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TRAVEL TIME DISTRIBUTIONS AND
CATCHMENT-SCALE TRANSPORT MODELS:
RECENT ADVANCES AND NEW CHALLENGES
GIANLUCA BOTTER
(gianlu...
thethethethe chemical responsechemical responsechemical responsechemical response is much more “damped” compared to theis ...
the hydrologic response to a rainfall event is chiefly made by waterthe hydrologic response to a rainfall event is chiefly...
THE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATER & WATER& WATER& WATER& WATER QUALITY ISSUESQUALITY ISSUES...
THE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATER & WATER& WATER& WATER& WATER QUALITY ISSUESQUALITY ISSUES...
THE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATER & WATER& WATER& WATER& WATER QUALITY ISSUESQUALITY ISSUES...
XXXX0
XXXXt(t;X0)
X1
X3
X2
INJECTION
AREA
CONTROLCONTROLCONTROLCONTROL
VOLUMEVOLUMEVOLUMEVOLUME
LagrangianLagrangianLagran...
“Time interval elapsed from the entry to the leave”
TRAVEL (or TRANSIT) TIME tT : the AGE when you die
“ Time spent by a w...
RESIDENCE TIME PDF evaluated at time t: pRT (tR , t )
( ) ( ) ( )∫∞−
−=
t
iiRTiINs
dttttptCtC ,
average storage concentrat...
RESIDENCE TIME PDF evaluated at time t: pRT (tR , t )
( ) ( ) ( )∫∞−
−=
t
iiRTiINs
dttttptCtC ,
average storage concentrat...
RESIDENCE TIME PDF: TEMPORAL EVOLUTION
STORAGE S(t)INPUT OUTPUT
low
high
N(tR,t)
N(tR,t) = S(t) pRT(tR,t)
number of partic...
RESIDENCE TIME PDF: TEMPORAL EVOLUTION
STORAGE S(t)INPUT OUTPUT
low
high
N(tR,t)
N(tR,t) = S(t) pRT(tR,t)
number of partic...
RESIDENCE TIME PDF: TEMPORAL EVOLUTION
N(tR,t)
RESIDENCE TIME tR
BOUNDARY CONDITION: N(tR=0,t)=IN(t) + AGEING: 0=
∂
∂
+
∂
...
RESIDENCE TIME PDF: TEMPORAL EVOLUTION
N(tR,t)
RESIDENCE TIME tR
BOUNDARY CONDITION: N(tR=0,t)=IN(t) + AGEING: 0=
∂
∂
+
∂
...
RESIDENCE TIME PDF: TEMPORAL EVOLUTION
N(tR,t)
RESIDENCE TIME tR
INPUTIN(t)
t
STORAGE S(t) OUTPUT
low
high
OUT(t)
t
)(),('...
The particles leaving the system are sampled among those in storage,The particles leaving the system are sampled among tho...
RAINFALL
DISCHARGE
EVAPO-
TRANSPIRATION
THE MASTER EQUATION FOR THE RESIDENCE TIME PDFTHE MASTER EQUATION FOR THE RESIDENC...
RAINFALL
DISCHARGE
EVAPO-
TRANSPIRATION
THE MASTER EQUATION FOR THE RESIDENCE TIME PDFTHE MASTER EQUATION FOR THE RESIDENC...
THE CASE OFTHE CASE OFTHE CASE OFTHE CASE OF RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (ωωωω=1=1=...
THE CASE OFTHE CASE OFTHE CASE OFTHE CASE OF RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (ωωωω=1=1=...
THE CASE OFTHE CASE OFTHE CASE OFTHE CASE OF RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (ωωωω=1=1=...
GENERAL MODELGENERAL MODELGENERAL MODELGENERAL MODEL STRUCTURE: TWOSTRUCTURE: TWOSTRUCTURE: TWOSTRUCTURE: TWO RS COMPARTME...
APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLIC...
APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLIC...
APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLIC...
OBSERVEDOBSERVEDOBSERVEDOBSERVED AND MODELEDAND MODELEDAND MODELEDAND MODELED DISCHARGES @ HUPSEL BROOKDISCHARGES @ HUPSEL...
OBSERVEDOBSERVEDOBSERVEDOBSERVED AND MODELEDAND MODELEDAND MODELEDAND MODELED Cl CONCENTRATIONS @ HUPSEL BROOKCl CONCENTRA...
TIME VARIANCE OF THE RESIDENCE TIME PDFTIME VARIANCE OF THE RESIDENCE TIME PDFTIME VARIANCE OF THE RESIDENCE TIME PDFTIME ...
APPLICATIONAPPLICATIONAPPLICATIONAPPLICATION 2.2.2.2. CHLORIDE TRANSPORTCHLORIDE TRANSPORTCHLORIDE TRANSPORTCHLORIDE TRANS...
APPLICATIONAPPLICATIONAPPLICATIONAPPLICATION 3.3.3.3. PESTICIDE TRANSPORT IN THE MONCHALTORF (CH)PESTICIDE TRANSPORT IN TH...
ANNUAL
DYNAMICS of
DISCHARGEDISCHARGEDISCHARGEDISCHARGE and
ATHRAZINEATHRAZINEATHRAZINEATHRAZINE
CONCENTRATIONCONCENTRATIO...
OBSERVEDOBSERVEDOBSERVEDOBSERVED AND MODELED At CONCENTRATIONS @ MONCHALTORFAND MODELED At CONCENTRATIONS @ MONCHALTORFAND...
CHALLENGESCHALLENGESCHALLENGESCHALLENGES
Derive analytical or numerical solutions forDerive analytical or numerical soluti...
CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS
timetimetimetime variance of travelvariance of travelvariance of travelvarian...
THE RESEARCH TEAM (PADOVATHE RESEARCH TEAM (PADOVATHE RESEARCH TEAM (PADOVATHE RESEARCH TEAM (PADOVA----LAUSANNE)LAUSANNE)...
TRAVEL TIME DISTRIBUTIONS AND
CATCHMENT-SCALE TRANSPORT MODELS:
RECENT ADVANCES AND NEW CHALLENGES
GIANLUCA BOTTER
(gianlu...
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Residence time theories of pollutants transport

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Gianluca Botter talked about the travel time distribution approach to catchment scale transport. A topic that intersects also the “old water paradox” querelle, but is, in general, pretty effective in getting the distribution of pollutants. This approach has a long story that put its roots, in Gedeon Dagan’s work, as well as in Rodriguez-Iturbe geomorphic unit hydrograph. Andrea own papers on Mass response function with Sandro Marani can also be considered at the foundations of this presentation.

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Transcript of "Residence time theories of pollutants transport"

  1. 1. TRAVEL TIME DISTRIBUTIONS AND CATCHMENT-SCALE TRANSPORT MODELS: RECENT ADVANCES AND NEW CHALLENGES GIANLUCA BOTTER (gianluca.botter@dicea.unipd.it) UNIVERSITA’ DEGLI STUDI DI PADOVA Department of Civil Architectural and Environmental Engineering (DICEA)
  2. 2. thethethethe chemical responsechemical responsechemical responsechemical response is much more “damped” compared to theis much more “damped” compared to theis much more “damped” compared to theis much more “damped” compared to the hydrologic signalhydrologic signalhydrologic signalhydrologic signal –––– different processesdifferent processesdifferent processesdifferent processes HYDROLOGIC vs CHEMICAL SIGNALSHYDROLOGIC vs CHEMICAL SIGNALSHYDROLOGIC vs CHEMICAL SIGNALSHYDROLOGIC vs CHEMICAL SIGNALS [Kirchner et al.., Nature 2000][Kirchner et al.., Nature 2000][Kirchner et al.., Nature 2000][Kirchner et al.., Nature 2000]
  3. 3. the hydrologic response to a rainfall event is chiefly made by waterthe hydrologic response to a rainfall event is chiefly made by waterthe hydrologic response to a rainfall event is chiefly made by waterthe hydrologic response to a rainfall event is chiefly made by water particles alreadyparticles alreadyparticles alreadyparticles already in storage before the event (old water)in storage before the event (old water)in storage before the event (old water)in storage before the event (old water) THE OLD WATERTHE OLD WATERTHE OLD WATERTHE OLD WATER PARADOXPARADOXPARADOXPARADOX TRACKS OF PAST RAINFALL EVENTS INTRACKS OF PAST RAINFALL EVENTS INTRACKS OF PAST RAINFALL EVENTS INTRACKS OF PAST RAINFALL EVENTS IN STREAMS…STREAMS…STREAMS…STREAMS… LASTING FOR MONTHS/YEARS (LONG MEMORY)LASTING FOR MONTHS/YEARS (LONG MEMORY)LASTING FOR MONTHS/YEARS (LONG MEMORY)LASTING FOR MONTHS/YEARS (LONG MEMORY) EVENTEVENTEVENTEVENT WATERWATERWATERWATER
  4. 4. THE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATER & WATER& WATER& WATER& WATER QUALITY ISSUESQUALITY ISSUESQUALITY ISSUESQUALITY ISSUES NUTRIENTSNUTRIENTSNUTRIENTSNUTRIENTS PESTICIDESPESTICIDESPESTICIDESPESTICIDES ECOSYSTEM IMPACTSECOSYSTEM IMPACTSECOSYSTEM IMPACTSECOSYSTEM IMPACTS SLUDGE SPILLSSLUDGE SPILLSSLUDGE SPILLSSLUDGE SPILLS
  5. 5. THE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATER & WATER& WATER& WATER& WATER QUALITY ISSUESQUALITY ISSUESQUALITY ISSUESQUALITY ISSUES NUTRIENTSNUTRIENTSNUTRIENTSNUTRIENTS PESTICIDESPESTICIDESPESTICIDESPESTICIDES ECOSYSTEM IMPACTSECOSYSTEM IMPACTSECOSYSTEM IMPACTSECOSYSTEM IMPACTS SLUDGE SPILLSLUDGE SPILLSLUDGE SPILLSLUDGE SPILL [Rinaldo et al., WRR 1989][Rinaldo et al., WRR 1989][Rinaldo et al., WRR 1989][Rinaldo et al., WRR 1989]
  6. 6. THE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATERTHE AGE OF WATER & WATER& WATER& WATER& WATER QUALITY ISSUESQUALITY ISSUESQUALITY ISSUESQUALITY ISSUES LAND MANAGEMENT AND CATCHMENT RESILIENCELAND MANAGEMENT AND CATCHMENT RESILIENCELAND MANAGEMENT AND CATCHMENT RESILIENCELAND MANAGEMENT AND CATCHMENT RESILIENCE
  7. 7. XXXX0 XXXXt(t;X0) X1 X3 X2 INJECTION AREA CONTROLCONTROLCONTROLCONTROL VOLUMEVOLUMEVOLUMEVOLUME LagrangianLagrangianLagrangianLagrangian transporttransporttransporttransport model:model:model:model: waterwaterwaterwater particlesparticlesparticlesparticles travelingtravelingtravelingtraveling throughthroughthroughthrough a control volumea control volumea control volumea control volume (MAINLY HILLSLOPES PRCESSES)(MAINLY HILLSLOPES PRCESSES)(MAINLY HILLSLOPES PRCESSES)(MAINLY HILLSLOPES PRCESSES) [e.g., Taylor, 1921;[e.g., Taylor, 1921;[e.g., Taylor, 1921;[e.g., Taylor, 1921; DaganDaganDaganDagan, 1989], 1989], 1989], 1989] FORMULATION ofFORMULATION ofFORMULATION ofFORMULATION of TRANSPORT AT THE CATCHMENT SCALETRANSPORT AT THE CATCHMENT SCALETRANSPORT AT THE CATCHMENT SCALETRANSPORT AT THE CATCHMENT SCALE ),( );( tXV dt XtdX t t =0 particle’s trajectory: INPUT OUTPUT
  8. 8. “Time interval elapsed from the entry to the leave” TRAVEL (or TRANSIT) TIME tT : the AGE when you die “ Time spent by a water/solute particle inside a catchment since entry” RESIDENCE TIME tR : the AGE RESIDENCE TIMES vs TRAVEL TIMES ...RANDOM VARIABLES (space-time heterogeneity of the relevant processes and enviroments)
  9. 9. RESIDENCE TIME PDF evaluated at time t: pRT (tR , t ) ( ) ( ) ( )∫∞− −= t iiRTiINs dttttptCtC , average storage concentration (STORAGE MEMORY of the INPUT) RESIDENCE TIMES vs TRAVEL TIMES AGE DISTRIBUTION of living people
  10. 10. RESIDENCE TIME PDF evaluated at time t: pRT (tR , t ) ( ) ( ) ( )∫∞− −= t iiRTiINs dttttptCtC , average storage concentration (STORAGE MEMORY of the INPUT) RESIDENCE TIMES vs TRAVEL TIMES TRAVEL TIME PDF conditional to the exit time: p’OUT (tT , t ) ( ) ( ) ( )∫∞− −= t iiOUTiINOUT dttttptCtC ,' output flux concentration (OUTPUT MEMORY of the INPUT) AGE DISTRIBUTION of living people AGE DISTRIBUTION of people dying
  11. 11. RESIDENCE TIME PDF: TEMPORAL EVOLUTION STORAGE S(t)INPUT OUTPUT low high N(tR,t) N(tR,t) = S(t) pRT(tR,t) number of particles with age tR at time t RESIDENCE TIME tR IN(t) OUT(t) t t PURE AGEING: 0= ∂ ∂ + ∂ ∂ R RR t ttN t ttN ),(),( PLAYPAUSE
  12. 12. RESIDENCE TIME PDF: TEMPORAL EVOLUTION STORAGE S(t)INPUT OUTPUT low high N(tR,t) N(tR,t) = S(t) pRT(tR,t) number of particles with age tR at time t RESIDENCE TIME tR IN(t) OUT(t) t t PURE AGEING: 0= ∂ ∂ + ∂ ∂ R RR t ttN t ttN ),(),( PLAYPAUSE
  13. 13. RESIDENCE TIME PDF: TEMPORAL EVOLUTION N(tR,t) RESIDENCE TIME tR BOUNDARY CONDITION: N(tR=0,t)=IN(t) + AGEING: 0= ∂ ∂ + ∂ ∂ R RR t ttN t ttN ),(),( PURE AGEING: 0= ∂ ∂ + ∂ ∂ R RR t ttN t ttN ),(),( INPUTIN(t) t STORAGE S(t) OUTPUT low high OUT(t) t PAUSEPLAY
  14. 14. RESIDENCE TIME PDF: TEMPORAL EVOLUTION N(tR,t) RESIDENCE TIME tR BOUNDARY CONDITION: N(tR=0,t)=IN(t) + AGEING: 0= ∂ ∂ + ∂ ∂ R RR t ttN t ttN ),(),( = ∂ ∂ + ∂ ∂ R RR t ttN t ttN ),(),( INPUTIN(t) t STORAGE S(t) OUTPUT low high OUT(t) t AGEING + SAMPLING VIA OUTPUT )(),(' tOUTttp ROUT − PAUSEPLAY
  15. 15. RESIDENCE TIME PDF: TEMPORAL EVOLUTION N(tR,t) RESIDENCE TIME tR INPUTIN(t) t STORAGE S(t) OUTPUT low high OUT(t) t )(),(' )],()([)],()([ tOUTttp t ttptS t ttptS ROUT R RRTRRT −= ∂ ∂ + ∂ ∂
  16. 16. The particles leaving the system are sampled among those in storage,The particles leaving the system are sampled among those in storage,The particles leaving the system are sampled among those in storage,The particles leaving the system are sampled among those in storage, and so their age:and so their age:and so their age:and so their age: w(tR, t)p’OUT(tR,t) = pRT(tR, t) AGES SAMPLED AGES AVAILABLE PREFERENCE AGE FUNCTIONAGE FUNCTIONAGE FUNCTIONAGE FUNCTION (MIXING)(MIXING)(MIXING)(MIXING) LOW AVAILABILITY or LOWLOW AVAILABILITY or LOWLOW AVAILABILITY or LOWLOW AVAILABILITY or LOW PREFERENCEPREFERENCEPREFERENCEPREFERENCE IMPLIES LOWIMPLIES LOWIMPLIES LOWIMPLIES LOW SAMPLINGSAMPLINGSAMPLINGSAMPLING –––– AGESAGESAGESAGES NOT REPRESENTED IN THE OUTPUTNOT REPRESENTED IN THE OUTPUTNOT REPRESENTED IN THE OUTPUTNOT REPRESENTED IN THE OUTPUT MIXING: LINKING RESIDENCE and TRAVEL TIME PDF ’sMIXING: LINKING RESIDENCE and TRAVEL TIME PDF ’sMIXING: LINKING RESIDENCE and TRAVEL TIME PDF ’sMIXING: LINKING RESIDENCE and TRAVEL TIME PDF ’s 1 SAMPLING through AGE functions 11 uniform preference over all ages ωωωω decreases for older ages ,,, =const ωωωω increases for older ages randomrandomrandomrandom samplingsamplingsamplingsampling preference for old waterpreference for old waterpreference for old waterpreference for old water preference for new waterpreference for new waterpreference for new waterpreference for new water
  17. 17. RAINFALL DISCHARGE EVAPO- TRANSPIRATION THE MASTER EQUATION FOR THE RESIDENCE TIME PDFTHE MASTER EQUATION FOR THE RESIDENCE TIME PDFTHE MASTER EQUATION FOR THE RESIDENCE TIME PDFTHE MASTER EQUATION FOR THE RESIDENCE TIME PDF )()()( )( tQtETtJ dt tdS −−= ),(),( ),(),( ttFttp t ttp t ttp RRRT R RRTRRT = ∂ ∂ + ∂ ∂ MASTER EQUATION FOR pRT:       −−+−= )( )( )],([ )( )( )],([ )( )( ),( tS tJ tt tS tQ tt tS tQ ttF RETRQR ωωωωωωωω 11 (WATER FLUXES, TYPE OF MIXING) where:
  18. 18. RAINFALL DISCHARGE EVAPO- TRANSPIRATION THE MASTER EQUATION FOR THE RESIDENCE TIME PDFTHE MASTER EQUATION FOR THE RESIDENCE TIME PDFTHE MASTER EQUATION FOR THE RESIDENCE TIME PDFTHE MASTER EQUATION FOR THE RESIDENCE TIME PDF )()()( )( tQtETtJ dt tdS −−= ),(),( ),(),( ttFttp t ttp t ttp RRRT R RRTRRT = ∂ ∂ + ∂ ∂ MASTER EQUATION FOR pRT:       −−+−= )( )( )],([ )( )( )],([ )( )( ),( tS tJ tt tS tQ tt tS tQ ttF RETRQR ωωωωωωωω 11 where: ................ ANALYTICAL SOLUTIONS forANALYTICAL SOLUTIONS forANALYTICAL SOLUTIONS forANALYTICAL SOLUTIONS for ωωωω=1=1=1=1 TRAVEL & RESIDENCE TIME PDF’s MUST BETRAVEL & RESIDENCE TIME PDF’s MUST BETRAVEL & RESIDENCE TIME PDF’s MUST BETRAVEL & RESIDENCE TIME PDF’s MUST BE CONSISTENTCONSISTENTCONSISTENTCONSISTENT WITH THEWITH THEWITH THEWITH THE SET OF AGES AVAILABLESET OF AGES AVAILABLESET OF AGES AVAILABLESET OF AGES AVAILABLE ANDANDANDAND THE INPUT/OUTPUTTHE INPUT/OUTPUTTHE INPUT/OUTPUTTHE INPUT/OUTPUT FLUXESFLUXESFLUXESFLUXES (WATER FLUXES, TYPE OF MIXING)
  19. 19. THE CASE OFTHE CASE OFTHE CASE OFTHE CASE OF RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (ωωωω=1=1=1=1))))       − − − = ∫− t tt T T TOUT T dx xS xJ ttS ttJ ttp )( )( exp )( )( ),(' TRAVEL TIME PDFTRAVEL TIME PDFTRAVEL TIME PDFTRAVEL TIME PDF [Botter et al., WRR 2010]
  20. 20. THE CASE OFTHE CASE OFTHE CASE OFTHE CASE OF RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (ωωωω=1=1=1=1))))       − − − = ∫− t tt T T TOUT T dx xS xJ ttS ttJ ttp )( )( exp )( )( ),(' TRAVEL TIME PDFTRAVEL TIME PDFTRAVEL TIME PDFTRAVEL TIME PDF [Botter et al., WRR 2010] Relationship with advection/dispersion models:
  21. 21. THE CASE OFTHE CASE OFTHE CASE OFTHE CASE OF RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (RANDOM SAMPLING (ωωωω=1=1=1=1)))) ANALYTICAL (WELL MIXED) NUMERICAL 3D SIMULATION C=Cmax C=0       − − − = ∫− t tt T T TOUT T dx xS xJ ttS ttJ ttp )( )( exp )( )( ),(' EMERGING FEATURES: 1. TIME VARIANCE 2. DEPENDENCE ON ECO- HYDROLOGICAL PROCESSES SERIES/PARALLEL OF MIXEDSERIES/PARALLEL OF MIXEDSERIES/PARALLEL OF MIXEDSERIES/PARALLEL OF MIXED STORAGES,STORAGES,STORAGES,STORAGES, ifififif necessarynecessarynecessarynecessary [Rinaldo et al., WRR 2011] TRAVEL TIME PDFTRAVEL TIME PDFTRAVEL TIME PDFTRAVEL TIME PDF
  22. 22. GENERAL MODELGENERAL MODELGENERAL MODELGENERAL MODEL STRUCTURE: TWOSTRUCTURE: TWOSTRUCTURE: TWOSTRUCTURE: TWO RS COMPARTMENTSRS COMPARTMENTSRS COMPARTMENTSRS COMPARTMENTS (Selective) ET(Selective) ET(Selective) ET(Selective) ET may increase c(t) )()()( )( tLtETtJ dt tds nZR −−= )()()( )( tMtMtF dt tdM LET s −−= ROOT ZONE DEEPER STORAGELEACHINGLEACHINGLEACHINGLEACHING
  23. 23. APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL) CHLORIDES introduced through FERTILIZERS... ...inducing high Cl concentrations in STREAMS
  24. 24. APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL) NEGATIVE CORRELATION between Q and C
  25. 25. APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL)APPLICATION 1. CHLORIDE TRANSPORT IN THE HUPSEL BROOK (NL) NO FERTILIZATIONS NEGATIVE CORRELATION between Q and C PERSISTENCY of the chemical signal, despite the input seasonality (long memory)
  26. 26. OBSERVEDOBSERVEDOBSERVEDOBSERVED AND MODELEDAND MODELEDAND MODELEDAND MODELED DISCHARGES @ HUPSEL BROOKDISCHARGES @ HUPSEL BROOKDISCHARGES @ HUPSEL BROOKDISCHARGES @ HUPSEL BROOK
  27. 27. OBSERVEDOBSERVEDOBSERVEDOBSERVED AND MODELEDAND MODELEDAND MODELEDAND MODELED Cl CONCENTRATIONS @ HUPSEL BROOKCl CONCENTRATIONS @ HUPSEL BROOKCl CONCENTRATIONS @ HUPSEL BROOKCl CONCENTRATIONS @ HUPSEL BROOK SHORT TERM FLUCTUATIONS RELATED TO THE ROOT ZONE (short travel times) in WINTER the Clin WINTER the Clin WINTER the Clin WINTER the Cl concentrationconcentrationconcentrationconcentration isisisis sustainedsustainedsustainedsustained by GW (longby GW (longby GW (longby GW (long traveltraveltraveltravel timestimestimestimes))))
  28. 28. TIME VARIANCE OF THE RESIDENCE TIME PDFTIME VARIANCE OF THE RESIDENCE TIME PDFTIME VARIANCE OF THE RESIDENCE TIME PDFTIME VARIANCE OF THE RESIDENCE TIME PDF ttttRRRR [[[[ ]]]]ttttRRRR [[[[ ]]]] ppppRTRTRTRT((((ttttRRRR,t,t,t,t))))[[[[]]]]ppppRTRTRTRT((((ttttRRRR,t,t,t,t))))[[[[]]]] ttttRRRR [[[[ ]]]] ppppRTRTRTRT((((ttttRRRR,t,t,t,t))))[[[[]]]] WINTERWINTERWINTERWINTER (WET)(WET)(WET)(WET) SUMMERSUMMERSUMMERSUMMER (DRY)(DRY)(DRY)(DRY)
  29. 29. APPLICATIONAPPLICATIONAPPLICATIONAPPLICATION 2.2.2.2. CHLORIDE TRANSPORTCHLORIDE TRANSPORTCHLORIDE TRANSPORTCHLORIDE TRANSPORT @ PLYNIMON (UK)@ PLYNIMON (UK)@ PLYNIMON (UK)@ PLYNIMON (UK) INCREASE or DECREASE of chloride concentrations during floods (depending on the season)
  30. 30. APPLICATIONAPPLICATIONAPPLICATIONAPPLICATION 3.3.3.3. PESTICIDE TRANSPORT IN THE MONCHALTORF (CH)PESTICIDE TRANSPORT IN THE MONCHALTORF (CH)PESTICIDE TRANSPORT IN THE MONCHALTORF (CH)PESTICIDE TRANSPORT IN THE MONCHALTORF (CH) Huge PESTICIDE LOADSPESTICIDE LOADSPESTICIDE LOADSPESTICIDE LOADS introduced through farming... high ATRAZINEATRAZINEATRAZINEATRAZINE CONCENTRATIONSCONCENTRATIONSCONCENTRATIONSCONCENTRATIONS in STREAMS during the SUMMER (ATRAZINE is CANCEROUS)
  31. 31. ANNUAL DYNAMICS of DISCHARGEDISCHARGEDISCHARGEDISCHARGE and ATHRAZINEATHRAZINEATHRAZINEATHRAZINE CONCENTRATIONCONCENTRATIONCONCENTRATIONCONCENTRATION APPLICATIONAPPLICATIONAPPLICATIONAPPLICATION 3.3.3.3. PESTICIDE TRANSPORT IN THE MONCHALTORF (CH)PESTICIDE TRANSPORT IN THE MONCHALTORF (CH)PESTICIDE TRANSPORT IN THE MONCHALTORF (CH)PESTICIDE TRANSPORT IN THE MONCHALTORF (CH)
  32. 32. OBSERVEDOBSERVEDOBSERVEDOBSERVED AND MODELED At CONCENTRATIONS @ MONCHALTORFAND MODELED At CONCENTRATIONS @ MONCHALTORFAND MODELED At CONCENTRATIONS @ MONCHALTORFAND MODELED At CONCENTRATIONS @ MONCHALTORF OBSERVED MODEL
  33. 33. CHALLENGESCHALLENGESCHALLENGESCHALLENGES Derive analytical or numerical solutions forDerive analytical or numerical solutions forDerive analytical or numerical solutions forDerive analytical or numerical solutions for arbitrary mixing functionsarbitrary mixing functionsarbitrary mixing functionsarbitrary mixing functions,,,, suitably parametrizedsuitably parametrizedsuitably parametrizedsuitably parametrized –––– relationship withrelationship withrelationship withrelationship with spatially distributedspatially distributedspatially distributedspatially distributed modelsmodelsmodelsmodels BetterBetterBetterBetter understandunderstandunderstandunderstand thethethethe rolerolerolerole ofofofof evapotranspirationevapotranspirationevapotranspirationevapotranspiration andandandand plantplantplantplant physiologyphysiologyphysiologyphysiology forforforfor thethethethe hydrohydrohydrohydro---- chemistrychemistrychemistrychemistry ofofofof riversriversriversrivers Let the age functions beLet the age functions beLet the age functions beLet the age functions be dependent on the catchment’dependent on the catchment’dependent on the catchment’dependent on the catchment’ statestatestatestate (e.g. wet(e.g. wet(e.g. wet(e.g. wet VS dry)VS dry)VS dry)VS dry) FLOODS DROUGHTS AGE functions
  34. 34. CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS timetimetimetime variance of travelvariance of travelvariance of travelvariance of travel &&&& residenceresidenceresidenceresidence time pdf’stime pdf’stime pdf’stime pdf’s @@@@ multiple timescalesmultiple timescalesmultiple timescalesmultiple timescales (variability(variability(variability(variability ofofofof fluxesfluxesfluxesfluxes and storages)and storages)and storages)and storages) Robustness of the approach,Robustness of the approach,Robustness of the approach,Robustness of the approach, suggested by the comparisonsuggested by the comparisonsuggested by the comparisonsuggested by the comparison with field datawith field datawith field datawith field data travel and residence time pdf’s aretravel and residence time pdf’s aretravel and residence time pdf’s aretravel and residence time pdf’s are related objectsrelated objectsrelated objectsrelated objects dependent on mixingdependent on mixingdependent on mixingdependent on mixing processes and hydrologic fluxesprocesses and hydrologic fluxesprocesses and hydrologic fluxesprocesses and hydrologic fluxes
  35. 35. THE RESEARCH TEAM (PADOVATHE RESEARCH TEAM (PADOVATHE RESEARCH TEAM (PADOVATHE RESEARCH TEAM (PADOVA----LAUSANNE)LAUSANNE)LAUSANNE)LAUSANNE) University of Padova, Italy Gianluca Botter Paolo Benettin EPFL, Lausanne, CH Andrea Rinaldo Enrico Bertuzzo
  36. 36. TRAVEL TIME DISTRIBUTIONS AND CATCHMENT-SCALE TRANSPORT MODELS: RECENT ADVANCES AND NEW CHALLENGES GIANLUCA BOTTER (gianluca.botter@dicea.unipd.it) UNIVERSITA’ DEGLI STUDI DI PADOVA Department of Civil Architectural and Environmental Engineering (DICEA)
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