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Application of deep learning to large scale riverine flow velocity estimation

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Abstract

Fast and reliable prediction of riverine flow velocities plays an important role in many applications, including flood risk management. The shallow water equations (SWEs) are commonly used for prediction of the riverine flow velocities. However, accurate and fast prediction with standard SWE solvers remains challenging in many cases. Traditional approaches are computationally expensive and require high-resolution measurement of riverbed profile (i.e., bathymetry) for accurate predictions. As a result, they are a poor fit in situations where they need to be evaluated repetitively due, for example, to varying boundary condition (BC) scenarios, or when the bathymetry is not known with certainty. In this work, we propose a two-stage process that tackles these issues. First, using the principal component geostatistical approach we estimate the probability density function of the bathymetry from flow velocity measurements, and then we use multiple machine learning algorithms in order to obtain a fast solver of the SWEs, given augmented realizations from the posterior bathymetry distribution and the prescribed range of potential BCs. The first step of the proposed approach allows us to predict flow velocities without any direct measurement of the bathymetry. Furthermore, the augmentation of the distribution in the second stage allows incorporation of the additional bathymetry information into the flow velocity prediction for improved accuracy and generalization, even if the bathymetry changes over time. Here, we use three different forward solvers, referred to as principal component analysis-deep neural network, supervised encoder, and supervised variational encoder, and validate them on a reach of the Savannah river near Augusta, GA. Our results show that the fast solvers are capable of predicting flow velocities with variable bathymetry and BCs with good accuracy, at a computational cost that is significantly lower than the cost of solving the full boundary value problem with traditional methods.

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References

  • Abdi G, Samadzadegan F, Reinartz P (2018) Deep learning decision fusion for the classification of urban remote sensing data. J Appl Remote Sens 12:016038

    Article  Google Scholar 

  • Agrafiotis P, Skarlatos D, Georgopoulos A, Karantzalos K (2019) DepthLearn: learning to correct the refraction on point clouds derived from aerial imagery for accurate dense shallow water bathymetry based on SVMs-Fusion with LiDAR point clouds. Remote Sens 11:2225

    Article  Google Scholar 

  • Antuono M, Brocchini M (2009) Solving the nonlinear shallow-water equations in physical space. J Fluid Mech 643:207–232

    Article  Google Scholar 

  • Benkhaldoun F, Seaid M (2010) A simple finite volume method for the shallow water equations. J Comput Appl Math 234:58–72

    Article  Google Scholar 

  • Benner P, Gugercin S, Willcox K (2015) A survey of projection-based model reduction methods for parametric dynamical systems. SIAM Rev 57:483–531

    Article  Google Scholar 

  • Berkooz G, Holmes P, Lumley J (1993) The proper orthogonal decomposition in the analysis of turbulent flows. Annu Rev Fluid Mech 25:539–575

    Article  Google Scholar 

  • Bishop CM (2006) Pattern recognition and machine learning. Springer, Berlin

    Google Scholar 

  • Bistrian D, Navon I (2015) An improved algorithm for the shallow water equations model reduction: dynamic mode decomposition vs POD. Int J Numer Methods Fluids 78:552–580

    Article  Google Scholar 

  • Casas A, Benito G, Thorndycraft V, Rico M (2006) The topographic data source of digital terrain models as a key element in the accuracy of hydraulic flood modelling. Earth Surf Process Landf J Br Geomorphol Res Group 31:444–456

    Article  Google Scholar 

  • Cea L, Blade E (2015) A simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications. Water Resour Res 51:5464–5486

    Article  Google Scholar 

  • Ceyhun O, Yalcin A (2010) Remote sensing of water depths in shallow waters via artificial neural networks. Estuar Coast Shelf Sci 89:89–96

    Article  Google Scholar 

  • Collins AM et al (2020) Bathymetric inversion and un1235 certainty estimation from synthetic surf-zone imagery with machine learning. Remote Sensing 12:3364

    Article  Google Scholar 

  • Corucci L, Masini A, Cococcioni M (2011) Approaching bathymetry estimation from high-resolution multispectral satellite images using a neuro-fuzzy technique. J Appl Remote Sens 5:053515

    Article  Google Scholar 

  • Cressie NAC (2015) Statistics for spatial data, revised. Wiley, Hoboken

    Google Scholar 

  • Crossley A, Lamb R, Waller S (2010) Fast solution of the shallow water equations using GPU technology. In: Third international symposium of British hydrological society (BHS), Newcastle, London, UK

  • De Lima RL, Abrantes JR, de Lima JL, de Lima MIP (2015) Using thermal tracers to estimate flow velocities of shallow flows: laboratory and field experiments. J Hydrol Hydromech 63:255–262

    Article  Google Scholar 

  • Delis A, Katsaounis T (2005) Numerical solution of the two-dimensional shallow water equations by the application of relaxation methods. Appl Math Model 29:754–783

    Article  Google Scholar 

  • Durakovic B (2017) Design of experiments application, concepts, examples: state of the art. Period Eng Nat Sci 5:421–439

    Google Scholar 

  • Emery L et al (2010) Autonomous collection of river parameters using drifting buoys. Oceans MTS/IEEE, Seattle, pp 1–7

    Google Scholar 

  • Garambois PA, Monnier J (2015) Inference of effective river properties from remotely sensed observations of water surface. Adv Water Resour 79:103–120

    Article  Google Scholar 

  • Gholamalifard M, Kutser T, Esmaili-Sari A, Abkar AA, Naimi B (2013) Remotely sensed empirical modeling of bathymetry in the southeastern Caspian sea. Remote Sens 5:2746–2762

    Article  Google Scholar 

  • Ghorbanidehno H et al (2020) Deep learning technique for fast inference of large-scale riverine bathymetry. Adv Water Resour 147:103715

    Article  Google Scholar 

  • Ghorbanidehno H, Kokkinaki A, Lee J, Darve E (2020) Recent developments in fast and scalable inverse modeling and data assimilation methods in hydrology. J Hydrol 591:125266

    Article  Google Scholar 

  • Hesthaven J, Ubbiali S (2018) Non-intrusive reduced order modeling of nonlinear problems using neural networks. J Comput Phys 363:55–78

    Article  Google Scholar 

  • Hilldale RC, Raff D (2008) Assessing the ability of airborne LiDAR to map river bathymetry. Earth Surf Proc Land 33:773–783

    Article  Google Scholar 

  • Hinton GE, Salakhutdinov RR (2006) Reducing the dimensionality of data with neural networks. Science 313:504–507

    Article  CAS  Google Scholar 

  • Horvath Z et al (2020) Comparison of fast shallow-water schemes on real-world floods. J Hydraul Eng 146:05019005

    Article  Google Scholar 

  • Jeong J, Park E (2019) Comparative applications of data-driven models representing water table fluctuations. J Hydrol 572:261–273

    Article  Google Scholar 

  • Karimi H et al (2019) Comparison of learning-based wastewater flow prediction methodologies for smart sewer management. J Hydrol 577:123977

    Article  Google Scholar 

  • Kingma DP, Welling M (2019) An introduction to variational autoencoders. Found Trends Mach Learn 12:307–392

    Article  Google Scholar 

  • Kitanidis PK, Lee J (2014) Principal component geostatistical approach for large dimensional inverse problems. Water Resour Res 50:5428–5443

    Article  CAS  Google Scholar 

  • Kramer MA (1991) Nonlinear principal component analysis using autoassociative neural networks. AIChE J 37:233–243

    Article  CAS  Google Scholar 

  • Kratzert F, Klotz D, Brenner C, Schulz K, Herrnegger M (2018) Rainfall-runoff modelling using long short-term memory (LSTM) networks. Hydrol Earth Syst Sci 22:6005–6022

    Article  Google Scholar 

  • Landon C, Wilson GW, Ozkan-Haller HT, MacMahan JH (2014) Bathymetry estimation using drifter-based velocity measurements on the Kootenai river, Idaho. J Atmos Oceanic Technol 31:503–514

    Article  Google Scholar 

  • Lane S, Richards K, Chandler J (1994) Developments in monitoring and modelling small-scale river bed topography. Earth Surf Proc Land 19:349–368

    Article  Google Scholar 

  • Lanzoni S, Siviglia A, Frascati A, Seminara G (2006) Long waves in erodible channels and morpho1056 dynamic influence. Water Resour Res 42:W06D17

    Article  Google Scholar 

  • Lee J et al (2018) Riverine bathymetry imaging with indirect observations. Water Resour Res 54:3704–3727

    Article  Google Scholar 

  • Lee H, Han S (2010) Solving the shallow water equations using 2D SPH particles for interactive applications. Vis Comput 26:865–872

    Article  Google Scholar 

  • Lee J, Kitanidis PK (2014) Large-scale hydraulic tomography and joint inversion of head and tracer data using the principal component geostatistical approach (PCGA). Water Resour Res 50:5410–5427

    Article  Google Scholar 

  • Li LPJ, Xu H, Lin G, Guo D, Wu H (2019) Water quality prediction based on recurrent neural network and improved evidence theory: a case study of Qiantang River, China. Environ Sci Pollut Res 26:19879–19896

    Article  Google Scholar 

  • matplotlib boxplot. https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.boxplot.html

  • Marcus WA (2002) Mapping of stream microhabitats with high spatial resolution hyperspectral imagery. J Geogr Syst 4:113–126

    Article  Google Scholar 

  • Matskevich NA, Chubarov LB (2019) Exact solutions to shallow water equations for a water oscillation problem in an idealized basin and their use in verifying some numerical algorithms. Numer Anal Appl 12:234–250

    Article  Google Scholar 

  • McKean J et al (2009) Remote sensing of channels and riparian zones with a narrow-beam aquatic-terrestrial lidar. Remote Sens 1:1065–1096

    Article  Google Scholar 

  • Misra A, Vojinovic Z, Ramakrishnan B, Luijendijk A et al (2018) Shallow water bathymetry mapping using Support Vector Machine (SVM) technique and multispectral imagery. Int J Remote Sens 39:4431–4450

    Article  Google Scholar 

  • Moses SA, Janaki L, Joseph S, Gomathi JP, Joseph J (2013) Lake bathymetry from Indian remote sensing (P6-LISS III) satellite imagery using artificial neural network model. Lakes Reserv Res Manag 18:145–153

    Article  CAS  Google Scholar 

  • Muste M, Fujita I, Hauet A (2008) Large-scale particle image velocimetry for measurements in riverine environments. Water Resour Res 44:W00D19

    Article  Google Scholar 

  • Negm A, Mesbah S, Abdelaziz T, Makboul O (2017) Nile river bathymetry by satellite remote sensing case study: Rosetta branch. Springer, The Nile River, pp 259–274

    Google Scholar 

  • Novikov EA (1987) An analytical solution of the shallow water equations. Phys Lett A 123:287–288

    Article  CAS  Google Scholar 

  • Poggio T, Mhaskar H, Rosasco L, Miranda B, Liao Q (2017) Why and when can deep- but not shallow- networks avoid the curse of dimensionality: a review. Int J Autom Comput 14:503–519

    Article  Google Scholar 

  • Puleo JA, McKenna TE, Holland KT, Calantoni J (2012) Quantifying riverine surface currents from time sequences of thermal infrared imagery. Water Resour Res 48:W01527

    Article  Google Scholar 

  • Ross DA, Lim J, Lin R-S, Yang M-H (2008) Incremental learning for robust visual tracking. Int J Comput Vis 77:125–141

    Article  Google Scholar 

  • Savant G, Berger C, McAlpin TO, Tate JN (2010) Efficient implicit finite-element hydrodynamic model for dam and levee breach. J Hydraul Eng 137:1005–1018

    Article  Google Scholar 

  • Singh J, Altinakar MS, Ding Y (2015) Numerical modeling of rainfall-generated overland flow using nonlinear shallow-water equations. J Hydrol Eng 20:04014089

    Article  Google Scholar 

  • Sit M et al (2019) A comprehensive review of deep learning applications in hydrology and water resources. EarthArXiv

  • Sonogashira M, Shonai M, Iiyama M (2020) Highresolution bathymetry by deep-learning-based image superresolution. PLoS ONE 15:e0235487

    Article  CAS  Google Scholar 

  • Stefanescu R, Sandu A, Navon I (2014) Comparison of POD reduced order strategies for the nonlinear 2D shallow water equations. Int J Numer Methods Fluids 76:497–521

    Article  Google Scholar 

  • Traganos D, Poursanidis D, Aggarwal B, Chrysoulakis N, Reinartz P (2018) Estimating satellite-derived bathymetry (SDB) with the Google earth engine and sentinel 2. Remote Sens 10:859

    Article  Google Scholar 

  • USGS 02197000 Savannah river at Augusta, GA https://waterdata.usgs.gov/ga/nwis/uv?site_no=02197000

  • Wang L, Liu H, Su H, Wang J (2019) Bathymetry retrieval from optical images with spatially distributed support vector machines. GI Sci Remote Sens 56:323–337

    Article  Google Scholar 

  • Westaway R, Lane S, Hicks D (2000) The development of an automated correction procedure for digital photogrammetry for the study of wide, shallow, gravel-bed rivers. Earth Surf Process Landf 25:209–226

    Article  Google Scholar 

  • Wilson GW, Ozkan-Haller HT (2012) Ensemblebased data assimilation for estimation of river depths. J Atmos Oceanic Technol 29:1558–1568

    Article  Google Scholar 

  • Xia X, Liang Q, Ming X, Hou J (2017) An efficient and stable hydrodynamic model with novel source term discretization schemes for overland flow and flood simulations. Water Resour Res 53:3730–3759

    Article  Google Scholar 

  • Yoon Y et al (2012) Estimating river bathymetry from data assimilation of synthetic SWOT measurements. J Hydrol 464:363–375

    Article  Google Scholar 

  • Yunus AP, Dou J, Song X, Avtar R (2019) Improved bathymetric mapping of coastal and lake environments using Sentinel-2 and Landsat-8 images. Sensors 19:2788

    Article  Google Scholar 

  • Zolezzi G, Seminarao G (2001) Downstream and upstream influence in river meandering. Part 1. General theory and application to overdeepening. J Fluid Mech 438:183–211

    Article  Google Scholar 

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Acknowledgements

The PCGA codes can be found in the https://github.com/jonghyunharrylee/pyPCGApyPCGA github repository, and the DNN codes can be found in the https://github.com/moji1369/DNN-based-fast-solver-of-SWEsDNN-SWEs github repository. This research was supported by the U.S. Department of Energy, Office of Advanced Scientific Computing Research under the Collaboratory on Mathematics and Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PhILMs) project, Grant #DE-SC0019453. Jonghyun Lee was supported by Hawai’i Experimental Program to Stimulate Competitive Research (EPSCoR) provided by the National Science Foundation Research Infrastructure Improvement (RII) Track-1: ’Ike Wai: Securing Hawai’i’s Water Future Award OIA #1557349. This work was also supported by an appointment to the Faculty and Postdoctoral Fellow Research Participation Program at the U.S. Engineer Research and Development Center, Coastal and Hydraulics Laboratory administered by the Oak Ridge Institute for Science and Education through an inter-agency agreement between the U.S. Department of Energy and ERDC. The Chief of Engineers has granted permission for the publication of this work.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

    Mojtaba Forghani & Eric F. Darve

  2. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, USA

    Yizhou Qian

  3. Department of Civil and Environmental Engineering and Water Resources Research Center, University of Hawaii at Manoa, Honolulu, HI, USA

    Jonghyun Lee

  4. U.S. Army Engineer Research and Development Center, Vicksburg, MS, USA

    Matthew W. Farthing & Tyler Hesser

  5. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, USA

    Peter K. Kitanidis

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  1. Mojtaba Forghani
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Forghani, M., Qian, Y., Lee, J. et al. Application of deep learning to large scale riverine flow velocity estimation. Stoch Environ Res Risk Assess 35, 1069–1088 (2021). https://doi.org/10.1007/s00477-021-01988-0

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