**4. Summary and conclusions**

*Advanced Evapotranspiration Methods and Applications*

*(a) Percent area of San Bernardino County covered by D0 and (b) monthly estimated ET values from the* 

possible to state that EWDI-NDVI estimated the drought condition better than EWDI-MOD. These results may be explained by comparing ET values shown in **Figure 10(b)**. The plot shows GG-NDVI ET against observed ET and the same with the modified GG estimates from 2012 to 2015. The results show that the pattern of ET from modified GG is much higher than observed ET, whereas GG-NDVI shows similar patterns with observed ET. The mean RMSE is 37 mm/month for modified

*quantity of r shown in figure means the correlation coefficient with USDM from 2001 to 2015.*

*Spatial distributions of USDM, EWDI, SPI, and PDSI results for major drought months in the CONUS. The* 

*modified GG and GG-NDVI models and mean monthly observed ET from 2012 to 2015.*

**90**

**Figure 11.**

**Figure 10.**

This study proposed an improved version of the Granger and Gray [4] using both the complementary relationship and the Budyko framework in Chapter 2. Then, existing limitation of the complementary relationship was identified by comparing remote sensing ET product. Lastly, the applicability of using accurate ET model as a drought index was addressed in Chapter 3.

In Chapter 2, the modified GG model developed by [5] was refined by using the Budyko framework based on [11]. The relative evaporation parameter in the original GG model was derived from limited sites under wet conditions in Canada [4]. To overcome this limitation, the Fu equation [11] was used instead of the relative evaporation parameter on the basis that the Fu equation can support the complementary relationship [9, 10]. This chapter used AmeriFlux eddy covariance tower sites in the United States to retrieve required meteorological data including precipitation. Also, NDVI were from the MODIS land subsets. Sites were divided into dry and wet climate conditions based on an aridity index from UNEP [13]. The proposed model, denoted as GG-NDVI, showed much lower RMSE in both dry and wet sites compared to the modified GG model (see details in [5]). More importantly, the validation in Chapter 2 provided an inherent limitation of the complementary relationship and validation through a direct comparison with the SSEBop (Operational Simplified Surface Energy Balance, [16]). The SSEBop ET data set retrieved from the USGS Geo Data Portal for the period 2000–2007 covering the United States and 60 AmeriFlux stations were used for validation of ET results from SSEBop and GG-NDVI. The results showed that GG-NDVI can produce similar or better accuracy than SSEBop. Based on the results, this study observed that the assumption of symmetric complementary relationship was a deficiency in GG-NDVI that produced poor results under certain condition. Under the symmetric complementary relationship, ET is close to ETW with increasing humidity, but natural surfaces even in the wettest regions will not approach saturation. Therefore, this study proposed a nonlinear correction function to the GG-NDVI to better describe the complementary relationship. This correction function improved the GG-NDVI model significantly especially, under conditions of high humidity and dense vegetation.

In Chapter 3, ET calculated from the latest version of GG-NDVI, denoted as Adjusted GG-NDVI, used to estimate drought conditions across the United States for the period of 2001–2015. The proposed drought index, EWDI, was calculated by using the difference between ETW and ET with the probability distribution function of [20] because this probabilistic approach allowed a consistent comparison between EWDI and other standardized indices. Also, the drought severity of EWDI was divided into five classes that are the same classes with the US Drought Monitor (USDM). Required meteorological data were from the PRISM at 4-km resolution covering the CONUS, and monthly NDVI data were retrieved from the NASA Earth Observations. The results of this chapter supported that the EWDI could capture drought conditions and using an accurate ET model can help to improve drought monitoring performance. One unanticipated finding was that within the complementary relationship when energy-limited conditions are present, ET and ETW

varied in a parallel trend and ET is closer to ETW, resulting in decreasing EWDI performances such as Minnesota (not shown in this study). Despite this limitation, EWDI could identify droughts over CONUS consistent with USDM from the major drought incidents of August 2007, November 2009, and July 2011.
