## 3 Temperature-Based ET Models: Advantages, Drawbacks, and Evolution of Research
### Contexture-Based ET Models
The approach incorporated visible and thermal satellite information to provide instantaneous spatial distribution of ET validated together with the employed EF, G, and instantaneous R\({}_{n}\) against EUROFLUX site data (March to October 1997). To compare different sensors, [PERSON] et al. 2006 conducted an extensive inter-comparison of ET estimates derived from MODIS and AVHRR sensors [93]. The comparison covered as well NDVI, Ts, EF and R\({}_{n}\). Despite differences in response functions and overpass times, the contextual space of the LST-NDVI diagram yielded comparable estimates of EF. [PERSON] et al. 2007 presented a methodology based on the EF concept for retrieving ET from low spatial resolution remote sensing data [94]. Comparison with high-resolution ET estimation showed good agreement, capturing the seasonal evolution of daily ET based on LST and VI. The MSG-SEVIRI high temporal resolution of the 15-minute acquisition intervals enables accurate estimation of the diurnal increase in LST during the morning, serving as a reliable proxy for overall daytime H. Using that, the improvement of the triangle method by [95] helped in estimating EF and thus the ET. By considering the diurnal change in LST and interpreting the LST-VI space, authors provided regional estimates of ET and the validation against field observations demonstrated low biases and good agreement. [PERSON] et al. 2008 aimed to improve the prediction of land surface heat fluxes and made two enhancements to an operational two-layer model [96]. The first improvement employed a SEB method to determine theoretical boundary lines in the scatter plot for surface temperature versus fractional vegetation cover (\(f_{c}\)) in mixed pixels. The second improvement introduced the assumption that the slope of temperature-vegetation cover curves is mainly controlled by soil water content. Validation against in situ measurements demonstrated the model's accuracy in predicting latent heat flux. Furthermore, [PERSON] et al. 2010 applied the LST-VI triangle method to estimate regional evapotranspiration in arid and semi-arid regions [97]. An algorithm was developed to quantitatively determine the dry and wet edges of the triangle space. Applying this algorithm to MODIS/TERRA datasets, good agreement was achieved between retrieved \(H\) and those measured by a Large Aperture Scintillometer (LAS). The Two-source Trapezoid Model for Evapotranspiration (TTME) was developed by [PERSON] and [PERSON] in 2012 by incorporating the fc-T\({}_{rad}\) space (T\({}_{rad}\) representing radiative surface temperature) and the concept of soil surface moisture availability isopleths [98]. TTME accurately estimated \(LE\) with a mean absolute percentage difference of around 10% and demonstrated comparable accuracy to the TSEB model. It required fewer inputs, avoided resistance network computations, and reduced overestimation of vegetation transpiration compared to the Priestley-Taylor equation. Sensitivity analysis revealed that TTME was most sensitive to T\({}_{rad}\) and T\({}_{a}\) while being less sensitive to other meteorological observations, variables, and derived parameters. In a different context, [PERSON] et al., 2013 developed the Temperature and Greenness Rectangle (TGR) model to estimate terrestrial ecosystem gross primary production (GPP) using MODIS satellite imagery [99]. The TGR model demonstrated good agreement with tower based GPP measurements, particularly for most vegetation types, except evergreen broadleaf forests. This model outperforms other models, providing superior GPP estimates, especially under dry climate conditions. It incorporates three significant advantages: (1) it adheres closely to the principles of the light use efficiency model while ensuring that each parameter possesses a tangible physical interpretation; (2) it mitigates the reliance on meteorological data obtained from ground-based sources; and (3) it prevents redundancy in information stemming from interrelated explanatory variables.