Abstract

Upscaling ecological information to larger scales in space and downscaling remote sensing observations or model simulations to finer scales remain grand challenges in Earth system science. Downscaling often involves inferring subgrid information from coarse-scale data, and such ill-posed problems are classically addressed using regularization. Here, we apply two-dimensional Tikhonov Regularization (2DTR) to simulate subgrid surface patterns for ecological applications. Specifically, we test the ability of 2DTR to simulate the spatial statistics of high-resolution (4 m) remote sensing observations of the normalized difference vegetation index (NDVI) in a tundra landscape. We find that the 2DTR approach as applied here can capture the major mode of spatial variability of the high-resolution information, but not multiple modes of spatial variability, and that the Lagrange multiplier (γ) used to impose the condition of smoothness across space is related to the range of the experimental semivariogram. We used observed and 2DTR-simulated maps of NDVI to estimate landscape-level leaf area index (LAI) and gross primary productivity (GPP). NDVI maps simulated using a γ value that approximates the range of observed NDVI result in a landscape-level GPP estimate that differs by ca 2% from those created using observed NDVI. Following findings that GPP per unit LAI is lower near vegetation patch edges, we simulated vegetation patch edges using multiple approaches and found that simulated GPP declined by up to 12% as a result. 2DTR can generate random landscapes rapidly and can be applied to disaggregate ecological information and compare of spatial observations against simulated landscapes.

Highlights

  • Upscaling estimates of ecosystem function from leaf to region to globe and downscaling remote sensing observations and general circulation model predictions to smaller scales remain basic research challenges across a wide range of Earth science disciplines

  • We explore the ability of 2DTR to downscale coarse-scale remote sensing data for the purpose of simulating fine-scale surface patterning, and provide an example by simulating landscape-level patterns of the normalized difference vegetation index (NDVI), leaf area index (LAI), and gross primary productivity (GPP) in tundra

  • The relationship approximates a generalized logistic function, and we fit such a function using nonlinear least squares to estimate the value of γ, approximately 100.85, that corresponds to the range of observed NDVI, 47.7 m

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Summary

Introduction

Upscaling estimates of ecosystem function from leaf to region to globe and downscaling remote sensing observations and general circulation model predictions to smaller scales remain basic research challenges across a wide range of Earth science disciplines. Scaling is a procedure that takes information at one scale in time and/or space and uses it to derive processes at another [1]. Following this definition, scaling inherently involves a transfer of information.

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