Analytical solutions for transport of decaying solutes in rivers with transient storage

Journal of Hydrology

Volumn 330, Issue 3-4, 2006, Pages 672-680

  De Smedt, F ^a  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

Analytical model; Dead zone; Decay; Solute transport; Stream flow

Indexed keywords

ANALYTICAL MODELS; DEAD ZONES; SOLUTE TRANSPORT;

BOUNDARY CONDITIONS; DISPERSIONS; MASS TRANSFER; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; RIVERS;

STREAM FLOW;

BOUNDARY CONDITIONS; DISPERSIONS; MASS TRANSFER; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; RIVERS; STREAM FLOW;

ADVECTION; BOUNDARY CONDITION; HYDROLOGICAL MODELING; NUMERICAL MODEL; REACTION RATE; RIVER CHANNEL; SOLUTE TRANSPORT;

EID: 33750005385     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2006.04.042     Document Type: Article

References (41)

1. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions (1970), Dover Publications Inc., New York 1046 pp.
2. Bencala K.E. Interactions of solute and streambed sediment. 2. A dynamic analysis of coupled hydrologic and chemical processes that determine solute transport. Water Resour. Res. 20 12 (1984) 1804-1814
3. Bencala K.E. Hyporheic exchange flows. In: Anderson M. (Ed). Encyclopedia of Hydrological Sciences vol. 3 (2005), John Wiley & Sons, Ltd 1733-1740 Pt. 10, Chap. 113
4. Bencala K.E., and Walters R.A. Simulation of solute transport in a mountain pool-and-riffle stream: a transient storage model. Water Resour. Res. 19 3 (1983) 718-724
5. Bencala K.E., McKnight D.M., and Zellweger G.W. Characterization of transport in an acidic and metal-rich mountain stream based on a lithium traces injection and simulations of transient storage. Water Resour. Res. 26 5 (1990) 989-1000
6. Carnahan C.L., and Remer J.S. Nonequilibrium and equilibrium sorption with a linear sorption isotherm during mass transport through an infinite porous medium: some analytical solutions. J. Hydrol. 73 (1984) 227-258
7. Chatwin P.C. Dispersion in natural streams. J. Hydraul. Div., ASCE 97 HY1 (1980) 71-83
8. Choi J., Harvey J.W., and Conklin M.H. Characterizing multiple timescales of stream and storage zone interaction that affect solute fate and transport in streams. Water Resour. Res. 36 6 (2000) 1511-1518
9. Czernuszenko W., and Rowinski P.M. Properties of the dead-zone model of longitudinal dispersion in rivers. J. Hydraul. Res. 35 4 (1997) 491-504
10. Czernuszenko W., Rowinski P.M., and Sukhodolov A. Experimental and numerical validation of the dead-zone model for longitudinal dispersion in rivers. J. Hydraul. Res. 36 2 (1998) 269-280
11. Davis P.M., Atkinson T.C., and Wigley T.M.L. Longitudinal dispersion in natural channels: 2. The roles of shear flow dispersion and dead zones in the River Severn, UK. Hydrol. Earth Syst. Sci. 4 3 (2000) 355-371
12. Day T.J. Longitudinal dispersion in natural channels. Water Resour. Res. 11 6 (1975) 909-918
13. De Smedt F., and Wierenga P.J. A generalized solution for solute flow in soils with mobile and immobile water. Water Resour. Res. 15 5 (1979) 1137-1141
14. De Smedt F., Brevis W., and Debels P. Analytical solution for solute transport resulting from instantaneous injection in streams with transient storage. J. Hydrol. 315 1-4 (2005) 25-39
15. Fernald A.G., Wigington Jr. P.J., and Landers D.H. Transient storage and hyporheic flow along the Willamette River, Oregon: field measurements and model estimates. Water Resour. Res. 37 6 (2001) 1681-1694
16. Goldstein F.R.S. On the mathematics of exchange processes in fixed columns I: Mathematical solutions and asymptotic expansions. Proc. Roy. Soc. London 219 (1953) 151-185
17. Goltz M.N., and Roberts P.V. Three-dimensional solutions for solute transport in an infinite medium with mobile and immobile zones. Water Resour. Res. 22 7 (1986) 1139-1148
18. Gooseff M.N., Bencala K.E., Scott D.T., Runkel R.L., and McKnight D.M. Sensitivity analysis of conservative and reactive transient storage models applied to field data from multiple-reach experiments. Adv. Water Resour. 28 5 (2005) 479-492
19. Hart D.R. Parameter estimation and stochastic interpretation of the transient storage model for solute transport in streams. Water Resour. Res. 31 2 (1995) 323-328
20. Harvey J.W., and Fuller C.C. Effect of enhanced Manganese oxidation in the hyporheic zone on basin-scale geochemical mass balance. Water Resour. Res. 34 4 (1998) 623-636
21. Harvey J.W., Wagner B.J., and Bencala K.E. Evaluating the reliability of the stream traces approach to characterize stream subsurface water exchange. Water Resour. Res. 32 8 (1996) 2441-2451
22. Hays, J.R., Krenkel, P.A., Schnelle, K.B., 1966. Mass transport mechanisms in open-channel flow. Technical Report No. 8, Dept. Civil Eng., Vanderbilt Univ., Nashville, Tennessee, 138 pp.
23. Huang, J., Goltz, M.N., Roberts, P.V., in press. Comment on 'Analytical solution for solute transport resulting from instantaneous injection in streams with transient storage' by F. De Smedt, W. Brevis, P. Debels, 2005. J. Hydrol. 315, 25-39. J. Hydrol., doi:10.1016/j.jhydrol.2006.04.007.
24. Jobson H.E. Predicting travel time and dispersion in rivers and streams. J. Hydraul. Eng. 123 11 (1997) 971-979
25. Keefe S.H., Barber L.B., Runkel R.L., Ryan J.N., McKnight D.M., and Wass R.D. Conservative and reactive solute transport in constructed wetlands. Water Resour. Res. 40 (2004) W01201 10.1029/2003WR002130
26. Laenen A., and Bencala K.E. Transient storage assessments of dye-tracer injections in rivers of the Willamette basin, Oregon. J. Am. Water Resour. Assoc. 37 2 (2001) 367-377
27. Lees M.J., Camacho L.A., and Chapra S.C. On the relationship of transient storage and aggregated dead zone models of longitudinal solute transport in streams. Water Resour. Res. 36 1 (2000) 213-224
28. Liu H., and Cheng H.D. Modified Fickian model for predicting dispersion. J. Hydraul. Div., ASCE 1 HY6 (1980) 1021-1040
29. Morrice J.A., Vallet M.H., Dahm C.N., and Campana M.E. Alluvial characteristics, groundwater-surface water exchange and hydrologic retention in headwater streams. Hydrol. Process. 11 (1997) 253-267
30. Nordin C.F., and Troutman B.M. Longitudinal dispersion in rivers: the persistence of skewness in observed data. Water Resour. Res. 16 1 (1980) 123-128
31. Ramaswami A., Milford J.B., and Small M.J. Integrated Environmental Modeling (2005), John Wiley & Sons, Inc.
32. Runkel R.L. Solution of the advective-diffusive equation: continuous load of finite duration. J. Environ. Eng. 122 9 (1996) 830-832
33. Runkel, R.L., 1998. One-dimensional transport with inflow and storage (OTIS): a solute transport model of streams and rivers. US Geol. Surv. Water Resour. Invest. Rep., 98-4018.
34. Runkel R.L., and Chapra S.C. An efficient numerical solution of the transient storage equations for solute transport in small streams. Water Resour. Res. 29 1 (1993) 211-215
35. Runkel R.L., McKnight D.M., and Rajaram H. Modeling hyporheic zone processes. Adv. Water Resour. 26 9 (2003) 901-905
36. Schmid B.H. On the transient storage equations for longitudinal solute transport in open channels: temporal moments accounting for the effects of first-order decay. J. Hydraul. Res. 33 5 (1995) 595-610
37. Schmid, B.H., 1997. Analytical solution of the transient storage equations accounting for solute decay. In: Proceedings of Theme B, Water for a Changing Global Community, The 27th Congress of the Int. Assoc. for Hydraulic Research, Water Resources Engineering Division/ASCE, August 10-15, 1997, San Francisco, CA, USA, pp. 15-20.
38. Schmid B.H. Temporal moments routing in rivers and streams with transient storage. Adv. Water Resour. 26 9 (2003) 1021-1027
39. Schmid B.H. Simplification in longitudinal transport modeling: case of instantaneous slug releases. J. Hydrol. Eng. 9 (2004) 319-324
40. Sneddon I.N. The Use of Integral Transforms (1972), Tata McGraw-Hill Publ. Co. Ltd., New Delhi 539 pp.
41. van Kooten J.J.A. A method to solve the advection-dispersion equation with a kinetic adsorption isotherm. Adv. Water Resour. 19 4 (1995) 193-206