NOAA Optimum Interpolation ¼ Degree Daily Sea Surface Temperature Analysis data (also known as Reynolds OI V2 SST data) were acquired from the NOAA´s NCDC webpage. AVHRR data were used due to its greater temporal coverage in relation to AVHRR/AMSRE data.

Daily files from 01-01-1982 to 12-31-2011, each bearing daily SSTs and associated standard deviations (SD), were imported into R as georrefered layers and stacked by chronological order. Data were retrieved separately for each coastal pixel (location) across the entire assemblage of temporal layers, worldwide. Coastal pixels were defined as those closer to land but with less than 50% of land contamination, which was assessed using full-resolution GSHHS coastline data. See the figure on the right.

An example showing 3 SST layers being sampled at a coastal location
       
  For each coastal pixel individually, average warming rates were computed as the slope of the linear regression of seasonally detrended SST vs. time, and expressed as ºC/decade ± s.e.m. To account for errors in the SST OI estimates, regression parameters were estimated using weighted least squares, with weights inversely proportional to the variance of the SST OI. To account for temporal autocorrelation, the degrees of freedom were adjusted using the Quenouille procedure, in which Neffective=N(1-r)/(1+r), with N representing the sample size and r the lag-1 autocorrelation coefficient of the residuals of the seasonally detrended time series.

The projected area of each ¼ degree pixel was used to standardize rates of change per unit of area, before reporting average rates of change over regions. Monthly SST changes were calculated in a similar way, but using monthly averages for each location. See an example on the right.

 
Example of weighted linear regression of SST against time
 
       
  For each location separately, 5 and 95 percentiles of standardized anomalies of the raw SST (1982-2010) were used to define extremely low and extremely high temperature thresholds. Yearly frequencies of daily anomalies exceeding the threshold values were calculated and regressed against time. The Quenouille procedure (see above) was used to correct the degrees of freedom whenever temporal autocorrelation was significant.

The figure on the right show the yearly frequency of extreme hot days plotted against time for one of the coastal pixels, yielding the average change in the number of extreme hot events in the last three decades for that location.

 
Average change in the number of extremely hot days at a given location
 
       
  This analysis was restricted to temperate latitudes between 60ºS and 30ºS and 30ºN and 60ºN. For each pixel in separate, the first Julian day in each year exceeding the 75th percentile of the entire SST dataset for that geographic location was recorded. For situations in which the Julian date of the first 75th percentile temperature occurred before 1 January (common situation in the southern hemisphere), it was necessary to transform the Julian dates to values < 0 in order to avoid spurious discontinuities in dates associated with the end of the year. These values were then regressed against time, and slopes expressed as the average change in date/decade ± s.e.m. The Quenouille procedure (see above) was used to correct the degrees of freedom when temporal autocorrelation was significant.

The figure on the right exemplifies this calculation for one of the locations. The top graph shows the timeseries for that location, with values exceeding the 75th percentile (representing the seasonal SST maxima) highlighted in orange. The first yearly occurrence was recorded and the corresponding julian day identified (vertical yellow arrows). The bootom graph shows the regression of the 1st yearly julian day exceeding the 75th SST percentile against time. This regression yielded the average change in the timing of the seasonal warming. The process was repeated for each pixel.

 
Average change on the timing of the seasonal warming at a given location