Model validation and analyses

The model was tested for the Yellow River basin for the period 1983 - 2000 after initializing the model until equilibrium was reached. Initially the model was run without considering the precipitation subgrid variability and the irrigation scheme. There are no big irrigation districts in the upstream Tangnaihai station. The discharge observations at Tangnaihai station is considered as the natural flow and compared with the simulated stream flow. Mean bias (BIAS), root mean squared error(RMSE), relative root mean squared error (RRMSE) and mean square skill score (MSSS) are used to evaluate the model performance. The BIAS is defined as:

BIAS = 5#56#67#7x_s - x_o8#8 (2)

and RMSE is defined as:

RMSE = 9#9 (3)

and RRMSE is defined as:

RRMSE = RMSE/10#106#6x_o/N11#11 (4)

and MSSS is defined as (Murphy, 1988):

MSSS = 1 - 12#12 (5)

where N is the total number of the time series for comparison, x_s is simulated values, x_o is observed cloud values. Mean monthly simulated and observed stream flow values are shown in Figure 4. The BIAS, RRMSE and MSSS are 4.5%, 0.26 and 0.840, respectively. The simulated and observed daily stream flow at the Tangnaihai station is shown in Figure 5. The RRMSE is 0.5 and MSSS is 0.685. The monthly and daily discharge is finely reproduced and the discharge simulation gives a reasonable performance for the estimation of irrigation water availability.

Figure 4: Simulated and observed mean monthly stream flow at the Tangnaihai station

13#13

Figure 5: Simulated and observed daily stream flow at the Tangnaihai station

14#14

For validation purposes, the irrigation scheme is implemented, and model-estimated net irrigation water consumption was compared to the statistical water consumption from several literatures. Liu and Zhang (2002) reported the water consumption in upper, middle, lower reaches of the Yellow River basin from the 1950s to 1990s, which may be larger the irrigation water consumption because the statistical water consumption took into account the water consumption in industry and drinking water. Li et al. (2004) provided the net irrigation water consumption in seven irrigation districts in upper and middle reaches of the Yellow River basin. In Table 1, the simulated and reported irrigation water consumptions are presented. The reported numbers are summarized in the 1980s and 1990s, while the simulation results are averages for the corresponding periods. The simulated water consumptions in upper reaches are less than reported ones because large amount of water is taken into the Hetao irrigation district and drained to an endoric lake and then evaporated into atmosphere (Li et al., 2004).

Table 1: Simulated and reported annual irrigation water consumptions (10⁹m³)

Time period	Upper reach1	Middle reach	Lower reach	Total
1980-1989 (reported)	12.11	6.21	11.29	29.61
1983-1989 (simulated)	8.15	7.90	11.06	27.11
1990-1995 (reported)	13.17	6.02	10.78	29.96
1990-1995 (simulated)	6.88	7.98	9.63	24.49

¹ The effect of an endoric lake was not considered in the simulations.

Model analyses were performed with a variety of modeling cases associated with natural and anthropogenic heterogeneity. Case 1: no irrigation without consideration of precipitation heterogeneity; case 2: no irrigation with precipitation heterogeneity; case 3: irrigation with precipitation heterogeneity. For all the modeling cases, the same SiB2 land cover from USGS Global Land Cover Characterization dataset was used. The same vegetation characteristics such as LAI and FPAR and related soil optical properties were used. Possible vegetation status variety because of irrigation is not taken into account in the model. The discharge at upstream station Tangnaihai is used to calibrate the precipitation heterogeneity parameters a, b, c in the equation 1. Parameters a = b = 4 was used in the cases taking into account precipitation heterogeneity in this study.