Simulatie van de overstroming van de Hupselse Beek met het Wageningen Model

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1 Simulatie van de overstroming van de Hupselse Beek met het Wageningen Model Claudia Brauer, Peter Kloosterman, Ryan Teuling, Remko Uijlenhoet Vakgroep Hydrologie en Kwantitatief Waterbeheer, Wageningen Universiteit NHV najaarsbijeenkomst, Haarlo, 15 november 2012

2 Aanleiding Brauer et al., HESS, 15, , 2011

3 Resultaat Brauer et al., HESS, 15, , 2011

4 Vervolgonderzoek Overstromingen in laaglandgebieden: I Begrijpen I Simuleren

5 Afstudeervak Peter Kloosterman Verglijking 5 gelumpte neerslag-afvoermodellen Q [mm d 1 ] Initial Q Peak Q Q [mm d 1 ] Obs. LSGI SWAP HBV Wag. Sac. 15 Aug 1 Sep 15 Sep

6 De geschiedenis van het Wageningen Model Ontwikkeld in jaren 70 bij Vakgroep Hydraulica en Afvoerhydrologie voor de Hupselse Beek

7 De geschiedenis van het Wageningen Model Sinds de jaren 70: toegepast op stroomgebieden in binnen- en buitenland talloze afstudeeronderzoeken Verschillende versies: reservoirs voor langzame en snelle afvoer vergelijkingen voor berekening verdampingsreductie talen/programma s: Fortran, Excel, R

8 De geschiedenis van het Wageningen Model Sinds de jaren 70: toegepast op stroomgebieden in binnen- en buitenland talloze afstudeeronderzoeken Verschillende versies: reservoirs voor langzame en snelle afvoer vergelijkingen voor berekening verdampingsreductie talen/programma s: Fortran, Excel, R Wat hebben we gebruikt voor de wedstrijd?

9 2. Conceptualisatie Precipitation Saturation Evapotranspiration Field capacity Soil moisture reservoir Influence Percolation Divider slow fast Capillary rise Groundwater reservoir Linear reservoir slow Discharge Linear reservoir fast

10 3+4. Schematisatie/discretisatie en randvoorwaarden Schematisatie/discretisatie a Ruimtelijk horizontaal: geen b Ruimtelijk verticaal: geen (reservoirs) c Temporeel: uurwaarden Randvoorwaarden: geen Beginvoorwaarden: voor de 4 reservoirs (gekalibreerd samen met parameters) Precipitation Saturation Evapotranspiration Field capacity Soil moisture reservoir Influence Percolation Divider slow fast Capillary rise Groundwater reservoir Linear reservoir slow Discharge Linear reservoir fast

11 5. Gebruikte code

12 1 2 3 ############################################################ 4 #################### WAGENINGEN MODEL #################### 5 ############################################################ ################# v e r s i o n 2 February 2012 ################## ############################################################ 12 # Author : Claudia Brauer 13 # Hydrology and Quantitative Water Management Group 14 # Wageningen University, The Netherlands 15 # address : Claudia. Brauer@wur. nl 16 # V i s i t i n g address : Droevendaalsesteeg 3, 6708 WB Wageningen 17 # Mail address : P.O. Box 47, 6700 AA Wageningen 18 ############################################################ ############################# 25 # Information and v e r s i o n l o g 26 ############################# 27 Hydrology and Quantitative Water Management Group Wageningen University, The Netherlands 25 June # This code i s n e a r l y the same as the s p r e a d s h e e t v e r s i o n o f the Wageningen Model. 29 # These s p r e a d s h e e t and R v e r s i o n s have two l i n e a r r e s e r v o i r s i n s t e a d o f 30 # the o r i g n i n a l j model and convection d i f f u s i o n r e s e r v o i r in the Fortran code # I made two changes to the spreadsheet version : 33 # 1. Surface r u n o f f added when SM>SAT. 34 # 2. Min and max f u n c t i o n s added f o r computation PEF or CAP 35 # ( so CAP i s not computed with formula f o r PEF) # Changes between the d i f f e r e n t v e r s i o n s o f the R code : 38 # : added : warming up period 39 # : added : lognash S u t c l i f f e and mean sum o f squares 40 # : added : extra i t e r a t i o n s to f i n d SM and PEF 41 # : added : run argument to g i v e the run a name ########## 49 # FUNCTION 50 ########## # This p a r a m e t r i c a l model c a l l e d WagMod i s a f u n c t i o n with two arguments : 53 # Argument f o r c : the f o r c i n g data frame 54 # Argument par : the parameter data frame 55 # Argument run : the name you want to g i v e to the model run WagMod = function ( forc, par, run ) 58 { # dummy v e c t o r s which have to be d e f i n e d b e f o r e the for loop s t a r t s 61 ETact = c ( ) # a c t u a l e v a p o t r a n s p i r a t i o n 2 [mm/d ] or [mm/h ] 62 PEF = c ( ) # e f f e c t i v e p r e c i p i t a t i o n [mm/d ] or [mm/h ] 63 SM = c ( ) # s o i l moisture content [mm] 64 Gstore = c ( ) # amount o f water s t o r e d in groundwater r e s e r v o i r [mm] 65 DIV = c ( ) # d i v i d e r between slow and quick r e s e r v o i r [ ] 66 in f a s t = c ( ) # flow i n t o f a s t r e s e r v o i r [mm/d ] or [mm/h ] 67 in slow = c ( ) # flow i n t o slow r e s e r v o i r [mm/d ] or [mm/h ] 68 Q f a s t = c ( ) # flow out o f f a s t r e s e r v o i r [mm/d ] or [mm/h ] 69 Q slow = c ( ) # flow out o f slow r e s e r v o i r [mm/d ] or [mm/h ] 70 Q s u r f = array ( 0, dim=length ( f o r c $P) ) # overland flow [mm/d ] or [mm/h ] 71 Q t o t = c ( ) # t o t a l outflow [mm/d ] or [mm/h ] # s e t i n i t i a l c o n d i t i o n s 75 SM [ 1 ] = par $SM0 # from par data frame 76 Gstore [ 1 ] = par$ Gstore0 # from par data frame 77 Q slow [ 1 ] = par$q slow0 # from par data frame 78 Q fast [ 1 ] = par$q fast0 # from par data frame # run for loop over each time step 82 f o r ( t in 1 : l ength ( f o r c $P) ) 83 { SM[ t +1] = SM[ t ] + f o r c $P[ t ] f o r c $ETpot [ t ] # f i r s t estimate new s o i l moisture content 86 # three s it ua t io ns : 87 # SM > SAT > surface runoff and percolation 88 # FC < SM < SAT > percolation 89 # SM < FC > capillary rise i f (SM[ t +1] >= par$fc) 92 { # p e r c o l a t i o n ( with or without s u r f a c e r u n o f f ) 93 ETact [ t ] = f o r c $ETpot [ t ] # no e v a p o t r a n s p i r a t i o n reduction > ETact = f o r c $ETpot 94 i f (SM[ t +1] > par$sat) # check for saturation { # situation SM > SAT > surface runoff and percolation 97 PEF[ t ] = par $REPA ( par $SAT par $FC) # maximum p e r c o l a t i o n 98 SM[ t +1] = SM[ t ] + f o r c $P[ t ] ETact [ t ] PEF[ t ] # new s o i l moisture minus p e r c o l a t i o n i f (SM[ t +1] > par$sat) 101 { # i f s t i l l SM>SAT 102 Q s u r f [ t ] = SM[ t +1] par $SAT # compute s u r f a c e r u n o f f 103 SM[ t +1] = par $SAT # s e t SM to s a t u r a t i o n 104 } } else { # situation FC < SM < SAT > percolation 107 PEF[ t ] = max(sm[ t +1] par $REPA (SM[ t +1] par $FC) / par $SAT, 0 ) # 1 s t estimate e f f e c t i v e p r e c i p i t a t i o n 108 SM [ t +1] = max(sm[ t ] + f o r c $P[ t ] f o r c $ETpot [ t ] PEF[ t ], 0) # 2nd estimate new s o i l moisture content 109 PEF[ t ] = max(sm[ t +1] par $REPA (SM[ t +1] par $FC) / par $SAT, 0 ) # 2nd PEF 110 SM [ t +1] = max(sm[ t ] + f o r c $P[ t ] ETact [ t ] PEF[ t ], 0 ) # 3 rd SM 111 PEF[ t ] = max(sm[ t +1] par $REPA (SM[ t +1] par $FC) / par $SAT, 0 ) # 3 rd PEF 112 SM [ t +1] = max(sm[ t ] + f o r c $P[ t ] ETact [ t ] PEF[ t ], 0 ) # 4 th SM 113 PEF[ t ] = max(sm[ t +1] par $REPA (SM[ t +1] par $FC) / par $SAT, 0 ) # 4 th PEF 114 SM [ t +1] = max(sm[ t ] + f o r c $P[ t ] ETact [ t ] PEF[ t ], 0 ) # 5 th SM 115 PEF[ t ] = max(sm[ t +1] par $REPA (SM[ t +1] par $FC) / par $SAT, 0 ) # 5 th PEF 116 SM [ t +1] = max(sm[ t ] + f o r c $P[ t ] ETact [ t ] PEF[ t ], 0 ) # 6 th SM 117 } } else { # situation SM < FC > capillary rise 120 PEF[ t ] = min( par $FOS ( par $FC SM[ t +1]) Gstore [ t ], 0 ) # f i r s t estimate e f f e c t i v e p r e c i p i t a t i o n 121 SM [ t +1] = max(sm[ t ] + f o r c $P[ t ] f o r c $ETpot [ t ] PEF[ t ], 0) # second estimate new s o i l moisture content 122 ETact [ t ] = f o r c $ETpot [ t ] ( cos (SM[ t +1] pi / par $FC) ) # e v a p o t r a n s p i r a t i o n reduction > compute ETact 123 PEF[ t ] = min( par $FOS ( par $FC SM[ t +1]) Gstore [ t ], 0 ) # 2nd PEF 124 SM [ t +1] = max(sm[ t ] + f o r c $P[ t ] ETact [ t ] PEF[ t ], 0 ) # 3 rd SM 125 PEF[ t ] = min( par $FOS ( par $FC SM[ t +1]) Gstore [ t ], 0 ) # 3 rd PEF 126 SM [ t +1] = max(sm[ t ] + f o r c $P[ t ] ETact [ t ] PEF[ t ], 0 ) # 4 th SM 127 PEF[ t ] = min( par $FOS ( par $FC SM[ t +1]) Gstore [ t ], 0 ) # 4 th PEF 128 SM [ t +1] = max(sm[ t ] + f o r c $P[ t ] ETact [ t ] PEF[ t ], 0 ) # 5 th SM 129 PEF[ t ] = min( par $FOS ( par $FC SM[ t +1]) Gstore [ t ], 0 ) # 5 th PEF 130 SM [ t +1] = max(sm[ t ] + f o r c $P[ t ] ETact [ t ] PEF[ t ], 0 ) # 6 th SM 131 } # d i v i d e water between r e s e r v o i r s 135 i f ( Gstore [ t ] >= 0 & PEF[ t ] >= 0) # IF groundwater s t o r a g e p o s i t i v e and p e r c o l a t i o n p o s i t i v e 136 { # THEN s o i l not very dry 137 DIV [ t ] = min ( ( Gstore [ t ] par $CR ),1) # and part o f water w i l l go through quick flow r o u t e s 138 } e l s e { # IF NOT, THEN s o i l very dry 139 DIV [ t ] = 0 # and no water w i l l go through quick flow rout es 140 } # l i n e a r r e s e r v o i r computations 144 in f a s t [ t ] = DIV [ t ] PEF[ t ] # i n f l o w f a s t r e s e r v o i r 145 in slow [ t ] = (1 DIV [ t ] ) PEF[ t ] # i n f l o w slow r e s e r v o i r 146 Q f a s t [ t +1] = max(q f a s t [ t ] exp( 1/ par $Kf ) + in f a s t [ t ] (1 exp( 1/ par $Kf ) ), 0 ) # outflow f a s t r e s e r v o i r 147 Q slow [ t +1] = max(q slow [ t ] exp( 1/ par $Ks) + in slow [ t ] (1 exp( 1/ par $Ks ) ), 0 ) # outflow slow r e s e r v o i r # new groundwater s t o r a g e 151 Gstore [ t +1] = max( Gstore [ t ] + in slow [ t ] Q slow [ t +1],0) } # end for loop # average s o i l moisture between time s t e p s 157 # ( because those v a r i a b l e s with i n i t i a l v a l u e s are computed f o r time step t +1) 158 SM = (SM [ 1 : ( length (SM ) 1)] + SM [ 2 : length (SM ) ] ) /2 159 Gstore = ( Gstore [ 1 : ( length ( Gstore ) 1)] + Gstore [ 2 : length ( Gstore ) ] ) /2 160 Q slow = (Q slow [ 1 : ( length (Q slow ) 1)] + Q slow [ 2 : length (Q slow ) ] ) /2 161 Q f a s t = (Q f a s t [ 1 : ( length (Q f a s t ) 1)] + Q f a s t [ 2 : length (Q f a s t ) ] ) / # t o t a l outflow i s sum o f 2 r e s e r v o i r s and s u r f a c e r u n o f f 165 Q tot = Q fast + Q slow + Q surf 166 # used to be : Q tot = Q fast + Q slow without surface runoff # bind output t o g e t h e r in a data frame date = f o r c $ date 171 P obs = f o r c $P 172 ETpot obs = f o r c $ETpot 173 Q obs = f o r c $Q 174 output = data. frame (cbind (date, P obs, ETpot obs, Q obs, ETact, PEF, SM, Gstore, 175 DIV, in fas t, in slow, Q fas t, Q slow, Q surf, Q tot ) ) # cut o f f the warming up period 178 output = output [ ( f o r c i n g $warm [1]+ 1 ) : nrow ( output ), ] # compute goodness o f f i t measures and put them in the same t a b l e 182 NS = 1 sum ( ( output$q obs output$q tot ) ˆ2) / sum ( ( output$q obs mean(output$q obs ) ) ˆ2) 183 logns = 1 sum ( ( log (output $Q obs ) log (output $Q tot ) ) ˆ2) / sum ( ( log (output $Q obs ) mean( log (output $Q obs ) ) ) ˆ2) 184 meanss = mean ( ( output $Q t o t output $Q obs )ˆ2) 185 output = cbind (output,ns, logns,meanss ) # w r i t e t a b l e s 189 write. table (output, paste ( output, run,. dat, sep= ), row.names=false) 190 write. table (par, paste ( parameters, run,. dat, sep= ), row.names=false) return ( output ) 194 } # end f u n c t i o n 6 5. Gebruikte code The Wageningen Model in R Claudia Brauer

13 6. Data en parameterisatie Invoer (uurwaarden) P : regenmeter op KNMI-station ET pot : dagsom met Makkink van KNMI-station (o.b.v. dagsom globale straling en daggemidelde temperatuur) disaggregeren met uursommen van straling Afvoer (om te kalibreren): stuw waterschap Rijn en IJssel omgerekend naar mm h 1 met 6.5 km 2 Parameters 7 parameters gekalibreerd 4 initiële waarden toestandsvariabelen gekalibreerd

14 7. Modelanalyse Gevoelig voor parameters over: percolatiesnelheid langzame reservoir snelle reservoir Parameterafhankelijkheid 7 parameters is al te veel Identificatie lastig: meer combinaties leiden tot hetzelfde resultaat Parameteronzekerheid 100 parametersets voor de Berkel (figuur: afstudeeronderzoek Herman Haaksma)

15 Q obs, Q mod [mm/h] ETpot, ETact [mm/h] P, Peff [mm/h] Q [mm/h] Kalibratie: 1 apr mrt 1999, NS=0.90 Q obs Q mod, NS = NA P ETpot ETact Soil moisture Field capacity and saturation P Peff Gstore Q obs Q mod Q slow Q fast Q surf P [mm/h] Soil moisture [mm] Gstore [mm]

16 7. Validatie: 1 apr mrt 2003, NS=0.83 Q obs, Q mod [mm/h] ETpot, ETact [mm/h] P, Peff [mm/h] Q [mm/h] Q obs Q mod, NS = NA P ETpot ETact Soil moisture Field capacity and saturation P Peff Gstore Q obs Q mod Q slow Q fast Q surf P [mm/h] Soil moisture [mm] Gstore [mm]

17 8. Simulatie: 1 apr mrt 2011: NS=0.82 Q obs, Q mod [mm/h] ETpot, ETact [mm/h] P, Peff [mm/h] Q [mm/h] Q obs Q mod, NS = 0.85 P ETpot ETact Soil moisture Field capacity and saturation P Peff Gstore Q obs Q mod Q slow Q fast Q surf P [mm/h] Soil moisture [mm] Gstore [mm]

18 8. Simulatie: 14 aug sept 2010: NS=0.86 Q obs, Q mod [mm/h] ETpot, ETact [mm/h] P, Peff [mm/h] Q [mm/h] Q obs Q mod, NS = 0.85 P ETpot ETact Soil moisture Field capacity and saturation P Peff Gstore Q obs Q mod Q slow Q fast Q surf P [mm/h] Soil moisture [mm] Gstore [mm]

19 8. Resultaten simulatie 2010 Piek Q RR Loop- Loop- Start Moment tijd 1 tijd 2 stijging Q piek Q [m 3 s 1 ] [-] [h] [h] Observatie /8 7:00 27/8 3:00 Model /8 5:00 27/8 4:00 Looptijd 1: zwaartepunt P - zwaartepunt Q Looptijd 2: zwaartepunt P - piek Q

20 9. Ervaringen Tijdsbesteding: Afstudeervak van 6 maanden, incl. de andere 4 modellen, analyses en rapportage, excl. schrijven R-code Rekentijden: 1 jaar uurwaarden doorrekenen kost

21 9. Ervaringen Tijdsbesteding: Afstudeervak van 6 maanden, incl. de andere 4 modellen, analyses en rapportage, excl. schrijven R-code Rekentijden: 1 jaar uurwaarden doorrekenen kost 6 seconden

22 Toekomst Wageningen Model verbeteren Slecht te verklaren onderdelen aanpassen Minder parameters? Consensuscode Open source, freeware en gemakkelijk toepasbaar Doel: een simpel, licht, conceptueel neerslag-afvoermodel dat geschikt is voor laaglandstroomgebieden

23 Toekomst (Afstudeer)onderzoeken over (simuleren van) overstromingen

24 Toekomst (Afstudeer)onderzoeken over (simuleren van) overstromingen

25 Meer informatie C.C. Brauer, A.J. Teuling, A. Overeem, Y. van der Velde, P. Hazenberg, P.M.M. Warmerdam, and R. Uijlenhoet, Anatomy of extraordinary rainfall and flash flood in a Dutch lowland catchment, Hydrology and Earth System Science, 15, , 2011 C.C. Brauer, A.J. Teuling, A. Overeem and R. Uijlenhoet, Extreme regenval en overstromingen in het stroomgebied van de Hupselse Beek, H2O, 18, 23-26, 2011 Diverse colloquia en scripties Brauer et al., HESS, 15, , 2011

26 Extra slides Brauer et al., HESS, 15, , 2011

27 Neerslag Rainfall depth [mm] Brauer et al., HESS, 15, , 2011

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36 Height [km] A 0 B A B' 50 A' B A' B' Reflectivity [dbz]

37 Radar Rainfall depth [mm] Gauge

38 Cumulative rainfall depth [mm] Used time series, automatic rain gauge Used time series, radar Hupsel Radar Hupsel Radar (link path) Microwave link Manual rain gauge :00 12:00 16:00 20:00 00:00 04:00 Time [UTC]

39 Neerslag-afvoerprocessen Brauer et al., HESS, 15, , 2011

40 Rainfall intensity [mm h -1 ] Groundwater level [cm below land surface] Discharge [m 3 s -1 ] ponding land surface 0 piezometer in local depression h saturation piezometer in local elevation 27 Aug 13:00 13 Sep 14: Soil moisture [vol. %] 0 24 Aug 25 Aug 26 Aug 27 Aug 28 Aug 29 Aug 30 Aug 31 Aug 01 Sep 02 Sep 03 Sep

41 Oppervlaktewateropstuwing I I road road road II V Brauer et al., HESS, 15, , 2011

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46 Respons Fase I: Bodemvochtaanvulling Fase II: Grondwaterstijging Fase III: Plasvorming en oppervlakte-afvoer drological Fase response IV: Oppervlaktewateropstuwing 0 Rainfall intensity [mm h -1 ] Groundwater level [cm below land surface] Discharge [m 3 s -1 ] ponding land surface piezometer in local depression Aug 25 Aug 26 Aug 8 h 27 Aug saturation 28 Aug 29 Aug 30 Aug 31 Aug piezometer in local elevation 27 Aug 13:00 13 Sep 14:00 01 Sep 02 Sep 03 Sep Soil moisture [vol. %] I II road Brauer et al., HESS, 15, , 2011

47 Discharge [m 3 s 1 ] a Groundwater level [cm below land surface] b land surface piezometer in local depression piezometer in local elevation µ= Catchment storage [mm above reference]

48 Saturation excess [mm] m Hupsel brook Secondary ditch Tertiary ditch Meteorological station Catchment outlet Sub catchment outlet

49 Extreme-waardenanalyse Brauer et al., HESS, 15, , 2011

50 24 h rainfall depth [mm] Hupsel 2010, excluded Hupsel 2010, included 3000 years 6000 years Return period [years]

51 Hoe extreem was deze afvoer? Dagwaarden Maximum: 21 mm d 1 Gumbelverdeling T = 98 years Voor T = 98 jaar, 95% betrouwbaarsheidsinterval: Q tussen 18 en 25 mm d 1 Piek 2010: 42 mm d 1 Niet mogelijk om herhalingstijd te berekenen! Brauer et al., HESS, 15, , 2011

52 cum. P [mm] Q [m 3 s 1 ] Initial Q Total P Peak Q Q [m 3 s 1 ] Aug Dec Nov Nov Dec Sep Hours before / after peak