**2.4 Results**

*Advanced Evapotranspiration Methods and Applications*

tion where parameter G is now defined as *Gnew*:

*Gnew* = \_\_\_\_ *ET*

*ETP* = \_\_\_\_ <sup>Δ</sup>

*ET* = \_\_\_\_\_\_ <sup>2</sup>*Gnew*

estimate ET from Eq. (10):

will be proposed.

**2.3 Data**

in Eq. (9):

framework is given in Eq. (7):

\_\_\_\_ *ET*

hypothesis through the Fu equation [9, 10]. The analytical solution of the Budyko

*ETP* <sup>−</sup> [<sup>1</sup> <sup>+</sup> (

where P is precipitation in mm and ETP is estimated using the Priestly and Taylor equation [6]. Parameter ω is constant and represents the land surface conditions, especially the vegetation cover [11]. Parameter ω is linearly correlated with the long-term average annual vegetation cover, and a model using NDVI can improve the estimation of ET (see details in [5]). Thus, Eq. (8) shows the Fu equa-

*ETP* <sup>=</sup> <sup>1</sup> <sup>+</sup> \_\_\_\_ *<sup>P</sup>*

Δ + *γ*

Having found *Gnew* from Eq. (8) and estimating ETW from Eq. (2), we can

Hereafter, this proposed model will be referred as the GG-NDVI model. This chapter used two phases to evaluate the performance of the proposed model. In phase 1, the GG-NDVI model compared with two CR models: the complementary relationship areal evapotranspiration (CRAE) model of [12] and the modified GG model of [5]. Moreover, comparisons are made between a commonly used remote sensing model and GG-NDVI model. In phase 2, a comparison of estimated ET from GG-NDVI with observed data from phase 1 will be performed to identify the weaknesses of the CR model, and appropriate corrections

ET estimation from GG-NDVI was generated using meteorological data and NDVI. Meteorological data required are temperature, wind speed, precipitation, net radiation, and elevation (pressure). Among these, net radiation (*Rn*) was calculated using the equations by [2]. This chapter proposes to use data from AmeriFlux eddy covariance sites in the United States because the US sites have wide variety of climate and physical conditions and land cover especially in dry regions. In phase 1, although we selected 75 sites of Level 2 data of AmeriFlux with fewer than 50% missing data and these data were obtained from the Oak Ridge National Laboratory's website (http://ameriflux.ornl.gov/), we used only 59 sites since only these sites have incident global radiation data required by the

*ETP* <sup>−</sup> [<sup>1</sup> <sup>+</sup> (

(*Rn* <sup>−</sup> *Gsoil*) <sup>+</sup> *<sup>γ</sup>* \_\_\_\_

Note *Gnew* in Eq. (8) is required and can be estimated using the Penman [1] given

\_\_\_\_ *P ETP*) *ω* ] 1/*ω*

*<sup>γ</sup>* <sup>+</sup> <sup>Δ</sup> *Ea* (9)

*Gnew* <sup>+</sup> <sup>1</sup> *ETW* (10)

\_\_\_\_ *P ETP*) *ω* ] 1/*ω*

(7)

(8)

*ETP* <sup>=</sup> <sup>1</sup> <sup>+</sup> \_\_\_\_ *<sup>P</sup>*

**80**

## *2.4.1 Phase 1: validation*

The CRAE model is considered as a simple, practical, and reliable model to estimate monthly ET [7]. The modified GG model had been validated by [5] that it showed better performance compared to the recently published works. Therefore, the phase 1 provides the opportunity to test both models compared to the proposed GG-NDVI model. The results of the comparison are given in **Table 1** and **Figure 2**. The GG-NDVI model showed the lowest mean RMSE across all models about 15 mm/month in dry sites and about 12 mm/month in wet sites. The results in general indicate that GG-NDVI can perform well in the dry conditions and even better


**Table 1.**

*Comparison of RMSE (mm/month) between different complementary relationship models.*

**Figure 2.**

*Comparison of RMSE (mm/month) between different complementary relationship models for 29 dry and 30 wet sites in the United States [15].*

in the wet conditions. These results also confirm that the estimation capability of ET reduces with increased aridity [5, 7, 14].

Overall, these results indicate that, among the ground-based methods, the GG-NDVI model can be used as a powerful methodology to estimate ET (see [15]).

While these findings are good within the realm of CR methods, some of the more commonly used ET estimation model now use remote sensing data. Therefore, we selected the operational Simplified Surface Energy Balance (SSEBop), which is one of the widely used remote sensing model developed by [16], and SSEBop can be easily retrieved from the USGS Geo Data Portal (http://cida.usgs.gov/gdp/). **Table 2** presents the yearly comparison of results between the SSEBop and GG-NDVI estimates. Compared with measured ET, the results indicate that the accuracy of SSEBop and GG-NDVI estimates show satisfactory R-square and RMSE values. R-square values for SSEBop and GG-NDVI are 0.65 and 0.61, respectively. The results demonstrate that the ET estimates from GG-NDVI ET at an annual time scale are reasonable.

According to **Table 2** and **Figure 3**, the mean RMSE of GG-NDVI ranged between 15 and 20, and GG-NDVI showed lower RMSE than SSEBop every year from 2000 to 2007. Although the magnitude of agreement (overestimation or underestimation) seems to vary from site to site and from season to season, **Figure 3** confirms that the occurrence of an RMSE less than 20 mm/month with GG-NDVI is more frequent than with SSEBop in both dry and wet sites. The mean RMSE across 24 dry sites for GG-NDVI and SSEBop is 19 and 22 mm/month, respectively.

Based on these results, we could conclude that GG-NDVI is a reliable approach for estimating ET showing a reasonable match with measured ET of AmeriFlux sites. However, GG-NDVI may not predict ET accurately when the vegetation cover

**83**

**Figure 3.**

mance of GG-NDVI.

*An Advanced Evapotranspiration Method and Application*

**R-square RMSE [mm/month]**

**SSEBop GG-NDVI SSEBop GG-NDVI**

 43 0.82 0.79 16 15 44 0.54 0.58 23 20 41 0.73 0.67 19 16 42 0.68 0.65 21 17 42 0.68 0.60 18 18 42 0.37 0.57 28 18 41 0.61 0.55 20 18 34 0.40 0.40 18 17 All years 44 0.65 0.61 19 18

*Comparison of monthly ET estimates between SSEBop and GG-NDVI using AmeriFlux data from 2000 to* 

changes significantly or is dense. A possible reason is that the relationship between NDVI and vegetation can be based where a Leaf Area Index (LAI) is less than 3. According to [7], a Soil-Adjusted Vegetation Index (SAVI) is recommended instead of NDVI when the LAI is less than 3. Thus, the limitations of NDVI to represent vegetation under specific conditions may be the reason for the decreased perfor-

*Histogram of RMSE (mm/month) of SSEBop and GG-NDVI for (a) 24 dry and (b) 36 wet sites.*

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

**[mm/month]**

**Year AmeriFlux mean** 

**Table 2.**

*2007.*


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

#### **Table 2.**

*Advanced Evapotranspiration Methods and Applications*

**Table 1.**

**Figure 2.**

*wet sites in the United States [15].*

ET reduces with increased aridity [5, 7, 14].

in the wet conditions. These results also confirm that the estimation capability of

*Comparison of RMSE (mm/month) between different complementary relationship models for 29 dry and 30* 

**29 dry sites 30 wet sites Min Mean Max Min Mean Max**

Modified GG 1.7 21.4 42.7 0.6 12.9 36.0 GG-NDVI 0.4 14.7 56.6 0.3 11.6 28.5 CRAE 0.5 18.9 53.9 0.8 22.3 62.3

*Comparison of RMSE (mm/month) between different complementary relationship models.*

Overall, these results indicate that, among the ground-based methods, the GG-NDVI model can be used as a powerful methodology to estimate ET (see [15]). While these findings are good within the realm of CR methods, some of the more commonly used ET estimation model now use remote sensing data. Therefore, we selected the operational Simplified Surface Energy Balance (SSEBop), which is one of the widely used remote sensing model developed by [16], and SSEBop can be easily retrieved from the USGS Geo Data Portal (http://cida.usgs.gov/gdp/). **Table 2** presents the yearly comparison of results between the SSEBop and GG-NDVI estimates. Compared with measured ET, the results indicate that the accuracy of SSEBop and GG-NDVI estimates show satisfactory R-square and RMSE values. R-square values for SSEBop and GG-NDVI are 0.65 and 0.61, respectively. The results demonstrate that the ET

estimates from GG-NDVI ET at an annual time scale are reasonable.

According to **Table 2** and **Figure 3**, the mean RMSE of GG-NDVI ranged between 15 and 20, and GG-NDVI showed lower RMSE than SSEBop every year from 2000 to 2007. Although the magnitude of agreement (overestimation or underestimation) seems to vary from site to site and from season to season, **Figure 3** confirms that the occurrence of an RMSE less than 20 mm/month with GG-NDVI is more frequent than with SSEBop in both dry and wet sites. The mean RMSE across 24 dry sites for GG-NDVI and SSEBop is 19 and 22 mm/month, respectively.

Based on these results, we could conclude that GG-NDVI is a reliable approach for estimating ET showing a reasonable match with measured ET of AmeriFlux sites. However, GG-NDVI may not predict ET accurately when the vegetation cover

**82**

*Comparison of monthly ET estimates between SSEBop and GG-NDVI using AmeriFlux data from 2000 to 2007.*

**Figure 3.** *Histogram of RMSE (mm/month) of SSEBop and GG-NDVI for (a) 24 dry and (b) 36 wet sites.*

changes significantly or is dense. A possible reason is that the relationship between NDVI and vegetation can be based where a Leaf Area Index (LAI) is less than 3. According to [7], a Soil-Adjusted Vegetation Index (SAVI) is recommended instead of NDVI when the LAI is less than 3. Thus, the limitations of NDVI to represent vegetation under specific conditions may be the reason for the decreased performance of GG-NDVI.

### *2.4.2 Phase 2: enhancement of GG-NDVI*

GG-NDVI increases the predictive power with increasing humidity similar to other CR models. One interesting finding is the RMSE of GG-NDVI increases slightly with the relative evaporation, parameter G, as shown in **Figure 4**. Considering this observation, phase 2 focused on the relationship between the performance of GG-NDVI and parameter G. Within the complementary relationship, increasing G means that climate is becoming wetter and ET is closer to ETW. When ET equals to ETW, surface has access to unlimited water as shown in **Figure 5**. However, natural surfaces in even the wettest regions may not approach complete saturation. Consequently, the magnitude of difference between ET and ETW is important in estimating ET. A possible explanation could be that the CR between ET and ETP is not symmetric. GG-NDVI has improved the performance of the Granger and Gray [4], but Eq. (10) still contains the value of two meaning of a symmetric complementary relationship as first developed by [3]. Furthermore, other studies question the use of the symmetric relationship [15, 17, 18]. Taking this into account, a correction function as a function of G is proposed as shown in **Figure 5** and Eq. (11):

$$ET = \frac{2Gnew}{Gnew \star 1} \times f(G) \times ETW \tag{11}$$

We expect the correction function to be nonlinear, similar to an exponential function, since the magnitude of the difference between ET and ETP decreases exponentially. The correction function can be calculated by Eq. (12), and we fitted 2772 data points to compute the values of *α* and *β* coefficients:

$$f(G) = \alpha \exp^{\beta G} \tag{12}$$

Regression analysis found *α* is 0.7895 and *β* is 0.9655. Hereafter, the GG model with the correction function given as Eq. (11) is called the Adjusted GG-NDVI model.

To evaluate the performance of Adjusted GG-NDVI, we compared the monthly ET estimations with SSEBop across 60 sites. **Figure 6** presents a histogram of RMSE from three models and shows a significant improvement attributed to the Adjusted GG-NDVI model. With the correction function, 38 sites have less than 15 mm/ month of RMSE, compared to 26 sites with GG-NDVI and 20 sites with SSEBop. The results demonstrate that the use of the correction function can significantly improve accuracy in estimation ET. In addition, Eq. (11) can be updated with the new definition of G as

$$ET + ETP = \mathcal{Z}f(G)ETW \tag{13}$$

**85**

**3.1 Introduction**

*Comparison of RMSE between different ET models.*

**Figure 6.**

**Figure 5.**

**Figure 4.**

*correction function, f(G).*

*An Advanced Evapotranspiration Method and Application*

*RMSE of GG-NDVI versus the relative evaporation, parameter G (ET/ETP).*

**3. Application of the evapotranspiration model in drought monitoring**

*A schematic representation of the complementary relationship between ET, ETP, and ETW with the proposed* 

Many operational drought indices focus on the effects of precipitation and temperature for drought monitoring, and the state-of-the-art drought monitoring indices were developed to address vegetation condition with advanced remote sensing technology. However, only a few are focused on the use of actual ET when a drought index is defined. The Standardized Evapotranspiration Deficit Index

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

The new formulation of the Adjusted GG-NDVI model described in Eq. (13) clearly shows that the relationship between ET and ETP is not symmetric with respect to ETW, further confirming the earlier conclusions that the idea of [3] needs to be extended and applied with appropriate corrections.

With an advanced ET model, we address the possibility of using ET as a proxy for drought monitoring through a new and reliable drought index than using potential evaporation in the next chapter.

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

**Figure 4.** *RMSE of GG-NDVI versus the relative evaporation, parameter G (ET/ETP).*

#### **Figure 5.**

*Advanced Evapotranspiration Methods and Applications*

GG-NDVI increases the predictive power with increasing humidity similar to other CR models. One interesting finding is the RMSE of GG-NDVI increases slightly with the relative evaporation, parameter G, as shown in **Figure 4**. Considering this observation, phase 2 focused on the relationship between the performance of GG-NDVI and parameter G. Within the complementary relationship, increasing G means that climate is becoming wetter and ET is closer to ETW. When ET equals to ETW, surface has access to unlimited water as shown in **Figure 5**. However, natural surfaces in even the wettest regions may not approach complete saturation. Consequently, the magnitude of difference between ET and ETW is important in estimating ET. A possible explanation could be that the CR between ET and ETP is not symmetric. GG-NDVI has improved the performance of the Granger and Gray [4], but Eq. (10) still contains the value of two meaning of a symmetric complementary relationship as first developed by [3]. Furthermore, other studies question the use of the symmetric relationship [15, 17, 18]. Taking this into account, a correction function as a function of G is proposed as shown in

We expect the correction function to be nonlinear, similar to an exponential function, since the magnitude of the difference between ET and ETP decreases exponentially. The correction function can be calculated by Eq. (12), and we fitted

*f*(*G*) = *α*exp*<sup>β</sup>*⋅*<sup>G</sup>* (12)

Regression analysis found *α* is 0.7895 and *β* is 0.9655. Hereafter, the GG model with the correction function given as Eq. (11) is called the Adjusted GG-NDVI

To evaluate the performance of Adjusted GG-NDVI, we compared the monthly ET estimations with SSEBop across 60 sites. **Figure 6** presents a histogram of RMSE from three models and shows a significant improvement attributed to the Adjusted GG-NDVI model. With the correction function, 38 sites have less than 15 mm/ month of RMSE, compared to 26 sites with GG-NDVI and 20 sites with SSEBop. The results demonstrate that the use of the correction function can significantly improve accuracy in estimation ET. In addition, Eq. (11) can be updated with the

*ET* + *ETP* = 2*f*(*G*)*ETW* (13)

The new formulation of the Adjusted GG-NDVI model described in Eq. (13) clearly shows that the relationship between ET and ETP is not symmetric with respect to ETW, further confirming the earlier conclusions that the idea of [3]

With an advanced ET model, we address the possibility of using ET as a proxy

for drought monitoring through a new and reliable drought index than using

needs to be extended and applied with appropriate corrections.

potential evaporation in the next chapter.

2772 data points to compute the values of *α* and *β* coefficients:

*Gnew* <sup>+</sup> <sup>1</sup> <sup>×</sup> *<sup>f</sup>*(*G*) <sup>×</sup> *ETW* (11)

*2.4.2 Phase 2: enhancement of GG-NDVI*

**Figure 5** and Eq. (11):

*ET* = \_\_\_\_\_\_\_ <sup>2</sup>*Gnew*

**84**

model.

new definition of G as

*A schematic representation of the complementary relationship between ET, ETP, and ETW with the proposed correction function, f(G).*

**Figure 6.** *Comparison of RMSE between different ET models.*
