The first published paper that we are aware of in this area Rutledge and Hobbs (1983). In this study, their kinematic cloud model used a bulk water formulation for the hydrometeors with categories for cloud water and ice, rain and snow. The initial thermodynamic fields were specified by rawinsonde data and allowed to adjust to the proscribed wind fields and diabatic sources and sinks of heating. In this regard this model and subsequent efforts does retrieve thermodynamic fields. The Rutledge and Hobbs (1983) study was designed to investigate the precipitation production mechanisms for warm fronts. Prior to this study, the mechanism that was proposed by many authors was that ice particles form in a so-called "seeder" zone and grow as they fall through a lower-level "feeder" zone. The model simulations allowed for an investigation of this "seeder-feeder" process both when the warm frontal ascent in the feeder zone is enhanced within a mesoscale rainband and when it is solely due to simply weaker frontal ascent. The simulations were two-dimensional and steady-state. The framework for the mesoscale rainband simulation is shown in Fig. 13.10 where the vertical motion is simply a smoothed profile of measured values applied over a mesoscale area:
In the other experiment, the vertical motions for the large-scale frontal ascent were obtained from compositing measured horizontal and vertical motions. Through these simulations and related sensitivity tests, Rutledge and Hobbs (1983) were able to show that the precipitation particles in the feeder zone in the weaker case grew due to vapor deposition. In contrast, the lifting in the rainband simulation was strong enough to produce liquid water in the feeder zone enabling the falling seeder particles to grow through riming. Following this study, Rutledge and Hobbs (1984) used a version of this model to investigate the precipitation production mechanisms within a narrow band and relatively shallow band of heavy precipitation that can occur along the leading edge of a cold front. In this study, the airflows were more closely tied to Doppler derived winds than in their previous study that used composite airflows.
While the method is a powerful technique for taking advantage of Doppler wind measurements to retrieve information about the microphysical processes taking place with cloud systems, the technique is not without limitations. One limitation is that there is not a consistent check for accuracy of the retrieved fields as was included in the previously described dynamic retrieval and related retrieval methods. In this regard however these early studies and subsequent work was able to compare observed precipitation rates and radar reflectivities with the model retrieved quantities. Another limitation is the steady state nature of the kinematic model. In order to be consistent with assumption, Rutledge and colleagues have applied this model to slowly evolving systems such as frontal rainbands in the two early works and in Rutledge (1989) and the stratiform precipitation regions in Rutledge (1986) and in Rutledge and Houze (1987). The technique also appears to be quite sensitive to errors in the Doppler derived air flows. For example through both comparisons of the retrieved microphysical fields with the output from a prognostic cloud model and of thermodynamic fields derived by the kinematic cloud model against the results of a dynamic retrieval, Barth and Parsons (1996) were able to detect significant errors in both the thermodynamic and microphysical fields of the kinematic modeling study of Rutledge (1989) due to errors in the Doppler derived vertical motions used as input.
The errors associated with retrievals of this type were also investigated by Ziegler (1985) and (1988). In this study the cloud model had some differences from the early work by Rutledge and Hobbs motivated no doubt by the different phenomena of interest. For example, in the Ziegler studies, the focus was convective storms so that the model needed to be three-dimensional and included a hydrometeor category for hail. In addition, the Ziegler work showed strong interested in the retrieved thermodynamic fields. In order to investigate the behavior of the errors in this approach, the winds from a cloud simulation were used as input so that the retrieved fields could be compared against a known standard. Efforts were made to make the characteristics of the input winds to be similar to a Doppler radar derived wind field through imposing observational errors that increased with height and by replacing missing winds outside the convective cell with estimated environmental values. The results were very encouraging since in these studies very close agreement was obtained between the known cloud model results and the retrieved thermodynamic and microphysical values as shown in the example in Fig. 13.11:
After exploring the accuracy of the technique, Ziegler et al. (1986, 1991) used this model to explore not only the thermodynamic and microphysical characteristics of the storm but also scientific issues associated the charging mechanisms for the electrification of convective clouds. An important distinction of these studies is that the steady-state assumption was no longer employed. In the first study, the input winds were obtained from a time varying conceptual model of the updraft in a convective storm constructed from single Doppler data. In the later study the input winds were interpolated in time from a series of multiple Doppler derived wind fields taken at three minute intervals over a period of 18 minutes. In both cases relatively favorable comparisons were obtained between the retrieved fields and in-situ data although periods of significant departure are also evident (Fig. 13.12):
In all the studies described thus far the radar measured reflectivities were not used in the retrieval process but rather used to validate the retrieved fields. Hauser and Amayenc (1986) developed a microphysical retrieval method that used the rain water content deduced from the radar reflectivity as an input to the model retrieval in addition to the Doppler derived wind fields. In addition, the unmeasured buoyancy field were deduced using the techniques by Roux that were described in the previous section. Hence, in using this approach the retrieved fields are more closely constrained by the radar observations, while one might argue that the cloud model is less sophisticated. The results appear physically plausible as noted for the retrieved cloud water and water vapor fields shown in (Fig. 13.13):
In a subsequent study, Hauser et al. (1988) coupled the thermodynamic and microphysical into a single method through an iterative process that links the retrieval of thermodynamic variables (temperature and pressure) to the microphysical variables of water vapor, cloud hydrometeors and precipitation. Thus in this approach, which essentially combines the approaches of Roux and co-workers with the method described in Hauser and Amayenc (1986), they used a complete set of governing equations including the momentum, thermodynamic and the various microphysical continuity equations. In this study, the precipitation fields were derived from the microphysical parameterization rather than being specified from the radar reflectivity as was done in Hauser and Amayenc (1986). In this study the retrieved surface rainfall rates and temperature perturbations are compared against observed in-situ values not used in the retrieval (Fig. 13.14):
We believe that the results are relatively favorable but some strong departures from the in-situ measurements are evident at times in the rainfall measurements. In particular we suspect that the radar measurements are not properly resolving the processes associated with the heavy rainfall at the leading edge of the system. The underestimation of the rainfall by the retrieval method (centered at X= 20 km) we suspect may be due to either errors in the wind field or in the microphysical parameterization. In terms of the later error source we note that such a comparison with observations would prove to be very difficult with a prognostic cloud model.
In the Hauser et al. (1988) study an attempt is also made to compare this approach against a method that uses only the thermodynamic equation and continuity equations to retrieve the microphysical variables and is thus more similar to the techniques of Rutledge and Ziegler. The results of this comparison include the conclusions that 1) the selection of a technique (thermodynamic retrieval, microphysical retrieval, or a combined approach) is largely dictated by the goals of the study, 2) the importance of keeping the thermal fields consistent with the wind field through including the momentum equations in the set of governing equations, favors the use of their combined approach, 3) the combined approach is more difficult to implement and computationally demanding. A combined thermodynamic and microphysical retrieval is also discussed in Geerts and Hobbs (1991).
A retrieval method closely related to the microphysical retrieval is to use the Doppler wind observations and radar reflectivity data to derive a water budget for convective systems. There are actually a number of different approaches that can be used. In one style of approach the water budget can be diagnosed directly from the methodology of microphysical retrieval. In this type of approach, Rutledge and Houze (1987) discuss a water budget for the stratiform area of a mid-latitude squall line closely related to their kinematic model. Also Chong and Hauser (1989) employed one of the retrieval methods of Hauser et al. (1988) (the one based only on the thermodynamic energy equation and continuity equations) to study convective and stratiform regions of a West African squall line. In the Gamache et al. (1993) water budget study of the inner core of hurricane,the retrieval of methods of Roux used to obtain the pressure and temperature perturbations which were subsequently used to determine the saturation mixing ratio. The microphysical retrieval were then based on the method of Hauser et al. (1988). In an alternate approach Gamache et al. (1993) used the reflectivity to diagnose the precipitation content and fallspeeds and the reflectivity data and the Doppler winds to determine the rate of precipitation production. Once the precipitation production is estimated, the cloud content can be determined from inverting the continuity equations for precipitation and cloud water. This technique is similar to the work of Churchill and Houze (1984) and others.