Bayesian Monte Carlo Integration Research Articles

A Novel Ice Cloud Retrieval Algorithm for Submillimeter Wave Radiometers: Simulations and Application to an Airborne Experiment

A retrieval methodology based on the Bayesian neural network (BNN) is presented that inverts the ice water path (IWP), mean mass-weighted diameter (D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">me</sub> ), and cloud height of ice clouds from sub-millimeter radiometer observations. The training dataset was created using collecting cloud profiles from the DARDAR (raDAR/liDAR) database and running simulations by the Atmospheric Radiative Transfer Simulator (ARTS) model. Since the effective radius (r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> ) is the size descriptor of ice particles in the DARDAR database, a look-up table of ice water content (IWC), D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">me</sub> , and r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> was constructed to convert r <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> profiles into D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">me</sub> profiles. In addition, random noises corresponding to the measurement uncertainties of the Compact Scanning Submillimeter-wave Imaging Radiometer (CoSSIR) during the TC4 experiment were added to the simulated brightness temperatures before training the BNN. The proposed retrieval method was first applied to the simulated testing database, and then to the observations of CoSSIR. Moreover, the retrieved IWP and D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">me</sub> were compared to the retrievals of the Bayesian Monte Carlo Integration (BMCI) method. The retrieved cloud height was assessed by cloud height extracted from the reflectivity data of the Cloud Radar System (CPS) flow on the same aircraft with CoSSIR. The comparison showed that the correlation coefficients of the retrieved IWP and D <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">me</sub> from the two methods are above 0.8, and the retrieved cloud height also showed good agreement with that extracted from the CPS.

Assessing synergistic radar and radiometer capability in retrieving ice cloud microphysics based on hybrid Bayesian algorithms

Abstract. The 2017 National Academy of Sciences Decadal Survey highlighted several high-priority objectives to be pursued in the decadal timeframe, and the next-generation Cloud, Convection and Precipitation (CCP) observing system is thereby contemplated. In this study, we develop a suite of hybrid Bayesian algorithms to evaluate two CCP remote sensor candidates including a W-band cloud radar and a (sub)millimeter-wave radiometer with channels in the 118–880 GHz frequency range for capability in constraining ice cloud microphysical quantities. The algorithms address active-only, passive-only, and synergistic active–passive retrievals. The hybrid Bayesian algorithms combine the Bayesian Monte Carlo integration and optimization process to retrieve quantities with uncertainty estimates. The radar-only retrievals employ the optimal estimation methodology, while the radiometer-involved retrievals employ ensemble approaches to maximize the posterior probability density function. A priori information is obtained from the Tropical Composition, Cloud and Climate Coupling (TC4) in situ data and CloudSat radar observations. End-to-end simulation experiments are conducted to evaluate the retrieval accuracies by comparing the retrieved parameters with known values. The experiment results suggest that the radiometer measurements possess high sensitivity to ice cloud particles with large water content. The radar-only retrievals demonstrate capability in reproducing ice water content profiles, but the performance in retrieving number concentration is poor. The synergistic observations enable improved pixel-level retrieval accuracies, and the improvements in ice water path retrievals are significant. The proposed retrieval algorithms could serve as alternative methods for exploring the synergistic active and passive concept, and the algorithm framework could be extended to the inclusion of other remote sensors to further assess the CCP observing system in future studies.

Assimilation of Satellite Microwave Observations over the Rainbands of Tropical Cyclones

AbstractA novel Bayesian Monte Carlo integration (BMCI) technique was developed to retrieve geophysical variables from satellite microwave radiometer data in the presence of tropical cyclones. The BMCI technique includes three steps: generating a stochastic database, simulating satellite brightness temperatures using a radiative transfer model, and retrieving geophysical variables such as profiles of temperature, relative humidity, and cloud liquid and ice water content from real observations. The technique also provides uncertainty estimates for each retrieval and can output the error covariance matrix of selected parameters. The measurements from the Advanced Technology Microwave Sounder (ATMS) on board Suomi National Polar-Orbiting Partnership (Suomi NPP) and the Global Precipitation Measurement (GPM) Microwave Imager (GMI) were used as input. A new technique was developed to correct the ATMS and GMI observations for the beam-filling effect, which is due to small-scale variability of precipitation and clouds when compared with the instrument footprint and also the nonlinear relation between the brightness temperature and precipitation. In addition, the assimilation of the BMCI retrievals into the NASA GEOS model is discussed for Hurricane Maria. The results show that assimilating the BMCI retrievals can influence the dynamical features of the cyclone, including a stronger warm core, a symmetric eye, and vertically aligned wind columns. Two possible factors that may limit the impact of the BMCI retrievals include 1) the resolution of the model (about 25 km), which was too coarse to show the potential of the BMCI data in improving the representation of tropical storms in the model forecast, and 2) the data assimilation system not being able to consider vertically correlated observation errors.

Synthesizing the Vertical Structure of Tropical Cirrus by Combining CloudSat Radar Reflectivity With In Situ Microphysical Measurements Using Bayesian Monte Carlo Integration

AbstractCreating synthetic ice cloud profiles that are distributed according to realistic probability density functions is fundamentally essential for submillimeter wave radiometer studies. In this paper, we develop an algorithm to create synthetic ice cloud profiles by combing in situ microphysics measurements and spaceborne radar reflectivity observations using Bayesian Monte Carlo Integration (MCI). We first conduct comprehensive studies of the in situ data from the Tropical Composition, Cloud and Climate Coupling (TC4) experiment based on a bimodal particle size distribution (PSD) scheme and the realistic particle scattering properties for different crystal habits. Ice water content and radar reflectivity simulations from the in situ PSD are compared with the in situ measurements qualitatively and quantitatively. We then evaluate the Bayesian MCI by applying the algorithm to the Cloud Radar System (CRS) during the TC4 campaign and compare the brightness temperature simulations for the retrievals with the Compact Scanning Submillimeter Imaging Radiometer (CoSSIR) measurements. Finally, we apply the Bayesian MCI to the Cloud Profiling Radar (CPR) measurements on CloudSat, and we use the cumulative distribution functions (CDFs) and empirical orthogonal functions (EOFs) to preserve the one‐point statistics and the two‐point statistics that allow for the creation of any number of synthetic ice cloud profiles that are statistically consistent with the Bayesian retrieval results. The synthesized profiles are a useful characterization of the ice cloud vertical structure that combines two disparate data sources, and the synthesis algorithm constitutes an essential initial step for producing critical information in submillimeter radiometry studies.

Towards an operational Ice Cloud Imager (ICI) retrieval product

Abstract. The second generation of the EUMETSAT Polar System (EPS-SG) will include the Ice Cloud Imager (ICI), the first operational sensor covering sub-millimetre wavelengths. Three copies of ICI will be launched that together will give a measurement time series exceeding 20 years. Due to the novelty of ICI, preparing the data processing is especially important and challenging. This paper focuses on activities related to the operational product planned, but also presents basic technical characteristics of the instrument. A retrieval algorithm based on Bayesian Monte Carlo integration has been developed. The main retrieval quantities are ice water path (IWP), mean mass height (Zm) and mean mass diameter (Dm). A novel part of the algorithm is that it fully presents the inversion as a description of the posterior probability distribution. This is preferred for ICI as its retrieval errors do not always follow Gaussian statistics. A state-of-the-art retrieval database is used to test the algorithm and to give an updated estimate of the retrieval performance. The degrees of freedom in measured radiances, and consequently the retrieval precision, vary with cloud situation. According to present simulations, IWP, Zm and Dm can be determined with 90 % confidence at best inside 50 %, 700 m and 50 µm, respectively. The retrieval requires that the data from the 13 channels of ICI are remapped to a common footprint. First estimates of the errors introduced by this remapping are also presented.

Prediction of cloud ice signatures in submillimetre emission spectra by means of ground-based radar and in situ microphysical data

Submillimetre down-looking radiometry is a promising technique for global measurements of cloud ice properties. There exist no observation data of sufficient size that can be used for detailed pre-launch studies of such an instrument and other means must be found to obtain data to optimise the instrument design and similar tasks. Several aspects of the observations make traditional retrieval methods not suitable and nonlinear multidimensional regression techniques (e.g. Bayesian Monte Carlo integration and neural networks) must be applied. Such methods are based on a retrieval database and to be successful the database must mimic relevant real conditions closely. A method to generate such databases of high quality is described here. Correct vertical distributions of cloud ice are obtained by basic data from ground-based radars. Cloud ice particle microphysical properties are generated randomly where statistical parameters are selected to mimic in situ measurement data closely. Atmospheric background fields from ECMWF are perturbed to account for variation on sub-grid scales. All these data, together with sensor characteristics, are fed into a state-of-the-art radiative transfer simulator (ARTS). The method was validated by a successful comparison with AMSU data. Copyright © 2007 Royal Meteorological Society

Computer-Based Research Advances in Economics

A set of four essays present research developments and computing in each of four areas of importance in economics. general equilibrium models, experimental economics, Bayesian Monte Carlo integration, and nonlinear stochastic growth models. Keywords : computing, economic models, general equilibrium models, experimental methods, Bayesian Monte Carlo integration, stochastic processes, nonlinear growth models.