A. Marshak

THE I3RC: Bringing Together the Most Advanced Radiative Transfer Tools for Cloudy Atmospheres

The interaction of clouds with solar and terrestrial radiation is one of the most important topics of climate research. In recent years it has been recognized that only a full three-dimensional (3D) treatment of this interaction can provide answers to many climate and remote sensing problems, leading to the worldwide development of numerous 3D radiative transfer (RT) codes. The international Intercomparison of 3D Radiation Codes (I3RC), described in this paper, sprung from the natural need to compare the performance of these 3D RT codes used in a variety of current scientific work in the atmospheric sciences. I3RC supports intercomparison and development of both exact and approximate 3D methods in its effort to 1) understand and document the errors/limits of 3D algorithms and their sources; 2) provide “baseline” cases for future code development for 3D radiation; 3) promote sharing and production of 3D radiative tools; 4) derive guidelines for 3D radiative tool selection; and 5) improve atmospheric science education in 3D RT. Results from the two completed phases of I3RC have been presented in two workshops and are expected to guide improvements in both remote sensing and radiative energy budget calculations in cloudy atmospheres.

Statistical Analysis of the Uncertainties in Cloud Optical Depth Retrievals Caused by Three-Dimensional Radiative Effects

Abstract This paper presents a simple yet general approach to estimate the uncertainties that arise in satellite retrievals of cloud optical depth when the retrievals use one-dimensional radiative transfer theory for heterogeneous clouds that have variations in all three dimensions. For the first time, preliminary error bounds are set to estimate the uncertainty of cloud optical depth retrievals. These estimates can help us better understand the nature of uncertainties that three-dimensional effects can introduce into retrievals of this important product of the Moderate Resolution Imaging Spectroradiometer instrument. The probability distribution of resulting retrieval errors is examined through theoretical simulations of shortwave cloud reflection for a set of cloud fields that represent the variability of stratocumulus clouds. The results are used to illustrate how retrieval uncertainties change with observable and known parameters, such as solar elevation or cloud brightness. Furthermore, the results i...

Cloud‐vegetation interaction: Use of normalized difference cloud index for estimation of cloud optical thickness

A new technique to retrieve cloud optical depth for broken clouds above green vegetation using ground-based zenith radiance measurements is developed. By analogy with the Normalized Difference Vegetation Index (NDVI), the Normalized Difference Cloud Index (NDCI) is defined as a ratio between the difference and the sum of two zenith radiances measured for two narrow spectral bands in the visible and near-IR regions. The very different spectral behavior of cloud liquid water drops and green vegetation is the key physics behind the NDCI. It provides extra tools to remove the radiative effects of the 3D cloud structure. Numerical calculations based on fractal clouds and real measurements of NDCI and cloud liquid water path confirm the improvements.

Fundamental Equations of Radiative Transfer in Leaf Canopies, and Iterative Methods for Their Solution

The theory of radiative transfer in turbid media was developed well enough for solving problems in astrophysics, nuclear physics and atmospheric physics (Davison 1958; Marchuk 1961 on the process of neutron transfer; Chandrasekhar 1950; Sobolev 1963 on astrophysical problems; Vladimirov 1961; Case and Zweifel 1967 for a mathematical description of transport theory). A formal way of developing radiative transfer theory in leaf canopies using the analogy of a turbid layer can be found in Shifrin (1953). Ross and colleagues further developed the theory in the mid 1960s (Ross 1962, 1964; Ross and Nilson 1963, 1965, 1967, 1968a, b: Nilson 1968a, b; Niilisk and Ross 1969).

Spectral Density of Cloud Liquid Water Content at High Frequencies

Abstract Aircraft measurements of liquid water content (LWC) made at sampling frequencies of 1 and 2 kHz with a particle volume monitor (PVM) probe from horizontal traverses in stratocumulus clouds during the Southern Ocean Cloud Experiment and cumulus clouds during the Small Cumulus Microphysics Study are described. The spectral density of the LWC measurements is calculated and compared to the −5/3 scaling law. The effect of PVM sampling noise is found to be small in most cases. Most measurements follow approximately the −5/3 law until cloud scales decrease below about 5 m in length. Below this length LWC variance can exceed that predicted by the −5/3 law. It is suggested that the enhanced LWC variance at small scales is related to entrainment of environmental air into the clouds, which changes primarily the droplet concentration.

Cloud three‐dimensional effects evidenced in Landsat spatial power spectra and autocorrelation functions

An analysis of nadir reflectivity spatial Fourier power spectra and autocorrelation functions for solar wavelengths and cloudy conditions is presented. The data come from Landsat thematic mapper (TM) observations, while Monte Carlo (MC) simulations are used to aid the interpretation of the observations and to examine sensitivity to various factors. We show that shortwave radiative processes produce consistent signatures in power spectra and autocorrelation functions. Power spectra take a variety of shapes not shown or explained in previous observational studies. We demonstrate that TM spectra can potentially be affected by radiative “roughening” at intermediate scales (∼1–5 km) and radiative “smoothing” at small scales (<1 km). These processes are wavelength-dependent, with systematic differences between conservative (for cloud droplets) TM band 4 (∼0.8 μm) and absorbing band 7 (∼2.2 μm). Band 7 exhibits more roughening and less smoothing than band 4 and faster decrease in autocorrelation. Roughening is more prevalent at large solar zenith angles due to optical and/or geometrical side illumination and shadowing. MC spectra illustrate that scale invariant optical depth fields can produce complex power spectra that take a variety of shapes under different conditions. Radiative roughening increases with decreasing single scattering albedo and increasing solar zenith angle (as in the observations). For low solar zenith angles, there is a clear shift in the radiative smoothing scale to smaller values as droplet absorption increases. Power spectra also show stronger decorrelations between optical depth and reflectivity when cloud top variations are more pronounced. Finally, it is shown that power spectral analysis is a useful tool for evaluating the skill of novel optical depth retrieval techniques in removing three-dimensional radiative effects. New techniques using inverse nonlocal independent pixel approximation and normalized difference of nadir reflectivity yield optical depth fields which better match the scale-by-scale variability of the true optical depth field.

A method for analyzing how various parts of clouds influence each other's brightness

[1]xa0This paper proposes a method for obtaining new information on three-dimensional (3-D) radiative effects that arise from horizontal radiative interactions in heterogeneous clouds. Unlike current radiative transfer models, it can not only calculate how 3-D effects change radiative quantities at any given point but can also determine which areas contribute to these 3-D effects, to what degree, and through what mechanisms. The new method uses Monte Carlo radiative transfer simulations to generate numerous photon trajectories through the cloud field, and then it examines the radiative processes along each trajectory. After describing the proposed method, the paper illustrates its new capabilities both for detailed case studies and for the statistical processing of large data sets. Because the proposed method makes it possible, for the first time, to link a particular change in cloud properties to the resulting 3-D effect, it can be used to develop new types of radiative transfer parameterizations. Encouraging initial results suggest that such parameterizations will be able to incorporate 3-D effects in practical applications currently limited to 1-D theory, such as remote sensing of cloud properties and dynamical cloud modeling.

Horizontal radiative fluxes in clouds and accuracy of the independent pixel approximation at absorbing wavelengths

In order to correctly interpret shortwave cloud radiation measured by satellites and ground-based radiometers, or by two aircraft flying above and below clouds, we need to better understand interactions between inhomogeneous clouds and solar radiation. The discrepancies between shortwave absorption inferred from measurements and predicted by models, between cloud optical depths estimated from satellites and ground measurements, between single scattering albedo retrieved from in situ radiation measurements and computed from measured droplet size distribution, among others, are strongly affected by cloud horizontal inhomogeneity. Net horizontal photon transport (i. e., horizontal fluxes) are a direct consequence of the inhomoqeneity in cloud structure. Horizontal fluxes and their effect on the accuracy of the pixel-by-pixel one-dimensional (1 D) radiative transfer calculations has recently undergone close scrutiny for conservative scattering. However, the properties and magnitude of horizontal fluxes in absorbing wavelengths are still poorly understood. As far as we are aware, only Ackerman and Cox and Titov discussed correlations between horizontal fluxes at absorbing wavelengths, though these were far from comprehensive. This paper partly fills this gap. We discuss here of whether the accuracy of the Independent Pixel Approximation (IPA), a 1 D radiative transfer approximation for each pixel, is a better model for multiple scattering at conservative or at absorbing wavelengths. Issues addressed here are: (1) dependence of net horizontal fluxes on single scattering albedo; (2) connection between pixel-by-pixel accuracy of the IPA and horizontal fluxes and (3) radiative smoothing and horizontal fluxes at absorbing wavelengths. In contrast to the traditional understanding of IPA, we study IPA accuracies not only for reflectance but also for transmittance and absorptance at both conservative and absorbing wavelengths. In spite of the apparent similarity between the three processes, dependence of IPA accuracies on single-scattering albedo is completely different. As a result, cloud optical properties retrieved from high resolution satellite images and ground-based measurements using IPA at absorbing channels will have different accuracies.

Spectrally-Invariant Approximation Within Atmospheric Radiative Transfer

AbstractCertain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These “spectrally invariant relationships” are the consequence of wavelength independence of the extinction coefficient and scattering phase function in vegetation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accurately describe the extinction and scattering properties of cloudy atmospheres. The validity of the assumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is ...