Explaining the Statistical Properties of Salt Intrusion in Estuaries Using a Stochastic Dynamical Modeling Approach

Determining the statistical properties of salt intrusion in estuaries on sub‐tidal time scales is a substantial challenge in environmental modeling. To study these properties, we here extend an idealized deterministic salt intrusion model to a stochastic one by including a stochastic model of the river discharge. In the river discharge model, two types of stochastic forcing are used: one independent (additive noise) and one dependent (multiplicative noise) on the river discharge state. Each type of forcing results in a non‐Gaussian response in the salt intrusion length, which we consider here as the distance of the 2 psu isohaline contour to the estuary mouth. The salt intrusion model including both types of stochastic forcing in the river discharge provides a satisfactory explanation of the multi‐year statistics of observed salt intrusion lengths in the San Francisco Bay estuary, in particular for the skewness of its probability density function.

[1]  H. Dijkstra,et al.  Estuarine salinity response to freshwater pulses , 2022, Journal of Geophysical Research: Oceans.

[2]  Jannis M. Hoch,et al.  Projections of salt intrusion in a mega-delta under climatic and anthropogenic stressors , 2021, Communications Earth & Environment.

[3]  H. Schuttelaars,et al.  A Unifying Approach to Subtidal Salt Intrusion Modeling in Tidal Estuaries , 2020 .

[4]  T. Jiang,et al.  A 439-year simulated daily discharge dataset (1861–2299) for the upper Yangtze River, China , 2020 .

[5]  R. Tian.  Factors controlling saltwater intrusion across multi-time scales in estuaries, Chester River, Chesapeake Bay , 2019, Estuarine, Coastal and Shelf Science.

[6]  Wenping Gong,et al.  Intraseasonal and interannual variabilities of saltwater intrusion during dry seasons and the associated driving forcings in a partially mixed estuary , 2019, Continental Shelf Research.

[7]  Miguel Á. Reyes-Merlo,et al.  Saltwater intrusion in a subtropical estuary , 2019, Estuarine, Coastal and Shelf Science.

[8]  S. Shreve,et al.  Stochastic differential equations , 1955, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  F. Wubs,et al.  A statistical significance test for sea-level variability , 2018 .

[10]  M. van der Wegen,et al.  Application of an unstructured 3D finite volume numerical model to flows and salinity dynamics in the San Francisco Bay-Delta , 2017 .

[11]  S. Monismith.  An integral model of unsteady salinity intrusion in estuaries , 2017 .

[12]  S. Monismith.  A Note on Delta Outflow , 2016 .

[13]  Miguel Á. Reyes-Merlo,et al.  On the relative influence of climate forcing agents on the saline intrusion in a well-mixed estuary: Medium-term Monte Carlo predictions , 2016 .

[14]  Shih-Nan Chen.  Asymmetric Estuarine Responses to Changes in River Forcing: A Consequence of Nonlinear Salt Flux , 2015 .

[15]  B. R. Noack.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 2013 .

[16]  M. Losada,et al.  Spatio‐temporal distribution, along‐channel transport, and post‐riverflood recovery of salinity in the Guadalquivir estuary (SW Spain) , 2013 .

[17]  Jian Shen,et al.  Salt intrusion during the dry season in the Huangmaohai Estuary, Pearl River Delta, China , 2013 .

[18]  Matthew C. Bowers,et al.  On the distributions of seasonal river flows: Lognormal or power law? , 2012 .

[19]  Pierre F. J. Lermusiaux,et al.  Dynamically orthogonal field equations for continuous stochastic dynamical systems , 2009 .

[20]  Younjoo J. Lee,et al.  Factors driving bottom salinity variability in the Chesapeake Bay , 2008 .

[21]  Floyd B. Hanson,et al.  Applied stochastic processes and control for jump-diffusions - modeling, analysis, and computation , 2007, Advances in design and control.

[22]  W. Rockwell Geyer,et al.  Mechanisms Driving the Time-Dependent Salt Flux in a Partially Stratified Estuary* , 2006 .

[23]  J. Newton,et al.  Dynamics of Willapa Bay, Washington: A Highly Unsteady, Partially Mixed Estuary , 2004 .

[24]  Shlomo Havlin,et al.  A stochastic model of river discharge fluctuations , 2003 .

[25]  Stephen G. Monismith,et al.  Structure and Flow-Induced Variability of the Subtidal Salinity Field in Northern San Francisco Bay , 2002 .

[26]  Frank Lunkeit,et al.  Regime Transitions in a Stochastically Forced Double-Gyre Model , 2001 .

[27]  P. MacCready.  Estuarine Adjustment to Changes in River Flow and Tidal Mixing , 1999 .

[28]  S. Monismith,et al.  Isohaline Position as a Habitat Indicator for Estuarine Populations , 1995 .

[29]  C. Kranenburg.  A Time Scale for Long-Term Salt Intrusion in Well-Mixed Estuaries , 1986 .

[30]  P. Chatwin.  Some remarks on the maintenance of the salinity distribution in estuaries , 1976 .

[31]  T. Faniran.  Numerical Solution of Stochastic Differential Equations , 2015 .

[32]  G. Weltje,et al.  A stochastic model for simulating long time series of river-mouth discharge and sediment load , 2007 .

[33]  P. MacCready.  Estuarine Adjustment , 2007 .

[34]  J..  VEGETATION AND RIVER CHANNEL DYNAMICS , 2007 .

[35]  H. Savenije.  Salt intrusion in alluvial estuaries , 2005 .

[36]  J. Simpson,et al.  The Salt Fluxes in a Tidally-Energetic Estuary , 2001 .

[37]  A. Kuo,et al.  Estuarine Circulation , 1989, Contemporary Issues in Science and Society.