Three-dimensional Broadband Solar Radiative Transfer in Small Tropical Cumulus Fields Derived from High-resolution Imagery

Timothy C. Benner and K. Franklin Evans
Program in Atmospheric and Oceanic Sciences
University of Colorado at Boulder

Motivation

• The determination of actual 3D cloud radiative transfer effects requires statistically representative sampling, not case studies.

• The Independent Pixel Approximation (IPA) provides a framework for accurate radiative transfer in stratiform clouds.

• The mean solar flux errors in cumulus cloud fields have been shown to be potentially large.

• The ARM SGP millimeter cloud radar has not been able to give cumulus cloud structure due to summertime insect contamination.

• We therefore constructed cumulus cloud structure with high-resolution imagery.

• Our statistical class is tropical central Pacific cumulus without overlying cirrus.

Cloud Structure Retrievals

• Visible (0.66 µm) and thermal infrared (11.0 µm) radiances, calibrated to high radiometric accuracy

• 150 scenes from thirteen legs of three flights, each 25x25 km (500x500 pixels) along nadir

• SZA mostly less than 52^o, with no overlying cirrus

Created lookup tables for each flight leg to relate MAS radiances to cloud thickness and liquid water path (LWP).

• Computed an adiabatic liquid water content (LWC) profile from a mean TOGA COARE sounding.

• Created 2D tables with a range of cloud thickness (h) and LWP. Defined an "adiabatic fraction" (f) to scale the adiabatic LWC profile, as a proxy for LWP. For each table entry, created a profile of LWC based on the appropriate h and f (Fig.1).

• Performed plane-parallel radiative transfer on each table entry to obtain modeled radiances corresponding to the two MAS channels (Fig.2).

• Included molecular scattering and absorption.

• Assumed 50 cloud droplets/cm³ and a gamma size distribution.

• Included appropriate geometry for sun angle and aircraft orientation, with a range of viewing angles.

• Limited the optical depth to 128.

Matched MAS radiances to lookup table radiances to obtain cloud thickness and LWP (via h and f) for each cloudy pixel in each scene (Fig. 3).

Constructed 3D LWC fields from the retrieved h and f fields, for each of the 150 scenes.

Cloud Scene Listing

Cloud Scene Statistics

Solar Radiative Transfer Modeling

• 3D cloud structure was obtained by scaling the adiabatic LWC profile (computed from the observed mean sounding) to match the retrieved liquid water path and cloud thickness for each pixel.

• Broadband calculations used Fu's correlated k-distribution, with four bands from 0.2 to 2.5 µm. (There is almost no reflected flux beyond this point).

• Cloud optical properties were computed with Mie theory.

• Maximal cross section Monte Carlo radiative transfer was performed for each scene, at five solar zenith angles (0^o, 27^o, 45^o, 56^o, and 63^o).

• Domain averaged reflected and column absorbed fluxes were calculated from the Monte Carlo results.

• 3D fluxes were compared with three approximations: plane-parallel with cloud fraction (PP), independent pixel approximation (IPA), and tilted independent pixel approximation (TIPA; Varnai and Davies).

Results

• The daytime averaged reflected flux errors of the three approximations are large for some scenes (Fig. 4).

• Averaged over all scenes, however, the 3D radiative effects are small (Fig. 5). Due to error cancellation the diurnal (day and night) errors for plane-parallel and IPA reflected fluxes are only about 0.5 W/m², the same as the TIPA error. This is due to the low occurrence of optically thick deeper clouds.

• For tropical oceanic cumulus, the IPA and TIPA errors are well correlated to cloud fraction (Fig. 6) and cloud side area (Fig.7). These errors are also well correlated with cloud fraction times mean optical depth, upwelling flux, and even cloud perimeter (Tables 1 & 2). The errors are substantially less for TIPA than for IPA.

• Because the IPA errors change sign as sun angle increases, the IPA correlations are low for daytime averages (Table 3). TIPA provides a better basis than IPA for a 3D radiative parameterization because it takes into account the larger effective cloud fraction for low sun angles, and its reflected flux error stays positive.

Correlations

Table 2:   Correlation and rms results for IPA and TIPA reflected flux error regressions. These results are for a solar zenith angle of 63^o.

Table 3:   Correlation and rms results for IPA and TIPA reflected flux error regressions. These results are for all five solar zenith angles.

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