9th International Conference on Urban Drainage Modelling Belgrade 2012

1

Weather radar and heavy rainfall - how to estimate the

real amount of precipitation?

Thomas Einfalt1

1 hydro & meteo GmbH & Co. KG, Breite Str. 6-8, D-23552 Lbeck, Germany (einfalt@hydrometeo.de)

ABSTRACT

Extreme precipitation often occurs on relatively small areas which are not sufficiently equipped with rain gauges to completely observe the occurred event. Therefore, radar data are extremely helpful to localise the most intense parts of the precipitation. However, radar data are prone to errors under extreme rainfall and bear higher uncertainties at higher rainfall intensities due to the non-linearity of the relationship between radar reflectivity and rainfall intensity and due to the unknown drop-size distribution of the rain cells. A case study illustrates a practical approach to test several assumptions on the drop-size distribution and important radar data quality considerations for high intensity precipitation.

KEYWORDS

Extreme events, radar rainfall, rain gauges, sparse network

1 INTRODUCTION

Local heavy precipitation is usually not captured by traditional point rainfall gauges. Weather radar, although less precise in rainfall volume at a point, permits a detailed view into spatial structures of precipitation. Therefore, weather radar plays an increasingly important role for the a-posteriori analysis of such events, in particular in presence of damage. For online data processing, different procedures are required.

Crucial points with radar are the potential measurement errors (Michelson et al., 2005) and the unknown drop size distribution required for a good estimation of rainfall amounts (Collier, 1989). For practical work with radar data in the urban context, a number of quality controls and data corrections need to be performed before a reliable result can be achieved (Einfalt et al., 2004).

2 RADAR DATA QUALITY CONTROL

As mentioned by Michelson et al. (2005), there are several sources of error which affect the ability of radars to measure precipitation and which influence the accuracy of the measurements. These errors

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are not always present in the radar measurement, but many of them appear only under certain meteorological conditions:

Attenuation: reduction of the measured reflectivity due to heavy precipitation (see 2.2),

Bright band: high values in the melting layer of the atmosphere when snow melts to rain,

Anomalous propagation: measurement of ground targets due to atmospheric conditions preventing a straight propagation of the radar beam.

Among (mostly) stationary influences on a correct radar measurement, ground clutter (see 2.1) and (partial) blockage of the radar beam by buildings or topography are the most frequent ones.

Readers interested in more details on error sources and their effects on radar measurements should refer to the document of Michelson et al. (2005).

2.1 Ground clutter

Ground clutter is usually strong due to the relative radar cross-section of the ground being much greater than that from meteorological targets. Ground clutter can be minimized through intelligent radar siting, Doppler suppression, and through the use of post-processing methods such as static clutter maps.

2.2 Attenuation of the radar signal

Heavy rain, graupel and hail can attenuate energy, leading to strong underestimation of precipitation intensities. Especially in hail the scattered energy can be attenuated to the point of virtual extinction of the signal. Shorter wavelengths (X and C bands) are more seriously affected.

Attenuation can be detected by a close look into measurements from rain gauges and radar (figure 1) and by visual inspection of the radar images (e.g. figure 2). The time series analysis shows during which time interval radar has seen considerably less precipitation than the rain gauge (in the red ellipse): the thin line shows the rain gauge measurement and the two bold lines radar measurement at two neighbouring points. It becomes obvious that radar has seen much less precipitation during the short time interval just before 18:00 hours.

Figure 1: Attenuation of the radar signal: detection through time series comparison to rain gauges

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Figure 2: Attenuation to the NW of the radar

2.3 Attenuation at the radar site (radome attenuation)

In heavy rain, a thin film of water will cover the radome, causing signal attenuation. In cold conditions, snow and ice may build up on top of the radome, also causing attenuation and limiting the quantitative use of reflectivity measurements.

Radome attenuation can best be observed in a sequence of radar images (figure 3 - left) where the decrease and later increase of the radar signal over the whole radar range can be observed. A counter measure is extremely difficult because the attenuation is not necessarily uniform over the different viewing directions of the radar. Else, a simple correction factor over the complete radar scope could sometimes save the data this manual method in some cases nevertheless improves the data (figure 3 - right).

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Figure 3: Uncorrected radar measurement with radome attenuation (left) and correction attempt (right)

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3 ESTIMATION OF THE PRECIPITATION AMOUNT

The relationship between the reflected radar signal in [dBZ] and the rainfall intensity [mm/h] depends on the drop size distribution of the precipitation. The drop size is related to the reflectivity by a power of 3, and to intensity by a power of 6, yielding a highly nonlinear relationship between reflectivity and intensity (Collier, 1989). Because the drop size distribution in practice is not known, assumptions have to be made in order to assess it: convective (summer thunderstorm) events are associated with a higher amount of large drops, whereas stratiform events are merely associated to smaller drops. These assumptions are important because intense precipitation corresponds to the higher reflectivities where the resolution of the radar in terms of mm/h is worse. Figure 4 shows for two examples, the Marshall-Palmer relationship for tropical wide spread rainfall and the original relationship of the German Weather service for convective type rainfall the difference: a reflectivity value of 50 dBZ may correspond to 50 mm/h or to 70 mm/h in intensity, depending on the weather type associated.

The large uncertainty in intensity values due to different assumptions about the unknown drop size distribution is the main reason that for quantitative use of radar data in hydrology it is indispensable to compare radar measurements to rain gauge data: the adjustment of radar to rain gauge values is the consequence of this.

In practice, the most realistic relationship to convert reflectivity to intensity is selected, and the resulting values are then fitted to the ground measurements at the rain gauge locations.

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60

Inte

nsi

ty [

mm

/h]

Reflectivity [dBZ]

Marshall-Palmer

DWD

Figure 4: Relationship between rainfall intensity [mm/h] and radar reflectivity [dBZ]

4 PRACTICAL WORK STEPS: ANALYSIS OF A CASE STUDY

4.1 The event of 28 August 2002

The event of 28 August 2002 produced damage in the area of Eitorf in North Rhine-Westphalia where a part of a highway was washed away. During the two hour event, rain gauges registered up to 70 mm of precipitation. Radar images suggest that the peak of the precipitation was higher.

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4.2 Radar adjustment to gauges

Since radar measurements are uncertain for estimating rainfall amounts correctly, rain gauges are used as an anchor point for a quantitative precipitation estimation. Figure 5 shows that rain gauges are measuring a higher amount at the rain gauge sites than radar for this case study (figure 6), regardless of the Z-R relationship employed. Radar on the other side clearly shows that the centre of the highest precipitation is situated between the four rain gauges with the highest amounts. Thus, a combination of both yields the best possible precipitation estimation.

Figure 5: Precipitation amount seen by the available rain gauges (event sum, inverse distance weighted (IDW) interpolation)

Figure 6: Rainfall amount seen by radar with a moderate Z-R relationship (left) and a convective Z-R relationship (right). The locations of the closest rain gauges are circled in red.

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In order to identify the Z-R relationship presumably closer to reality, a cross validation of the four main rain gauges has been performed during the adjustment process: Each of the gauges has been skipped in turn, and the results have been compared with the results from the adjustment with all gauges. Due to the selected Brandes type adjustment scheme (Wilson / Brandes, 1979), the radar values at the gauge locations correspond to the rain gauge amounts.

The statistics chosen to analyse the results are

The absolute difference between the gauge measurements and the adjusted radar amounts,

The mean percentage difference, allowing to detect systematic deviations,

The absolute percentage difference, giving a larger weight to gauges with smaller rainfall amounts than the first criterion.

Table 1 shows that the rain gauge with the highest observed rainfall amount (Eitorf) is the most difficult to reach by both Z-R relationships. Although the differences between the two selected Z-R relationships are not very large, all statistics show that the convective Z-R relationship appears to be more appropriate to use for this event.

Table 1: Results of the cross validation of the adjustment for the four main rain gauges and two Z-R relationships

mod. conv. mod. conv. mod. conv.

Eitorf 70.3 57.42 61.99 12.88 8.31 -18.32 -11.82 18.32 11.82

Lascheid 50.4 54.65 56.74 4.25 6.34 8.43 12.57 8.43 12.57

Hanfmhle 31.3 31.77 30.21 0.47 1.09 1.52 -3.50 1.52 3.50

Kuchenbach 36.5 41.23 38.42 4.73 1.92 12.96 5.27 12.96 5.27

Parameter Sum 22.33 17.66 4.58 2.53 41.22 33.16

Gauge

mod.

[mm]

conv.

[mm]

Radar absolute

difference

mean percentage

difference

absolute percentage

difference

Rain at

gauge

[mm]

The use of the convective type Z-R relationship resulted in a maximum value at the point with the highest precipitation amount of 103 mm (Figure 7), whereas the moderate relationship would have yielded 95 mm as event sum for the maximum pixel. Figure 7 also demonstrates the necessity to adjust the radar data: without this procedure, radar would have estimated the precipitation to be lower by approximately a factor of 2.

.

Figure 7: Original (left) and gauge adjusted (right) rainfall amounts based on radar data with the convective type Z-R relationship

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5 CONCLUSIONS AND OUTLOOK

Radar data are a required source of information for the analysis of small scale heavy precipitation. The measurements of both radar and rain gauges are to be checked for errors in a detailed manner for such events. Then radar is able to give a good estimate of the precipitation between the rain gauge locations. A method to cross compare the use of different Z-R relationships and their quality to assess the amount of rainfall has been presented.

An automated cross-validation check of the type presented in Table 1 and using a small catalogue of likely Z-R relationships has the capability of improving quantitative precipitation estimates.

6 REFERENCES

Collier, C.G., 1989: Applications of Weather Radar Systems a Guide to Uses of Radar Data in Meteorology and Hydrology, Ellis Horwood Limited, Chichester, England.

Einfalt, T., Arnbjerg-Nielsen, K., Golz, C., Jensen, N.E., Quirmbach, M., Vaes, G., Vieux, B. (2004). Towards a Roadmap for Use of Radar Rainfall data use in Urban Drainage. Journal of Hydrology, 299, pp. 186-202.

Michelson D., Einfalt T., Holleman I., Gjertsen U., Friedrich K., Haase G., Lindskog M., Jurczyk A., 2005: Weather radar data quality in Europe quality control and characterisation. Review, COST Action 717 - Use of radar observations in hydrological and NWP models, Luxembourg.

Wilson, J.W., Brandes E.A. (1979). Radar measurement of rainfall A summary, American Meteorological Society, 60, 1048-1058.

9th International Conference on Urban Drainage Modelling Belgrade 2012

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Radar-raingauge data combination techniques: a

revision and analysis of their suitability for urban

hydrology

Li-Pen Wang1, Susana Ochoa2, Nuno Simes3, Christian Onof4, edo Maksimovi5

1 Imperial College London, United Kingdom, li-pen.wang08@imperial.ac.uk 2 Imperial College London, United Kingdom, s.ochoa-rodriguez@imperial.ac.uk 3 Imperial College London, United Kingdom & University of Coimbra, Portugal, nuno.simoes08@imperial.ac.uk 4 Imperial College London, United Kingdom, c.onof@imperial.ac.uk 5 Imperial College London, United Kingdom, c.maksimovic@imperial.ac.uk

ABSTRACT

The applicability of the operational radar and raingauge networks for urban hydrology is insufficient. Radar rainfall estimates provide a good description of the spatiotemporal variability of rainfall; however, their accuracy is in general insufficient. It is therefore necessary to adjust radar measurements using raingauge data, which provide accurate point rainfall information. Several gauge-based radar rainfall adjustment techniques have been developed and mainly applied at coarser spatial and temporal scales; however, their suitability for small-scale urban hydrology is seldom explored. In this paper a review of gauge-based adjustment techniques is first provided. After that, two techniques, respectively based upon the ideas of mean bias reduction and error variance minimisation, were selected and tested in an urban catchment (865 ha) in North-East London. The radar rainfall estimates of four historical events (2010-2012) were adjusted and applied to the hydraulic model of the study area. The results show that both techniques can effectively reduce mean bias; however, only the technique based upon error variance minimisation can correctly reproduce the spatial and temporal variability of rainfall, which proved to have a significant impact on the associated hydraulic outputs. This suggests that error variance minimisation methods may be more appropriate for urban hydrological/hydraulic applications.

KEYWORDS

Gauge-based adjustment, merging/combination, pluvial flooding, radar, rainfall, urban hydrology.

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1 INTRODUCTION

Rainfall constitutes the main input for urban pluvial flood models and the uncertainty associated to it dominates the overall uncertainty in the modelling and forecasting of this type of flooding (Golding, 2009). The rainfall events which generate pluvial flooding are often associated with thunderstorms of high intensity and small spatial scale ( 10 km), whose magnitude and spatial distribution are difficult

to monitor and predict (Collier, 2009; Golding, 2009; Vieux and Imgarten, 2011).

The sensors that are commonly used for estimation and prediction of rainfall at catchment scales are raingauges and radars (Cole and Moore, 2008); however, the applicability (i.e. achievable accuracy and resolution) of the currently operational radar and raingauge networks for urban hydrology is insufficient. In general, raingauges provide accurate point rainfall estimates near the ground surface; nonetheless, they cannot capture the spatial variability of rainfall which has a significant impact on the physical processes and thus on modelling of urban pluvial flooding (Tabios and Salas, 1985; Syed et al., 2003). Moreover, since dense raingauge networks cannot cover large areas, it is difficult to forecast rainfall with longer lead time based on raingauge data only (Looper and Vieux, 2012). In contrast, radars can survey large areas and can capture the spatial variability of the rainfall, thus improving the short-term predictability of rainfall and flooding. However, the accuracy of radar measurements is in general insufficient, particularly in the case of extreme rainfall magnitudes (Einfalt et al., 2005; Harrison et al., 2009); this has a tremendous effect on the subsequent rainfall forecast (which uses radar estimates as starting point) and on the associated flood forecast (whose main input is the rainfall forecast) (Ligouri et al., 2011). The low accuracy of radar measurements is mainly due to the fact that, unlike raingauges, which directly collect rain droplets, radar devices obtain rainfall measurements through an indirect process, which introduces more uncertainty. This indirect process comprises the following sub-processes: (i) noise filtering, (ii) identification of clutter and occultation, (iii) removal of anomalous propagation, (iv) attenuation correction, (v) calibration or conversion of reflectivity to rain rate and (vi) raingauge-based adjustment. The last two sub-processes involve calibration or adjustment of radar estimates based on raingauge measurements; nonetheless, the scale at which this is done cannot ensure that radar estimates capture high intensities and local conditions accurately. The conversion of reflectivity to rain rate (i.e. Z - R conversion function) is the result of a calibration process based on the comparison of a large number of coincidental observations of radar and raingauges. In order to obtain statistically optimal results, the conversion function has to compromise the capacity of deriving extreme values since the frequency of their occurrence is relatively low; hence, the Z - R conversion performs poorly at capturing intense rainfall rates in particular (Einfalt et al., 2004, 2005), which is vital for urban applications. In addition, the conversion functions are in general static; i.e. they are not dynamically updated (they only change according to the storm type; however, for each storm type the conversion function is fixed). After the conversion or calibration process and with the purpose of further enhancing the suitability of radar estimates for hydrological and hydraulic applications, gauge-based adjustment techniques, also referred to as re-calibration, combination or merging in the literature (Einfalt et al., 2004), are widely used to dynamically correct the bias between radar estimates and the coincidental raingauge measurements (Fulton et al., 1998; Seo et al., 1999; Harrison et al., 2009). However, these adjustment techniques are mostly applied in catchments of large area (~1000 km2) and use hourly rainfall rates, and although they provide benefits for hydrological applications at large scales, the suitability of the resulting rainfall estimates for urban hydrological applications is still insufficient. For example, Smith et al (2007) re-investigated 35 rainfall events selected from the US NEXRAD (network of 159 high resolution Doppler weather radars operated by the US National Weather Service (Fulton et al., 1998)) during the period 2003 - 2005, and compared them with the coincidental point observations recorded by a dense network of raingauges (one raingauge per km2 in average) over a small urban area

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( 14.3 km2). In this comparison large and event-varying bias were observed over the study catchment even though NEXRAD rainfall products had been dynamically adjusted with raingauge measurements (similar to the UK Nimrod rainfall data and adjusted based upon hourly scales).

Moreover, the feasibility of applying the existing gauge-based adjustment techniques at smaller spatial and temporal scales (i.e. for urban applications) has not yet been fully analysed.

In this paper a review of gauge-based adjustment techniques is first provided. After that, two of these techniques were selected and applied to a study urban catchment in North-East London, with the purpose of assessing their ability to improve operational radar measurements for urban applications.

2 REVIEW OF GAUGE-BASED ADJUSTMENT TECHNIQUES

Gauged-based adjustment techniques aim at combining the advantages and overcoming the drawbacks of radar and raingauge rainfall estimates; that is, to retain the accuracy of the point rainfall information provided by raingauges and at the same time the broader description of the spatial and temporal variations of rain-fields provided by radar. As previously mentioned, the final purpose of these techniques is to enhance the suitability of rainfall estimates for hydrological and hydraulic applications, including flood modelling and forecasting.

After reviewing different gauge-based adjustment techniques, it was noticed that, in general, they can be classified into two types: (i) mean bias reduction techniques and (2) error variance minimisation techniques. A review of these two types of gauge-based adjustment techniques is provided.

2.1 Mean bias reduction techniques

Mean bias is the difference between the mean radar rainfall estimates and the mean raingauge measurements at the locations of raingauges for a given time period. In the literature it is also termed systematic error and is thought to be the most important source of uncertainty affecting the suitability of radar rainfall estimates for hydrological and hydraulic applications (Vieux and Bedient, 2004). Consequently, many adjustment techniques focus on reducing raingauge-radar mean bias in order to improve radar rainfall estimates. The idea of the mean bias adjustment is to analyse the differences between raingauge observations and the coincidental radar measurements over a given period, and then apply this event-varying difference directly to each radar rainfall grid.

An example of this is the adjustment method implemented in the operational UK Nimrod system, where an adjustment ratio, based on comparisons between processed radar and raingauge hourly rainfall is applied to the entire domain of each radar site and is updated on an hourly basis (Harrison et al., 2009). A similar adjustment technique is used in the US NEXRAD system (Seo et al., 1999). As mentioned before, the adjustments carried out in the Nimrod and NEXRAD systems provide benefits for large scale hydrological applications; however, the resulting rainfall estimates are not accurate enough for urban applications (Vieux and Bedient, 2004; Smith et al., 2007).

Mean bias adjustment techniques have also been used at smaller scales in order to further improve radar rainfall estimates (which may have already been adjusted at larger scales, as in the case of Nimrod and NEXRAD products). For instance, in the above mentioned work by Vieux and Bedient (2004) over a 260 km2 urban catchment. They evaluated the hydrological prediction uncertainty caused by rainfall input errors through event re-construction. Five events were selected from NEXRAD during the period 1998 2003. These events were re-constructed by applying a simple ratio to reduce the mean bias between radar and the co-located raingauge observations. This simple ratio was derived from the comparison between mean radar rainfall estimates and mean local raingauge

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measurements at the locations of raingauges over the duration of a rainfall event. Results show that the corresponding flow prediction could be significantly improved by using mean bias adjusted (corrected) radar rainfall estimates as inputs. A similar work was carried out by Smith et al. (2007) but over a relatively small catchment (14.3 km2), in which 35 rainfall events were re-investigated and significant bias were observed between NEXRAD products and raingauge data. Similarly, the authors reduced bias by applying a simple ratio to scale up or down the radar rainfall rates to approximate the coincidental raingauge records. These works suggest that mean bias is the most important uncertainty source decreasing the suitability of radar rainfall estimates for urban hydrological and hydraulic applications. In addition, they suggest that the suitability of rainfall data for these applications could be massively improved through locally and dynamically adjusting radar rainfall estimates using co-located raingauge records. However, this simple mean bias adjustment was carried out through post-event (or historical rainfall records) comparisons. It is therefore more suitable for improving the applicability of historical rainfall events to hydrological and/or hydraulic design, rather than for short-term real-time forecasting. If intended for real-time flood forecasting applications, this method would require a very dense raingauge network (or a larger area) and a longer temporal comparison basis (i.e. hourly) to obtain a more reliable ratio to scale the radar rainfall (Anagnostou and Krajewski, 1999; Seo et al., 1999). It is therefore more suitable for coarser spatial- and temporal-resolution rainfall adjustment.

A methodology for improving the local and dynamic capacity of conventional mean bias adjustment methods was proposed by Moore et al. (1989) and further modified by Wood et al. (2000). A dynamic calibration factor was introduced to carry out 15-min radar rainfall adjustment in real time. This factor is based on the comparison of raingauge and radar estimates at each time step in synergy with a positive correction value and a static calibration factor , where and are long-term derived constants. Cole and Moore (2008) further examined the applicability of this methodology over two UK catchments (Darwen and Kent, respectively 135.7 and 212.3 km2). In this work three types of gauge-based adjustment techniques were used to correct radar estimates: (i) static adjustment, (ii) standard dynamic adjustment, and (iii) dynamic adjustment including mean bias. The first one is similar to the aforementioned simple mean-bias adjustment, but based upon a long-term radar-raingauge comparison. The second and third techniques are respectively based upon the original local adjustment methodology (Moore et al., 1989) and the modified one (Wood et al., 2000). Results suggest that the applicability of radar rainfall estimates can be significantly improved by the local adjustment methodology (i.e. the second and third techniques).

More recently, a geostatistical merging method which also focuses on reducing mean bias was developed by Ehret et al. (2008) and applied to real-time small-scale flood forecasting in the Goldersbach catchment, Germany ( 75 km2). At each time step, the point raingauge records are interpolated into a rainfall field and further merged with the coincidental radar image. The Block Kriging interpolation technique was employed to ensure that the synthetic rainfall field is unbiased. A deviation ratio field can be then obtained by comparing the interpolated rainfall and radar rainfall at each radar grid. This deviation field is then adjusted to ensure that its mean is equal to 1 and it is further applied to the interpolated rainfall field (in this way it is ensured that the raingauge totals are retained). A merged rainfall field is therefore obtained at each time step and further used as input for flood forecasting. The quality of radar rainfall was significantly improved by this merging process and, consequently, the accuracy of the rainfall and flood forecasts was also largely improved.

Although the mean bias adjustment methods mentioned above have proven to significantly improve rainfall estimates and the associated flow estimates and forecasts, they have some common drawbacks. First, the spatial structure (e.g. spatial variability) of radar rainfall fields could be altered by simply multiplying a ratio to the rainfall estimate at each radar grid. The ability to characterise the spatial

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variations in rainfall is however one of the most reliable features of radar sensors and should therefore be retained. Second, the mean bias adjustment methods have difficulty in correcting the temporal and spatial profiles of radar rainfall. For example, if the original radar rainfall estimates fail to capture the time of the rainfall peaks, this error will not be corrected by the mean bias adjustment methods since these focus on the correction of quantitative differences (see Figure 4 of Ehret et al. (2008)).

2.2 Error variance minimisation techniques

Another type of gauge-based adjustment techniques focuses on minimising the error variances. The error herein represents the difference between true (or raingauge) and radar rainfall estimates. The concept of minimising the error variances is similar to maximum likelihood approaches; therefore, in addition to mean bias, the spatial and temporal patterns of rainfall are also taken into account in the adjustment process (Krajewski, 1987; Todini, 2001; Mazzetti, 2004; Gerstner and Heinemann, 2008). In general, these techniques assume that there is a true (or best estimated) rainfall field at each time step, made up of grids whose rainfall volume is the (linear) combination of the coincidental radar and raingauge estimates. The total rainfall of this true rainfall field is equal to the raingauge total; this means that the raingauge records are unbiased. However, it is seldom possible to have at least one raingauge per radar grid; therefore, some further assumptions are necessary. For example, Gerstner and Heinemann (2008) defined that the rainfall volume at a specific grid of the true rainfall field as follows:

K

kiirkkgikiiriia yxPyxPwyxPyxP

1

,,,, (1)

where Pa(xi, yi) and Pr(xi, yi) are, respectively, the true and radar rainfall at the grid point (xi, yi); Pg(xk, yk) is the raingauge measurement at the raingauge position (xk, yk); wik is the to-be-determined weight and K is the number of raingauges. Through minimising the error variances, wiks can be estimated and their values are in general inversely proportional to the distance between raingauge and radar grids. Results show that this weighting technique can effectively reflect the local point information to radar rainfall. However, the study was carried out on a daily basis and its applicability to sub-daily and sub-hourly radar rainfall adjustment is therefore unknown.

Different from Gerstner and Heinemann (2008), Krajewski (1987) and Todini (2001) employed the (Block-) Kriging interpolation technique to generate point raingauge information at each radar grid before merging it with radar estimates. In Krajewski (1987)s Cokriging combination technique, the best rainfall estimate V*(x0, y0) at a specific location was defined as follows:

iiN

iiRii

N

iiG yxRyxGyxV

R

i

G

i,,,

1100

*

(2)

where NG and NR are the numbers of raingauges and radar grids around location (x0, y0) and Gi(xi, yi) and Ri(xi, yi) are the associated measurements at location (xi, yi). In the process of deriving Gi and Ri, the information of the covariances between true and raingauge rainfall CovVG and between true and radar rainfall CovVR are required; however, it is impossible to obtain them. They are therefore approximated by the forms CovVG = GCovGG and CovVR = RCovRR, where CovGG and CovRR are the covariances respectively between raingauges and radar grids and G and R are two to-be-determined constants ranging from 0 to 1. This approximation however largely decreases the applicability of the Cokriging technique because the values of G and R are usually determined subjectively or through a large number of simulations.

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Todini (2001), different from Krajewski (1987), employed the Kalman filter algorithm to merge the interpolated raingauge and radar rainfall field to obtain the true rainfall field at each time step. This method (called Bayesian combination), instead of using CovVG and CovVR, uses the covariance of errors Covt to help deriving the true rainfall field. The error t is estimated by comparing the co-located Block-Kriged and radar rainfall estimates; a Covt matrix can be therefore constructed in real time to update the original radar estimates to produce the true rainfall field. This Bayesian combination method has been applied to a 1051 km2 river catchment near Bologna (Italy), where 1 km2 C-band radar images and point rainfall information recorded by a network of 26 raingauges are available. Results show that the bias and variance between radar and observed rainfall estimates were significantly reduced. This application however was undertaken in an hourly basis and its potential to be used in sub-hourly rainfall adjustment needs to be further examined.

3 METHODOLOGY

In this work, one of each type of gauge-based adjustment techniques was selected and tested at the urban scale, with the purpose of assessing and comparing their ability to improve operational radar measurements for urban applications. The selected adjustment methods are next described.

3.1 Mean bias reduction method selected for testing at the urban scale

As mentioned above, the bias between raingauge and radar rainfall estimates is widely regarded as the dominative factor in the uncertainty of the corresponding hydrological and hydraulic modelling. A mean bias adjustment method was therefore implemented in this work to evaluate the impact of bias reduction on the corresponding hydraulic outputs of an urban catchment.

The implemented technique is a post-event one, where the mean sample bias is defined as the ratio of the mean raingauge accumulations to the co-located mean radar rainfall accumulations on an event total basis, i.e.,

myxR

mRGB

m

j jji

m

j ij

i

1

1

, (3)

where Bi is the sample bias for the i-th event, m is the number of raingauges, RGij is the rainfall accumulation (in mm) for the i-th event at the j-th raingauge, (xj, yj) is the geographical location of the j-th raingauge and Ri(xj, yj) denotes the radar rainfall accumulation (in mm) for the i-th event at location (xj, yj).

In order to correct the mean bias, the event sample bias Bi is applied to each radar rainfall grid over the study area for each selected rainfall event (the adjusted values will be referred to as Corrected radar estimates).

3.2 Error variance minimisation method selected for testing at the urban

scale

In this work, the Bayesian combination method proposed by Todini (2001) was selected for testing in an urban catchment. The reasons for selecting this method are the following:

1. It has a strong theoretical background and relatively little approximation

2. The software is available and well maintained

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3. It does not require numerous simulations and historical rainfall events to determine parameters

This is a dynamic method intended for real-time applications. The first step of the method is to, for each time step, interpolate the real-time raingauge measurements into a synthetic rainfall field using the Block Kriging (BK) interpolation method. After that, the interpolated rainfall field is merged with the coincidental radar image using the Kalman filter algorithm (Todini, 2001; Mazzetti, 2004).

The idea of the BK interpolation method is to synthesise a rainfall field whose semi-variogram curve is very similar to the semi-variogram curve empirically estimated from the associated point rainfall information, where the semi-variogram curve is a function used to characterise the degree of spatial dependence of a spatial random field (e.g. a rainfall field). In other words, the Block Kriged rainfall field contains not only accurate point rainfall estimates but also the spatial dependences between these point estimates over a specific area. This information can reflect the spatial structure of rainfall right above the ground; this can be very useful to correct the spatial structure observed by radar, which is at a given elevation above the ground and could be horizontally shifted by wind advection. This idea of using spatial dependences estimated from raingauge observations to improve the generation of rainfall processes has been widely used in the hydrological field (Wheater et al., 2005; Yang et al., 2005).

The Kalman filter algorithm used for carrying out the actual merging comprises two steps: predict and update (Kalman, 1960). In the predict step, the a priori estimates and status at the current time step are firstly predicted based upon the estimates and status at the previous time step. These a priori estimates and status are then updated using real-time observations and the a posteriori estimates and status can be obtained by minimising the variance between the a priori estimates and the observations (termed error variance). In the method proposed by Todini (2001), the radar image represents the a priori estimates and the interpolated rainfall field constitutes the observations to update the predicted estimates for obtaining the output field (a posteriori estimate) at each time step.

4 EXPERIMENTAL SITE AND DATASET

4.1 Cranbrook Catchment

The above mentioned gauge-based adjustment techniques were tested in the Cranbrook catchment. This catchment is located within the London Borough of Redbridge (North-East part of Greater London - see Figure 1). It is predominantly urbanised and has a drainage area of approximately 865 hectares; the main water course is about 5.75 km long, of which 5.69 km are piped or culverted. This area has experienced several pluvial, fluvial and coincidental floodings in the past.

4.2 Radar (Nimrod) Data

The Cranbrook catchment is in the coverage of two radars, Chenies and Thurnham (Figure 1(a)). The radar data are measured by the C-band radar network operated by the UK Met Office through the British Atmospheric Data Centre (BADC) with spatial and temporal resolutions of 1 km and 5 min, respectively. The radar (Nimrod) data have been quality-controlled by the UK Met Office following the correction techniques proposed by Harrison et al. (2009) to account for all the errors inherent to radar rainfall measurements.

4.3 Local Monitoring System: raingauges and level gauges

A real time accessible monitoring system is installed covering this catchment since April 2010. It includes three tipping bucket rain gauges, one pressure sensor for monitoring water levels at the

8

Roding River (downstream boundary condition of the catchment), two sensors for water depth measurement in sewers and one sensor for water depth measurement in open channels (Figure 1(b)).

4.4 Hydrological/Hydraulic Model of the Study Area

The focus of our work is on urban pluvial flooding, which, as was mentioned before, is one of the major issues in the Cranbrook catchment. For this reason, a pluvial flood model was implemented for the study area. The model is a dual-drainage, physically-based one and was set up in InfoWorks CS 10.5. In this model the urban surface was modelled in 2D (2-dimensions), using a triangular mesh. The model of the surface was coupled with a 1D (1-dimensional) model of the sewer system (Figure 1(c)) and the interactions between the two models take place at the manholes. The implemented model was calibrated using the rainfall and water level measurements collected through the local monitoring system (Section 4.3).

Rain gaugeLevel gauge in sewer

Level gauge in open channel

Pressure sensor for river level

Beal High School

Chadwell Heath Foundation School

Ursuline High School

Valentine Sewer

(a) (b) (c)

Figure 1. Cranbrook catchment (a) location of the catchment in relation to radars and the Roding River catchment; (b) monitoring system; (c) sewer network

4.5 Rainfall events selected for testing of gauge-based adjustment methods

Four rainfall events occurring between August 2010 and January 2012 were selected to test the gauge-based adjustment methods. The dates and statistics of these events are summarised in Table 1. In this table RG Total is the mean raingauge accumulation, Radar@RG Total is the co-located mean radar rainfall accumulation, Radar Total is the mean radar accumulation over the whole catchment and Peak Flow Depth corresponds to the maximum flow depth recorded in the Valentine Sewer (located in the mid-stream section of the catchment, see Figure 1(b)) for each event.

Table 1. Statistics of rainfall events selected for testing of adjustment methods.

Date Duration (h)

RG Total (mm)

Radar@RG Total (mm)

Radar Total

(mm)

Peak Flow Depth (m)

23/08/2010 8 23.53 7.29 6.80 0.633

26/05/2011 9 15.53 5.10 4.88 0.672

05-06/06/2011 24 20.87 9.43 9.48 0.346

03/01/2012 13 8.93 7.72 7.55 0.547

5 RESULTS AND DISCUSSION

As can be seen from Table 1, large and event-varying bias between raingauge and radar measurements were observed in the four rainfall events that were selected for testing. In order to correct this, the two

9

adjustment methods described in Section 3 were applied to each rainfall event. Due to space limitations, only the results associated with the event on 23/08/2010 will be presented. However, similar results were obtained for all events.

In this section, the corrected radar estimates obtained with the mean bias reduction method are referred to as Corrected Radar 1 km and the results of the error variance minimisation method are referred to as Bayesian Radar 1 km. Raingauge measurements are usually denoted RG and the original radar (Nimrod) estimates are referred to as Radar 1 km.

Figure 2 shows the results for the entire Cranbrook catchment for the 23/08/2010 event: i.e. it shows mean values of raingauge, radar and adjusted radar estimates, as well as the associated hydraulic results. Figure 3 shows the 5-min rainfall profiles and accumulations of the adjusted radar estimates, the coincidental raingauge records and the original radar rainfall estimates at the location of one of the raingauge sites (Chadwell Heath Foundation School) for the 23/08/2010 event. Similar results were obtained for the other 2 raingauge sites, but these are omitted due to space limitations.

From Figures 2 and 3 it can be seen that radar rainfall rates and rainfall accumulations, both at a specific raingauge location as well as for the entire catchment, were largely improved by both adjustment methods. In terms of total rainfall accumulation (see Figures 2(b) and 3(b)), the Corrected Radar 1 km produced slightly better results than the Bayesian Radar 1 km. For the rainfall profiles, however, the Bayesian method produced significantly better results than the mean bias one. For example, in Figures 2(c) and 3(a) some underestimation (e.g. around 00:05 - 02:05), overestimation (e.g. around 03:05 - 04:05) and faulty timing of rainfall peaks can be observed in the rainfall profiles of the Corrected Radar 1 km, as compared to the RG profiles. In contrast, the profiles of the Bayesian Radar 1 km fit the RG profiles significantly better. Moreover, in Figures 2(b) and 3(b) it can be noted that the shape of the cumulative rainfall for the Bayesian Radar 1 km is very similar to that of the RGs, as opposed to the shape produced by the mean bias corrected estimates (Corrected Radar 1 km). This conclusion is further strengthened by the q-q plot of Figure 1(a): it can be seen that the Bayesian Radar 1 km estimates provide a better fit to the RG observations, particularly for high rain rates (it can be noted that the markers of Bayesian Radar 1 km estimates are more concentrated around and closer to the straight line with slope equal to 1, as compared to the Corrected Radar 1 km estimates). The faulty reproduction of rainfall profiles by the mean bias adjusted estimates is due to the fact that this adjustment method fully relies on correcting the accumulated difference between radar and raingauge measurements over the entire rainfall event, without taking into account the temporal variation within a storm process.

In addition to the rainfall (temporal) profiles, Figure 2(d) also demonstrates that the spatial structures of rainfall fields are largely altered by simply multiplying a given constant (i.e. the sample mean bias) to the original radar rainfall fields. In contrast, it can be seen that the spatial structure of the rainfall field is preserved when the Bayesian adjustment technique is applied. As previously mentioned, the ability to reflect the spatial variability of a rainfall field is one of the main advantages of radars and it is desirable to retain it. After carrying out the rainfall adjustment, the different rainfall estimates were applied to the dual-drainage model of the Cranbrook catchment. The associated flow levels in one of the sewers (located in the mid-stream part of the catchment) are shown in Figure 2(c). As can be seen, the hydraulic outputs obtained with the adjusted radar measurements are quantitatively much more similar to the RG outputs and to the observed water levels, as compared to the outputs resulted from the radar rainfall estimates before adjustment. This demonstrates the predominant role of rainfall mean bias in hydrological and hydraulic modelling. However, it can also be observed that, as compared to the hydraulic outputs of the Corrected Radar 1 km, the outputs of the Bayesian Radar 1 km show better agreement with the RG outputs and with the flow level measurements, particularly regarding the timing and magnitude of flow level peaks. It is mainly due to the better reproduction of rainfall

10

profiles (both in quantity and geometry) achieved with the Bayesian adjustment method. These results suggest that, in addition to rainfall mean bias, the spatial and temporal variability of rainfall is also an important factor which has a significant impact on the associated urban hydrological/hydraulic applications.

(a) (b)

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Spatial Variability: 23/08/2010 event

Radar 1km

Bayesian Radar 1km

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(d)

Figure 2. Results for the entire Cranbrook catchment for the 23/08/2010 event: (a) Quantile-quantile (q-q) comparison of mean raingauge, radar and adjusted radar rainfall estimates (mm) per 5-min time step; (b) q-q comparison of cumulative mean raingauge, radar and adjusted radar rainfall estimates (mm); (c) Mean raingauge, radar and adjusted radar rainfall profiles and associated hydraulic outputs,

11

as represented by water depth at the Valentine Sewer Pipe 463.1 of the hydraulic model; (d) Spatial variability as represented by the standard deviation of the original and adjusted radar rainfall fields.

Figure 3. Comparison of 5-min rainfall profiles and accumulations for the Chadwell Heath Foundation School raingauge and the coincidental original and adjusted radar estimates 23/08/2010 event.

6 CONCLUSIONS AND FUTURE WORK

In this work, a detailed review of state-of-the-art gauged-based radar rainfall adjustment techniques was firstly conducted with the purpose of analysing their theoretical foundation. In general, rainfall adjustment techniques can be classified into two types: (i) mean bias reduction techniques and (ii) error variance minimisation techniques. Moreover, the existing techniques have mainly been applied at large scales and on hourly or daily basis; however, their suitability for smaller spatial and temporal scales (i.e. for urban applications) has not been fully analysed.

After this review, one technique of each type was selected and tested in a small urban catchment (865 ha) in North-East London. The radar rainfall estimates of four historical events occurring between August 2010 and January 2012 were adjusted using point rainfall measurements recorded by three in situ raingauges. The adjusted rainfall estimates were applied to the physically-based dual-drainage model of the catchment and the associated outputs were compared to flow level records in addition to the outputs resulted from raingauge measurements and the original radar data.

In these case studies, the method based upon error variance minimisation performed better, as it not only reduced mean bias, but it managed to correctly reproduce the spatial and temporal variability of rainfall, which proved to have a significant impact on the associated hydraulic outputs. These results suggest that error variance minimisation methods may be more appropriate for small scale urban hydrological/hydraulic applications. However, before further conclusions can be drawn, more work should be done to deeply understand the impact of parameters such as catchment size and geometry, raingauge network size, density and relative location. Moreover, the feasibility of using these techniques in real-time and its potential benefits for rainfall and flood forecast should be further studied.

7 ACKNOWLEDGEMENTS

The authors would like to thank Dr Cinzia Mazzetti and Prof Ezzio Todini, from Progea and the University of Bologna (Italy), for making freely available to us the RAINMUSIC software package for

12

meteorological data processing and data interpolation. The authors would also like to thank the UK Met Office for providing the radar data and Innovyze for providing the InfoWorks CS software. The first author would like to acknowledge the support of the European Unions Interreg IVB NWE Programme to the RainGain project (PSC8-236H), of which this research is part.

8 REFERENCES

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Ehret, U., Gotzinger, J., Bardossy, A. and Pegram, G. G. S. (2008). Radar based flood forecasting in small catchments, exemplified by the Goldersbach catchment, Germany. International Journal of River Basin Management, 6(4), 323-329.

Einfalt, T., Arnbjerg-Nielsen, K., Golz, C., Jensen, N.-E., Quirmbach, M., Vaes, G. and Vieux, B. (2004). Towards a roadmap for use of radar rainfall data in urban drainage. Journal of Hydrology, 299(3-4), 186-202.

Einfalt, T., Jessen, M. and Mehlig, B. (2005). Comparison of radar and raingauge measurements during heavy rainfall. Water Science and Technology, 51(2), 195-201.

Fulton, R. A., Breidenbach, J. P., Dong-Jun, S. and Miller, D. A. (1998). The WSR-88D rainfall algorithm. Weather and Forecasting, 13(2), 377-395.

Gerstner, E.-M. and Heinemann, G. (2008). Real-time areal precipitation determination from radar by means of statistical objective analysis. Journal of Hydrology, 352, 296-308.

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Liguori, S., Rico-Ramirez, M. A., Schellart, A. N. A. and Saul, A. J. (2011). Using probabilistic radar rainfall nowcasts and NWP forecasts for flow prediction in urban catchments. Atmospheric Research, 103, 80-95.

Looper, J. P. and Vieux, B. E. (2012) An assessment of distributed flash flood forecasting accuracy using radar and rain gauge input for a physics-based distributed hydrologic model. Journal of Hydrology, 412-413(0), 114-132.

Mazzetti, C. (2004). Report on performance of the new methodology. Deliverable 7.4, MUSIC Project (Multiple Sensor Precipitation Measurements, Integration, Calibration and Flood Forecasting), European Commission.

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Moore, R. J., Watson, B. C., Jones, D. A. and Black, K. B. (1989). London Weather Radar Local Calibration Study: Final Report, Contract report prepared for the National Rivers Authority Thames Region, NERC/Institute of Hydrology, Wallingford, UK.

Seo, D.-J., Breidenbach, J. P. and Johnson, E. R. (1999). Real-time estimation of mean field bias in radar rainfall data. Journal of Hydrology, 223, 131-147.

Smith, J. A., Baeck, M. L., Meierdiercks, K. L., Miller, A. J. and Krajewski, W. F. (2007). Radar rainfall estimation for flash flood forecasting in small urban watersheds. Advances in Water Resources, 30(10), 2087-2097.

Syed, K. H., Goodrich, D. C., Myers, D. E. and Sorooshian, S. (2003). Spatial characteristics of thunderstorm rainfall fields and their relation to runoff. Journal of Hydrology, 271(1-4), 1-21.

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Todini, E. (2001). A Bayesian technique for conditioning radar precipitation estimates to rain-gauge measurements. Hydrology and Earth System Sciences, 5(2), 187-199.

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Vieux, B. E. and Imgarten, J. M. (2011). On the scale-dependent propagation of hydrologic uncertainty using high-resolution X-band radar rainfall estimates. Atmospheric Research, 103(0), 96-105.

Wheater, H., Chandler, R., Onof, C., Isham, V., Bellone, E., Yang, C., Lekkas, D., Lourmas, G. and Segond, M. L. (2005). Spatial-temporal rainfall modelling for flood risk estimation. Stochastic Environmental Research and Risk Assessment, 19(6), 403-416.

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9th International Conference on Urban Drainage Modelling Belgrade 2012

1

Improving urban drainage modelling with path-average rainfall from telecommunication microwave links Martin Fencl1, Jrg Rieckermann2, David Strnsk1, Vojtch Bare1

1Czech Technical University in Prague, Department of Sanitary and Ecological Engineering, Thkurova 7, Praha 2Swiss Federal Institute of Aquatic Science and Technology (Eawag) and Swiss Federal Institute of Technology (ETH), 8600 Dbendorf, Switzerland

ABSTRACT

Incomplete knowledge about spatio-temporal rainfall dynamics causes input uncertainty in rainfallrunoff modelling. This is especially critical in urban areas, where subcatchments are small and runoff is generated extremely fast on the impervious areas. Networks of telecommunication microwave links (MWL) are very dense in urban areas and therefore could provide novel rainfall information which has the potential to reduce input uncertainty in urban drainage modelling. In this study, we therefore investigate how the better information on spatio-temporal rainfall variability from MWL observations improves pipe flow predictions. Specifically, we perform numerical experiments with virtual rainfall fields and compare the results of MWL rainfall reconstructions to those of rain gauge observations. For a case study of a suburb in Prague, Czech Republic, we are able to show that MWL networks in urban areas are sufficiently dense to provide good information on spatio-temporal rainfall variability. Total rainfall volumes are reproduced very well, with errors of about 6 %. Although peak rainfall intensities are still systematically underestimated by approximately 30%, this clearly outperforms rain gauge observations. Also, we find that peak flows from MWL observations are only biased by 6 %, whereas rain gauge observations cause a bias of 16 %. In our study, we did not include effects of uncertainties in both MWL and rain gauge measurements, which, arguably, can be high. Nevertheless, MWL networks could provide hundreds of rainfall sensors, which would be available at virtually no cost. As demonstrated, MWLs can significantly reduce input uncertainties in future rainfall-runoff modeling and thus improve discharge predictions.

KEYWORDS

Rainfall estimation, rainfall spatial dynamics, telecommunication microwave links, urban drainage modelling

2

1 INTRODUCTION

Commercial microwave links from telecommunication networks (MWL) are new source of rainfall information which has a potential to improve incomplete knowledge about spatio-temporal rainfall dynamics especially in urban areas (Messer et al., 2006). Traditional rain gauges provide data with sufficient temporal resolution, but usually cannot reflect the spatial variability of rainfalls. Similarly, weather radar data provides insight into the spatial distribution of precipitation, but only have limited accuracy for urban rainfall monitoring. For example, in Czech Republic, operational radar observes precipitation with a resolution of about 2.5 x 2.5 km2 every 5 min. Recent Local Area Weather Radars, which can provide higher spatial resolution of rainfall, are not always available. In addition they are potentially affected by significant sources of error (Thorndahl, 2011).

Similar to weather radars, MWL operate in the microwave range, where the rain drops are the major source of signal attenuation. Therefore, rain-induced MWL attenuation can be used to compute path-averaged rainfall intensities using a simple power law model (Berne and Uijlenhoet, 2007). Using MWL in urban drainage modeling is conceptually interesting, because MWL networks i) are already built and could provide rainfall information at virtually no additional cost, ii) observe near-surface precipitation a few tens of meters above ground, and iii) have a high density in urban areas (Rieckermann et al., 2009). In addition, MWL provide path-average rain intensities, which, given typical length scales from a few hundred meters to a few kilometers, should conceptually correspond very well to the scale of urban subcatchments.

In this manuscript, we therefore investigate for the first time how data from commercial telecommunication networks can improve urban drainage modeling. Specifically, we analyze in how far the better information about spatio-temporal rainfall variability improves pipe flow predictions. Our analysis for a suburb of Prague, Czech Republic, shows that MWL networks in urban areas are sufficiently dense to provide good information on spatio-temporal rainfall variability. Although peak rainfall intensities are still systematically underestimated, we find that MWL rainfall estimates predict pipe flows more accurately than point rainfall measurements.

2 METHODS AND MATERIAL

To assess the potential of MWL in urban drainage modeling, we investigate how runoff predictions using MWL rainfall improve in comparison to those using rain gauges. As proposed previously, we here present the results based on realistic numerical experiments. First, we compute reference rainfall fields and, second, extract point intensities as measured by a rain gauge. Third, we compute path-averaged rainfall intensities and reconstruct space-time rainfall as seen by a MWL network. These three datasets are then propagated through a hydrodynamic model to compare the influence of different rainfall monitoring techniques on predicted pipe flows. As we only investigate input uncertainties due to spatial rainfall variability, we disregard any other uncertainties.

2.1 Reconstruction of space-time rainfall

Reference rainfall fields: The reference areal rainfall intensities are simulated using a virtual drop size distribution (DSD) generator (Schleiss et al., 2012). The simulator estimates the medium and large scale rainfall variability (1-50 km) and advection direction and velocity using radar data. The small scale variability (0.1-1 km) of the DSD is parameterized based on disdrometer data.

Rain gauge observations: Virtual rain gauge measurements are extracted from the reference rainfall at one particular cell of a rainfall field.

3

MWL rainfall reconstruction: The rain-induced MWL attenuation contains information on the path-averaged rainfall intensity. As a typical network contains MWLs of different lengths and orientations, the two dimensional rainfall spatial variability can be reconstructed to some extent from joint analysis of nearby MWL data. For simplicity, we used the algorithm by Goldshtein et al., (2009) which is straightforward to implement: Each i-th MWL is divided into Ki equal subsections of approximately 0.5 km. Each subsection is substituted by a data point Mj, located at its centre. Each link is thereafter represented as a set of Ki data points (Figure 1). The mean rainfall intensity of all points along a link has to correspond to the path-averaged intensity:

ii

MWLijj

R=L

r (1)

The rainfall distribution between points (Mj, Mj+1, ..., Mj+ki) representing i-th link is approximated from data points belonging to neighboring links as follows (Figure 1):

MWLikk

MWLikkk

jl

lr= 2

2 )( (2)

where j is the rainfall estimate at Mj of the i-th link, rk is a rainfall at each neighboring point Mk which does not belong to the i-th link and lk is a distance of point Mj to the neighboring point Mk. The distribution of rainfall intensity along the i-th link is thereafter corrected by minimizing the cost function:

MWLij

jj r=F2)( (3)

under the condition (1). Here, the procedure is applied to each link and iterated 20 times as suggested by Goldshtein, (2009). To obtain two dimensional reconstructed rainfall field the iterated rainfall intensities at data points Mi are transformed to the regular grid. The rainfall intensity of particular grid point is calculated as a mean of intensities of data points weighted by square distance between grid point and respective data point Mi, analogically to (2).

To propagate the three sets of rainfall information through a hydrodynamic model, each subcatchments in the model requires the input of a specific rainfall time series. For our case study, the areal rainfall intensity over each subcatchment is therefore calculated by averaging the corresponding cells of the rainfall field proportionally to the area of intersection.

2.2 Urban rainfall runoff modelling

To investigate the potential of MWL information to better predict pipe flows, we use a standard 1D-hydrodynamic model. Details on the surface runoff and pipe flow modules are given below.

2.3 Performance assessment

To compare the different monitoring techniques, we compute relevant performance statistics of rainfall reconstruction and pipe flow in comparison to the reference rainfall case. For each rainfall event and input data set, we compute a) the peak intensity (Rmax), and b) the rainfall volume (RV), considering only the rainfall cells restricted by the catchment area. From the corresponding runoff hydrograph we compute c) outflow volume (QV) and d) peak flow at the catchment outlet (Qmax).

4

Z=0 z = 1 z = 20 z = 0

Figure 1. Rainfall reconstruction from MWL data. Left: Initial distribution of a rainfall between data points representing particular links. Middle: Distribution of a rainfall along links after first iteration of a rainfall intensity at the first link. Right: The reconstructed rainfall distribution along the links after last iteration (z).

We use the relative error to compare estimated values of respective magnitude with its reference value. The mean value of the relative error represents the bias and its standard deviation the uncertainty due to limited spatial information of each measuring technique.

2.4 Cases study Urban Catchment in Prague, Czech Republic

The case study area is located in a suburb of Prague. The investigated catchment has an area of 2.33 km2, with an impervious area of about 64 %, which is drained by a separate sewer system. The Prague urban area is covered by a dense network of many hundred MWL. We selected 29 MWLs owned by T-Mobile using Ericsson MINI-LINK platform which are located in the direct vicinity of the catchment (see below).

The reference rainfall fields are sampled every 5 minutes and have a spatial resolution of 0.1 x 0.1 km2. The original size of a rainfall field is 40 x 40 km2. As the response of the catchment fundamentally depends on the rainfall characteristics, we generated three convective rainfall events with different storm velocities and intermittencies: first of advection velocity 10 m/s to the North-East intermittency of 55 %, second of advection velocity 7.7 m/s to the South-East and intermittency of 50 %, third of advection velocity 5.5 m/s to the North East and intermittency of 70 %. The duration of each event is 50 minutes. To eliminate the influence of positioning of the rainfall field over the study area, the relative position of the catchment to the rainfall fields was repeatedly changed to cover 25 different locations uniformly distributed over the field. This finally resulted in a comprehensive set of 75 reference areal rainfalls of a size of 7 x 7 km2. From these, we computed rain gauge data and MWL reconstructions as follows.

For the rain gauge information, we only used one rain gauge, as this would correspond to the information in a typical consultant study. Also, the available hydrodynamic model was calibrated based on a single gauge.

In the study area, we selected a network of 29 MWLs with a total length of 54.3 km (Figure 2). For the MWL rainfall reconstruction analysis, we first chose all links which intersect with the catchment boundary polygon. Then, some links are filtered out to obtain a more regular structure of the MWL network and improve the coverage of the subcatchment. We found that this improves the reconstruction, because a) links which intersected the catchment boundary polygon only by a small

5

proportion spun the mass of the rainfall outside of the polygon and b) links of a similar length and orientation biased the iteration of a rainfall distribution along the path of links (2).(Figure 2). After filtering, the remaining 15 MWL have a median length of about 1 km. 10 operate at 38 GHz, one pair on 32 GHz and one pair on 26 GHz and one link at 23 GHz.

The rainfall reconstruction algorithm splits the 15 MWL into 39 data points, from which three links are represented by a single point only. The longest link is subdivided into 5 points. The number of iterations is set to 20. The reconstructed rainfall field has a size of 7 x 7 km2 and spatial resolution of 0.25 x 0.25 km2.

As described above, we use a standard hydrodynamic model for the rainfall-runoff simulations. It has been implemented in the commercial solver MIKE URBAN with computational engine MOUSE (MOUSE, 2009). The model is owned by the municipality of Prague and was constructed for the general drainage masterplan for Prague. The model has been carefully calibrated on data from a rain gauge and an ultrasonic Doppler flow meter, which have been collected from April 2006 to June 2006. The model comprises 188 subcatchments with a median area of 0.34 ha and has 517 manholes with pipe length of around 18.2 km. Diameters ranges from 0.3 to 1.6 m. The surface runoff module uses the simple time-area method (Type A). From this, pipe flows are computed by the dynamic Saint-Venant equations. The routing time step varies between 5 and 10 seconds.

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Figure 2. Study catchment and MWL network (left), the links displayed by the solid line were used for the rainfall spatial reconstruction. Right: Data points representing links used in the spatial reconstruction algorithm (right).

To guarantee a realistic evaluation, only those events were considered in performance assessment, where the reference peak flow (Qmax,ref) exceeded 10 l/s, because those flows are relevant from an engineering viewpoint. The events with an estimated peak flow (Qmax,est) lower than 5 l/s were also not included, since the runoff is very sensitive to small changes in model parameters (e.g., pipe roughness coefficients) and discharge predictions at such low flows are not robust.

6

3 RESULTS

In general, we found that the ability to predict runoff dynamics of a storm event depends on the estimation of total rainfall volume, its spatial stratification and temporal dynamics.

Regarding the spatio-temporal characteristics of the rainfall fields, we found that the MWL reconstruction in general correctly reproduces the location of peak rainfall intensities. However, peak intensities are generally averaged and therefore underestimated (Figure 3). In contrast, low intensities are overestimated. In comparison to reference rainfall volumes, RVMWL are systematically overestimated by only 6 %, with a standard deviation of 38 percent points (Table 1). On average, Rmax MWL is underestimated by 31 % (17 %). In our view, this is a very good result, considering that we deliberately chose convective events with a rather high intermittency (Table 1). In contrast, RVRG are systematically underestimated by 9 %. The lack of information about spatial variability of rainfall shows in the peak intensity estimates, Rmax RG,, which underestimate the reference values by almost 50%.

Regarding the performance to predict sewer discharges, the threshold for evaluating the rainfall induced flows (Qmax ref> 10 l/s and Qmax est> 5 l/s) was exceeded by 33 rain events. For these, we found that the MWL-based flow predictions match the runoff from reference rainfall considerably better than those from rain gauge data. (Table 2).

Table 1. Performance statistic of rainfall reconstruction in comparison to the reference rainfall (standard deviation is given in brackets)

RV

mean rel. error

Rmax

Mean rel. error

RG -9 % (32 %) 48 % (25 %)

MWL 6 % (38 %) -31 % (17 %)

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Figure 3. Example of ref. rainfall (left) and MWL reconstruction (right) - Event No. 26, t = 06:35.

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Table 2. Statistical comparison of estimated peak flows and flow volumes

QV mean rel. error

Qmax mean rel. error

RG 25 % (115 %) 16 % (85 %)

MWL -2 % (38 %) -6 % (23 %)

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Figure 4. Scatter in peak flow estimates (left) and absolute outflow volume estimates (right)

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RGMWLmean RGmean MWL

Figure 5. Relative peak flow error for different reference peak flows (left). Relative outflow volume error for different outflow volumes (right)

The outflow volume from MWL rainfall measurements is biased only off by -2 %, with a standard deviation of 38 percent points (Table 2). In contrast, the rain gauge overestimates the runoff volume by 25 %, with a much higher standard deviation. Similarly, the peak flows are only biased by 6 % using MWL fields, whereas rain gauge observations cause a bias of 16 %. Interestingly, the highest relative errors occur for both MWL and rain gauge data at low reference discharges (Figure 4, Figure 5). In summary, despite slight systematic under- and overestimation of rainfall fields, MWL observations considerably reduce input errors in hydrodynamic modeling, which leads to more accurate pipe flow predictions in comparison to traditional rain gauge observations (Figure 6).

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06:30 07:00 07:30 08:00

050

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time [hh:mm]

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/s]

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Figure 6. Example of the sewer hydrograph resulting from rain event No. 26 fromthe reference rainfall (solid), MWL reconstruction (dashed) and rain gauge observations (dotted). The better spatial resolution of the MWL data visibly reduces the input uncertainty due to incomplete rainfall observations.

4 DISCUSSION

The time-area method used for rainfall-runoff transformation smoothes the temporal variability of rainfall fallen on a particular subcatchment. This corresponds to the behavior of real-world subcatchments, where larger subcatchments lead to comparably smoother hydrographs, because the rainfall-runoff dynamic is averaged over the time. In addition, runoff dynamics are further smoothed during wave routing in the drainage system. Therefore, the averaging of peaks in reconstructed rainfall fields significantly influences the accuracy of pipe flow predictions.

Since a rain gauge measures the rainfall only at one point it easily misses the rainfall intensity peak. In contrast to peak averaging, this systematically underestimates the total rainfall volume and, consequently, has a much greater impact on the predicted rainfall-runoff. The uncertainty in the rain gauge measurement is, however, enhanced in our study also by the coarse temporal sampling of the rainfall fields. Since there is a relationship between spatial and temporal rainfall dynamics (Schleiss et al., 2012) the monitoring techniques which reflect the spatial variability do not require such a high sampling frequency as point measurements. This is, because discontinuities in temporal rainfall dynamics are compensated by its spatial dynamics. Consequently, the rain gauge cannot compensate the loss of information about temporal rainfall dynamics by rainfall spatial information.

While our results are based on virtual data, MWL rainfall estimates from real power level measurements contain additional uncertainties. The most significant errors are caused by the baseline determination, quantization noise, wet antenna effect and model structure deficits of the power law rainfall-attenuation relation (Zinevich et al, 2010; Fencl, 2011). In general, the uncertainty in MWL rainfall estimation grows with the rainfall intensity because of the rainfall-attenuation power law relationship. This negative effect is reduced for frequencies around 30 GHz, where the attenuation-rainfall relation is almost linear (Berne and Uijlenhoet, 2007). Although MWL reconstructions under real world conditions will always be less accurate than reported here, the uncertainties could be minimized i) by combining the MWL information with rain gauge and weather radar information ii) by implementing a more sophisticated reconstruction algorithm.

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Also, it is well known that traditional rain gauges are also affected by uncertainties. While they can measure moderate rainfalls very accurately, heavy and very heavy rainfall observations are often systematically underestimated. Especially for tipping bucket gauges, this can be partly filtered out by proper calibration (Stransky et al., 2007).

Future research is needed to investigate how the uncertainty is related to the link length, which, as shown, governs the averaging and location detection of peak rainfall intensities. Based on our results, we suggest to further improve rainfall reconstruction algorithms. This should include a better selection of data points and weights for the rainfall intensity iterations (Eq. 2), as well as better consideration of the redundant information from parallel links and the irregular ray-like structure of a MWL network. The rainfall reconstruction technique used in this study also reconstructs the rainfall fields separately. More sophisticated methods should take advantage of the spatio-temporal correlation of different observations (Zinevich et al., 2008) and use a rain field model, possibly in combination with radar data. In addition, this approach enables short term forecasting which can find a great use in drainage system real time control applications.

5 CONCLUSION

In our study, we found that the better information from Telecommunication Microwave Links about spatio-temporal rainfall variability has the potential to improve pipe flow predictions compared to those based on traditional rain gauge observations. Our results show, first, that MWL rainfall reconstruction underestimates extreme rainfall peak intensities, but very well reproduces areal averaged rainfall intensities. Second, for urban drainage applications, we found that the averaging of rainfall peaks over a larger area from MWL observations does not influence the runoff dynamics as significantly as missed rainfall peaks by rain gauges. Rain gauges often miss peak intensities of a storm cell, especially for convective high-intensity events and, here, generally produced too low runoff. These results do not yet include effects of uncertainties in both MWL and rain gauge measurements, which can be very high. Especially for short MWL, wet antenna and quantization effects can lead to biased and imprecise observations. On the other hand, we found that MWL networks can be extremely dense in urban areas, where many rainfall sensors could be available at virtually no cost. Thus, considering the redundant information from many links seems promising to improve the accuracy of MWL observations. In the future, the MWLs have potential to complement rain gauge point measurements with the missing spatial rainfall information. Thus, they can reduce input uncertainties in rainfall-runoff modeling and improve discharge predictions.

6 ACKNOWLEDMENTS

This work was supported by the project of Czech Technical University in Prague project no. SGS12/045/OHK1/1T/11. Further, we would like to thank T-Mobile Czech Republic a.s. for kindly providing us with information on the MWL network. The Prazska Vodohospodarska spolecnost, a. s. is acknowledged for providing us with their hydrodynamic model. People from Veolia Voda, a.s. were very helpful in selecting the appropriate case study area. We would also like to thank the employees of Hydroprojekt, a. s. and DHI, a. s. for consulting regarding the rainfall-runoff model. Last but not least we thank Marc Schleiss, EPFL, Lausanne, for providing us with DSD fields for the numerical experiments.

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7 REFERENCES

Berne A., Uijlenhoet R. (2007). Path-averaged rainfall estimation using microwave links: Uncertainty due to spatial rainfall variability. Geophys. Res. Lett. 34(7).

Fencl M. (2011). Reducing the uncertainty in rainfall-runoff modelling using commercial microwave links. Master's Thesis. Department of Sanitary and Ecological Engineering, Czech Technical University in Prague, Czech Republic.

Goldshtein O., Messer H. Zinevich A. (2009). Rain rate estimation using measurements from commercial telecommunications links. Signal Processing, IEEE Transactions on 57, 16161625.

Messer, H., Zinevich, A., Alpert, P. (2006). Environmental Monitoring by Wireless Communication Networks. Science 312, 713713.

MOUSE (2009). User Guide. DHI. http://www.hydroasia.org/jahia/webdav/site/hydroasia/shared/

Document_public/Project/Manuals/US/MOUSE_UserGuide.pdf (accessed 7 April 2012)

Rieckermann J., Lscher R. and Krmer S. (2009). Assessing Urban Precipitation using Radio Signals from a Commercial Communication Network, 8th International Workshop on Precipitation in Urban Areas, 10-13 December, 2009, St. Moritz, Switzerland..

Schleiss, M., J. Jaffrain and A. Berne (2012), Stochastic simulation of intermittent DSD fields in time, J. Hydrometeorol., vol.13, No.2, 621-637.

Stransky D., Bares V., and Fatka P. (2007). The effect of rainfall measurement uncertainties on rainfall-runoff processes modelling. Water science and technology, 55 (4), 103111.

Thorndahl, S., Rasmussen, M.R. (2011), Marine X-band weather radar data calibration, Atmospheric Research, vol. 103, 33-44.

Zinevich, A., Alpert, P., Messer, H. (2008). Estimation of rainfall fields using commercial microwave communication networks of variable density. Adv. Water Resour. 31, 14701480.

Zinevich A., Messer H. and Alpert P. (2010). Prediction of rainfall intensity measurement errors using commercial microwave communication links. Atmospheric Measurement Techniques 3, 13851402.

9th International Conference on Urban Drainage Modelling Belgrade 2012

1

State-space adjustment of radar rainfall and stochastic

flow forecasting for use in real-time control of urban

drainage systems

Roland Lwe1 , Peter Steen Mikkelsen2, Michael R. Rasmussen3, Henrik Madsen4

1 Department of Informatics and Mathematical Modelling, Technical University of Denmark (DTU), Denmark, rolo@imm.dtu.dk 2 Department of Environmental Engineering, Technical University of Denmark (DTU), Denmark, psmi@env.dtu.dk 3 Department of Civil Engineering, Aalborg University, Denmark, mr@civil.aau.dk 4 Department of Informatics and Mathematical Modelling, Technical University of Denmark (DTU), Denmark, hm@imm.dtu.dk

ABSTRACT

Merging of radar rainfall data with rain gauge measurements is a common approach to overcome problems in deriving rain intensities from radar measurements. We extend an existing approach for adjustment of C-band radar data using state-space models and use the resulting rainfall intensities as input for forecasting outflow from two catchments in the Copenhagen area. Stochastic greybox models are applied to create the runoff forecasts, providing us with not only a point forecast but also a quantification of the forecast uncertainty. Evaluating the results, we can show that using the adjusted radar data improves runoff forecasts compared to using the original radar data and that rain gauge measurements as forecast input are also outperformed. Combining the data merging approach with short term rainfall forecasting algorithms may result in further improved runoff forecasts that can be used in real time control.

KEYWORDS

Flow forecast, greybox model, radar rainfall, state space model

1 INTRODUCTION

Radar observations are increasingly used for measuring rainfall in urban areas. The good spatial coverage, however, comes along with problems in determining the rainfall intensity due to problems such as beam attenuation and the drop size dependency of the relation between reflectivity and rain intensity. Merging the radar measurements with gauge observations is a practitioners approach to this problem.

2

Classically, radar rainfall measurements are adjusted with mean field bias to reflect ground measurements as good as possible. Thorndahl et al. (2010) follow this approach in a two-step adjustment that is used operationally within the real time control framework in the Copenhagen area (Grum et al. (2011)). Uncertainties of the ground measurements are thereby neglected. Further, assumptions need to be made on how to apply rain gauge point measurements to the radar rainfall plane. Integrating gauge and radar rainfall measurements using state space models has been proposed by several authors in the past. Chumchean et al. (2006) and Costa and Alpuim (2009) use these techniques for temporal updating of the mean field bias. Brown et al. (2001) integrate spatial interaction into their model via a vector autoregressive process. Similarly Grum et al. (2002) construct a simple state space model that implicitly enables spatial interaction between the pixels and allows for the integration of a multitude of measurement types that can be related to the rainfall process.

We adopt this last approach due to its ability to incorporate spatial interaction and various measurement types and extend the uncertainty structure. The reconstruction of the rainfall process is then used to create stochastic runoff forecast from a simple grey-box model. We evaluate the quality of different forecasts using skill scores.

2 METHODOLOGY

2.1 Data and Catchments

We consider two catchments in the Copenhagen area. The Ballerup catchment has a total area of approx. 1300 ha. It is mainly laid out as a separate system but has a small combined part. The runoff in this area is further strongly influenced by rainfall dependent infiltration.

The Damhusen catchment is located close to Ballerup but drains to a different treatment plant. We consider the northern part of the catchment with a total area of approx. 3000 ha. The catchment is laid out as a combined sewer system and a multitude of CSOs are located in the area. Flow measurements are available from both catchments in 5 min resolution.

A C-band radar is operated by the Danish Meteorological Institute (DMI) in Stevns approx. 45 km south of the considered catchments. The spatial resolution of the radar pixels is 2x2 km. The provided radar data are rain intensities derived using the Marshall Palmer relationship, where the coefficients have been adjusted such that the average rainfall depth observed by the radar during the considered period matches selected gauge measurements (Thorndahl et al. (2010)). We denote these data unadjusted radar data. We consider an area of 9x11 pixels that covers the whole Copenhagen area (Figure 1).

Within the catchments online rain gauge measurements are available from the Danish SVK network (Jrgensen et al. (1998)). The gauges marked red in Figure 1 are used to adjust the radar measurements. Only few of the available gauges are used for this purpose as one objective for using radar rainfall data is to derive rain intensities from as few ground measurements as possible. To make results comparable, we use the same gauges that are used for radar adjustment in a real time control project in the Copenhagen area (Grum et al. (2011)). A reference simulation is performed where flow forecasts are generated using rain gauge measurements as an input. The gauges for these simulations were selected with respect to their location to the catchment as marked in Figure 1.

We have selected a 3-month period of measurements from 25/06/2010 until 29/09/2010 for this study. The period contains several summer storms that should be relevant for control applications in urban

3