On the determination of variance in modeled and observed surface irradiance

Description

Satellites view the entire Earth over relatively short periods of time, allowing for reasonable observation of the Earth’s radiation budget at the top of the atmosphere (TOA). At the Earth’s surface, however, we are necessarily restricted to observations of irradiance at essentially a handful of sites located primarily over northern hemisphere continental regions. Hence, to determine the global budget of irradiance at the surface we must rely on radiative transfer models driven by 4-dimensional space/time re-analyses of the atmospheric state over time. Modeled and observed surface irradiances have been compared in many studies (e.g., Rossow and Zhang 1995, Rose et al. 2006, Charlock et al. 2006, Wang and Pinker 2009, Niu et al. 2010). The RMS difference between modeled and observed irradiances at surface sites can be used as a measure of uncertainty, though their relationship is complex. The noise of temporal and spatial mismatch between observed surface irradiances can dominate in the comparisons, especially shortwave irradiances, and uncertainty might be overestimated if the surface site does not represent the grid box where the site is located.

We separate the RMS difference of modeled minus observed irradiance into three components: r^2= r(s)^2+r(t)^2+r(m)^2 where r is the RMS difference computed with the difference between modeled gridded monthly mean irradiance and observed monthly mean irradiance. r(s) is the RMS difference due to variability of surface irradiance within the grid (spatial sampling), r(t) is the uncertainty due to temporal resolution of modeled irradiance, and r(m) is modeling error and the noise due to matching modeled irradiances with surface observations. The spatial RMS error r(s) arises because observations at a surface site measure the irradiance at one location that may not be representative of a larger area such as a global climate model grid box. Temporal uncertainty arises because model input is often based on observations that are typically limited to several times a day. Modeling error includes the error in the inputs and assumptions in the model. Using various satellite-based model calculations of surface downward irradiance at several different time and space scales, we attempt to determine the components of the above equation to quantify the uncertainty in such model versus observation comparisons.