Improved Representations of Longwave Surface Emissivity to Reduce Surface and Atmospheric Heating Biases in Earth System Models

Abstract

Many Earth system models (ESMs) approximate surface emissivity as a broadband constant. This approximation reduces the computational burden, yet omits the spectral structure of emissivity and atmospheric absorption. Neglecting spectral variation in surface emission introduces biases in longwave (LW) atmospheric fluxes and heating. Biases are strongest over surfaces with strongly varying emissivity and minimal atmospheric opacity. We examine these biases over water, ice, and snow surfaces. We partition spectral emissivity into the 16 spectral bands utilized by a single-column atmospheric radiative transfer model (RRTMG_LW) commonly used in ESMs. We quantify flux and heating biases introduced by broadband assumptions relative to the spectrally resolved case for standard atmospheric profiles over each surface type. Current assumptions tend to overestimate upwelling surface fluxes; for example, the greybody assumption overestimates flux by 1.6 W/m² ($\sim$0.52%) at the bottom of a mid-latitude winter atmosphere over ice, and by 2.33 ${\text{W/m}}^2$ ($\sim$1.0%) at the top of atmosphere. The blackbody assumption tends to artificially cool Earth's surface, stabilizing the lower troposphere. Interestingly, the optimal broadband emissivity can deviate from the Planck-weighted mean by up to 3% depending on surface type and atmospheric profile. We investigate bias sensitivity to surface temperature, cloud water path, and atmospheric water vapor. Bias is most sensitive to water vapor content, and least sensitive to cloud water path. Lastly, we show that a modified greybody method with updated broadband values can reduce total surface flux bias up to 1.69 ${\text{W/m}}^2$, comparable to a five-band approach and at a fraction of the computational cost.