Urban run-off volumes dependency on rainfall measurement method - Scaling properties of precipitation within a 2x2 km radar pixel L. Pedersen 1 *, N. E. Jensen 2, M. R. Rasmussen 3 and M. G. Nicolajsen 4 1 NIRAS Water and Sanitation, Consulting Engineers and Planners A/S, Vestre Havnepromenade 9, DK-9 Aalborg, Denmark 2 DHI Water & Environment, Science Park, Gustav Wieds Vej 1, DK-8 Aarhus C, Denmark 3 Aalborg University, Department of Civil Engineering, Hydraulic and Coastal Engineering, Sohngaardsholmsvej 57, DK-9 Aalborg, Denmark 4 The Municipality of Aalborg, Wastewater Department, Stigsborg Brygge 4, DK-94 Noerresundby, Denmark *Corresponding author, e-mail lip@niras.dk ABSTRACT Urban run-off is characterized with fast response since the large surface run-off in the catchments responds immediately to variations in the rainfall. Modeling such type of catchments is most often done with the input from very few rain gauges, but the large variation in rainfall over small areas suggests that rainfall needs to be measured with a much higher spatial resolution (Jensen and Pedersen, 24). This paper evaluates the impact of using high-resolution rainfall information from weather radar compared to the conventional single gauge approach. The radar rainfall in three different resolutions and single gauge rainfall was fed to a MOUSE run-off model. The flow and total volume over the event is evaluated. KEYWORDS MOUSE; Precipitation measurements; rainfall; spatial distribution; weather radar; urbanrunoff. INTRODUCTION Rainfall data used in connection with modeling of urban catchments is usually from rain gauges, but since rain gauges only measure over a very small area (less than hundred cm 2 ) the approach induces a large element of uncertainty. The spatial variability is most important when single rain events are being modeled due to the fact that spatial variability is large when relatively short time scales are considered [Jensen and Pedersen, 24]. The spatial variability of rainfall therefore becomes an important factor when run-off from urban catchments is being modeled since the concentration time of the catchment is of the same order of magnitude as the duration of the design rainfall event. In 23-24 an experimental study showed that even within a relatively small area of 5x5 meters the spatial variability of rainfall was so large that the rainfall could not be regarded as uniformly distributed and thereby could not be represented by one point measurement [Jensen and Pedersen, 24]. The same tendency was found by Goodrich et. al (1995), that states that the normal assumption of spatial rainfall uniformity in relatively small areas (5 ha) is invalid. Pedersen et al. 1
To measure rainfall with a resolution fine enough to intercept the spatial variability at small scales, an unrealistic high number of rain gauges would be necessary. A solution to this problem could be the application of a Local Area Weather Radar (LAWR) rainfall radar. The LAWR radar type is typically capable of operating with pixel sizes of 5x5 meter, 25x25 meter and 1x1 meter as illustrated on figure 1. The LAWR pixel sizes are shown in relation to a pixel size of 2x2 km used by normal weather radars. In figure 1 a rain event is shown to illustrate the problem with rain gauges because the rain event is capable of passing over large parts of an urban catchment without being intercepted by rain gauge. Figure 1 A scale indication: 1x1 m pixel superimposed on the city of Frejlev, near Aalborg, Denmark. The drainage system is indicated on top of the map with black. North is up. In order to analyse the impact that the distribution of rainfall has to run-off from an urban catchment, the LAWR data has been applied to an existing well-tested MOUSE model of a typical small Danish village. In this case an existing MOUSE model of Frejlev was used (Frejlev is a suburb with approximately 25 inhabitants). The sewage system is a combination of combined and separate sewers and has only one outlet to the north of the village to the intercepting sewer. Just before the intercepting sewer there is a weir. In order to test a well-tested MOUSE model with verified radar rainfall, the MOUSE model has been placed at the site where the variability measurements in Jensen and Pedersen (24) were conducted. Due to this transplant, the results can only be regarded relatively. The topographic conditions at the two sites are very similar. 2 Urban run-off volumes dependency on rainfall measurement method
The hydrographs presented in this paper are extracted from the pipe just upstream the weir, marked in figure 1 as extraction point. METHOD At the Frejlev site two rain gauges normally would have been available, but not in this case since the data has been moved. Instead radar data from the corresponding 1 x 1 m cells are used as point measurements. The point measurements established in this way would tend to underestimate peak intensities due to the fact that a radar measurement reflects the average of rainfall over the pixel area compared to the area of a rain gauge. In order to analyse the effect of applying distributed rain to an urban run-off model compared to the normal approach with rain gauges the run-off hydrographs and the accumulated outflow are compared based on the LAWR and the rain gauges, respectively. Rainfall measured with LAWR The rainfall used in this paper was measured with the Søsterhøj Radar located south of Århus in the period 17 th -18 th of November 24. Two separate rainfall events have been used for analysing the consequences of using a small number of rain gauges to simulate urban run-off, cf. table 1. The spatial variability is expressed with the fractional standard deviation, which expresses the standard deviation in form of percent of the mean. The >1 % variation also found in other events from this site (Jensen and Pedersen, 24) is also found in this event (see figure 3 5: 5 mm accumulated in the lower left compared to 1 mm in the upper right). A large fractional standard deviation value for a rainfall event indicates that the spatial variability is large. The fractional standard deviation, δ is a measure of the dispersion of the sample variables and is defined as (Ayyub and McCuen, 1997): n n 2 1 = = 2 1 x i x i n 1 i 1 n S i 1 δ = = (1) n X 1 x i n i= 1 S: Standard deviation, which is the square of the variance X : Mean x i : Sample n: Number of samples Table 1 Rainfall data for event I and II. Event I Event II Start 17.11.24 1.45 17.11.24 2.35 Stop 17.11.24 16.5 18.11.24 6.45 Measuring resolution [meters] 5x5 25x25 1x1 5x5 25x25 1x1 Minimum precipitation [mm] 2.24 2.4 1.95 5.57 5.6 4.9 Maximum precipitation [mm] 3.55 3.81 3.92 8.49 8.82 9.2 Mean precipitation [mm] 2.7 2.82 2.9 6.61 6.74 6.89 Fractional Standard Deviation [% ] 16.65 22.19 23.63 13.68 18.66 2.1 Pedersen et al. 3
As shown in table 1 the fractional standard deviation is increasing with decreasing measuring scale and thereby illustrating that the spatial scale of rainfall is smaller than the 2x2 km measuring area offered by traditional weather radars. The variability within a 5x5 meter LAWR pixel was determined in 23-24 using 9 high resolution optical rain gauges to be in the order of 25-3 % and sometimes considerably higher if individual rain events were considered (Pedersen, 24). This states that rainfall measured over a 2x2 km surface cannot be regarded as uniform and it is therefore highly uncertain to use one rainfall measurement for representing an area of this size. This goes for both the use of traditional weather radar and the traditional use of one single rain gauge for measuring the rainfall for a whole town or a several square kilometers large area if the temporal scale is in the order of hours or days. To illustrate the spatial distribution within a 2x2 km area different measuring resolutions of the LAWR are compared with data from Event II. Each pixel can be regarded as a synthetic rain gauge. The accumulated rainfalls measured with the LAWR with the three possible pixel resolutions are shown in figure 3 to 5 for event II. For comparison the mean values are shown in figure 2. The mean value corresponds to the resolution of a traditional weather radar and the assumed distribution if a rain gauge is used. Figure 2 Mean value of event II within a 2x2 area. Figure 3 Distribution of accumulated rainfall in event II within a 2x2 area on basis of LAWR-5 data. Figure 4 Distribution of accumulated rainfall in event II within a 2x2 area on basis of LAWR-25 data. Figure 5 Distribution of accumulated rainfall in event II within a 2x2 area on basis of LAWR-1 data. 4 Urban run-off volumes dependency on rainfall measurement method
Rainfall measured with rain gauges In order to compare run-off based on distributed rainfall and run-off based on point measurements (rain gauge), the time series from the two 1x1 meter pixels overlaying the location of the two rain gauges in Frejlev (see figure 6) has been extracted for events I and II and are used for modelling run-off on the basis of point measurements. This approach will make the rain gauges more representative for the area since they represents 1, m 2 compared to the normal few cm 2 found on real-lift rain gauges. Figure 6 The drainage system in Frejlev with the 1x1 meter pixel grid overlay. The two hatched pixels are used to extract rain gauge time series. The time series from the two rain gauges for the two events are shown in figure 7 and figure 8..9 Rainfall from North "gauge" Rainfall from South "gauge".9 Rainfall from North "gauge" Rainfall from South "gauge".8.8.7.7.6.6 Rainfall [µ m s -1 ].5.4 Rainfall [µ m s -1 ].5.4.3.3.2.2.1.1 9: 12: 15: 18: Event I 17 th of November 24 Figure 7 Rainfall from the North and South gauge from event I. 18: 21: : 3: 6: 9: Event II 17-18 th of November 24 Figure 8 Rainfall from the North and South gauge from event II. The differences in the North and the South gauge in figure 7 and 8 are due to the before mentioned spatial variability. It should be remarked that this tendency also has been observed in data from real rain gauge placed even close together; less than 2 m (Pedersen, 24). Pedersen et al. 5
MOUSE configuration The MOUSE simulations of surface run-off have been performed with use of the default Time-Area curve and default parameter set. The pipe flow computation is based on the full dynamic equation. The Frejlev model consists of 31 catchments which all are well defined with a catchment area, the number of inhabitants and impervious area. The catchment data are based on maps, physical observations and data from the municipality of Aalborg. RESULTS AND DISCUSSION The run-off hydrographs for events I and II based on the 5 different types of rainfall input are shown in figure 9 and figure 1. For event I it can be seen in figure 9 that if the run-off only was based on the North rain gauge it would be overestimated, while the opposite is the case if the South gauge was used. The dependency in relation to the selected radar pixel size is less. The difference in the run-off hydrographs can be explained by the spatial distribution on the rainfall as illustrated in figures 3 to 5 for event II, where it can be seen that the north gauge is intercepting 9 mm while the south gauge only measures 5 mm of rain..14.12 16 5x5 meter pixels 64 25x25 meter pixels 4 1x1 meter pixels North Gauge South Gauge.14.12 16 5x5 meter pixels 64 25x25 meter pixels 4 1x1 meter pixels North Gauge South Gauge.1.1 Run-off [m 3 /s].8.6 Run-off [m 3 /s].8.6.4.4.2.2 12:: 15:: 18:: 21:: :: Event I 17 th of November 24 Figure 9 Run-off hydrographs based on distributed rainfall for event I and the two gauges. 18: 21: : 3: 6: 9: 12: Event II 17-18 th of November 24 Figure 1 Run-off hydrographs based on distributed rainfall for event II and the two gauges. If the accumulated outflow is considered the tendency is even clearer as illustrated in figure 11 and figure 12. 6 Urban run-off volumes dependency on rainfall measurement method
9 25 8 7 2 Accumulated outflow of system [m 3 ] 6 5 4 3 Accumulated outflow of system [m 3 ] 15 1 2 16 5x5 meter pixels 64 25x25 meter pixels 1 4 1x1 meter pixels North Gauge South Gauge 12:: 15:: 18:: 21:: :: Event I 17 th of November 24 Figure 11 Accumulated outflow from the system for event I and the two gauges. 5 16 5x5 meter pixels 64 25x25 meter pixels 4 1x1 meter pixels North Gauge South Gauge 18: 21: : 3: 6: 9: 12: Event II 17-18 th of November 24 Figure 12 Accumulated outflow from the system for event II and the two gauges. The variation shown in figures 9 12 is quantified in table 2 where the deviation in percent from the 1x1 meter LAWR resolution is calculated. The 1x1 meter resolution is used as reference value since it is regarded as the best available measure of the rainfall. Table 2 Variability of peak discharge and total outflow in relation to 1x1 meter resolution given in % from the 1x1 meter resolution. 5x5 25x25 North gauge South gauge meter pixels meter pixels Maximum peak in Event I [%] 5.1 16.5 59.5-6.3 Maximum peak in Event II [%] -1.9 33.3-17.1 Total outflow Event I [%] -1.3 8.1 5.3-12.5 Total outflow Event II [%].7 5.1 46-13.3 The figures and the table values clearly show how uncertain it is to model urban run-off based on a single rain gauge if impacts of a specific rain event are attempted to be modelled. Faurés et al. (1995) examined the run-off from a 4.4 ha catchment and they also detected very large variations in the total run-off volume from the catchment, when comparing the results from using input from a single rain gauge with a relatively dense network of rain gauges. The duration of a rain event throughout the catchment may be as important as the distribution of the rainfall intensity. Figure 13 shows the duration of the rainfall event II based on the 1x1 m resolution. When using rain gauges alone, the duration over the entire catchment is assumed to be the same. In this case it can be seen that the duration using the North rain gauge alone would be some 475 minutes compared to a duration of 455 minutes if the rainfall duration was based on the South gauge. The actual duration over the catchment ranges from 435 minutes in the western side of the catchment to 55 minutes on the eastern side. Pedersen et al. 7
Figure 13 Rainfall duration in minutes shown in relation to pixels for event II for the 4 1x1 pixels. Both spatial and temporal variation in the rainfall contributes to the effects on the simulation results. It would be relevant to investigate whether effort spent on radar calibration (intensities estimates) are better spent that effort spent on achieving high (1x1 m) resolution. CONCLUSION Not surprisingly detailed knowledge on spatial and temporal distribution of precipitation is essential to modelling of urban run-off. Few rain gauges may yield reasonable results but it may also result in substantial over- or underestimation of the catchments run-off and there is no way of knowing the quality of the single simulation, since earlier calibrations may have compensated for a particular deficiency in precipitation knowledge. The usage of high-resolution radar rainfall data combined with rain gauge measurements is a feasible approach for accurate simulation of urban run-off since this approach provides both spatial and temporal knowledge on the boundary data to the model. REFERENCES Ayyub B., Mccuen R., CRC Press, Inc. 1997,: Probability, Statics, & Reliability for Engineers, CRC Press, New York, ISBN -8493-269-7 Faurés, J., D.C. Goodrich, D.A. Woolhiser, S. Sorooshian, 1995, Impact of small-scale rainfall variability on run-off modeling, Journal of Hydrology 173 (1995) Goodrich, D.C., J. Faurés, D.A. Woolhiser, L.J. Lane, S. Sorooshian, 1995, Measurements and analysis of small-scale convective storm rainfall variability, Journal of Hydrology 173 (1995) Jensen N. E., Pedersen L. 24; Spatial variability of rainfall; Atmospheric Research -in press Pedersen. L; 24; Scaling Properties of Precipitation experimental study using weather radar and rain gauges, M.Sc. Thesis from Department of Civil Engineering, Aalborg University. Can be downloaded from www.exigo.dk 8 Urban run-off volumes dependency on rainfall measurement method