##
**Splitting the Solar Spectrum: Sometimes Less Is Better Than More**

Pawlak, D. T., Pennsylvania State University

General Circulation and Single Column Models/Parameterizations

Cloud Modeling

Pawlak, DT, EJ Clothiaux, MF Modest, and JNS Cole. 2004. Full-Spectrum Correlated-k Distribution for Shortwave Atmospheric Radiative Transfer. *Journal of the Atmospheric Sciences* 61: 2588-2601.

Of all the physical and dynamical calculations required in numerical weather prediction and climate modeling, radiation calculations consume the most computational time. This is because the radiation transfer physics of the atmosphere involve molecular absorption that occurs in narrowly defined absorption bands of the electromagnetic spectrum. The exact location in the spectrum of each absorption line may change in response to the conditions that exist at a given altitude, so radiation calculations must be done separately at different levels in the atmosphere. Each absorption band must be accurately accounted for in radiative calculations and this accounting is known as a line-by-line (LBL) calculation. The contribution from individual absorption lines may be summed in whatever order is most convenient mathematically, as long as the underlying source of the radiation (the solar spectrum) is relatively constant over the range being summed. The constraint that the solar spectrum be relatively constant dictates that a relatively large number of individual summations must be made across relatively narrow regions of the spectrum. This is because the solar source function changes rapidly in some wavelength bands. As a result of the need to make many calculations, radiation subroutines are usually invoked far less often than the time scale on which clouds evolve in the models.

In a study sponsored by the DOE's Atmospheric Radiation Measurement Program, researchers demonstrated a new technique whereby the characteristics of the solar source function can be accounted for before the absorption lines are summed to determine the radiation transfer through the atmosphere. By weighting the individual absorption lines by the amount of incoming energy normally expected in that particular band, the strict constraint of a relatively constant solar spectrum is effectively removed. Sophisticated mathematical manipulations are required to apply this weighting, but the end result is that the contributions from all of the individual lines can be summed in a single calculation, rather than a number that is dictated by the underlying solar spectrum. Using the new technique, the total number of calculations can be reduced substantially without losing significant accuracy relative to the traditional approach of broadband line-by-line (LBL) calculations. As reported in the *Journal of the Atmospheric Sciences *(November 2004), their study compared heating rates and broadband shortwave fluxes calculated from a traditional LBL radiative transfer scheme and the modified radiative transfer approach—called the "full spectrum correlated k distribution" or FSCK.

In comparing both clear sky and cloudy sky cases, the researchers used vertical profiles of pressure, temperature, water vapor, and ozone from subarctic winter, midlatitude winter, and tropical atmospheres for their calculations. By separating the shortwave spectrum into two bands (band 1 from 0.24-0.68 um and band 2 from 0.68-4.60 um), the results showed broadband FSCK clear sky fluxes and heating rates accurate to better than 1% and 3%, respectively, when compared with traditional computationally-intensive LBL models. Computationally intensive LBL models may require that the visible and infrared spectrum be subdivided into as many as 8,192 individual segments to properly account for all of the absorption lines. The new FSCK technique allows the full spectrum to be represented by summing contributions in as few as 5 or 10 segments to achieve differences of 1% and 7% respectively, when compared to the computationally intensive LBL calculations (8,192 segments). Similarly, for low- and hi-cloud test cases, the researchers found FSCK to sufficiently reproduce the LBL generated fluxes and heating rates (which used spectrally varying cloud absorption and scattering properties) to approximately 1% and 8% respectively.

The study demonstrates that the FSCK method represents an accurate and efficient alternative to LBL calculations for shortwave atmospheric radiative transfer. The FSCK method represents a 60%-90% reduction in computational overhead from models used currently. In addition, by explicitly accounting for spectral variability of the solar source function, the FSCK method has the potential for improving accuracy relative to the traditional correlated k distribution model that assume constant solar emissions over each band. The next step toward application of the FSCK method to shortwave atmospheric radiative transfer is to develop a robust radiative transfer module that may be used in operational numerical weather production or global climate models.