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

Analyses directionnelles multivariées de la qualité des précipitations sur la région de Québec

La question des précipitations acides est devenue une des principales préoccupations environnementales de ce siècle. Les dommages engendrés touchent l'ensemble des composantes atmosphérique, aquatique et terrestre de notre écosystème. Dans cet article, l'intérêt est tourné vers le transport des substances polluantes en faisant intervenir le vecteur des précipitations acides: le vent. Il existe une croyance populaire, largement répandue dans l'est du Canada, consistant à admettre que les vents d'est ou du nord sont associés à des précipitations faiblement chargées en éléments acides, contrairement aux vents du sud-ouest qui transporteraient les charges plus contaminées des industries situées dans le Midwest nord-américain. Une confirmation expérimentale de la réalité du phénomène est présentée ici.Une analyse factorielle des correspondances permet de mettre en évidence des relations entre la direction des vents et la composition chimique des précipitations. Des analyses de variance permettent ensuite de montrer la signification de l'effet de la direction des vents sur les concentrations de sulfates et de nitrates, en plus de mettre en évidence un effet saisonnier significatif pour ces deux variables. Les concentrations de nitrates et de sulfates associées aux vents de l'ouest sont respec- tivement de 0,33 mg/l-¹ et 1,73 mg/l-¹ comparativement à 0,24 mg/l-¹ et 1,48 mg/l-¹ pour les vents provenant de l'est. En ce qui concerne l'effet saisonnier, les concentrations moyennes de nitrates sont plus élevées durant les mois de janvier et de mars alors que les concentrations de sulfates sont plus elevées durant les mois d'été.The problem of acidic precipitation has become an important environmental concern; related damages can affect atmospheric, terrestrial and aquatic components of our ecosystem. This paper focuses on wind-driven atmospheric transport of contaminants, notably niirates and sulfates. Conventional wisdom in eastern Canada holds that winds originating from the east bring precipitation less loaded with acidic components than winds originating from the southwest; the latter carry contarninants generated by industries located in the American Midwest.An experimental confirmation of this phenomenon is presented here. SPERBER (1987) showed that hourly series of piecipitation content and wind direction, measured at a reception site are adequate to represent the lagrangian history of precipitating systems (New York City region). Following this result, we suppose that the northesastern continental atmospheric system is homogeneous enough so that winds measured at our reception site (Québec City region) are representative of the whole system. Thus, our experiment is performed in eulerian coordinates.The data bank used in the statistic alana|yses contains 10 time series: the weekly concentrations of 9 compounds found in the precipitation (H, Ca, Cl, K, Mg, Na, NO3, NH4 and SO4) gathered at the local Montmorency site and a s:ries ofweekly prevailing winds measured at the nearby Québec City airport. The time series contain 312 observations covering a full six year period (December 1981 to December 1987). As the original data bank of corcentrations is episodic, i.e. an obsercvation is available for each day with a significant precipitation event, volumes and loadings are used to derive the average weekly values of concentrations. In contrast, hourly series of direction (projected in 36 directions) and velocity of the prevailing winds are used to build, via a vectorial addition, a weekly series of wind direitions projected on a 12 point wind rose where directions corespond to the nind origin and not its destination.Classic statistical methods are used to deal with this data bank. Principal component analysis studies relationships between series of concentrations in the precipitations, while correspondence analysis highrights the relationships betwlen tile series of precipitation content and the series ofwind direction. The final statistical method, analysis of variance, is used to test the signilïcance of relationships higtrlighted by the correspondence analysis.The principal component analysis shows that all variables were positively correlated with the first component which reflects the fact that a higtrly loaded precipitation event will show high concentrations for each ofthe nine variables. The second component discriminates two groups of variables: one includes NO3, NH4 and SO4, the other Ca, Mg and Cl. The acidity variable, H, is nearer to the acid ion group (NO3, NH4 and SO4) than to the other ion group (Ca, Mg and Cl).The correspondence analysis shows that high concentrations of acidic compounds (NO3, NH4 and SO4) are highly rerated to winds from the W and WSW directions; conversely lower concentrations of the same compounds are associated with winds from the E and ENE directions. The elements Ca, Mg and Cl, reputed to be of oceanic origin, show high functional relationships between high concentrations and E, ENE winds and also between low concentrations and W, WSW winds. These results support the popular belief initially presented that acid precipitation is largely associated with winds from the southwest.The analyses of variance show that precipitation concentrations (NO3 and SO4) are significantly different according to the wind directions. Nitrate and sulfate concentrations associated with winds originating from the west are respectively 0.33-mg.l-l and 1.73 mg.l-l compared, to 0.24 mg.l-l and 1.48 mg.l-l for winds originating from the east. The analyses ofvariance also indicate a significant seasonal effect where mean monthly concentrations in nitrates are hilhest for winter months and early spring whereas sulfate concentrations are highest for the summer months

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

Dewetting of thin polymer films near the glass transition

Dewetting of ultra-thin polymer films near the glass transition exhibits unexpected front morphologies [G. Reiter, Phys. Rev. Lett., 87, 186101 (2001)]. We present here the first theoretical attempt to understand these features, focusing on the shear-thinning behaviour of these films. We analyse the profile of the dewetting film, and characterize the time evolution of the dry region radius, $R_{d}(t)$, and of the rim height, $h_{m}(t)$. After a transient time depending on the initial thickness, $h_{m}(t)$ grows like $\sqrt{t}$ while $R_{d}(t)$ increases like $\exp{(\sqrt{t})}$. Different regimes of growth are expected, depending on the initial film thickness and experimental time range.Comment: 4 pages, 5 figures Revised version, published in Physical Review Letters: F. Saulnier, E. Raphael and P.-G. de Gennes, Phys. Rev. Lett. 88, 196101 (2002

Dewetting of Glassy Polymer Films

Dynamics and morphology of hole growth in a film of power hardening viscoplastic solid (yield stress ~ [strain-rate]^n) is investigated. At short-times the growth is exponential and depends on the initial hole size. At long-times, for n > 1/3, the growth is exponential with a different exponent. However, for n < 1/3, the hole growth slows; the hole radius approaches an asymptotic value as time tends to infinity. The rim shape is highly asymmetric, the height of which has a power law dependence on the hole radius (exponent close to unity for 0.25 < n < 0.4). The above results explain recent intriguing experiments of Reiter, Phys. Rev. Lett, 87, 186101 (2001).Comment: 4 pages, 5 figures, RevTe

Effective Mitigation of Anchoring Bias, Projection Bias, and Representativeness Bias from Serious Game-based Training

AbstractAlthough human use of heuristics can result in ‘fast and frugal’ decision-making, those prepotent tendencies can also impair our ability to make optimal choices. Previous work had suggested such cognitive biases are resistant to mitigation training. Serious games offer a method to incorporate desirable elements into a training experience, and allow the use of mechanisms that enhance learning and retention. We developed a game to train recognition and mitigation of three forms of cognitive bias: anchoring, a tendency to be inordinately influenced by one piece of information; projection, an implicit assumption that others think or know what you do; and representativeness, judging the likelihood of a hypothesis by how much the available data resembles it. Participants were randomly assigned to play the training game once, twice spaced by 10 to 12 days, or a control condition that used a training video. External questionnaire-based assessments were given immediately post-training and 12 weeks later. Superior training was seen from the game. An independent group using our training game with their own novel bias assessment instruments (to which the researchers and game-developers had no access or content information) validated the key finding. These results demonstrate the viability and high value of using serious computer games to train mitigation of cognitive biases

Soluble tumor necrosis factor receptor 1 and 2 predict outcomes in advanced chronic kidney disease : a prospective cohort study

Background : Soluble tumor necrosis factor receptors 1 (sTNFR1) and 2 (sTNFR2) have been associated to progression of renal failure, end stage renal disease and mortality in early stages of chronic kidney disease (CKD), mostly in the context of diabetic nephropathy. The predictive value of these markers in advanced stages of CKD irrespective of the specific causes of kidney disease has not yet been defined. In this study, the relationship between sTNFR1 and sTNFR2 and the risk for adverse cardiovascular events (CVE) and all-cause mortality was investigated in a population with CKD stage 4-5, not yet on dialysis, to minimize the confounding by renal function. Patients and methods : In 131 patients, CKD stage 4-5, sTNFR1, sTNFR2 were analysed for their association to a composite endpoint of all-cause mortality or first non-fatal CVE by univariate and multivariate Cox proportional hazards models. In the multivariate models, age, gender, CRP, eGFR and significant comorbidities were included as covariates. Results : During a median follow-up of 33 months, 40 events (30.5%) occurred of which 29 deaths (22.1%) and 11 (8.4%) first non-fatal CVE. In univariate analysis, the hazard ratios (HR) of sTNFR1 and sTNFR2 for negative outcome were 1.49 (95% confidence interval (CI): 1.28-1.75) and 1.13 (95% CI: 1.06-1.20) respectively. After adjustment for clinical covariables (age, CRP, diabetes and a history of cardiovascular disease) both sTNFRs remained independently associated to outcomes (HR: sTNFR1: 1.51, 95% CI: 1.30-1.77; sTNFR2: 1.13, 95% CI: 1.06-1.20). A subanalysis of the non-diabetic patients in the study population confirmed these findings, especially for sTNFR1. Conclusion : sTNFR1 and sTNFR2 are independently associated to all-cause mortality or an increased risk for cardiovascular events in advanced CKD irrespective of the cause of kidney disease

Search for Exclusive Charmless Hadronic B Decays

We have searched for two-body charmless hadronic decays of $B$ mesons. Final states include $\pi\pi$, $K \pi$, and $KK$ with both charged and neutral kaons and pions; $\pi\rho$, $K \rho$, and $K^*\pi$; and $K\phi$, $K^*\phi$, and $\phi\phi$. The data used in this analysis consist of 2.6~million $B\bar{B}$~pairs produced at the $\Upsilon(4S)$ taken with the CLEO-II detector at the Cornell Electron Storage Ring (CESR). We measure the branching fraction of the sum of $B^0 \rightarrow \pi^+\pi^-$ and $B^0 \rightarrow K^+\pi^-$ to be $(1.8^{+0.6+0.2}_{-0.5-0.3}\pm0.2) \times 10^{-5}$. In addition, we place upper limits on individual branching fractions in the range from $10^{-4}$ to $10^{-6}$.Comment: 33 page LATEX file, uses REVTEX and psfig, 14 figures in a separate uuencoded postscript file, postscript version also available through http://w4.lns.cornell.edu/public/CLN