NAVAL POSTGRADUATE SCHOOL Monterey, California ..uniO IN THERMAL S _ ,,,.-ivjorHt THE MODIFICATION OF STRUCTURE DURING THE :RIC FOR( THE UPP COOLING DING ER OCEAN SEASON by Norman Thomas Camp Dep artment of Oceanogrc December 1 976 iphy Thesis Advi sor: R. L. El sberry Approved for public release; distribution unlimited. T1779A6 SECURITY CLASSIFICATION OF THIS PAGE (When Data Sntered) Ciim fy v REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER 4. TITLE fand Su6MC»*) The Role of Strong Atmospheric Forcing Events in the Modification of the Upper Ocean Thermal Structure during the Cooling Season 5. TYPE OF REPORT ft PERIOO COVERED Ph.D. Dissertation December 1976 • PERFORMING ORG. REPORT NUMBER 7. AUTHOR^,) Norman Thomas Camp ft. CONTRACT OR GRANT NUMBER*-*.) >. PERFORMING ORGANI Z ATION NAME AND ADDRESS Naval Postgraduate School Monterey, California 93940 10. PROGRAM ELEMENT, PROJECT, TASK AREA ft WORK UNIT NUMBERS 11. CONTROLLING OFFICE NAME AND AOORESS Naval Postgraduate School Monterey, California 93940 12. REPORT DATE December 1 976 13. NUMBER OF PASES 175 14. MONITORING AGENCY NAME * AOORESSf// different from Controlling Office) Naval Postgraduate School Monterey, California 93940 18. SECURITY CLASS, (ot thlc report) Unclassi f ied IS*. DECLASSIFICATION. DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of tMa Report) Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (of the abetraci entered In Block 30, It dtttoront from Report) 18. SUPPLEMENTARY NOTES IS. KEY WORDS (Continue on rererce aide it neceaeaty and Identity by block number) Mixed layer Extratrop ica 1 cyclone Thermal structure Entrainment Sea-surface temperature Turbulent kinetic energy Mixed- layer models Non-penetrative convection 20. ABSTRACT (Continue on rarer** aide It naceaaaty mnd Identity by block member) The role of strong atmospheric forcing events in determining the evolution of the upper ocean during the fall and early winter cooling season was investigated. The historical series of surface and near-surface marine observations at three mid-latitude ocean weather ships [PAPA (OWS P), NOVEMBER (OWS N), and VICTOR (OWS V)] support the hypothesis that the integrated effects of these events dominate this evolution. For example, periods when the mechanical DO ,^r7, 1473 (Page 1) EDITION OF I NOV «» IS OBSOLETE S/N 0102-014- S601 | SECURITY CLASSIFICATION OF THIS PAOE (When Date Kntered) fuCuWlTv CLASSIFICATION OF This P»GEr*>i«n D»«» Enffd forcing was greater than the long-term mean accounted for approxi- mately 35$ of the time in the record examined at the three stations. However 85$/68#/57# of the sea-surface temperature change at OWS N/ OWS P/OWS V occurred during these periods. Forty-nine data sets were examined and modeled during periods of intense fall and winter forcing. The significant thermal struc- ture modifications observed during these strong events were simu- lated successfully using three modifications of the Kraus and Turner (1967) one-dimensional model. Evidence is presented which demon- strates that the amount of mechanically-generated turbulent kinetic energy available for entrainment decreases as the mixed-layer depth increases. Furthermore, in agreement with Gill and Turner (1976), these case studies suggest that only a small percentage of the con- vective I y-generated turbulent kinetic energy is available for in- creasing the potential energy of the ocean by entrainment. DD Form 1473 , 1 Jan 73 S/N 0102-014-6601 SECURITY CLASSIFICATION OF THIS F 8Cs(x.,t) -sQ]} (2-3) where I dp D I dp a = -tt=f , and 3 = — v~ • p 3T ' p ds The coefficients, a and B, are taken as constants throughout this thesis as a = 2.5 x I0"4(°C)_I, and 6 = 7.5 x I 0~4(°/oo)~ ' . It will be assumed that the fractional generation of heat and mole- cular heat transfer processes are negligible compared with typical values of radiant solar energy and the turbulent heat fluxes exchanged between the ocean and atmosphere. Therefore a simplified form of the first law of thermodynamics may be expressed as: 3T j 9T I 3R(z) fn .. ^T + U . tt = = 5 (2-4) dt J 8x . p C dz J o p According to Jerlov (1968), the total downward irradiance in the spectra range of 300-2500 nm decreases to 50$ of its surface value in the first meter of the ocean, virtually irrespective of the water type considered. 18 Therefore, in this study, the absorption of short wave radiation below the initial meter will be approximated by: R(z) = RQ eyz (2-5) where y represents a total extinction coefficient (taken as 0.3 m ), R represents the surface absorption. R = .5 0 , where 0 is the o r o s . s total solar flux at the surface. The final expression necessary to complete the system is the equa- tion for conservation of salt. Once again neglecting molecular diffu- sion, it may be simply represented as: ||+ u.|i =o (2-6) J J B. THE ONE-DIMENSIONAL HYPOTHESIS The basic assumption of the one-dimensional hypothesis is that the ocean is horizontally homogeneous in all its properties (u., s, T). This assumption restricts the domain of applicability to time and space scales over which the vertical fluxes of mass and momentum dominate the horizontal fluxes. Because of the sparsity of open ocean measurements this assumption is difficult to verify a priori . However, the one-dimen- sional hypothesis is desirable at this point because three-dimensional models are not only far more complicated and expensive, but the frequency of observations (especially oceanic) prohibits proper initialization, calibration, and validation. 19 C. TURBULENT FORM OF THE BASIC EQUATIONS The turbulent components are introduced into the basic equations through the Reynolds decomposition technique, whereby the variables are expressed as a time averaged mean and a fluctuation about the mean (i.e. T = T + T'). The prime denotes the fluctuation and the overbar represents the mean; At - i r 2 T = AT J T d+ ' (2"7) At 2 for example. The integral time scale, At, should be short compared with the time in which the mean field properties are changing, but long relative to the time scale of the fluctuations. Applying this technique to the basic set of equations (neglecting the mean vertical motion W ) results in the following: 3c .,- 3w'c' ,~ Q. -ttt + i f c = * (2-8) 3t 3z 3T ^- (R(z) - p C w'T') (2-9) 3t pC 3z Ko p o p ||=-^- (2-10) 8t 3z Equation (2-8) is the equation of mean motion expressed in complex notation (c = u + iv) with the geostrophic component removed. Equa- tions (2-9) and (2-10) are the conservation relations for mean tempera- ture (T) and salinity (s), while expressions w'c', w'T', and w's' represent the turbulent fluxes of momentum, temperature, and salt re- spectively. The parameterization of these fluxes will be accomplished, 20 in part, by examining the turbulent kinetic energy budget for the upper ocean, which is derived from the Navier-Stokes equation. If (2-1) is multiplied by u. and subjected to Reynolds decomposi- tion, the resulting expression will represent the conservation of total kinetic energy. The conservation of mean kinetic energy is formulated by the decomposition of (2-1) multiplied by the time averaged mean velocity U. . The turbulent kinetic energy equation is obtained by subtracting the mean from the total equation and the resulting expression 3U 8 q*". d r . ,p' q*\-| — i — r a „ w'p' „ fn i . <, Tr(^-) + -^-rLw t (■£— + -^— ) J = - u_ ' w ' -^ g — ~ e (2-11) 9t 2 3?" p 2 J a dz a p 2 « t where q = u . Tu. ' , and ua = tu, V) , £ = v/3un 2 l^j j The first term on the left is the local time rate of change of turbu- ent kinetic energy while the second, the divergence term, specifies the vertical redistribution of the turbulent kinetic energy w'(p'/p + q /2) by the turbulence. This energy is generated primarily by breaking waves at the surface and by the Reynolds stresses acting on the mean flow. The right hand terms represent the three ways in which turbulent kinetic energy is either gained or lost. The first of these, which is usually positive, is the rate at which mean kinetic energy is converted to turbu- »w» lent kinetic energy by the working of_the Reynolds stresses -p u 'w 3U ° a ct against the mean velocity gradient ■* — . The second, the covariance 21 between the fluctuations in density and the vertical velocity, may be positive or negative. If the basic density distribution is statically unstable, then fluid elements moving upwards tend to be less dense than those descending, and a release of potential energy takes place by free convection (-g w'p'/p > 0). If, on the other hand, the density distri- bution is stable, the reverse is true and -g w'p'/p < 0. This covariance then represents the rate at which turbulent kinetic energy is expended by mixing the less dense fluid downward, thus increasing the potential energy. The last term (e) is the rate at which turbulent kinetic energy is dissipated by viscosity and always represents a loss. To solve the system (2-8) - (2-11) requires specification of the vertical structure of the properties and the boundary conditions imposed on the domain. Moreover, this involves parameterization of turbulent processes and addi- tional simplifications will be necessary to make the problem tractable. D. THE BULK MODEL HYPOTHESIS In this thesis the one-dimensional dynamic processes that affect the evolution of the upper ocean will be studied in terms of the energetics associated with the turbulent kinetic budget. The parameterization of these energetics is accomplished by idealizing the upper ocean structure with the assumptions of the bulk model hypothesis (depicted in Fig. 2-1). The quantities C , T , S represent the vertically averaged values of velocity, temperature, and salinity, defined for example as o C = -4-f f cdz (2-12) s h + 6 J -h-6 With this concept, the density structure (T , S ) directly below the wind blown ocean surface is assumed vertically homogeneous to a depth of 22 ? TURBULENT A _^, „ HEAT FLUX sOLAR (Qe.Qh) RADIATION (Qs) SURFACE STRESS (r.) [ BACK RADIATION (Qb) I PRODUCTION ZONE s~az Figure 2-1. Schematic of the oceanic mixed layer, 23 z = -h. Below this level there is a discontinuity in the density fol- lowed by a stable density profile. The mean velocity structure is modeled as being vertically uniform and fully turbulent in the mixed layer and negligibly small and nonturbulent below. Deviations from this vertical structure occur at the top and bottom of the layer where shear zones are formed. These shear zones are formed at the top due to the action of the wind on the water, and at the bottom due to the slab-like motion of the mixed layer over the quiescent water in the pycnocline. The surface shear zone is known as the production zone, where turbulent kinetic energy is generated by the working of the Reynolds stresses against the mean velocity gradient. The bottom shear zone is an entrap- ment zone of thickness 6. There is a vertical flux of mass and momentum at the top (z = -h') while none leaks out the bottom (z = -h-5). It is further assumed that the Reynolds stresses are also capable of generat- ing turbulence in this zone. Thus the bulk model concept assumes that variations from the structure of the upper ocean depicted in Fig. 2-1 may be neglected and the vertical mean quantities may be predicted, with sufficient accuracy, by specification of the turbulent transfer processes at the boundaries. To maintain these homogeneous profiles throughout the mixed layer a continual vertical flux of turbulent energy is necessary throughout the layer. When there is a convergence of turbulent energy at z = -h, the entrainment zone is destabilized and the excess turbulent kinetic energy is expended by entraining fluid from below as the layer deepens. With a downward buoyancy flux at the surface (excess heating or precipitation), it is possible that an insufficient flux of turbulent kinetic energy may be available to mix the fluid homogeneously to the existing mixed layer depth. In this case a new mixed layer depth is established at the level 24 where the downward vertical turbulent flux vanishes. Since this level is higher than the previous layer depth, this formation is called layer retreat. The turbulent motions below this level are assumed to be shut off from the energy source, and become nonturbulent by viscous forces on a dissipation time scale. It is therefore envisioned that the mixed layer is being constantly re-established from the surface, and that shallowing mixed layers are not the result of the interface moving upward, but are the consequence of net surface heating and an insufficient down- ward flux of turbulent kinetic energy. E. BOUNDARY CONDITIONS The boundary conditions will be specified as a function of time and the overbar on the mean quantities will be dropped. The surface stress is denoted as x and s T + io s - w'c'(o) = -= (2-13) po while ( Bi^l - VrfT) (o) = S n a (2-14) pC / p C \ o p / 'o p The terrrj Q is the sum of the turbulent fluxes of latent (Q ) and sensible (0.) heat and the effective long wave back radiation (0,). The short wave solar energy (Q ) is always taken as a positive value. The surface flux of salt is - w's'(o) = s(E-P) (2-15) where P is the rate of precipitation, and E is the evaporation rate. 25 The boundary conditions at the bottom of the mixed layer are derived by integrating (2-8) - (2-10) over the entrainment zone (-h-6 < z < -h). Thus 8h wfc'(-h) = - gj Ac where Ac = c(-h) - c(-h-6) Since only one-dimensional effects are considered in this model, -~ is the time rate of change of the mixed layer depth (h) due to turbulent processes. As this expression implies an upward momentum flux for ^— < 0 (an impossibility in this system), it is rewritten as dt 8h w'c'(-h) = - A -^ Ac (2-16) where A is the Heaviside unit step function defined as (2-17) The fluxes of heat and salt at tne base of the mixed layer are similarly derived and are \ R e"Yh Riil _ ^Tjr) (.h) = o + A 3h AT poCp / poCP 9+ w^C-h) = -A ~ As (2-19) 26 F. THE INTEGRATED MASS, MOMENTUM, AND ENERGY BUDGETS Equations (2-8) - (2-10) may now be integrated over the mixed layer to form the mass and momentum budgets of the region. The results are: 8C ■a— + ifC dt S 3t T + s - A IK] Q -Q -R e s a o -yh P c L op "A8t AT (2-20) (2-21 ) 5 _ I 3t h s(E-P) -A |£ As (2-22) These equations are subject to simple interpretation. Equation (2-20) shows that the mean motion of the mixed layer is modified in time by rotation and the vertical fluxes of momentum at the surface and base of the slab. The surface flux may add or subtract momentum depending on the relative directions of t and C . During the period when the mixed layer is s s 3 v deepening the flux of momentum at the base is always a sink for energy (Ac - C _> 0) and represents the energy necessary to impulsively accele- rate the entrained fluid to the velocity of the mixed layer. For deepen- ing mixed layers the density, specified by (2-21) and (2-22), will normally increase due to the turbulent flux of density at the surface and base of the mixed layer, while it normally decreases for shallowing layers. For stable temperature and salinity structures, deepening layers normally become cooler and more saline while the reverse is true for the retreating case. To close this system the time rate of change of the mixed layer depth Oh/9t) must be specified. This may be accomplished through the 27 integration of the turbulent kinetic energy equation over the mixed layer. It is at this point where most modern one-dimensional bulk models differ and the procedure will be given careful consideration. One may start by defining the terms of (2-11) as follows: ■*-£} dz (2-23) G* = -h-6 D* = Po f e dz -h-6 P* = o p / w'b' dz -h-6 s* = °o f It - Q - R F(yh) s Ya o ' P Co o p - s(E-P) a ■] (2-30) Ab = pQgaAT - pQg3 As , (2-31) and F(Yh) =^[l -e^h]-e^h (2-32) 29 The process modeled by — ~— A rr represents the amount of turbulent kinetic energy expended to deepen the mixed layer and increase the poten- tial energy of the column of water (raise the center of gravity) by en- B h training denser fluid from below. — — is the turbulent kinetic energy (released potential energy) generated when B < 0 and free convection occurs. When B > 0 , it represents the energy expended during forced convection to mix the buoyant surface water downward and increase the po- tential energy. The function F(yh) reflects the penetration of solar energy to some depth with the property that F(yh) -»• 0 as yh -*■ °° (complete absorption in the layer), and F(yh) -*■ I as yh -*• 0 (complete penetration through the layer). Substituting (2-29) into (2-28) results in an expression for the time rate of change of the mixed-layer depth in terms of G* , D* , S^ and the surface fluxes of heat and salt; in - i rwRoF(^h) + 1(E P) + 2 The first two terms represent the mechanical production at the surface due to atmospheric perturbations and breaking waves (term I), and the work performed against the mean velocity gradient by the Reynolds stresses (term 2). The third term is the shear production in the entrain- ment zone as the layer deepens. Niiler (1975) carefully performed these integrations to show that the contribution of the first two terms is 31 proportional to the cube of the friction velocity (w*), while the third *h ic r is approximately A -trr -y . Therefore Ic I2 G* = m„p w* + mTp Avr -y (2-39) * 2 o * 3 o dt 2 and the nondimensiona I constants m„ and m, are both of order unity. The total integrated turbulent kinetic budget is obtained by substi' tuting (2-29), (2-35), and (2-39) into (2-28). 2 pom|w* 3h hAb . _3Ji 2 3t 2 3t , m7p C ». B h 3 3 o1 s1 . ah o ,_ ... m„p w„ + = A vr it- ~ D* (2-40) z o * z at z * 1 1 1 G. CLASSES OF MIXED LAYER MODELS I . The Prototype Turbulent Bulk Model Most modern mixed layer models can be classified as to which terms of (2-40) are used to predict changes in the mixed layer proper- ties. Kraus and Turner (1967), hereafter KT, formulated the prototype turublent bulk model, assuming a balance between terms II, III, and V in (2-40) and neglecting the rest as follows: hAb . 3h „ 3 o n ,,, — A 37= P0w* -— (2-41) 32 When the sum of the terms on the right are positive, the layer deepens according to _. 2p w„ - B h lH = ° 2_ (2-42) 8t hAb K Ci However, during periods of weak winds and surface heating, the right hand side becomes negative and 3 • 2p w* hr - -g2_ (2-43) o is a prognostic equation which calculates the retreating mixed layer depth proportional to the Moni n-Obukhov length scale (L). Incidentally, Kita igorodski (I960), using a steady state model and dimensional analy- sis, reasoned that this should be the proper length scale. Kraus and Turner demonstrated that this model was capable of simulating the annual evolution of the mixed layer with a saw tooth heating function and constant wind stress. Denman and Miyake (1973) applied a numerical version of KT to a 12-day period at ocean station PAPA with favorable results. Using observed forcing they were able to simulate both the daily and weekly changes in mixed layer temperature and depth during a period of moderate synoptic scale winds, apparently without any significant effects from vertical or horizontal advection. On the other hand, Dorman (1974) applied the same model to cases of spring heating and fall cooling at ocean station NOVEMBER with limited success, and attributed the model's poor performance to horizontal advection. However, these few simulations are not conclusive evidence for the validity of the one-dimensional bulk model (in particular KT) and 33 a primary objective of this work will be to attempt a large number of experiments to gather such evidence. In addition to KT, the model of Kim (1976) and the model of Elsberry, Fraim, and Trapnell (1976), here- after KIM and EFT, will be evaluated. Both of these models assume the dominance of surface production and are therefore of the KT type. Kraus and Turner originally determined that KT predicted exces- sive mixed layer depths when mechanical production and free convection were considered together. They concluded that either their parameteri- zation of mechanical production was in error or the effects of dissipa- tion could not be neglected, or both. Turner (1969) found that the fraction of the total energy, imparted during an impulsive wind event, that is used to increase the potential energy by entrainment was larger than p w^ , as originally reasoned by Kraus and Turner from dimensional analysis. He suggested that much of the kinetic energy goes into drift currents and is eventually used to deepen the layer; however he did not specify the mechanism for this deepening. 2. The Prototype Inertia I Bulk Model In an attempt to explain the rapid deepening of the mixed layer in response to strong impulsive forcing, as reported by Turner (1969), Pollard, Rhines, and Thompson (1973), hereafter PRT, formulated a model quite different from KT. Assuming the density was a function of tempera- ture only, they neglected the turbulent kinetic energy budget and con- sidered only the time rate of change of total kinetic (KE) and potential (PE) energy as follows: 9PE 3KE , . / o /i /i \ -ttt- + -prr— = t u(o) (2-44) at at s 34 Further, they implied that at the onset of heavy winds the mixed layer would respond and move as a slab, and through the mechanism of mean flow instability the mixed layer would deepen. They postulated that the mean flow would remain unstable as long as the bulk Richardson number (R. ) was less than or equal to unity. * = gahAT< , (2_45) C I2 The PRT model predicts continual deepening as long as x u(o) is posi- * r 2 tive and R. <_ I . If w'c'(o) = -w* +io , a particular solution for (2-19) is [sin ft - id - cos ft)] (2-46) 's fh At time t = ir/f (half the inertial period), t u(o) becomes negative, the energy f low to increase h ceases, and since the water cannot unmix, # h must remain constant and R. > I . The PRT model predicts a maximum mixed layer depth for a constant w^ as I .7 w^. h = (2-47) max M 2 where N = gar and N is the Brunt-Va i sa la frequency. Niiler (1975) concluded that the PRT model, in reality, assumes a balance between terms II and IV in (2-40). If m, = I , then this balance simply reduces to (2-45). The model is most effective in causing mixed-layer depth changes during periods of relatively shallow mixed layers and strong impulsive winds. However, a major difficulty with this 35 model is that it fails to account for the gradual deepening that takes place during periods of weak forcing or when the initial layer depth is qreater than h . It is entirely possible that the deepening of 3 max 7 a the mixed layer may occur as a combination of KT and PRT and that the geophysical situation (magnitude of the wind, layer depth, and ocean stability) will dictate which process will dominate. In section IV the one-dimensional bulk models of KT, EFT, and KIM will be applied to data sets obtained during the autumn and winter season in the North Pacific. The PRT model was not included in this study because the calculations shown in Table 2-1 indicate that the bulk Richardson number remains greater than un i ty dur i ng all but a small num- ber of observations during these periods (h > 30 m). In performing these calculations it was assumed that at time t = 0, h = h , and o both PRT and KT type deepening occur simultaneously. Additionally sur- face heat fluxes were neglected, a constant temperature gradient was hrT assumed, and AT was approximated by —^- . The values of R. (as a function of wind speed) are calculated at t = ir/f . Therefore values * of R. < I indicate situations when the PRT model would have deepened a greater amount than the KT model. Also, it has not been clearly # established that the mean flow positively becomes unstable at P.. = I and, in fact, the instability may be initiated at much lower values (see Turner, 1973, pp. 97-102). H. NON-PENETRATIVE FREE CONVECTION Returning to the KT model two difficulties are yet to be resolved. The first of these involves the percentage of turbulent kinetic energy generated during free convection that is actually utilized for entrap- ment. Kraus and Turner followed Ball (I960) and assumed that 100 percent 36 TABLE 2-1. R. as a function of wind speed (Uiri) and initial layer U|r)(m/sec) 5 10 15 20 25 30 35 40 45 50 depth (h ). o h = o 30 m h = o 40 m h = o 50 m h = 60 m o 4.2x io4 1 .3x IO5 3.2x10^ 6.7xl05 70.0 2.2xlOZ 5.2xl02 1 . Ox 1 03 5.6 15.1 35.0 70.0 1.9 3.9 8.0 15.0 1. 1 1.9 3.2 5.6 1.0 1.2 1.8 2.9 .8 1.0 1.3 1.8 o7 .8 I.I 1.4 .7 ■ .8 .9 I.I .7 .7 .8 1.0 .7 .7 .8 .9 37 is used. However, laboratory work by Deardorff, Willis, and Lilly (1969), and a more recent field experiment by Farmer (1975) indicate that only a small fraction of this energy (1-3$) is actually converted to potential energy through entrainment. Furthermore, Gill and Turner (1975) demonstrated that a fraction equal to 0.15 was adequate to achieve annual cyclic steady state in the potential energy balance. The reason becomes evident by considering a simple case where solar radiation is neglected and density is a function of temperature only. Then, -pQga C w'T' dz (2-48) 9PE at -h 3pe pogah r Q 3t 2 p C [&-'«"] (2-49) Writing (2-33) as Q, 2(G*- D*- S*) A 15- AT = r —2- H dt p C p gah o p o3 where r is the fraction of convect i vel y-generated turbulent kinetic energy utilized for entrainment, (2-49) becomes 8PE. P^M . ^a_ p n . 8t ~ 2 r; p C ' * U*~ b* (2-51) o P The KT model assumes r = I and neglects D* and S* . 3t~ = G* = PQW* (2-52) 38 Equation (2-52) demonstrates clearly that a cyclic steady state balance is impossible in the KT model and, except when the wind stops blowing, the potential energy increases continually. The consequences are exces- sive mixed layer depths and downward heat flux into the deep layers. As the entrainment process takes place, a continual downward heat flux into the deeper layers occurs. Before the seasonal thermocline may be reestablished, during the spring and summer heating cycle, this heat must be removed by non-penetrative free convection (cooling without deep- ening ). The KT model cannot accomplish this process and, when inte- grated over several annual cycles, will eventually erode away the thermo- cline. Therefore, the conclusion is drawn that non-penetrative free convection (r < I) must be an integral part of any mixed layer model and, following Gill and Turner (1975), a value of r = 0.15 will be used in all the models evaluated in this thesis (including KT). The theory explaining how such a large percentage (85%) of the kinetic energy is lost is not complete. A certain amount is dissipated by vis- cosity, and atmospheric investigations such as Townsend (1968) and Stu I I (1975) indicate th3t internal waves generated by convection are capable of radiating energy away from the mixed layer interface into the gradient region. I. DISSIPATION ENHANCEMENT The second difficulty with KT is that excessive deepening is pre- dicted, even when free convection is neglected. This is a consequence of not properly parameterizing dissipation. A tank experiment by Thompson and Turner (1975) demonstrated that the entrainment rate pro- duced by a stirring grid is not directly related to the velocity of the stirrer, but to the turbulent velocity near the interface. They reasoned 39 that the turbulent kinetic energy density decays with depth and that less is available for mixing as the layer deepens and the entrai nment zone gets further away from the surface production zone. The first model to include this process was that of Elsberry, Fraim, and Trapnell (1976). Total dissipation was assumed to increase exponentially as a function of layer depth, h, and a scale depth, Z, and G* - D* = p w*3 e"h/Z (2-53) In this model G* - D* is nearly equal to the downward energy flux from the atmosphere (according to KT) if the mixed layer is shallow (h « Z) while it tends towards zero for very deep layers. A more recent model by Kim (1976) also uses a depth dependent dis- sipation parameterization and additionally includes the storage term. G* - D* =. 1.25 pQw*3 - pQDbh (2- 53a) where D. is a constant background dissipation. The surface production term is parameterized according to Kato and Phillips (1969), and D, calculated from the dissipation data of Grant, Moilliet, and Vogel (1968). Kim's model has the additional interesting property of being able to predict steady state in the potential energy balance for neutral conditions (no heating or cooling). For the KIM model (2-51) becomes 8PE PogahM , 9a il ,_ 3 n . I 2 9h ,- ... TZ~ = ~ n ( ,-r) rT~ +1 .25 p W„ -p D, h- Tlll.p W» -rrr (2-54) dt 2 p C o * o b 2 I o * 3t o p 40 and for -^r— = 0 , and Q = 0 dT a . ot, 3 I 2 3h I .25 w* - j m w* ^r h = fr— - — ! — , (2-55) b with solution Db + I 2 1 1.25 w* \2 V* / + (2-56) b and C is a constant determined by initial conditions. 2 m. w^ Thus, neutral steady state is predicted for t » — ^=- — ; this means b that a constant wind is only capable of deepening the layer to a depth described by (2-56). J. VERTICAL DIFFUSION The prototype turbulent bulk model has the undesirable tendency to predict abnormally large temperature gradients at the base of the mixed layer (see Denman and Miyake, 1973, Fig. 6). This is a consequence of the zero-flux condition imposed at the base of the entrainment zone. An attempt will be made in. this research to overcome this difficulty by assuming that the thermocline is weakly diffusive. The temperature be- low the mixed layer will be specified by |I = A i!l (2-57) at v gz2 where A is the vertical diffusion coefficient. The KT, KIM, and EFT will be evaluated with this diffusion tendency to determine its effec- tiveness. 41 K. SALINITY EFFECTS An additional assumption, made throughout this thesis, is that the density structure is a function of temperature only and that buoyancy flux (wfbf) is synonymous with heat flux (wfTf) . This assumption is necessary (but certainly not desirable) because the data used In this investigation included neither salinity structure information nor ob- served precipitation rates. The errors introduced into the system by this assumption are reflected by (2-33), and (2-40). These equations indicate that salinity changes may be an important consideration depend- ing on the season, geographical location, and vertical depth scale over which the model is applied. An attempt will be made to determine to what extent this assumption affects model performance. In summary, the fundamental principles governing the evolution of the mixed layer have been reviewed in some detail, and the assumptions of the one-dimensional bulk model specified. The expressions that will be used to examine the physical processes responsible for observed changes in the mixed layer are (2-21), (2-33), and (2-40). 42 III. CHARACTERISTICS OF THE ATMOSPHERIC FORCING AND OCEANIC STRUCTURE AT OCEAN WEATHER SHIPS (OWS) PAPA (P), NOVEMBER (N) AND VICTOR (V) A. DATA SOURCES One of the largest data sets for investigating the upper ocean ther- mal response to atmospheric forcing is the meteorological and oceano- graphic observations taken at ocean weather ships. To examine the physi- cal mechanisms responsible for changing the thermal structure, it was decided to focus the analysis on the data gathered at Ocean Weather Ships PAPA (50N, I45W), NOVEMBER (30N, HOW), and VICTOR (34N, I64E) in the North Pacific. Furthermore, since the objective of this thesis is to examine these processes during the fall and early winter cooling season, only data collected during September through December will be considered. The near-surface marine observations were provided by the National Weather Records Center and the three-hourly data included measurements of sea-surface temperature (T ), air-temperature (T ), dew point (T ), wind speed (u ), and visual estimates of total cloud cover (C). Table a (3-1) lists the years when data were available and includes approximate- ly 96$ of the possible three-hourly records. TABLE 3-1. Availability of data at the ocean weather stations. Station Atmospheric Observations Mechanical BT's P 1946, 1948-1970 1946, 1948-1970 N 1946-1951 1947-1950 1953-1954 1954-1970 1956-1970 V 1956-1970 1956-1970 43 Information regarding the evolution of the oceanic thermal structure was obtained through analysis of mechanical bathythermograph (MBT) records provided by the National Oceanographic Data Center. The years for which MBT data were available are also listed in Table (3-1); however, the fre- quency of these observations was highly variable, and usually numbered less than a few hundred per season. B. FORMULAS FOR COMPUTING ATMOSPHERIC FORCING Examination of (2-21), (2-31), and (2-38) indicates that the atmos- pheric forcing necessary for modeling the response of the upper ocean includes a measure of turbulent kinetic energy flux (w* ), the effective solar radiation (Q ), the turbulent fluxes of sensible (Q, ) and latent heat (Q ), and the net back radiation (Q, ). These variables may be esti- mated using the measured atmospheric parameters in the following bulk aerodynamic formulas: u* = Jcl (u x I02) (cm/sec) (3-1) * Da Q = 3,767 Cn (0.98 E - E ) u (ly/day) (3-2) e D w a a 1 7 Q, = 2,488 Cn (T - T ) u (ly/day) (3-3) h ' D w a a ' ' Q, = 1.14 x I0'7(273.I6+T )4(0.39-0.05v/E~) ( I -0.6C2) ( I y/day ) (3-4) b w a where u* is the friction velocity of the atmosphere and is related to w* by w* = (— )l/2 u* (3-5) w The non-dimensional drag coefficient (CR) was assumed constant (1.3 x 10 ) throughout this study and the saturation vapor pressure of the marine atmosphere (E ) in direct contact with the ocean was estimated 44 from the observed sea-surface temperature. The final quantity (E ) is a the saturation vapor pressure of the atmosphere at a height of approxi- mately 10 meters and was estimated from the dewpoint temperature. Additionally a daily estimate of the effective solar radiation was com- puted from the formula developed by Seckel and Beaudry (1973). A more complete description of the empirical formulas is presented in Appendix A, along with a discussion of their underlying assumptions. C. CHARACTERISTIC ATMOSPHERIC AND OCEANIC CONDITIONS AT THE WEATHER STATIONS Before proceeding to the details of modeling the upper ocean, the general character of the marine atmospheric forcing and oceanic response at the ocean weather stations will be examined to place this study in perspect i ve. During the fall and winter, the mean atmospheric circulation at OWS P and OWS V is dominated by a large barometric low pressure system (Aleutian Low), and the mean flow is generally westerly. The mean sur- face winds at OWS N are under the influence of the subtropic high and are generally northeasterly. However, the most outstanding feature of the mid-latitude atmosphere in the North Pacific is the fluctuations in the atmosphere associated with the frequency and intensity of travelling I extratrop ica I cyclones. An analysis of historical storm tracks, presented in the U.S. Navy Marine Climatic Atlas (1957), indicates that OWS V and OWS P lie in close proximity to the preferred path of the major storm centers, while OWS N is located a considerable distance to the south. The influence that these storms have on air-sea interactions is therefore expected to be most pronounced at OWS V and OWS P and weakest at OWS N. 45 Figures 3-1 present a comparison of the long-term mean atmospheric forcing and oceanic thermal response at the three ocean stations. The atmospheric forcing and sea-surface temperature were computed from the three-hourly surface and near-surface observations while the bathyther- mograph file was used to establish the mixed-layer depth (defined as the depth at which the temperature was 0.2°C less than the sea-surface tem- perature). Each point represents the daily average of all available data (see Table 3-1) smoothed by a 7-day running mean (for display pur- poses on ly) . These figures are presented merely to illustrate the relative magni- tude and variability of the atmospheric forcing and oceanic response that we might anticipate at the three stations. An important observa- tion that should be made is that the air-sea interactions in the North Pacific are highly dependent upon geographical location. Since we are interested in evaluating model performance under a variety of geophysi- cal situations, these three stations appear ideally suited for this study. It is also important to observe that there is a significant cor- relation between the strong, variable forcing and large oceanic response at OWS P and OWS V and the relatively weak, steady forcing and response at OWS N. In Chapter V a detailed analysis of these data will be per- formed, designed to understand the principal mechanisms by which these evolutions take place. The North Pacific has been divided into distinctive ocean regimes (Tu My, 1964) based on similarities in the characteristic temperature and salinity structures in these regions. OWS P is located in the Paci- fic Subarctic region while OWS V and OWS N are located in the Pacific Subtropic. Figures 3-2 illustrate schematically the major features of the ocean structure to be found in these regions. 46 27 24 - cr D £18 a 2 LU H15 LU a §12 < LU If) A . >. '" — — ■— ^..J*^ _ - "v^"" _ '%_ / owsv OWSN ^ ** «* ** OWSP 1 1 I 1 i i i i 9 6 - 1 15 SEP 1 15 OCT 1 15 NOV 15 30 DEC 600 i £ -650 - -900 - -1150 - -1400 150 *• . -400 - ' >»^- V.-*..'^\ J I L J I I L 15 SEP 1 15 OCT 15 NOV 15 30 DEC -20 B -120 - -140 - -160 24 21 18 b 5 15 n a LU to -,' 12 S y n * 3 9 J I L 1 15 1 15 1 15 1 15 30 SEP OCT NOV DEC \ J A' A / ' * i t\r-. /v. / v .A / V S:\ 1 15 1 15 1 15 1 15 30 SEP OCT NOV DEC Figure 3-I. Long-term mean atmospheric forcing and oceanic thermal response at OWS P, OWS V, and OWS N. 47 T(°C) 6 8 10 12 32 S(%o) 33 p(gm/cm2) 34 1.024 1.026 1 300 J4 T(°C) 18 22 26 34 S(%o) p(gm/cm2) 35 361.024 1.026 100- Q. LU Q 200 300 I I I I II I I I ^/ I s^ in J l I i I V i \ i i - / I I *** \ i \ i \ - / AUG \ DEC • B Figure 3-2. Major features North Pacific. of the ocean thermal structure in the (A) Pacific Subarctic Region (B) Pacific Subtropic Region (after Tul ly, I 964) . 48 The Pacific Subarctic region is distinguished by excess precipita- tion (E-P < 0), large upward surface heat fluxes, and strong mechanical forcing through most of the cooling season. These quantities interact to create a unique temperature and salinity structure and the most dis- tinctive feature to be noted in Fig. 3-2A is the existence of a stable salinity gradient in the upper ocean. Throughout this region the density structure is a function of both the temperature and salinity structure in the upper 100 m, with the salinity becoming increasingly more impor- tant at depths approaching the permanent halocline. At OWS N and OWS V very similar temperature and salinity structures are observed (Fig. 3-2B) which are very different from OWS P. The Sub- tropic region is characterized by large surface heat fluxes and values of E-P > 0 through most of the cooling season. Consequently both tem- perature and salinity decrease with depth in the upper ocean and the den- sity structure is primarily a function of the temperature structure in this region. OWS P offers a unique opportunity to examine and model the effects that intense winter storms have on the upper ocean thermal structure. The largest vertical flux of turbulent kinetic energy (Fig. 3-ID) may be expected at this station throughout the season, and makes this an ideal location for examining the parameter i zat ions of dissipation postulated by Kraus and Turner (1967), Kim (1976), and Elsberry, et aj_. (1976). Additionally, it should prove instructive to determine if the major ther- mal structure changes may be accounted for with a model that assumes that the density structure may be represented by only the temperature struc- ture, and surface buoyancy flux by only the heat flux. The study of the processes which control the evolution of the upper ocean at OWS V and OWS N offers an opportunity to examine these mechanisms 49 under different conditions than at OWS P. OWS V wi I I be characterized by the largest upward surface heat fluxes (Fig. 3-IC) observed at any station together with large and variable energy fluxes. Therefore, both mechanical mixing and free convection may be expected to play important roles in modifying the thermal structure. OWS N, on the other hand, is an excellent location for testing the model's performance under rather weak and steady forcing. Because of the characteristic ocean structure in the subtropics, neglecting salinity should not introduce any severe limitations on model performance at either OWS V or OWS N (see Dorman, 1974). 50 IV. RESPONSE OF THE UPPER OCEAN TO STRONG ATMOSPHERIC FORCING; OBSERVATIONS AND SIMULATIONS A. INTRODUCTION In this chapter we investigate the oceanic thermal response asso- ciated with strong autumn and early winter atmospheric forcing events at the three ocean weather stations. Denman and Miyake (1973) presented data from OWS P (13-24 June 1970) which illustrated the behavior of the upper ocean during the passage of several synoptic-scale weather systems. Further, they were able to simulate the major features of the mixed layer response to these summer storms using a numerical version of the Kraus- Turner model (1967). However, the response of the upper ocean to the strong fall and winter storm events has not been adequately investigated and has never been successfully simulated. The atmospheric forcing associated with the strong events that occur during the fall and early winter seasons is typically much more energetic than the forcing observed during the strong summer events. In addition to large downward fluxes of mechanical energy, the fall and winter events are frequently characterized by large upward turbulent fluxes of latent and sensible heat. Therefore, mechan i ca I mixing and convection play an increasingly important interactive role in the mixed layer evolution during the autumn and early winter seasons. The principal objectives of this chapter are to examine data sets representing air-sea interactions at OWS P, OWS N, and OWS V to: I. show that significant upper ocean thermal structure modifica- tions occur during periods of strong fall and early winter forc- ing at the three ocean weather stations; 51 2. demonstrate that a modified version of the Kraus-Turner model (parameterized to account for dissipation enhancement and non- penetrative convection) is capable of simulating a large per- centage of these changes; 3. establish the relative importance of the mechanical and convec- tive processes that characterize the strong fall and early winter forcing events at the three ocean weather stations. In this research the three one-dimensional, bulk models (specifical- ly KT, EFT, and KIM), discussed in Chapter II, were evaluated at the three ocean weather stations. Successful simulation of the response of the upper ocean depends upon adequate parameterization of the principal physical processes which govern the response. The relative capabilities of the three models in simulating the mixed layer evolutions will be discussed in terms of the importance of properly parameterizing dissipa- tion enhancement and non-penetrative convection. B. PARAMETERIZATION OF THE MODELS A modification of the algorithm presented by Thompson (1976) was de- veloped to parameterize the KT, EFT, and KIM models in a consistent manner. The scheme was designed to calculate the potential energy changes resulting from the vertical fluxes of heat and turbulent kinetic energy that occur in the upper ocean. The sources and sinks of turbulent kine- tic energy, specified in (2-40), are parameterized according to the KT, EFT, and KIM models. The modifications of the thermal structure by these vertical heat and energy fluxes are accomplished in a manner de- scribed in detail in Appendix B. 8T The time rate of change of the mixed layer temperature (-^r— ) and depth (-yp) , specified by (2-21) and (2-33), are specified by the 52 vertical redistribution of heat by the turbulent energy fluxes. In Thompson's algorithm the temperature profile is stored in N equally- spaced grid intervals [-(n-l) Az, -nAZH, where n=l,2,...,N and AZ = 2.5 m. At each time step (At = I hr) the mixed-layer temperature is taken to be the temperature in the first interval. The scheme does not explicitly calculate the mixed-layer depth and it is simply defined (in the model and the BT data) as the depth at which the temperature is 0.2°C less than the mixed layer temperature. The basic algorithm was evaluated by Thompson (1976) for the case of mechanical mixing with no radiation, and for surface cooling with no mechanical forcing. Numerical results from this scheme were equivalent to the analytical calculations for these cases. A desirable property of' Thompson' s algorithm is that it conserves heat and potential energy at each time step. This property is important because it allows us to isolate and compare the relative importance of mechanically generated turbulent kinetic energy and free convection in the modification of the upper ocean thermal structure. C. INPUT DATA The atmospheric forcing (w^ , Q , Q , Q , Q ) was estimated from the routine meteorological observations using the bulk formulas described in Chapter III and Appendix A. The turbulent energy fluxes (w* , Q , 0, ) were calculated every three hours and linearly interpolated to hourly values corresponding to the integration time-step used* in the models. The calculated daily value of effective long-wave radiation (Q, ) was distributed uniformly over the 24 hours. The value of net short wave radiation (Q ), however, varied as a function of the solar altitude. To approximate this effect, the estimated daily value was distributed sinusoidal ly from sunrise to sunset. 53 Since the forcing was calculated from the observed surface and near- surface parameters, there was no feedback possible between the ocean and the atmosphere. The models were purposely run in this uncoupled state to insure that each model received the same forcing. The different model responses may, therefore, be compared in terms of the differences in the internal physical mechanisms specified by each model. Additionally, since any errors in the forcing are introduced in each model, they should not adversely affect the relative comparison of the different model results. The models were initialized using mechanical BT data from the NODC historical file at the three ocean weather stations. In choosing data sets for testing the performance of the models, the lack of BT data was the most limiting factor. During many strong forcing events the BT data were completely missing. Therefore, some data sets could only be initialized using observations which were available before the events and the results of the models validated using data obtained a few days after the events had passed. After examining many data sets, it was observed that the morning BT (within 2 hrs of 0800) provided a reliable indicator of the trend in the mixed-layer depth and temperature during the strong fall and winter events. The individual morning BT observations were examined and a number of simple gross error checks were made to insure that the obser- vations were realistic. The trend in the sea-surface temperature in the BT observations was compared with the trend in the bucket temperature reported in the marine deck. If these two trends were not comparab le, the data set was rejected. Addi tiona I I y, the trend in the mixed-layer depth was examined to insure that it was compatible with the character of the computed atmospheric forcing. Finally, to guard against any single BT observation seriously biasing the results (especially the initial obser- vation), the profiles used in the model were smooth by hanning. This 54 morning sampling rate prohibits resolution of model performance during time scales of less than one day. Therefore the analysis will focus on the relative capabilities with which the models simulate the general trend in the mixed layer changes on time scales of a few days to a few weeks. Some of the variation in the mixed-layer depth in the individual BT observations can be attributed to internal waves with periods ranging from the Brunt-Va isa la period (1-10 min in the upper ocean) to the local inertia I period (between 15.7 hrs at OWS P to 24 hrs at OWS N). The atmospheric events investigated in this study were primarily selected to include periods with impulsive increases in the wind speed. Inertial waves, investigated by Pollard (1970), and Pollard and Millard (1970), which are generated by these moving atmospheric disturbances probably ■ account for some of the differences in mixed- layer depth between the model and data. However, since these internal oscillations have relative small effects on the sea-surface temperature, they are easily distinguish- able from the changes over several days that are due to the turbulent processes parameterized in the models. A total of 49 data sets (20 at OWS P, 16 at OWS N and 13 at OWS V) were finally accepted and modeled using the KT, KIM, and EFT models. The scale depth, Z, for the EFT model (see Eq. 2-53) was calibrated to six data sets (two from each ocean weather station). A va I ue of Z = 50 m gave the best fit to the mixed layer depth, in these calibration experi- ments, and was used in all further applications of the EFT model. It should be noted, however, that none of the data sets chosen for presenta- tion were among the six calibration sets. In this chapter a total of five data sets will be presented (three from OWS P, and one each from OWS V and OWS N). They are i I lustrative of 55 the different atmospheric forcing and oceanic response characteristics that were observed at the three ocean weather stations during this study. The first four data sets were selected during periods when the mixed layer response appeared to be largely one-dimensional. That is to say, the local heat budget was maintained and a one-dimensional mixed-layer model, adequately parameterized to account for dissipation enhancement and partially-penetrative convection, was capable of simulating the mixed layer response. The relative performance of the three models will be examined using these data sets to gain insight into the problem of pro- perly parameterizing the important vertical processes. The final data set was selected to illustrate the capability of the one-dimensional model during periods when non-local processes (e.g., advection) play a significant role in the evolution of the thermal structure. D. CHARACTERISTICS OF THE ATMOSPHERIC FORCING AND OCEANIC RESPONSE AT OWS P In this section three data sets from OWS P are examined to illustrate the characteristics of the upper ocean thermal response under the follow- ing set of atmospheric and oceanic conditions: 1. abnormally strong, impulsive mechanical forcing events occurring relatively early in the fall when the mixed layer is shallow; 2. steady atmospheric forcing (equal to the cl i matolog ical average) occurring in the late fall when the mixed layer is deep; 3. alternate periods of strong and weak mechanical forcing, in the early fall, whi I e the ocean is being heated. The first example was selected from the period 7-19 October 1954. It is representative of the large upper ocean thermal structure modifica- tions that were observed during periods of strong, impulsive mechanical 56 forcing events occurring early in the cooling season (10 of the 20 data sets at OWS P had similar forcing). Figures 4-1 to 4-2A present the relationships between the atmospheric forcing, the observed mixed layer response, and the relative performance of the KT, EFT, and KIM models in simulating the response. In Fig. 4— I A the atmospheric forcing is represented as daily averages of the surface stress (x ), the effective insolation (0 ), the sum of the s ' ^s ' latent and sensible heat (Q_) , and the net heat exchange at the sea sur- face (Q ). In this chapter a positive heat flux represents an upward flux. To illustrate the relative strength of the forcing during this experiment it was determined that 10% of the turbulent kinetic energy and 81$ of the net surface heat fluxes for the month of October 1954 were ex- changed during the period 7-19 October {42% of the month). Furthermore, comparing the forcing received during October 1954 with the long-term mean forcing for October (see Fig. 3-1) showed that the turbulent kinetic energy flux was 120$ I arger than norma I while the net surface heat flux was about average during October 1954. The surface stress is characterized by three distinct peaks (events) centered on II, 14, and 17 October 1954. The net surface cooling (Qy) has only one peak on II October 1954 which does not occur with the largest peak in the stress. The magnitude of Q_, as specified by (3-2) and (3-3), depends to a large degree upon the magnitude of the air-sea temperature and vapor pressure differences, in addition to the wind speed. These air-sea differences were smaller during the second event than during the first and third events. The response of the mixed layer during this period is depicted in Fig. 4- IB, along with the response of the KT, EFT, and KIM models. The 57 C^iCO _ > to en en CL i — (Tl A /' V ' y\ \. -r ' ' 1 i i I i \ i ? IU Li lib la Figure 4-1. Atmospheric forcing and observed and predicted mixed layer response at OWS P during the period 7-19 October 1954. 58 long-term mean trend (CLIM) is displayed as a basis for comparing the mixed layer response. During this experiment the observed mixed-layer depth and temperature (30-52 m, I3.9-I0.8°C) were abnormally large com- pared with CLIM (30-39 m, I 3.9- 1 2.6°C) . It should also be observed that the mixed layer response predicted by the EFT model compared favorably with the general trend in the data (30-55 m, 1 3.9-1 0.9°C) . The KIM model (30-73 m, I3.9-9.9°C) and KT model (30-81 m, I3.9-9.6°C) predicted excessive deepening and cooling. Figure 4-2 depicts the capability of the EFT model in predicting the thermal structure modifications during the period. The agreement between the data and model temperature profile is generally quite good with the exception of the abnormally large temperature gradient predicted below the mixed layer. In .an attempt to correct this undesirable property, vertical diffusion was added to the models. The temperature change due to diffusion was specified according to: |I= A 14 (4-1) at v 8Z2 where A is the vertical diffusion coefficient. A constant value of 2 -I A = 0.5 cm -sec , as used by Haney and Davies (1976), gave acceptable results in the data sets modeled in this study. The diffusion tendency was calculated at each time step with the Euler scheme and added to the profile after the turbulent mixing processes were calculated. A zero- flux condition was assumed at the top and bottom of the profile. The resulting accumulation of heat at the bottom was not significant for the integrations performed in this study (less than a month in all cases). Figure 4-2A shows the results of the EFT model including diffusion. It is clear that the model with diffusion more realistically represents 59 ^r-^ u - i_ A ai en 03 r^. tQ CO? ld Lu CC ncc 2=Q ^ u 0 OS 00T OST (SfcG13WJ HldBG ^r ^ 0 OS 001 OST [StGl3H) HidSG a> i_ 3 +- u 3 — I- (0 +- o 01 — +- — !_ 03 L. CD -C -C +- +- — 2 *"N * CD sz 0) i- ■+- 3 CD M- 01 i_ 4- -Q O • — O M- ■a • CN "fr L0 .J EG ^_J ^r- 0 03 001 OST (SU313W) HiddQ >- — +■ u Q. CD CD to O XCsl 0) F O CM 1 in CD < « — ••w U_ "O 01 CD 10 X3 3 CD — E 0 to c CO • — • (O CM <3- 0 , the ^n ^n ' contribution during the deepening would be to increase A and therefore Qn must be subtracted. If Q < 0 , Q is added to the heat content in n Tn n area A. If the local heat balance is maintained during this evolution, then this calculation will be representative of the entrainment heat flux. Both measurement errors and non-local processes contribute to errors in this estimate of entrainment heat flux. 62 Figure 4-3A indicates that the cumulative entrainment heat flux cal- culated by the EFT model (-8350 ly) was in good agreement with BASE/OBS (-9200 ly). The KT (-16,850 ly) and KIM (-15,400 ly) models calculated unreal i stical ly large entrainment heat fluxes because of the excessive mixed-layer depth predicted by these models. It should be noted, however, that the entrainment heat flux, calculated by the EFT model, is much larger in magnitude than the surface heat flux (+2400 ly) during this period. Therefore, according to (2-21), the principal mechanism account- ing for the large sea-surface temperature change observed in the data was the downward flux of heat occurring during entrainment. The impor- tant implication is that during these large mechanically forced events, an accurate prediction of the sea-surface temperature depends, to a large extent, on the accurate specification of the entrainment heat flux. This is synonymous, in the models, with an accurate determination of the potential energy changes that result from mechanical mixing and convec- tion (see Eq. 2-49). Figure 4-3B depicts the changes in the potential energy as calculated by the EFT model. It should be observed in Figs. 4- I B and 4-3A that the 8h curves representing -sr and w'T'(h) are mirror images of the changes ot in potential energy due to mechanical mixing represented in Fig. 4-3B. It is significant to note, however, that in Fig. 4- I B the curve depicting o ' - gu 8PE -^t— is also similar in shape to -ttt , w'T'(h) and -^p- (the time rate of change of total potential energy). The similarity in the shape of these curves is characteristic of all data sets in which the vertical heat fluxes at the base of the layer dominated the heat budget of the mixed layer. The differences in the performance of the EFT, KT and KIM models may be examined in terms of the potential energy budgets calculated by each 63 o i in _ SURPRCE. _ BRSFvEFT _j* BflSfyKIM Figure 4-3. (A) Relative importance of the vertical heat fluxes and OB) Potential energy modifications calculated by the EFT model during the period 7-19 October 1954. 64 model. Table 4-1 presents a comparison between the total surface heat flux (ZO ) and the total entrainment heat flux (Z w'T'(h)) estimated n from the data and from the model results. The final three columns repre- sent the total potential energy change (ZAPE), the total potential energy increase due to mechanical mixing (ZAPE ), and the total reduction in potential energy due to convection (ZAPE ). These three quantities are related as fol lows: ZAPE = ZAPE + (l-r) ZAPE , (4-2) m c where r is the fraction of convectivel y-generated turbulent kinetic energy available for entrainment and is taken as 0.15. Comparing ZAPE for the three models it may be observed that in the KT and KIM models, considerably more turbulent kinetic energy is available for entrainment than in the EFT model. It should also be noted, comparing ZAPE with ZAPE , that convection was not as important as mechanical mixing during this period. An examination of ZAPE shows that the largest reduction in potential energy is calculated by the KT model because the mixea layer is deepest and therefore convection occurs over a deeper depth (see Eq. 2-51). The net result is that ZAPE is largest in the KT model and smallest in the EFT model. I It may easily be demonstrated that the abnormally large mixed-layer depth and temperature changes predicted by the KT and KIM models are due to the large amount of turbulent kinetic energy available for entrainment. One may express (2-33) as ~, 2(G* - D* - S*) %>m * hAb (4"3' where Ab = p gaAT . 65 t ~ O CN H | •^ r- rH X 0 •^r (N rH ^—^ • • • o o) rH rH rH * W Cn <3 3 1 1 1 W — ' f ~ O CN H | in -tf >£> x p VD ^ V^) "-— ' • • • g X I • • • *— •* 0) o 00 00 * W Cn rH a, >-4 + + + < a; W — ' f s ,w a> o o o o b H in *tf m o ^h Cn 00 ■^f ro CN H £ *» •^ *» «* 12 S3 V£> in CO w h -H H 1 1 1 1 >l c t- 0) O -Q h- E CD +- U Q. CD (D Q U X Csl 0 — — I I in CD o\ s_ — C7) !_ — CD Li_ -Q E CO CD (U > o CD ^ E ro cn CO CN CD L. Q- 1?- 0 ^+ 9+ £T+ 9 £ 0 SS9dlG 69 C\J o <^ o m CO C\J IT, CM LO CM .J CM c° CM ■o 0 s_ CD Q. • r- CD in JZ CTi +- — s_ i_ O CD 4- £1 F -f- CD Q. U CD CD U Q X CD CN (0 CN 1 "vT r* in CD On 1_ — 3 en L. •— 1) lj- .Q E co CD rn > 0 CD z E CO CN CO CN • LP* -3- CD L. 3 O) 0 OS 00T OST (Sti313W) Hld3Q 0 03 GOT 051 (SU313W) Hid3Q 70 only predicted approximately the correct mixed-layer temperature and depth, but accurately simulates the reduction in the temperature gra- dient (AT) immediately below the mixed layer. As shown by Gill and Turner (1976) the reduction of AT during these deepening events is pri- marily caused by non-penetrative convection. Equation (4-3) may be examined to verify that a reduction in AT results in the reduction of 9h hAb and, therefore, an increase in (-^— ) . The reduction in AT is at m the principal mechanism by which convection interacts with mechanical mixing to permit further mechanical deepening of the mixed layer. In Fig. 4-6A and Table 4-2 it should be observed that during this period the total net surface heat flux (+5497 ly) was considerably larger than the entrainment heat flux estimated from the data (-2972 ly), or calculated by the EFT model (-3481 ly). Note also that the entrain- ment heat flux calculated by the EFT model is again in good agreement with the estimate from the data. The KT (-10240 ly) and KIM (-8132) models again calculated abnormally large entrainment fluxes (because of ri h inadequate dissipation) and as a consequence overestimated ^r • ot The potential energy change observed in Fig. 4-6B and Table 4-2, calculated by the EFT model, is very different than in the previous data set (see Fig. 4-2B and Table 4-1). With the exception of the initial increase during the first few days, the general trend is for the poten- tial energy to decrease during the period. As a result the characteris- tic shapes of the curves representing -ttt- , -^p , and -^r— are not similar as in the previous example. This property is characteristic of the EFT model when convection plays a dominant role in the evolution of the upper ocean. The potential energy changes calculated by the KT and KIM models may be examined in Table 4-2 to see that a total increase in 71 V £ Z T 0 -T- z- e- p- l9-**0T)*i;i**Nj/G0tG) .IDNbhD 3 d ^nutnrMia 31 6 9 e o e- 9- ^-**0T)*(Z**^rj.""ib'j) xnid 1U3H 3niiU"inwnG ■o 0 L. CD • Q_r- in CD CT> JZ — +- !_ L. CD O -Q 4- ;- CD +- o CL (!) © Q u X CN CD — ro 1 «* r~ LO 0) Q\ i_ — ^ en L. . — CD u_ -Q E 01 CD ro > O CD Z E ro CN CO CM vO CD !_ CD L 72 3 i - O (N •H | LO i ON •^r iS P ""■ m • • • U K «* ro en ■K W Cn S 5-1 <3 0) 1 1 1 Kl — ' f ~ O CN H | o LD * r KD en 00 • ■ <£> wg ft o r-~ • * i W (T> iH CN CU J-l + + + < 0) w — fV o r-1 E n 00 VO r» ~ L C7> CN <-\ ^r r* i *■. ^ * CTi a a O 00 m •. , W t-1 H Q4 , 1 1 1 1 >. C 0) O <-i j tji r*» r-» r» r- 'Xi c • CD vO CN VO i o> sf — i_ OS 001 QGT (SfcG13W) HlcGCj OG DOT DST 78 r c z I 0 T- Z- 33NbH3 .1 d z o z- p- 9~ 8~ tnnwna -a 0 !_ e — V£> 2< r o ; si CD o m CN h <-* KO CN \D fen Cn m CXi CO *- C *» *» ^ 15 ft KD m •^ * l W M i 1 1 1 1 >. i C * 1 1 1 1 1 ! 1 DEL E- 1 1 s « 1 S 80 a departure from the previous data sets and may be understood by an examination of the dissipation enhancement parameterization in each model . We may express (2-53) and (2-53a) in the following form P n I Z = 0 for XT j- = e ' ( Z = 50 m for EFT (4-5) P w* o * G* " D* D h j- = 1.25 -2j (4-6) PQW* w* Equations (4-5) and (4-6) represent the ratio of turbulent kinetic energy (G*-D*) available for mixing to the surface production accord- ing to the KT model (p w^ ). The ratios in (4-5) and (4-6) are plotted in Fig. 4-10 as a function of various wind speeds and layer depths. They may be interpreted as the percentage of mechanical pro- duction of turbulent energy (relative to surface production of the KT model) available for entrainment in the various models. In the KT model dissipation enhancement is not parameterized and G*-D* is always equal to p w^ . In the EFT model G*-D* is equal to p w* only for the trivial case of h=0 . In general G*-D* < p w* according to (4-5) and therefore the KT model always predicts a deeper, cooler mixed layer than the EFT model. However, because the surface produc- tion in the KIM model was parameterized according to the Kato and Phillips (1969) experimental results, it is 25$ larger than in the KT and EFT models. Dissipation enhancement is parameterized in the KIM model as a linear function of depth and a constant background 81 (G»-D»)/p0^ .5 1 20 40 I UJ O 60 80 100 i — i — i — i — i — i — i — i — r Figure 4-10. Values G*-D* normalized by p w^ as a function of depth and wind speed for the EFT, KT, and KIM models, 82 dissipation (see Eq. 2-53a). In Fig. 4-10 it should be observed that there are combinations of wind speeds and mixed layer depth for which the amount of kinetic energy available for entrainment predicted by the KIM model may be greater or smaller than either the KT or EFT models. During the events characterized by strong mechanical forcing, the response of the KIM model is very similar to the KT model and excessive mixed-layer depths are predicted. However, during periods of weak mechanical forcing, the mixed-layer depths predicted by the KIM model are too shallow and consequently the mixed-layer temperatures are too warm. These model results further suggest that the exponential para- meterization of G*-D* , in the EFT model, may be calibrated for a wider range of wind speeds and layer depths than the linear parameteri- zation in the KIM model. E. IMPORTANCE OF NON-PENETRATIVE CONVECTION In the previous three examples the percentage of convectivel y- generated turbulent kinetic energy available for entrainment was set equal to \5% (r = 0.15 in Eq. 2-50) following Gill and Turner (1976). In this section it will be demonstrated that non-penetrative convection (cooling of the mixed layer without deepening) should be an integral part of any turbulent bulk model. Furthermore, this property is absolutely essential during the fall and winter cooling seasons to pre- vent the models from predicting excessive deepening and cooling rates. Gill and Turner reported that the potential energy of the upper 250 m at nine ocean weather stations in the Atlantic reaches a maximum by early October and decreases during the October to March period. They were successful in simulating these potential energy changes with a 83 modified version of the KT model with r = 0.15. The experiments of Deardorff, et a I . (1969) and Farmer (1975) suggest that r is of the order 0.01-0.15 but there were uncertainties in their estimates. How- ever, the essential feature that must be simulated by the models is a decrease in the total potential energy during periods when the upward surface heat flux is larger than the entrainment heat flux. The data set chosen to illustrate this point is from OWS V during the period 7-19 October 1963. It was selected because it is typical of the response of the upper ocean at OWS V during periods when the net surface heat flux is positive and larger than the entrainment heat flux (10 of the 13 data sets examined at OWS V are in this category). In this experiment, only the EFT model was used and the fraction of convec- tively-generated turbulent kinetic energy available for entrainment was varied between \5% and 100$. Figures 4-11 to 4-13 depict the calculated forcing and the relative capability of the EFT model with varying amounts of non-penetrative convection. The atmospheric forcing (Fig. 4-1 IA) is characterized by a peak in the stress and surface cooling (Q_) centered on 14 October. Com- pared with the forcing in the first example presented (Fig. 4-IA), the turbulent kinetic energy flux was nearly five times smaller, but the net surface heat flux was larger by 550 ly. In the next chapter it will be demonstrated that large upward heat fluxes are common at OWS V because of the extremely large air-sea temperature and vapor pressure differences during the fall and early winter seasons. In Fig. 4- | | B it should be observed that a significant mixed layer response occurred (42-60 m, 24.3-23.5°C) . It should also be noted that the EFT model (r = 0.15) simulates this response with excellent agreement 84 Figure 4-11. Same as Figure 4-1 except for OWS V during the period 7-! 9 October 1963. 85 CO s o !_ o H- +- Q. o © to (J ^o X o> CD — to s_ CN CD 1 ^2 ■* 0 += CD u i_ o 3 CD CT\ U_ 1 r- 01 CO -H o CD ■ — E s_ (0 CD GO CL CN I CD I_ CD Sd31dW) Hiddd 0 OS DOT D5T (Sd3idWi HiddG 86 CO _ en- i * CD CM V I CO o X OJ or. LU 3 TT CLcO -J i CD i Figure 4-13. Same as Figure 4-3 except for OWS V during the period 7-19 October 1963. 87 with the data (42-61 m, 24.3-23.4°C) . Note also in Fig. 4-12 the good agreement between the EFT model (r = 0.15) profiles and the data pro- files. However, the EFT model with r = 0.5 (42-68 m, 24.3-23.2°C) and r = 1.0 (42-74 m, 24.3-23.0°C) predicted deepening and cooling rates that were too large. In Fig. 4-I3A and Table 4-4 it should be observed that the net surface heat flux (+3000) was larger than the entrainment heat flux estimated from the data (-1870). As previously mentioned, this should result in a total decrease in the potential energy and Fig. 4- I 3B and Table 4-4 show that the EFT model with r = 0.15 predicts this response. An examina- tion of the potential energy modifications by the three variations of the EFT model (Table 4-4) illustrates the importance of properly parameteriz- ing non-penetrative convection. It is important to observe that for r = 0.15 ( I 5% of the convecti ve ly-generated turbulent kinetic energy available for entrainment) and r = 0.5 the total potential energy (EAPE) is decreased in the model, while for r = 1.0 it is increased. In fact, as discussed in Chapter II (see 2-51), a model with full penetrative convection (r = 1.0) must increase the potential energy. In accordance with the findings of Gill and Turner (1976) a model with r = 1.0 will not be useful for seasonal integrations. The present results from the EFT model with r = 1.0 indicates that, in certain circumstances, it will also be wrong for very short integrations during the cooling season. The results from the EFT model with r = 0.15 suggest this model (with an exponential dissipation parameterization) reasonably simulates this process. An additional reason for presenting this data set is because its time frame (7-19 October) is the same as the first example (Fig. 4-1) 88 CO X> as L -p • as 3 3 JS i> * c 3J 5 3 0 8 U-l -M > J/J +3 j? tfl CD -U 3 • J c -|J .: 3 3^ fH, -rH •H (1) CD -U a I O CM u W OS O a s CH CN as ■— * 1 x 6 00 ■*— * CN e m • W Cn H a, n + ro (N CN O O O ro + in e. o CN I as o + as CD O en a\ — CN u_ I CO ro ~o O CD — E 1- (0 CD co a. CD Z3 CD J- *>- 0 P+ 9+ c.T + 9 E 0 i-3-ixua^T] xnid iUjh .:]9Udans (s**w3/*a) ss^ais 92 ■ J en r j 0) CD c L. ^XJg 00 o o ■v.. CJ ON X — 0) L. (0 CD O <- 2: en on — CN UL. I ON u° E !- to © CO Q_ I CD [l j CL G v Z2 h- wUj -^"■■"■.^ Gi *— ( i : I 0 OS 00T D9T (Sb3l3H) HidSG 0 OS 001 OST (Sh3l.dN] HidSG 93 8 9 f> Z 0 Z- fr- 9- 8- 9-**0T)*(Z**M3''S0tm dONbHj 3 d 3nilUTlWna 0) jC +- Ol c s_ 3 ■o z CO 3: o !_ o •+- • +- LT» CL MD CD C^ o — X CD !_ CD t^\ jO | E **■ CD > CD O I_ -z. 3 en on — CM u_ 1 CTi CO CO T3 O CD • — E S_ (U CD CO Q. 9 vO — " 1 CD s_ 3 CD 8 9 p c 0 c- ?- 9- 8- (e-**0T)*(2**W3''iti3) xn^j iujh Bniiuinwm 94 energy and net surface flux exchanged during these events were very strong compared with climatology (total u* for November 1965 was 205$ of the c I imatologica I mean for November and total Q was 160$ of the mean). During the period 9-29 November 1965, 95$ of the total monthly turbulent kinetic energy and 80$ of the net surface heat flux were exchanged. It-should be observed in Fig. 4-I4B and 4-15 that the EFT model accurately simulates the evolution of the mixed layer through November 19 and suggests that the local heat balance was maintained during this period. The estimate of cumulative entrainment heat flux from the data (Fig. 4-1 5A) on November 19 also supports this suggestion. However after November 19-20 the observed mixed-layer temperature decreased signifi- cantly, relative to all the models, while the mixed-layer depth was simulated quite well by the EFT model. Furthermore, in Fig. 4- I 6A it may be observed that the entrainment heat flux, estimated from the data from November 19-29, appears to be too large. The layer depth, accord- ing to the data, only increased 8 m during the period November 19-29. This small -?rr coupled with the weak temperature gradient immediately below the mixed layer (Fig. 4-15), would not support BASE/OBS (Fig. 4- I5A) during this period. The reason for the difference between the observed and model mixed layer temperature during November 20-29 is presumed to be due to a hori- zontal intrusion of a cold water mass into the region. This presumption is based upon the observations from Fig. 4-15 that the entire data pro- file (even below the mixed layer) is colder relative to the EFT model. During this period the ocean weather ship reported its position to within 10 NM of 30N - I40W and therefore ship drift was not responsible for the temperature changes. Since the temperature changes observed in Fig. 4-15 95 can not be due to vertical mixing, it is suggestive of a horizontal heat flux. During this period the EFT model was able to simulate the mixed- layer depth quite well and the characteristic slope of the temperature profile was maintained. If the principal motivation for this forecast was to predict the thermal structure modifications, say for predicting the resulting changes in the acoustic properties, then the EFT model results would be very useful. These model results further suggest that if the horizontal heat fluxes were specified, say from an ocean general circulation model, then the EFT model would be capable of predicting the total response of the upper ocean with adequate accuracy. G. RELATIVE PERFORMANCE OF THE EFT, KT, AND KIM MODELS AT OWS P, OWS N, AND OWS V In this section the relative performance of the EFT, KT, and KIM models will be evaluated at the three ocean weather stations. Figures 4-17 to 4-19 depict the daily observed mixed-layer depths versus the predicted depths for the three models at the three ocean weather sta- tions. The diagonal lines are drawn to aid in relating model results to the locus of perfect prediction. In Tab-le 4-5 the RMS and mean errors for the mixed-layer temperature (MLT) and mixed-layer depth (MLD) are presented for the three models at the three stations. A negative mean error in MLD indicates that the model, on the average, predicted a deeper MLD. A negative MLT indicates that, on the average, the model predicted MLT was warmer than the observations. The RMS and mean errors are based on the daily (morning) observed and predicted MLT and MLD and are based on 313 values at OWS P, 238 at OWS N, and 208 at OWS V (this includes all 49 cases studied). 96 120 100 - 80 - Q LU y 60 Q 111 (X a 40 20 •'.•L'y' yvW" &C" : OWS P EFT £- 1 1 l_ i 20 40 60 80 100 OBSERVED MLD (M) 120 \±K) »*S . / • * • / • • ' / 100 • •' • •* / 2 • • ••••". Q It • ■ •• **y ^ 80 »v . ••• . *• " / S. •• « • •?•*•/• Q LU " • i • '"'** / O 60 •• • • /; 5 *• n+y~ LU : *!''/% • K •v» ^ a 40 '.*?• ' OWS P A KT 20 ".'. OWS P Xv ' KIM 20 I C. i i i ' 20 40 60 80 100 OBSERVED MLD (M) 120 Figure 4-I7. Predicted vs. observed mixed layer depths (MLD) at OWS P. 97 120 20 40 60 80 100 120 OBSERVED MLD (M) 120 100 d 80 Q HI O 60 Q HI cr 11 40 20 ~ .. .«» - ••:' C; .•- ; •X . •V >** V %* ••, * • , , N. % *^f y* / ' f , ' 1 1 1 OWSN KT 1 120 100 - 80 - Q ill O 60 Q UJ cr Q. 40 - 20 40 60 80 100 120 OBSERVED MLD (M) 20 - 1 ••/^•" - • a, wVi«« • »'-«*' ,#" \> .; • *♦• * • VI - ! I OWSN KIM i . i 20 40 60 80 100 OBSERVED MLD (M) 120 Figure 4-I8. Same as 4-I7 except for OWS N, 98 120 20 40 60 80 100 OBSERVED WILD (M) 120 \zv •• ** • • / 100 - .♦ / 80 60 - • • *.*t 40 on i i OWS V KT i j 120 20 40 60 80 100 OBSERVED MLD (M) 120 20 40 60 80 100 OBSERVED MLD (M) 120 Figure 4-I9. Same as 4-I7 except for OWS V. 99 TABLE 4—5. Comparison of mean and EMS errors of the models at the three ocean weather stations. OWS P Model MLT HMS(°C) MLT Mean Error (°C) MLD RMS(m) MLD Mean Error (m) EFT KIM KT 0.36 0.49 0.72 +0.16 +0.32 +0.54 6.8 13.8 19.9 -2.9 -7.6 -15.6 OWS N Model MLT RMS(°C) MLT Mean Error ( °C) MLD RMS(m) MLD Mean Error (m) EFT KIM KT 0.34 0.35 0.37 -0.01 -0.02 +0.04 6.7 8.9 10.0 +1.6 +2.2 -2.8 OWS V Model MLT RMS(°C) MLT Mean Error (°C) MLD RMS(m) MLD MEAN Error (m) EFT KIM KT 0.65 0.66 0.75 +0.02 +0.05 +0.18 9.8 11.2 14.1 -1.3 -4.2 -9.1 RMS and MEAN ERROR based on comparison of daily observed and predicted mixed -layer depth (MLD) and mixed -layer temperature (MLT) . Statistics are computed from 313 comparisons at OWS P, 238 at OWS N and 208 at OWS V. 100 It should be observed in Table 4-5 that the RMS and mean errors for MLT and MLD are consistently smallest for the EFT model and largest for the KT model. At OWS P, for example, the scatter observed in Fig. 4-17 and the mean MLT and MLD errors in Table 4-5 show that the models are all biased toward predicting a mixed layer that is too cool and too deep. However the RMS and mean errors, and the magnitude of the scatter in Fig. 4-17, demonstrate clearly that the EFT model simulates MLT and MLD more accurately at OWS P. During the fall and early winter, OWS P is characterized by the largest mechanical forcing observed at the three stations (see Fig. 3-IC). The performances of the EFT model rela- tive to the KT and KIM models suggest that the exponential parameteriza- tion of dissipation enhancement (EFT) was most effective in preventing excessive deepening. At OWS N the mean errors in MLT and MLD, observed in Table 4-5, and the scatter in Fig. 4-18 indicate that the EFT and KT predict MLT and MLD, on the average, too warm and too shallow. The KT model is again biased toward predicting MLT and MLD too deep and too cool. At OWS N considerably less mechanical energy is transferred to the ocean than at OWS P (again see Fig. 3-IC). Therefore, at OWS N, one would expect con- vection to play a more dominate role in the mixed-layer evolution and the performance of the three models to be more similar. The similarity in the scatter in Fig. 4-18 and the RMS and mean errors in Table 4-5 should be observed to be very similar at OWS N. An interesting observa- tion may be made by comparing the relative magnitude of the RMS and mean errors at OWS P and OWS N. At OWS P the relationships between the mean and RMS MLT and MLD errors suggest that the increasing RMS errors are largely due to the increasing bias of the EFT, KT, and KIM models. At 101 OWS H, however, the large RMS errors, relative to the mean errors (most obvious in MLT), would suggest that the errors are more random at OWS N than at OWS P. At OWS V the scatter observed in Fig. 4-19 and the RMS and mean errors in Table 4-5 indicate that the models are all biased toward pre- dicting MLD and MLT too deep and too cool. Again it should be observed that the scatter in Fig. 4-19 and the RMS and mean error for MLD are smallest for the EFT model and largest for the KT model. As indicated previously, mechanical energy and convection are strong at OWS V. The increasing RMS and mean MLD errors for the EFT, KT, and KIM may once again be related to the parameterization of dissipation enhancement in each model. Again it should be observed that the relationship between the RMS and mean errors in MLT would suggest that a considerable amount of the RMS MLT error is random. The data presented in Figs. 4-17 to 4-19 and Table 4-5 clearly indi- cate that the EFT model is capable of predicting a larger percentage of the observed MLT and MLD changes observed in the data sets modeled in this study. The exponential parameterization of dissipation enhancement coupled with an adequate estimate of non-penetrative convection appears to be most reasonable for predicting the changes associated with large atmospheric forcing events. Table 4-6 presents a comparison of the accuracy with which the EFT model predicted the total observed MLT change during the 49 data sets examined in this study. The values in Table 4-6 represent the number of data sets during which the EFT model predicted the various percentages of the total observed MLT change. For example, at OWS P, in 7 out of the 20 data sets, greater than 90$ of the observed MLT change was pre- dicted by the EFT model. It may be observed in Table 4-6 that the EFT 102 TABLE 4—6. Ccmparison of MLT predictions by the EFT model at the ocean weather stations. Percentage of MLT Change Predicted Number of aws >90% >75% >50% >25% Data Sets p 7* 12 18 18 20 N 2 7 12 14 16 V 6 7 10 11 13 *Values in the table are the number of data sets which predict the prescribed percentage of MLT. 103 model showed reasonably good capability in predicting the MLT. For ex- ample, in nearly 50$ of the data sets modeled, the EFT model was capable of predicting greater than 1% of the observed MLT changes. Additionally in 18 out of 20 cases at OWS P, 12 out of 16 at OWS N, and 10 out of 13 at OWS V the one-dimensional model accounted for greater than 50$ of the observed MLT change. It should be noted that in this study only a mini- mum of calibration was performed with the EFT model. The performance of the model was still quite good and suggests that greater reliability could be obtained with more extensive calibration. In addition to providing reasonable estimates of MLT and MLD changes, the one-dimensional model provides a means of separating the contribu- tions of the vertical heat fluxes to the total heat budget of the mixed layer. As may be seen in Fig. 4-I6A (BASE/OBS), the estimation of the entrainment heat flux from the data is very unreliable during periods when non-local processes are important. In the next section we will ex- amine EQ and £ w'T' (-h) from the EFT model results in an attempt to determine the relative importance of these heat fluxes at the three weather stations. H. RELATIVE IMPORTANCE OF THE SURFACE AND ENTRAINMENT HEAT FLUXES In this section an attempt will be made to determine the relative importance of the surface and entrainment heat fluxes during the periods modeled in this study. In the first four examples presented in this chapter, it was demonstrated that during periods when the local heat budget was maintained, the EFT model predicted the mixed layer depth and temperature quite accurately. Furthermore estimates of the entrainment heat flux from the data were in good agreement with model calculations. 104 Since the thermal structure modifications calculated by the model agreed closely with the data, it is assumed the potential energy changes calcu- lated in the model are representative of the potential energy changes occurring in the ocean. Additionally it will be assumed that during periods when non-local processes are important the vertical turbulent heat fluxes are still represented accurately by the EFT model. Figure 4-20A depicts the relative magnitudes of the total cumulative net surface and entrainment heat fluxes calculated by the EFT model. In Fig. 4-20B the total potential energy change (ZAPE) is plotted against the total upper ocean heat content change (ZQ ) calculated by the EFT model. Since the model is one-dimensional AH = ZQ . The data in n Figs. 4-20A,B is representative of the total changes calculated by the model in a I I but three data sets at the ocean weather stations. One data set at OWS P, presented earlier in this chapter, and two at OWS V were examples of weak surface heating periods and the entrainment heat flux totally dominated the heat budget of the mixed layer. These two figures may be interpreted in light of the four one- dimensional data sets previously presented. If EAPE > 0 (Fig. 4-20B) during these periods, then the mechanical mixing by the wind was the dominant vertical turbulent process, and normally this will be indicated in Fig. 4-20A by Z wTTr(-h) > ZQ . If, however, ZAPE < 0 then convection was the dominant vertical turbulent process and |Z w'T' (-h) < |ZQ I. The relationships depicted in Fiqs. 4-20 indicate that the n atmospheric forcing events examined at OWS P were mainly dominated by mechanical mixing. In 15 of the 19 cases examined, Z w'T'(-h) > ZQ and ZAPE _> 0 . At OWS N and OWS V, however, the large majority of the atmospheric forcing events were dominated by convection. In 12 of the 105 X OWSP • OWSV A OWSN v (A) A A t • X x >w X N. A • • • X X • xx X 1 1 ■ x , A >s 10 - 8 9 X >- 4 c a w -2 -10 -8 -6 -4 £ W'T'l-hCLYXIO"3) -2 "AT- XA —2^ X OWSP • OWSV A OWSN (B) X X • A A ■■-4 X ..-6 -L _L -3 4H(LYX10'J) -8 -6 -8 ± ± Figure 4-20, -4 -2 0 2 4 Ez1PE(ERGS-CM~2x10-6) Relative magnitude of the cumulative heat fluxes and total potential energy change at the three ocean stations, (A) Cumulative net surface heat flux (£QR) vs. cumulative entrainment heat flux (Zw'Tf Oh) ) (B) Total potential energy change (EAPE) vs. ocean heat content change (AH). All points calculated by EFT model for total duration of data set. 106 16 data sets at OWS N |Z w'T'(-h)| < |ZQ | and EAPE <_ 0 , and at OWS V 10 of II cases Indicated \Z w'T'(-h)| < \lQ I and EAPE < 0 . i * * n ■ — It has been demonstrated that the large forcing events, whether domi- nated by mechanical forcing or surface cooling, are capable of causing extremely large changes in the mixed layer in relatively short periods. It has further been illustrated that the response during these large events is largely one-dimensional. Additionally, it has been shown that a one-dimensional model, properly parameterized to include dissipation enhancement and non-penetrative convection, is capable of predicting a large percentage of the observed changes. In the next chapter we will attempt to determine how significant Is the role of the large forcing events in the total seasonal evolution of the upper ocean. 107 V. ROLE OF STRONG ATMOSPHERIC FORCING EVENTS IN THE SEASONAL EVOLUTION OF THE UPPER OCEAN A. INTRODUCTION In the previous chapter it was demonstrated that significant changes may take place in the upper ocean thermal structure in response to strong atmospheric forcing events. Further it was shown that the one-dimensional processes, when modeled properly, are capable of predicting a large per- centage of these observed changes in the three locations studied. In this chapter the historical series of surface and near-surface marine ob- servations will be examined in a new and rather unique way, and the principal objectives will be to: 1. determine the significant characteristics of the atmospheric forc- ing during the fall and early wi nter cool i ng season at the three ocean weather stations; 2. demonstrate that the major features of the upper ocean thermal response during the cooling season are explainable in terms of one-dimensional processes; 3. quantify the relative importance of strong atmospheric forcing events to the total evolution of the upper ocean at OWS P, OWS N, and OWS V. B. CHARACTERISTICS OF THE MARINE ATMOSPHERE AT THE OCEAN WEATHER STATIONS To determine the distribution and variability of the atmospheric forc- ing at the three ocean weather stations, values representative of wind speed (u*), turbulent kinetic energy flux (u* ), and upward turbulent heat flux (Q ) were computed from every available three-hourly record, a These values were grouped into equal (32) class intervals (ranked in order of increasing values) and the resulting frequency distributions are 108 depicted in Figs. 5-1 and 5-2. Additionally Table 5-1 lists the signi- ficant statistical quantities which characterize these distributions. In all future discussions a negative heat flux will represent a heat loss by the ocean. The non-gaussian nature of these distributions is evidenced by their characteristic shape and the values of skewness and kurtosis presented in Table 5-1. It will be demonstrated that the large, relatively rare values (reflected by the long tails in the distributions) account for a considerable amount of the total energy exchange. The means of the u* and u* distributions show that the strongest winds and largest turbulent kinetic energy exchanges occur at OWS P while the weakest mechanical interactions are observed at OWS N. From the distribution of 0 it is a observed that the largest turbulent heat fluxes take place at OWS V and the smallest at OWS P. Additionally, Table 5-1 shows that the mean of the u^ distribution, at all stations, is approximately double its stan- dard deviation. This relationship is also valid for 0 at OWS N, while a at OWS P and OWS V the distribution of Q_ has more relative variance a than u*. This implies that the variability of the turbulent heat fluxes is more closely coupled to the variability of the wind at OWS N than at the other stations. It will be demonstrated that the increased variance in Q at OWS P and OWS V is the result of a larger variabi I ity in the air-sea temperature and vapor pressure differences at these stations. These distributions indicate that the characteristics of the marine atmos- pheric forcing are similar at OWS P and OWS V but quite different at OWS N» The similarities and differences in these characteristics may be explained by considering the principal air-sea parameters in terms of the geographical locations of the three ocean weather stations. 109 110 0 2 4 6 8 20 15- S5 > o in a UJ at u. 5-1 -J I 1 1 1 (B) OWS N 100 18 34 48 58 74 90 0 1.4 2.8 4.2 5.6 20 15 ID- S' - ~L — i _r (C) OWS V 1 1 1 100 20 38 56 74 U* (CM /SEC) 92 110 0 2 4 6 8 l4(x10~5)CM3/SEC3 Figure 5- I . Histograms of wind speed (u*) and turbulent kinetic energy flux (u*3) at OWS P, OWS N, and OWS V. Vertical dashed lines represent the mean of the distri bution. 110 20 15 O 2 10 D 0 LU IX 5- (B) OWS N — i * i mz i i -1.40 -1.12 ■84 -.56 -.28 20 15 - 10 5- -1.90 -1.52 -1.14 -.76 QA(x102) LY/SEC _ (C) OWS V J~^ J- 1 1 *""i 1 1 -.38 Figure 5-2. Histograms of upward turbulent heat flux (QQ) at OWS P, OWS N, and OWS V. The vertical dashed lines represent the mean of the distribution. Ill TABLE 5-1. Statistical characteristics of the histograms of wind (u.,J , turbulent kinetic energy (u.,. ) , and turbulent heat flux (Q ). a OWS P Distribution Mean Std. Dev. Skewness Kurtosis u*( cm/sec) 41.9 20.0 0.5 3 . 5x10 _1 Uj. (cm /sec ) 1.3xl05 1.8 x 105 4.2 32.5 Q (ly/sec) -3.2xl0"3 2.2 x 10"3 -1.1 1.6 OWS V Distribution Mean Std. Dev. Skewness Kurtosis u.v(cm/sec) 30.3 15.8 0.9 1.6 uft (cm /sec ) 5. 4x10 ^ 1.1 x 105 11.7 264 Q (ly/sec) -5.5xl0"3 3.7 x 10"3 -1.3 2.1 OWS N Distribution Mean Std. Dev. Skewness Kurtosis uA( cm/ sec) 23.2 11.7 0.9 2.3 uA (cm /sec ) 2.3X104 5.0 x 104 19.9 680 Q (ly/sec) -4.3xl0"3 2.2 x 10"3 -1.4 3.3 112 Tables 5-2 to 5-4 present a summation of the monthly means, and standard deviations about these means, of the principal air-sea para- meters used to determine the atmospheric forcing depicted in the histo- grams. A smaller percentage of vapor pressure differences (E -E ) were calculated (see note 2) because atmospheric moisture information was not always recorded. The marine winds (u ) are strongest at OWS P and weakest at OWS N, a which accounts for the relative magnitudes of the u* and u* distribu- tions. However a more significant observation is that at OWS P and OWS V the increase in the magnitude of the winds, from September to December, is nearly double that observed at OWS N. The air-sea tempera- ture difference (T -T ) and saturated vapor pressure difference (E -E ) w a r r w a are the additional parameters that are important for determining the turbulent heat fluxes. Tables 5-2 to 5-4 show that both of these para- meters are significantly larger at OWS V and OWS N than at OWS P. As a consequence the smallest turbulent heat fluxes occur at OWS P, despite the largest observable winds. The magnitudes of these air-sea differences are related to the loca- tion of the three stations relative to the mean atmospheric circulation in the North Pacific. The general westerly flow at OWS V and northeasterly flow at OWS N, together with the subsidence associated with the subtropical high pressure belt, continuously brings cold, relatively dry air in con- tact with the warm ocean at these two stations. At OWS P, however, the mean flow is westerly, the air mass has had considerable contact with the underlying ocean, and consequently the air-sea temperature and vapor pres- sure differences are small. Additionally it should be observed that these differences are much more variable at OWS P and V than at OWS N (compare the means and standard deviations at each station in Table 5-1). This 113 TABLE 5-2. Variability of atmospheric and oceanic parameters at OWS P. VARIABLE SEPT OCT NOV DEC u (m/sec) a 9.5 (4.6) 11.7 (5.5) 12.5 (5.7) 12.6 (5.6) T -T (°C) w a 0.1 (1.0) 0.5 (1.3) 0.7 (1.4) 0.5 (1.5) E -E (mb) w a 1.9 (1.8) 2.6 (2.0) 2.3 (1.6) 1.5 (1.4) NOTE: (1) Eirst value represents the monthly /seasonal mean of the three-hourly readings while the second (in parenthesis) is the standard deviation. (2) Statistics are based upon 90% (21,030) of the possible three-hourly observations of E -E and 96% (25 ,524 ) of the remainder of the variables. 114 TABLE 5-3. Variability of atmospheric and oceanic parameters at OWS V. VARIABLE SEPT OCT NOV DEC u (m/sec) a 6.7 (3.7) 7.8 (3.8) 9.2 (4.4) 10.1 (4.8) T -T (°C) w a 1.0 (1.4) 1.3 (1.6) 2.0 (2.0) 2.4 (2.2) E -E (mb) w a 8.1 (4.2) 7.9 (4.4) 8.7 (4.3) 8.0 (4.2) NOTE: (1) Eirst value represents the monthly /seasonal mean of the three-hourly readings while the second (in parenthesis) is the standard deviation. (2) Statistics are based upon 75% (10,930) of the possible three-hourly observations of E -E and 96% (14,065) of the remainder of the variables. 115 TABLE 5-4. Variability of atmospheric and oceanic parameters at OWS N. VARIABLE SEPT OCT NOV DEC u (m/sec) a 5.6 (2.9) 5.9 (2.9) 6.9 (3.3) 7.3 (3.4) T -T (°C) w a 0.9 (1.0) 1.2 (1.2) 1.5 (1.3) 1.5 (1.4) E -E (mb) w a 8.1 (2.3) 8.4 (2.7) 8.2 (2.9) 7.2 (3.0) NOTE: (1) Eirst value represents the monthly /seasonal mean of the three-hourly readings while the second (in parenthesis) is the standard deviation. (2) Statistics are based upon 76% (17,146) of the possible three-hourly observations of E -E and 95% (23,377) of the remainder ol the variables. 116 would explain the additional variance in Q at these two a stations. The magnitude and variability in these data suggest strongly that the characteristics of the marine atmosphere at OWS P and OWS V are closely related to the frequency and intensity of the large winter storms that occur at these locations. The atmospheric forcing at OWS N, on the other hand, is more closely coupled to the properties of the mean ci rculation. To examine the relative distribution of the turbulent kinetic energy and the turbulent heat fluxes, the percentage of these quantities along with the percentage of observations in each class interval were computed, For examp le N 3 PEj = 100 £ u/ / £ u*3 (5-1) k=l represents the percentage of turbulent kinetic energy that occurs in the j interval, n is the number of observations in the interval, and N is the total number of observations. Percentages of the turbulent heat fluxes (Q ) and wind (u*) were calculated with similar expressions. These percentages were accumulated from the smallest to the largest values and are compared in Fig. 5-3 in the form of cumulative frequency diagrams. The values for the cumulative percentage of u* and Q are determined from the upper scale of the abscissa, while the cumulative percentage of obser- vations are obtained from the lower scale. For example, Fig. 5-3A indi- 3 5 3-3 cates that a I I observations of u^ less than 10 cm -sec account for 74#/90$/97# of the total observations at OWS P/V/N, but account for only 117 3x105 10 100 U3* (CM3/SEC3) 106 107 3x107 (UPPER SCALE) OBS (LOWER SCALE) 3x10' 10' -3x10-2 -10-2 10 a Uj (CM3/SEC3) QKLY/SEC) -10'3 10< 3x10* -10 -4 -3x10 -4 100 80 LU §60 Z LU o LU a40 20 o* K% ,P COOLING (UPPER SCALE) \ \ \ \\ \ w \ w * w w V' Vx \x \ V (LOWER SCALE) 0 -3x10 -1 -10 -1 ■£ -io-2 QKLY/SEC) -10" -3x10 -3 Figure 5-3. Cumulative percentage of turbulent kinetic energy (TKE), surface cooling, and observation at OWS P, OWS N, and OWS V. (See text for explanation,) 118 30$/56$/83# of the turbulent kinetic energy flux computed from these re- cords. Similar comparisons can be made regarding the distribution of the turbulent heat fluxes from Fig. 5-3B (except that increasing values are read to the left). The horizontal displacement in these curves indi- cates that the turbulent kinetic energy exchange at the three stations increases from a minimum at OWS N to a maximum at OWS P, while the turbu- lent heat fluxes are smallest at OWS P and largest at OWS V. The example just presented indicates that at all -stations a large percentage of the observations account for a relatively smaller percentage of the turbulent kinetic energy fluxes. It is easily verified from Fig. 5-2B that this is also valid for the turbulent heat fluxes. Furthermore the characteristic shape of the u* curves suggest that although the magnitude of the turbulent kinetic energy f I ux is different at each station its di stri but ion is quite similar. The shape of the 0 curves would indicate that the distributions of turbulent a heat fluxes are similar at OWS V and OWS P but slightly different at OWS N. Additional information may be obtained by plotting the cumulative per- centages of Ufc , Q . and u* against the cumulative percentages of observa- a tions, as in Fig. 5-4. The first important observation from these curves is the relative invariance in the d ilstr i but ion of u# and u* at the three stations (in these figures there is less than 3$ scatter). Although these curves were constructed from the entire sample of values, curves drawn from the individual monthly values were nearly identical, and indi- cate that these distributions are also invariant with respect to month during the cooling season. The distribution of Q was identical to u* at OWS N while at OWS P and OWS V the curves indicate a higher percentage of 119 100 co 80 * D Li. O LU o 0 > Q > and Q were summed and the monthly totals are presented in the first four columns of Tables 5-5 to 5-7. The next two columns show the long-term mean monthly changes in the sea-surface temperature (ASST) and the mixed layer depth (AMLD). The relative contribution of the net surface heat flux (ZQ ) to the mean sea-surface temperature change is presented in the last column as ASST(ZQ ). This contribution was esti- n mated by distributing ZQ over the mean layer depth at the beginning of the month (upper value), and at the end of the month (lower value). Since the layer deepens between these two depths, the actual contribution of ZQ is somewhere between these two extremes. 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As expected, the largest flux of turbulent kinetic energy (Zu* ) is received at OWS P and the smallest at OWS N, with a general increase in magnitude during the season at all stations. At OWS P and OWS V, however, Zu* increases rather abruptly in October and November respectively. It is quite evident that at OWS N no abrupt changes in Zu* occur during the cooling-season in any month. This is rather suggestive that at OWS P and OWS V these abrupt increases in Zu* mark the onset of the winter storm season at these stations. At OWS N the trend in Zu* would suggest a slow intensification of the wind, which would be indicative of the wintertime strengthening of the mean circula- tion. The monthly Q values at the three stations show the same relation- ' a ships as previously noted in the histograms (Fig. 5-2). The most intense turbulent heat fluxes occur at OWS V and the weakest at OWS P. By compar- ing the mean and standard deviations of ZQ at the three stations, it may a be noted again that the turbulent heat fluxes are more variable at OWS P and OWS V than at OWS N. As expected, the effective solar insolation, ZQ , decreases throughout the season and with latitude. Additionally it should be observed that the insolation at OWS P has much more variability than at the other stations. Since this can only be introduced by the total cloud cover (see Appendix A), it is indicative of the changes in the cloud patterns that accompany the cyclonic storms at OWS P. At OWS P the cloud-types are normally low stratus and the sky frequently covered by heavy overcast throughout this season. The exception to this pattern occurs in the cold, dry air mass behind the cold front where the cloud patterns are broken and, therefore, allow more insolation to reach the sea surface. At OWS V and OWS N, however, the sky is not normally overcast 126 and the storm systems do not introduce as much variability in the total cloud amounts. Finally the net heat gain or loss by the ocean is re- flected in the fourth column of Tables 5-5 to 5-7 as EQ . There is a n net heat gain, at a I I stations, during September and this downward heat flux is largest at OWS N and smallest at OWS V. During the remaining three months ZQ is increasingly negative, at all stations, and is most negative at OWS V and least negative at OWS N. The oceanic thermal response has characteristic trends, at each sta- tion, that we will attempt to explain with one-dimensional reasoning. The total mixed layer depth change (AMLD) is largest at OWS P and smallest at OWS N; however, the trend is similar at all three stations. The deep- ening rate increases early in the season and is reduced at the end. The seasonal sea-surface temperature change (ASST) is comparable at OWS V and OWS P, but significantly smaller at OWS N. It should be noted that the trend in ASST is different at OWS P than at OWS V and OWS N. At OWS V and OWS N, ASST increases throughout the season, while at OWS P ASST in- creases during October and decreases in the final two months. If one-dimensional reasoning is applied to the long-term forcing and oceanic response, a considerable amount of the observed changes are ex- plainable. Consider first the amount of the monthly sea-surface tempera- ture change (ASST) that may be explained by the net surface flux (EQ ). September, at all stations, marks the transition between the heating and cooling seasons and the data indicate that the surface fluxes increase the heat content of the upper ocean at all stations. This occurs during a period when the sea-surface temperature is normally decreasing at OWS P and OWS V, and unchanging at OWS N. Therefore the sea-surface tempera- ture change, during September, cannot be explained (and certainly not predicted) in terms of the surface heat fluxes alone. The net surface 127 fluxes become increasingly negative from October to December; however, ASST(ZQ ) increases from October to November and then decreases in Decem- n ber. This is because the ratio of the net surface fluxes to the mixed layer depth increases from October to November and decreases in December (i.e. ASST (ZQ ) - r- ZQ ) . This illustrates the importance of the mixed n h n r layer depth in determining the effect of surface fluxes on the sea- surface temperature change. The relative importance of the surface fluxes to the total sea-sur- face temperature change may be ascertained by comparing the cumulative contribution of ASST (ZQ ) in Tables 5-5 to 5-7, for the final three n months, with the total sea-surface temperature change during these months. At OWS V and OWS N greater than one-half of ASST may be directly explain- able by ASST (ZQ ), while at OWS P only one-third is explainable. Final- ly, as a measure of the dominance of the surface fluxes, consider the months during which ASST (ZQ ) accounts for greater than 50$ of ASST. At OWS V and OWS N these fluxes become dominant during November while at OWS P this does not occur until December. It is evident that, even during the months when these surface fluxes appear dominant, they are not capable of explaining the total sea-surface temperature change. The other significant vertical process which might explain the differ- I ence between ASST and ASST (ZQ ) is the heat flux at the base of the mixed n layer that occurs during entrainment. In fact, during large deepening events, the entrainment heat flux may actually dominate the surface heat flux, as was demonstrated in the previous chapter. Since this heat flux cannot be computed from these data, we must infer its relative magnitude from the turbulent kinetic energy flux (Zu* ), the mixed layer depth change (AMLD), and the characteristic thermal structure at the three ocean weather stations. 128 It is important to observe that nearly twice the turbulent kinetic energy is transferred to the ocean at OWS P as at OWS V, and greater than five times as much as at OWS N. Additionally, the maximum seasonal residuals between ASST and ASST (ZQ ) that must be explained are -5.2°C, -3.7°C, and -2.4°C at OWS P, OWS V, and OWS N respectively. The rela- tive magnitudes of these fluxes and residuals are understandable in terms of (2-49), (2-50), and the fundamental differences in the thermal structure at the three stations, illustrated in Fig. 5-5. The character- istic shape of the profiles at OWS V and OWS N are quite similar, but considerably different than the profile at OWS P. This is because at both OWS V and OWS N the parent water mass is North Pacific Central (Sverdrup, 1942), while the water mass at OWS P is Pacific Subarctic. However, the important difference to be observed in the three profiles is the magnitude of the temperature gradient immediately below the mixed layer. The temperature change from 70-80 meters is approximately 2.5°C /2.I°C/I.5°C at OWS P/OWS V/OWS N. The relative magnitudes of the temperature difference (AT) at the base of the mixed layer is in the same proportion at the beginning of September. Equations (2-49) and (2-50) indicate that the largest amount of tur- bulent kinetic energy would be required to mix the upper layers of the ocean at OWS P and the least at OWS N. This is completely consistent with the relative magnitudes of Zu* noted previously in Tables 5-5 to 5-7. Additionally, comparing AMLD and AT at each station, we should ex- pect the largest entrainment heat flux (rr AT) at OWS P and the smallest a T at OWS N. This is consistent with the relative magnitudes of the sea- surface temperature residuals computed at the three stations. The seasonal trend in the mixed-layer depth is understandable in terms of the magnitude of Zu* and the concept of dissipation enhancement, 129 17 20 18 TEMP(°C)OWSV&N 19 20 T T 21 -FT 22 OWSP OWSN OWSV 5 6 7 TEMP(°C) OWSP 8 Figure 5-5. Typical mid-season temperature profiles at the three ocean weather stations. 130 discussed in the previous chapter. As the layer deepens, the entrainment zone is displaced from the surface production zone, and a greater percent- age of the turbulent kinetic energy is dissipated. In accordance with (2-33) as the ratio of G*-D* and h decreases the mixed layer deepening rate also decreases. This occurs in November at OWS P and OWS N and in December at OWS V0 It is encouraging to note the major trends in these data are consis- tent with simple one-dimensional reasoning. However, it is important to realize that these trends are not explainable solely in terms of the surface forcing. It is necessary to be able to specify both the surface heat flux and the entrainment heat flux to accurately describe the sea- sonal mixed layer evolution. The entrainment heat flux will dominate the surface heat flux early in the season when -^— and AT are large and the surface heat fluxes are small. By the end of the season the large surface heat fluxes become the dominant factor in changing the sea- surface temperature. D. IMPORTANCE OF LARGE ATMOSPHERIC FORCING EVENTS IN DETERMINING THE SEASONAL EVOLUTION OF THE MIXED LAYER In this section the seasonal evolution of the mixed layer will be ex- amined relative to the long-term mean trend to illustrate the importance of large atmospheric forcing events in changing the upper ocean thermal structure. The purpose of this analysis will be to demonstrate that the timing of the first large storms (whether they occur early or late in the season) is very important to the seasonal evolution of the mixed layer. Evidence will be presented to illustrate that the underlying thermal structure is as important as the surface forcing. Two cooling seasons, taken from the OWS P record, were chosen to demonstrate these principles, 131 because both the atmospheric forcing and the thermal structure were very different during these two years. Mid-October temperature profiles (Fig. 5-6) illustrate that the mixed layer was deeper and cooler during 1963 than during 1959. Notice also that the temperature gradient at the base of the layer during 1963 was considerably weaker than during 1959. The final observation is that in 1963 there was a much stronger thermal gradient below 60 meters during 1963 than in 1959. Figures 5-7 and 5-8 depict the observed forcing and oceanic response during these two seasons, with the long-term mean trends superimposed. In Table 5-8 the strength of the forcing and response characteristics are presented and compared with the long-term mean. In Figs. 5-7A,B it is observed that at the start of the 1959 season the mixed layer was considerably deeper and cooler than the long-term mean. However, at the beginning of September 1963 a very warm, shallow layer is present (Figs. 5-8A,B). The character and timing of the atmospheric forcing during these two seasons may be observed in Figs. 5-7C,D and 5-8C,D. During 1963, the period from 15 October to I November marks the beginning of the winter storm season. In 1959, with the exception of the one significant event in mid-October, the large forcing events do not begin until mid-November. The difference in these storm patterns coupled with the different initial temperature structures result in the evolution of the upper ocean being quite different during these two seasons (compare Figs. 5-7A,B and 5-8A,B) In the previous chapter, it was demonstrated that large forcing events that occur early in the season produce much larger oceanic thermal re- sponses than events occurring late in the season. This is consistent with what is observed in Figs. 5-7 and 5-8, and we will examine the 132 20 40 jE 60 Q. LU D 80 100 120 5 TEMPERATURECC) 7 9 T T -OWSP 1963 -OWSP 1959 11 13 Figure 5-6. Mid-October temperature profile at OWS P. 133 24 - A . p 2 21 - s D 1- < %U... %«a %Q xs %Q xn %AMLT %AMLD Sept 12 20 42 -11 25 21 Sept 15 14 42 -12 -6 -16 Oct 40 40 34 UQ 51 51 Oct 21 21 30 14 27 27 Nov 23 26 15 41 16 J* Nov 35 25 16 33 38 it Dec 25 14 9 21 8 3C Dec 29 40 12 65 41 •♦• 'Missing Data 1963 Forcing and Response (as a percentage of the long-term mean) 1959 Month %u* %\ %Q xs %Q xn %AMLT %AMLD Month %u* %^a %Q xs %Q n %aml: %AMLI Sept 95 134 119 8: 248 150 Sept 115 9: 99 lit -28 -80 Oct 176 156 130 1-: 174 154 Oct 83 8*- 95 69 51 58 Nov 86 96 107 ' i 7- * Nov 121 ^5 97 94 98 •:c Dec 99 56 106 4 c ^6 j. Dec 104 16C 118 171 181 * Season 114 108 12 'J gu 137 100 Season 1C6 109 99 121 76 71 Oceanic Response (j.962) Month MLT(°C) MLD(M) Oceanic Response (1959) Month MLT(°C) MLD(M) Sept 15.3-12.9 " 3-33 Sept 12.5-12.8 45-37 Oct 12.9- 8.1 -70 Oct 12.8-11.4 37-51 Nov 8.1- 6.6 70- ' Nov 11. u- 9.4 51-* Dec 6.6- 5.8 * -yo Dec 9.4- 7.2 - -96 Month _e ~'ct Nov Dec Oceanic Response (long-term mean) MLT(°C) 13.3-12.3 12.3- 9.5 9.5- 7.5 7.5- 6.3 MLD(M) 28-38 38-62 62-^3 83-100 136 oceanic evolution during these two seasons to show that the major features are explainable by one-dimensional reasoning. During 1963 the month of September had weaker than normal downward fluxes of turbulent kinetic energy (u* ) and heat (Q ) (compare percentage of long-term mean in Table 5-8). The mixed layer, however, deepened and cooled more than the long-term mean. The larger than normal deepening and cooling rate was the result of the layer being warm and very shallow at the beginning of the period. Because the layer was shallow, only a rela- tively small amount of turbulent kinetic energy was dissipated, which resulted in the large entrainment rate. As would be expected, the verti- cal re-distribution of the heat in this warm layer resulted in a larger than normal entrainment heat flux and consequently abnormal sea-surface temperature change. During October 1963 the large winter storms are responsible for an energy exchange between the atmosphere and ocean which is significantly larger than the long-term mean. These large fluxes force the mixed layer to deepen and cool, such that by the end of the month the layer is deeper (8 m) and cooler ( I ,4°C) than the long-term mean. During these first two months 52%(60$) of the seasonal u* (Q ) was received by a the ocean, which is \0% greater than the long-term average. However, this abnormal forcing accounted for 75% of the mixed layer response during the season, which is 25% greater than normal. Th i-s large response occurred because the strong forcing came early in a season when a large heat storage had taken place in a very shallow mixed layer. The final two months of 1963 were characterized by weaker than normal forcing. The upward heat fluxes (Q ) account for only 40$ of the seasonal total (10$ less than normal) and this is a consequence of the anomalously cool sea-surface temperatures. The turbulent kinetic energy flux (u* ) received during the final two months is less than the long-term average 137 but is actually about the same amount received during the first two months (48$ of the seasonal total). However, the response of the layer is only 25$ of the seasonal total. The turbulent kinetic energy flux received during the final two months is simply not sufficient to accom- plish any significant deepening. Evidently this is because the entrap- ment zone is deeper than normal, a larger percentage of the turbulent kinetic energy is dissipated, and the ratio of G*-D* to h is less than norma I . Examination of the total seasonal forcing (Table 5-8) shows that greater turbulent kinetic energy and smaller net heat fluxes were ex- changed at the air-sea interface during the 1963 season, which resulted in a normal seasonal deepening rate but a I arger-than-norma I sea-surface temperature change. This is consistent with our earlier findings that a temperature structure that has a large heat storage in the near surface layers will require a large amount of energy flux to deepen the layer. Additionally this deepening will be accompanied by a large entrainment heat flux and, consequently, a large sea-surface temperature change. This example demonstrates clearly that the energy fluxes received early in the season results in a much larger mixed layer response than comparable energy fluxes received late in the season. An additional ob- servation is that during September and October the anomalously large up- ward heat fluxes (Q ) are accompanied by significantly I arger-than-norma I a downward fluxes of solar radiation (Q ). This supports our previous suggestion that the large variance in Q (Table 5-5) at OWS P is due to the large winter storms. The air mass is generally cold and dry during stormy periods and there is usually less cloud cover than the mean winter conditions. 138 The evolution of the mixed layer during the 1959 season was quite different than during 1963 (Figs. 5-8A,B). Since the mixed layer was deeper and cooler than normal at the start of the season, it is pre- sumed that a significant re-distribution of the heat was accomplished by strong summer forcing (evidence will be presented to support this presumption). The turbulent kinetic energy was stronger than normal during September 1959, but so was the downward net surface heat flux (see Table 5-8). As a result, the .mechanica I energy was insufficient to mix this additional heat to the old mixed layer depth and a new shallower mixed layer formed above the old one (see Figs. 5-8A,B). By the end of the month the layer depth had retreated to near the long- term mean while the temperature is warmer than normal. The forcing re- ceived during October 1959 is much weaker than normal and only a weak mixed layer response takes place. The forcing received during the month of November is characterized by extremely strong mechanical forcing while the upward heat fluxes are smaller than normal. Because of the gap in the bathythermograph record it was not possible to determine the mixed layer depth at the end of the month. However, Fig. 5-8B would seem to indicate that the deepening rate is larger than normal. Because the net surface flux (Q ) is less than normal the sea-surface tempera- ture decreases on I y a normal amount and at the end of the month the /layer is probably deeper but significantly warmer than normal. December 1959 is characterized by average mechanical forcing but extremely larger upward turbulent heat fluxes. The sea-surface temperature change is much larger than the long-term mean as a result of the large surface heat fluxes. At the end of the season the layer depth is about normal but the sea-surface temperature is approximately I °C warmer than normal. 139 The seasonal totals in Table 5-8 show that the forcing was actually stronger than the long-term mean and yet less than normal oceanic re- sponse occurred. This is primarily the result of the deep mixed layer that was present at the beginning of the season. The forcing during the first two months was not sufficient to establish the normal deepening and cooling rate. The large winter storms came late in the season and were not able to reduce the sea-surface temperature the additional amount necessary to bring the ocean back to the long-term mean. These two examples illustrate that the timing of the strong atmos-r pheric forcing events coupled with the characteristics of the underlying thermal structure are of primary importance in determining the evolution of the upper ocean during the cooling season. Once again it should be noted that the large forcing events produce a much greater oceanic re- sponse when the mixed layer depth is shallow (usually early in the season) It may be seen in Fig. 5-5 that the temperature structure is quite different at OWS P than at OWS N and OWS V. Furthermore Fig. 5-6 shows that the thermal structure may have considerable variability from year to year at a particular location. Since the seasonal thermocl ine is estab- lished during the spring and summer, these figures would suggest that the mechanisms responsible for its formation may vary depending on loca- tion and year. The spring and summer forcing, observed during 1959 and 1963 at OWS P, were compared to see if the differences in the temperature structure, depicted in Figs. 5-6, 5-7A,B, and 5-8A,B, are explainable in terms of one-dimensional processes. The mechanical forcing observed during the spring in 1959 was much weaker than observed in 1963. However, the synoptic patterns observed during the summer indicates that the 1959 season was characterized by a high incidence of strong storm activity 140 while the forcing was extremely weak during 1963. Consequently the layer retreated very rapidly during the spring of 1959 and because very little heat was mixed below 60 meters, the seasonal thermocline below this level was nearly isothermal. On the other hand, during 1963 a considerable amount of heat was mixed into the deep layers by the strong spring forcing, and a relatively strong thermal gradient was established below 60 meters (see Fig. 5-6). The strong summer forcing during 1959 caused a large downward transfer of heat and resulted in a very deep, cool mixed layer at the beginning of September (see Fig. 5-7A,B). The weak forcing during the summer of 1963 was insufficient to maintain a normal summertime mixed layer depth and a very warm, shallow layer developed (see Fig. 5-8A,B). This simple analysis suggests that the synoptic storms may be as important to the establishment of the seasonal thermocline during the heating season as they are to the subsequent erosion that takes place during the fall and winter cooling season. The evolution of the upper ocean during the cooling season is determined to a large extent by the nature of the stability of the thermocline. Therefore it is important to realize that the entrainment process may be influenced by the nature of the forcing during the previous spring. A simple conclusion would be that the spring and summer heating season should be examined in detail to determine the relationship between the principal mechanisms that govern the formation of the seasonal thermocline. E. IMPORTANCE OF THE STRONG ATMOSPHERIC FORCING EVENTS AT THE THREE OCEAN WEATHER STATIONS In this final section the total record (see Table 3-1) of the surface and near-surface parameters will be examined to determine the relative 141 importance of large forcing events to the total evolution of the upper ocean thermal structure. The objectives of this analysis will be to determine: (1) the principal characteristics of the large events at the three stations; (2) the percentage of the total energy that is exchanged during these events. Figure 5-9 is presented to explain how the analysis was performed. An event will be defined as those individual periods when the forcing was greater than the long-term mean. For example, in Fig. 5-9 there are 12 individual events during the season. If the forcing is greater than the long-term mean at the beginning or end of the season it is counted as an event. If an event takes place during two months (for example events 3 and 9), the amount of energy received during each month is calculated and the event is credited to the month in which the largest energy exchange occurs. For example the third event in Fig. 5-9 would be credited to October and the ninth event to November. The duration of an event is defined as the time during which the forcing is greater than the long-term mean. An additional parameter was the ratio of the peak value of the forcing to the long-term daily mean. This peak-to- mean ratio (Pk) was used to examine the effects of the larger events. For instance we might only examine events where Pk > 1.5, etc. The analysis was performed first by defining the forcing events in terms of the u^ curves (mechanical events). Next the analysis was repeated with the events defined by the Q curves (cooling events). The results a from both of these definitions will be presented. The response of the ocean thermal structure was estimated from the seasonal sea-surface temperature change (based on the surface marine 142 Figure 5-9, Characteristic of events, 143 observations) that occurred during each event. The ratio of the cumula- tive changes in sea-surface temperature taking place during the events to the total seasonal change is the percentage of the total response that occurs during the events. In a similar manner, the percentage of the total duration, u* and Q occurring during these events was calcu- lated. The large data gaps in the bathythermograph record would not per- mit analysis of mixed layer depth during these events. However, the examples presented earlier in this chapter, and the results from the numerical models indicate that large changes in sea-surface temperature are normally accompanied by large changes in the mixed layer depth. In the first part of this analysis we will examine the percentage of the monthly forcing and response that takes place when the forcing Ceither u^ or Q ) is greater than the long-term mean. The results of this analysis is presented in Tables 5-9 to 5-11 and is based upon the 24/23/15 seasonal records considered at OWS P/OWS N/OWS V. The data presented in these tables is consistent with our original hypothesis that a significant percentage of the atmospheric forcing and oceanic response takes place during periods when the forcing is strong. The first observation is the relative invariance in the duration of the forcing at all stations. The mechanical events characteristically are shorter in duration than the cooling events because large air-sea tern- perature and vapor pressure differences persist longer than the strong winds. The relationship between the duration and the percentage of tur- bulent kinetic energy exchanged during these periods is also very consis- tent at a I I stations. At a I I stations a large percentage of u* takes place during a relatively short time frame. Although the magnitudes of these large energy events are significantly different at the three 144 t ■M -P CO +-> I CO 13 TD ON I LO (1) § en bO o CT> CM H CO rein than 2 =t CO CO r-~ o Uh ^ CD O TJ £ en ro CM c*» CD O d" cn o r- bfl bO rH •M ft) rcen en Q £ w zt- CM CO H CD JZ CO j- CO 1 CM 0- 3 rH s CD CD cn 6 c _ O a b a ro o CM LO CO CO W o CD H CD CO bO C •5 5 2 CO r~- rf LO O -M £ §| •H uh rd B CO CD CO CO o g CD bO ro en o ro CO LO CO •m -:« s J r_ g 6 w LO o o CO CD rC CO ro c-» CM o 0* 2 H bO / •5 / p / CD C ^ / i— 1 0 •~\ ^^ /— s o / ■a •H o\° o\° o\° Pm / ■M <-^ v_^ ^^ *»_• •H ftf o\° co H B H v— ' 3 o^ 00 CO > " o 145 i 03 T3 LO a d) § CO OJ C 6 a e w r- if c*- if 03 C Q CO LO CD LO d re g-te S § H > bfl O LO CM CD H rein than 2 id- CD C»> r- 0 <+h b 0) o o if O CM CD •5 2 CO [*- LO CD O -M u-i 5 4-> mh " < 146 S3 rH a; 3 rC 1 4-> H 5 • 3 S TJ C/D nj ^ fa O M -P O ft) o o 0) • iii B a 4-> CU E en 8 en rH | d 5) n) -p 4-> JLj o | 3 ■M bO c rd >i o u rH H d) x: Qh4- CU p c rC 4-> y ■4-J CU (U B y -1 Hi -p 4-> 4h § 4-4 fa () CU cn -H I cn fl a; CO 01 V 4-> g, s s$ O 3 fa bfl •5 & Mh lo 3 CU § cn a) C E a e w CM rH o H cn C Q zr CO oo CO d re g-te § o rH > bO o rH CD CO CO rein than z: d- CD CO r~ o IN fa CU 4-1 4-> o (d CJ CO H r>- CO CU o d- C-» CO o CU fa bfl bO rH rH -M rtf rcen en Q E CO w CO =t LO cn CU Xi GO It CO rH CO CU 5 1 rH B CU cy cn E C ^ CJ a g w r- LO CD OO Q CO t>« LO LO cn cu 2 V bO -a c r3 rH > o r- CD CD CD bO C •5 J s CO [>■ CD CO O 4-J fa 4-i aj 4-J 4h 1) £ r> CD O zt o a, CU bO rtf co o CO O- LO rH CD 4-- -k C 3 1 cu P-I o q £lj 'fa v_^ s^^s n— y •H rO o\° CO H £ C_i \ ■ ^" aP 00 00 > " < 147 stations, these data would support the suggestion, made from the histo- grams, that the distribution of u* is fairly invariant at the three stations. Because 0 includes both Q and Q it is much more variable Yn a Ys than u* . During September, for instance, when there is normally a net downward heat flux, a net upward heat flux takes place during these strong forcing periods (compare Q at each station). This simply means that in September the surface cooling that does take place probably occurs during these strong forcing periods. It is also evident from these data that there is net heating taking place during October at all stations. This is reflected by Q being greater than 1 00% during these months. As ex- pected u* is larger in the mechanical events and Q is larger in the cool i ng events. The final, and most significant observation, is that during all months (mechanical and cooling events) a significant percentage of the sea-surface temperature changes (ASST) takes place during a relatively short duration. Also the general trend in these data is that ASST de- creases as the seasons progress. This is true for both the mechanical and the cooling events. This once again supports the argument that the large atmospheric forcing produces a larger oceanic response early in the season when the mixed layer is shallow. The second part of the analysis was designed to determine the charac- teristics of these large events and their relative importance to the seasonal evolution of the thermal structure. The results of this analysis are presented in Tables 5-12 to 5-14 in the order of increasing peak-to-mean ratios (Pk). Therefore the statistics in Table 5-12 repre- sent every period in the record identified as an event, while those in Tables 5-13 and 5-14 represent only those events where Pk > 1.5 and 148 CD en »-n O ' 2g C CD f *J S3 as x: •H en •3 Id •H > CD X) en § cu en C en a- en en cu ££ a, bfl o & en O cu O 'fO •H > •M w en •H fc • CD o +-> . &s 6S CN t LO 2 •— \ •~\ ^-N to o CO J- CD CD cn H rH H CD oo j- • • O0 rH CO zf • • CO CO CO LO • oo rH • ■ - — — — N_^ \^ s_/ en -M s > bO /•"X ^^ s-\ CO 3 rH CD LO O CD 00 CO CO • • =t 1— I CO CM • • CM CM -3" CM rH • •5 rH 8 >»• v— • Nw^ o a. •~\ <•"> /*N o CD CO CD 00 CO J- oo • • CM rH • • CO CO J" CD • CO H • s ^"N s~\ /— N en CO 3 CO CO CD LO 00 00 j- • • CO rH CD J" • • CM CM rH CO • • CM LO -P ^-/ N^ s_^ C 0) > > 0 •H /* \ «""\ ^"> CO 3: o OO CO CO CO rH CO LO • • J" rH co r-~ • • CM rH CD CO • • rH rH g ^-y s_ y ^-^ CD S a. <~\ i»~\ ^> CO O CO CO O CO LO 00 CO rH CO • • LO rH cm r>- • • CM rH CO CO • CD rH • /~N £ x— V o\° P (4h cn e O > o cu rH ■8 •H > g •H o k en a) -p tion t (Da •H 1 -H 0 /— s /"N •"> a J" CM CO o CD 00 CO O- o CO ro • • • • • OO 3 H ro J- oo H H 0O CN H • bfl o ^^ ^^ v-^ 5 iH (X, (•"N •— \ •~\ J- H OO LO CD CD s CD J- LO r-~ • • • • • OO rH oo =T oo rH rH zt oo H • o v«^ N— ' N— ' 2: CD OO CO r-« o j- CO CM LO rH c~^ • • • • • • 3 CM LO <>■ LO H H OO CN oo p> 10 o \w> s^> v_^ 4-» C > . W > •""\ f^ /— \ ■a Zt LO CO CO LO O CO O =t c-» H • • • • • • o 3 CN zf CO 00 CM H CM i— 1 cn cm •H . O «H s /— \ dp 1 s3 o ^ -to- Rati -9 •H aP C*P >^-p* u to •H 4-> V 1 Vari tJ m **• H CO is 2 S 3S •K 3 o^ CO <3 la Q W 150 £-. Q) +J rd 5. CO "-> o • ■H § ft) U A 6 SJi gj +j 6 I P o 3 ■H 0 ■£"* 8.8 o .C'H -P P •H rrj 3-H > CO CD P T3 TD •5 5 ^ CO -d

+j w CO ■H H • CU o p • 0 es 23 rTlS 64? 2 /— V /"■s 00 3 m m oj OJ CO rH Ol -3" 00 rH co ^O • co • • vo m OJ • CO 0 v~"' w W " - P B > ^^ /-v <»"s £ 00 5 m o> m 1— 1 O r-~ oi m o> • CO # # CO rH Ol • , { O ^w' ■^^ 8 CJ ft •-\ /— S /""» 00 r^ r-\ H W > /-v /•"S /m^ O ■H 00 s en rH 00 vO oj in 1—1 H 00 Ol m OJ Ol OJ r^ r-{ OJ rH co oi ■s , J3 0 •H CD e •^ s S Q A t! H 5 X-N dP \ 0 w 0 rd P (X ■a •H o\° •— \ ^.^ ?H CO •H +-> w dP 0) P P P 1 •H > (5 CO ^-/ rH 00 is ss ^§ ^ 3 O^ CO < la aa CD 0) ft s I r>H 151 Pk > 2.0 respectively. The first four entries in these tables (duration, uj', Q , ASST) are the percentage of the seasonal totals that occur dur- * n ing these events. The final three entries are useful for comparing the characteristics of the events at each station. The data in these tables supports the hypothesis that a significant percentage of the energy exchange takes place during these large atmos- pheric forcing events and results in a large oceanic thermal response. This may be easily verified by comparing the relationship between dura- tion. u*3, 0 , and ASST for both the mechanical and cooling events listed ' * ' n' in Table 5-12. Once again it may be observed from this table that, con- sidering all possible events, the percentage of duration of the cooling events is larger than the mechanical events. Comparing these same rela- tionships in Tables 5-13 and 5-14 shows the importance of the larger events to the upper ocean evolution. The general trend is for the larger mechanical events to remain significant while the larger cooling events become less important. For example the cooling events with Pk _> 2.0 are almost insignificant. The exception to this trend is OWS V. It should be observed in Tables 5-13 and 5-14 that for Pk _> 1.5 ASST is only 31$ at OWS V, and for Pk > 2.0 SST is reduced to only 22$. These percentages are significantly smaller than at OWS P and OWS N. It was noted previous- ly that the intensification of the atmospheric forcing does not occur until November at OWS V. Therefore it is possible that the large events (Pk > 1.5) occur later in the season at OWS V and this would account for the smaller sea-surface temperature response. Before discussing the characteristics of the events one additional observation may be made by comparing u* and Q during the mechanical events in the three tables. At OWS P and OWS V, the percentage of u* is consistently larger than QR 152 while at OWS N it is consistently smaller. This is additional evidence that the surface cooling at OWS N is more closely coupled to the wind at OWS N than at OWS P and OWS V. The final part of this analysis was to determine the principal charac- teristics of the large events. The final three quantities (number of events/month, duration of the events, and peak-to-mean ratio) will demon- strate that the character of the events is very similar at OWS P and OWS V but quite different at OWS N. In fact these quantities support the hypothesis that these events are directly related to the properties of the large winter storms at OWS P and OWS V, while they are related to changes in the mean circulation at OWS N. Table 5-12 shows that the average number of mechanical and cooling events is largest at OWS P and smallest at OWS N. At all stations a larger number of mechanical events occur than cooling events but have a shorter duration and a larger peak- to-mean ratio. However it is important to observe that, for the mechani- cal events, the duration and Pk (mean and standard deviation) are very similar at OWS P and OWS V and noticeably different at OWS N. This be- comes even more apparent for the larger events as may be seen in Tables 5-13 and 5-14. The larger mechanical events at OWS P and OWS V appear to be well organized on time scales of 2-3 days, have similar Pk, and occur at the same frequency each month. These large events at OWS N however, occur less frequently, are of longer duration, and exhibit a very large and variable peak- to-mean ratio. These are exactly the nature of the statistics that would be expected if the events at OWS P and OWS V were directly associated with the passage of extratrop ica I cyclone systems. The statistics at OWS N are compatible with the presumption that the events are related to a pulsing of the mean circulation. 153 The important implication from this analysis is that these large events occur frequently during the fall and winter at all stations. Furthermore they play a significant role in determining the character- istic evolution of the upper ocean thermal structure. Therefore they deserve special attention in any prediction scheme that attempts to reproduce this evolution. 154 VI . CONCLUSIONS The principal objective of this research was to examine the upper ocean thermal structure modifications that take place in response to strong atmospheric forcing events during the fall and early winter cool- ing seasons. The motivation was the fact that there was a serious gap in our fundamental knowledge regarding the role that these strong events play in the total thermal structure evolution during the fall and early wi nter. The one-dimensional hypothesis was evaluated at the three North Pacific Ocean weather stations using modified versions of the Kraus and Turner (1967), Kim (1976), and Elsberry, eta[. (1976) models. The performance of the three models was evaluated using 49 independent data sets from the historical series of marine observations at OWS P, OWS N, and OWS V. Additionally the EFT model was used to isolate and examine the relative importance of the principal one-dimensional mechanisms at the three stations. Finally, the large body of surface and near-surface marine observations were examined at the three North Pacific Ocean weather stations. A new analysis technique was employed to determine the relative importance of strong atmospheric forcing events in the tota fall and early winter thermal structure modifications at these stations. From the analysis the following significant conclusions were drawn. I. The integrated effect of the strong fall and winter atmospheric forcing events is the dominant factor in the modification of the upper ocean thermal structure at OWS P, OWS N, and OWS V. For example, these strong events occurred during approximately 35% of the time at the three 155 ocean weather stations. However, 85$/68%/57$ of the sea-surface tempera- ture change at OWS N/OWS P/OWS V occurred during these periods. Observa- tions from the individual data sets indicate that one can expect similar responses for mixed layer depth changes. It was therefore concluded that these strong events can not be excluded from any forecast scheme developed to simulate upper ocean response during the cooling season. 2. The response of the upper ocean during the strong events investi- gated in this study was largely one-dimensional. Additionally, a modi- fied version of the EFT model consistently demonstrated better agreement with observations than either the KT or KIM models. The KT model consis- tently predicted mixed-layer temperature and depth changes which were much larger than the observations. This result suggests that the fraction of turbulent kinetic energy that is available for entrainment is not a constant fraction of the turbulent kinetic energy transferred to the ocean by the wind, as postulated by Turner (1969). The superior perform- ance of the EFT and KIM models relative to the KT model suggests that the amount of wind-generated turbulent kinetic energy arriving at the mixed layer interface decreases as the mixed-layer depth increases. However, the exponential parameterization of dissipation enhancement employed in the EFT model was found to be more effective in preventing excessive deepening rates than the linear representation in the KIM model. It was further concluded that the convecti vel y-generated turbulent kinetic energy is largely non-penetrative, in agreement with Gill and Turner (1976). 3. During these strong forcing events a large component of the sea- surface temperature change is due to the vertical fluxes of heat at the surface and at the base of the deepening mixed layer. Depending on the magnitude of the turbulent fluxes of kinetic energy, the heat exchanged 156 JXlMP tM&£- C\Jc!*L ^UT bE06S at the air-sea interface, and the depth of the mixed layer, either of these heat fluxes may dominate the local heat budget of the mixed layer. However the important conclusion that may be drawn from this research is that an accurate specification of both fluxes is essential to understand- ing and predicting the sea-surface temperature changes. The effect of entrainment mixing is most evident during early season events when the sea-surface temperature decreases while the net surface heat flux is down- ward. This means that a forecast scheme must be capable of predicting the changes in the mixed layer depth to predict the sea-surface tempera- ture evol ution. 4. The data sets examined in this study suggest that at OWS P the large forcing events are largely dominated by mechanical mixing. This is evidenced by the entrainment heat flux exceeding the surface heat flux, and the increase of potential energy of the upper ocean. At OWS V and OWS N, however, the large majority of the cases showed that the strong forcing events are dominated by the convective process. 5. The adequacy with which the EFT model simulated the evolution during these strong events suggests that a properly parameterized turbu- lent bulk model will be useful for predicting the thermal structure changes over a period of a few weeks. Even during periods when non-local processes were important, the EFT model was capable of predicting changes in the thermal gradient. This property should be useful for estimating the changing acoustic properties of the upper ocean due to storm activity, 6. In agreement with the findings of Dorman (1974) the modeling of data sets at OWS N and OWS V suggests that the inclusion of salinity effects may not be necessary to simulate the upper ocean thermal struc- ture changes in the subtropics. Moreover, the results at OWS P suggest that a model that neglects salinity effects is capable of simulating the 157 changes in the temperature structure during the early cooling season in the subarctic region as well. 7. The examination of the seasonal trends in the mixed layer evolu- tion suggests that a large percentage of the changes are understandable in terms of one-dimensional processes. Additionally, the capability of the modified EFT model to simulate layer retreat suggests that it should be useful for simulating thermal structure changes during the spring and summer heating seasons. 8. The examination of the forcing terms showed that the distribu- tion of the marine winds and turbulent heat fluxes are non-Gaussian at the three ocean weather stations. The analysis showed that although the magnitude of the mechanical forcing is largest at OWS P and smallest at OWS N, its frequency distribution is similar at all stations. The dis- tribution of the turbulent heat fluxes were similar at OWS P and OWS V, but different at OWS N. It was demonstrated that this is related to the fact that the large forcing events at OWS P and OWS V are very similar and are closely correlated to the extratropica I cyclones that pass in close proximity to these two stations. At OWS N, however, cyclone activ- ity is rare and the events are related to a pulsing of the mean flow. This pulsing is probably due to a strengthening of the north-south pres- sure gradient as the large storms pass north of OWS N. 9. The final conclusion is that the timing of the large fall and winter events and the characteristics of the underlying thermal structure are important to the seasonal evolution of the upper ocean. It was demonstrated that the strong forcing events that occur early in the cooling season result in a much larger mixed layer response than compar- able events occurring later in the season. This is because less turbulent 158 kinetic energy is available for entrai nment when the layer is deep (dis- sipation enhancement). It was further demonstrated that changes in the mixed layer will be quite different depending on the strength of the thermocline. Cursory examination of records from OWS P suggests that the strength or weakness of the seasonal thermocline depends on the characteristics of the forcing during the spring and summer heating sea- son. It is possible, therefore, that the large forcing events are equally important in the formation of the thermocline, during the spring and summer, as they are in its subsequent erosion during the fall and winter. It is recommended that future research be conducted during the spring and summer periods to demonstrate the role of strong events during these seasons. 159 APPENDIX A COMPUTATIONAL FORMULAS FOR SURFACE FORCING A. RADIATIVE FLUXES AT THE SEA SURFACE The heat gained or lost by the oceans at the air-sea interface by radiant energy falls into two spectral regions. The first, ranging -4 from 0.1 to 4 microns (10 cm), is the short wave radiation received from the sun. The long wave, 4 to 50 microns, is commonly known as the back radiation and represents a net loss of heat from the ocean to the atmosphere or space. These two spectral ranges are virtually exclusive, thus permitting computations of these radiative fluxes to be performed separate I y. A number of empirical formulas are available for computing the in- solation arriving at the sea surface and Reed (1975) has reviewed and evaluated the most commonly used expressions. Reed found that results obtained from the formula developed by Seckel and Beaudry (1973), were consistently in better agreement with data collected at five coastal stations. Therefore this expression is used to calculate the clear-sky radiation (Q ) in this study, o 0o = AQ+ A( coscf) + B. sincj) + A„ cos 2 + B2 s i n 2 (A- 1) where Q is in langley (ly) per day, *=f^(t-2l) , and t is the Julian day of the year. The coefficients (A , etc.) were o calculated by a harmonic representation of the values presented in the 160 Smithsonian Meteorological Tables (List, 1958). This clear-sky value must be corrected for the presence of clouds and reflection from the sea surface. Gunter Seckel (personal communication) has suggested that the cubic cloud correction of Laevastu (I960) and a reflection coeffi- cient modeled after Anderson (1952) are suitable at the ocean stations. Therefore, Qs = QQ K (I - R) (A-2) calculates the solar energy penetrating the air-sea interface and K = I - .66 C3 R = a a The coefficient C is the total observed cloud cover (in tenths) and a is the mid-day elevation angle of the sun. The constants, a and b , are adopted from Tabata (1964), and for C < 0.5 , a = 0.-33 and b = -0.42 , whi le for C _> 0.5 , a = 0.21 and b = -0.29 . The largest source of error in (A-2) is the parameterization of the effects of cloud cover and the subjectivity involved in observation. Moreover, the application of this expression for averages less than mean monthly values introduces another possible source of error, as discussed by Reed and Ha I pern (1975). In this research (A-2) was used to estimate Q on a daily basis with C taken as the mean cloud cover during the daytime. The net long wave radiation (Q ) is a function of the radiation emitted from the sea surface to the atmosphere, minus the energy radiated from the air mass and absorbed by the ocean. Both of these quantities depend upon the fourth power of the absolute temperature of the emitting 161 body (Stephan Boltzman Law) with suitable correction factors for cloud cover and vapor content of the atmosphere. A representative formula reported by Husby and Seckel (1975) is Qu = I. I4xl0'7(273. 16+T )4 (0.39-0.05 /E~) ( I -0.6C2) (A-3) Tb s a where Q is in ly/day, T is the sea-surface temperature (°C), and E is the saturated vapor pressure of the atmosphere (at a height of a 10 m) in millibars. This vapor pressure was calculated using the Goff- Gratch (1946) formulation of the C I aus i us-CI apeyron equation, using the dew point temperature (T.) as the entering argument. Equation (A-3) is the modified Brunt (1932) formula with the empirical constants of Budyko (1956), and the largest uncertainties are introduced through the cloud correction factor and the use of overland constants. B. TURBULENT FLUXES OF HEAT AND MOMENTUM The turbulent fluxes of latent heat (Q ), sensible heat (Q^,) , and momentum (t ) at the air-sea interface were represented by the so-called bulk aerodynamic formulas. t = p Cn (u x I02) (dynes/cm2) (A-4) s Ka D a 7 Q = 3,767 C^ (0.98 E -E ) u (ly/day) (A-5) e ' D s a a ' ; Q, = 2,488 Cn (T -T ) u (ly/day) (A-6) n u s a a where u is the mean wind speed (m/sec), T is the air temperature a a (°C), E_ is the saturated vapor pressure of the marine air directly in contact with the sea surface (0.98 corrects for salt effects), and C_ is the non-dimensional drag coefficient. A constant drag coefficient 162 (1.3 x 10 ) is used in all computations in this thesis and is consis- tent with the range of values reported in the literature. The accuracy of these expressions has been the subject of many de- tailed studies and the main sources of error are the underlying assump- tions of a neutrally stable atmosphere and constant and equal exchange coefficients (moisture, momentum, and heat). Businger, et a I . (1971), from overland values, and Paulson, et a I . (1972), from data collected at sea, have demonstrated that the moisture and heat coefficients are nearly equal but quite different from the coefficients of momentum ex- change. Furthermore, studies by Deardorff (1968), DeLeonibus (1971), and Davidson (1974) have found that these coefficients are very depen- dent on the stability of the marine boundary layer and the roughness of the sea surface. Nevertheless, they afford the only practical means for computing these fluxes, using the meteorological observations avail- able in the ocean weather station file, and are used throughout this research. 163 APPENDIX B THE NUMERICAL SCHEME FOR THE ONE- DIMENSIONAL TURBULENT BULK MODELS A simple numerical scheme was developed which is capable of incor- porating the various assumptions of the Kraus-Turner (1967), Elsberry, et al. (1976), and Kim (1976) models in a consistent manner. This rou- tine is a modification of the algorithm presented by Thompson (1976), and is designed to calculate the potential energy modifications due to the vertical fluxes of heat and turbulent kinetic energy. The NODC mechanical bathythermographs that were used to initialize and validate the models were digitized in five meter increments starting at the sea-surface. In the model, this temperature profile is stored in N equally-spaced grid intervals [-(n-l) AZ, -nAZ_], where n=l,2,...,N, and AZ = 2.5 m. For a profile in which the temperature is well mixed to a depth of -nAZ , the first n-values of T are equal to T. . Dur- ing initialization it was assumed that the temperature varied linearly with depth in each five meter increment in the BT profile, and the model profile was chosen to conserve the heat content of the BT profile. In the model the potential energy (PE) per unit area may be expressed as PE = "PQga J Tzdz (B-l ) -D where D is a depth which is deeper than the maximum penetration of the vertical turbulent processes (typically the deepest level in the model). If non-local processes are small relative to the vertical fluxes, and if density changes due to salinity changes can be ignored, and a is 164 constant, changes in the potential energy calculated by (B-l) will be representative of the changes in the potential energy per unit area of the ocean. After mixing the top n grid intervals a further mixing of the layer to a depth -(n+!)AZ will result in a change in potential energy (APE) of the column by APE(n) = i pQgan(AZ)2 (Tp - T+|) (B-2) For T - T > 0 , this mixing increases the potential energy and n n+l APE (n) will represent the amount of turbulent kinetic energy that must m be expended to accomplish the mixing. However, if the column is unstable (T - T < 0), this mixing will release potential energy, and APE (n) n n+l will represent the turbulent kinetic energy generated by free convection. At the beginning of each time step (At = I hr) the surface heat fluxes are added to obtain * ■*■ * T,(t+At) = Tn(t)+At[Qa(t )+Qs(o,t )-Q£(AZ,t )]/pQCp (B-3) T (t+At) = T (t)+At[Q (-nAZ,t*)-Q(-(n+l)AZ,t*)I]/p C (B-4) n n s s ^ \-> for n=2,3,...,N, and t = t + i At . The effective insolation (QM was distributed by assuming 50% absorption in the first meter and the re- mainder taken to decay as exp(-yZ). The average extinction coefficient (y) was assumed constant at 0.003 cm" , which is the value used by Den- man and Miyake (1973). If the resulting temperature profile is unstable (T. < T?) the first two intervals are mixed and the resulting turbulent kinetic energy (APE ) generated by the convection is calculated according 165 to CB-I). This process continues until a stable temperature profile is established (T, > T, . ) and the upper layer is isothermal to a depth Z = -kAZ . At the end of this evolution the potential energy of the column will be reduced by k-l V APEc(n) , (B-5) n=l which is also equal to the total generation of turbulent kinetic energy by free convection. Further mixing will require an expenditure of turbulent kinetic energy. The algorithm must also be modified to account for dissipation en- hancement (EFT and KIM), the storage of turbulent kinetic energy (KIM), and the fraction of convectively generated turbulent kinetic energy that is utilized for entrainment (KT, EFT, and KIM). We start by defining the total amount of turbulent kinetic energy, Ey(n), available for mix- ing the first n levels with level n+l as Ex(n) = E (n) + E - E (n) - E (n) (B-6) T m c p s The mechanically generated turbulent kinetic enerqy is E (n) ; E is 1 a a/ m c the fraction of (B-5) available for entrainment, E (n) is the amount P of turbulent kinetic energy previously expended to mix the layer to level n, and E (n) is the amount of turbulent kinetic energy that is stored as the layer deepens to a depth -nAZ . For the KIM model , E (n) = (1.25 p w„3(t ) - p D.nAZ) At , (B-7) m o * ob 166 -4 2 where D, is a constant background dissipation equal to 2 x 1 0 cm - sec . For the KT and EFT models, E (n) = [p w*3(t*) exp(-nAZ/Z] At , (B-8) with 00 for KT (B-9) 50 m for EFT Therefore (B-7), (B-8), and (B-9) express the depth dependence of dissi- pation (dissipation enhancement) formulated by Kim (1976) and Elsberry, et a I . (1976). In the Kraus and Turner (1967) model dissipation is 3 * neglected, and the amount of surface production, p w» (t ) , available for mixing is independent of depth. Further, k-l = -r V APE (n) (B-10) n= I where r is the fraction of the convectively generated turbulent kinetic energy utilized for entrainment. In all models used in this study r = .15 following Gill and Turner (1976). Therefore the KT model here is equivalent to a modified version discussed by Gill and Turner (1976). Fina I ly, n-l Ep(n) = X APEm(I) > (B-ll) i=k 167 and E = s n-l I 4. 5 p AZ w„ (t ), for KIM \=l ( B- 1 2 ) 0 , for KT and EFT Thus (B-ll) is used to calculate the turbulent kinetic energy expended to deepen the layer from the free-convection depth to -nAZ . For KIM, (B-12) calculates the amount of turbulent kinetic energy stored as the mixed layer deepens beyond the mixed layer depth of the previous time step [i.e., £AZ(t+At) > h(t)]. If E_(n) > APE (n) , there is enough energy to mix T through T ,,. T — m 3 3 n+l If there is insufficient energy to mix completely, ET(n) < APE (n) , then we follow Thompson (1976) and partially mix; i.e., set a = nE (n) (n+l )APE (n) m T = [aT + (n-a) T ]/n n+l n TT = a Tn + ( l-a) T n+l then set T. = T , for i=l,2,...n, T . = T1 . The mixed-layer tempera- ture at each time step is equal to T., but since the algorithm does not calculate the mixed layer depth, it is defined as the depth at which the temperature is 0.2°C less than T. . The relative importance of mechanical mixing and free convection to the evolution of the mixed layer were investigated by comparing the rela- tive contribution of APE and APE to APE. An important part of m c this study was to quantify the relative magnitudes of the surface and entrainment heat fluxes. The surface heat fluxes were calculated, as 168 described in Appendix A, from the surface marine observations. The en- trainment heat flux (-A 4r AT) was calculated, in the models, as the heat gained by the profile (during each time step) in levels n+ I to n+m as the mixed layer deepens between levels n and n+m. 169 BIBLIOGRAPHY 1. Anderson, E. R., 1952: Energy budgets studies. Water loss studies: Volume I, Lake Hefner studies. U. S. Navy Electron Lab., Tech. Rep. 327, pp. 71-1 12. 2. Brunt, D., 1932: Notes on radiation in the atmosphere. Meteorol . Soc. Lond., 58, 389-420. 3. Budyko, M. I., 1956: The heat balance of the earth's atmosphere. 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K., 1975: An evaluation of formulas for estimating clear- sky insolation over the ocean. NOAA Tech. Rept. ERL 352-PMEL26, 25 pp. 32. Reed, R. K. , and D. Halpern, 1975: Insolation and net long-wave radiation off the Oregon coast. J. Geophys. Res., 80, 839-844. 33. Seckel, G. R., and F. H. Beaudry, 1973: The radiation from sun and sky over the North Pacific Ocean. (Abstract 0-33) EOS, Trans. Am. Geophys. Union, 54:1114. 34. Simpson, J., 1969: On some aspects of sea-air interaction in middle latitudes. Deep-Sea Res., Suppl. to Vol. J_6, 233-261. 35. Stu I I , R. B. , 1975: Temperature inversions capping atmospheric boundary layers. Ph.D. thesis, University of Washington. 36. Sverdrup, H. V., M. W. Johnson, and R. H. Fleming, 1942: The Oceans Their Chemistry, Physics, and General Biology. Prentice- Hall , New York, 1087 pp.- 37. Tabata, S., 1964: A study of the main physical factors governing the oceanographic conditions of station P in the northeast Pacific Ocean, Doctor, Sci. thesis, Univeristy of Tokyo, 264 p. 38. Thompson, S. M., and J. S. Turner, 1975: Mixing across an inter- face due to turbulence generated by an oscillating grid. J. Fluid Mech., 64, 349-367. 39. Thompson, R.O.R.Y., 1976: C I imatologica I numerical models of the surface mixed layers of the ocean. J. Phys. Oceanogr., 6_, 496-503. 40. Townsend, A. A., 1968: Excitation of internal waves in a stably- stratified atmosphere with considerable wind-shear. J. Fluid Mech., 32, 145-171. 41. Tully, J. P., 1964: Oceanographic regions and assessment of tem- perature structure in the seasonal zone of the North Pacific Ocean, . 21 (5), 941-970. 42. Turner, J. S., and E. B. Kraus, 1967: A one-dimensional model of the seasonal thermocline, I. A laboratory experiment and its interpretation. Tel I us, I 9, 88-97. 43. Turner, J. S., 1969: A note on wind mixing at the seasonal thermo- cline. Deep-Sea Res., Suppl. to Vol. j_6, 297-300. 44. Turner, J. S., 1973: Buoyancy Effects in Fluids, Cambridge University Press, London, 367 pp. 172 INITIAL DISTRIBUTION LIST No. Copies 1. Defense Documentation Center 2 Cameron Station Alexandria, Virginia 22314 2. Library (Code 0142) 2 Naval Postgraduate School Monterey, California 93940 3. Department of Oceanography, Code 68 3 Naval Postgraduate School Monterey, California 93940 4. Department of Meterology, Code 63 1 Naval Postgraduate School Monterey, California 93940 5. Oceanographer of the Navy 1 Hoffman Building No. 2 200 Stoval 1 Street 6. Office of Naval Research 1 Code 410 N0RDA, NSTL Bay St. Louis, Mississippi 39520 7. Dr. Robert E. Stevenson 1 Scientific Liaison Office, 0NR Scripps Institution of Oceanography La Jolla, California 92037 8. Library, Code 3330 1 Naval Oceanographi c Office Washington, D. C. 20373 9. SI0 Library ' 1 University of California, San Diego P. 0. Box 2367 La Jolla, California 92037 10. Department of Oceanography Library 1 University of Washington Seattle, Washington 98105 11. Department of Oceanography Library 1 Oregon State University Corvallis, Oregon 97331 173 12. Commanding Officer Fleet Numerical Weather Central Monterey, California 93940 13. Commanding Officer Naval Environmental Prediction Research Facility Monterey, California 93940 14. Department of the Navy Commander Oceanographi c System Pacific Box 1390 FPO San Francisco 96610 15. Di rector Naval Oceanography and Meteorology National Space Technology Laboratories Bay St. Louis, Mississippi 39520 16. N0RDA Bay St. Louis, Mississippi 39520 17. Assoc, Prof. R. L. Elsberry, Code 63Es Department of Meteorology Naval Postgraduate School Monterey, California 93940 18. Lcdr N. T. Camp, USN Staff, Commander Fleet Air Mediterranean FPO New York 09521 19. Professor C. Comstock, Code 53Zk Department of Mathematics Naval Postgraduate School Monterey, California 93940 20. Assoc. Prof. E. B. Thornton, Code 68Tn Department of Oceanography Naval Postgraduate School Monterey, California 93940 21. Assoc. Prof. R. L. Haney, Code 63Hy Department of Meteorology Naval Postgraduate School Monterey, California 93940 22. Asst. Prof. R. H. Bourke, Code 68Bf Department of Oceanography Naval Postgraduate School Monterey, California 93940 174 23. Professor G. H. Jung, Code 68Jg Department of Oceanography Naval Postgraduate School Monterey, California 93940 24. Assoc. Prof. W. Denner, Code 68Ds Department of Oceanography Naval Postgraduate School Monterey, California 93940 25. Adjunct Asst. Prof. R. W. Garwood, Code 68Gd Department of Oceanography Naval Postgraduate School Monterey, California 93940 26. Mr. Gunter Seckel National Marine Fisheries Monterey, California 93940 175 / '7 -fe 2U >V5'3 Thesis CI 9323 c.l Camp 63790 The cation of *-h« ocean t-h Upper Lean thermal stru_ l7/1^? 2^ 9 tin Thes is 16979J C193 23 Camp c.l The role of strong atmospheric forcing events in the modifi- cation of the upper ocean thermal struc- ture during the cool- ing season.