Downscaling of remotely sensed soil moisture with a modified fractal interpolation method using contraction mapping and ancillary data

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Abstract

Previous work showed that remotely sensed soil moisture fields exhibit multiscaling and multifractal behavior varying with the scales of observations and hydrometeorological forcing (Remote Sens. Environ. 81 (2002) 1). Specifically, it was determined that this multiscaling behavior is consistent with the scaling of soil hydraulic properties and vegetation cover, while the multifractal behavior is associated with the temporal evolution of soil moisture fields. Here, we apply these findings by directly incorporating information on the spatial structure of soil texture and vegetation water content to the spatial interpolation of remotely sensed soil moisture data.

A downscaling model is presented which consists of a modified fractal interpolation method based on contraction mapping. This methodology is different from other fractal interpolation schemes because it generates unique fractal surfaces. It is different from other contraction mapping models because it includes spatially and temporally varying scaling functions as opposed to single-valued scaling factors. The scaling functions are linear combinations of the spatial distributions of ancillary data. The model is demonstrated by downscaling soil moisture fields from 10 to 1 km resolution using remote-sensing data from the Southern Great Plains 1997 (SGP'97) field experiment.

Introduction

In remote-sensing applications, as in physically based modeling of land-surface processes, the representation (inclusion) of subgrid-scale variability in coarse resolution data remains an elusive challenge. The problem is one of spatial interpolation, or downscaling. The challenge results from the discrepancy between the coarse spatial scales (and often temporal scales) of available data and the fine scales necessary for meaningful research and applications. In this paper, we focus specifically on the downscaling of remotely sensed soil moisture fields.

The statistical characteristics of remotely sensed soil moisture images were analyzed by Rodriguez-Iturbe et al. (1995), Hu, Islam, & Cheng (1997), and Kim & Barros (2002) among others. Using soil moisture data from the Little Washita '92 experiment, Rodriguez-Iturbe et al. (1995) concluded that the spatial variance of soil moisture fields follows a power law decay as a function of the spatial scale. They also suggested that the scaling behavior of soil moisture could be related to the scaling behavior of soil porosity. Hu et al. (1997) estimated the Hurst exponent of soil moisture fields at about 0.1 using the same data. This reflects the lack of persistence in the soil moisture images because of the succession of wetting and drying cycles in response to rainfall, and due to the subgrid-scale heterogeneity of soils. Kim & Barros (2002) showed that large-scale soil moisture images from SGP'97 (Southern Great Plains 1997 field experiment) do not exhibit scale invariance at spatial scales larger than 10 km (β-scale range) (Fig. 1). They also found that the multiscaling properties of soil moisture imagery could be explained through the scaling characteristics of land-surface attributes such as soil texture and vegetation water content, and that this scaling behavior changed with time as a function of changes in soil moisture level (multifractal scaling). The immediate implication of these results is that any downscaling model designed to improve upon the spatial resolution of remotely sensed soil moisture data must capture this multifractal and multiscaling behavior. That is, a robust downscaling algorithm should reflect the association between the spatial structure of soil moisture and relevant ancillary data. For this purpose, we introduce here a modified fractal interpolation model based on contraction mapping principles. The model includes spatially and temporally varying scaling functions derived from the spatial distributions of soil texture and vegetation indices. We examined and tested model performance using data from the Southern Great Plains experiment in the summer of 1997 (SGP'97). The model formulation is presented in Section 2. Section 3 describes the data, while results and error analysis are discussed in Section 4. The manuscript concludes in Section 5 with a brief summary and assessment of further research needs.

Section snippets

Rationale

Typical interpolation such as linear averaging, kriging and polynomial interpolation produce smoothed versions of the original data at a different (and finer) spatial resolution. Because the complex spatial structure of environmental data is often charged with physical meaning, efforts to preserve the spatial variability of original data in transferring information across scales have been many (e.g., Mandelbrot, 1982 among others). For example, Bindlish & Barros (1996) used a fractal

Description of data

The Southern Great Plains 1997 (SGP'97) Hydrology Experiment was a cooperative experiment between NASA, USDA, and several other government agencies and universities, and it was conducted between June 18 and July 17, 1997 in Oklahoma over a 10,000 km2 area (Fig. 3). The Electronically Scanned Thinned Array Radiometer (ESTAR) passive imagery corresponds to a mapping area of 40×250 km2 at a resolution of 0.8×0.8 km2. Because of weather and calibration problems, only 16 of the 29 days of the

Fractal interpolation design

To investigate the model performance, we used 15 soil moisture images from SGP'97. The application was designed to downscale soil moisture fields from 10 km (the best anticipated resolution of a future soil moisture mission) to a target resolution of 825 m (the actual resolution of the SGP'97 data). The coarse images were obtained by averaging the original data projecting an area corresponding to 12×12 pixels at 825 m resolution to 1 pixel at 10 km resolution. This process is consistent with

Summary

A downscaling model is presented which consists of a modified fractal interpolation method with contraction mapping. The model is different from other fractal interpolation schemes because it generates unique fractal surfaces. The model is different from other contraction mapping models because it includes spatially and temporally varying scaling functions as opposed to single-valued scaling factors. These scaling functions are linear combinations of the spatial distributions of ancillary data.

Acknowledgements

This work was supported in part by NASA under Contract NAG5-7547 and by a Merck Faculty Fellowship to the second author.

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Currently at Department of Civil Engineering, Kyungpook National University, Taegu, Korea.

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