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Studies have demonstrated that remotely sensed land surface temperature (LST) and solar insolation observations from the geostationary satellites could provide reliable information to derive ET and drought conditions routinely (Anderson et al., 1997, 2007, 2011). The ALEXI model was specifically designed to minimize the need for ancillary meteorological data while maintaining a physically realistic representation of land–atmosphere exchange over a wide range in vegetation cover conditions. These advantages make the ALEXI model capable of routine, long‐term mapping of ET and soil moisture stress to develop a Evaporative Stress Index (ESI).

The ALEXI model is built on the TSEB model developed by (Norman et al., 1995). It has been found that two‐source models represent advancement over single‐layer models, which typically use the radiometric temperature to be representative of the aerodynamic temperature (Gash, 1987; Hall et al., 1992; R. D. Jackson, 1982). The relationship between the surface radiometric temperature and the aerodynamic temperature can be represented more accurately when the net surface flux is partitioned between the soil and canopy components (Anderson et al., 1997). Another significant improvement with the two‐source model is that the variation of surface radiometric temperature with sensor view angle can be predicted because the individual temperatures of both the soil and canopy are extracted from the composite temperature (Anderson et al., 1997).

The ALEXI model is made up of two atmospheric components, a surface‐layer component and an atmospheric boundary layer (ABL) component (Anderson et al., 1997). Figure 2.1 shows a schematic representation of both the surface and atmospheric boundary layer component of the ALEXI model. The implementation of an atmospheric boundary layer component was motivated by documented relationships between the rise in temperature and height of the mixed layer to the time‐integrated influx of sensible heating from the surface (Culf, 1993; Diak, 1990; Diak & Whipple, 1995; Mecikalski et al., 1999; Tennekes, 1973).

Flux partitioning in the ALEXI model is guided by time changes in surface brightness temperature, where the amplitude of the diurnal surface temperature wave has been found to be a good indicator of surface flux partitioning; wetter surfaces warm more slowly and expend more energy in evaporation (Diak, 1990; Idso et al., 1975; Mecikalski et al., 1999; Wetzel et al., 1984). The use of a time‐differential temperature signal reduces the impact of errors in sensor‐based calibration errors, atmospheric corrections, and assumed surface emissivity (Anderson et al., 1997; Mecikalski et al., 1999). This represents a significant upgrade over models that use observations of absolute temperature in their computations.

The radiometric temperature of a vegetated surface is the ensemble average of the individual thermodynamic temperature of the soil (T _s), and the vegetation (T _c), weighted by their contribution to the brightness temperature:

(2.1)

where f( ϕ ) is the fraction of the sensor view angle occupied by vegetation when viewed at an angle ϕ from nadir (Norman & Becker, 1995). For a canopy with a random distribution of leaves, a spherical distribution of leaf angles, and a leaf area index F,

(2.2)

The net balance of energy at the Earth’s surface can be represented by

(2.3)

where R _n is the net radiation above the vegetated surface, and H, LE, and G are the net fluxes of sensible, latent, and ground conduction heating, respectively.

Using brightness temperature measurements at times t ₁ and t ₂, and initial estimates of near‐surface temperature, the surface component of the ALEXI model yields instantaneous sensible heat flux estimates, H ₁ and H ₂ (Anderson et al., 1997). Assuming a linear rise in sensible heat during the morning hours, which has been found to be valid when advection is negligible, a time‐integrated heat flux can be computed by

Figure 2.1 (a) A schematic description of the surface‐layer component of the ALEXI model. (b) The surface‐layer model component is applied at times t₁ and t₂ during the morning hours, returning instantaneous sensible heat flux estimates. The time‐integrated sensible heat flux during this interval serves to heat and grow the atmospheric boundary layer.

(Source: From Mecikalski, J. M., G. R. Diak, M. C. Anderson & J. M. Norman (1999). Estimating fluxes on continental scales using remotely sensed data in an atmosphere–land exchange model. Journal of Applied Meteorology, 38, 1352–1369. © American Meteorological Society.)

(2.4)

The ABL component of ALEXI is a simple slab model which describes the dynamics of the atmospheric boundary layer and is used as a closure technique to evaluate the morning evolution of air temperature, Ta, in the surface layer. It is assumed that all the air within the mixed layer is at a uniform potential temperature, and this value is related to the surface air temperature by

(2.5)

where p is the atmospheric pressure (in kPa) at the surface and R/c _p = 0.286 (Anderson et al., 1997). Tennekes (1973) showed that the height of the convective boundary layer at any time is uniquely defined by the current surface air temperature and a morning temperature sounding. McNaughton and Spriggs (1986) presented a simplified conservation equation describing the growth of a convective boundary layer over time, assuming no subsidence and horizontal advection:

(2.6)

where θ _m,1 is the potential temperature within the mixed layer and θ _s(z) is the potential temperature profile above the mixed layer at time t ₁. The time‐integrated sensible heat flux from the ABL component of the ALEXI model is computed given a value of θ _m,2. Because differential surface temperature measurements are more reliable than absolute temperature measurements, in practice z ₁ is fixed at some small value (~50 m), and the change in modeled θ _m is allowed to govern the growth of the boundary layer based on the lapse rate profile above the mixed layer height, z ₁ (Anderson et al., 1997). The sensible heat flux estimates from both the surface and ABL components of the ALEXI model are iterated until the time‐integrated sensible heat flux estimates from both components converge (Anderson et al., 1997). Based on the computation of sensible heat flux for the soil (H _S) and the canopy (H _C), the canopy transpiration (LE _C), the ground heat flux (G), and net radiation (R _n), the value for direct soil evaporation (LE _S) is solved as a residual to the surface energy budget calculation. Under drier conditions this can result in a direct soil evaporation of less than zero, which in unlikely during the midday period. This condition implies that the earlier assumption of the canopy transpiring at its potential rate is invalid, and in this case the canopy transpiration term is scaled back until the direct soil evaporation term is zero (Anderson et al., 1997). A number of primary data sources are needed for regional implementation of the ALEXI model and these data sources are summarized in Table 2.1.

Table 2.1 Major inputs data for GET‐D system

Data source	Specifications	Resolution	Format	Example file names	Size (MB)
GOES East and West	Band 02	4 km	McIDAS	1350954623.goes13.2014.001.061520.BAND_02	~25
GOES East and West	Band 04	4 km	McIDAS	1350954623.goes13.2014.001.061520.BAND_04	~25
GSIP	L2 product	4 km	NetCDF	gsipL2_goes13_GENHEM_2014198_1145.nc.gz gsipL2_goes15_GWNHEM_2014198_1400.nc.gz	~20–30
VIIRS	Global NDVI and EVI	375 m	HDF5	GVF‐ASEVI‐P2_s20120726_e20120801_h00v01.h5	~800
IMS	Daily Northern Hemisphere Snow and Ice Analysis	24 km	ASCII	ims2014017_24km.asc	~1