Relationship between nutrients and temperature Good relationships between nutrients and temperature were found in the surface ocean by Kamykowski and Zentara (1985, 1986), Takahashi et al. (1993), and many others. We explored nutrient-temperature relationships for the NODC data sets for the upper 500 m of the ocean to see if they could be used for filtering and extrapolation of the nutrient data. We found that nutrient-temperature relationships varied spatially, so we partitioned the ocean into eight regions. For each region, we defined parabolic least-squares fits for temperature below 25°C, and linear fits for temperature between 25° and 30°C. We assumed that for temperature greater than 30°C, nutrient concentrations were zero. The eight regions used were: North Pacific (15N - 60N), North Atlantic including Arctic ocean (north of 15N), Tropical Pacific, Tropical Atlantic, (15N - 15S for both of them), Tropical Indian, (North of 15S), South Pacific, South Atlantic and South Indian (south of 15S). We found that segregation of the data as a function of time and depth did not noticeably improve the regressions. r² values varied from 0.50 to 0.85. The best fits were obtained for the high Southern latitudes and the North Pacific. 

Filtering the data We took advantage of the extensive quality control procedures performed by Conkright et al. (1998) and used only those data that passed all of their tests. This left us with 287,554 phosphate profiles, 171,141 silicate profiles and 66446 nitrate profiles. We still found, however, that many outliers remained in the data, so we conducted additional filtering using the nutrient-temperature relationships described above. We simply deleted all nutrient data that were more than a defined deviation from the least squares fit for each region. The deviations were a function of temperature; as we didn't want to smooth the seasonal signal of the nutrients, we took larger intervals of tolerance (two to three standard deviationa) for cold waters (where the seasonal signal is strong) and moderate intervals (about one standard deviation) for warm waters. 

Vertical interpolation We vertically interpolated the data to the top 14 NODC standard levels (0, 10, 20, 30, 50, 75, 100, 125, 150, 200, 250, 300, 400 and 500 m) using the monotonic scheme of Steffen (1990), as described in Najjar and Keeling (1997). In some cases interpolation could not be performed because of poor vertical resolution of the measurements. The final number of profiles of nutrients used for the mapping were: 

PO4: 183,451 profiles (discarded 42% of the initial profiles) 
NO3: 48,254 profiles (discarded 34%) 
SiO2: 121,124 profiles (discarded 40%) 

Binning the data on the equal-area grid The equal-area grid described in Najjar and Keeling (1997) was used for the horizontal spacing of the nutrient maps. The grid is 2 degrees in latitude and variable in longitude (2 degrees at the equator to 120 degrees at the poles). For each depth level an average was computed for each grid point containing an observation. We did this for each month, and then we also used these binned data to create three- and five-month moving averages. For example, for January, we have one binned field representing data in January, a second representing data from December to February, and a third representing data from November to March.

Horizontal interpolating and smoothing To fill in undefined values of the five month moving average maps, the nutrient-temperature relationships described above and the temperature climatology of Levitus and Boyer (1994a) were used. Following Najjar and Keeling (1997), distance weighted averaging with a 1000 km Cressman function was used to smooth the monthly binned fields. Where data density allowed it, the map obtained was filled with the three-month moving averages or preferably one-month averages. The Cressman function was used to smooth the fields once more. A final test on the maps was used to calculate the difference between regression-data blend fields and regression-only fields. A new interval of tolerance was defined as a function of latitude. Where this interval was not respected, the data from the blended fields was replaced by the regression estimate. A final smoothing was done by using the Cressman function.

Transferring the data from the equal area grid to a regular 2X2 degree grid A simple scheme of zonal linear interpolation was taken. The resulting monthly 3D fields between 0 and 75 m are available.

Kamykowski D. and S.-J. Zentara, 1985. Nitrate and silicic acid in the world ocean: patterns and processes. Mar. Ecol. Prog. Ser., vol 26, 47-59. 

Kamykowski D. and S.-J. Zentara, 1986. Predicting plant nutrient concentrations from temperature and sigma-t in the upper kilometer of the world ocean. Deep-Sea Res., 33, 1, 89-105. 

Levitus S. and T.P. Boyer, 1994a. World Ocean Atlas, Volume 4: Temperature. NOAA Atlas NESDIS 4, 117 pps. 

Najjar R.G. and R.F. Keeling, 1997. Analysis of the mean annual cycle of the dissolved oxygen anomaly in the world ocean. Journal of Marine Research, 55, 117-151. 

Steffen M., 1990. A simple method for monotonic interpolation in one dimension. Astron. Astrophys., 239, 443-450. 

Takahashi T., J. Olafsson, J.G. Goddard, D.W. Chipman and S.C. Sutherland, 1993. Seasonal variations of CO2 and nutrients in the high-latitudes surface oceans : a comparative study. Global Biogeochemical Cycles, 7, 843-878.