The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation based on the Lee catchment, UK

Journal of Hydrology (2007) 347, 116– 131

available at www.sciencedirect.com

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The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation based on the Lee catchment, UK Marie-Laure Segond *, Howard S. Wheater, Christian Onof Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AB, United Kingdom Received 9 October 2006; received in revised form 18 July 2007; accepted 5 September 2007

KEYWORDS Rainfall; Runoff; Semi-distributed modelling; Spatial variability; Scale

In the context of flood management, this paper investigates the relationship between spatial rainfall and runoff production, based on 15 years of radar data, 16 raingauges and 12 flow stations from the 1400 km2 Lee catchment, UK. Event-based, semi-distributed rainfall–runoff modelling is undertaken. Alternative rainfall estimators (radar data and raingauge networks of various density) are considered and their effects on simulated runoff evaluated as a function of rainfall type, catchment type and catchment scale. An index of spatial variability is defined, based on the difference between the reference rainfall (defined by the full raingauge network) and alternative rainfall estimators. A modified Nash–Sutcliffe efficiency criterion measures the performance of the simulated runoff with respect to reference simulated runoff. Results show a complex picture. The dominant effect is the spatial variability of the rainfall. No clear pattern emerges as a function of catchment scale, or response time, except that the impact of spatial variability is damped at the whole catchment scale. The sensitivity to spatial rainfall is enhanced on urbanised catchments. ª 2007 Elsevier B.V. All rights reserved. Summary

Introduction Rainfall is the primary input to most hydrological systems, and a key issue for hydrological science and practice is to assess the importance of the spatial structure of rainfall and its representation for flood runoff generation. This can be * Corresponding author. Tel.: +33 130136091. E-mail address: [email protected] (M.-L. Segond).

expected to depend on complex interactions between the type of event, the nature of the catchment and the spatial scale (i.e. catchment area) of the problem. However, although the literature on the relationship between spatial rainfall and runoff response is extensive, results have been contrasting and sometimes contradictory. In a recent review, Singh (1997) concluded that the spatial and temporal variability of rainfall can significantly influence the flood hydrograph and shape, and that the importance of this variability varies as a function of catchment rainfall properties.

0022-1694/$ - see front matter ª 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2007.09.040

The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation However, as in most similar studies, no general conclusions were drawn in assessing the impact of spatial rainfall on runoff generation. This illustrates the complexity of the problem, which is compounded by the fact that the effects of rainfall spatial variability are usually assessed indirectly, via a watershed model. While hydrological models provide a powerful tool to test the sensitivity of the catchment to various rainfall patterns (Grayson and Blo ¨schl, 2000), their calibration at a fixed spatial scale introduces uncertainties in relating the rainfall input to the simulated flow (Morin et al., 2001; Koren et al., 1999). Given the lack of guidance, this paper explores the importance of spatial rainfall representation for rainfall– runoff modelling as a function of rainfall type, catchment type and catchment scale, with emphasis on humid temperate regions in general, and the UK in particular. The paper addresses the spatial resolution requirements for rainfall at different catchment scales, and the results are of practical relevance to the design of raingauge and radar networks for flood estimation, as well as flood models. ‘‘Review of the significance of spatial data for flood runoff generation’’ presents a summary of the literature on the significance of spatial data for flood runoff generation. This provides guidance for a numerical investigation carried out on the 1040 km2 Lee catchment, UK. ‘‘The case-study area’’ describes the study area and the substantial dataset of radar, raingauge and flow data used in this investigation. Calibration of an event-based semi-distributed rainfall–runoff model fitted to 7 individual sub-catchments, and to the catchment as a whole is addressed in ‘‘Calibration of the upper lee catchment rainfall–runoff model’’. Results of the rainfall–runoff investigation are presented in ‘‘The significance of spatial data’’. Finally, the conclusions are presented in ‘‘Discussion and conclusions’’.

Review of the significance of spatial data for flood runoff generation Urban catchments On impervious areas, a high proportion of the rain becomes effective and produces runoff whereas on pervious areas, rainfall variations are damped by the integrating response of the catchment. A reasonable prior hypothesis is therefore that for urban catchments, effects of spatial rainfall on streamflow will be greater than for rural areas, with similar results for other fast-responding catchments. It could be expected that the effects would decrease with increasing catchment scale, due to increased catchment damping, although this is clearly conditional on the scale-dependence of the spatial structure of the rainfall. Numerous studies of urban catchments show that the runoff response is sensitive to storm variability in space and time and is also affected by storm movement (Singh, 1997). The runoff peak can be enhanced when the storm moves in the direction of flow and at low speed (de Lima and Singh, 2002). Hydrological modelling therefore requires fine temporal and spatial rainfall resolution. For instance, Berne et al. (2004) suggested a resolution of 3–6 min in time and 2– 4 km in space for urban catchments of 1–10 km2, with higher resolution for smaller catchments. In addition, Ngirane-

117

Katashaya and Wheater (1985) showed that smaller catchments are more sensitive to storm movement.

Semi-arid regions with convective rainfall For evidence of fast-responding natural catchments, we can turn to semi-arid areas characterised by a dominance of Hortonian overland flow; these are commonly associated with convectively dominated rainfall. Studies conducted on the Walnut Gulch watershed in Arizona, across a range of size from 4 ha to 150 km2 (Faure `s et al., 1995; Lopes, 1996; Michaud and Sorooshian, 1994), revealed that spatial rainfall is important at all scales and that its importance increases as the scale decreases. This was also confirmed by Ogden and Julien (1994) who observe larger deviations due to rainfall aggregation as basin scale decreases. In addition, the basin response is sensitive to the magnitude of events (Michaud and Sorooshian, 1994; Syed et al., 2003). Overall, it is concluded that a density of 4 raingauges is required to model adequately a 4.4 ha catchment (Faure `s et al., 1995), and at least 5 raingauges are necessary at the 6.7 km2 scale (Lopes, 1996). Michaud and Sorooshian (1994) used rainfall input from 58 raingauges at the 150 km2 scale and suggested 2 km resolution to model 50– 500 km2 watersheds. Ogden and Julien (1994) recommended a spatial resolution less than 0.4 the square root of the watershed area. (i.e. 1 km resolution for a 10 km2 watershed, 4 km resolution for a 100 km2 watershed). Although not semi-arid, Arnaud et al. (2002) reported results from Mexico City (2000 km2), which has pronounced dry and wet seasons associated with heavy convective rainfall, and a fast-responding catchment. The findings are therefore presented here to illustrate effects at larger catchment scale. In contrast to the previous results, higher differences in flow were observed for more frequent events compared to extreme events, and higher relative errors were observed for the largest basins in comparison to the smallest ones, which suggest that the sensitivity of the runoff to spatial variability of rainfall increases with catchment size. This seems to be a particular feature of Mexico City and may highlight the complexity introduced when mixed weather and catchment conditions are considered.

Temperate climate Turning to natural catchments in temperate areas, effects of rainfall spatial variability are likely to be less clear-cut. The catchment response is a trade-off between the impact of spatial variability of rainfall and the smoothing effect due to the heterogeneity of the catchment. The importance of spatial rainfall depends on how variable the rainfall is and whether there is enough variability to overcome the damping and filtering effect of the basins (Smith et al., 2004; Obled et al., 1994). The rainfall variability depends on the type of event. Bell and Moore (2000) observed lower variability in rainfall and runoff response during stratiform as opposed to convective events on the 135 km2 Brue catchment, UK. On the 1645 km2 Watts basin in North America, Ajami et al. (2004) concluded that knowledge of spatial rainfall is important when modelling extreme events and convective events in summer.

118 When there is not enough variability in rainfall to overcome the damping effect of the catchment, detailed knowledge of rainfall spatial variability is not required to model the catchment response, although reliable information of catchment-averaged rainfall is important (Woods and Sivapalan, 1999; Smith et al., 2004; Andre ´assian et al., 2001; Naden, 1992). For instance, Smith et al. (2004) observed that improvement in model efficiency using a distributed model is observed when spatial variability of rainfall is included to model the 795 km2 Blue catchment, whereas a lumped approach using catchment-averaged rainfall is suitable to model the 1645 km2 Watts basin. The Blue basin is characterised by variable precipitation and low level of basin filtering whereas the Watts show higher level of filtering and more uniform precipitation. Some authors (Beven and Hornberger, 1982; Obled et al., 1994; Pessoa et al., 1993) argue that the most important factor affecting the reproduction of the hydrograph is the volume of rainfall. Flow routing and the distribution of rainfall-excess with flow distance control the catchment response. Woods and Sivapalan (1999) proposed an analytical method to identify the importance of different components of storm response, based on a 420 km2 catchment in New Zealand. The method is illustrated for a 10-h storm using hourly radar rainfall data at 1 km grid resolution and a lumped rainfall–runoff model. They concluded that if the space and time covariance between rainfall and runoff generation are negligible then methods for estimating catchment average rainfall and runoff generation may be more important than methods for estimating their variability. Apparently, substantial spatial variations in rainfall did not seem to have any significant influence on the timing of catchment response. For the small sub-catchments the space pattern of excess rainfall was unimportant because it only influenced channel routing, and the timescale of channel routing in those catchments was small compared to storm duration. For larger catchments, spatial variability of rainfall had little influence; for this event, at each flow distance, there was a wide range of rainfall depths so the distance-averaged rainfall excess was relatively uniform. Obled et al. (1994) reached similar conclusions. In a study conducted on a 71 km2 catchment in France, they found that spatially-uniform rainfall estimated from five raingauges was enough to estimate the streamflow hydrograph because of the large damping behaviour of the basin. They argued that because the runoff generation mechanism is predominantly of the Dunne type in this area, the water infiltrates and local variation of the rainfall input is smoothed and delayed within the soil. Similarly, the underlying geology is important and can mask the impact of spatial rainfall. Naden (1992) concluded that a lumped approach is appropriate to model the 7000 km2 Thames catchment; the hillslope component of runoff has a much longer residence time than the channel routing, due to the large proportion of limestone and chalk. Dodov and Foufoula-Georgiou (2005) found that including information on rainfall spatial distribution improves the prediction performance of streamflow, but less for a catchment with presence of limestone aquifer. Effects of rainfall spatial variability are also likely to vary, depending on the effect of antecedent catchment conditions on catchment response. Based on results from a 10 km2 catchment in the UK, Shah et al. (1996) observed

M.-L. Segond et al. that under dry conditions, higher errors in runoff prediction (14% and 8% in peak flow and volume) are obtained with a spatially averaged rainfall input compared to the case with wet conditions (6% and 3%). The importance of spatial rainfall on runoff generation is also a function of catchment scale. More precise areal rainfall estimates are required at small scales (Shah et al., 1996; Andre ´assian et al., 2001; Carpenter et al., 2001). Obled et al. (1994) recommended 5 raingauges for a 71 km2 basin in the South of France. The study of Bell and Moore (2000) suggested a 2 km grid rainfall resolution to model the 132 km2 Brue catchment. As the scale increases, in the case where knowledge of spatial rainfall improves the runoff prediction, a crude resolution of rainfall is adequate. Smith et al. (2004) used 4 km rainfall grid resolution to model a 800 km2 basin. Carpenter et al. (2001) suggested a rainfall resolution of 80 km2 (i.e. a 9 km grid) for catchment scales greater than 800 km2 and recommended a smaller one for a 280 km2 catchment. At the larger scale, Dodov and Foufoula-Georgiou (2005) suggested that aggregation of rainfall at the sub-catchment scale captures enough spatial information to improve the prediction performance of streamflow by about 10–15% and 3–8% for two catchments of 4800 and 7300 km2, respectively. They used catchment-averaged rainfall over sub-catchments of 530 km2 (9 subdivisions scheme) and 1600 km2 (3 subdivisions scheme) for the 4800 km2 basin, and sub-catchments of 735 km2 (10 subdivisions scheme) and 2450 km2 (3 subdivisions scheme) for the 7300 km2 basin. As noted earlier, further complexity in unscrambling the effect of spatial rainfall on runoff is added when using a rainfall–runoff model. Obled et al. (1994) noted that the sensitivity of a particular model to the spatial variability of precipitation is not necessarily the same as the sensitivity of the actual basin. Koren et al. (1999) concluded that lumped hydrologic models are scale-dependent and that scale-dependency decreases when spatial variation of rainfall is accounted for in the model structure. Using a semi-distributed model, Chaubey et al. (1999) showed that large uncertainties in model parameters are introduced due to the spatial variability of rainfall. Shah et al. (1996) found that larger errors in runoff prediction arise when a lumped instead of a distributed model is applied to the catchment, compared to averaging the rainfall as input to a distributed model. To conclude, the runoff response is the result of a complex interaction between rainfall spatial variability and heterogeneous catchment properties, such as soils, geology and channel morphology, that determine runoff generation and channel flow routing. Effects will also vary depending on antecedent conditions. The importance of spatial rainfall generally decreases with catchment scale. The relative importance of spatial rainfall is dependent upon the modelling strategy; hence the impact of the model should be quantified and kept to a minimum. A fine catchment discretisation is preferable to avoid loss of rainfall information due to averaging at too large-scale.

Direction of research This brief overview has identified various factors that define the importance of spatial rainfall representation for rainfall–runoff modelling, but clear guidelines are not available

The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation for temperate humid areas. Hence a numerical investigation is undertaken (a) to test whether spatial rainfall is important to model medium to large-scale catchments in humid areas, (b) assuming that it is important, to investigate the rainfall spatial resolution required at catchment scale, for a range of scales and catchment types and (c) to identify the modelling needs. The 1040 km2 catchment of the Upper Lee, north of London was selected. The sub-catchments include a range of geology, land use and scales. Distributed streamflow monitoring data are available, together with a relatively dense raingauge network and an extensive record of radar rainfall. A semi-distributed rainfall–runoff model is needed to test the significance of spatial rainfall. The event-based RORB (RunOff Routing B6700), model was selected; it has been used extensively in practice to model the Lee catchment (Lotufo Conejo, 1979; Flynn and Rothwell, 1991a,b; Hawnt, 1987a,b) and model configuration files were available for several of the sub-catchments.

The case-study area The 1040 km2 Upper Lee catchment (Fig. 1) has a humid temperate climate with a mean annual rainfall of 632 mm; elevation ranges from 20 to 250 masl. The Upper Lee to Feildes Weir is mainly rural, characterised by arable farming. However, the area has seen significant housing growth since the 1950s, with urban areas now covering 15% of the upper catchment. From West to East, the main tributaries of the

Figure 1

119

upper catchment are the Upper Lee, the Mimram, the Beane, the Ash, the Rib and the Stort (see Table 1 for summary properties). The Upper Lee, a chalk catchment, is substantially urbanised and is joined by the Mimram at Hertford. The Mimram drains a mostly rural area and is also predominantly chalk, characterised by low natural stormflow runoff. The Beane joins the Middle Lee just downstream in the centre of Hertford. Low runoff from chalk areas is augmented by runoff from overlying boulder clay and by urban runoff from the town of Stevenage. The Rib catchment is underlain by Chalk, but with extensive overlying deposits of boulder clay, stormflow runoff is moderately high, albeit characterised by a marked lag. The Ash catchment is almost entirely rural and has similar runoff characteristics to the Rib. Finally, the Stort joins the Middle Lee immediately upstream of Feildes Weir. Runoff rates from the Stort vary considerably, being high on the clay and much lower on the chalk. The Stort presents a mainly rural upper catchment, but includes substantial urban development in the valley. The flow regime is influenced by interactions between the river and the canalised Stort Navigation. The river is relatively slow flowing and when the lock is in use by the boats it creates a reverse flow (Flynn and Rothwell, 1991a), which makes the calibration of the Stort difficult (negative flowrate or erratic flowrate curve). Continuous records of radar, raingauge and flow data were provided by the Environment Agency of England and Wales for the period 1987–2002. In this investigation, all data are aggregated to an hourly time-step to be used as in-

Map of the upper catchment of the Lee.

120

M.-L. Segond et al.

Table 1 Percentage distribution of hydrogeological characteristics, main components of drift and urbanisation of the upper catchment of the Lee Upper Lee

Mimram

Beane

Rib

Ash

Stort

Feildes Weir

Permeability (%) High (fissured) Low Mixed

90.1 6.0 3.9

97.1 – 3.0

96.1 – 3.9

93.9 – 6.1

63.9 10.5 25.5

24.1 70.8 5.1

71.4 22.1 6.4

Drift (%) Sand and gravel Boulder clay Clay with flints

22.3 13.5 9.8

14.9 9.3 35.6

14.9 41.8 7.5

12.5 81.3 –

14.9 77.2 –

18.4 76.2 –

18.4 50.8 7.2

Urbanisation (%)

34.7

12.7

12.9

3.5

3.5

12.9

14.9

Source: http://www.nerc-wallingford.ac.uk/ih/nrfa/spatialinfo/Index/indexEAThames.html.

put to the rainfall–runoff model. Two kilometers grid resolution data from the Chenies radar in the Thames region are calibrated following the procedure developed by Moore et al. (1994) and reported in Wheater et al. (2005). Data from a network of 17 raingauges are used in this study. Due to the proximity of two sites (1.7 km distance) and the fact that their period of record is complementary, they are taken as a single gauge for this investigation. These are complemented with flow data from 12 stations. The location of the raingauges and flow stations on the Lee catchment can be found in Fig. 1.

Calibration of the upper lee catchment rainfall–runoff model RORB (Laurenson and Mein, 1988) is a semi-distributed, event-based hydrologic simulation model. From the total event rainfall over a subarea, losses (initial loss followed by a constant proportional loss or a continuing loss rate) are deducted to derive an rainfall excess hyetograph. This is converted to a stormflow runoff hydrograph and routed to the catchment outlet. The storage–discharge relation for both runoff generation and routing is represented by a non-linear element S ¼ kQ m

ð1Þ

where S represents storage in the sub-catchment or river reach, Q is the discharge and k and m are constant parameters. k is the product of two factors, a catchment-wide parameter kc and a dimensionless relative delay time kr, calculated automatically from relative reach lengths (or userdefined if special storages are required). Hence the program has four main parameters to be identified: the event-dependent initial loss (IL) and runoff coefficient (RC, or constant loss rate) and the parameters m and kc. Note that RC and kr can be modified within the programme using prespecified parameters to account for runoff from urban areas and for channel improvements, and that the programme distributes k values to subareas based on the kr calculation. The upper catchment of the Lee was subdivided into the 6 major sub-catchments discussed above. In order to minimise the impact of model discretisation, a relatively fine subdivision of the sub-catchments into subareas of about

10 km2 was used (Fig. 2), except for the Mimram. This is baseflow dominated due to the chalk geology, and does not justify such detailed subdivision; subareas of 20– 30 km2 were used. The flow from each sub-catchment was then combined and routed to the outlet of the catchment at Feildes Weir. The impact of spatial rainfall can thus be studied as a function of sub-catchment type, sub-catchment scale (80–280 km2) and catchment scale (1000 km2). Since the model is semi-distributed, a spatially-variable rainfall is used for its calibration. Radar data can be unstable and the derivation of accurate quantitative precipitation estimates is still the subject of ongoing research (Tetzlaff and Uhlenbrook, 2005). In this application, following Moore et al. (1994) an adjustment procedure against the raingauges was applied (see Wheater et al., 2005) to the radar data. However, the spatially variable rainfall derived from the full raingauge network was perceived as a more robust estimator. It was therefore considered as the reference rainfall to be used as input for calibration purposes. Since a relatively dense network of representative raingauges is available, a simple method to derive the sub-areal precipitation was selected. Spatial interpolation used the Thiessen Polygons method; the temporal pattern applied to each subarea was given by the nearest raingauge. The simulated flow driven by the reference rainfall is referred to as the reference flow. The calibration of the rainfall–runoff model was based on a total of 28 events that span the whole dataset. Stormflow runoff is required for RORB calibration and as a first approach a simple linear separation method was applied (Chow et al., 1988) to each flow event to remove the baseflow component. Model parameter calibration and validation was based on three criteria: the reproduction of the peak outflow (Qp), time to peak (Tp) and the well-known Nash–Sutcliffe Efficiency (NSEobs) (Nash and Sutcliffe, 1970), which is sensitive to hydrograph peak error. The aim of the calibration was to identify model parameters which provide a suitable basis for analysis of model sensitivity to precipitation inputs, hence an exhaustive calibration exercise was not justified. Manual calibration was undertaken, varying the model parameters m, kc and IL for the range of events to achieve a close match between the observed and calculated hydrograph. RC is calculated by the program by iteratively achieving a volume balance of rainfall-excess with measured surface runoff.

The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation

Figure 2

Subcatchment subdivisions.

For a particular sub-catchment, it was not possible to determine a unique parameter set for all events. The fitted kc generally increased with the size of the flow event. A summary of the calibrated model parameters for each sub-catchment is presented in Table 2. ‘‘Standard’’ refers to the default parameter set fitting most events, ‘‘Low’’ and ‘‘Large’’ refer to the parameter set required to represent low or large flows as specified in Table 2. As shown in Table 3, a relatively good fit was achieved for all tributaries with NSEobs on average for all sub-catchments and events of 0.88 and 0.89 in calibration and validation mode, respectively. This was considered a suitable performance basis to support the subsequent sensitivity analysis.

Table 2

121

Following validation of the individual sub-catchments, they were incorporated into an integrated catchment model. Simulated runoff from each sub-catchment was modelled independently, used as inflow to a Middle Lee model and routed to generate the total runoff at the 1040 km2 catchment scale (Feildes Model). A common set of events was defined in order to test the combined calibration at Feildes Weir. Due to data availability and the manual calibration procedure, these were limited to five individual storm events (Table 4) of medium to large rainfall depth. The largest rainfall event in the database, 11th October 1993, was included, leading to the highest peak flow. The others were taken at different times of the year, represen-

Calibrated parameter results Upper Lee

Mimram

Beane

Rib

Ash

Stort

Middle Lee

–

–

0.8–7 <1 m3/s

–

0.8–7 <1 m3/s

0.8–17 <3 m3/s

0.6–7 <10 m3/s

Standard m  kc

0.8–21

0.8–7

0.8–21

0.8–16

0.8–15

0.8–37

0.6–21

Large m  kc Flow

0.8–33 >5 m3/s

0.8–17 >3 m3/s

–

0.8–21 >15 m3/s

0.8–21 >7 m3/s

–

0.6–35 >50 m3/s

IL (mm)

3

0

5

9

7

0

0

Low m  kc Flow

122

M.-L. Segond et al.

Table 3

Calibration results in terms of NSEobs Upper Lee

Mimram

Beane

Rib

Ash

Stort

Middle Lee

Calibration No. of events Min NSEobs Max NSEobs Mean NSEobs

5 0.78 0.94 0.88

5 0.64 0.97 0.86

4 0.78 0.97 0.92

4 0.62 0.96 0.81

6 0.83 0.96 0.91

4 0.77 0.97 0.85

5 0.87 0.95 0.92

Validation No. of Events Min NSEobs Max NSEobs Mean NSEobs

4 0.92 0.95 0.94

2 0.81 0.90 0.85

3 0.92 0.95 0.94

4 0.74 0.95 0.88

3 0.73 0.95 0.88

4 0.75 0.88 0.83

3 0.80 0.98 0.88

0.55 0.65 0.64 0.61 0.84

0.54 0.83 0.97 0.78 0.92

0.96 0.86 0.85 0.78 0.51

0.94 0.84 0.97 0.22 0.73

0.75 0.88 0.88 0.59 0.23

Feildes Weir 0.84 0.95 0.87 0.92 0.88

Validation of the integrated catchment 11 October 1993 0.92 03 February 1994 0.92 08 January 1996 0.94 16 May 1995 0.73 30 July 2002 0.61

Table 4

Characteristics of selected events

Events

Duration (h)

Mean (mm)

CV (%)

Direct runoff cumecs

11 03 08 16 30

65 8 19 25 30

62.7 12.1 20.3 17.1 21.4

16.9 16.5 14.3 11.1 42.7

109.1 28.8 30.7 4.3 4.2

October 1993 February 1994 January 1996 May 1995 July 2002

tative of frontal and convective rainfall and associated with high, medium and low flows. The coefficient of variation of rainfall is large for the event of 30th July 2002, which is characterised by a high temporal and spatial variability. Using the calibrated parameters, the results in terms of NSEobs for the 5 selected events are also displayed in Table 3. The performance at interior points is lower in the case of extreme and summer events. Examples of observed and reference flow are illustrated in Fig. 3 for a frontal (a–c) and a convective (d–f) event. The observed flow in the case of summer events for the Stort has low maxima (<1.5 m3/s) and the flow curve is very erratic. This is most probably due to the presence of boats in the canal, which would explain the lower performance in summer displayed in Table 3. Overall, a reasonable fit is achieved with NSEobs of 0.77 on average for all sub-catchments and events. These five events constitute a reference set against which alternative rainfall representations based on radar data and subsets of the raingauges were tested to assess the significance of spatial rainfall data for runoff generation.

The significance of spatial data Measures of rainfall variability and basin response The reference rainfall was defined above. In order to analyse the effects of various rainfall representations, the following rainfall inputs were tested on each sub-catchment:

• Raingauge network: – Single raingauge per sub-catchment, with uniform sub-catchment rainfall. The raingauge nearest to the centroid of the sub-catchment was selected. Hence at the catchment scale, the flow at Feildes Weir is driven by seven raingauges (SG7). – Single raingauge for the whole Upper Lee catchment, i.e. with uniform catchment rainfall. The raingauge nearest to the centroid of the Feildes Weir catchment was selected (SG1). • Spatially variable rainfall from radar data calibrated using the network of supporting raingauges (Wheater et al., 2005). The areal rainfall on each sub-area is estimated from the average of the pixels included in the subarea. The temporal pattern applied to each subarea is given by the hourly averaged radar rainfall estimate for the sub-area. For the practitioner, a central question is to assess the importance of the spatial structure of rainfall in rainfall– runoff modelling and evaluate what is necessary to characterise this in terms of observational data. Hence one objective of this investigation is to determine the requirement in terms of type of data and raingauge density for rainfall– runoff application. SG7 and SG1 represent a degradation of spatial information in comparison to the reference rainfall consequently lower model performance is expected. The use of radar data represents an improvement in terms of spatial information but since the model is calibrated using the reference rainfall, similar model performance is expected. The rainfall estimators are selected to give insight into the requirements for spatial rainfall and its modelling for hydrological applications (i.e. a full spatial– temporal rainfall field based on radar data, a multisite description based on a raingauge network, a point estimate using one gauge). Large uncertainties can results from the calibration of the model parameters (Chaubey et al., 1999), which can also compensate for the biases in rainfall. In order to minimise the impact of modelling errors, the

The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation Mimram

Feildes 40

6

1.5

Beane

123

Reference

30

5

Radar 1.0

SG1

20

Observed

0.5

Flow cumecs

Flow cumecs

4 3 0

20

40

60

80

100

0

0

0.0

1

10

2

Flow cumecs

SG7

0

20

40

60

80

100

0

20

40

60

80

time (h)

time (h)

time (h)

(a) Mixed Chalk and Clay catchment

(b) Chalk catchment

(c) Catchment scale

Feildes

0

20

40

60

80

100

0

0.0

0.0

1

0.5

2

3

Flow cumecs

1.0

Flow cumecs 0.5

Flow cumecs

4

1.0

1.5

5

6

2.0

Mimram

1.5

Beane

100

0

20

time (h) (d)

Figure 3

60

80

100

time (h) (e)

0

20

40

60

80

100

time (h) (f)

Observed, reference and simulated flows for the event of 03/02/94 (a–c) and the event of 30/07/02 (d–f).

same parameter sets derived for the reference rainfall were used when testing alternative rainfall descriptors. Hence the errors between the reference flow and the observed flow can be seen as a model error whereas the errors between the reference flow and the simulated flow (driven by radar data, SG7 or SG1) represent the relative errors introduced by the tested rainfall representation in comparison to the reference rainfall. A Spatial Deviation Index (SDI) (Quasem, 2004) was defined for each storm; and for each of the 6 sub-catchments and the entire catchment draining to the Feildes weir (referred to as (sub)catchment) as a measure of spatial variability over a (sub)catchment. It measures the deviation between the sub-areal reference rainfall and the (sub)catchment-averaged areal rainfall as follows: SDI ¼

40

N 1 X j Pri  P T j N i¼1 PT

ð2Þ

where Pri represents the reference areal precipitation (i.e. as defined by the full raingauge network) for sub-area i in mm, PT the (sub)catchment Thiessen averaged areal precip-

itation based on the full raingauge network in mm, and N the number of sub-areas for a given (sub)catchment. A Reference Spatial Deviation Index (SDIR) compares the rainfall spatial deviation between the sub-areal estimates from the tested rainfall representation to the reference sub-areal precipitation estimates. SDIR ¼

N 1 X j P i  Pri j N i¼1 P ri

ð3Þ

where Pi represents the areal precipitation from either radar data or subsets of the gauges for sub-area i in mm, Pri the reference areal precipitation in mm for sub-area i, and N the number of sub-areas. Various indices have been derived to measure runoff variability in relation to rainfall (Woods and Sivapalan, 1999; Ogden and Julien, 1993; Smith et al., 2004; Morin et al., 2001). The basic hydrograph characteristics used here are hydrograph peak, hydrograph volume and the lag time between rainfall and flow, which is a measure of the catchment response time and expresses the average travel time from all points on the catchment to the outlet. Following

124

M.-L. Segond et al.

where Ci and Ri are the calculated and reference discharge at hour i.

May 95 event are closer to the reference rainfall than the radar. The event of 30th July 2002 leads to the highest deviations, of the order of 30%, for all rainfall representations. Hence results indicate that radar data capture a rainfall information which differs from the raingauge network in the case of extreme and summer events, otherwise both spatially variable rainfall descriptors are in agreement. This may be due to discrepancies in the sampling mode, an inappropriate relationship converting the radar reflectivity into rainfall rate being applied for these types of event (Pessoa et al., 1993) or the raingauge network failing to capture the rainfall patterns.

Rainfall spatial variability

Rural catchment results

For each sub-catchment, the events defined in Table 4 were used to test the model sensitivity to the rainfall representations defined above. The rainfall characteristics in terms of SDI (%) and SDIR (%) are presented in Table 5. Across all events and sub-catchments, the SDI ranges between 2.3% and 25.3%. As expected, larger discrepancies are introduced for the more variable event of 30th July 2002. SDIR ranges between 2% and 42%. Radar data lead to the largest deviation in areal rainfall, compared to SG7 and SG1 for the event of 11th October 1993. For the events of January 1996 and February 1994, a closer agreement is seen between the reference rainfall and radar data, and the discrepancies are worse when SG1 is used. All the SG7 values for the 16th

Effect of spatial rainfall resolution Radar, SG7 and SG1 rainfall fields were input to the rainfall–runoff model with the parameters calibrated to the reference rainfall. Simulated runoff is compared to the reference streamflow as illustrated in Fig. 3. The results in terms of NSEref can be found in Table 6 and express the errors in reproducing the reference flow introduced by the rainfall representation. On average for all sub-catchments and events, NSEref values of 0.95, 0.91 and 0.80 are observed for Radar, SG7 and SG1, respectively. The corresponding values for NSEobs are 0.73, 0.73 and 0.60, respectively, but it is difficult to interpret these results since the average value of NSEobs between the reference

NERC (1975), the time from the centroid of total rainfall to the peak flow is adopted here (in case of multipeaked events, the centroid of total rainfall to the ‘‘centroid of peaks’’, averaged over the five events). A modified definition of NSE is introduced at this stage to measure the performance of the simulated runoff in comparison to the reference flow according to: PM ðCi  Ri Þ2 NSEref ¼ 1  Pi¼1 ð4Þ M 2 i¼1 ðRi  RÞ

Table 5

Rainfall spatial variability measured in terms of SDI (%) for the reference rainfall and SDIR (%) for radar, SG7 and SG1 Upper Lee

Mimram

Beane

Rib

Ash

Stort

Feildes

11-October-93 Reference Radar SG7 SG1

11.3 11.5 18.0 14.6

5.5 18.6 9.3 17.5

10.0 11.6 12.9 18.4

7.9 18.6 10.0 8.7

2.3 10.8 2.2 4.7

9.1 18.9 12.5 9.1

8.1 15.9 10.9 10.8

03-February-94 Reference Radar SG7 SG1

6.6 7.8 4.0 8.5

5.2 11.3 5.5 6.3

8.3 7.9 12.5 22.8

9.7 8.2 15.6 33.5

7.2 6.8 9.2 24.8

5.9 5.0 5.0 22.9

7.3 6.8 8.3 19.3

08-January-96 Reference Radar SG7 SG1

6.9 7.4 9.0 7.2

8.3 2.8 10.6 10.4

8.6 7.2 9.1 9.3

13.1 10.4 20.7 26.4

4.6 4.2 4.8 11.3

10.6 10.3 21.9 19.2

8.3 8.2 12.9 13.0

16-May-95 Reference Radar SG7 SG1

4.4 10.8 8.8 22.6

4.1 15.6 9.2 13.4

5.2 7.8 5.2 30.1

3.2 12.7 4.0 33.5

2.6 8.2 3.3 36.5

3.8 10.4 4.1 33.7

4.6 9.8 6.1 27.4

30-July-02 Reference Radar SG7 SG1

19.6 30.0 39.9 21.2

11.6 34.6 15.4 21.2

11.2 28.5 20.8 27.1

11.7 22.0 11.8 19.0

25.3 16.2 17.3 24.8

25.0 27.1 32.8 42.3

19.0 25.0 26.3 29.2

The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation Table 6

125

Results in terms of NSEref for the rural catchments Upper Lee

Mimram

Beane

Rib

Ash

Stort

Feildes

11-October-93 Radar SG7 SG1

0.98 0.91 0.97

0.97 1 0.89

0.99 0.96 0.96

0.86 0.95 0.96

0.83 0.97 0.96

0.94 0.96 0.95

0.97 0.98 0.96

03-February-94 Radar SG7 SG1

0.92 0.93 0.97

1 0.99 1

0.99 0.93 0.73

0.99 0.88 0.36

0.98 0.99 0.74

1 1 0.89

0.99 0.99 0.86

08-January-96 Radar SG7 SG1

0.99 0.97 0.98

1 0.99 0.96

1 0.98 0.99

0.98 0.82 0.69

0.99 1 0.99

0.99 0.72 0.79

1 0.98 0.92

16-May-95 Radar SG7 SG1

0.90 0.82 0.42

0.97 0.98 0.92

0.94 0.98 0.54

0.97 0.99 0.69

0.99 1 0.54

0.99 0.99 0.74

1 0.94 0.65

30-July-02 Radar SG7 SG1

0.74 0.06 0.35

0.98 0.97 0.93

0.73 0.75 0.53

0.97 0.96 0.99

0.98 0.97 0.77

0.9 0.78 0.61

0.95 0.98 0.85

and observed flow is 0.77, which can be seen as a model error. Radar data always lead to high performance at both catchment and sub-catchment scale (usually NSEref > 0.95). Considering the variation overall events, lower performance is observed for the extreme event of 11th October 1993 on the Rib and the Ash (NSEref of 0.86 and 0.83, respectively) and during summer events (NSEref of 0.74 and 0.73 on the Upper Lee and the Beane on 30th July 2002). As mentioned earlier, the rainfall information captured by the radar data differs from that of the network of 16 raingauges in the case of the extreme and summer events studied. SG7 also generally gives high values of NSEref at catchment scale, with somewhat lower performance on the Rib on 3rd February 1994 (NSEref of 0.88), the Rib and the Stort on 8th January 1996 (NSEref of 0.82 and 0.72, respectively), the Upper Lee on 16th May 1995 (NSEref of 0.72), the Upper Lee and the Beane on 30th July 2002 (NSEref of 0.06 and 0.75, respectively). The SG7 performance is always high for the Mimram, the Ash and the Beane. This suggests that one gauge per tributary may be adequate for the Mimram, a medium size Chalk basin and the Ash, an entirely rural small basin. A network of seven raingauges may be suitable to model the more heterogeneous large-scale catchment (i.e. the flow at the catchment outlet only, no interior point). SG1 gives lower results for all events at both catchment and sub-catchment scale, except for the Mimram. Hence this confirms that the model for the Mimram does not show much sensitivity to spatial rainfall and therefore can be run using rainfall from one raingauge. These findings are illustrated in Fig. 3 for three catchments for the event of 3rd February 1994. These are complemented with the percentage change in peak discharge (Qp), peak time (Tp) and runoff volume (V) in comparison

to the reference flow for the three rainfall representations. Results in Table 6 show that the relative error in Qp, Tp and V is less with radar data and increases with SG7 and SG1. In conclusion, radar data lead to high values of NSEref at all scales and to the smallest variations in Qp, Tp, and V. SG7 leads to high NSEref values at the catchment scale but occasionally lower performance at sub-catchment scale. This representation does not seem to affect the average Tp but compared to radar data, increases the errors in Qp and V. Lower performance in terms of NSEref, Qp, Tp and V are observed at sub-catchment and catchment scales with SG1. Lower performance is observed for the extreme event of 13th October 1993 and the summer events. The relative importance of spatial rainfall, basin damping and basin scale is assessed in the following sections. Impact of rainfall spatial variability Fig. 4 plots the model performance in terms of NSEref against SDIR for all five events and all basins. A correlation between the increase in SDIR and the decrease in NSEref is observed. The top graph illustrates the impact of the three rainfall representations on model performance. Up to an SDIR value of about 10%, the NSEref remains close to 1 for all rainfall scenarios. As SDIR increases, the NSEref remains high for radar data whereas for SG7 it decreases for SDIR greater than 15% and for SG1 decreases more sharply for SDIR greater than 10%. The bottom graph lumps all rainfall representation but distinguishes between winter and summer events. It can be seen that the NSEref performance is high (above 0.9) for winter events up to SDIR values of 20% and remains above 0.7 up to SDIR values of 30%. For summer events, the results are less consistent with a larger spread of NSEref values for SDIR greater than 10%. Hence, precipitation dominates the hydrological response and its

M.-L. Segond et al. 20

1.0

126

Radar

10

t_c (h)

0.6 0.4

NSE_ref

15

0.8

Rural catchments Urban catchments

0.2

SG7

0.0

5

SG1

10

20

30

40

0

0

SDIR (%)

400

1.0

200

800

1000

1.0

0.6

0.8

Figure 5 Response time of existing and urbanised basins against catchment area.

0.4

NSE_ref

600 Area (km2)

Winter

30

40

SDIR (%)

0.0

Figure 4 Impact of rainfall spatial variability on NSEref. Influence of rainfall representation (top) and type of rainfall events (bottom).

0.6

20

NSE_ref

10

0.2

0

0.4

0.0

0.8

0.2

Summer

patterns are dependent on the type of rainfall representations and storms. Results indicate that a SDIR greater than 10% affects the reproduction of the hydrograph and that above 20% it reduces the NSEref below 0.80. Effect of catchment response The response time of each (sub)catchment is given in Table 7 and is plotted against catchment area in Fig. 5. If the basins were homogeneous, we would expect the catchment response time to increase with the scale of the basin. For instance, Berne et al. (2004) fitted a power law relationship between the lag time and surface area for 6 urban sub-basins of 38 ha to 105 km2 in the Southwest of France. However in this case, differences between the basins (see Table 1) appear to mask any relationship between the response time and area. Fig. 6 displays the results in terms of NSEref, lumped for all rainfall representations (radar data, SG7 and SG1), for the five selected events and for each sub-catchment ranked

Table 7 Percentage change of peak flow, time to peak and hydrograph volume for the rural catchments

Qp (%) Tp (%) V (%)

Radar

SG7

SG1

12.6 5.6 7.4

15.3 5.8 12.4

28.1 8.0 21.6

Mimram Upper Lee Beane

Ash

Feildes

Stort

Rib

Figure 6 Model performance for rural (white boxplots) and urbanised (grey boxplots) basins ranked according to the catchments’ response time.

according to their characteristic lag time. In total, there are 15 observations per sub-catchment. The boxplot represent the median, upper and lower quartile, the whiskers extend to the NSEref value within 1.5 times the interquartile range from the box. Outliers are represented by the open circles. As highlighted in the review of the literature, contrasting observations arise from the studies in humid areas. No clear pattern emerges. Models for the Mimram and the Lee catchment to Feildes Weir are less sensitive to spatial rainfall with NSE values close to 1, which highlights the damping effect due to the chalk geology of the Mimram and the integrating effect at the large catchment scale for the Lee. This supports the hypothesis that detailed knowledge of spatial rainfall is not required for basins characterised by a high level of dampening of the rainfall input signal (Obled et al., 1994; Smith et al., 2004; Woods and Sivapalan, 1999; Naden, 1992). In conclusion, this case-study suggests that the controls on the catchment response time are the extent of runoff contributing areas (i.e. the extent of urbanisation and boulder clay drift), which can be moderated by their location with respect to the travel flow to the outlet, and the scale of the catchment. Attention should be focused on these

The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation 132

134

156

176

278

1033

Urban catchment results

0.6 0.4 0.0

0.2

NSE_ref

0.8

1.0

79

127

Ash

Mimram

Rib

Upper Lee

Beane

Stort

Feildes

Figure 7 Model performance for rural (white boxplots) and urbanised (grey boxplots) basins ranked according to catchment scale.

interactions when modelling sub-humid basins in temperate regions. As in Woods and Sivapalan (1999), an analytical framework could be used to assess the relative importance of these interactions. Effect of catchment scale Results displayed in Fig. 7 are similar to those presented in Fig. 6, but with the sub-catchments ranked by size (upper axis in km2). Again the empty circles represent the outlier values. The graph is difficult to interpret. It may be that the sensitivity of the basin to variation in spatial rainfall increases up to the scale of the Beane (175 km2), then decreases with scale as the catchment presents more spatial heterogeneity. At the catchment scale (1040 km2), the integrating effects of the catchment result in less sensitivity to variation in spatial rainfall with NSEref values mostly comprised between 0.8 and 1. However, lower performance is reached with SG1 in the case of the convective summer event (NSEref = 0.65), which indicates that knowledge of spatial rainfall is important at the catchment scale even though a detailed representation is not necessary. In our case, if the interest is in modelling the catchment outlet only, a network of 7 raingauges seems adequate. This is in agreement with the findings of Andre ´assian et al. (2001) who recommend a density of 8 raingauges at the 1120 km2 scale (using lumped modelling). Conclusion Results on existing, predominantly rural, catchments reveal that the models for the behaviour of the basins are sensitive to the type of rainfall events, rainfall representation, catchment scale and catchment type. The findings show a clear relationship between the increase in spatial variability of rainfall and the decrease in model performance. More variability is introduced when extreme or summer events occur. Spatially variable rainfall defined by the reference rainfall and radar data lead to similar flow response whereas larger discrepancies are introduced when using input data from a subset of the raingauges (SG7 and SG1). Results are worse when using a single gauge (SG1) to model the whole catchment. Less sensitivity is observed at the catchment scale.

The primary effects of urbanisation on storm runoff are due to (i) increase in impervious area which increases the amount of runoff, and (ii) hydraulic improvement of flow paths (e.g. roofs, roadways, gutters, pipes and channel) which speeds up the response. Within RORB the runoff coefficient can be varied by changing the percent impervious coefficient (with assumed 90% runoff) and the hydraulic improvement is dealt with by modifying the stream routing parameter according to the type of reach (Laurenson and Mein, 1988). As a numerical experiment to investigate the effects of catchment response, the sub-catchments are turned artificially into urban basins by applying a fraction imperviousness of 30% to all subareas to ensure a faster response, and with the exception of the Stort, by changing the reach type from Natural to Lined (or Piped) with a slope of 0.1%. The same rainfall estimators are tested and the simulated runoff is compared as before to the flow obtained with the reference rainfall. Effect of spatial rainfall resolution Table 8 presents the results in terms of NSEref for urban catchments. Fig. 8 illustrates that urban catchments are faster responding than the existing natural basins. The hydrograph is characterised by a narrow shape and a high peak flow. Further, the urban response is sensitive to the temporal distribution of rainfall, with bursts of rainfall reflected in the hydrograph shape. The average NSEref for all catchments and events is 0.95, 0.92 and 0.73 for radar, SG7 and SG1, respectively. In comparison to rural basins, the performance is maintained for radar data and SG7 but decreases with SG1. As mentioned by Young (2006), the NSE statistic is biased towards the fit of high flows and tends to increase as the length of simulation period decreases. However, these results serve as a first point of comparison and are complemented by the percentage change in Qp, Tp and V. In comparison to rural catchments, the error in Qp and Tp decreases for radar data (9.7% and 5.4% for urban catchments compared to 12.6% and 5.6% for rural catchments) and increases for SG7 (16.5% and 9.8% for urban catchments compared to 15.3% and 5.8% for rural catchments) and SG1 (38.5% and 12.7% for urban catchments compared to 28.1% and 8% for rural catchments). However errors in hydrograph volume increase slightly for radar data (8% for urban catchments compared to 7.4% for rural catchments) and decreases for SG7 (11.1% for urban catchments compared to 12.4% for rural catchments) and SG1 (18.4% for urban catchments compared to 21.6% for rural catchments). The event of 30th July 2002 leads to more variation in the catchment response with a percentage peak change up to 120% compared to 80% for rural catchments. Impact of spatial variability of rainfall The graph in Fig. 9 presents a similar trend as in the case of existing predominantly rural catchments (see Fig. 4) with SG1 leading to lower performance compared to the other rainfall representations. Summer events are characterised by lower NSEref values, especially for SG7 and SG1 (Table 9).

128 Table 8

M.-L. Segond et al. Mean lag time (tc) for existing and artificially urbanised catchments Upper Lee

Mimram

Beane

Rib

Ash

Stort

Feildes

0.97 0.93 0.95

0.92 0.95 0.93

0.98 0.97 0.89

0.81 0.90 0.92

0.95 0.89 0.92

0.97 0.98 0.88

0.98 0.99 0.98

03-February-94 Radar 0.97 SG7 0.95 SG1 0.98

0.97 1 0.98

0.99 0.96 0.83

1 0.94 0.62

1 0.98 0.86

1 1 0.86

1 0.99 0.93

08-January-96 Radar SG7 SG1

0.99 0.95 0.98

0.99 0.79 0.85

0.92 0.93 0.98

0.99 0.91 0.75

1 0.99 0.92

1 0.99 0.89

1 0.99 0.96

16-May-95 Radar SG7 SG1

0.98 0.93 0.82

0.99 0.99 0.77

0.98 0.96 0.69

0.93 0.97 0.66

0.99 0.96 0.40

0.97 0.94 0.81

0.99 1 0.83

30-July-02 Radar SG7 SG1

0.91 0.47 0.16

0.96 0.72 0.72

0.59 0.76 0.01

0.80 0.68 0.04

0.98 0.82 0

0.90 0.95 0.15

0.94 0.94 0.46

11-October-93 Radar SG7 SG1

Feildes

Reference Radar SG7 SG1

20

40

60

50 0

0 0

100

Flow cumecs

40

Flow cumecs

20

40 0

20

Flow cumecs

150

60

60

200

80

Mimram

80

Beane

0

20

40

60

0

20

40

time (h)

time (h)

time (h)

Mixed Chalk and Clay catchment

Chalk catchment

Catchment scale

Figure 8

60

Reference and simulated flow at urban catchment outlets on 30/07/02.

Influence of catchment response time and catchment scale Table 8 presents the response time of the urbanised catchments. The response times of the existing and urbanised basins are plotted against catchment area in Fig. 5. It can be seen that the impact of urbanisation decreases the catchment response time by about 50% on average across all basins. The graph in Fig. 6 compares the model performance in terms of NSEref for the rural and urban sub-catchments. The basins are ranked according to the rural catchment re-

sponse time. The impact of urbanisation has increased the interquartile range in NSEref for the Mimram, the Ash and the Rib (i.e. the chalk and the two entirely rural basins) whereas the range has decreased for the upper Lee, the Beane, the Stort and the upper catchment to Feildes Weir (i.e. the more heterogeneous basins including a mixture of clay and chalk and zones of urban developments). Similarly, Fig. 7 compares the performance of rural and urban catchments but ranked by size. The results show that urbanisation has an impact on the model performance at sub-basin scale. At catchment scale, the NSEref remains high using

The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation

0.6 0.4

NSE_ref

0.8

1.0

dar data. SG7 leads to high NSEref (0.92) but higher errors in Qp (16.5%) and Tp (9.8%). Lowest model performance characteristics are obtained with SG1.

Discussion and conclusions

Radar SG7

0.0

0.2

SG1

0

10

20

30

40

30

40

0.6 0.4

Winter Summer

0.0

0.2

NSE_ref

0.8

1.0

SDIR (%)

0

10

20

SDIR (%)

Figure 9 Impact of rainfall spatial variability on NSE. Influence of rainfall representation (top) and type of rainfall events (bottom).

Table 9 Percentage change of peak to peak and hydrograph volume for the urbanized catchments

Qp (%) Tp (%) V (%)

129

Radar

SG7

SG1

9.7 5.4 8.0

16.5 9.8 11.1

38.5 12.7 18.4

SG7 and radar data. Lower performance is observed using SG1 during summer events. Conclusion In conclusion, results show that radar data lead to similar performance on rural and urban catchments. SG7 applied on urbanised basins leads to similar NSEref values as in the case of rural basins but to larger errors in Qp and Tp. The discrepancies are enhanced for SG1, especially in the case of summer events. The effect of urbanisation decreases the lag time by 50% on average for all sub-catchments. However, the impacts of the lag time and the catchment scale on the runoff response are not clearly evidenced. Only at the catchment scale, less sensitivity to spatial rainfall (using radar data and SG7) is observed. A summary of the model performance characteristics obtained on average for all catchments and events and for all rainfall representations on urbanised catchments is presented in Table 8. Higher NSEref performance (0.95) and lower errors in Qp (9.7%) and Tp (5.4%) are obtained with ra-

The literature on the significance of spatial rainfall for runoff estimation is complex and sometimes contradictory. Effects can be expected to vary depending on the nature of the rainfall, the nature of the catchment, and the spatial scale of the catchment and rainfall. Runoff from urban areas is extremely sensitive to spatial rainfall, and the same is true for arid areas, where rapid flow response is generated from spatially localised convective rainfall. This is problematic, since the required density of raingauges to capture the spatial variability exceeds that normally available from routine monitoring networks. For temperate regions, the review highlighted the trade-off in terms of catchment response between the impact of spatial variability of rainfall and the smoothing effect due to the heterogeneity of the catchment. Hence it was observed that as the scale increases, the importance of spatial rainfall decreases and there is a transfer from spatial variability of rainfall to catchment response time distribution as the dominant factor governing runoff generation. Following the guidance from the literature, a numerical experiment was conducted on the Lee catchment and the main findings of this study are summarised below: • The dominant effect for runoff production is the spatial variability of rainfall; as this increases, so does the significance of appropriate rainfall characterisation. The catchment response is a complex relationship between the spatially variable input and the watershed heterogeneity. For a range of representative events, spatial deviations in rainfall of up to 40% were observed depending on the type of data available and this was reflected in the simulated hydrograph. At the subcatchment scale, spatial deviations in rainfall above 10% led to variations greater than 20% in the peak flow and 10% in the volume of the hydrograph. Spatial deviation in rainfall above 20% led to NSE performance below 0.8. Results showed that more variability in the rainfall distribution was introduced when extreme or summer events occurred. • Spatially variable rainfall and radar data led to similar flow responses whereas larger discrepancies were introduced when using input data from a subset of the raingauges. Using radar data, results in terms of NSE were robust and remained high (usually above 0.9). Using one gauge per tributary achieved high NSE value at the catchment scale but could lead to low NSE values at the sub-catchment scale. When a unique rain gauge was used to model the catchment response, the results worsened at both sub-catchment and catchment scales and also affected the reproduction of the hydrograph. Since the model was calibrated using spatially variable rainfall defined by the full raingauge network, the performance of radar data over the spatially variable rainfall could not be assessed. However, results for the largest summer event suggested that

130

•

•

•

•

large spatial deviations in rainfall (about 30%) could be observed between the radar data and the full raingauge network. The damping behaviour of the modelled basin was characterised by the catchment response time. The dominant controls on runoff response were the size of the catchments and the extent of runoff contributing areas. Their location with flow distance to the outlet was incorporated in the modelling framework. However, the catchments were highly heterogeneous, so that it was not possible to assess the relative importance of these interactions. As a result, no clear pattern emerged as a function of catchment scale, or response time. Further work is required to identify their importance quantitatively. The sub-catchments varied greatly in geology and runoff response. It was found that the models of the clay and/or partly urban sub-catchments were more sensitive to the spatial distribution of rainfall, whereas the chalk rural sub-catchment, the Mimram, exhibited a damping behaviour of the rainfall input. At a catchment scale of 1000 km2, the impact of spatial variation of rainfall on runoff was less than at the sub-catchment scale of 80– 280 km2. This underlines the integrating effect of the catchment as the size increases. However, the catchment modelling still benefits from spatial information in the case of convective summer events. When the existing sub-catchments were artificially turned into fast-responding urban basins, a decrease in the catchment response time (about 40% on average for all subcatments) was observed and the discrepancies in terms of reproduction of peak flow and runoff volume were enhanced for the most variable events. This confirms that urban catchments require a fine spatial and temporal resolution to adequately reproduce the streamflow. It is concluded that, for largely rural catchments, a network of 16 raingauges seems appropriate at 1000 km2 scale; between 4 and 7 gauges are required at 80– 280 km2 but this recommendation may not be appropriate for summer convective events. As urbanisation increases, the requirements become greater because urban basins are more sensitive to the spatial and temporal distribution of rainfall. It seems that sub-hourly data and a spatial resolution of the order of a few kilometers are required and there is therefore a need for radar data.

Improvement in the modelling strategy would include automatic calibration, incorporation of a larger number of subdivisions in the model structure and the possibility of varying model parameters at sub-catchment scale automatically. A simple spatial interpolation scheme based on the Thiessen polygon method was used here to calculate the areal rainfall. Methods that take into account the distance between the estimation point and the observation stations, such as inverse distance weighting and multiquadratics, may be more suitable to model summer events. Possible extension of this work involves the use of continuous simulation to assess the sensitivity of the catchment response to the rainfall estimators under various catchment and storm conditions, and facilitate the derivation of flood frequency curves.

M.-L. Segond et al. Hence the importance of rainfall spatial variability is confirmed but further investigation on the impact of catchment scale on runoff generation should be undertaken. The catchments used in this investigation are very heterogeneous: thus the impact of catchment properties may have masked the impact of catchment scale. It would be interesting to redo the analysis on a more homogeneous catchment and run different rainfall scenarios at various sub-catchment scales. Further, an analysis at an intermediate catchment scale (about 500 km2) is required.

Acknowledgments M.-L. Segond was in receipt of a UK Natural Environment Research Council research studentship, and has been partially supported by research contract FD2105 between Imperial College London and University College London and the UK Department for Environment, Food and Rural Affairs. The data have been made available by the Environment Agency of England and Wales for use in this study. The authors would like to thank R. Chandler and V. Isham for valuable discussions and E. Bellone for her assistance with the use of radar data. The authors are grateful to R. Mein for his advise with the use of the RORB model and to R. Hawnt for providing some model configuration datafiles of the Lee catchment; and would also thank W. Quasem for his contribution to the rainfall–runoff calibration of the Lee catchment. The authors thank the two anonymous reviewers for their useful comments that helped improving the manuscript.

References Ajami, N., Gupta, H., Wagener, T., Sorooshian, S., 2004. Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system. Journal of Hydrology 298, 112– 135. Andre ´assian, V., Perrin, C., Michel, C., Usart-Sanchez, I., Lavabre, J., 2001. Impact of imperfect rainfall knowledge on the efficiency and the parameters of watershed models. Journal of Hydrology 250, 206–223. Arnaud, P., Bouvier, C., Cisneros, L., Dominguez, R., 2002. Influence of rainfall spatial variability on flood prediction. Journal of Hydrology 260, 216–230. Bell, V., Moore, R., 2000. The sensitivity of catchment runoff models to rainfall data at different spatial scales. Hydrology and Earth System Sciences 4 (4), 653–667. Berne, A., Delrieu, G., Creutin, J.-D., Obled, C., 2004. Temporal and spatial resolution of rainfall measurements required for urban hydrology. Journal of Hydrology 299, 166–179. Beven, K., Hornberger, G.M., 1982. Assessing the effect of spatial pattern of precipitation in modelling stream flow hydrographs. Water Resources Bulletin 18 (5), 823–829. Carpenter, T., Konstantine, P., Sperfslagea, J., 2001. On the parametric and nexradradar sensitivities of a distributed hydrologic model suitable for operational use. Journal of Hydrology 253, 169–193. Chaubey, I., Hann, C., Grunwald, S., Salisbury, J., 1999. Uncertainty in the model parameters due to spatial variability of rainfall. Journal of Hydrology 220, 48–61. Chow, V., Maidment, D., Mays, L., 1988. Applied Hydrology. McGraw-Hill.

The significance of spatial rainfall representation for flood runoff estimation: A numerical evaluation de Lima, J., Singh, V., 2002. The influence of the pattern of moving rainstorms on overland flow. Advances in Water Resources 25, 817–828. Dodov, B., Foufoula-Georgiou, E., 2005. Incorporating the spatiotemporal distribution of rainfall and basin geomorphology into nonlinear analyses of streamflow dynamics. Advances in Water Resources 28, 711–728. Faure `s, J., Goodrish, D., Woolhiser, D., Sorooshian, S., 1995. Impact of small-scale spatial rainfall variability on runoff modeling. Journal of Hydrology 173, 309–326. Flynn, Rothwell, 1991a. Report on hydraulic modelling (ONDA) of the River Stort. Report to Thames Region, National Rivers Authority, London, UK. Flynn, Rothwell, 1991b. Report on hydrologic modelling (RORB) of Middle Lee. Report to Thames Region, National Rivers Authority, London, UK. Grayson, R., Blo ¨schl, G., 2000. Spatial modelling of catchment dynamics. In: Grayson, R., Blo ¨schl, G. (Eds.). Spatial Patterns in Catchment Hydrology: Observations and Modelling. Cambridge press, pp. 51–81. Hawnt, R., 1987a. Catchment runoff control study, Report on the evaluation of the hydrological response of the Mimram and Beane catchments. Technical Report, Thames Water, Rivers Division. Hawnt, R., 1987b. Catchment runoff control study, Report on the evaluation of the hydrological response of the catchments of the Rib and Ash. Technical Report, Thames Water, Rivers Division. Koren, V., Finnerty, B., Schaake, J., Smith, M., Seo, D.-J., Duan, Q.-Y., 1999. Scale dependencies of hydrologic models to spatial variability of precipitation. Journal of Hydrology 217, 285–302. Laurenson, E., Mein, R., 1988. RORB version 4 Runoff Routing program, User Manual. Technical Report, Monash University, Department of Civil Engineering. Lopes, V., 1996. On the effect of uncertainty in spatial distribution of rainfall on catchment modelling. CATENA 28, 107–119. Lotufo Conejo, J., 1979. Hydrologic simulation and flood routing models: a case study. Technical Report, Imperial College London. Michaud, J., Sorooshian, S., 1994. Effect of rainfall-sampling errors on simulations of desert flash floods. Water Resources Research 30 (10), 2765–2775. Moore, R.J., May, B., Jones, D., Black, K., 1994. Local calibration of weather radar over London. In: Advances in Radar Hydrology. European Commission, pp. 186–195. Morin, E., Enzel, Y., Shamir, U., Garti, R., 2001. The characteristic timescale for basin hydrological response using radar data. Journal of Hydrology 252, 85–99. Naden, P., 1992. Spatial variability in flood estimation for large catchments: the exploitation of channel network structure. Journal des Sciences Hydrologiques 37 (1), 53–71.

131

Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models, part 1 – a discussion of principles. Journal of Hydrology 10 (3), 282–290. NERC, 1975. Flood Studies Report, Hydrological Studies, vol. 1. Natural Environment Research Council, UK. Ngirane-Katashaya, G., Wheater, H., 1985. Hydrograph sensitivity to storm kinematics. Water Resources Research 21 (3), 337–345. Obled, C., Wendling, J., Beven, K., 1994. The sensitivity of hydrological models to spatial rainfall patterns: an evaluation using observed data. Journal of Hydrology 159, 305–333. Ogden, F., Julien, P., 1993. Runoff sensitivity to temporal and spatial rainfall variability at runoff plane and small basin scales. Water Resources Research 29 (8), 2589–2597. Ogden, F., Julien, P., 1994. Runoff model sensitivity to radar rainfall resolution. Journal of Hydrology 158, 1–18. Pessoa, M.L., Bras, R.L., Williams, E.R., 1993. Use of weather radar for flood forecasting in the Sieve river basin: a sensitivity study. Journal of Applied Meteorology 32, 462–474. Quasem, W.M., 2004. Effect of spatial variability of rainfall on runoff for the lee catchment. Master’s thesis, Imperial College London. Shah, S., O’Connel, P., Hosking, J., 1996. Modelling the effects of spatial variability in rainfall on catchment response. 2. Experiments with distributed and lumped models. Journal of Hydrology 175, 89–111. Singh, V., 1997. Effect of spatial and temporal variability in rainfall and watershed characteristics on stream flow hydrograph. Hydrological Processes 11, 1649–1669. Smith, M., Koren, V., Zhang, Z., Reed, S., Pan, J., Moreda, F., 2004. Runoff response to spatial variability in precipitation: an analysis of observed data. Journal of Hydrology 298, 267–286. Syed, K., Goodrich, D., Myers, D., Sorooshian, S., 2003. Spatial characteristics of thunderstorm rainfall fields and their relation to runoff. Journal of Hydrology 271, 1–21. Tetzlaff, D., Uhlenbrook, U., 2005. Effects of spatial variability of precipitation for process-oriented hydrological modeling: results from two nested catchments. Hydrology and Earth System Sciences 9, 29–41. Wheater, H., Isham, V., Chandler, R., Onof, C., Stewart, E., Bellone, E., Yang, C., Lekkas, D., Lourmas, G., Segond, M.-L., Frost, A., Prudhomme, C., Crooks, S. 2005. Improved methods for national spatial–temporal rainfall and evaporation modelling for BSM. R&D Technical Report F2105/TR for DEFRA, Imperial College London and University College London. Woods, R., Sivapalan, M., 1999. A synthesis of space-time variability in storm response: rainfall, runoff generation and routing. Water Resources Research 35 (8), 2469–2489. Young, A., 2006. Stream flow simulation within UK ungauged catchments using a daily rainfall–runoff model. Journal of Hydrology 320, 155–172.