There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Data Mining - Concepts and Techniques.

Abstract A two-dimensional version of the Pennsylvania State University mesoscale model has been applied to Winter Monsoon Experiment data in order to simulate the diurnally occurring convection observed over the South China Sea. The domain includes a representation of part of Borneo as well as the sea so that the model can simulate the initiation of convection. Also included in the model are parameterizations of mesoscale ice phase and moisture processes and longwave and shortwave radiation with a diurnal cycle. This allows use of the model to test the relative importance of various heating mechanisms to the stratiform cloud deck, which typically occupies several hundred kilometers of the domain. Frank and Cohen's cumulus parameterization scheme is employed to represent vital unresolved vertical transports in the convective area. The major conclusions are: Ice phase processes are important in determining the level of maximum large-scale heating and vertical motion because there is a strong anvil componen...

Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model [presentation]

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

A new bulk microphysical parameterization (BMP) has been developed for use with the Weather Research and Forecasting (WRF) Model or other mesoscale models. As compared with earlier single-moment BMPs, the new scheme incorporates a large number of improvements to both physical processes and computer coding, and it employs many techniques found in far more sophisticated spectral/bin schemes using lookup tables. Unlike any other BMP, the assumed snow size distribution depends on both ice water content and temperature and is represented as a sum of exponential and gamma distributions. Furthermore, snow assumes a nonspherical shape with a bulk density that varies inversely with diameter as found in observations and in contrast to nearly all other BMPs that assume spherical snow with constant density. The new scheme’s snow category was readily modified to match previous research in sensitivity experiments designed to test the sphericity and distribution shape characteristics. From analysis of four idea...

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Explicit Forecasts of Winter Precipitation Using an Improved Bulk Microphysics Scheme. Part II: Implementation of a New Snow Parameterization

Considering that the statistics of the phase and the power of weather signals in the spectral domain are different from those statistics for echoes from stationary objects, a spectrum clutter identification (SCI) algorithm has been developed to detect ground clutter using single polarization radars, but SCI can be extended for dual-pol radars. SCI examines both the power and phase in the spectral domain and uses a simple Bayesian classifier to combine four discriminants: spectral power distribution, spectral phase fluctuations, spatial texture of echo power, and spatial texture of spectrum width to make decisions as to the presence of clutter that can corrupt meteorological measurements. This work is focused on detecting ground clutter mixed with weather signals, even if the clutter power to signal power ratio is low. The performance of the SCI algorithm is shown by applying it to radar data collected by University of Oklahoma-Polarimetric Radar for Innovation in Meteorology and Engineering.

A New Approach to Detect Ground Clutter Mixed With Weather Signals

Ensemble-based probabilistic forecasts are performed for a mesoscale convective system (MCS) that occurred over Oklahoma on 8–9 May 2007, initialized from ensemble Kalman filter analyses using multinetwork radar data and different microphysics schemes. Two experiments are conducted, using either a single-moment or double-moment microphysics scheme during the 1-h-long assimilation period and in subsequent 3-h ensemble forecasts. Qualitative and quantitative verifications are performed on the ensemble forecasts, including probabilistic skill scores. The predicted dual-polarization (dual-pol) radar variables and their probabilistic forecasts are also evaluated against available dual-pol radar observations, and discussed in relation to predicted microphysical states and structures.Evaluation of predicted reflectivity (Z) fields shows that the double-moment ensemble predicts the precipitation coverage of the leading convective line and stratiform precipitation regions of the MCS with higher probabiliti...

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Ensemble Probabilistic Prediction of a Mesoscale Convective System and Associated Polarimetric Radar Variables Using Single-Moment and Double-Moment Microphysics Schemes and EnKF Radar Data Assimilation

[1] The theoretical accuracy of baseline winds, estimated using spaced antennas (SA) and a full correlation analysis (FCA) method to process signals in the presence of noise, is derived assuming horizontally isotropic refractive index perturbations with a horizontal scale small compared to the transmitting antenna diameter D. This performance of the FCA method is compared with the theoretical performance of another correlation-based approach (i.e., the cross-correlation ratio method, CCR). The theoretical results of the error analysis are supported with numerical simulations and experimental data. It is shown that the theoretical analysis is valid and the results can be applied to improve wind estimates obtained from SA signals contaminated with additive white noise. The theory shows that the effect noise has on SA wind estimates depends on system configuration and lag spacing, and cannot be correctly accounted by a reduced correlation coefficient due to noise as hypothesized by May [1988].

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Performance of correlation estimators for spaced‐antenna wind measurement in the presence of noise

It is becoming widely accepted that radar polarimetry provides accurate and informative weather measurements, while phased array technology can shorten data updating time. In this paper, a theory of phased array radar polarimetry is developed, and the relationship between the wave field at the radar antenna coordinate and that at the hydrometeors is established, along with the correction matrix to the scattering matrix. The challenges and opportunities for the weather sensing are discussed.

Phased Array Radar Polarimetry for Weather Sensing: Challenges and Opportunities

The U.S. weather radar network is currently being upgraded with dual-polarization capability. Weather radar polarimetry is an interdisciplinary area of engineering and meteorology. This paper presents efficient ways to learn weather radar polarimetry through several basic and practical topics. These topics include: 1) hydrometeor scattering model and calculation of radar variables; 2) characteristics of polarimetric radar measurements and radar echo classification; and 3) rain microphysics retrieval. The supporting files, data, codes, and results are provided on the Web site http://arrc.ou.edu/~guzhang/Polarimetry/main.html. The study modules provide hands-on experience in the area of weather radar polarimetry and related fields.

Guifu Zhang

Papers

A New Approach to Detect Ground Clutter Mixed With Weather Signals

Ensemble Probabilistic Prediction of a Mesoscale Convective System and Associated Polarimetric Radar Variables Using Single-Moment and Double-Moment Microphysics Schemes and EnKF Radar Data Assimilation

Performance of correlation estimators for spaced‐antenna wind measurement in the presence of noise

Phased Array Radar Polarimetry for Weather Sensing: Challenges and Opportunities

Efficient Ways to Learn Weather Radar Polarimetry