Paper for the Inter-Agency Committee on the Hydrological Applications of Weather Radar
Submitted : 3rd December 2004
The use of dual-frequency microwave links for
measuring path-averaged rain
by
A.R. Holt & C.G. Collier
G.J.G. Upton, A.R. Rahimi, R.J. Cummings & G.L. Robbins
Summary
This paper details the experiments which have been carried out to test the theory that the use of
dual-frequency microwave links can provide an accurate estimate of path-averaged attenuation. It
gives examples of event analysis, as well as scattergrams of gauge estimates and link estimates.
Problems are detailed, and examples given. The potential use of links for correcting radar data at
X-band is described. Research in the use of links in hydrological models is presented. Advantages
are disadvantages of links are summarised, and future work is described.
1. Introduction
The proposal to use dual-frequency microwave links for measuring path-averaged rainfall grew from the
analysis of data from the Olympus satellite [Hardaker et al 1997].
After a pilot study
[NERC/GR9/03366], a full experiment was funded by NERC [GR3/C0035] in the Bolton region. This
region was chosen since there was already a network of rain gauges in the urban region, as well as flow
data from the River Croal. Moreover at the time the proposal was submitted, the region was covered by
two C-band radars, one being the Met Office radar at Hameldon Hill, and the other being a C-band radar
belonging to North West Water/United Utilities. In the event, the latter radar ceased operations before the
project began.
The project was supported by United Utilities, the Environment Agency, the Met Office (who provided
gauge and AWS data), and by Crown Castle International and Your Communications (who assisted with
antenna placements). The Radiocommunications Agency funded an extension of the experiment for their
own purposes, but made a data exchange agreement.
Funding from the European Union under Framework 5 (the MANTISSA project) enabled the experiment
to be extended to mainland Europe, with three links – one in an industrial region of Germany, one in a
steep-sided valley in the Italian Alps, and the third in the foothills of the Appenines. All the microwave
equipment, both for Bolton and for Mantissa was built by the RadioCommunications Research Unit at the
Rutherford Appleton Laboratory.
Throughout the work, dual-frequency microwave links have been seen as a complement to, rather than as
a replacement for, links and radar.
In conjunction with the experimental data, hydrological modelling has been developed. In the Bolton
region the purpose of this was to compare the usefulness of microwave links with that of gauges for the
Bolton Town Centre Urban Drainage System.
In the MANTISSA project, European partners have developed a new stochastic state-space model (Water
Aspects), which seeks to exploit information from various sources, including links and gauges.
2. Theoretical and Practical Considerations
It has been shown [Hardaker et al 1997, Rahimi et al 2003] that, provided the frequencies and
polarisations are suitably chosen, the attenuation difference between two frequencies can be a linear
function of rain rate that is relatively insensitive to the unknown parameters such as drop size distribution.
Consequently, the total on-path attenuation difference yields a true path-averaged attenuation difference,
and hence a path-averaged rainrate. It is estimated that the maximum error in the derived rain rate due to
the unknown physical parameters such as drop shape, temperature and drop size distribution is 15%. This
is not the case for single frequency attenuation, which generally has a power-law relationship with rain
rate.
In Bolton, the links installed varied from 9km to 23km in length. In Germany, the link was 30km long,
whereas the links in Italy were short – 3.5km and 7km. The longer links used lower frequencies than the
short links.
Any theory is always limited by practical considerations, and the following have proved important:

Attenuation due to atmospheric effects must be distinguished from that due to precipitation.

Clear-air attenuation appeared to be dependent on the time of year, over and beyond that
anticipated from variations in temperature/humidity/pressure.

It is necessary to establish baseline attenuation levels for each event. On some occasions the preevent baseline was significantly different from the post-event baseline. This could have been the
result of antenna wetting.

Events containing sleet gave the appearance of prolonged heavy rain – a similar effect to the bright
band in radar studies.

On a few occasions the attenuation at the high frequency was greater than the dynamic range of the
receivers, and hence the signal was lost. However, on no occasion did the low frequency link
saturate.
To take the above problems into account, we have:
Made use of rain detectors (gauges or radar) to help determine whether it is raining.

Used the correlation between the two attenuations. Correlation is high in rain and low in
atmospheric effects.

Interpolated baselines through an event.

Used the low frequency attenuation, suitably scaled, to estimate rainfall in periods when the high
frequency was saturated.

Used the ratio of the estimates of path rainfall derived from the single frequencies as an indicator
of the presence of sleet.
Verification of link-derived estimates of path-averaged rain rate is not easy. The gauge-based values of
the path-averaged rainfall must not be regarded as “truth”, but as estimates. They were derived by using a
Thiessen-weighted average of the records from nearby functioning rain-gauges. Raingauges are prone to
blockage and other malfunctions, so that the number of relevant gauges varied from three to five, with
some gauges being as much as 2 km from the link.
Installation of equipment needs suitable towers, or buildings, with an access to power supply, and a safe
environment for link equipment and data collection. Cost of building receivers and transmitters would
depend on the number being built. For a custom-built dual-frequency link, the current estimate of
transmitters, receivers, and data acquisition system is £32K + VAT, and its installation would be
approximately £2.5K + VAT. If a number of such links were to be built, the costs might be around £5K
less per dual-frequency link. These estimates have been provided by John Goddard of the Rutherford
Appleton Laboratory.
To gain an idea of the coverage provided by a link, we have conducted a limited analysis of Cartesian data
from the Hameldon Hill radar. We have estimated the path-averaged rainfall along two parallel links and
have studied the extent to which the values agree. We find that, as expected, agreement improves with
increases in link length or integration time, but decreases as the distance between the links increases. Our
measure of accuracy is the APD (the difference between the values, expressed as a percentage of their
average). Specimen results are:
 For a 1-hour storm falling on the Bolton sub-catchment (21km2), a centrally placed 10km link
should be able to achieve an APD of less than 15%.
 For a 5-hour storm falling on a catchment of 10 km by 10 km, a centrally placed link ought to be
able to achieve an APD of around 15%.

For a 5-hour storm falling on a 20km link, the APD of 25% might provide useful information for
as much as 500 km2.
The links in Bolton used either 17.6GHz & 12.8GHz (Hameldon Hill- Clarke’s Hill) or 22.9GHz &
13.9GHz. In Essen the frequencies were 17.5GHz & 10.5GHz, whilst in Italy they were 24.1GHz &
13.5GHz.
3. Results
3.1 Hameldon Hill – Clarke’s Hill
To illustrate the results, we firstly give in Figure 1 the time series of attenuations, and both the time series
and cumulative estimates of path-averaged rainfall for an event on 10th February 2000, which saw the
passage of a front across the link from Hameldon Hill south to Clarke’s Hill, a distance of 23km. The
gauge estimates came from four gauges.
Figure 1. Times series of link attenuations in dBs (————17.6GHz —————12.8GHz),
rainrate estimates (———— link ———— gauges), and cumulative rainfall for an event on
10Th February 2000 on Hameldon Hill link
In Figure 2 we give the same quantities as in Figure1, but for a long-duration event on 7th-8th March 2000
when approximately 40mm fell in 30hrs.
Figure 2. Legend as in Figure 1, but for an event on 7th-8th March 2000.
The agreement between link and gauges in both these events is very satisfactory, particularly
remembering that the four gauges were not equally spaced along the link. In both cases the difference
between the estimates is about 10%. It is noteworthy that the gauges did not see the peak of the front on
10th February.
In Figure 3 we show the times series of link attenuations, rainrate estimates, and temperature for an event
on 2nd-3rd March 2000. It will be seen that, at the beginning of the event, both attenuations rise to a peak of
more than 20dB, and are comparable in size, whereas later in the event the ratio of the attenuations is
much larger, though the attenuations themselves are much smaller. The derived rainrate estimates show
that in the early part of the event, the link estimates are much greater than the gauge estimate. Turning to
the temperature chart, we see that when the attenuations were large, the temperature was no more than
3°C. The temperatures were measured at the Clarke’s Hill site, which is 250m lower in altitude than
Hameldon Hill. Assuming a lapse rate of 6°C/km, this suggests that the temperature at Hameldon was
around 1.5°C. This suggests that much of the link was experiencing sleet.
Figure 3. Time series of attenuations, rainrate estimates and temperature for 2nd/3rd March 2000
In Figure 4 we show a scatterplot of gauge and link estimates of event rainfall for 249events. We have
separately marked with a + those events where the temperature at the receiver fell below 4°C, since these
are events which are very likely to include sleet. We also show the line of equality of the estimates,
together with ±15% error bounds.
Figure 4. Scatterplot of Gauge and Link estimates of cumulative path-averaged rainfall (in mm) for
249events on Hameldon Hill link. ------------- exact agreement ------------- 15% error bounds
The agreement is encouraging, given the fact that the gauges do not provide a good coverage of the link
(one gauge may have represented 8km of the link). However, it is clearly important to know whether there
has been sleet, since the figure suggests that the link may substantially overestimate the amount of
precipitation when sleet is occurring.
3.2 Heather Hall – Clarke’s Hill
The second link across Bolton was from Heather Hall to Clarke’s Hill, a distance of some 14GHz. As
stated above, somewhat higher frequencies were used for the shorter link. Since the transmitters were
somewhat lower in altitude than those at Hameldon Hill, and the link was operating for a shorter period
than that from Hameldon Hill, rather few occurrences of sleet were observed. In Figure 5 we give the
scatterplot of gauge and link estimates of cumulative path-averaged rainfall for this link. It should be
noted that there were up to 5 gauges covering this link, and hence the gauge estimates should be
somewhat better than those for the Hameldon link. Indeed, the overall agreement does seem better than for
the 23km Hameldon link, the agreement generally being close to, or within the ± 15% bounds as predicted
by theory
Figure 5. Scatterplot of link and gauge estimates of path-averaged rainfall (mm) for 99 events on HeatherHall-Clarke’s Hill link. Legend as in Figure 4.
It should be noted that there was a second link across Bolton at these frequencies, somewhat shorter
(<9km). The results from this link were less satisfactory, with the link fairly consistently overestimating
the rainfall. However, when the link was taken down, it was found that the antennas on this link were full
of water, which had presumably caused an increase in attenuation, thus giving rise to the overestimate.
This is a matter that needs careful consideration in an operational situation.
3.3 Reckinghausen to Essen (Germany)
This link was financed under the EU-funded MANTISSA project. The local water company (EGLF) has
an X-band radar situated in Essen (with analysis help from the University of Hannover); the idea behind
placing a link here was to investigate the possibility of correcting for attenuation. The area is industrial,
and the link was chosen to be between Essen and a tall industrial chimney at Recklinghausen, a distance
of nearly 30km, in a NE direction. There were five gauges close to the link, but these were all fairly
central on the link. Consequently the gauge estimates for this link may well be in error on occasions when
only the ends of the link are affected by rain. In Figure 6 we show the scatterplot of path-averaged event
rainfall for 61 events. Since the link was virtually horizontal, we have assumed that the criterion for likely
sleet was a temperature of 2°C. Two such events where the temperature fell below 2°C are seen to have
had a major effect on the link estimates. Otherwise the link and gauge estimates are in surprisingly good
agreement.
Figure 6 : Scatterplot of link and gauge estimates of path-averaged event rainfall (in mm) for 61 events for
link between Essen and Reckinghausen. Legend as in Figure 4.
The X-band radar suffered severe attenuation in convective events, and on occasions the radar was
reporting no echo from a region in which the gauges were recording rain. In the study, we were able to use
the 10.5GHz vertical polarisation attenuation to estimate the total 9.47GHz radar attenuation on the link.
This was then used as a constraint, and a backwards correction process was used to correct the radar data.
The corrected radar data were then used to estimate the path-averaged rainrate, and also for comparison
with the data from a gauge situated very close to the path of the link. The agreement obtained was
encouraging, and a paper has been submitted (Rahimi et al 2004b).
3.4 Sondrio valley (Italy)
This link was managed by our Italian partners in MANTISSA, the Politecnico di Milano. The link, 7km in
length, was installed in a steep-sided Alpine valley, with the object of seeing whether such a link might be
able to provide early warning of flash flooding; it appears that the Lombardy civil defence organisation is
interested in extending the duration of the experiment. Because of the nature of the terrain and the
probability of snow cover, the three gauges had to be placed on poles, and were therefore several metres
above ground level. The uppermost gauge (at 1240m) was heated, the other two (at 720m and 650m) were
not, which resulted in interesting effects in comparing gauge traces. In several events, our criteria for
deciding the end of a rain period suggested that the links were experiencing attenuation, which gradually
subsided, long after the rain had ceased. This could have been due to antenna wetting, or possibly to low
cloud occurring on the link. In Figure 7 we display the scatterplot of the rain estimates for 17 events for
this link. The agreement is understandably worse than for the other links.
Figure 7. Scatterplot of path-averaged link and gauge estimates of event rainfall (in mm) for link in
Sondrio valley in the Italian Alps
3.5 Summary
Experiments have been performed in a number of different geographical locations/regions to compare
estimates of path-averaged rainfall from both dual-frequency links and gauges. A very encouraging
agreement has been obtained. Simulation suggests that links can provide an estimate of areal rainfall if
time integration is performed. Generally, links, gauges and radar are seen to be complementary. Some of
the results have been given in Rahimi et al (2003, 2004a)
4.Hydrological Modelling
4.1 Background
Research at the University of Salford assessed the ability of one, or a combination of microwave links to
provide useful rainfall input to hydrological models. The representation of high spatial variability within
the rainfall over a catchment is critical to achieving adequate model flow predictions for use in real time
flood prevention and monitoring. Traditional estimates made by networks of rain gauges have proved to
provide precise rain depth information, however because this technique is limited to interpolation between
a multitude of point measurements, important variations within the rainfall structure may be missed. The
use of weather radar represents the spatial structure well however this technique is subject to many errors
(see Collier, 1996) that often lead to poor estimates of rain depth at a particular point in space and time.
Microwave links may provide a compromise between the high depth precision of the rain gauges and the
good spatial coverage of the radar. In what follows, two experiments are described, one comparing the
rain gauge, radar and microwave link estimates of rainfall as inputs to a hydro-dynamic model of an urban
drainage system. The second uses a stochastic state-space model to assess various combinations of all
three rainfall estimation techniques to model river flow.
4.2 A Hydro-dynamic Model of the Bolton Town Centre Urban Drainage System
Effective real time control of urban drainage systems (UDS) is often essential for the reduction of
combined sewer overflows. These occur when insufficient capacity in the UDS leads to quantities of
untreated storm-water and sewage being discharged into water courses, and in the worst cases flooding
streets and properties. Detailed knowledge of the rainfall structure allows flows within the UDS to be
controlled using adjustable weirs or detained using huge off-line storage tanks. This experiment attempts
to compare the ability of the Heather Hall – Clarkes Hill (HH-CH; section 3.1; table 1) and Cow Lane –
Height Barn (CL-HB; table 1) microwave links to provide UDS model flow predictions against the 2 km x
2 km resolution Hameldon Hill C-band weather radar (section 1) and several rain gauges. A Hydroworks
based hydro-dynamic model of the Bolton Town Centre UDS was provided by United Utilities. The
location of this with respect to the rain gauges and microwave links is shown in figure 8.
Link
Heather Hall – Clarke’s Hill (HH-CH)
Cow Lane – Height Barn (CL-HB)
Hameldon Hill – Clarke’s Hill (HamH – CH)
Length (km)
13.95
8.89
23.29
Frequency (GHz)
12.8/17.6
13.9/22.9
17.6/12.8
Table 1: Microwave link properties. The HamH-CH link is referred to in section 4.3.
Rainfall measurements from fifty five events between March 2000 and September 2001 were assimilated
into the Hydroworks model. For each event several model runs were made, each using rainfall inputs from
a different observing system The hydrographs predicted at the UDS output (figure 8) were compared. The
observing systems used were the WS, SM and LE rain gauges (figure 8) operating alone, the LR, TH and
GT gauges operating as a network, the HH-CH and CL-HB microwave links operating alone and as a
combination, and the Hameldon Hill weather radar. Due to the unavailability of any flow measurements
during the period of study, the predicted hydrographs from each observing system were compared to that
predicted using the WS, SM and LE gauges operating as a network. These three gauges are considered to
provide a good representation of the rainfall due to their central location with respect to the UDS area and
therefore the resultant flow prediction provides a quality standard with which predictions using other
observing systems may be compared. We now consider an example case study of 13th September 2001.
Figure 8: The Bolton Town Centre UDS and Hydrometeorological Network. The green dots show nodes
in the UDS model structure and the black square represents the UDS outlet where predicted flows are
compared. The red lines are microwave links and the blue circles are rain gauges with those in blue
forming the quality standard network. The squares represent the 2 km x 2 km Cartesian pixels from the
Hameldon Hill weather radar.
It can be seen that the CL-HB link generally estimates higher rainfall intensities than HH-CH (figure 9).
This is possible because CL-HB is shorter than HH-CH therefore averaging the rainfall over a shorter link
path. Similar rainfall information is also estimated by the WS SM and LE gauges.
14
10
WS
LE
SM
8
6
4
2
0
04:00
06:00
08:00
10:00
Date:Time
12:00
14:00
16:00
Rainfall Intensity (mm/hr)
Rainfall Intensity (mm/hr)
14
12
12
10
HH-CH
CL-HB
8
6
4
2
0
04:00
06:00
08:00
10:00
12:00
14:00
16:00
Time
Figure 9: Rain gauge and microwave link rain fall measurements over Bolton, 13/09/2001.
Despite the relatively similar rainfall patterns described by the gauges and the microwave links (figure 9),
there are some noticeable differences in the flow predictions (figure 10). All networks predict the flow
shape fairly well, although HH-CH often under predicts especially during the second half of the event. SM
predicts poorly the initial rises and falls of the events. WS performs the best out of the single gauge
networks. The microwave links generally perform very well, with CL-HB generally providing the closest
match of the two links working alone, although at some instances (e.g. 09:30 and 11:50) HH-CH provides
the better predictions. The combination of links matches the quality standard well, and despite not always
predicting flows that are closer to the quality standard as the links operating alone, the larger errors in the
combination’s prediction are never as great as those in the individual link predictions.
3
2.5
Flow (m3/s)
2
WS SM LE
WS
SM
LE
HH-CH
CL-HB
MW
RADAR
1.5
1
0.5
0
04:00
06:00
08:00
10:00
12:00
14:00
16:00
18:00
20:00
22:00
00:00
02:00
04:00
Time
Figure 10: Model flow predictions at the Bolton Town Centre UDS outlet from a variety of rainfall
observing systems, 13-14/09/2001.
It is evident in the case of the HH-CH microwave link, that an under-prediction at one peak is carried
forward to the following peak. This remains true, unless the sensor begins to over predict at some point,
which is not the case in this example.
An objective function (F; equation 1) quantifies the difference between the predicted and quality standard
hydrographs. It is defined as:
F  e  where,

t
QOi  QPi
1
,

  1 i t 
QOi
(1)
(2)
t is the discrete clock time and is the event duration in time-steps. Unlike the previous objective
functions described the F value gives an indication of the relative error between different flows over the
duration of the event. The calculations will give values between 1 and 0, where 1 indicates a perfect match
between the two flows. The F value decreases with the performance of the flow prediction. Values of F
are compared for different event types defined in terms of an objective parameter R representing rainfall
variability as follows;
2

N
1



I

I

i( j)
( j)
 N( j) 1 
j 1
i 1

R
G
G

I( j) 

j
(3)
,
where Ii(j) is the rainfall intensity (mm/hr) measured by gauge j at time step i, I ( j ) is the mean rainfall
measured by gauge j, N(j) is the number of time steps between the start and end of rainfall event measured
by gauge j over the duration of the event, and G is the number of gauges. Figure 11 shows a plot of F
against R for various rainfall observing systems.
F vs Rainfall Variability for Networks
1
0.95
F Value
0.9
WS
LE
SM
LR TH GT
MW
HH-CH
CL-HB
RADAR
0.85
0.8
0.75
0.7
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Variability
Figure 11: Objective function F against variability for Bolton UDS flow predictions.
It is shown that using rain gauges with in the catchment (WS, SM and LE) produces flows with the
smallest errors when the rainfall variability is low (stratiform) but the errors get larger as the variability
increases. It is not surprising that these rain gauges perform best because they form part of the network
with which all rainfall observing systems are compared and therefore a comparison between these and
other networks will clearly be biased towards these gauges being awarded higher performance values.
The ability of a microwave link operating alone to provide flow estimates for UDS flow prediction is
better than that of a rain gauge positioned just outside of the catchment (SM). The fact that the microwave
links perform better than any of the quality standard component gauges suggests that there is a close
agreement with the microwave link and rain gauge flow estimations. The relative performance of the two
links operating alone is affected by their location and orientation with respect to the catchment. The CLHB link is the shorter of the two links and a greater proportion of this link spans the catchment compared
to the HH-CH link. These two facts are contributory to the CL-HB link being the better performer of the
two links. The link spanning across (CL-HB), as opposed to along the catchment (HH-CH), achieves the
higher performance.
Two links in combination consistently perform well, whereas the single links are sometimes subject to
very poor performance. The two links operating in combination will intercept any rainfall that falls across
the catchment. If only one link were operating it could be possible for rain to move alongside but never
cross the path of a link. This would provide no rise in model predicted flows even though rain would be
falling over some part of the catchment. The relative orientations of the two links may also be important
although this remains untested. Despite the increase in spatial coverage offered by the two links operating
in combination, any spatial variability is lost due to the path-averaged rainfall estimate provided by the
links. Therefore only two rainfall profiles are assimilated into the model. This, however does not result in
poor flow predictions because the variability is included but just lumped together in the attenuation
measurement. The microwave link rainfall estimates may differ from those made by the quality standard
rain gauge network in one of two ways:
i) The links may begin to measure rainfall before it reaches the rain gauge network but it’s peak intensity
may not be as high as the rain gauges due to the path-averaging of the rainfall. This will result in rainfall
estimates over a longer period of time, but at lower intensities than the rain gauges.
ii) Heavy rainfall in an event may be intercepted by the microwave links but missed by the gauges,
resulting in a higher rainfall estimate by the links than the gauges.
The recognised ability of a radar to represent the spatial variability of the rainfall leads it to perform well
in higher variability events in which the better representation of the spatial variability appears more
important than the magnitude of the rainfall estimates for effective flow prediction. The microwave links
and rain gauges provide estimates of lower variability rainfall that are superior to the radar.
4.3 Stochastic State-Space Model of the River Croal Catchment
A stochastic state-space modeling approach has been developed for the combined exploitation of the
information content in several different types of rainfall and hydrological measurement. This not only
promises to provide the optimal rain plane given the set of measurements but will also update the system
state using flow measurements. A sub catchment upstream of a flow or level gauge could also be
considered a rain gauge assuming that one is able to give a fair description of the lumping and delay that
takes place. This implies that model predictions of a hydrograph may continue to be improved even after
the rain has stopped falling. The stochastic modelling technique applied in this study has been presented
theoretically by Grum et al. (2002). It has been incorporated into a hydrological modelling package,
WaterAspects (www.WaterAspects.org) that provides a frame work within which a model of the Croal
catchment was constructed.
The Croal catchment is 143 km2 and surrounds the Bolton Town Centre UDS described in section 4.2 and
has a dense hydrometeorological network shown by figure 12. This includes 16 tipping bucket rain
gauges, the HH-CH, CL-HB and HamH-CH dual frequency microwave links and the Hameldon Hill
weather radar. This study aims to consider the performance of the model using several combinations of
these instruments and these are listed in table 2.
Figure 12: The Croal catchment and associated hydrometeorological network.
Network
Full Network
Radar & RG
5 RG
MW
MW & RG
All RG
Radar
Radar & MW
Constituent
All rain recording devices
Radar and all rain gauges
Five Rain gauges; LR WS HW RD CG (figure 12)
All microwave links
All microwave links and all rain gauges
All rain gauges
Radar alone
Radar and all microwave links
Table 2: Hydrometeorological networks used in the stochastic state-space modelling.
A rain plane was constructed for each observing system comprising one pixel for each rainfall
measurement made (i.e. a microwave link, rain gauge or radar pixel measurement). If several rainfall
estimates are made at the same geographical location then these are averaged to provide a single intensity
observation for that pixel. A simple model predicts the rainfall intensities one step ahead for each pixel of
the rain plane, and this prediction is based on the notion that the rainfall in a particular pixel at a particular
time step will probably be similar to the rainfall in the proceeding time step. Therefore at every time step
the rainfall model predicts the rainfall intensity based on knowledge from the previous time step.
A simple rainfall-runoff hydrological model is also constructed using two series of linear reservoirs
running parallel to each other to represent the fast and slow flows through the catchment. A single rain
profile determined from the rain plane model and the observations is assimilated into the hydrological
model. A Kalman filter considers estimates of the likely errors present in the observations (rainfall and
flow) and the system states (reservoir volumes). Model predictions (both rainfall and flow) are then
updated using knowledge of these errors and the observed values. Likely initial error standard deviations
were predetermined using an optimisation procedure.
A chosen case study is a frontal rainfall event with embedded convection occurring 12th – 15th September
2001 (figure 13a). Flow predictions are provided at regular intervals from the start of the event and these
are compared to the observed flow at the catchment outlet. The flow predictions are compared using three
techniques; the modelling efficiency (Nash & Sutcliffe, 1970; figure 13b), a comparison of the time of
peak flow (figure 13c) and the peak flow magnitude (figure 13d). This is similar to the F objective
function (section 4.2), returning a value of 1 for a perfect match between the observed and modelled
hydrographs. A value of 0 is returned if the model predicts a hydrograph that is not better than simply the
mean of the observations.
Time
08:00:00
0
18:00:00
04:00:00
14:00:00
1
00:00:00
10:00:00
14
12
20
Rainfall (mm/hr)
40
8
50
6
60
70
Flow (m3/s)
10
30
Rain
Observed
50
350
700
Modelling Efficiency
0.5
10
4
Full Network
Radar & RG
5 RG
MW
MW & RG
All RG
Radar
Radar & MW
0
-0.5
-1
End of
Rainfall
-1.5
80
2
90
-2
100
0
0
50 100 150 200 250 300 350 400 450 500 550 600 650 700
Time-step
Time
200
End of
rainfall
180
140
Full Network
Radar & RG
5 RG
MW
MW & RG
All RG
Radar
Radar & MW
Peak flow
120
100
80
60
40
20
0
0
50
150
250
350
Time-steps
450
550
650
700
Peak Flow Error (m3/s)
Peak Time Error (min)
160
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
Zero Line
Full Network
Radar & RG
5 RG
MW
MW & RG
All RG
Radar
Radar & MW
End of rainfall
0
50
150
250
350
Peak flow
450
550
650
700
Time-step
Figure 13 (a-d clockwise from top left hand graph). a: Model predictions at regular time-steps throughout
the event using the full network. Graphs b, c and d show modelling efficiency, comparisons of peak flow
timing and peak flow errors respectively for flow predictions made at regular intervals throughout the
event using various rainfall observing systems.
The predictions using each hydrometeorological network provide a closer match to the observations the
later they are made after the onset of the rainfall (figure 13a). The flow reconstructions continue to
improve after it has ceased to rain (13/09/2001 16:00; time-step 385) due to information from the flow
measurements that updates the system states (figure 13b). Increases in performance of all networks at the
50 and 350 time-step forecasts illustrates the rain plane model’s ability to predict the subsequent rise in
flow. In the forecast made at time-step 350 (175 minutes before the end of the rainfall and 200 minutes
before the flow peak), each network, except for the rain gauge and microwave combination, predicts the
peak flow magnitude within 20%, and the time of peak flow within 30 time-steps (150 minutes) of the
observations (figures 13c and 13d). Forecasts made after time-step 350 are split between those networks
including the radar and those that do not.
Generally the microwave links, the rain gauges and the combination of these two techniques produce good
flow reconstructions. Close estimates of the peak flow magnitude (10.35 m3s-1) are predicted at the 350
time-step forecast. The microwave link and rain gauge combination fail to predict the time of peak flow
until after the end of the rainfall in this particular example only, because predictions of the first rainfall
peak are higher than those of the second, which has a higher magnitude according to the observed flow.
The radar is one of the poorer performers in terms of the peak flow magnitude prediction however the
predicted time is very close. The overestimations in peak flow magnitude made using the radar based
networks are 2-3 times the magnitude of the underestimations made by the other networks. This illustrates
spatial structure within the rainfall is well represented by the radar although the actual depth of rainfall is
not estimated so well.
The radar tends to dominate the rain depth estimations since the radar combination, with either the
microwave links or the rain gauges, fails to provide a peak flow magnitude prediction that is closer to the
observations. The combination of the full network only slightly improves this flow prediction.
Hydrometeorological networks not including the radar produce better peak flow predictions and generally
provide closer matches to the flow observations.
The results suggest that the microwave links and rain gauges produce the better flow reconstructions in
this particular rain-plane and model configuration. The radar does not perform so well and this has an
effect on predictions using the full hydrometerological network and combinations of the radar with the
rain gauges or the microwave links. These results are limited and based on the study of a single event over
a single catchment. They only serve to demonstrate the possible performance a stochastic state space
modeling technique such as this could achieve. Future work will consider this technique over a multitude
of rainfall events. The entire Irwell catchment (554 km2) will also be considered by combining similar
model of all five subcatchments to form a semi-distributed model of the larger river system.
4.4 Summary
It is shown, using the two different modelling techniques above, that a combination of several microwave
links can provide rainfall input into a hydrological model that is of a similar or better quality than rain
gauges or weather radar. When combined with radar and/or rain gauge measurements the microwave link
rainfall information offers some improvement to the model flow estimation, especially when combined
with the rain gauges.
5.Advantages and disadvantages of the link method
The main advantages are that one link seems to be equivalent to several gauges, as far as getting a pathaveraged rainfall is concerned. For an area average, the link will be expected to give a good representation
of areal rainfall if time integration is considered. The accuracy depends on the parameters of the link. The
link should be less accessible to vandals, and easier to place in urban situations, where there is a potential
for mounting on buildings. It could also be placed in regions where the topography makes it difficult to
use gauges or radar. Research has shown that a link gives a much improved estimate, certainly for
hydrological purposes, on that provided by a single gauge, and hence a link may be particularly worth
considering in sparsely gauged catchments. A link should require less maintenance. In theory, it should
be possible to use, or augment, existing telecommunications links to obtain rainfall information, but the
practicality remains to be explored. The use of a link to correct radar data for attenuation has been
demonstrated, and the use for radar calibration is about to be tested.
The main disadvantages are cost, both of capital equipment, and also for installation and maintenance if
towers are required. It does not give a point rainfall, only a path average. It needs a power supply at both
ends of the link. Currently, good accuracy requires a gauge or a rain detector to help distinguish between
rain and atmospheric effects, though it is believed that this is not essential. The link data requires
processing to remove atmospheric effects, and to identify any occurrence of sleet.
Future Work in the UK
A second experiment has been funded by NERC, with support from the Met Office, The Environment
Agency, YourCommunications, & United Utilities. The purpose here is two-fold. Firstly to seek to use the
Hameldon Hill link to calibrate the Met Office Hameldon Hill radar, and secondly to use the combination
of transmission of the lower frequency at 45º polarisation together with two receivers to obtain total path
differential phase, as well as additional attenuation information. It is hoped that these measurements will
distinguish rain events from those containing sleet, will identify the occurrence of snow, and will help to
better determine the baseline attenuations for each event. In conjunction with this, the hydrological model
will be extended to take into account the effects of snow.
References
Collier, C.G. (1996):Applications of weather radar systems, John Wiley & Sons, Chichester.
Grum, M., Harremoes, P., and Linde, J.J.(2002): Assimilating a multitude of rainfall and runoff data using
a stochastic state space modelling approach. 91CUD, Portland, Oregon.
Hardaker, P.J., Holt, A.R. and Goddard, J.W.F. (1997) Comparing modelled and measured rainfall rates
obtained from a combination of remotely sensed and in situ observations, Radio Science, 32 (5), 17851796.
Nash, J.E., and Sutcliffe, J.V. (1970): River flow forecasting through conceptual models. Part 1 – a
discussion of principals, Journal of Hydrology, 10, 282-290.
Rahimi A.R.,Holt A.R., Upton G.J.G., and Cummings R.J. (2003): Use of dual-frequency microwave links
for measuring path-averaged rainfall . J. Geophys Res. – Atmos., 108(D15), art no. 4467
Rahimi A.R., Upton G.J.G and Holt A.R. (2004a): Dual-frequency links – a complement to gauges and
radar for the measurement of rain. J. Hydrology 278, 197-212
Rahimi A.R., Holt A.R., Upton G.J.G., Krämer S., Redder A and Verworn H-R. (2004b): Attenuation
Calibration of an X-band Weather Radar using a Microwave Link. Submitted to J.Atmos & Oceanic
Technology Nov 2004
Acknowledgements; We are very grateful for the considerable support we have received from our
partners, in particular the Radiocommunications Research Unit of RAL, and our industrial sponsors the
Met Office, United Utilities, YourCommunications, the Environment Agency, and the
Radiocommunications Agency. In MANTISSA, we have worked closely with the University of Hannover,
the Politecnico di Milano, Emschergenossenschaft/Lipperverband, and PH-Consult.