The checkerboard method of Winckler, Reick and Pongratz (2017) separates the local (in-grid-box) biogeophysical temperature effects of land-cover change (LCC) from the nonlocal effects of altered atmospheric circulation, but its original demonstration was limited to a single model (MPI-ESM) with prescribed sea surface temperatures. Later work - the multi-model fully coupled LAMACLIMA (Land MAnagement for CLImate Mitigation and Adaptation) simulations and separations based on CMIP6 (the Coupled Model Intercomparison Project Phase 6) - has established that the sign and latitudinal structure of the isolated local effects are largely consistent across Earth system models and with observations. What remains open is completing the framework's domain of validity: (i) whether the original finding that local effects are independent of the areal extent of LCC survives when the ocean and sea surface temperatures are interactive, so that amplified background change can feed back onto the in-box response; (ii) how to design sampling and interpolation schemes that reduce, beyond the chessboard recommendation of Winckler et al. (2017), the interpolation errors larger than 1 K in the surroundings of mountain ranges such as the Andes or the Himalayas; and (iii) how to decompose a nonlocal response pattern into contributions from individual remote LCC source regions. These three components jointly determine when the separated local signal - the quantity compared against observations and used in mitigation assessments - can be trusted.

Background

Land-cover change (LCC), such as deforestation or afforestation, alters climate biogeophysically by changing surface albedo (reflectivity), evapotranspiration, and surface roughness, in addition to any carbon-cycle effects. In a climate model, the temperature response in a grid box where LCC occurred mixes two physically different contributions: the local effect, caused by the altered surface properties within that box, and the nonlocal effect, caused by changes in wide-ranging atmospheric (and, in coupled runs, ocean) circulation that LCC induces everywhere. Observations can only ever see the local effect plus whatever background state they share, so model-based separation is prerequisite to any like-for-like comparison with satellite or station data. Winckler, Reick and Pongratz (2017, Journal of Climate 30, 1159–1176) introduced a robust separation for global climate models: land surface properties are changed only in selected 'LCC boxes' arranged in a regular sub-sampled pattern - the 'checkerboard' approach, e.g. alternating affected and unaffected boxes at a 1/2 areal fraction, with sparser and more extensive regular sub-sampled patterns also tested - so that unaffected boxes carry the pure nonlocal signal, and the local effect is recovered by differencing against a reference simulation without LCC. In the Max Planck Institute Earth System Model (MPI-ESM), run with prescribed sea surface temperatures (SSTs), they found the isolated local effects to be largely independent of the number of LCC boxes, i.e. of the areal extent of the perturbation, and concluded this holds 'as long as sea surface temperatures are not affected'. A Dynamic Global Vegetation Model (DGVM) is a model component that simulates vegetation cover interactively; land surface schemes differ across models in albedo, evapotranspiration efficiency, roughness and subgrid heterogeneity - the representation of several land-cover types (tiles) inside one grid box, each with its own surface temperature. Since 2017 the framework has been extended: the LAMACLIMA (Land MAnagement for CLImate Mitigation and Adaptation) simulations (De Hertog et al. 2023, Earth System Dynamics 14, 629–667) applied the checkerboard in fully coupled (interactive-ocean) runs of three Earth system models - CESM (the Community Earth System Model), MPI-ESM, and EC-EARTH (the European consortium Earth system model) - for idealized afforestation, cropland expansion, wood harvest and irrigation; studies based on CMIP6 (the Coupled Model Intercomparison Project Phase 6) and its Land Use Model Intercomparison Project (LUMIP) (Liu et al. 2023; Luo et al. 2024; Mileva et al. 2025) separated local and nonlocal effects across up to eleven models using LUMIP's idealized global-deforestation experiment (deforest-glob) and regression-based variants; and Zhao et al. (2026) intercompared the existing separation methods. This later work resolved much of the original multimodel question: a consensus emerged that local effects of deforestation produce boreal cooling and tropical warming consistent with observations, while intermodel spread is dominated by the nonlocal component. Three elements of the original open agenda, however, remain without a direct answer, and they define the problem addressed here.

Problem Statement

The problem is to complete the domain of validity of the local/nonlocal separation framework for the biogeophysical effects of land-cover change (LCC), by answering three linked questions left open by Winckler, Reick and Pongratz (2017): (1) Interactive-ocean areal-extent robustness - in fully coupled simulations where sea surface temperatures and ocean circulation respond to LCC, does the isolated local (in-grid-box) effect remain independent of the areal extent of LCC, as it does under prescribed SSTs ('at least as long as sea surface temperatures are not affected'), or do ocean-feedback-amplified background changes alter the in-box local response? This requires coupled experiments that vary the areal extent or patch fraction of LCC (for example sub-sampled fractions such as 1/8 and 1/4 versus full coverage, or checkerboard versus contiguous LCC of the same total area) and quantify any dependence of the separated local signal on extent against internal variability. (2) Sampling and interpolation in high-gradient regions - Winckler et al. (2017) already recommend a chessboard-like pattern of one out of two LCC boxes, relying on interpolation from directly adjacent grid boxes, which reduces the global root-mean-square interpolation difference to 0.29 K; yet the interpolation errors remain larger than 1 K in the surroundings of mountain ranges such as the Andes or the Himalayas, and at coasts, where values on at least one side are missing, nearest-neighbor extrapolation is applied. How should the spatial sampling pattern and the interpolation of local effects from LCC boxes to non-LCC boxes be designed (denser, adaptive, or alternative patterns, or coupling to higher-resolution regional simulations) so that these residual high-gradient-region errors are further reduced below the 1 K level currently reported in these high-gradient and coastal regions, preserving the physical interpretation of the local signal, with the global root-mean-square level of 0.29 K achieved by Winckler et al. (2017) as an aspirational target rather than a requirement? (3) Source attribution of nonlocal effects - for a given nonlocal response pattern, how can the contributions of individual remote LCC source regions (specific spatial subsets of LCC) be separated and quantified, addressing the limitation noted by Winckler et al. (2017) that 'for the nonlocal effects of one concrete geographical distribution of LCC, we cannot determine the relative importance of LCC of each grid box for triggering those nonlocal effects', for example through targeted single-source or leave-one-out experiment ensembles or a source–receptor reconstruction? These questions serve the applications that motivate a robust isolation: a consistent comparison of LCC effects against observations and an assessment in an adaptation/mitigation context, with the nonlocal component traceable to its sources. Each of the three questions is a required, independently judged part of a complete answer: resolving only one or two of them does not by itself complete the framework's domain of validity.

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