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

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

A completely new nonhydrostatic model system known as the Advanced Regional Prediction System (ARPS) has been developed in recent years at the Center for Analysis and Prediction of Storms (CAPS) at the University of Oklahoma. The ARPS is designed from the beginning to serve as an effective tool for basic and applied research and as a system suitable for explicit prediction of convective storms as well as weather systems at other scales. The ARPS includes its own data ingest, quality control and objective analysis packages, a data assimilation system which includes single-Doppler velocity and thermodynamic retrieval algorithms, the forward prediction component, and a self-contained post-processing, diagnostic and verification package. The forward prediction component of the ARPS is a three-dimensional, nonhydrostatic compressible model formulated in generalized terrain-following coordinates. Minimum approximations are made to the original governing equations. The split-explicit scheme is used to integrate the sound-wave containing equations, which allows the horizontal domain-decomposition strategy to be efficiently implemented for distributed-memory massively parallel computers. The model performs equally well on conventional shared-memory scalar and vector processors. The model employs advanced numerical techniques, including monotonic advection schemes for scalar transport and variance-conserving fourth-order advection for other variables. The model also includes state-of-the-art physics parameterization schemes that are important for explicit prediction of convective storms as well as the prediction of flows at larger scales. Unique to this system are the consistent code styling maintained for the entire model system and thorough internal documentation. Modern software engineering practices are employed to ensure that the system is modular, extensible and easy to use. The system has been undergoing real-time prediction tests at the synoptic through storm scales in the past several years over the continental United States as well as in part of Asia, some of which included retrieved Doppler radar data and hydrometeor types in the initial condition. As the first of a two-part paper series, we describe herein the dynamic and numerical framework of the model, together with the subgrid-scale turbulence and the PBL parameterization. The model dynamic and numerical framework is then verified using idealized and realistic mountain flow cases and an idealized density current. Other physics parameterization schemes will be described in Part II, which is followed by verification against observational data of the coupled soil-vegetation model, surface layer fluxes and the PBL parameterization. Applications of the model to the simulation of an observed supercell storm and to the prediction of a real case are also found in Part II. In the latter case, a long-lasting squall line developed and propagated across the eastern part of the United States following a historical number of tornado outbreak in the state of Arkansas.

/pdf/the-advanced-regional-prediction-system-arps-a-multi-scale-4ndsy21x71.pdf

The Advanced Regional Prediction System (ARPS) – A multi-scale nonhydrostatic atmospheric simulation and prediction model. Part I: Model dynamics and verification

A Short Course in Cloud Physics

Weather radars with conventional antenna cannot provide desired volume scan updates at intervals of one minute or less, which is essential for significant improvement in warning lead time of impending storm hazards. The agile-beam multimission phased array radar (MPAR) discussed herein is one potential candidate that can provide faster scanning. It also offers a unique potential for multipurpose use to not only sample weather, but support air traffic needs and track noncooperative airplanes, thus making it an affordable option. After introducing the basic idea behind electronic beam steering, the needs for frequent observations of convective weather are explained. Then, advantages of the phased array radar (PAR) for weather monitoring and improving data quality are examined. To explore and develop weather-related applications of the PAR, a National Weather Radar Testbed (NWRT) has been established in Norman, Oklahoma. The NWRT's main purpose is to address the advanced capabilities anticipated within the n...

Agile-Beam Phased Array Radar for Weather Observations

This paper proposes a new method of dual-Doppler radar analysis based on a variational approach. In it, a cost function, defined as the distance between the analysis and the observations at the data points, is minimized through a limited memory, quasi-Newton conjugate gradient algorithm with the mass continuity equation imposed as a weak constraint. The analysis is performed in Cartesian space. Compared with traditional methods, the variational method offers much more flexibility in its use of observational data and various constraints. Using the radar data directly at observation locations avoids an interpolation step, which is often a source of error, especially in the presence of data voids. In addition, using the mass continuity equation as a weak instead of strong constraint avoids the error accumulation and the subsequent somewhat arbitrary adjustment associated with the explicit vertical integration of the continuity equation. The current method is tested on both model-simulated and observed datasets of supercell storms. It is shown that the circulation inside and around the storms, including the strong updraft and associated downdraft, is well analyzed in both cases. Furthermore, the authors found that the analysis is not very sensitive to the specification of boundary conditions and to data contamination. The method also has the potential for retrieving, with reasonable accuracy, the wind in regions of single-Doppler radar coverage.

/pdf/a-variational-method-for-the-analysis-of-three-dimensional-4t0xlqnivt.pdf

A Variational Method for the Analysis of Three-Dimensional Wind Fields from Two Doppler Radars

A theory is presented for the Great Plains low-level jet in which the jet emerges in the sloping atmospheric boundary layer as the nocturnal phase of an oscillation arising from diurnal variations in turbulent diffusivity (Blackadar mechanism) and surface buoyancy (Holton mechanism). The governing equations are the equations of motion, mass conservation, and thermal energy for a stably stratified fluid in the Boussinesq approximation. Attention is restricted to remote (far above slope) geostrophic winds that blow along the terrain isoheights (southerly for the Great Plains). Diurnally periodic solutions are obtained analytically with diffusivities that vary as piecewise constant functions of time and slope buoyancies that vary as piecewise linear functions of time. The solution is controlled by 11 parameters: slope angle, Coriolis parameter, free-atmosphere Brunt–Vaisala frequency, free-atmosphere geostrophic wind, radiative damping parameter, day and night diffusivities, maximum and minimum surfa...

A Unified Theory for the Great Plains Nocturnal Low-Level Jet

A new three-dimensional single-Doppler velocity retrieval is introduced and tested with reflectivity and radial velocity data gathered during the Phoenix II field program near Boulder, Colorado. This retrieval is based on reflectivity conservation (with provision for raindrop fall speed), the incompressibility condition, and a temporal constraint on the velocity field. Two temporal constraints are considered: velocity stationarity and Taylor's frozen turbulence approximation (velocity stationarity in a moving reference frame). It is demonstrated that either of these temporal constraints can be used to derive a second conserved scalar from the original conserved scalar (reflectivity). This two-scalar system is, in general, overdetermined, but a least-squares formulation reduces the problem to a Poisson equation for a pseudostreamfunction. The requisite boundary conditions arise naturally from the least-squares formulation and require only single-Doppler measurements for their evaluation. The new r...

Alan Shapiro

Papers

Agile-Beam Phased Array Radar for Weather Observations

A Variational Method for the Analysis of Three-Dimensional Wind Fields from Two Doppler Radars

A Unified Theory for the Great Plains Nocturnal Low-Level Jet

Single-Doppler Velocity Retrievals with Phoenix II Data: Clear Air and Microburst Wind Retrievals in the Planetary Boundary Layer

A Unified Theory for the Great Plains Nocturnal Low-Level Jet