ALEXI Energy Partitioning Algorithm

Solving the system and component energy budgets

So far, we have only discussed the estimation of the system (soil+canopy) sensible heat flux (H). The ALEXI model estimates all major components of the system energy budget:

RN = H + LE + G,

the canopy energy budget:

RNc = Hc + LEc,

and the soil energy budget:

RNs = Hs + LEs + G,

where RN is the net radiation, LE is the latent heat flux, G is the soil heat flux, and the subscripts c and s refer to the canopy and soil components of the system, respectively, and

H = Hs + Hc
LE = LEs + LEc
RN = RNs + RNc.

The methods for estimating these component fluxes are described briefly below; see Anderson et al, (1997) and Mecikalski et al. (1999) for greater detail.

Net Radiation

The system net radiation is given by

RN = (LWdn - LWup) + (SWdn + SWup)

where LW and SW are long- and shortwave radiation fluxes, respectively, in the downwelling (dn) and upwelling (up) directions.

In a regional-scale application, downwelling short and longwave fluxes are derived from visible, near-infrared and thermal imagery acquired with a geostationary satellite. Upwelling longwave emission depends on the soil and canopy temperatures diagnosed by the two-source model, and the component emissivities. Upwelling shortwave depends on surface albedo. In ALEXI, surface emissivity and albedo are tied to landcover class and fractional vegetation cover.

Mecikalski et al (1999) describe the partitioning of RN into the canopy divergence (RNc) and the net radiation above the soil surface (RNs).

Soil Heat Flux

Choudhury et al. (1987) provide a simple parameterization of the soil heat flux as a fraction of the net radiation at the soil surface:

G = 0.3 RNs

While this approximation is fairly crude, and does not recognize the phase difference between the diurnal RN and G curves, it yields an adequate estimate given that G is typically small in comparison with the other energy budget components. The approximation improves when extrapolated to a daytime total basis (see X).

Latent Heat Flux

In the two-source model, as described by Norman et al (1995), a first guess at the canopy evapotranspiration is obtained using the Priestley-Taylor approximation applied to the divergence of net radiation within the green portion of the canopy:

LEc = 1.3 fg RNc (s/s+gamma)

where fg is the greenness fraction, s is the slope of the saturation vapor pressure vs. temperature curve, and gamma is the psychometric constant. This is a reasonable approximation of the canopy ET provided the vegetation is not stressed and the canopy is transpiring at it's potential rate.

Given a measurement of the composite surface radiometric temperature, estimates of G, RNc and LEc, and an initial estimate of H (refined through iteration), all components of the energy budget can be solved for, with LEs as the final residual.

This residual is used as a check on the assumption that the modified Priestley-Taylor is a good representation of LEc, ie that the canopy is not stressed. Stress will cause the canopy temperature, and therefore the sensible heating flux, to increase. Before long, LEs will go negative in attempts to balance the soil energy budget. Under normal atmospheric conditions, we do not expect condensation on the soil to occur midday, so this is taken as a signal that the Priestley-Taylor equation is overestimating canopy ET, and LEc is throttled back.

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