AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-9-3837-2016Close-range radar rainfall estimation and error analysisvan de BeekC. Z.remco.vandebeek@meteogroup.comLeijnseH.https://orcid.org/0000-0001-7835-4480HazenbergP.UijlenhoetR.https://orcid.org/0000-0001-7418-4445MeteoGroup, Wageningen, the NetherlandsRoyal Netherlands Meteorological Institute, De Bilt, the NetherlandsAtmospheric Sciences Department, University of Arizona, Tucson, AZ, USAHydrology and Quantitative Water Management Group, Wageningen University, the NetherlandsC. Z. van de Beek (remco.vandebeek@meteogroup.com)18August201698383738509March201616March201617July201618July2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/9/3837/2016/amt-9-3837-2016.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/9/3837/2016/amt-9-3837-2016.pdf
Quantitative precipitation estimation (QPE) using ground-based weather radar
is affected by many sources of error. The most important of these are
(1) radar calibration, (2) ground clutter, (3) wet-radome attenuation,
(4) rain-induced attenuation, (5) vertical variability in rain drop size
distribution (DSD), (6) non-uniform beam filling and (7) variations in DSD. This study presents an attempt to separate and quantify
these sources of error in flat terrain very close to the radar (1–2 km),
where (4), (5) and (6) only play a minor role. Other important errors exist,
like beam blockage, WLAN interferences and hail contamination and are
briefly mentioned, but not considered in the analysis. A 3-day rainfall event
(25–27 August 2010) that produced more than 50 mm of precipitation in De
Bilt, the Netherlands, is analyzed using radar, rain gauge and disdrometer
data.
Without any correction, it is found that the radar severely underestimates the
total rain amount (by more than 50 %). The calibration of the radar
receiver is operationally monitored by analyzing the received power from the
sun. This turns out to cause a 1 dB underestimation. The operational
clutter filter applied by KNMI is found to incorrectly identify precipitation
as clutter, especially at near-zero Doppler velocities. An alternative simple
clutter removal scheme using a clear sky clutter map improves the rainfall
estimation slightly. To investigate the effect of wet-radome attenuation,
stable returns from buildings close to the radar are analyzed. It is shown
that this may have caused an underestimation of up to 4 dB. Finally, a
disdrometer is used to derive event and intra-event specific Z–R
relations due to variations in the observed DSDs. Such variations may result
in errors when applying the operational Marshall–Palmer Z–R relation.
Correcting for all of these effects has a large positive impact on the
radar-derived precipitation estimates and yields a good match between radar QPE and
gauge measurements, with a difference of 5–8 %. This shows the
potential of radar as a tool for rainfall estimation, especially at close
ranges, but also underlines the importance of applying radar correction
methods as individual errors can have a large detrimental impact on the QPE
performance of the radar.
Introduction
Rainfall is known to be highly variable, both in time and space. Traditional
measurements by single rain gauges or networks only provide accurate
information of the rainfall at their locations. While interpolation of these
data is possible, the spatial information is often too sparse for accurate
meteorological and hydrological applications
. Furthermore, rain gauges are often
seen as “ground truth”, but these instruments also suffer from errors
.
Radar, on the other hand, does provide far better coverage in space and often
also in time. However, a problem with radar systems is the larger number of
error sources, which makes quantitative estimations based solely on radar
difficult, unless these error sources are correctly addressed. Error sources
that can be identified are radar calibration, clutter, wet-radome
attenuation, rain-induced attenuation, vertical profile of reflectivity
(VPR), non-uniform beam filling
e.g., and errors in
derived surface rain rate from the measured reflectivity aloft due to
uncertainties in the rain drop size distribution (DSD) , the impact of wind drift and
differences in instrumental characteristics (i.e., radar beam volume vs.
point-based rain gauge). These variations in the error sources have been
studied and described extensively in the past
e.g.,. Polarimetric
radars offer new variables that allow greater insight in precipitation and
new ways to deal with these error sources, but are not considered in this
paper .
Clutter results from the main beam or side lobes (partially) reflecting off
the terrain or atmospheric objects (e.g., buildings or trees, airplanes,
insects and birds). Close to the radar, ground clutter from objects can lead
to overestimation of rainfall reflectivities. Another source of clutter
results from atmospheric conditions bending the emitted radar beam towards
the surface (i.e., anomalous propagation (“anaprop”)). This source of
clutter can be highly variable in time, but its overall effect is generally
limited. In the past many clutter correction schemes have been developed
that reduce the impact of clutter with varying degrees of success
e.g.,.
Attenuation of the transmitted signal during a rainfall event can lead to
strong underestimation of the rain rate. The amount of attenuation along the
path of the transmitted signal is strongly dependent on the rain rate as well
as on the transmitted wavelength. X-band radars are relatively inexpensive
and easy to install, but suffer quite strongly from attenuation
e.g.,. Radars operating at longer wavelengths, like
C-band and S-band radars, suffer less from attenuation. However, during intense
precipitation events, C-band radar rainfall retrievals also tend to
underestimate precipitation rate e.g.,.
Correction for rain-induced attenuation was first proposed by
. Since then, other schemes have been developed that use
a path-integrated attenuation constraint
e.g.,.
Even though this study is based on a single-polarization radar, it is worth
noting that the differential-phase measurements from polarimetric radars
allow new methods e.g.,. Another source of
attenuation is caused by precipitation on the radar radome, resulting in a
liquid film of water. This film attenuates the signal and its effect becomes
more pronounced during stronger precipitation intensities. Wet radome
attenuation is highly dependent on the wind direction and the state of the
radome, as the attenuation depends on whether a film of water can form on the
radome .
Vertical variations in precipitation as observed with radar give rise to the
so-called vertical profile of reflectivity (VPR). The VPR has an important
impact on the measurement characteristics of the radar, even though close to
the surface, the role of the VPR tends to be limited. For stratiform
precipitation, the melting of snowflakes and ice crystals aloft results in
relatively large droplets. Within this melting layer region, the returned
radar signal intensifies (bright band), leading to an overestimation of the
precipitation intensity, while measurements above the melting layer typically
lead to an underestimation
e.g.,.
Non-uniform beam filling can also cause significant errors. This effect of
course depends on the size of the radar measurement volume and the spatial
heterogeneity of the rainfall. Because the relation between radar
reflectivity and rainfall intensity is nonlinear and not unique (depending
on the DSD), spatial rainfall variability within the radar measurement volume
can cause errors . The DSD also
directly influences the relation between the radar reflectivity and specific
attenuation. In case rain-induced attenuation is not corrected for, the radar
product is prone to result in erroneous rainfall estimates
.
The conversion from measured reflectivity values to rain rates at ground
level can be quite challenging as rain is highly variable in terms of its DSD
e.g.,. In general, the reflectivity value
(Z) is converted into a rainfall rate (R) using a power-law relation:
Z=aRb.
Locations of the rain gauge, disdrometer and radar at De Bilt with
0.5 km range rings around the radar (dashed lines). The blue section is the
1–2 km radar bin that is used in this study. The inset in the upper right
corner shows the locations of radar and instruments at De Bilt and at Hupsel,
which is the location of maximum rainfall measured during the event studied.
Data by OpenStreetMap.org contributors under CC BY-SA 2.0
license.
To date, the Marshall–Palmer (M–P) equation with
Z=200R1.6 is the most commonly used Z–R relationship and is
generally assumed to be representative of stratiform precipitation. It
should be noted that other Z–R relations have been derived as well, more
suitable during different types of precipitation and for other locations
e.g.,.
Estimates of the DSD can be obtained by surface disdrometers, from which both
Z and R can be inferred. Based on these estimates, it then becomes
possible to infer the actual Z–R relationship for the event of study at
the location of the instrument
e.g.,. However, the benefit
of applying disdrometer observations for weather radar rainfall correction
application is still uncertain, as their point-based character might not be
representative of the larger scale precipitation system aloft.
showed that using a disdrometer to determine the actual
Z–R relation did lead to improved results for convective precipitation.
At the same time, making use of disdrometer observations for the Netherlands
was shown to lead to improved precipitation estimates for widespread
stratiform precipitation
Beam blockage is definitely among the main error sources in complex terrain
scenarios, even more than attenuation (at least for C-band radar), considering the
latter as a transient phenomenon whose effects over medium to long
accumulation intervals might not be detrimental, even if not corrected. Beam
blockage, despite quantifiable and correctable to a given extent, affects the
adopted scan strategy and the height of measurements above ground.
WLAN interference is increasingly becoming an issue for weather radar
measurements, but is not considered in this paper. A recent publication on
this topic is, e.g., .
Hail can also heavily affect radar observations in terms of both scattering and
absorption enhancement. For C-band radar, melting hail can be responsible for
attenuation enhancement that can lead to signal extinction.
This paper studies the possibilities of quantitative precipitation estimation
(QPE) at close ranges (1–2 km) for a C-band weather radar operated by the
Royal Netherlands Meteorological Institute (KNMI) in the center of the
Netherlands. At these distances, the effects of VPR, rain-induced attenuation
and non-uniform beam filling are limited. Their impact was therefore ignored
in this work. Section describes the instruments and the data
used in this study, which are the same as used by .
Section describes the rain event that is analyzed. On
Sect. the reflectivity correction methods and their effects
are discussed, together with a verification. Finally,
Sect. contains conclusions and recommendations.
Instruments and data
The precipitation event analyzed in this paper was observed by the radar
during the late afternoon on 25 August 2010 and lasted for about 2 days and
is well known for the large amount of precipitation that fell, especially in
the east of the Netherlands at Hupsel . A
number of instruments, located at KNMI in De Bilt, the Netherlands, are used
in this paper. These are a rain gauge, an optical disdrometer and an
operational C-band Doppler weather radar. The instruments are located in a
field south of the radar at KNMI. The instrument locations as well as the
radar distance bin that has been used for the comparison are shown in
Fig. .
The employed rain gauge is an automatic gauge with a surface area of 400±5 cm2 installed in a pit . The height of
a float in the reservoir of the gauge is measured every 12 s with a
resolution of 0.001 mm. The gauge can report the precipitation intensity in
steps of 0.006 mm h-1. The rain is accumulated and stored at 10 min
intervals, using guidelines set by and .
The disdrometer is a first-generation OTT Parsivel®. The Parsivel® measures the
size and velocity of droplets by the extinction caused by droplets passing
through a sheet of light with a surface area of around 50 cm2. It can
measure particles from 0.2 to 25 mm diameter with velocities between 0.2 and
20 m s-1. The beam between transmitter and receiver has been oriented
perpendicular to the prevailing southwesterly wind direction in the
Netherlands. The data from the disdrometer are logged every minute
. The first-generation Parsivel® disdrometer is known to
have some issues . Most notable is the
overestimation that occurs for higher rainfall intensities and large
raindrops. note that the Parsivel® starts to overestimate
the number of drops larger than 2.44 mm diameter when intensities exceed
2.5 mm h-1 and the drop concentrations exceed 400 min-1. The
number of drops in this diameter class (i.e., larger than 2.44 mm) is
limited throughout the event presented below, so the effect is expected to be
minor.
The radar operated by KNMI is a Doppler C-band radar from SELEX-SI (Meteor
AC360). It is located at 52.108∘ N, 5.178∘ E on top of a
tower at 44 m above sea level. It operates at 5.6 GHz (wavelength of
5.3 cm). The radar performs a full 14-elevation volume scan every 5 min.
The resolution is 1∘ in azimuth and 1 km in range. For details about
the radar and the scan schedule, see . For this study we
use the first distance bin between 1 and 2 km from the radar at an azimuth
of 230∘ (see Fig. ) of the 0.8∘
elevation scan. The analyzed data are from a range in the far field of the
radar. The T/R limiter might cause some tenths of a decibel additional attenuation
at the close range considered. The limited effect is confirmed, however, as
the final rainfall estimates are seen to correspond well with disdrometer and
rain gauge measurements .
Description of the rain event
Synoptic situation for 26 August 2010,
12:00 UTC.
Daily precipitation sum and duration on 25–27
August.
De Bilt Hupsel Sum (mm)Duration (h)Sum (mm)Duration (h)25 Aug6.45.71.63.026 Aug50.618.3142.319.527 Aug3.05.514.64.5Total60.029.5158.527.0
Between 25 and 27 August 2010, a narrow band of low pressure passed over the
Netherlands from the direction of the English Channel towards southern
Denmark, between high pressure zones over southern Europe and Scotland. During
26 August, the triple point remained near the southern coast of the
Netherlands for most of the day with the warm front moving very slowly
northward. This caused large temperature differences in the Netherlands
between the north, with cold air, and the south, with warmer air behind
the warm front. During the afternoon of the 26th the low pressure zone began
moving eastwards, leading to calmer weather (see Fig. ).
Top panel: time series of the rain event, with the rain rate from the
rain gauge in black, and in red, the rain rate derived from the radar
reflectivity using the Marshall–Palmer Z–R relation (M–P). The
vertical dashed lines divide the event into eight different episodes. Bottom
panel: cumulative sum of rainfall from the three instruments before any
correction of the radar and using the M–P relation.
DSD during the rain event. The black dashed lines illustrate the
identified rain episodes of the event.
During the passage of these low-pressure areas, a mesoscale convective system
containing large fields of alternately stratiform and convective
precipitation passed over the Netherlands. This led to both large
precipitation amounts and long durations for most of the Netherlands.
Table illustrates the amounts and durations for De Bilt, where the radar and instruments are located, and for Hupsel, located in
the east of the Netherlands. At Hupsel, an extremely large amount of
precipitation of nearly 160 mm within 24 h was measured (return
period > 1000 years) for this event
see. At the location of the radar in De
Bilt, which is the focus of this study, the total precipitation accumulation
was less, although still considerable, with 50.6 mm over a period of 18.3 h
of continuous rain return period 5–10 years;
see.
The time series of precipitation is shown in the top panel of
Fig. and in Fig. . There is no
precipitation until the late afternoon on the 25th. A long period of rain,
with low to moderate rain rates, was observed at De Bilt (episode 1 in
Fig. ). The highest intensity cores were mostly observed
just south of the radar and therefore not observed by the surface instruments
used here. After a short dry period, more precipitation passes over the radar
with variable intensities. This period has been subdivided into two phases: a
first phase with moderate intensities of around 5 mm h-1 (episode 2
in Fig. ), and a second one containing heavier rainfall
rates up to 25 mm h-1 (episode 3 in Fig. ). This
period also gave rise to the largest number of raindrops measured by the
Parsivel® disdrometer (see Fig. ). The large peak in episode 4
was the edge of an active squall line that began to form south of the radar
and was advected eastwards, which caused large precipitation sums near Hupsel
. For episodes 5–8, rain intensities decreased within the
trailing stratiform part of the squall line, resulting in sporadic rainfall
observed close to the radar. The total accumulations are shown in the bottom
panel of Fig. . The two disdrometers and the gauge are
closely related, but the radar clearly underestimates rainfall accumulations.
Radar reflectivity (left panel) and amount of clutter corrected by
the Doppler notch filter (right panel) for the most intense rainfall peak of
episode 4 on 26 August 2010 at 12:10 UTC. Images shown are for the
0.8∘ elevation scan.
Methodology and results
As explained in the introduction, various error sources affect rainfall
measurements by weather radar. Since this work focuses on the performance of
the weather radar at close ranges, it was decided not to focus on the impact
of rain-induced attenuation and VPR, as at close ranges these are expected to
be negligible. Therefore, the current section specifically focuses on the
effects of correcting for calibration, ground clutter and wet-radome
attenuation. Furthermore, this section also presents the impact of accounting
for DSD variations as inferred from disdrometer observations.
Calibration
As explained in the introduction, the absolute radar calibration can have an
impact on the QPE performance of weather radar
. In the current work, we make use of the
sensitivity of the receiver and the alignment of the radar to get accurate
information on the possible calibration issues for the current event. The
emitted signal from the sun is easily detectable by the radar as it is
constant over all range bins. This signal can then be used to monitor the
absolute calibration of the radar. This method is used operationally by KNMI
. These analyses showed that the receiver calibration was
off by approximately 1 dB, resulting in an underestimation by the radar. The
transmitter calibration is regularly checked and is therefore assumed to be
correct. To account for this error source, a value of 1 dB was added to the
observed radar reflectivity values.
Top-left panel: reflectivity of the studied range bin between 1 and
2 km from the radar of the uncorrected reflectivity (black) and the static-clutter-corrected reflectivity (blue). Here the red dashed line is the
average reflectivity when there is no rain. Top right panel: the cumulative
rain sums for the rain gauge (blue) and the Doppler clutter-corrected
reflectivity (black), together with the uncorrected (red) and the static-clutter-corrected
reflectivity (green) using the Marshall–Palmer Z–R relation with 1 dB
added to compensate for calibration errors. Bottom panel: time series of the
rain gauge, Doppler clutter-corrected and the static-clutter-corrected rain
rates.
Clutter correction
The operational ground clutter correction algorithm uses a time-domain
Doppler notch filter. A drawback of this automatic procedure is that it
incorrectly identifies some precipitation as clutter
e.g.,, leading to an underestimation of rainfall
intensities as measured by the radar. An example is clearly shown in
Fig. , where images of both the radar reflectivity
factor and the amount of clutter correction are shown. The zero-isoDop, the
region where the velocity is perpendicular to the radar and therefore zero,
is clearly visible in the right-hand panel of this image, and the amount of
filtering in such areas can be as high as 3–4 dB. For other areas, the
amount of incorrect identification of precipitation as ground clutter is
limited, although its effect can still be significant, on the order of
1–2 dB (i.e., a factor of 1.15–1.33 in terms of rainfall intensity given
the Marshall–Palmer Z–R relation).
As an alternative procedure to correct for the impact of ground clutter,
use was made of a dry weather clutter map technique, consisting of the
average dry weather reflectivity value. To correct for the impact of ground
clutter during the precipitation event, this map is subtracted from the
observed reflectivity values. Normally such a technique is applied to every
pixel within the radar map, but for this study it has only been applied to
the bin of interest. A main underlying assumption of making use of a static
dry weather clutter map is that the clutter reflectivity does not change
during rain (e.g., because objects become wet). This method (also called a
clutter map) will not remove all clutter; however, it identifies less
precipitation as clutter compared to a Doppler filter.
Figure illustrates the effect of the operational
clutter removal scheme and the use of the static dry weather clutter map. In the
top-left panel, the raw uncorrected reflectivity values are shown in black. It
can be observed that the average background reflectivity values during clear
sky situations are around 15.6 dBZ (dashed red line). Subtraction of the
mean value of Z (mm6 m-3) (i.e., not dBZ) from the uncorrected
reflectivity results in the simple static clutter removal (blue line). This
has the greatest impact for low reflectivities, with no or very little rain.
In the top-right panel of Fig. , the cumulative
rainfall sums are shown for both rain gauge and radar rainfall (using the
M–P relation) data. Radar accumulations are shown without clutter
correction, and after applying either an operational Doppler scheme or the
static dry-weather clutter correction method. Note that these results are
obtained after applying 1 dB calibration correction. Results show that the
uncorrected radar reflectivities produce the largest rainfall accumulations,
as results are overestimated due to the identification of ground clutter as
precipitation. Of the two clutter correction schemes, applying the
operational Doppler scheme results in the largest reduction of precipitation,
whereas the static scheme is more conservative. As explained before, it is
anticipated that the operational Doppler scheme incorrectly identifies some
precipitation as ground clutter and as such results in the lowest
precipitation accumulations. Therefore, in the remainder of the paper, use is made of the static-clutter correction scheme.
In the bottom panel of Fig. , the time series of
the Doppler and static-clutter-corrected radar-derived rain rates are shown,
together with those of the rain gauge. As expected, the static-clutter-corrected time series shows higher rainfall intensity peaks than those of the
Doppler corrected time series and is generally closer to the rain gauge
measurements. The small dip that is present in the peak of the Doppler corrected rain rate with very heavy rain in episode 4 of
Fig. disappears in the static-clutter-corrected
time series. This is a good illustration of the Doppler clutter removal
scheme being too sensitive at times. There are a few exceptions to the
underestimation by the radar, most notably the two highest peaks in episode
5, where the radar actually overestimates the rain rate compared to the rain
gauge. A possible cause might be that the studied range bin lies further
south than the other instruments, located at the measurement field of KNMI,
and most of the strongest precipitation passed just south of the radar,
especially during the formation of the squall line at the end of the rain
event.
Wet radome attenuation
Top-left panel: reflectivity of a strongly reflective clutter pixel
near the radar. Here the red dashed line is the average reflectivity when
there is no rain. Top right panel: the cumulative rain for the rain gauge
(blue), the Doppler clutter-corrected (black) and the wet-radome-attenuation-corrected rain rate using the Marshall–Palmer Z–R relation using the
static-clutter- and calibration-corrected data (red). Bottom panel: time
series of the rain gauge, KNMI (Doppler filter) clutter-corrected and the
wet-radome-attenuation-corrected rain rates.
Since for the current event, precipitation with considerable intensities was
observed at the location of the radar for a large period of time, it is
highly likely that the resulting formation of a thin layer of water on top of
the radome caused significant attenuation of the signal. The effect of the
wet radome needs to be corrected and is achieved by using a strong clutter
pixel observed close to the radar, caused by a tall building. Due to its
close proximity to the radar (only 3 km away), it is assumed that the impact
of the rain-induced attenuation is negligible. We relate a decrease in the
measured reflectivity value of this static clutter pixel during a
precipitation event to the amount of attenuation caused by the wetting of the
radome. While the wetting of the clutter object and precipitation at the
clutter location may also influence the measured reflectivity, these factors
are assumed to be much smaller than the effect of the wetting of the radome.
Figure presents the impact of wet-radome attenuation on
the measurement capabilities of the radar. The top-left panel shows the
measured reflectivity from the clutter pixel at a range between 3 and 4 km
from the radar. The dashed red line presents the average reflectivity during
dry periods. The reflectivity can be seen to fluctuate by about 0.5 dB
around this mean value; however a larger drop in measured reflectivity values
can be observed at the onset of the event in the late afternoon on 25 August.
The difference between the average dry and observed reflectivity values is
assumed to represent the impact of wet-radome attenuation, which reaches its
greatest value during the peak of very heavy rainfall. After having corrected
for calibration error and clutter, the impact of wet-radome attenuation
correction is shown in the top-right panel of Fig. . As
expected, the correction of the attenuated radar reflectivity results in a
larger estimated rain rate, closer to that of the rain gauge.
Left panel: reflectivity (Z) measured by the radar and derived
from the Parsivel®, where the black circles are the operationally corrected
values and the red circles the fully corrected data described in this paper.
Right panel: same as left panel but on a logarithmic
scale.
Z–R relations
The corrections applied so far have all had a positive impact on the radar QPE
performance. As a last aspect, the current section focuses on the impact of
DSD variations. Figure compares the reflectivity
measurements of the radar to those inferred from the disdrometer. While DSD
sampling effects (both in terms of number of drops per unit time and diameter
class widths) are relevant aspects, it is not expected to greatly influence
the results in this paper
. The corrections
clearly have a positive impact, especially for high values of reflectivity
(left panel of Fig. ). If the M–P Z–R relation is
used, the accumulated rainfall increases from 25.8 mm for the uncorrected
data to 47.1 mm after applying the corrections for calibration error, ground
clutter and wet-radome attenuation (see Fig. ). While
this is still below the accumulated rain sum of 56.3 mm for the rain gauge,
the net effect is considerable. Since the current precipitation event was
highly variable in space and time, the applied M–P relationship is expected
not to be suitable as it is representative of stratiform precipitation
conditions. Therefore, further improvements in the quality of the rainfall
estimates by radar can presumably be obtained using the Z–R relationship
inferred from the disdrometer measurements.
Z–R relations derived from the 1 min data of the Parsivel®
for the different rainfall episodes distinguished in
Fig. using linear regression on the logarithmic values
(green curves) and nonlinear regression (red
curves).
Z–R relation derivation
Both the radar reflectivity Z (mm6 m-3) and the precipitation
intensity R (mm h-1) can be expressed as integral variables of the
raindrop size distribution N(D) (mm-1 m-3), where
Z=∫0∞D6N(D)dD,
and
R=6π×10-4∫0∞D3v(D)N(D)dD,
where v (m s-1) is the terminal raindrop fall velocity. Hence, both
Z and R are functions of the DSD.
The relation between radar reflectivity and rainfall intensity can be
expressed as a power-law function :
Z=aRb.
The observations obtained by the Parsivel® disdrometer are analyzed in more
detail here, as from the measurement taken by this instrument, joint estimates
of Z and R are obtained. These observations enable one to study the
impact of event- and intra-event-based variations of the Z–R relation
different from the M–P relationship.
In Fig. the Z–R
relationships which are obtained from the 1 min disdrometer data for
each of the identified episodes are presented. Multiple methods have been
presented to derive the Z–R relationship
. The simplest approach is
to apply a least squares linear regression procedure on the logarithms of Z
and R. However, this approach tends to give more weight to smaller rainfall
intensities. Therefore as a second approach, in the current work, a
nonlinear least squares fitting procedure was also applied and the results are
presented in Table . From
Fig. it can be observed that
the applied fitting technique has a large impact on the estimated values of
the prefactor a and exponent b. The Z–R relation varies greatly
between episodes. For episode 1, a clear split in the observed Z–R values
is visible, suggesting that this episode can be better represented by two
separate Z–R relations. However, on the basis of an in-depth analysis
using both the radar pseudo-CAPPI images (not shown here) as well as the DSD
data (see Fig. ), it was impossible to accurately distinguish
between these periods. Therefore, it was decided that this would be treated as a single
episode. For the other episodes, such a clear distinction cannot be observed,
although some episodes show more scatter than others.
In the remainder of this work it was decided to apply the estimates of a
and b (see Eq. 4) obtained by the nonlinear least squares approach, as
higher values obtain a larger weight by this procedure.
Z–R relations derived from the 1 min data of the Parsivel®
for the rainfall episodes shown in
Fig. using linear regression
on the logarithmic values and nonlinear regression.
Left panel: all nonlinear fits together with the Marshall–Palmer
Z–R relation. Right panel: accumulated rain for different Z–R
relations applied to reflectivity data that are corrected for calibration,
static clutter and wet-radome attenuation.
The nonlinear power-law fits, together with the Marshall–Palmer Z–R
relation, are shown in the left panel of Fig. . For
the current rainfall event, the optimal Z–R relationship varies
considerably between the different episodes. As expected, the
Marshall–Palmer relation is not representative of any of the eight
episodes. Therefore, applying this relation results in an overall
underestimation of the actual rain rate by the weather radar. This especially
holds for episodes 3 and 4. These episodes contained predominantly convective
precipitation. By making use of the effective Z–R relations shown in
Fig. , much larger precipitation
values are obtained. Furthermore, since these two episodes contain the rain
with the highest rainfall intensities observed for this event at the location
of the radar, these larger estimates have a strong effect on the total
accumulated rainfall. The Marshall–Palmer relationship overestimates the
amount of rainfall only during three episodes. Episodes 6 and 7 produce much
less rain than would be expected using the Marshall–Palmer relation (M–P),
while episode 2 yields slightly less rain compared to M–P for higher
reflectivities. These results clearly illustrate the impact of DSD
variability on the effective Z–R relations and the limited effectiveness
of a applying a single static relation.
Application of Z–R relations
The effects of applying the derived Z–R relations are shown in the right
panel of Fig. . In this figure, three different
approaches have been applied. First, the standard Marshall–Palmer
relationship is used (similar to Fig. ). As a second
approach, the event-based Z–R relation, obtained from all Z and R
data collected by the Parsivel® during this event, is used (top-left panel of
Fig. ). Using a single
representative Z–R relationship leads to considerably more precipitation
(59.6 mm) than M–P (47.1 mm) and results in an overestimation of about
6 % in total accumulation as compared to the nearby rain gauge. As a
third procedure, the eight individual, optimal intra-event power-law
relationships were applied. This leads to a total precipitation accumulation
of 61.0 mm, which is an overestimation by 8.3 %. The results clearly reveal the
positive impact of applying an event-based Z–R relationship, which for
the current event could successfully be derived from surface observations
obtained by a single disdrometer. It should also be noted that even though
considerable variations in the DSD are observed between the different
episodes, leading to variations in the effective Z–R relationship, this
does not further improve the event-based precipitation estimates.
Verification of the correction methods
Several statistical parameters were selected to give a summary of the overall
quality of the radar improvements compared to the rain gauge. These are the
sum, relative mean bias and the coefficient of variation.
The sum is defined as the accumulated rain sum found from the different radar
corrections:
Sum=∑i=1NR(i)Δt,
where R(i) is the rain intensity of the radar for the current time step and
Δt is the time interval in hours (i.e., 0.1667 h for 10 min values).
The relative mean bias is defined as the mean difference between 10 min
rainfall intensities from the radar and the rain gauge, normalized by the
average gauge intensity:
Bias=∑i=1N(R(i)-G(i))∑i=1NG(i)×100%,
where G(i) is defined as the rain intensity of the gauge for the current
time step.
The coefficient of variation (CV) is defined as the standard deviation of the
gauge–radar differences of 10 min intensities, normalized by the average
10 min gauge intensities:
CV=1N∑i=1NR(i)-G(i)-1N∑i=1N(R(i)-G(i))21N∑i=1NG(i)×100%.
Rainfall sum (mm) from the radar, together with relative mean bias
(%) and coefficient of variation (CV) (%) of 10 min rainfall
intensities from the rain gauge and the radar for different correction
combinations. Here, operational means the operational Doppler clutter-corrected data,
raw means the uncorrected data, static the static-clutter-corrected data and wet the wet-radome-corrected data. M–P is
the rain rate derived using the Marshall–Palmer equation. Pars means the
rain rate derived using the Z–R relation found from all data of the
Parsivel®. Finally, Pars steps is the same, but for all episodes of the
event, the derived Z–R values are used.
Table illustrates the above-mentioned statistics for
several combinations of corrections. The operational product (applied M–P
and Doppler clutter filter) gives rise to a large underestimation
by the radar and the worst performance. Not performing any kind of clutter
correction leads to better results as compared to the operational product,
both in total rainfall, standard deviation as well as bias. If a wet-radome
correction is applied to the static-clutter-corrected images, all statistics
improve and the difference between rain gauge and radar decreases from 38.8
to 16.3 %. By converting the corrected reflectivity data using the
Parsivel®-inferred Z–R relation, further improvements in the quality of
the radar product are obtained. Now the differences become very small, both
in terms of bias and coefficient of variation. This is also apparent from the
difference in rainfall accumulations. While the radar now slightly
overestimates the gauge, this value is much closer to the rainfall
accumulation than when using M–P. Finally, the use of a different
Parsivel®-derived Z–R relation for each episode gives a larger
overestimation compared to the rain gauge. The coefficient of variation also
decreases with each improvement. The effect would have been even larger if
time steps without precipitation were removed from the data. This reduces
the CV for the full correction from 123 to 81 %.
The final results for both correction methods based on the Parsivel®-derived
Z–R relations are comparable to the observations by the rain gauge. The
comparison between both instruments is remarkably close, especially if
one takes the differences between both instruments, their effective sampling
volumes and the impact of elevation differences into account. It should be
noted that rain gauges give point measurements over a period and radar data
are instantaneous measurements of a volume in the air, so comparison is not
straightforward . While the sampling
time interval can cause errors in radar rainfall estimation, especially
during convective situations , the space–time structure of
the precipitation for this event was such that this had only a minor effect
on the results.
Summary and conclusions
In the current study, close-range quantitative precipitation estimation (QPE)
by radar was analyzed. By focussing specifically on regions close to the
radar, the effects of rain-induced attenuation, VPR and non-uniform beam
filling are expected to be small, allowing errors due to calibration, clutter, wet-radome attenuation and Z–R
variability to be addressed. It was found that for this event the operational
clutter-corrected radar product underestimated the rainfall accumulation by
54.1 % compared to the rain gauge using a standard Marshall–Palmer
Z–R relation. The operational time-domain Doppler clutter filter used by
KNMI is shown to erroneously filter some of the rain as well. By correcting
radar volume data for clutter using a simple static clutter filter, the
underestimation reduces to 38.8 %. Further improvement is obtained when
the data are corrected for wet-radome attenuation by using a stable clutter
target close to the radar as reference. These two corrections, along with a
correction for calibration error, jointly give an optimal estimated reflectivity from
the radar. Applying M–P, this resulted in a 16.3 % underestimation with
respect to the rain gauge.
Finally, the Z–R relation was analyzed in detail to investigate if this
could improve results. This was done by fitting a power-law function using
Z and R values obtained from the Parsivel® disdrometer and applying this
to the fully corrected radar reflectivities. This resulted in a slight
overestimation of 5.9 %. Additionally, the event was split up into eight
different episodes based on DSD data and radar images. A dedicated Z–R
relation was derived for each episode, again based on the Parsivel® data. The
optimal Z–R relation was found to be highly variable over the event.
Applying these Z–R relations to the fully corrected radar reflectivity
data gave a slightly larger overestimation compared to the rain gauge. The
standard deviation of the difference between gauge and radar, using a
different Z–R relation for each episode, is slightly lower than when
applying a single Z–R relation for the entire event.
The results presented in this work clearly show that the rainfall estimation
capabilities of the radar have tremendous potential, if errors can be
properly corrected for. Even at close ranges from the radar, multiple sources
of error are shown to significantly affect radar rainfall estimates. The
multiplicative nature of most of these errors means that their effect on
rainfall estimates is greatest at high rainfall intensities. It is shown here
that using a time-domain Doppler clutter filter on all radar pixels causes
significant underestimation. Using an operational algorithm that is more selective
in clutter filtering e.g., CMD; see, or using a Doppler
filter with spectral reconstruction e.g., will likely
reduce this problem. Application of the technique used to correct for the
wet-radome attenuation to an entire radar image is not recommended because
wet-radome attenuation may be strongly dependent on azimuth, which probably
depends on the wind speed and direction. It is relevant to study this in
more detail because wet-radome attenuation can cause major (i.e., 3–4 dB;
see Fig. ) underestimation of precipitation. As both
convective and stratiform precipitation were observed in this study, it is
expected that the results also hold for more than just this event and can be
considered to be quite general. This case did not contain solid precipitation, like
hail or snow, at ground level. It would therefore be very interesting to also
explore the effect of these precipitation types.
The availability of a disdrometer enabled the derivation of intra-event
Z–R relations for selected periods. The current study showed that this
led to improved rainfall estimates as obtained from the radar, instead of
using the standard Marshall–Palmer relationship. The current work only
focussed on the impact of an event-based Z–R relationship close to the
radar. Recently, extended this
approach to the whole radar domain for summertime precipitation, identifying
the benefits and limitations of using the disdrometer information. For
convective precipitation, the potential benefit of these instruments was
small. This is because the locations of these cells do not correspond to the
location of the disdrometer. However, for widespread stratiform
precipitation, by making use of observations obtained by a single
disdrometer, a much better correspondence with the rain gauges was observed
as compared to applying a single static Z–R relationship. These results
show both the possibilities and limitations of making use of disdrometer
observations to derive information on the event-based Z–R relationship.
Data availability
Weather radar data are available from the KNMI Data Centre
(http://data.knmi.nl). Rain gauge and disdrometer data are available upon request by sending an e-mail to
hidde.leijnse@knmi.nl.
Acknowledgements
Financial support for this work was provided by the Netherlands Space Office
(NSO) and Netherlands Organization for Scientific Research (NWO) through
grant EO-058. The authors would also like to thank Marijn de Haij of KNMI for
providing the disdrometer data used in this paper. Edited by: G. Vulpiani Reviewed by: M.
Rico-Ramirez, N. I. Fox, M. Montopoli and one anonymous referee
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