Assessing models for parameters of the Ångström–Prescott formula in China

Application of the Ångström–Prescott (A–P) model, one of the best rated global solar irradiation (Rs) models based on sunshine, is often limited by the lack of model parameters. Increasing the availability of its parameters in the absence of Rs   measurement provides an effective way to overcome this problem. Although some models relating the A–P parameters to other variables have been developed, they generally lack worldwide validity test. Using data from 80 sites covering three agro-climatic zones in China, we evaluated seven models that relate the parameters to annual average of relative sunshine (n/N¯) (models 1–2), altitude (model 7), altitude and n/N¯ (model 3), altitude, n/N¯ and latitude (model 4), altitude and latitude (model 5) and annual average air temperature (model 6). It was found that model 7 performed best, followed by models 6, 1, 3, 2 and 4. The better performance of models 7 and 6 and the fact that they used fewer sites and variables in their establishment demonstrated that using a large dataset in developing the A–P parameter model or having more variables included is no guarantee of wider applicability, and that the local climatic regime may override other factors in the parameter modeling. This also suggests that applicability of a Rs model is not proportional to its complexity. The common feature of the better performing models suggests that accurate modeling of parameter a is more important than that of b. Therefore, priority should be given to parameter models having higher accuracy for a. Comparison of predicted against the calibrated A–P parameters revealed many unrealistic predictions by model 5, with which it was possible to obtain meaningful Rs   estimates. To ensure that a parameter model is conceptually consistent and related to reality, it is necessary to check the modeled parameters against the calibrated ones. Models 1, 6 and 7 showed an advantage in keeping the physical meaning of their modeled parameters due to the small magnitude of n/N¯ and the use of the relation of (a + b) versus other variables as a constraint, respectively. All models tended to perform best in zone II and poorest in zone I in predicting Rs, indicating larger errors in humid climates. Since most productive agricultural areas in China are located in zone I, developing parameter models tailored to this zone would be valuable to improve Rs accuracy.

► Seven parameter models for the Ångström–Prescott formula were assessed in China.
► The better performing models and agro-climatic zones were revealed.
► Accurate modeling of parameter a is more important than that of b in predicting Rs.
► Size of dataset in developing a parameter model related less to its applicability.
► The model including more variables is no guarantee of its wider applicability.