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
(1) School of Civil Engineering (Dept. DICAM) University of Bologna, Italy.
(2) Department of Physical Geography, University of Utrecht, Utrecht, Netherlands.
(3) 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
The prediction of low-flows indices in ungauged basins is a critical
task in a number of engineering applications related to surface water
resources planning and management.
Hydrological predictions generally have to deal with the inadequacy
or deficiency of observations for the site of interest (see the decade
on Prediction in Ungauged Basins promoted by the International
Association of Hydrological Sciences – IAHS; Sivapalan et al., 2003).
Ridracoli Dam
2007 historical minimum
Recent studies highlight
that geostatistical
interpolation can be
effectively applied to the
problem of regionalization
of hydrometric information.
“Geostatistical regionalization of low-flows: Top-kriging vs. PSBI”
S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl
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.
 ij  0.5  Var ( z ( Ai )  z ( A j )) 
 1
 0.5   2
 Ai
(a)
(b)
(c)
1
Ai A j
   P ( xi  x j )dxi dx j 
Ai A j
 
P
( xi  x j )dxi dx j 
Ai A j
1
A 2j

   P ( xi  x j )dxi dx j 
Ai A j

Example of catchment size effect (a)
and the effect of nesting (b and c) in
the estimation of i.
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
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
Top-kriging vs. PSBI
Top-kriging:
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 poolinggroups of sites.
“Geostatistical regionalization of low-flows: Top-kriging vs. PSBI”
S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl
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.
a) 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.
b) 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
Study area
a)
The region includes 51 unregulated
basins for which daily streamflows are
available for different observation periods
with a minimum record length of 5 years;
b)
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
Descriptor
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).
Physiographical space:
(xi ;yi) = f(A, L, P, Hmax, Hmean, Hmin, ΔH, τc, MAP)
Explain about 70% of the
variability of the original
set of physiographic and
climatic descriptors
“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):
1.
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
Top-kriging
Top-kriging
5
5
4
4
Stimati [log(l/s)]
Stimati [log(l/s)]
PSBI
PSBI
3
2
3
2
1
1
0
0
0
1
2
3
4
5
0
1
Empirici [log(l/s)]
2
3
4
Empirici [log(l/s)]
Performance
indices
PSBI
Top-kriging
E
0.88
0.90
MRE
1.09
1.14
RRMSE
2.56
2.28
“Geostatistical regionalization of low-flows: Top-kriging vs. PSBI”
S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl
Performance
indices from the
exclusion of
these three
basins
5
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: dataset
1°
Application of
GIS Processing
Top-kriging
4°
GIS Processing
DEM (90 x 90 m)
Sub-basin divides
2°
P
Lithological map
3°
GIS Processing
GIS Processing
MAP
Thiessen Polygon
A, L, Hmax, Hmean Hmin, ΔH, tc
Rain Gauges
Application of PSBI
“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
PSBI:
Q355 (m3/s)
Top-kriging:
Q355 (m3/s)
0.00 - 0.05
0.00 - 0.05
0.05 - 0.10
0.05 - 0.10
0.10 - 0.15
0.10 - 0.15
0.15 - 0.25
0.15 - 0.25
0.25 - 0.35
0.25 - 0.35
0.35 - 0.55
0.35 - 0.55
0.55 - 0.75
0.55 - 0.75
0.75 - 0.95
0.75 - 0.95
0.95 - 1.50
0.95 - 1.50
1.50 - 2.20
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)
0.00 - 0.05
PSBI
Top-kriging:
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
MRE =0.10
MRE =0.54
MRE =0.12
MRE =0.52
1.50 - 2.20
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: along river network
Q355 (m3/s)
0.00 - 0.05
PSBI
MRE =0.40
MRE =3.02
Top-kriging:
0.05 - 0.10
0.10 - 0.15
0.15 - 0.25
0.25 - 0.35
0.35 - 0.55
MRE =1.20
MRE =0.01
0.55 - 0.75
0.75 - 0.95
0.95 - 1.50
1.50 - 2.20
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)
0.00 - 0.05
PSBI
Larger river branches
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
Top-kriging:
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
“Geostatistical regionalization of low-flows: Top-kriging vs. PSBI”
S. Castiglioni, A. Castellarin, A. Montanari, J. O. Skøien, G. Laaha, G. Blöschl
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 Topkriging 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