Monthly calibration and optimization of Ångström-Prescott equation coefficients for comprehensive agricultural divisions in China

doi:10.1007/s11442-021-1882-4

Abstract

Abstract:

?ngstr?m-Prescott equation (AP) is the algorithm recommended by the Food and Agriculture Organization (FAO) of the United Nations for calculating the surface solar radiation (R_s) to support the estimation of crop evapotranspiration. Thus, the a_s and b_s coefficients in the AP are vital. This study aims to obtain coefficients a_s and b_s in the AP, which are optimized for China’s comprehensive agricultural divisions. The average monthly solar radiation and relative sunshine duration data at 121 stations from 1957-2016 were collected. Using data from 1957 to 2010, we calculated the monthly a_s and b_s coefficients for each subregion by least-squares regression. Then, taking the observation values of R_s from 2011 to 2016 as the true values, we estimated and compared the relative accuracy of R_s calculated using the regression values of coefficients a_s and b_s and that calculated with the FAO recommended coefficients. The monthly coefficients, a_s and b_s, of each subregion are significantly different, both temporally and spatially, from the FAO recommended coefficients. The relative error range (0-54%) of R_s calculated via the regression values of the a_s and b_s coefficients is better than the relative error range (0-77%) of R_s calculated using the FAO suggested coefficients. The station-mean relative error was reduced by 1% to 6%. However, the regression values of the a_s and b_s coefficients performed worse in certain months and agricultural subregions during verification. Therefore, we selected the a_s and b_s coefficients with the minimum R_s estimation error as the final coefficients and constructed a coefficient recommendation table for 36 agricultural production and management subregions in China. These coefficient recommendations enrich the case study of coefficient calibration for the AP in China and can improve the accuracy of calculating R_s and crop evapotranspiration based on existing data.

Key words: solar radiation, coefficient calibration, ?ngstr?m-Prescott equation, least-squares regression, agricultural divisions, China

XIA Xingsheng, PAN Yaozhong, ZHU Xiufang, ZHANG Jinshui. Monthly calibration and optimization of Ångström-Prescott equation coefficients for comprehensive agricultural divisions in China[J].Journal of Geographical Sciences, 2021, 31(7): 997-1014.

Figures/Tables 10

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Table 1

Monthly optimal values for the coefficients of the AP for each agricultural subregion in China

Region ID	Jan.		Feb.		Mar.		Apr.		May.		Jun.		Jul.		Aug.		Sep.		Oct.		Nov.		Dec.
Region ID	a_s	b_s	a_s	b_s	a_s	b_s	a_s	b_s	a_s	b_s	a_s	b_s	a_s	b_s	a_s	b_s	a_s	b_s	a_s	b_s	a_s	b_s	a_s	b_s
A1	0.36	0.32	0.20	0.62	0.32	0.48	0.18	0.62	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.19	0.62	0.21	0.62	0.36	0.29
A2	0.28	0.46	0.31	0.44	0.26	0.49	0.25	0.50	0.26	0.44	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.30	0.41	0.33	0.35
A3	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50
A4	0.33	0.25	0.26	0.40	0.13	0.62	0.14	0.60	0.20	0.51	0.22	0.46	0.25	0.37	0.16	0.55	0.20	0.50	0.18	0.53	0.21	0.45	0.28	0.31
B1	0.47	0.24	0.43	0.32	0.37	0.39	0.29	0.46	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.27	0.50	0.26	0.53	0.37	0.38	0.45	0.25
B2	0.40	0.27	0.20	0.56	0.25	0.49	0.25	0.50	0.25	0.50	0.27	0.39	0.38	0.20	0.23	0.49	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50
B3	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.23	0.49	0.25	0.48	0.25	0.50	0.32	0.38
C1	0.19	0.50	0.21	0.49	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.21	0.46	0.16	0.54
C2	0.23	0.46	0.25	0.50	0.31	0.37	0.13	0.66	0.26	0.43	0.22	0.48	0.25	0.50	0.25	0.39	0.27	0.37	0.20	0.52	0.19	0.54	0.22	0.47
C3	0.20	0.50	0.23	0.48	0.25	0.50	0.25	0.50	0.22	0.46	0.25	0.50	0.25	0.50	0.25	0.50	0.19	0.52	0.25	0.50	0.18	0.52	0.25	0.50
C4	0.21	0.43	0.18	0.52	0.25	0.50	0.21	0.47	0.17	0.55	0.21	0.46	0.20	0.47	0.20	0.46	0.25	0.50	0.17	0.54	0.17	0.53	0.18	0.47
D2	0.22	0.46	0.25	0.38	0.25	0.36	0.28	0.30	0.26	0.37	0.21	0.48	0.22	0.47	0.20	0.50	0.18	0.52	0.20	0.47	0.21	0.46	0.22	0.47
D3	0.24	0.44	0.25	0.50	0.25	0.50	0.18	0.55	0.15	0.60	0.14	0.61	0.18	0.55	0.18	0.54	0.15	0.59	0.13	0.62	0.19	0.52	0.17	0.54
D4	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.13	0.67	0.22	0.51	0.21	0.52	0.25	0.50	0.19	0.56	0.25	0.50	0.25	0.50	0.25	0.50
E1	0.16	0.55	0.12	0.64	0.10	0.69	0.14	0.60	0.18	0.53	0.17	0.52	0.16	0.55	0.15	0.56	0.16	0.55	0.17	0.55	0.15	0.57	0.14	0.58
E2	0.25	0.50	0.25	0.50	0.25	0.50	0.21	0.46	0.23	0.43	0.22	0.47	0.21	0.51	0.19	0.53	0.16	0.60	0.14	0.60	0.16	0.54	0.25	0.50
E3	0.10	0.73	0.11	0.70	0.11	0.67	0.12	0.63	0.17	0.55	0.17	0.55	0.18	0.53	0.15	0.59	0.11	0.71	0.19	0.53	0.16	0.58	0.16	0.56
E4	0.10	0.68	0.10	0.71	0.11	0.65	0.16	0.46	0.15	0.58	0.20	0.45	0.23	0.44	0.21	0.48	0.19	0.52	0.18	0.52	0.15	0.58	0.12	0.65
E5	0.13	0.73	0.19	0.52	0.16	0.60	0.20	0.52	0.18	0.61	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.21	0.53	0.18	0.59
E6	0.13	0.63	0.12	0.63	0.11	0.65	0.13	0.55	0.14	0.60	0.19	0.48	0.18	0.50	0.23	0.42	0.17	0.56	0.21	0.48	0.16	0.58	0.17	0.52
F1	0.16	0.59	0.19	0.51	0.18	0.55	0.35	0.17	0.26	0.40	0.20	0.54	0.24	0.48	0.19	0.59	0.15	0.68	0.18	0.56	0.24	0.37	0.22	0.48
F2	0.15	0.53	0.15	0.64	0.16	0.59	0.17	0.52	0.19	0.49	0.17	0.55	0.19	0.49	0.18	0.50	0.16	0.53	0.17	0.52	0.16	0.57	0.14	0.62
F3	0.14	0.53	0.13	0.58	0.11	0.64	0.14	0.54	0.16	0.52	0.18	0.50	0.19	0.49	0.23	0.41	0.21	0.43	0.18	0.45	0.15	0.55	0.14	0.54
F4	0.11	0.77	0.12	0.73	0.25	0.50	0.14	0.61	0.25	0.50	0.25	0.50	0.25	0.50	0.20	0.46	0.16	0.54	0.25	0.50	0.12	0.76	0.13	0.62
F5	0.20	0.56	0.25	0.50	0.13	0.63	0.19	0.53	0.20	0.52	0.22	0.48	0.23	0.46	0.21	0.51	0.22	0.51	0.25	0.50	0.18	0.59	0.16	0.61
G1	0.15	0.59	0.14	0.62	0.13	0.65	0.15	0.58	0.16	0.55	0.19	0.43	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50
G2	0.17	0.58	0.15	0.62	0.16	0.54	0.17	0.57	0.19	0.50	0.21	0.48	0.22	0.45	0.22	0.46	0.22	0.48	0.27	0.41	0.21	0.52	0.20	0.53
G3	0.25	0.50	0.25	0.50	0.23	0.45	0.30	0.33	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.27	0.42
G4	0.19	0.54	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50	0.34	0.28	0.25	0.50	0.28	0.34	0.25	0.50	0.25	0.50	0.21	0.50
H1	0.25	0.50	0.25	0.50	0.41	0.29	0.35	0.38	0.25	0.50	0.25	0.50	0.27	0.47	0.23	0.53	0.25	0.50	0.25	0.50	0.25	0.50	0.25	0.50
H2	0.25	0.50	0.25	0.50	0.25	0.50	0.37	0.30	0.17	0.60	0.30	0.42	0.27	0.44	0.24	0.49	0.25	0.50	0.21	0.53	0.23	0.52	0.26	0.47
H3	0.25	0.50	0.25	0.50	0.25	0.50	0.29	0.42	0.34	0.35	0.35	0.34	0.30	0.40	0.32	0.37	0.34	0.36	0.31	0.42	0.25	0.50	0.27	0.43
I1	0.16	0.73	0.34	0.49	0.39	0.39	0.25	0.50	0.40	0.36	0.43	0.32	0.35	0.45	0.35	0.45	0.38	0.39	0.25	0.50	0.25	0.50	0.25	0.50
I2	0.24	0.60	0.27	0.52	0.25	0.50	0.30	0.42	0.28	0.45	0.28	0.46	0.23	0.60	0.21	0.64	0.22	0.60	0.17	0.69	0.30	0.52	0.31	0.50
I3	0.33	0.47	0.48	0.29	0.49	0.24	0.27	0.55	0.27	0.53	0.26	0.53	0.26	0.54	0.30	0.47	0.29	0.50	0.29	0.53	0.28	0.56	0.25	0.50
I4	0.39	0.39	0.32	0.48	0.22	0.59	0.34	0.39	0.28	0.47	0.30	0.45	0.24	0.54	0.34	0.38	0.30	0.46	0.43	0.35	0.22	0.61	0.23	0.60

Table 1

Figure 7

Figure 8

Figure 9

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