1. GEOSTATISTICAL REGIONALIZATION OF LOW-FLOWS: TOP-KRIGING VS. PSBI
EGU Leonardo Topical Conferences Series on the hydrological cycle 2010 Luxembourg, 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.

2. 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

3. 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

4. “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

5. “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

6. “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 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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 (
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

13. Top-kriging vs. PSBI: along river network
Q355 (m3/s)
Q355 (m3/s)
“Geostatistical regionalization of low-flows: Top-kriging vs. PSBI”
S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl

14. Top-kriging vs. PSBI: along river network
Q355 (m3/s)
MRE =0.40
MRE =3.02
PSBI
Top-kriging:
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

15. Top-kriging vs. PSBI: complementary methods?
Q355 (m3/s)
Larger river branches
PSBI
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

16. “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

17. 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