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Cost-benefit analyses (CBA) of flood management plans usually require estimating expected annual flood damages on a study area and rely on a complex modelling chain, including hydrological, hydraulic and economic modelling, as well as geographic information system-based spatial analysis. As most model-based assessments, these CBA are fraught with uncertainty. In this paper, we consider as a case study the CBA of a set of flood control structural measures on the Orb Delta, France. We demonstrate the use of variance-based global sensitivity analysis to (i) propagate uncertainty sources through the modelling chain and assess their overall impact on the outcomes of the CBA, and (ii) rank uncertainty sources according to their contribution to the variance of the CBA outcomes. All uncertainty sources prove to explain a significant share of the overall output variance. Results show that the ranking of uncertainty sources depends not only on the economic sector considered (private housing, agricultural land, other economic activities), but also on a number of averaging-out effects controlled by the number and surface area of the assets considered, the number of land use types or the number of damage functions.

Variance-based global sensitivity analysis (GSA) is used to study how the variance of the output of a model can be apportioned to different sources of uncertainty in its inputs. GSA is an essential component of model building as it helps to identify model inputs that account for most of the model output variance. However, this approach is seldom applied to spatial models because it cannot describe how uncertainty propagation interacts with another key issue in spatial modeling: the issue of model upscaling, that is, a change of spatial support of model output. In many environmental models, the end user is interested in the spatial average or the sum of the model output over a given spatial unit (for example, the average porosity of a geological block). Under a change of spatial support, the relative contribution of uncertain model inputs to the variance of aggregated model output may change. We propose a simple formalism to discuss this issue within a GSA framework by defining point and block sensitivity indices. We show that the relative contribution of an uncertain spatially distributed model input increases with its correlation length and decreases with the size of the spatial unit considered for model output aggregation. The results are briefly illustrated by a simple example.

Oil palm is the most rapidly expanding tropical perennial crop. Its cultivation raises environmental concerns, notably related to the use of nitrogen (N) fertilisers and the associated pollution and greenhouse gas emissions. While numerous and diverse models exist to estimate N losses from agriculture, very few are currently available for tropical perennial crops. Moreover, there is a lack of critical analysis of their performance in the specific context of tropical perennial cropping systems. We assessed the capacity of 11 models and 29 sub-models to estimate N losses in a typical oil palm plantation over a 25-year growth cycle, through leaching and runoff, and emissions of NH3, N2, N2O, and NOx. Estimates of total N losses were very variable, ranging from 21 to 139 kg N ha−1 yr−1. On average, 31 % of the losses occurred during the first 3 years of the cycle. Nitrate leaching accounted for about 80 % of the losses. A comprehensive Morris sensitivity analysis showed the most influential variables to be soil clay content, rooting depth, and oil palm N uptake. We also compared model estimates with published field measurements. Many challenges remain in modelling processes related to the peculiarities of perennial tropical crop systems such as oil palm more accurately.

International audience; In this paper, we investigate the use of the contribution to the sample mean plot (CSM plot) as a graphical tool for sensitivity analysis (SA) of computational models. We first provide an exact formula that links, for each uncertain model input Xj , the CSM plot Cj(·) with the first-order variance-based sensitivity index Sj . We then build a new estimate for Sj using polynomial regression of the CSM plot. This estimation procedure allows the computation of Sj from given data, without any SA-specific design of experiment. Numerical results show that this new Sj estimate is efficient for large sample sizes, but that at small sample sizes it does not compare well with other Sj estimation techniques based on given data, such as the effective algorithm for computing global sensitivity indices method or metamodel-based approaches.

International audience; We investigate how hazard spatial datasets and land use spatial datasets can be overlaid in natural risk assessments. Based on a case-study of a flood damage assessment on the Orb River, France, we show that the variability of spatial overlay techniques considered as a spatial model uncertainty may result in significant uncertainty in natural risk assessments.

International audience; Flood hydraulic simulation aims to reproduce the flood wave, i.e. the water level, the flood duration or the flow velocity at any site of the channels and floodplain. Hydraulic model outputs may later be used in studies to delineate risk areas, to characterize impacts in cost-benefit analyses of a flood prevention project, or to alert inhabitants before flood event. To support the robustness of these studies, uncertainties of hydraulic outputs over floodplain, especially a spatially explicit representation of uncertainties may be required (Saint-Geours et al., 2013). However, due to the flood data scarcity, the available observed water level data are rather used to calibrate hydraulic model parameters rather than to validate the model. Thus, epistemic uncertainties of simulated maxima flood levels over floodplain are rarely measured, except on some points along the main channel. Nevertheless, hydraulic modellers are able to deduce general rules and ranges on flood level uncertainties from modelling experiences. These rules are built up in regards with the frequencies of the modelled events and the floodplain morphology. The translation of this expert knowledge to spatial pattern models that are able to simulate spatial explicit uncertainties has thus to be addressed. In this paper, we explored the translation of the downstream Rhône river hydraulic modellers expertise in ad hoc stochastic spatial, i.e. geostatistical models. Expertise rules were only devoted to 1D floodplain modelling using a storage cells network framework. It concerned i) the magnitude of flood level errors depending on the riverbed location (floodplain or channel) of storage cells, ii) the water level measurement accuracies, iii) the spatial dependencies on errors between connected storage cells, and iv) some additional constraints on orders between flood levels on connected storage cells. Three continuous or discrete uncertainties simulation approaches were investigated using different levels of constraint: i) multi-Gaussian random fields on storage cells centroids within an anisotropic and curvilinear euclidean 2D space, ii) multi-Gaussian random fields on storage cells lattice and iii) Gaussian Markov random fields on storage cells lattice (Rue and Held, 2004). Identical spatial 2D covariance models were used in order to respect the expert rules on the water level error spatial structure in the same conditions for the three investigated approaches. The theoretical limitations of these approaches are first identified and discussed. Resulting maps of uncertainties are thus shown and discussed. Finally, in order to discuss the importance to refine spatial hydraulic uncertainty simulation methods, the measure of the impact of hydraulic un-1 certainties in a flood-risk project cost-benefit analysis is computed in addition to other sources of uncertainties (stakes uncertainties, flood frequency uncertainties, damage curve uncertainties, etc.). This latter sensitivity analysis results allows to balance the impact of flood level errors in comparison to other sources of uncertainties. Acknowledgements: This work has benefited from the support of Plan Rhône (FEDER funding).

[Departement_IRSTEA]Territoires [TR1_IRSTEA]SYNERGIE; International audience; This work aimed to prospect future space-borne LiDAR sensor capacities for global bathymetry over inland and coastal waters. The sensor performances were assessed using a methodology based on waveform simulation. A global representative simulated waveform database is first built from the Wa-LiD (Water LiDAR) waveform simulator and from distributions of water parameters assumed to be representative at the global scale. A bathymetry detection and estimation process is thus applied to each waveform to determine the bathymetric measurement probabilities in coastal waters, shallow lakes, deep lakes and rivers for a range of water depths. Finally, with a sensitivity analysis of waveforms, the accuracy and some limiting factors of the bathymetry are identified for the dominant water parameters. Two future space-borne LiDAR sensors were explored: an ultraviolet (UV) LiDAR and a green LiDAR. The results show that the bathymetric measurement probabilities at a 1 m depth is 63%, 54%, 24% and 19% with the green LiDAR for deep lakes, coastal waters, rivers and shallow lakes, respectively, and 10%, 22%, 1% and 0% with the UV LiDAR, respectively. The threshold values of dominant water parameters (sediment, yellow substance and phytoplankton concentrations) above which bathymetry detection fails were identified and mapped. The accuracy on the bathymetry estimates for both LiDAR sensors is 2.8 cm for one standard deviation with negligible bias (approximately 0.5 cm). However, these accuracy statistics only include the errors coming from the digitizing resolution and the inversion algorithm.

International audience; Flood risk mapping is recognized as an effective tool in flood risk management, and the elaboration of flood risk maps is now required for all major river basins in the European Union (Euro-pean directive 2007/60/EC). Flood risk maps can be based on the computation of potential damage due to different flood events, estimated for each individual stake over the study area. Mean Annual Damage indicator (MAD) is a synthetic indicator obtained by averaging over time, using the return period of each event, that can be mapped too. The issue of uncertainty associated with these flood damage maps should be carefully scrutinized, as they may be used to inform the relevant stakeholders or to design flood mitigation measures. Flood damage maps are based on the combination of hydrological, hydraulic, geographic and economic modeling efforts. Consequently, numerous sources of uncertainty propagate in their elaboration. Recent studies describe these various sources of uncertainty. Some authors propagate these uncertainties through the flood risk modeling chain and estimate confidence bounds around the resulting flood damage estimates. It is of great interest to go a step further by identifying which sources of uncertainty account for most of the uncertainty in flood damage maps. We demonstrate the use of variance-based global sensitivity analysis to rank sources of uncertainty in flood risk mapping, taking into account spatial scaling. We use a quasi-Monte-Carlo scheme to propagate input uncertainties through the process of flood damage map elaboration and to compute importance measures (Sobol' sensitivity indices) for each source of uncertainty. The variability of the damage or MAD indicator and the associated sensitivity indices are estimated at different spatial scales: individual stake, district, whole floodplain. This approach is illustrated on a case study on the Orb River, France. By mapping the uncertainty of damage and MAD indicator, we identified zones where flood damage estimates were less accurate. Then, sensitivity indices allowed ranking the sources of uncertainty at different scales. For instance, the accuracy of the digital elevation model proved to be the key source of uncertainty when estimating the MAD indicator on an individual stake (e.g. a single building), whereas return period of flood events were the most influential when examining the accuracy of total MAD over a larger zone. Finally, maps of sensitivity indices showed the spatial variability of sensitivities over the study area.

Environmental models often involve complex dynamic and spatial inputs and outputs. This raises specific issues when performing uncertainty and sensitivity analyses (SA). Based on appli- cations in flood risk assessment and agro-ecology, we present current research to adapt the methods of variance-based SA to such models. After recalling the basic principles, we propose a metamodelling approach of dynamic models based on a reduced-basis approximation of PDEs and we show how the error on the subsequent sensitivity indices can be quantified. We then present a mix of pragmatic and methodological solutions to perform the SA of a dynamic agro-climatic model with non standard input factors. SA is then applied to a flood risk model with spatially distributed inputs and outputs. Block sensitivity indices are defined and a precise relationship between these indices and their support size is established. Finally, we show how the whole support landscape and its key features can be incorporated in the SA of a spatial model., Les modèles environnementaux contiennent souvent des entrées-sorties complexes de par leur nature dynamique et spatiale, ce qui soulève des problèmes spécifiques pour leurs analyses d'incertitude et de sensibilité (AS). A partir d'applications en évaluation des risques d'inondation et en agro-écologie, nous présentons des recherches en cours pour adapter les méthodes d'AS à de tels modèles. Après un rappel des principes de base, nous proposons une approche de métamodélisation de modèles dynamiques basée sur une approximation par base réduite d'EDPs et nous montrons comment l'erreur sur les indices de sensibilité qui en découle peut être quantifiée. Nous présentons ensuite un cocktail de solutions pragmatiques et méthodologiques pour l'AS d'un modèle agro-climatique dynamique avec des facteurs d'entrée non standards. Puis l'AS est appliquée à un modèle de risque d'inondation avec des entrées-sorties spatialisées. On définit des indices de sensibilité par bloc et une relation précise est établie entre ces indices et leur taille de support. Enfin, nous montrons comment l'ensemble du paysage et de ses caractéristiques clés peut être incorpore à l'AS d'un modèle spatial.

[Departement_IRSTEA]Territoires [TR1_IRSTEA]SYNERGIE [TR2_IRSTEA]ARCEAU; International audience; Geostatistical simulations are used to perform a global sensitivity analysis on a model Y = f(X1 ... Xk) where one of the model inputs Xi is a continuous 2D-field. Geostatistics allow specifying uncertainty on Xi with a spatial covariance model and generating random realizations of Xi. These random realizations are used to propagate uncertainty through model f and estimate global sensitivity indices. Focusing on variance-based global sensitivity analysis (GSA), we assess in this paper how sensitivity indices vary with covariance parameters (range, sill, nugget). Results give a better understanding on how and when to use geostatistical simulations for sensitivity analysis of spatially distributed models.

International audience; Complex spatial models are developed to support decision making in various fields of environmental management. These models use environmental data that is spatially distributed, including 2D fields derived from sampled data. These spatial inputs are always partly uncertain. In order to provide confidence in these models, it is necessary to assess the impact of all input uncertainties. Performing sensitivity analysis (SA) can achieve this goal: SA techniques will allow the robustness of the model predictions to be checked and the input factors that account for most of the model output variability to be identied. The variance-based Sobol' approach is one of the few sensitivity analysis techniques that is suitable for complex models with spatially distributed inputs, non-linear effects and interactions between factors. It is based on a wide random exploration of the uncertainty space of the input factors,through Monte-Carlo sampling schemes. Spatially distributed inputs can be included in the analysis by associating randomly generated map realizations to scalar values. This allows complex description of spatial uncertainty to be applied. Spatial uncertainty on continuous fields, such as land elevation or rainfall elds, can come from diverse sources: measurement errors in data acquisition, interpolation errors, etc. To simulate this uncertainty, geostatistical unconditional or conditional simulations can be used to generate random realizations of the continuous 2D elds used as model inputs. Yet spatial Sobol' methods need a large number of model runs to compute sensitivity indices. With time consuming models, it is necessary to get the most accurate sensitivity indices with the fewest model runs. One way to reach better efficiency in the computation of sensitivity indices is by using a better sampling design in the space of the input factors. This issue has been widely discussed in the case of models with scalar inputs. Latin hypercube sampling (LHS) has been documented as an efficient option, along with other sampling schemes (quasi-random, winding stairs). Yet, in the case of sensitivity analysis of models with spatial inputs, the influence of the sampling scheme used to generate geostatistical simulations has not, up to now, been discussed. Some techniques have been developed to apply LHS to sample geostatistical simulations (e.g. Pebsema and Heuvelink, 1999 and Xu, 2005). Using a spatial sampling technique such as these may lead to better efficiency in the computation of sensitivity indices on spatial models. The aim of this paper is to compare the accuracy and bias of Sobol sensitivity indices on a model with continuous 2D spatial inputs, with a) different sampling designs of geostatistical simulations for spatial model inputs (simple random sampling, Latin hypercube sampling), b) increasing sample size.

[Departement_IRSTEA]RE [TR1_IRSTEA]GES / USAGES [TR2_IRSTEA]METHODO / SYNERGIE; National audience; Cost-Benefit Analysis based on the damage avoided approach gives rise to several synthetic indicators measuring either the flood exposure of an area (mean annual damage), or the interest to conduct a flood prevention policy (mean annual damage avoided, net present value). Those indicators are the outcome of a combination of hydrological, hydraulic, geographic and economic models. Although it is recommended to study the precision of these indicators, this is rarely done in practice, as the combined models which are needed are relatively complex. In this article, we present an approach which is based on Monte-Carlo analysis, and discuss the insights which can be drawn from it on the validity of the indicators.; L'analyse coût-bénéfice basée sur la simulation des dommages évités permet d'obtenir des indicateurs synthétiques sur l'exposition d'un territoire aux inondations (les dommages moyens annualisés), ainsi que l'intérêt ou non de mener une politique de prévention des inondations (les dommages évités moyens annualisés, la valeur actuelle nette). Ces indicateurs sont issus de la combinaison de modélisations hydrologiques, hydrauliques, géographiques et économiques d'un territoire. Bien qu'il soir recommandé d'en étudier la précision et la sensibilité, cette étape n'est que très rarement effectuée en pratique, notamment du fait de la complexité de la combinaison des différents modèles mobilisés. Dans cet article, au travers d'un exemple, nous proposons une approche reposant sur la technique de Monte-Carlo et analysons les enseignements concernant la validité des indicateurs.