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Abstract: The potential of Local Sensitivity Analysis (LSA) for analysis of uncertainty with respect to two major risks in river hydrodynamics – flash flood and dam failure – is assessed. LSA, implemented as an equation-based method, is compared to a Global Uncertainty Analysis (GUA) consisting in running Monte Carlo simulations with a hydrodynamic model. For a given statistical distribution of the model input parameters, the mean and standard deviation of the output variables are estimated with the two methods. In all single or multiple parameter cases investigated, including as much as±80% relative variation, LSA provides similar results to GUA, while requiring only one simulation instead of several hundreds or thousands. Only within a few meters of the shock (flow discontinuity) generated by the breaking of a dam do the two methods depart. This paper shows that despite the non-linearity of river flow processes, the first order, local approach remains generally valid for uncertainty analysis of hydrodynamic risks, even in the case of large parameter uncertainty. The contrast in importance of the various parameters on both sides of a shock is also highlighted. [Copyright &y& Elsevier]

Emerging tools for automatic differentiation (AD) of computer programs should be of great benefit for the implementation of many derivative-based numerical methods such as those used for inverse modeling. The Odysse´e software, one such tool for Fortran 77 codes, has been tested on a sample model that solves a 2D non-linear diffusion-type equation. Odysse´e offers both the forward and the reverse differentiation modes, that produce the tangent and the cotangent models, respectively. The two modes have been implemented on the sample application. A comparison is made with a manually-produced differentiated code for this model (MD), obtained by solving the adjoint equations associated with the model's discrete state equations. Following a presentation of the methods and tools and of their relative advantages and drawbacks, the performances of the codes produced by the manual and automatic methods are compared, in terms of accuracy and of computing efficiency (CPU and memory needs). The perturbation method (finite-difference approximation of derivatives) is also used as a reference. Based on the test of Taylor, the accuracy of the two AD modes proves to be excellent and as high as machine precision permits, a good indication of Odysse´e's capability to produce error-free codes. In comparison, the manually-produced derivatives (MD) sometimes appear to be slightly biased, which is likely due to the fact that a theoretical model (state equations) and a practical model (computer program) do not exactly coincide, while the accuracy of the perturbation method is very uncertain. The MD code largely outperforms all other methods in computing efficiency, a subject of current research for the improvement of AD tools. Yet these tools can already be of considerable help for the computer implementation of many numerical methods, avoiding the tedious task of hand-coding the differentiation of complex algorithms. [Copyright &y& Elsevier]

Abstract: The sensitivity of a model output (called a variable) to a parameter can be defined as the partial derivative of the variable with respect to the parameter. When the governing equations are not differentiable with respect to this parameter, problems arise in the numerical solution of the sensitivity equations, such as locally infinite values or instability. An approximate Riemann solver is thus proposed for direct sensitivity calculation for hyperbolic systems of conservation laws in the presence of discontinuous solutions. The proposed approach uses an extra source term in the form of a Dirac function to restore sensitivity balance across the shocks. It is valid for systems such as the Euler equations for gas dynamics or the shallow water equations for free surface flow. The method is first detailed and its application to the shallow water equations is proposed, with some test cases such as dike- or dam-break problems with or without source terms. An application to a two-dimensional flow problem illustrates the superiority of direct sensitivity calculation over the classical empirical approach. [Copyright &y& Elsevier]

Abstract: MOD17A2 provides operational gross primary production (GPP) data globally at 1km spatial resolution and 8-day temporal resolution. MOD17A2 estimates GPP according to the light use efficiency (LUE) concept assuming a fixed maximum rate of carbon assimilation per unit photosynthetically active radiation absorbed by the vegetation (εmax). Minimum temperature and vapor pressure deficit derived from meteorological data down-regulate εmax and constrain carbon assimilation. This data is useful for regional to global studies of the terrestrial carbon budget, climate change and natural resources. In this study we evaluated the MOD17A2 product and its driver data by using in situ measurements of meteorology and eddy covariance GPP for 12 African sites. MOD17A2 agreed well with eddy covariance GPP for wet sites. Overall, seasonality was well captured but MOD17A2 GPP was underestimated for the dry sites located in the Sahel region. Replacing the meteorological driver data derived from coarse resolution reanalysis data with tower measurements reduced MOD17A2 GPP uncertainties, however, the underestimations at the dry sites persisted. Inferred εmax calculated from tower data was higher than the εmax prescribed in MOD17A2. This, in addition to uncertainties in fraction of absorbed photosynthetically active radiation (FAPAR) explains some of the underestimations. The results suggest that improved quality of driver data, but primarily a readjustment of the parameters in the biome parameter look-up table (BPLUT) may be needed to better estimate GPP for African ecosystems in MOD17A2. [Copyright &y& Elsevier]

Abstract: One of the most frequently applied methods for integrating controls on primary production through satellite data is the light use efficiency (LUE) approach, which links vegetation gross or net primary productivity (GPP or NPP) to remotely sensed estimates of absorbed photosynthetically active radiation (APAR). Eddy covariance towers provide continuous measurements of carbon flux, presenting an opportunity for evaluation of satellite estimates of GPP. Here we investigate relationships between eddy covariance estimated GPP, environmental variables derived from flux towers, Moderate Resolution Imaging Spectroradiometer (MODIS) enhanced vegetation index (EVI) and GPP across African savanna ecosystems. MODIS GPP was found to underestimate GPP at the majority of sites, particularly at sites in the Sahel. EVI was found to correlate well with estimated GPP on a site-by-site basis. Combining EVI with tower-measured PAR and evaporative fraction (EF, a measure of water sufficiency) improved the direct relationship between GPP and EVI at the majority of the sites. The slope of this relationship was strongly related to site peak leaf area index (LAI). These results are promising for the extension of GPP through the use of remote sensing data to a regional or even continental scale. [Copyright &y& Elsevier]