areal rainfall estimation using moving cars as rain … · ﬁelds is sampled with a conventional...

Hydrol. Earth Syst. Sci., 14, 1139–1151, 2010www.hydrol-earth-syst-sci.net/14/1139/2010/doi:10.5194/hess-14-1139-2010© Author(s) 2010. CC Attribution 3.0 License.

Hydrology andEarth System

Sciences

Areal rainfall estimation using moving cars as rain gauges– a modelling study

U. Haberlandt1 and M. Sester2

1Institute of Water Resources Management, Hydrology and Agricultural Hydraulic Engineering,Leibniz University of Hannover, Hannover, Germany2Institute of Cartography and Geoinformatics, Leibniz University of Hannover, Germany

Received: 28 May 2009 – Published in Hydrol. Earth Syst. Sci. Discuss.: 3 July 2009Revised: 21 March 2010 – Accepted: 25 June 2010 – Published: 2 July 2010

Abstract. Optimal spatial assessment of short-time step pre-cipitation for hydrological modelling is still an important re-search question considering the poor observation networksfor high time resolution data. The main objective of this pa-per is to present a new approach for rainfall observation. Theidea is to consider motorcars as moving rain gauges withwindscreen wipers as sensors to detect precipitation. Thisidea is easily technically feasible if the cars are provided withGPS and a small memory chip for recording the coordinates,car speed and wiper frequency. This study explores theoret-ically the benefits of such an approach. For that a valid re-lationship between wiper speed and rainfall rate consideringuncertainty was assumed here. A simple traffic model is ap-plied to generate motorcars on roads in a river basin. Radardata are used as reference rainfall fields. Rainfall from thesefields is sampled with a conventional rain gauge network andwith several dynamic networks consisting of moving motor-cars, using different assumptions such as accuracy levels formeasurements and sensor equipment rates for the car net-works. Those observed point rainfall data from the differentnetworks are then used to calculate areal rainfall for differentscales. Ordinary kriging and indicator kriging are appliedfor interpolation of the point data with the latter consider-ing uncertain rainfall observation by cars e.g. according to adiscrete number of windscreen wiper operation classes. Theresults are compared with the values from the radar observa-tions. The study is carried out for the 3300 km2 Bode riverbasin located in the Harz Mountains in Northern Germany.The results show, that the idea is theoretically feasible andmotivate practical experiments. Only a small portion of thecars needed to be equipped with sensors for sufficient areal

Correspondence to:U. Haberlandt([email protected])

rainfall estimation. Regarding the required sensitivity of thepotential rain sensors in cars it could be shown, that oftena few classes for rainfall observation are enough for satis-factory areal rainfall estimation. The findings of the studysuggest also a revisiting of the rain gauge network optimisa-tion problem.

1 Introduction

Rainfall is the most important input information for hydro-logical planning and water resources management. Espe-cially the modelling of highly dynamic and nonlinear pro-cesses like floods, erosion or wash out of pollutants reliesheavily on good information about precipitation. Due to itshigh variability in space and time observation of rainfall isstill a challenging task. While the classical networks of non-recording rain gauges with a daily observation interval havereached a sufficient density and a good standard, the avail-ability and density of recording rain gauges for the observa-tion of short time step rainfall is still inadequate. Even for de-veloped European countries like Germany the network den-sity of recording rain gauges considering stations with longerrecords from the German Weather Service (DWD, MI net-work) is only about one station per 1800 km2 compared to adensity of about one station per 90 km2 for non-recordingrain gauges. Weather radar is a very important new datasource for measuring rainfall. However, despite the high spa-tial resolution of radar data there is often a large space-timevariable bias in radar rainfall estimates (Smith et al., 2007;Krajewski and Smith, 2002). So, a sufficient point precipi-tation network is still needed for calibration. Other specialand innovative methods for rainfall observation use satellites(Grimes and Diop, 2003; Wardah et al., 2008), microwave

Published by Copernicus Publications on behalf of the European Geosciences Union.

http://creativecommons.org/licenses/by/3.0/

1140 U. Haberlandt and M. Sester: Areal rainfall estimation using moving cars as rain gauges

links (Leijnse et al., 2007; Messer et al., 2006) or rain gaugesaboard moving ships to measure rainfall at sea (Hasse et al.,1998; Yuter and Parker, 2001). Utilising rainfall informationfrom different sources together and applying sophisticatedinterpolation or merging methods can further improve pre-cipitation estimation for hydrological applications (Gouden-hoofdt and Delobbe, 2009; Chiang et al., 2007; Goovaerts,2000; Haberlandt, 2007; Ehret et al., 2008).

The main objective of this paper is to present a new ideafor measuring precipitation using moving cars as rain gaugeswith windscreen wipers as sensors to detect precipitation.This idea would easily be technically feasible if the cars wereprovided with a GPS and a small memory chip for recordingtime, car velocity and wiper frequency. Alternatively, alsoan online transmission of the sensed information via mobilephones could be realized. The potential of such a conceptbecomes immediately clear considering the high and everincreasing traffic density worldwide with a huge number ofcars; e.g. in Germany exist more than 40 million cars (EU-ROSTAT, 2009).

This study explores theoretically the benefits of such anapproach. A simple statistical traffic model is applied to gen-erate car traffic on main roads in a river basin. Radar rain-fall data are used as reference rainfall fields. Rainfall fromthese fields is sampled with a conventional rain gauge net-work and with a dynamic network consisting of moving mo-torcars. Those observed point rainfall data from the two net-works are then used to calculate areal rainfall for differentscales using geostatistical interpolation methods. The resultsare compared with the reference values from radar observa-tions.

2 Methodology

2.1 Traffic generation model

The traffic flow of the moving cars is determined in a sim-ple stochastic simulation process. The necessary data for thetraffic flow model is geometric information about roads withassociated information about traffic density at different timesof the day. Furthermore, assumptions about the relative num-ber of cars that is equipped with a rain sensor are needed. Fi-nally, a factor determines the sampling rate, i.e. the frequencyof measurements in time.

Based on these assumptions, cars are randomly generatedfor each road segment. From their starting position, the carsvirtually drive with the given velocity towards the end-nodeof the road segment. Their position is interpolated accordingto the given sampling rate, here in intervals of 5 minutes.This leads to a collection of car positions on the roads in theform: x, y and time. Subsequently, rainfall observations areassigned to the car positions and areal rainfall is estimatedusing interpolation (see below).

2.2 Rainfall observation by cars

Rainfall observation by cars could be realised using the wind-screen wipers as sensors. The cars need to be equipped witha GPS system to obtain the geographical position. In addi-tion a memory chip is necessary to register time, location,car speed and wiper frequency. A crucial task for this sys-tem to work is the derivation of a relationship between wiperspeed (W ) and rainfall intensity (R). This relationship willbe called in the following W-R relationship. In general therainfall intensity to be estimated depends on the wipers fre-quency, the car speed, the specific properties of the car andthe driver’s preferences operating the car. The influence ofthe latter could be avoided if photocell rain detectors installedin modern cars for automatic set up of wiper speed are useddirectly as sensors.

In order to establish a W-R relationship calibration is re-quired. The calibration of the W-R relationships using ob-served data from rain gauges would have some similaritiesto the procedure for calibration of radar data using the Z-Rrelationship. The main difference is that each car has its ownspecific W-R relationship which is primarily related to thewiper system, the driver, the cars speed and the local condi-tions. To test the idea of areal rainfall estimation by cars W-Rrelationships are needed. In the following possible ways toestablish W-R relationships are briefly discussed:

a. Assuming error free W-R relationships.As base line scenario a correct W-R relationship withexact rainfall measurement by cars is assumed. Thepoint error for rainfall observation by cars is zero in thiscase. This allows assessing the impact of point obser-vation errors on the total uncertainty of areal rainfall es-timation by comparison of this base line scenario withthe following cases, where point errors are taken intoaccount. For this reference case the total error differ-ences in areal rainfall estimation from gauges and carsdepends only on the interpolation error from the dif-ferent observation networks. Note, that for this and allother cases error free observation of rainfall at the raingauges is assumed.

b. Assuming W-R relationships with uncertainty.Simple W-R relationships with uncertainty will be as-sumed. Here, the point observation error is taken intoaccount by considering only a limited number of rainfallclasses with constant observed wiper speed for the cer-tain ranges of rainfall. For instance rainfall observationsbased on 4 classes, corresponding to less accurate mea-surements (“more old fashioned cars”) and 10 classes,corresponding to rather precise measurements (“moremodern cars”) could be considered. The assumed pointerror is uniformly distributed within the classes and canbe taken into account e.g. by taking mid class values asobserved car rainfall or by using indicator kriging forinterpolation (see below).

Hydrol. Earth Syst. Sci., 14, 1139–1151, 2010 www.hydrol-earth-syst-sci.net/14/1139/2010/

U. Haberlandt and M. Sester: Areal rainfall estimation using moving cars as rain gauges 1141

c. Estimating W-R relationships from laboratoryexperiments.A set of basic W-R relationships for different cars andwiper systems might be derived in laboratory exper-iments. Climate-wind tunnels may be employed forthat allowing exact definition of rainfall intensities, carspeed, etc. A simple model for the point errors couldbe assumed considering e.g. normal distribution for theerrors. Those errors can be estimated from average andvariance of the single relationships derived as outcomeof the experiments. To consider this point error in thesimulation experiments realisations of wiper frequen-cies belonging to the truth rainfall are drawn from nor-mal distributions providing in return the uncertain pointestimations of rainfall for subsequent interpolation.

d. Estimating W-R relationships from field experiments.For field experiments some cars could be equipped withGPS and devices for recording car speed, location andwiper frequency. If rainfall intensities are available acalibration of the W-R relationships similar to Z-R rela-tionships can be tried. Rainfall intensities can be takenfrom nearby rain gauges or from radar observations.However, both methods involve also significant uncer-tainties to estimate the reference rainfall for the car lo-cations. When using nearby rain gauges as reference theinterpolation errors have to be considered. In case ofusing radar as reference the uncertain transformation ofreflectivity into rain rate needs to be taken into account.Also a merged precipitation product could be used asreference (e.g. Goudenhoofdt and Delobbe, 2009). Thecalibration can be carried out in a re-analysis mode us-ing “historic” data or in an on-line mode using rainfallrates obtained from nearby automatic rain gauges withremote transmission capabilities. The latter would al-low a dynamic updating of the transformation functionsand an adaptation to different conditions like differentdrivers of the cars. Such a system could be further im-proved by allowing a communication between the carspropagating such information through the whole “sen-sor network” (Stefanidis and Nittel, 2004).

Investigations for establishing valid relationships betweenwiper frequency and rain rate from laboratory or field exper-iments (cases c. and d.) are beyond the scope of this pilotstudy and need quite an amount of further research. Here,it will be assumed, that such relationships exist, either er-ror free as reference (case a.) or with assumed uncertaintybased on a restriction of the continuous rainfall intensities tosome discrete observable classes (case b.) The uncertaintyin the W-R relationship is one important source or errors forareal rainfall estimation by car networks. The other impor-tant source is the interpolation error mainly related to the lim-ited number of observation points to estimate areal rainfall,which is discussed in the following and which is the mainfocus of the paper.

2.3 Areal rainfall assessment

Rainfall interpolation is required to estimate raster basedcontinuous rainfall fields in space from point observationsand to calculate areal rainfall for regions or catchments.For rainfall interpolation two geostatistical methods ordinarykriging (OK) and indicator kriging (IK) are employed. OKis used for the interpolation of rainfall from the stationarygauge network and as reference method assuming continu-ous observation ability of the moving rain gauges. IK is usedfor the interpolation of rainfall measured by the cars con-sidering their discrete observation ability in practice. It isassumed, that using the moving cars as rain gauges only alimited accuracy is possible providing rainfall observationsin discrete classes. In the following a brief overview of theinterpolation methods OK and IK and their implementationfor this investigation is given. A more detailed descriptionabout the theory of the methods can be found in geostatisti-cal textbooks (e.g. Goovaerts, 1997; Isaaks and Srivastava,1989).

Ordinary Kriging (OK) is the best known and most usedgeostatistical interpolation method (Matheron, 1971). Forusing OK the requirements of the intrinsic hypothesis haveto be met. That means, first, the expected value of the vari-ableZ is constant in the whole domain

E [Z(u)] = m for all u ∈ D (1)

and, second, the variance of the differences [Z(u + h) −

Z(u)] between two points depends only on the distance vec-tor h and not on the locationsu andu+h

γ (h) =1

2Var[Z(u+h)−Z(u)] u ∈ D. (2)

The functionγ (h) is called here variogram (exact semivar-iogram), characterising the spatial variability of the targetvariable. The linear estimator for the unknown pointu0 isa weighted sum of the observations from then surroundingpointsui :

Z∗(u0) =

n∑i=1

λiZ(ui). (3)

The weightsλ are calculated using the OK kriging system

n∑j=1

λjγ (ui −uj )+µ = γ (ui −u) i = 1,...,n

n∑j=1

λj = 1, (4)

whereλ are the variogram values andµ is a Lagrange pa-rameter. Considering that time series of precipitation need tobe processed a variance weighted average experimental vari-ogram is calculated assuming isotropy

γ ∗(h) =1

m ·2n(h)

m∑t=1

1

s2t (Z)

n(h)∑i=1

[Z(ui,t)−Z(ui+h,t)

]2, (5)

www.hydrol-earth-syst-sci.net/14/1139/2010/ Hydrol. Earth Syst. Sci., 14, 1139–1151, 2010


wherem is the number of time stepst and s2t is the vari-

ance for each time step. In this case only one experimentalvariogram is obtained, for which the fitting of the theoreticalmodel can be done manually. The combination of a nuggeteffect with an exponential model is used here uniformly astheoretical variogram model:

γ (h) = c0+c ·

[1−exp

(−

3h

ae

)], (6)

whereae is the effective range,c is the partial sill andc0 isthe nugget variance.

For indicator kriging (IK) (Journel, 1983) the observedvariableZ(u) is first transformed into a binary indicator vari-ableIα according to

Iα =

{1 if Z(u) ≤ α

0 otherwise. (7)

Using several thresholdsαk with k = 1,...,K gives a vectorof indicator variablesIα,k. Variograms have to be inferredfor all indicator variables separately. Considering ordinaryindicator kriging the interpolation is done for each indicatorusing the OK framework, which gives in the end an estima-tion of the cumulative distribution function (cdf) ofZ(u).Order relation deviations are corrected a posteriori followingthe approach of Deutsch and Journel (1992, p. 81). The meanof the cdf approximated by its discrete sum provides then anestimate for the observed variable:

Z∗(u) = Iα0(u)α0+

K∑k=0

[I ∗αk+1

(u)−I ∗αk

(u)]·αk+1−αk

2,(8)

whereα0 andαk+1 are the minimum the maximum values ofthe Z-range, respectively.

2.4 Performance assessment

To compare the performance of the moving car networkwith the performance of conventional rain gauges for estima-tion of areal precipitation space-time high resolution rainfallfields are required as reference or “true” rainfall. Stochasti-cally generated rain fields could be employed for this purpose(e.g. Seo et al., 1990). However, here it is preferred to useweather radar rainfall, since those data are probably closerto reality regarding space-time dynamics, and avoid the ad-ditional introduction of a stochastic weather generator. Arealrainfall estimates based on moving car networks and basedon a stationary gauge network are then compared against“true” areal rainfall calculated from the reference radar data.Precipitation from both networks is interpolated on a regu-lar raster for each time step using the methods described inSect. 2.2 and then aggregated to areal averagesZ∗

A(t) con-sidering different spatial scales

Z∗

A(t) =1

N

N∑i=1

Z∗(t,ui), (9)

whereN is the number of raster cells within the area andt is the time step. For evaluation of the areal precipitationestimates the following performance criteria are used:

the total bias Bias=m∑t=1

[Z∗

A(t)−ZA(t)], (10)

the relative standard error normalised with the average of thereference areal value

RSE=1

ZA

·

√√√√ 1

m

m∑t=1

[Z∗

A(t)−ZA(t)]2 (11)

and the coefficient of correlation

Cor=Cor

[ZA(t),Z∗

A(t)]√

Var[ZA(t)] ·Var[Z∗

A(t)] , (12)

whereZ∗

A is the estimated areal precipitation,ZA the ref-erence areal precipitation andm the number of time stepsconsidered for error calculation.

The performance of the areal rainfall estimation dependson the network density. To quantify the density of the stationnetwork and the car network the following kernel density es-timator is applied to all cellsi = 1,...,N of the 1 km× 1 kmgrid (Silverman, 1986):

Di =1

πr2

n∑j=1

kj with kj =

{3(1−

(dr

)2)2

for d ≤ r

0 ford > r,(13)

wheren is the number of stations within the search radiusr

andk is a quartic kernel weighting the stations according totheir distanced from the cell centre. The total network den-sity for one specific area or subbasinDsub is then calculatedby averagingDi over all raster cells within the consideredcatchment. The kernel density is chosen here as estimatorto consider all appropriate stations, also those located out-side the catchment boundaries and to weigh the individualstations differently according to their distance from the sub-basin.

2.5 General steps for analysis

For the analysis the following steps are carried out based onrainfall time series with a temporal discretisation of 5 min:

1. Areal reference rainfall time series are calculated for se-lected catchments from radar rainfall fields.

2. Point precipitation time series are extracted for a sta-tionary rainfall gauge network from the radar rainfallfields.

3. Cars are randomly generated on roads according to tem-poral traffic density variations but with uniform spatialdensity considering different sensor equipment rates.



4. Point precipitation time series are extracted for the mov-ing car networks from the radar rainfall fields consider-ing the discrete observation ability of the car sensors.Rainfall from that raster cell in which the gauge is lo-cated or which the car is just crossing at the observationtime interval is taken as observed point value.

5. The point rainfall time series from the gauge net-work are interpolated using ordinary kriging (OK) on a1 km× 1 km raster for the whole study area and are sub-sequently aggregated over selected catchments to arealrainfall time series.

6. The point rainfall time series from the different car net-works are interpolated using ordinary kriging (OK), in-dicator kriging with 4 rainfall classes (IK4) and in-dicator kriging with 10 rainfall classes (IK10) on a1 km× 1 km raster each. Then they are subsequentlyaggregated over the selected catchments to areal rain-fall time series.

7. Error statistics are calculated by comparisons of theareal rainfall time series from gauge and car networkseach with the reference areal radar rainfall time seriesfor the selected catchments.

3 Study region and data

3.1 Study region

The study is carried out for the 3300 km2 Bode riverbasin located in the Harz Mountains in Northern Germany(Fig. 1). The considered Bode region has elevations between1140 m a.s.l. at the top of the Brocken Mountain and about80 m a.s.l. Mean annual rainfall varies between 1700 mm/yrand 500 mm/yr. Four mesoscale catchments of different sizesare selected for areal rainfall estimation, which comprise theTrautenstein (40 km2), the Selke (102 km2), the Holtemme(167 km2) and the Gr. Graben (812 km2) catchments. Thestationary rainfall observation network consists of 14 record-ing rain gauges with 6 stations operated all year and 8 sta-tions operated only during the summer time. The all yearstation network represents a typical recording rain gauge net-work density in Germany. In addition, a weather radar stationis located at Ummendorf covering the whole area within itsobservation range.

For the car networks road data from the topographic infor-mation system (here, the German ATKIS) are used, where theroads are given according to different road categories rangingfrom highways to side roads. In order to make conservativeestimations, only the highest road categories, namely high-ways and federal roads are considered here (see Fig. 1).

25

Figure 1. Study region showing the selected four catchments for the estimation of areal rain-

fall, the stationary raingauge network and the location of highways and freeways used for the

simulation of the car network

Fig. 1. Study region showing the selected four catchments for theestimation of areal rainfall, the stationary raingauge network andthe location of highways and freeways used for the simulation ofthe car network.

3.2 Traffic data

Traffic statistics were taken from a study related to noisepropagation (R.-D. Mummenthey, Trade Office Hildesheim,personal communication, September 2008). Table 1 showsthe traffic data which are used in this study. Assumed aver-age speed of the cars on major roads is 80 km/h. Three dif-ferent classes of traffic density with respect to different timesof the day are used. For simplification all traffic statisticaldata are applied uniformly within the whole study area. Thisis motivated by the fact, that only one type of road, namelymajor roads, are used neglecting all smaller roads. If otherroads were also included it would increase the spatial traf-fic variability but it would also further increase the potentialof the car network for improved rainfall estimation, i.e. ourassumptions are conservative (see also Sect. 4.1). Only a cer-tain fraction of all cars will be prepared to measure precip-itation. For that four different sensor equipment rates be-tween 0.5% and 4% are assumed here (see Table 1). Thewindscreen wipers are used as sensors to detect and measureprecipitation. The rainfall intensity can be derived from thewipers frequency. As currently there is no known relation-ship between the wiper frequency and the rainfall intensitysimple assumptions are made. The first one is to have anexact observation of the rainfall intensity as reference for po-tential maximum accuracy (case a. from Sect. 2.2). The otherassumptions are to use different rainfall observation classes,e.g. corresponding to the wiper frequency intervals that canbe manually set in the cars (case b. from Sect. 2.2).



Table 1. Traffic data used for car generation.

Road types Highways, Federal Roads

Velocity 80 km/h

Density Day (6 a.m.–5 p.m.) Evening (5 p.m.–10 p.m.) Night (10 p.m.–6 a.m.)1100 cars/h 700 cars/h 180 cars/h

Sampling rate 5 min

Sensor equipment rates 0.5%, 1%, 2%, 4%

3.3 Rainfall data

To provide reference rainfall fields for the simulation experi-ments radar data from the C-band instrument at Ummendorfare utilised. The data were provided by the German WeatherService (DWD) as raw reflectivities with a spatial polar res-olution of 1 km× 1◦ and a time discretisation of 5 min. Thereflectivities are converted into rainfall intensities applyingthe Marshall-Palmer Z-R relationship (Marshall and Palmer,1948)

Z = 200·R1.60, (14)

whereZ is the reflectivity in mm6/m3 andR the rainfall in-tensity in mm/h. The rainfall intensities are interpolated to a1 km× 1 km rectangular grid. Here a simple a nearest neigh-bour approach is used for those raster cells containing nomore than one radar point; otherwise the mean value fromall available radar points within a raster cell is taken. Theradar data have been corrected for attenuation and clutter er-rors (Kramer, 2008), although this was not really necessaryfor this exercise. A bias correction of the radar data e.g. usingthe observations has not been applied here.

The heavy summer storm lasting from 16 July 2002 to19 July 2002 has been selected for this analysis. It is charac-terised by high temporal and spatial rainfall variability with“observed” rainfall sums over the four days between 31 mmand 125 mm sampled at the 14 rainfall station locations fromthe radar fields. Rainfall data are used at a temporal reso-lution of 5 min for this analysis. Figures 2 and 3 illustratethe spatial and temporal variability of the event based on theradar precipitation data. Most rainfall occurs at the secondday of the event, however with a high temporal variability.Note also that there are quite pronounced differences be-tween the time series of areal rainfall for the four selectedcatchments. For further analyses only the time steps from 51to 700 of the event are considered (see Fig. 3), which coverthe most significant rainfall period.

26

16/07/2002

X

Y

0.0

5.0

10.0

15.0

20.0

25.017/07/2002

X

Y

0.0

20.0

40.0

60.0

80.0

100.

18/07/2002

X

Y

0.0

2.0

4.0

6.0

8.0

10.019/07/2002

X

Y

0.0

1.0

2.0

3.0

4.0

5.0

Figure 2. Spatial distribution of the reference radar rainfall in mm/d for the Bode river basin

accumulated over the four days of the storm event

Fig. 2. Spatial distribution of the reference radar rainfall in mm/dfor the Bode river basin accumulated over the four days of the stormevent.

27

0

0.3

0.6

0.9

1.2

1.5

50 150 250 350 450 550 650

Time step [5 min]

Rai

nfa

ll [m

m/5

min

]

Trautenstein

Selke

Holtemme

Gr. Graben

Figure 3. Time series of areal rainfall derived from the reference radar fields for the selected four catchments considering only the time period of the event with significant rainfall over the particular catchments between time steps 51 and 700

Fig. 3. Time series of areal rainfall derived from the reference radarfields for the selected four catchments considering only the time pe-riod of the event with significant rainfall over the particular catch-ments between time steps 51 and 700.



28

#

#

#

#

#

#

#

#

##

#

##

#

#

#

#

#

#

#

##

#

##

#

# #

#

#

#

#

#

##

#

#

#

#

##

#

#

#

#

#

#

#

#

##

#

#

#

#

#

#

#

#

##

#

#

#

#

#

#

#

#

#

#

#

# #

#

#

#

#

#

#

#

#

#

#

#

##

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

###

#

#

#

#

#

#

#

#

##

#

#

#

#

#

#

##

#

# #

#

#

##

#

##

#

#

#

#

#

# #

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

##

##

#

#

#

#

##

#

#

#

#

#

### ##

#

#

###

#

###

#

#

#

##

##

##

#

#######

##

#

#

##

#

#

#

#

#

###

#

#

#

#

#

#

##

#

##

#

##

#

#

#

#

#

#

##

#

#

#

#

#

##

#

#

#

#

###

#

#

#

###

#

##

##

###

#

#

##

#

#

#

#

#

##

#

#

#

#

##

#

#

##

###

##

#

#

####

##

#

#

#

#

##

##

#

#

##

###

#

#

#

#

#

#

##

#

#

#

#

##

#

##

##

####

##

#####

#

#

#

#

##

###

#

##

###

#

#

#

##

#

###

#

#

# #

#

#

#

#

#

#

#

#

#

#

###

#

#

#

#

##

##

#

###

#

#

####

##

##

#

#

#

##

#

#

#

#

##

#

##

#

#

#

###

#

##

#

#

##

#

######

##

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

##

#

##

##

#

##

##

#

#

#

#

#

## #

#

##

#

##

#

#

#

#

#

#

#

#

#

#

#

#

#

#

##

####

#

#

#

#

#

##

#

##

#

#

#

##

#

#

#

#

#

#####

#

#

###

#

#

#

##

###

##

#

#

####

#

##

##

#

#

##

#

#

##

#

#

#

#####

#

#

#

#

###

#

###

#

###

#

#

#

#

##

#

#

####

#

#

##

#

#

#

##

#

## #

#

#

#

##

###

#

#

##

#

####

#

##

##

#

#

#

#

##

#

##

#

###

#

#

#

##

#

####

#

#

#

#

#

##

#

#

#

#

#

####

#

#

#

#

##

#

#

#

#

#

##

###

##

#

#

#

#

##

#

#

#

#

#

#

#

#

####

#

##

#

#

#

####

#

#

#

#

##

#

#

#

#

#

#

#

#

##

#

#

#

###

#

#

#

##

#

###

#

#

#

##

#

##

#

#

#

#

#

#

####

#

#

##

#

#

#

##

#

#

#

#

#

#

##

#

#

#

#

###

###

#

#

#

#

###

#

#

#

#

#

#####

##

#

#

#

#

#

#

#

## ##

#

# ##

###

#

#

#

#

##

#

#

###

#

##

#

###

###

#

##

##

#

#

#

#

###

#

##

##

####

#

##

##

#

#

##

#

#

###

##

#

#

#

##

#

#

## #

#

#

#

#

#

#

###

#

###

#

#

#

#

#

##

#

###

###

#

# ####

#

#

#

#

#

#

#

#

##

##

#

#

#

##

##

#

######

#

##

##

#

#

#

#

##

#

##

#

#

##

#

#

#

#

##

#

#

#

#

#

##

#

#

##

##

#

#

#

#

##

##

##

#

#

##

#

##

#

##

#

#

#

###

#

#

# #

#

####

#

#####

##

#

#

#

#

#

#

#

#

##

#

#

#

#

#

#

#

#

###

#

#

#

#

#

#

#

#

#

#

###

###

##

#

#

#

#

#

#

#

#

#

#

##

##

#

#

#

#

#

##

#

#

##

# ####

#

##

##

#

#

##

#

#

#

##

##

##

#

#

#

####

#

####

###

##

#

##

#

#

#

#

##

##

#

#

##

#

#

#####

#

#

#

#

##

##

#

#

##

##

#

#

#

##

#

#

##

#

###

##

#

#

##

#

#

#

#

###

#

#

#

#

#

#

#

###

#

###

#

##

#

#

#

#

####

#

##

##

###

#

#

#

##

#

##

#

#

#

#

####

##

#

#

#

#

#

#

##

# #

#

#

#

#

#

#

###

#

##

#

#

##

#

##

#

#

#

###

##

#

#

#

#

#

#

###

#

##

##

#

#

#

##

#

###

####

##

#

#

#

#

##

#

##

#

#

#

#

#

####

##

#

#

#

#

###

#

#

#

#

#

#

#

#

#

#

#

#

##

#

#

#

#

#

#

#

#

##

#

#

#

##

# ##

#

#

#

#

#

#

#

#####

#

#

###

#

#

#

##

###

###

#

#

###

#

#

#

#

##

#

#

#

#

##

#

##

#

###

#

#

#

######

##

#

#

####

##

#

###

##

#

#

#

#

## #

#

##

#

## ##

###

#

#

#

#

##

#

###

#####

##

#

### ###

#

##

###

##

#

#

#

#

#

#

#

###

###

##

#

#

#

#

#

#

##

#

##

### ##

#

#

#

##

#

#

#

##

#

#

#

#

###

#### #

#

#

#

#

##

####

#

#

####

#

#

##

#

##

##

##

#

##

#

##

##

#

#

##

#

##

##

##

#

#

#

#

#

##

#

##

##

#

#

#

#

###

#

##

#

#

#

#

##

# #

#

###

#

# ##

##

#

######

###

##########

# ####

#

#

##

#

###### ##

##### ###

###

#

#######

#

###

##

##

#

#

#

#

###

##

##

#

#

###

####

#

#

## #

###

##

##

#

##

#

###

#

#

###

##

###

###

##

##

#

###

#

#

#

#

#

#

#

#

#

#

##

#

#

##

##

#

#

###

#

#

#

#

##

###

##

###

#

#

#

#

##

#

#

#

# ####

####

#

##

##

#

#

##

##

#

###

#

#

###

#

## #

###

## ##

#

##

#

#

#

##

#

#

#

#

#####

######

##

#

#######

#

##

#

##

#

##

####

#

###

# ## #

#

#

###

##

####

##

#

#

##

#

###

#

###

#

#

#

##

#

#

#

####

#

#

###

####

#

#

#

##

#

#

###

#

#

##

###

##

##

#

###

#

#

#

#

#

#

#

####

##

#

#

#

#

##

####

#

#

###

#

##

### #

####

#

#

#

#

#### #

#

######

####

##

########

##

#

#

#

#

####

#

#

#

#

#

##

#

#

#

#

#

#

#

# ##

#

#

#

###

#

#

##

#

#

#

###

#

#

##

#

#

##

#

#

### #

### #########

##

#

##

#

###

##

### #

#

##

##

#####

#

###

##### #

# #

##

#

#

#

###

##

###

#

#

#

###

##

#

##

#

##

####

##

##

#

#

## ##

##

## ##

#

#####

##

#

####

#

#### ##

#

## # #

#

######

#

#

###

#

#

#

#

#

#

####

#

#

######

##

####

#

#### ##### ##

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

##

##

# #

####

#

#

#

#

#

#

#

#

#

#

#

#

##

##

#

##

#

#

#

#

##

#

#

#

#

#

#

# #

#

#

#

#

###

#

#

#

#

##

#

#

# #

#

#

#

#

#

#

#

#

#

#

##

#

#

#

#

##

#

#

#

##

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

# # #

#

#

#

#

#

#

#

##

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

# #

#

#

#

#

##

#

#

#

#

#

# #

#

#

#

#

#

#

#

#

##

#

##

#

#

#

#

#

#

#

#

#

# #

##

#

#

#

#

###

##

#

#

##

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

##

##

# #

#

#

#

#

###

#

#

##

#

#

#

#

###

# #

#

#

#

#

#

#

##

#

##

#

#

##

#

#

#

#

#

#

#

#

##

#

#

#

## #

#

#

##

##

##

#

#

#

#

#

#

#

#

##

#

#

#

##

###

#

#

#

#

##

##

#

#

#

##

#

##

#

#

##

#

#

#

#

#

#

#

#

##

#

#

#

#

# #

#

# # #

#

## #

#

##

#

#

##

#

#

#

#

#

#

#

#

#

##

#

##

#

#

###

##

#####

#

##

##

#

##

#

#

# #

# #

#

####

#

#

##

Figure 4: Example for car distributions considering traffic with a sensor equipment rate of 1% on the road network during day (upper row) and night (lower row). On the left is the situation at one particular sampling time (5 min time step), on the right is the information of an accu-mulated sampling result of one hour.

Fig. 4. Example for car distributions considering traffic with a sen-sor equipment rate of 1% on the road network during day (upperrow) and night (lower row). On the left is the situation at one partic-ular sampling time (5 min time step), on the right is the informationof an accumulated sampling result of one hour.

4 Application and results

4.1 Car networks

Figure 4 shows examples of the distribution of cars consid-ering a sensor equipment rate of 1% during day and night atone time step and accumulated over 1 h, respectively. Thedifferent car densities between day and night time are clearlyvisible. The figure also suggests that with a dynamic networkthe number of observation points in space can be virtuallyincreased if measurements are integrated over time. Assum-ing that the change of the car locations with time (i.e. thespeed of the cars) is greater than the change of the rainfallintensity with time at one location a moving network wouldprovide advantages compared to a stationary network of thesame density. In fact one car could measure rainfall at severallocations before the rainfall intensity changes.

If the roads are now travelled by cars equipped with rainsensors at a rate of 1% and rainfall is sampled every 5 min,the absolute car densities for the Bode river basin can be cal-culated as given in Table 2. The values in this table are theresult of empirical counting of discrete car positions in thewhole area within a time interval of one hour for three timephases of the day (day, evening, night). The values in the sec-ond column are computed by normalizing the first values bythe whole area, resulting in an average car position densityper hour and km2. For different equipment rates the valuesin Table 2 have to be multiplied with these rates. Note, thatthe figures in Table 2 are in fact the number of car locations(and not the number of cars) counted within one hour for adiscrete observation time interval of 5 min. The difference is

Table 2. Number of cars (i.e. number of car positions accumulatedover 5 minute intervals per hour) for the whole Bode river basinconsidering highways and federal roads and a sensor equipment rateof 1%.

Time of day Absolute numberof cars [h−1]

Specific numberof cars [h−1 km−2]

Day (6 a.m.–5 p.m.)Evening (5 p.m.–10 p.m.)Night (10 p.m.–6 a.m.)

21741423360

0.660.430.11

visualized in Fig. 4, where on the left panels the real numberof cars is shown and on the right panels the integration of carpositions used for observations over one hour.

Only the highways and federal roads having a total lengthof about 1300 km within the Bode river basin are used inthis study. To the minor roads, which are not consideredhere, belong the state and district roads with a total lengthof 3100 km as well as the side roads with a total length of10 300 km. Those figures give an impression what potentialwould be available additionally for measuring rainfall withcar networks in this region.

4.2 Rainfall sampling and variogram inference

Rainfall for the stationary gauge and moving car networksis sampled every 5 min from the reference radar field fromthose raster cells were rain gauges and cars, respectively, arelocated (cp. Fig. 1, Fig. 4). For the stationary gauges an ex-act rainfall measurement without errors is postulated. Forrainfall observations by cars imprecision is assumed, whichis related to various factors e.g. a restricted number of wind-screen wiper frequency classes, non-unique features for dif-ferent car types, calibration uncertainties etc. This is takeninto account by a limited number of rainfall classes for whichthe sampling can be made. Rainfall observations based on 4classes, corresponding to less accurate measurements (“moreold fashioned cars”) and 10 classes, corresponding to ratherprecise measurements (“more modern cars”) are analysedhere. The definition of the rainfall intervals has been donehere quite subjectively based on simple assumptions aboutwiper frequencies and a rough examination of several ob-served storms in the Bode region. Table 3 lists the assumedrainfall ranges for the two classification schemes.

Prior to the application of the geostatistical interpolationmethods variograms have to be estimated, which characterisethe spatial variability of the rainfall fields. The variogramsare inferred here a priori from the radar data. This is a certainsimplification as the radar data represent the truth, which isusually not known. However, since the focus of the analysisis on relative comparisons of the performance between thestationary gauge network and different dynamic car networks



Table 3. Rainfall discretisation into classes, thresholds used for interpolation with indicator kriging (IK) and corresponding variogramparameters. For ordinary kriging (OK) the variogram No. 0 without threshold is applied. The upper bounds are included in the classes.

No Classes for IKwith 10 intervals[mm/5 min]

Classes for IKwith 4 intervals[mm/5 min]

Threshold[mm/5min]

Nugget[–]

Sill[–]

EffectiveRange[km]

012345678910

–0.00.0 – 0.10.1–0.30.3–0.50.5–1.01.0–1.51.5–2.02.0–3.03.0–4.04.0–5.0

–0.0––0–0.5––0.5–2.02.0–5.0

None0.00.10.30.51.01.52.0

0.00.10.10.10.10.10.10.1

1.10.90.90.950.90.80.650.35

3060302012865

29

γ

Distance [km]

Original variable

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.40

0.80

1.20

γ

Distance [km]

Threshold 1: alpha=0.0

0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.40

0.80

1.20

γ

Distance [km]


0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.40

0.80

1.20

γ

Distance [km]


0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.40

0.80

1.20

γ

Distance [km]


0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.40

0.80

1.20

γ

Distance [km]


0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.40

0.80

1.20

γ

Distance [km]


0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.40

0.80

1.20

γ

Distance [km]


0.0 10.0 20.0 30.0 40.0 50.0 60.00.00

0.40

0.80

1.20

Figure 5. Average standardized variogram of the original variable rainfall and indicator variograms for 7 rainfall thresholds given in mm/5min estimated from observed radar data

Fig. 5. Average standardized variogram of the original variable rainfall and indicator variograms for 7 rainfall thresholds given in mm/5 minestimated from observed radar data.

and the variograms are used uniquely for both networks thisis tolerable.

Average experimental variograms are calculated based onEq. (5) for rainfall as continuous variableZ(u) and for dif-ferent rainfall indicator variablesIαk(u) with k = 1,...,K.For the estimation of the indicator variograms radar rainfallis discretised into seven classes taking into account the pre-defined rainfall observation intervals. The combination of anugget effect with an exponential model is fitted manually toall experimental variograms. Figure 5 shows the experimen-

tal and fitted theoretical variograms forZ(u) andIαk(u) forall selected thresholds. Table 3 lists the estimated variogramparameters and indicates which variograms are used for OKand for IK considering either 4 classes or 10 classes. Com-paring the indicator variograms it can be seen that the rangebut also the sill decrease with increasing rainfall thresholds.Larger rainfall intensities have smaller extent which explainsthe decreasing range. For the highest thresholds there areonly a few observed values beyond the threshold, which ex-plains the low variance. For that reason variograms with



30

0

0.2

0.4

0.6

0.8

1

50 150 250 350 450 550 650

Time step [5 min]

Ra

infa

ll [

mm

/5m

in] true

stats_OK

0

0.2

0.4

0.6

0.8

1

50 150 250 350 450 550 650

Time step [5 min]

Ra

infa

ll [

mm

/5m

in] true

cars_IK4

0

0.2

0.4

0.6

0.8

1

50 150 250 350 450 550 650

Time step [5 min]

Ra

infa

ll [

mm

/5m

in] true

cars_IK10

0

0.2

0.4

0.6

0.8

1

50 150 250 350 450 550 650

Time step [5 min]

Ra

infa

ll [

mm

/5m

in] true

cars_OK

Figure 6. Areal rainfall time series for the Gr. Graben catchment estimated from the stationary gauge network using ordinary kriging (stats_OK) and estimated from the car network with 4% sensor equipment rate using indicator kriging with 4 rainfall classes (cars_IK4), using IK with 10 rainfall classes (cars_IK10) and using OK without rainfall classification (cars_OK). Reference areal rainfall is from radar data (true).

Fig. 6. Areal rainfall time series for the Gr. Graben catchment estimated from the stationary gauge network using ordinary kriging (statsOK)and estimated from the car network with 4% sensor equipment rate using indicator kriging with 4 rainfall classes (carsIK4), using IK with10 rainfall classes (carsIK10) and using OK without rainfall classification (carsOK). Reference areal rainfall is from radar data (true).

31

0

0.3

0.6

0.9

1.2

1.5

50 150 250 350 450 550 650Time step [5 min]

Ra

infa

ll [

mm

/5m

in] true

stats_OK

0

0.3

0.6

0.9

1.2

1.5

50 150 250 350 450 550 650Time step [5 min]

Ra

infa

ll [

mm

/5m

in] true

cars_IK4

0

0.3

0.6

0.9

1.2

1.5

50 150 250 350 450 550 650

Time step [5 min]

Ra

infa

ll [

mm

/5m

in] true

cars_IK10

0

0.3

0.6

0.9

1.2

1.5

50 150 250 350 450 550 650

Time step [5 min]

Ra

infa

ll [

mm

/5m

in] true

cars_OK

Figure 7. Areal rainfall time series for the Holtemme catchment estimated from the stationary gauge network using ordinary kriging (stats_OK) and estimated from the car network with 4% sensor equipment rate using indicator kriging with 4 rainfall classes (cars_IK4), using IK with 10 rainfall classes (cars_IK10) and using OK without rainfall classification (cars_OK). Reference areal rainfall is from radar data (true).

Fig. 7. Areal rainfall time series for the Holtemme catchment estimated from the stationary gauge network using ordinary kriging (statsOK)and estimated from the car network with 4% sensor equipment rate using indicator kriging with 4 rainfall classes (carsIK4), using IK with10 rainfall classes (carsIK10) and using OK without rainfall classification (carsOK). Reference areal rainfall is from radar data (true).

higher thresholds thanα = 2.0 mm/5 min are not estimated.For interpolation of indicator variables with higher thresh-olds the last estimated indicator variogram is then applied(see Table 3).

4.3 Comparisons of areal rainfall estimation

Figures 6 and 7 show exemplarily areal rainfall time seriesfor the Gr. Graben and the Holtemme catchments estimatedfrom the rain gauge network and the car network with 4%

sensor equipment rate. For the 800 km2 large Gr. Grabencatchment the areal rainfall estimation using the stationaryrain gauge network is poor. All approaches employing thecar network provide significantly better areal rainfall esti-mation. This is not surprising considering that no station-ary gauges are available within the basin boundaries for thatcatchment. For the Holtemme catchment areal rainfall esti-mation from the car network using IK4 provides slightly bet-ter results compared to the estimation from the rain gauge



32

Selke

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

4 2 1 0.5

Sensor equipment rate [%]

RS

E [

-]

0

20

40

60

80

100

120

140

160

Ds

ub [

10

-3 k

m-2

]

Holtemme

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

4 2 1 0.5


RS

E [

-]

0

20

40

60

80

100

120

140

160

Ds

ub [

10

-3 k

m-2

]

Gr. Graben

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

4 2 1 0.5


RS

E [

-]

0

20

40

60

80

100

120

140

160

Ds

ub [

10

-3 k

m-2

]

Trautenstein

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

4 2 1 0.5


RS

E [

-]

0

20

40

60

80

100

120

140

160

Ds

ub [

10

-3 k

m-2

]

Figure 8. Performance of areal rainfall estimation from the rain gauge network (horizontal red line) and from the 4 car networks with different sensor equipment rates (bars). For interpola-tion of the car rainfall observations IK4 (heavy dotted bars), IK10 (medium dotted bars) and OK (light dotted bars) are used. In addition the average network densities Dsub for the station network (blue triangles) and the car networks (blue squares) for each subbasin are provided.

Fig. 8. Performance of areal rainfall estimation from the rain gauge network (horizontal red line) and from the 4 car networks with differentsensor equipment rates (bars). For interpolation of the car rainfall observations IK4 (heavy dotted bars), IK10 (medium dotted bars) and OK(light dotted bars) are used. In addition the average network densitiesDsub for the station network (blue triangles) and the car networks (bluesquares) for each subbasin are provided.

network. Using IK10 however improves significantly theareal rainfall estimation. OK used as reference method as-suming no errors in rainfall observation from car observato-ries gives here only an additional rather small improvement.

In Table 4 all calculated performance measures for arealrainfall estimation are listed considering the four catchments,the different car sensor equipment rates and interpolationmethods. Table 5 shows the corresponding kernel densitycalculations of the networks. In addition, a visual com-parison of the relative standard errors for areal rainfall es-timation and the associated network densities is given inFig. 8. For the largest test catchment Gr. Graben all carnetworks perform significantly better compared to the sta-tion network no matter what sensor equipment rate or inter-polation approach is used. The error from the station net-work is highest (RSE = 0.66) and the station density is low-est (Dsub= 0.6) compared to the other catchments. For thesmallest catchment Trautenstein the error from the stationnetwork (RSE = 0.6) is still almost always higher than the er-rors from the car networks, which is also related to a very lowstation density (Dsub= 1.5). For the Holtemme catchmentthe error from the station network is smaller (RSE = 0.34) asconsequence of a higher rain gauge density (Dsub= 7.7). Forthat catchment, the car networks perform better only for thelarger sensor equipment rates of 2% and 4% although thecar network density is always superior compared to the sta-tion density. The car network for the Selke catchment canhardly do better than the traditional rain gauge network al-though the average car density is higher for all sensor equip-

ment rates which are greater or equal to 1%. One reasonfor that could be that the locations of the rain gauges in theSelke basin are optimal compared to the locations of the cars,which are forced on roads with possibly disadvantageous po-sitions e.g. in valleys.

From Table 4 it can bee seen, that the bias for the indicatorapproaches is usually higher compared to OK. This comeslikely from the suboptimal rainfall classification, required bythe fixed rainfall observation classes e.g. according to thewiper frequencies. This rainfall discretisation does neitherguarantee an equal number of values per class nor an equaldistribution of the values within the classes. Especially themaximum limit of the highest interval is a critical assump-tion (cp. Table 3). All this leads to a biased estimation of themean value from the cumulative distribution function, whichhas been obtained from the interpolation of the indicators us-ing Eq. (8). This bias decreases usually with increasing num-ber of classes (cp. results for IK4 and IK10 in Table 4).

Cars can only travel on roads. So the car precipitation net-work is restricted to roadways. Considering the preferred lo-cation of road lines e.g. in valleys and the relation of rainfallto elevation (i.e. on average higher rainfall for higher loca-tions) the car network forced on roads might e.g. underesti-mate precipitation. For that reason one additional computerexperiment is carried out generating cars anywhere withinthe catchment area ignoring roadways. The results are shownexemplarily for two sensor equipment rates in Fig. 9. It be-comes clear, that a random positioning of the cars within thecatchments does not improve the estimation performance for



Table 4. Performance of areal rainfall estimation based on the rain gauge network (Stations) and the car networks (Cars) with differentsensor equipment rates (SER) in comparison with the radar reference rainfall. For interpolation ordinary kriging (OK) and indicator kriging(IK) with 4 and 10 rainfall classes are used. All values between time steps 51 and 700 with reference rainfall intensity greater or equal to 0.1mm/5min are considered for error calculations.

Stations OK Cars IK4 Cars IK10 Cars OK

SER[%]

Bias[mm]

RSE[–]

Cor[–]

Bias[mm]

RSE[–]

Cor[–]

Bias[mm]

RSE[–]

Cor[–]

Bias[mm]

RSE[–]

Cor[–]

Catchment Trautenstein (39 km2)

4210.5

−6.7−6.7−6.7−6.7

0.600.600.600.60

0.580.580.580.58

15.112.113.512.0

0.490.500.560.63

0.870.800.780.69

−5.9−7.7−6.0−6.7

0.220.340.370.46

0.960.900.870.80

0.0−1.4−0.7−3.2

0.150.300.350.44

0.980.910.870.81

Catchment Selke (102 km2)

4210.5

0.10.10.10.1

0.230.230.230.23

0.950.950.950.95

16.917.114.515.8

0.460.560.540.60

0.900.800.780.76

−4.7−4.8−4.5−3.1

0.220.350.380.42

0.960.880.860.81

−0.9−0.90.40.4

0.150.330.300.44

0.980.890.900.81

Catchment Holtemme (167 km2)

4210.5

−15.8−15.8−15.8−15.8

0.340.340.340.34

0.860.860.860.86

17.512.64.4–6.6

0.280.290.340.40

0.950.920.880.79

−10.3−15.2−20.2−28.1

0.180.250.340.44

0.970.940.890.82

−1.6−4.9−8.1−15.7

0.160.240.340.43

0.970.930.870.78

Catchment Gr. Graben (812 km2)

4210.5

−4.1−4.1−4.1−4.1

0.660.660.660.66

0.160.160.160.16

12.912.37.73.4

0.300.330.340.45

0.910.840.750.50

−6.9−7.2−10.7−13.3

0.180.230.320.47

0.950.890.800.52

−1.1−1.2−4.1−6.2

0.140.190.240.45

0.950.900.860.53

Table 5. Kernel network densitiesDsub for the stationary raingauge network (Stations) and averaged over time for the dynamiccar networks (Cars) for the four selected catchments consideringdifferent sensor equipment rates (SER).

Catchment DsubStations[10−3 km−2]

DsubCars with SER of[10−3 km−2]

4% 2% 1% 0.5%

TrautensteinSelkeHoltemmeGr. Graben

1.520.17.70.6

107.3127.6153.1124.7

53.964.477.362.0

28.431.538.331.0

13.317.119.315.4

areal rainfall. For the Selke basin even the opposite seemstrue. For those four catchments it can be concluded that usingthe roadways for measuring rainfall is not suboptimal com-pared to a pure random network of the same density. Still,this does not disprove the possibility that the existent station

locations are optimal compared to a random distribution ofgauges.

The error for areal rainfall estimation from the car net-works seems not strongly related to the catchment size atleast for considering the interpolation approaches IK10 andOK. The interpolation based on only 4 rainfall intervals usingIK4, however, tends to give smaller estimation errors for thetwo larger catchments, Gr. Graben and Holtemme, comparedto the two smaller ones, Selke and Trautenstein. Althoughfor the largest basin (Gr. Graben) IK4 produces higher errorscompared to the second largest basin (Holtemme).

Figure 10 shows the absolute number of cars together withobserved and estimated areal rainfall time series for the Selkebasin. It becomes clear, that there is a high variability in thecar network density with changing levels for day, eveningand night times. The figure shows also, that the car networkdensity is poor for the largest peak of the event (during nighttime) which leads to a significant underestimation of rainfall.This could also contribute to the superiority of the actual sta-tion network in this catchment.



33

Figure 9. Relative standard errors for areal rainfall estimation using OK interpolation with regular moving cars on roads (heavy dotted) and randomly redistributed cars (light dotted) for two sensor equipment rates

0.5% Sensor equipment rate

0

0.2

0.4

0.6

0.8

Selke Holtemme Gr. Graben Trautenstein

RS

E [

-]

2% Sensor equipment rate

0

0.2

0.4

0.6

0.8

Selke Holtemme Gr. Graben Trautenstein

RS

E [

-]

Fig. 9. Relative standard errors for areal rainfall estimation usingOK interpolation with regular moving cars on roads (heavy dotted)and randomly redistributed cars (light dotted) for two sensor equip-ment rates.

34

Figure 10: Absolute number of cars (no. of cars) generated on roads in the Selke catchment with 4% sensor equipment rate in comparison with time series of observed (true) and esti-mated areal rainfall (cars_ik10)

0

10

20

30

40

50

60

50 150 250 350 450 550 650

Time step [5 min]

Nu

mb

er o

f c

ars

[-]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Rai

nfa

ll [m

m/5

min

]

no. of cars true cars_ik10

Fig. 10. Absolute number of cars (no. of cars) generated on roadsin the Selke catchment with 4% sensor equipment rate in compari-son with time series of observed (true) and estimated areal rainfall(carsik10).

5 Summary and conclusions

The main objective of this paper was to present a new ap-proach for rainfall observation. The idea was to considermotorcars as moving rain gauges with windscreen wipers assensors to detect precipitation. This study has explored the-oretically the benefits of such an approach. A simple traf-fic model was applied to generate motorcars on roads in the3300 km2 Bode river basin. Rainfall from radar data fieldswere sampled with a conventional rain gauge network andwith several dynamic networks consisting of moving motor-

cars. Calculated areal rainfall for four different catchmentsusing ordinary kriging and indicator kriging was comparedagainst the reference values from radar observations. Themain results can be summarised as follows:

1. In general, the idea of using cars as rain gauges is theo-retically feasible and would improve the assessment ofareal rainfall compared to stationary gauge networks.

2. The error for areal rainfall estimation depends on thenetwork density and decreases with growing number ofcars. Considering the current traffic density obtainedfrom statistical data a small sensor equipment rate be-tween 0.5 and 4% was sufficient for areal rainfall es-timation in the selected mesoscale catchments of theBode river basin.

3. The imprecision in rainfall observation by the cars canbe considered in areal estimation using indicator krig-ing based on rainfall classes. For the Gr. Graben and theTrautenstein catchments even as little as 4 discrete inter-vals for rainfall observation provide better areal rainfallestimation then the stationary gauge network with con-tinuous observations. Using 10 rainfall intervals givesoften almost as good results as with assumed continu-ous rainfall observation by the car network.

4. A problem with the imprecision of rainfall observationusing cars is the prior definition of suitable rainfall inter-vals according to the expected range of the event. Thisleads likely to an additional bias in rainfall estimation.

5. A simulation study has shown that locations of the mainroads have no disadvantageous effect on the position ofcars regarding rainfall observation compared to a the-oretical random distribution of cars in space with thesame network density.

6. The results for the Selke catchment indicate that theremight be optimal positions for rain gauges which reducethe required network density significantly compared toan arbitrary location of the gauges.

For this pilot study valid relationships between wiper speedand rainfall rate were assumed considering the point obser-vation error only in a very simple way. So, the focus of thestudy was on interpolation uncertainty given different net-work densities (e.g. how many cars are needed) and regard-ing the required discretisation of the rainfall sensors in cars.In order to quantify point measurement errors using the carsas rain gauges and to confirm assumed discretisation accura-cies for car rainfall observations practical experiments haveto be carried out in the next step.

Future investigations should also consider different rain-fall events, other regions and complete road networks to fur-ther test the presented ideas. Especially higher samplingrates for the cars and the integration of observations over time



need to be explored. The findings also suggest a revisitingof the rain gauge network optimisation problem. Future re-search might also consider a merging of rainfall informationfrom the three sources radar, stations and cars. Eventually,practical feasibility studies are required to answer questionsabout applicability of the ideas in praxis.

Acknowledgements.The authors thank the German WeatherService (DWD) for providing the meteorological data and theassociate editor as well as three anonymous referees for theirhelpful and critical comments to improve the paper.

Edited by: A. Shamseldin

References

Chiang, Y.-M., Hsu, K.-L., Chang, F.-J., Hong, Y., and Sorooshian,S.: Merging multiple precipitation sources for flash flood fore-casting, J. Hydrol., 340, 183–196, 2007.

Deutsch, C. V. and Journel, A. G.: GSLIB: Geostatistical softwarelibrary and user’s guide, Oxford University Press, New York,340 pp., 1992.

Ehret, U., Gotzinger, J., Bardossy, A., and Pegram, G. G. S.: Radar-based flood forecasting in small catchments, exemplified by theGoldersbach catchment, Germany, Intl. J. River Basin Manage-ment, 6, 323–329, 2008.

EUROSTAT: European Commission Statistics Database,http://epp.eurostat.ec.europa.eu, last access: 2 May 2009.

Goovaerts, P.: Geostatistics for natural resources evaluation, OxfordUniversity Press, New York, Oxford, 483 pp., 1997.

Goovaerts, P.: Geostatistical approaches for incorporating elevationinto the spatial interpolation of rainfall, J. Hydrol., 228, 113–129,2000.

Goudenhoofdt, E. and Delobbe, L.: Evaluation of radar-gaugemerging methods for quantitative precipitation estimates, Hy-drol. Earth Syst. Sci., 13, 195–203, doi:10.5194/hess-13-195-2009, 2009.

Grimes, D. I. F. and Diop, M.: Satellite-based rainfall estimationfor river flow forecasting in Africa. I: Rainfall estimates and hy-drological forecasts, Hydrol Sci. J., 48, 567–584, 2003.

Haberlandt, U.: Geostatistical interpolation of hourly precipitationfrom rain gauges and radar for a large-scale extreme rainfallevent, J. Hydrol., 332, 144–157, 2007.

Hasse, L., Grossklaus, M., Uhlig, K., and Timm, P.: A Ship RainGauge for Use in High Wind Speeds, J. Atmos. Ocean. Tech., 15,380–386, 1998.

Isaaks, E. H. and Srivastava, R. M.: Applied Geostatistics, OxfordUniversity Press, New York, 1989.

Journel, A. G.: Non parametric estimation of spatial distributions,Math. Geol., 15, 445–468, 1983.

Krajewski, W. F. and Smith, J. A.: Radar Hydrology: rainfall esti-mation, Adv. Water Resour., 25, 1387–1394, 2002.

Kramer, S.: Quantitative Radardatenaufbereitung fur die Nieder-schlagsvorhersage und die Siedlungsentwasserung, Mitteilun-gen, Heft 92, Inst. of Water Resources Management, LeibnizUniversity of Hannover, Hannover, 391 pp., 2008.

Leijnse, H., Uijlenhoet, R., and Stricker, J. N. M.: Rain-fall measurement using radio links from cellular com-munication networks, Water Resour. Res., 43, W03201,doi:03210.01029/02006WR005631, 2007.

Marshall, J. S. and Palmer, W. M.: The distribution of raindropswith size, J. Meteorol., 9, 327–332, 1948.

Matheron, G.: The Theory of Regionalized Variables and its Appli-cations, Les Cahiers du Centre de Morphologie Mathematique,Fasc. 5, 1971.

Messer, H., Zinevich, A., and Alpert, P.: Environmental Monitor-ing by Wireless Communication Networks, Science, 312, p. 713,doi:10.1126/science.1120034, 2006.

Seo, D.-J., Krajewski, W. F., and Bowles, D. S.: Stochastic in-terpolation of rainfall data from raingages and radar using co-kriging: 1. Design of experiments, Water Resour. Res., 26, 469–477 (489WR02984), 1990.

Silverman, B. W.: Density estimation for statistics and data analy-sis, Chapman and Hall, London, 1986.

Smith, J. A., Baeck, M. L., Meierdiercks, K. L., Miller, A. J.,and Krajewski, W. F.: Radar rainfall estimation for flash floodforecasting in small urban watersheds, Adv. Water Resour., 30,2087–2097, 2007.

Stefanidis, A. and Nittel, S.: GeoSensorNetworks, CRC Press,Boka Raton, Florida, 2004.

Wardah, T., Abu Bakar, S. H., Bardossy, A., and Maznorizan, M.:Use of geostationary meteorological satellite images in convec-tive rain estimation for flash-flood forecasting, J. Hydrol., 356,283–298, 2008.

Yuter, S. E. and Parker, W. S.: Rainfall Measurement on Ship Re-visited: The 1997 PACS TEPPS Cruise, J. Appl. Meteorol., 40,1003–1018, 2001.


http://epp.eurostat.ec.europa.eu

http://epp.eurostat.ec.europa.eu

areal rainfall estimation using moving cars as rain … · ﬁelds is sampled with a conventional...

Documents