Introduction 130 

The results and discussion of rainfall data, including the criteria for selecting remote sensing products for hydrological forecasting, are presented. The comparison between satellite rainfall estimates and observed point rainfall and the extent to which they were used as input for the stream flow predictions is also presented. Two satellite derived estimates were evaluated against the observed rainfall data in terms of spatial and temporal resolution and these were: the Climate Prediction Centre (CPC-RFE 2.0) and Tropical Rainfall Measuring Mission (TRMM 3B42) products. The comparison was done for the period 1999 – 2008. This process was first done by comparing the daily CPC-RFE 2.0 and TRMM 3B42 data (extracted from pixels where the station is located, with the station data itself after interpolated to ensure use of the same pixels). The interpolation of observed data was done at 8 km x 8 km and 25 km x 25 km, using the Kriging method in GIS, chosen to optimise the smoothness of the fitted values. Secondly, a continuous verification statistic (which included the Coefficient of Determination ( ), Relative bias (Rbias), Relative Root Mean Square Error (RRMSE) and the Index of Agreement (IA) was carried out to obtain a quantitative assessment for each set of validated data (Ebert, 2007; Ebert et al., 2007). The validated Satellite Rainfall Estimate (RFE) data are of fundamental importance in this study because they were used to fill in data missing from the observed records for the modelling application/s. Fundamental difficulties existed when comparing gauge measurements and satellite estimates and these included: retrieval errors of satellite algorithms; sampling errors caused by different sampling schemes; and systematic gauge errors related to instruments (Ciach and Krajewski, 1999; Bowman, 2005). The aim of this study, however, is not to quantify the errors of satellite estimates in individual rain events, but to evaluate the overall performance of the two satellite products when compared with using rain gauge data as input into hydrological model. This evaluation was used to gather information on the type of product to recommend for input into hydrological modelling studies in the Zambezi River Basin. In the Zambezi Basin, the comparison of TRMM 3B42 and CPC-RFE 2.0 estimates with the in situ station records, at a monthly time scale, indicated that TRMM often underestimates (by up to 50%) during the wet season and overestimates (by up to 50%) during dry months, whereas the CPC-RFE 2.0 showed less bias (Winsemius et al., 2006; Liechti et al., 2011). Based on the divergent results obtained from previous studies and the lack of validation at the daily time scale, one of the objectives of this study has been to provide a comparison and evaluation of the different sources of input data that can be used for the hydrological modelling and flood forecasting of the Zambezi Basin at the daily time step.

5.2. Statistical methods for comparison of rain gauge and satellite

rainfall estimates

The first part of the analysis focused on the comparison of the different satellite estimates against rain gauge based rainfall estimates to highlight both the similarities and the discordances. The Pearson Correlation Coefficient (R ) was used to compare the time series between the rain gauge data and the satellite data in the same pixel from 1999 – 2008. Twenty selected rain gauge stations were analysed (Table 3.1, Section 3.4.2.1). For these rain gauge stations, the Global Telecommunication System (GTS) was excluded from the analysis, because GTS may have influenced the statistics agreement when compared with the CPC-RFE 2.0. The original grid size for each product was used to extract the satellite rainfall values. As most of the observed rain gauge data contains large gaps, only those time series with a minimum of at least 20 continuous daily values were used in the analysis at a daily time step. The correlation between satellite products and rain gauge data was evaluated by applying the Coefficient of Determination ( ), Bias and Relative bias, the Relative Root Mean Square Error (RRMSE), and the Index of agreement (IA) (Daren and Smith, 2007) (Equation 5.1 to Equation 5.5). ∑ 0 0 ̅ ∑ 0 ∑ ̅ Equation 5.1 0 Equation 5.2 ∑ 0 ∑ 0 Equation 5.3 1 ∑ 0 Equation 5.4 1 ∑ ∑ | | Equation 5.5

where “Si” is the satellite data, “oi” the observed data and “0” the mean of the observed data.

The Coefficient of Determination: R is a standard correlation statistic designed to

determine the strength of the linear relationship between simulated and observed data (Legates and McCabe, 1990; Ebert et al., 2007; Moriasi et al., 2007). This statistic describes the proportion of the total variance in the observed data which can be explained by the model and the ranges is expressed between 0 and 1, with higher values indicating the ability of the model to explain more variance in the observed data.

The Bias: Bias is the difference between the estimator's expected value and the true value of the parameter being estimated. An estimator (or decision rule) with zero bias is called unbiased – otherwise the estimator is said to be biased. For this study the acceptable range for data validation was chosen to be ±0.50.

The Relative bias (Rbias): Rbias is an error index that measures the individual and average

deviation of the satellite mean daily rainfall from the observed rain gauge data (Moriasi et al., 2007). Zero is the optimal value of both bias and relative bias and the deviation from this value, whether positive or negative, indicates errors in the model prediction. For this study the acceptable range for data validation was chosen to be ±0.20.

The Relative Root Mean Square Error (RRMSE): RRMSE is used to measure the

differences between values predicted by the satellites and those by observed rain gauge data. If the RRMSE is high, then the observed rain gauge values are not close to the satellites values; if the RRMSE is low, the satellite values are well predicted (Moriasi et al., 2007).

The Index of Agreement (IA): IA is a standardised measure of the degree of model prediction

error and varies between 0 and 1 (Legates and Willmott, 1990). A value of 1 indicates a perfect match, and 0 indicates no agreement at all. For this study the acceptable range for data validation was 0.5.The comparison between satellite and rain gauge data was also done temporally through a time series comparison and a probability of exceedence, from October 1999 to 2008. Spatial comparisons were also performed for the wet seasons from 1999 to 2008.