U.S. DEPARTMENT OF COMMERCE/Environmental Science Services Administration COLLECTED REPRINTS ESSA INSTITUTE FOR OCEANOGRAPHY -, No. 12, 9ib-94l. 7. McFadden, James D. , and Robert A. Ragotzkie, Climatological significance of albedo in Central Canada, J. Geophys. Res. 72, No. 4, Il3b-ll43. MARINE GEOLOGY AND GEOPHYSICS 8. Anikouchine, William A. , Dissolved chemical substances in com- pacting marine sediments, J. Geophys. Res. J72, No. 2, 505-509. 9. Anikouchine, William A. , and Hsing-Yi Ling, Evidence of turbidite accumulation in trenches in the Indo-Pacific region, Marine Geol. 5, 141-154. in 10. Burns, Robert E. , and Paul J. Grim, Heat flow in the Pacific off Central California, J. Geophys. Res T2, No. 24, 6239-6247. 11. Dietz, Roberts., Astroblemes, McGraw-Hill Yearbook of Science and Technology, 109-111 (McGraw-Hill Book Co. , Inc., New York, N.Y.). 12. Dietz, Robert S. , Craters and legends, Medical Opinion and Rev. _3, No. 1, 50-57. 13. Dietz, Robert S. , More about continental drift, Sea Frontiers 1 3 , No. 2, 66-82. 14. Dietz, Robert S. , Passive continents, spreading sea floors and continental rises; A reply, Am, J. Sci. 265, 231-237. 15. Dietz, Robert S. , Shatter cone orientation at Gosses Bluff astro- bleme, Nature 2l6_, 1082-1084, Dec. 1967. 16. Harbison, R. N. , De Soto Canyon reveals salt trends, Oil and Gas J. 6_5, No. 8, 124-128. 17. Harrison, W. , Environmental effects of dredging and soil deposition, Proc. World Dredging Conf. , 535-539. 18. Harrison, W. , and A. M. Richardson, Jr. , Plate-load tests on sandy marine sediments, Lower Chesapeake Bay, Marine Geotechnique, 274-290 (Univ. of Illinois Press, Urbana, 111.). 19. Keller, G. H. Pleistocene-recent boundary in the Malacca Strait, Southeast Asia, Proc. Seventh Internatl. Sedimentological Congress. 20. Keller, George H. , and Adrian F. Richards, Sediments of the Malacca Strait, Southwest Asia, J. Sed. Pet. _37, No. 1, 102-127. 21. Ling, Hsing-Yi, and W. A. Anikouchine, Some spumellarian radio- laria from Java, Philippines, and Mariana trenches, J. Paleon- tology 41_, No. 6, 1481-1491. 22. Malloy, R. J. , Vertical crustal movement associated with the 1964 Alaskan earthquake, Proc. Eleventh Pacific Science Congress in Vol. 2 Oceanography, Tokyo. IV 2 3. Perry, R. B. , and Haven Nichols, Submarine geology of the Aleutian Arc, Alaska, Proc. Eleventh Pacific Science Congress in Vol. 2 Oceanography, Tokyo. 24. Peter, G. , D. Elvers, and O. Dewald, Results from a geophysical survey in the North-East Pacific Ocean, Proc. Eleventh Pacific Science Congress in Vol. 2 Oceanography, Tokyo. 25. Sokolowski, T. J., andG. R. Miller, Automated epicenter locations from a quadripartite array, Bull. Seismol. Soc. Am. _57, No. 2, 269-275. 26. von Huene, Roland, Richard J. Malloy, George G. Shor, Jr. , and Pierre St-Amand., Geological structures in the aftershock region of the 19&4 Alaskan earthquake, J. Geophys. Res. _72, No. 14, 3649-3660. 27. "Weeks, L. A., R. N. Harbison, andG. Peter, Island arc system in Andaman Sea, Am. Assoc. Petrol. Geol. Bull. 51_, No. 9, 1803-1315. PHYSICAL OCEANOGRAPHY 28. Butler, J. P. , Double-humped waves on a sloping beach, HIG-67-16, ESSA/JTRE-2 - Univ. of Hawaii. 29. Chew, Frank, On the cross-stream variation of the k-factor for geomagnetic electrokinetograph data from the Florida current off Miami, Limn, and Ocean. 12_, No. 1, 73-78. 30. Gassaway, John D. , New method for Boron determination in sea water and some preliminary results, Internatl. J. Ocean, and Limn. !_, No. 2, 85-90. 31. Munk, W. H. , and B. D. Zetler, Deep-sea tides: A program, Sci. 158_, No. 3003, 884-886. 32. Nelson, Raymond M. , Sensing ocean currents from space: Ocean Industry 2, No. 5, 40-42. 33. Seelinger, P. E. , R. A. Wallston, B. H. Erickson, J. E. Master son, and W. E. Hoehne, An oceanographic data collection system, Trans. Second Internatl. Buoy Technol. Symp. , Marine Technol. Soc, Washington, D. C. 34. Vitousek, M. J., and G. R. Miller, Low-frequency wave study in the Meso-deep ocean, HIG-67-11, ESSA/JTRE - Univ. of Hawaii. 35. Zetler, Bernard D. , Tides and other long period waves, U.S.Natl. Rept. 1963-1967 to 14th Gen. Assembly, IUGG, Trans. A.G.U. , 591-595. 36. Zetler, B. D. , and G. W. Lennon, Some comparative tests of tidal analytical processes, Internatl. Hydro. Rev. _44, No. 1, 139-147. 37. Zetler, B. D. , and R. A. Cummings, A harmonic method for pre- dicting shallow water tides, Proc. Eleventh Pacific Science Congress in Vol. 2, Oceanography, Tokyo. 38. Zetler, B. D. , and R. A. Cummings, A harmonic method for pre- dicting shallow water tides, J. Marine Res. _2_5, No. 1, 10 3-114. GENERAL 39. Schuldt, M. D. , C. E. Cook, and B. W. Hale, Photogrammetry applied to photography at the bottom, Part of Deep Sea Photo- graphy, ed. J. B. Her sey, (Johns Hopkins Univ. Press, Baltimore, Md.). 40. Stewart, Harris B. , Jr. , Seafloor Geology 1968 Yearbook Directory, Oceanol. Internatl., June, 30-31. 41. Stewart, Harris B. , Jr., Killer at the seashore, ESSA World_2, No. 3, 30-31, U. S. Dept. of Commerce, Rockville, Md. 42. Stewart, Harris B. , Jr., Sea science ships, The Miamian, Sept. 1967, p. 27. PUBLICATIONS NOT INCLUDED GENERAL Stewart, Harris B. , Jr. , True-life adventures: dive to a mountain- top, Summer Senior Weekly Reader 6_, No. 5, 6. Stewart, Harris B. , Jr., Underwater worlds of tomorrow, Presidents Assoc. , Inc. VI lA Reprinted from PROCEEDINGS THE ELEVENTH PACIFIC SCIENCE CONGRESS Volume 2 Oceanography, Tokyo, 1966 -13- A CRITICAL SURVEY OP THE STORM SURGE PROTECTION PROBLEM D. Lee Harris Institute for Oceanography Environmental Science Services Administration, United States of America The goal of a disaster warning service is to provide the maximum protection to the public with a minimum of inconvenience. It is necessary to consider the uncertainties in both basic data and predictions in decid- ing on the level of protection required. For storm surge protection, these uncertainties include those related to the movement and development of the storm, the relation between wind velocity and wind stress, and those arising from the uncertainties resulting from approximations and assumptions made in the computation of the response of the sea to atmospheric stresses. These uncertainties will be reviewed both from the standpoint of identifying areas in which more basic research is needed and from the standpoint of showing how these uncertainties should affect the operation- al natural disaster warning service. Reprinted from PROCEEDINGS THE ELEVENTH PACIFIC SCIENCE CONGRESS Volume 2, Oceanography, Toyko 1966 -49- THE DRAG COEFFICIENT BETWEEN WIND AND WATER D. Lee Harris. Institute for Oceanography, Environmental Science Services Administra- tion, U. S. A. Two of the most popular techniques for determining the stress between wind and water are to record the slope of a water surface exposed to the wind and to analyze the profile of the wind speed above the water according to the Prandtl boundary layer theory or some extension of it which allows for the effects of buoyancy when the lapse rate is not adiabatic. Determinations of the drag coefficient by the first technique are characteristi- cally larger than those determined by the second. It will be shown that second order phenomena normally overlooked in the application of these techniques act to produce an overestimate of the stress coefficients derived by the first technique and to produce an underestimate of the stress coefficient derived by the second technique. 740 Reprinted from MONTHLY WEATHER REVIEW Vol. 95 No. 11 Vol. 95, No. 11 NUMERICAL COMPUTATIONS OF STORM SURGES WITH BOTTOM STRESS CHESTER P. JELESNIANSKI Institute for Oceanography, ESSA, Silver Spring, Md. ABSTRACT A linear form of the transport equations of motion is used to compute numerically storm surges generated by model tropical storms traveling across model basins. The storms move in any fixed direction and speed relative to a straight line coast and have a restricted number of physical parameters to fix their strength and size. These param- eters are readily available in most weather stations. A dissipating mechanism, introduced by Platzman, using only an eddy viscosity coefficient is modified to include a bottom slip current by means of a bottom slip coefficient. These two coefficients are used to control the amplitude of resurgences on the sea following the passage of tropical storms. Numerical values for the coefficients are empirically determined by comparing computed and observed resurgences off Atlantic City. Nomograms prepared from the computations may have some skill in forecasting future storm surges. 1. INTRODUCTION The storm surge prediction problem is concerned with I he rise of coastal waters brought about by meteorological storms. The rising waters not only inundate coastal areas but also act as a pathway for short surface or wind waves to move and break farther inland. It is the purpose of this paper to provide some further insight into the mechanics and prediction of storm surges. The response of the sea, from driving forces generated by a moving tropical storm, is of such complexity that practical results are obtained only through bold assump- tions and empirical tests using numerical computations; an electronic computer, therefore, is viewed as a laboratory to compute storm surges using model storms traveling across model basins. The entire response of the sea, however, is much too general for storm surge computations and only portions of the response are considered. In the natural oceans there is a basic flow composed of the general circulation, varying seasonally, and the daily astronomical tide. The present state of knowledge and data acquisition for hurricane conditions on the open coast does not permit a direct incorporation of the basic flow into the storm surge computations, nor provide the ability to consider nonlinear interactions with storms. For this reason, and as a great matheinatic convenience, only linearized forms of the equations of motion are used in the present study. The basic flow can be partially accounted for in the computations by appending the predicted astronomical tide and the observed, extrapolated, or predicted seasonal variations of the sea surface to the computed storm surge via the superposition principle (Harris [3]). This is feasible il the effects of nonlinear interactions are small; in any case these corrections can be applied only at shore stations where data are available and not in the open sea. Model tropical storms have been used by Jelesnianski [6] to compute storm surges but without considering bottom stress in the storm surge equations of motion. The computed surges were found to be reasonable for fast moving storms making landfall but had serious deficiencies for storms moving slowly or traveling parallel to the coast at any speed. Computations therefore were restricted to storms traveling at moderate or higher speeds and with direction of travel at not too acute a crossing angle to the coast. For convenience, storms moving from land to sea were omitted even though the computed surges were reasonable. A detailed description is given in this paper to surges generated by storm travel inadmissible in the previous paper [6]. These particular surges are complicated in space and time. The techniques developed in [6] to predict storm surges using a restricted number of meteorological parameters are extended to consider storms crossing the coast at any angle and speed, as well as storms traveling parallel to the coast at any speed and distance from the coast. To consider this broad spectrum of storm velocity relative to a coast, methods of applying bottom stress in the numerical computations are necessary. The methods used are useful palliatives in the absence of a sound theory for bottom stress and dissipating mechanisms. The addition of a bottom stress in the equations of motion does not significantly change the results of [6] but does have a commanding effect with storm travel inad- missible in [6]. Storms traveling parallel to the coast at any speed, or landfalling at slow speeds, form second order surge oscillations due to initialization effects and special wave phenomena, all of significant amplitude; these are superimposed on the generated surge and can be controlled by a dissipating mechanism. Test computations show that certain portions of the coastal surge profile are almost unaffected when using any November 1967 Chester P. Jelesnianski 741 bottom friction law, including a no-friction law if the storm is not moving too slowly. For an observer on sea, facing land, and watching a storm landf ailing, the coastal pro- file and peak surge to the right of landfall are not greatly affected; on the other hand, the profile to the left of land- fall is sensitive to the type of bottom stress law used. 2. EQUATIONS OF MOTION FOR STORM SURGE COMPUTATIONS The model in this study corresponds to that of the previous report [6], except for the addition of bottom stress, and consists of an analytically described storm traveling across a rectangular shaped, variable depth" basin that is open to the sea on three sides. Initially the sea in the basin is assumed at rest, and the storm is al- lowed to grow to maturity from zero strength in a rapid but continuous manner. In storm surge computations, we are primarily in- terested in the height of the sea surface and only casually in the current field. It is convenient then to transform the equations of motion to two-dimensional transport fields. This transformation, however, presents serious problems with bottom stress. For future use we shall need a continuity transport equation which can be written as (Welander [20]) : dh where a: (U, 10= (w, v)dz', i.e., transport components ft = storm surge (height of mean sea surface above equilibrium level) u, v = horizontal components of current field 7}=depth of the sea x, ?y, z' — right hand coordinate system [z' in antic- ipation of scaling) . The momentum equations of motion (not yet in trans- port form) with hydrostatic approximation can be written in linear and complex form (Welander [20]) as: where w=u-\-iv, q- -[ d a(ft-fto) dx (2) +i d(ft-fto)' p = vertical kinematic eddy viscosity /=Coriolis parameter (constant) Tb=V dw ds7 complex form of surface, bottom stress (4) W= complex form for transports Q=Dq. The surface stress can be formulated as a function of the wind, but the bottom stress depends on the vertical gradient of the bottom current. Since only transport terms are available if (3) is used directly, it has been cus- tomary to assume the bottom stress as a simple quadratic function of transport in conformity with experiments from pipe or channel flow ; corrections to such an empirical law for a system under the influence of a surface wind stress has been given by Reid [16]. This type of bottom stress will not be considered since computational experiments gave results that were not always satisfactory. Other systems of representing bottom stress, which are linear in nature, have been designed by Nomitsu [91, [10], [11], [12]; Nomitsu and Takegami [13], [14]; and Platzman [15]. Platzman's scheme is more convenient for nu- merical computations. In what follows, we will adhere to the notation given by Platzman whenever possible. Let the surface boundary condition be v(dw/dz')\z-=o = R, where 7? is the complex form of the surface wind stress, taken as R=^\V. W where Fs = complex wind, pa, p = air, water density, C is assumed to be a constant drag coefficient, and Cpjp — 3 X 10~6. We formulate the bottom boundary condition as dw b~7 = SW\-' = -D (5) where s is a slip coefficient; here we are assuming a "gliding" current above a very thin boundary or skin layer, where for practical purposes the depth of the skin layer is taken as zero. If only one friction parameter consisting of an eddy viscosity coefficient is used, then computations show that the storm surge is somewhat sensitive to small changes of the parameter. The introduction of a slip coefficient as a second friction parameter greatly reduces this sensitivity 742 MONTHLY WEATHER REVIEW Vol. 95, No. 11 and also gives more freedom when working with dependent data to better fit computed and observed surge profiles. It is convenient to make the vertical coordinate non- dimensional by the transformation z=z'/D. If the time derivative in (2) is treated as an operator, and the resulting second order differential equation with variable z is solved with surface and bottom boundary conditions, then i-, sinh az „ . cosh crz , , „ , . 1 n wD= R-\ ^-j — (cosh o7f— sw>_iH -2 V r)„v T],a sum a y\va where v>=v/D2 ''=«=' 0+1) a-R+ (sinh a)Q (6) W_,= »[ y\v sinh a-\-y;(j cosh '] = complex bottom current. If (6) is now integrated in the vertical (with respect to z from — 1 to 0) , the result is where 7l,WJrG{«)]M=QMl + H{a)]R (7) M= complex transport (equivalent to dimensionalized W in (3)) G(*y- H(. Then dt 2£eif/K+«)=^3iEei(0«+*) 752 MONTHLY WEATHER REVIEW Vol. 95, No. 11 so that the effect of operating with d/dt is just the effect of multiplying by if3. An operator formed as a "function" J (d/dt) has, on the operand Ee'^'+*), the effect of multi- plying by /(?/?), for the operand Ee'^'+v the operator d/dt "takes on the value" i/3. In general, the operands will not be of the form £V!*<0'+*> ; however, at any time t for which the operand is not zero, there is an exponential function which fits most closely to the operand. If the values of E, /3, of the approximating exponential do not rapidly change with time, tl u it i> reasonable to approximate d/dt with the value i|8. The values of E, /3, depend on the operands and the time t for which the "evaluation of d/dt" is performed and are different for the operands M and R. If /3 is real, so that the opera nd is neither increasing or decreasing in value, the values of G and H will be finite and bounded. Figures 19 a-b give the real and imaginary parts of G and H against a2, with a2 = iD2(j-\-fi)/v (i.e., replacing d/dt by i/3) . These figures indicate that a linear approxima- tion to G and H may be acceptable, provider ji is not large. We first examine our experimental computations to determine for which values of /3 the actual oper- ands approximate exponentials. (If M=E W+*\ then dM/dl=ipM, so 0=(l/iM)dM/dt where Mis i egarded as a complex valued function of time and space.) Empirically it was noticed that the transport field usually consists of a train of vortices along the storm's path; in general, these vortices do not travel or increase in strength with any great rapidity, suggesting that for the trans] ort operand M, the value of /3 remains small, and a linear approxima- tion may be acceptable. The storm model used in this study is a previously determined analytic function, and moves with a uniform rectilinear motion. For this case, the time derivative of the forcing function can be written in the form dt' =-v..v (12) Figure 19. — (a) Plot of real and imaginary parts of G(,S-B*(", T(p))*(v)ATt(v, u*(p, C), T) ;=1 i=\ m IS^, T(p0))(rt(v, U*(p, w), T)rt{v, u*(p, C), T.) (1) i = l The effects of other radiatively active gases such as ozone and nitrous oxide in the wavelength regions considered are insignificant, amounting to less than 1 percent of the upward irradiance, and are not considered. Equation (1) is employed in deducing the quantity of atmospheric water vapor from measurements of upward irradiance for a particular spectral interval. An iteration procedure resulting in a direct solution of the water vapor transmissivity, tw{v, p, T), is used. Since the water vapor transmissivity is a function of the quantity of water vapor, w, beneath a given reference level, and since the amount of water vapor is a function of the mixing ratio, the solution yields the mixing ratio. The iteration procedure requires calculations of irradi- ance with a stepped series of trial values of water vapor (equation (1)) until the difference between calculated and observed upward irradiance is minimized. Carbon dioxide emission and transmission are calculated assuming a constant mixing ratio. A first approximation for the water vapor profile is described by a power law expression of the form, w=wa{piPoy (2) after Smith [8]. X, the exponent of a power law expression, changes the water vapor profile as required in the iteration. For tropical soundings W0 is assumed to be 5.0 gm./kg., certainly a lower bound. For mid-latitude summer sound- ings, W0 is assumed to 0.6 gm./kg. For mid-latitude winter soundings W0 is assumed to be 0.06 gm./kg. In other words, a lower bound is chosen to start the compu- tations. The iteration procedure, involving repeated solutions of equation (1), requires minimizing the quantity, i Stepwise changes in X, (equation (2)) for subsequent successive increases in WQ provide the repeated input of the "trial" water vapor quantities required for equation (1). The computer evaluates Ft] from an initial "mini- mum" profile of W0 shaped by an initial X value of 0.5. The X values are stepped upward to a maximum value of 3.0 and then the process repeats with a new stepped increase in W0. Negative values of X will allow the mixing ratio profile to increase with altitude above the surface. The changing of the entire water vapor profile by the power function approximation of equation (2) imposes a stabilizing constraint on the solution of equation (1). This same procedure has been used by Kuhn and Cox [2] to infer stratospheric water vapor profiles. It should be noted that the constraint of equation (2) does not preclude convergence at every level, within reason, since the step- wise variation of X allows, literally, almost any charac- teristic shape to the W profile to obtain. Average computer solution time is 0.3 min. (CDC-1604) for 10 levels, over the spectral range 4.39 to 20.83ju (480-2280 cm.-'). 3. UNIQUENESS OF THE SOLUTION FOR INFERRED WATER VAPOR In view of the rate of change of the water vapor slab transmissivity, rF, with changes in the amount of atmos- pheric water vapor, u*, it is necessary to establish the uniqueness of the radiometrically inferred water vapor quantity. Figure 1 gives the water vapor slab or irradiance transmissivity as a function of the sum of the logarithm of «*, the pressure and temperature scaled optical thick- ness, and the logarithm of the generalized absorption coefficient L, (Elsasser [9]). This is expressed by, tv=tf (logio «*+logio L). (3) From this figure it is evident that the greatest change in transmissivity for a given change in log u*-\-log L occurs between values of —1.50 and 0.50 for log u*+\og L. Assuming a mean value for log L of —0.50, this represents August 1967 Peter M. Kuhn and James D. McFadden 567 WAVENUMBER (CM"') -2 -I 0 LOG U + LOG L Figure 1. — Water vapor beam transmissivity vs. (logi0M* + logioi). an optical thickness range of from approximately 0.1 gm./cm.2 to 10.0 gm./cm.2 Aerosol contamination is clearly evident as a sharp discontinuity in the observed moisture profile. In fact, detection of thin clouds at night is possible with these instruments. 4. IRRADIANCE OBSERVATIONS The primary instrument employed in this research was a chopper bolometer radiometer having a 30° optical field of view, germanium optical flat-front lens with a spectral bandpass from 4.39 to 20.83ju (480 to 2280 cm.-1). The mean band transmissivity is 0.50. The relative resolution and special characteristics of the primary radiometer used in these experiments are given in table 1. Various optical companies can provide bolometer radiometers with resolution of at least 0.025°C, twice the resolution of the unit used. Thus for a 0.025°C. change in target temperature at 5.0°C the corresponding Table 1. — Radiometer specifications Spectral passband Average filter transmissivity Field of view Maximum temperature resolution Irradiance change behind germanium flat filter for 0.05'C. change at 5.0°C. Temperature range Recorder output.. 4.39 to 20.83 ». 0.58 30°. 0.05°C. 0.7 micro watt/cm.' (.007 watt/m.') -40.0°C. to + 30.0°C. 0-50 millivolts full scale into 1000 ohms 00 1500 14 13 12 1 IOOO . 300 800 700 , , , |, | ' ' O 10 gm/cm2 THRU 2000" 80 V j o 60 , X o , i 1 gm/cm2 THRU 3000 40 !tf |\ 20 •iily^i! \ Jpi^ V--x, ,x> v///////i '/M&Ss*o. ~*« 8 9 10 II 12 13 WAVELENGTH (MICRONS) IRW-FILTER TRANSMISSIVITY Figure 2. — Window radiometer filter transmissivity vs. wavelength. 2500 WAVE NUMBER (CM"') 1000 625 500 •- 4 6 8 10 12 14 16 18 20 WAVELENGTH (MICRONS) Figure 3. — Broad-band radiometer filter transmissivity vs. wave- length. \og10L vs. wavelength. irradiance change behind the optical flat filter is 0.0035 watt/m.2 For an average tropospheric sounding to 20,000 ft., this would correspond to a mean water vapor mixing ratio resolution of 0.05 gm./kg. or 50 parts per million for a moderately dry atmosphere. Throughout, we are considering air-borne radiometers at costs not exceeding $10,000. The absolute accuracy of the broad bandpass radiometer is 0.028 watt/m.2 The absolute accuracy of the "window" radiometer is 2°C. above 0°C. The curves of the filter transmissivity of the "window" radiometer and the primary broad-band earth and atmos- phere self emission radiometer are shown in figures 2 and 3. The solid angle aperture of the surface temperature monitor "window" radiometer is 3°. The radiometers were calibrated against a hemispherically symmetrical black source. We then have, F\?=^ B(v, TtMv)dv. (4) The equivalent blackbody temperature Teq, can be determined from equation (4). B(v,Teq) is the hemisphere blackbody irradiance. The curves of radiometer power versus equivalent blackbody source temperature are 568 MONTHLY WEATHER REVIEW Vol. 95, No. 8 10 5 0 _ -5 o V10 -15 -20 ! • ' .•' CALIBRATION 7.35 - 3 16 u 1.6 1.8 2.0 2.2 2.4 2.6 2.8 (MICRO WATTS/CENTIMETER BAND IRRADIANCE 30 2* 3.2 Window radiometer calibration curve, equivalent temperature vs. micro watts/square centimeter. CALIBRATION 30' FIELD OF VIEW Figure 4.— blackbody 6.0 7.0 8.0 9.0 10.0 SPECTRAL IRRADIANCE (WATTS/METER2 ) Figure 5. — Broad-band radiometer calibration curve, equivalent blackbody temperature vs. watts/square meter. reproduced in figures 4 and 5 for the window and broad bandpass radiometers, respectively. Reference to figure 2 shows the considerable oveilap of the water vapor absorption band in the bandpass area, 7.1 to 9.5m- To show the closing effects of this band, ir- radiance calculations for received power were run for the June mean monthly sounding at Saidt Ste. Marie, Mich., from sea level to 18,000 ft. Figure 6 illustrates the influ- ence of water vapor absorption for this sounding in the shorter-wave end of the filter used on the window radiom- eter (7.35-13. 16/u), and the lesser influence in the 10.00 to 12.05-/. bandpass of a curiently available "window" radiometer. The deduced surface temperature error for the narrow pass filter is about half that of the window radiometer used in this experiment when observing the surface at 700 mb. (or 10,000 ft.). In addition, a tempera- ture and moisture inversion below 900 mb. has consider- ably less effect in the narrower bandpass region. These facts are, of course, not new, but in light of the fact that 500 - 600 - 700 - SSM JUNE © © 10.00 12.05 MIC "" 1 \ ® TARGET - » TEMP. 1 © T \ \ \ \ © © \ \ s © \ \ \ \ © © ©. 50 2. 93 -4.80 1.87 -6.00 0.72 -4.03 September 1967 Bernhard Lettau 629 NORTH ^ \ ) \ \ ^\ \ / \ ">^>\ \ \ / ^~\^ Y- J s — L-'-^""/-' \ \ ^-^" \ s-\ / \ ^\ --- Wind Seed Imps) ^-^ s. Xs 0 12 3 4 5 x Wind Sh.or (mp5/km) Figure 2. — Directional distribution of the surface wind vectors, frictionally produced shear vectors, and thermal wind vectors. Summer. \ \ , NORTH 1 / 1 k \ \ \ f" / / y 4 (y V— --"~ ' \ ^~ \ \ / w.nd Speed Imps) ^ I 0 12 3 4 5 -yj' Wind Sheer Imps /km) ~~~~~'—-.. ^ Figuke 3. — Directional distribution of the surface wind vectors frictionally produced shear vectors, and thermal wind vectors. Winter. The separation of the two shear vectors is most straight- forward if opposed wind directions are paired, as is shown in the example in figure 1. Vectors of surface wind and observed shear are drawn so that the heads of the observed shear vectors coincide. In this hypothetical Southern Hemisphere case, the east wind VI; turns sharply to the left, while the west wind V2, turns slowly to the right with altitude. The following will explain the method in more detail. Since the thermal wind vector is assumed to be the same in both observations, and since the observed shear vectors were drawn to one point, we may allow the head of the thermal wind vector to fall on that point. It then follows that the heads of the frictional shear vectors for the two surface winds must also fall on one point, which must be the tail of the thermal wind vector. The second assump- tion, that the angles between the surface winds and the frictional shear vectors are the same, requires that this triple point lie on the line joining the heads of the two surface wind vectors. The third assumption, that the magnitude of each frictional shear vector is proportional to the corresponding surface wind, requires that this point coincide with the intersection of the lines joining the heads and the tails of the two surface wind vectors. In this example the frictional shear vector displaces the 1,000-m. wind vector 16° to the left of the surface wind vector, while the thermal wind vector displaces it toward the southeast. This has the effect of augmenting the rate of turning in the one case, and reversing it in the other. Figures 2 and 3 show the observed shear vectors for the Little America data separated into frictional and thermal components in summer and winter. The frictional shear invariably has the effect of turning the wind vector to the left and increasing the speed with height. The amount of frictional turning of the wind vector from the surface to 1,000 m. varies from 17° to 28° in summer, and from 23° to 36° in winter. The seasonal difference may reflect greater hydrostatic stability in the boundary layer in winter, since the other effects on which the surface wind angle depends are either not applicable — variation with latitude — nor not very pronounced — variation with surface roughness (cf. Johnson [3]). The angles themselves are somewhat greater than would be expected from theory. A representative geostrophic wind speed of 550 cm. /sec, a Coriolis parameter of 1.42X 10~4 sec."1, and surface roughness of 0.01 cm., which is typical of an Antarctic snow field, will produce an angle between the wind at the surface and at the top of the boundary layer of 15° (cf. H. Lettau [4]). The effect of the thermal wind is to turn the surface wind vector toward an azimuth of 91° in summer, and toward an azimuth of 42° in winter. The effect is less pronounced for north or south winds than for east and west winds in both seasons, presumably because the effect of the temperature gradient at the edge of the ice near Little America is suppressed within a homogeneous air mass moving perpendicular to the shore. The largest thermal shears occur with zonal winds in summer, when the ice edge is much closer to the station and of nearly east-west orientation. The change in direction of the thermal wind from sum- mer to winter is related to the magnitude of the annual temperature variation in the area surrounding Little America. A shift such as that observed requires a much greater seasonal temperature contrast to the west and southwest than to the east and northeast of the station. 630 MONTHLY WEATHER REVIEW Vol. 95, No. 9 WINTER I I I SE S SW Surface Wind Direct! Figure 4. — Source region temperature as a function of the surface wind direction. The shaded areas show the directions of minimum and maximum seasonal temperature contrast. Although the air temperatures in the vicinity of the station are not known directly, the seasonal contrast may be investigated by assuming that the mean temper- ature observed at the station with each wind direction is representative of thermal conditions some distance up- wind. As shown in figure 4, the seasonal temperature contrast does vary with the wind direction, ranging from a minimum of about 18° C. for north-northeast winds to a maximum of about 28° C. for winds generally from the west. It is suggested therefore that both the orientation of the thermal wind vectors and the change from summer to winter are direct results of the local temperature distribution, rather than spurious geometrical values introduced by the method of analysis. 4. DETAILED WIND PROFILES A more complete representation of the boundary layer may be obtained by a detailed analysis of the observed wind profiles. Since the thermal wind is apparently insensitive to changes in wind direction, this section has been limited to the examination of the mean profiles observed with north and south winds at the surface for both the summer and the winter seasons. The theoretical background for the analysis of boundary layer wind profiles which include a constant thermal wind has been given by H. Lettau [5], H. Lettau and Hoeber [6], and Johnson [3]. The assumptions are made that the large-scale motion is uniform and unaccelerated over level terrain of constant surface roughness, that there are no mean vertical motions, and that there are no inertial forces, and that the vertical density variation can be neglected. The wind velocity is then a function only of the pressure gradient and the vertical derivative of the shearing stress. If the coordinate system is oriented with the y-axis parallel and the x-axis normal to the direction of the surface stress, which is also the direction of the surface wind, the vertical variation of the geo- strophic component parallel to the surface wind is con- strained by the fact that the surface stress has no compo- nent normal to they-direction, and that the shearing stress becomes negligible at height H. If v(z) is the observed wind profile in the y-direction, and V(z) the geostrophic wind profile in the same direction, then (V— v)dz=0. With the assumption of a constant thermal wind and geostrophic ambient conditions at z=H=l,000 m., V{z) is represented by a straight line tangent to v(z) at z= 1,000 m., such that the algebraic sum of the differences (V—v) (z) is zero. A similar line of reasoning will not give the analogous U(z) since the surface stress parallel to the surface wind is not zero. It is now possible to determine the vertical profile of 7V, T* = Pf£ (V-V)dz (1) where p is the air density, and/ is the Coriolis parameter. A similar expression can be written for t,„ l>- )dz (2) where U(z) is the geostrophic wind profile and u{z) the observed wind profile in the x-direction, although the relation is not very useful at the moment since neither the vertical profile of r„ nor that of U(z) is known. One may, however, also express the shearing stress at any level as the product of air density, wind shear, and eddy diffusivity. Both components of the wind shear are known and there is no reason to suppose the diffusivity to vary with direction. Thus for all values of z, du/bz 'dv/dz (3) in which r„ is the only unknown. A convenient value to use is z=z*, the height at which V(z) and v(z) intersect, which is the height of maximum rx. Thus U(z) is obtained by the straight line tangent to ii(z) at 2=1,000 m., such that € = Pf\ (U-u)dz. (4) Figures 5 through 8 show the above constructions for smoothed mean northerly and southerly wind profiles in September 1967 I000 Bernhard Lettau 6 7 8 Wind Speed Parallel to Surface Wind Direction (mps —4 —3 —2 —I Wind Speed Normal to Surface Wind Direction (mps) Figure 5. — Observed ambient mean wind profile and computed linear geostrophic wind profile separated into components parallel and normal to the surface wind direction. North winds in winter. winter and summer. For the most part the differences among the four cases are minor, and related to directional rather than seasonal differences, suggesting that the ice surface produces its own characteristic wind distribution. The component parallel to the surface wind increases with height immediately above the surface in all four cases, but reaches a maximum below 400 m. and decreases slowly with height above that level. The geostrophic wind decreases continuously in the boundary layer indicating that this component of the thermal wind is antiparallel to the surface wind. Its magnitude however is relatively small, ranging from 0.3 to 1.5 m. sec."1 km.-1 The height at which tt reaches a maximum is approximately 160 m., with the exception of southerly winds in summer when tx reaches a maximum at 200 m., and the maximum value attained ranges from 0.17 and 0.25 dyne/cm.2 The component normal to the surface wind shows a definite directional difference, caused by the relatively fixed thermal wind vector. For the southerly winds this component increases from the surface to roughly 500 m., then decreases to the top of the boundary layer, the devia- tion being to the left of the surface wind. For the northerly winds the component value in summer increases con- tinuously to the left of the surface wind through the boundary layer; in winter the profile is very similar with the exception of a slight relative maximum at 600 m. The geostrophic wind increases to the left for the northerly components, and to the right for the southerly components, implying an eastward-directed thermal wind for all cases. Table 2. — Derived boundary layer -parameters at Little America Height of maximum r?.__ Surface geostrophic wind.. . . Surface stress.. Surface geostrophic wind angle. Thermal wind vector magnitude. . ... . . azimuth. Surface Rossby number Geostrophic drag coefficient.. Energy dissipation Roughness length V,o Ros C E m./sec. dyne/cm.- degrees m. sec.-1 km.-i degrees watts/m.- cm. North Winds Winter Summer 155 8.78 0.81 1.72 30 8. 32 x 10° 0.025 0.61 0.8 160 5.81 0.64 24 1.24 75 2. 76 x 106 0.033 0.33 1.6 South Winds Winter Summer 162 6.23 0.56 23 1.47 108 4. 57 x 10« I 0. 030 0.31 1. 1 202 6.15 0.94 34 1.42 108 0. 045 x 10e 0.041 0.40 105 632 MONTHLY WEATHER REVIEW Vol. 95, No. 9 000 - 800 -600 Z - 400 5 - 200 3 4 5 6—4 Wind Speed Parallel to Surface Wind Direction (mps) —3 —2 Wind Speed Normal to Surface Wind Direction (mps) Figure 6. — Observed ambient mean wind profile and computed linear geostrophic wind profile separated into components parallel and normal to the surface wind direction. North winds in summer. The magnitude of the normal component of the thermal wind is again relatively small, ranging from 0.8 to 1.4 m. sec. km."1 A number of other boundary layer parameters, given in table 2, may be determined either directly or sequen- tially from the observed and the geostrophic wind pro- files. Those determined directly include the surface geostrophic wind, \gQ, obtained as the vector sum of the two geostrophic components at the surface, the surface stress, T0, determined from the relation T0=f>f( (U-u)dZ ,/n (5) and the angle, a0, between the surface geostrophic wind and the surface stress, determined by the arctangent of the ratio U0/V0- Derived parameters include the surface Rossby number, Ro0, which is a unique function of the angle an, the geostrophic drag coefficient, C, determined by the relation r- h l (6) the energy dissipated in j the boundary layer, E, which may be obtained from the geostrophic wind and the surface stress (cf. H. Lettau [4]), and the roughness length, z0, from the relation Zo-- 'RooJ (7) The tabulated values are internally reasonably con- sistent with the exception of those parameter values de- rived from the surface geostrophic wind angle for the mean south wind profile in summer. The relatively much higher value for this angle produces a much lower surface Rossby number and consequently a much higher and quite spurious roughness length. Similar analyses of wind profiles in the boundary layer have been undertaken by Johnson [3] for kite wind data from four stations in the midwestern United States, and by H. Lettau and Hoeber [6] for pilot balloon profiles ob- tained on Helgoland in the North Sea. Although all three studies are in reasonable agreement with one another, re- sults of the first study are generally indicative of more vigorous flow over a rougher surface than that at Little America, while the second study shows more rapid air motion over a surface comparable to that at Little America. The differences in the surface stress and in the frictional energy dissipation within the boundary layer specifically emphasize these conclusions. At the inland stations in the first study the surface stress always exceeds 0.8 dyne/cm.2 and generally ranges from 1.5 to 2.0 dyne/ cm.2, while the energy dissipation generally exceeds 1 Bernhard Letrau 3 4 5 6 Wind Speed Parallel to Surface Wind Direction (mps) -3 —2 —I 0 Wind Speed Normal to Surface Wind Direction (mps) Figure 7. — Observed ambient mean wind profile and computed linear geostrophic wind profile separated into components parallel and normal to the surface wind direction. South winds in winter. watt/m.2 On the ice shelf at Little America the stress ranges from about 0.6 to 0.9 dyne/cm.2, and the energy dissipation from 0.3 to 0.6 watt/m.2, lower by a factor of roughly three. The Helgoland data, which essentially represent wind profiles over a water surface, produce surface stress values of 0.6 and 0.9 dyne/cm.2, and energy dissipation values of 0.6 and 1.4 watt/m.2 Since the sur- face stress value can be said to be determined by the shape of the wind profile components in the boundary layer, it is evident that these are roughly the same for the Helgo- land and the Little America data. The energy dissipation values, on the other hand, also depend on the mean geo- strophic wind in the boundary layer, which at Helgoland exceeds that at Little America by a factor of about two. Thus the observed difference is entirely due to the observed higher wind speed at Helgoland. The computed angles between the surface geostrophic wind and the surface stress in the Little America data do not follow the similarity pattern described above. These are more nearly equal to those found for the inland data, which average about 25°, than to those found for the littoral data (9.5° and 11.2°). From this point of view the ice shelf is better described as a land surface than as a water surface. A second point of similarity between the midwestern United States data and the Little America data is that the observed angles exceed by roughly 7° the values theoretically predicted by independently derived rough- ness lengths. If one takes the roughness length obtained as typical for the snow surface at the South Pole by Dalrymple et al. [1], 20=0.014 cm., together with the observed wind speeds, one obtains a surface Rossby number of 3X108, which corresponds to an angle between the surface geostrophic wind and the surface stress of 17°. The difference, as obtained by Johnson [3], was attributed to a real height variation of the thermal wind which would become obscured by the method of analysis, rather than to topographical or other external effects. A similar real height variation of the thermal wind should be expected in the Little America data because of the complex thermal structure of the boundary layer which would produce a number of abrupt wind velocity changes rather than the smooth transition that has been shown here. The diabatic effects which should be con- sidered on the ice shelf include radiational cooling near the ice surface, and temperature profiles which sometimes change from inversion to lapse conditions within the lowest 1,000 m. MONTHLY WEATHER REVIEW 3 4 5 6-4 Wind Speed Parallel to Surface Wind Direction (mps) -3 —2 Wind Speed Normol to Surface Wind Direction (mps) Figure 8. — Observed ambient mean wind profile and computed linear geostrophic wind profile separated into components parallel and normal to the surface wind direction. South winds in summer. 5. DISCUSSION A hypothetical example of precisely such diabatic influences on the wind spiral near a snow surface has been prepared by H. Lettau [4]. Here a surface cooling rate of 26 langleys/day produced a significant reduction in the surface wind speed, and a correspondingly greater angle between the surface stress and the surface geostrophic wind vector than under adiabatic conditions. Although a surface inversion is in fact one of the major characteristics of the Antarctic boundary layer, it is not possible to investigate this diabatic effect in the Little America I and II data, since almost no free-air temperatures were obtained by the Byrd Antarctic Expeditions. Subsequent scientific efforts in the Antarctic have of course obtained simultaneous temperature and wind profiles, although none has matched the nearly 1,000 boundary layer profiles that have been used in this study to provide reliable mean values. REFERENCES P. C. Dalrymple, H. H. Lettau, and S. H. Wollaston, "South Pole Micromctcorology Program, Part II, Data Analysis," Report No. 20, Institute of Polar Studies, Ohio State Univer- sity, 1963, 94 pp. G. Grimminger and W. C. Haines, "Meteorological Results of the Byrd Antarctic Expeditions 1928-30, 1933-35: Tables," Monthly Weather Review Supplement No. 41, 1939, 377 pp. W. B. Johnson, Jr., "Climatology of Atmospheric Boundary Layer Parameters and Energy Dissipation," Studies of the Three-Dimensional Structure of the Planetary Boundary Layer, Dept. of Meteorology, University of Wisconsin, 1962, pp. 125-158. II. II. Lettau, "Notes on Theoretical Models of Profile Structure in the Diabatic Surface Layer," Studies of the Three-Dimensional Structure of the Planetary Boundary Layer, Dept. of Meteor- ology, University of Wisconsin, 1962, pp. 195-226. H. II. Lettau, "Windprofil, innere Ucibung, und Energic Umsatz in den unteren 500 m. iiber dem Mccr," Beitrdge zur Physik der Almosphdre, vol. 3D, No. 2, 1957, pp. 78-96. H. II. Lettau and II. Ilocber, "Uber die Bestiinmung der Hohenvertcilung von Schubspannung und Austauschkocffi- zienten in der atmospharischen Heibungsschicht," Beitrage zur Physik der Almosphdre, vol. 37, No. 2, 1964, pp. 105-118. [Received May SI, 1967; revised June 15, 1967] May 1967 Reprinted from MONTHLY WEATHER REVIEW Vol. 95, No. 5 299 SEA-SURFACE TEMPERATURES IN THE WAKE OF HURRICANE BETSY (1965) JAMES D. McFADDEN Sea-Air Interaction Laboratory, Institute for Oceanography, ESSA, Silver Spring, Md. ABSTRACT Following the passage of hurricane Betsy (1965) through the Gulf of Mexico two flights were made five days apart aboard a research ah craft to collect sea-surface temperatures with an infrared radiometer. The purpose was to study the effects of a hurricane on the sea-surface temperatures field. Data from the first flight, which occurred one to two days after the hurricane passage, showed two cores of colder water to the right of the storm's track and very little structure to the left. The flight made five days later still showed a core of colder water to the right, but by this time its shape had been badly distorted by the surface current system. These results are compared with the findings of other investigators, and the value of real-time synoptic coverage with the use of aircraft is pointed out. The plan for an experiment utilizing aircraft and airborne oceanographic techniques to provide a 3-dimensional picture of the ocean temperature structure prior to and following a hurricane is also presented. 1. INTRODUCTION There has been considerable interest shown in recent years in the effects of the passage of a hurricane on sea- surface temperature. While it is agreed that the hurri- cane causes a cooling of the sea surface of up to 5° C, there appears to be some disagreement as to the mechanics involved. Fisher [1] noted that pools of cold water were created behind some hurricanes during parts of their lives, and that this phenomenon is apparently produced by upwelling in the ocean where the top layers are thermally stratified. Jordan [5], working with ship temperature data obtained prior to and following several typhoons in the Pacific, concluded that vertical mixing is the primary factor in the cooling of the surface layers and that mechan- ical stirring is probably more important than organized upwelling in this cooling process. He reached these con- clusions mainly because the cooling was much more pronounced on the right side of the storm, (relative to the forward motion) the region of most intense wind and wave action. Stevenson and Armstrong [9], by measuring sea tem- peratures in a zone of low-salinity shallow water near the coast in the northwestern Gulf of Mexico after the pas- sage of hurricane Carla (1961), observed that bathy- thermograph traces revealed temperature inversions as great as 2.5° C. extending as deep as 83 m. They hy- pothesized that these inversions were formed in the surface waters through a lowering of the water temperature by a loss of heat to the hurricane. Leipper [7] made the most complete study to date in his detailed oceanographic investigation of that portion of the western Gulf through which hurricane Hilda (1964) passed. His observations indicated that the hurricane caused surface waters to be transported away from its center, cooling and mixing them to a slight degree as they moved. Convergence outside the storm area resulted in downwelling to 80 to 100 m. in that area, while water on the order of 5° C. colder upwelled from about 60 m. in the central region of the storm. Hidaka and Akiba [3] developed a theory to explain cold water areas observed after hurricane passages which indicates a considerable amount of upwelling in the center of the storm. Ichiye [4], basing his results on fairly rigorous mathematical treatment, shows weak descending motion ahead of the storm, reaching somewhat larger though negligible values near the center, followed by strong vertical ascending motion thereafter. Gutman [2] and O'Brien [8] have also done some modeling of these phenomena. Gutman's solutions, which are obtained using variable stress as a function of time and then com- puting upwelling using continuity considerations, show maximum upwelling to occur at the center of the storm. O'Brien, on the other hand, derived a non-linear, theo- retical model which describes upwelling and mixing induced in a stratified, rotating two-layer ocean by mo- mentum transfer from a stationary, axially symmetric hurricane, and concluded that maximum upwelling occurs in the region of maximum turbulent shearing stress. O'Brien, however worked with a stationary model while Gutman incorporated forward movement of the system in his model. Thus, some question remains as to the origin of these cold spots observed in the wakes of hurricanes. Leipper's conclusion that upwelling is responsible is certainly rea- sonable based on the results of his cruise following the passage of hurricane Hilda (1964), but his inference that this upwelling occurred in the central region of the storm is still not completely proven. The "after Hilda" data 300 MONTHLY WEATHER REVIEW Vol. 95, No. 5 were collected on a seven-day cruise, which means that the information obtained was not synoptic. Uncertainties of interpretation may have resulted from the fact that no consideration was given to the effects of the Gulf circu- lation on the thermal structure in the interval between the passage of the hurricane and the time the observations were made. 2. OBJECTIVES During the past 12 yr. there have been only 11 hur- ricanes that have qualified as "great hurricanes", i.e., hurricanes with central pressure less than 950 mb. (Kraft [6]). Hurricane Betsy (1965) was one of these. It had qualified for this category before entering the Gulf of Mexico on September 8 and continued as an intense storm until shortly after landfall on September 10. Its maximum surface wind speed averaged about 120 kt. during the Gulf transect, and the eye diameter varied between 25 and 80 n. mi. during this period (see fig. 1). Because of the size and intensity it was immediately recognized that this storm should have a profound effect on the thermal structure of the surface of the ocean. On September 9, the Director of the National Hurricane Research Laboratory, ESSA, agreed to support the Sea Air Interaction Laboratory's efforts to study these effects by making available a research aircraft from ESSA's Research Flight Facility for two nights to obtain sea-surface temperature data with an infrared radiometer in the wake of the storm. These missions were successfully completed on September 10 and 15. The objective of this paper is to present the essentially real-time sea-surface temperature patterns obtained from these two flights, to discuss the similarities and differences between these results and those of previous investigators, and to suggest an investigation that could possibly lead to a more thorough understanding of the effects of the storm on the ocean thermal structure. 3. DATA COLLECTION ESSA's Research Flight Facility is adequately equipped with multi-engine aircraft (two DC-6's, a DC-4, and a B-57) suitable for long-range reconnaissance and especially for hurricane research. The aircraft are outfitted with a system of meteorological sensors, radars, and photo- graphic equipment as well as digital tape, analog, and photo-recording devices. For obtaining sea-surface tem- peratures from the DC-6 aircraft a Barnes IT-2 radiom- eter is employed, and the infrared (IR) data are recorded on an oscillographic recorder. This sensor is shock mounted vertically on a frame which fits inside the drop- sonde chute during normal operation but which can easily be removed at any time during flight in order that in-flight calibration checks of the radiometer can be made. Two-point calibration checks are made ap- proximately every 30 min. during flight using two agitated FLIGHT TRACK 10-11 SEPT 1965 ALONG PATH OF HURRICANE BETSY Figure 1. — Flight track of September 10-11, 1965, superimposed on the path of hurricane Betsy. Dashed lines define width of eye as determined by radar and reconnaissance aircraft. SEA SURFACE TEMPERATURE DISTRIBUTION 10-11 SEPT 1965 + MERCHANT SHIP DATA (WithinJ2 hr. of IlighMilt I Figure 2. — Sea-surface temperature distribution on September 10-11, 1965. water baths of different temperatures. This rather frequent calibration helps to minimize readout errors resulting from changes in detector bias voltages, detector responsivity, amplifier gain, and amplifier drift of the radiometer. Such changes otherwise could lead to errors in the analysis of the data, which from experience could be as much as 1.5° to 2° C. The track of the first flight, superimposed over the path of Betsy, is shown in figure 1. The times of three turning points are given for comparison with the hurricane time coordinates. The dashed lines denote the eye width as May 1967 James D. McFadden 301 determined by radars at Key West and New Orleans and by reconnaissance aircraft. Greater emphasis was placed on the right side of the storm track, although the left portion was adequately covered for detection of any colder water zones in that region. A DC-6 research aircraft departed Miami on September 10 at 2225 gmt and returned after completing the mission at 0600 gmt on September 11. A flight altitude of between 800 and 1000 ft. was maintained throughout the flight. In addition to the IR data, meteorological information was also obtained throughout the flight at a sampling frequency of once every 10 sec. This information included: temperature, pressure, humidity, pressure alti- tude, radar altitude, and wind direction and wind speed as determined by the Doppler navigational system. Precise positioning was provided by means of Loran. The second flight on September 15, with the exception of the flight track, was conducted in the same manner as the first flight, 4. RESULTS The sea-surface temperature distribution as measured on September 10-11 is shown in figure 2. The solid lines are isotherms drawn with a reasonable degree of certainty while the dashed lines, exclusive of the eye size indication, are extrapolated isotherms. The four temperatures at positions denoted by plus signs were obtained by merchant ships within 12 hr. of the time in which the IR data were collected. They were not used in analyzing the data and positioning the isotherms and are presented only for comparison with the airborne IR measurements for this flight, At a glance the cold water zone induced by the hur- ricane is immediately the outstanding feature of this figure. It may be noted, however, that all of this cold water appears to the right of Betsy's path and farther from the center than the eye wall. Another interesting feature is the existence of two cores of cold water rather than one continuous trough. The northward curl of isotherms in the eastern core is of importance as will be shown below. The lowest temperature detected by the radiometer was slightly less than 25° C. This indication was recorded several miles north of the intersection of the leg of the flight occurring after the 2331 gmt turning point with the leg made prior to the 0404 gmt turning point on both tracks. The temperatures recorded on both tracks at each of the two intersections were in agreement with each other, thus indicating relative validity of all of the IR flight data. Based on preliminary results of the first flight, a second plan was drawn up to cover some of the major features which had been observed. Major emphasis was placed on the north (right) side of the hurricane's path. At 0500 gmt on September 15, a DC-6 research aircraft departed Miami on another mission to collect sea-surface temperature data. Figure 3 shows the track of that FLIGHT TRACK 15 SEPT 1965 Figure 3. — Flight track of September 15, 1965, superimposed on the path of hurricane Betsy. Figure 4. — Sea-surface temperature distribution on September 15, 1965. flight, The aircraft returned to Miami at 1200 gmt after completing the second of the two nighttime flights made during the operation. The major feature of the second flight shown in figure 4 is an elongation to the northeast of the cold core detected on the earlier flight as indicated by the northward curl of the isotherms shown in figure 2. The data also indicate that during the five-day interval between flights the cold-core surface temperatures increased about 0.5° to 1.0° C. Another interesting feature is the relatively small cold water area southwest of St. Petersburg and Tampa Bay. The shape of the isotherms indicates that this 302 MONTHLY WEATHER REVIEW Vol. 95, No. 5 temperature structure is possibly associated with the bay circulation and may result from relatively cool rain- water runoff. On the latter flight the aircraft did not traverse the area of the Gulf where the second cold core was detected on the western legs of the first flight. 5. CONCLUSIONS The results of this experiment lead to two conclusions. First, they confirm the observations of the other investi- gators, as was expected, that hurricanes do cause well defined areas of cold water to occur at the sea surface in their wakes. The surface temperature data alone, however, do not establish whether maximum upwelling occurs in the central region of the storm, as concluded by Gutman [2] and Leipper [7], or whether it occurs in the region of maximum turbulent shearing stress as concluded by O'Brien [8]. Certainly the positions of the cold water areas observed on these flights fit more closely positions of cold water zones described for Pacific typhoons by Jordan [5], but again it is not obvious from the IR data that vertical mixing induced by mechanical stirring is more important than organized upwelling in this cooling process as he concluded. Perhaps even more important than the first observation above, at least from a data collection standpoint, is the rapid deformation of the eastern cold water core observed in the interval between the two flights. This temperature pattern change could have been realized by a northeast- ward flowing current of less than 1 kt. Such a current, the Yucatan Current, is a feature of the surface circulation of the Gulf of Mexico. The emphasis here is on the sampling time involved in acquiring data for the solution of this particular problem. On the one hand a research ship can obtain, in addition to surface temperatures, sub-surface data which are essential to answering the questions concerning upwelling and mixing. A voyage to obtain this information, how- ever, requires a considerable amount of time — about 10 days to cover such an area as discussed here. The aircraft, on the other hand, covered the area in less than 10 hr., but it was not suitably equipped to obtain sub-surface temperatures. It would be desirable, then, to combine the speed of the aircraft with the versatility demonstrated by the ship for success! ully attacking the problem. Wilkerson [10] points out that with an airborne infrared sensor and an air-droppable expendable bathythermograph, observations can now be made of sea-surface temperatures and temperatures with depth, thus providing a near-synoptic picture of the thermal structure of the first few hundred meters of the ocean over a large area. It would take several ships at considerably greater expense to duplicate such observa- tions. The Sea-Air Interaction Laboratory plans in the near future to employ these techniques of airborne oceanography in a more detailed synoptic study of the effects of a hurricane on the thermal structure of the ocean by measuring surface and sub-surface temperatures both ahead of and behind the storm. ACKNOWLEDGMENTS The author expresses his thanks to the National Hurricane Research Laboratory for making the flight time available, to ESSA's Research Flight Facility, in particular to Dr. Gerald Conrad, for collecting the data, and to Mr. Feodor Ostapoff and Dr. Donald V. Hansen of the Institute for Oceanography for their comments and suggestions. REFERENCES 1. E. L. Fisher, "Hurricanes and Sea-Surface Temperature Field," Journal of Meteorology, vol. 15, No. 3, June 1958, pp. 328-333. 2. G. Gutman, "A Preliminary Study of Ocean Conditions as Affected by a Hurricane Passage," Paper presented at the Fourth Technical Conference on Hurricanes and Tropical Meteorology, Miami Beach, Fla., Nov. 22-24, 1965. 3. K. Hidaka and Y. Akiba, "Upwelling Induced by a Circular Wind System," Records of Oceanographic Works ■ in Japan, vol. 2, No. 1, Mar. 1955, pp. 7-18. 4. T. Ichiye, "On the Variation of Oceanic Circulation, Part 5," Geophysical Magazine, Tokyo, vol. 26, No. 4, Aug. 1955, pp. 283-299. 5. C. L. Jordan, "On the Influence of Tropical Cyclones on the Sea Surface Temperature Field," Proceedings, Symposium on Tropical Meteorology, J. W. Hutchins (ed.), New Zealand Meteorology Service, Wellington, 1964, pp. 614-622. 6. R. H. Kraft, "Great Hurricanes, 1955-1965," Mariners Weather Log, vol. 10, No. 6, Nov. 1966, pp. 200-202. 7. D. F. Leipper, "Observed Ocean Conditions and Hurricane Hilda, 1964, "Journal of the Atmospheric Sciences, 1967 (in press). 8. J. J. O'Brien, "The Non-Linear Response of a Two-Layer, Baroclinic Ocean to a Stationary, Axially-Symmetric Hurri- cane," Texas A&M University, Department of Oceanography, Reference 65-34T, Dec. 1965, 98 pp. 9. R. E. Stevenson and R. S. Armstrong, "Heat Loss From the Waters of the Northwest Gulf of Mexico During Hurricane Carla," Geofisica Internacional, vol. 5, No. 2, 1965, pp. 49-57. 10. J. W. Wilkerson, "Airborne Oceanography," Geo-Marint Technology, vol. 2, No. 8, Sept. 1966, pp. 9-16. [Received February 9, 1967 ; revised March 3, 1967] 936 Reprinted from MONTHLY WEATHER REVIEW Vol. 95, No. 12 Vol. 95, No. 12 COMPATIBILITY OF AIRCRAFT AND SHIPBORNE INSTRUMENTS USED IN AIR-SEA INTERACTION RESEARCH JAMES D. McFADDEN Sea Air Interaction Laboratory, ESSA, Silver Spring, Md. and JOHN W. WILKERSON U.S. Naval Oceanographic Office, Washington, D.C. ABSTRACT On June 16, 1966, an experiment was performed off the east coast of Florida that involved two research aircraft, one from the Naval Oceanographic Office and one from ESSA's Research Flight Facility, and the USCGSS Peirce, aboard which were two scientists from ESSA's Sea Air Interaction Laboratory, and the Weather Bureau Airport Station at Jacksonville, Fla. The purpose of this investigation was to determine the comparability of data for air-sea interaction research as determined by aircraft temperature, humidity, pressure, and wind sensors; airborne IR radiom- eters; a tethered boundary layer instrument package, radiosondes, rawinsondes, and dropsondes. Results showed generally good agreement (within listed instrumental accuracies) between comparisons of aircraft and radiosonde temperature and humidity observations, fair agreement of wind observations, and very poor comparisons between dropsondes and radiosondes. The sea surface temperature readings obtained by the airborne radiation thermometer aboard the Navy aircraft were well within ±0.4° C. operational accuracy of the instrument when compared with bucket temperature measurements taken aboard the Peirce. Whether the accuracies of these presently available instruments are good enough for mesoscale and macroscale ocean-atmosphere interaction investigations now being planned will have to await studies of the environments in which these experiments will take place. 1. INTRODUCTION A major, comprehensive, field investigation is now being planned by ESSA, the primary focus of which will be on the problem of ocean-atmosphere interaction, as well as related topics in physical oceanography and microscale and mesoscale meteorology. The primary objectives of this experiment are: 1) to study the total fluid environ- ment within a limited area, and 2) to provide a realistic pilot field study for the planning and execution of a suc- ceeding major Tropical Ocean Area Study within the framework of the World Weather Watch. The plans for this experiment call for among other things the deployment of several ships on fixed stations several hundred miles apart, a roving ship for making meteorolog- ical and oceanographic measurements within the study area, and several research aircraft that will be used in a variety of measurement programs, such as vertical pro- filing, making line integral observations, and obtaining sea surface and subsurface temperature data. Further, these plans call for the utilization of ship launched rawinsondes, for obtaining vertical soundings of temper- ature, pressure, humidity, and winds; tethered boundary layer instrument packages for obtaining both profiles of temperature, humidity, pressure, and winds and the time variation of these quantities at any height up to 2000 m.; and air released dropsondes for obtaining vertical profiles of temperature, humidity, and pressure. Before the investigation can be initiated, however, there are certain preliminary steps that must be taken. These include: 1) an evaluation of the compatibility of the variety of instruments mentioned above, 2) an improve- ment in our knowledge of the environment in the region of the experiment, and 3) a test of the major instrument systems in the experimental area. This paper concerns itself with the first of these steps. In June 1966 an experiment was performed to evaluate the comparability of existing operational instruments of the types planned for use in future mesoscale and macro- scale ocean-atmosphere interaction studies. The objectives of this investigation were to observe the comparability of the data obtained by the various methods mentioned above, to ascertain whether observed differences between any two readings of a given parameter were within the quoted accuracies of the measuring instruments, and to arrive at a conclusion regarding the use of these state-of- the-art instruments for air-sea interaction research. 2. INSTRUMENTATION AND DATA ACQUISITION Because of the nature of this experiment a variety of organizations was called upon to pool their efforts toward accomplishing the mission. The U.S. Naval Oceano- graphic Office provided the services of its Ocean Aerial Survey Unit of the ASWEPS program and ESSA was represented by the Weather Bureau Airport Station at Jacksonville, Fla., the USCGSS Peirce, the Research December 1 967 James D. McFadden and J. W. Wilkerson 937 Flight Facility (RFF) of the Institute for Atmospheric Sciences, and the Sea Air Interaction Laboratory (SAIL) of the Institute for Oceanography. The Navy aircraft was a Lockheed Super-G Constella- tion which, as one of the airborne platforms, was used to obtain measurements of air temperature, pressure, and humidity and sea surface temperature. The air tempera- ture and pressure aboard this aircraft are obtained by a meteorological set (AN/AMQ 17) which consists in pari of a platinum wire resistor vortex thermometer and a bellows mechanically linked to a potentiometer. The operational accuracies listed for this device are 0.5° C. for the thermometer and 5 mb. for the pressure sensor. Humidity data are obtained by an infrared absorption hygrometer system designed and built by the Weather Bureau's Equipment Development Laboratory. Basically this hygrometer is an optical instrument designed to measure the absolute humidity of the atmosphere by measuring the absorption of radiant energy over a given optical path in the spectral region of the infrared water vapor absorption band. A full description of this system is given in [1]. A relatively large console model airborne radiation thermometer (ART) developed by Barnes Engineering Co. is used to obtain sea surface temperature aboard the Navy aircraft. Radiation from the sea surface in the 8 to 13-/z region is detected by a thermistor bolometer and this received energy, which is proportional to the fourth power of the sea surface temperature, is translated into temperature readings by electronic processing. The operational accuracy of this system is listed as ±0.4° C. These instruments represent just three of a large array of devices designed for oceanographic research from the Navy aircraft. A complete description of this aerial platform and its capabilities is given in [2]. ESSA's Research Flight Facility provided this project with a DC-6 aircraft instrumented primarily for hurricane research. This aircraft was used as a platform from which air temperature, pressure, and humidity; wind speed and direction; and sea surface temperatures were obtained and from which dropsondes to measure temperature, pressure, and humidity were released. An AMQ-8 vortex thermometer system is used aboard the RFF aircraft to measure the free-air temperature in flight. System accuracy is quoted to be 0.5° C. Ambient pressure is measured by a pressure transducer operating on an independent static source. Humidity is measured by a system identical to that described for the Navy aircraft. An interesting secondary objective of this experiment was to obtain data from which a thorough evaluation of the in-flight capabilities of these two absorption hygrometers could be made. The infrared hygrometer, while used on both aircraft as the primary source of humidity information, is still classed as a special purpose device. It has three outstanding features that make it desirable for use aboard aircraft, high sensitivity at low water-vapor concentrations, fast speed of response for all water-vapor concentrations, and ability to effect a humidity measurement without altering the sample concentration by either adding or subtracting water or changing the state of any part of the sample. Wind speed and direction, along with latitude and longitude information, are determined by a Doppler navigation and wind-computing system (APN-82) manu- factured by General Precision Laboratories. The Research Flight Facility, from operational experience quotes for this system an accuracy of ± 3 kt. for the wind speed and an error function in degrees of roughly (150 -h- wind speed) for wind direction. The dropsonde system used aboard the RFF DC-6 is a military type (AN/AMT-3) and is used to obtain soundings of temperature, pressure, and humidity from aircraft flight level to the surface. Following launch from the aircraft the instrument descends by parachute at a rate of approximately 1,200 ft./min. During this descent the package transmits measurements of temperature, humidity, and pressure in International Morse Code approximately 12 times a minute, and these transmissions are hand copied aboard the aircraft. The temperature element consists of a bimetallic strip, the humidity element of several strips of hair; and the pressure element is a double-bellows aneroid cell. RFF experience with this system indicates that pressures determined by this instrument are accurate to within plus or minus 2 mb., and that temperature and humidity data are comparable in accuracy to conventional radio- sondes. To obtain sea surface temperatures the RFF employs a Barnes IT-2 infrared thermometer. In principle this device operates similarly to the ART on the Navy aircraft, being a thermistor bolometer with a spectral bandpass of 8 to 13 /x. Physically, however, the unit is much smaller and can be hand held. The sensing head of the radiometer is mounted in the dropsonde chute of the DC-6. A more detailed description of its operation is given in [3]. The manufacturer lists a resolution of 1° F. and an absolute accuracy of 2° F. for this instrument. The USCGSS Peirce was used as a platform from which scientists from SAIL launched conventional radiosondes, obtained sea surface temperatures for comparison with aircraft infrared-sensed temperatures, and gathered air temperature and humidity data at 1,000-ft. and 500-ft. heights with a boundary layer instrument package being- developed in-house. This device, which was in the early stages of development at that time, consisted of a stand- ard 403-mHz. radiosonde package supported at the given heights by a pair of kytoons tethered to the ship. The aneroid switch had been replaced with a small clock switch and this permitted alternate transmission of tem- perature and relative humidity data to a standard radio- sonde receiver-recorder located on the ship. (Subsequent to this experiment a more sophisticated package has been developed by SAIL which can be used to measure and 938 MONTHLY WEATHER REVIEW Vol. 95, No. 12 transmit temperature, humidity, and wind speed data simultaneously to receivers on the ship from any height from the surface to 2000 m. The development of this sys- tem is the subject of a forthcoming report now in prepara- tion within the laboratory.) The Weather Bureau participation in this experiment consisted of a rawinsonde launch from the Airport Station at Jacksonville, Fla. A 1200-gm. balloon was released at this station shortly before the arrival of the aircraft over Jacksonville and was tracked by GMD radar to an altitude of about 32,000 ft. Air temperature, pressure, and humidity, of course, were also obtained on this flight. On June 16, 1966, under ideal weather conditions the instrument comparison test was performed. The operation, as shown in figure 1, proceeded in the following manner. The two aircraft departed Miami, Fla., about 1345 gmt and proceeded at an altitude of 5,000 ft. to a point north of Cape Kennedy staying a few miles inland at all times. This route was necessitated by a launch from the Cape which had been rescheduled from the prior day. After reaching this point the research aircraft turned eastward, descended to 1,000-ft. altitude and continued on the course shown to the USCGSS Peirce while maintaining a separation between them of 2 to 3 mi. Upon arriving at the ship and making an initial pass past the boundary layer instrument package tethered at 1,000 ft. the RFF aircraft began its climb to the 500-mb. level while the Navy aircraft made three additional passes over the Peirce before beginning its climb. After completing the ascent to the desired altitude, personnel aboard the DC-6 released a dropsonde while simultaneously a radiosonde was released from the ship. By the completion of the radiosonde and dropsonde soundings the Navy plane had arrived at the same level as the RFF aircraft, and both planes began a 500-ft./min. spiral descent to 500 ft. where four additional passes were made over the ship. A southwesterly flight path was then followed from the Peirce to Jacksonville, Fla. Enroute, the Navy plane flew at an altitude of 1,000 ft. collecting sea surface temperature data while the RFF plane climbed to 15,000 ft. for a second dropsonde release about halfway between the ship and the airport station. After reaching Jacksonville the DC-6 made a short ascent to 18,000 ft. and released a third dropsonde, as indicated in figure 1, while the Constellation was completing its climb from 1,000 ft. to the same height. Both aircraft then made a spiral descent as described before to 1,000 ft. just seaward of the coast and east of Jacksonville. After completing the spiral descent, the Navy Constellation terminated its data acquisition operation and returned to its home base at Patuxent River, Md. The RFF DC-6 proceeded on a southerly course toward its home base at Miami, breaking off data acquisition at Daytona Beach. 3. RESULTS Figures 2-8 and table 1 present the results of this experiment. A quick glance at these graphs makes it CLIMB & DESCEND US C&GS PIERCE Figure 1. — Flight plan of Navy and Research Flight Facility aircraft on June 16, 1966. Table 1. — Comparison of aircraft sensors with boundary layer instrument package and sea surface temperature thermometer Air temperature (°C.) Humidity (gm./m.3) Sea surface temperature (°C.) Altitude(ft.) Navy RFF Peirce RFF Peirce Navv (ART) Peirce (Bucket) 1000 24.0 23.8 23.7 23.7 24.6 24.6 24.7 24.7 24.0 a e 5 24.8 24.8 24.8 24.6 24. 1 24.3 24.0 25.1 24.7 25.0 25.0 IS. 3 No data 27.3 27.3 27.3 27.3 27.4 27.4 27.4 27.5 27.2 27.4 27.4 27.3 500 18.5 18.5 18.5 18.5 16.8 16.1 15.0 16.8 27.3 27.2 27.3 27.3 December 1967 James D. McFadden and J. W. Wilkerson 939 immediately apparent that there are no data for some of the instruments originally planned to be used and de- scribed in the previous section. Unfortunately, there were equipment malfunctions during the flight and even more unfortunate no back-up systems for substitution. This will be discussed further, later. Figure 2 depicts sea surface temperatures measured by the ART on the Navy plane and a plane-to-plane compari- son of air temperatures on the Cape Kennedy-to-ship leg of the flight. As mentioned earlier the lateral separation between the two aircraft was 2 to 3 mi. which possibly could account for some of the observed differences (maximum 0.5° C.) in the air temperature record. Perhaps the greatest interest, particularly in the Navy Oceanographic Office and the Research Flight Facility, lay in the comparison of the infrared radiometers and the absorption hygrometers of the two aircraft. It is sad to say that neither of these comparisons could be made AIR TEMPERATURES NAVY AIRCRAFT RFF AIRCRAFT 1530 1540 1550 1600 Figure 2. — Sea surface temperatures as measured by Navy ART and air temperatures as measured by both aircraft on Cape Kennedy to USCGSS Peirce leg of the flight. \J \ RFF NA\ AIRCRAFT r AIRCRAFT \ ^ SHIP sf \ I \ AIR TEMPERATURE C v, 1 *L \\ RFF AIRCRAFT \ \ RADIOSONDE 600 \ \^ *v ^ \ \ JAX ^ SHIP a oo \ r \ 11' v \\ \\ 900 1000 \ \\ V \ t- \ I TtMPEHAIUBt Figure 4. -Comparison of radiosonde temperature profile RFF aircraft profile. with 500 \ OROPSONDE \ x HA 3IOSONDE \\ \L \ \\ V = JAX \ \ SHIP \ |jk ^ \ V V 900 \ \ 1000 vx ^ Is p1 N 20 30 Figure 5. — Comparison of radiosonde and dropsondc temperature sounding. 500 1 If 1 1 \ 1 J \f i !V JAX \ SHIP RADIOS ONDE \ \ / / \ \ \ \ \l \\ 1 \ \ \ \ ^ \ \l \\ V s \ I \ \ \ V 1 \ \ \ \ \ \ v\ \\ s \ \ \ \ \ N s HUMIDITY (G/MJ Figure 3. — Comparison of air temperature profiles measured by Figure 6. — Comparison of RFF aircraft and radiosonde humidity both aircraft. sounding. 940 MONTHLY WEATHER REVIEW Vol. 95, No. 12 I I RFF AIRCRAFT 0 0 JAX RAWINSONDE 500 VP* i 5>"~p U ~" -jrv -- -° __LZ 900 0 *~~*~^ 40 < 1 „ < < 20 EA CLE o - u S 1 £ LAKE CONDITION FROZEN PARTLY FROZEN UNFROZEN NO LAKES COVER SNOW NO SNOW Fig. 1. Albedo means and ranges for tundra region. Sky condition for each set of measure- ments is also shown. field of view. At an altitude of 500 feet the beam albedo system will instantaneously sample an area 35 feet in diameter, while the hemisphere system samples over the entire solid angle. In a general way, values from the two dif- ferent systems can be compared. Bauer and Dutton [1962] and Dutton [1962] observed that for a fresh layer of snow on a lake, which they assumed to be a homogeneous and isotropic surface, the measured hemispheric and beam albedo values were in agreement and that a calibration factor of 1.294 for the beam reflector incorporated all deviations from the ideal para- bolic reflector. Further, they showed that for various terrain surfaces, excluding water, with- out snow cover the ratio of hemispheric albedo to (beam albedo X 1.294) was very close to unity. One should expect, then, that the albedo values reported herein for areas with no snow and for a snow covered tundra would be in agreement with beam albedo values, incorporat- ing the calibration factor above. A comparison of beam albedo values obtained by Kung et al. [1964] and hemispheric values obtained by the authors for similar type terrain in southern Manitoba, under like conditions and at approxi- mately the same date, showed that the values were almost equal after the calibration correc- tion was made. The beam albedo averages for swamps, fields, and wooded farms in this area ranged from 12 to 14%, whereas the corrected '00 80 oe < e*T _i < U < c£ t— U o 60 o _ m < >. < < > 1 t X t— IM < X ea I— 40 at < < as - i— < T u o i 1— < T 13 as 20 i ! -L LAKE CONDITION FROZEN PARTLY FROZEN NO LAKES SNOW COVER SNOW NO SNOW LIGHT SNOW NO SNOW Fig. 2. Albedo means and ranges for boreal forest region. Sky condition for each set of meas- urements is also shown. hemispheric averages ranged from 11.8 to 14.4%. The uncorrected values ranged from 15.2 to 18.6%. Results Representative sections from the albedo rec- ords obtained on various flights and covering horizontal distances of 15 to 50 miles over the 100 80 O 2 60 CO < 40 20 ( 1 SXY CONDITION 1 - I - CLEAR BUT HAZY 5 TERRAIN FARMS WOODS FARMS FARMS, WOODS, AND BOGS PLOWED FIELDS SNOW COVER SNOW NO SNOW Fig. 3. Albedo means and ranges for northern hardwood-conifer forest and farmland mixture. 1138 McFADDEN AND RAGOTZKIE TABLE 2. Albedo Means, Standard Deviations, and Ranges in Per Cent for Various Surfaces Date Time, CST1 Area Description Standard Mean Deviation Range July 13, 1962 1714 Kazan River, tundra, clear sky, altitude 2200 ft2 1800 Tundra and lakes, clear sky 1830 Tundra and lakes, clear sky, altitude 2000 ft 1845 Tundra and lakes, altitude 2000 ft July 15, 1962 1103 Hudson Bay water (no ice) 1120 Fog banks over Hudson Bay 1130 Fog banks over Hudson Bay 1130 Ice flow on Hudson Bay 1130-1200 Marshy tundra and lakes, coastal lowlands, high percentage of lakes 1200 Tundra and small lakes, stratus3 1210 Tundra and lakes, 70% lakes mostly ice covered; thin stratus 1220 Tundra and lakes, some ice on lakes, 40-50% lakes, 63°30'N, thin stratus 1330 White Hills Lake, ice covered 10/10 cirrus 1330 Tundra and few lakes, north of Rossby Lake 1445 Chantrey inlet, floating ice 1450 Chantrey inlet, light colored water 1530 Sherman inlet, ice; Alto-stratus clouds 3500 ft 1530 Sherman inlet, ice, 3500 ft Alto-stratus 1730 Tundra and lakes, 3500 ft 1830 Dabawnt Lake, ice; stratus 1920 Tundra and lakes, near Ennadai 1950 Tundra east of Ennadai May 22, 1963 1100-1200 Spruce trees, no snow, frozen lakes, darkish ice, bogs, clear sky 1300-1345 Spruce forest, lakes, no ice, bogs, altitude 8000 ft June 9, 1963 1215 Kasba Lake, ice covered, stratus, thinning, heavy snow cover 1230 Ennadai Lake, ice cover, stratus, thinning, heavy snow cover 1325 Large lake surrounded by rocky tundra, ice, no snow, clear 1420 Spruce forest, heavy snow cover, lakes open, stratus thinning June 12, 1963 0835-0922 North of Winnipeg, farms and marshes, no snow, stratus, var. thickness 0922-0941 Lake Winnipeg, stratus-var. thickness 1015-1030 55°40'N, 98°W, spruce forest, no snow 1225-1245 Mostly trees, some bogs (may be tundra), lakes open, stratus 1250-1308 (Mostly trees) mixed forest-tundra, lakes partly frozen, stratus 1308-1508 (Mostly trees) mixed forest-tundra, lakes partly frozen, thinning stratus 1508-1528 Marsh and bogs, east of Lake Winnipeg stratus June 14, 1963 0835-0853 Bog and marshy area NNW of Winnipeg, some scattered lakes, clear 0855-0915 Bog and marshy area NNW of Winnipeg, some scattered lakes, clear 0933-0937 Lake Winnipegosis, clear 0941-0945 Cedar Lake 53°15'N, 100°W, clear 17.1 1.82 11.8-21.3 19.9 1.24 18.0-21.8 19.1 1.00 18.3-19.6 20.4 1.26 17.4-23.7 4.9 0.616 4.6-5.1 9.0 0.436 7.7-10.1 10.2 0.995 8.5-11.4 28.7 3.94 24.5-33.1 10.8 1.14 7.9-12.4 16.1 2.28 12.3-19.3 16.7 2.42 13.5-21.4 15.4 2.24 11.5-20.0 27.5 0.773 26.8-28.8 14.9 1.14 13.8-16.5 21.7 1.60 18.3-23.8 13.4 0.894 11.3-15.3 25.8 2.10 23.4-29.0 25.1 2.09 20.6-27.7 16.0 0.949 12.6-19.1 31.7 0.671 29.7-33.4 20.0 2.561 16.4-25.6 18.5 1.76 13.6-22.7 12.3 1.31 10.2-18.9 10.4 1.23 7.2-12.2 60.1 3.16 57.5-63.0 63.7 3.85 58.6-70.8 29.4 7.5 17.7-38.7 23.0 3.38 16.7-28.4 17.8 1.55 16.2-20.3 11.1 1.18 9.7-12.4 10.5 1.45 7.6-11.8 14.2 1.38 11.3-17.0 13.3 2.09 8.6-16.1 18.2 2.72 14.5-29.4 17.2 2.72 12.5-27.2 15.2 1.23 11.0-16.9 14.2 1.38 12.6-15.7 8.0 0.77 7.8-8.5 7.3 0.84 6.8-8.1 CLIMATOLOGICAL SIGNIFICANCE OF ALBEDO TABLE 2 (Continued) 1139 Date Time, CSTi Area Description Standard Mean Deviation Range 1023-1029 1334-1344 June 15, 1963 0905-0945 June 29, 1963 0900-0920 0940 0950 1035 1145-1200 1200-1245 1245-1255 1325-1410 1420 July 1, 1963 1108-1112 1115-1121 1150-1210 1225-1238 1245 1630 Oct. 15, 1963 1407-1447 Forests, lakes, and some open areas near Cranberry Portage Dubawnt Lake, ice, light colored, heavy stratus Cultivated fields South of Winnipeg, prairies, no lakes, clear sky Tundra, open lakes, clear sky Tundra, open lakes, clear sky Tundra, open lakes, clear sky Lakes and Tundra McLeod Bay, open but with some small ice floes, clear Rocky tundra and lakes north of Great Slave Lake, most lakes open, some partly frozen Rocky tundra north of Great Slave Lake, some lakes open, more frozen, clear Mostly tundra, some small lakes and some ice, clear Lakes with fairly dark ice, tundra small lakes open, stratus Mostly light brown and green tundra, very little water, just south of Aberdeen Lake, clear Mostly light brown and green tundra, but more lakes and ice. Just north of Aber- deen Lake, clear Greenish tundra with some sandy areas, lakes, 0.5 ice north of Gary L., clear (some cumulus) 67°25'N, 97°-98°W. Dark brown tundra, lakes, partly open, some light ice, some snow banks Sea ice in Chantrey Inlet, clear Hudson Bay, open waters, under thin stratus near Churchill 63°30' to 64°30'N, tundra, frozen lakes, snow cover, under stratus 15.2 53.1 17.7 12.7 12.7 13.1 11.6 6.6 1.95 5.93 1.32 1.34 1.70 1.72 1.79 0.028 12.7-18.0 41.8-64.2 15.2-21.1 9.4-14.8 8.2-15.2 10.1-15.3 8.0-14.8 6.1-8.7 14.6 2.57 8.9-28.7 24.9 8.82 15.2-47.1 16.2 1.10 14.1-20.4 32.7 9.54 20.1-48.7 14.8 0.95 13.5-15.6 14.9 2.38 13.0-20.2 16.4 4.29 12.0-31.6 16.8 2.72 13.2-25.7 47.5 1.84 45.5-49.8 10.9 0.539 9.7-11.6 77.7 3.45 70.5-83.2 ay be estimated by (3 X time 1 Where time intervals are given distance of transect in nautical miles may be estimated by interval in minutes). 2 All values obtained at aircraft height of 1000 ft or lower except where indicated. 3 Aircraft below cloud level in all cases. thrqe regions mentioned above were selected. The mean, standard deviation, relative variance, and range of the albedo for each of these sec- tions are given in Table 1 and shown graphically in Figures 1, 2, and 3. Additional values of albedo for various regions are presented in Table 2. Relative variance, or coefficient of vari- ability (see Steel and Tome [1960] and Kung et al. [1964]), which is the ratio of standard deviation to mean in per cent, expresses gen- erally the variation of the reflectivity caused by the heterogeneity of the surface. The tundra region of Canada, because of the general absence of trees, exhibits the highest seasonal range of albedo of the three major areas studied (see Figure 1). The numerous lakes in this region do not, however, have a large effect on the horizontal variation of albedo in the winter or the summer seasons. During the winter when all lakes are frozen, the surface 1140 McFADDEN AND RAGOTZKIE can be considered continental, and, with a snow cover, it has a high albedo with a low coefficient of variability. During the summer the albedo of the tundra is low enough so that the addition of lakes causes only a slight decrease in the mean reflectivity of the surface. However, in spring and autumn, when the lakes are partially frozen with no snow cover on the ground, there is a pronounced lake effect on the albedo. During the spring and autumn, the albedo is extremely variable, and the standard deviation and rela- tive variance are very high. In the boreal forest region (Figure 2) the seasonal changes of albedo are not as great as in the tundra, but the lake effect is larger as indicated by wider ranges of values and gen- erally higher coefficients of variability. Consid- ering the nature of the terrain this is under- standable. The crowns of the trees do not support the generally dry and powdery snow, and the forest appears dark during both winter and summer, particularly when viewed from the di- rection parallel with the incident solar radia- tion. Interspersed throughout the forest are numerous lakes and bogs. In the winter when these are frozen and snow covered, they appear as light areas, raising the average albedo of the region by a factor of 2 or more compared with forest areas without lakes and bogs (Figure 4). As mentioned earlier, the method of obtain- ing albedo information for an essentially uni- form or isotropic surface is not too critical. For a snow covered forest that is clearly anisotropic, as Figure 4 shows, careful consideration must be given to whether the values of reflected radia- tion were obtained with a beam or a hemi- speric radiometer. The reflectivity of a snow covered forest of the type observed in central Canada is much higher when viewed from above than from an angle, because more of the lighter snow covered ground is visible. A beam solarim- eter, then, would probably give higher reflected values over this region than a hemisphere de- vice, because the hemisphere instrument also 'sees' the darker ground at an angle. Actually, the surface might absorb more energy than either albedo method would indicate because the hemispheric solarimeter also receives most of its energy from the vertical. When consider- ing the amount of energy absorbed by the boreal Fig. 4. View of snow covered terrain in boreal forest region. CLIMATOLOGICAL SIGNIFICANCE OF ALBEDO 1141 forest and by the tundra in the autumn and spring, the albedo measurements obtained by either method, and in particular by the beam method, might tend to indicate smaller absorbed energy differences between the two regions than actually exist. Using values of direct and diffuse solar radia- tion from Bernhardt and Phillips [1958], an observed mean surface albedo value under a stratus cloud condition for diffuse radiation, and a computed estimate of direct radiation, based on a knowledge of the albedo of the trees and snow covered lakes and bogs, it is possible to conclude what the true albedo of an area in a boreal forest region similar to that shown in Figure 4 would possibly be in early November at 55°N latitude under a cloudless sky. An ob- served value of 34.5% (Table 1) was used in the estimate for the albedo of this area for diffuse radiation. For the direct radiation a value of about 28% was computed, using albedo values of 12% for the conifers and 77% for the snow covered open areas, and a land cover ratio of 3 to 1 in favor of the trees. At that time of year and for that location, half the radiation incident on the earth's surface is direct and half is diffuse. Thus, the estimated true albedo would be approximately 31%, indicating that the measured mean values (Table 1) are possibly too high by a factor of about 35%. Albedo values obtained from the northern hardwood-conifer forest and farm land mixture region (Figure 3) are included primarily for comparison with values obtained over similar areas by Bauer and Dutton [1960] and Kung et al.. [1964]. Kung et al., for example, give November albedo values (converted by means of the ^eam-to-hemispheric calibration factor of 1.294) for Wisconsin farmland of approximately 18 to 22%, which compares favorably with values given in Table 1, also obtained during November. Climatological Significance Of significance to the meteorologist are the effects that seasonal changes of albedo have on regional climate and general circulation patterns. For example, Bryson and Lahey [1958] have suggested that a rapid and drastic change of the albedo of the tundra in June might trigger the change from one natural season to another. By using albedo values given above, snow observa- TABLE 3. Effect of Observed Albedo on Effective Solar Radiation for Tundra Region June 1 June 21 Albedo of lnnd, % 83 15 Albedo of lakes (15% of surface), % 83 40 Solar radiation at surface under average cloud con- ditions (estimated from Bernhardt and Philipps [1958]), ly/day 352.8 446.4 Radiation absorbed per unit area, ly/day Land 60.0 379.4 Lakes 60.0 267.8 Land-lake combination 60.0 362.6 tions from Operation Breakup 1963 \McFadden, 1965], and solar radiation values estimated from the results of Bernhardt and Phillips [1958], it is possible to estimate the change in absorbed solar radiation between snow and no snow con- ditions. The results shown in Table 3 were com- puted for the tundra area of northern Canada lying south of the sixty-eighth parallel and west of Hudson Bay. On the flight of May 22, 1963, the snow line was observed some 250 miles south of the forest- tundra border, and on the flight of June 14, no snow was observed as far north as 64°N, or 450 miles north of the May 22 snow line position. No snow was observed on the July 1 flight to the Arctic Ocean. It is reasonable to assume from these three observations that the tundra was still completely snow covered as late as June 1 and probably snow free no later than June 21. During this 3-week period the albedo of the tundra dropped from an average of approximately 83% to about 20% (15% for the land surface and about 40% for the partly open lakes that constitute up to 15% of the tundra surface). This decrease in the reflectivity of the surface plus the increase in incident radia- tion at the surface between June 1 and 21 re- sulted in a 600% increase in the absorbed radia- tion of from 60 to 363 ly/day during this period. Whether this sudden and drastic change of albedo actually served as a triggering mecha- nism for the atmosphere will have to await further study, but it seems plausible that this tremendous increase of energy occurring sud- denly and at about the same time in all the 1142 McFADDEN AND RAGOTZKIE TABLE 4. Heat Balance Estimate for Tundra Region 1963, ly/day June 1 June 21 Incoming solar radiation 352 . 8 446 . 4 Reflected solar radiation —292.8 —66.9 Effective long wave radiation — 131 . 0 — 132 . 5 Net radiation -71.0 247.0 Heat storage (land) 2.5 Heat required to melt perma- frost (0.5 cm/day) 36.0 Heat for evaporation (latent)* —160.4 Sensible heat* -48.1 * Using Bryson and Kuhn's Bowen ratio value (0.30). tundra regions of the northern hemisphere should produce a noticeable effect. To obtain some idea of the partitioning of this energy absorbed by the tundra and the amount available as sensible and latent heat, the heat balance for the area was estimated (Table 4). The equation for estimating the net radiation at the tundra surface is given by RN = Rr + Rr + Ri where RN = net radiation. Ri = incoming short-wave radiation. RR = reflected short-wave radiation. RLelt = effective long-wave radiation. The values of incoming solar radiation and albedo are the same as given in Table 3, and the formula for computing effective long-wave ra- diation is that of Budyko [1958]. The heat balance equation for estimating sensible and latent heat transfer over the land surface is given by S+M = RV+Q + E where S — heat stored in the soil. M = permafrost melt (estimated at 0.5 cm/ day from in situ measurements). Q = sensible heat. E = heat for evaporation (latent heat). For estimating the storage and melting terms of the heat budget equation, Larsen's [1965] values for permafrost depths and soil tempera- tures in tussock muskeg material for the period June 1-21, 1963, near Ennadai, Northwest Territories, were used. The July Bowen ratio estimate (0.30) of Bryson and Kuhn [1962] for the region from Norman Wells, Northwest Territories, to Fort Smith, Alberta, was used for determining the sensible and latent heat terms because a ratio estimate for June was not avail- able. Applying the estimated value for sensible heat transfer to the atmosphere, 48.1 ly/day, to a column of air 1000 meters in height and with a mean temperature of 0°C gives a heating rate of approximately 1.6°C per day. This heat- ing rate does not appear to be unrealistic. From radiosonde data obtained at Baker Lake on June 20, 1963, the average temperature increase between 0600 and 1800 hours CST in the lower 1000 meters was computed to be 1.3°C. An average temperature increase of 1.85°C per day for this layer was also computed for the period between 1800 hours on June 17 and 1800 hours on June 21. This increase agrees quite well with the results in Table 4. Winds at this station during this period were very light to calm and more northerly in frequency. Conclusion Whereas the major change in the albedo of central Canada was a result of the presence or absence of snow, the effects of lakes were strik- ingly different in the tundra and boreal forest regions. Lakes caused very little horizontal vari- ation in either the summer or winter in the tundra, but they produced a large effect during the transition months of fall and spring. In the boreal forest region lakes also had little effect on the range of albedo in the summer. Small horizontal range was noted during the fall as lakes were freezing and prior to the first snow. The largest variation of albedo was obtained over this region in the winter, when the lakes were frozen and there was a good snow cover on the ground. A large range was also noted in the spring after the snow had melted but before the lakes had thawed. The rapid disappearance of snow from the tundra observed in June 1963 caused an esti- mated 600% increase in the absorbed radiation at the surface. Whether this rather sudden and drastic change in absorbed radiation occurring over the entire tundra region had any effect on CLIMATOLOGICAL SIGNIFICANCE OF ALBEDO 1143 the general circulation pattern must await fur- ther study. The estimated heating of 1000 meters of atmosphere by an average of 1.6°C per day during this period agrees fairly well with radiosonde observations at Baker Lake, Northwest Territories. Acknowledgments. The authors are grateful to Professors Bryson and Horn for their advice and criticism, to the U. S. Navy, in particular the officers and crew of P2V 128362, and to Messrs. Bernhard Lettau, David Drury, James Peterson, Wayne Wendland, Dennis Finke, Ben Bullock, and Robert Knollenberg for their efforts toward col- lecting and reducing the data. This research was supported by the Geography Branch, Office of Naval Research Contract Nonr 1202 (07) with the Department of Meteorology, University of Wisconsin. References Bauer, K. G., and J. A. Dutton, Flight investiga- tions of surface albedo, Tech. Rept. 2, Contract DA-36-039-SC-S0282, Department of Meteorol- ogy, University of Wisconsin, Madison, 1960. Bauer, K. G., and J. A. Dutton, Albedo variations measured from an airplane over several types of surface, J. Geophys. Res., 67(6), 2367-2376, 1962. Bener, P., Untersuchung iiber die Virkungsweise des Solarigraphen Moll-Gorezynski, Arch. Mete- orol., Geophys., Bioklimatol., Ser. B, 2, 188-249, 1951. Bernhardt, F., and H. Phillips, Die Raumliche und Zeitliche Verteilung der Einstrahlung, der Ausstrahlung und der Strahlungsbilanz im Meeresniveau, 1, Die Einstrahlung, Abhandl. des Meteor ologischen Hydrologischen, Dienstes der Deutschen Demokratischen Republik, NR. 45, Akademie-Verlag, Berlin, 1958. Bryson, R. A., and P. M. Kuhn, Some regional heat budget values for northern Canada, Geo- graph. Bull. 17, 57-66, 1962. Bryson, R. A., and J. F. Lahey, The march of the seasons, Final Rept. Department of Meteorol- ogy, University of Wisconsin, Madison, Contract AF 19-(604)-922, 1958. Budyko, M. I., The heat balance of the earth's surface, (translated from Russian), Office of Technical Services, U. S. Department of Com- merce, Washington, D. C, 1958. Dutton, J. A., An addition to the paper 'Albedo variations measured from an airplane over sev- eral types of surface,' J. Geophys. Res., 67(13), 5365-5366, 1962. Fritz, S., The albedo of the ground and the at- mosphere, Bull. Am. Meteorol. Soc, 29, 303, 1948. Hanson, K. J., and H. J. Viebrock, Albedo meas- urements over the northeastern United States, Monthly Weather Rev., 92(b), 223-234, 1964. Kung, E. C, R. A. Bryson, and D. H. Lenschow, Study of a continental surface albedo on the basis of flight measurements and structure of the earth's surface cover over North America, Monthly Weather Rev., 92(12), 543-564, 1964. Larsen, J. A'., The vegetation of the Ennadai Lake area, N.W.T., Studies in subarctic and arctic bioclimatology, Ecological Monographs, 35, 37- 39, 1965. McFadden, J. D., The interrelationship of lake ice and climate in central Canada, Tech. Rept. 20, ONR Contract Nonr 1202(07), Department of Meteorology, University of Wisconsin, Madi- son, 1965. Steel, R. G. D., and J. T. Torrie, Principles and Procedures of Statistics, McGraw-Hill Book Co., New York, 1960. (Received August 25, 1966.) Reprinted from JOURNAL OF GEOPHYSICAL RESEARCH Vol. 72, No. 2 The American Geophysical Union 8 Journal of Geophysical Research Vol. 72, No. 2 January 15, 1967 Dissolved Chemical Substances in Compacting Marine Sediments1 William A. Anikouchine Joint Oceano graphic Research Group Institute for Oceanography, ESSA University of Washington, Seattle A mathematical description of the distribution of a dissolved chemical species in inter- stitial water of clayey marine sediments is obtained by applying the equation of the distribu- tion of a scalar variable to a constantly accumulating column of marine sediments. An equa- tion describing compaction, and hence interstitial water velocity, is obtained empirically from porosity data. When the space coordinates are transformed to the moving sediment- water interface, the advection term vanishes and a simple equation involving diffusion, re- action, and local change describes the distribution of chemical species dissolved in interstitial water. This equation is solved to obtain a steady-state distribution of dissolved silicate and the diffusive flux of dissolved manganese across the sediment-water interface, and agree- ment between theoretical predictions and empirical data is found. The validity of assump- tions used in developing the mathematical model is discussed. Introduction Several mathematical models have been de- vised to describe the depth distribution of con- centration of various chemical species dissolved in the interstitial water of marine sediments [Koczy, 1961; Goldberg and Koide, 1963; Berner, 1964, 1966]. These models include the effects of diffusion, reaction, and moving space coordinates, but no provision has been made for the movement of interstitial water caused by compaction of the sediments. This provision is included in the model described in this paper. The procedure used is (1) to state a dis- tribution equation in terms of coordinates fixed with respect to a fixed basement, (2) to derive an advection term from an empirical porosity- depth relationship, (3) to transform to moving coordinates to include the effects of sediment accumulation, (4) to solve the resulting equa- tion under steady-state conditions, and (5) to compare the solution with data on interstitial water. Development of the Model The distribution of dissolved chemical spe- cies in interstitial water is dependent upon 1 Contribution 398 from the Department of Oceanography, University of Washington; JORG contribution 6. diffusion, advection, and reaction within the interstitial water (or between the interstitial solution and sediment grains). The dependence is expressed by the equation for local change dc/dt of concentration: The second-order term describes Fickian dif- fusion with a constant coefficient of diffusivity, D. Advection at a point h above the fixed basement is described by the product of- vK, the velocity of expelled interstitial water, and dc/ dh, the concentration gradient. The reaction term is the product of the first-order reaction rate constant fo and the extent-of-completion parameter (c — cr), which is the difference between c, the concentration at h, and the final or saturation concentration c,. The combined effects of sediment accumu- lation and compaction of the sediments cause the sediment-water interface to move upward from the fixed basement. In a hypothetical case (Figure 1) the interface moves upward at a constant rate K after sufficient time has elapsed. Experimental evidence [Long, 1961] suggests that clayey sediments behave simi- larly. Because sediment properties are normally measured relative to the sediment-water inter- face, the space coordinate of (1) is transformed to move with the interface by substituting 505 506 WILLIAM A. ANIKOUCHINE ZONE OF .COMPACTION MOVING UPWARD THROUGH SPACE AT A CONSTANT RATE, K FIXED BASEMENT AT h = 0 V COMPACTION IS ESSENTIALLY COMPLETE IN THIS REGION ' i > —t £ * '•" I"" '■' _l I I I I I I L U AFTER THIS TIME, THE r*^ INTERFACE BUILDS UPWARD AT ALMOST A CONSTANT RATE, K Fig. 1. Compaction behavior of a hypothetical column of sediment. Solid lines are tra- jectories of individual sediment particles. Vertical distances between adjacent dotted curves represent the sediment porosity at that time and place. z = h - Kt (2) t = T (3) The change with time T of concentration c at a depth z below the interface is described by the transformed equation : dc dc d2c dc . s ( . w-KTz=D-&-v7z-k^-Cf) (4) The interstitial water velocity (with respect to the interface v) is determined by consider- ing that the sediment compacts so that the profile of porosity n with depth z remains un- changed as indicated in Figure 1. Porosity is piaue. assumed to vary with depth as follows [Athy, 1930] : n = n0 exp —(mz) (5) The porosity at the interface n* and the com- paction factor m are derived empirically. The continuity equation dn dt ds dz (6) relates the time rate of change of porosity and the gradient of superficial velocity s. The su- perficial velocity is the flow of interstitial water per unit cross-sectional area of sediment. The DISSOLVED CHEMICALS IN MARINE SEDIMENTS 507 rate of change is found, from (2) and (5), to be dn dt — mKn0 exp (mz) (7) Substituting (6) and integrating yields s = Kn0 exp (mz) + d (8) The constant of integration Cj is evaluated by assuming that the sediments are infinitely thick and are totally compacted at depth, so that s — > 0 z — > - oo (9) Under these conditions, Ci is zero and s = Kn0 exp (mz) (10) The interstitial water velocity v and the super- ficial velocity s are related by the equation v = s/n (11) Hence (10) becomes v = K (12) and the distribution equation (4) becomes £-*§-**-«) 03) The advection term disappears because move- ment of water toward the interface is count- ered by interface movement during sediment accumulation. Equation 13 is solved by assuming that a steady state exists and that diffusion balances reaction. The boundary conditions are C—*Ct g — > — oo (14) C = Co 2=0 (15) and the solution is f^f- = exp [z(h/D)1/2] C0 — Cf (16) Discussion Several assumptions are made in obtaining equation 16: 1. The rate of accumulation of sediments is constant. 2. Sediments are homogeneous and have uniform mineral and chemical composition. 3. Interstices are filled with liquid, and no gas phase is present. 4. There is lateral homogeneity in the sys- tem, and a one-dimensional treatment is ade- quate. 5. The effects of temperature and pressure are negligible. 6. A steady state is attained ultimately. 7. Chemical reactions obey first-order ki- netics. 8. The diffusivity coefficient is constant. 9. Interstitial water flow is laminar. 10. Sediment grains and interstitial water are incompressible. 11. After sufficient time, the sediment-water interface moves upward at a constant rate, and the depth profile of porosity remains station- ary with respect to the interface. 12. The empirical porosity-depth relation- ship applies to clayey marine sediments. 13. The sediment column can be approxi- mated by an infinitely thick column. Assumptions about the physical nature of the system are most nearly valid for sediments in an environment free of disruptive effects such as variable sediment supply and changes in thermal conditions. Assumptions about the kinetics of chemical reactions are valid for reactions involving substances that are present in excess. Although the reactions in the system modeled here are heterogeneous, empirical first- order kinetics are suggested by the apparent success of the model in the case of dissolved silicate considered later in this paper. The re- maining assumptions are necessary to provide a mathematically tractable model. A dimensionless form of (13) is aZ dr It is obtained by applying the transforms (17) r = ktT (18) Z ~ KZ (19) c-c~Cf Co Cf (20) The dimensionless constant, represents the ratio of advective effects to dif- 508 WILLIAM A. ANIKOUCHINE Fig. 2. Theoretical distribution of silicate in interstitial water fitted to data of Siever et al. [1965]. fusion and reaction. This ratio has a value of about 3 X 10"5 in the case to be considered, which indicates that a simple diffusion-reaction model should suffice to describe the distribution of dissolved substances in interstitial water. Comparison of Theoretical Result and Empirical Data The validity of (16) can be examined by- comparing results based on (16) with empirical data from the literature. Measurements of sili- cate concentrations in interstitial water in sev- eral sediment cores were reported by Siever et al. [1965]. Two of these cores that exhibit uniform lithology and low degree of scatter of silicate concentrations were compared with the theoretically derived silicate concentration dis- tribution. The cores are L-139, a diatomaceous clay from the Gulf of California, and 258-5, a gray clay (upper part only) from the con- tinental shelf off Cape Cod, Massachusetts. The silicate concentrations in these two cores are fitted (Figure 2) by the curve c = 63 - 26 exp (1.9 X 10~2z) (21) If we assume a diffusivity coefficient of 0.3 X 10"* cm3 sec"1, the reaction rate given by (16) is 10 X 10"10 sec"1. This is smaller than the re- sults of Grill [1961] and Lewin [1961], who obtained constants of between 10"7 and 10"8 sec"1 in vitro silica dissolution experiments. It appears that the dissolution of silica in in- terstitial water is suppressed, perhaps by large concentrations of dissolved iron and aluminum [Lewin, 1961]. The model can be used in calculating the diffusive flux of a substance dissolved in in- terstitial water. The appropriate expression is -Z)|= -{kxDY%0 -C/) •expKV-D)"2] (22) To illustrate the use of (22), we consider the distribution of dissolved manganese. If ex- tremely slow dissolution (k\ = 10"12 sec"1) is assumed to control the distribution of dissolved manganese, the diffusive flux of manganese at the sediment-water interface is 1.7 X 10"" g cm"2 sec"1. This means that each year about 0.5 gram of manganese is transferred from the sediments to each square meter of bottom. The values for c0 and cf used in this calculation, 10"* g cm"3 and 10"3 g cm"3, are the concen- trations observed in seawater [Harvey, 1963] and in argillaceous rocks [Rankama and Sa- hama, 1950]. The diffusivity coefficient is as- sumed to be 0.3 x 10"5 cm2 sec"1. If the manganese in the interstitial water precipitates as nodules upon contact with the seawater and if it is assumed that the diameter of the nodules is 6 cm, their density is 2.8 g/cm3, and the manganese content is 19%, about 14 x 103 years would be required for the accumulation of 120 nodules/ma. The growth rate of these nodules is about 2 mm/ 1000 yr, a little larger than the rates (0.01 to 1 mm/1000 yr) reported for rapidly growing, shallow-water nodules [Manheim, 1965]. These results suggest that, within the limitations of the model developed here, the source of man- ganese nodules is the interstitial water of the underlying sediments. Conclusions If compaction is included in a model of the interstitial water system, a simplification of the mathematics results even though advection caused by compaction is a negligibly small ef- fect. The diffusion-reaction, steady-state model yields distribution profiles that agree with empirical data on dissolved silicates and growth of manganese nodules. If assumptions made in developing the model are valid, empirical con- centration profiles can be examined for anoma- DISSOLVED CHEMICALS IN MARINE SEDIMENTS 509 lies. In this way the model can be used in interpreting the geochemistry of marine sedi- ments. Acknowledgments. I should like to thank Dr. M. G. Gross for his critical reading of the manu- script and for his helpful suggestions. References Athy, L. F., Density, porosity and compaction of sedimentary rocks, Bull. Am. Assoc. Petrol. Geologists, 14, 1-24, 1930. Berner, R. A., An idealized model of dissolved sulfate distribution in recent sediments, Geo- chim. Cosmochim. Acta, 28, 1497-1503, 1964. Berner, R. A., Chemical diagenesis of some mod- ern carbonate sediments, Am. J. Sci., 264, 1-36, 1966. Goldberg, E. C, and M. Koide, Rates of sediment accumulation in the Indian Ocean, in Earth Science and Meteoritics, compiled by J. Geiss and E. D. Goldberg, pp. 98-100, North Holland Publishing Company, Amsterdam, 1963. Grill, E. V., A chemical study of nutrient regen- eration from phytoplankton decomposing in sea water, M.S. thesis, Department of Oceanog- raphy, University of Washington, Seattle, 1961. Harvey, H. W., The Chemistry and Fertility of Sea Waters, 2nd ed., pp. 146-147, Cambridge University Press, 1963. Koczy, F. F., Radioactive tracers in oceanogra- phy, Intern. Union Geodesy and Geophys. Monograph 20, 1961. Lewin, J. C, The dissolution of silica from diatom walls, Geochim. Cosmochim. Acta, 21, 182-198, 1961. Long, D. V., Mechanics of consolidation with reference to experimentally sedimented clays, Ph.D. thesis, California Institute of Technology, Pasadena, 1961. Manheim, F. T., Manganese-iron accumulations in the shallow marine environment, Occasional Publ. 30, pp. 217-276, Narragansett Marine Lab- oratory, University of Rhode Island, 1965. Rankama, K., and Th. G. Sahama, Geochemis- try, p. 652, The University of Chicago Press, 1950. Siever, R., K. C. Beck, and R. A. Berner, Com- position of interstitial waters of modern sedi- ments, J. Geol., 78, 39-73, 1965. (Received July 25, 1966.) Reprinted from MARINE GEOLOGY Vol. 5 Marine Geology - Elsevier Publishing Company, Amsterdam - Printed in The Netherlands EVIDENCE FOR TURBIDITE ACCUMULATION IN TRENCHES IN THE INDO-PACIFIC REGION1 WILLIAM A. ANIKOUCHINE AND HSIN-YI LING Joint Oeeanographic Research Group, University of Washington, Seattle, Wash. (U.S.A.) Department of Oceanography, University of Washington, Seattle, Wash. (U.S.A.) (Received June 29, 1966) SUMMARY Sedimentary evidence in three cores taken from the Java, Mindanao and Mariana Trenches indicates that the Java and Mindanao Trenches are receiving sediments that are mostly turbidites. The Mariana Trench is receiving mostly pelagic muds with minor, but significant additions of sediments transported by turbidity flows. INTRODUCTION In 1964, cores (Fig.l) from the Java, Mindanao and Mariana Trenches, were taken from the ship U.S.C. and G.S. "pioneer" as part of the International Indian Ocean Expedition. The sediments in these eores exhibit unexpected textural and compositional features that indicate they are turbidites. METHODS The cores were taken with a large-diameter (3-inch) piston corer operated without a piston deactivator. The lower portions of the cores were disturbed, and were not analyzed. Analyses were performed by the senior author at the Pacific Oeeanographic Laboratory (POL), Institute for Oceanography, Environmental Science Services Administration, Seattle, Washington. The upper portions were logged (U. S. Department of Commerce, 1965), analyzed granulometrically, and examined under a stereomicroscope ( X 60). A summary of these data is presented in Fig.2, 3 and 4. The cores, both reference and working halves, are stored at POL. 1 Contribution No. 2, Joint Oeeanographic Research Group and Contribution No. 389, Department of Oceanography, University of Washington, Seattle, Wash. (U.S.A.). Marine Geo!., 5 (1967) 141-154 142 W. A. ANIKOUCHINE AND H. Y. LING 140° CHALLENGER SNELLIUS EXPEDITION CORES SWEDISH DEEP SEA EXPEDITION CORES PIONEER (USCaGS) TRENCH CORE POSITIONS ^MINDANAO '/, TRENCH /264 ■ 108 -271 225 ,/M MARIANA - TRENCH - , 2 — 29 — 59 _ 63 — 69 — 83 — 91 — 119 — 151 — 178 — 210 — 249 — 7.58 8.05 7.72 6.61 5.35 4.69 7.48 7.43 7.84 7.89 623 7.64 □ LUTITE SILT HEAVY FRACTION LIGHT FRACTION TOTAL FRACTION PRESENT ABUNDANT FLOOD TRACE |2T 3H /3L 4T t X X A 28.5 ? A X F F t t i2T /3T I/4T A X t 36.2 F ///3H //3L f//4T t t X 30.0 X t t ///3H //3L I/4H i 4L X 2.16 'I X X I7.0 A t 2.04 '] A A X /3H /3L ' 4T X X t t 8.2 2.27 % F t t 1.63 ' 1.04*; /3H ' 3L \4T F F t 2.6 0.57 C F t X 3H \ 3L X t 2.23 k X X A 1 t 32.3 X X X X A \ t t t I 2T \ 3H \3L \\4T X X X X t A 28.6 2.41 k, X X A t A A X A X 3H \ 3L \\4H \\4L X 2.08v X A t t X t 39.0 X X X X A t A A l.70v \3H \\3L A X X X t t X X X 35.5 X t t F X t t 2.21 . \3H ,\3L \*T X X t t I4.9 A t X \ 3H \ 3L \4T X X A 30.0 A A Fig.2. Java Trench core (PI-442-64-33) sediment analysis data. Numerical values in mean grain size, sorting and size fraction columns are in phi units. Marine Geol, 5 (1967) 141-154 144 W. A. ANIKOUCHINE AND H. Y. LING /3H X 3L X t A 35.8 \ 4H X \4L X X A t ^3H X X 3L X X 1 1.9 \ 4H X X X A X \4L t A A ^2T F X v 3T A X X 26.4 \4T A A t t t /2T X t X /3T A A X t X 35.0 / 4T X t / 2T 7.4 \4T X A A t X A /IT F X ' 2T A F 30.1 \ 3T iA_ A \4T A t t /2T A X \ 3T A F t 46.7 \4T A X X X /it /2T A X t X 40.1 / 3T ^A X t X 4T A X X X '/3H X 1 / 3L t F X t t 35.6 4H t X X X ^4L X A /IT X F X <* 2T F A 47.4 > 3T X F X X \4T X F X X t I-2T X OT X X IT t A X 33.8 2T A X \ 3T X X A t "--\41 F F \ IT A X \\ 2T A t t X 35.8 \\ 3T A X X t X X t \\4T A X X X X X X X t \ 3T F X X 41.5 \4T F X X X X X I I LUTITE IH^ MUD LUMPS EE3 SILT E551 DIATOM OOZE P77I WOOD H HEAVY FRACTION L LIGHT FRACTION T TOTAL FRACTION X PRESENT A ABUNDANT F FLOOD t TRACE Fig.3. Mindanao Trench core (PI-442-64-35) sediment analysis data. Numerical values in mean size, sorting ana size fraction columns are in phi units. Marine Geol., 5 (1967) 141-154 INDO-PACIFIC TURBIDITES 145 0 20 S 40 ? 60 I 80 o_ LU 100 Q 120- 140 I0YR6/2 I0YR4/2 I0YR5/2 I0YR4/2 7YR4/2 5YR5/4 13 — 30 — 60- 105 ■ 139 — 5.53 4.04 7.74 5.99 6 55 6.01 6.10 4.10 2.95' 4.10, □ LUTITE m MUD LUMPS m SILT H HEAVY FRACTION L LIGHT FRACTION T TOTAL FRACTION X PRESENT A ABUNDANT F FLOOD t TRACE f3H X A [3L X X t t 13.8 4H X t A t 4L A X X X /3H t X X t X t t t t 3L X X t A X t X t t t 19.4 4T X X t X X A X X /3H X X X t ;3L t A t A t 30.7 4H X A X A X 41 1 t t A X X X ,'2T t X t X X 3H X X X X X 22.7 3L J^ X X X X X t A X X t 4T X X X X X X t F t t Ah A A X A X t 3L X X X X X X X t 37.7 4H X X X t 4L t X X A X t X X X t 3H F A X X A 3L A X X X A t t t X X 29.2 4H t A A t \4I X X X t X X 3H F A t 3L t A X A t X 35.1 L4H 1 X X X X A t \4L X X X t X X 3H X A X t 3L t A X 19.1 i4H F X A A X 4L A A A t X A Fig.4. Mariana Trench core (PI-442-64-36) sediment analysis data. Numerical values in mean grain size, sorting and size fraction columns are in phi units. Sorting The generally poor sorting in these cores does not agree with the moderate to good sorting cited by Kuenen (1964a, p. 10) as typifying deep-sea sands. The disparity probably is caused by excessive amounts of lutite in the trench core sediments. Inorganic constituents Beside clay minerals, the most abundant component, trench sediments contain angular quartz, mica, feldspar and pyrite. These are all cited (Kuenen, 1964) as existing in turbidites. These materials are not diagnostic of their depth of original Marine Geol , 5 (1967) 141-154 146 W. A. ANIKOUCHINE AND H. Y. LING deposition but the presence of rock fragments and feldspar suggests that the materials have undergone few sedimentary cycles. Origin and distribution of organic constituents Organic materials in the trench sediments are mostly the remains of siliceous planktonic organisms. Foraminifera in the Java Trench core occur principally in fine-textured layers. In the Mindanao Trench core, the diatom, Ethmodiscus rex (Plate IB, C), occurs only in certain coarse-textured layers (Plate 1A). All other organic remains (Radiolaria, sponge spicules, .fish teeth and wood occur in both fine and coarse-textured layers. Fish teeth and fish bone fragments occur throughout the Mariana Trench core, but most of the Radiolaria occur in layers containing abundant mud lumps. Of all organic constituents in these sediments, the wood is unquestionably of terrestrial origin. Fish bones and sponge spicules might be of neritic origin. It is difficult to interpret the origin of the few tubular, arenaceous Foraminifera found in Java Trench core or of the other organic constituents in the Mindanao and Mariana Trench cores. Lamination The sediments from the Java Trench and Mindanao Trench cores are strongly and irregularly laminated. Laminae range in thickness from a few millimeters to as much as 20 cm. Alterations in sediment laminae are marked by changes in color and texture or, in silt streaks, by changes in mean grain size. Layering in the Mariana Trench core is marked by changes in texture and by subtle changes in color. Textural changes reflect changes in the amounts of mud lumps present in the laminae. The thickness of lamina of lutite is similar to the other trench cores. Silt occurs in streaks about 1 mm thick or layers as much as 20 cm thick. Distorted beds These are found in the sediments from the Java Trench and Mariana Trench cores. Sediments with contorted bedding lie between layers having normal bedding in the Java Trench core. In the Mariana Trench core there are irregular silty lenses lying about 50° to the core axis. These lenses lie between layers having bedding normal to the core axis. Ripple lamination A structure resembling cross-bedding occurs in the core from the Java Trench. Streaks of fine sand, 1-2 cm apart, accentuate bedding surfaces tangential to the underlying layer and truncated by the overlying layer. This structure is about 5 cm thick and may be a portion of a large-scale ripple mark. No ripple marks were found in the other two trench cores. Marine Geol., 5 (1967) 141-154 PLATE I H* A 3*?$t?52E ' icSt. t? '•■tf-^w B 5wSSSBt'j*sC?^fiS8»S!a<W-C0NFIDENCE "LOW ▲ WW£"£7?-C0NFIDENCE "HIGH" A ^/O/Vff/P-CONFIDENCE "LOW" D PREVIOUS REPORTS (VH)-VON HER2EN. 1964 (F)-FOSTER, 1962 Fig. 1. (Top) Map of Upper Mantle Project area off California. Fourteen heat flow stations, shown below, lie along A-A'. Bathymetry and the total magnetic field were obtained along A-A' , B-B', C-C, and D-D'. The hatched areas represent areas having relief of over 100 meters. Physiographic provinces are based on the map of Menard [1964]. (Bottom) Heat flow values to the nearest tenth in cal cm"2 sec"1 X 10"6. Previously published values by Foster [1962] and Von Herzen [1964] are indicated by F and VH. Pioneer stations are shown by triangles; Surveyor stations, by circles. Solid circles or triangles indicate high-confidence values and open circles or triangles indicate low-confidence values, as explained in the text. (The remaining figures in this paper, which show heat flow, use this method of identification.) Station numbers from Pioneer and Surveyor are in parentheses and correspond to numbers in Table 1. Contours, in meters, are from the map by Menard [1964]. grad [Gerard et al., 1962; Langseth, 1965]. The equipment and the many uncertainties inherent in the general method of estimating heat flow have been discussed at length by many previous investigators (see for example, Lachenbruch and Marshall [1966] and Langseth [1965]), and these aspects will not be discussed in this paper. The thermal conductivities were determined from thermal resistivity estimates based on water content of the sediments collected by the coring device, using the linear relationship re- ported by Bullard and Day [1961]. The results of the measurements are tabulated in Table 1. The values of heat flow reported in Table 1 are simply the products of the conductivity and the gradient. The indicated confidence has been HEAT FLOW IN PACIFIC OCEAN 6241 estimated by alternative methods, depending on how many thermistors actually penetrated the bottom. When three thermistor probes were in the sediment, independent estimates of heat flow were made over the two intervals between the thermistors. Using the notation of Lachenbruch and Marshall [1966], where (q) is the average and Aq is the difference of the two heat flow values, 'high' confidence is indicated for values of Aq/2(q) less than 10% and 'low' confidence is indicated for values greater than 10%. When only two probes were in the sediment, the estimate of confidence is based on the un- certainty in the determination of both the thermal gradient and the thermal conductivity. When temperature differences between the two probes were read from several places on the record and were equal or differed by less than 0.01 °C, the temperature gradient was consid- ered high confidence; a greater range was con- sidered low. For conductivity, where AK is the range of values and (K) the average, values of AK/2(K) of less than 10% were considered high confidence; a value greater than 10% (or if there was only one determination of K) was considered low. The confidence estimate in Table 1, for the stations in which only two probes penetrated the sediment, is reported high only if both the temperature gradient and the thermal conductivity were accepted with high confidence. In the cases (stations P-10, P-15, P-22) where no sediment sample was obtained, the reported (K) is the regional mean, and the listed heat flow is considered a low confidence estimate. If the eight measurements of heat flow pre- viously reported from the area (see Figure 1) are included, a total of thirty-nine heat flow measurements are now available from the UMP TABLE 1. Heat Flow Measurements Taken during Upper Mantle Project Marine Geophysical Survey Station* North Latitude West Longitude Depth, m No. Conductivity Probes Conductivity X 10' cal/cm in Mud Samples sec °C Heat Flow Gradient X 10«, X 108, °C/cm cal/cmJ sec Confidence S-l 39°01.6' 129 "59 .7' 4456 3 S-2 35°29 0' 132 "00. 4' 5167 3 S-3 35 "29. 5' 130 "58. 6' 5090 3 S-4 35 "29. 7' 130 °01 7' 4858 3 S-5 35°29.2' 128°59.0' 4796 2 s-e 37°28 2' 123°50.5' 3514 3 S-7 37°59.7' 124°53.2' 3959 3 S-8 38 "10. 2' 125°28.0' 3937 3 S-9 38°24.1' 126 "02. 2' 4264 3 S-10 38°29.3' 126°43.0' 4467 2 S-12 38 "35 3' 127 "30. 9' 4613 2 S-14 38°45.1' 128°59.0' 4533 2 S-16 38 "31. 4' 127°08.3' 4551 3 S-19 38°29.1' 126 "43.0' 4494 2 S-20 38 "27. 4' 126 "28. 9' 4403 3 S-21 35 "48. 3' 122 "59. 7' 3710 3 S-22 36°59.9' 123 "38. 0' 3425 3 S-23 36 "59. 5' 124°22.4' 4052 2 S-24 36°49.7' 124 "45. 9' 4290 2 S-25 36 "39.0' 125 "10. 5' 4194 2 P-3 36 "56. 9' 127 "55. 3' 4635 4 P-10 38°35.1' 127 "15. 9' 4462 3 P-12 38 "19 1' 124 "01 .8' 3273 2 P-13 38 "30.1' 124 "15. 3' 3438 3 P-15 37 "55. 5' 123 "49. 9' 3310 3 P-16 37 "47. 5' 124 "16. 9' 3465 3 P-17 38°25 2' 126 "08. 2' 4370 3 P-18 38°25.6' 126 "19 .8' 4224 3 P-20 38°29.3' 126 "47. 6' 4370 2 P-21 38°31.9' 127 "03. 6' 4416 2 P-22 38 "34. 3' 127 "12 7' 4452 3 1.94 0.30 0.58 High 1.95 0.98 1.91 High 1.91 2.40 4.58 High 1.86 0.84 1.56 High 1.82 1.18 2.14 High 2.00 0.98 1.96 High 1.95 0.86 1.68 High 1.83 0.97 1.77 High 1.88 0.97 1.82 High 1.95 0.73 1.42 High 2.00 0.15 0 30 High 1.88 0.25 0.47 Low 1.99 0.64 1.27 Low 1.98 0.72 1.42 Low 1.93 0.93 1.79 Low 1.98 0.86 1.70 High 1.82 0.70 1.27 High 1.98 0.74 1.46 Low 1.78 0.19 0.33 High 1.92 0.98 1.88 High 1.96 1.32 2.58 High (1.91) 0.40 0.76 Low 1.73 1.01 1.74 High 1.87 0.90 1.68 High (191) 0.99 1.89 Low 1.89 1.06 2.00 Low 1.86 1.50 2.79 High 1.74 1.18 2.05 Low 2.42 1.07 2.58 High 1.81 0.37 0.66 High (191) 0.46 0.87 Low * S prefix for Surveyor stations; P prefix for Pioneer stations. 6242 BURNS AND GRIM area. These measurements are not evenly dis- tributed and can be discussed by considering a subdivision based on spatial grouping. Eastern Part of Continental Rise This subdivision covers the eastern parts of the Delgada and Monterey fans and is arbi- trarily defined as being east of the 4,000-meter isobath (see Figure 1). Earlier measurements from this region indicated a relatively high heat flow ((Q) = 2.2 jucal cm"2 sec"1) with low spatial variability. These earlier stations are clustered in a relatively small portion of the area, and one of the objectives of the present investigation was to determine whether they are representa- tive of this part of the continental rise. Conse- quently, additional heat flow measurements were made at stations P-12, P-13, P-15, P-16, S-6, S-7, S-8, S-21, S-22, and S-23. The mean regional heat flow estimated from the data ob- tained at these ten stations is 1.7 iical cm"2 sec"1 (s = 0.2 tical cm"2 sec"1), and, if the previous data are included, the mean is 1.8 /teal cm-2 sec"1 (s = 0.3 jucal cm-2 sec"1) . From these estimates, heat flow in the eastern part of the continental rise, as defined here, appears to be slightly high (