Calibrating 1D hydrodynamic river models in the absence of cross-section geometry using satellite observations of water surface elevation and river width

Hydrodynamic modeling has been increasingly used to simulate water surface elevation which is important for flood prediction and risk assessment. Scarcity and inaccessibility of in situ bathymetric information have hindered hydrodynamic model development at continental-to-global scales. Therefore, river cross-section geometry is commonly approximated by highly simplified generic shapes. Hydrodynamic river models require both bed geometry and roughness as input parameters. Simultaneous calibration of shape parameters and roughness is difficult, because often there are trade-offs between them. Instead of parameterizing cross-section geometry and hydraulic roughness separately, this study introduces a parameterization of 1D hydrodynamic models by combining cross-section geometry and roughness into one conveyance parameter. Flow area and conveyance are expressed as power laws of flow depth, and they are found to be linearly related in log–log space at reach scale. Data from a wide range of river systems show that the linearity approximation is globally applicable. Because the two are expressed as power laws of flow depth, no further assumptions about channel geometry are needed. Therefore, the hydraulic inversion approach allows for calibrating flow area and conveyance curves in the absence of direct observations of bathymetry and hydraulic roughness. The feasibility and performance of the hydraulic inversion workflow are illustrated using satellite observations of river width and water surface elevation in the Songhua river, China. Results show that this approach is able to reproduce water level dynamics with root-mean-square error values of 0.44 and 0.50 m at two gauging stations, which is comparable to that achieved using a standard calibration approach. In summary, this study puts forward an alternative method to parameterize and calibrate river models using satellite observations of river width and water surface elevation.

Geological evolution of the Mississippi River into the Anthropocene

The Mississippi River maintains commercial and societal networks of the USA along its >3700 km length. It has accumulated a fluvial sedimentary succession over 80 million years. Through the last 11,700 years of the Holocene Epoch, the wild river shaped the landscape, models of which have become classic in geological studies of ancient river strata. Studies of the river were led by the need to develop infrastructure and to search for hydrocarbons, through which, these models have become quite sophisticated. However, whilst the models demonstrate how the wild river behaves, a monumental shift in fundamental controls on the entire fluvial system, broadly coinciding with the proposed mid-20th century onset of the Anthropocene Epoch, has generated new geological patterns that are becoming globally ubiquitous, and which the Mississippi River typifies. As such, whilst classic Holocene river models may be compared to human-modified systems such as the Lower Mississippi River (and others worldwide), locally the models may now only directly apply to its fossilized components preserved in the sub-surface. Such river models need adapting to better understand the present dynamics, and future evolution of these landscapes.

Selected Topics on Reaction-Diffusion-Advection Models from Spatial Ecology

We discuss the effects of movement and spatial heterogeneity on population dynamics via reaction–diffusion-advection models, focusing on the persistence, competition, and evolution of organisms in spatially heterogeneous environments. Topics include Lokta-Volterra competition models, river models, evolution of biased movement, phytoplanktongrowth, and spatial spread of epidemic disease. Open problems and conjectures are presented.P arts of this survey are adopted from the materials in [89,108,109], and some very recent progress are also included.

Discharge and bathymetry estimations of rivers from altimetry and datasets by hybrid computational methods

<p>We present the Hierarchical Variational Discharge Inference (HiVDI) algorithm [1,2] and its capabilities to estimate the discharge and bathymetry of rivers from altimetry measurement, more particularly from the forthcoming SWOT space mission. The last version algorithm is based on hierarchical flow models and hybrid computational approaches : 1) a dedicated satellite-scale low-complexity model relating the discharge Q(x,t), the bathymetry b(x) and the friction parameter K [2]; 2) an advanced Variational Data Assimilation (VDA) formulation based on a relatively complete physics (Saint-Venant’s equations) [2,4] ; 3) deep neural networks based estimations obtained from recently enriched databases [1]. The resulting algorithm turns out to be robust and relatively accurate. Passed the assimilation of a hydrological cycle (~ 1 year variations, considered as a “learning period) the identified parameters (b(x), K) are identified; next given newly acquired satellite measurements, the low complexity model enables to estimate Q(x,t) in real-time [1,2].</p><p>Numerical results on numerous river datasets are analyzed in detail including for relatively complex flows and multi-satellite datasets [1,2,3].</p><p>References</p><p>[1] K. Larnier, J. Monnier. "Hybrid data assimilation - deep learning approaches to estimate rivers discharges from altimetry". Submitted.</p><p>[2] K. Larnier, J. Monnier, P.-A. Garambois, J. Verley. "River discharge and bathymetry estimations from SWOT altimetry measurements". Revised (nov. 2019).</p><p>[3] P.-A. Garambois, K. Larnier, J. Monnier, P. Finaud-Guyot, J. Verley, A. Montazem, S. Calmant. "Variational inference of effective channel and ungauged anabranching river discharge from multi-satellite water heights of different spatial sparsity". J. of Hydrology 2019.</p><p>[4] P. Brisset, J. Monnier, P.-A. Garambois, H. Roux. "On the assimilation of altimetry data in 1D Saint-Venant river models". Adv. Water Ress. 2018. </p><p>[5] "DassFlow: Data Assimilation for Free Surface Flows", open-source computational software. INSA - IMT, CNRS, CNES, CS group. http://www.math.univ-toulouse.fr/DassFlow</p>