***** ^■"•' ,rr *JJ , J5L NPS55-84-014 NAVAL POSTGRADUATE SCHOOL Monterey, California FEDDOCS D 208.14/2: NPS-55-84-014 A PILOT DATA ANALYSIS OF SEA SURFACE TEMPERATURES AND WIND SPEEDS MEASURED ON OCEANIC WEATHER SHIP PAPA - A SUMMARY by P. A. Jacobs July 1984 Approved for public release; distribution unlimited Prepared for: Chief of Naval Research Arlington, VA 22217 NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA Commodore R. H. Shuinaker David A. Schrady Superintendent Provost This work was supported in part by the Naval Postgraduate School Foundation Research Program which was funded by the Chief of Naval Research Reproduction of all or part of this report is authorized. ilFIED iv Classification of this page rwhen uete Entered) REPORT DOCUMENTATION PAGE RT NUMBER -84-014 2 GOVT ACCESSION HO READ INSTRUCTIONS BEFORE COMPLETING FORM 3 RECIPIENT** CATALOG NUMBER i (and Sutytitimi LOT DATA ANALYSIS OF SEA SURFACE TEMPERATURES WIND SPEEDS MEASURED ON OCEANIC WEATHER SHIP ^ - A SUMMARY S Tv*>E OF REPORT 4 PERIOD COVERED Technical » PERFORMING ORG. REPORT NUMBER ORf»J I CONTRACT OR GRANT NUMBER, t) \. Jacobs ORMING ORGANIZATION NAME AND AODRESS il Postgraduate School terey, CA 93943 10. PROGRAM ELEMENT. PROJECT. T ASK AREA ft «ORK UNIT NUMBERS 61152N: RR000-01-00 N001484WR41001 TROLLING OFFICE NAME AND ADDRESS ef of Naval Research ington, VA 22217 12. REPORT DATE July 1984 '3 NUMBER QF PAGES % ITORINC AGENCY NAME 4 ACORESSri' dlllereni from Controlling Ottice) 15. SECURITY CLASS, (ot tttla report) Unci ass i fied ISa. DECl AS SI FICATION 'DOWNGRADING SCHEDULE RIBUTiON STATEMENT (ol thit Report) -nved for puhlic release: distribution unlimited WlBuTlON STATEMENT (ol the abstract entered In Block 20. II dlllereni trom Report) LEMENTARY NOTES WORDS (Continue on rereree aid* II neceeaery and Identity by block nuaabet) surface temperatures, wind speeds, oceanic mixed layer depth, data ysis RACT (Contlnum on reveree aid* It neceeeary and Identity by block rrumber) lis note describes the results of an exploratory data-analytic study of sea 5 temperatures and wind speeds measured on Oceanic Weather Ship PAPA, il analysis indicates that sea surface temperatures and wind speeds have il effects. Detrended sea surface temperatures and wind speeds exhibit the ing association. Positive changes between days t and t-1 in the inverse il sea surface temperature are associated with large residual wind speeds t and large residual sea surface temperatures on day t-1. This association explained by the behavior of the oceanic mixed layer depth. ' M ?J 1473 EDITION OF 1 NOV 63 IS OBSOLETE S/N 102-014- 6601 ' UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Dele Entered) A Pilot Data Analysis of Sea Surface Temperatures and Wind Speeds Measured on Oceanic Weather Ship PAPA - A Summary by P. A. Jacobs Operations Research Department Naval Postgraduate School 1 . Introduction This note describes the results of an exploratory data- analytic study of sea surface temperatures and wind speeds meas- ured on Oceanic Weather Ship PAPA. The data consist of 15 years (1955-1969) of measurements taken every three hours. Two of the measurements recorded were of wind speed and sea surface tempera- ture, uther measurements taken include air temperature and wind direction . In Section 2 the results of a spectral analysis of the lb years of sea surtace temperatures are described. It indicates that sea surface temperatures exhibit noticeaole 1 year, 6 month, 24 hour, and 12 hour cyclic components. The 24 hour and 12 hour components are modulated by yearly and seasonal effects. In Section 3 the results of an analysis of average daily sea surface temperatures and average daily wind speeds during the Spring and Summer for three years Iy64-b6 are reported. After the two series were detrended, it was found that positive changes between days t and t-1 in the inverse residual sea surface temperature are associated with large residual wind speeds on day t and large residual sea surface temperatures on day t-1 . This association can De explained by the behavior of the oceanic mixed layer depth. 1 . Sea Surface Temperatures In this section we describe a spectral analysis of sea sur- face temperatures taken on Ship PAPA. The data consist of 15 years (1955-1969) of measurements taken every three hours. The 5 leap days were removed leaving a data set of length 43,800 readings . Figure 1 shows the data set. The most apparent feature of sea surface temperatures is the strong yearly cycle. Another feature is the change in the measurement reporting procedure which occurs 8 years into the record. The first 8 years of data appear to be more discrete than the last 7 years. Prior to 1963 the data were recorded with a 1° Fahrenheit resolution and then converted to degrees Celsius. Starting in 1963 the data were recorded with a 0.1° C resolution. The data record also appears to contain erroneous measurements and interpolations. The Zn (normalized periodogram) of the entire record of sea surface temperatures appears in Figures 2-5; (cf. Cox and Lewis [1966] p. 99). Figure 2 shows the entire Jin periodogram; the horizontal line is at the Jin 95% quantile of the maximum of 21,900 independent unit exponentials. Figure 3 shows the first hundred values of the Jin (periodogram). The two peaks occur at p = 15 and 30 which correspond to cycles of 1 year and 6 months respectively. Figure 4 shows the values of the Jin (periodogram) for p-values around the peak at p = 547 5 which is the 24 hour cycle. Notice the local peaks at p = 5490 and 5460 which are 1 year side lobes. A second pair of side lobes occur at p = 5408 and 5542 which correspond to 81.7 day side lobes or seasonal side lobes. Figure 5 gives the in (per iodogram ) for values of p around the peak at 10950, the 12 hour cycle. Again there are side lobes at p = 10945, 10965 (1 year) and p = 10882, 11018 (80.5 days or seasonal). The side lobes indicate tnat sea surface temperatures are modulated by yearly and seasonal effects. It suggests that the sea surtace temperatures in the same season in different years are statistically different; (ct. bloomfield [I9"?b] pp. 99-100). R. w. Garwood has provided the following explanation tor the year to year variability. The variability in sea surface tem- peratures in the same season of different years is due to the variability of the mixed layer depth in the ocean. The mixed layer depth is a function of surface heating of the ocean and ocean mixing by turbulence due to storms. The times between passage of, and the strength of, the storms varies from year to year. The surface heating is a function of the season of the year . In summary, the In ( per iodogram ) of 15 years of sea surface temperatures indicate that the record has noticeable 1 year, b month, 24 hour, and 12 hour cyclic components. The 24 hour and 12 hour cycle components are modulated by year and seasonal effects . Associations between average daily Sea burface Temperatures and Averaye Daily wind Speed In this section we will report on a pilot study of associa- tions between averaye daily sea surface temperature and averaye daily wind speeds during the Spriny and Summer (Julian days 91-2 7 2) for the years 1964 (year 1U), lybb (year 11), and 196b (year 12 ) . P. A. W. Lewis and his associates have done a spectral anal- ysis of 15 years (1955-1969) of Ship P wind speed data which was measured every three hours ( Lewis 1 1983 ]) . The analysis sug- gests that the wind speed data has cyclic components of 1 year, 6 month, 12 hours and 6 hours. Associations between the averaye daily sea surface tempera- tures and average daily wind speeds may be confounded by the non- stationarity of the two series. Thus, the two series were de- trended. In order to detrend the series in the same manner, the average daily sea surface temperatures and average daily wind speeds for Julian aays 91-2 7 2 for each of years 1U-12 were put into two-way tables having 26 rows (weeks) and 7 columns (days). The two-way tables were median polished (cf. McNeil [ly77j) to obtain expressions of the form Data = typical value + day effect + week effect + residual. The residuals from the median polish were taken as the detrended series. Since both average daily sea surface temperatures and average daily wind speeds were treated in the same manner by this procedure, the residual series are comparable. figure 6 (respectively 7) shows a plot ot the median polish residuals ot average daily sea surface temperatures (respectively wind speeds) for year 12. The plots for the other years are similar. The plots exhibit no apparent nonstat ionari ty and show the typical pattern of many small values due to the use of median polish. The periodogram (not shown) of the residual sea surface temperature for year 12 shows a significant peak at 7 days which may be due to the fact that the median polish was done on a two-way table with rows of length 7 days. The periodograms of residual sea surface temperatures for the other two years do not show this effect. The first 50 serial correlations were computed for each residual series. There is some correlation in the residual series particularly in the residual average sea surface tempera- tures in year 12. There appears to be a pattern in the correla- tions again suggesting possible nonstat ionari ty introduced by the median polish. However, the correlation was judged not to be substantial enough to affect the results of this exploratory study. Let W(t) (respectively S(t)) denote the residual from median polish of the average daily wind speed (respectively sea surface temperature) on day t . Put H(t) = suTTT ' -- " 91 272 - where the constant 1 in the denominator was arbitrarily chosen to ensure that H(t) is finite. The surface mixed layer depth of the ocean during the Spring and Summer is related to the in- verse of sea surface temperature; (Garwood [1983]). Thus, H(t) should be related to mixed layer depth. Let and D(t) = H(t) - H(t-l) , t = 92,. ..,272 X(t) = £n(S(t) +1) t = 91, ...,272. D(t) is related to chanyes in mixed layer deptn. we will con- centrate on associations between D(t) and W(t) and x(t-l). For each year the quantiles of residual sea surface tempera- ture (s(t) ; t = 91, ...,271} were used to categorize {(D(t), W(t)), t = 92,... ,272} in the following manner. Category I contains those (D(t), W(t)) such that S(t-l) is less than or equal to the lower quartile of |s(t); t = 91 , . . . , 2 7 2 } ; Category II contains those data such that S(t-l) is greater than the lower quartile but less than or equal to the median; Category III contains those data such that S(t-l) is greater than the median but less than the upper quartile; and Category IV contains the remainder of the data. In brief, Category I is "very low"; Category II is "low"; Category III is "high"; and Category IV is "very high" as ordered by sea surface temperature on the previous day. Figures a-lu show plots of residual wind speed W(t) versus L)(t) by residual sea surface temperature category for each of the three years. For each year the plot in the upper (lower) left hand corner corresponds to Category I (Category III); the plot in the upper (lower) right hand corner corresponds to Category II (Category IV) . All of the plots suggest that larger residual wind speeds are associated with larger values in the differences D(t). Further the association looks roughly linear. There is no strong indication that the association changes for different sea surface temperature categories . For each year the quartiles of |w(t); t = 91,. ..,272} were used to categorize {(D(t), X(t-l)), t = 92,. ..272} in the same manner. The categorical plots of X(t-l) versus D(t) are shown in Figures 11-13, the arrangement of the plots by category is the same as for Figures 8-10. Once again the plots indicate that larger values of D(t) are associated with larger values of X(t-l). The association appears roughly linear. Again there is no strong indication that the association is different in different categories . Regressions of the form D(t) = a + b W(t) + cX(t-l) t = 92,... ,272 were fit to the data in each of the three years using two pro- cedures. One is least-squares, a classical procedure which is sensitive to possible outlying values in the data; (cf. Mosteller and Tukey [1977]). The second is a biweight procedure (cf. Mosteller and Tukey [1977] pp. 205) which is less sensitive to outlying values. The estimated coefficients can be found in Table 1. Plots of the residuals from the regression versus pre- dicted D(t) showed little structure. This suggests that the regression has removed most that is systematic or explainable in the data. Regressions containing an interaction term of the form D(t) = a + b W(t) + cX(t-l) + d(X(t-l) x W(t)) were also fit. The estimated values appear in Table 2. Table 1 Estimated Values for the Coefficients of D( t) = a + b W(t) + cX( t-1) Year 10 11 12 Least Squares Estimates (Std. Error) U.0141 (.017) 0.0144 (0.027) 0.0125 (0.024 ) 0.2027 ( .048) 0.1325 (0.074) 0.14^5 ( 0.063) 0.6510 ( .090) 0.8969 (0.108) 0.7368 (0.092) Biweiyht Estimates a b c -0.0081 0.1267 0.b510 -0.0214 0.1319 0.6120 -0.0179 0.1368 0.4254 Table 2 Estimated Values for the Coefficients of D(t) = a + b w(t) + cX(t-l) + d(X(t-l) x w(t)) Year 10 11 12 Least squares Estimates (Std. Error) 0.0188 (0.017) 0.0153 ( 0.027) 0.0314 ( 0.024) 0.2175 (0.048) 0.1504 (0.075) 0.1933 (0.062) 0.6298 ( 0.090) 0.8328 (0.115) 0.7193 (0.089) -0.6047 (0.311) 0.4474 (0.272) -0.9222 ( 0.236) Biweiyht Estimates a b c 0.0104 0.1144 0.5202 d ,2b -0.0210 0.1346 0.6114 -0.09 -0.0202 0.1312 0.4023 0.20 The regressions indicate that larger differences in the inverse residual sea surface temperature, D(t) , are associated with larger residual wind speeds, W(t) and larger in (residual sea surface temperature) the day before, S(t-l) . There appears to be no significant interaction term of the form W(t) * X(t-l) . The standard errors for the least squares estimates should be viewed with caution because of the correlation in the series |S(t)} and (W(t)} . There is no suggestion that the association is different in the different years. An explanation for the relationship suggested by R. W. Garwood is as follows. The mixed layer depth of the ocean during the Spring and Summer is related to the inverse of sea surface temperature. Thus D(t) should be related to the change in mixed layer depth of the ocean between days t and t-1 . Further X(t-l) = £n(l + S(t-l)) is related to the mixed layer depth on day t-1 . Thus the above association suggests that deepening (shallowing) of the ocean mixed layer depth during the Spring and .Summer (Julian days 92-272) is associated with larger (smaller) wind speeds and shallower (deeper) mixed layer depths the day before. During the Spring and Summer the mixed layer depth of the ocean is a function of solar warming and turbulant mixing attri- butable to storms. During periods of light (strong) winds the mixed layer becomes shallower (deeper). However, the effect of a storm on the mixed layer depth depends on "how deep the mixed layer is already". A storm of the same strength will cause a larger drop in sea surface temperature if the surface mixed layer is shallow than if it is deep. The association found here agrees with a simpler related association found by Elsberry and Raney (1978) also using bhip P data. They defined sustained periods of above or below normal wind forcing as events and calculated the surface temperature change for each event. They found an association between an increase (decrease) in sea surface temperature and below (above) average wind speeds. 1U i . Conclusions (1) Spectral Analyses of 15 year records of sea surface temperatures and wind speeds from ship P showed strong yearly, seasonal and time of day effects. The Spring-Summer periods of three years 1964-1966 were chosen for further study. (2) After average daily sea surface temperatures and wind speeds for the period were detrended and the residuals examined, it was found that large changes between days t and t-1 in the inverse residual sea surface temperature are associated with large wind speeds on day t and large sea surface temperatures on day t-1 . The association can be explained by the behavior of the oceanic mixed layer depth. 11 4 . Acknowledgments The research of P. A. Jacobs was supported by the Naval Postgraduate School Foundation. The author would like to thank R. Ellsberry, R. W. Garwood, D. P. Gaver, and P. A. W. Lewis for their helpful discussions. Figures 1-13 were produced by an experimental APL package GRAFST3 which the Naval Postgraduate School is using under a test agreement with IBM Watson Research Center, Yorktown Heights, N. Y. Thanks also go to Dr. P. D. Welch and Dr. P. Heidelberger for making this package available. 12 References P. Bloomf ield . Fourier Analysis of Time Series ; An Introduction John Wiley and Sons, Inc. 1976. D. R. Cox and P. A. W. Lewis. The Statistical Analysis of Series Events . Methuen and Co. 1966. R. L. Elsberry and S. D. Raney. Sea Surface temperature response to variations in atmospheric wind forcing. J^ Phys . Oceanogr . 8 (1978) 881-887. R. W. Garwood. Personal Communication, 1983. P. A. W. Lewis. Personal Communication, 1983. D. R. McNeil. Interactive Data Analysis . John Wiley and Sons, 1977. F. Mosteller and J. W. Tukey. Data Analysis and Regression . Addison-Wesley , 1977. 13 CO (X X ro >- LU > LU Q UJ q: Z> CO < CO LU C£ Z> < LU GL LU < LU CO CO q: >- m 6l 8 SdW3l V3S 14 00 cr >- Q_ LJ a; u •H Pn S- OL ^VdOOQOId3d Nl 15 o o o CO a. LxJ < 01 Ld o m cu u p ■H fa o 8 o JU WVdOOQOI&Bd Nl 16 en CL LU < LU 00 CO > < DC O o g LU CL o o CD o m m -r dj o u o a m Di m ■H En o in Z- V- 9- WVd00CI0ld3d N1 o o in 17 T3 w O CL 0) ^ CL LU k- 1— 3 o < £. 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Gaver 1 Code 55Gv Naval Postgraduate School Monterey, CA 93943 Professor P. A. W. Lev/is 1 Code 55Lw Navy Postgraduate School Monterey, CA 93943 Professor R. Garwood 1 Department of Oceangraphy Naval Postgraduate School Monterey, CA 93943 Professor R. Elsberry 1 Department of Meteorology Naval Postgraduate School Monterey, CA 93943 Dr. P. D. Welch 1 Room 31-139 Thomas J. Watson Research Center IBM Yorktown Heights, NY 10598 Chief of Naval Research 1 Arlington, VA 222] 7 DUDLEY KNOX LIBRARY - WESEAHCH REPORTS 5 6853 01071704 4