Geostatistical interpolation of runoffJon Olav Skøien and Günter Blöschl
Institute of Hydraulic and Water Resources EngineeringVienna University of Technology
Conclusion
Spatio-temporal geostatistical interpolation offers an alternative to regionalisation of rainfall-runoff model parameters for ungauged catchments (PUB)! Method uses real catchment boundaries! No information in addition to runoff data and catchment boundaries needed! To do:
- Consider other aggregation schemes
- Preserve variance in a better way
Motivation
& Common practice to use deterministic models for prediction of runoff in hydrology& Stochastic models have been used for regionalisation of model parameters
C We suggest a geostatistical interpolation method for runoff taking into account:- Runoff from neighbouring catchments
- True catchment boundaries - Network structure
Estimating variance between catchments
Time
T1
A1
T1
A1 T2
A2
T2
A2
hths
hths
hthshs
1500
350
100
25
6
1.5
0.5
0
0 5 12 20 35 55 80 120 200 300
0
0.0003
0.0006
0.0009
0.0012
0.0015
0.0018
0.0021
0.0024
0.0027
0.003
Temporal lag(hours)
Spatial lag (km)
Spatio-temporal sample variogram of runoff
- Variogram cloud of the catchment pairs
- Binned temporal distances
=>Point variogram found by joint fitting of the spatio-temporal variances between catchments
Type of variability Our approach
Soil and vegetation
Channel network
Euclidian
Euclidian
} Variogram
Tree structure Boundaries
mm/day
ò ò ò òò ò ò ò ----+-+=A T A TA T A T
tstsst dsdrdtdtrsTA
dsdrdtdhtrhsTA
Thah ttgttgg ),(1
),(1
),(2222
Catchment: can be seen as a set of points in space and time
! Variance between catchments - The average of point variances
! Variances dependent on spatial and temporal distancesC Regularisation
100 km2
49 km2
25 km2
9 km2
25 km2
20 km
2100 km
249 km
225 km
29 km
225 km
20 km
0.40
0.28
0.19
0.13
Kriging weights
Block to beinterpolated
EGU General AssemblyVienna, April 25-29, 2005Contact: Jon Olav Skø[email protected]
÷÷
ø
ö
çç
è
æ--+--
---=
ò ò ò òò ò ò ò
ò ò ò ò
ttgttg
ttgg
dsdrdtdtrsTA
dsdrdtdtrsTA
dsdrdtdtrsTTAA
j j j ji i i i
i i j j
A T A TjjA T A Tii
A T A Tjiji
ij
),(1
),(1
5.0
),(1
2222 ÷÷
ø
ö
çç
è
æ--+--
---=
ò ò ò òò ò ò ò
ò ò ò ò
ttgttg
ttgg
dsdrdtdtrsTA
dsdrdtdtrsTA
dsdrdtdtrsTTAA
j j j ji i i i
i i j j
A T A TjjA T A Tii
A T A Tjiji
ij
),(1
),(1
5.0
),(1
2222
Results
Two interpolated runoff hydrographs as examples! Hourly runoff 1998 interpolated! Only showing 35 day period! Nash-Sutcliffe for all catchments.0.75-0.97
& The catchment filters the signal from the atmospheric forcing - The smoothing is stronger from a large catchment than from a small one
& Also temporal filtering takes place, due to the residence time in the catchmentb
& The residence time simplified as T=aA , A is area and a and b parameters& We assume a simple aggregation within the catchment
- Runoff at outlet is average of runoff generated within the catchment during time T
Regularisation of a variogram in space and time:
Back-calculation of a point variogram:
The influence of support on interpolation
A spatial example - Four neighbour blocks with equal centre-to-centre distance
! Largest catchment will get largest kriging weight! Smallest catchment get smallest weight! Size of interpolated block does not come into account in symmetric case
Block Kriging
! Gamma value in kriging matrix calculated separately for each pair of catchments! Kriging matrix solved as normally! The kriging matrix is only solved once for each ungauged catchment.
Data
! Interpolation of 17 stations from Innviertel, Austria- marked with black circles, numbered C1-C17
! Yearly runoff relatively homogenous (small green numbers)! Also other neighbouring catchments used for interpolation
Litz
Alfenz
Alfenz
Alvier
Lutz
Frutz
Ehbach
Dornbirnerach
Rheintalbinnenkanal
Bregenzerach
Bregenzerach
Subersach
Weißach
RotachRuggbachLeiblach
ZürsbachLech
Schwarzach
Gillbach
Mühlbach
Bizauerbach
Ehbach
Lech
Hornbach
Lech
Isar
Vils
Loisach
Schalklbach
Inn
Inn
Trisanna
RosannaRosanna
Inn
Salvesenbach
Inn
RofenacheVenterGurgler
Ötztaler
Ötztaler
Ötztaler
InnInn
Obernberger
Schmirnbach
Gschnitzbach
SillNavisbach
Sill
WattenbachWeerbach
Inn
Tuxbach
Ziller
ZillerGerlosbach
Ziller
Inn
Brandenberger
Walchentaler
Kelchsauer
Brixentaler
Inn
Weißache
Kitzbüheler
AschauerKitzbühelerFieberbrunner
Gerlosbach
Zamserbach
Sanna
Pitze
ZirmbachLängentalbach
Gurglbach
Leutascher
Stampfangerbach
Gießenbach
Windauer
Sill
Ruetz
Vils
Loisach
Leutasch
Tiroler
Großache
SalzachObersulzbach
Untersulzbach
Mühlbach Salzach
Felber
Salzach
Fuscher
Fuscher
Hüttwinkelache
Rauriser
Dientenbach
Naßfelder
Gasteiner
Großarler
Kleinarler
Fritzbach
LammerLammer
TorrenerSalzach
Tauglbach
Almbach
Berchtesgad.Ache
Salzach
Glanbach
Saalach
Urschlaubach
Leogangbach
Saalach
Loferbach
Saalach
Salzach
Moosache
Kraftwerk
Saalach
Habach
Hainbach
Enns
Taurachbach
MurMur
Taurach
Weißpriach
TaurachMur
Thomatalbach
Zederhausbach
Pladenbach Oichtenbach
Obersulzbach
Salzach
Forstaubach
Schwarzbach
WeißenbachSchwarzbach
Mur
Stuhlfeldnerbach
Göriachbach
Lessachbach
Löhnersbach
Eugenbach
Moosache
Moosache
MühlbergerSchwemmbach
Mattig
Waldzeller
Mettmach
Lochbach
Ach
Oberach
Rieder
Osternach
Inn
Pram
PfudabachPfudabachDiersbachPram
Ranna
Große
Große
Steinerne
Innbach
InnbachTrattnach
StillbachTrattnach
Innbach
Dürre
Aschach Großer
Waldbach
Traun
Langbathbach
Griesler
Äusserer
Vöckla
Frankenburger
Vöckla
Dürre
Vöckla
Aurach
Staiger
TraunSchwaiger
Alm
Aiterbach
Grünbach
Schmiedleitnerbach
Sipbach
Krems
Krems
Ipfbach
Gaflenzbach
Reichramingbach
Enns
Steyr
KrummeSteyr
Steyr
Teichl
DambachTeichl
Teichl
Steyrling
Steyr
Paltenbach Krumme
Krumme
Enns
Feldaist
Rettenbach
Waldaist
Aist
Große
Kleine
Naarn
Schwemmbach
SchwemmbachSchalchener
Pram
Aschach
Sarmingbach
Messenbach
Ottnanger
LaudachSchwemmbach
Pram
Enns
Reichramingbach
Gusen
Dürre
Weißenbach
Pyhrnbach
Alm
Vorderer
Hintersteinerbach
Maltsch
Große
Feldaist
Ramingbach
Hörschinger
Mitterweißenbach
Enknach
Stambach
Pettenbach
GroßeDiestlbachWald-(Schwarze)
Berndorfer
LochbachMoosbach
Hainbach
Mühlheimer
Laussabach
Kleine
Trattenbach
Grünbach
Antiesen
Sulzbach
Hinterer
Schwemmbach
Kleine
Donau
Donau
Donau
Donau
DonauDonau
March
March
Donau
DonauIsper
Ybbs
Kleine
Ybbs
Urlbach
Große
Ötscherbach
Lassingbach
GroßeGamingbach
Jeßnitz
Kleine
Erlauf
Weitenbach
Mank
Melk
Pielach
Pielach
Sierningbach
Krems
Fladnitz
Traisen
Gölsen
Traisen
ZwettlKamp
KampPurzelkamp
Purzelkamp
Kamp
Perschling
Große
Schmida
Göllersbach
Wien
Schwechat
Mödling
Triesting
Triesting
LiesingSchwechat
Kalter
Fischa
Fischa
Fischa
Piesting Piesting
Piesting
Piesting
Fischa
Reisenbach
Fischa
Rußbach
Rußbach
Lainsitz
Braunaubach
Reißbach
Deutsche
Thaya
Pulkau
Thaya
Weidenbach
Schwarza
NaßbachSchwarza
Sierning
SierningSchwarza
GroßerFeistritz
Pitten
Pitten
Große
Leitha
WarmeWarme
Leitha
Leitha
RomaubachThaya
Zaya
Melk
Große
Erlabach
Rußbach
Leitha
Warme
Taffa
Petersbach
Liesing
Türnitztraisen
Hochberggraben
Laimbach
Schopfgraben
Schliefaubach
Hagenbach
Maisbirbaumer
Staffbach
Halbach
Zaya
Weidlingbach
Schwechat
Perschling
Lainsitz
Spitzer
Pulkau
Unrechttraisen
Schlattenbach
Ois
Kleine
FrauenbachProssetbach
Mährische
Gablitzbach
TaxenbachDeutsche
Mauerbach
Liesing
WienHalterbach
Leitha
Rabnitz
Rabnitz
Stoob
Wulka
Wulka
Wulka
Stögersbach
Lafnitz
Pinka
Pinka
Tauchenbach
Tauchenbach
Pinka
Strem
Strem
Zöbernbach
Güns
Wulka
Eisbach
Lafnitz
Pinka
Raab
Strem
Nodbach
Rabnitz
Augstbach
Ödenseetraun
Unterthaler
Enns
Gulling
EnnsPaltenbach
Enns
Enns
Erzbach
Salza
Radmerbach
Salza
Moderbach
Weizbach
Raab
Raab
Lafnitz
Lafnitz
Safenbach
Feistritz
Ilzbach
Feistritz
Mur
Mur
Pusterwaldbach
Pöls
Mur
LiesingbachMur
Vordernberger
Mürz
Mürz
Thörlbach
MürzLamingbach
Mur
Kainach
Kainach
Schwarze
Weiße
Laßnitz
Sulm
Schwarzaubach
Mur
Gnasbach
Krumbach
Mur
Raab
Prätisbach
Saifenbach
Übelbach
Saggaubach
Laßnitz
Lafnitz
Raab
Raab
Mur
Feistritz
Granitzenbach
Mur
Pinka
LaßnitzGleinzbachWildbach
Liesingbach
Stainzbach
Stanzbach
Mur
Rabnitzbach
Stiefing
Sulm
Rittscheinbach
Ingeringbach
Feistritzbach
Schwarzenbach
Drau
IselIslitz
GschlößbachTauernbach
Isel
Schwarzach
DorferbachTeischnitzbach
Isel
Isel
Winkeltalbach
Drau
DrauMödritschbach
Drau
Möll
Mallnitzbach
Möll
Möll
Lieser
Hochalmbach
Malta
Lieser
Gail
Gail
Gail Gösseringbach
GailGail
BodenbachLoiblbach
Vellach
GurkGurk
Gurk
Metnitz
Görtschitz
Görtschitz
Glan
Steiner
Glan Gurk
Lavant
Lavant
Treffner
Möll
GurkRieger
Drau
Lieser
Drau
Tiebelbach
Wimitz
Wimitz
Metnitz
Weißenbach
Glan
Moosburger
Silberbach
Lavant
Lavant
Wölfnitzbach
Gurk
Olsabach
Zickenbach
Goldbach
Inn
Inn
Inn
Radurschlbach Pitze
Fagge
Ötztaler
Fundusbach
Alpeinerbach
Längentaler
Kraspesbach
Melach
Ruetz
Dürrach Grundache
Mühlbach
DrauVillgratenbach
0
0
1
1
0
0
0
0
0
0
0
0
1
000
00
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
11
1
1
1
000
0
0
0
11
0
0
0
00
0
00
1
1
1
1 1
1
1
0
0
1
0
1
0
0
0 0 0
1
0
1
1
10
0
0
0
0
0
-1
0
0
0
0
0
0
10
0
0 0
0
1
1
0
1
0
0
1
0
0
-1
0
00
00
0
1
-1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
10
0
0
00
0
0
0 0
0
0
0
0
00
0
0
0
0
0
0
0
0
00
-1
0
0
0
0
-1
0
0
1
0
000
0
1
0
0
0
0
00
00
0
0
0 0
0
-1
-1
-1
0
0
0
0
0
0
0
0
00
0
00
0
0
0
0
0
0
0
0
0
0 0
0
0
00
0
0
1
0 0
0
0
0
0
0
0
0
0
0
0
00
0
0
-1
0
0
00
0
1
0
0
0
0
0
-1
0
0
0
0
0
0
0
0
0
0
0
000
0
00
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
11
1
1
1
11
0
0
1
0
-1
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
00
0
1
0
0
0
0
0
0
0
0
0
00
0
0
0
0
0 0
0
0
0
0
0
0
0
0
-1
0
0
0
0
0
0
0
00
0
00
00
0
0
1
0
00
0
0
-1 1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
00
0
0
00
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-1
1
0
10
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
01
0
0
0
0
00
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0 00
1
1
0
1
0
0
0
0
0
0
0
0
00
00
0
0
00
0
0
0
0
00
0
1
0
1
1
0
0
1
1
0
0
0 0
00
0 0
0
00
0
0
0
0
0
0
-1 -1
0
0
0
0
00
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0 0
0
0
0
0
0
0
1
0
00
0
10
0.0464
0.053
0.0415
0.0377
0.0631
0.0658
0.048
0.0562
0.0268
0.0696
0.0605
0.0757
0.0354
0.04380.03660.0307
0.06510.0609
0.0438
0.0269
0.0189
0.0482
0.0397
0.0561
0.063
0.0453
0.0373
0.0414
0.0326
0.0274
0.0283
0.0324
0.0239
0.03870.036
0.0125
0.0414
0.0295
0.04640.04470.0519
0.039
0.0378
0.035
0.0290.0292
0.0335
0.0311
0.0385
0.03250.0268
0.0297
0.02980.0316
0.0304
0.0293
0.0446
0.04350.0427
0.0413
0.0316
0.0386
0.0454
0.0394
0.0347
0.0324
0.0269
0.0364
0.03440.03540.0433
0.045
0.0463
0.0284
0.0193
0.01450.0394
0.0258
0.0313
0.0272
0.0113
0.0419
0.0217
0.042
0.0458
0.0269
0.0335
0.0365
0.0423
0.03350.0560.0518
0.0330.0398
0.0423
0.0433
0.0473
0.037
0.037
0.0404
0.0368
0.0217
0.0475
0.0349
0.0361
0.025
0.03230.0453
0.05050.039
0.0323
0.0454
0.0425
0.0394
0.0415
0.0341
0.0362
0.0251
0.0355
0.0477
0.0386
0.0392
0.0125
0.0546
0.0342
0.0476
0.0109
0.0335
0.0515
0.03420.0261
0.0343
0.0327
0.02880.0251
0.019
0.0239
0.0105 0.0185
0.0805
0.0175
0.0268
0.1112
0.02270.3855
0.0247
0.0358
0.0259
0.0307
0.038
0.0287
0.0188
0.0122
0.01230.0126
0.0107
0.0224
0.017
0.0087
0.017
0.0148
0.0156
0.0142
0.028
0.0143
0.01690.01550.0134
0.0145
0.0227
0.0242
0.0216
0.0146
0.0126
0.01110.0148
0.01390.0123
0.0119
0.0115
0.0141 0.0157
0.0816
0.0549
0.0313
0.0352
0.0714
0.0266
0.0204
0.0215
0.0196
0.0198
0.0272
0.0159
0.03910.01
0.0406
0.01050.0084
0.0202
0.0146
0.0338
0.0209
0.0103
0.0211
0.0367
0.0328
0.0608
0.14730.0828
0.0531
0.0612
0.02760.0368
0.0446
0.0259
0.0486
0.0278 0.0305
0.0308
0.0344
0.0086
0.0494
0.0117
0.0104
0.0127
0.0122
0.0119
0.0142
0.00540.0284
0.0166
0.0135
0.0131
0.0144
0.0148
0.01710.0085
0.0144
0.0317
0.04
0.0087
0.0144
0.0329
0.0336
0.0544
0.0598
0.0166
0.0105
0.0097
0.0082
0.0208
0.0039
0.0576
0.004
0.0303
0.182
0.01280.0190.0137
0.0216
0.01310.012
0.0095
0.017
0.04
0.0158
0.0313
0.0089
0.0142
0.0147
0.0745
0.0094
0.0086
0.0181
0.0113
0.0226
0.0118
0.01130.0134
0.0041
0.0042
0.0221
0.01550.0129
0.0378
0.0272
0.0272
0.0133
0.0266
0.0402
0.0323
0.03470.0258
0.022
0.0164
0.0245
0.007
0.0126
0.0094
0.0371
0.0211
0.0068
0.0055
0.0023
0.0243
0.0158
0.0183
0.00730.0083
0.01190.0089
0.0069
0.0056
0.0052
0.0057
0.0012
0.001
0.0092
0.0086
0.0041
0.0103
0.0096
0.00530.0078
0.0231
0.0836
0.0219
0.034
0.019 0.0107
0.0083
0.0077
0.016
0.0067
0.0142
0.0015
0.0035
0.008
0.0069
0.0081
0.0062
0.0051
0.0009
0.003
0.0016
0.0183
0.02170.0203
0.0109
0.00830.0038
0.01210.0108
0.0101
0.0085
0.0342
0.0024
0.00190.0015
0.0057
0.0053
0.00830.0039
0.0013
0.013
0.0327
0.0093
0.0032
0.002
0.0235
0.0028
0.0031
0.0104
0.0293
0.1404
0.0123
0.0121
0.0209
0.0505
0.0242
0.011
0.0197
0.0015
0.0046
0.0121
0.0074
0.0094
0.003
0.0021
0.0248
0.0046
0.0386
0.004
0.01070.0032
0.0041
0.0066
0.00520.0049
0.006
0.0051
0.00720.009
0.004
0.0052
0.004
0.0039
0.0032
0.0022
0.0028
0.0051
0.0068
0.0076
0.0053
0.0048
0.004
0.0051
0.0036
0.0036
0.0064
0.0057
0.0029
0.0034
0.0079
0.0085
0.0078
0.0037
0.0023
0.0041
0.0515
0.0617
0.0404
0.0335
0.0294
0.03010.0244
0.0306
0.0304
0.0381
0.0261
0.036
0.0344
0.0101
0.0113
0.0082
0.0079
0.0098
0.0084
0.0057
0.0125
0.0058
0.0096
0.0205
0.0192
0.0258
0.0205
0.0193
0.0220.0175
0.0183
0.0307
0.0189
0.015
0.01620.0168
0.0173
0.0126
0.0124
0.0231
0.0176
0.0129
0.0141
0.0079
0.0153
0.0074
0.0302
0.0166
0.0091
0.0076
0.0086
0.0143
0.0138
0.0177
0.0101
0.0098
0.0094
0.0208
0.0216
0.0161
0.0175
0.0122
0.01540.01370.011
0.0297
0.0121
0.0115
0.0171
0.0077
0.0072
0.0172
0.007
0.021
0.0227
0.0227
0.0234
0.04990.0561
0.07670.0685
0.0395
0.0325
0.05010.036
0.0325
0.0374
0.0261
0.0287
0.0280.023
0.0266
0.0195
0.0418
0.0239
0.0081
0.0182
0.0593
0.0135
0.017
0.0287
0.0298
0.0306 0.0245
0.03190.0327
0.02350.0402
0.0304
0.01810.0163
0.0134
0.011
0.0133
0.0118
0.0092
0.0075
0.0116 0.0114
0.014
0.0124
0.0128
0.0259
0.01110.0172
0.0293
0.0195
0.027
0.0196
0.0099
0.0093
0.0133
0.0124
0.0102
0.0104
0.0064
0.0137
0.0122
0.0122
0.0117
0.0103
0.0052
0.0053
0.0279
0.03
0.0311
0.0332 0.0514
0.05
0.0356
0.034
0.0493
0.0421
0.0397
0.0199
0.0338
0.0445 0.0312
0.0336
0.02040.0289
200048
200071
200089
200097
200105
200154
200162
200204
200220
200246
200253
200287
200303
200311200345200352
200360200378
200428
200469
200485
200493
200527
201012
201053
201087
201095
201111
201152
201160
201178
201194
201236
201251201277
201293
201301
201319
201350201368201376
201392
201418
201434
201459201525
201533
201558
201566
201574201582
201624
201657201665
201681
201723
201749
201756201772
201780
201806
201822
201830
201848
201863
201889
201897
201913
201921201939201947
201970
201996
202036
202044
202077202093
202101
202127
202135
202143
202218
202275
202283
202291
202309
202317
202341
202382
203026203034203042
203067203075
203083
203125
203133
203141
203158
203166
203174
203190
203208
203224
203232
203257
203265203307
203315203323
203331
203349
203364
203398
203422
203463
203471
203489
203497
203505
203521
203539
203547
203554
203570
203596
203638
203703
203737
203745203752
203760
203778
203786203794
203810
203828
203836 203844
203893
203901
203919
203927
203935203943
203976
203984
203992
204008
204016
204024
204529
204545
204602204628
204677
204685
204693
204701
204719
204727
204735
204768
204776
204784
204826204834204842
204859
204875
204891
204917
204925
204958
204966204974
204990205021
205039
205047
205054 205096
205120
205153
205229
205294
205336
205377
205385
205393
205401
205419
205435
205443
205468205476
205500
205534205559
205583
205609
205625
205641
205690
205732
205740
205757
205765
205773205781
205799
205807
205815205823
205831
205856
205864
205872 205880
205898
205922
205948
205955
205971
205989
205997
206003
206029
206052
206078206086
206102
206169
206227
206268
206284
206292206318
206326
206342
206367
206375
206383
206425
206466
206508
206524
206532
206557
206573
206581
206599
206607
206615
206623
206631
206649
206656206664206680
206698
206706206722
206730
206748
206763
206771
206789
206797
206805
206813
206821
206839
206854
207035
207126
207134
207175
207274207282
207308
207324
207357
207399207613
207654
207662
207688
207696
207704
207712
207720
207738207746
207787
207795
207803
207811
207829
207837
207845
207852
207860
207878
207886
207894
207902
207910
207936207944
207951207969
207977
207993
208009
208017
208041
208058
208066
208090
208108
208116
208124
208132208157
208181
208207
208231
208249
208272 208280
208306
208330
208413
208421
208439
208447
208454
208462
208579
208603
208611
208629
208637
208645
208678
208686
208694208702
208736
208744208785
208819208827
208835
208843
208850
208884
208918208926
208991
209007
209064209171
209189
209197
209213
209247
209262
209288
209296
209338
209346
209353
209361
209379
209387
209395
209403
209411
209429
209437
209445
209452
209460
209478
209486
209494
209502
209510
209536
209544
209551
209569
209585209593
209601
209627
209734209742
209890
209908
209916209932
210013
210039
210054
210062
210070
210088
210096
210203
210211
210229
210237
210245
210252
210260
210286
210294
210302
210310
210328
210393
210401
210419
210468
210476
210492
210500
210559
210583
210625
210641
210773
210799210815
210823
210849
210856
210864
210880
210898
210955
210963
210971
210989
210997
211003
211011
211029
211037
211045
211086
211102
211110
211128
211136
211169211185
211193
211227
211243
211250
211268211276
211292
211334
211342
211383
211391
211441
211458
211474
211490
211508
211540
211573
211599
211623
211631
211649
211656
211664
211680
211698
211706
211714
211722
211730
211763
211771
211797211805211813
211821
211854
211862
211870
211888
211896
211904
211912
211920
211938
211946
212027
212043212050
212068212076
212092
212100
212118212126
212167
212183
212225
212316
212324212340
212357
212373
212381
212399
212407
212431
212456
212498
212530
212613
212647
212670 212704
212753212787
212829212837
212852
212860212878
212886
212894
212928
212936
212951
213017
213033 213041
213082
213090
213116
213124
213157213181
213199
213207
213215
213231
213249
213256
213306
213314
213322
213330
213355
213363
213371
213389
213397
213405
215012
215020
230011
230078
230102
230110 230177
230300
230342
230383
230409
230466
230581
230706
230714
230722 230896
230904
231092231100
km
Rieder
Osternach
Inn
Pram
PfudabachPfudabach
Ranna
Große
Steinerne
Innbach
InnbachTrattnach
StillbachTrattnach
Innbach
Dürre
Aschach
Pram
Aschach
MessenbachPram
Kleine
Antiesen
Donau
0
0.0156
0.0142
0.028
0.0143
0.0169
0.0155
0.01340.0145
0.0227
0.0216
0.0146
0.0126
0.01110.0148
0.0139 0.0123
0.0119
0.0115
0.0141
0.0166
0.0135
0.01440.0144
0.0158
0.0142
0.0181
C1
C2
C3C4
C5
C6
C7
C8C9
C10C11
C12
C13
C14
C15C16
C17
Pram
Atmospheric forcing
Hydrographs from some of the neighbours used for interpolation
10
20
30
40
31/10 07/11 14/11 21/11 28/11
Interpolated runoffObserved runoff
10
20
30
40
C4 - Taufkirchen
Interpolated runoffObserved runoff
mm/day
Peak satisfying interpolated despite large variance in peaks of neighbouring catchments
10
20
30
40
31/10 07/11 14/11 21/11 28/11
Interpolated runoffObserved runoff
10
20
30
40
C14 - Neumarkt im Hausruckkreis
Interpolated runoffObserved runoff
Second peak largest in interpolated catchment => underestimation! Method is not able to preserve variance of a time series! Kriging gives the best linear unbiased estimator for each time step
Neighbours
Neighbours
Spatio-temporal point variogram of runoff