This thesis develops an optimal interpolation method that takes daily precipitation values collected from weather stations and produces precipitation estimates on a grid. The method, called Hybrid 2.0, combines EOF-based linear interpolation with the nearest-station method. Gridded monthly precipitation is first obtained via EOF, then distributed among days via nearest station. Hybrid 2.0 builds on an earlier method, called Hybrid 1.0, that applies an inverse-distance weighting method to obtain gridded monthly values. Hybrid 2.0 uses these monthly Hybrid 1.0 values as inputs when constructing EOF functions. The data used in this thesis were obtained from the Meteorological Service of Canada. Few weather stations were located in the northern and mountain regions of Alberta prior to 1950. As a result, the Hybrid 1.0 gridded results underestimate precipitation in these regions for that period. The main contribution of Hybrid 2.0 is a substantial reduction in this bias, obtained by implicitly taking topographic elevation into account. Bias reduction is achieved by extracting EOFs from Hybrid 1.0 output for 1951-2002, when many more stations were present in the northern and mountain regions. Hybrid 2.0 is shown to be more accurate in interpolating both monthly and daily precipitation in Alberta, when compared with Hybrid 1.0 and other methods. The thesis also provides detailed analyses of precipitation trends and droughts using the gridded Hybrid 2.0 daily values. Optimality of the selected EOF modes and sensitivity to data error in the EOF-based linear reconstruction are also discussed in this thesis. Agricultural uses of historical climate data have become extremely important. Applications include: enabling prompt, optimal decisions on market prices and disaster aid, designing future agricultural practices such as adaptation to climate and technology changes, and managing risks for agricultural producers and governments in areas such as drought monitoring. Many applications require a reliable interpolation technique to accurately reconstruct daily climate estimates onto grids of various resolutions. The gridded Hybrid 2.0 daily precipitation values produced by this thesis satisfy this requirement and can be used as inputs for many agricultural applications. / Applied Mathematics

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Thesis (MSc (Geography and Environmental Studies))--University of Stellenbosch, 2007. / Due to the relative scarcity of weather stations, the climate conditions of large areas are not adequately represented by a weather station. This is especially true for regions with complex topographies or low population densities. Various interpolation techniques and software packages are available with which the climate of such areas can be calculated from surrounding weather stations’ data. This study investigates the possibility of using the software package ANUSPLIN to create accurate climate maps for the Western Cape, South Africa. ANUSPLIN makes use of thin plate smoothing splines and a digital elevation model to convert point data into grid format to represent an area’s climatic conditions. This software has been used successfully throughout the world, therefore a large body of literature is available on the topic, highlighting the limitations and successes of this interpolation method. Various factors have an effect on a region’s climate, the most influential being location (distance from the poles or equator), topography (height above sea level), distance from large water bodies, and other topographical factors such as slope and aspect. Until now latitude, longitude and the elevation of a weather station have most often been used as input variables to create climate grids, but the new version of ANUSPLIN (4.3) makes provision for additional variables. This study investigates the possibility of incorporating the effect of the surrounding oceans and topography (slope and aspect) in the interpolation process in order to create climate grids with a resolution of 90m x 90m. This is done for monthly mean daily maximum and minimum temperature and the mean monthly rainfall for the study area for each month of the year. Not many projects where additional variables have been incorporated in the interpolation process using ANUSPLIN are to be found in the literature, thus further investigation into the correct transformation and the units of these variables had to be done before they could be successfully incorporated. It was found that distance to oceans influences a region’s maximum and minimum temperatures, and to a lesser extent rainfall, while aspect and slope has an influence on a region’s rainfall. In order to assess the accuracy of the interpolation process, two methods were employed, namely statistical values produced during the spline function calculations by ANUSPLIN, and the removal of a selected number of stations in order to compare the interpolated values with the actual measured values. The analysis showed that more accurate maps were obtained when additional variables were incorporated into the interpolation process. Once the best transformations and units were identified for the additional variables, climate maps were produced in order to compare them with existing climate grids available for the study area. In general the temperatures were higher than those of the existing grids. For the rainfall grids ANUSPLIN’s produced higher rainfall values throughout the study region compared to the existing grids, except for the Southwestern Cape where the rainfall values were lower on north-facing slopes and high-lying area