procedure gives somewhat greater weight to an observa- 

 tion near a grid point than would a weighting of 1-R 2 , 

 where R is the distance in fractions of a grid length.) If 

 there is only one observation within a unit grid area and 

 there are no observations in any of the surrounding grid 

 areas, the observed value would be assigned to each of 

 the four nearest grid points. 



The middate of the observations in a given section was 

 assigned to its corresponding grid field for later use in 

 determining harmonic coefficients. Thus the maximum 

 time error for data at either end of the section would be 

 about 2.0 to 2.5 days. 



2. Least squares harmonic fit. — In order to establish 

 a smooth mean seasonal cycle for each gridpoint, a least 

 squares fit was made for the harmonic function 



T tJ = (A„). . + 2 (A n cosnwt + B n amnut) ij 



where oj = 2tt/365, t is the day of the year, and i and; are 

 gridpoint indices. Robinson (1976) also used the first 

 three harmonics of the Fourier function for time smooth- 

 ing of monthly mean values of mechanical bathyther- 

 mograph data (to 400 ft) for the North Pacific Ocean. 

 Since our initial gridded fields were not distributed at 

 equal intervals in time, the terms which normally disap- 

 pear in harmonic analysis of evenly spaced data (due to 

 orthogonality) are not zero when applying the least 

 squares fit. Seven simultaneous equations for least 

 squares fit were solved to determine the seven unknown 

 constants to represent the mean temperature and thel2-, 

 6-, and 4-mo cycles. 



To avoid overweighting certain years because of 

 greater sampling frequency, a set of harmonic constants 

 was determined for each of three time periods: June 

 1966-December 1970, 1971-73, and 1974. The first period 

 was selected because of the consistency of the sampling 

 mentioned earlier. The year 1974 was analyzed separate- 

 ly because of the unusually high-density sampling. The 

 observations from 1971 and 1972 were considered as 1 yr 

 and combined with 1973. 



Constants from the three periods were weighted and 

 combined by Dorman to provide the mean constants 

 representative of the 1966-74 period. Weights assigned to 

 the periods were as follows: 



equally spaced times throughout a year. (For con- 

 venience of identification these are labeled as 01 

 January, mid-January, 01 February, etc., to mid- 

 December.) 



The data field for each of the 24 mean vertical sections 

 was reconstructed from the harmonic functions at each 

 grid point. Because the time smoothing by the least 

 squares fit was independent from point to point, a spatial 

 smoothing was applied to the grid field before contour- 

 ing. 



The spatial smoothing was done with one pass of a 5 X 

 5 point (370 km by 40 m) smoother in the EDMAP pro- 

 gram. The smoother was a two-step numerical filter, 

 after Shapiro (1970), which was mostly effective for 

 reducing amplitudes of perturbations with wave lengths 

 of less than about four grid lengths. Its response was zero 

 at a wave length of two grid lengths, 0.45 at three grid 

 lengths, and 0.75 at four grid lengths. The response was 

 0.96, or greater, at wave lengths of seven grid lengths or 

 more. 



The contouring part of the EDMAP program divided 

 each grid square into 25 subsquares, whose corner values 

 were determined by Bessel's central difference formula 

 for double quadratic interpolation. The intersection of 

 each contour with the boundary of a subsquare it 

 transects was determined by linear interpolation. The 

 isotherms were computer plotted and are reproduced 

 herein, with drafting touch-up only for clarity of presen- 

 tation. The isotherms were not changed subjectively. 



The major changes in the seasonally varying mean 

 temperature were found to occur in the upper 200 m of 

 the water column. The figures of Appendix 1 also show 

 the distribution of the "30-day" temperature changes for 

 the upper 200 m. The changes were computed from the 

 spatially smoothed data (described on page 7) and are 

 centered on the date of the vertical section in the upper 

 panel. Note that there is a 50% overlap between two con- 

 secutive temperature change charts. 



4. Tables of mean temperature. — Mean temperature 

 values, in °C, for selected depths and alternating grid 

 points (intervals of 185 km) are presented in Appendix 2. 

 The values are those reconstructed from the fitted har- 

 monics for the given grid point (distance and depth) and 

 extracted before the grid was spatially smoothed for con- 

 touring. The tables are identified as 01 January, mid- 

 January, etc., to mid-December, as were the vertical sec- 

 tions of Appendix 1 . 



Period Weight 



June 1966-December 1970 4.5 



1971-1973 2.0 



1974 1.0 



3. Vertical sections of mean temperature and mean 

 temperature change. — Appendix 1 contains vertical 

 sections of the mean temperature structure along the 

 Honolulu-San Francisco route, to depths of 500 m, for 24 



RESULTS 



This section discusses some of the general features of 

 the mean temperature distributions in Appendix 1. 

 Further, we have selected seven locations, each of which 

 has vertical temperature structure and cycles 

 characteristic of a part of the route. For each of these, 

 Figure 3a-g shows the seasonally varying mean 

 temperature for eight depths from the surface to 500 m, 

 and Figure 4a-g shows the mean monthly vertical profiles 

 of temperature for the warming and cooling periods. 



