Newtonian nudging for a Richards equation-based distributed hydrological model |
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| Institution: | 1. Institut National de la Recherche Scientifique (INRS), 490 de la Couronne, Quebec City (QC) G1K 9A9, Canada;2. Intragaz, 6565 boul. Jean XXIII, Trois-Rivières (QC) G9A 5C9, Canada;1. College of Physical Science and Technology, Sichuan University, Chengdu 610064, China;2. Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064, China;3. Sino-British Joint Materials Research Institute, Sichuan University, Chengdu 610064, China;1. Department of Earth System Science, University of California, Irvine, CA 92697, USA;2. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA;3. Department of Space, National Atmospheric Research Laboratory, Government of India, Tirupati, India;4. Institute Center for Water and Environment (iWATER), Masdar Institute of Science and Technology, P.O. Box 54224, Abu Dhabi, United Arab Emirates;5. INRS-ETE, National Institute of Scientific Research, Quebec City, QC G1K9A9, Canada;6. Department of Electronics and Communication Engineering, Sree Narayana Gurukulam College of Engineering, Ernakulam, Kerala, India;7. Department of Physics, Sri Venkateswara University, Tirupati, India |
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| Abstract: | The objective of data assimilation is to provide physically consistent estimates of spatially distributed environmental variables. In this study a relatively simple data assimilation method has been implemented in a relatively complex hydrological model. The data assimilation technique is Newtonian relaxation or nudging, in which model variables are driven towards observations by a forcing term added to the model equations. The forcing term is proportional to the difference between simulation and observation (relaxation component) and contains four-dimensional weighting functions that can incorporate prior knowledge about the spatial and temporal variability and characteristic scales of the state variable(s) being assimilated. The numerical model couples a three-dimensional finite element Richards equation solver for variably saturated porous media and a finite difference diffusion wave approximation based on digital elevation data for surface water dynamics. We describe the implementation of the data assimilation algorithm for the coupled model and report on the numerical and hydrological performance of the resulting assimilation scheme. Nudging is shown to be successful in improving the hydrological simulation results, and it introduces little computational cost, in terms of CPU and other numerical aspects of the model’s behavior, in some cases even improving numerical performance compared to model runs without nudging. We also examine the sensitivity of the model to nudging term parameters including the spatio-temporal influence coefficients in the weighting functions. Overall the nudging algorithm is quite flexible, for instance in dealing with concurrent observation datasets, gridded or scattered data, and different state variables, and the implementation presented here can be readily extended to any of these features not already incorporated. Moreover the nudging code and tests can serve as a basis for implementation of more sophisticated data assimilation techniques in a Richards equation-based hydrological model. |
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