Multi-scalar analysis of geospatial agricultural data for sustainability

Concerns for environmental sustainability are leading to a growing interest understanding geospatial data. At the same time, the availability of high-resolution imagery from satellites and unmanned air systems is increasing rapidly. However, the processing techniques that are available within geographic information systems are not yet adapted to big data challenges and opportunities. We propose a logarithmically scaling alternative to widely used window aggregation techniques, and integrate it with the localized computation of regression lines and correlations. Our approach, furthermore, enables a multi-scalar analysis at no additional computational cost. We demonstrate the potential for the proposed technique in the context of agriculturally relevant relationships, in particular between yield and vegetation indexes, which have the goal of reducing fertilizer use through a targeted application of nitrogen during the season. To demonstrate scaling and general usefulness of our techniques we furthermore examine relationships between different bands of remotely sensed data.

I. Introduction

For decades, the 30m resolution of Landsat satellites drove the development of algorithms for remotely sensed data, and the techniques that are available in geographic information systems, such as GRASS GIS [14], reflect the performance requirements for such data. In agricultural applications, the number of data points that cover one agricultural field that is imaged at 30m resolution is in the hundreds of data points, which does not require special optimizations and is well within reach of statistical data analysis techniques. Window-based aggregation in GRASS iterates through each window [17], and thereby has a linear scaling in the number of data points within each window. While window-based results may then be further combined at higher levels, such approaches do not allow applying the same basic statistical operators over arbitrarily many length scales. Modern satellites like RapidEye, with a typical 5m-resolution, add 1–2 orders of magnitude to the data volume, and for unmanned air systems the pixel size can be as small as a few centimeters, resulting in data quantities that are far beyond traditional aggregation and statistical evaluation techniques, and squarely place processing tasks into the big data realm. Getting the most information from this type of data requires a fundamental rethinking of techniques involving both performance and objectives. In this setting, it may not be clear initially, at what length scales the most relevant dependencies are to be expected, and the results should not depend on any assumptions that are used initially. I.e., there is not initial window-size that can be expected to appropriate for processing. At centimeter resolutions there may be four orders of magnitude to bridge to even recover Landsat resolution, and the information that is available at the highest resolution may not directly reflect variations due to parameters like soil type or fertilization but rather actual plant geometry. In fact, soil type and fertilization themselves are expected to vary at different length scales. If an initial window size was picked small enough to have acceptable performance for the conventional averaging algorithm, that window size may not even cover a plant fully. Our approach resembles the aggregation in the fast Fourier transform algorithm, where the scope of aggregation doubles in each step, and an overall logarithmic performance emerges,