**6. Model evaluation**

In both the experimental watersheds surface runoff volumes and sediment yields were eval‐ uated at the event scale; in the Cannata watershed the analysis of surface runoff was extend‐ ed to the monthly and annual scale.

Model performance was assessed by qualitative and quantitative approaches. The qualita‐ tive procedure consisted of visually comparing observed and simulated values. For quanti‐ tative evaluation a range of both summary and difference measures were used (Table 4).

The summary measures utilized were the mean and standard deviation of both observed and simulated values. Given that coefficient of determination, r2 , is an insufficient and often misleading evaluation criterion, the Nash and Sutcliffe (1970) coefficient of efficiency (E) and its modified form (E1) were also used to assess model efficiency (Table 4). In particular, E is more sensitive to extreme values, while E1 is better suited to significant over- or underpre‐ diction by reducing the effect of squared terms (Krause et al, 2005). As suggested by the same authors, E and E1 were integrated with the Root Mean Square Error (RMSE), which de‐ scribes the difference between the observed values and the model predictions in the unit of the variable. Finally, the Coefficient of Residual Mass (CRM) was used to indicate a preva‐ lent model over- or underestimation of the observed values (Loague and Green, 1991).

The values considered to be optimal for these criteria were 1 for r2 , E and E1 and 0 for RMSE and CRM (Table 4). According to common practice, simulation results are considered good for values of E greater than or equal to 0.75, satisfactory for values of E between 0.75 and 0.36 and unsatisfactory for values below 0.36 (Van Liew and Garbrecht, 2003).


**Values**

**Mean (mm)**

Observed 78.54 40.25

Observed 7.71 15.91

Observed 0.25 2.42

Observed 158.74 145.05

Observed 13.23 34.43

Observed 0.43 5.37

scales for calibration and validation tests at the Cannata watershed.

high-intensity convective storms over dry soils (Latron et al., 2003).

[a] Default simulation [b] Calibrated model.

**Std. Dev.**

**(mm) r2 <sup>E</sup> E1**

Prediction of Surface Runoff and Soil Erosion at Watershed Scale: Analysis of the AnnAGNPS Model

**Calibration test** *Annual scale (1997 to 2000)*

Predicted[a] 107.05 43.05 0.59 -0.13 -0.10 38.19 -0.40 Predicted [b] 77.17 39.81 0.72 0.70 0.53 6.30 0 *Monthly scale (Oct. 1996 to Dec. 2000)*

Predicted [a] 10.79 19.50 0.75 0.59 0.48 10.15 -0.40 Predicted [b] 7.70 15.98 0.78 0.77 0.61 7.61 0 *Event scale (Oct. 1996 to Dec. 2000)*

Predicted [a] 0.36 2.79 0.83 0.76 0.52 1.18 -0.40 Predicted [b] 0.25 2.36 0.85 0.84 0.64 0.96 0 **Validation test** *Annual scale (Jan. 2001 to Dec. 2003)*

Predicted [b] 108.38 80.79 0.99 0.62 0.54 72.74 0.32 *Monthly scale (Jan. 2001 to Dec. 2003)*

Predicted [b] 9.03 24.20 0.93 0.85 0.66 13.27 0.32 *Event scale (Jan. 2001 to Dec. 2003)*

Predicted[b] 0.30 4.00 0.87 0.83 0.58 2.21 0.32

**Table 5.** Values of the coefficients, summary and difference measures applied to runoff volumes at different time

The simulated total runoff volume for the period of October 1996 to December 2000 (405.72 mm) was only slightly higher than the observed value (393.23 mm), showing a runoff pre‐ diction capability for long periods, which was also detected by other Authors (Yuan et al., 2001). The improvement in the annual runoff volume predictions after the calibration is due to the reduction of the cumulated volume overprediction relative to events with smaller runoff (Figure 5). In some cases, at the beginning of the wet season, runoff was generated by AnnAGNPS but not observed (Figure 6). This was probably due to the peculiarity of the hy‐ drological processes governing runoff formation in Mediterranean regions, depending not only on catchment characteristics but also on antecedent hydrological conditions and char‐ acteristics of the rainfall events, with low runoff coefficients as a result of short-duration,

**RMSE (mm)**

**CRM**

http://dx.doi.org/10.5772/50427

17

Oi , Pi = observed and predicted values at the time step i.

Ō = mean of observed values.

**Table 4.** Coefficients and difference measures for model evaluation and their range of variability.
