## 5 Reformulating SVAT models to accommodate new data sources  
[PERSON] [49] described the history of evaporation research over the past 30 years as a series of loosely-linked conceptual and technical advances leading to the present state of the science. Carbon flux studies parallel that history [16, 37]. [PERSON] and [PERSON] [37] pointed to the historical connection between SVAT parameters and what could be measured at the time the models were developed. Historically, SVAT and SEB models have taken a \"bottom-up\" approach, attempting to scale leaf level measurements to whole canopies and stands of plants [16]. For example, the Penman-Monteith \begin{table}
\begin{tabular}{l l c c c c c} \hline
**Tower Site** & **Vegetation** & **EVI** & **NDVI** & **T\({}_{\text{a}}\)** & **P** & **EVI + T\({}_{\text{a}}\)** & **EVI + P** \\ \hline Riparian & & & & & & & \\ San Pedro 1 & Mesquite & 0.87 & 0.83 & 0.77 & - & 0.88 & - \\ San Pedro 2 & Mesquite & 0.86 & 0.82 & 0.77 & - & 0.90 & - \\ San Pedro 3 & Sacaton & 0.94 & 0.82 & 0.77 & - & 0.97 & - \\ Rio Grande 1 & Saltcedar & 0.83 & 0.68 & 0.84 & - & 0.88 & - \\ Rio Grande 2 & Saltcedar & 0.84 & 0.52 & 0.82 & - & 0.89 & - \\ Rio Grande 3 & Cottonwood & 0.84 & 0.74 & 0.86 & - & 0.90 & - \\ Rio Grande 4 & Cottonwood & 0.82 & 0.77 & 0.89 & - & 0.89 & - \\ Colorado 1 & Saltcedar & 0.83 & 0.64 & 0.92 & - & 0.92 & - \\ Colorado 2 & Arrowweed & 0.64 & 0.50 & 0.76 & - & 0.79 & - \\ Upland & & & & & & & \\ Grassland & Grama & 0.82 & 0.80 & - & 0.66 & - & 0.84 \\ Shrubland & Mixed & 0.87 & 0.78 & - & 0.72 & - & 0.90 \\ Mean & & 0.83 & 0.72 & 0.82 & 0.69 & 0.89 & 0.87 \\ \hline \end{tabular}
\end{table} 
Table 1: Correlation coefficients between evapotranspiration measured at moisture flux towers and MODIS vegetation indices and relevant meteorological data in the southwestern U.S. T\({}_{\text{a}}\) is maximum daily temperature and P is precipitation. Correlation coefficients for combined variables are for the multiple linear regression equation of best fit for combined riparian (EVI + T\({}_{\text{a}}\)) or upland (EVI + P) sites. From data in [31, 34, 76]. equation [11] for ET treats the canopy as a series of resistances, starting with individual stomata at the leaf level then proceeding to the canopy level, where the atmospheric resistance term is applied. Figure 5: Stomatal resistance of cottonwood, willow and saltcedar plants under stressed and unstressed conditions. Clusters of plants (6 per species) were grown outdoors in Tucson, Arizona. Sap flow sensors measured plant transpiration over an eight day period in summer, and micrometeorological data were used to model the diurnal course stomatal resistance for each species based on potential ET. Plants were then subjected to drought or salt stress (3 per treatment) for the final 3 days of the measurement period. Stomatal resistance was calculated based on sap flow measurements at three time points in the mid-day period, and plotted against unstressed stomatal resistance calculated from meteorological data. Plants are combined across replicates and stress treatments in the plot. From data in [36]. Carbon flux models usually start at the leaf level as well, sometimes assuming Michaelis-Menton kinetics for carbon fixation as functions of light intensity and carbon dioxide concentration as starting points, then using radiation transfer models to scale light intensity and photosynthesis over the layers of leaves in the canopy [16]. These models were developed when leaf-level measurements of photosynthesis and stomatal conductance were becoming feasible. The bottom up approach has encountered some problems in remote sensing applications, however. First is the complexity of actual plant canopies, especially in mixed stands of plants, compared to what can be determined from remote sensing measurements. Second is the problem of equifinality, the tendency of models with different levels of complexity and different starting assumptions to produce similar results [82].