Statistical prediction of the monthly mean sea surface temperature over the northwestern of the Indian Ocean

The variability of sea surface temperature (SST) is used as a valuable climate index for the prediction of precipitation in far and near areas from the sea. The prediction of SST in the north western of the Indian Ocean is the main goal of this study. This water region including 81 gridpoints with 2˚×2˚ grid in the geographical location of 10-30N and 45-76˚E. The SST was extracted from the National Oceanic and Atmospheric Administration (NOAA) for the period 1951–2007. The principal components analysis technique was used to identify the main patterns of SST and data reduction. The PCA performed was based on the correlation matrix. The number of row and column of the input file for the correlation matrix was, respectively, the number of months and gridpoints. The four principal components that explained 98% of the SST total variance were extracted. The first, second, third and fourth principal components explained 79, 8/9, 5/9 and 4% of the SST total variance, respectively. These four principal components as four regions over the area of interest were studied. The first, second and third regions were geographically located in 16-24˚Nand 58-72˚E, 10-14˚N and 48-76˚E, and 14-16˚N and 50-74˚E. Also, the fourth region was the Persian Gulf. The spatial average of SST within each region was considered as a regional index. As the linear stochastic models, the “seasonal auto-regressive integrated moving average” (SARIMA) models were used to predict the monthly time series of the regional indices of SST patterns. The dataset for the monthly time scale for the 1951–2000 period was used to construct SARIMA models for each region. There is a linear trend in SST time series over three regions which indicate that the monthly SST over these regions is non-stationary. Since ARMA models prefer stationary time series data as their input files, a differencing procedure was considered as a smart approach for transforming these non-stationary series into the stationary ones.  On the basis of the corrected Akaike information criterion (AIC) and significant coefficients, the best seasonal auto-regressive integrated moving average model was separately selected for each region. The auto-correlation function plots of the residuals for the selected models have indicated that the residuals are uncorrelated. The selected model for each region had a minimum value of AIC and its parameters were significantly different from zero. For example, SARIMA(1,1,0)×(1,1,0)₁₂ model was identified for SST time series over the northwestern parts of the study area. As the independent data of training period, the SST time series for the 2001–2007 period was predicted at lead times ranging from one to 12 months and then was evaluated. For example, the value of Pearson correlation between the observed and the predicted SST over the northwestern parts of the study area with SARIMA(1,1,0)×(1,1,0)₁₂ model for the test period (84 months) was 0.94. Also, the corresponding root mean square error was 0.46 degrees Celsius. In all of the regions, the correlation coefficient between the observed and the predicted SST for the independent dataset is higher than 0.9. Therefore, the time series models have a valuable ability in forecasting the monthly time series of SST in each region.