The non-parametric (N-P) method expresses evapotranspiration as a function of net radiation, ground heat flux, air temperature, and surface temperature (T_s). This method is relatively new and attractive for estimating evapotranspiration, especially for T_s measurements from remote sensing. The purpose of this study is to investigate the limitations of this method and compare its performance with those of the Penman–Monteith (P–M) and Priestley–Taylor (P–T) equations. Field experiments were carried out to study the evapotranspiration rates and sensible heat fluxes above three different ecosystems: grassland, peat bog, and forest. The results show that above the grassland and peat bog, the evapotranspiration rates were close to the equilibrium evaporation. Though the forest is humid (average humidity ≈ 89%; annual precipitation ≈ 2600 mm), the evapotranspiration was only 69% of the equilibrium evaporation. In terms of model predictions, it was found that the P–M and P–T equations were able to predict the water vapor and sensible heat fluxes well (R² ≈ 0.60–0.92; RMSE ≈ 30 W m⁻²) for all the three sites if the canopy resistance and the P–T constant of the ecosystem were given a priori. However, the N-P method only succeeded for the grassland and peat bog; it failed above the forest site (RMSE ≈ 60 W m⁻²). Our analyses and field measurements demonstrated that for the N-P method to be applicable, the actual evapotranspiration of the site should be within 0.89–1.05 times the equilibrium evaporation.

Ground heat flux may play an important role in surface energy balance. In this study we evaluate the performance of the objective hysteresis model (OHM) for estimating ground heat flux from net radiation and compare it with the linear regression model. The experimental sites include residential roofs (concrete), campus grassland, agricultural grassland, and peat bog. Our field measurements show that the mean partition coefficient from net radiation to ground heat flux varied from 0.47 (concrete roof) to 0.079 (agricultural grassland). The mean hysteresis (lag) factors for residential roof, campus grassland, and peat bog were 0.55, 0.26, and −0.11 h, respectively; and the hysteresis factor at the agricultural site was only 0.032 h. However, the partition and hysteresis coefficients in the OHM were found to vary with time for the same surface. Our measurements and analysis show that when the hysteresis factor is larger than 0.11 h, ground heat flux estimates from net radiation can be improved (17–37% reduction in the root mean square error) by using OHM instead of a simple linear regression model.

Canopy resistance is a key parameter in the Penman–Monteith (P–M) equation for calculating evapotranspiration (ET). In this study, we compared a machine learning algorithm–support vector machine (SVM) and an analytical solution (Todorovic, 1999) for estimating canopy resistances. Then, these estimated canopy resistances were applied to the P–M equation for estimating ET; as a benchmark, a constant (fixed) canopy resistance was also adopted for ET estimations. ET data were measured using the eddy-covariance method above three sites: a grassland (south Ireland), Cypress forest (north Taiwan), and Cryptomeria forest (central Taiwan) were used to test the accuracy of the above two methods. The observed canopy resistance was derived from rearranging the P–M equation. From the measurements, the average canopy resistances for the grassland, Cypress forest, and Cryptomeria forest were 163, 346, and 321 (s/m), respectively. Our results show that both methods tend to reproduce canopy resistances within a certain range of intervals. In general, the SVM model performs better, and the analytical solution systematically underestimates the canopy resistances and leads to an overestimation of evapotranspiration. It is found that the analytical solution is only suitable for low canopy resistance (less than 100 s/m) conditions.