particles as for example hail, attenuation also plays an important role for C band systems. For the polarimetric quantities, differences in attenuation between the horizontal and verti- cal channel because of oriented hydrometeors such as rain drops or ice crystals have to be
considered. While the specific attenuationk gives the attenuation of the horizontal channel,
the specific differential attenuationAdp (dB km−1) is defined as the difference in attenuation
in the horizontal and vertical channel. The attenuated polarimetric quantities can then be calculated as (Bringi and Chandrasekar (2001))
ZHH =ZHHo −2k r, (3.26)
ZDR =ZDRo −2ADP r, (3.27)
LDR =LoDR+ 2ADP r. (3.28)
Within SynPolRad, the specific and the specific differential attenuation are calculated to- gether with the polarimetric quantities by the scattering module solving the equations for the transmission matrix (Oguchi (1983), Vivekanandan (1986)). For the simulation of the beam propagation in the model domain, total attenuation and total specific attenuation are applied on the synthetic polarimetric quantities following Equations 3.26 to 3.28.
3.6
Interpolation of the Observations
Typically, a radar samples the atmosphere by so-called PPI scans (plan position indicator) varying the azimuth angle at a fixed elevation angle or RHI scans (range height indicator) varying the elevation angle at a fixed azimuth angle. If a complete volume is scanned, this is normally done by executing several PPI scans at different elevations. The spatial resolution of the radar is very fine in the surroundings of the instruments while the scanned volume increases with range because of beam broadening. According to the scanning technique and the irregular spatial resolution, the radar observations are executed and stored in polar coordinates. In order to simulate PPI and RHI scans, SynPolRad computes the polarimetric quantities as introduced in Section 3.2 at the grid points of the model. Then, the variables are interpolated to a polar coordinate system for the simulation of beam propagation (Section 3.4) including attenuation (Section 3.5) along its path. Finally, both, the observed and the synthetic polarimetric radar data, are transferred back to the model grid for evaluation. This is done because successful and fair comparisons of observations and simulations are only possible in the same spatial resolution allowing the application of the same statistical methods on the two fields. There are several reasons for transferring the radar data back to the model grid. The resolution of the radar is finer than the model resolution and, therefore, by averaging from the finer to the coarser resolution, the sub-grid variability as well as extreme values of the radar measurements are smoothened. A further advantage of the model grid lies in its regular horizontal resolution which allows to do statistics on the number of pixels.
Choosing the right grid for RHI scans is more difficult because both, the observations and the model data, are given at an irregular vertical resolution. The resolution of the model is very fine in the first thousand meters in order to describe well the processes of the planetary boundary layer. This is also true for the radar with a fine resolution near the radar becoming
40 3. Synthetic Polarimetric Radar
Figure 3.6: Comparison of POLDIRAD RHI scan in its original resolution (left) and interpolated on a vertical resolution of 200 m (right).
coarser due to beam broadening. Therefore, looking at RHI scans both, observations and simulations are interpolated at grid boxes with a constant height of 200 m. Figure 3.6 shows an example of a POLDIRAD RHI scan in its original resolution on the left and averaged on the 200 m vertical resolution on the right where the fine structures and extreme values are smoothened due to the averaging.
Chapter 4
Linking SynPolRad to the NWP
Model
In the last chapter, the polarimetric radar forward operator SynPolRad has been introduced as a novel tool for the evaluation of microphysical processes in NWP models. However, a successful evaluation of the model physics is only achievable if the link between the model and the forward operator conforms as closely as possible to the model assumptions. Ide- ally, all the input variables of the forward operator are determined by the weather forecast model and if this is not the case these free parameters have to be defined such that no arti- facts are included in the synthetic observables endangering a successful evaluation. Section 2.3.2 showed that polarimetric signatures depend on the spectrum of particle sizes relative to wavelength, particle shapes, particle dielectric constants, and particle falling behavior which affects the orientation of the particle relative to the direction of the incident wave and its polarization state. In order to successfully simulate polarimetric quantities out of model forecast, information on these quantities has to be provided by the NWP model to SynPolRad.
NWP models predict precipitation in bulk quantities of a given number of hydrometeor types where microphysical properties are derived using fixed assumptions regarding DSD and ice density. For the simulation of polarimetric quantities, SynPolRad requires information on the drop size distribution, the particle shape and falling behavior, as well as its dielectric constant given by the composition of the hydrometeor regarding the portions of ice, air, and water. Thus, there exists a number of free input parameters that are neither predicted nor defined by the mesoscale model but have significant importance for the simulations of polarimetric radar quantities. These are the parameters describing the shape and falling behavior of the particle as well as in the case of ice the degree of melting determining the dielectric constant. The link between the mesoscale model and SynPolRad is summarized as a conceptual overview in Figure 4.1.
In the case of rain, SynPolRad can easily be applied because the free parameters can be defined as a function of diameter. The problems simulating polarimetric radar signatures arise in the ice phase due to the natural variability in density, shape, and falling behavior for the different ice hydrometeor types. In order to overcome these problems and, nevertheless, simulate polarimetric radar parameters out of model forecasts, strategies of defining the free parameters will be discussed. This will be done on theoretical terms studying the impact of
42 4. Linking SynPolRad to the NWP Model
Figure 4.1: Conceptual view of the link between the NWP model and the polarimetric radar forward operator SynPolRad showing the input parameters defined by the model as well as the free parameters.
the single input parameters on the simulation of the polarimetric quantities using sensitivity studies. The results will be employed to determine the free parameters such that they re- present physical considerations accordingly to the model assumptions. In the following, the input parameters of SynPolRad for rain and the determination of the free parameters for the ice hydrometeors will be discussed. Then, the focus will be set on the representation of brightband aspects and the chapter will finish with an evaluation of the polarimetric radar forward operator SynPolRad.