Geodesic
A river routing scheme for an Earth system model
Numerical methods and programming, Tome 20 (2019) no. 4, pp. 396-410.

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A new version of the INM RAS-MSU land surface scheme is presented which includes a module for the thermo- and hydrodynamics of rivers. The river dynamics is described by the diffusion wave equations, whereas the river thermodynamics is simulated by the one-dimensional heat equation. The object-oriented implementation of the river routing scheme allows one to use arbitrary solvers of one-dimensional river dynamics problems, for example, the Saint-Venant equations. The snow cover thermodynamics is supplemented by the effects of liquid moisture percolation and freezing. The set of model updates significantly improved simulation of the annual cycle of water discharge and temperature for Severnaya Dvina river.
Keywords: Earth system model, land surface scheme, river network, snow melting. 
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     author = {V. M. Stepanenko and A. I. Medvedev and I. A. Korpushenkov and N. L. Frolova and V. N. Lykosov},
     title = {A river routing scheme for an {Earth} system model},
     journal = {Numerical methods and programming},
     pages = {396--410},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2019_20_4_a4/}
}
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V. M. Stepanenko; A. I. Medvedev; I. A. Korpushenkov; N. L. Frolova; V. N. Lykosov. A river routing scheme for an Earth system model. Numerical methods and programming, Tome 20 (2019) no. 4, pp. 396-410. http://geodesic.mathdoc.fr/item/VMP_2019_20_4_a4/