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

An Example of the Use of Interdigital PVDF Transducers to Generate and Receive a High Order Lamb Wave Mode in a Pipe

From a non-destructive evaluation point of view, Lamb waves are a highly attractive means of inspecting a large area of a structure from a single point. Interdigital PVDF transducers have been used previously in signal processing applications [1] to generate acoustic waves in piezoelectric substrates. This paper in conjunction with that of Monkhouse et al [2] aims to provide an overview of the work accomplished so far at Imperial College in the use of interdigital PVDF transducers to transmit and receive Lamb waves in certain structures for non-destructive evaluation purposes. Interdigital PVDF transducers may be permanently bonded to either flat of curved surfaces and this attribute together with their low cost means that they are potentially suitable for“smart structure” applications

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 Thor´e 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.JRC.G.9-Econometrics and applied statistic

Feature-guided waves for monitoring adhesive shear modulus in bonded stiffeners

Adhesively bonded stiffeners are employed in aerospace applications to increase structural stiffness. The potential of feature-guided wave modes for the verification of adhesion and curing state in difficult-to-access regions has been investigated. The properties of guided wave modes propagating along a T-shaped stiffener bonded to an aluminium plate were calculated using the Semi-Analytical Finite Element (SAFE) method. Feature-guided modes dominated by shearing motion were identified to be well suited, with energy concentrated at the stiffener and bond line, limiting energy radiation into the plate and thus maximising inspection length. The influences of the bond line stiffness and thickness on the guided wave behaviour were investigated using SAFE and 3D Finite Element calculations, and found to be significant. Experiments were conducted to measure the properties of the guided waves during the curing of an epoxy joint attaching a stiffener to a plate. The feature-guided mode was excited using a piezo-electric shear transducer and measured using a laser interferometer. The measured phase speed changed significantly during curing. The frequency dependency was found to match well with the SAFE calculations for a variation of the shear (Coulomb) modulus of the adhesive. The potential of the feature-guided shear wave mode for bond line inspection and monitoring has been shown and the choice of guided wave mode and frequency range for good sensitivity to the bond line state discussed

Arabidopsis Roots and Shoots Show Distinct Temporal Adaptation Patterns toward Nitrogen Starvation

Nitrogen (N) is an essential macronutrient for plants. N levels in soil vary widely, and plants have developed strategies to cope with N deficiency. However, the regulation of these adaptive responses and the coordinating signals that underlie them are still poorly understood. The aim of this study was to characterize N starvation in adult Arabidopsis (Arabidopsis thaliana) plants in a spatiotemporal manner by an integrative, multilevel global approach analyzing growth, metabolites, enzyme activities, and transcript levels. We determined that the remobilization of N and carbon compounds to the growing roots occurred long before the internal N stores became depleted. A global metabolite analysis by gas chromatography-mass spectrometry revealed organ-specific differences in the metabolic adaptation to complete N starvation, for example, for several tricarboxylic acid cycle intermediates, but also for carbohydrates, secondary products, and phosphate. The activities of central N metabolism enzymes and the capacity for nitrate uptake adapted to N starvation by favoring N remobilization and by increasing the high-affinity nitrate uptake capacity after long-term starvation. Changes in the transcriptome confirmed earlier studies and added a new dimension by revealing specific spatiotemporal patterns and several unknown N starvation-regulated genes, including new predicted small RNA genes. No global correlation between metabolites, enzyme activities, and transcripts was evident. However, this multilevel spatiotemporal global study revealed numerous new patterns of adaptation mechanisms to N starvation. In the context of a sustainable agriculture, this work will give new insight for the production of crops with increased N use efficiency

Variational methods

International audienceThis contribution presents derivative-based methods for local sensitivity analysis, called Variational Sensitivity Analysis (VSA). If one defines an output called the response function, its sensitivity to inputs variations around a nominal value can be studied using derivative (gradient) information. The main issue of VSA is then to provide an efficient way of computing gradients. This contribution first presents the theoretical grounds of VSA: framework and problem statement, tangent and adjoint methods. Then it covers pratical means to compute derivatives, from naive to more sophisticated approaches, discussing their various 2 merits. Finally, applications of VSA are reviewed and some examples are presented, covering various applications fields: oceanography, glaciology, meteorology

Elastic Wave Scattering from a Rough Strip-Like Crack

Ultrasonic nondestructive testing is a widely used method for searching for defects, e.g. cracks, in the nuclear power industry. Even though the method can be considered as wellestablished the theoretical understanding is far from complete, especially when more complicated situations are considered. Consequently, it is advantageous to have access to a good mathematical model of the testing procedure. Such a model can, for instance, be used to perform parametric studies, to develop testing procedures, for qualification purposes, and for education. Furthermore, systematic use of a well tested and validated simulation program will most likely result in a better physical understanding of the process. It should also be emphasized that experimental work is a very expensive alternative to mathematical modeling

Cloning and Characterization of Maize miRNAs Involved in Responses to Nitrogen Deficiency

Although recent studies indicated that miRNAs regulate plant adaptive responses to nutrient deprivation, the functional significance of miRNAs in adaptive responses to nitrogen (N) limitation remains to be explored. To elucidate the molecular biology underlying N sensing/signaling in maize, we constructed four small RNA libraries and one degradome from maize seedlings exposed to N deficiency. We discovered a total of 99 absolutely new loci belonging to 47 miRNA families by small RNA deep sequencing and degradome sequencing, as well as 9 new loci were the paralogs of previously reported miR169, miR171, and miR398, significantly expanding the reported 150 high confidence genes within 26 miRNA families in maize. Bioinformatic and subsequent small RNA northern blot analysis identified eight miRNA families (five conserved and three newly identified) differentially expressed under the N-deficient condition. Predicted and degradome-validated targets of the newly identified miRNAs suggest their involvement in a broad range of cellular responses and metabolic processes. Because maize is not only an important crop but is also a genetic model for basic biological research, our research contributes to the understanding of the regulatory roles of miRNAs in plant adaption to N-deficiency stress