Quantitative Precipitation Estimation from Radar Data â A ... - einfalt.de

MUSIC – Multiple-Sensor Precipitation Measurements, 

Integration, Calibration and Flood Forecasting 

A Project supported by the European Commission 

under Contract N o EVK1-CT-2000-00058 

Published is here the Deliverable 4.1 

titled 

Quantitative Precipitation Estimation 

from Radar Data – 

A Review of Current Methodologies 

by Ronald Hannesen 

Gematronik GmbH 

resulting from 

WP 4 

Gematronik GmbH 

Raiffeisenstr. 10 

41470 Neuss 

Germany 

Tel.: (+49) 2137 782 0 

Fax: (+49) 2137 782 11 

EMail: Info@Gematronik.com 

Web: www.gematronik.com 

Assessment of presently available radar estimation techniques and 

implementation of improved techniques for radar rainfall estimates

Contents 

Contents ..................................................................................................................... 2 

1 Scope of this paper ............................................................................................. 3 

2 Basic Principles of Radar Meteorology................................................................ 5 

3 Quantitative Precipitation Estimation I – Aspects of Rainfall Rate Derivation...... 7 

3.1 Drop Size Distributions and Z-R-Relations ...................................................... 7 

3.2 Clutter Filtering and Speckle Removing........................................................... 9 

3.3 Attenuation..................................................................................................... 11 

3.4 Vertical Profiles and Beam Blocking Corrections........................................... 13 

3.5 Orographic Enhancement.............................................................................. 14 

3.6 Bright Band, Snow and Hail ........................................................................... 14 

3.7 Stratiform and Convective Precipitation......................................................... 16 

3.8 Dual Polarisation Radars ............................................................................... 17 

3.9 Dual Wavelength Radars............................................................................... 20 

3.10 Scan Strategy............................................................................................. 21 

3.11 Operational Applicability............................................................................. 22 

4 Quantitative Precipitation Estimation II – Accumulated Rain: Aspects of 

Integration in Time.................................................................................................... 24 

4.1 Scan Strategy and Time Steps between Single Scans.................................. 24 

4.2 Speckle Filtering ............................................................................................ 27 

4.3 Handling of Missing Scans............................................................................. 27 

5 Outlook: Future Work in the MUSIC Project...................................................... 28 

References ............................................................................................................... 29 

MUSIC · Deliverable 4.1 · 8 th Oct. 2001 Page 2

1 Scope of this paper 

Introduction 

1 · Scope of this paper 

Precipitation measurement is an essential task for many purposes. The amount and 

the horizontal distribution of precipitation strongly influence evaporation from the 

earth’s surface, which triggers the global atmospheric circulation. For example 

farmers and forest authorities need precipitation information to control irrigation 

devices for optimal agricultural use. Hydrologists need precipitation data as input for 

river stage forecasts, flood warnings or waste water flow regulation. 

If much rain falls in a short time, the soil will not allow it all to infiltrate. The resulting 

surface runoff may result in floods causing a large amount of damage. The extent of 

a flood depends on the precipitation type. Convective precipitation systems, which 

seldom last longer than a few hours, can have very intense small-scale rain events 

causing hazardous flash floods in small subcatchments. The 1993 Brig flash flood is 

an example (e.g. Benoit and Desgagné, 1996). 

To recognise the danger of a potential flood, operational weather forecasts are 

necessary as well as sufficiently dense networks of precipitation measuring stations. 

Denser networks are required to observe rain events with higher intensity and 

smaller spatial extent. The observation of strong convective precipitation in large 

areas might require too much gauges, and therefore, use of weather radar data is 

essential. 

A weather radar provides information about the intensity of precipitation with a spatial 

resolution of less than a kilometer and a temporal resolution of about one minute. An 

area of several hundred kilometers can be observed with one device. A radar gives 

the chance to identify dangerous precipitation regions before they appear at a 

specific site. The three-dimensional data sets allow the investigation of vertical 

structures and of dynamics of precipitation systems. The problem, that the rain 

intensity itself cannot be measured directly, has resulted in a wide range of research 

fields with the aim of making precipitation estimates from weather radars as good as 

possible (Atlas, 1990). 

The MUSIC Project 

The main goal of the MUSIC (Multiple-Sensor Precipitation Measurements, 

Integration, Calibration and Flood Forecasting) Project is to develop an innovative 

technique to improve weather radar, weather satellite and rain gauge derived 

precipitation data, resulting in an integrated prototype flood forecasting system. The 

Project is subdivided into different work packages (WP). One of these, WP 4, has the 

aim of assessing available methodologies and of developing enhanced weather radar 

precipitation estimates. The present paper summarises the results of the first part of 

this package, namely a review of currently available methods in Quantitative 

Precipitation Estimation (QPE) from weather radar data. 


1 · Scope of this paper 

Very often radar precipitation estimates are adjusted by other-sensor data like rain 

gauge data, or are combined with numerical models. These methods will not be 

described in this paper. It is the task of other work packages within the Project to 

combine weather radar, weather satellite and rain gauge data by applying the Block 

Kriging and Bayesian combination techniques. Thus the radar data must not be 

adjusted by rain gauges or other-sensor data when using these methods. 

This paper presents an overview of currently used methods in Quantitative 

Precipitation Estimation (QPE) from weather radar data alone. Chapter 2 gives a 

basic introduction to radar meteorology. QPE can be divided into two steps: i) 

derivation of rainfall intensity from single- or multiple-parameter radar data; and ii) 

accumulation, i.e. integration in time of rainfall intensities. Chapter 3 reviews current 

techniques with respect to the first step, i.e. derivation of rainfall intensities from radar 

data. Chapter 4 lists aspects of the second step, namely the integration in time of 

rainfall intensity data. The last Chapter presents an outlook to future work within the 

MUSIC Project. 


2 · Basic Principles of Radar Meteorology 

2 Basic Principles of Radar Meteorology 

The basic principle of a weather radar is its ability to derive quantitative information of 

precipitation particles from the characteristics of electromagnetic radiation which is 

transmitted and received by such a device. The intensity of precipitation can be 

derived from the amplitude of the received radiation. Doppler radars measure the 

phase shift of the electromagnetic wave, which is used to obtain information about 

the atmospheric circulation. Some radars can measure polarimetric parameters, 

which give hints on the type and shape of the hydrometeors. A detailed review of the 

development in radar meteorology can be found in the articles collected in Atlas 

(1990). Further details of the theory of radar meteorology can be found in e.g. Battan 

(1973), Rinehart (1991), Sauvageot (1992) or Doviak and Zrnic (1993). 

This chapter will present the most important equations for the measurement of the 

reflectivity. The derivation of rainfall parameters will be handled in the next chapter 

(section 3.1), which gives an overview of techniques used therefor. The theory of 

polarimetric measurements will also be introduced in the next chapter (section 3.8). 

With a pulsed weather radar, the atmosphere – containing many scattering 

particles – is “illuminated” with a short pulse of electromagnetic radiation. The Radar 

Equation gives the relation between the transmitted power Pt and the received power 

Pr (after Sauvageot, 1992): 

2 

2 

2 

Pt G λ L c τ η 4 

Pr = ∫ f ( θ, 

ϕ) 

dΩ 

. (2.1) 

3 

2 

( 4π) 

2 r Ω 

Here G is the so-called antenna gain, which describes the ratio between the radiation 

intensity of a beam collected by the antenna reflector and an isotropic transmission of 

radiation. λ is the wavelength of the radiation. 1–L is the fraction of radiation lost by 

extinction (mostly called attenuation) on a single trip between the antenna and the 

scattering particles. c is the speed of light and τ the pulse duration. η is the volume 

specific backscattering cross section of the particles and is called radar reflectivity. 

r is the distance to the radar, which results from the time since pulse transmission. 

f 2 (θ,φ) is the normalised radiation intensity at the azimuth angle θ and the zenith 

angle φ (given relative to the beam axis, thus f 2 (0,0) = 1). The right-hand integral of 

eq. (2.1) extends over the complete solid angle Ω of the pulse volume, assuming 

homogeneous distribution of the scatterers. 

For spherical water droplets with a diameter D « λ, the backscattering cross section σ 

of the individual drops can be calculated using the Rayleigh approximation. We then 

find for the radar reflectivity 

Dmax 

η = ∫ σ ( D) 

n( 

D) 

dD ≈ dD ) D ( n D | K | 

π 2 6 

4 ∫ 

, (2.2) 

λ 

0 

5 

where Dmax is the maximum diameter of the droplets. n(D) is the drop size distribution 

and |K| 2 the dielectric coefficient (|K| 2 ≈ 0,93 for water and |K| 2 ≈ 0,18 for ice). The 

Rayleigh approximation is valid in most cases, as weather radars typically operate at 

X-Band (≈3 cm wavelength), C-Band (≈5 cm) or S-Band (≈10 cm). 

MUSIC · Deliverable 4.1 · 8 th Oct. 2001 Page 5 

Dmax 

0

2 · Basic Principles of Radar Meteorology 

Eq. (2.2) in combination with eq. (2.1) implies the definition of the radar reflectivity 

factor Z (which is usually shortly expressed as reflectivity): 

Dmax 

D 

6 

Z = ∫ n( 

D) 

dD. 

(2.3) 

0 

The real reflectivity Z of the particles has to be distinguished from the measured Zm, 

which can be calculated from the received power Pr and the distance r from eq. (2.1): 

1 2 

Zm = Pr r , (2.4) 

C 

with C being the radar constant: 

5 

2 

2 

2 

2 π Pt 

G L λ c τ 4 

C = | K| 

∫ f ( θ, 

φ) 

dΩ 

. (2.5) 

4 

3 

λ ( 4π) 

2 Ω 

The radar constant is mainly a hardware-dependent quantity. For the calculation of 

the measured reflectivity Zm according to eq. (2.4), usually the dielectric coefficient 

for water is used, and the attenuation losses are assumed by standard gaseous 

attenuation. 

The values of the reflectivity Z extends over several orders of magnitude. Thus it is 

used usually on a logarithmic scale: 

⎛ Z ⎞ 

DBZ = 10 log ⎜ ⎟ 

10⎜ 

6 −3 ⎟ 

(2.6) 

⎝ mm m ⎠ 

This dimension-less quantity is usually called reflectivity as well. The statement that 

“reflectivity is 1000 mm 6 m –3 “ is synonymous to “reflectivity is 30 dBZ”. Both means: 

Z = 1000 mm 6 m –3 ⇔ DBZ = 30 = 30 dBZ. (Note that dBZ is a dimension-less “unit”). 

The measured reflectivity Zm derived in such way is not necessarily equal to the real 

reflectivity Z. The simplification used in eqs. (2.2) to (2.5) can result in some 

problems, e.g. for non-liquid precipitation or strong attenuation. The consequences of 

such problems will be discussed in the next chapter. At the beginning of that 

chapter, the derivation of rainfall data will be discussed. Later in that chapter, basic 

principles of polarimetric measurements will be presented. 


3 · QPE I – Aspects of Rainfall Rate Derivation 

3 Quantitative Precipitation Estimation I – Aspects 

of Rainfall Rate Derivation 

In the last chapter, the basic principles of reflectivity measurements have been 

introduced. Several steps are only valid if certain assumptions are true. This present 

chapter will deal with the consequences of situations where the assumptions are not 

true in reality. 

The derivation of rainfall data from reflectivity measurements has not been presented 

in the previous chapter, even though it is an important point of radar meteorology. 

This topic is dealt with in this chapter for the reason that the assumptions necessary 

for the derivation of rainfall rate are never given exactly. The reasons and 

consequences of this are given in the same section as the derivation of rainfall data 

(section 3.1). 

As already stated in the first chapter, the derivation of precipitation amounts from 

radar data can be divided into two steps 

i) the derivation of rainfall intensity data (valid for a certain time point); and 

ii) the accumulation of rainfall intensity data, i.e. integration in time. 

This chapter presents different possible error sources and issues that have to be 

considered during the derivation of rainfall intensity data. Available algorithms to 

overcome such errors are listed. One section deals with the problem of operability, 

i.e. real-time application of algorithms. Problems that arise with the accumulation in 

time will be discussed in the following chapter. Algorithms to adjust radar data by 

other-sensor data will not be presented at all, as they are not appropriate to WP 4. 

3.1 Drop Size Distributions and Z-R-Relations 

In the last chapter, the definition of the reflectivity Z was given in eq. (2.3); and the 

way how to measure it (or, better, how to derive the measured reflectivity Zm) was 

given in eq. (2.4). Assuming that the measured reflectivity is same than the real, the 

rainfall intensity R may be derived. R is defined as 

∞ 

6 ∫ 

0 

π 3 

R = D v( 

D) 

n( 

D) 

dD , (3.1) 

where v(D) denotes the fall velocity of a drop of the diameter D. To calculate the 

rainfall rate R from reflectivity Z, the fall velocity has to be known as well as the drop 

size distribution n(D). Of course these are given only in seldom cases. But lots of 

measurements have shown that the drop size distribution roughly follows an 

exponential law: n(D) = N0e -ΛD (e.g. Marshall and Palmer, 1948). If the rain drop fall 

velocity is expressed as v(D) = v0·(D/D0) P , for reflectivity Z and rainfall intensity R 

follows: 

Z = 6! N0 Λ –7 , (3.1a) 


R = 

π v 

6 D 

0 

P 

0 

N 

0 

Γ( 

4 + P) 

Λ 

−4−P 

where Γ is the gamma function. 

Marshall and Palmer (1948) found 

Λ = 4,1 mm –1 (R / mm·h –1 ) –0,21 


, (3.1b) 

and N0 = 8000 mm –1 m –3 , 

which gives from eq. (3.1a) 

Z = 296 mm 6 m –3 (R / mm·h –1 ) 1,47 (3.2) 

Substituting Λ from eq. (3.1b) with the result from Marshall and Palmer (1948) gives 

for the fall velocity relation P = 0,76 and v0 = 3,34 m/s (for D0 = 1 mm). This fall 

velocity relation is nearly identical to that one derived by Liu and Orville (1969) with 

direct measurements; they found P = 0,8 and v0 = 3,35 m/s for D0 = 1 mm. For very 

large drops (with diameters above about 4 mm) this relation gives too high velocities. 

The equation from Atlas et al. (1973) give better results then. The found a fall velocity 

relation of the form v(D) = v0 – v1·e –(0,6 D/mm) with v0 = 9,65 m/s and v1 = 10,3 m/s 

(note that this relation gives erroneous results for small drops). 

It is a common way in radar meteorology to express the relation between reflectivity 

and rainfall rate in a Z-R-relation of the form Z = a·R b (cf. eq. (3.2)), where reflectivity 

Z is expressed in mm 6 m –3 and rainfall rate R in mm h –1 . Battan (1973) lists several 

dozen Z-R-relations. The application of a certain Z-R-relation always implies a certain 

drop size distribution and a certain fall velocity law. The deviation of the reality from 

these assumptions may result in large errors of R. 

Such errors can be reduced, if the precipitation type is classified e.g. as 

“thunderstorm” or “drizzle” (Fiser, 2001) and then applying different Z-R-relations 

(see also section 3.7 for that topic). Austin (1987) found that the Z-R-relation has only 

small variations within one precipitation event of the same genesis, even if R and Z 

vary over a wide range. But this method may sometimes lead to wrong results: 

Kreuels (1988) analysed Z-R-relations of more than ten years continuous 

measurements with a Joss-Waldvogel distrometer and found no correlation between 

precipitation type and Z-R-relation nor between season and Z-R-relation. 

For this reason, individual drop size distributions measured by distrometers may be 

taken as input for improved, site- and time-dependent Z-R-relations. This procedure 

must not be confused with adjustment: adjustment means that radar derived R data 

are corrected in a post-processing step, whereas selections of distrometer-derived Z- 

R-relations do not care about the absolute values of R from the distrometer and the 

corresponding radar data. 

Another problem arises with inhomogeneous beam filling and with data interpolation. 

If the scatterers do not fill the pulse volume homogeneously, the radar will measure a 

mean reflectivity factor. Due to the non-linearity of the Z-R-relation, the rainfall 

intensity derived from that mean reflectivity will be different from a mean rainfall rate 

derived from the Z-distribution within the pulse volume (if the latter could be 

measured at all). 

In a similar way data interpolation influences the results. Whereas the measured data 

are based on a polar grid, rainfall data mostly have to be derived on a cartesian 



system. If a cartesian grid point is interpolated from several polar co-ordinates, the 

interpolation could be done in the Z data, or in the DBZ data, or in the R(Z) data. 

Again, three different results will occur and the interpolation in R does not always 

give the best results. 

3.2 Clutter Filtering and Speckle Removing 

Clutter Filtering 

Clutter refers to all non-meteorological echoes that influence the radar data quality. 

Very often clutter is used as a synonym for ground clutter, meaning all returns from 

the earth’s surface. The echoes from the ground are usually the strongest of all 

echoes, at least close to the radar. This makes removal or at least reduction of clutter 

necessary. 

Different techniques of clutter filtering may be used: 

• Doppler filter or statistical filter (applied in the signal processor): In the first case, 

the Doppler spectrum of the received signal is analysed and a narrow band width 

around zero velocity is removed or interpolated. Doppler filter require a Doppler 

radar, which fortunately has become standard in recent years. In the latter case, 

the long correlation time of ground clutter is used to identify clutter by the pulseto-pulse 

changes of reflectivity samples. 

• Clutter maps (usually applied as a post-processing after the signal processor): 

The reflectivity values sampled at fair-weather conditions are store in a file. For all 

subsequent scans, the clutter map amount is subtracted from the measured 

reflectivity. 

• Sophisticated clutter suppression schemes which are a combination of the above 

mentioned and may take into account other information like terrain data. An 

example is described in Lee et al. (1995). 

It must be noted that no clutter filter will work perfectly. Of course the solid earth is 

not moving, but the radar antenna is, and so are plants blown by the wind. Thus 

clutter signals have a velocity and spectrum width differing from zero and may 

sometimes not be separable from a weather echo. The clutter intensity is not 

constant over time, but changing e.g. due to a wet coating. A clutter filter may also 

remove large parts of the weather signal, often if the radial velocity of the weather is 

close to zero and if the spectrum of the weather signal is narrow (as e.g. in stratiform 

snow). 

Sea clutter caused by waves is a severe problem, because it has velocities 

significantly differing from zero (see figure 3.1). But as in all ground clutter, it is 

strongest in the lowest elevation scans and always related to the same positions. 

Thus it can be identified by special algorithms. 



Figure 3.1: Examples of sea clutter. In the upper image showing reflectivity data from a Norwegian 

radar, the sea clutter is visible only in those sectors, where the valleys in the vicinity of the radar allow 

direct sight to the sea. The data of the lower images were obtained from a radar in Taiwan located at 

the coast line. Thus the sea clutter covers a wide range up to about 50 km distance, beyond which the 

earth curvature became effective. The velocity data (lower right image) illustrate the wave motion of 

about 4 m/s from the Northeast. 

Other clutter may appear from time to time at random locations and thus is not 

removable by real-time algorithms. Such clutter types are 

• Echoes from birds or insects 

• Echoes from aircraft, balloons, ships or trains 

• Echoes from artificial atmospheric tracers (chaff) 

But even the normal clutter of a given radar site may sometimes be enlarged 

significantly: In cases of anomalous beam propagation (refraction), caused e.g. from 

low-level temperature inversions, the radar beam may hit the ground at places were 

this is not possible under normal conditions. In such cases, application of clutter 

maps may fail completely. Nevertheless algorithms have been developed to identify 

such conditions and to reduce the clutter influence (Harrison et al., 2000; Kessinger 

et al., 2001). 



In general it can be stated that the clutter contamination is less for higher elevation 

angles. Thus the use of higher elevation angles may be applicable for some 

purposes. See section 3.10 (scan strategy) for more aspects on this topic. 

Speckle removing 

As even the best clutter removal techniques may fail in some conditions, clutter 

contaminated data may remain. Such data may come up as isolated speckles or as 

points with abnormally large magnitude and can be interpolated by surrounding 

measurements. Receiver noise speckles can be eliminated in the same way. Speckle 

removing can be set up in the signal processor or can be applied as a postprocessing 

step (e.g. Fulton et al., 1998). 

3.3 Attenuation 

Attenuation is a serious problem in radar meteorology. Every material on the way 

between antenna and target interfere with the radiation. Some part of the radiation is 

lost due to this interference. Attenuation consists of absorption and scattering. The 

atmospheric gases cause attenuation as well as the radome used for protection of 

radars. The scattering of radiation in atmospheric particles is used to measure 

reflectivity; this implies that meteorological targets cause attenuation as well. Some 

attenuators have effects which are more or less constant with time and thus can be 

corrected quite easy. Attenuation is dependent of the radar’s wavelength; for 

precipitation, it is strong for X-Band radars and weak for S-band radars. The most 

important attenuation effects are listed in this section. 

Radome Attenuation 

The attenuation caused by the a dry radome depends only weakly from antenna 

direction and thus can be considered as constant. It can be corrected in the radar 

calibration itself. Nevertheless caution must be taken at radome design for the 

arrangement of radome joints; they shall produce as least scatter as possible (Manz 

et al., 1998). 

For precipitation estimates, the change of radome attenuation due to water on its 

surface may become quite large: one-way attenuation of several dB even for 

moderate rain has been reported (Manz et al., 1998; Löffler-Mang and Gysi, 1998); 

for strong rain, this might make a quantitative rainfall estimation impossible. For such 

reasons, radome surfaces usually have hydrophobic coating. Radomes should be 

cleaned from time to time, because dirt could eliminate the hydrophobic coating 

effect completely. 

Attenuation in Gases (Air) 

The attenuation in atmospheric gases is depending on air density which mainly is a 

function of height. Additionally the composition of air, mainly the amount of water 



vapour, influences the gaseous attenuation. Typically values of two-way gas 

attenuation lie around 1dB / 100km (for S-Band radars). For this values being small 

compared to possible attenuation in rain and because the variations are not very 

large, the gas attenuation is usually corrected in the signal processor, where the 

product of a hardware-specific constant and the distance is added to the measured 

values. 

Attenuation in Precipitation 

If the precipitation particles consist of drops being small compared to the radar 

wavelength, the Rayleigh approximation can be applied. Then the absorption is 

proportional to the integral over the drops’ diameter to the power of 3, and the 

scattering is proportional to the integral over the drops’ diameter to the power of 6. 

Thus for the attenuation, which is the sum of absorption and scattering, the extinction 

coefficient σE can be approximated by 

∞ 

∫ 

0 

α 

σE = c D n( 

D) 

dD , (3.3) 

where c is a constant and α an exponent between 3 and 6 (in most cases between 

3.5 and 4.0), depending from the wavelength. From the Marshall and Palmer (1948) 

results, the rainfall rate can be written as 

∞ 

2 ∫ 

0 

3. 

76 

R = c D n( 

D) 

dD, 

(3.4) 

(cf. the discussion of the eqs.(3.1) to (3.2)). This indicates, that for typical weather 

radars, the absorption might be directly proportional to the rainfall rate and 

independent of the drop size distribution, namely if α = 3.76. This statement is best 

fulfilled for K-band radars (≈1 cm wavelength). For other wavelengths, attenuation 

relations of the form σE = c3·R β can be applied (with β around 1.0). See Doviak and 

Zrnic (1993) for further details. 

Such formulas can be used to calculate the attenuation from rainfall rate, which is 

calculated from the measured reflectivity. With this method, each ray of radar data 

can be corrected step by step. 

It has to be noted that the above considerations are only valid for small raindrops. In 

case of large raindrops, when the Rayleigh approximation becomes invalid, or in 

presence of snow or hail, attenuation correction formula may give wrong results. For 

C-Band radars, the attenuation from light rain can be neglected, for S-Band radar 

even from moderate to strong rain. In such cases, only strong rain cells give 

significant attenuation in relatively small sectors. The echoes from behind the cell in 

this sectors can be compared with neighboured, not attenuated rays to derive the 

total attenuation from one rain cell (Upton and Fernández-Durán, 1998). However, 

such method is difficult to implement on real-time processing. 



3.4 Vertical Profiles and Beam Blocking Corrections 

Radars which are located in mountain regions have to deal with the difficulty that 

several valleys cannot be “seen” by the radar. Thus information from upper-level 

elevations have to be extrapolated to the ground. A first attempt is to assume 

constant reflectivity. This gives good results only if no major microphysical processes 

take place in the atmospheric layers below the lowest accessible elevation. But 

several processes may change the reflectivity Z or the rain rate R during the falling of 

hydrometeors, which gives different vertical profiles (e.g. Huggel et al., 1996): 

• Evaporation decreases Z and R 

• Condensation increases Z and R 

• Particle type conversion (e.g. melting snow) changes Z but not R 

• Particle coagulation or disruption changes Z but not R 

• Increasing friction through denser air increases Z but does not change R 

Usually several of this processes will happen simultaneously. For such effects, a 

vertical profile correction which is depending on location, time, season or weather 

condition may give better results than assuming constant reflectivity (Germann, 1998; 

Germann and Joss, 2001; Germann and Joss, 2000). Such profiles can be derived 

from radar volume data or may be set up by the radar operator. 

If a radar is surrounded by mountains, several rays at lower elevations will be 

blocked totally by mountains as described above. But a lot of beams will be blocked 

only partially. If the blocked part is not too large, the corresponding reflectivity data 

can be corrected from geometric consideration of the beam using high-precision 

digital terrain data. For this correction, inhomogeneous scatterer distribution may also 

be considered (Hannesen, 1998, chapter 3; Hannesen and Löffler-Mang, 1998). See 

figure 3.2 for an example. 

a) 

Precipitation im mm derived from 

non-corrected radar data 

25 

20 

15 

10 

5 

Distance smaller than 60 km 

Distance between 60 and 90 km 

Distance larger than 90 km 

0 

0 5 10 15 20 25 

Precipitation in mm at ground 

b) 

Precipitation in mm derived from 

corrected radar data 

0 

0 5 10 15 20 25 

Precipitation in mm at ground 

MUSIC · Deliverable 4.1 · 8 th Oct. 2001 Page 13 

25 

20 

15 

10 

5 

Distance smaller than 60 km 

Distance between 60 and 90 km 

Distance larger than 90 km 

Figure 3.2: Comparison of 24h radar derived rainfall data (left axis) with rain gauge data (abscissa) 

(from Hannesen, 1998, chapter 3). The left image shows uncorrected radar data. For the right image, 

the radar date were corrected for partial beam filling. Solid squares indicate gauges closer than 60 km 

to the radar, open squares between 60 and 90 km, and crosses more than 90 km away from the radar.


It should be noted, that even in flat terrain a vertical profile correction may be 

necessary. If the lowest elevation angle is set e.g. to 0.5 degree, this results in an 

altitude of about 1,5 km above the radar in 100 km distance, and of about 4 km in 

200 km distance. If the area of investigation is very small and close to the radar, the 

assumption of constant reflectivity may give sufficient results. 

3.5 Orographic Enhancement 

If warm, moist air is flowing over hills, condensation processes can occur. Sometimes 

this condensation increases significantly already falling precipitation from upper 

altitudes. This additional condensation is very often limited to a shallow layer directly 

above the surface and is called orographic enhancement. Due to the condensation 

processes, the drop size distribution is changed significantly and thus also reflectivity 

Z, rainfall rate R and the Z-R-relation itself. These phenomena are related to certain 

weather conditions as the warm sector of extra-tropical cyclones (Kitchen et al., 

1994; Neimann et al., 2001; White et al., 2001). 

Due to their small height, areas of orographic enhancement are difficult to detect. 

Furthermore, the corresponding radar data may be contaminated by ground clutter 

from the mountains that cause the enhancement. As orographic enhancement is 

correlated to special weather conditions, algorithms for their correction may need 

other information besides radar data alone. The correction algorithms have to take 

into account the specific site conditions, mainly orography, as well. Nevertheless, 

some real-time correction schemes exist (e.g. Kitchen et al., 1994). 

3.6 Bright Band, Snow and Hail 

In the previous sections, the assumption of small liquid water droplets has often been 

made to describe phenomena or correction schemes. In reality, non-liquid 

precipitation particles like snow or hail may occur in those layers which are taken for 

the rainfall rate estimation from reflectivity data. In such cases, the simple equations 

presented in the preceding sections may be not valid. The consequences will be 

discussed in this section. 

The Bright Band 

When snow flakes or ice crystals begin to melt, the cover with a thin water film. Due 

to the fact that the dielectric coefficient |K| 2 for water is about five times higher than 

for ice, the reflectivity increases. Theoretical calculations have shown that a small 

water film may result in nearly the same backscattering cross section of the particle 

as if it was completely liquid. Snow flakes contain large parts of air, but regarding the 

backscattering cross section these parts have no large effect: they appear as if they 

were completely filled with ice. During the melting phase, the particles tend to 

accumulate together which increases Z further. 

When the particles continue to fall down, they become more and more liquid. Thus 

their volume decreases and their fall speed increases until they have become liquid 



droplets. Both effects reduce Z significantly: the volume loss because of the D 6 

dependence, and the increasing fall velocity because the volume-specific particle 

density is decreased. 

The above described effects result in a horizontal layer of increased reflectivity (e.g. 

Austin and Bemis, 1950), which is called the Bright Band. This name comes from the 

early time of radar meteorology with analogue displays, where the brightness 

represented the reflectivity. The bright band appeared in vertical cross sections as a 

thin band of very bright echo display. Fig. 3.3 shows an example of a bright band. 

Fig. 3.3: Vertical cross section through a bright band. The used grey scale would make the name 

“Dark Band” more appropriate here (from Hannesen, 1998). 

The above mentioned decrease of reflectivity due to volume reduction and increased 

fall speed at the final stages of the melting process are stronger pronounced in 

stratiform precipitation, which mainly consists of slow falling ice crystals and snow 

flakes above the freezing level, than in convective precipitation, which mainly contain 

faster falling grauple-like particles in the ice phase. These different precipitation types 

cause different microphysical processes below the bright band; thus typical bright 

band profiles for different precipitation types can be obtained (Huggel et al., 1996). 

If radar data are not corrected for the effects of bright band, too high rainfall 

estimates will be the result in those measurement points that are affected. Thus 

several bright band identification and correction algorithms have been developed 

(e.g. Kitchen et al., 1994; Gysi et al., 1997), which provide significant improvements 

in radar rainfall estimates. Such algorithms also have to care about far-distance 

measurements, where the vertical extent of the radar beam is much larger than the 

bright band thickness, and for the data from above the bright band with ice particles, 

where snow Z-R-relations should be applied (see also below). 

Bright band detection algorithms may be used as an estimator for the freezing level 

and provide information for forecasters. On the other hand, if the freezing level is 

known and given as information supplement for a bright band detection algorithm, the 

algorithm will have more reliable results than if it would only perform on radar data. 


Snow 


Snow flakes and ice crystals cannot be described by a simple radar equation 

because of their irregular shape and orientation. The effect of the different dielectric 

constant may easily be taken into account, but snow flakes can become as large as 

5 cm, whereas ice crystals typically have sizes of about one mm. As mentioned 

above, the large amounts of air inside snow flakes do not allow a common relation 

between the particle diameter and its backscattering cross section. Thus a reflectivity 

as in eq. (2.3) makes no sense for snow flakes. So for ice particles, reflectivity 

usually means measured reflectivity. Instead of rainfall rate, the equivalent rain rate is 

taken, which basically means the amount of liquid water if the ice was melted. 

Due to the variations of snow shape, orientation and size, the parameters of 

applicable Z-R-relations cover a wide range. Several Z-R-relations for different snow 

types have been obtained and are given in the literature (e.g. Battan, 1973). But it 

must be noted that the errors affecting precipitation estimates from radar derived 

snow reflectivity data usually are larger than for liquid rain. 

Hail 

Hail can cause strong damage on agricultural plants and on infrastructure. It can 

occur in all heights of the troposphere and is thus difficult to detect by singleparameter 

radar. Probabilities of hail occurrence can be derived regarding the 

following theoretical assumption: Above the freezing level, besides hail only supercooled 

water droplets and ice crystals and snow flakes can occur. Super-cooled 

water droplets are very small and thus have negligible reflectivity. Snow flakes may 

have large sizes (and thus large reflectivity values) only around the melting layer, 

where coagulation is very likely. Thus if strong echoes appear somewhat above the 

freezing level, the occurrence of hail is very likely. The hail probability is larger, the 

larger the vertical extent of such data above the freezing level is (Waldvogel et al., 

1979). It must be kept in mind, that for typical summer thunderstorms, the hail will 

melt in most cases on its way down to the earth’s surface. 

Hail has no large direct influence on hydrology, but it affects the Z-R-relation: A few 

large hailstones will result in very large values of Z, but the corresponding R remains 

too weak; thus R may be over-estimated. Large hail does no longer fulfil the Rayleigh 

approximation, even for S-Band radar. As a consequence, not only the R estimation 

may be erroneous in case of hail, but also attenuation correction algorithms may fail 

completely. These errors can be reduced if the presence of hail can be identified with 

sufficient accuracy; some hail Z-R-relations exist in literature. As described above, a 

single-parameter radar has only limited chances to detect hail. Much better results 

are obtained using polarimetric radars (see section 3.8) 

3.7 Stratiform and Convective Precipitation 

The meteorological conditions and thus microphysical processes are different for 

stratiform and convective precipitation. The main difference is the vertical air velocity, 

which is much larger in convective cases (a few m/s compared to several cm/s). The 

microphysical processes result in different drop size distributions for stratiform and 



convective precipitation and thus in different Z-R-relations. Battan (1973) lists Z-Rrelations 

for various weather types. But it must be kept in mind that sometimes the 

correlation between the weather type and the Z-R-relation is poor (Kreuels, 1988; 

see section 3.1). 

Due to the meteorological forcing, stratiform precipitation events exhibit different 

patterns than convective precipitation. In the first case, horizontal variations of the 

reflectivity are small, and a bright band is likely to appear (if the clouds top over the 

freezing level). In the latter case, the horizontal fluctuations are quite large, whereas 

vertical reflectivity gradients are weaker, at least in the lowest few kilometers. So 

three-dimensional properties of the reflectivity data can be used so separate 

convective from stratiform precipitation (Rosenfeld et al., 1995; Hannesen, 1998, 

chapter 4; Germann and Joss, 2001). The results can be used to apply for different 

Z-R-relations or for different vertical profile corrections in case of blocked lowelevation 

beams. 

3.8 Dual Polarisation Radars 

Conventional weather radars transmit a horizontally polarised electromagnetic wave. 

Some type of radars use dual polarisation techniques: they have the capability to 

transmit and receive horizontally and vertically polarised radiation. This allows the 

measurement of several polarimetric quantities (e.g. Doviak and Zrnic, 1993; Zrnic 

and Ryzhkov, 1999): 

The differential reflectivity ZDR is defined as 

10 h Zv 

= ⎜ 

⎛ 2 

2 

10 log s 

⎟ 

⎞ 

hh svv 

, (3.5) 

⎝ 

⎠ 

where Zh is the reflectivity from horizontal polarisation, and Zv from vertical 

polarisation. sij are members of the backscattering matrix of the particles (i,j = h,v). 

Spherical particles like small drops give Zh = Zv, thus ZDR = 0. Large drops are oblate 

and thus give positive values of ZDR. 

ZDR = log ( Z ) 

The linear depolarisation ratio LDR is defined as 

10 hv Zh 

= ⎜ 

⎛ 2 

2 

10 log s 

⎟ 

⎞ 

hv shh 

, (3.6) 

⎝ 

⎠ 

where Zhv is the reflectivity received on the vertical channel at transmission on the 

horizontal channel. For spherical particles as well as for oblate particles with 

horizontal axis, Zhv vanishes and thus LDR becomes negative infinite. But if oblate 

particles are tumbling and thus have a tilted axis, Zhv becomes different from zero. It 

is typically some orders of magnitude smaller than Zh, thus LDR lies somewhere 

between -40 dB and -20 dB. 

LDR = log ( Z ) 

The differential phase ΦDP is defined as 

ΦDP = Φhh – Φvv, (3.7) 

where Φhh and Φvv are the integrated phase shift of radiation along the transmission 

path for horizontal and vertical polarisation, respectively. 



The specific differential phase KDP is defined as 

∆ ΦDP 

KDP = . (3.8) 

2 ∆r 

It is the change of the differential phase with range. From theoretical considerations, 

KDP is almost proportional to the rain rate and only little dependent of the drop size 

distribution. 

The correlation coefficient (at zero lag) ρHV is defined as 

ρHV = s vvs* 

hh 

⎡ 

⎢ 

⎣ 

2 

shh 

1/ 

2 

svv 

2 

1/ 

2 ⎤ 

⎥ , 

⎦ 

(3.9) 

where s*hh is a member of the backscattering covariance matrix. 

The reader is referred to Doviak and Zrnic (1993), Chapter 8, for further theoretical 

background and details of these quantities. 

Quantitative precipitation estimation can be improved significantly, if polarimetric 

measurements are taken into account. To illustrate this, let us consider the following 

example: Two drop size distributions may be given which result in the same rainfall 

rate, but the first one contains some large drops and relatively few small drops (like in 

a light shower), whereas the second distribution consists of many small drops and no 

large drops (as in a dense drizzle). Due to the power-of-6 law, the reflectivity of the 

first distribution will be larger than for the second. With Z-R-relations, this problem 

cannot be solved. Now the large drops are oblate, thus the first distribution will give a 

higher differential reflectivity ZDR than the second one. This means that taking ZDR 

data into account, deviations from a standard drop size distribution may be resolved 

at the rainfall estimation and give better results than using Z-R relations (e.g. 

Ryzhkov et al., 2001). 

Several Z-ZDR-R-relations have been derived from theoretical calculations and 

measurements. Table 3.1 shows an example which also illustrates our above 

example considerations (using R = 0.0076 Z 0.93 10 –0.281 ZDR ; from Gorgucci et al., 

1994): Same R values result from higher reflectivity, if ZDR increases. The table also 

contains R data obtained from a standard Z-R-relation (Z = 200 R 1.6 ). These values 

are denoted by the thin green line across the Z-ZDR-table. A look at the 

corresponding ZDR scale shows, that these standard Z-R-relation implies differential 

reflectivity around zero (being typical for small drops), if the reflectivity is weak, 

whereas ZDR rises up to a few dB for high reflectivity values (caused by several large, 

oblate drops) according to a standard Z-R-relation based on a standard exponential 

drop size distribution. 

Table 3.1 gives a hint to the danger that lies in the application of such Z-ZDR-Rrelations: 

by the red lines, the border of rain rate values within a factor of five around 

the standard case are indicated (for constant DBZ). One can see that for a given 

reflectivity value, a change of ZDR by about 2 dB causes a factor of five in rainfall rate. 

This must be compared with the necessary change in reflectivity: for DBZ, a change 

of 7 dB is necessary (for constant ZDR) to change the rain rate by a factor of five, and 

using standard Z-R-relations, DBZ needs a change of about 10 dB to bias R by such 



Standard Z-R a = 200 b = 1.6 

R (mm/h) 0,2 0,3 0,6 1,3 2,7 5,6 11,5 23,7 48,6 99,9 205,0 421,1 864,7 

R (mm/h) dBZ 

ZDR (dB) 10 15 20 25 30 35 40 45 50 55 60 65 70 

5 0,0 0,0 0,0 0,1 0,2 0,5 1,6 4,6 13,4 39,0 113,7 331,8 967,9 

4,75 0,0 0,0 0,0 0,1 0,2 0,6 1,8 5,4 15,7 45,8 133,7 390,0 1137,8 

4,5 0,0 0,0 0,0 0,1 0,3 0,7 2,2 6,3 18,5 53,9 157,1 458,5 1337,6 

4,25 0,0 0,0 0,0 0,1 0,3 0,9 2,6 7,4 21,7 63,3 184,7 539,0 1572,4 

4 0,0 0,0 0,0 0,1 0,4 1,0 3,0 8,7 25,5 74,4 217,2 633,6 1848,5 

3,75 0,0 0,0 0,0 0,1 0,4 1,2 3,5 10,3 30,0 87,5 255,3 744,8 2173,0 

3,5 0,0 0,0 0,1 0,2 0,5 1,4 4,1 12,1 35,3 102,9 300,1 875,6 2554,5 

3,25 0,0 0,0 0,1 0,2 0,6 1,7 4,9 14,2 41,5 120,9 352,8 1029,4 3003,1 

3 0,0 0,0 0,1 0,2 0,7 2,0 5,7 16,7 48,7 142,2 414,8 1210,1 3530,3 

2,75 0,0 0,0 0,1 0,3 0,8 2,3 6,7 19,6 57,3 167,1 487,6 1422,5 4150,1 

2,5 0,0 0,0 0,1 0,3 0,9 2,7 7,9 23,1 67,3 196,5 573,2 1672,3 4878,8 

2,25 0,0 0,0 0,1 0,4 1,1 3,2 9,3 27,1 79,2 231,0 673,9 1965,9 5735,4 

2 0,0 0,1 0,2 0,4 1,3 3,7 10,9 31,9 93,1 271,5 792,2 2311,1 6742,4 

1,75 0,0 0,1 0,2 0,5 1,5 4,4 12,9 37,5 109,4 319,2 931,2 2716,8 7926,2 

1,5 0,0 0,1 0,2 0,6 1,8 5,2 15,1 44,1 128,6 375,2 1094,7 3193,8 9317,8 

1,25 0,0 0,1 0,2 0,7 2,1 6,1 17,8 51,8 151,2 441,1 1287,0 3754,6 ###### 

1 0,0 0,1 0,3 0,8 2,5 7,2 20,9 60,9 177,8 518,6 1512,9 4413,8 ###### 

0,75 0,0 0,1 0,3 1,0 2,9 8,4 24,6 71,6 209,0 609,6 1778,5 5188,8 ###### 

0,5 0,0 0,1 0,4 1,2 3,4 9,9 28,9 84,2 245,6 716,7 2090,8 6099,8 ###### 

0,25 0,1 0,2 0,5 1,4 4,0 11,6 33,9 99,0 288,8 842,5 2457,9 7170,7 ###### 

0 0,1 0,2 0,6 1,6 4,7 13,7 39,9 116,4 339,5 990,4 2889,4 8429,7 ###### 

-0,25 0,1 0,2 0,6 1,9 5,5 16,1 46,9 136,8 399,1 1164,3 3396,8 9909,8 ###### 

-0,5 0,1 0,3 0,8 2,2 6,5 18,9 55,1 160,8 469,2 1368,7 3993,1 ###### ###### 

-0,75 0,1 0,3 0,9 2,6 7,6 22,2 64,8 189,0 551,5 1609,0 4694,2 ###### ###### 

-1 0,1 0,4 1,1 3,1 8,9 26,1 76,2 222,2 648,4 1891,5 5518,4 ###### ###### 

Table 3.1: Rainfall rates R derived from Z and ZDR. R values from a standard Z-R-relation are given at 

the top, the corresponding values are indicated by the green line in the Z-ZDR-table. The red lines 

illustrate the border of all R data within a factor of five around the standard Z-R data. 

amount. This illustrates that the ZDR measurement and the corresponding calibration 

must be done very precisely (better than 0.2 dB) to obtain reliable results. 

But even with such precise equipment, Z-ZDR-R-relations give erroneous results in 

case of hail or snow. If for example a strong thunderstorm contains a few large hail 

stones, these hail causes very high reflectivity. Compared to standard Z-R-relations, 

the real rainfall rate is then smaller, thus too high rain rates would be obtained. But 

applying a Z-ZDR-R-relations as in table 3.1 would make this estimation much worse: 

hail stones are random oriented and thus ZDR will be around zero. For high 

reflectivity, the corresponding rainfall rate may be more than one order of magnitude 

higher than R derived by a standard Z-R-relation from reflectivity data alone. And 

even this R is too high compared to reality. 

For C-Band radars, attenuation becomes a severe problem, because the attenuation 

is stronger for horizontal reflectivity than for vertical in the case of large, oblate drops; 

thus ZDR is biased to negative values. 

According to theoretical considerations, KDP is almost proportional to the rainfall rate 

and only weakly dependent of the drop size distribution. Thus deriving R from KDP is 

more reliable than using Z-R-relations or Z-ZDR-R-relations. Furthermore KDP 

measurements are very robust to partial beam blocking and attenuation effects. 



Reliable results have also been obtained using ZDR-KDP-R-relations, i.e. deriving 

rainfall rate from differential reflectivity and specific differential phase data. This has 

been proven in several measurements (e.g. Ryzhkov et al., 2001). 

KDP-R-processing has one major disadvantage: As KDP is a derivative, noise may 

have significant influence and could cause negative KDP data. This makes it 

necessary to average the measurements in radial direction, losing the advantage of 

high resolution (Illingworth, 2001). Furthermore, anisotropic scatterers or non- 

Rayleigh conditions will bias KDP-R- or ZDR-KDP-R-relations. 

Besides more accurate rainfall estimates, dual polarisation data offer the possibility to 

identify the main hydrometeor type within a radar pulse volume. Hail can be detected 

from dual polarisation radars (e.g. Nanni et al., 1998). Sophisticated precipitation 

type determination algorithms use all available polarimetric quantities to distinguish 

between rain, drizzle, hail, dry snow, wet snow and so on (e.g. Lim et al., 2001). 

Until now, only few dual polarisation radars are available, but polarimetric 

measurements cover a wide range of present research. So in future possibly dual 

polarisation radar become available also for operational observations. 

3.9 Dual Wavelength Radars 

As discussed in section 3.3, attenuation due to precipitation is stronger for X-Band 

than for S-Band radars. For S-Band radars it can be neglected for all cases except 

very intense rain cells. This circumstances can be used for the application of dual 

wavelength radars: If a radar has for example the possibility to detect reflectivity data 

from and S-Band and X-Band system simultaneously, the total attenuation of the X- 

Band data can be calculated for each position in each ray. Differentiating with respect 

to the range, the attenuation coefficient for the X-Band can be derived for each 

measurement point. According to eqs. (3.3) and (3.4), this attenuation can be 

calculated into rainfall rate R with very robust relations, which are almost 

independent of the drop size distributions (Doviak and Zrnic, 1993). 

The rainfall rate is derived from a differential, thus even weak noise in the reflectivity 

data might cause significant errors, maybe even negative rain rates. Some radial 

averaging may become necessary to overcome these errors. But this means a loss in 

one of the major advantages of the radar: its high spatial resolution. Fortunately the 

noise effects are negligible in case of strong precipitation, correlated to strong 

differential attenuation. And these are the important cases for hydrological purposes, 

where the robustness of this method has its advantages compared to rainfall 

estimation from single parameter radars. Unfortunately only few dual wavelength 

radars are available. 

Again it should be noted that in some weather conditions this method may become 

erroneous: The attenuation-rainfall-relation is based on the assumption of liquid 

water, thus snow, hail or melting particles do not allow for such kind of precipitation 

estimation. 


3.10 Scan Strategy 


Reflectivity data for Z-R conversion should be measured close to ground, but they 

should not be contaminated by ground clutter, nor should they be blocked 

completely, to avoid as much errors as possible which might bias the data by 

application of different correction schemes. Very often the scan strategy is not only 

determined by the need to obtain quantitative precipitation estimates, but also other 

meteorological phenomena may be essential to be detected. Rainfall intensity data 

can be obtained from three different type of scans: 

• PPI-scan, i.e. data from one elevation angle only are considered 

• Pseudo-PPI-scan: one elevation with azimuth-dependent tilting elevation angle 

• Volume-scan, i.e. a scan with several subsequent elevations 

The PPI-scan with one elevation only is a simple and rapid possibility to measure a 

horizontal distribution of reflectivity data. It can be repeated within a very short time 

and thus provides the opportunity to observe even rapidly changing weather 

phenomena. But taking only PPI-scans brings up some major disadvantages: The 

height above ground is varying strongly with range, and thus e.g. clutter 

contamination is much larger close to the radar than far away. In mountain regions, 

either areas with beam blocking will appear (if the elevation angle is set low) or there 

are areas, where the measurement position is too high above the ground (if the 

elevation angle is set high) or even both. If only one PPI angle is used, individual 

vertical profiles cannot be obtained from the radar data, and the application of bright 

band detection algorithms becomes very difficult or impossible. 

One disadvantage of the single-PPI-scan with fixed elevation angle can be overcome 

by using a varying elevation angle: into directions with flat terrain, a low elevation 

angle is used. This angle is shifted slightly upward when the antenna turns to 

directions with mountain areas. This procedure can give a good compromise 

between the need of being close to the ground and not to block the antenna beam. 

Such scan type is used by the German Weather Service with elevation angles 

between 0.5 and 1.8 degrees for precipitation estimates (Schreiber, 1998). The main 

disadvantage of such scan compared to the previous type is that any correction 

algorithms become more complicated due to the azimuth-dependence of the 

elevation angle (e.g. for bright band detection or anomalous propagation correction), 

which means that more CPU time is needed (with possible negative impact on 

operational applicability). 

Finally precipitation data may be derived using volume-scans, i.e. scans with multiple 

elevations. Such three-dimensional data sets allow to avoid clutter contamination 

close to the radar, because data from upper elevation angles can be obtained there. 

Usually the data are taken from different elevation angles, which are determined by 

the horizontal distribution of the terrain height. A best fit between the need to have 

data close to the ground, but not clutter-contaminated nor totally beam-blocked can 

always be obtained. This type of precipitation estimation is used by the NEXRAD 

system (Fulton et al., 1998) and the SRI product (Surface Rainfall Intensity) of 

Rainbow ® . Volume scans provide much better chances for bright band detection 

algorithms and for vertical profile analysis and correction; they are essential for some 

sophisticated wind retrieval or phenomena detection algorithms which often have to 



be performed on the same radar data as the rainfall estimation algorithms. Volume 

scans have one severe disadvantage compared to the others: they require much 

more time. This may prevent the detection and analysis of fast-developing 

phenomena. 

Modern radar control and data evaluation software allows interlaced scan strategy: a 

volume scan with several elevations for three-dimensional analysis (like vertical 

profile, wind algorithm, phenomena detection) is interrupted several times by a lowlevel 

scan with one (or a few) elevations for precipitation estimation. This allows a 

compromise between the need of small time steps between precipitation scans and 

the need of three-dimensional data. The first chapter of the next section will focus on 

the effects of different time steps between precipitation scans in more detail. 

3.11 Operational Applicability 

In the previous sections, many concepts for the improvement of rainfall intensity 

estimation have been presented. The most important constraints were listed. Of 

course this review is far away from being complete. Details about the correction 

schemes can be found in the referenced literature. One final point should given 

attention here: the applicability of rainfall estimation on real-time. 

The possibility or the need to use certain correction steps is first of all limited by the 

radar hardware and the signal processor: For example, dual-polarisation techniques 

cannot be applied for the most operational radars. A Doppler clutter filter requires a 

Doppler radar; many radars have to use statistical filters and clutter maps. S-band 

radars are affected by attenuation through precipitation only very weakly; 

corresponding correction algorithms can be omitted without severe loss of data 

quality. 

Some correction steps are necessary only at specific site conditions: 

• Climate: In the tropics is no need for bright band correction or snow Z-R-relations, 

if the area of interest is not too large (thus elevation heights remaining small). 

Snow will seldom fall below 4 km above MSL in the tropics. 

• Orography: In flat terrain is minor need to extrapolate radar data from upper levels 

to the surface than in mountain areas with the problems of beam blocking. Thus 

less sophisticated vertical profile corrections may be applied or can be omitted 

totally. This could even mean that no three-dimensional scans are necessary 

which gives the chance of rapid repetition. 

• Coastal sites: If a radar is located close to an ocean or large lake, algorithms for 

sea-clutter reductions are necessary. Some oceans favour the appearance of 

low-level temperature inversions; thus increased problems with anomalous 

propagation may occur. 

These circumstances require that operational rainfall estimating algorithms should be 

constructed modular, it means that they should have the possibility to apply or omit 

different correction steps independently. 

Usually other real-time radar data processing is running simultaneously on the same 

platform, and other processing require correction steps as well. This gives some 



limitation for the CPU time consumption of all algorithms for radar data processing. 

For this reason it is sometimes necessary to skip a highly sophisticated correction 

step and use a simpler scheme instead, whose resulting data quality may be a few 

percent less than from the sophisticated algorithm. 


4 · QPE II – Accumulated Rain: Aspects of Integration in Time 

4 Quantitative Precipitation Estimation II – 

Accumulated Rain: Aspects of Integration in 

Time 

In the previous chapter, methods currently available to estimate quantitative rainfall 

rate from weather radar data have been presented. Important sources of possible 

errors have been discussed, possible solutions were shown. The effects of used 

radar hardware were discussed as well: influence of different wavelengths as well as 

the ability of Doppler measurements or of obtaining polarimetric quantities. 

If all necessary correction steps have been applied to derive the best rainfall rate 

data from radar measurements, an important step towards hydrological application of 

such data has been made. But there remains another problem, which will be 

discussed in this chapter: the integration of rainfall data in time. A rain gauge is 

measuring continuously, thus instantaneous rainfall rates as well as accumulations 

over selectable time intervals can be available. Radar derived rainfall intensities exist 

only in discrete time steps. Information about the development between these steps 

is not directly available. 

The present chapter deals with different ways of filling this gap of information. Some 

aspects of data quality control will be given as well. 

4.1 Scan Strategy and Time Steps between Single Scans 

To obtain accumulated precipitation amounts from radar derived rainfall rates R, the 

R data have to be integrated in time. A common way to do this is to multiply the 

instantaneous R data with the time interval between the scans. This method is simple 

and consumes only little CPU time, thus real-time application is no problem. 

However, the time ∆t between the scans must be small enough. A first estimate is 

that 

∆t < X / V (4.1) 

will give sufficient accuracy, with X being a measure for the horizontal extent of 

precipitation patterns and V being their propagating speed. In stratiform precipitation 

events, X is of the order of 10 km, whereas rain cells can be as small as 1 km or 

even less. Considering a propagation speed of 10 m/s, this would result in a time 

step of about 15 minutes or less for the first case, and about one and a half minute or 

less for the second case. The smaller the time step ∆t, the better the resulting 

accumulates will be. 

If the time step between scans is much longer, the accumulated data will show some 

discrete patterns in the horizontal distribution. If for example a small rain cell 

propagates across the radar coverage, those places where the cell was at each scan 

time will experience too high rain amounts, whereas the places between will miss a 

large portion of the data. As a result not only hydrological use of such accumulated 

data will give wrong results, but also any radar-raingauge comparison must fail. 



Fig. 4.1a: 75 minute precipitation accumulation with a time step of 15 minutes (for details see text). 

Fig. 4.1b: As fig. 4.1a, but with a time step of 6 minutes. 



Fig. 4.1c: As fig. 4.1a, but with a time step of 1:30 minutes. 

The effect of too large time steps is illustrated in the figures 4.1a to 4.1c: each image 

shows the accumulated rainfall data of 75 minutes of observation. The individual 

rainfall rate data were multiplied by the time step between the scans. In the first case 

(fig. 4.1a), only one scan was taken every fifteen minutes. Random distributed areas 

with high precipitation amounts are the consequence. For the second image, more 

than twice the scans were taken with a time step of 6 minutes. Now the propagation 

path of different rain cells can be seen (from Southwest to Northeast), but several 

regions with high and low precipitation alternate along the paths. In the last case (fig. 

4.1c), the time between scans was only one and a half minutes. The result is a good 

reflection of the real precipitation swaths. 

Very fast repetition of scans (one minute or less) is only possible, if just one or a few 

elevations are sampled in each scan with a high antenna speed. But due to other 

requirements this may not be possible. In such cases, other methods have to be 

applied to avoid unrealistic peaks from small-scale cells as in figure 4.1a. The time 

step between scans can be reduced artificially by deriving inter-scan images or, 

equivalently, by tracking the individual precipitation patterns from one image to the 

next and considering their movement and intensity changes in the time integration. 

Fabry (1994, chapter V) reported very promising results. However, tracking of 

precipitation patterns, especially by cross-correlation methods, is a very CPUintensive 

task and thus may face limitations for operational application. As a simpler 

and much faster method, the precipitation pattern propagation might be 

approximated by a mid-tropospheric mean wind vector derived from Doppler velocity 

data. It will be a main task of the future work within the MUSIC Project to investigate 

such methods with respect to the quality of derived precipitation accumulation and 

with respect to the operational applicability regarding the CPU time consumption. The 



best precipitation estimating algorithm coming out from these investigations will be 

used for radar derived rainfall data within the Project. 

4.2 Speckle Filtering 

Speckle filtering was a task carried out during the derivation of rainfall rates (see 

section 3.2), but it might be necessary to apply some speckle filtering again on the 

accumulated data. Even the best clutter filter will not work perfectly, thus small parts 

of clutter contamination may remain in the reflectivity data and pass all other filtering. 

Accumulated over long time, these small parts may come out as significant 

precipitation amounts. If the real precipitation was very weak, the clutteraccumulation 

may be a multiple of it and appear as speckles of very high 

precipitation amount. Such speckles can be thresholded down to an upper limit which 

depends on the site, season and integration time, or may be interpolated by mean 

values of the surrounding. 

4.3 Handling of Missing Scans 

If the radar operation is interrupted for some reasons and thus the time interval 

between the last step before and the first one after interruption becomes too large 

(e.g. more than half an hour), no accumulation technique can be applied for the 

corresponding time. Thus the precipitation accumulation must be stopped at the 

beginning of the interruption and restarted when the radar starts its operation again. 

For several purposes, precipitation accumulation with varying observation time are 

not useful: typically hourly or daily precipitation amounts are required for further 

hydrological processing. For this purposes, any information about missing scans 

should be given in the precipitation accumulation data set. This could be done by 

giving the loss time as percentage of the total observation time, or by noting the 

missing times explicitly. For further hydrological modelling, the radar derived 

precipitation amounts might be multiplied with a correction factor depending on the 

missing time percentage, or if other sensor data are taken as well and if the missing 

times are given explicitly, other interpolation techniques may be used. However, such 

is no task of radar rainfall estimation in the context of this paper. 


5 · Outlook: Future Work in the MUSIC Project 

5 Outlook: Future Work in the MUSIC Project 

The previous chapters gave an overview of problems that arise when radar data has 

to be transformed to rainfall data. Several algorithms have been presented, which 

reduce the errors arising from such problems. Gematronik’s radar data calculation 

and visualisation software Rainbow ® is able to apply most of these correction steps in 

real-time. This software is going to be implemented in the MUSIC Project. 

Some steps in rainfall data derivation will be improved using enhanced algorithms 

that will be developed in the Project within the next months. The beam blockage 

correction for example can be automated and gives better results, when highresolution 

digital terrain data are used from WP 3 (data bank). 

The most significant improvement of radar rainfall estimation will be achieved using 

new schemes for integration of radar rainfall data in time (see also section 4.1): 

Tracking of rain cells provides vector information that will be used to obtain better 

accumulated data (following the instructions of Fabry (1994)). This step will be 

performed in collaboration with WP 5 (UniNEW), who derive storm, rain cell and rain 

band properties interactively using automated stochastic models . 

All new algorithms will have a special focus on their operational applicability; they 

must be able to run in real-time on quite large data sets. 

Finally these new algorithms will be provided to the MUSIC users on a UNIX 

workstation (SUN) that will also contain the implementation of the improved rainfall 

estimation estimators into the Rainbow ® radar data visualisation software, together 

with a standard set of conventional meteorological radar products. The 

corresponding radar data will be supplied in the file format specified by WP 2 

(“Hydro-Meteorological Data Collection and Supply”). This format will also provide the 

interface to the work packages WP 3 (Data Bank), WP 7 (Block Kriging, Bayesian 

combination) and WP 9 (3D Visualisation). 


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