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

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

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

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

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

Local variance reduction 6 Strict-Lipschitz Condition Monotonic Condition Loose-Lipschitz Condition MultiDimensional Scaling (MDS)

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

 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

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

Local Variance Reduction K=4

Neighboring CatchmentsTransfer parameter set

 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

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

 Is the Euclidean Space feasible? NOT entirely E E E E E E Eigenvalues of YY T Summary and discussion cont. 15 Catchment Similarity MDS reconstructed

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

20,000 Monte-Carlo Simulations, NS coefficient (Cat. 16 vs. 22)

20,000 Monte-Carlo Simulations, NS coefficient (Cat. 10 vs. 17)

Lehrstuhl für Hydrologie und Geohydrologie Prof. Dr. rer. nat. Dr.-Ing. habil. András Bárdossy