Radar techniques for identifying precipitation type and
estimating quantity of precipitation
Document of COST Action 717, WG 1
Task WG 1-2
Milan Šálek1
, Jean-Luc Cheze2
, Jan Handwerker3
, Laurent Delobbe4
, Remko Uijlenhoet5
1
Czech Hydrometeorological Institute
2
Météo France
3
Institut für Meteorologie und Klimaforschung, FZ Karlsruhe
4
Royal Meteorological Institute of Belgium
5
Wageningen University
July 2004
1 Background
The early era of weather radar research was accompanied by enthusiasm about the capability
of measuring precipitation by radar systems. Since its birth, weather radar has been offering
prompt overviews of precipitating clouds, their structure and development. Considerable
effort was taken in the second half of 20th
century to use more quantitative information that
could be used in other hydrometeorological information systems, especially in hydrological
modelling and numerical weather prediction (NWP). In the beginning, expectations about the
accuracy of radar measurement of precipitation were high but nowadays it is apparent that
weather radar measurement is often accompanied with non-negligible and sometimes large
errors; hence the radar can be referred as a semi-quantitative measurement device (Joss et al,
1998). The errors stem from the nature of the measurement and are highly influenced by the
meteorological conditions, especially by precipitation processes and by the size distribution of
precipitation particles. Nevertheless, radar still provides very useful information; its real-time
coverage and prompt availability of the data are particularly valuable.
Since rainfall constitutes the main source of water for the terrestrial hydrological
processes, accurate measurement and prediction of the spatial and temporal distribution of
rainfall is a basic issue in hydrology. As a result of the gradual development of radar
technology over the past 50 years, ground-based weather radar is now finally becoming a tool
for quantitative rainfall measurement instead of merely for qualitative rainfall estimation.
Potential areas of application of ground-based weather radar systems in operational hydrology
include storm hazard assessment and flood forecasting, warning, and control (Collier, 1989).
The current attention for land surface hydrological processes in the climate system has
stimulated research into the spatial and temporal variability of rainfall as well. A potential
area of application of ground-based weather radar in this context is the validation and
verification of sub-grid rainfall parameterizations for atmospheric mesoscale models and
general circulation models.
Regarding the quantitative precipitation estimation (QPE), there is an extensive literature
because QPE was an issue since the first radar meteorological observations and it is still one
of the very important ones, and because it has not been solved satisfactorily. To get a good
Radar techniques for identifying precipitation type and estimating quantity of precipitation 1
overview of QPE issues we recommend looking at Zawadzki (1984) and Joss and Waldvogel
(1990). Although radar technology has improved since that time (most radars have a Doppler
facility nowadays), the descriptions of the fundamental physical mechanisms are still valid.
For an overview of the state of the art of radar data processing, see the final report of the
COST 75 action (Collier, 2001) and the recently printed textbook of Meischner et al. (2003).
These references can also be used to find further literature about several error correction
procedures.
A good scan strategy and appropriate data processing may improve data quality in every
application. However, hydrological applications have often to utilize radar data that are
gathered primarily for another purpose, e.g. qualitative nowcasting. Here, we describe the
steps that may improve data quality during the measurement and explain the errors which can
be expected if the measuring procedure is not specifically designed for the hydrological
applications.
One of the aims of COST Action 717 is to evaluate the potential of weather radar to
provide hydrological simulation and forecasting systems with information regarding primarily
quantitative precipitation estimation. The quality of the estimates is related to the precipitation
type and thus the quantitative precipitation estimate should be accompanied with information
on the precipitation type, either derived only from the radar measurement or provided by
other information sources (measurement networks, NWP models).
While the principle of radar precipitation estimation are relatively well known and
routinely used in many operational systems, the classification of precipitation type by radar is
not so widespread and is generally done with dual polarization (or dual wavelength) methods
which are still limited mainly to research experiments (with some exceptions). However,
some nowcasting systems provide and use the categorization of precipitation type with the
help of other information sources, especially surface and/or upper air observations or NWP
models.
This text aims to provide an introduction to the state of the art of radar quantitative
precipitation estimation for hydrological applications and a brief review of the techniques of
radar precipitation measurement and methods for the identification of the precipitation type.
The latter topic will be a little enlarged to mention the importance of multisource
(multisensor) methods that integrate radar measurements and other meteorological data.
Quantitative precipitation forecasting (QPF) is beyond the scope of this text and is covered in
a review already published (Mecklenburg et al., 2002).
2 Principles of radar measurement of precipitation
Radar measurement of precipitation is a complex issue and only the main principles will be
presented here. For a more detailed treatment see for instance, Doviak and Zrnic (1993),
Collier (1996), Sauvageot (1992), Bringi and Chandrasekhar (2001) or Rinehart (1997).
Weather radar obtains volume information by rotating an antenna with a variable vertical
angle according to a predefined scanning strategy. The radar antenna emits a short pulse of
electromagnetic radiation in a known direction and a small fraction of this energy is reflected
by targets (meteorological and non-meteorological) back to the radar antenna. The backscattered
mean power rP received by the radar is proportional to the reflectivity factor Z
(provided the scattering particles are considerably – by order of magnitude – smaller then the
wavelength and are of spherical shape), and to the factor
2
2
2
2
2
1
+
−
=
m
m
K , which is a function
Radar techniques for identifying precipitation type and estimating quantity of precipitation 2
of complex refractivity index m and thus dielectric constant of the target. The received power
is also proportional to the radar constant C (including e.g. the emitted power) and inversely
proportional to the square of the target distance r2
and the square of the one-way atmospheric
attenuation LAtm. The simplified form of the radar equation is then (e.g. Joss and Waldvogel,
1990):
2
2
2
r
ZK
L
C
P
Atm
r = (1)
The radar constant reflects the radar properties as the emitted power, pulse length, 3-dB
beam shape, antenna gain and attenuation of the radar hardware including the attenuation of
amplifiers within the receiver. As the radar constant must be determined, the parameters
mentioned above have to be known. Some of these values are assumed (hoped) to be constant
and thus are measured once by the manufacturer. The distortion of beam by the radome is
mostly neglected and some of these values are measured and/or calibrated regularly.
Since the dielectric constant changes with the particles’ phase, the
2
K value for water is
approx. 0.93 whilst its value for ice is about 0.18; the difference should be taken into account
if radar measures precipitation where the solid phase of precipitation is important (see section
4.2.4).
Z (mm6
m-3
), the radar reflectivity factor, is hereafter simply referred to as radar
reflectivity. All radar properties are contained in C, and all raindrop properties in
2
K and Z.
Z is related to the size distribution of the raindrops in the radar sample volume according to
(e.g. Battan, 1973)
( )∫
∞
=
0
6
,dDDNDZ V (2)
where (the subscript V standing for volume) represents the mean number of
raindrops with equivalent spherical diameters between D and
( )dDDNV
dDD + (mm) present per unit
volume of air1
. The corresponding units of ( )DNV are mm-1
m-3
. Hence, although Z is called
the radar reflectivity factor, it is a purely meteorological quantity that is independent of any
radar property. Because in practice the variations in radar reflectivity may span several orders
of magnitude, it is often convenient to use a logarithmic scale. The logarithmic radar
reflectivity is defined as and is expressed in units of dBZ (e.g. Battan, 1973).Zlog10
However, the radar equation is accurate only under specific assumptions (e.g. physical
properties of the target, beam filling with the randomly scattered precipitation particles,
uniform factor Z through the sample volume, etc., see Collier, 1996) that often do not occur in
the real environment. Especially the assumption that hydrometeors are water spheroids with
diameter inside the Rayleigh scattering region is often far from the reality. Therefore a
quantity called the effective (or equivalent) radar reflectivity Ze is used. The quantity Ze is
defined as the summation per unit volume of the sixth power of the diameter of spherical
water drops in the Rayleigh scattering region, which would backscatter the same power as the
measured reflectivity (Collier, 1996).
1
The raindrop diameter integration limits have been assumed to be zero and infinity, respectively. In other
words, the effects of truncation of the raindrop size distribution (e.g. Ulbrich, 1985) have been disregarded.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 3
3 Parameterization of raindrop size distributions and radar
reflectivity – rain rate relationships2
A fundamental problem before radar-derived rainfall amounts can be used for hydrological
purposes is to make sure that they provide accurate and robust estimates of the spatially and
temporally distributed rainfall amounts. The branch of hydrology dealing with this problem is
now starting to be known as radar hydrology. The crucial step in tackling the so-called
observer’s problem associated with radar remote sensing of rainfall is the conversion of the
radar reflectivities measured aloft to rain rates at the ground. The exact manner in which this
conversion is carried out will obviously affect the accuracy of the obtained radar rainfall
estimates. Various aspects of the associated assumptions, error sources, and uncertainties are
discussed by Zawadzki (1984), Andrieu et al. (1997), Creutin et al. (1997), Wood et al.
(2000), and Sanchez-Diezma et al. (2001), among others.
At the heart of the problem of radar hydrology lies the conversion of the radar reflectivity
factor Z (mm6
m-3
) to rain rate R (mm h-1
). The former can in principle be inferred from
conventional (so-called single-parameter) weather radar measurements, whereas the latter is
the variable of interest to hydrologists3
. It has been common practice for over 50 years now
(Marshall and Palmer, 1948) to take for this conversion a simple power law relationship
between Z and R. It is the purpose of this contribution to explain that the fundamental reason
for the existence of such power law relationships is the fact that the radar reflectivity factor Z
and the rain rate R are related to each other via the raindrop size distribution (DSD).
3.1 The definitions of radar reflectivity and rain rate
3.1.1 Radar reflectivity
As noted in previous chapter, the weather radar equation describes the relationship between
the received power, the properties of the radar, the properties of the targets, and the distance
between the radar and the targets. In this treatment, the targets are assumed to be raindrops.
Equation (1) can be used to convert weather radar measurements of the spatial and
temporal distribution of the mean received power rP to that of Z according to
.2
22
CK
LPr
Z Atmr
= (3)
Of course, estimates of Z obtained with this equation will only be perfect if the hypotheses
on which it is based are satisfied. This implies among others a perfect radar calibration,
Rayleigh scattering and the absence of additional attenuation, beam shielding and anomalous
propagation. In reality, these conditions are hardly ever met, as explained elsewhere in this
report. Therefore, in practice, one often speaks of the effective (or equivalent) radar
reflectivity factor Ze in the context of Eq. (3) (e.g. Battan, 1973). Nevertheless, even a perfect
measurement of Z does not yet imply a perfect estimate of the rain rate R, as will be shown
next.
2
Parts of this contribution have appeared before in Uijlenhoet, R. (1999), Parameterization of rainfall
microstructure for radar meteorology and hydrology, Doctoral dissertation, Wageningen University, The
Netherlands, and in Uijlenhoet, R. (2001), Raindrop size distributions and radar reflectivity – rain rate
relationships for radar hydrology, Hydrol. Earth System Sci., 5, 615-627.
3
Multi-parameter (e.g. polarization diversity) weather radar is beyond the scope of this contribution.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 4
3.1.2 Rain rate
If the effects of wind (notably updrafts and downdrafts), turbulence, and raindrop interaction
are neglected, the (stationary) rain rate R (in mm h-1
) is related to the raindrop size
distribution according to( )DNV
( ) ( )∫
∞
−
×=
0
34
,106 dDDNDvDR Vπ (4)
where represents the functional relationship between the raindrop terminal fall speed in
still air v (m s
( )Dv
-1
) and the equivalent spherical raindrop diameter D (mm). The simplest and
most widely used form of the -relationship is the power law( )Dv
( ) .γ
cDDv = (5)
Atlas and Ulbrich (1977) demonstrated that Eq. (5) with 778.3=c (if v is expressed in
m s-1
and D in mm) and 67.0=γ provides a close fit to the data of Gunn and Kinzer (1949)
in the range mm (the diameter interval contributing most to rain rate). Although
more sophisticated relationships have been proposed in the literature (e.g. Atlas et al., 1973),
the power law form for the -relationship is the only functional form that is consistent
with power law relationships between rainfall-related variables, notably between Z and R
(Uijlenhoet, 1999).
0.55.0 ≤≤ D
( )Dv
A comparison of Eq. (4) with Eq. (2) demonstrates that it is the raindrop size distribution
(and to a lesser extent also the( )DNV ( )Dv -relationship) that ties Z to R. This is the reason
why the analysis of raindrop size distributions and the associated Z–R relationships is of
interest to hydrologists (Smith and Krajewski, 1993; Steiner et al., 2004). In hydrological
applications, it is clearly not the spatial and temporal distribution of Z that is of interest, but
rather that of the rain rate R. A complicating factor in this respect is the fact that the
measurements of Z are made aloft, whereas estimates of R are generally needed at ground
level. The difference between the value of Z aloft and that at the ground is determined by the
vertical profile of reflectivity. Only at ranges close to the radar, where the height of the radar
beam above the ground is small, can this factor be neglected. Even then, the time it takes the
raindrops to fall from the radar sample volume down to the ground should often be taken into
account.
Even if weather radar were to provide perfect measurements of the spatial and temporal
distributions of Z at ground level, the radar rainfall measurement problem would not be
solved completely. First of all, the relationship between the radar reflectivity factor Z and the
rain rate R is generally not a unique relationship. Secondly, even if it were unique, it would
generally be unknown. This fundamental uncertainty in the Z–R relationship provides a lower
limit to the overall uncertainty associated with radar rainfall estimation. In the absence of any
other error source affecting the radar estimation of Z, the rainfall measurement problem for
single-parameter weather radar reduces therefore to optimally using the information Z is
supplying about the raindrop size distribution for the estimation of R.
3.2 Empirical radar reflectivity – rain rate relationships
On the basis of measurements of raindrop size distributions at the ground and an assumption
about the -relationship (such as Eq. (5)), it is possible to derive Z–R relationships (via
regression analysis). There exists overwhelming empirical evidence (e.g. Battan, 1973) that
such relationships generally follow power laws of the form
( )Dv
Radar techniques for identifying precipitation type and estimating quantity of precipitation 5
,b
aRZ = (6)
where a and b are coefficients that may vary from one location to the next and from one
season to the next, but that are independent of R itself. These coefficients will in some sense
reflect the climatological character of a particular location or season, or more specifically the
type of rainfall (e.g. stratiform, convective, orographic) for which they are derived.
Battan’s (1973) standard treatise on radar meteorology quotes a list of 69 of such empirical
power law Z–R relationships derived for different climatic settings in various parts of the
world (his Table 7.1, p. 90-92). Figure 1a provides all these relationships in one single plot.
For reference, the linear Z–R relationship proposed by List (1988) for equilibrium rainfall
conditions (which have been observed during ‘steady tropical rain’) is included as well.
Figure 1b shows that, although there is an appreciable variability in the coefficients of these
Z–R relationships associated with differences in rainfall climatologies, there seems to be a
well-defined envelope comprising most relationships. A naive approach (taking the geometric
mean of the individual prefactors a and the arithmetic mean of the exponents b –
corresponding to averaging the linear – relationships) leads to the mean power
law relationship
Zlog Rlog
.238 50.1
RZ = (7)
Figure 1b compares this relationship with the so-called Marshall-Palmer Z–R relationship,
6.1
200RZ = (8)
(Marshall and Palmer, 1948; Marshall et al., 1955). The correspondence is close, particularly
for rain rates between 1 and 50 mm h-1
. This may be an explanation for the success of Eq. (8)
for many different types of rainfall in many parts of the world, even though the MarshallPalmer
Z–R relationship is based on measurements of raindrop size distributions in Montreal,
Canada, mainly in stratiform precipitation.
The question is whether the coefficients a and b of the power law Z–R relationships are
systematically different for different types of rainfall. Figure 2 shows a plot of b versus a for
Battan's 69 Z–R relationships. On the basis of the remarks given by Battan (in his Table 7.1),
it is possible to associate 25 of these Z–R relationships unambiguously with a particular type
of rainfall. Using the same stratification as Ulbrich (1983), 4 of the relationships can be
associated with ‘orographic’ rainfall, 5 with ‘thunderstorm’ rainfall, 10 with ‘widespread’ or
‘stratiform’ rainfall, and 6 with ‘showers’. The remaining 44 relationships cannot be
unambiguously associated with a particular type of rainfall, either because they correspond to
mixtures of different rainfall types or because the rainfall type is not specified at all. Figure 2
provides some indication that the orographic and thunderstorm Z–R relationships form
coherent groups in the -phase space. On average, orographic rainfall tends to be
associated with smaller prefactors and larger exponents, whereas for thunderstorm rainfall the
opposite seems to be the case. For the Z–R relationships associated with the other rainfall
types, it is less obvious to make unambiguous statements about their positions in the
( ba, )
( )ba, phase
space. A physical interpretation of the coefficients a and b in terms of the parameters of
the corresponding raindrop size distributions may help to explain their variability.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 6
Figure 1: (a) The 69 power law Z–R relationships quoted by Battan (1973; p. 90-92), including five
deviating relationships (dashed lines), four of which have prefactors a significantly smaller than 100 and one of
which has an exponent b as high as 2.87. The bold line indicates the linear relationship (List, 1988).
(b) The mean of Battan’s relationships, (bold solid line), the reference relationship
(Marshall et al., 1955; bold dashed line), and the envelope (thin solid lines) of 64 (the thin solid
lines in (a)) of Battan’s 69 Z–R relationships (Uijlenhoet, 1999, 2001).
b
aRZ =
RZ 742=
50.1
238RZ =
6.1
200RZ =
Radar techniques for identifying precipitation type and estimating quantity of precipitation 7
Figure 2: The coefficients a and b of the 69 power law Z–R relationships (with Z expressed in mm
b
aRZ = 6
m-3
and R in mm h-1
) quoted by Battan (1973), stratified according to rainfall type: orographic (circles);
thunderstorm (triangles); widespread/stratiform (stars); showers (squares); no unambiguous identification
possible (dots). The dashed lines correspond to the reference relationship (Marshall et al., 1955);
the dash-dotted lines correspond to Marshall and Palmer’s (1948) relationship , which almost
equals the mean of Battan’s relationships, (Uijlenhoet, 1999, 2001).
6.1
200RZ =
50.1
237RZ =
50.1
238RZ =
3.3 Parameterization of the raindrop size distribution
3.3.1 The exponential raindrop size distribution
Since, according to Eqs. (2) and (4), both Z and R are related to the raindrop size distribution
, it should be possible to express a and b as functions of the parameters of( )DNV ( )DNV .
Although many different parameterizations for ( )DNV have been proposed in the literature,
notably the gamma (Ulbrich, 1983) and lognormal (Feingold and Levin, 1986) forms, the
exponential raindrop size distribution introduced by Marshall and Palmer (1948) has found
the widest application. There exists empirical evidence showing that averaged raindrop size
distributions indeed generally tend to the exponential form (Joss and Gori, 1978; Ulbrich and
Atlas, 1998). Note that the exponential parameterization will be used here merely as an
example of a family of raindrop size distributions. A general approach to deriving Z–R
relationships, independent of any a priori assumption regarding the exact functional form of
the raindrop size distribution, is presented later.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 8
Figure 3: Experimental size distributions (circles, crosses) of raindrops present in a volume of air and fitted
exponential parameterization (solid lines) according to Eqs. (9-11) for different rain rates (A: 1.0 mm h-1
; B: 2.8
mm h-1
; C: 6.3 mm h-1
; D: 23.0 mm h-1
) (after Marshall and Palmer, 1948).
In their classical paper, Marshall and Palmer (1948) proposed a simple negative
exponential parameterization for the raindrop size distribution ( )DNV as a fit to filter-paper
measurements of raindrop size spectra for rain rates between 1 and 23 mm h-1
,
( ) ( ),exp0 DNDNV Λ−= (9)
where (mm0N -1
m-3
) is a shorthand notation for ( )0VN and Λ (mm-1
) is the slope of the
-curve on a semi-logarithmic plot (Fig. 3). An alternative interpretation of( )DNV Λ is the
inverse of the mean diameter of raindrops present in a volume of air (Uijlenhoet and Stricker,
1999). Marshall and Palmer found that was approximately constant for any rain rate,0N
,100.8 3
0 ×=N (10)
and that decreased with increasing rain rate R (mm hΛ -1
) according to the power law
.1.4 21.0−
=Λ R (11)
Although the filter paper raindrop size measurements to which the Marshall-Palmer
parameterization was adjusted corresponded to rain rates not exceeding 23 mm h-1
, it has been
found to remain a realistic representation of averaged raindrop size distributions for much
higher rain rates.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 9
3.3.2 Scaling law for the raindrop size distribution
Sempere Torres et al. (1994; 1998) have demonstrated that many previously proposed
parameterizations for the raindrop size distribution are special cases of a general formulation,
which takes the form of a scaling law4
. In this formulation, the raindrop size distribution
depends both on the raindrop diameter (D) and on the value of a so-called reference variable,
commonly taken to be the rain rate (R). The generality of this formulation stems from the fact
that it is no longer necessary to impose an a priori functional form for the raindrop size
distribution. Moreover, it naturally leads to the ubiquitous power law relationships between
rainfall integral parameters, notably that between the radar reflectivity factor (Z) and R.
According to the scaling law formalism, raindrop size distributions can be parameterized
as (Sempere Torres et al., 1994; 1998)
)/(),( βα
RDgRRDNV = , (12)
where (mm( RDNV , ) -1
m-3
) is the raindrop size distribution as a function of the (equivalent
spherical) raindrop diameter D (mm) and the rain rate R (mm h-1
), α and β are
(dimensionless) scaling exponents, and ( )xg is the general raindrop size distribution as a
function of the scaled raindrop diameter . In agreement with common practice, R is
used as the reference variable in Eq. (12), although any other rainfall integral variable could
serve as such (notably Z). According to this formulation, the values of
β
RDx /=
α and β and the form
and dimensions of depend on the choice of the reference variable, but do not bear any
functional dependence on its value.
( )xg
The importance of the scaling law formalism for radar hydrology stems from the fact that it
allows an interpretation of the coefficients of Z–R relationships in terms of the values of the
scaling exponents and the shape of the general raindrop size distribution. Substituting Eq. (12)
into the definition of Z in terms of the raindrop size distribution, Eq. (2), leads to a power law
Z–R relationship, Eq. (6), with
∫
∞
=
0
6
)( dxxgxa , (13)
and
βα 7+=b (14)
(Uijlenhoet, 1999, 2001). Hence, the prefactors of power law Z–R relationships are entirely
determined by the shape of the general raindrop size distribution (they are in fact its 6th
moment), whereas a linear combination of the values of the scaling exponents completely
determines the exponents of such power law Z–R relationships.
In a similar manner, the scaling law formalism leads to power law relationships between
any other pair of rainfall integral variables. In particular, substituting Eq. (12) into the
definition of R in terms of the raindrop size distribution, Eq. (4), and assuming a power law
raindrop terminal fall speed parameterization, Eq. (5), leads to the self-consistency constraints
1)(106
0
34
=× ∫
∞
+−
dxxgxc γ
π , (15)
and
4
Recently proposed approaches to normalizing raindrop size distributions using two reference variables (Testud
et al., 2001; Illingworth and Blackman, 2002; Lee et al., 2004) are beyond the scope of this contribution.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 10
( ) 14 =++ βγα (16)
(Sempere Torres et al., 1994). Hence, ( )xg must satisfy an integral equation (which reduces
its degrees of freedom by one) and there is only one free scaling exponent. Substitution of the
self-consistency constraint on the scaling exponents, Eq. (16), into the definition of b in terms
of those scaling exponents, Eq. (14), yields
( )βγ−+= 31b (17)
in terms of the scaling exponent β , or an equivalent expression in terms of the scaling
exponent α (Uijlenhoet, 1999, 2001). For 67.0=γ (Atlas and Ulbrich, 1977), Eq. (17)
reduces to β33.21+=b . Hence, the exponents of power law Z–R relationships can be
expressed explicitly in terms of both scaling exponents [which are related to each other via
the self-consistency constraint Eq. (16)], independent of any assumption regarding the shape
of the general raindrop size distribution. To obtain equivalent explicit expressions for the
prefactors of power law Z–R relationships, however, a particular functional form for ( )xg
needs to be assumed.
Consider an exponential parameterization for the general raindrop size distribution,
( ) ( ).exp xxg λκ −= (18)
In this general form, is not an admissible description of the general raindrop size
distribution, because it does not satisfy the self-consistency constraint on , Eq. (15).
Substitution of Eq. (18) into (15) yields a power law relationship of
( )xg
( )xg
κ in terms of λ ,
( )[ ] ,4106 414 γ
λγπκ +−−
+Γ×= c (19)
or an equivalent power law relationship of λ in terms of κ (Uijlenhoet, 1999, 2001).
Equation (19) provides an explicit form of the self-consistency constraint on for the
special case of an exponential parameterization. For the applied units, with and
( )xg
778.3=c
67.0=γ (Atlas and Ulbrich, 1977), Eq. (19) reduces to .67.4
50.9 λκ =
Hence, the self-consistency constraint on ( )xg reduces its number of free parameters by
one. Since the exponential parameterization for ( )xg , Eq. (18), has only two parameters,
namely κ and λ , the number of free parameters that remains, is only one (either κ or λ ). In
the same manner as Eq. (16) describes a unique relationship between the scaling exponents α
and β (depending only on the value of γ ), Eq. (19) describes a unique relationship between
the parameters of the exponential form for the general raindrop size distribution (depending
only on the values of c and γ ). As a result, for the special case of an exponential
parameterization for , the total number of free parameters that is required to
unambiguously describe the scaling law, Eq. (12), and any derived (power law) relationship
between rainfall-related variables (notably Z–R relationships) is two: on the one hand either
( )xg
α or β , and on the other hand either κ or λ (Sempere Torres et al., 1994; 1998). Note that
relationships similar to Eq. (19) can be developed for any other functional form for the
general raindrop size distribution, notably the gamma and lognormal parameterizations
(Uijlenhoet, 1999; Uijlenhoet et al., 2003a,b).
A general expression for the prefactors of power law Z–R relationships for the special case
of an exponential parameterization for ( )xg can be obtained by substituting Eq. (18) into
(13). This yields
Radar techniques for identifying precipitation type and estimating quantity of precipitation 11
( ) .7 7−
Γ= κλa (20)
To guarantee that a satisfies the self-consistency constraint on ( )xg , Eq. (19) needs to be
substituted into Eq. (20). This yields a power law relationship of a in terms of λ ,
( ) ( )[ ] ( )
.41067 314 γ
λγπ −−−−
+Γ×Γ= ca (21)
This equation (or an equivalent power law relationship of a in terms of κ ) complements Eq.
(17) and together they form an internally consistent pair of relationships for the estimation of
the prefactors and exponents of power law Z–R relationships in terms of the parameters of the
exponential raindrop size distribution. For the applied units, with and778.3=c 67.0=γ
(Atlas and Ulbrich, 1977), Eq. (21) reduces to .33.23
1084.6 −
×= λa
3.3.3 Comparison of the scaling law with the exponential raindrop size
distribution
It is of considerable interest to establish a link between the scaling law formalism and the
traditional analytical parameterizations for the raindrop size distribution. For the special case
of the exponential raindrop size distribution, this can be achieved through substituting Eq.
(18) into (12). This yields
( ) ( ).exp, DRRRDNV
βα
λκ −
−= (22)
A comparison with Eq. (9) shows that Eq. (22) reduces to the classical exponential
parameterization for the raindrop size distribution if and0N Λ depend on R according to the
power laws
α
κRN =0 (23)
and
.β
λ −
=Λ R (24)
As opposed to Eq. (9), Eq. (22) is an intrinsically self-consistent form of the exponential
raindrop size distribution. This is because, as has been demonstrated above, only two of the
four parameters ( λκβα ,,, ) that define ( )RDNV , according to Eq. (22) can actually be
chosen freely. More concretely, the coefficients of the power law –R and0N Λ –R
relationships defined by Eqs. (23) and (24) cannot be chosen without restrictions, but have to
satisfy the self-consistency constraints imposed by Eqs. (16) and (19).
Now consider Marshall and Palmer’s (1948) assumption of a constant
independent of the rain rate R, Eq. (10). Equation (23) shows that this special case
corresponds to
,100.8 3
0 ×=N
κ=0N , or equivalently 0=α . Substituting Atlas and Ulbrich’s (1977) values
for c and γ (for the applied units: 778.3=c and 67.0=γ ) and Marshall and Palmer’s (1948)
value for into the self-consistency relations Eqs. (16) and (19) yields for the0N Λ –R
relationship, Eq. (24), For the corresponding Z–R relationship, Eq. (6) with a
according to Eq. (21) and b according to Eq. (17), the same substitution yields .
Interestingly, the coefficients of this relationship are almost exactly the same as those of the
mean of Battan’s 69 Z–R relationships, Eq. (7). Finally, direct substitution of Eqs. (9)-(11) in
.23.4 214.0−
=Λ R
50.1
237RZ =
Radar techniques for identifying precipitation type and estimating quantity of precipitation 12
Eq. (2) yields an expression reported by Marshall and Palmer (1948) as well.,296 47.1
RZ =
These calculations show that the Marshall-Palmer Λ –R relationship, Eq. (11), is actually
not fully consistent with Atlas and Ulbrich’s (1977) values for c and γ and with the MarshallPalmer
value for (at least not for diameter integration limits of 0 and ∞ ). More
importantly, they also show that Eq. (8), although it is commonly known as the MarshallPalmer
Z–R relationship, is not consistent with the Marshall-Palmer parameterization for the
raindrop size distribution, Eqs. (9)-(11).
0N
3.4 Raindrop size distributions from empirical radar reflectivity –
rain rate relationships
Equations (17) and (21) resolve the issue of relating the coefficients of power law Z–R
relationships to the parameters of the raindrop size distribution. Equation (21) can be inverted
to estimate λ [and κ via Eq. (19)] from given values of a, in much the same way as Eq. (17)
can be inverted to estimate β [and α via Eq. (16)] from given values of b. This approach
provides the opportunity to investigate the dependence of the parameters of the (selfconsistent
exponential) raindrop size distribution on the type of rainfall using the coefficients
of the 69 power law Z–R relationships quoted by Battan (1973) that have been discussed
before. Figure 4a presents the results for the coefficients of the corresponding Λ –R
relationships (parameterized as withβ
λ −
=Λ R Λ expressed in mm-1
and R in mm h-1
), Fig.
4b for the coefficients of the corresponding –R relationships ( with in mm0N α
κRN =0 0N -1
m-3
and R in mm h-1
). Figure 4b clearly demonstrates that Marshall and Palmer’s (1948)
assumption of a constant is too restrictive in practice. Although the mean value of0N α
seems to be close to zero (indicating a constant ), there is a significant amount of
variability between different rainfall climatologies.
0N
Both in terms of the –R relationship and in terms of the –R relationship, orographic
rainfall tends to be associated with larger prefactors and smaller exponents. For thunderstorm
rainfall, the opposite seems to be the case (Table 1). Recall that
Λ 0N
Λ is the inverse of the mean
diameter of raindrops present in a volume of air and that represents the concentration of
the smallest raindrops, Eq. (9). Bearing this in mind, the observations indicate that, at a given
rain rate, orographic rainfall would exhibit smaller mean raindrop sizes and larger
concentrations, whereas thunderstorm rainfall would be associated with larger mean drop
sizes and smaller concentrations. This is exactly what one would expect for these types of
rainfall. Moreover, it provides an explanation for the differences between the coefficients of
the Z–R relationships corresponding to these rainfall types (Table 1, Fig. 2).
0N
Radar techniques for identifying precipitation type and estimating quantity of precipitation 13
Figure 4: (a) The coefficients λ and β− of power law Λ –R relationships (with expressed in
mm
β
λ −
=Λ R Λ
-1
and R in mm h-1
) for the 69 exponential raindrop size distributions consistent with Battan’s (1973) Z–R
relationships, stratified according to rainfall type: orographic (circles); thunderstorm (triangles);
widespread/stratiform (stars); showers (squares); no unambiguous identification possible (dots). The dashed lines
correspond to the relationship , consistent with (Marshall et al., 1955); the
dash-dotted lines correspond to the relationship , consistent with (Marshall
and Palmer, 1948). (b) Idem for the coefficients
258.0
55.4 −
=Λ R 6.1
200RZ =
214.0
23.4 −
=Λ R 50.1
237RZ =
κ and α of the 69 corresponding power law –R0N
Radar techniques for identifying precipitation type and estimating quantity of precipitation 14
relationships (with expressed in mm
α
κRN =0 0N -1
m-3
and R in mm h-1
). The dashed lines correspond to the
relationship , consistent with (Marshall et al., 1955); the dash-dotted
lines correspond to the relationship , consistent with (Marshall and Palmer,
1948).
203.04
0 1013.1 −
×= RN 6.1
200RZ =
3
0 1000.8 ×=N 50.1
237RZ =
Table 1: Mean values of the parameters of the self-consistent exponential raindrop size distribution, Eq. (22),
and the corresponding mean values of the Z–R coefficients, as derived from Battan’s (1973) 69 Z–R
relationships, stratified according to rainfall type. The category ‘Rest’ contains all relationships for which an
unambiguous identification of rainfall type is impossible, ‘nr.’ denotes the number of relationships in each
category (Uijlenhoet, 1999).
Rainfall type nr. α β κ λ a b
Orographic 4 -0.219 0.261 2.02×105
8.44 47 1.61
Thunderstorm 5 0.136 0.185 3.44×103
3.53 361 1.43
Widespread/
stratiform
10 0.117 0.189 7.74×103
4.20 241 1.44
Showers 6 -0.499 0.321 7.32×103
4.15 248 1.75
Rest 44 0.057 0.202 7.85×103
4.21 240 1.47
All 69 0.005 0.213 9.63×103
4.40 216 1.50
The relationships presented in Table 1 for orographic, thunderstorm and
widespread/stratiform rainfall correspond quite closely to those provided by Battan (1973) as
being ‘typical’ for these types of rainfall. Moreover, the entries under ‘All’ indicate that the
Marshall-Palmer Z–R relationship, Eq. (8), and the Marshall-Palmer parameterization for the
raindrop size distribution, Eqs. (9)-(11), are reasonable approximations for average
conditions.
3.5 Summary and conclusions regarding the parametrizations of the
raindrop size distributions
Many previously proposed parameterizations for the raindrop size distribution are special
cases of a general formulation, which takes the form of a scaling law. Using this scaling law
framework for describing raindrop size distributions and their properties, it has been shown
(1) that the definitions of Z and R naturally lead to power law Z–R relationships, and (2) how
the coefficients of such relationships are related to the parameters of the raindrop size
distribution.
Using the classical exponential family of raindrop size distributions as an example, the 69
empirical Z–R relationships quoted by Battan (1973) have been analyzed in the scaling law
framework. The objective was to verify whether there exist any systematic differences in the
coefficients of Z–R relationships and the corresponding parameters of the (exponential)
raindrop size distribution between different rainfall types. It was found that, at a given rain
rate, orographic rainfall tends to exhibit smaller mean raindrop sizes and larger
concentrations, whereas thunderstorm rainfall tends to be associated with larger mean
raindrop sizes and smaller concentrations, which is exactly what one would expect for these
types of rainfall. This interpretation provided an explanation for the smaller values of the
prefactors and the larger values of the exponents of the Z–R relationships reported for
orographic rainfall as compared to those reported for thunderstorm rainfall. Finally, the
Marshall-Palmer Z–R relationship and the Marshall-Palmer parameterization for the raindrop
size distribution were found to be reasonable approximations for average conditions.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 15
4 Errors of the single parameter radar precipitation estimates
Quantitative precipitation estimates by radar have a number of errors that stem from the
nature of this kind of measurement. The quantification of the errors in radar is difficult
because there are several independent error sources. Their relative importance varies greatly
with weather conditions, distance to the radar, scan strategy, temporal and spatial resolution,
orography, data processing or amount and quality of maintenance the radar is given. This
makes it impossible to give a number like “the accuracy of radar precipitation estimates is
x%”.
Discussing error characteristics we have to distinguish between systematic and random
errors. The latter ones are reducing with the increasing size of the area and the increasing
duration of the integration. The former ones might be reduced by the use of so called “ground
truth” data from rain gauge networks or by correction using vertical profiles of reflectivity
(see section 4.2.2).
The quality of radar data is often assessed by comparing radar rainfall estimates to rain
gauge measurements. For this comparison it is common to compare the measurement error of
a gauge with that of a single radar value (mean rainfall accumulation of an areal element,
usually of side length of several hundreds meters or several kilometers). These comparisons
suffer mainly from the problem of rain gauge representativity (sampling problem). Short term
comparisons on the basis of minutes, hours or even days show a significant scatter because
the radar averages over an area of the order of 1 km2
, whereas the rain gauge uses an area that
is roughly 10 orders of magnitude smaller. Especially in convective precipitation, when very
steep horizontal gradients of precipitation are observed, the information of the rain gauges can
be misleading.
It must be stressed that radar and rain gauges are not competitive but complementary
sensors. The best results are achieved by a combination of the information from both
measurement systems. This improves not only the quality of the data, but it puts redundancy
into the game, giving still some information on the precipitation when one of the two systems
is malfunctioning.
The radar measurement errors may be classified into instrumental (or non-meteorological)
errors and errors caused by changes in the meteorological conditions (meteorological errors)
including the above mentioned drop size distribution.
Most of the discrepancies between ground-based measurements (such as from a dense
network of rain gauges) and radar precipitation estimates are because the radar measures the
precipitation in a relatively large sample volume at some height above the ground. The
characteristics of precipitation, as e.g. liquid water content, can significantly change with
height and hence the precipitation estimation aloft may not be representative of what the
ground surface receives.
4.1 Non-meteorological errors of the single parameter radar
precipitation estimates
Non-meteorological errors are caused by beam propagation, clutter, radar hardware and
overall data processing, which is not a simple task. The radar system must consistently cope
with electrical power across twenty orders of magnitude. An example of the simplification
whose effects are often neglected is the gaussian shape of the radar beam whose boundaries
are artificially determined as a power by 3dB (50 %) less than the peak power; another
example is the often neglected influence of side lobes in the vicinity of the radar.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 16
4.1.1 Calibration of the radar
Several parts of the radar parameters, e.g. antenna gain, radar transmitter and receiver
characteristics etc. must be carefully calibrated and typical calibration errors can be up to
several tenths of dB. The calibration measurement tasks require at least the use of a signal
generator, a power meter and several attenuators. These devices are not necessarily more
stable than the radar itself. Thus, it is not trivial to ensure the long-term stability of the radar.
Meischner et al. (1998) and Joss et al. (1995) report that it is possible to ensure a stability of
system parameters during normal operation well within 0.2 dBZ but this quality is based on
the proper, operational use of modern equipment to monitor the radar performance. The
availability of this equipment is not yet the standard, thus significantly larger variations of the
calibration errors should be assumed. As reported by Gekat et al. (2003), the error might be of
the order of 2 dB. Comparisons of radars in different countries around the Baltic Sea showed
a disagreement up to 7dB during the early stage of the BALTEX experiment (Koistinen et al.,
1999 in Michelson et al., 2000).
The temporal scale on which these errors vary is of the order of months or years and they
contribute as a uniform error affecting the entire radar image. This is why these errors are not
of great impact: They can be easily removed by comparing the long-term accumulated rainfall
from radar with so-called ground truth.
The different levels of calibration of particular radars, usually those maintained by
different operators, is usually seen in composite radar images as artificial “borders” within the
radar image.
To use the radar as a measuring instrument, it is necessary to calibrate it with care to know
the accurate values of the constants of the radar equation. If it is difficult to obtain a more
accurate absolute calibration than 1 or 2 dB, it can be useful to compare radar data with rain
gauge data over a long period (about 1 year) to check if the weather radar tends to
overestimate or underestimate. In addition, it is important to check periodically the behaviour
of the radar. For that, electronic calibration of the receiver has to be performed as often as
possible (at least every month) and comparisons with rain gauge data can be carried on, for
example on a monthly basis.
It must be noted that the calibration of radar is usually done for (and often within) the
radar system itself and the main goal of the calibration is to achieve the reproducibility (or
stability) of the radar measurement. The term calibration should be distinguished from the
adjustment of the original radar precipitation estimate that uses some external quantity,
mostly rain gauge data, in order to achieve more accurate precipitation estimate. The
adjustment is not intended to be used for immediate change of the radar constant with the
exception that long-term (months, years) adjustment factor can indicate problems connected
with radar calibration. The adjustment can also reflect the influence of meteorological
conditions. However, some authors do not differentiate between both terms and use only the
term calibration.
4.1.2 Errors caused by beam propagation
Beam propagation is influenced by meteorological conditions, mainly by temperature and the
vertical profile of humidity in the atmosphere, but, on average, the beam follows a path which
is approximately a straight line compared to a sphere with a radius equal to four thirds of the
Earth's radius. It means that under normal meteorological conditions the height and width of
the beam is increasing with distance from the radar site which causes one of the most
important systematic errors of radar precipitation measurement: underestimating the
precipitation rates at long ranges, i.e. mostly beyond 100 km. On average, the reflectivity
Radar techniques for identifying precipitation type and estimating quantity of precipitation 17
decreases with height (with a maximum often in the melting layer) but the reflectivity
gradient depends on particular precipitation processes. The effect is less pronounced in
convective systems in which the average reflectivity profile does not usually show such a
steep decrease with height but in stratiform rainfall (or snowfall) the underestimation at long
ranges can be two orders of magnitudes (Koistinen et al., 2003). This effect will be dealt with
in more detail in section 4.2.2.
For example, consider a one-degree beam with an elevation angle of 0.5°. At 120 km range
the beam width is about 2 km and the height of the beam center is 2 km above the radar site,
which results in a sampled volume extending from one to three kilometers above the radar
altitude. At 230 km range, the 0.5-degree elevation beam (if not blocked) yields a beampattern-weighted
average reflectivity from the layer 1.6-5.6 km above the radar altitude,
which means that the observed radar reflectivity can be very different from ground values.
4.1.2.1 Anaprop
In a standard atmosphere, the radar beam is lightly curved downward relative to straight line.
This is a convenient effect, because it reduces the height of the beam above the ground and
thus, we measure the reflectivity at a lower height than we would in a homogeneous
atmosphere. The standard case uses the so-called 4/3 Earth: The height of the real (i.e. curved)
beams over the real earth is approximately the same as the height of straight lines above an
Earth of 4/3 the radius of the real Earth (i.e. 8500km instead of 6400km radius).
A difficulty connected with beam propagation is its dependence on the vertical profiles of
temperature and humidity due to their influence on the refractive index of the atmosphere. In
the case of anomalous propagation (anaprop) the beam may be higher then assumed from the
average state of the atmosphere (subrefraction), or it can be bent further towards the Earth
surface (superrefraction, ducting), which can significantly worsen clutter problems.
Superrefraction and/or ducting occur when a moist and relatively cool surface layer is present,
especially in the nights and mornings when a surface inversion forms (see e.g. Doviak and
Zrnic, 1993, Keeler, 1998, Koistinen et al., 2003). The term anaprop is usually used for the
superrefraction (as it is in the following text) because subrefraction has usually much less
impact on the radar-based QPE.
Detection of spurious echoes due to anomalous propagation can be performed by trained
users, using loops of a series of radar images or comparison with satellite imagery. Clutter
filtering also works well on anaprop. Anaprop often occurs at locations where in a standard
atmosphere the radar beam cannot hit the ground.
Anaprop-induced clutter occurs more rarely than “normal” ground clutter and thus it is
usually not so harmful. Luckily during precipitation events the stratification of the refractivity
is quite often not too far from the standard atmosphere, so in these cases anaprop effects are
not too common.
4.1.2.2 Shielding
Ground clutter appears at the place where the beam intersects the earth surface or ground
objects. Behind this location the radar beam is attenuated by the fraction of energy that was
lost on the ground, and in the worst case all of the radar beam energy is lost. This leads to a
probable severe reduction in the measured reflectivity values behind the obstacle. If this
reduction is ignored, the intensity of the rain in that area is underestimated.
Totally shielded regions can be identified by inspecting long series of radar data in polar
coordinates for (parts of) beams that never contain a signal. The detection of partial beam
Radar techniques for identifying precipitation type and estimating quantity of precipitation 18
shielding is more complicated, because in this case there are still (weak) echoes. In these
cases only an advanced investigation on the plausibility of the vertical profiles or a
straightforward calculation of the elevation angle of the horizon can help.
As long as only a minor fraction of the beam is shielded, a correction of the data is
possible. Using very precise information about mountain heights, Hannesen (1998; see also
Hannessen and Löffler-Mang, 1998) calculated the power reduction due to mountain
shielding. Besides the directivity pattern of the antenna, an estimate of the vertical profile of
reflectivity is an important input to this algorithm. As long as enough power is received by the
radar, the data can be significantly improved by this procedure. If more than 0.3° of the beam
(beam width 1°) is shielded, the loss of information is too strong and the data should be
removed.
In these cases an extrapolation of the reflectivity profile from higher elevations is
necessary. If the precipitation is too shallow, a total loss may occur.
The effect of power reduction due to mountain shielding is described by Delrieu et al.
(1995) and more general discussion about the challenges of the hydrological application of
weather radar in mountainous terrain is given by Andrieu et al. (1997) and Creutin et al.
(1997).
4.1.3 Errors caused by ground clutter
Reflections from the ground, buildings, trees and other fixed bodies are called ground clutter
whilst reflections from sea surfaces are known as sea clutter. Clutter contaminates the radar
measurement severely. Clutter can be much more intense than the strongest meteorological
signal and it can even overamplify the receiver of the radar.
Very strong clutter stems from reflections from the main axis of the antenna when the
beam hits the ground (e.g. a mountain). This sort of ground clutter can be easily removed by
demanding a certain minimum height of valid measurements above the ground.
More problematic are reflections from sidelobes of the antenna. They may occur even
when the antenna axis does not approach the ground. Because the radar software has to
assume that the reflected echo belongs to scatterers in the main axis of the antenna, these
ground echoes are recorded at any height above the ground.
Clutter from sidelobe reflections is reduced by using an antenna with strong sidelobe
suppression. Nevertheless, a finite antenna always produces finite sidelobes. Typical antennas
have sidelobes which are 30 dB and more below the main lobe (one way). Nevertheless,
reflections from large objects may be more intense even in the sidelobe than reflections from
hydrometeors in the main lobe.
The clutter elimination is not an easy task and even with the help of sophisticated
techniques including Doppler or statistical filtering, thresholding of the received signal,
clutter maps etc., there are some remnants of clutter that are not removed (for algorithms of
ground clutter suppression, see e.g. Germann and Joss, 2003, Wessels and Beekhuis, 1995).
Additional problems arise in areas where clutter prevents the radar from viewing the
precipitation close to the ground. Quantifying the error caused by residual clutter is rather
difficult but in some extreme cases (anomalous propagation along with failure of Doppler
filtering etc.) the error can reach tens of dBZ (i.e. up to tens of mm/h). Usually an isolated
radar element (pixel) with residual clutter may not introduce serious error if the precipitation
estimate is averaged over a sufficiently large area. However, if the clutter filtering fails to
remove a considerable percentage of clutter, then the radar precipitation estimate can be
useless. Moreover, the influence of this error can be considerable if a clutter-contaminated
Radar techniques for identifying precipitation type and estimating quantity of precipitation 19
pixel is paired with a collocated rain gauge measurement in a gauge adjustment processing.
There are at least 4 different approaches to identify and to correct clutter data:
• Use of a clutter map. To produce a clutter map one uses the clutter reflections within a
radar image where surely no precipitation occurs. Clutter maps may be recorded for every
radar even without Doppler facility. Nevertheless, the locations of clutter depends on the
stratification in the troposphere and thus, clutter maps are valid only for a very limited time
period. They only serve as the “poor man’s” solution.
• Statistical filtering is based on the different temporal variability of ground clutter
compared to rain echoes. It can be implemented on conventional radars. A rejection of 25 to
35 dB of ground clutter can be obtained, but it remains difficult to perform accurate rain
estimates over areas contaminated by strong clutter.
• Doppler filtering uses the assumption that the ground has a vanishing velocity relative
to the radar. Using a Doppler facility, the complex reflectivities (containing the phase of the
wave) are recorded. The complex reflectivities from several pulses are high-pass filtered
before calculating the average. This procedure has to be implemented in the radar processor,
because the complex reflectivity values of single pulses are not available afterwards.
• Dual polarization measurements. Probably the best result that can be obtained by dual
polarization is clutter rejection. E.g. Zawadzki et al. (2001) use a fuzzy-logic approach to
identify and remove clutter to a degree “where it was virtually impossible for trained
personnel to identify ground targets that had not been detected by the algorithm.”
Unfortunately, clutter rejection is often equated with removing all signal at the affected
range bins, i.e. setting rain intensity to zero. This might be worse than leaving the cluttered
data in the data set. Using Doppler filtering one will lose some precipitation that moves
perpendicular to the viewing direction (if there were near-zero vertical velocity of the
precipitation particles, the Doppler filtering would reject all precipitation that moves
perpendicular to the viewing direction). In regions where clutter is regularly observed, the
precipitation will be systematically underestimated. If the clutter identification is not able to
estimate the uncluttered reflectivity (it should be with Doppler facility and with dual
polarization), at least the average of the ambient rain intensities should be used as a better
estimation than “no precipitation” at the location (radar areal element).
MeteoSwiss uses rather advanced Doppler filter, which is described in detail in Joss et al.
(1998). It uses a decision tree in which, for each range gate, up to seven conditions have to be
evaluated. This algorithm works on Dopplerized radars but it has to be implemented in the
signal processor, because it uses the data before an averaging over several pulses.
Finally we have to mention sea clutter as a special type of reflection from the lower
boundary. Doppler filtering is mostly ineffective because the sea waves have usually
sufficient velocity, which results in the returning signal not being recognized as clutter. Thus,
the removal of sea clutter is even more difficult than the identification of ground clutter. For
hydrological purposes, the error, however large, is not too serious because the extra artificial
rainfall caused by sea clutter is usually not too important. However, this effect should not be
forgotten if calculating water balance of a lake where the sea (‘lake’) clutter can appear
(although it is not assumed to be too important, either). The sea clutter is much more
significant for nowcasting purposes.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 20
4.1.4 Wavelength issues
Following the discussion on attenuation and “ground contact” of the beam, a short note on the
choice of the optimum wavelength has to be repeated (see Joss and Waldvogel, 1990). A long
wavelength improves the performance of a radar in terms of attenuation. Whereas X-band
radars suffer severely from attenuation, S-band radars are affected much less. The difference
increases with increasing rain intensity because the attenuation coefficient grows nearly
linearly with the rain intensity at S-band, but grows with R1.31
at X-band.
Another benefit of long wavelengths is the extension of the Rayleigh region up to larger
particles. Large drops and more than that snow, graupel and hail are not totally within the
Rayleigh region of a C-band radar.
On the other hand, ground clutter problems increase with wavelength. This is because for
small objects (Rayleigh approximation) the reflectivity decreases with 1/λ4
(λ being the
wavelength). For large objects (geometric region), as e.g. ground, the reflectivity is
independent of the wavelength. Thus, the signal to clutter relation worsens with increasing
wavelength.
4.1.5 Rotational speed
An additional condition implied in Eq. (1) demands that the scatterers are distributed
randomly within the scattering volume. Otherwise, if the phases of the backscattered waves
from each individual scatterer interfere constructively or destructively, the total power
deviates significantly from the sum of the individual backscattered powers.
To increase the degree of independence (and to reduce the impact of noise), the reflectivity
is not calculated from a single pulse but the radar averages over several consecutive pulses
(time sampling) and over adjacent range gates (range sampling) to obtain a single reflectivity
value. Obviously, the statistical errors decrease with increasing time and range sampling but
on the other hand the time needed to take a volume scan increases.
In this connection, the important physical parameter is the decorrelation time, which is
given by νσλτ /2.0= , where λ is the wavelength and νσ is the standard deviation of the
radial velocity. The latter is of the order of 0.5 m/s (snow), 1 m/s (rain) and up to 5 m/s in
convective storms (Sauvageot, 1992). The decorrelation time for C-Band is of the order of
10 ms. If we demand 20 independent pulses to get a reliable reflectivity value, this procedure
needs 0.2 s for each single direction. A volume scan consisting of typically 360 azimuthal
directions and 10 elevations then takes 12 minutes (neglecting the time required to position
the radar at the different elevations).
This time is normally shortened by combining time sampling with range sampling. The 20
independent pulses might be gathered by a time sampling of 5 and a range sampling of 4, so
the volume scan needs only 3 minutes and taking the positioning times into account can be
performed within 5 minutes.
If we try to increase the number of independent pulses by increasing the time sampling, the
time step between two volumes scans increases. So we have to balance the number of
independent pulses gathered for a single volume scan and the number of volume scans we can
collect in a time span. To get an optimum measurement of the total amount of precipitation
within a certain time, it might be useful to accept some noise within a single volume scan but
to increase the number of (independent) scans performed in that time.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 21
For shortening of the scanning process, it is possible to use an ‘interlaced’ volume scan:
Only some elevations (e.g. the lowest two elevations and then the every second elevation) are
used for a short time period (say, 5 minutes) and the rest (plus the lowest two elevations,
again) are taken in the following 5-minute time period. Then, in the 10 minutes we have full
volume scan and reduced volume reflectivity fields (and reflectivities from the lowest
elevations which are suitable for QPE) are available every five minutes.
4.1.6 Spatial resolution
The physical quantity that should be averaged is the rain intensity but the primarily measured
quantity is the reflectivity, which is nonlinearly related to the rain intensity. Thus averaging in
reflectivity introduces a bias. This bias increases with the inhomogeneity of the reflectivity
field and with the size of a recorded range gate, i.e. it increases especially with distance from
the radar. The largest values are reached when the bright band is partially included in the
scattering volume and in convective storms, when horizontal gradients are strong.
Zawadzki et al. (1999) used highly resolved data from a vertically pointing X-band radar to
calculate the reflectivity values a radar with a resolution of 1 degree would measure from a
distance of 60 km. The standard deviation was between 1.43 dB and 4.34 dB, indicating that
the coarse spatial resolution of a radar is in certain situations a significant source of
uncertainties.
4.1.7 Additional issues
Other errors that can be present in the radar precipitation estimation include reflections
received from various non-meteorological targets that include insects, birds, aircrafts, chaffs,
solar radiation etc. These errors are usually not too serious but there are some considerable
exceptions. Specific problems, especially for nowcasting, can be caused by ships that are
difficult to distinguish from meteorological targets automatically (Koistinen et al., 2003).
There can be problems related to the time discretization of the radar measurement. If the
precipitation systems move or develop sufficiently fast, then the integration from the discrete
rain rate estimations results in a precipitation field that is artificially discontinuous. Hannesen
and Gysi (2002) proposed a correction method which is based on derived motion vectors and
the integration along the path which passes the areal element (pixel) between two successive
radar images. This problem has also been discussed by Fabry et al. (1994) and by Blanchet et
al. (1991).
4.2 Errors of radar-based QPE due to changing meteorological
conditions
Removing all the non-meteorological targets, however difficult, is only a first step towards
reasonable radar-based QPE. Even if it were successfully completed, it could not be
guaranteed that the precipitation estimate is accurate or stable. This is because of the large
variety of meteorological conditions and processes influencing the precipitation; they are
sometimes beneficial and improve the precipitation estimate but in other cases they can have
adverse effects in terms of reliable radar detection. For successful utilization of radar
estimates, good knowledge of these errors and theirs characteristics according to the particular
meteorological situation is crucial.
Some of the “meteorological” errors are schematically depicted at Figure 5; note that the
meteorological errors are also influenced by the beam propagation.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 22
Figure 5. Diagram of typical meteorological errors of radar-based QPE of stratiform (top) and convective
(bottom) precipitation. The influence of vertical profile of reflectivity and type of precipitation (along with
range-dependent width and height of the radar beam) dominates in stratiform region while the QPE in convective
processes is often influenced by the presence of the updrafts, downdrafts and hail. Precipitation-induced
attenuation depends on the position of the particular storm cells and the radar site(s) and is significant especially
in heavy rainfalls. High wind increases the possibility of pronounced seeder-feeder orographic enhancement,
typical rather for stratiform precipitation.
Remark: The horizontal extent of the storm cells (bottom) is artificially amplified for better depiction.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 23
4.2.1 Z-R relationship, particle size distribution
The Z-R relation ( ) is surely the best-known error source for most users. Each
hydrometeor contributes to the radar reflectivity proportional to the 6
b
aRZ =
th
power of its diameter d
whereas it contributes to rain intensity roughly with the 3.7th
power of d, see Eqs. (2), (4) and
(5). Thus, as long as one only measures the integral reflectivity, one needs assumptions on the
drop size distributions.
Nowadays, it is common practice to apply a single or time-conservative, seasonallydependent
Z-R relationship. The values of a and b are usually 200 and 1.6, respectively,
which was proposed by Marshall and Palmer. E.g. the German weather service uses
Z=256R1.42
. Battan (1973) lists several dozens of Z-R relations in which the precipitation
intensity R differs for the same reflectivity Z typically by tens of percents, in some cases by
hundreds of percents (Doviak and Zrnic, 1993, see also section 3).
Keeping in mind that Z is calculated by solving Eq. 1 for the reflectivity, tuning of the
parameter a is identical to a recalibration of the radar constant. Doelling et al. (1996) argue
that parameter b only varies between 1.4 and 1.6 in nearly all cases; therefore it is
recommended to leave the b parameter within these values. On the other hand, the value of
the b parameter is closely linked to the type of precipitation (see Fig. 2, section 3). For
instance, in equilibrium (tropical) rainfall, where there is a balance between coalescence and
collisional and spontaneous breakup of drops such that the raindrop size distribution reaches a
stationary state, the Z-R relation may even become linear (see Uijlenhoet et al., 2003a).
There are approaches that use tuned Z-R relations that reflect different meteorological
situations, e.g. of stratiform and convective precipitation (see Table 1, section 3). To apply
those corrections, the different types of precipitation have to be identified e.g. on the basis of
absolute reflectivity values, presence of a bright band, strong horizontal gradients of
precipitation and vertical extent of the radar echo.
A recent approach is called ‘climatologically tuned Z-R relations’. The method consists in
deriving the Z-R relations with respect to long time series of rain gauge data and allows a
correction of the range effect, also reflecting the precipitation regime from the climatological
point of view.
Using short-term measurements to fit the Z-R relation very often degrades the quality
because they lack sufficient representativeness. Deviations due to inhomogeneities in the
precipitation are not averaged out over the short durations and unrepresentative gauge or
disdrometer measurements are generalized over larger areas. This makes online calibrations
tricky and sometimes unreliable.
Collecting more information about the precipitation, e.g. by polarimetric measurements
(see section 6) is another way to obtain estimates of the drop size distribution and thus on the
Z-R relation.
Finally, the probability matching method (PMM, Rosenfeld et al., 1993) or window
probability matching method (WPMM, Rosenfeld et al., 1995) should be mentioned. These
procedures assign reflectivities and rain intensity with the same probability density to each
other. When fitting the parameters a and b of a standard Z-R relation, medium rain intensities
contribute the most to the signal. Thus, outliers of very strong precipitation or very weak
precipitation are not managed reliably. Because the PMM allows a much more complicated
relation between Z and R, these outliers are better represented.
Studies to find the most suitable Z-R relationship for each precipitation type were
motivated by the idea that most of the errors of the precipitation estimate are due to improper
Radar techniques for identifying precipitation type and estimating quantity of precipitation 24
Z-R relationships. As it turned out in last two decades of the 20th
century, this was a rather
misleading paradigm (see e.g. Joss and Waldvogel, 1990). As Zawadzki (1984) showed, the
Z-R related error is a relatively minor factor affecting the accuracy of radar estimates of rain
rate. On the average the vertical profile, i.e. the extrapolation from the lowest elevation seen
by the radar to the ground, and the problem of visibility are probably the most important
effects diminishing the quality of radar measurements.
Current work on improving precipitation measurement from single polarization radar is
now oriented towards corrections using vertical profile(s) of reflectivity (Germann and Joss,
2003, Koistinen et al., 2003), see also following section 4.2.2.
4.2.2 Variability of the vertical profile of reflectivity, profile correction
The formation and modification of atmospheric precipitation particles during their lifecycle is
a complex process that depends on the physical and chemical properties of the atmosphere
and on the precipitation particles themselves, especially their phase and size. The change of
the physical properties of precipitation considerably affects the measured reflectivity and
derived precipitation rate. The significance of the vertical profile, especially in widespread
precipitation and at larger distances, was realized only roughly a decade ago (e.g. Joss and
Waldvogel, 1990).
What we want to feed into the Z-R relation is the reflectivity value at surface height (0 m
above the ground). But what we measure is an average of reflectivity values within the
(lowest usable) beam at a certain height given by the height of the beam axis above ground.
This averaging in the inappropriate quantity (reflectivity instead of rain intensity) produces an
additional bias depending on the variability within each range bin (see also section 4.1.6).
The average vertical profile of reflectivity (VPR) exhibits a general decrease with
increasing height, typically by 10 to 20 dBZ to mid-troposphere (Gekat et al., 2003, see also
Fig. 6). A well-known feature of the vertical profile of reflectivity is the maximum found in
the melting layer (where falling ice particles melt to rain) of typical thickness of a few
hundreds meters, called bright band. The enhanced reflectivity in the melting layer can cause
an overestimation by a factor of five if used as an estimate of the precipitation on the ground
(Joss and Waldvogel, 1990). The influence of the melting layer is especially pronounced in
the vicinity of the radar (up to several tens of km) where the bright band has a vertical depth
similar to the beam width. At a larger distance from the radar, the influence of the bright band
decreases as it can fill only part of the beam that is broadening with the distance. As the radar
beam gets more into the snow region above the melting layer at larger ranges, the bright band
can partly compensate for the general range-dependent underestimation of precipitation rate
(when the bright band is approximately 1 km above the antenna, see Koistinen et al., 2003).
At further ranges, the bright band is in nearly all cases below the lowermost height seen by
radar (see also Figure 5).
Radar techniques for identifying precipitation type and estimating quantity of precipitation 25
Figure 6. Daily mean vertical reflectivity profiles for the radar Skalky (C-band, eastern part of the Czech
Republic), 30-80 km from the radar site, July-August 1997. From (Kráčmar et al., 1998).
The most important factors influencing the vertical profile are:
• The development of precipitation within the cloud but below the lowest beam element.
• Variations of the dielectric factor due to a change in the physical state of the
hydrometeors.
• Variations of the particles’ concentration due to a changing velocity of the
hydrometeors. This is partly caused by the changing physical state and partly due to the
change of air density.
• Coagulation and break up of hydrometeors.
• Evaporation in dry air below the cloud.
The fastest changes occur below the zero degree height where the bright band forms.
The diameter of the beam is of the order of 1km roughly 60km from the radar. Thus the
measured reflectivity at 60 km distance is the average over the vertical reflectivity profile
weighted with the beam function (which describes the beam pattern) over the width of at least
one kilometre. The beam function smears out the features within the vertical profile. The
degree of this smearing depends on the diameter of the beam, which again depends on the
distance from the radar. Thus, the observed vertical profile at a certain distance is not identical
to the vertical profile in the vicinity of the radar, even if both profiles are taken in the same
meteorological circumstances.
Especially at ranges of more than 100km from the radar site the quantitative precipitation
estimation typically improves by several dB when the correction is based on the vertical
profile of reflectivity (Koistinen 1991).
Radar techniques for identifying precipitation type and estimating quantity of precipitation 26
Large errors - requiring large corrections in radar estimates of surface precipitation - are
likely to occur in the following meteorological situations:
1. If precipitating clouds are shallow, i.e. in cold climates or temperate climates during
the winter, the radar beam is only partially filled with precipitation at ranges far from the
radar (Kitchen and Jackson 1993). Additional underestimation occurs if ice particles fill the
measurement volume aloft while the dielectric factor, which is actually used in the radar
equation, is that of water (see section 4.2.4). It is not uncommon for the error in surface
estimates of rainfall or in radar reflectivity factor to exceed 5 dB at a range of 100 km and to
increase dramatically at farther ranges. The effect of beam overshooting is further pronounced
if part of the radar beam is blocked. In the worst case the precipitation is not seen by the radar
at all and no correction is possible (see e.g. Koistinen et al., 2003).
2. If the beam intercepts the bright band this may lead to overestimation of surface
rainfall up to 5-10 dB. The overestimation can cover (i) a ring-shaped area at a fixed range
from a radar (if the rainfall product is based on a PPI image and the bright band is spatially
homogeneous) or (ii) it can behave stepwise as a function of range (if the selected CAPPI
level coincides with the height of the melting level and no interpolation has been applied
when the CAPPI is calculated from rings of the original PPI measurements). For description
of this effect, see e.g. Sanchez-Diezma et al. (2000).
3. Strong evaporation below the observation height leads to overestimation of the
precipitation reaching the ground. This is typical in widespread frontal Altostratus clouds
preceding warm and occluded fronts or at the trailing edge of cold fronts of ana-type.
4. In hilly or mountainous terrain orographic growth of hydrometeors below the height of
a radar measurement may result in considerable (up to 6dB) underestimation of precipitation
at the ground. This orographic enhancement is dealt with in more detail in section 4.2.3.
The main problem in the operational application of a correction scheme is the unknown
vertical profile of reflectivity (VPR) or precipitation profile i.e. the ratio of observed beam
smoothed values aloft and the ground truth at each location in each moment of measurement.
Prior to any vertical reflectivity profile correction one should consider how accurately the
time-space structure of the profile should be known in order to improve radar derived
precipitation amounts significantly. The experience gained to date suggests that profiles
derived from measurements near the radar and integrated over much longer time periods than
the actual accumulation period of precipitation will help considerably.
A coarse way to take into account the mean beam overshooting and shielding due to
mountains and earth curvature is to determine empirical range dependent adjustment factor
based on long-term gauge-radar comparisons at the same locations.
The next step is to use seasonal mean profiles (Joss and Pittini, 1991) or climatological
classes based on synoptic weather types (Brown et al., 1991). These profiles can be estimated
without actually calculating the mean of all measured profiles during a season. If the large
synoptic scale variation of the melting level height is taken into account, the averaging time of
reflectivity profiles cannot be longer than approximately one day. It was found that the use of
mean daily reflectivity profiles reduced the bias in radar-derived daily rainfall estimates by up
to 6 dB (Koistinen, 1991).
Accurate correction of the effect of error in the vertical profile, especially in cases of very
short accumulation periods (e.g. 10 minutes) requires knowledge of the time-space
distribution of the profile. Much research is being carried out on in various countries
(Switzerland, Spain, France, USA, …) to develop acceptable correction algorithms based on
the availability of volume scans.
For a thorough discussion of the determination of the VPR with respect to the radar beam
Radar techniques for identifying precipitation type and estimating quantity of precipitation 27
geometry and sampling scheme see e.g. Andrieu and Creutin (1995) who propose a method
that is less affected by the radar beam geometry and smoothing. Leaving aside the issues
regarding the identification of the profile by the radar, the weakest point of these schemes is
still the lack of representativeness of the profile for the areas where the VPR correction is
applied. Although the uncertainty about the ‘true’ but unknown profile in the area of interest
(where the VPR correction is applied) remains relatively large, the correction is still able to
reduce the range dependency of the bias (see e.g. Novák and Kráčmar, 2001). Then it makes
the radar estimate more suitable for the mean field adjustment by the rain gauges
measurements. Otherwise, if the VPR correction is not applied, then the possible rain gauge
adjustment must often utilize a bias that is dependent on the range (see, e.g. Michelson et al.,
2000), which can be also considered as a coarse VPR correction (see above).
4.2.3 Errors of radar estimates caused by orographic seeder-feeder precipitation
enhancement
Complex orography not only reduces radar visibility but, under favourable conditions,
induces also significant change of precipitation intensity and duration. The orographic
enhancement of precipitation can be divided into three categories (after Grey and Seed, 2000):
a) Orography-induced autoconversion (growth of the droplets through collision and
coalescence), which can produce only light rain.
b) Seeder-feeder mechanism; the low level cloud is maintained by upslope winds and
provide the moisture source that is collected by the drops falling from aloft from ‘seeder’
clouds.
c) Triggered convection that is caused by the wind flow over the hills which triggers
potential instability; the convection can be also activated by heating of the slopes in relatively
cold air.
The autoconversion is usually not too important from the hydrological point of view and
triggered convection can be well captured by radar due its vertical extent. The seeder-feeder
enhancement often causes significant error in the radar estimates because it takes place
mainly within a few hundred meters above the ground. Even 50 m high hills can produce an
enhancement of 10-40% in the lowest 500 m (Grey and Seed, 2000). The seeder-feeder
mechanism causes two types of problems for radar estimates: (i) the radar detection often
suffers from reduced visibility in mountainous areas and (ii) at the same time significant
enhancement can occur very close to the ground, at the heights that are barely seen by the
radar. The lowest usable beam is then often able to capture only the seeder clouds and at most
only a part of the feeder area, which results in very significant underestimation (Collier, 1996,
Gray and Seed, 2000). Moreover, the orographic precipitation usually shows specific type of
the drop size distribution, which further worsens the radar underestimation (Rosenfeld and
Ulbrich, 2002, see also section 3).
Collier (1996) advises that the radar should be sited so that it can observe the low level
precipitation directly, but this is not always possible. For more successful assessment and
anticipation of this error additional information sources are needed, e.g. direct observation
and NWP models. Even a climatologically derived relationship between humidity and wind at
800 m above sea level and the magnitude of the seeder-feeder enhancement can partly help
(Kitchen et al., 1994, Harrison et al., 2000). However, the orographic enhancement effect is
not simple, as Grey and Seed note, and they also add: ‘If radar were to be used to increase the
lead-time for flood forecasting, then it would necessary to forecast, in advance, the manner in
which the enhancement will be manifestated.’
Radar techniques for identifying precipitation type and estimating quantity of precipitation 28
4.2.4 Dielectric Factor
Knowledge of the dielectric factor
2
K provides information about the physical state of the
hydrometeors. The value of
2
K for water is approximately 0.93 (depending weakly on
temperature and wavelength), for ice it is roughly 0.18, i.e. 5 times smaller. The radar
software always assumes as a default setting that precipitation consists of liquid drops, thus it
calculates with a fixed dielectric factor of 0.93. This leads to an underestimation of the
reflectivity within convection (see Eq. 1). Nevertheless, this is only one of several problems
due to graupel and hail (see also sections 4.2.8, 4.2.9 and 5.2).
In stratiform precipitation there is a clear separation of ice and water: Above the bright
band ice particles dominate, below you find water phase and the bright band contains a
mixture of both constituents. In these cases the dielectric factor contributes to the vertical
profile and the VPR correction (see above) deals with it inherently.
In convective cells the different states are mixed and the separation is not possible. Dual
polarization radars might provide an estimate of the mixing ratio of the liquid and frozen
components (see section 6) but without a dual polarization facility this ratio is not available.
There are techniques to identify areas with convection within radar images. High
reflectivity values, large horizontal gradients, vertical profile and large vertically integrated
liquid water contents are used to separate these areas from the rest. Nevertheless, even if one
can identify a thunderstorm, no information about the relative proportions of ice and water is
available from a single polarization radar.
4.2.5 Errors caused by attenuation in precipitation
Radar radiation is attenuated by atmospheric gases and hydrometeors. Attenuation is strongly
dependent on the wavelength; S-band radar (approx. 10 cm wavelength) is much less affected
by attenuation then X-band (approx. 3 cm wavelength).
Among the gases in the atmosphere, oxygen and water vapour cause the most attenuation.
In most cases, the attenuation due to oxygen (which is of the order of 7×10-3
dB/km) is more
intense then that caused by water vapour. This static part of attenuation is normally corrected
for by the radar signal processor, which uses a user-defined value for the attenuation
coefficient to correct the data.
The more intense and more problematic part of the attenuation is due to the precipitation
itself. It is possible to estimate the attenuation by power laws of the form
K=aRb
, (25)
where K is the attenuation coefficient in dB/km and R the rain rate in mm/h. In case of rain
these laws read (see Sauvageot, 1992) as K=0.3×10-3
R1.00
at S-band, K=2.2×10-3
R1.17
at Cband,
and K=7.4×10-3
R1.31
at X-band for one-way attenuation. At a range of 100 km and a
(constant) rain rate of 1 mm/h a two-way attenuation of 0.06 dB, 0.44 dB and 1.48 dB is
observed for S, C and X bands, respectively. A cell with a diameter of 5 km and a rain
intensity of 40 mm/h produces a two-way attenuation of 0.12 dB, 1.6 dB and 9.3 dB,
respectively. In snow the attenuation is weaker and in the bright band it can be even more
intense. For further reading, see Delrieu et al. (1991).
Due to this sensitivity and the effect that an overestimation of the attenuation in a nearer
range gate produces an even worse overestimation in a further range gate, the gate-to-gate
correction schemes prove to be unstable in many cases (e.g. Hildebrand, 1977, Hitschfeld and
Radar techniques for identifying precipitation type and estimating quantity of precipitation 29
Bordan, 1953, Bringi and Chandrasekhar, 2001). The chance for instabilities increases with
the attenuation that has to be removed from the data: The more we need attenuation correction
the worse it works. This is the reason why attenuation correction is not operational at any
weather service. Although occasional attempts of a correction scheme are still reported (see
e.g. a proposal to use a variational method by Berenguer et al., 2002), the most promising
algorithms are based on the use of the differential phase shift for dual-polarization radars.
4.2.6 Additional attenuation by water on the radome
Water on the radome causes an additional attenuation and a broadening of the beam width.
These effects are well known not only in the radar community but also e.g. in the (satellite)
communication field (Anderson, 1975). As long as the water stays in the form of droplets on
the radome, the effect is not very strong. Separate droplets behave as additional rain. But as
soon as the water forms rivulets or even a closed film on the radome, the attenuation increases
significantly.
Therefore, radomes are manufactured with a repellent coating, which should inhibit the
formation of water films. This coating degrades due to dirt and dust and physical and
chemical interaction with the environment. The water film thickness at a certain point on the
radome depends on the rain intensity, wind speed and direction, state of the radome surface
and the position of that point (especially the slope).
The variation of the film thickness causes an additional beam distortion that can be
disturbing, especially if it leads to additional ground clutter in the echoes.
This effect is difficult to be removed, mainly because exact information on the water film
thickness is not available. Experiments with artificial precipitation from a fire brigade on a
radome produced an attenuation of roughly 5 dB (one direction) due to an estimated
equivalent rain rate of about 100 mm/h on a 5-year-old radome (Manz et al., 1999). This
attenuation corresponds to an error of a factor 4.5 in the rain rate.
This additional attenuation can obviously be very important. It varies with azimuth and
elevation of the antenna and it changes in time as rapidly as the rain rate varies at the radar
location. Nevertheless, there is no operational service applying any correction routine to deal
with this error. It is not easy to remove this error afterwards, because it varies with time and
with the direction from the radar. Thus it is a rather inhomogeneous distortion on short time
scales.
4.2.7 Shape of the rainfall droplets
The derivation of Eq. 1 uses the assumption, that the scatterers are spherical. This is realistic
for small drops but the drops of the order of 1 mm or larger get oblate. Frozen hydrometeors,
especially snow, grow in a nearly arbitrary shape and the error is larger. In snow this error is
one of several additional errors in determining the (equivalent) rain rate. No investigation that
separates this error from the other problems in snow is known to the authors.
The deviation of the large drops from the spherical shape is used in dual polarization radars
to estimate information about the drop size distribution through the difference of reflectivity
of horizontal vs. vertical polarisation. This difference is measured as the differential
reflectivity ZDR:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
V
H
DR
Z
Z
Z log10 , (26)
Radar techniques for identifying precipitation type and estimating quantity of precipitation 30
where ZH
and ZV
denote the reflectivity of a horizontally or vertically polarized signal,
respectively. ZDR reaches values of up to 5 dB in rain. The details will be discussed in the
section 6.
4.2.8 Precipitation Particles of size beyond Rayleigh approximation
To allow the reflectivity of a single scatterer to be calculated by the Rayleigh approximation,
as it is done in radar meteorology, the scatterer has to be small compared to the wavelength.
Small means that the diameter should be 10 to 16 times smaller than the wavelength. This
means that the largest particle should be smaller than 10mm, 5mm and 3mm for S-, C- and
X-band, respectively. In moderate climates raindrops are normally smaller than 5 mm. In
tropical rain, drops of 8mm are often observed. Frozen hydrometeors may be even larger than
10 mm. These large particles do reflect much less than assumed by the Rayleigh
approximation. Thus, they are estimated to be smaller than they are in reality. On the other
hand, these large particles are not properly described by the usual drop size distributions that
underlie the Z-R relation.
Finally, hailstones produce much less precipitation than rain of the same reflectivity. An
example: A hailstone of 10 mm produces (in Rayleigh approximation) a reflectivity of 106
mm6
. Due to the fact, that it is not in the Rayleigh region we assume it to reflect only half this
value: 5× 105
mm6
. Its volume is 535mm3
.
To produce the same reflectivity we need 32 drops with a diameter of 5 mm. Their total
volume is nearly 2100 mm3
, roughly 4 times the volume of the hailstone. Thus, they
contribute much more rain than the hailstone, notwithstanding their smaller fall velocity.
Large hailstones violate the Rayleigh approximation as well as the Marshall-Palmer drop
size distribution. Finally, they lead to a severe overestimation of rain intensity. There are
heuristic methods to reduce this overestimation. Among the simplest ones you can find using
the ‘hail cap’, i.e. truncation of the maximum used reflectivity/rainrate to predefined value
(e.g. Fulton et al., 1998, see also Table 2). Another approach assumes that rain intensities of
more than 200 mm/h should be corrected by unkorrkorr RhmmR 200]/[ = .
In fact, these very intense events last in most cases only for short durations so the
integrated amount of rain is normally not large. On the other hand this infrequency makes it
difficult to find more sophisticated correction themes than the one cited above.
4.2.9 Errors caused by different precipitation type
As noted in previous sections, the Z-R relationship and the radar equation assume liquid water
and a spherical shape of the droplets of size not exceeding some limits. However, these
assumptions are often far from the reality; especially in cold climate (or cold season in
temperate climate) the radar frequently measures snowfall and instead of using the Z-R
relationship for rainfall, Ze-S (equivalent reflectivity – snowfall [mm/h]) relationship with
different coefficients should be applied. For detailed studies and independent sampling of
precipitation rate one must not forget the problem of a different factor
2
K for water and ice
(see section 4.2.4) that is usually kept constant all year round.
However, the error caused by unsuitable use of Z-R/Ze-S relationship is usually less
important than more serious problems connected with snowfall. The general decrease in
vertical depth of snowfall-producing clouds in a cold climate (or season) results in more
Radar techniques for identifying precipitation type and estimating quantity of precipitation 31
severe underestimation at long ranges. More information about these effects and possible
corrections can be found in Koistinen et al. (2003).
One of the difficulties that are usually encountered in warm seasons is the presence of hail
as mentioned in the previous chapter (see also chapter 4.2).
4.2.10 Updrafts and downdrafts
According to Gunn and Kinzer (1949, in Doviak and Zrnic, 1993), the typical vertical
velocities of raindrops in stagnant air are between 2 and 8 m/s; the raindrops of the 0.6 mm
and 4 mm diameter fall at the speed 2 m/s and 8 m/s, respectively (at the air pressure of
1013 hPa and air temperature of 20ºC). In the middle of the troposphere the raindrop
velocities are about 30-40% higher due to less air density.
The Z-R relation requires assumption that the raindrops are falling in a still air. The
situation changes in convective storms where updrafts and downdrafts up to tens of m/s occur
(see also Fig. 5). In an updraft the radar must overestimate surface precipitation rate because
the air current suspends the precipitation particles in the air. In the downdraft the situation is
more complex. It is obvious that at the height typical for radar measurement of precipitation,
roughly about 1 km above the surface or more, the rainfall rate relative to the earth surface is
greater than the radar estimate that assumes still air because of the vertical velocity of the
falling air. However, the vertical velocity of the air at the horizontal earth surface is zero. It
means that the downdrafts diverges at the surface and thus increases the area that is hit by the
precipitation present in the downdraft (Kessler, 1987, Lee, 1988 in Doviak and Zrnic, 1993).
Then the downdraft presence mainly results in underestimating the area hit by the heavy
precipitation. Only if hail is present, the underestimation caused by downdraft may not be so
pronounced (Collier, 1996).
The errors caused by downdrafts and updrafts, which can be up to several dB (Collier,
1996, Joss and Waldvogel, 1990), can be reduced by integrating the rainfall over a
sufficiently large area where these effects are likely to compensate. Thus, the recommended
reasonable area for mean areal estimates should be equal or more than the typical area of
convective storm cells, which is typically about ten square kilometres. If smaller areas are
used when analysing convective precipitation, these effects are likely to be more significant.
4.2.11 Additional problems
In addition to the previous list of errors, we have to mention drift by the upper wind, threebody
scattering signature caused by additional scattering between hail and ground and second
trip echo caused by intensively backscattering targets beyond the maximum unambiguous
range (see e.g. Doviak and Zrnic, 1993). However, these types of error are generally smaller
than the ones described above.
4.2.12 Summary of the meteorological errors
The meteorological errors are summarized in Table 2 which is adapted from Austin, 1987 (in
Collier, 1996). It gives the overview of the expected magnitudes of the errors and the
proposed action that may be taken or the compensating effects which can occur.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 32
Table 2. The effects of meteorological factors on values of equivalent rainfall rate deduced from radar
measurements and conditions under which they are significant (adapted from Collier, 1996).
Factor
Magnitude of the effect and
situations where it is significant
Methods for compensations
Drops larger than average in intense
convective storms;
reflectivity increased by 1-2 dB
Use of relation Z=400R1.3
or similar *;
raingauge adjustment
Drops smaller than average in warmfrontal
rain;
reflectivity decreased by 3-4 dB
Use of relation Z=100R1.4
or similar *;
raingauge adjustment
Variations in the
raindrop-size
distributions
Any other deviation from average
drop-size distribution is usually too
small to be detected or is masked by
other effects
Predominant factor in intense
convective storms (Max Z ≥ 53 dBZ);
may increase reflectivity in storm
cores by 10 dB or more above that of
the rain alone
Limiting R (or Z) to a maximum value
(“hail cap”);
usually Rmax ≈100 mm/h (from 75 to
150 mm according to the climate type
– Fulton et al., 1998);
some compensation by downdraft
effect **
Enhancement of
signal by presence
of hail
Probably 4-5 dB enhancement in
moderate convective storms
(45 dBZ ≤ max Z ≤ 53 dBZ)
which are non-frontal
Automatically compensated for by
downdraft effect **
Predominant factor in moderately
convective storms which are
associated with cold fronts or
stationary fronts. Reflectivity in storm
cores diminishes by 4-5 dB
Use of relation Z=230R1.2
*;
Some compensation by updraft
(overestimating) effect **
Diminution of
reflectivity by
downdrafts
associated with
heavy rain in
convective cells
Similar effect in intense convective
storms and in non-frontal moderate
convective storms
Automatically compensated for by
hail effect or updraft effect **
Signal enhancement
by melting snow
Significant factor in all stratiform
rain. When ‘bright band’ is in the
radar beam, reflectivity may be
1-5 dB stronger than that of the rain
alone
Limiting measurement to region
below the melting layer; correction
procedures using estimates of
reflectivity profile
Low-level growth of
raindrops in fog or
stratus clouds
Occurs when fog or low stratus is
present. Increase in rainfall rate
unlikely to be more than 25 % in light
rain or 15 % in heavy rain (except
orographic enhancement – see below)
Recognition of possible
underestimation by radar when fog is
present;
raingauge adjustment;
correction procedures using
knowledge of reflectivity profile
Radar techniques for identifying precipitation type and estimating quantity of precipitation 33
Factor
Magnitude of the effect and
situations where it is significant
Methods for compensations
Orographic seederfeeder
enhancement
(intense
low-level growth of
raindrops in fog or
stratus clouds in the
mountains)
Significant factor in heavy rainfall
when accompanied with high wind;
occurs usually in widespread
(stratiform) rain; underestimation can
reach 1-5 dB according to the height
of the beam above the ground and the
intensity of the enhancement;
Recognition of possible
underestimation by radar when fog
and high wind in the mountains are
observed;
local (possibly altitude-dependent)
raingauge adjustment;
correction procedures using
knowledge of reflectivity profile or
using climatology of the enhancement
(dependency on the wind vector and
humidity);
Low-level
evaporation of drops
in relatively dry air
Unlikely to be a significant factor
except ahead of warm fronts
Recognition of possible
overestimation when relative humidity
is low; raingauge adjustment
*) Although it is mentioned here, the change of the Z-R relationship is probably not the most
preferred method of compensation
**) The downdraft-updraft-hail compensation takes effect only if sampled (or averaged) area
of QPE is equal or bigger than storm cell. Note that the compensation is not always able to
diminish the error to desirable extent.
5 Identifying the precipitation type
The identification of precipitation type can be helpful for the improvement of the quantitative
precipitation estimate. However, the identification made by a single polarization radar is
limited to the recognition of hail, bright band (and hence snowfall/rainfall layers) and
delineation of regions of prevailing stratiform or convective precipitation. It has to be stressed
that the radar is not the only means to determine the precipitation phase and hence we
nowadays see more integration with other sources of meteorological information.
5.1 Identification of the precipitation phase by bright band detection
Bright band detection can be achieved using the full volume data and vertical profile of
reflectivity or with help of image analysis or independent data such as radiosonde temperature
measurement. The identification of the bright band leads to more accurate determination of
areas where the radar (at particular beam elevation) is measuring rainfall, areas where the
beam measures snow and areas where the radar is likely to overestimate the rainfall rate
because of the bright band effect (Collier, 1996). An example of the bright band detection can
be found in (Gourley and Calvert, 2003). It has to be stressed that the quality of the bright
band detection depends on the vertical resolution of the radar and hence is confined to only
several tens of kilometres from the radar site. According to Gourley and Calvert (2003), the
WSR-88D uses reflections from the range 10-30 km for detection of bright band and the
height and depth of the bright band was in good agreement with other verification sources
(vertically pointing radar, radiosondes).
Radar techniques for identifying precipitation type and estimating quantity of precipitation 34
5.2 Identification of hail
5.2.1 Introduction
Hail precipitation is associated with very high radar reflectivities. The conversion to
precipitation rates using the conventional Z-R relationship will generally give rise to a
significant overestimation of the on-ground precipitation accumulation as mentioned in
section 4.2.8. Besides, hail precipitation is responsible for relatively high attenuation of the
radar beam through absorption and scattering. As a result, radar estimates of precipitation
behind these hail cells can be significantly underestimated. For these reasons, a reliable
detection of the presence of hail is of great importance for hydrological applications.
5.2.2 Hail development processes
The microphysical processes responsible for hail development are not yet completely
understood. Ice particles may form in a cloud if the temperature drops below zero. However,
the transformation to ice does not take place readily and the ice phase is frequently observed
only as cloud temperatures approach –20°C (Pruppacher and Klett, 1997). Liquid water that is
colder than 0°C is called supercooled. At temperatures below 0 °C, the coexistence of
supercooled water drops and ice particles is an important factor for the development of
hailstones. Three different mechanisms are responsible for the growth of ice particles.
The first mechanism is the collision and aggregation of ice particles. This mechanism is
often referred to as clumping and is mainly active at the initial stage of the particle growth.
The second mechanism is deposition, i.e. water vapour diffusion to the ice particles. The
presence of liquid water ensures the diffusional growth of ice crystals at the expense of water
drops through the Bergeron process (Bergeron, 1933). This process relies primarily on the
fact that the saturation vapour pressure with respect to ice is less than the saturation vapour
pressure with respect to water. The last mechanism is riming, i.e. the collection and freezing
of water drops colliding with ice particles. The initial growth of ice crystals is primarily
through clumping and vapour deposition until they are large enough to begin riming (Jameson
and Johnson, 1990). When riming of an ice particle has proceeded to the stage where the
features of the original ice crystal are no longer visible, the ice particle is referred to as a
graupel. Rimed particles that have reached a diameter larger than 5 mm are called hailstones.
The production of large hailstones needs a rapid growth of ice particles through the abovementioned
mechanisms. Favourable conditions are found in intense thunderstorms where
water and ice coexist in the central updraft. There is a positive relationship between the
apparent strength of a storm (strength and size of updraft) and the size of hail that it produces
(Ray, 1990). Growth of hailstones is highly influenced by the flow dynamics within the
thunderstorm (Heymsfield et al., 1980; Nelson, 1983). The interactions between
microphysical processes and thunderstorm flow fields are complex. The trajectories of
hailstones depend on the type of storm. In supercell storms, it is thought that most hail mass is
acquired during a single pass across the updraft (e.g. Browning and Foote, 1976). More
complex trajectories can be found in multicells where hailstones may recirculate in different
cells of the thunderstorm complex, resulting in successive growth cycles. Nelson (1983)
concludes that the most critical storm feature for large hail to be produced is the presence of a
broad area of moderate updraft ensuring a sufficient residence time in a favourable growth
environment.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 35
5.2.3 Radar-based hail detection methods
The most efficient technique for discrimating hail from water is given by dual polarization
radars (e.g. Seliga et al., 1982). Reflectivities in the horizontal (ZH) and vertical polarizations
(ZV) are similar for spherical hailstones, which is not the case for non-spherical raindrops. The
widely used parameter in this technique is the differential reflectivity (see Eq. 26).
Very large reflectivities together with low values of differential reflectivity are the
signature of hail precipitation.
Another technique for hail detection is the dual-wavelength algorithm that was first
proposed by Atlas and Ludlam (1961). This method is based on the measurements from a dual
wavelength radar and makes use of the reflectivity dependence on the wavelength, which is
much higher for hailstones than for water drops. This technique does not receive the same
degree of attention as the dual polarization but some new developments have been recently
published (Feral et al., 2003).
Most radars of currently operational networks are single wavelength and single
polarization radars. Various methods have been proposed for detecting hail using reflectivity
measurements from this type of radar. In this section, we give a short overview of the
currently used methods. An extended review can be found in Holleman (2001).
The most straightforward way for detecting hail is based on the Pseudo Constant Altitude
Plan-Position Indicator product (Pseudo CAPPI). This product is generated from a radar scan
at multiple elevations. The Pseudo CAPPI represents the reflectivity values at a given altitude
above mean sea level. It is produced by interpolating between the reflectivity data from
different elevations. At short ranges, where the highest radar beam is lower than the selected
altitude, the reflectivity data are taken from the highest elevation. At long ranges, where the
lowest beam is above the selected altitude, the data are taken from the lowest elevation. For
the radar of Wideumont, the selected altitude is 1500 m and the Pseudo-CAPPI is generated
every 5 minutes from a scan at 5 elevations (Fig. 7).
Figure 7. Pseudo-CAPPI 1500 m for the radar of Wideumont (Belgium) derived from 5 scans at different
elevation angles (in degrees).
Large hail stones give rise to very high reflectivities that could not be obtained from rain
drops. Mason (1971) proposes a reflectivity threshold of 55 dBZ for distinguishing between
Radar techniques for identifying precipitation type and estimating quantity of precipitation 36
rain and hail. This method is successful in case of severe hailstorms but cannot distinguish
between heavy rain and relatively light hail.
A slightly different method makes use of the Maximum-reflectivity product (MAX)
instead of the Pseudo CAPPI. The MAX product gives the highest measured reflectivity
value for each vertical column. This product allows detecting high reflectivity values present
at higher levels than the Pseudo-CAPPI level. In principle, a threshold criterion based on this
product can detect hail in developing thunderstorms cells before hail precipitation reaches the
ground.
Some methods make use of radar observations together with other sources of information.
Auer (1994) proposes a method which combines radar reflectivity data with infrared cloudtop
temperature from satellite imagery. This method has been extensively tested on hail cases
in New Zealand and performs much better than the CAPPI method. The cloud top
temperature provides additional information on the vertical extension of the thunderstorm
cells.
In the United States, the so-called Weather Surveillance Radar-1988 Doppler (WSR-88D)
system is the operational radar network system producing meteorological and hydrological
analysis products (Crum and Alberty, 1993). The original hail detection algorithm used in the
WSR-88D system is based on the presence of seven hail indicators (Smart and Alberty, 1985).
After testing is completed, a storm is given one of the following four hail labels (positive,
probable, negative or unknown).
An enhanced hail detection algorithm has been developed at the National Severe Storms
Laboratory (NSSL, USA) and now replaces the original algorithm (Kessinger et al., 1995;
Witt et al., 1998). The new algorithm estimates the probability of hail (any size), probability
of severe-size hail (diameter ≥ 19 mm), and maximum expected hail size for each detected
storm cell.
The detection of hail of any size is based on the criterion proposed by Waldvogel et al.
(1979). The probability of hail is derived from the difference between the maximum height at
which a reflectivity of 45 dBZ is observed (HZ45) and the height of the freezing level (HT0)
(Fig. 8). When the height difference is larger than 1.4 km, a positive indication of hail exists.
The probability of hail increases with the height difference (Fig. 9). A 100 % probability is
obtained for a height difference of 6 km.
Height(km)
Distance (km)
Vertical cross section of a thunderstorm cell
∆H
HZ45
HT0
Height(km)
Distance (km)
Vertical cross section of a thunderstorm cell
∆H
HZ45
HT0
Figure 8. Criterion of hail detection proposed by Waldvogel et al. (1979). From Iwan Holleman (KNMI).
Radar techniques for identifying precipitation type and estimating quantity of precipitation 37
The new algorithm has been evaluated through comparison with ground-truth data
collected during a field experiment in the summer months of 1992 and 1993. Kessinger et al.
(1995) note a significant improvement with respect to the initial version. The hail detection
method based on Waldvogel has been operationally implemented at KNMI (Royal
Netherlands Meteorological Institute) and tested on an extended verification dataset in the
summer months of 1999 and 2000 (Holleman, 2001). The results show that this method
performs substantially better than any other tested methods. The verification results have been
used to adjust the function that relates the probability of hail (POH) to the height difference
between the freezing level and the maximum height of the 45 dBZ reflectivity.
The following expression is currently used in the operational hail detection algorithm at
KNMI:
045),(133.0319.0 ZTZ HHHkmHPOH −=∆∆+= (27)
As can be seen on Figure 9, the linear expression obtained by Holleman (2001) differs
significantly from the original relation used by Witt et al. (1998). This is probably due to
differences in climatological conditions associated with hail.
-1-2 -1-2
Figure 9. Probability of hail as a function of the difference between the maximum height at which a reflectivity
of 45 dBZ is observed (HZ45) and the height of the freezing level (HT0). The black stepwise line gives the relation
used by Witt et al. (1998) and the blue line the expression obtained by Holleman (2001). Figure adapted from
Witt et al. (1998).
In particular, the climatology of the height of the freezing level may significantly influence
the POH relation. The method of Waldvogel using the formulation (1) has been implemented
at the Royal Meteorological Institute of Belgium and tested on reported hail events in the
summer 2002 (Delobbe et al., 2003). For 22 cases out of 23, a probability of hail at least equal
to 50 % was found at less than 10 km from locations where hail fall was reported.
As mentioned above, the NSSL has also developed algorithms for the detection of severe
hail (diameter ≥ 19 mm), and the prediction of maximum expected hail size (Witt et al.,
1998). The severe hail algorithm is based on a severe hail index (SHI) derived from the
Radar techniques for identifying precipitation type and estimating quantity of precipitation 38
vertical profiles of reflectivity and temperature. The vertical profile of reflectivity is first
converted into a vertical profile of hail kinetic energy flux and then vertically integrated using
a temperature-based weighting function. The maximum expected hail size is also derived
from the SHI using a simple empirical relationship. It must be noted that the verification of
severe hail detection algorithms and even more of maximum size predictions is extremely
difficult given the highly sporadic nature of severe hail reports.
Vertically integrated liquid water (VIL) is another indicator of the severity of a storm cell
which was introduced by Greene and Clark (1972). Reflectivity values can be converted to
liquid water contents using a semi-empirical relationship similar to the Z-R relationship used
for the conversion of reflectivities to precipitation rates. The vertical integration of the liquid
water content is the VIL. However, discriminating between thunderstorms with and without
hail using VIL only is not straightforward since there is a large variability in the VIL
threshold associated with the presence of hail. A normalized VIL has been proposed by
Amburn and Wolf (1997) : the VIL is divided by the height of the top of the thunderstorm
cell. This top can be for example determined as the maximum height with a 7 dBZ reflectivity
value. The threshold for the normalized VIL is supposed to be more universal than the VIL
threshold. Nevertheless there is still no agreement on the most appropriate threshold for
operational hail detection method using a normalized VIL indicator.
5.3 Determination of stratiform/convective type of precipitation
Stratiform (large-scale, synoptic-scale) precipitation is caused by upward vertical motion over
large areas (thousands of sq. kilometres and more) of typical velocities of cm/s as the result of
synoptic-scale forcing. From the radar point of view, it usually exhibits well-defined bright
band (if the surface precipitation is liquid) and rather low horizontal gradients of precipitation
(with some notable exceptions, among others due to orographic enhancement). Detection of
such precipitation by radar often encounters significant systematic errors due to bright band
effects, attenuation over the large areas of continuous precipitation and rather low vertical
depth of the precipitation region, i.e. steep vertical gradient of reflectivity, which results in a
pronounced range dependent bias (significant systematic underestimation at far ranges).
Under favourable conditions, seeder-feeder orographic enhancement can occur.
Convective precipitation, on the other hand, is caused by nearly vertical air motions of
typical velocities of 1 m/s to tens of m/s caused by the atmosphere instability. Convective
precipitation shows very high horizontal gradients and large vertical depth. These
characteristics mean that the weather radar is the best tool for detecting convective
precipitation, but the presence of different types of hydrometeors, especially hail, and storm
dynamics (magnitude of updrafts and downdrafts) resulting in fast varying VPR usually result
in considerable random error in quantitative precipitation estimates. Large differences can be
found especially when comparing rain gauge and radar estimates because of the high temporal
and spatial variability of the convective storm and related vertical profile of reflectivity.
However, it is not always possible to strictly categorize all the precipitation system into
stratiform and convective classes because of common transition between the prevailing
forcing mechanisms and related characteristics. If the conditional or potential instability is
sufficient, embedded convection can be found in stratiform regions, while convective
development sometimes results in widespread precipitation with clear bright band signature.
Therefore a ‘transition’ or ‘no signature’ class must also be used (e.g. Sempere-Torres et al.,
2000, Uijlenhoet et al., 2003b).
Despite the ambiguity that can sometimes occur, categorization of the precipitation events
or regions into the ‘thermodynamical’ classes described above provides the users with
additional information about the anticipated rainfall characteristics (intensities, predictability,
Radar techniques for identifying precipitation type and estimating quantity of precipitation 39
reliability/usefulness of the radar estimate).
An algorithm for the identification of convective areas can be found in Steiner et al.
(1995), which was used by Sempere-Torres et al. (2000) for analyses of DSD and Z-R
relations. Steiner’s scheme uses gridded data from a CAPPI level and the classification is
based on the absolute magnitude of the echo (if more than 40dBZe, the echo is convective)
and the relative magnitude over the background reflectivity, averaged over a circular area of
11-km radius. Depending on their echo intensity, areas adjacent to the convective cells may
be classified as convective. The background-exceedance algorithm of Steiner et al. (1995)
was refined by Biggerstaff and Listenmaa (2000) who incorporated VPR into the scheme.
The work was motivated by the need for a better assessment of the magnitude of the
atmospheric diabatic heating caused by different processes.
Another procedure for identifying convective and stratiform types can be found in Seo et
al., 2002. Their convective/stratiform separation algorithm relies much more on the spatial
statistics (autocorrelation) of reflectivity, apparent height of convective echo and the third
variable is the maximum reflectivity in vertical direction. Moreover, the vertically integrated
liquid water (VIL) was found to be also a good parameter for the identification of convective
and stratiform regions, but it should not be used separately. This procedure is about to be
implemented operationally in the overall WSR-88D precipitation processing system.
The use of formal identification of stratiform/convective types of precipitation for the
purposes of quantitative precipitation estimation is not too common. It may be so because
crude identification of these classes can be made intuitively by visual inspection of the radar
images, often along with a lightning detection system if available. One of the exceptions is
discrimination between rainfall types on the basis of temporal evolution of adjustment factor
as proposed and temporarily introduced by Collier in the United Kingdom (Collier et al.,
1983, in: Collier, 1996). The harmonic analysis of the factor allowed identification of
following types: frontal (i.e. stratiform), showers (i.e. convective) and ‘Welsh shadow’ (warm
frontal sector). Depending on the precipitation type identified, different Z-R relationships
were applied.
5.4 Multisource method of identification of precipitation type
Single polarization radar has only a modest capability of determination the precipitation type;
e.g. the phase of the precipitation can be estimated only indirectly by height and depth of the
melting layer if the bright band signature is pronounced enough. However, much better
information can be achieved if other sources of meteorological data are used. For instance,
hail detection algorithms by single polarization radars generally use a temperature profile (at
least the height of the freezing level, see chapter 4.2.3). National weather services are
nowadays running comprehensive observation networks and can simultaneously utilize NWP
models, satellite measurements, lightning detection etc. Thus, the radar measurement has to
be considered as a complementary tool in the overall monitoring system whose aim is to show
the most accurate image of the atmospheric state and processes.
From this point of view, except for hail detection, single polarization radar plays a rather
minor role in the determination of the precipitation type, especially in operational
applications. In the systems that integrate more information for the identification of the
precipitation type and quantity, the radar measurements are usually corrected using other
meteorological information. For example, the determination of the freezing level over Finland
is operationally made using space-interpolated radiosondes and/or NWP data and the freezing
level height is used for the VPR correction. Vertical profile of temperature is also very useful
in separating shallow precipitation from clear air echoes (see Koistinen, 2003). The explicit
determination of the precipitation type on the ground is based on surface weather (SYNOPRadar
techniques for identifying precipitation type and estimating quantity of precipitation 40
coded) observations and the Z-R/Ze-S relationships are adjusted according to the probability of
snowfall on the ground (Koistinen, 2003).
Another attempt to identify the precipitation type using radar has been reported by Costa et
al. (1995) who found that radar-derived precipitation estimates can be improved if the
correction regression equations include relative vorticity from the ECMWF model. The role
of the vorticity in the radar performance is not fully explained but it was suggested that the
vorticity value might reflect the spatial organization of precipitating clouds.
An example of a ‘multisource’ system that integrates observations, NWP models and
remote sensing data is the UK Met Office’s NIMROD system (Golding, 1998). The primary
goal of NIMROD is to provide the customer with very short-range forecasts including the
precipitation quantity and type. Whilst the radars produce mainly the initial field of
precipitation which is then extrapolated, the precipitation product utilizes the NWP outputs
and observations for determining the precipitation type, including the occurrence of hail.
6 Dual polarization radars
Although this paper is devoted primarily to single polarization radars, we have to shortly
mention also the possibilities provided by more sophisticated dual polarization radars. In the
following text we rely mostly on information available in Collier et al, 2001.
Linear polarisation radars can generally transmit pulses that are alternately polarised in the
horizontal and vertical, and can measure the two co-polar returns Zh
(horizontal polarized), Zv
(vertical polarized); if a cross polar receiver channel is installed, then the cross-polar return
ZHV
is also available. In addition, if the radar is Dopplerized, then the phase of the returns
with horizontal and vertical polarisation, Φh
and Φv
, can be estimated.
The four parameters we shall discuss are: the differential reflectivity, ZDR
; the specific
differential phase shift, KDP
; the linear depolarisation ratio, LDR
; and the co-polar correlation,
ρ2,hv.
ZDR
– differential reflectivity ( )/log(10 vh ZZ= ) is a measure of mean particle shape.
ZDR
is particularly useful for rain, because small raindrops are spherical but larger ones
become increasingly oblate. If we assume a simple Marshall-Palmer raindrop size
distribution , where D0
is the equivolumetric median drop
diameter, then the value of D0
can be estimated from ZDR
. Once D0
is known, then the
value of N0
is fixed by the observed value of Z. An empirical Z-R relationship is equivalent
to assuming that N0
is constant, but the use of Z and ZDR
to fix both N0
and D0
should
result in more accurate rainfall estimates (Seliga and Bringi, 1976). Here, for this method
to work, ZDR
must be measured to about 0.2dB accuracy, and at C-band the attenuation by
the oblate raindrops is appreciably higher in the horizontal than the vertical and this
differential attenuation leads to an increasingly negative bias of ZDR
with range in heavy
rain.
)/67.3exp()( 00 DDNDN −=
Ice particles have lower dielectric constants and so even if they are oblate they tend to
have low values of ZDR
, particular if, as is the case of snow, they are a low density mixture
of air and ice. Once particles are wet the value of ZDR
increases, and so the bright band is
Radar techniques for identifying precipitation type and estimating quantity of precipitation 41
associated with high values of ZDR
. In addition, supercooled raindrops in vigorous
convection can be recognised by narrow vertical columns of positive ZDR
extending above
the freezing level.
KDP
– the specific differential phase arises because the speed of the horizontally
polarised wave through a regions containing oblate raindrops is lower than the speed of the
vertically polarised wave, and as a result the phase of the horizontal return, Φh
, lags
progressively behind the phase of the vertical return, Φv
, and as a result the differential
phase, ΦDP
=Φv
-Φh
, increase with range. KDP
is the rate of change of ΦDP
with range
measured in degrees/km. The advantage of KDP
is that it is more linearly related to the
rainfall rate than is Z. In addition, when hail is present it can dominate Z and lead to very
high values of Z, which are difficult to interpret in terms of a rainfall rate, but hail tumbles
as it falls so it gives no contribution to KDP
. KDP
can be quite difficult to measure as the
phase shifts at S-band in light rain are quite small, but as KDP
scales with frequency the
phase shifts are larger at C-band.
ρ2,hv – the correlation of the time series of the Zh
and Zv
returns, which provides a
measure of the range of particle characteristics present, i.e. the range of the ratio of the
horizontal to the vertical back scattering amplitude. Raindrops are usually Rayleigh
scatterers, have similar shapes and exhibit a high degree of common orientation and so
they are generally associated with high values of correlation very close to unity. ρ2,hv
values tend to be lower in the bright band because of the range of particle shapes present
there. In theory, the value of ρ2,hv can be used to estimate the breadth of the raindrop size
distribution and the degree of tumbling, but this seems to require a very good antenna.
Another application of the correlation coefficient is to distinguish precipitation from
ground clutter; this could be particularly useful for recognizing anomalous propagation.
Ground clutter has a correlation which is essentially zero.
LDR
- the linear depolarisation ratio ( )/log(10 hhv ZZ= ), the ratio of the cross-polar to
the co-polar return. The cross-polar return is high only for wet oblate ice particles falling
with their axes inclined to the horizontal. LDR
depends on the mode of fall of the particles
and is an excellent indicator of wet ice. It is a good indicator of the presence of the bright
band. At C-band LDR
may well be affected by depolarisation of the beam, so that as it
passes through a region of finite LDR
some of the incident radiation is transferred to the
cross-polar channel, which is subsequently reflected very efficiently by targets. This will
cause the apparent value of LDR
to rise with distance.
To sum up, one can say that dual polarized radars provide additional information on the
precipitation. These additional parameters may be used to improve the estimation of the rain
rate. The big advantage is, that some dual polarization parameters are independent of
attenuation, because they use the phase of the signal. Nevertheless, these parameters are hard
to measure, because the signals are rather small and are sometimes determined as the
difference between two large signals. With proper adjustment of the radar a calibration of the
reflectivity signal to 0.5dB (10%) seems to be possible.
The performance of QPE of a WSR-88D radar that has added dual polarization capability
is evaluated in Ryzhkov et al., 2003. Following their results, the improvement due to
utilization of above-mentioned parameters is remarkable, especially when using a ‘synthetic’
Radar techniques for identifying precipitation type and estimating quantity of precipitation 42
algorithm using values of Z, KDP and ZDR. The benefit is especially pronounced in heavy
rainfalls and areal estimates. Concerning the range, the polarimetric methods of QPE clearly
outperform the conventional one especially up to 125 km from the radar site. The farther from
the radar, the less apparent the improvement is, and beyond 200 km the performance of all
algorithms is poor because of the dominant (in)visibility problem of low levels.
In Europe, where weather radars are mostly in the C-band, efforts have been made also to
correct for attenuation by heavy rain. For example, the ZPHI algorithm, based on Φh
and Φv
,
has the objective to improve QPE by the correction of attenuation by heavy rain, a capacity of
self-calibration of radar data and a low sensitivity to drop size distributions (Testud, 2000 and
Le Bouar, 2001).
The operational use of dual polarization radars for QPE is not common, mainly because of
the overall cost of the equipment (including maintenance) which is much higher then that of
single polarization radars. However, the benefit of improved QPE may in the future outweigh
the cost of dual polarization radars, especially when the more accurate QPE and additional
parameters are effectively utilized for better warning systems. It has to be mentioned that the
U.S. National Weather Service plans to equip their WSR-88D radar network with dual
polarization facilities in about the year 2007 (Fulton, 2003). There are also some plans in
Europe; for example, in 2004 Meteo-France will install a new radar equipped with dual
polarization that will be used to evaluate the benefits of this technique in a quasi-operational
context (Parent du Châtelet et al., 2003)
When planning to introduce dual polarization radars, it should not be forgotten that these
instruments are limited by the visibility as well as conventional radars. In places where
shielding poses a big problem, the dual polarization will not help very much.
7 Conclusion
The digital revolution at the end of the 20th
century was reflected in a new generation of
radars with fully digitized outputs, which has considerably facilitated the quantitative use of
radar information. However, errors in radar measurements became more apparent, which
could result in a loss of faith in the ability of radar to measure precipitation effectively. In
fact, the initial expectations of the potential of radar were probably too high, especially for
quantitative precipitation measurement. Nowadays, when the limitations of weather radars,
including sophisticated multiparameter (dual polarization) radar, are better known, the role of
radar has to be a slightly redefined. It should be no longer considered as a competitor of rain
gauges but rather as a complementary source of information that must be used in conjunction
with other relevant meteorological (and hydrological) information. This has already been
reflected in literature and even some operational systems use the “multisensor” approach
(Fulton et al., 1995, Golding, 1998).
The use of radar for quantitative precipitation estimation has to be accompanied also by
information that can provide some assessment of data quality. For instance, one of the basic
indices can be the “time coverage” or “radar scans availability” (the ratio of number of real
measurements to the theoretically possible; if the radar measures without failures or gaps, the
percentage is 100%). Although it is not easy to define a more general “quality index” of the
reliability of the radar measurement, considerable effort in this field was taken in the
framework of COST 717 Action (Michelson et al., 2004). Nevertheless, at least visual
inspection of the radar performance in comparison with other data (e.g. rain gauges or
satellites) is highly recommended, along with an assessment of upcoming precipitation
processes with the help of NWP models and observations.
Radar techniques for identifying precipitation type and estimating quantity of precipitation 43
The partial solution of the problem of quantifying the QPE-related error can be to express
the QPE in a probabilistic form, i.e. to assign probabilities to some predefined threshold
values. Although this is not a trivial task, some preliminary activities in the field are already
reported (Krajewski and Ciach, 2003).
The user of the radar precipitation estimates has to be aware that in some adverse
meteorological situations the ‘raw’ radar precipitation estimate can be of little use (e.g. in case
of pronounced seeder-feeder enhancement with a radar underestimation by one order of
magnitude) but under different conditions the radar information can be invaluable. Even if the
quantitative information is not accurate enough, the radar can still provide good qualitative
image of the atmospheric situation, which is also useful. The user has to be trained enough to
be able to assess the quality of the radar QPE at the moment of utilizing the estimates.
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