Improving a Penman–Monteith evapotranspiration model by incorporating soil moisture control on soil evaporation in semiarid areas

Figures & data

Figure 1. Flowchart of the PM-SMI ET algorithm for calculating daily ET.

Table 1. Location, soil type and land cover of study sites.

Site	Lat	Lon	Land cover
E7_Elk_Falls	37.383 N	96.18 W	Grass
E8_Coldwater	37.333 N	99.309 W	Grass
E9_Ashton	37.133 N	97.266 W	Grass
E13_Lamont	36.605 N	97.485 W	Crop
E15_Ringwood	36.431 N	98.284 W	Grass
E20_Meeker	35.564 N	96.988 W	Grass
E27_Earlsboro	35.269 N	96.740 W	Grass
Duke Forest Hardwoods	35.974 N	79.100 W	Mixed forest
North Carolina Loblolly Pine	35.803 N	76.668 W	Mixed forest
Walker Branch	35.959 N	84.287 W	Deciduous broad-leaf forest

Table 2. The mean NDVI, mean LAI, max NDVI, max LAI and mean soil water content for each site. The mean and max values of NDVI and LAI were obtained from the MODIS NDVI and LAI products. The mean soil water content was obtained from surface soil moisture measurements taken at 5 cm. The data from SGP sites was collected from 2004 and the data from AmeriFlux sites was collected from 2005.

Site	Mean NDVI	Mean LAI	Max NDVI	Max LAI	Mean soil water content (m^3/m^3)
E7	0.54	1.4	0.75	3.1	0.37
E8	0.45	0.8	0.52	1.5	0.14
E9	0.49	0.6	0.62	1.1	0.32
E13	0.53	0.9	0.67	2.1	0.32
E15	0.48	0.64	0.60	1.0	0.11
E20	0.55	1.2	0.73	2.6	0.32
E27	0.56	1.1	0.74	2.3	0.18
Duke FH	0.67	2.42	0.85	5.9	0.33
North CLP	0.63	2.27	0.86	6.3	0.33
Walker B	0.68	2.44	0.88	6	0.2

Table 3. Available days, root mean square error (RMSE: mm/day), absolute bias (bias: mm/day), and square of correlation coefficient (R²) of four ET algorithms for each site. (1) PM-Mu2007; (2) PM-Mu2011; (3) PM-Yuan; and (4) PM-SMI.

Site	ECR	Available days	RMSE1	RMSE2	RMSE3	RMSE4	Bias1	Bias2	Bias3	Bias4	R^21	R^22	R^23	R^24
E7	–	148	1.30	1.08	1.22	0.74	−1.01	−0.71	−0.95	−0.05	0.79	0.81	0.81	0.86
E8	–	161	1.48	1.49	1.44	1.05	−1.14	−1.20	−1.11	0.43	0.44	0.55	0.46	0.58
E9	–	162	1.69	1.64	1.67	0.39	−1.49	−1.34	−1.45	−0.03	0.94	0.87	0.95	0.95
E13	–	153	1.89	1.95	1.88	0.97	−1.35	−1.23	−1.29	0.18	0.60	0.40	0.54	0.75
E15	–	161	1.38	1.49	1.39	0.98	−1.05	−1.07	−1.04	0.57	0.73	0.69	0.74	0.76
E20	–	149	1.02	0.87	0.96	0.83	−0.76	−0.46	−0.71	0.34	0.82	0.81	0.84	0.85
E27	–	127	1.22	1.01	1.18	0.90	−0.91	−0.67	−0.85	0.26	0.83	0.86	0.84	0.81
SGP	–		1.40	1.37	1.37	0.91	−1.06	−0.93	−1.02	0.33	0.69	0.64	0.69	0.77
Duke FH	0.81	180	0.56	0.93	0.53	0.58	−0.05	−0.43	−0.02	0.09	0.93	0.84	0.93	0.91
North CLP	0.70	158	0.88	1.46	0.86	0.68	−0.67	−0.89	−0.66	−0.38	0.91	0.72	0.91	0.89
Walker B	0.64	98	1.31	0.82	1.30	1.42	0.76	0.37	0.78	0.98	0.74	0.80	0.73	0.68
Forest	–		0.99	1.20	0.97	0.96	−0.12	−0.45	−0.10	0.15	0.75	0.69	0.75	0.74
All	–		1.31	1.33	1.28	0.88	−0.82	−0.80	−0.78	0.24	0.66	0.64	0.66	0.78

Figure 2. Scatterplots between observed ET and estimated ET.

Figure 4. Comparisons of 8-day ET measurements to PM-SMI 8-day ET estimates and the MODIS 8-day ET product.

Figure A1. T_s−F_v trapezoid space. The upper solid line is the dry edge, estimated from the energy balance formula, representing extreme water stressed conditions. The lower solid line is the wet edge, representing saturated soil water conditions.