FE 537. Catchment Modeling. Oregon State University

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1 Catchment Modeling

2 This section An experimentalist s s view of models and their development in catchment hydrology Example of a model that captures dominant runoff processes Using our new process knowledge to build the model and calibrate the model How to judge the worth of a model with our process knowledge Bringing detailed processes (that we cannot observe!) into the model

FE The 537 need for a design discharge The Prehistory Examples: the Rational Method and the Time Area Curve the Unit Hydrograph, the Effective Rain and Separation of

3 FE The 537 need for a design discharge The Prehistory Examples: the Rational Method and the Time Area Curve the Unit Hydrograph, the Effective Rain and Separation of Hydrographs the Linear Models: the linear channel, the linear reservoir, the Nash cascade only for small and impervious catchments very strong assumptions (e.g. linearity) Mario Martina

the SACRAMENTO model the continuous API model the CLS

4 The conceptual models FE 537 The Middle Ages Examples (WMO Intercomparison, 1976): the STANFORD model IV the SACRAMENTO model the continuous API model the CLS the parameters are physically meaningless Mario Martina

Model the SHETRAN breakthrough in hydrological modelling physical processes

5 The physically based models The Renaissance Examples: the R.A. Freeze Model the Systeme Hydrologique Europeen the Institute of Hydrology Model the SHETRAN breakthrough in hydrological modelling physical processes are now represented too many parameters, too many information needed for the calibration Mario Martina

The FE 537 Variable Contributing Area models The Romanticism A probabilistic representation of spatially distributed variables Examples: the Probability

6 The FE 537 Variable Contributing Area models The Romanticism A probabilistic representation of spatially distributed variables Examples: the Probability Distributed Soil Capacity model the Xinanjiang Model the VIC model few parameters, but they are not directly related to measurable quantities Mario Martina

Geomorphologic Unit Hydrograph the TOPMODEL few parameters and they can

7 FE The 537 derived from topography models The Modern Age TOPMODEL Topographic Index Examples: the Soil Conservation Number model the Geomorphologic Unit Hydrograph the TOPMODEL few parameters and they can be related to measurable quantities but are they really physically based? Mario Martina

FE New 537 physically based / process oriented models The Contemporary Age Examples: the Representative Elementary Watershed (REW) model the Tracer Aided Catchment Distributed (TAC D ) model the

8 FE New 537 physically based / process oriented models The Contemporary Age Examples: the Representative Elementary Watershed (REW) model the Tracer Aided Catchment Distributed (TAC D ) model the TIN-based Real-time Integrated Basin Simulator (tribs) the TOPographic KInematic wave APproximation and Integration (TOPKAPI) Physically-based distributed representation of the dominant processes (synthesis) sometimes a coupled conceptual/physically based approach Mario Martina

9 Complexity / Predictability Grayson & Bloschl (Advances in Water Resources, 2002) More complex does not always mean better!

10 Different scales Measures Phenomena (and theory) Models Mario Martina

11 Process assumptions that we have reviewed (and rejected!) FE 537 (a) Topography Saturated Area Not steady state Bloody Hell! T 0 ln(a/tanβ) Depth (b) Index Bedrock topography (c) Depth to WT Threshold connections Z Preferential flow T Z = T e 0 Z

12 Remember this slide from the Introduction? FE 537 Runoff (l/s) Q Efficiency /30 10/20 11/9 11/29 12/19 1/ Date K (m/d) Vache et al., 2004 GRL

13 This is what such uncertainty can mean for something we (now) know about

14 If an experimentalist was to build a catchment model After much whittling down, this is my most parsimonious catchment model structure.

15 If an experimentalist were to build a model for real P E P E P E U min Hillslope box U max U Hollow box Riparian box Runoff Coupled saturated and unsaturated storage Linear outflow equations Threshold level in hollow box Seibert and McDonnell, 2002 WRR

16 Example Planar slope hollow Hillslope throughflow trench 3 ha catchment 17 ha catchment Stream and riparian zones Downstream

17 The sat and unsat zone need to be coupled from what we have examined today Initial condition Falling water table Rising water table n d Unsaturated zone Unsaturated zone intput Unsaturated zone ΔW Saturated zone Water table depth W Soil depth D output Saturated zone ΔW Saturated zone n Volume: Mass exchange: Mass exchange: V sat = W A n V unsat = ( D W ) A ( n n d ) Δm = m V sat sat Δw A ( n n d ) Δm = m V unsat unsat Δw A ( n n d ) Weiler and McDonnell, 2003 JoH

18 Why three boxes in this application? Hillslope Hollow Riparian Zone

19 K (μmol/l) Riparian Zone Geochemical End Members Hillslope Na (mol/l) Stream Rain Riparian Zone Soil-Ridge Soil-Hollow Hollow Elsenbeer et al., unpub data

20 Cluster Analysis of Deuterium Concentration in Subsurface Water Hillslope Hollow Riparian McDonnell et al.,1991 WRR

21 A non-linear reservoir in the hollow box P E P E P E U min Hillslope box U U max Hollow box Hillslope type discussed earlier Riparian box Runoff Seibert and McDonnell, 2002 WRR

22 Effect of drainable porosity decline on hillslope response to rainfall (and mixing) n d z ( z) = n0 exp m Σδ 18 Storm Rainfall Σδ 18 Ο = 10 ο / οο n d z) z = n exp m ( 0 ψ<0 δ Ο = 4.5 ο / οο ψ<0 Oregon McD, 1990 State WRR; University McD et al 1996 EOS; Freer et al WRR δ Ο = 5 ο / οο

23 Model efficiency : 0.93 Groundwater level [m] Hillslope Hollow Riparian Q [mm/h] 4 2 Observed Q Simulated Q 0 28-Sep 8-Oct 18-Oct 28-Oct 7-Nov 17-Nov 27-Nov

24 It works, eh? Runoff efficiency GW hard GW soft Parameter values New water Q A1 Q and soft GW A1 and A2 Q and new water Goodness measure A1, A2 and A3

25 Model efficiency : 0.93 Groundwater level [m] Hillslope Hollow Riparian Q [mm/h] 4 2 Observed Q Simulated Q 0 28-Sep 8-Oct 18-Oct 28-Oct 7-Nov 17-Nov 27-Nov

26 Model efficiency : 0.92 Groundwater level [m] Hillslope Hollow Riparian Q [mm/h] 4 2 Observed Q Simulated Q 0 28-Sep 8-Oct 18-Oct 28-Oct 7-Nov 17-Nov 27-Nov

27 Model efficiency : 0.93 Groundwater level [m] Hillslope Hollow Riparian Q [mm/h] 4 2 Observed Q Simulated Q 0 28-Sep 8-Oct 18-Oct 28-Oct 7-Nov 17-Nov 27-Nov

28 The internal tug-of of-war what about field experience?! we need real data for model calibration! reviewers

29 What is soft data? Qualitative knowledge from the geoscientist that cannot be used directly for model calibration (or validation) (e.g. new water contribution [%] to peak flow, maximum groundwater level, mean soil depth, reservoir volume, etc) Storage Rainfall z Bypass flow and mixing Pipeflow of old water

30 Dialog between the experimentalist and modeler P E P E Seibert and McDonnell, 2002 AGU Monograph P E Hillslope box U max U Hollow box Riparian box Runoff U min Experimentalist Evaluation rules Modeler Values for evaluation rules

31 Dialog between experimentalist and modeler Experimentalist Evaluation rules Values for evaluation rules (a i ) Modeler Degree of acceptability a a 2 a a 4 New water contribution to peak flow [-] (30/9/87 event, McDonnell et al WRR)

32 Soft data and degree of acceptability μ ( x) = 0 x a2 1 a a4 0 4 a 1 a 1 x a Degree of acceptability 3 if if if if if x a a x 2 a 1 3 > a 1 x a x x 4 < < < a a 3 a Fuzzy Rules - new water at peak - reservoir volumes, K sat etc - range of gw levels - hollow threshold level a 1 a 2 a 3 a 4 Seibert and McDonnell, 2002 AGU Monograph

33 Different ways of evaluating model acceptability based on hard (A1) and soft (A2 and A3) data Acceptability according to: Example Measure A 1 Fit between simulated and Runoff Efficiency observed data A 2 Agreement with perceptual New water Percentage of (qualitative) knowledge contribution peak flow A 3 Reasonability of parameter Spatial extension Fraction of values of riparian zone catchment area Combined objective function: A = n A n A n2 A n with n = n + n + n 1 2 3

34 Model performance Goodness measure Runoff efficiency GW hard GW soft Parameter values New water 0 A1, A2 and A3 A1 and A2 Q and new water Q and soft GW A1 Q Increasing amount of soft data

35 Best overall performance a a little less right but for the correct process reasons Groundwater level [m] Hillslope Hollow Riparian Q [mm/h] 4 2 Observed Q Simulated Q 0 28-Sep 8-Oct 18-Oct 28-Oct 7-Nov 17-Nov 27-Nov

36 Other reservoir assemblages (it s s a soft model approach that you can use in your area) It is physically-based

37 Other modeling examples at the hillslope scale (where we can use our new process knowledge)

38 Pipeflow Pipeflow is mostly preevent water but, applied line sources of tracer often show rapid lateral breakthrough through the pipe/hillslope system.

Our simple model Lateral subsurface flow Dupuit-Forchheimer

cell approach (Wigmosta, 1994 WRR) Water and mass balance

Simple infiltration (soil water content, power law) and

39 Our simple model Lateral subsurface flow Dupuit-Forchheimer assumption (slope of water table) 2-D D explicit grid by grid cell approach (Wigmosta, 1994 WRR) Water and mass balance within the saturated and unsaturated zone in each grid cell Simple infiltration (soil water content, power law) and evapotranspiration z z) = n exp b n d ( 0 K( z) q SSF m 1 z = Ko 1 D ( t) = T ( t) β w

40 Combining this with the process understanding Experimental commonality**: Pipe diameter within a narrow range. Uchida et al WRR Pipe length and connectivity mapping shows discontinuous pipe sections (max. length < some meters) Kitihara 1994 Bull. FFPRI Pipe location within the soil profiles is mostly within a narrow band above the soil-bedrock interface. Uchida et al HP; Water flow in the pipe Sidle et al JoH: q p = k ( h) 0. 4 **from review by Uchida et al 2001 HP

41 How to model the unknown pipe system? Spatial pipe geometry Pipe height within starting cell slope z Despite the limited length of preferential flow structures (e.g. pipes), they can connect by water flow from micro-meso meso-macro macro porosity.

42 Visualizations - Maimai Pipe Flow Line tracer movement Pipe Flow Matrix Flow Runoff Concentration Relative flow in soil pipes 0 max Relative concentration in soil column 0 max

43 Runoff (mm/h) Average with Pipes Ensembles with Pipes Without Pipes Measurements Maimai 0.0 Runoff (mm/h) Total Pre-event runoff Average with Pipes Ensembles with Pipes Without Pipes Evaluation Criteria* Flow 0.0 Tracer Recovery (%) Average with Pipes Ensembles with Pipes Without Pipes Time (h) Event Water % Tracer Recovery *Consistency more important than optimality

44 More Questions How does soil depth variation affect flow? How can place-based experimental knowledge be coupled with the model approach?

45 Remember this site from before. Soil depth mapped at 2 m grid Average: 0.63 m Std: 0.3 m Correlation length: 12 m Subsurface flow measured at 10 2-m 2 wide trench sections

46 Subsurface flow (mm/hr) Model results: total subsurface flow /6/02 2/1/02 2/7/02 2/15/02 2/8/02 3/1/02 2/9/02 3/15/02 2/10/02 3/29/02 2/11/024/12/02 2/12/02 Time Observed Model: mapped soil depth Model: uniform soil depth Soil depth variability has a very large influence on modeled subsurface storm flow volume Precipitation (mm/hr)

47 Subsurface flow (mm/hr) FE Model results: statistical representation Multiple realizations of a model with statistical representations of soil 0 depth represent observed subsurface Model: statistical representations Observed Model: mapped soil depth - 20 m long trench Model: mapped soil depth - 28 m long trench Model: uniform soil depth 0.0 2/6/02 2/7/02 2/8/02 2/9/02 2/10/02 2/11/02 Time Precipitation (mm/hr) 5 storm flow better than a model with average soil depth 10

48 Subsurface flow (mm/hr) Moving to larger segments of the landscape For larger hillslopes the effect of soil 70 x 100 m wide hillslope depth variability on total subsurface flow Model: statistical representations is less than Average for the of smaller statistical representations hillslope but the Model: uniform soil depth 5 effect on timing of subsurface flow is large /6/02 2/7/02 2/8/02 2/9/02 2/10/02 2/11/02 Time 10 Precipitation (mm/hr)

49 Other modeling examples where we can use our new process knowledge

50 Use this expert knowledge to constrain our models also m n Init. Sat. Keff Vache et al GRL 2005

51 Rejecting nonsense dots Red dots = % new water < 50 Black dots = % new water > 50 Identifies parameter sets that produce the efficient results for the wrong reasons m Init. Sat. Vache et al GRL 2005 n Keff

52 Other modeling examples where we can use our new process knowledge to determine how much complexity is warranted in the model

53 Towards more orthogonal measures for model structural improvement and uncertainty reduction A Multi-Criteria Evaluative Strategy Soil Water MRT Discharge Stream Water MRT Gordon Grant s Blob

54 aptures flow path heterogeneity

55 Maimai: : The simplest of our various experimental watersheds Planar slope hollow Hillslope throughflow trench 3 ha catchment 17 ha catchment Stream and riparian zones Downstream

56 The simplest of models to start Grid-based, highly simplified with 3 tunable parameters Precipitation Evapotranspiration Lateral Subsurface Stormflow Vache et al., 2004 GRL The volume of water within each reservoir is accounted for using the familiar continuity equation: dv dt = P ET SS out SOF out + SS in

57 Streamwater residence time (120 days) but also soil water residence time Annual Data P 2250 mm Q 1350 mm E 850 mm Average Data Slope 34 o Relief m 5 m/hr K sat Soils Data Depth 1 m Strong catenary sequence Pit A Pit 5 Raingauge Near Stream Tensiometer Network ln(a/tanβ) Precipitation Soil Water -4 Soil water -4-8 Residence -8 Time Average 94 δ 18 O δ 18 O

58 Pit A Pit 5 Raingauge Near Stream FE 537 ln(a/tanβ) MRT and distance from the divide Tensiometer Network Mean Residence time (days MRT = 1.9(Distance) r^2 = Distance from divide (m) Based on data from Stewart and McDonnell, 1991 WRR

59 Regionalized MRT to the entire basin based on a 2 meter elevation grid using a single direction D8 algorithm

60 Model output 100 Runoff (l/s) 10 1 Measured Run1426 Run /30 10/20 11/9 11/29 12/19 1/8 100 Date Runoff (l/s) Measured Run1426 Run /30 10/20 11/9 11/29 12/19 1/8 Date 1750 runs, cutoff NS > 0.75

61 Precipitation FE 537 Evapotranspiration Tracer in the model Lateral Subsurface Stormflow Then defined as a mass balance of some arbitrary conserved tracer: dm dt t = MRT pc = 0 0 p + tcdt Cdt qc in qc The mean residence time is derived by the concentration breakthrough: out i.e. time averaged C normalized by total mass of the tracer

62 Simulated tracer breakthrough Breakthrough (mg/l) /2 10/12 11/21 12/31 2/9 3/20 4/29 Time Directly simulated MRT over the prior parameter range varied from 30 to 95 days.

63 the slide you saw earlier 0.9 Q Efficiency Mean Residence Time (days) Vache and McDonnell, 2005 WRR

100 75 FE 537 Runoff (l/s) 50 25 Model output from before Measured Run1426 Run1836 0 9/30 10/20

64 FE 537 Runoff (l/s) Model output from before Measured Run1426 Run /30 10/20 11/9 11/29 12/19 1/8 Date we would reject this model recall that our measured range was days

65 Residence time as a process-based model rejection tool Model 1 Model 3 Precipitation Precipitation Evapotranspiration Saturated Zone Effective Porosity Explicit Unsaturated Zone Evapotranspiration # Tuned Parameters Model 1 Yes Lateral Subsurface Stormflow No No 3 Lateral Subsurface Stormflow Model 2 Yes Yes No 4 Model 2 Model 3 Yes No Model 4 Yes 5 Model 4 Precipitation Yes Yes Yes 6 Precipitation Evapotranspiration Evapotranspiration Lateral Subsurface Stormflow Lateral Subsurface Stormflow

66 Runs with NS > 0.7

67 Breakthroughs Note early time and late time differences between Models 1-4

68 How much detail is warranted? Complementary measures for evaluation Vache and McDonnell, 2005 WRR

69 Take a virtual field trip that deals with catchment scale hydrology at

Towards a better process representation of catchment hydrology in conceptual runoff modelling

Towards a better process representation of catchment hydrology in conceptual runoff modelling Jan Seibert, Jeff McDonnell Oregon State University, Department of Forest Engineering, Corvallis OR 97331,