K. Franklin Evans

A Bayesian algorithm to retrieve profiles of cloud ice water content (IWC), ice particle size (D_me), and relative humidity from millimeter-wave/submillimeter-wave radiometers is presented. The first part of the algorithm prepares an a priori file with cumulative distribution functions (CDFs) and empirical orthogonal functions (EOFs) of profiles of temperature, relative humidity, three ice particle parameters (IWC, D_me, distribution width), and two liquid cloud parameters. The a priori CDFs and EOFs are derived from CloudSat radar reflectivity profiles and associated ECMWF temperature and relative humidity profiles combined with three cloud microphysical probability distributions obtained from in situ cloud probes. The second part of the algorithm uses the CDF/EOF file to perform a Bayesian retrieval with a hybrid technique that uses Monte Carlo integration (MCI) or, when too few MCI cases match the observations, uses optimization to maximize the posterior probability function. The very computationally intensive Markov chain Monte Carlo (MCMC) method also may be chosen as a solution method. The radiative transfer model assumes mixtures of several shapes of randomly oriented ice particles, and here random aggregates of spheres, dendrites, and hexagonal plates are used for tropical convection. A new physical model of stochastic dendritic snowflake aggregation is developed. The retrieval algorithm is applied to data from the Compact Scanning Submillimeter-wave Imaging Radiometer (CoSSIR) flown on the ER-2 aircraft during the Tropical Composition, Cloud and Climate Coupling (TC4) experiment in 2007. Example retrievals with error bars are shown for nadir profiles of IWC, D_me, and relative humidity, and nadir and conical scan swath retrievals of ice water path and average D_me. The ice cloud retrievals are evaluated by retrieving integrated 94 GHz backscattering from CoSSIR for comparison with the Cloud Radar System (CRS) flown on the same aircraft. The rms difference in integrated backscattering is around 3 dB over a 30 dB range. A comparison of CoSSIR retrieved and CRS measured reflectivity shows that CoSSIR has the ability to retrieve low-resolution ice cloud profiles in the upper troposphere.

The spherical harmonics discrete ordinate method for plane-parallel data assimilation (SHDOMPPDA) model is an unpolarized plane-parallel radiative transfer forward model, with corresponding tangent linear and adjoint models, suitable for use in assimilating cloudy sky visible and infrared radiances. It is derived from the spherical harmonics discrete ordinate method plane-parallel (SHDOMPP, also described in this article) version of the spherical harmonics discrete ordinate method (SHDOM) model for three-dimensional atmospheric radiative transfer. The inputs to the SHDOMPPDA forward model are profiles of pressure, temperature, water vapor, and mass mixing ratio and number concentration for a number of hydrometeor species. Hydrometeor optical properties, including detailed phase functions, are determined from lookup tables as a function of mass mean radius. The SHDOMPP and SHDOMPPDA algorithms and construction of the tangent-linear and adjoint models are described. The SHDOMPPDA forward model is validated against the Discrete Ordinate Radiative Transfer Model (DISORT) by comparing upwelling radiances in multiple directions from 100 cloud model columns at visible and midinfrared wavelengths. For this test in optically thick clouds the computational time for SHDOMPPDA is comparable to DISORT for visible reflection, and roughly 5 times faster for thermal emission. The tangent linear and adjoint models are validated by comparison to finite differencing of the forward model.

Submillimeter-wave radiometry is a new technique for determining ice water path (IWP) and particle size in upper-tropospheric ice clouds. The first brightness temperatures images of ice clouds above 340 GHz were measured by the Compact Scanning Submillimeter Imaging Radiometer (CoSSIR) during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers (CRYSTAL) Florida Area Cirrus Experiment (FACE) campaign in July 2002. CoSSIR operated with 12 channels from receivers at 183, 220, 380, 487, and 640 GHz. CoSSIR and the nadir-viewing 94-GHz Cloud Radar System (CRS) flew on the NASA ER-2 airplane based out of Key West, Florida. A qualitative comparison of the CoSSIR brightness temperatures demonstrates that the submillimeter-wave frequencies are more sensitive to anvil ice cloud particles than are the lower frequencies. A Bayesian algorithm, with a priori microphysical information from in situ cloud probes, is used to retrieve the IWP and median mass equivalent sphere particle diameter (Dme). Microwave scattering properties of random aggregates of plates and aggregates of frozen droplets are computed with the discrete dipole approximation (DDA) and an effective medium approximation tuned to DDA results. As a test of the retrievals, the vertically integrated 94-GHz radar backscattering is also retrieved from the CoSSIR data and compared with that measured by the CRS. The integrated backscattering typically agrees within 1–2 dB for IWP from 1000 to 10 000 g m−2, and while the disagreement increases for smaller IWP, it is typically within the Bayesian error bars. Retrievals made with only the three 183- and one 220-GHz channel are generally as good or better than those including 380 ± 6.2 and 640 GHz, because the CoSSIR submillimeter-wave channels were much noisier than expected. An algorithm to retrieve profiles of ice water content and Dme from CRS and CoSSIR data was developed. This Bayesian algorithm also retrieves the coefficients of an IWC–radar reflectivity power-law relation and could be used to evaluate radar-only ice cloud retrieval algorithms.

Due to the spatially inhomogeneous nature of clouds there are large uncertainties in validating remote sensing retrievals of cloud properties with traditional in situ cloud probes, which have sampling volumes measured in liters. This paper introduces a new technique called in situ cloud lidar, which can measure extinction in liquid clouds with sampling volumes of millions of cubic meters. In this technique a laser sends out pulses of light horizontally from an aircraft inside an optically thick cloud, and wide-field-of-view detectors viewing upward and downward measure the time series of the number of photons returned. Diffusion theory calculations indicate that the expected in situ lidar time series depends on the extinction and has a functional form of a power law times an exponential, with the exponential scale depending on the distance to the cloud boundary. Simulations of 532-nm wavelength in situ lidar time series are made with a Monte Carlo radiative transfer model in stochastically genera... Abstract Due to the spatially inhomogeneous nature of clouds there are large uncertainties in validating remote sensing retrievals of cloud properties with traditional in situ cloud probes, which have sampling volumes measured in liters. This paper introduces a new technique called in situ cloud lidar, which can measure extinction in liquid clouds with sampling volumes of millions of cubic meters. In this technique a laser sends out pulses of light horizontally from an aircraft inside an optically thick cloud, and wide-field-of-view detectors viewing upward and downward measure the time series of the number of photons returned. Diffusion theory calculations indicate that the expected in situ lidar time series depends on the extinction and has a functional form of a power law times an exponential, with the exponential scale depending on the distance to the cloud boundary. Simulations of 532-nm wavelength in situ lidar time series are made with a Monte Carlo radiative transfer model in stochastically genera...

A retrieval method has been developed to directly retrieve statistics of cloud parameters from Geostationary Operational Environmental Satellite (GOES) visible and infrared imager data. This method retrieves cloud parameter probability density functions (PDFs) directly from distributions of multichannel satellite-observed radiances. For example, the joint probability distribution of ice water content and effective radius can be retrieved from a four-dimensional histogram of GOES radiances. A forward radiative transfer model creates a mapping from cloud parameter space to satellite radiance space. The cloud parameter space is described by vertically inhomogeneous liquid and ice cloud layers with variable liquid water path, effective radius, height, and thickness. A Monte Carlo procedure uses the mapping to transform probability density from the observed satellite radiance histogram, or radiance PDF, to a two-dimensional cloud property PDF. An estimate of the uncertainty in the retrieved PDF is cal... Abstract A retrieval method has been developed to directly retrieve statistics of cloud parameters from Geostationary Operational Environmental Satellite (GOES) visible and infrared imager data. This method retrieves cloud parameter probability density functions (PDFs) directly from distributions of multichannel satellite-observed radiances. For example, the joint probability distribution of ice water content and effective radius can be retrieved from a four-dimensional histogram of GOES radiances. A forward radiative transfer model creates a mapping from cloud parameter space to satellite radiance space. The cloud parameter space is described by vertically inhomogeneous liquid and ice cloud layers with variable liquid water path, effective radius, height, and thickness. A Monte Carlo procedure uses the mapping to transform probability density from the observed satellite radiance histogram, or radiance PDF, to a two-dimensional cloud property PDF. An estimate of the uncertainty in the retrieved PDF is cal...

Given the substantial radiative effects of cirrus clouds and the need to validate cirrus cloud mass in climate models, it is important to measure the global distribution of cirrus properties with satellite remote sensing. Existing cirrus remote sensing techniques, such as solar reflectance methods, measure cirrus ice water path (IWP) rather indirectly and with limited accuracy. Submillimeter-wave radiometry is an independent method of cirrus remote sensing based on ice particles scattering the upwelling radiance emitted by the lower atmosphere. A new aircraft instrument, the Far Infrared Sensor for Cirrus (FIRSC), is described. The FIRSC employs a Fourier Transform Spectrometer (FTS), which measures the upwelling radiance across the whole submillimeter region (0.1–1.0-mm wavelength). This wide spectral coverage gives high sensitivity to most cirrus particle sizes and allows accurate determination of the characteristic particle size. Radiative transfer modeling is performed to analyze the capabili... Abstract Given the substantial radiative effects of cirrus clouds and the need to validate cirrus cloud mass in climate models, it is important to measure the global distribution of cirrus properties with satellite remote sensing. Existing cirrus remote sensing techniques, such as solar reflectance methods, measure cirrus ice water path (IWP) rather indirectly and with limited accuracy. Submillimeter-wave radiometry is an independent method of cirrus remote sensing based on ice particles scattering the upwelling radiance emitted by the lower atmosphere. A new aircraft instrument, the Far Infrared Sensor for Cirrus (FIRSC), is described. The FIRSC employs a Fourier Transform Spectrometer (FTS), which measures the upwelling radiance across the whole submillimeter region (0.1–1.0-mm wavelength). This wide spectral coverage gives high sensitivity to most cirrus particle sizes and allows accurate determination of the characteristic particle size. Radiative transfer modeling is performed to analyze the capabili...

A new algorithm for modeling radiative transfer in inhomogeneous three-dimensional media is described. The spherical harmonics discrete ordinate method uses a spherical harmonic angular representation to reduce memory use and time computing the source function. The radiative transfer equation is integrated along discrete ordinates through a spatial grid to model the streaming of radiation. An adaptive grid approach, which places additional points where they are most needed to improve accuracy, is implemented. The solution method is a type of successive order of scattering approach or Picard iteration. The model computes accurate radiances or fluxes in either the shortwave or longwave regions, even for highly peaked phase functions. Broadband radiative transfer is computed efficiently with a k distribution. The results of validation tests and examples illustrating the efficiency and accuracy of the algorithm are shown for simple geometries and realistic simulated clouds.

A new algorithm for modeling radiative transfer in inhomogeneous three-dimensional media is described. The spherical harmonics discrete ordinate method uses a spherical harmonic angular representation to reduce memory use and time computing the source function. The radiative transfer equation is integrated along discrete ordinates through a spatial grid to model the streaming of radiation. An adaptive grid approach, which places additional points where they are most needed to improve accuracy, is implemented. The solution method is a type of successive order of scattering approach or Picard iteration. The model computes accurate radiances or fluxes in either the shortwave or longwave regions, even for highly peaked phase functions. Broadband radiative transfer is computed efficiently with a k distribution. The results of validation tests and examples illustrating the efficiency and accuracy of the algorithm are shown for simple geometries and realistic simulated clouds. Abstract A new algorithm for modeling radiative transfer in inhomogeneous three-dimensional media is described. The spherical harmonics discrete ordinate method uses a spherical harmonic angular representation to reduce memory use and time computing the source function. The radiative transfer equation is integrated along discrete ordinates through a spatial grid to model the streaming of radiation. An adaptive grid approach, which places additional points where they are most needed to improve accuracy, is implemented. The solution method is a type of successive order of scattering approach or Picard iteration. The model computes accurate radiances or fluxes in either the shortwave or longwave regions, even for highly peaked phase functions. Broadband radiative transfer is computed efficiently with a k distribution. The results of validation tests and examples illustrating the efficiency and accuracy of the algorithm are shown for simple geometries and realistic simulated clouds.

The scattering properties of cirrus clouds at submillimeter-wave frequencies are analyzed and characterized in this paper. This study lays a theoretical foundation for using radiometric measurements to investigate and monitor cirrus properties from high-flying aircraft or satellite. The significance of this capability is that it would provide data on the global distribution of cloud ice mass that is currently required to validate climate models. At present, these needs remain unmet by existing and planned observational systems. In this study the brightness temperature depression (ΔTb) of upwelling radiation due to cirrus clouds is simulated at 150, 220, 340, 500, 630, and 880 GHz. The effects of a range of size distributions, eight ice particle shapes, and different atmospheric profiles are modeled. The atmospheric transmission is high enough in the submillimeter windows to allow upper-tropospheric sensing from space, but absorption by water vapor reduces the sensitivity to lower cirrus clouds in... Abstract The scattering properties of cirrus clouds at submillimeter-wave frequencies are analyzed and characterized in this paper. This study lays a theoretical foundation for using radiometric measurements to investigate and monitor cirrus properties from high-flying aircraft or satellite. The significance of this capability is that it would provide data on the global distribution of cloud ice mass that is currently required to validate climate models. At present, these needs remain unmet by existing and planned observational systems. In this study the brightness temperature depression (ΔTb) of upwelling radiation due to cirrus clouds is simulated at 150, 220, 340, 500, 630, and 880 GHz. The effects of a range of size distributions, eight ice particle shapes, and different atmospheric profiles are modeled. The atmospheric transmission is high enough in the submillimeter windows to allow upper-tropospheric sensing from space, but absorption by water vapor reduces the sensitivity to lower cirrus clouds in...

Vertical profiles of drop size distribution (DSD) parameters are produced from data collected with the National Oceanographic and Atmospheric Administration 915- and 50-MHz Doppler radars at Darwin, Australia, for the 1993–94 monsoon season. An existing algorithm is used to retrieve gamma size distribution parameters from the VHF and UHF Doppler radar spectra. The clear-air mean velocities and spectral widths obtained from the VHF radar are used to fit DSDs accurately to UHF spectra. Uncertainties in retrieved precipitation parameters are estimated from errors in both VHF and UHF spectra. The statistics of the retrieved profiles of DSD parameters are summarized and compared with surface disdrometer data from a site near Darwin. Retrieved vertical profiles of gamma DSDs are input to a microwave radiative transfer model to determine realistic variations in upwelling 10- and 19-GHz brightness temperatures due to uncertainties in drop size distribution. These brightness temperature variations are then used to estimate the error in simple emission-based passive microwave remote sensing algorithms for tropical rainfall due to the Marshall–Palmer assumption. For a viewing angle of 53.1° and for vertical polarization, the two-sigma scatter in brightness temperature is estimated to be ±7.0 K at 10 GHz and ±6.8 K at 19 GHz. The rms difference in brightness temperatures from the Marshall–Palmer brightness temperature, rain rate curve is estimated to be 6.7 K at 10 GHz and 4.9 K at 19 GHz. It is concluded that the scatter in the modeled brightness temperatures is primarily due to variations in the retrieved DSDs, though some scatter can be attributed to vertical inhomogeneity within the DSD profiles. The rms difference in the brightness temperature–rain rate relationship from Marshall–Palmer is consistent with a systematic shift in the retrieved DSDs toward smaller raindrops for a given rain rate than is predicted with the Marshall–Palmer DSD.