An Investigation into Transient Storage Model Structures of One Dimensional Transport in Streams

The Significance of Model Structure in One-Dimensional Stream Solute Transport Models with Multiple Transient Storage ZonesThe Significance of Model Structure in One-Dimensional Stream Solute Transport Models with Multiple Transient Storage ZonesThe Significance of Model Structure in One-Dimensional Stream Solute Transport Models with Multiple Transient Storage ZonesThe Significance of Model Structure in One-Dimensional Stream Solute Transport Models with Multiple Transient Storage ZonesThe Significance of Model Structure in One-Dimensional Stream Solute Transport Models with Multiple Transient Storage Zones Masters Defense of:Patrick Corbitt Kerr

Advisor:Michael Gooseff1

Committee Members:Peggy Johnson1Diogo Bolster2

1 Department of Civil and Environmental Engineering, The Pennsylvania State University, State College, PA, USA2 Department of Civil Engineering and Geological Sciences, University of Notre Dame, IN, USA

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MotivationLow-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.

2Vannote. 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: 130-13711MotivationThe hydraulic characteristics and biogeochemical conditions of low-order streams are different than for high-order streams.Biogeochemical processing is dependent on hydrodynamic transport.Residence TimeTravel PathResidence Conditions

3Stream Corridor Restoration: Principles, Processes, and Practices. 1998. Federal Interagency Stream Restoration Working Group.22MotivationWe 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

MotivationThese 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.

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Preston, S.D., Alexander, R.B., Woodside, M.D., and Hamilton, P.A., 2009, SPARROW MODELINGEnhancing Understanding of the Nations Water Quality: U.S. Geological Survey Fact Sheet 20093019, 6 p.33

Transient Storage Model

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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.4545Previous WorkBencala, 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. 45.71-SZ Inadequacy1-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.

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June SlugMultiple Storage ZonesSurface Transient Storage (STS)Light, Aerobic, Particulate, Diurnal TemperatureHyporheic Transient Storage (HTS)Dark, Anaerobic , Dissolved, Temperate

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Competing Model Structure

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Nested Model Structure11

HTSMCSTSNumerical ModelRunkels OTIS was converted to Matlab, multiple storage zones and a GUI were added.F.D. (Crank-Nicholson)

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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. 91-01.66

A :1.8 mAHTS :0.5 mASTS :1 mD :0.006 m/sQ :0.01 m/sSTS :0.00005 s-1HTS :0.000005 s-1U/S Boundary Condition: 1.0 g/m Step1-8hr @ 200m U/S13Conceptual Comparison of Competing versus Nested Transient Storage Module Structure using Identical ParametersStudy SiteLaurel Run: 1st order streamStudy Reach: 460-m Drainage Area is 4.66 km of valley-ridge topography, old-growth deciduous trees and mountain laurel.Chesapeake Bay Watershed

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Tracer ExperimentsConservative Tracer: Cl-3 Constant Rate Injections: June, July, AugustHigh->Low Flow3 Control Sections: 0m, 75m, 460mCampbell Scientific CR-1000 data loggers with CS547A Cond/Temp Probes2 Piezometers with Trutrack WT-HR Capacitance Rods15

MC/STS Parsing2-SZ model requires 2more parameters(AHTS, HTS)

Solution:Second BTC in STSASTS EstimationVelocity TransectsA/ASTS Ratio

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Field Results17

Breakthrough Curves of Solute in Main ChannelA) June, B) July, C) AugustParameterJuneJulyAugustA/ASTS2.02.02.6Q (x10-2 m/s)5.762.900.87Qlat (x10-6 m/s)6.3818.00.73Optimization ProcessGlobal Optimization Algorithm: SCE-UA (1992)(Shuffled Complex Evolution Method University of Arizona)18IndividualPoint1Family/GroupSimplexN+1Community/TribeComplexM=2.N+1PopulationSampleS=P.(2N+1)N = Dimension of ProblemM = Size of ComplexP = Number of ComplexesS = Size of Sample1-SZ Parameters: D, A, AS, 2-SZ Parameters: D, A, ASTS, STS, AHTS, HTSSCE-UA Optimization Process19

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, 265-284.66SCE-UA Optimization Process20

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, 265-284.66SCE-UA Optimization Process21

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, 265-284.66SCE-UA Optimization Process22

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, 265-284.66SCE-UA Optimization Process23

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, 265-284.66

Parameter Optimization24

Color Coded Parameter Optimization for July First Iteration - BLUE, Last Iteration - RED1-SZCompeting 2-SZNested 2-SZOptimized ParametersParameterJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZD (m/s) 0.8310.9081.080.2010.2260.3200.5030.7450.8620.0060.006 (x10^-5 s-1)5.4111.63.73STS (x10-5 s-1)4385502102401602105.005.00HTS (x10-5 s-1)9.1917.78.2714.94.7811.40.5000.500A (m)0.6180.4110.4180.4710.3310.3390.1870.1340.1371.801.80AS (m)0.3300.1290.125ASTS (m)0.2060.2090.1650.1700.05150.05291.001.00AHTS (m)0.5890.6060.1450.1290.1510.1550.5000.500RMSE0.3060.3510.3530.4490.3510.3540.2760.4400.4635Q (x10-2 m/s)5.762.900.871.00Qlat (x10-6 m/s)6.3818.00.730.0025Optimized ParametersParameterJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZD (m/s) 0.8310.9081.080.2010.2260.3200.5030.7450.8620.0060.006 (x10^-5 s-1)5.4111.63.73STS (x10-5 s-1)4385502102401602105.005.00HTS (x10-5 s-1)9.1917.78.2714.94.7811.40.5000.500A (m)0.6180.4110.4180.4710.3310.3390.1870.1340.1371.801.80AS (m)0.3300.1290.125ASTS (m)0.2060.2090.1650.1700.05150.05291.001.00AHTS (m)0.5890.6060.1450.1290.1510.1550.5000.500RMSE0.3060.3510.3530.4490.3510.3540.2760.4400.4635Q (x10-2 m/s)5.762.900.871.00Qlat (x10-6 m/s)6.3818.00.730.0026Optimized ParametersParameterJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZD (m/s) 0.8310.9081.080.2010.2260.3200.5030.7450.8620.0060.006 (x10^-5 s-1)5.4111.63.73STS (x10-5 s-1)4385502102401602105.005.00HTS (x10-5 s-1)9.1917.78.2714.94.7811.40.5000.500A (m)0.6180.4110.4180.4710.3310.3390.1870.1340.1371.801.80AS (m)0.3300.1290.125ASTS (m)0.2060.2090.1650.1700.05150.05291.001.00AHTS (m)0.5890.6060.1450.1290.1510.1550.5000.500RMSE0.3060.3510.3530.4490.3510.3540.2760.4400.4635Q (x10-2 m/s)5.762.900.871.00Qlat (x10-6 m/s)6.3818.00.730.0027Optimized ParametersParameterJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZD (m/s) 0.8310.9081.080.2010.2260.3200.5030.7450.8620.0060.006 (x10^-5 s-1)5.4111.63.73STS (x10-5 s-1)4385502102401602105.005.00HTS (x10-5 s-1)9.1917.78.2714.94.7811.40.5000.500A (m)0.6180.4110.4180.4710.3310.3390.1870.1340.1371.801.80AS (m)0.3300.1290.125ASTS (m)0.2060.2090.1650.1700.05150.05291.001.00AHTS (m)0.5890.6060.1450.1290.1510.1550.5000.500RMSE0.3060.3510.3530.4490.3510.3540.2760.4400.4635Q (x10-2 m/s)5.762.900.871.00Qlat (x10-6 m/s)6.3818.00.730.0028Optimized ParametersParameterJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZD (m/s) 0.8310.9081.080.2010.2260.3200.5030.7450.8620.0060.006 (x10^-5 s-1)5.4111.63.73STS (x10-5 s-1)4385502102401602105.005.00HTS (x10-5 s-1)9.1917.78.2714.94.7811.40.5000.500A (m)0.6180.4110.4180.4710.3310.3390.1870.1340.1371.801.80AS (m)0.3300.1290.125ASTS (m)0.2060.2090.1650.1700.05150.05291.001.00AHTS (m)0.5890.6060.1450.1290.1510.1550.5000.500RMSE0.3060.3510.3530.4490.3510.3540.2760.4400.4635Q (x10-2 m/s)5.762.900.871.00Qlat (x10-6 m/s)6.3818.00.730.0029BTC Comparisons30

JuneJulyAugustSingle Storage Zone MetricsMain channel residence time

Storage zone residence time

Mean travel time31

Computation of 2-SZ MetricsTransform PDEs to ODEs 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:

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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. 268-277Metric1-SZNested 2-SZCompeting 2-SZMain channel residence timeStorage zone residence time

Mean travel timeNew 2-SZ Metrics33

2-SZ MetricsMetricJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZTmean (s)758095499838834988998900167631811418741150742150742Tstr (s)184842241828621458417268106074761818220000Tsto (s)987035523613681792172316667TSTS (s)114892372032401801111110526THTS (s)155941638152975093235752570255556100000342-SZ MetricsMetricJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZTmean (s)758095499838834988998900167631811418741150742150742Tstr (s)184842241828621458417268106074761818220000Tsto (s)987035523613681792172316667TSTS (s)114892372032401801111110526THTS (s)155941638152975093235752570255556100000352-SZ MetricsMetricJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZTmean (s)758095499838834988998900167631811418741150742150742Tstr (s)184842241828621458417268106074761818220000Tsto (s)987035523613681792172316667TSTS (s)114892372032401801111110526THTS (s)155941638152975093235752570255556100000362-SZ MetricsMetricJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZTmean (s)758095499838834988998900167631811418741150742150742Tstr (s)184842241828621458417268106074761818220000Tsto (s)987035523613681792172316667TSTS (s)114892372032401801111110526THTS (s)155941638152975093235752570255556100000372-SZ MetricsMetricJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZTmean (s)758095499838834988998900167631811418741150742150742Tstr (s)184842241828621458417268106074761818220000Tsto (s)987035523613681792172316667TSTS (s)114892372032401801111110526THTS (s)155941638152975093235752570255556100000382-SZ MetricsMetricJuneJulyAugustConceptual1-SZC-SZN-SZ1-SZC-SZN-SZ1-SZC-SZN-SZC-SZN-SZTmean (s)758095499838834988998900167631811418741150742150742Tstr (s)184842241828621458417268106074761818220000Tsto (s)987035523613681792172316667TSTS (s)114892372032401801111110526THTS (s)15594163815297509323575257025555610000039ConclusionsMultiple 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.

40ConclusionsData 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.

41ConclusionsHowever, in comparison to the Competing model, the Nested model resulted in slightly higher values for D, STS, and HTS. Mean Travel Time Metric is identical for Nested and Competing models.Optimized Parameters show strong similarityStorage Time Metrics equations differ for Nested and Competing models.

42ConclusionsThe 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.

43AcknowledgementsUSGS Water Resources Research Investigation (WRRI) entitled Controls on nitrogen and phosphorous transport and fate in northern Appalachian streams.44

Main Channel(MC)
Transient Storage
Exchange due to Transient Storage
Lateral Inflow
Lateral Outflow
Dispersion
Dispersion
Advection
Advection

Main Channel(MC)
Surface Transient Storage(STS)
Exchange due to Transient Storage
Lateral Inflow
Lateral Outflow
Dispersion
Dispersion
Advection
Advection
Hyporheic Transient Storage(HTS)
Exchange due to Transient Storage

Main Channel(MC)
Surface Transient Storage(STS)
Exchange due to Transient Storage
Lateral Inflow
Lateral Outflow
Dispersion
Dispersion
Advection
Advection
Hyporheic Transient Storage(HTS)
Exchange due to Transient Storage