Sensitivity analysis of the evaporation module of the E-DiGOR model
derivatives. In other words, sensitivity coefficients, as defined by equations given in the sub-section “Derivation of formulas for relative sensitivity”, were calculated on a daily basis for the study periods to cover the entire possible range of the input variable values. However, the magnitude of this measure of sensitivity is only relative (i.e. change in model output due a change in model input). In order to give the readers an idea of the importance of input variables, the relative sensitivity coefficients were pooled for each variable and the average values of the coefficients and their confidence limits were determined (Spiegel 1961).
The values of potential soil evaporation estimated by the Penman-Monteith equation for the bare soil surface throughout the study period are plotted in Figure 1 together with the relative sensitivity coefficients. The daily sensitivity coefficients exhibited a seasonal variation. Actual soil evaporation estimated by Aydın’s equation for the bare soil during a period of 34 days and the sensitivity coefficients are given in Figure 2. Predicted soil water potential and its relative sensitivity to potential soil evaporation are presented in Figure 3. Water potential at air-dryness and its sensitivity to air-humidity during the first-half of the year are depicted in Figure 4. It can be seen from the figures that the coefficients varied daily depending on the values of all input variables and outputs. The mean values of the coefficients together with their confidence limits (Spiegel 1961) are given in Table 2.
According to the Penman-Monteith equation, all the sensitivity coefficients were relatively stable when potential soil evaporation was the highest (Figure 1). As indicated by van Griensven et al. (2006), local techniques concentrate on estimating the local impact of a parameter on the model output. This means that the analysis focuses on the impact of changes in a certain parameter value. A change in net radiation (Rn) significantly affected the output (Ep) of the Penman-Monteith model used for bare soil. In other words, the Ep estimates were very sensitive to Rn, with
a mean value of 0.82 (Table 2). This confirms that the radiation term is generally dominant over the aerodynamic term in the prediction equation as reported by Beven (1979). The sensitivity to Gs was small during the summer season. However, Gs had a significant impact during the winter months when net r a d i a t i o n w a s l o w . T h e s l o p e o f s a t u r a t e d v a p o u r p r e s s u r e – t e m p e r a t u r e c u r v e ( ∇ ) i n c r e a s e d o r decreased the value of Ep. The changes in S∇ between p o s i t i v e a n d n e g a t i v e v a l u e s w e r e t h e r e s u l t o f t h e o c c u r r e n c e o f ∇ i n b o t h t h e n u m e r a t o r a n d d e n o m i n a t o r o f t h e P e n m a n - M o n t e i t h e q u a t i o n . T h e e f f e c t s o f t h e v a p o u r p r e s s u r e d e f i c i t ( δ ) , w h i c h increases the evaporation, reached higher levels during the winter months. In the case of Sra, the values constantly had a negative sign. However, the pattern of yearly change in Sra was becoming more negative during the winter days. Our results are not directly comparable to those of other sensitivity analyses since the predictions for vegetation surfaces (Beven 1979; Saxton 1975) or open-water surfaces (McCuen 1974) were considered in the other available papers. However, all studies (McCuen 1974; Saxton 1975; Coleman and DeCoursey 1976; Beven 1979) showed that potential evaporation/evapotranspiration was much more sensitive to radiation, humidity, and temperature. In addition, Piper (1989) emphasised that the sensitivity of Penman estimates of evaporation to input variables could have seasonal fluctuations.
In Aydın’s equation, the dependent variable (Ea), was initially very sensitive to a change in the |ψ| value; hence a change in |ψ| significantly affected the Ea rate in the wet soil (Figure 2). The sensitivity decreased progressively during the drying period. The coefficients were constantly negative, with a mean value of –0.19 (Table 2), and exhibited a regular pattern during the study period. In contrast, the values of S|ψad| remained small in the wet soil and became higher in the drier soil. The sensitivity coefficient used to measure the effect of potential (Ep) on actual evaporation (Ea) was observed to be a constant value. From the equation of Aydın and Uygur (Aydın et al. 2008), it was clear that in the wet soils Ep greatly affected the output of the model, ψ (Figure 3). However, in Kelvin’s equation, it was observed that an increase in the absolute temperature