together with the isentropic data. Examples of these 

 curves for 1967 (a year with large data gaps) and 1971 (a 

 year with small data gaps) are shown in Figures 3 and 4. 

 Questionable values are revealed as large discrepan- 

 cies from the fitted curve. The questionable values were 

 usually associated with the previously mentioned poor 

 vertical sampling interval at individual stations or with 

 stations that were occupied outside the 60 nmi quad- 

 rangle about the nominal position of OWS-V (Fig. 2). Us- 

 ing this quality control procedure, 38 stations were re- 

 jected from the 6-yr series. 



After this quality control procedure the harmonic coef- 

 ficients were calculated for the temperature, salinity, 

 and depth at a, levels between 22.0 and 27.4 with inter- 

 vals of 0.2 a, units, as well as for the surface temperature, 

 salinity, and a,. Although the analyses were carried out 

 to the 52d harmonic, resolving fluctuations with a 7-day 

 duration, only the first 12 harmonic coefficients are listed 

 in Appendix I. Also listed are the slope M, and initial 

 values, /(I), for the linear trend at each level. Thus, using 

 the values of Appendix I in Equation (3), expected values 

 for any day of the year for any of the given levels can be 

 obtained. 



Because of the seasonal variation in the density of the 

 upper layers, properties at the lower a, values will not oc- 

 cur throughout the year. For these situations the dates of 

 the first and last observation are given in the tabulation 

 of Appendix I and derived values will be valid only for 

 the duration bounded by these dates. 



Statistical Characteristics of 

 the Harmonic Analyses 



Figures 3 and 4 show qualitatively that the fitted 

 curves follow the observed values very well, as they 

 should, because a Fourier series approximation is a least 



squares fit regardless of the number of harmonics used in 

 the summation (Jenkins and Watts 1968). A quantitative 

 measure of the goodness of fit is provided by the unex- 

 plained variance. 



S, =■ 



f =1 



(5) 



T-1 



Equation (5) is an estimate of the mean square error or 

 variance of the difference between the observed values 

 and the Fourier series approximation. With an increas- 

 ing number of harmonics used in the approximation, 

 S,., the standard error of the estimate, should decrease. 

 These quantitative aspects are presented in Table 2 and 

 illustrated in Figures 5, 6, and 7 by graphs of S,, as a 

 function of the number of harmonics used in the 

 analyses of the temperature, salinity, and depth for 

 1971. 



Considering the temperature and salinity graphs (Figs. 

 5, 6) first, there is a marked reduction in S, at the shal- 

 lower levels as n increases to 6, 6\. then decreases slowly 

 with increasing n. For example, at a, 25.2, S,. for the 

 temperature is 0.28°C at « = 1, 0.135°C at n = 6, and 

 0.12°C at n = 20. In the deeper layers the decrease in S^ 

 with increasing harmonic used in the fitting procedure is 

 relatively small. For example, at a, 26.4, S, for the 

 temperature is 0.13°C at n = 1, 0.115°C at n = 6 and 

 0.11°C at n = 20. The greater variability of the prop- 

 erties at the shallower levels may reflect, in part, low fre- 

 quency variability in the air-sea interaction processes 

 directly affecting the upper layer of the ocean to approxi- 

 mately the (T, 25.8 level. 



Figure 7 shows that the standard error of estimate for 



Table 2.— Standard errors of estimate. S, . for Fourier series summations (n = 12) on a, 25.0-27.4 levels of temperature, °C, (upper 

 panel); salinity, */.., (middle panel); and depth, m, (lower panel). 5^ was computed only for times of actual observations, exclud- 

 ing interpolated values, 1966-71. 



