As a pixel is made up of the sum of its fractional surface components, we assume that the temperature of a pixel can be modeled by a linear mixture of its thermal components, that is, the sum of the LST for each of those components multiplied by their fractional portion of the pixel. To capture thermal variability within surface covers, each of the three components is broken down into sub-classes that are expected to share similar thermal properties, referred to as thermal classes going forward. These thermal classes resulted in each of the three surface covers having more than one thermal endmember, one for each thermal class. The endmembers that were used to model the expected temperature of each pixel were determined by the classes that were contained in that given pixel. To further evaluate crop-specific patterns of LST, we tested two hypotheses: 1) Crops with higher LST residuals, on average, will show declining yields over the study period, as would be indicative of stress; and 2) Crops with higher ET rates will shed more energy through latent heat flux and therefore have lower average LST values than crops with lower ET rates. To test the first hypothesis, yield data were obtained at the county level from the four counties that were part of the study area using annual agricultural statistics reports .The overall productivity for each crop type was calculated using an average of the county statistics, weighed by the relative area of that crop in each county. Because yield data are not available at the field-scale, county-level statistics were the closest proxy of productivity in the study area that could be obtained. Therefore, while the yield data and crop LST residuals are not directly relatable since the residuals only refer to a spatial subset of what is reported by the yield data,growing blackberries in containers the yield data is expected to give a general sense of which crops were faring well and which were most stressed within the study area.

To test the second hypothesis, we evaluated the correlation between average crop LST and the daily ET rate of each crop. ET rates were calculated as the product of the daily reference ET, as reported by the Belridge CIMIS station for each of the three dates, and the crop coefficient for each of the studied species, as calculated for June in the Southern San Joaquin Valley of California in a dry year . An evaluation of mean crop temperatures of pure pixels of each species by year showed that the temperature of each species relative to one another did not deviate greatly from year to year . The almonds had one of the top two coolest mean temperatures in each of the three years. The three citrus species, orange, lemons and tangerines, consistently had the three highest temperatures in each year. Cherries always had the highest average temperature of any crop except citrus. Every crop showed its highest mean temperature in 2014, likely attributable to the later flight time. The consistency suggests that thermal patterns are indicative of core biophysical properties, physiological properties, or irrigation practices that stay constant and allow for detailed analysis between species across time.Crops with higher residuals showed warmer measured temperatures than would be expected while crops with low residuals showed cooler temperatures than expected. High residuals are assumed indicative of stress. On average, crop residuals increased from 2013 to 2015 with average residuals of 0.14, 0.97, and 1.1 °C respectively. This positive year-to year trend of residuals indicates an increase in relative stress from the 2013 scene to the 2015 scene. This trend may be indicative of larger environmental and political consequences of the progressing drought with increased stress due to reduced irrigation and increased water restrictions. Alternately, the increase in relative stress could be resultant from more local scene and date-specific factors such as irrigation timing, differences in radiation load, or vapor pressure deficit.Fig 3.11 illustrates that the species-level trends in crop productivity from 2013-2015, as measured by yield per unit area, were captured well by the LST residual data. The percentage change in yield per unit area from 2013 to 2015 was compared with the average residual for each crop over all three years. We expected crops with higher LST residuals to have greater declines in yields, as would be the result of stressed vegetation.

Cherries and pistachios both showed the highest residuals and the largest declines in yields, a result that supported our hypothesis that high temperature residuals indicate unhealthy crops. Crops with the lowest residuals were hypothesized to be the least-stressed and therefore expected to have a relatively stable yield or an increase in yield. The crops with the lowest residuals did not have the largest increases in yield, however there was general agreement between the two trends overall with an inverse relationship apparent. While between-crop residual and yield data from 2013-2015 showed agreement, within-crop changes in residuals from year to year did not correlate with within-crop changes in yields. For example, both the average residual and the average yield of pistachio trees declined from 2013 to 2014, changes in stress that are opposite in implication. This suggests that this method is more suitable for comparing relative stress between crops than comparing stress of one crop over time .We calculated an expected LST for each pixel as a function of its fractional cover of soil, NPV, and GV and the expected temperature for the thermal classes contained within it. Although deviations from this relationship were presumed to indicate relative levels of plant stress, there may have been other factors that contributed to the deviations from the expected GV/LST pattern. For full interpretation of the residual results, the effect of various factors on the modeled, expected LST will be discussed: a) non-linearity of GV fraction estimation, b) shade effects, c) plant stress, d) error in fractional cover estimates, e) timing of flights, f) spatial variability in environmental variables and g) choice of thermal groups. First, expected LST is estimated using pixel fractions derived from MESMA, a linear spectral mixture model. However, in actuality spectral mixing is nonlinear due to multiple scattering of photons . This effect is expected to be prominent in agricultural orchards due to the vertical structure of the canopy, density of trees, and transmittance of radiation through the leaves . As shown in Somers et al., , tree-soil mixtures within a citrus orchard canopy as modeled by a linear mixture analysis will lead to an underestimation of GV for < 50% GV cover and an overestimation of green vegetation when GV cover is >50%.

These errors will likely be smaller with dark soils than bright soils because there are fewer photons reflected by darker objects . Nonlinearity can result in RMSE values of between 4 and 10% in citrus orchards for cover fractions . This error in GV fraction will lead the LST model to overestimate temperatures when pixels contain less than 50% GV and underestimate temperatures when the GV fraction exceeds 50% . Subsequently, pixels with low GV fraction will overestimate temperature, reducing the residual, while pixels with a high GV fraction will underestimate temperature,square pot increasing the negative residual. However, the errors due to multiple scattering in this study are expected to be low because canopy endmembers were used in the linear unmixing and these endmember already capture multiple scattering. Second, just as the linear spectral mixture does not account for photon interactions when estimating fractional cover, the linear thermal model used to model LST is also subject to nonlinear effects. Shade will cause error in soil temperature estimation that can lead to an overestimation of soil temperatures in mixed pixels. Thermal soil endmembers for the model were calculated based on the average temperature for pure soil pixels. A pure soil pixel is unlikely to be influenced by shadows, and its temperature will be a function of full solar radiation. However, as vegetation cover increases in a pixel, a larger percentage of the present soil will be shaded, up until the vegetation fraction reaches 100% and the effect cancels out . Shaded soil would be expected to be cooler than non-shaded soil, therefore the soil endmembers that are being used to model the soil temperature will be warmer than the actual shaded soil in mixed pixels. This will lead the temperatures of mixed pixels to be modeled as too warm, and the corresponding residuals to be too low. Similarly, vegetation is subject to shading effects as well as differences in structure and orientation that influence LST. Jones et al. found that leaf temperatures vary by as much as 15°C between full sun and deep shade. Therefore, factors such as the orientation of the leaves, canopy structure, and row spacing are all important controls on plant temperatures as they influence the amount of vegetation in a field that is shaded. These factors also affect the surface aerodynamic roughness, which governs how readily vegetation can transfer heat and moisture to the atmosphere. The height and structure of a crop canopy determines its aerodynamic roughness, with rougher vegetation being more tightly coupled to the atmospheric moisture deficit, which increases plant ET and decreases canopy temperature . In an aerodynamically rougher crop canopy, heat is also more readily transferred to the atmosphere by sensible heat flux. For these reasons, the remotely sensed surface temperature depends not only on the fractional cover of a pixel, but also on the composition of vegetation within a pixel. Two pixels with the same fractional cover of vegetation can have different thermal behaviors due to differences in the distribution of that vegetation, its height, and structure . The model aims to account for these influences by using canopy-level image endmembers and creating multiple thermal classes for different groups of perennial crops, so the overall error attributable to canopy shading is assumed to be small. Third, plant stress will alter the GV/LST relationship in a way that, while not introducing error, will lead LST residuals to vary by GV fraction. If a plant is stressed, its actual temperature will be warmer than expected, leading to a positive residual. While the model is designed for such a result, the side effect is that pixels with larger fractions of stressed vegetation will have higher residuals than pixels that have small fractions of stressed vegetation, as indicated by the increasing LST residuals with GV fractions in Fig 3.13C. Therefore, if plants are stressed, we expect that GV fraction and LST residual will have a positive correlation. We examined the relationship between LST residual and GV fraction for each of the studied crops in Figure 3.13 and found a trend of increasing residuals with increasing fractional cover, a result that we believe is indicative of crop stress. The relationship between residuals and GV fraction is shown by the positive linear trend lines in Figure 3.14 and the growing shaded area with fractional cover between the modeled and observed lines in Figure 3.13C. Fourth, an under or over estimation of fractional cover will propagate into LST residual errors; however, we do not believe that the distribution of errors will change the robustness of the results. Given mean LST values of 306.3 K, 321.3 K and 326.6 K for GV, NPV and soil respectively over all years and within the fields studied, the largest LST residual errors would result from a fraction error between soil and GV. MESMA has proven high fractional estimation accuracy for green vegetation. When looking at spectral separability between turfgrass, tree, paved, roof, soil, and NPV, Wetherley et al. found that mixtures of tree/soil were the second most separable pair after turfgrass/soil. Using synthetic mixtures, this study observed that soil, when mixed with tree, had a fractional accuracy of 0.976 while tree, when mixed with soil, had a fractional accuracy of 0.896. Therefore, we believe that fraction errors between GV and soil will be less than 10%. Furthermore, partitioning the landscape into soil and green vegetation is a necessary step in estimating crop stress and water use, and is therefore included in comparable models such as the VHI and WDI.