Added-value from a multi-criteria selection of donor catchments in the prediction of continuous streamflow series at ungauged pollution control-sites

Abstract

We explore the potential of a multi-criteria selection of donor catchments in the prediction of continuous streamflow series by the spatial proximity method. Three criteria have been used: (1) spatial proximity; (2) physical similarity; (3) stream gauging network topology. An extensive assessment of our spatial proximity method variant is made on a 149 catchment-data set located in the Rhine-Meuse catchment. The competitiveness of the method is evaluated against spatial interpolation of catchment model parameters with ordinary kriging. We found that the spatial proximity approach is more efficient than ordinary kriging. When distance to upstream/downstream stream gauge stations is considered as a second order criterion in the selection of donor catchments, an unprecedented level of efficiency is reached for nested catchments. Nevertheless, the spatial proximity method does not take advantage from physical similarity between donor catchments and receiver catchments because catchments that are the most hydrologically similar to each catchment poorly match with the catchments that are the most physically similar to each catchment.

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Proc. IAHS, 373, 6972, 2016 proc-iahs.net/373/69/2016/ doi:10.5194/piahs-373-69-2016 Author(s) 2016. CC Attribution 3.0 License.

Open Access

Added-value from a multi-criteria selection of donor catchments in the prediction of continuous streamow series at ungauged pollution control-sites

Gilles Drogue1, Wiem Ben Khediri1, and Cline Conan2

1Laboratoire LOTERR, Universit de Lorraine, Metz, 57045 CEDEX 1, France

2Agence de lEau Rhin-Meuse, Moulins Ls Metz, 57161 BP 30019, France

Correspondence to: Gilles Drogue ([email protected])

Published: 12 May 2016

Abstract. We explore the potential of a multi-criteria selection of donor catchments in the prediction of continuous streamow series by the spatial proximity method. Three criteria have been used: (1) spatial proximity;(2) physical similarity; (3) stream gauging network topology. An extensive assessment of our spatial proximity method variant is made on a 149 catchment-data set located in the Rhine-Meuse catchment. The competitiveness of the method is evaluated against spatial interpolation of catchment model parameters with ordinary kriging. We found that the spatial proximity approach is more efcient than ordinary kriging. When distance to upstream/downstream stream gauge stations is considered as a second order criterion in the selection of donor catchments, an unprecedented level of efciency is reached for nested catchments. Nevertheless, the spatial proximity method does not take advantage from physical similarity between donor catchments and receiver catchments because catchments that are the most hydrologically similar to each catchment poorly match with the catchments that are the most physically similar to each catchment.

1 Introduction

Because quantitative hydrological information contribute to the understanding of short and medium-term uctuations in pollutants concentrations recorded in river ows (e.g. Burt et al., 2010), there is a strong demand to reconstruct continuous ow time series at ungauged pollution-control sites for short (i.e. up to 15 days) and medium (i.e. up to 180 days) lead times, before and after the river water sampling has occurred. The best way to handle this problem would be to set up a coordinated monitoring network in order to get continuous streamow series at the point where water quality data are collected. Unfortunately, different brakes like nancial costs, logistics and most often diverging interest between water ow managers prevent the design of such a coordinated data-acquisition network. Therefore, rainfall-runoff modelling strategies can be viewed as surrogate models for reconstructing and simulating continuous ow time series at ungauged pollution control-sites. In the French part of the Rhine-Meuse catchment, we made different attempts

to produce daily streamow series through regionalisation of catchment model parameters (Drogue and Plasse, 2014; Plasse et al., 2014). In the worst case, where no hydrological information is available at the point of interest, we came to the conclusion that, in our temperate non Mediterranean area, the spatial proximity method is the best approach to solve the regionalisation problem of hydrograph prediction provided for the hydrological network is sufciently dense(i.e. 1 station per 250 km2). But our results have also shown that there is still a considerable room for progress in reducing the prediction error in such hydrological information at un-gauged catchments. For that reason and also because there is an important part of nested catchments in our catchment-data set, we test a variant of the spatial proximity approach where the donor catchments are not only selected according to their spatial proximity but also according to their physical similarity and gauging network connectivity from the receiver catchment.

Published by Copernicus Publications on behalf of the International Association of Hydrological Sciences.

70 G. Drogue et al.: Prediction of river ows for ungauged pollution-control sites

2 Setting the scene: study area and datasets

2.1 Study area

The investigated territory corresponds to the French part of the Rhine-Meuse catchment (North-Eastern part of France).The presence of the Vosges Mountains induces climatic gradients among highest of France. Considering the weak inuence of snow on the hydrological regime of the upstream mountain rivers, the snow component is not taken into account in the regionalisation study reported in this paper.

2.2 Datasets

We split the entire period of observations (19902002) into two periods: from 1 January 1990 to 31 December 1995 and from 1 January 1996 to 31 December 2002. Warm up periods of one year has been used in both cases. For the efciency estimation of the catchment model regionalisation we used the second sub-period as a conrmatory period.

2.2.1 Catchment-data set

We made an extensive assessment of our regionalisation scheme on a dense stream gauging network (approximately 1 gauging station for 250 km2) comprising 149 reliable stations gauging non-regulated rivers and providing daily streamow values validated on the target period 19902002. More than half of these stations are also dedicated to water quality monitoring. The drainage areas lie between 5 and 11 500 km2.

The catchment set includes 40 % of nested catchments (i.e. 60 % of adjacent catchments). The territory covered by our catchment sample is approximately 38 000 km2. This accounts for 15 % of the total drainage area of the Rhine-Meuse catchment ( 200 000 km2 at the outlet).

2.2.2 Climate forcings and rainfall-runoff model

In addition to streamow data, we also collected daily precipitation and potential evapo-transpiration from the SAFRAN gridded climatology data. The daily lumped GR4J rainfall runoff model (Perrin et al., 2003) has been calibrated over the training period (19901995) by using the BroydenFletcherGoldfarbShanno algorithm (hill climbing optimization technique; see Byrd et al., 1995). Parameters have been optimized with the NashSutcliffe coefcient computed on the square root of the daily streamow series (NSsqrtQ).

This power transformation makes possible to dene a parameter set representative of the catchment behaviour on all the streamow range. The repetition of the split-sample test for all the catchment-data set allows setting up a regional library containing 149 vectors of four optimal parameters.

3 How strengthening the spatial proximity approach?

In a rst simulation experiment, we optimized the performance of the spatial proximity approach allowing the output averaging option and four geographic neighbours (Plasse et al., 2014). In this basic version of the spatial proximity approach, we lter out poorly modelled donor catchments,i.e. the ones having a NSsqrtQ below 0.7 in calibration mode. In this study we go one step further by selecting geographic neighbours according to a regional composite rank mixing elementary ranks related to spatial proximity, physical similarity and stream gauging network topology. The experiment design is described in Fig. 1.

As for a truly ungauged catchment, streamow hydro-graph is unkown, we apply a method that introduces hydro-logical catchment behaviour in the assessment of catchment physical similarity (Oudin et al., 2010). We compute two catchment classications (a hydrological one and a physical one) where similarity is dened as an Euclidean distance in the catchment property space: for the hydrological classication we use seven hydrological signatures calculated on the 19902002 period (runoff coefcient, lag time, Base Flow Index, slopes of the Flow Duration Curve for the high ow range, the low ow range and the medium ow range, rising limb density); for the physical classication we use 70 catchment attributes related to climate, geology, land cover, hydrology and morphology and a weighted version of the Euclidean distance for estimating the catchment similarity. Then, we sought physical attributes allowing the best matching between both classications according to the Adjusted Rand Index ARI (Hubert and Arabie, 1985). We also incorporate the hydraulic connectivity of nested catchments in the composite rank calculation (Fig. 1). We proceed in a very simple way: for a target point having upstream/downstream neighbour(s), we assign a topological rank to neighbour(s) according to the stream network distance between the target point and its neighbours. The closest is the gauging station the smallest is the rank. For adjacent stations, we add one to the rtopo value of the furthest upstream/downstream neigh-bour(s) rank value. For an adjacent receiver catchment, the topological rank is set to 0. We examine the efciency of our regionalisation method by jakknife cross validation (Fig. 1). As the catchment-data set is quite large, a [1; 1] bounded

version of the NSsqrtQ criterion (called C2M) is calculated for efciency estimation (Mathevet et al., 2006). For sake of robustness evaluation, the GR4J model parameters are also regionalised by ordinary kriging (OK). The variogram properties of GR4J model parameters are summarized in Table 1. As the X2 parameter has no spatial autocorrelation, the median value is used.

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G. Drogue et al.: Prediction of river ows for ungauged pollution-control sites 71

Euclidean distance between catchment centrods (Spatial proximity)

Step 1 : Selection of a receiver catchment i

Step 2 : Ranking of donor catchments according to

Step 5 : Sensitivity analysis to weights in calculation

(increment of 0.2)

Optimal number of donor catchmentsand weights in composite rank calculation leading to the best C2M quantiles (149 values)

Hydrologically intelligent physical attributes (Physcial similarity)

Upstream/downstream distance to the outlet of the catchment i (Gauging network topology)

rgeo rphys rtopo

Step 4 : Streamflow prediction and output averaging for n= 1 to 149

Best weights for calculation according to the C2M criterion

Best combination of donor catchments according to the

C2M criterion

Step 3 : Calculation of a composite rank for the donor catchments

For n = 1 to 149 receiver catchments

Figure 1. Flowchart of the regionalisation scheme applied to our catchment-data set.

Table 1. Variogram models used to interpolate the X1, X3 and X4 GR4J model parameters in the study area.

model parameter Denition Variogram model

X1 (mm) maximal capacity of the production reservoir spherical; range: 100 km; sill: 250 000 mm2

X3 (mm) capacity of the non linear routing reservoir spherical; range: 37 km; sill: 3100 mm2

X4 (day) unit hydrograph time base spherical; range: 35 km; sill: 0.25 day2

Table 2. Physical attributes maximizing the Adjusted Rand Index (ARI) computed between the classication based on physical attributes and the classication based on hydrological signatures.

Iterations Physical attributes Number of Weights in Euclidean Adjusted Rand Index ()

clusters distance metric

1 Catchment perimeter 13 1 0.333

2 Catchment perimeter (CP) + 13 CP: 0.5 0.545

proportion of Strahler stream order 5 (SSO5) SSO5: 0.5

4 Results and discussion

4.1 Which physical attribute(s) of catchment could be used as proxie(s) for hydrological similarity?

The catchment classication based on hydrological signatures leads to nine clusters. The two physical attributes optimizing the ARI index are the catchment perimeter and the proportion of Strahler stream order 5 (Table 2). Nevertheless, the intermediate value of ARI (0.545) shows that physical catchment characteristics are poor proxies for describing hydrological behaviour similarity patterns. In order to orient future researches, a focus should be made on hydrological signatures that discriminate the most hydrologically similar catchments and physically similar catchments (Oudin et al., 2010).

4.2 Overall performance of the multi-criteria spatial proximity approach

Looking at Fig. 2 we can see that the spatial proximity method produces less prediction error than OK over the conrmatory period. An improvement of model hydrograph prediction at ungauged sites could be obtained when using the multi-criteria selection approach with four donor catchments, especially for well regionalised catchments (Fig. 2). Optimal weights in composite rank leading to that result are respectively 1 = 0.8 for rgeo (spatial proximity), 2 = 0.1 for rphys

(physical similarity) and 3 = 0.1 for rtopo (distance between

upstream/downstream gauging stations). It means that for the considered monitoring stream gauge network, physical similarity and network topology have a second order effect in the selection of pertinent donor catchments in comparison to Euclidean distance between catchment centroids. Therefore, as a rst guess and with the specicity of our study area,

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72 G. Drogue et al.: Prediction of river ows for ungauged pollution-control sites

0.0

A tsite calibration

Ordinary kriging

Spatial proximity (output averaging with four neighbours)

Spatial proximity (multi criteria selection and output averaging with four neighbours)

1.0

0.9

0.8

Cumulative frequency

0.7

0.6

0.5

0.4

0.3

0.2

0.1

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Model efficieny (C2M)

Figure 2. Cumulative distribution functions (CDFs) of GR4J model efciencies using model parameters regionalised by three methods. CDF for at-site calibration efciencies is also shown. Results are given in validation mode.

the simple spatial proximity method can be regarded as good enough (see also Parajka et al., 2005).

5 Conclusions

We tested a multi-criteria variant of the spatial proximity approach for daily hydrograph prediction at ungauged sites. Three criteria were used to choose the neighbours of a target catchment: spatial proximity, physical similarity (conditioned by catchment hydrological similarity patterns) and distances between upstream/downstream neigh-bours for nested catchments. No added value comes up from using physical similarity in the selection process of donor catchments. Poorly regionalised catchments do not take advantage from the multi-criteria approach. For well modelled nested catchments, prediction error of hydrograph in ungauged conditions could be reduced by prioritizing upstream/downstream neighbours among the closest donor catchments. In light of these results, hydrograph prediction over ungauged catchments through catchment model region-alisation denitely appears as a learning process.

Acknowledgements. We would like to thank Mto France for providing the SAFRAN reanalysis data, the SCHAPI for providing access to the HYDRO streamow archive, the German Federal Waterways and Shipping Administration as well as the German Federal Institute of Hydrology (BfG) for providing the German streamow data, and the Service public de Wallonie, Direction gnrale oprationnelle Mobilit et Voies hydrauliques, Direction de la Gestion hydrologique intgre, Service dEtudes Hydrologiques (SETHY) for making the Belgian streamow data freely available. We also would like to acknowledge the Rhine-Meuse French Water Agency for its nancial support (Grant no. 15C54112) and the two anonymous reviewers for their thorough review.

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