Fred J. Kopp

Numerical Simulation of the Life History of a Hailstorm

Abstract A two-dimensional, time-dependent cloud model has been used to simulate the evolution of hail cells and hailstorms. The model has been under development for several years tested on a few days of real data, and gives reasonable predictions of the convective characteristics and essential precipitation processes for both severe and nonsevere convection days. Hydrodynamic equations for. deep convection are integrated over a 20 km square grid with 200 m spacing between grid points. Cloud formation and precipitation processes employing bulk water techniques are simulated in the model. Autoconversion and accretion are used to transform cloud water to rain. Precipitating ice (hail) is formed by the freezing of rain and through an approximation to the Bergeron-Findeisen process to transform cloud liquid to precipitating ice. Accretion of cloud water by rain, and accretion of cloud water, cloud ice and rain by hail are modeled. Wet and dry growth of hail and the shedding of rain from hail are simulated. Cl...

Specification of the scale and magnitude of thermals used to initiate convection in cloud models

Abstract Boundary layer similarity techniques are employed to specify the scale and intensity of a thermal perturbation used to initialize a cloud in a numerical cloud model. Techniques are outlined to specify the needed similarity variables from external information. Finally, the cloud model response using the similarity scaled thermal is analyzed employing variations in the similarity variables giving an indication of the importance of the correct specification of the initiating thermal.

Numerical simulation of the effects of cooling tower complexes on clouds and severe storms

Abstract A two-dimensional, time-dependent model has been developed which gives realistic simulations of many severe storm processes—such as heavy rains, hail and strong winds. The model is a set of partial differential equations describing time changes of momentum, energy, and mass (air and various water substances such as water vapor, cloud liquid, cloud ice, rainwater and hail). In addition, appropriate boundary and initial conditions (taken from weather sounding data) are imposed on a domain approx. 20 km high by 20 km wide with 200 m grid intervals to complete the model. Modifications have been made to the model which allow additional water vapor and heat to be added at several lower grid points, simulating effluents from a power park. Cases have been run which depict realistic severe storm situations. One atmospheric sounding has a strong middle-level inversion which tends to inhibit the first convective clouds but gives rise later to a severe storm with hail and heavy rains. One other sounding, is taken from a day in which a severe storm occurred in the Miami area. A third sounding depicts atmospheric conditions in which severe storms formed in the vicinity of Huron, South Dakota. The results indicate that a power park emitting 80 % latent heat and 20 % sensible heat has little effect on the simulated storm. A case with 100 % sensible heat emission leads to a much different solution, with the simulated storm reduced in severity and the rain and hail redistributed. A case in which water vapor is accumulated in a region and released over a broad depth results in slightly more rain from a severe storm.

Numerical Simulation of Dry Ice Cloud Seeding Experiments

Abstract The application of a two-dimensional, time-dependent cloud model to describe the effects of dry ice cloud seeding is demonstrated. A conservation equation and associated auxiliary equations for the mixing ratio of dry ice (CO2) are presented. The importance of identical time steps in both seeded and unseeded cases is discussed. Small convective clouds are seeded at about the −10°C level and the seeding agent (CO2) traced as it falls through the cloud creating a mass of cloud ice in its trail. The cloud ice transforms to snow and the snow to graupel/hail which then melts into rain as it falls below the zero degree isotherm level. Precipitation starts about 6 min earlier in the seeded cloud and the timing of the rain fallout affects the interaction with a second cell. Approximately 20% more rain falls from the seeded cell in a very light shower.

The Use of a Two-Dimensional, Time-Dependent Cloud Model to Predict Convective and Stratiform Clouds and Precipitation

Abstract A two-dimensional, time-dependent cloud model has been used in two field projects to forecast the convective development during the day from the morning sounding. In effect, the cloud model gives a dynamic analysis of the sounding as affected by heating and evaporation at the earths surface, divergence of the winds throughout the atmosphere, and cloud shadow effects. During the initial project, the Cooperative Huntsville Meteorological Experiment, the results were mixed. Model runs were easily made when soundings were available, but displaying the results in a meaningful and useful way was the limiting factor. In a later experiment, the North Dakota Thunderstorm Project, the problem of displaying results was overcome and soundings were available from the local weather service forecast office with a high degree of reliability. The experimental model correctly forecasts convective development about 80% of the time, and precipitation or no precipitation more than 70% of the time.

Observations and Model Simulations of Transport and Precipitation Development in a Seeded Cumulus Congestus Cloud

Abstract Observations made by three instrumented aircraft, a Doppler radar, and other data sources were used to follow the initiation and development of precipitation in a small cumulus congestus cloud. The cloud was seeded at its base using an airborne silver iodide solution burner. Sulfur hexafluoride tracer gas was released along with the seeding material. Analyzers on two instrumented aircraft detected the tracer gas during subsequent cloud penetrations as it was carried up into the cloud along with the seeding agent. Ice developed initially in the upper regions of the cloud near the −10°C level ∼15 min after the commencement of seeding. This is consistent with primary nucleation by the seeding agent. The cloud developed millimeter-size graupel within the following few minutes. A radar echo approaching 40 dBZ subsequently developed. The echo was observed to descend through the cloud as the cloud dissipated. One-dimensional, steady-state and two-dimensional, time-dependent bulk water models were used t...

A Simulation of Alberta Cumulus

Abstract A two-dimensional cloud model was used to simulate an Alberta, Canada, seeding experiment that was conducted on 24 July 1979, by the Alberta Research Council. The simulation reproduced some of the characteristics of the silver iodide seeded cloud in the actual case studies. This simulated cloud was also allowed to develop naturally and, in a third simulation, as a CO2 seeded cloud. A stratus layer was reproduced in the simulations, as well as the cloud used in the seeding simulations. The model was similar to those in previous papers, but there have been enhancements. Cloud ice was simulated as a bulk field with the total mass of ice; this was the sole predictor in the previous papers, while here an additional predictor, total number of ice crystals, was added. In the seeding simulations, the silver iodide produced a longer lasting seeding effect than the carbon dioxide. The carbon dioxide fell out of the cloud in minutes, while the silver iodide was carried around by the air flow for an indefini...

A Numerical Simulation of the 22 July 1979 HIPLEX-1 Case

Abstract A HIPLEX- A cloud case has been used to describe the effects of ice-phase cloud seeding on a cold base cloud. The cast was used at the First International Cloud Modeling Workshop/Conference held in 1985 in Irsee, Federal Republic of Germany, to provide modelers with a well-observed cloud-seeded case. Solid dry ice pellets (CO2) were dropped into the cloud at about the −10°C level. Aircraft and radar observations of the cloud were obtained over approximately 40 min of its life history. Seeding produced clear ice seeding signatures in this continental type cloud. Graupel formed within 10 min and rain was observed at the +10°C level 13 min after seeding. About 9.4 kT of rain was estimated to fall from the cloud. The modeling results also show enhanced ice in the seeded cloud and can be compared with an unseeded model cloud (not available in nature). The precipitation path from cloud ice to snow to graupel/hail to rain from the melted graupel is evident. The Bergeron process was important for snow in...

Fields of motion and transport within a sheared thunderstorm

Abstract The fields of motion within a small, strongly sheared High Plains thunderstrom are examined using measurements of reflectivity and velocity from an airborne Doppler radar and other in situ measurements. The measurements are complemented by a high resolution two-dimensional numerical simulation of the storm. Implications for predicting storm characteristics, delivery and effectiveness of seeding material, and precipitation efficiency are examined. The numerical model run was made in the forecasting mode 5 h before initial storm development and 7 h before the observations of the mature stage. The main features of the simulated storm structure and motions are very similar to those measured, except that the model produced a vertically and temporally compressed storm. The characteristics of the measured and the modeled storm, in combination, are consistent with other theories and observations that precipatation efficiency is low and a large portion of the processed water substance is transported out through the anvil in thunderstorms that develop in an environment with strong wind speed shears in the vertical. The measurements and the model reveal a quasi-steady-state organization during the mature stage. Although the storm formed in response to surface heating, the simulation and the radar measurements in combination indicate that the relative importance of inflow directly from the surface was diminished during the mature stage and completely cut off during the dissipation stage. Despite the modest size and intensity of this storm, the actual circulation within it was highly three dimensional and this, of course, could not be directly simulated by the two-dimensional model. Mature-stage inflows between about 3 and 6 km above ground level from a south-flank feeder cell field contributed significantly to the main updraft. Effective delivery of cloud seeding material to a storm like this would be influenced by the three-dimensionality and the relative importance of surface feeding in relation to inflows from levels above the surface. Such features would have to be determined in real time and state-of-the-art technologies offer the means to do this.

On the Computation of Gradients from Observations over Complex Terrain

A mathematical scheme is developed to compute the gradients of observations taken over complex terrain. The method is applied to an artificial example to demonstrate the scheme. An application is made to surface pressure observations between Little Rock, Arkansas, and Amarillo, Texas. Divergence computations are made with the scheme using observed wind data over the Black Hills of South Dakota.