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This paper presents an approach using the GEneralized Nonlinear Retrieval Analysis (GENRA) tool and general inverse theory diagnostics including the maximum likelihood solution and the Shannon information content to investigate the performance of a new spectral technique for the retrieval of cloud optical properties from surface based transmittance measurements. The cumulative retrieval information over broad ranges in cloud optical thickness (_{e}_{e}_{e}

The radiative energy incident at the Earth’s surface comes from two sources, the Sun and the atmosphere. Clouds are the predominant atmospheric constituent impacting the flow of this radiant energy by absorption and by scattering some of the incoming shortwave (300–4,000 nm) radiation to space, and by emitting infrared radiation. Clouds may either cool or warm the surface depending on their altitude (temperature), thickness and composition. While much has been learned about global cloud coverage, cloud top heights, optical thickness and droplet size from passive remote sensing, a determination on whether clouds will enhance or counteract warming temperatures in a changing climate has not yet been achieved [

Shortwave cloud reflectance results from scattering and absorption near cloud top. In contrast, transmitted cloud radiation, which can only be measured from below the cloud, interacts with all layers of a cloud [

Regardless of the perspective from which the remote measurements are made, the radiative impacts of the clouds depend upon their optical thickness and droplet effective radius, the ratio of the third to second moment of the particle size distribution (e.g., [

To improve the sensitivity of the retrieval to droplet effective radius, McBride

We employ the GEneralized Nonlinear Retrieval Analysis (GENRA) [

Shannon information content (SIC) analysis of shortwave cloud retrievals has been applied in other recent studies. L’Écuyer

In this study we define the transmittance retrieval methods and wavelengths (

In the visible and very near-infrared (approximately 350–1,000 nm) where liquid water does not absorb, cloud reflectance and transmittance depend primarily upon the cloud optical thickness through scattering. In the near-infrared, liquid water absorption increases and scales with the product of the bulk absorption coefficient and cloud droplet or ice crystal size. This forms the basis of the standard retrieval used in many operational satellite cloud retrievals to date ([

With surface measurements of zenith cloud

We use a measurement-based definition of transmittance, _{trans}^{−2}·nm^{−1}·sr^{−1}) and normal incident solar radiance, _{0}F_{0}/π_{0}

_{e}_{0}

(_{0}

The impacts of surface albedo on transmittance are demonstrated through a direct comparison to McBride

Note that the cloud optical thickness defined in the forward calculations used to generate the look-up tables plotted in

To improve the sensitivity to droplet effective radius, McBride

The retrieval wavelengths were carefully chosen (a) to be outside the strong gas absorption bands (predominantly water vapor) so differences between modeled and measured gas absorption do not impact the cloud retrieval, and (b) to exhibit linear behavior in transmittance over a broad range in cloud optical thickness and effective radius. Figure 5 of [

_{0}

Throughout the remainder of this work, we apply the definitions of McBride

For cloud optical thickness from 1 to 100 and droplet effective radius from 1 to 30 ^{−2}·nm^{−1}) and nadir and zenith radiance (W·m^{−2}·nm^{−1}·sr^{−1}) in a cloudy atmosphere using a plane-parallel radiative transfer model. The calculations were performed with a variable step size in optical thickness from 0.5 to 100 and 1

The plane-parallel radiative transfer model [

The cloud droplet extinction, single-scattering albedo, and the first 16 moments of the Legendre series coefficients of the scattering phase function were computed using a Mie scattering code [

For _{0}

In the look-up table approach to cloud retrievals described above, the cloud optical properties are determined by a best-fit solution between the measured and calculated values of cloud reflectance or transmittance. Retrieval errors are typically evaluated through error propagation methods. An alternative approach is to apply error estimation theory [

The GEneralized Nonlinear Retrieval Analysis (GENRA) [

GENRA requires a look-up table as the discretized transfer function [_{1}(_{e}_{e}_{e}_{e}

Realistic distributions of measurements (_{2}(_{2}(_{e}

The joint posterior solution to the generalized inverse problem is represented by the integration over the measurement space,

The GENRA algorithm introduces measurements at each retrieval wavelength sequentially. At each incremental step, the pdfs on the right hand side of Equation (2) are computed. The spectral ordering in which the measurements are introduced is irrelevant to the joint posterior pdf. The combination of the model pdfs (_{e}_{e}_{e}_{e}

There are two approaches to the treatment of the

The joint posterior pdf contains the information about the probability of the discrete values of _{e}_{e}

The Shannon information content [_{e}_{e}

Uncertainty in the retrieved parameters can come from measurement errors and from errors in the input parameters to the radiative transfer model that is used to simulate the measurements. An additional source of errors is the approximations inherent to the radiative transfer model itself, such as plane-parallel assumptions. In this work, we investigate the error contributions of the first two sources.

In assigning the measurement pdf, we assume the simulated SSFR measurements are subject to a 3% systematic radiometric error offset [

We also investigate the impact of uncertainty due to natural variability in forward model inputs on the simulated transmittance. In this study, we derive the sensitivity of the transmitted cloud radiation to water vapor amount and to the magnitude and spectral shape of the underlying surface albedo only. The sensitivity in the transmittance to these variables will have spectral, cloud property, and solar angle dependencies. We report the sensitivities as standard deviations in the transmittance and the spectral slope of the transmittance relative to the baseline calculations discussed in

Coddington _{e}

_{e}_{0}

The sensitivities provided in _{e}

Transmitted radiation is dependent on the albedo of the surface surrounding the instrument and preliminary calculations by McBride

(

The measured and retrieved surface albedo spectra shown in

If we assume no prior knowledge about surface type, the resulting standard deviations in transmittance to the broad range in surface albedo boundary conditions shown in

In

Using the results of

(

The minimum, maximum and baseline of the surface albedo at 515, 1,565, 1,600, and 1,634 nm used in forward modeling calculations to derive the standard deviation in transmittance at these wavelengths due to changing surface conditions. Baseline values are from measurements over a vegetated surface [

Wavelength (nm) | Minimum | Maximum | Baseline |
---|---|---|---|

515 | 0.0377 | 0.1377 | 0.0379 |

1,565 | 0.1085 | 0.2085 | 0.1585 |

1,600 | 0.1096 | 0.2311 | 0.1773 |

1,634 | 0.1106 | 0.2669 | 0.1942 |

_{0}

_{e}_{0}

In this section, we investigate the various sources of measurement and modeling errors (

Firstly, we investigate variability in water vapor as the sole source of model error. This allows us to verify the GENRA output while also testing the relative impacts of systematic and random measurement error. In _{e}

Marginal pdfs in effective radius (r_{eff}, in _{e}_{e}_{e}_{0}

In the results shown in _{e}_{e}_{e}

The measurement systematic error is the dominant factor in the differences in the maximum likelihood solutions of the marginal and joint pdf solutions. The grid points in the transmittance look up tables (_{e}_{e}

The forward modeling errors resulting from uncertainty in surface albedo (

We define a retrieval bias as the difference between the maximum likelihood solution of the joint posterior pdf and the ‘true’ value. Since the Shannon information content is inversely related to error variance, a low value indicates a broad, imprecise, distribution of _{e}_{e}

Despite the larger errors due to surface variability compared to that of water vapor, the slope retrieval method is able to retrieve cloud optical thickness within ±2 for clouds of τ greater than 5 and less than 60, and within ±5 for thicker clouds. The standard method has biases exceeding 5, and approaching 50, for clouds of τ > 40. Although the slope method is more accurate than the standard method for retrieving effective radius, in agreement with the results of McBride _{e}_{e}

Surface plots of retrieval biases in effective radius and optical thickness (biases are defined as the difference between the maximum likelihood solution of the joint posterior pdf in _{e}_{0 }

In _{e}

1-dimension marginal pdfs in optical thickness and effective radius and the joint posterior pdfs for _{e}_{e}_{e}_{e}_{e}_{0}_{e}

Recall that the maximum likelihood solution of the joint posterior pdf in _{e}_{e}_{e}

There is a solar angle dependency in the retrieved cloud properties using the slope method. This dependency is greatest for clouds with _{e}

The dependency in the marginal pdfs in cloud optical thickness and droplet effective radius on solar zenith angle for _{e}_{e}_{e}_{e}_{e}_{0}_{0}_{0}_{0 }

_{0}

In this study, we quantify the variance in transmittance resulting from ±30% variability in atmospheric water vapor content and spectral surface albedo spanning soil to vegetated surface types for a broad range of cloud optical thickness and droplet effective radius. The variance is quantified at a visible and near infrared wavelength and in the slope of the normalized transmittance over a near infrared wavelength channel (1,565 nm to 1,634 nm). Using an application based on general inverse theory called the GEneralized Nonlinear Retrieval Analysis (GENRA), the retrieved cloud optical properties using a new spectral slope method developed by McBride

The new spectral algorithm, which exploits the spectral shape of transmittance in the near infrared, is more accurate than the standard method for retrieving effective radius. For clouds with an optical thickness between 5 and 60 and droplet size less than approximately 20

The results suggest ground-based measurements of transmittance, though more difficult because there is no one-to-one mapping between transmittance and optical thickness as occurs with measurements of cloud reflectance, can be utilized for cloud retrievals when the variability in surface albedo is constrained. A ground-based viewpoint allows for studies of clouds at higher temporal resolution than available from satellite. The MODIS BRDF/albedo product would be one good candidate to provide independent prior knowledge of surface albedo, potentially providing a constraint on surface type and thereby improving retrieval convergence. Future retrieval algorithms may consider a joint retrieval of cloud and surface properties because there is a clear influence of the surface properties on the downward radiation field below cloud. A new Shannon information content study may evaluate the feasibility of such a method.

This work did not investigate the impacts of snow-covered surfaces on the variability in transmittance. Snow covered surfaces have larger and more variable albedos at visible wavelengths [

We gratefully acknowledge Shi Song for assistance in compiling the forward modeling results and Bruce Kindel for computing the linear mixtures of soil and vegetated surface reflectance spectra. This work was accomplished under NASA grant numbers NNX08AI83G and NNX11AK67G. We would like to thank three anonymous reviewers for their helpful comments, which improved this manuscript.