Improvement of Interpolation Using Information From Rainfall Stations and Comparison of Hydroclimate Changes (1913-1938)/(1986-2016)

The primary objective of this study is to use a better method for rainfall mapping in areas with low density rain gauge networks. Secondly, to identify and study hydro-climatic change in the semi-arid high plains of eastern Algeria on the basis of a comparative mapping approach. The latter concerns the annual rainfall map produced by the authors of this paper for the period studied (1986/2016) and the annual rainfall map for the period 1913/1938, prepared by Chaumont and Paquin (1971). The results of this analysis show that isohyets between 300 mm and 350 mm cover a large part of the study area, they occupy an area of 14444 Km2, followed by isohyets between 200 mm and 300 mm with an area of 5298 Km2. In addition, the comparative analysis between the periods showed that hydro-climatic change was clear for the 200 mm, 300 mm and 400 mm isohyets, whereas there are no major changes for the 500 mm and above isohyets. Data processing based on a combination of statistical and geostatistical analysis (multiple linear regression and kriging) has once again shown the value of taking into account other parameters in the design of rainfall maps, such as geomorphological and geographical parameters.


 Prospecting and data collection
In order to highlight the characteristics of the region, prospecting and investigation work in the agropedoclimatic context was necessary for the identification and selection of the most reliable informations. Investigations were carried out to highlight previous work carried out in the study area. This research mainly concerned work related to natural data and the physical environment, in particular for any variable data over time, such as climate data (Tab.1). These latter are collected, for the most part, from the professional and auxiliary weather stations belonging to the National Office of Meteorology, also from some rainfall stations belonging to the National Agency for Water Resources (NAWR).  The observation allowed identifying some stations whose periods of observation or operation are very heterogeneous and contain data gaps in their time series. Thus, this situation poses problems to constitute a climate dataset, which makes it possible to study the evolution of climatic parameters at the scale of the region. Given that the objective is to produce thematic maps based on complete reference data, we have selected the most reliable ones, which are 65 rainfall stations (Tab.2).  Approch adopted for rainfall mapping Currently, in the study area, the density of the climate network remains low. Only professional stations in aerodromes measure all climate parameters. Faced with such a situation of lack of rainfall data and a poor spatial representation of climate stations ( Fig. 1), which can lead to errors or even aberrations in data interpolation, mapping becomes difficult to achieve consistency. To overcome this problematic, the authors have put in place a reflection on the methodology and the tools that must be used to estimate the precipitation parameter in the region of study following a very specific framing (Fig.2). To this end, we have adopted a methodology wich consists in expressing the rainfall variable (P) from a multiple regression equation to three (03) simple type factors.

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the estimator of the mean Z on 0 x . Z (x i ), the known value Z at the point x i . nb N are a number of data points used for estimation and λ i , are kriging weights which are estimated as solution of the kriging system. The weightings involved in the linear combination are obtained by solving the minimization problem whose equations depend on the theoretical variogram and the geometric configuration of rainfall data point's knowledge [29]. The equation of Semi-variogram is expressed as: Where h is the distance between X i and X j , m is the number of pairs which are separated by the distance h. The

III. RESULTS AND DISCUSSIONS  Multiple regression analysis
It was discussed to adjust the explanatory model for precipitation (P) by multiple regression. A rain-specific MLR model is developed from all 65 rain gauging stations and, using cumulated yearly rainfall variables of each station. With X, Y and Z are respectively longitude, latitude and altitude  Represents error. With X, Y and Z are respectively latitude, longitude and altitude.  Represents error of estimation 53.2. Table 3 displays the regression coefficients values and the validation tests of the MLR model. According to Table 3

 Geostatistical study and numerical precipitation mapping
According to [30], the adjustment step is the most delicate step of spatial interpolation. The directional variogram obtained at the annual scale is presented in Figure 5.    The mapping approach is based on the simple kriging interpolation method to perform isohyets from 220 study points representing reel raingauging station (65 stations) and estimated values from (155 fictional stations).   .6). This situation shows that these two wilayas have become, over time, more arid.

IV. CONCLUSION
The measurements of the rainfall heights of the 1986-2016 period, recorded in the selected rainfall network, showed that the average annual rainfall varies from one station to another. We can say that rain mapping, based on MLR model and geostatistics, allows to optimize rainfall estimation at any point of a considered area and has given good results. This method provides a much better interpolation than that made from the usual interpolation methods. Furthermore, the comparative analysis between the map of yearly rainfall for the period (1986-2016) and the map of isohyets produced by Chaumont and Paquin (1971) showed that there is no great change over time for the 500 mm isohyet and that the change is clear for the 200 mm, 300 mm and 400 mm isohyets. Given the extent of the study area which is characterized by a geomorphological and even pedological diversity, the results obtained lead to reflect on the importance of strengthening and extending the current climate network by adopting statistical methods and GIS tools.