Master’s Defense of: Patrick Corbitt Kerr Advisor: Michael Gooseff 1 Committee Members:

1. The Significance of Model Structure in One-Dimensional Stream Solute Transport Models with Multiple Transient Storage Zones The Significance of Model Structure in One-Dimensional Stream Solute Transport Models with Multiple Transient Storage Zones The Significance of Model Structure in One-Dimensional Stream Solute Transport Models with Multiple Transient Storage Zones The Significance of Model Structure in One-Dimensional Stream Solute Transport Models with Multiple Transient Storage Zones 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 Gooseff1 Committee Members: Peggy Johnson1 Diogo Bolster2 • 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

2. Motivation 1 • 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. 1 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

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 2 2 Stream Corridor Restoration: Principles, Processes, and Practices. 1998. Federal Interagency Stream Restoration Working Group.

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.

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. 3 3 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.

6. Transient Storage Model 4 5 4 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. 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.

8. 1-SZ Inadequacy June Slug • 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.

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

10. Competing Model Structure

11. Nested Model Structure STS MC HTS

12. Numerical Model • Runkel’s OTIS was converted to Matlab, multiple storage zones and a GUI were added. • F.D. (Crank-Nicholson) 6 6 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.

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

14. Study Site • Laurel Run: 1st 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

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

16. MC/STS Parsing 2-SZ model requires 2 more parameters (AHTS, αHTS) Solution: • Second BTC in STS • ASTS Estimation • Velocity Transects • A/ASTS Ratio

17. Field Results Breakthrough Curves of Solute in Main Channel A) June, B) July, C) August

18. Optimization Process • Global Optimization Algorithm: SCE-UA (1992) • (Shuffled Complex Evolution Method – University of Arizona) • Individual Point 1 • Family/Group Simplex N+1 • Community/Tribe Complex M=2.N+1 • Population Sample S=P.(2N+1) • N = Dimension of Problem • M = Size of Complex • P = Number of Complexes • S = Size of Sample • 1-SZ Parameters: D, A, AS, α • 2-SZ Parameters: D, A, ASTS, αSTS, AHTS, αHTS

19. SCE-UA Optimization Process 6 6 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.

20. SCE-UA Optimization Process 6 6 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.

21. SCE-UA Optimization Process 6 6 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.

22. SCE-UA Optimization Process 6 6 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.

23. SCE-UA Optimization Process 6 6 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.

24. Parameter Optimization 1-SZ Competing 2-SZ Nested 2-SZ Color Coded Parameter Optimization for July First Iteration - BLUE, Last Iteration - RED

25. Optimized Parameters

26. Optimized Parameters

27. Optimized Parameters

28. Optimized Parameters

29. Optimized Parameters

30. BTC Comparisons July June August

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

32. Computation of 2-SZ Metrics • 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. • Mean residence times can be found from the first moment of the impulse response: 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. New 2-SZ Metrics

34. 2-SZ Metrics

35. 2-SZ Metrics

36. 2-SZ Metrics

37. 2-SZ Metrics

38. 2-SZ Metrics

39. 2-SZ Metrics

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.

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, ASTS, and AHTS. Therefore either model structure can be used to approximate area parameters.

42. Conclusions • However, in comparison to the “Competing” model, the “Nested” model resulted in slightly higher values for D, αSTS, and αHTS. • 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.

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.

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