GEOSTATISTICAL REGIONALIZATION OF LOW-FLOWS: TOP-KRIGING VS. PSBI EGU Leonardo Topical Conferences Series on the hydrological cycle 2010 Luxembourg, 10-12 November 2010 GEOSTATISTICAL REGIONALIZATION OF LOW-FLOWS: TOP-KRIGING VS. PSBI S. Castiglioni1, A. Castellarin1, A. Montanari1, J. O. Skøien2, G. Laaha3, G. Blöschl4 School of Civil Engineering (Dept. DICAM) University of Bologna, Italy. Department of Physical Geography, University of Utrecht, Utrecht, Netherlands. Institute of Applied Statistics and Computing, Univ. of Natural Resources and Applied Life Sciences, BOKU Vienna, Austria (4) Inst. for Hydraul. and Water Resour. Eng., Vienna Univ. of Technology, Vienna, Austria.

Introduction: Top-kriging Top-kriging, or Topological kriging, predicts the variable of interest along river networks taking both the area and nested nature of catchments into account. Example of catchment size effect (a) and the effect of nesting (b and c) in the estimation of i. (a) (b) (c) Example of the estimate of the normalised specific 100-year flood from Top-kriging colour coded on the stream network of the Mur region (Skøien et al., 2006). “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Introduction: PSBI (xi ;yi) = physiographical space PSBI (Physiographic-Space Based Interpolation) performs the spatial interpolation of the desired streamflow index (e.g., annual streamflow, low-flow index, flood quantile, etc.) in the space of catchment descriptors. GEOMORPHOCLIMATIC CATCHMENT DESCRIPTORS (xi ;yi) = physiographical space The literature reports successful applications of PSBI to the problem of regionalization of flood frequency regime (Chokmani and Ouarda, 2004) or parameters of rainfall-runoff models (Hundecha et al., 2008) and low-flows (Castiglioni et al., 2009). X Y “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

“Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” Physiographic Space-Based Interpolation (PSBI): X Y Although rather different in their approach to regionalization, these methodologies share a common background idea: both methodologies perform the regionalization of streamflow indices without defining or identifying homogeneous regions or pooling-groups of sites. “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

“Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” Objectives This study compares these two innovative geostatistical approaches for the prediction of low-flows in ungauged basins. The comparison is performed at two different spatial scales: (a) regional scale; (b) catchment scale. We assess the ability of each technique to predict Q355 through a comprehensive leave-one out cross validation procedure for an entire study region of interest. We apply both methodologies to a large catchment of the study area to better analyse and interpret their accuracy and reliability for prediction of Q355 along the stream network. “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

“Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” Study area The region includes 51 unregulated basins for which daily streamflows are available for different observation periods with a minimum record length of 5 years; Concerning the catchment scale application, our study focuses on the Metauro catchment that counts 7 stream gauges for 1043.6 km2 Metauro basin “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Physiographic and climatic descriptors Denomination Max Mean Min A [km2] Drainage area 3082 350 14.4 L [km] Main channel length 160 36 5.3 P [%] Percentage of permeable area 99 49 0.1 Hmax [m s.l.m.] Maximum elevations 2914 2086 279 Hmean [m s.l.m.] Mean elevations 1950 959 178 Hmin [m s.l.m.] Minimum elevations 1103 364 3 ΔH [m] Average elevation relative to Hmin 1543 595 150 τc [hours] Concentration time (Giandotti’s empirical formula) 18.9 6.4 0.9 MAP [mm/year] Mean annual precipitation 1530 1099 820 “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Physiographical space Physiographic and climatic descriptors: A, L, P, Hmax, Hmean, Hmin, ΔH, τc, MAP Principal Component Analysis (PCA, Basilevsky, 1994). Explain about 70% of the variability of the original set of physiographic and climatic descriptors Physiographical space: (xi ;yi) = f(A, L, P, Hmax, Hmean, Hmin, ΔH, τc, MAP) “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Spatial interpolation PSBI: (PC1; PC2) = physiographical space Universal Kriging: spherical variogram (Castiglioni et al., 2009) Top-kriging: (x; y) = geographical space Top-kriging: modified exponential variogram (Skøien et al., 2006) “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Cross-validation procedure We assessed the reliability of the techniques and the uncertainty of the associated predictions of Q355 in ungauged basins by applying a leave-one-out cross-validation procedure (see e.g., Zhang and Kroll, 2007; Brath et al., 2003): assume one of the N basins, let us say site i, to be ungauged; 2. predict the Q355 value for this site on the basis of the remaining N-1 observations; 3. repeating this step N times, considering in turn each of the basins as ungauged, we obtain N cross-validation estimates of Q355 which can be compared with the corresponding observations. “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Top-kriging vs. PSBI: regional scale Performance indices PSBI Top-kriging E 0.88 0.90 MRE 1.09 1.14 RRMSE 2.56 2.28 Performance indices from the exclusion of these three basins “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Top-kriging vs. PSBI: catchment scale The catchment-scale application of both methodologies required the preliminary identification of the stream network and the evaluation of the nine considered geomorphologic and climatic descriptors for all identified subcatchments. DEM, SRTM 90m Digital Elevation Data (http://csi.cgiar.org/index.asp) Subcatchment boundaries (Amin>10 Km2) “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Top-kriging vs. PSBI: along river network Q355 (m3/s) Q355 (m3/s) 0.00 - 0.05 0.05 - 0.10 0.10 - 0.15 0.15 - 0.25 0.25 - 0.35 0.35 - 0.55 0.55 - 0.75 0.75 - 0.95 0.95 - 1.50 1.50 - 2.20 0.00 - 0.05 0.05 - 0.10 0.10 - 0.15 0.15 - 0.25 0.25 - 0.35 0.35 - 0.55 0.55 - 0.75 0.75 - 0.95 0.95 - 1.50 1.50 - 2.20 “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Top-kriging vs. PSBI: along river network Q355 (m3/s) MRE =0.40 MRE =3.02 PSBI Top-kriging: 0.00 - 0.05 0.05 - 0.10 0.10 - 0.15 0.15 - 0.25 0.25 - 0.35 0.35 - 0.55 0.55 - 0.75 0.75 - 0.95 0.95 - 1.50 1.50 - 2.20 MRE =1.20 MRE =0.01  MRE PSBI Top-kriging Min 0.10 0.01 Mean 0.38 0.77 Max 1.20 3.04 “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Top-kriging vs. PSBI: complementary methods? Q355 (m3/s) Larger river branches PSBI 0.00 - 0.05 0.05 - 0.10 0.10 - 0.15 0.15 - 0.25 0.25 - 0.35 0.35 - 0.55 0.55 - 0.75 0.75 - 0.95 0.95 - 1.50 1.50 - 2.20 Basin code MRE of PSBI MRE of Top-kriging 801 0.12 0.54 901 0.23 0.02 902 0.34 0.39 1002 1.20 0.01 1004 0.40 3.04 1701 0.10 0.52 2101 0.30 0.91 Mean 0.38 0.77 Headwater catchments Top-kriging: “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

“Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” Conclusions The results of our study point out that the performances of Top-kriging and PSBI are very similar: both methodologies represent an effective alternative to traditional regionalization approaches (i.e. multiregression models). Concerning the catchment scale, the Metauro application of PSBI and Top-kriging demonstrated that the latter technique is easier to implement. The comparison between jack-knife predictions and empirical values of Q355 point out that PSBI slightly outperforms Top-kriging. Finally the analysis shows a complementariness of the two estimation methods (complementary in terms of the basic principle of spatial interpolation, complementary in terms of data requirements and complementary in terms of predictive performances). “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

Thanks for your attention! “Geostatistical regionalization of low-flows: Top-kriging vs. PSBI” S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl