1. www.uni-stuttgart.de Application of a Non-parametric Classification Scheme to Catchment Hydrology Lehrstuhl für Hydrologie und Geohydrologie Prof. Dr. rer. nat. Dr.-Ing. habil. András Bárdossy HE, Yi Helen BÁRDOSSY, András ZEHE, Erwin

2. www.uni-stuttgart.de Outline of the Talk2 1.Underlying assumption 2.Catchment Classification Scheme and its model dependency 3.Summary and discussion Lehrstuhl für Hydrologie und Geohydrologie Prof. Dr. rer. nat. Dr.-Ing. habil. András Bárdossy

3. www.uni-stuttgart.de Catchment Classification Scheme 3 3. Models are able to capture similarity Basic Assumptions: BA‘s Three Laws similarly 1. Similar catchments behave similarly 2. Similarity 2. Similarity can be described with catchments’ characteristics Lehrstuhl für Hydrologie und Geohydrologie Prof. Dr. rer. nat. Dr.-Ing. habil. András Bárdossy

4. www.uni-stuttgart.de Entire German Section of the Rhine Basin 109,330 km 2 12 sub-basins; 101 catchments Credit: Hundecha, 2005 Study Domain

5. www.uni-stuttgart.de Drainage Area; Drainage Slope; Drainage Shape(length 2 /area); Four Land-use Area: Forest; Urban; Agricultural land; Water Bodies; Six Soil-Class Area: Lithosol; Ranker; Gleysol; Cambisol; Luvisol; Podzol. Lehrstuhl für Hydrologie und Geohydrologie Prof. Dr. rer. nat. Dr.-Ing. habil. András Bárdossy Catchment Classification Scheme cont. 5

6. www.uni-stuttgart.de Local variance reduction 6 Strict-Lipschitz Condition Monotonic Condition Loose-Lipschitz Condition MultiDimensional Scaling (MDS)

7. www.uni-stuttgart.de MDS - Recovery of coordinates 7 Shepard-Kruskal algorithm k Distance in the transformed k space U Distance computed from Pool- adjacent violator method

8. www.uni-stuttgart.de  HOW does it help in hydrologic prediction? Catchments share similar problems  Model parameters can be transferred  Regional extreme (flood/drought) value statistics Applications 8 Lehrstuhl für Hydrologie und Geohydrologie Prof. Dr. rer. nat. Dr.-Ing. habil. András Bárdossy

9. www.uni-stuttgart.de HBV-IWS Model 20,000 Monte-Carlo Simulations Calibration: 22 headwater cat. in Yellow Validation: 5 headwater cat. in Green

10. www.uni-stuttgart.de Local Variance Reduction K=4

11. www.uni-stuttgart.de Neighboring CatchmentsTransfer parameter set

12. www.uni-stuttgart.de

13.  Local Variance Reduction (LVR)  MultiDimensional Scaling (MDS)  Model dependency Model-captured-similarity Minimum Variance == Cluster of Similar Objects Determine dimension of the embedded space Catchment Classification Scheme cont. 13 Examine dependency of similar catchment pairs on the HBV and Xinanjiang Models

14. www.uni-stuttgart.de Lehrstuhl für Hydrologie und Geohydrologie Prof. Dr. rer. nat. Dr.-Ing. habil. András Bárdossy Significant difference indicates needs of re-examination of model structures and dominant hydrological processes

15. www.uni-stuttgart.de  Is the Euclidean Space feasible? NOT entirely 2.59481 0.694520.26766 0.332890.12829 0.164250.063299 0.0931440.035897 0.058080.022384 0.0436720.016831 0.0356910.013755 0.0118270.004558 0.0063970.002465 0.0024110.000929 0.0011520.000444 0.0009830.000379 0.00040.000154 0.0001816.98E-05 6.02E-182.32E-18 -2.87E-05-1.11E-05 -0.00021-8.00E-05 -0.00127-0.00049 -0.00366-0.00141 -0.02772-0.01068 Eigenvalues of YY T Summary and discussion cont. 15 Catchment Similarity MDS reconstructed

16. www.uni-stuttgart.de Summary and discussion cont. 16  Can similarity be better defined? Introducing the idea of copula to define catchment similarity

17. www.uni-stuttgart.de 20,000 Monte-Carlo Simulations, NS coefficient (Cat. 16 vs. 22)

18. www.uni-stuttgart.de 20,000 Monte-Carlo Simulations, NS coefficient (Cat. 10 vs. 17)

19. www.uni-stuttgart.de Lehrstuhl für Hydrologie und Geohydrologie Prof. Dr. rer. nat. Dr.-Ing. habil. András Bárdossy