Modified Aver'yanov's phreatic evaporation equations under crop growing

Phreatic evaporation is an important component of the water balance in irrigated areas, and accurate estimates of phreatic evaporation are useful in regional water resources assessments and irrigation water management. Aver'yanov's equation with high accuracy is one of the most widely used empirical equations for estimating phreatic evaporation. To improve the calculation accuracy of phreatic evaporation under the crop growth conditions, the concept of crop influencing coefficient was introduced in this paper and two modified Aver'yanov equations were proposed based on the fact that the ratio of phreatic evaporation from crop-covered and bare soils regularly increases when the crop grows. The modified Aver'yanov Equation I used the crop coefficient estimating crop water requirements, reflecting the influences of crop growth on the phreatic evaporation. The crop has less impact on phreatic evaporation in the initial stage, and the impact gradually enhances the phreatic evaporation in the middle stage with phreatic evaporation maintaining at a relatively high level. At last, the effect of crop on phreatic evaporation drops down due to the maturity of the crop. In the second equation, the modified Aver'yanov Equation II, the effect of crop growth on the change of extinction depth was taken further into consideration. Lysimeter experiments were conducted at the Huibei Water Science Experiment Station during 2005-2007 in Henan Province, and the daily weather data and infiltration, runoff, evaporation data were collected, and then phreatic evaporation was calculated. Three statistical indicators, mean absolute error, root mean square error and correlation coefficient, were adopted to evaluate the performance of the modified equations. Experimental data were used to verify the values of parameters of the modified equations in crop growing season for 2007-2008. The results showed that the values of the empirical index, extinction depth and crop influencing coefficients of the modified Aver'yanov Equation I were within the reasonable range. For the verification period, the mean absolute error was 0.30-0.59 mm·d-1, the root mean square error was 0.57~0.87 mm·d-1, and the correlation coefficient was 0.58-0.72. The values of statistical indicators indicated that the modified Aver'yanov Equation I performed better than the equation reported in a previous study and Aver'yanov Equation II. The modified Aver'yanov Equation I has a rational structure and explicit physical meaning and this equation could be recommended calculating phreatic evaporation.