Coupling principal component analysis and geostatistics in the creation of rainfall maps for north-central Algeria
The spatial distribution of annual rainfall in north-central Algeria was mapped by combining principal component analysis (PCA) and the theory of regionalized variables. The study of the spatial distribution of a natural phenomenon often requires a network of specific measurements. The extension of site-collected and fragmentary data over the whole study area is essential for mapping the variation of the parameter in space. The theory of the regionalized variables is used to account for the structural characteristics of a natural phenomenon in a suitable mathematical form. North-central Algeria, a region covering 390 km from west to east and 360 km from north to south, was the subject of this study. The region contains the Cheliff watershed, coastal Algeria and parts of the Isser and Zahrez watersheds. Ninety-seven rainfall measurement stations were retained, taking into account the quantity and quality of the precipitation data, which covered the time period from 1921/22 to 1960/61 and from 1968/69 to 1998/99, i.e., altogether 70 years but with some gaps. Using PCA, two regional vectors with a multiple correlation coefficient of 0.87, explaining 75% of the total variance, were identified. A linear combination between yearly precipitation and the two regional vectors was established, allowing us to fill the gaps in data among the 97 stations. Two regional vectors, representing the most likely trend in rainfall used in the homogenization of the data, were identified. A rainfall return period of five to ten years was estimated in order to complete information given by the annual rainfall values. According to the literature, the annual rainfall distribution in Algeria has a positive skewness for which the root normal distribution led to the best fitting of extreme values. The estimation of the variability in rainfall in the study area required field knowledge. The inadequate distribution of the rainfall network gave a poor representation of the rainfall measurement stations with respect to the altitude. For this reason, a model of the relationship between rainfall and altitude was developed. The altitude was initially analyzed using a digital elevation model (MNT) that samples the elevation using the nodes of a network with a square grid of 2 km x 2 km with the objective of identifying a certain number of morphologic parameters able to explain rainfall variability. The mapped zone was a rectangle oriented from east to west with 35,476 sampled elevations. We chose the model that identifies Lambert co-ordinates (X, Y) and hypsometric (elevation (Z), slope and orientation) parameters. To take into account the orientation of the slopes and the entrenchment of the site, six parameters (TG1, TGE, TGN, TGNE, TGW and TG3) were identified, the calculation of which was based on differences in level. They were identified on the basis of a regular grid (2 km x 2 km) of 25 nodes centered on the rainfall measurement station using a tangent (TG) function. The calculation of smoothed elevation (ZfS) was performed using the TG function and required the construction of a regular grid of nine nodes centered on a rainfall measurement station at an elevation of Z. The best models of the relationship between rainfall and altitude were identified using multiple linear regressions, by comparing the coefficient of determination (r2) and the sum of residuals. The models obtained were validated by independence and residual normality tests. Some morphologic parameters explaining rainfall variability were also identified, to be used for the estimation of rainfall at any point in the study area using multiple regressions. These models allowed us to extend the series to the nodes (2 km x 2 km) for which the X, Y and Z coordinates are known. A functional relationship between observed and model estimated rainfall was developed. The observed variable «rainfall» can only be accurately defined with the nodes of the grid if the corresponding residuals are established, making the study of the node residuals essential. The knowledge of the regression residuals extended to all grid nodes remains necessary for the mapping of our parameters and allows us to better interpret the resulting variograms. The interpolation between nodes of the grid (2 km x 2 km) was carried out by kriging, following the investigation of their spacial structure by the calculation of experimental variograms. This spatial structure represented the variance of the differences between the residuals of regression between two distant points of h. To study anisotropy, the north-south and west-east directions were retained. The exponential model provided a good fit to the regression residuals. The variogram of the residuals has a net spatial structure. Variographic parameters were defined by kriging and fitted for interpolation between rainfall measurement stations. Starting with the elevation grid, as defined by the digital elevation model, the spatial rainfall pattern was obtained by combining the estimated rainfall grids, obtained from the digital elevation model, and the residuals grid. Automatic mapping yielded annual, five-year and ten-year isohyet maps.