Probabilistic solution to two-dimensional stochastic solute transport model by the Fokker-Planck equation approach

Tu T., Ercan A., Kavvas M. L.

JOURNAL OF HYDROLOGY, vol.580, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 580
  • Publication Date: 2020
  • Doi Number: 10.1016/j.jhydrol.2019.124250
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Aerospace Database, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), Artic & Antarctic Regions, BIOSIS, CAB Abstracts, Communication Abstracts, Compendex, Environment Index, Geobase, INSPEC, Metadex, Pollution Abstracts, Veterinary Science Database, Civil Engineering Abstracts
  • Keywords: Two-dimensional, Stochastic solute transport, Fokker-Planck Equation, Upscaling, Monte Carlo simulation, OPEN-CHANNEL FLOW, UNSTEADY, SIMULATION, SCHEME
  • Middle East Technical University Affiliated: No


The study of solute transport in rivers is of environmental significance, since solute transported in river flows may affect the river water quality conditions. Solute transport in natural flows is a challenging process to be investigated, given natural flows usually indicate uncertainty in space and time. Two-dimensional models are more preferable to one-dimensional models, especially when the underlying flow field is complex. In this study, a stochastic horizontally two-dimensional solute transport model is developed. The proposed model can account for the effect of uncertain two-dimensional flow field and solute loading conditions on the uncertainty of the solute transport. The governing equation of the proposed model is in the form of Fokker-Planck equation, which characterizes the spatiotemporal evolution of the probability density function of the state variables of the solute transport process. Consequently, the mean and standard deviation behavior of the ensemble solute transport under uncertain conditions can be quantified. The numerical solutions of the proposed model are validated with the Monte Carlo simulations under uncertain flow fields. The comparison of the results by the two methods indicate the developed two-dimensional stochastic solute transport model can sufficiently express the spatial variability of the solute transport process and adequately capture the ensemble solute transport behavior by the complete probabilistic description of the solute transport process under uncertain conditions.