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The Significance of Model Structure in One- Dimensional Stream Solute Transport Models with Multiple Transient Storage Zones Master’s Defense of: Patrick.

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Presentation on theme: "The Significance of Model Structure in One- Dimensional Stream Solute Transport Models with Multiple Transient Storage Zones Master’s Defense of: Patrick."— Presentation transcript:

1 The Significance of Model Structure in One- Dimensional Stream Solute Transport Models with Multiple Transient Storage Zones Master’s Defense of: Patrick Corbitt Kerr Advisor: Michael Gooseff 1 Committee Members: Peggy Johnson 1 Diogo Bolster 2 1 Department of Civil and Environmental Engineering, The Pennsylvania State University, State College, PA, USA 2 Department of Civil Engineering and Geological Sciences, University of Notre Dame, IN, USA 1

2 Motivation Low-order streams are at the head of the river continuum and are the primary interface between the river network and its drainage basin. These streams feature a strong connectivity with the riparian ecosystem due to channel complexity and stream gradient. 2 Vannote. R.L., G. W. Minshall, K. W. Cummins, J. R. Sedell, and C. E. Cushing. 1980. The river continuum concept. Can. J. Fish. Aquat. Sci. 37: 130-137 1 1

3 Motivation The hydraulic characteristics and biogeochemical conditions of low-order streams are different than for high-order streams. Biogeochemical processing is dependent on hydrodynamic transport. Residence Time Travel Path Residence Conditions 3 Stream Corridor Restoration: Principles, Processes, and Practices. 1998. Federal Interagency Stream Restoration Working Group. 2 2

4 Motivation We seek to understand hydrodynamic and biogeochemical processes, so we try to model it. Simulation of hydrodynamic transport requires conceptual models to approximate the complex geometry and physics. Tracer experiments are used to populate parameters in the solute transport model as well as verify model physics. 4

5 Motivation These models can provide insight into areas of the stream difficult to observe. Interpretation of models can also lead to metrics, a means to quantify biogeochemical and hydraulic characteristics. These metrics can used at the local, reach, or watershed scale to investigate processes such as nutrient cycling. 5 Preston, S.D., Alexander, R.B., Woodside, M.D., and Hamilton, P.A., 2009, SPARROW MODELING—Enhancing Understanding of the Nation’s Water Quality: U.S. Geological Survey Fact Sheet 2009–3019, 6 p. 3 3

6 Transient Storage Model 6 Thackston, E. L., and K. B. Schnelle, J. (1970). "Predicting effects of dead zones on stream mixing." J. Sanit. Eng. Div. Am. Soc. Civ. Eng., 96(SA2), 319-331. Hays, J. R., Krenkel, P. A., and K. B. Schnelle, J. (1966). Mass transport mechanisms in open-channel flow, Vanderbilt Univer., Nashville, Tenn. 4 5 4 5

7 Previous Work Bencala, K. E., and Walters, R. A. (1983). "Simulation of solute transport in a mountain pool-and-riffle stream: a transient storage model." Water Resources Research, 19(3), 718-724. Stream_Solute_Workshop. (1990). "Concepts and methods for assessing solute dynamics in stream ecosystems." Journal of the North American Benthological Society, 9, 95-119. Runkel, R. L., and Broshears, R. E. (1991). "One dimensional transport with inflow and storage (OTIS): A solute transport model for small streams ", Center for Adv. Decision Support for Water Environ. Syst., ed., Tech Rep. 91-01. D'Angelo, D. J., Webster, J. R., Gregory, S. V., and Meyer, J. L. (1993). "Transient storage in Appalachian and Cascade mountain streams as related to hydraulic characteristics." Journal of the North American Benthological Society, 12(3), 223-235. Choi, J., Harvey, J. W., and Conklin, M. H. (2000). "Characterizing multiple timescales of stream and storage zone interaction that affect solute fate and transport in streams." Water Resources Research, 36(6), 1511-1518. Harvey, J. W., Saiers, J. E., and Newlin, J. T. (2005). "Solute transport and storage mechanisms in wetlands of the Everglades, south Florida." Water Resources Research, W05009, doi:10.1029/2004WR003507. Gooseff, M. N., McKnight, D. M., Runkel, R. L., and Duff, J. H. (2004). "Denitrification and hydrologic transient storage in a glacial meltwater stream, McMurdo Dry Valleys, Antarctica." Limnology and Oceanography, 49(5), 1884-1895. Ensign, S. H., and Doyle, M. W. (2005). "In-channel transient storage and associated nutrient retention: Evidence from experimental manipulations " Limnology and Oceanography. Lautz, L. K., and Siegel, D. I. (2007). "The effect of transient storage on nitrate uptake lengths in streams: an inter-site comparison." Hydrological Processes, 21(26), 3533-3548. Briggs, M. A., Gooseff, M. N., Arp, C. D., and Baker, M. A. (2008). "Informing a stream transient storage model with two-storage zones to discriminate in-channel dead zone and hyporheic exchange." Water Resources Research, Vol. 45. 7

8 1-SZ Inadequacy 1-SZ models lump the stream into only 2- zones, mobile and immobile. Breakthrough Curves in the channel are not uniform. Discrimination of immobile zones can lead to better models. 8 June Slug

9 Multiple Storage Zones Surface Transient Storage (STS) Light, Aerobic, Particulate, Diurnal Temperature Hyporheic Transient Storage (HTS) Dark, Anaerobic …, Dissolved, Temperate 9

10 Competing Model Structure 10

11 Nested Model Structure 11 HTS MC STS

12 Numerical Model Runkel’s OTIS was converted to Matlab, multiple storage zones and a GUI were added. F.D. (Crank-Nicholson) 12 Runkel, R. L., and Broshears, R. E. (1991). "One dimensional transport with inflow and storage (OTIS): A solute transport model for small streams ", Center for Adv. Decision Support for Water Environ. Syst., ed., Tech Rep. 91-01. 6 6

13 A :1.8 m² A HTS :0.5 m² A STS :1 m² D :0.006 m²/s Q :0.01 m³/s α STS :0.00005 s -1 α HTS :0.000005 s -1 U/S Boundary Condition: 1.0 g/m³ Step 1-8hr @ 200m U/S 13 Conceptual Comparison of Competing versus Nested Transient Storage Module Structure using Identical Parameters

14 Study Site Laurel Run: 1 st order stream Study Reach: 460-m Drainage Area is 4.66 km² of valley-ridge topography, old-growth deciduous trees and mountain laurel. Chesapeake Bay Watershed 14

15 Tracer Experiments Conservative Tracer: Cl- 3 Constant Rate Injections: June, July, August High->Low Flow 3 Control Sections: 0m, 75m, 460m Campbell Scientific CR- 1000 data loggers with CS547A Cond/Temp Probes 2 Piezometers with Trutrack WT-HR Capacitance Rods 15

16 MC/STS Parsing 2-SZ model requires 2 more parameters (A HTS, α HTS ) Solution: Second BTC in STS A STS Estimation Velocity Transects A/A STS Ratio 16

17 Field Results 17 Breakthrough Curves of Solute in Main Channel A) June, B) July, C) August ParameterJuneJulyAugust A/A STS 2.0 2.6 Q (x10-2 m³/s) 5.762.900.87 Q lat (x10-6 m²/s)6.3818.00.73

18 Optimization Process Global Optimization Algorithm: SCE-UA (1992) (Shuffled Complex Evolution Method – University of Arizona) 18 IndividualPoint1 Family/GroupSimplexN+1 Community/TribeComplexM=2.N+1 PopulationSampleS=P.(2N+1) N = Dimension of Problem M = Size of Complex P = Number of Complexes S = Size of Sample 1-SZ Parameters: D, A, A S, α 2-SZ Parameters: D, A, A STS, α STS, A HTS, α HTS

19 SCE-UA Optimization Process 19 Duan Q., Sorooshian, S., Gupta, V. K. 1994. Optimal Use of the SCE-UA Global Optimization Method for Calibrating Watershed Models. Journal of Hydrology, Vol. 158, 265-284. 6 6

20 SCE-UA Optimization Process 20 Duan Q., Sorooshian, S., Gupta, V. K. 1994. Optimal Use of the SCE-UA Global Optimization Method for Calibrating Watershed Models. Journal of Hydrology, Vol. 158, 265-284. 6 6

21 SCE-UA Optimization Process 21 Duan Q., Sorooshian, S., Gupta, V. K. 1994. Optimal Use of the SCE-UA Global Optimization Method for Calibrating Watershed Models. Journal of Hydrology, Vol. 158, 265-284. 6 6

22 SCE-UA Optimization Process 22 Duan Q., Sorooshian, S., Gupta, V. K. 1994. Optimal Use of the SCE-UA Global Optimization Method for Calibrating Watershed Models. Journal of Hydrology, Vol. 158, 265-284. 6 6

23 SCE-UA Optimization Process 23 Duan Q., Sorooshian, S., Gupta, V. K. 1994. Optimal Use of the SCE-UA Global Optimization Method for Calibrating Watershed Models. Journal of Hydrology, Vol. 158, 265-284. 6 6

24 Parameter Optimization 24 Color Coded Parameter Optimization for July First Iteration - BLUE, Last Iteration - RED 1-SZCompeting 2-SZNested 2-SZ

25 Optimized Parameters Parameter JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ D (m²/s)0.8310.9081.080.2010.2260.3200.5030.7450.8620.006 α (x10^-5 s -1 )5.4111.63.73 α STS (x10-5 s -1 )4385502102401602105.00 α HTS (x10-5 s -1 )9.1917.78.2714.94.7811.40.500 A (m²)0.6180.4110.4180.4710.3310.3390.1870.1340.1371.80 A S (m²)0.3300.1290.125 A STS (m²)0.2060.2090.1650.1700.05150.05291.00 A HTS (m²)0.5890.6060.1450.1290.1510.1550.500 RMSE0.3060.3510.3530.4490.3510.3540.2760.4400.4635 Q (x10-2 m³/s) 5.762.900.871.00 Q lat (x10-6 m²/s)6.3818.00.730.00 25

26 Optimized Parameters Parameter JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ D (m²/s)0.8310.9081.080.2010.2260.3200.5030.7450.8620.006 α (x10^-5 s -1 )5.4111.63.73 α STS (x10-5 s -1 )4385502102401602105.00 α HTS (x10-5 s -1 )9.1917.78.2714.94.7811.40.500 A (m²)0.6180.4110.4180.4710.3310.3390.1870.1340.1371.80 A S (m²)0.3300.1290.125 A STS (m²)0.2060.2090.1650.1700.05150.05291.00 A HTS (m²)0.5890.6060.1450.1290.1510.1550.500 RMSE0.3060.3510.3530.4490.3510.3540.2760.4400.4635 Q (x10-2 m³/s) 5.762.900.871.00 Q lat (x10-6 m²/s)6.3818.00.730.00 26

27 Optimized Parameters Parameter JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ D (m²/s)0.8310.9081.080.2010.2260.3200.5030.7450.8620.006 α (x10^-5 s -1 )5.4111.63.73 α STS (x10-5 s -1 )4385502102401602105.00 α HTS (x10-5 s -1 )9.1917.78.2714.94.7811.40.500 A (m²)0.6180.4110.4180.4710.3310.3390.1870.1340.1371.80 A S (m²)0.3300.1290.125 A STS (m²)0.2060.2090.1650.1700.05150.05291.00 A HTS (m²)0.5890.6060.1450.1290.1510.1550.500 RMSE0.3060.3510.3530.4490.3510.3540.2760.4400.4635 Q (x10-2 m³/s) 5.762.900.871.00 Q lat (x10-6 m²/s)6.3818.00.730.00 27

28 Optimized Parameters Parameter JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ D (m²/s)0.8310.9081.080.2010.2260.3200.5030.7450.8620.006 α (x10^-5 s -1 )5.4111.63.73 α STS (x10-5 s -1 )4385502102401602105.00 α HTS (x10-5 s -1 )9.1917.78.2714.94.7811.40.500 A (m²)0.6180.4110.4180.4710.3310.3390.1870.1340.1371.80 A S (m²)0.3300.1290.125 A STS (m²)0.2060.2090.1650.1700.05150.05291.00 A HTS (m²)0.5890.6060.1450.1290.1510.1550.500 RMSE0.3060.3510.3530.4490.3510.3540.2760.4400.4635 Q (x10-2 m³/s) 5.762.900.871.00 Q lat (x10-6 m²/s)6.3818.00.730.00 28

29 Optimized Parameters Parameter JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ D (m²/s)0.8310.9081.080.2010.2260.3200.5030.7450.8620.006 α (x10^-5 s -1 )5.4111.63.73 α STS (x10-5 s -1 )4385502102401602105.00 α HTS (x10-5 s -1 )9.1917.78.2714.94.7811.40.500 A (m²)0.6180.4110.4180.4710.3310.3390.1870.1340.1371.80 A S (m²)0.3300.1290.125 A STS (m²)0.2060.2090.1650.1700.05150.05291.00 A HTS (m²)0.5890.6060.1450.1290.1510.1550.500 RMSE0.3060.3510.3530.4490.3510.3540.2760.4400.4635 Q (x10-2 m³/s) 5.762.900.871.00 Q lat (x10-6 m²/s)6.3818.00.730.00 29

30 BTC Comparisons 30 June July August

31 Single Storage Zone Metrics Main channel residence time Storage zone residence time Mean travel time 31

32 Computation of 2-SZ Metrics 1) Transform PDE’s to ODE’s in Laplace space, solve for particular solution, normalize, apply B.C.’s, restrict to temporal/spatial domains, and solve for concentration. 2) Mean residence times can be found from the first moment of the impulse response: 32 Aris, R. (1958). “On the dispersion of linear kinematic waves." Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 246, No. 1241, pp. 268-277

33 Metric1-SZNested 2-SZCompeting 2-SZ Main channel residence time Storage zone residence time Mean travel time New 2-SZ Metrics 33

34 2-SZ Metrics Metric JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ T mean (s) 758095499838834988998900167631811418741150742 T str (s) 184842241828621458417268106074761818220000 T sto (s) 987035523613681792172316667 T STS (s) 114892372032401801111110526 T HTS (s) 155941638152975093235752570255556100000 34

35 2-SZ Metrics Metric JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ T mean (s) 758095499838834988998900167631811418741150742 T str (s) 184842241828621458417268106074761818220000 T sto (s) 987035523613681792172316667 T STS (s) 114892372032401801111110526 T HTS (s) 155941638152975093235752570255556100000 35

36 2-SZ Metrics Metric JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ T mean (s) 758095499838834988998900167631811418741150742 T str (s) 184842241828621458417268106074761818220000 T sto (s) 987035523613681792172316667 T STS (s) 114892372032401801111110526 T HTS (s) 155941638152975093235752570255556100000 36

37 2-SZ Metrics Metric JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ T mean (s) 758095499838834988998900167631811418741150742 T str (s) 184842241828621458417268106074761818220000 T sto (s) 987035523613681792172316667 T STS (s) 114892372032401801111110526 T HTS (s) 155941638152975093235752570255556100000 37

38 2-SZ Metrics Metric JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ T mean (s) 758095499838834988998900167631811418741150742 T str (s) 184842241828621458417268106074761818220000 T sto (s) 987035523613681792172316667 T STS (s) 114892372032401801111110526 T HTS (s) 155941638152975093235752570255556100000 38

39 2-SZ Metrics Metric JuneJulyAugust Conceptual 1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZ T mean (s) 758095499838834988998900167631811418741150742 T str (s) 184842241828621458417268106074761818220000 T sto (s) 987035523613681792172316667 T STS (s) 114892372032401801111110526 T HTS (s) 155941638152975093235752570255556100000 39

40 Conclusions Multiple transient storage zone models have the ability to discriminate the transport processes within the zones and thus potentially the biogeochemical processes too. Model structure determines the process by which particles pass through zones and for how long they remain in them. Particles would travel uniquely different paths between these two different model structures. Not well illustrated by breakthrough curves. 40

41 Conclusions Data collection for both model structures is identical. Both 1-SZ and 2-SZ models can accurately simulate the observed BTC in the main channel. But only the 2-SZ models can also accurately simulate the observed BTC in the STS. The BTC in the HTS differs for each model. The 1-SZ and 2-SZ models feature different main channel area, A. Both 2-SZ models had similar parameter values for A, A STS, and A HTS. Therefore either model structure can be used to approximate area parameters. 41

42 Conclusions However, in comparison to the “Competing” model, the “Nested” model resulted in slightly higher values for D, α STS, and α HTS. Mean Travel Time Metric is identical for “Nested” and “Competing” models. Optimized Parameters show strong similarity Storage Time Metrics equations differ for “Nested” and Competing” models. 42

43 Conclusions The pathway, residence time, and HTS BTC are the significant differences in the two model structures. Both model structures have the ability to discriminate processes between the different zones. It was not determinable from the tracer experiments if one model was more appropriate. The differences in conceptual transient storage interactions are significant to the interpretation of residence times and discrimination of biogeochemical processes within each zone. 43

44 Acknowledgements USGS Water Resources Research Investigation (WRRI) entitled “Controls on nitrogen and phosphorous transport and fate in northern Appalachian streams.” 44


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