Spatial distribution of main parameters of Hargreaves formula in typical time scales in Huang-Huai-Hai Plain

Abstract: In order to improve the applicability and accuracy of Hargreaves formula in different regions, and improve the estimation precision of regional crop water requirement and the level of irrigation management, the nonlinear fitting for the main parameters of the Hargreaves model in typical time scales (annual scale and quarter scale) was combined with the Kriging method in this study. The dependent variable was the reference crop evapotranspiration (ET0) calculated with the Penman-Monteith model, and the independent variables were the maximum and minimum temperature, and the atmospheric solar radiation. The long series of daily weather data from 1961 to 2012 was collected from 54 meteorological stations in the Huang-Huai-Hai Plain. Results indicated that the annual dynamics of the transformation coefficient K of the Hargreaves model was similar with the variation of K in summer. The K value increased gradually from the northwest to southeast in the Huang-Huai-Hai Plain. The key geographic factors controlling the distribution of K in the scale of year and summer were longitude and latitude, the correlation coefficient between K value and longitude all were 0.42, and which between K value and latitude were -0.37 and -0.47. However, the K value in spring, autumn and winter was opposite to the variation in summer, decreasing gradually from the northwest to southeast in this region, the correlations between K value and latitude in spring, between K value and elevation in autumn, between K value and longitude in winter were better, and the correlation coefficients were 0.43, 0.38, -0.48, respectively. The main meteorological factors controlling the distribution of K were the minimum temperature, sunshine hour and relative humidity. Changes in the exponential coefficient n in the scale of year and summer were similar, which increasing from the southeast to northwest in the Huang-Huai-Hai Plain gradually. The key geographic factors controlling the distribution of n in the scale of year was longitude, the correlation coefficient was -0.53, and in summer the key geographic factors were longitude and latitude, the correlation coefficient were -0.59 and 0.44. However, the n value in spring, summer and winter increased from the northeast to southwest in this region gradually, and there was a better correlation between n value and latitude in these seasons, the correlation coefficients were -0.71, -0.64, -0.40, respectively. The key factors controlling the distribution of n were maximum temperature, sunshine hour and relative humidity. The values of temperature offset Toff increased gradually from the southwest to northeast in this region. Toff increased gradually from the south to the north in the scale of year, spring, summer and autumn, increased with the increase in latitude. While in winter, Toff increased gradually from the west to the east. The key meteorological factors influencing the distribution of Toff were solar radiation, sunshine hour, and maximum temperature. The correlation index between the calibrated Hargreaves model and P-M model was 0.79 in the scale of year, 0.70 and 0.71 in spring and autumn, and 0.46 in winter. The standard error of parameters calibrated with the nonlinear fitting was decreased to a very low level. The standard error of K, n and Toff was lower than 0.001, 0.72, and 10.0, respectively. The statistical analysis indicated that the calibrated Hargreaves model had a high goodness-of-fit and improved the estimation accuracy of the corresponding parameters.