scholarly journals Statistical approaches to error identification for plane-parallel retrievals of optical and microphysical properties of three-dimensional clouds: Bayesian inference

2009 ◽  
Vol 114 (D6) ◽  
Author(s):  
P. Gabriel ◽  
H. W. Barker ◽  
D. O'Brien ◽  
N. Ferlay ◽  
G. L. Stephens
2013 ◽  
Vol 6 (3) ◽  
pp. 539-547 ◽  
Author(s):  
E. Jäkel ◽  
J. Walter ◽  
M. Wendisch

Abstract. The sensitivity of passive remote sensing measurements to retrieve microphysical parameters of convective clouds, in particular their thermodynamic phase, is investigated by three-dimensional (3-D) radiative transfer simulations. The effects of different viewing geometries and vertical distributions of the cloud microphysical properties are investigated. Measurement examples of spectral solar radiance reflected by cloud sides (passive) in the near-infrared (NIR) spectral range are performed together with collocated lidar observations (active). The retrieval method to distinguish the cloud thermodynamic phase (liquid water or ice) exploits different slopes of cloud side reflectivity spectra of water and ice clouds in the NIR. The concurrent depolarization backscattering lidar provides geometry information about the cloud distance and height as well as the depolarization.


2014 ◽  
Vol 53 (2) ◽  
pp. 437-455 ◽  
Author(s):  
Steven D. Miller ◽  
John M. Forsythe ◽  
Philip T. Partain ◽  
John M. Haynes ◽  
Richard L. Bankert ◽  
...  

AbstractThe launch of the NASA CloudSat in April 2006 enabled the first satellite-based global observation of vertically resolved cloud information. However, CloudSat’s nonscanning W-band (94 GHz) Cloud Profiling Radar (CPR) provides only a nadir cross section, or “curtain,” of the atmosphere along the satellite ground track, precluding a full three-dimensional (3D) characterization and thus limiting its utility for certain model verification and cloud-process studies. This paper details an algorithm for extending a limited set of vertically resolved cloud observations to form regional 3D cloud structure. Predicated on the assumption that clouds of the same type (e.g., cirrus, cumulus, and stratocumulus) often share geometric and microphysical properties as well, the algorithm identifies cloud-type-dependent correlations and uses them to estimate cloud-base height and liquid/ice water content vertical structure. These estimates, when combined with conventional retrievals of cloud-top height, result in a 3D structure for the topmost cloud layer. The technique was developed on multiyear CloudSat data and applied to Moderate Resolution Imaging Spectroradiometer (MODIS) swath data from the NASA Aqua satellite. Data-exclusion experiments along the CloudSat ground track show improved predictive skill over both climatology and type-independent nearest-neighbor estimates. More important, the statistical methods, which employ a dynamic range-dependent weighting scheme, were also found to outperform type-dependent near-neighbor estimates. Application to the 3D cloud rendering of a tropical cyclone is demonstrated.


2013 ◽  
Vol 6 (4) ◽  
pp. 6329-6369
Author(s):  
N. B. Wood ◽  
T. S. L'Ecuyer ◽  
F. L. Bliven ◽  
G. L. Stephens

Abstract. Estimates of snow microphysical properties obtained by analyzing collections of individual particles are often limited to short time scales and coarse time resolution. Retrievals using disdrometer observations coincident with bulk measurements such as radar reflectivity and snowfall amounts may overcome these limitations; however, retrieval techniques using such observations require uncertainty estimates not only for the bulk measurements themselves, but also for the simulated measurements modeled from the disdrometer observations. Disdrometer uncertainties arise due to sampling and analytic errors and to the discrete, potentially truncated form of the reported size distributions. Imaging disdrometers such as the Snowflake Video Imager and 2-D Video Disdrometer provide remarkably detailed representations of snow particles, but view limited projections of their three-dimensional shapes. Particle sizes determined by such instruments underestimate the true dimensions of the particles in a way that depends, in the mean, on particle shape, also contributing to uncertainties. An uncertainty model that accounts for these uncertainties is developed and used to establish their contributions to simulated radar reflectivity and snowfall rate. Viewing geometry effects are characterized by a parameter, φ, that relates disdrometer-observed particle size to the true maximum dimension of the particle. Values and uncertainties for φ are estimated using idealized ellipsoidal snow particles. The model is applied to observations from seven snow events from the Canadian CloudSat CALIPSO Validation Project (C3VP), a mid-latitude cold season cloud and precipitation field experiment. Typical total uncertainties are 4 dBZ for reflectivity and 40–60% for snowfall rate, are highly correlated, and are substantial compared to expected observational uncertainties. The dominant sources of errors are viewing geometry effects and the discrete, truncated form of the size distributions. While modeled Ze-S relationships are strongly affected by assumptions about snow particle mass properties, such relationships are only modestly sensitive to φ owing to partially compensating effects on both the reflectivity and snowfall rate.


Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem


Author(s):  
Amit Singer

The power spectrum of proteins at high frequencies is remarkably well described by the flat Wilson statistics. Wilson statistics therefore plays a significant role in X-ray crystallography and more recently in electron cryomicroscopy (cryo-EM). Specifically, modern computational methods for three-dimensional map sharpening and atomic modelling of macromolecules by single-particle cryo-EM are based on Wilson statistics. Here the first rigorous mathematical derivation of Wilson statistics is provided. The derivation pinpoints the regime of validity of Wilson statistics in terms of the size of the macromolecule. Moreover, the analysis naturally leads to generalizations of the statistics to covariance and higher-order spectra. These in turn provide a theoretical foundation for assumptions underlying the widespread Bayesian inference framework for three-dimensional refinement and for explaining the limitations of autocorrelation-based methods in cryo-EM.


2016 ◽  
Author(s):  
E. J. Spreitzer ◽  
M. P. Marschalik ◽  
P. Spichtinger

Abstract. Ice clouds, so-called cirrus clouds, occur very frequently in the tropopause region. A special class are subvisible cirrus clouds with an optical depth lower than 0.03. Obviously, the ice crystal number concentration of these clouds is very low. The dominant pathway for these clouds is not known well. It is often assumed that heterogeneous nucleation at solid aerosol particles is the preferred mechanism although homogeneous freezing of aqueous solution droplets might be possible. For investigating subvisible cirrus clouds as formed by homogeneous freezing we develop a simple analytical cloud model from first principles; the model consists of a three dimensional set of ordinary differential equations, including the relevant processes as ice nucleation, diffusional growth and sedimentation, respectively. The model is integrated numerically and is investigated using theory of dynamical systems. We found two different states for the long-term behaviour of subvisible cirrus clouds, i.e. an attractor case and a limit cycle scenario. The transition between the states constitutes a Hopf bifurcation and is determined by environmental conditions as vertical updraughts and temperature. In both cases, the microphysical properties of the simulated clouds agree reasonably well with simulations using a complex model, with former analytical studies and with observations of subvisible cirrus. In addition, the model can also be used for explaining complex model simulations close to the bifurcation qualitatively. Finally, the results indicate that homogeneous nucleation might be a possible formation pathway for subvisible cirrus clouds.


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