General aspects of local radar data

The German Weather Service, abbreviated as DWD (Deutscher Wetterdienst), runs a net- work of 17 operational weather radars which are equipped with the latest dual polariza- tion Doppler technology. The 17 weather radars cover the whole Germany, providing many products for high resolution precipitation analysis and forecast. The scan strategy for the DWD’s radar network can be referred to under https://www.dwd.de/EN/ourservices/ radar products/radar products.html. The scanning cycle starts with the so-called precipitation scan, namely a near-surface scan during which the antenna follows the orography.

Fig. 2.9 shows the 17 radar network of DWD, with the study domain marked as a purple square. The study domain is covered by three radars. Among them, available data are from Radar T ¨urkheim and Radar Feldberg — see Table 2.2 for further details of the two radars. The 150 km coverage of the two radars are highlighted with two purple circles.

Weather radar takes snapshots of reflectivity distribution over large area from which the distribution of precipitation intensity is estimated. The snapshots of reflectivity are expressed as plan position indicators, or PPIs. There is a systematic change of PPIs in the observation height with range. As the domain is relatively small (a square with the side length of 19 km), the change in the elevation is neglected. The center of the domain is around 45 km from Radar T ¨urkheim and around 113 km from Radar Feldberg. With the elevation angle as low as possible to avoid ground echoes, according to equ (2.8), the measurement heights of Radar T ¨urkheim and Radar Feldberg for the study domain are respectively 1280 m and 2280 m above the ground (m. a. g.) under the normal propagation condition.

Table 2.2:Specification of Radar T ¨urkheim and Radar Feldberg

Item Specification Location T ¨urkheim 9.783◦ W, 48.585◦ N, 767.62 m.a.s.l. Location Feldberg 8.004◦ W, 47.874◦ N, 1516.10 m.a.s.l. Measured variables Radar reflectivity in dBZ, radio velocity Radar frequency 5.6 GHz

Elevation angle 0.5 – 1.8◦

(follow orography) Reflectivity quantization -32.5 up to 95.0 dBZ with 0.5 dBZ

increment Spatial resolution 1◦

×1 km (azimuth, range)

Range 128 km

Figure 2.9:Radar network of DWD, where the blue dot denotes each radar site and the blue circle indicates the radar coverage of 150 km range. The study domain is marked as a purple square with the side length of 19 km. The coverages of Radar T ¨urkheim and Radar Feldberg are highlighted with two purple circles. Reprinted from Deutscher Wetterdienst (Wetter und Klima aus einer Hand), weather fore- casting, numerical modeling. https://www.dwd.de/EN/research/weatherforecasting/ num modelling/bilder/02 datenassimilation abb09 en.html

The German Weather Service uses the DX file format to encode local radar sweeps. Raw, unprocessed DX products are in polar coordinates with the unit dBZ. The processing chain of DX products in this study is composed of (arranged in order): clutter removal, attenuation correction, conversion of reflectivity to precipitation rate, rainfall accumulation, re-projection from polar coordinates to Cartesian grid and clip the square data for the study domain. Some complementary descriptions about the processing chain are listed below.

• For clutter removal, despite the application of a Doppler filter at the signal proces- sor, the radar data still contains residual clutter (dynamic clutter), which can become considerable source of instability for the subsequent attenuation correction procedure [Kr¨amer and Verworn, 2008]. Therefore, the residual clutter is filtered out by the scheme proposed by Gabella and Notarpietro [2002], based on a texture filter that de- tects strong reflectivity gradients.

• For attenuation correction, the constrained gate-by-gate attenuation correction scheme is applied ([Kr¨amer and Verworn, 2008]; [Jacobi and Heistermann, 2016]).

• For the conversion of reflectivity to precipitation rate, the Z-R relation is parameterized asZ = 256R1.42_{, consistent with the parameterization adopted by DWD.}

• For the re-projection from polar coordinates (Resolution: 1◦

×1 km) to Cartesian grid (Resolution: 500 m×500 m), nearest neighbor method is applied, no interpolation is conducted.

All the radar data processing steps in this study are operated under the environment of

wradlib, an open source library for weather radar data processing. wradlib is written in the free programming language Python, and a tutorial on a typical workflow for radar-based rainfall estimation is available underhttp://docs.wradlib.org/en/latest/notebooks/basics/wradlib workflow.html.

3.1 Introduction

Unlike rain gauges which record accumulated precipitation depth in a point-wise manner, weather radars take snapshots of reflectivity distribution over large area from which the distribution of precipitation intensity is estimated. The field of reflectivity or precipitation intensity evolves with time. The evolution is generally reflected in two aspects: the evolu- tion in the magnitudes of the radar reflectivity or precipitation intensity and the evolution in the spatial pattern of the field.

It happens on occasions that the sampling frequency of weather radar is not capable of cap- turing the evolution details of the rainfall event to a satisfying degree, especially when the air motion is relatively strong. For example, when the horizontal wind speed is at 10 m/s, given the sampling frequency of every 5 min (e.g. the C band radars operated by DWD), the precipitation field will have a horizontal displacement of 3 km within the 5 minutes’ time in- terval. As shown by Pfaff [2013], precipitation accumulation obtained by directly adding up the 5-min-intervalled precipitation intensity maps will end up with some visually unsatisfy- ing, as described by the author, ripple-like structure in the accumulated precipitation maps, due to the large displacements between successive radar scans. The displacement between successive radar scans is normally caused by the wind. In this study, the displacement or the evolution of the field in terms of the spatial pattern is named as thewind displacement. The study distinguishes two kinds of wind displacement: the horizontal and the vertical displacement. The above is an reflection of the horizontal displacement. Since the radar im- ageries are measured at a constant altitude, namely a time series of horizontal maps sampled at fixed frequency.

Changing from the horizontal to a vertical point of view, the wind also imposes an influence on the precipitation field over the vertical distance. Hydrometeors, as they precipitate in the atmosphere, are very likely to be displaced by the wind. The effect of displacement by the wind is more pronounced for particles of less weight and larger surface area, such as snowflakes. As suggested by Mittermaier et al. [2004], observational evidence in their study shows that the fall streaks in the snow can lead to a displacement of the order 10 - 20 km. And even for raindrops, with a relatively high fall speed (0 - 9 m/s) due to large bodyweight, the drift driven by the air motion could be over considerable distances [Lack and Fox, 2007]. It is common practice to compare rain gauge data with the collocated radar data by assum- ing the vertical descending of the hydrometeors. The wind-induced displacement of the hydrometeors can result in large errors when comparing with the collocated rain gauge ob- servations on the ground. The phenomenon of the displacement of hydrometeors between

radar contributing layer in the air and the ground surface caused by the air motion is usu- ally referred to as “wind drift” by previous authors such as [Collier, 1999]; [Mittermaier et al., 2004]; [Lack and Fox, 2007] and [Rasmussen et al., 2003]. To avoid confusion and for the sake of consistency, the displacement along the vertical distance is termed as vertical displacement. Note the vertical distance is not necessarily between the radar contributing layer and the Earth’s surface, but also between any two layers in the air.