Systematic Correlation Matrix Evaluation (SCoMaE) – a bottom–up, science-led approach to identifying indicators

Abstract

Abstract. This study introduces the Systematic Correlation Matrix Evaluation (SCoMaE) method, a bottom–up approach which combines expert judgment and statistical information to systematically select transparent, nonredundant indicators for a comprehensive assessment of the state of the Earth system. The methods consists of two basic steps: (1) the calculation of a correlation matrix among variables relevant for a given research question and (2) the systematic evaluation of the matrix, to identify clusters of variables with similar behavior and respective mutually independent indicators. Optional further analysis steps include (3) the interpretation of the identified clusters, enabling a learning effect from the selection of indicators, (4) testing the robustness of identified clusters with respect to changes in forcing or boundary conditions, (5) enabling a comparative assessment of varying scenarios by constructing and evaluating a common correlation matrix, and (6) the inclusion of expert judgment, for example, to prescribe indicators, to allow for considerations other than statistical consistency. The example application of the SCoMaE method to Earth system model output forced by different CO2 emission scenarios reveals the necessity of reevaluating indicators identified in a historical scenario simulation for an accurate assessment of an intermediate–high, as well as a business-as-usual, climate change scenario simulation. This necessity arises from changes in prevailing correlations in the Earth system under varying climate forcing. For a comparative assessment of the three climate change scenarios, we construct and evaluate a common correlation matrix, in which we identify robust correlations between variables across the three considered scenarios.