Water temperature modeling in the Garonne River (France)

Stream water temperature is one of the most important parameters for water quality and ecosystem studies. Temperature can influence many chemical and biological processes and therefore impacts on the living conditions and distribution of aquatic ecosystems. Simplified models such as statistical models can be very useful for practitioners and water resource management. The present study assessed two statistical models – an equilibrium-based model and stochastic autoregressive model with exogenous inputs – in modeling daily mean water temperatures in the Garonne River from 1988 to 2005. The equilibrium temperature-based model is an approach where net heat flux at the water surface is expressed as a simpler form than in traditional deterministic models. The stochastic autoregressive model with exogenous inputs consists of decomposing the water temperature time series into a seasonal component and a short-term component (residual component). The seasonal component was modeled by Fourier series and residuals by a second-order autoregressive process (Markov chain) with use of short-term air temperatures as exogenous input. The models were calibrated using data of the first half of the period 1988–2005 and validated on the second half. Calibration of the models was done using temperatures above 20 ◦C only to ensure better prediction of high temperatures that are currently at stake for the aquatic conditions of the Garonne River, and particularly for freshwater migrating fishes such as Atlantic Salmon (Salmo salar L.). The results obtained for both approaches indicated that both models performed well with an average root mean square error for observed temperatures above 20 ◦C that varied on an annual basis from 0.55 ◦C to 1.72 ◦C on validation, and good predictions of temporal occurrences and durations of three temperature threshold crossings linked to the conditions of migration and survival of Atlantic Salmon

Data assimilation method for real-time flash flood forecasting using a physically based distributed model

The MARINE model (Roux et al, 2011) is a physically based distributed model dedicated to real time flash flood forecasting on small to medium catchments. The infiltration capacity is evaluated by the Green and Ampt equation and the surface runoff calculation is divided into two parts: the land surface flow and the flow in the drainage network both based on kinematic wave hypothesis. In order to take into account rainfall spatial-temporal variability as well as the various behaviours of soil types among the catchment, the model is spatially distributed, which can also help to understand the flood driving processes. The model integrates remote sensing data such as the land coverage map with spatial resolution adapted to hydrological scales. Minimal data requirements for the model are: the Digital Elevation Model describing catchment topography and the location and description of the drainage network. Moreover some parameters are not directly measurable and need to be calibrated. Most of the sources of uncertainties can be propagated thanks to variational method (Castaings et al, 2009) and finally help to determine time dependent uncertainty intervals. This study also investigates the methodology developed for real-time flash flood forecasting using the MARINE model and data assimilation techniques. According to prior sensitivity analyses and calibrations, parameters values were determined as constants or initial guess. Then a data assimilation method called the adjoint state method is used to update some of the most sensitive parameters to improve accuracy of discharges predictions. The forecast errors are evaluated as a function of lead time and discussed from an operational point of view. Multiple strategies in term of updatable parameters set, length of time window, parameters bounds and observation threshold used to trigger the assimilation method are discussed regarding accuracy, robustness and real-time feasibility

Study of flow through rockfill in channel = Etude des écoulements dans une mèche en canal

We present the results of an experimental, theoretical, and also numerical study of free surface buried flows that we have undertaken in the laboratory LSTE of INAT. This work was conducted as part of collaboration with the engineering international office MECATER which included the construction of a new channel with large section in INAT, this channel was designed to study the losses in porous media with high porosity for which Darcy's law is no longer applicable. The experiments consisted in determining the evolution of the free surface for different geometrical characteristics of riprap and different flow rates. These tests were used to verify different laws of head loss proposed in the literature, by performing numerical simulations of the evolution of the water surface for each experiment. The analysis of our results shows that the Stephenson’s formula is relevant to calculate the non-linear head loss for flows with high Reynolds number of pore. Furthermore, the simulations have highlighted the important role of porosity. These results should be confirmed by further tests to assess in particular the influence of the slope and to analyze the behavior of the flow at the inlet and outlet of the riprap

Sensitivity analysis and parameter estimation for distributed hydrological modeling: potential of variational methods

Variational methods are widely used for the analysis and control of computationally intensive spatially distributed systems. In particular, the adjoint state method enables a very efficient calculation of the derivatives of an objective function (response function to be analysed or cost function to be optimised) with respect to model inputs. In this contribution, it is shown that the potential of variational methods for distributed catchment scale hydrology should be considered. A distributed flash flood model, coupling kinematic wave overland flow and Green Ampt infiltration, is applied to a small catchment of the Thoré basin and used as a relatively simple (synthetic observations) but didactic application case. It is shown that forward and adjoint sensitivity analysis provide a local but extensive insight on the relation between the assigned model parameters and the simulated hydrological response. Spatially distributed parameter sensitivities can be obtained for a very modest calculation effort (~6 times the computing time of a single model run) and the singular value decomposition (SVD) of the Jacobian matrix provides an interesting perspective for the analysis of the rainfall-runoff relation. For the estimation of model parameters, adjoint-based derivatives were found exceedingly efficient in driving a bound-constrained quasi-Newton algorithm. The reference parameter set is retrieved independently from the optimization initial condition when the very common dimension reduction strategy (i.e. scalar multipliers) is adopted. Furthermore, the sensitivity analysis results suggest that most of the variability in this high-dimensional parameter space can be captured with a few orthogonal directions. A parametrization based on the SVD leading singular vectors was found very promising but should be combined with another regularization strategy in order to prevent overfitting

Characterization of process-oriented hydrologic model behavior with temporal sensitivity analysis for flash floods in Mediterranean catchments

This paper presents a detailed analysis of 10 flash flood events in the Mediterranean region using the distributed hydrological model MARINE. Characterizing catchment response during flash flood events may provide new and valuable insight into the dynamics involved for extreme catchment response and their dependency on physiographic properties and flood severity. The main objective of this study is to analyze flash-flood-dedicated hydrologic model sensitivity with a new approach in hydrology, allowing model outputs variance decomposition for temporal patterns of parameter sensitivity analysis. Such approaches enable ranking of uncertainty sources for nonlinear and nonmonotonic mappings with a low computational cost. Hydrologic model and sensitivity analysis are used as learning tools on a large flash flood dataset. With Nash performances above 0.73 on average for this extended set of 10 validation events, the five sensitive parameters of MARINE process-oriented distributed model are analyzed. This contribution shows that soil depth explains more than 80% of model output variance when most hydrographs are peaking. Moreover, the lateral subsurface transfer is responsible for 80% of model variance for some catchment-flood events’ hydrographs during slow-declining limbs. The unexplained variance of model output representing interactions between parameters reveals to be very low during modeled flood peaks and informs that model parsimonious parameterization is appropriate to tackle the problem of flash floods. Interactions observed after model initialization or rainfall intensity peaks incite to improve water partition representation between flow components and initialization itself. This paper gives a practical framework for application of this method to other models, landscapes and climatic conditions, potentially helping to improve processes understanding and representation

Flash flood modeling with the MARINE hydrological distributed model

International audienceFlash floods are characterized by their violence and the rapidity of their occurrence. Because these events are rare and unpredictable, but also fast and intense, their anticipation with sufficient lead time for warning and broadcasting is a primary subject of research. Because of the heterogeneities of the rain and of the behavior of the surface, spatially distributed hydrological models can lead to a better understanding of the processes and so on they can contribute to a better forecasting of flash flood. Our main goal here is to develop an operational and robust methodology for flash flood forecasting. This methodology should provide relevant data (information) about flood evolution on short time scales, and should be applicable even in locations where direct observations are sparse (e.g. absence of historical and modern rainfalls and streamflows in small mountainous watersheds). The flash flood forecast is obtained by the physically based, space-time distributed hydrological model "MARINE'' (Model of Anticipation of Runoff and INondations for Extreme events). This model is presented and tested in this paper for a real flash flood event. The model consists in two steps, or two components: the first component is a "basin'' flood module which generates flood runoff in the upstream part of the watershed, and the second component is the "stream network'' module, which propagates the flood in the main river and its subsidiaries. The basin flash flood generation model is a rainfall-runoff model that can integrate remotely sensed data. Surface hydraulics equations are solved with enough simplifying hypotheses to allow real time exploitation. The minimum data required by the model are: (i) the Digital Elevation Model, used to calculate slopes that generate runoff, it can be issued from satellite imagery (SPOT) or from French Geographical Institute (IGN); (ii) the rainfall data from meteorological radar, observed or anticipated by the French Meteorological Service (Météo France); and (iii) the spatially distributed soil and other surface properties viewed from space (land cover map from SPOT or LANDSAT, main rivers, ...). The stream flood propagation model simulates flood propagation in main rivers by solving 1-D Saint Venant equations. The data required for this part of the model are the river morphology, topography and roughness. The MARINE model has already been used previously for real time flash floods forecasting in the frame of the PACTES project on "forecasting and anticipation of floods with spatial techniques'' (funded by the CNES and the French Ministry of Research) concerning the catastrophic 1999 flash flood that occurred in the South of France. The main advantages of MARINE are its ability to run on insufficiently gauged basins (with the help of satellite information) and to run in an operational mode for real-time flood forecasting

A physically-based parsimonious hydrological model for flash floods in Mediterranean catchments

A spatially distributed hydrological model, dedicated to flood simulation, is developed on the basis of physical process representation (infiltration, overland flow, channel routing). Estimation of model parameters requires data concerning topography, soil properties, vegetation and land use. Four parameters are calibrated for the entire catchment using one flood event. Model sensitivity to individual parameters is assessed using Monte-Carlo simulations. Results of this sensitivity analysis with a criterion based on the Nash efficiency coefficient and the error of peak time and runoff are used to calibrate the model. This procedure is tested on the Gardon d'Anduze catchment, located in the Mediterranean zone of southern France. A first validation is conducted using three flood events with different hydrometeorological characteristics. This sensitivity analysis along with validation tests illustrates the predictive capability of the model and points out the possible improvements on the model's structure and parameterization for flash flood forecasting, especially in ungauged basins. Concerning the model structure, results show that water transfer through the subsurface zone also contributes to the hydrograph response to an extreme event, especially during the recession period. Maps of soil saturation emphasize the impact of rainfall and soil properties variability on these dynamics. Adding a subsurface flow component in the simulation also greatly impacts the spatial distribution of soil saturation and shows the importance of the drainage network. Measures of such distributed variables would help discriminating between different possible model structures

On the assimilation of SWOT type data into 2D shallow-water models

In river hydraulics, assimilation of water level measurements at gauging stations is well controlled, while assimilation of images is still delicate. In the present talk, we address the richness of satellite mapped information to constrain a 2D shallow-water model, but also related difficulties. 2D shallow models may be necessary for small scale modelling in particular for low-water and flood plain flows. Since in both cases, the dynamics of the wet dry front is essential, one has to elaborate robust and accurate solvers. In this contribution we introduce robust second order, stable finite volume scheme [CoMaMoViDaLa]. Comparisons of real like tests cases with more classical solvers highlight the importance of an accurate flood plain modelling. A preliminary inverse study is presented in a flood plain flow case, [LaMo] [HoLaMoPu]. As a first step, a 0th order data processing model improves observation operator and produces more reliable water level derived from rough measurements [PuRa]. Then, both model and flow behaviours can be better understood thanks to variational sensitivities based on a gradient computation and adjoint equations. It can reveal several difficulties that a model designer has to tackle. Next, a 4D-Var data assimilation algorithm used with spatialized data leads to improved model calibration and potentially leads to identify river discharges. All the algorithms are implemented into DassFlow software (Fortran, MPI, adjoint) [Da]. All these results and experiments (accurate wet-dry front dynamics, sensitivities analysis, identification of discharges and calibration of model) are currently performed in view to use data from the future SWOT mission

Relations between streamflow indices, rainfall characteristics and catchment physical descriptors for flash flood events

Flash flood is a very intense and quick hydrologic response of a catchment to rainfall. This phenomenon has a high spatial-temporal variability as the generating storm often hits small catchments (few km²). Given the small spatial temporal scales and high variability of flash floods, their prediction remains a hard exercise as the necessary data are often scarce. This study investigates the potential of hydrologic indices at different scales to improve understanding of flash floods dynamics and characterize catchment response in a model independent approach. These hydrologic indices gather information on hydrograph shape or catchment dynamic for instance and are useful to examine catchment signature in function of their size. Results show that for middle-size (>100 km²) catchments response shape can be correlated to storm cell position within the catchment contrarily to smaller catchments. In a multi-scale point of view, regional characteristics about catchment geomorphology or rainfall field statistics should provide useful insight to find pertinent hydrologic response indices. The combined use of these indices with a physically-based distributed modelling could facilitate calibration on ungauged catchments

Using a multi-hypothesis framework to improve the understanding of flow dynamics during flash floods

A method of multiple working hypotheses was applied to a range of catchments in the Mediterranean area to analyse different types of possible flow dynamics in soils during flash flood events. The distributed, process-oriented model, MARINE, was used to test several representations of subsurface flows, including flows at depth in fractured bedrock and flows through preferential pathways in macropores. Results showed the contrasting performances of the submitted models, revealing different hydrological behaviours among the catchment set. The benchmark study offered a characterisation of the catchments’ reactivity through the description of the hydrograph formation. The quantification of the different flow processes (surface and intra-soil flows) was consistent with the scarce in situ observations, but it remains uncertain as a result of an equifinality issue. The spatial description of the simulated flows over the catchments, made available by the model, enabled the identification of counterbalancing effects between internal flow processes, including the compensation for the water transit time in the hillslopes and in the drainage network. New insights are finally proposed in the form of setting up strategic monitoring and calibration constraints