Their errors were calculated as the average of the four RMSE values respectively. The climatology of each of the above‐mentioned soil moisture data sets were generated by assembling the variable values for a particular calendar week for all years of the study periods. Once the climatology was assembled, the standardized anomalies (ψ) were computed for week w, year y, and grid location (i, j), as
(2.27)
where
(2.28)
(2.29)
(2.30)
where Π indicates the true drought status, and μ , ω . and ρ denote the unknown errors in the MWSM, the ESI based on thermal remotely sensed evapotranspiration, and NLSM. The ESI data from GET‐D were generated only for the North America domain as described in the previous section. For this study we have developed a new and novel method of using twice‐daily observations from polar sensors such as the MODIS and Visible Infrared Imaging Radiometer Suite (VIIRS) to estimate the mid‐morning rise in LST that is used to drive the energy balance estimations within the ALEXI model (Hain et al., 2017). This allows the method to be applied globally using the sensors onboard polar‐orbiting satellites rather than a global composite of all available geostationary data sets. The global ALEXI model ESI product is available at a spatial resolution of 5 km and a period of record from 2001 to 2014, reprocessed to weekly time steps and 25 km resolution for this study.
Assuming that the three kinds of errors are uncorrelated and
(2.31)
we obtain the RMSE values for MWSM ( ξ MWSM), ESI ( ξ ESI), and NLSM ( ξ NLSM) as the following (Miralles et al., 2010; Scipal et al., 2008; Stoffelen, 1998):
(2.32)
(2.33)
(2.34)
Thus, based on the TCEM, the monthly RMSEs for each of the data sets can be estimated grid by grid regionally or globally.
The procedure of generating the best Blended Drought Index (BDI_b) for each pixel in the global domain is described in Figure 2.5. Each pixel is filled by the retrieval that is estimated to have the lowest RMSE estimated from the TCEM, which ensures that all pixels across the global domain can be covered by the best available drought estimation information, instead of integrating the evaluations by building their weights. The monthly TCEM‐based RMSE for each of the six soil moisture retrievals used in this study can characterize their time series throughout the year.
The severe drought caused by the great Russian heat wave of 2010 lead to extensive wildfires and thousands of human deaths (Barriopedro et al., 2011). The 2010 western Russia drought started in May and lasted through November in response to the record‐breaking high temperature caused by a very strong La Niña event (Barriopedro et al., 2011; Kogan et al., 2013). The monthly BDI_b results effectively capture the documented droughts in western Russia in 2010 (Figure 2.6).
Figure 2.5 The procedure for constructing the BDI_b using the RMSEs estimated from the triple collocation error model implemented for each grid in each calendar month. RMSEmin is the minimum RMSE for a grid, and RMSESMOPS, RMSENLSM, and RMSEESI are the monthly RMSE values for soil moisture data sets from SMOPS, NLSM, and ESI cases, respectively.
(Source: From Yin, J., Zhan, X., Hain, C. R., Liu, J., & Anderson, M. C. (2018). A Method for Objectively Integrating Soil Moisture Satellite Observations and Model Simulations Toward a Blended Drought Index. Water Resources Research, 54(9), 6772–6791. © 2018, John Wiley & Sons.)
The 2011 drought over the Southern Great Plains of the United States seriously affected agriculture, severely impacted crop and livestock sectors, and significantly influenced food prices at the retail level (Grigg, 2014; Tadesse et al., 2015) with the State of Texas experiencing its driest year since 1895 (Hoerling et al., 2014). This severe drought started in November 2010 and lasted through October 2011, and the dry situation was mitigated across the southeast Texas Panhandle and eastern Rolling Plains in November 2011 by heavy precipitation (Tadesse et al., 2015). The BDI_b perfectly exhibits the drought episodes (Figure 2.7).
With respect to the reported drought records and the drought monitoring benchmarks including the US Drought Monitor, the Palmer Drought Severity Index and the standardized precipitation evapotranspiration index products, the BDI_b was compared with the simple average BDI and the RMSE‐weighted average BDI (Yin et al., 2018). The BDI_b performs more consistently with the drought monitoring benchmarks. With respect to the official drought records, the developed BDI_b shows the best performance on tracking drought development in terms of time evolution and spatial patterns of the 2010 Russia, 2011 United States, 2013, and New Zealand droughts, as well as other reported agricultural drought occurrences over the 2009–2014 period (Yin et al., 2018).
Figure 2.6 Monthly BDI_b for the Russian (from 40°N, 20°E to 70°N, 80°E) domain in 2010.
(Source: From Yin, J., Zhan, X., Hain, C. R., Liu, J., & Anderson, M. C. (2018). A Method for Objectively Integrating Soil Moisture Satellite Observations and Model Simulations Toward a Blended Drought Index. Water Resources Research, 54(9), 6772–6791. © 2018, John Wiley & Sons.)
2.6. DISCUSSION
In this chapter we briefly reviewed the history of studies of estimating land surface evapotranspiration at local to global scales using remote sensing approaches. The thermal remote sensing approach using the ALEXI model is categorized as probably one of the most reliable. Based on the ALEXI model the GET‐D product system using GOES‐13 and GOES‐15 observations
