Spectral Mixture Analysis as a Unified Framework for the Remote Sensing of Evapotranspiration

This study illustrates a unified, physically-based framework for mapping landscape parameters of evapotranspiration (ET) using spectral mixture analysis (SMA). The framework integrates two widely used approaches by relating radiometric surface temperature to subpixel fractions of substrate (S), vegetation (V), and dark (D) spectral endmembers (EMs). Spatial and temporal variations in these spectral endmember fractions reflect process-driven variations in soil moisture, vegetation phenology, and illumination. Using all available Landsat 8 scenes from the peak growing season in the agriculturally diverse Sacramento Valley of northern California, we characterize the spatiotemporal relationships between each of the S, V, D land cover fractions and apparent brightness temperature (T) using bivariate distributions in the ET parameter spaces. The dark fraction scales inversely with shortwave broadband albedo (ρ < −0.98), and show a multilinear relationship to T. Substrate fraction estimates show a consistent (ρ ≈ 0.7 to 0.9) linear relationship to T. The vegetation fraction showed the expected triangular relationship to T. However, the bivariate distribution of V and T shows more distinct clustering than the distributions of Normalized Difference Vegetation Index (NDVI)-based proxies and T. Following the Triangle Method, the V fraction is used with T to compute the spatial maps of the ET fraction (EF; the ratio of the actual total ET to the net radiation) and moisture availability (Mo; the ratio of the actual soil surface evaporation to potential ET at the soil surface). EF and Mo estimates derived from the V fraction distinguish among rice growth stages, and between rice and non-rice agriculture, more clearly than those derived from transformed NDVI proxies. Met station-based reference ET & soil temperatures also track vegetation fraction-based estimates of EF & Mo more closely than do NDVI-based estimates of EF & Mo. The proposed approach using S, V, D land cover fractions in conjunction with T (SVD+T) provides a physically-based conceptual framework that unifies two widely-used approaches by simultaneously mapping the effects of albedo and vegetation abundance on the surface temperature field. The additional information provided by the third (Substrate) fraction suggests a potential avenue for ET model improvement by providing an explicit observational constraint on the exposed soil fraction and its moisture-modulated brightness. The structures of the T, EF & Mo vs SVD feature spaces are complementary and that can be interpreted in the context of physical variables that scale linearly and that can be represented directly in process models. Using the structure of the feature spaces to represent the spatiotemporal trajectory of crop phenology is possible in agricultural settings, because variations in the timing of planting and irrigation result in continuous trajectories in the physical parameter spaces that are represented by the feature spaces. The linear scaling properties of the SMA fraction estimates from meter to kilometer scales also facilitate the vicarious validation of ET estimates using multiple resolutions of imagery.


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Earth's lithosphere, atmosphere, and biosphere are unified by the movement of water.

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Southern Oscillation [5], as well as direct relationships between soil moisture and temperature [6].

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In addition to its importance for understanding fundamental Earth system processes, ET also 37 has clear practical applications. ET has long been recognized as practical indicator of plant water 38 stress [7][8][9]. In agricultural settings, near real-time ET monitoring can improve predictions of 39 irrigation need and regulatory estimates of water use. In natural environments, ET can inform 40 studies of ecosystem health and biodiversity. For recent reviews of the potential applications of ET 41 monitoring, as well as outstanding unresolved questions, see [10] and [11].

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(α). The relationships among these three quantities can be understood in the context of their 55 bivariate distributions. The distribution of V vs T gives information about plant-based 56 evapotranspirative cooling and is fundamental to the physical basis of many popular ET models 57 (e.g. [13][14][15][16]). The distribution of α vs T has also been long recognized [17], and provides 58 information about soil moisture ([18,19]) and roughness [20]. α vs T has been incorporated into a 59 popular ET model by [21]. Recent work by [22] has developed a model based on fusion of both the V 60 vs T and α vs T relationships, with encouraging results.

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For the vast majority of current ET estimation algorithms and associated 62 Surface-Vegetation-Atmosphere Transfer (SVAT) models, vegetation abundance is computed with a 63 spectral index. The specific index used varies from model to model. Many models (e.g. [23,24]) rely 64 directly upon the Normalized Difference Vegetation Index (NDVI). However, all spectral indices use 65 only a small subset of the information present in multispectral imagery. NDVI in particular has a 66 number of known flaws, including scaling nonlinearities ([2,25,26]), sensitivity to both soil 67 background and atmospheric effects ([27,28]), and saturation effects over a wide range of vegetation 68 fractions [28]. In response to these problems, NDVI is often normalized using linear (e.g. [29]) or 69 quadratic (e.g. [30][31][32]) transformations. Each spectral index, transformed or untransformed, gives 70 different estimates of vegetation abundance, which then result in differences in estimated ET. If 71 these metrics could be improved and standardized, ET models could be made more accurate and 72 cross-model standardization could be more effective.

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Spectral Mixture Analysis (SMA; [33][34][35]) is a physically-based method that uses the full 74 reflectance spectrum, rather than a small subset of bands, to estimate V. SMA-based estimates of V 75 mitigate many of the problems with spectral indices. SMA explicitly accounts for illumination effects 76 as well the reflectance of the soil & NPV background, substantially improving estimates at low 77 vegetation abundance [27]. Because SMA relies on area-weighted linear mixing of radiance from 78 materials within the pixel, V estimates are relatively insensitive to sensor spatial resolution and have 79 been shown to scale linearly from 2 m to 30 m ([26,28]) as well as from meter-scale field 80 measurements [25]. This simple linear scaling could be a key advantage for ET studies, given the 81 widely recognized scaling nonlinearities of ET estimates (e.g. [36][37][38][39][40][41]). SMA fraction estimates are 82 sensitive to the spectra of the endmember (EM) materials, but previous work has characterized the 83 global multispectral mixing space and proposed generic EMs which well-describe the majority of the 84 Earth's land environments and are calibrated across sensors ([28,42,43]).

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In addition to providing enhanced estimates of V, SMA simultaneously provides accurate 86 estimates of two additional physically meaningful quantities: 1) the areal abundances of soil, rock 87 and NPV Substrates (S), and 2) Dark features (D) such as shadow, water, and low-albedo surfaces.

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These estimates are made at subpixel resolution and with trivial computational cost. D fraction 89 estimates represent the effects of albedo (α), illumination geometry, atmospheric opacity, and soil 90 moisture content, thereby modulating the overall amplitude of the reflectance signal. S fraction 91 estimates provide information about the compositional properties of the soil and NPV substrate 92 background at each pixel. To our knowledge, SMA has not yet been used in ET estimation 93 algorithms. This could represent a missed opportunity. When compared against coincident T 94 measurements, SVD fractions can provide a unifying framework which incorporates two major 95 existing approaches to ET estimation (V vs T and α vs T), and also includes a novel, potentially 96 useful supplement (S vs T).

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This article is a non-peer reviewed preprint published at EarthArXiv The primary purpose of this analysis is to explore the SVD model as an innovative conceptual 98 framework for ET estimation. We illustrate the relationships between each fraction and T, as well as

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Despite their different sets of assumptions and governing equations, all these models generally 122 require vegetation abundance estimates, and rely on spectral indices to provide them.

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The above summary of models is not intended to be comprehensive. Rather, it is designed to

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SMA assumes area-weighted linear mixing of upwelling radiance within the IFOV of each 154 multispectral pixel. While not always a valid assumption, linear mixing has been shown by [52][53][54] 155 to have solid theoretical and observational basis for practical application. SMA treats each pixel 156 spectrum as a linear combination of pure EM spectra and inverts a set of linear mixing equations to 157 accurately estimate the subpixel abundance of each EM material.

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Theoretically, as many materials could be mapped as wavelengths measured by the 159 multispectral imager (4 to 12). In practice, however, 6-band Landsat spectra have been shown to

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Optical and thermal image data were calibrated to exoatmospheric reflectance and apparent 182 brightness temperature, respectively, using the standard calibration procedures described in the

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NDVI* better fills the physically meaningful 0 to 1 range expected of fractional vegetation cover, but 256 still has notable overestimation and roll-off effects. NDVI* 2 is even more linear than NDVI*, but the

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Bivariate distributions of NDVI*, NDVI* 2 , and V versus T* are shown in the right panel of

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The left and center columns of Figure 5 show the bivariate distribution of D vs T* and α vs T* 316 for each image, respectively. The two distributions have obvious visual similarity and give similar 317 information. Clearly, the D fraction well represents broadband shortwave albedo in these images.

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This article is a non-peer reviewed preprint published at EarthArXiv

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Variations in V fraction and T images are manifest in the EF and Mo images (center and bottom,

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The overestimation in the rice is even more severe for NDVI* 2 , although the underestimation in the

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SMA also has the advantage of being grounded in a straightforward physical basis and accounts for 417 the effects of soil reflectance, moisture content and shadow explicitly. In general, it is reasonable to 418 expect the relationship between the true subpixel areal abundance of land cover and the estimate 419 given by SMA to be more accurate, and scale more linearly, than the estimate given by a spectral

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The SVD approach provides users with additional information about potential thermal EMs by

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Clustering in the feature space is also the foundation for discrete image classification. By

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The focus of this analysis on a single study area may beg the question of generality of results.

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While the persistence of the feature space structure over several years is encouraging, it does not 478 guarantee that the method will perform as well in other environments. However, the global analysis