**3.4 Results**

The Pearson correlation coefficient was used to determine which ET method is the best estimating drought. Like SPI and other drought indices, EWDI can be estimated at different time scales from which specific time aggregated versions are selected. **Figure 7** provides the results obtained from the correlation coefficient between two EWDI results and USDM for years 2001–2015. EWDI using the GG-NDVI ET model generally shows a stronger relationship with UDSM across CONUS. The area-averaged correlation coefficient over all pixels for EWDI-MOD is 0.58, whereas EWDI-NDVI produced 0.72. Also, correlations between EWDI-NDVI and USDM are strongest over much of the southern and northern rockies and plains of the US climate regions and highest in Texas (r > 0.8). This observation is consistent with the regions where soil moisture on land surfaces makes the largest contributions to ET, referred as "hot spot" of land-atmosphere coupling by [27]. It can be clearly seen from **Figure 7** that a significant improvement is attributed to the GG-NDVI model in northwest, upper midwest, and northeast climate regions of the United States. Moreover, the improved performance of EWDI-NDVI over the CONUS can be seen from **Figure 8**. The drought conditions of EWDI-NDVI are similar to that estimated by USDM as shown in **Figure 8(a)**. Also, EWDI-NDVI produced extreme drought conditions much better than EWDI-MOD as shown in **Figure 8(b)**. It is very much plausible that these improved results are due to the use of an accurate ET model.

To further study these results, the San Bernardino County in California was selected as shown in **Figure 9**. The area-averaged correlation coefficient over all pixels in California is 0.55 for EWDI-MOD and 0.70 for EWDI-NDVI. The EWDI-MOD showed lower correlation (0.4–0.6) for most of San Bernardino County, and even the northern county values (r < 0.2) were much lower than the county

#### **Figure 7.**

*Correlation coefficient between two EWDIs and USDM. EWDI-MOD (left) represents EWDI using the modified GG [5], and EWDI-NDVI (right) represents EWDI using GG-NDVI [15]. The area-averaged correlation coefficient over all pixels for EWDI-MOD and EWDI-NDVI is 0.58 and 0.72, respectively.*

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**Figure 8.**

**Figure 9.**

*County (black line).*

*from 2001 to 2015.*

*An Advanced Evapotranspiration Method and Application*

area-averaged correlation coefficient of 0.51. However, the correlation coefficients of EWDI-NDVI were between 0.6 and 0.8 for most of California, and the county

*Correlation coefficient for EWDI-MOD (left) and EWDI-NDVI (right) for California and San Bernardino* 

*Percent area of CONUS (a) covered by D0 (abnormally dry) and (b) covered by D4 (exceptional drought)* 

To compare the temporal drought patterns of EWDI-MOD and EWDI-NDVI, **Figure 10** presents percent area of San Bernardino County covered by D0 from 2012 to 2015. This time period was selected because observed ET data are only available from 2012 to 2015. As shown in **Figure 10(a)**, both produced similar drought conditions until the middle of 2012. Thereafter, EWDI-MOD overestimated drought until May 2013 and underestimated compared to USDM in 2014 and 2015. It is therefore

area-averaged values increased by 40% compared to EWDI-MOD.

*DOI: http://dx.doi.org/10.5772/intechopen.81047*

*An Advanced Evapotranspiration Method and Application DOI: http://dx.doi.org/10.5772/intechopen.81047*

**Figure 8.**

*Advanced Evapotranspiration Methods and Applications*

as *ET* = *LE*/λ, where LE is the latent heat flux (W/m<sup>2</sup>

vaporization (2.45 MJ/kg).

of an accurate ET model.

**3.4 Results**

droughtmonitor.unl.edu/Home.aspx), and four indices are resampled to match the 4-km resolution of EWDI using bilinear interpolation in the ArcMap software. We also used EC flux tower data (in mm/month) from FLUXNET stations to perform a comparison of modified GG and GG-NDVI ET products. The latent heat flux data were collected from the Oak Ridge National Laboratory's AmeriFlux website (http://ameriflux.ornl.gov/, last accessed on November 23, 2016). The tower-measured monthly latent heat flux data were calculated using the equation

The Pearson correlation coefficient was used to determine which ET method is the best estimating drought. Like SPI and other drought indices, EWDI can be estimated at different time scales from which specific time aggregated versions are selected. **Figure 7** provides the results obtained from the correlation coefficient between two EWDI results and USDM for years 2001–2015. EWDI using the GG-NDVI ET model generally shows a stronger relationship with UDSM across CONUS. The area-averaged correlation coefficient over all pixels for EWDI-MOD is 0.58, whereas EWDI-NDVI produced 0.72. Also, correlations between EWDI-NDVI and USDM are strongest over much of the southern and northern rockies and plains of the US climate regions and highest in Texas (r > 0.8). This observation is consistent with the regions where soil moisture on land surfaces makes the largest contributions to ET, referred as "hot spot" of land-atmosphere coupling by [27]. It can be clearly seen from **Figure 7** that a significant improvement is attributed to the GG-NDVI model in northwest, upper midwest, and northeast climate regions of the United States. Moreover, the improved performance of EWDI-NDVI over the CONUS can be seen from **Figure 8**. The drought conditions of EWDI-NDVI are similar to that estimated by USDM as shown in **Figure 8(a)**. Also, EWDI-NDVI produced extreme drought conditions much better than EWDI-MOD as shown in **Figure 8(b)**. It is very much plausible that these improved results are due to the use

To further study these results, the San Bernardino County in California was selected as shown in **Figure 9**. The area-averaged correlation coefficient over all pixels in California is 0.55 for EWDI-MOD and 0.70 for EWDI-NDVI. The EWDI-MOD showed lower correlation (0.4–0.6) for most of San Bernardino County, and even the northern county values (r < 0.2) were much lower than the county

) and λ is the latent heat of

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**Figure 7.**

*Correlation coefficient between two EWDIs and USDM. EWDI-MOD (left) represents EWDI using the modified GG [5], and EWDI-NDVI (right) represents EWDI using GG-NDVI [15]. The area-averaged correlation coefficient over all pixels for EWDI-MOD and EWDI-NDVI is 0.58 and 0.72, respectively.*

*Percent area of CONUS (a) covered by D0 (abnormally dry) and (b) covered by D4 (exceptional drought) from 2001 to 2015.*

#### **Figure 9.**

*Correlation coefficient for EWDI-MOD (left) and EWDI-NDVI (right) for California and San Bernardino County (black line).*

area-averaged correlation coefficient of 0.51. However, the correlation coefficients of EWDI-NDVI were between 0.6 and 0.8 for most of California, and the county area-averaged values increased by 40% compared to EWDI-MOD.

To compare the temporal drought patterns of EWDI-MOD and EWDI-NDVI, **Figure 10** presents percent area of San Bernardino County covered by D0 from 2012 to 2015. This time period was selected because observed ET data are only available from 2012 to 2015. As shown in **Figure 10(a)**, both produced similar drought conditions until the middle of 2012. Thereafter, EWDI-MOD overestimated drought until May 2013 and underestimated compared to USDM in 2014 and 2015. It is therefore

#### **Figure 10.**

*(a) Percent area of San Bernardino County covered by D0 and (b) monthly estimated ET values from the modified GG and GG-NDVI models and mean monthly observed ET from 2012 to 2015.*

#### **Figure 11.**

*Spatial distributions of USDM, EWDI, SPI, and PDSI results for major drought months in the CONUS. The quantity of r shown in figure means the correlation coefficient with USDM from 2001 to 2015.*

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

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dense vegetation.

*An Advanced Evapotranspiration Method and Application*

model as a drought index was addressed in Chapter 3.

GG and 7 mm/month for GG-NDVI. The overestimated ET from modified GG, which brings a small water deficit, results in a corresponding drought that is underestimated compared to USDM. Taken together, these results indicate that the water deficit derived from the complementary relationship can be used as a drought index and the use of an accurate ET method can improve the performance of EWDI (**Figure 11**).

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

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

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

*DOI: http://dx.doi.org/10.5772/intechopen.81047*

**4. Summary and conclusions**

GG and 7 mm/month for GG-NDVI. The overestimated ET from modified GG, which brings a small water deficit, results in a corresponding drought that is underestimated compared to USDM. Taken together, these results indicate that the water deficit derived from the complementary relationship can be used as a drought index and the use of an accurate ET method can improve the performance of EWDI (**Figure 11**).
