Equation discovery for climate impact: emulating impact models for unexplored climate scenario with interpretable symbolic regression

Abstract. Projected impacts of climate change are assessed with impact models, such as ecological or hydrological models, driven by climate projections. Uncertainties of projected impacts are estimated by driving impact models with a large ensemble of plausible future climate projections. However, most of the time, this is not possible for practical reasons: computing time, data availability. To fix this issue, we propose an approach that links climate projections to impacts with an interpretable equation. First, this equation is discovered based on simulations of the impact model and their corresponding climate projections. Then, we consider that this equation can be used to emulate the impact model for other climate projections. Specifically, the discovered equation maps each year climate indicators, i.e. a list of yearly and seasonally-averaged climate model variables, to a yearly-averaged impact indicator, i.e. a variable computed from the impact model outputs. In our application, the impact indicator is the annual mean Net Primary Production (NPP) of a risk-relevant regional oceanic area located in the North-Western Mediterranean basin. It is computed from the outputs of a biogeochemical model of the Mediterranean Sea, which is driven by climate projections of a coupled regional climate model of the Mediterranean area. In our methodology, we run nine validation schemes each one providing one equation to predict this impact indicator. Our results show that all discovered equations are linear, even though non-linearity is allowed, and that most of them contain four climate indicators that can be interpreted physically: the sea surface temperatures in winter and spring, the sea surface salinity in spring, and the net downward shortwave flux in winter. Based on these four indicators, we fit a linear equation on the historical period (1986–2005) and the scenario RCP8.5 (2006–2099) that reproduces well the trend and the year-to-year correlation of the impact indicator for the scenario RCP4.5 (2006–2099), which was not used for the fit. The predictions of the linear equation however underestimate the interannual variance of NPP. As a perspective, this equation allows us to approximate the impact indicator at a neglected computational cost, i.e. without running the costly biogeochemical impact model, for any regional climate model outputs available.