Numerous modifications to the Kain‐Fritsch convective parameterization have been implemented over the last decade. These modifications are described, and the motivating factors for the changes are discussed. Most changes were inspired by feedback from users of the scheme (primarily numerical modelers) and interpreters of the model output (mainly operational forecasters). The specific formulation of the modifications evolved from an effort to produce desired effects in numerical weather prediction while also rendering the scheme more faithful to observations and cloud-resolving modeling studies.

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The Kain–Fritsch Convective Parameterization: An Update

This comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability. It incorporates all aspects of environmental computer modeling including an historical overview of the subject, equations of motion and their approximations, a modern and clear description of numerical methods, and the determination of initial conditions using weather observations (an important science known as data assimilation). Finally, this book provides a clear discussion of the problems of predictability and chaos in dynamical systems and how they can be applied to atmospheric and oceanic systems. Professors and students in meteorology, atmospheric science, oceanography, hydrology and environmental science will find much to interest them in this book, which can also form the basis of one or more graduate-level courses.

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Atmospheric Modeling, Data Assimilation and Predictability

A compilation of the optical constants of ice Ih is made for temperatures within 60 K of the melting point. The imaginary part mim of the complex index of refraction m is obtained from measurements of spectral absorption coefficient; the real part mre is computed to be consistent with mim by use of known dispersion relations. The compilation of mim requires subjective interpolation in the near-ultraviolet and microwave, a temperature correction in the far-infrared, and a choice between two conflicting sources in the near-infrared. New measurements of the spectral absorption coefficient of pure ice are needed, at temperatures near the melting point, for 185–400-nm, 1.4–2.8-μm, 3.5–4.3-μm, 33–600-μm, and 1–100-mm wavelengths.

Optical constants of ice from the ultraviolet to the microwave

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.

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

Because of its simplicity, the empirical relation A = aR^{b} between the specific attenuation A and the rainrate R is often used in the calculation of rain attenuation statistics. Values for the frequency-dependent parameters a and b are available, however, for only a limited number of frequencies. Some of these values, furthermore, were obtained experimentally, and may contain errors due to limitations in the experimental techniques employed. The aR^{b} relation is shown to be an approximation to a more general relation, except in the low-frequency and optical limits. Because the approximation is a good one, however, a comprehensive and self-consistent set of values for a and b is presented in both tabular and graphical form for the frequency range f = 1-1000 GHz. These values were computed by applying logarithmic regression to Mie scattering calculations. The dropsize distributions of Laws and Parsons, Marshall and Palmer, and Joss et al., were employed to provide calculations applicable to "widespread" and "convective" rain. Empirical equations for some of the curves of a(f) and b(f) are presented for use in systems studies requiring calculations at many frequencies. Some comparison is also made with experimental results, and suggestions are given regarding application of the various calculations.

The aR b relation in the calculation of rain attenuation

A critical survey of the literature is presented. An empirical model of the complex refractive indices for ice and liquid water is constructed from this review. The model is applicable from -20 degrees C to 0 degrees C for ice and from -20 degrees C to 50 degrees C for water. The spectral interval for which the model applies extends from 2 micro, to several thousand kilometers in wavelength for ice and from 2 micro to several hundred meters in wavelength for water.

Broadband Complex Refractive Indices of Ice and Water

The use of one, two, three or more Doppler radars has become increasingly common in research programs. The advantage in increasing the number of radars is in the increased area covered and the accuracy with which wind estimates may be obtained. Although multiple-radar systems can yield special quantitative insight, a great deal of information can still be determined in real time from a single radar. It should be noted that the interpretation of radial velocity estimates from a single radar are not always unambiguous. Color displays of single-Doppler radial velocity patterns aid in the real-time interpretation of the associated reflectivity fields and can reveal important features not evident in the reflectivity structures alone. Such a capability is of particular interest in the identification and study of severe storms. A display utilizing a 5 cm Doppler radar is used to illustrate the patterns seen from several tornadic storms that occurred in central Oklahoma on 20 May 1977. Interpretation of ...

Single- and Multiple-Doppler Radar Observations of Tornadic Storms

Through the interactive use of Doppler-radar analyses and a three-dimensional numerical storm simulation the detailed structure of a supercell, tornadic storm is analyzed. This storm, named the Del City storm, occurred in central Oklahoma on 20 May 1977. The storm exhibits certain important features which are essential to maintaining its longevity and which promote the storm's transition to its tornadic phase. These features are strongly influenced by the rotational character of the storm separates the precipitation from the updraft and which orients the resulting downdrafts to which reinforce low-level convergence along the gust front and sustain the storm. Analyses of air parcel and rain trajectories within the storm provide a detailed visualization of this internal structure. These trajectories reveal that. air parcels rising through the cyclonically rotating updraft actually turn anticyclonically with height owing to the influence of the storm relative environmental wind field. Downdraft traj...

Observed and numerically simulated structure of a mature supercell thunderstorm

In 1984, the American Meteorological Society, the Cooperative Institute for Mesoscale Meteorological Studies, and the National Oceanic and Atmospheric Administration cosponsored the Intensive Course on Mesoscale Meteorology and Forecasting, held in Boulder, Colorado. This volume is an edited version of the lectures, including complete illustrations and extensive bibliographic references. The 31 chapters consider all aspects of mesoscale meteorology. After an introduction that discusses mesoscale classifications and typical forecast problems, the volume is organized in sections on observing techniques and systems, internally generated circulations, mesoscale convective systems, externally forced circulations, modeling, and short-range forecasting techniques and technology. As a textbook of mesoscale meteorology it will serve both practicing and student meteorologists.

Mesoscale Meteorology and Forecasting

The role of noninductive graupel-ice charge separation in the early electrification of the July 31, 1984, New Mexico mountain thunderstorm is assessed with a three-dimensional kinematic cloud model along with multiple Doppler radar and in situ measurements. Observations of the early electrification rate and the electric field distribution are consistent with modeled values that result when the noninductive mechanism works under the influence of convective motions and precipitation growth. An increase in ice particle concentrations and sizes, arising from vigorous precipitation growth, accelerates graupel-ice collision rates and hence the noninductive charging rate. Growing graupel particles experience increasing fall speed as they rise toward the top of the updraft. The resulting vertical flux convergence of graupel containing charge from previous noninductive collisions is a significant factor in the growth of the main negative charge density. This implies that a combination of air motion, precipitation interaction, and sedimentation contributes to the rapid intensification of storm electric fields. The linear electrification phase, which begins with the cessation of convective growth, is caused by a roughly constant noninductive charging rate and by the separation of negatively charged graupel and positively charged smaller ice particles by differential sedimentation, downdrafts, and horizontal advection in vertically sheared flow. When the sign reversal temperature for noninductive charging is assumed to be −10°C, the model results are characterized by a main negative charge in middle levels and provide the best overall agreement with the in situ field measurements in the July 31 storm. For a sign reversal temperature of −21°C the model results are characterized by a main positive charge center in middle levels, and the electric field polarity is opposite to the polarity measured at low and middle levels of the storm. The model and observational data, combined with findings of some laboratory studies, support the hypothesis that the actual reversal temperature in the July 31 storm is around −10°C. When the model includes the inductive graupel-droplet charging mechanism in addition to the noninductive mechanism, the effect of inductive charging is secondary to that of noninductive charging. The net effect of adding induction is dissipative. For example, the maximum field strength at the location of the aircraft measurements is slightly less than in the case where the noninductive mechanism acts alone. Weak charge screening layers were found to develop on the boundary of the modeled cloud.

Peter S. Ray

Papers

Broadband Complex Refractive Indices of Ice and Water

Single- and Multiple-Doppler Radar Observations of Tornadic Storms

Observed and numerically simulated structure of a mature supercell thunderstorm

Mesoscale Meteorology and Forecasting

A model evaluation of noninductive graupel‐ice charging in the early electrification of a mountain thunderstorm