Discrete Ordinates Spectral Model for Clear-Sky Longwave Surface Irradiance

PURPOSE AND BACKGROUND

The atmosphere and Earth’s surface absorb/scatter shortwave radiation (< 4 μm) coming from the Sun and absorb/emit/scatter longwave radiation (> 4 μm). The balance between the shortwave radiation and the longwave radiation determines the global temperature. Therefore the surface downwelling longwave irradiance plays a critical role in modeling of weather and climate variability as well as in the heat balance design of solar power plants and radiant cooling systems. The downward longwave atmospheric irradiance can be measured directly by pyrgeometers, but they are not equipped widely in weather stations because they are relatively expensive and require extensive calibration and adjustments to exclude the longwave radiation emitted by surroundings. Therefore, the focus of this work is to develop a model that can calculate the atmospheric downwelling longwave radiation at the ground level for different locations, and also examine the effects of water vapor and aerosols on the surface downwelling longwave irradiance with high spectral and spatial resolutions.

METHODOLOGY

A spectrally resolved discrete ordinates radiative model is developed and used to calculate surface downwelling longwave (DLW) irradiance (0 ~ 2500 cm^-1) under clear-sky (cloud free) conditions. The wavenumber spectral resolution of the model is 0.01 cm^-1 and the atmosphere is represented by 18 non-uniform plane-parallel layers with the pressure of each layer being determined by a constant σ coordinate system. The standard AFGL profiles for temperature and atmospheric gas concentrations have been adopted with the correction for current surface atmospheric gas concentrations. The model utilizes the most up-to-date HITRAN molecular spectral data for 5 atmospheric gases: H₂O, CO₂, O₃, CH₄ and N₂O. The MT_CKD model is used to calculate water vapor continuum absorption coefficients. The downwelling and upwelling monochromatic fluxes of each layer are calculated by integrating diffuse radiation from all directions via exponential integral.

For scattering atmosphere (with aerosols), the aerosol concentration is assumed to be constant below 1 km and decays exponentially above 1 km. Aerosol size distribution is assumed to follow a bimodal distribution. The size and refractive index of aerosols will change as they absorb water, therefore the size distribution and refractive index are corrected for different surrounding water vapor concentrations (relative humidities). The absorption coefficients, scattering coefficients and asymmetry factor of aerosols are calculated from refractive index and size distribution by Mie scattering theory. With the aerosol absorption and scattering within each layer, the radiosity and irradiance of each layer is calculated by energy balance equations using transfer factors with the assumption of isotropic scattering (asymmetry factor is calculated to be smaller than 0.03). The monochromatic downwelling and upwelling fluxes of each layer are further calculated from radiosity and irradiance by modifying the transfer factors. Broadband fluxes are integrated using k-distribution method for both non-scattering and scattering atmosphere.

RESULTS AND CONCLUSION

For a non-scattering atmosphere, a resolution of 18 vertical layers is found to achieve grid convergence. The calculated surface DLW irradiance agrees within 2.5% with the mean values from Intercomparison of Radiation Codes in Climate Models (ICRCCM) program, and the spectral density difference is smaller than 0.03 W/(m² cm^-1). Outside the atmospheric spectral windows, water vapor resided below 300 m is found to be heating the surface while that above 300 m is found to be cooling the surface.

For a scattering atmosphere with typical aerosol loading (surface number density about 350/cm³). Within the atmospheric spectral window, aerosol below 3.5 km is found to be heating the surface while that above 3.45 km is found to start cooling the surface. This effect is enhanced with less water vapor present (Figure 1). The broadband surface DLW irradiance increases by around 4 W/m² when compared with non-scattering conditions. When the scattering model is applied to 7 climatologically diverse SURFRAD stations, the modeled DLW irradiance agrees within 3.27% relative error when compared to measured values. This relative error is smaller than a calibrated parametric model regressed from data for those same 7 stations, i.e., the discrete-ordinates model captures the climatological differences between stations, making it a valuable tool to theoretically calculate DLW at any locations across the contiguous United States where measurements are not readily available.