Dynamics of frontal circulations  Applications of Dynamic Retrieval  Boundary layer investigations

Dynamics of precipitating convection and downdraft forcing

There have been a number of studies of deep convective systems using the dynamic retrieval concept including the work of Lin and Pasken (1984), Lin et al. (1986), Hane and Ray (1985), Knupp (1988), and Kingsmill and Wakimoto (1991). These researchers and others were able to use the more complete set of variables afforded by the dynamic retrieval to better understand convective dynamics. For example, Kingsmill and Wakimoto (1991) used thermodynamic retrieval to study the lifecycle of an air mass thunderstorm revising the classical conceptual model of this type of convective event.

The inclusion of precipitation and associated processes results in several changes to the governing equations from the system described thus far and those used in Gal-Chen and Kropfli (1984). For example, the equations of motion (13.5), (13.6), and (13.7) are rewritten in anelastic form defining pressure as an Exner function $\pi$. The derivation of this form of the anelastic system of equations can be found in Ogura and Phillips (1962) and Wilhelmson and Ogura (1972). Extending our previously defined convention, the equations in three dimensional vector form in this system of equations appear as

$$\rho_{0}(z)\left({{d{\bf {V}}} \over {dt}}+{\bf {f_{i}}}\righ......eta_{v0}{\bf {\nabla} \pi^\prime} + {\bf {k} g \beta^\prime}$$ (13.19)

 

with c_p denoting the specific heat of air at constant pressure, $\bf f_{i}$ other measured forces such as Coriolis and mixing, and $\bf {k}$ the unit vector in the vertical direction Note also that the buoyancy force ${\rho}^\prime$ in the vertical equation of motion (13.7) was rewritten to include the buoyancy forces, $\beta$, that arise due in an atmosphere with clouds and precipitation so that

$${\beta}^\prime={\theta_{v}^\prime\over \theta_0} - q_{c} - q_{r}$$ (13.20)

 

where ${\theta}^\prime_{v}$ is the virtual temperature deviation, q_c is the mixing ratio of cloud water and q_r the mixing ratio of precipitation. The virtual temperature is in turn defined in the standard sense as (1.0 + 0.61 q_v)$\theta$ with q_v the water vapor mixing ratio. The continuity equation in this anelastic system of equations can be written as

$${\bf {\nabla} \cdot {\rho_{0} (z)}} {\bf V} = 0 \ \ .$$ (13.21)

  

A number of studies (Lin and Hughes 1987; Kessinger et al. 1988; Parsons and Kropfli 1990; Lee et al. 1992) used the dynamic retrieval within this system of equations to focus on microburst downdrafts within convective storms. A microburst is a short-lived (less than 5 minutes), small-scale (less than 4 km) strong downdraft below cloud base within a convective cloud. These downdrafts and the low-level wind shear associated with the strong horizontal flows resulting when the downdraft nears the surface has resulted in many aircraft accidents (Fujita and Byers 1977). Dynamic retrieval, coupled with in-situ measurements, showed that microbursts were forced by negative buoyancy and in turn that the contributions to the negative buoyancy from precipitation loading, evaporative cooling and cooling from melting depended upon the characteristics of the cloud (i.e., the precipitation rate, the height of cloud base, the aspect ratio of the downdraft) and the vertical lapse rates of temperature and humidity in the sub-cloud environment.

In the study of microburst downbursts, the mixing ratio of cloud water can often be neglected if the investigations are concentrated below cloud base. The contribution to the buoyancy from the precipitation mixing ratio can be calculated from the radar reflectivity using various equations termed Z-R relationships. For details on these relationships the reader is referred to the retrieval studies cited in this subsection. The neglect of the cloud water and the removal of the precipitation loading using the Z-R relationships allowed the investigators to solve directly for the virtual temperature fluctuations and to compare those to the contributions from rainfall to understand microburst forcing. An example of such an approach is shown in Fig. 13.5 from the study of Parsons and Kropfli (1990):

 

Figure 13.5: Results of a thermodynamic retrieval in a microburst downdraft in eastern Colorado created from taking the thermodynamic perturbations near the microburst center at different analysis times. a) Contribution to negative buoyancy from water loading. b) Virtual temperature contributions. (from Parsons and Kropfli 1990).

In this figure buoyancy deviations due to precipitation loading (Fig. 13.5a) and virtual temperature fluctuations (Fig. 13.5b) are both shown. The data were taken near the center of a microburst downdraft at different analysis times. From this figure and other data discussed in the text, Parsons and Kropfli were able to show that the microburst downdraft was driven increasingly by evaporative cooling as it moved downward through the boundary layer. This result is consistent with the deep dry adiabatic temperature lapse rate present in the ambient environment.

A different application of dynamic retrieval to microbursts was carried out by Lin and Coover (1988) who calculated the various terms in the kinetic energy budget. Traditionally the correlation between the vertical pressure gradient and the vertical velocity is calculated as a residual, but in this study it was calculated from a least-squares solution to the horizontal equations of motion. From the study it was concluded that correlation term mentioned above is important. This is is to be contrasted with a Rotta-type approximation (Donaldson, 1973) where the velocity-pressure correlation contribution in the budget of the Reynolds stresses is assumed to be of secondary importance.

Despite the collective success of these studies, the application to microbursts also illustrates several limitations of the retrieval analysis process. First a number of difficulties arise since the events are small-scale and short-lived as the Doppler radars simply cannot scan rapidly enough to obtain a ``snapshot" of the downburst and/or the parent convective storm at sufficiently high spatial resolution. The temporal resolution issue also arises in applying the retrieval technique as the local time derivatives in the momentum equations (13.19) begin to approach the advective terms in magnitude. Hence, careful treatment of the local time derivatives, such as calculating the local time derivative only after placing successive radar volumes in a frame of reference selected to minimize the local time changes, is necessary. Even with careful treatment of the time derivatives, the E_r consistency check is sometimes large within certain regions of analysis domain with values in excess of 0.5 often found. Recalling that the value of E_r is a measure of the signal-to-noise ratio one could take the approach of using a spatial filter to remove the noise and thereby lower the value of E_r to more acceptable levels. Such an approach is frequently used in this analysis technique with a Leise (1981) filter commonly selected to remove the fluctuations at the smallest scales. However, the small scale of the microburst precludes the use of spatial filters to reduce the noise as the signal can also be negatively impacted.

With the issue of accuracy of the retrieval process in mind, the reader is referred to the studies of Hane and Scott (1978) and Hane et al. (1981). These studies both deal with investigating the accuracy of the retrieval approach using the output from model simulations of convective systems which has the advantage of the retrieved fields being known. These papers contains important insight concerning such topics as the impact of observational errors on the retrieval process, on the time resolution needed for accurate retrieval and the impacts of filtering. Notable discussions on these issues can also be found in Gal-Chen (1978).

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