Incorporating bias error in calculating solar irradiance: Implications for crop yield simulations

Solar irradiance is an important input parameter to many crop simulation models. It is not measured at the same spatial density as air temperature and precipitation, which has lead to the development of algorithms to calculate solar irradiance from air temperature and precipitation data. Fourteen algorithms were evaluated using 10 yr of measured air temperature, precipitation, and solar irradiance data from Mead, NE. All algorithms had similar root mean square errors (RMSE). When the bias error (the difference between measured and simulated values) was plotted against day of year, only one version of the algorithm showed a simple pattern not dependent on fitting a Fourier series to the data. This pattern of the bias error formed the basis for a correction factor that was applied to all calculations of solar irradiance. Using independent meteorological data from nine locations in eastern and western portions of Kansas, Nebraska, and South Dakota, the corrected algorithm developed from the Mead data calculated solar irradiance with RMSE ranging from 3.6 to 4.7 MJ m^-2 d^-1 Using the Erosion Productivity Impact Calculator, simulated yields of wheat (Triticum aestivum L.), maize (Zea mays L.), and soybean [Glycine max (L.) Merr.] were significantly different when using the measured and uncorrected solar irradiance; however, the yields were not significantly different when using the measured and modified solar irradiance. Using this modification, solar irradiance measured at one location can be used to calculate solar irradiance at locations up to 600 km away in the U.S. Great Plains.