Towards an Assessment of Realism (Validity) of Short-Wave Radiation Transport Schemes in GCMs using Pathlength Statistics from Fine O2 A-Band Spectroscopy

How can we assess the realism or "validity" of GCM short-wave (SW) radiation parameterizations that predict domain-average heating rate profiles and boundary fluxes? Efforts to date [1] focus on predictions of broadband quantities since, ultimately, they matter the most. Model errors can, however, be introduced both spectrally (optical properties) and spatially (media properties). Since wavelengths do not interact directly, this challenge can be broken into two independent parts: broadband spectral integration and spatial transport, the latter generally being treated uniformly across wavelengths (e.g., a multi-layer 2-stream model). Here we scrutinize only that spatial "core" of this challenge which is responsible for capturing the impacts of partial cloudiness, unresolved cloud water variability, cloud overlap in the vertical, and maybe even spatial correlations in the horizontal.

Molecular oxygen is a major constituent of air but has negligible impact on radiation budgets in spite of a deep-but-narrow spectral feature (the "A-band") at 0.7677-0.7717 μm. This is near the maximum of spectral solar flux when expressed in photons/s/m²/μm. While the better-known yellow-green peak in W/m²/μm matters for energetics, this alternate maximum is optimal for instrumental diagnostics designed around photon-counting detectors. Because oxygen is a well-mixed gas, its absorption is directly related to geometrical path, at least layer-by-layer. It has been demonstrated theoretically [2-4] and empirically [5-10] that the spatial structure of cloudiness has a first-order effect on pathlength statistics for solar photons (mean and RMS pathlengths, or its variance). Conversely, this observational signature gives us a unique validation metric for SW radiative transfer schemes in GCMs. This is a relevant standard of comparison for modeling solar heating-rate profiles since it is entirely about gaseous absorption and the amount of gas is known accurately.

How could we use pathlength statistics in a principled iterative validation exercise [11] for SW parameterizations? We illustrate a possible approach with an evolving model based on a one-parameter modification of the fundamental transport kernel, Beer's Law of exponential attenuation. This generalized transmission law accounts for unresolved spatial variability in the entire cloudy column [12]. Because it is by construction a full-column stochastic model, this scheme is not well-suited for incorporation into GCMs. It does prove, however, to be skilled at explaining certain invariance properties of solar photon pathlength distributions observed from ground under a wide variety of cloud conditions. The new model also makes interesting predictions about how these properties change when observed using A-band detectors in space with a sufficiently large (or degraded) foot-print. This capability will become available with sufficient resolution (λ/Δλ = 17,500) in 2008 when NASA's Orbiting Carbon Observatory (OCO) [13] joins forces with CloudSat, Calipso, and other essential cloud observing assets in the A-train.

Although many details about how to elaborate a productive validation protocol for SW transport parameterizations (including the role of 3D radiative transfer simulations for given cloud fields) remain open for discussion, we urge solar GCM radiation modelers to support the emerging capabilities in high-resolution O₂ A-band spectroscopy and its derived pathlength products. To access the proposed observational framework for assessing the performance of solar radiative transfer models regarding the 3D spatial distribution of cloudiness, one need only extract the model's transport core and incorporate it into generic "wrapper" code designed to predict O₂ spectroscopic observables, photon pathlength distributions, or simply moments thereof. Based on our experience, these diagnostics will help improve the credibility of the representation of clouds in large-scale SW transport models.

References:

[1]    H.W. Barker and 31 co-authors, 2003: Assessing 1D Atmospheric Solar Radiative Transfer Models: Interpretation and Handling of Unresolved Clouds, J. Climate, 16, 2676-2699.

[2]    A. Davis and A. Marshak, 1997: Lévy Kinetics in Slab Geometry: Scaling of Transmission Probability, in Fractal Frontiers, M. M. Novak and T. G. Dewey (Eds.), World Scientific, Singapore, pp. 63-72.

[3]    A.K. Heidinger and G.L. Stephens, 2002: Molecular Line Absorption in a Scattering Atmosphere - Part III: Path Length Characteristics and the Effects of Spatially Heterogeneous Clouds, J. Atmos. Sci., 59, 1641-1654.

[4]    G.L. Stephens, A.K. Heidinger, and P.M. Gabriel, 2005: Photon Paths and Cloud Heterogeneity: An Observational Strategy to Assess Effects of 3D Geometry on Radiative Transfer, in 3D Radiative Transfer in Cloudy Atmospheres, A. Marshak and A. B. Davis (Eds.), Springer-Verlag, Heidelberg (Germany), pp. 587-616.

[5]    K. Pfeilsticker, F. Erle, O. Funk, H. Veitel, and U. Platt, 1998: First Geometrical Pathlength Distribution Measurements of Skylight Using the Oxygen A-band Absorption Technique - I, Measurement Technique, Atmospheric Observations, and Model Calculations, J. Geophys. Res., 103, 11483-11504.

[6]    Q.-L. Min and L.C. Harrison, 1999: Joint Statistics of Photon Pathlength and Cloud Optical Depth, Geophys. Res. Lett., 26, 1425-1428.

[7]    K. Pfeilsticker, 1999: First Geometrical Pathlength Distribution Measurements of Skylight Using the Oxygen A-band Absorption Technique - II, Derivation of the Lévy-Index for Skylight Transmitted by Mid-Latitude Clouds, J. Geophys. Res., 104, 4101-4116.

[8]    Q.-L. Min, L.C. Harrison, and E.E. Clothiaux, 2001: Joint Statistics of Photon Path Length and Cloud Optical Depth: Case studies, J. Geophys. Res., 106, 7375-7385.

[9]    Q.-L. Min, L.C. Harrison, P. Kiedron, J. Berndt, and E. Joseph. A High Resolution Oxygen A-Band and Water Vapor Band Spectrometer, J. Geophys. Res., 109, 2202, doi:10.1029/2003JD003540, 2004.

[10]  T. Scholl, K. Pfeilsticker, A.B. Davis, H.K. Baltink, S. Crewell, U. Löhnert, C. Simmer, J. Meywerk, and M. Quante, 2006: Path Length Distributions for Solar Photons Under Cloudy Skies: Comparison of Measured First and Second Moments with Predictions from Classical and Anomalous Diffusion Theories, J. Geophys. Res. – D (accepted).

[11]  D. Sornette, A.B. Davis, K. Ide, K.R. Vixie, V. Pisarenko, and J.R. Kamm, 2006: An Algorithm for Validation: Theory and Implementation, Proc. Nat. Acad. Sci. (submitted). Preprint available online at URL http://arxiv.org/abs/physics/0511219.

[12]  A.B. Davis, 2006: Effective Propagation Kernels in Structured Media with Broad Spatial Correlations, Illustration with Large-Scale Transport of Solar Photons Through Cloudy Atmospheres, in Computational Methods in Transport – Granlibakken 2004, F. Graziani (Ed.), Springer-Verlag, New York (NY), pp. 85-140.

[13]  D. Crisp and 30 co-authors, 2004: The Orbiting Carbon Observatory (OCO) Mission. Advances in Space Research, 34, 700-709.