Characterizing the multi–scale spatial structure of remotely sensed evapotranspiration with information theory

Abstract

Abstract.A more thorough understanding of the multi-scale spatial structure of land surface heterogeneity will enhance understanding of the relationships and feedbacks between land surface conditions, mass and energy exchanges between the surface and the atmosphere, and regional meteorological and climatological conditions. The objectives of this study were to (1) quantify which spatial scales are dominant in determining the evapotranspiration flux between the surface and the atmosphere and (2) to quantify how different spatial scales of atmospheric and surface processes interact for different stages of the phenological cycle. We used the ALEXI/DisALEXI model for three days (DOY 181, 229 and 245) in 2002 over the Ft. Peck Ameriflux site to estimate the latent heat flux from Landsat, MODIS and GOES satellites. We then applied a multiresolution information theory methodology to quantify these interactions across different spatial scales and compared the dynamics across the different sensors and different periods. We note several important results: (1) spatial scaling characteristics vary with day, but are usually consistent for a given sensor, but (2) different sensors give different scalings, and (3) the different sensors exhibit different scaling relationships with driving variables such as fractional vegetation and near surface soil moisture. In addition, we note that while the dominant length scale of the vegetation index remains relatively constant across the dates, the contribution of the vegetation index to the derived latent heat flux varies with time. We also note that length scales determined from MODIS are consistently larger than those determined from Landsat, even at scales that should be detectable by MODIS. This may imply an inability of the MODIS sensor to accurately determine the fine scale spaCorrespondence to: N. A. Brunsell (brunsell@ku.edu) tial structure of the land surface. These results aid in identifying the dominant cross-scale nature of local to regional biosphere-atmosphere interactions.

Quantification of land‐surface heterogeneity via entropy spectrum method

“…Due to the nature of the method, one needs physical values that are ordered on a grid. That means that the methods works best when applied to high-resolution measurements (e.g., MODIS data, [Brunsell and Anderson, 2011] or model simulations, like large eddy simulations).…”

“…Anisotropy refers to the directional dependence of heterogeneity and may play an important role in the atmospheric responses. The decomposition method used in this study retains the anisotropic features of the land surface data, and an explicit treatment of anisotropy is not necessary see [Brunsell and Anderson, 2011]. In this study, our focus is on the information aspect of heterogeneity.…”

Assessing Regional Climate and Local Landcover Impacts on Vegetation with Remote Sensing

“…Information theory has been previously used to examine land-atmosphere interactions [25][26][27]. Entropy is a measure of the statistical uncertainty of the random field X as described by the probability density function (pdf).…”

“…Previous studies such as Brunsell and Gillies [44] and Brunsell and Young [25] have applied wavelet analysis to assess the relationship between water and energy cycling and vegetation in terms of spatial variability and distribution. In this study, we followed the method of [27] and examined NDVI and PPT to ascertain temporal variabilities of the land surface and precipitation. We quantified the variability of precipitation and landcover as a function of temporal scale, and PPT and NDVI signals were compared at each level of decomposition.…”

“…Our proposed methodology, multiscale information theory metrics, which have been developed by Brunsell and Young [25], Brunsell [26] and Brunsell and Anderson [27], is a set of metrics to assess the spatial and temporal variability of hydrological processes and is able to be applied to land-surface hydrology and ecology [26]. As discussed by Stoy et al [28] this method can quantify the appropriate scales for observations and modeling studies.…”