Identification of the parameters of rainfall-runoff models at ungauged locations: can we benefit from the regionalization of flow statistics?

Transcription

1 Identification of the parameters of rainfall-runoff models at ungauged locations: can we benefit from the regionalization of flow statistics? Gianluca Boldetti (1), Vazken Andréassian (1), Ludovic Oudin (2), Charles Perrin (1) (1) Cemagref, Antony, France (2) Université Pierre et Marie Curie, Paris, France EGU Leonardo 2010 Luxembourg, November

2 Context A four-parameter lumped RR model (GR4J) An ungauged catchment for which only the streamflow record is unknown Many gauged catchments Our objective here is to identify one suitable parameter set. The efficiency criterion used here is NSE, calculated on square-rooted flows 2 EGU Leonardo 2010 Luxembourg, November

3 Different regionalization approaches DIRECT METHODS regression INDIRECT METHODS One regionalizes flow statistics first catchment-similarity measures On this basis, candidate ( behavioural ) parameter set(s) can be identified spatial proximity Several recent studies (Yadav et al., 2007; Bardossy, 2007; etc ) 3 EGU Leonardo 2010 Luxembourg, November

4 Different approaches DIRECT METHODS regression INDIRECT METHODS One regionalizes flow statistics first catchment-similarity measures On this basis, candidate ( behavioural ) parameter set(s) can be identified spatial proximity Several recent studies (Yadav et al., 2007; Bardossy, 2007; etc ) 4 EGU Leonardo 2010 Luxembourg, November

5 Behavioural parameter set In our case we are looking for the (single) parameter set that best reproduces some previously regionalized statistics which (we hope!) will also be a NS-efficient set What is the impact of the statistics regionalization efficiency? Where do we look for candidate parameter sets? Do we want a broad library or a more constrained one? Is such a method robust? 5 EGU Leonardo 2010 Luxembourg, November

6 Our Data We worked on 794 catchments, all located in France. For each catchment, we had at least 80% of streamflow data between 1986 and 2005 (we only used data from this 20 year period). Daily time step Forest % Slope (etc...) For each catchment, several physiographic descriptors were available. 6 EGU Leonardo 2010 Luxembourg, November

7 Flow statistics used Q [ mm] Average runoff /01/ /12/ /12/ Q0, Q10,Q100 fdc quantiles, normalized by the average daily flow 10 Slopes of the FDC Q/Qav % exceedence LAG : time shift for which the correlation between rainfall and runoff records is the highest 7 EGU Leonardo 2010 Luxembourg, November

8 Flow statistics used Q [ mm] Average runoff /01/ /12/ /12/ Q0, Q10,Q100 fdc quantiles, normalized by the average daily flow 10 Slopes of the FDC Q/Qav % exceedence LAG : time shift for which the correlation between rainfall and runoff records is the highest 8 EGU Leonardo 2010 Luxembourg, November

9 Flow statistics used Q [ mm] Average runoff /01/ /12/ /12/ Q0, Q10,Q100 fdc quantiles, normalized by the average daily flow 10 Slopes of the FDC Q/Qav % exceedence LAG : time shift for which the correlation between rainfall and runoff records is the highest 9 EGU Leonardo 2010 Luxembourg, November

10 Flow statistics used Q [ mm] Average runoff /01/ /12/ /12/ Q0, Q10,Q100 fdc quantiles, normalized by the average daily flow 10 Slopes of the FDC Q/Qav % exceedence LAG : time shift for which the correlation between rainfall and runoff records is the highest 10 EGU Leonardo 2010 Luxembourg, November

11 Regionalization of statistics Two steps: 1. Stepwise regression between statistics and physiographic descriptors (log-transformed worked best) ln( Q ˆ) = a + b ln( x1) IDW interpolation of the residuals (ratios between empirical and regression-generated statistic) ϑ = Q / Q ˆ b n ln( x 1 n ) (jack-knife) 11 EGU Leonardo 2010 Luxembourg, November

12 Evaluation of parameter sets, step one x 1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 x1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 we work with a library constituted by the calibrated parameter sets of all our catchments (other than the single catchment we treat as ungauged) x 1 x 2 x 3 x 4 parameter sets x 1 x 2 x 3 x 4 x1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 x1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 For each parameter set, our model is run with the rainfall record of the ungauged catchment x 1 x 2 x 3 x 4 Flow statistics are calculated on the simulated streamflow record Q m,q 100, 12 EGU Leonardo 2010 Luxembourg, November 0

13 Evaluation of parameter sets, step two For each statistic, we calculate the difference between simulation-generated and regionalized values. (This error is normalized by the variation range of each statistic) err = Qˆ sim Qˆ reg A penalty score is calculated, as a weighted sum of all errors (the weights are calibrated to maximize the median NSE) p = α w i err i In the end, we keep the parameter set with the lowest score 13 EGU Leonardo 2010 Luxembourg, November

14 What is the impact of regionalization efficiency? benchmarks NSE st neighbour ideal We would like to do better than just borrowing the closest neighbour s parameters % exceedence In any way, we could not do better than the black line (this method cheats, and chooses the best possible parameter set in the library) 14 EGU Leonardo 2010 Luxembourg, November

15 What is the impact of regionalization efficiency? regression-estimated signatures NSE st neighbour ideal With regressionestimated flow statistics, we don t satisfy our objective of beating the first neighbour case. 0.1 regression % exceedence Average Runoff 1.0E+01 Q30 Q30-Q70 2.0E+03 regression 1.0E+03 regression 5.0E+00 regression 5.0E E E E E E E E E E E E+00 data data data 15 EGU Leonardo 2010 Luxembourg, November

16 What is the impact of regionalization efficiency? regression+idw estimated signatures NSE Using the regression+idw estimates yelds a small (but noticeable) improvement st neighbour ideal regression+idw Still, the first neighbour isn t beaten % exceedence Average Runoff 1.0E+01 Q30 Q30-Q70 regression+idw 2.0E E+03 regression+idw 5.0E+00 regression+idw 5.0E E E E E E E E E E E E+00 data 16 EGU Leonardo 2010 Luxembourg, November data data

17 What is the impact of regionalization efficiency? NSE signatures of the observed record (cheat) 1st neighbour ideal regression+idw cheat % exceedence We cheated, using the flow statistics we had calculated on the actual runoff record (forgetting our catchment is ungauged ) In this case, the result would be satisfying! 17 EGU Leonardo 2010 Luxembourg, November

18 where do we look for parameter sets? Do we want a broad parameter set library or is it worth to constrain it? As our network is very dense, we tested a constraint based on spatial proximity (of course not the only possibility) 18 EGU Leonardo 2010 Luxembourg, November

19 where do we look for parameter sets? NSE sets from first 7 neighbours 1st neighbour ideal regression+idw % exceedence We tried limiting the available parameter sets to those of the closest 7 gauged catchments. It seems easier to identfy efficient parameter sets, we re finally doing better than the first neighbour method. 19 EGU Leonardo 2010 Luxembourg, November

20 where do we look for parameter sets? NSE sets from first 7 neighbours ideal regression+idw cheat % exceedence The impact of flow statistics estimation efficiency is slightly less dramatic than without constraints. Even when cheating we get better results here than without constraint. 20 EGU Leonardo 2010 Luxembourg, November

21 where do we look for parameter sets? sets from first 7 neighbours NSE ideal 7 neigh. regression+idw cheat However, there is a drawback : the potential of an ideal case, where we always pick the best possible parameter set, is diminished (smaller margin for improvement) % exceedence 21 EGU Leonardo 2010 Luxembourg, November

22 Is such a method robust? 794 catchments over France : a very spatially-dense gauging network 100 closest neighbours % non-exceedence distance [km] 22 EGU Leonardo 2010 Luxembourg, November

23 Is such a method robust? The red-circled catchments sit in the middle of an hydrological desert. We can artificially put other catchments of our dataset in the same situation, by preventing them to see their closest neighbours 23 EGU Leonardo 2010 Luxembourg, November

24 Is such a method robust? No hydrological desert This is what happened without simulating the hydrological desert situation NSE st neighbour all sets 7 neighbours For this case and the following two, we used regression-estimated flow statistics (no IDW) % exceedence 24 EGU Leonardo 2010 Luxembourg, November

25 Is such a method robust? hydrological desert : closest neighbour at 20 km In this case, we only accepted parameter sets from catchments being at least 20 km away NSE st neighbour all sets 7 neighbours % exceedence While pure spatial proximity loses interest, the two options using flow statistics keep almost unchanged performances 25 EGU Leonardo 2010 Luxembourg, November

26 Is such a method robust? hydrological desert : closest neighbour at 50 km 50 km hydrological desert 0.8 NSE st neighbour all sets 7 neighbours constraining the choice of parameter sets on a spatial-proximity base starts to be less interesting, even if not yet detrimental. % exceedence 26 EGU Leonardo 2010 Luxembourg, November

27 Conclusions There is a strong dependence on the signature s regionalization efficiency There s a clear advantage in combining this method with at least another way of selecting candidate sets (in this case, spatial proximity) This method seems a good choice for spatially sparse networks, provided that flow signatures can still be satisfactorily estimated at ungauged locations 27 EGU Leonardo 2010 Luxembourg, November

28 Developments testing more signatures Will our conclusions hold on a different country? (possibly one with a less-dense gauging network) Application with a different model Discussing the weights that statistics get : dependence on the objective function dependence on the statistic s estimation efficiency dependence on the model? 28 EGU Leonardo 2010 Luxembourg, November

29 Thank You! (and blame him!) 29 EGU Leonardo 2010 Luxembourg, November

30 en plus confrontation avec une bibliothéque plus riche (10 random sets par bassis, ça ne change rien du tout!!!) distance 1,2,3,7 voisin 30 EGU Leonardo 2010 Luxembourg, November

31 Which statistics? Which weights? At first, we tested the possibility of giving each statistic the same weight Then, we tested calibrating the weights so that the median efficiency was maximized 31 EGU Leonardo 2010 Luxembourg, November

32 What happens when we change our criterion? peut etre ajouter ici une figure qui montre la performance en régionalisation de chaque statistic : on pourreit ainsi discuter l influence de la performance et l influnce de la pertinence au critère sur le poids de chaque sig. 32 EGU Leonardo 2010 Luxembourg, November

33 Bassin P(mm) ETP(mm)T( C) Vent(m/s) Hum(g/kg) S Zmin Zmoy Zmax Z_0.1 Z_0.2 Z_0.3 Z_0.4 Z_0.5 Z_0.6 Z_0.7 Z_0.8 Z_0.9 PenteMin PenteMoy PenteMax P_0.1 P_0.2 P_0.3 P_0.4 P_0.5 P_0.6 P_0.7 P_0.8 P_0.9 URBAN AGRICOLE FRUIT HYBRIDE FOREST OTHER 33 EGU Leonardo 2010 Luxembourg, November