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The Structure of the ALEXI Model
ALEXI is a coupled 2-source landsurface - 1-dimensional atmospheric boundary layer (ABL) model. The lower boundary conditions for the 2-source model are provided by thermal IR observations taken at 2 times during the morning hours. The ABL model then relates the rise in air temperature above the canopy and the growth of the ABL to the time-integrated influx of sensible heating from the surface.
The Two-Source Model
"Two-source" refers to the treatment of an inhomogeneous landsurface as having two sources of heat and water vapor flux: the soil, and the vegetative canopy (see Fig. 1). Each of these sources can have a different turbulent coupling with the overlying atmosphere, and fluxes from each source are assumed to add in series.
The two-source representation was a giant step forward from single-source models that were originally employed to interpret radiometric temperature signals from heterogeneous landpatches, which typically required site-specific, empirical adjustments to the surface-to-air coupling resistances (Norman et al., 1995).
Given an estimate of the fraction of vegetation cover within the scene, the directional cover fraction, fc(theta), from the viewpoint of the thermal sensor can be deduced. This fractional cover is used to deconvolve the composite radiometric temperature observed by the satellite (Trad(theta)) into its soil and canopy components (Ts and Tc, respectively).
Another advantage of the two-source representation is that it can account for off-nadir radiometric observations: a surface with partial vegetation cover will tend to appear cooler when viewed at off-nadir angles, where the typically hotter soil is more obscured by the cooler vegetation.
Coupled Two-Source-ABL Model
In ALEXI, the two-source model (TSM) is applied to radiometric temperature observations taken at two times during the morning hours, and two corresponding air temperatures are computed given an initial guess at the sensible heat curve. The atmospheric boundary layer model then grows the boundary layer up an early-morning temperature profile, provided by radiosonde, and determines the time-integrated sensible heat influx required to achieve this change in air temperature. Assuming a linear rise in sensible heating during the morning hours, revised sensible heats at times 1 and 2 (H1 and H2) are returned to the surface model, and the process continues until it converges (see Fig 2).
Importantly, unlike many landsurface models, the air temperature in the surface layer (Ta, at ~50m) is not defined as a boundary condition - Ta is diagnosed by the model and responds to feedback from both the surface fluxes and the atmospheric profile. The upper model boundary is moved up into the well-mixed atmospheric boundary layer, where conditions are more uniform at the 5km scale.
The ABL representation used in ALEXI is a 1-dimensional slab model with a very simple diagnostic entrainment parameterization (McNaughton and Spriggs, 1986).
Time-Differential vs. Absolute Inputs
Because the ALEXI model is sensitive primarily to time-changes in surface temperature, any time-independent biases in the remote surface temperature data are absorbed into the modeled air temperature, leaving the true surface-to-air temperature difference intact and the model fluxes relatively unaffected. Errors due to atmospheric corrections and surface emissivity specification are significantly reduced by using time-differential measurements rather than single, absolute measurements.
A simple experiment demonstrates this advantageous property of the ALEXI model. In the sequence of model runs shown in Fig. 3 (based on data gathered during the 1987 FIFE field experiment in Kansas), surface temperatures were artificially increased by 5o C at both observation times, simulating a time-independent bias. Results on the vertical axis were obtained using these biased temperatures, while the horizontal axis shows results obtained when unmodified temperatures are used. Most of the bias in surface temperature was absorbed in the computed air temperatures, leaving the sensible heat flux estimates essentially unaltered.
Choosing an optimal pair of thermal observation times
The two morning thermal observations used in ALEXI have been timed to optimize the correlation between the temperature change signal and the daytime integrated sensible heat flux (Anderson et al., 1997). Furthermore, these observations must also lie within the morning linear rise portion of the diurnal sensible heat curve, to satisfy our assumptions linking the instantaneous fluxes at times t1 and t2 to the time-integrated heat flux (see above).
Immediately after sunrise, the surface sensible heat is channeled into dissipating the shallow surface inversion that has developed overnight, and the equations in the simple slab ABL model do not hold. The first observation should therefore occur at least an hour after sunrise. The linear rise in sensible heat assumption constrains the second observation to at least an hour before local noon.
Numerical simulations with the Cupid soil-plant-atmosphere model (Norman and Campbell, 1983), using data collected during the July IFC of FIFE '87 (Kansas), suggest an optimal time pair satisfying these criteria is 1.5 and 5.5 hours past local sunrise. Because this choice will vary with date and latitude, a more generic form is selected for regional scale ALEXI applications: 1 hour past local sunrise and 1.5 hours before local noon.
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