The relationship between daily and monthly pan evaporation and rainfall totals in Southern Africa

Recent droughts in South Africa have highlighted the vulnerability of the economy to water restrictions. However, the degree of surface aridity in southern Africa is not only a function of precipitation, but also one of evaporation. The quantitative assessment of evaporative loss is important since it is a major component of the water budget. For example, in southern Africa, evaporation accounts for 79.5% of the hydrological water budget. As the cost of water resource development increases, so there has been an increasing demand for hydrological modelling to optimise project planning. Reliable estimates of evaporation are essential to significant improvements in the practice of hydrology and particularly in a country like South Africa which is prone to the adverse effects of drought. It is difficult to adequately measure potential evaporation over an area as large and as sparsely populated as southern Africa. Despite the research that has been undertaken to estimate evaporation from related meteorological and physical variables, generally, the estimation of evaporation in southern Africa has been unsatisfactory. There are a number of methods for estimating potential evaporation. However, a major problem tends to be the incompatibility between the data requirements of some of the more physically-based models, and the actual data that is available and collected on a routine basis at a sufficient number of stations. In existing water resources estimation models, evaporation is often incorporated as a time series input of pan evaporation, using daily or monthly values. The lack of a nearby record of pan evaporation often necessitates the use of published regionalised mean monthly pan values. This technique of using the mean monthly evaporation values in water resources estimation models tends to overestimate or underestimate the actual evaporation that is occurring, depending on the actual amount of rain occurring in a specific month. This is because no attempt has been made to correct these mean evaporation values for the amount of rainfall that occurs in a specific month, in a specific region. The regional rainfall/evaporation relationships (that vary spatially and temporally) are not taken into account. A need was identified for an assessment of the value of grouping data by rainfall as a better tool for estimating evaporation. Here, the monthly evaporation and the mean monthly evaporation for a specific rainfall group category will be estimated using daily data. Due to data availability, the most appropriate time scale to use is one day. Therefore, in this study an attempt has been made to relate rainfall amounts to evaporation values and to develop rainfall/evaporation relationships, identifying variations by season and region. It is important to identify and quantify these relationships and assess the possibility of incorporating these variations into existing Water Resource Estimation Models. The ability to derive and develop meaningful relationships between daily rainfall and daily evaporation for each season, and for a number of sites considered representative of the climatological zones for southern Africa was assessed. The first approach was to compare daily evaporation plotted against daily rainfall, and in the process develop a quantitative rainfall/evaporation relationship. Unfortunately, no direct linear relationships were identified. The second approach was to test the performance of the water resource estimation model using the following possible choices, (i) a real daily input (COREVAP1) - here the estimated monthly evaporation is the sum of the product number of days within each month * mean daily evaporation for each specified raingroup category, (ii) a distributed mean monthly input (COREVAP2) - here evaporation is estimated using a random sampling procedure to draw samples from a restricted part of the daily evaporation distribution for each raingroup and is defined by the mean and standard deviation, and (iii) a distributed mean monthly input and correction (COREVAP3) - here samples are drawn from the full distribution of daily evaporation for each raingroup category. The performance of the COREVAP programs was analyzed in terms of the improvement effected by estimating evaporation using the mean monthly evaporation regardless of rain. COREVAP1 produced the best simulations of monthly evaporation. This was expected as the program uses the straight-forward mean evaporation value multiplied by the number of days to simulate the monthly evaporation values. However, the COREVAP programs did not perform well when using the monthly evaporation data based on daily infilled values using the transformed parameters. Any regionalisation of parameter files would mean that a range of parameters in a region would now be represented by a single value. The need to assess the effect of this change from a regional range of values to a single representative value was identified. This was done by conducting a sensitivity analysis, in terms of what effect a percentage increase or decrease in the lambda, mean evaporation and mean rainfall values would have on the resultant simulated monthly evaporation and coefficient of efficiency values. A sensitivity analysis was conducted on COREVAP1 to determine which parameters of the model had the greatest influence on the simulations. This was done with reference to the percentage error of monthly evaporation and the monthly and accumulative coefficient of efficiency values. Generally, the percentage increase/decrease in mean evaporation values that are acceptable for the representative stations are low. In contrast, fairly high percentage changes in mean rainfall values are tolerated. The objective of the regionalisation of parameters was to determine whether general characteristics can be applied to some stations that are significantly different compared to other stations, so that the stations may be combined to represent a separate region. The demarcation of regions was conducted on the basis of the regional relative mean evaporation values (per raingroup, per season), the daily mean evaporation values per month and the average number of days within each raingroup, per season. Intra-station and inter-region variability was analysed using the Kruskal-Wallis H test and the Friedman Fr test. The regional parameters were then used as input into the COREVAP programs and the simulation results were analysed in terms of whether the simulations still produce positive accumulative coefficient of efficiency values. The results obtained when substituting the regional parameters were not good. Based on these results, it has been concluded that the hypothesis that grouping data by rainfall may be a better tool for estimating evaporation compared to simply using the mean monthly evaporation, may be rejected