Improving the S-Shape Solar Radiation Estimation Method for Supporting Crop Models

Table 3

Comparison of the radiation estimates obtained with the indicated methods for the validation sites (Figure 2). Parameters of S^0-2-1-4 were set according to Section 3.3. The DC, DB, HKS, and LS methods were parameterized for each site separately.

Estimation method	Error index	Columbus, OH	Fort Smith, AR	Jackson, MS	Kansas City, MO	Louisville, KY	Memphis, TN	Omaha, NE	Springfield, IL	Waterloo, IA	Wichita, KS	Average
	𝑅^2	0.723	0.757	0.708	0.773	0.734	0.708	0.760	0.748	0.763	0.777	0.745
DC	RMSE	4.01	3.58	3.69	3.76	3.83	3.94	4.00	4.02	4.02	3.65	3.85
	PIdoy	0.951	0.946	2.270	0.755	1.210	2.090	1.040	1.210	2.070	0.329	1.287
	𝑅^2	0.698	0.759	0.731	0.743	0.722	0.714	0.734	0.715	0.734	0.758	0.731
DB	RMSE	4.10	3.53	3.57	3.92	3.92	3.99	4.11	4.16	3.99	3.72	3.90
	PIdoy	0.779	0.581	0.316	0.881	0.585	0.609	0.891	0.953	1.070	0.688	0.735
	𝑅^2	0.802	0.813	0.792	0.806	0.804	0.791	0.792	0.801	0.816	0.814	0.803
HKS	RMSE	3.21	3.04	3.08	3.32	3.21	3.30	3.55	3.35	3.19	3.17	3.24
	PIdoy	0.986	0.740	0.972	0.789	1.010	1.090	0.965	0.894	0.973	0.677	0.910
	𝑅^2	0.829	0.831	0.812	0.838	0.834	0.823	0.816	0.832	0.836	0.835	0.829
LS	RMSE	2.98	2.90	2.95	3.03	2.96	3.05	3.33	3.08	3.01	2.99	3.03
	PIdoy	0.465	0.608	0.997	0.534	0.689	0.888	0.824	0.621	0.975	0.413	0.701
	𝑅^2	0.831	0.828	0.805	0.839	0.836	0.825	0.816	0.836	0.840	0.832	0.829
S^0-2-1-4	RMSE	3.03	2.94	3.01	3.07	2.94	3.22	3.35	3.06	2.98	3.03	3.06
	PIdoy	0.612	0.585	0.253	0.521	0.210	0.971	0.397	0.149	0.198	0.329	0.423