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(1996). Courault et al. (2005) reviewed four categories of ET estimation approaches developed from local to regional spatial scales primarily for water management and agricultural applications: (a) direct empirical relationship, (b) energy budget residual, (c) deterministic complex model, and (d) vegetation index approaches.

      Vinukollu et al. (2011) have evaluated three process‐based approaches for global estimation of ET for climate research: Surface Energy Balance System (SEBS), Penman–Monteith algorithm (PM), and the Priestley–Taylor algorithm (PT). Using only remote‐sensing‐based data for inputs and forcing, they generated ET data products from each of these three approaches for the years 2003–2006 and compared them with measurements in situ over various watersheds around the world. The SEBS type model they used is the single source energy balance model evaluated in Su et al. (2005). In their evaluation the PM type algorithm they used is that by Mu et al. (2007) to generate a time series of global ET data product based on Moderate‐Resolution Imaging Spectroradiometer (MODIS) observations. The PT type algorithm they evaluated is that by Fisher et al. (2008). With these data products, Vinukollu et al. (2011)showed that the average of the three model ET estimates for 2003–2006 well represented the seasonal cycle over the continents, and the ET suppression during major droughts in Europe, Australia, and the Amazon were identified.

      Among the various satellite‐based ET estimation techniques, the Surface Energy Balance Algorithms for Land (SEBAL; Bastiaanssen, Menenti, et al., 1998; Bastiaanssen, Pelgrum, et al., 1998)_and its enhancement, Mapping EvapoTranspiration at high Resolution with Internalized Calibration (METRIC; Allen et al., 2007, 2011), have been widely adopted and routinely used to monitor irrigation, determine drought, and estimate consumptive use in agricultural areas around the world. The SEBAL and METRIC techniques are widely used with Landsat data to estimate ET at the field level in agricultural areas. Both these techniques determine ET as a residual of sensible fluxes in net radiation. The novelty of these techniques is that several key parameters that drive energy fluxes, such as the gradient between surface temperature and air temperature and surface resistance to sensible and latent heat transfer, are determined directly from the imagery itself while compensating for uncertainties in measurements, such as satellite estimates of surface temperature, the determination of surface albedo, and ground‐based measurements of windspeed fields. These two approaches have been widely validated and routinely used with Landsat data, which has 30 m spatial resolution over agricultural areas where the assumptions of micrometeorology incorporated in to the SEBAL and METRIC techniques are valid. Nevertheless, extending these techniques to coarse resolution satellite imagery at continental scales is yet to be demonstrated, as the land cover types are seldom homogeneous within a pixel and parametrization schemes for such heterogeneous environments, where both the surface types and the atmosphere vary substantially within a single satellite image that extends thousands of kilometers, are difficult to establish.

      Using ground flux tower measurements of ET from irrigated cropland in Oregon, Tang et al. (2009) found that a variation of the MODIS ET product algorithm, based on near real time MODIS and NOAA GOES data products of land cover, vegetation indices, land surface temperature, albedo, and surface radiation budget, may estimate instantaneous and daily ET with biases less than 10% and 15%, respectively. For seasonal ET, they found the MODIS‐based ET could underestimate while the METRIC‐based algorithm (Allen et al., 2007) may overestimate.

      2.3.1. The ALEXI Model

      Studies have demonstrated that remotely sensed land surface temperature (LST) and solar insolation observations from the geostationary satellites could provide reliable information to derive ET and drought conditions routinely (Anderson et al., 1997, 2007, 2011). The ALEXI model was specifically designed to minimize the need for ancillary meteorological data while maintaining a physically realistic representation of land–atmosphere exchange over a wide range in vegetation cover conditions. These advantages make the ALEXI model capable of routine, long‐term mapping of ET and soil moisture stress to develop a Evaporative Stress Index (ESI).

      The ALEXI model is built on the TSEB model developed by (Norman et al., 1995). It has been found that two‐source models represent advancement over single‐layer models, which typically use the radiometric temperature to be representative of the aerodynamic temperature (Gash, 1987; Hall et al., 1992; R. D. Jackson, 1982). The relationship between the surface radiometric temperature and the aerodynamic temperature can be represented more accurately when the net surface flux is partitioned between the soil and canopy components (Anderson et al., 1997). Another significant improvement with the two‐source model is that the variation of surface radiometric temperature with sensor view angle can be predicted because the individual temperatures of both the soil and canopy are extracted from the composite temperature (Anderson et al., 1997).

      Flux partitioning in the ALEXI model is guided by time changes in surface brightness temperature, where the amplitude of the diurnal surface temperature wave has been found to be a good indicator of surface flux partitioning; wetter surfaces warm more slowly and expend more energy in evaporation (Diak, 1990; Idso et al., 1975; Mecikalski et al., 1999; Wetzel et al., 1984). The use of a time‐differential temperature signal reduces the impact of errors in sensor‐based calibration errors, atmospheric corrections, and assumed surface emissivity (Anderson et al., 1997; Mecikalski et al., 1999). This represents a significant upgrade over models that use observations of absolute temperature in their computations.

      The radiometric temperature of a vegetated surface is the ensemble average of the individual thermodynamic temperature of the soil (T s), and the vegetation (T c), weighted by their contribution to the brightness temperature:

      (2.1)equation

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