Academia.eduAcademia.edu

Outline

Stage‐discharge relationship in tidal channels

2017, Limnology and Oceanography-methods

https://doi.org/10.1002/LOM3.10168

Abstract

Long-term records of the flow of water through tidal channels are essential to constrain the budgets of sediments and biogeochemical compounds in salt marshes. Statistical models which relate discharge to water level allow the estimation of such records from more easily obtained records of water stage in the channel. Here we compare four different types of stage-discharge models, each of which captures different characteristics of the stage-discharge relationship. We estimate and validate each of these models on a two-month long time series of stage and discharge obtained with an Acoustic Doppler Current Profiler in a salt marsh channel. We find that the best performance is obtained by models that account for the nonlinear and time-varying nature of the stage-discharge relationship. Good performance can also be obtained from a simplified version of these models, which captures nonlinearity and nonstationarity without the complexity of the fully nonlinear or time-varying models.

References (39)

  1. Aravkin, A. Y., J. V. Burke, and G. Pillonetto. 2013. Linear system identification using stable spline kernels and PLQ penalties. 52nd IEEE Conference on Decision and Control. doi:10.1109/cdc.2013.6760701
  2. Bayliss-Smith, T., R. Healey, R. Lailey, T. Spencer, and D. Stoddart. 1979. Tidal flows in salt marsh creeks. Estuarine and Coastal Marine Science 9: 235-255. doi:10.1016/0302- 3524(79)90038-0
  3. Beven, K., and J. Davies. 2015. Velocities, celerities and the basin of attraction in catchment response. Hydrological Processes 29: 5214-5226. doi:10.1002/Hyp.10699
  4. Blanton, J. O., G. Lin, and S. A. Elston. 2002. Tidal current asymmetry in shallow estuaries and tidal creeks. Continental Shelf Research 22: 1731-1743. doi:10.1016/S0278-4343(02)00035-3
  5. Boon, J. D. 1975. Tidal discharge asymmetry in a salt marsh drainage system. Limnology and Oceanography 20: 71-80. doi:10.4319/lo.1975.20.1.0071
  6. Botter, G., E. Bertuzzo, and A. Rinaldo. 2010. Transport in the hydrologic response: Travel time distributions, soil moisture dynamics, and the old water paradox. Water Resources Research 46: W03514. doi:10.1029/2009wr008371
  7. Burnham, K. P., and D. R. Anderson. 2002. Model selection and multimodel inference, Springer.
  8. Bühlmann, P. 2002. Bootstraps for time series. Statist. Sci. 17: 52-72. doi:10.1214/ss/1023798998
  9. Cai, W.-J. 2011. Estuarine and coastal ocean carbon paradox: CO2 sinks or sites of terrestrial carbon incineration? Ann. Rev. Marine. Sci. 3: 123-145. doi:10.1146/Annurev- Marine-120709-142723
  10. Carey, J. C., and R. W. Fulweiler. 2014. Salt marsh tidal exchange increases residence time of silica in estuaries. Limnology and Oceanography 59: 1203-1212. doi:10.4319/lo.2014.59.4.1203
  11. Chmura, G. L., S. C. Anisfeld, D. R. Cahoon, and J. C. Lynch. 2003. Global carbon sequestration in tidal, saline wetland soils. Global Biogeochemical Cycles 17: 1111. doi:10.1029/2002GB001917
  12. Duarte, C. M., J. J. Middelburg, and N. Caraco. 2005. Major role of marine vegetation on the oceanic carbon cycle. Biogeosciences 2: 1-8. doi:10.5194/Bg-2-1-2005
  13. Fagherazzi, S. 2002. Basic flow field in a tidal basin. Geophysical Research Letters 29: 62-1 -62-3. doi: 10.1029/2001GL013787
  14. Fagherazzi, S., P. L. Wiberg, and A. D. Howard. 2003. Tidal flow field in a small basin. Journal of Geophysical Research: Oceans 108: 16-1 -16-10. doi: 10.1029/2002JC001340
  15. Fagherazzi, S., M. Hannion, and P. D'Odorico. 2008. Geomorphic structure of tidal hydrodynamics in salt marsh creeks. Water Resources Research 44: W02419. doi:10.1029/2007wr006289
  16. Fagherazzi, S., P. L. Wiberg, S. Temmerman, E. Struyf, Y. Zhao, and P. A. Raymond. 2013. Fluxes of water, sediments, and biogeochemical compounds in salt marshes. Ecological Processes 2: 3. doi:10.1186/2192-1709-2-3
  17. Franz, M. O., and B. Schölkopf. 2006. A unifying view of Wiener and Volterra theory and polynomial kernel regression. Neural Computation 18: 3097-3118. doi:10.1162/Neco.2006.18.12.3097
  18. Ganju, N. K., M. L. Kirwan, P. J. Dickhudt, G. R. Guntenspergen, D. R. Cahoon, and K. D. Kroeger. 2015. Sediment transport-based metrics of wetland stability. Geophysical Research Letters 42: 7992-8000.
  19. Ganju, N. K., N. J. Nidzieko, and M. L. Kirwan. 2013. Inferring tidal wetland stability from channel sediment fluxes: Observations and a conceptual model. Journal of Geophysical Research: Earth Surface 118: 2045-2058. doi:10.1002/jgrf.20143
  20. Gardner, L. R. 1975. Runoff from an intertidal marsh during tidal exposure-recession curves and chemical characteristics. Limnology and Oceanography 20: 81-89. doi:10.4319/Lo.1975.20.1.0081
  21. Harman, C. J. 2015. Time-variable transit time distributions and transport: Theory and application to storage-dependent transport of chloride in a watershed. Water Resources Research 51: 1-30. doi:10.1002/2014wr015707
  22. Healey, R., K. Pye, D. Stoddart, and T. Bayliss-Smith. 1981. Velocity variations in salt marsh creeks, norfolk, england. Estuarine, Coastal and Shelf Science 13: 535-545. doi:10.1016/S0302-3524(81)80056-4
  23. Hocking, R. R. 1976. The analysis and selection of variables in linear regression. Biometrics 32: 1-49.
  24. Hopke, P. K., C. Liu, and D. B. Rubin. 2001. Multiple imputation for multivariate data with missing and below-threshold measurements: Time-series concentrations of pollutants in the arctic. Biometrics 57: 22-33. doi:10.1111/j.0006-341x.2001.00022.x Kelley, C. T. 1999. Iterative methods for optimization, Society for Industrial & Applied Mathematics (SIAM).
  25. Kennedy, E. J. 1984. Discharge ratings at gaging stations. U.S. Geological Survey Techniques of Water-Resources Investigations.
  26. Little, R. J. A., and D. B. Rubin. 2002. Statistical analysis with missing data, 2nd ed. Wiley-Blackwell.
  27. Ljung, G. M., and G. E. P. Box. 1978. On a measure of lack of fit in time series models. Biometrika 65: 297-303. doi:10.1093/biomet/65.2.297
  28. Morris, J. T., P. V. Sundareshwar, C. T. Nietch, B. Kjerfve, and D. R. Cahoon. 2002. Responses of coastal wetlands to rising sea level. Ecology 83: 2869-2877. doi:10.1890/0012-9658(2002)083[2869:ROCWTR]2.0.CO;
  29. Mueller, D. S., C. R. Wagner, M. S. Rehmel, K. A. Oberg, and F. Rainville. 2009. Measuring discharge with acoustic doppler current profilers from a moving boat. U.S. Geological Survey Techniques; Methods.
  30. Myrick, R. M., and L. B. Leopold. 1963. Hydraulic geometry of a small tidal estuary. US Geological Survey.
  31. Pethick, J. 1980. Velocity surges and asymmetry in tidal channels. Estuarine and Coastal Marine Science 11: 331-345. doi:10.1016/S0302-3524(80)80087-9
  32. Pillonetto, G., and G. De Nicolao. 2010. A new kernel-based approach for linear system identification. Automatica 46: 81-93. doi:10.1016/J.Automatica.2009.10.031
  33. Rugh, W. J. 1981. Nonlinear system theory, Johns Hopkins University Press Baltimore.
  34. Ruhl, C. A., and M. R. Simpson. 2005. Computation of discharge using the index- velocity method in tidally affected areas. US Geological Survey.
  35. Speer, P., and D. Aubrey. 1985. A study of non-linear tidal propagation in shallow inlet/estuarine systems. Part II: Theory. Estuarine, Coastal and Shelf Science 21: 207- 224. doi:10.1016/0272-7714(85)90097-6
  36. Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological) 267-288.
  37. Wold, S., A. Ruhe, H. Wold, and W. Dunn III. 1984. The collinearity problem in linear regression. the partial least squares (pls) approach to generalized inverses. SIAM Journal on Scientific and Statistical Computing 5: 735-743.
  38. Xu, R., and D. Wunsch. 2009. Clustering, John Wiley & Sons.
  39. Zou, H., and T. Hastie. 2005. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67: 301-320.