maximum principles and singular elliptic inequalities abstract in this paper we present a version of the omori yau maximum principle a liouville type result and a phragmen lindeloff type theorem for a class of singular elliptic operators on a riemannian manifold which include the p laplacian and the mean curvature operator some applications of the results obtained are discussed

recursive bayesian estimation of conceptual rainfall runoff model errors in real time prediction of streamflow conceptual rainfall runoff models account for the spatial dynamics of hydrological processes in a basin using simple spatially lumped storage flow relations such rough approximations introduce model errors that are often difficult to characterize here we develop and apply a methodology that recursively estimates and accounts for model errors in real time streamflow prediction settings by adding time dependent random noise to the internal states storages of the hydrological model magnitude of the added noise depends on a precision inverse variance parameter that is estimated from rainfall runoff data a recursive bayesian technique is used for estimation posteriors of hydrological parameters and states are updated through time with an ensemble kalman filter whereas the posterior of the precision parameter is updated recursively using a novel gamma density approximation technique applying this algorithm to different model error scenarios allows identification of the main source of model errors the methodology is applied to short term streamflow prediction with the hymod rainfall runoff model in a semi cold semi humid basin in iran results show that i streamflow prediction in this snow dominated basin is more affected by model errors in the slow flow than the quick flow component of the model ii accounting for model errors in the slow flow component improves both low and high flow predictions and iii predictive performance further improves by accounting for hymod parameter uncertainty in addition to model errors overall accounting for model errors increased nash sutcliffe efficiency by 1 5 reduced mean absolute error by 2 43 and improved probabilistic predictive performance by 50 80

development of a formal likelihood function for improved bayesian inference of ephemeral catchments 1 the application of formal bayesian inferential approaches in hydrologic modeling is often criticized for requiring explicit assumptions to be made about the distribution of the errors via the likelihood function these assumptions can be adequate in some situations but often little attention is paid to the selection of an appropriate likelihood function this paper investigates the application of bayesian methods in modeling ephemeral catchments we consider two modeling case studies including a synthetically generated data set and a real data set of an arid australian catchment the case studies investigate some typical forms of the likelihood function which have been applied widely by previous researchers as well as introducing new implementations aimed at better addressing likelihood function assumptions in dry catchments the results of the case studies indicate the importance of explicitly accounting for model residuals that are highly positively skewed due to the presence of many zeros zero inflation arising from the dry spells experienced by the catchment specifically the form of the likelihood function was found to significantly impact the calibrated parameter posterior distributions which in turn have the potential to greatly affect the uncertainty estimates in each application the likelihood function that explicitly accounted for the nonconstant variance of the errors and the zero inflation of the errors resulted in 1 equivalent or better fits to the observed discharge in both timing and volume 2 superior estimation of the uncertainty as measured by the reliability and sharpness metrics and 3 more linear quantile quantile plots indicating the errors were more closely matched to the assumptions of this form of the likelihood function

probabilistic optimization for conceptual rainfall runoff models a comparison of the shuffled complex evolution and simulated annealing algorithms automatic optimization algorithms are used routinely to calibrate conceptual rainfall runoff crr models the goal of calibration is to estimate a feasible and unique global set of parameter estimates that best fit the observed runoff data most if not all optimization algorithms have difficulty in locating the global optimum because of response surfaces that contain multiple local optima with regions of attraction of differing size discontinuities and long ridges and valleys extensive research has been undertaken to develop efficient and robust global optimization algorithms over the last 10 years this study compares the performance of two probabilistic global optimization methods the shuffled complex evolution algorithm sce ua and the three phase simulated annealing algorithm sa sx both algorithms are used to calibrate two parameter sets of a modified version of boughton s 1984 sfb model using data from two australian catchments that have low and high runoff yields for the reduced well identified parameter set the algorithms have a similar efficiency for the low yielding catchment but sce ua is almost twice as robust although the robustness of the algorithms is similar for the high yielding catchment sce ua is six times more efficient than sa sx when fitting the full parameter set the performance of sa sx deteriorated markedly for both catchments these results indicated that sce ua s use of multiple complexes and shuffling provided a more effective search of the parameter space than sa sx s single simplex with stochastic step acceptance criterion especially when the level of parameterization is increased examination of the response surface for the low yielding catchment revealed some reasons why sce ua outperformed sa sx and why probabilistic optimization algorithms can experience difficulty in locating the global optimum

momcmc an efficient monte carlo method for multi objective sampling over real parameter space in this paper we present a new population based monte carlo method so called momcmc multi objective markov chain monte carlo for sampling in the presence of multiple objective functions in real parameter space the momcmc method is designed to address the multi objective sampling problem which is not only of interest in exploring diversified solutions at the pareto optimal front in the function space of multiple objective functions but also those near the front momcmc integrates differential evolution de style crossover into markov chain monte carlo mcmc to adaptively propose new solutions from the current population the significance of dominance is taken into consideration in momcmc s fitness assignment scheme while balancing the solution s optimality and diversity moreover the acceptance rate in momcmc is used to control the sampling bandwidth of the solutions near the pareto optimal front as a result the computational results of momcmc with the high dimensional zdt benchmark functions demonstrate its efficiency in obtaining solution samples at or near the pareto optimal front compared to moscem multiobjective shuffled complex evolution metropolis an existing monte carlo sampling method for multi objective optimization momcmc exhibits significantly faster convergence to the pareto optimal front furthermore with small population size momcmc also shows effectiveness in sampling complicated multi objective function space

state and parameter estimation of hydrologic models using the constrained ensemble kalman filter 1 data assimilation techniques such as the kalman filter kf and its extensions update state variables based on the kf type of algorithms but state space models usually have relevant physical laws or settings the updated states by the kf may violate some physical constraints which can be equality or inequality and linear or nonlinear constraints this paper presents three methods the naive method the projection method and the accept reject method to incorporate constraints into the ensemble kalman filter enkf essentially the projection method projects the updated ensemble members from the unconstrained enkf to the feasible space characterized by the constraints the accept reject method tries to enforce the updated states to obey the constraints by resampling the observation error and model error the three methods are applied to a conceptual hydrologic model for state estimation and sequential parameter learning with specific treatment of inequality constraints both the reject accept and projection methods perform better than the naive method which treats the hard constraint in a simple way and ignores other constraints it is easy to implement the accept reject method the performance of which is comparable to the projection method regarding both the estimation quality and the computational time with the case study

efficient prediction uncertainty approximation in the calibration of environmental simulation models 1 this paper is aimed at improving the efficiency of model uncertainty analyses that are conditioned on measured calibration data specifically the focus is on developing an alternative methodology to the generalized likelihood uncertainty estimation glue technique when pseudolikelihood functions are utilized instead of a traditional statistical likelihood function we demonstrate for multiple calibration case studies that the most common sampling approach utilized in glue applications uniform random sampling is much too inefficient and can generate misleading estimates of prediction uncertainty we present how the new dynamically dimensioned search dds optimization algorithm can be used to independently identify multiple acceptable or behavioral model parameter sets in two ways dds could replace random sampling in typical applications of glue more importantly we present a new practical and efficient uncertainty analysis methodology called dds approximation of uncertainty dds au that quantifies prediction uncertainty using prediction bounds rather than prediction limits results for 13 14 26 and 30 parameter calibration problems show that dds au can be hundreds or thousands of times more efficient at finding behavioral parameter sets than glue with random sampling results for one example show that for the same limited computational effort dds au prediction bounds can simultaneously be smaller and contain more of the measured data in comparison to glue prediction bounds we also argue and then demonstrate that within the glue framework when behavioral parameter sets are not sampled frequently enough latin hypercube sampling does not offer any improvements over simple random sampling

a new bayesian recursive technique for parameter estimation 1 the performance of any model depends on how well its associated parameters are estimated in the current application a localized bayesian recursive estimation lobare approach is devised for parameter estimation the lobare methodology is an extension of the bayesian recursive estimation bare method it is applied in this paper on two different types of models an artificial intelligence ai model in the form of a support vector machine svm application for forecasting soil moisture and a conceptual rainfall runoff crr model represented by the sacramento soil moisture accounting sac sma model support vector machines based on statistical learning theory slt represent the modeling task as a quadratic optimization problem and have already been used in various applications in hydrology they require estimation of three parameters sac sma is a very well known model that estimates runoff it has a 13 dimensional parameter space in the lobare approach presented here bayesian inference is used in an iterative fashion to estimate the parameter space that will most likely enclose a best parameter set this is done by narrowing the sampling space through updating the parent bounds based on their fitness these bounds are actually the parameter sets that were selected by bare runs on subspaces of the initial parameter space the new approach results in faster convergence toward the optimal parameter set using minimum training calibration data and fewer sets of parameter values the efficacy of the localized methodology is also compared with the previously used bare algorithm

assessing the impacts of parameter uncertainty for computationally expensive groundwater models 1 computational requirements often limit the assessment of uncertainty in complex environmental models monte carlo based techniques such as generalized likelihood uncertainty estimation glue and bayesian uncertainty assessment are limited in applicability because of their heavy computational demands this paper presents a computationally efficient method that combines automatic calibration using function approximation based global optimization with importance weighting for assessing parametric uncertainty in model outputs for computationally expensive models we call this method automatic calibration and uncertainty assessment using response surfaces acuars the bias introduced during optimization because of oversampling of high goodness of fit regions of the parameter space is corrected using a multidimensional cell declustering technique the proposed method is applied to two hypothetical examples in enhanced bioremediation of chlorinated ethenes in groundwater that differ in computational requirements and the number of parameters that were calibrated the results from the simpler example in which uncertainty of three model parameters in model outputs was considered showed that for a given acceptability threshold and a given number of permissible model simulations acuars finds many more representative parameter sets than glue glue produced only half the number of acceptable parameter sets for uncertainty assessment even after 10 times as many simulations as acuars was performed for glue further the median output of acuars predicted the true value of the outputs more closely than glue for a more complicated numerical example where noisy data were used for calibration of seven model parameters glue required 2400 simulations to find 31 acceptable parameter sets while acuars found 46 acceptable parameter sets in only 300 simulations for a moderately stringent threshold this enabled a more accurate estimate of uncertainty by providing closer estimates of the true outputs

multivariate calibration of a water and energy balance model in the spectral domain 1 the objective of this paper is to explore the possibility of using multiple variables in the calibration of hydrologic models in the spectral domain a simple water and energy balance model was used combined with observations of the energy balance and the soil moisture profile the correlation functions of the model outputs and the observations for the different variables have been calculated after the removal of the diurnal cycle of the energy balance variables these were transformed to the frequency domain to obtain spectral density functions which were combined in the calibration algorithm it has been found that it is best to use the square root of the spectral densities in the parameter estimation under these conditions spectral calibration performs almost equally as well as time domain calibration using least squares differences between observed and simulated time series incorporation of the spectral coefficients of the cross correlation functions did not improve the results of the calibration calibration on the correlation functions in the time domain led to worse model performance when the meteorological forcing and model calibration data are not overlapping in time spectral calibration has been shown to lead to an acceptable model performance overall the results in this paper suggest that in case of data scarcity multivariate spectral calibration can be an attractive tool to estimate model parameters

separately accounting for uncertainties in rainfall and runoff calibration of event based conceptual hydrological models in small urban catchments using bayesian method 1 uncertainty analysis of hydrological models is usually based on model calibration and the bayesian method is a popular way to evaluate the uncertainty the traditional bayesian method usually uses lumped model residuals to form the likelihood function where uncertainty in inputs rainfall is not explicitly addressed this paper compares three approaches based on bayesian inferences considering rainfall uncertainty either implicitly or explicitly in calibration consistent parameter estimation and reliable quantification of predictive uncertainty are mainly examined when rainfall uncertainty is explicitly treated in calibration several rainfall observations at one minute time steps are grouped to share one multiplier to consider the possible observation errors the appropriate grouping strategy that balances the representativeness and the complexity of the problem is suggested the application of the methods considered in this study focuses on small urban catchments 200 ha with a small temporal scale 1 min time step in contrast to most literature studies dealing with larger catchments monitored at larger time steps it is found that uncertainty in rainfall has a minor contribution to the total uncertainty in runoff estimation and this minor role can be explained by the low pass filter effect of the linear reservoir model however the approach explicitly accounting for input uncertainty results in more informed knowledge for uncertainties related with hydrological model calibrations which can possibly provide an estimation of uncertainty attributed to rainfall records it should be noted that rainfall error estimates can compensate model structural uncertainty that is not explicitly addressed in this study

baker campbell hausdorff relations for supergroups one parameter subgroups the exponential mapping and canonical coordinates have previously been defined for connected supergroups in this paper a technique for obtaining analytical expressions linking different coordinate schemes for supergroups is presented these are the baker campbell hausdorff relations the method is illustrated in detail with the examples of supergroups based on the supersymmetric quantum mechanical superalgebra sqm 2 and on the inonu wigner contraction isop 1 2 of the simple superalgebra osp 1 2

global properties of supermanifolds we construct new examples of supermanifolds and determine the vector bundle structure of the supermanifolds commonly used in physics we show that any supermanifold admits a foliation whose leaves are locally tangent to the soul directions in the coordinate charts and which is one of a nested sequence of foliations we point out that the existence of these foliations implies restrictions on the possible topologies of supermanifolds for example a compact supermanifold with a single even dimension must have vanishing euler characteristic we also show that a globally defined superfield on a nice compact supermanifold must be constant along the leaves of the foliations by this mechanism the global topology of a supermanifold can be used to impose physically interesting constraints on superfields as an example we exhibit a supermanifold which has the local geometry of flat superspace but is such that all globally defined superfields are chiral

a hybrid shuffled complex evolution approach based on differential evolution for unconstrained optimization numerous optimization methods have been proposed for the solution of the unconstrained optimization problems such as mathematical programming methods stochastic global optimization approaches and metaheuristics in this paper a metaheuristic algorithm called modified shuffled complex evolution msce is proposed where an adaptation of the downhill simplex search strategy combined with the differential evolution method is proposed the efficiency of the new method is analyzed in terms of the mean performance and computational time in comparison with the genetic algorithm using floating point representation gaf and the classical shuffled complex evolution sce ua algorithm using six benchmark optimization functions simulation results and the comparisons with sce ua and gaf indicate that the msce improves the search performance on the five benchmark functions of six tested functions

reducing hydrologic model uncertainty in monthly streamflow predictions using multimodel combination 1 model errors are inevitable in any prediction exercise one approach that is currently gaining attention in reducing model errors is by combining multiple models to develop improved predictions the rationale behind this approach primarily lies on the premise that optimal weights could be derived for each model so that the developed multimodel predictions will result in improved predictions a new dynamic approach mm 1 to combine multiple hydrological models by evaluating their performance skill contingent on the predictor state is proposed we combine two hydrological models abcd model and variable infiltration capacity vic model to develop multimodel streamflow predictions to quantify precisely under what conditions the multimodel combination results in improved predictions we compare multimodel scheme mm 1 with optimal model combination scheme mm o by employing them in predicting the streamflow generated from a known hydrologic model abcd model orvicmodel with heteroscedastic error variance as well as from a hydrologic model that exhibits different structure than that of the candidate models i e abcd model or vic model results from the study show that streamflow estimated from single models performed better than multimodels under almost no measurement error however under increased measurement errors and model structural misspecification both multimodel schemes mm 1 and mm o consistently performed better than the single model prediction overall mm 1 performs better than mm o in predicting the monthly flow values as well as in predicting extreme monthly flows comparison of the weights obtained from each candidate model reveals that as measurement errors increase mm 1 assigns weights equally for all the models whereas mm o assigns higher weights for always the best performing candidate model under the calibration period applying the multimodel algorithms for predicting streamflows over four different sites revealed that mm 1 performs better than all single models and optimal model combination scheme mm o in predicting the monthly flows as well as the flows during wetter months

effective and efficient global optimization for conceptual rainfall runoff models the successful application of a conceptual rainfall runoff crr model depends on how well it is calibrated despite the popularity of crr models reports in the literature indicate that it is typically difficult if not impossible to obtain unique optimal values for their parameters using automatic calibration methods unless the best set of parameters associated with a given calibration data set can be found it is difficult to determine how sensitive the parameter estimates and hence the model forecasts are to factors such as input and output data error model error quantity and quality of data objective function used and so on results are presented that establish clearly the nature of the multiple optima problem for the research crr model sixpar these results suggest that the crr model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets next the performance of three existing global search procedures are evaluated on the model sixpar finally a powerful new global optimization procedure is presented entitled the shuffled complex evolution sce ua method which was able to consistently locate the global optimum of the sixpar model and appears to be capable of efficiently and effectively solving the crr model optimization problem

a multisignal automatic calibration methodology for hydrochemical models a case study of the birkenes model most hydrochemical models employ immeasurable or artificial parameters that need to be estimated from calibration data a methodology is presented here for the automatic calibration of artificial parameters which improves parameter identifiability through increasing the information available for determining the parameter values instead of calibrating the model using only one signal e g the hydrograph multiple signals e g chemical signals as well as the hydrograph are considered simultaneously either a simple least squares or a weighted least squares objective function may be used the methodology is applied to the hydrologic module of the birkenes hydrochemical model using artificial data from a wide range of starting points a gradient search optimization technique is able to consistently locate the correct parameter values uniformly better when using two signals the hydrograph and a conservative tracer than when only one signal the hydrograph is used

keller osserman conditions for diffusion type operators on riemannian manifolds abstract in this paper we obtain essentially sharp generalized keller osserman conditions for wide classes of differential inequalities of the form l u b x f u l u and l u b x f u l u g u h u on weighted riemannian manifolds where l is a non linear diffusion type operator prototypical examples of these operators are the p laplacian and the mean curvature operator the geometry of the underlying manifold is reflected via bounds for the modified bakry emery ricci curvature by growth conditions for the functions b and l a weak maximum principle which extends and improves previous results valid for the laplacian is also obtained geometric comparison results valid even in the case of integral bounds for the modified bakry emery ricci tensor are presented

state and bias estimation for soil moisture profiles by an ensemble kalman filter effect of assimilation depth and frequency 1 an ensemble kalman filter for state estimation and a bias estimation algorithm were applied to estimate individual soil moisture profiles in a small corn field with the clm2 0 model through the assimilation of measurements from capacitance probes both without and with inclusion of bias correction the effect of the assimilation frequency the assimilation depth and the number of observations assimilated per profile were studied assimilation of complete profiles had the highest impact on deeper soil layers and the optimal assimilation frequency was about 1 2 weeks if bias correction was applied the optimal assimilation depth depended on the calibration results assimilation in the surface layer had typically less impact than assimilation in other layers through bias correction the soil moisture estimate greatly improved in general the correct propagation of the innovations for both the bias blind state and bias filtering from any layer to other layers was insufficient the approximate estimation of the a priori bias error covariance and the choice of a zero initialized persistent bias model made it impossible to estimate the bias in layers for which no observations were available

locally conformally flat quasi einstein manifolds in this paper we prove that any complete locally conformally flat quasi einstein man ifold of dimension n 3 is locally a warped product with n 1 dimensional fibers of constant curvature this result includes also the case of locally conformally flat gradient ricci solitons

improving the shuffled complex evolution scheme for optimization of complex nonlinear hydrological systems application to the calibration of the sacramento soil moisture accounting model 1 an innovative algorithm shuffled complexes with principal components analysis sp uci is developed to overcome a critical deficiency of the shuffled complex evolution scheme population degeneration population degeneration means that during the evolutionary search process the population of search particles may degenerate into a subspace of the full parameter space thereby missing the capacity of fully exploring the parameter space being confined in a subspace may even lead the particle population to converge to nonstationary points which is a fatal malfunction to overcome this problem sp uci employs the principal components analysis to detect the occurrence of population degeneration and remedy the adverse effects the ensemble of calibrations of the sacramento soil moisture accounting model with the sp uci method over the leaf river basin mississippi retrieves the optimal parameter values with the lowest recorded root mean squared error of simulated daily runoff against the observation moreover the result also provides consistent narrow ranges model parameter distribution which results in a better understanding of the model s behavior given the watershed s hydrologic features

corruption of accuracy and efficiency of markov chain monte carlo simulation by inaccurate numerical implementation of conceptual hydrologic models conceptual rainfall runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics reliance on first order explicit fixed step integration methods leads to computationally cheap simulation models that are easy to implement computational speed is especially desirable for estimating parameter and predictive uncertainty using markov chain monte carlo mcmc methods confirming earlier work of kavetski et al 2003 we show here that the computational speed of first order explicit fixed step integration methods comes at a cost for a case study with a spatially lumped conceptual rainfall runoff model it introduces artificial bimodality in the marginal posterior parameter distributions which is not present in numerically accurate implementations of the same model the resulting effects on mcmc simulation include 1 inconsistent estimates of posterior parameter and predictive distributions 2 poor performance and slow convergence of the mcmc algorithm and 3 unreliable convergence diagnosis using the gelman rubin statistic we studied several alternative numerical implementations to remedy these problems including various adaptive step finite difference schemes and an operator splitting method our results show that adaptive step second order methods based on either explicit finite differencing or operator splitting with analytical integration provide the best alternative for accurate and efficient mcmc simulation fixed step or adaptive step implicit methods may also be used for increased accuracy but they cannot match the efficiency of adaptive step explicit finite differencing or operator splitting of the latter two explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically as the splitting method then loses its advantage

on the role of gradient terms in coercive quasilinear differential inequalities on carnot groups abstract in the sub riemannian setting of carnot groups this work investigates a priori estimates and liouville type theorems for solutions of coercive quasilinear differential inequalities of the type g u b x f u l u prototype examples of g are the subelliptic p laplacian and the mean curvature operator the main novelty of the present paper is that we allow a dependence on the gradient l t that can vanish both as t 0 and as t our results improve on the recent literature and by means of suitable counterexamples we show that the range of parameters in the main theorems are sharp

application of temporal streamflow descriptors in hydrologic model parameter estimation 1 this paper presents a parameter estimation approach based on hydrograph descriptors that capture dominant streamflow characteristics at three timescales monthly yearly and record extent the scheme entitled hydrograph descriptors multitemporal sensitivity analyses hydmus yields an ensemble of model simulations generated from a reduced parameter space based on a set of streamflow descriptors that emphasize the timescale dynamics of streamflow record in this procedure the posterior distributions of model parameters derived at coarser timescales are used to sample model parameters for the next finer timescale the procedure was used to estimate the parameters of the sacramento soil moisture accounting model sac sma for the leaf river mississippi the results indicated that in addition to a significant reduction in the range of parameter uncertainty hydmus improved parameter identifiability for all 13 of the model parameters the performance of the procedure was compared to four previous calibration studies on the same watershed although our application of hydmus did not explicitly consider the error at each simulation time step during the calibration process the model performance was in some important respects found to be better than in previous deterministic studies

estimating effective model parameters for heterogeneous unsaturated flow using error models for bias correction 1 estimates of effective parameters for unsaturated flow models are typically based on observations taken on length scales smaller than the modeling scale this complicates parameter estimation for heterogeneous soil structures in this paper we attempt to account for soil structure not present in the flow model by using so called external error models which correct for bias in the likelihood function of a parameter estimation algorithm the performance of external error models are investigated using data from three virtual reality experiments and one real world experiment all experiments are multistep outflow and inflow experiments in columns packed with two sand types with different structures first effective parameters for equivalent homogeneous models for the different columns were estimated using soil moisture measurements taken at a few locations this resulted in parameters that had a low predictive power for the averaged states of the soil moisture if the measurements did not adequately capture a representative elementary volume of the heterogeneous soil column second parameter estimation was performed using error models that attempted to correct for bias introduced by soil structure not taken into account in the first estimation three different error models that required different amounts of prior knowledge about the heterogeneous structure were considered the results showed that the introduction of an error model can help to obtain effective parameters with more predictive power with respect to the average soil water content in the system this was especially true when the dynamic behavior of the flow process was analyzed

on the theory of one parameter subgroups of supergroups the one parameter subgroups of supergroups are defined and their primary properties are delineated parametrization schemes analogous to those used in lie group theory are investigated in particular exponentiation is introduced and related to the one parameter subgroups canonical coordinates of three kinds are investigated the third of which has no analog in conventional lie theory we illustrate our results with the examples of the supersymmetric quantum mechanical superalgebra sqm 2 and the simple superalgebra osp 1 2

efficient regularization and uncertainty analysis using a global optimization methodology 1 the concept of the pareto front has received considerable attention in the model calibration literature particularly in conjunction with global search optimizers that have been developed for use in contexts where objective function surfaces are pitted with local optima or characterized by multiple broad regions of attraction in parameter space in this paper use of the pareto concept in such calibration contexts is extended to include regularization and model predictive uncertainty analysis both of these processes can be formulated as constrained optimization problems in which a trade off is analyzed between a set of constraints on model parameters on the one hand and maximization minimization of one or a number of model outputs of interest on the other hand in both cases the optimal trade off point though being calculable on a theoretical basis for synthetic cases must be chosen subjectively when working with real world models two cases are presented to illustrate the methodology one a synthetic groundwater model and the other a real world surface water model

correcting for forecast bias in soil moisture assimilation with the ensemble kalman filter 1 land surface models are usually biased in at least a subset of the simulated variables even after calibration bias estimation may therefore be needed for data assimilation here in situ soil moisture profile observations in a small agricultural field were merged with community land model clm2 0 simulations using different algorithms for state and forecast bias estimation with and without bias correction feedback simple state updating with the conventional ensemble kalman filter enkf allows for some implicit forecast bias correction it is possible to estimate the soil moisture bias explicitly and derive superior soil moisture estimates with a generalized enkf that uses a simple persistence model for the bias and assumes that the a priori bias error covariance is proportional to the a priori state error covariance for the case of bi weekly assimilation of the entire profile of soil moisture observations bias estimation and correction typically reduces the rmse in soil moisture over the standard enkf without bias correction by around 60 percent however under the above assumptions significant improvements are limited to state variables for which observations are available therefore it is crucial to measure the state variables of interest the best variant for state and bias estimation depends on the nature of the model bias and the output of interest to the user in a model that is only biased for soil moisture large and frequent increments for soil moisture updating may be required which in turn may negatively impact the water balance and output fluxes it is then better to post process the soil moisture with the bias analysis without updating the model state

bayesian calibration of a large scale geothermal reservoir model by a new adaptive delayed acceptance metropolis hastings algorithm 1 the aim of this research is to estimate the parameters of a large scale numerical model of a geothermal reservoir using markov chain monte carlo mcmc sampling within the framework of bayesian inference all feasible parameters that are consistent with the measured data are summarized by the posterior distribution and hence parameter estimation and uncertainty quantification are both given by calculating expected values of statistics of interest over the posterior distribution it appears to be computationally infeasible to use the standard metropolis hastings algorithm mh to sample the high dimensional computationally expensive posterior distribution to improve the sampling efficiency a new adaptive delayed acceptance mh algorithm adamh is implemented to adaptively build a stochastic model of the error introduced by the use of a reduced order model this use of adaptivity differs from existing adaptive mcmc algorithms that tune proposal distributions of the metropolis hastings algorithm mh though adamh also implements that technique for the 3 d geothermal reservoir model we present here adamh shows a great improvement in the computational efficiency of the mcmc sampling and promising results for parameter estimation and uncertainty quantification are obtained this algorithm could offer significant improvement in computational efficiency when implementing sample based inference in other large scale inverse problems

calibration of a water and energy balance model recursive parameter estimation versus particle swarm optimization 1 it is well known that one of the major problems in the application of land surface models is the determination of the various model parameters in most cases only one or a limited number of variables are used to estimate these parameters this study evaluates the use of two fundamentally different global optimization methods multistart weight adaptive recursive parameter estimation mwarpe and particle swarm optimization pso for the estimation of hydrologic model parameters on the basis of data for multiple variables mwarpe iteratively uses the linear recursive filter equations in a monte carlo setting and therefore does not rely on the explicit minimization of an objective function however a major drawback of the mwarpe method is the high dimensionality determined by the number of observations of the matrix to be inverted on the other hand pso is a stochastic optimization method based on the collective strength of a population of individuals with flocking or herding behavior as observed in a wide number of biological systems in situ observations of net radiation latent sensible and ground heat fluxes and the soil moisture profile are used to determine the parameters of a simplified water and energy balance model both optimization methods are analyzed in terms of model performance and computational efficiency comparable results expressed in terms of the root mean square error values were obtained for both methods however it was found that mwarpe tends to slightly overfit the data

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

geometric convergence and central limit theorems for multidimensional hastings and metropolis algorithms we develop results on geometric ergodicity of markov chains and apply these and other recent results in markov chain theory to multidimensional hastings and metropolis algorithms for those based on random walk candidate distributions we find sufficient conditions for moments and moment generating functions to converge at a geometric rate to a prescribed distribution by phrasing the conditions in terms of the curvature of the densities we show that the results apply to all distributions with positive densities in a large class which encompasses many commonly used statistical forms from these results we develop central limit theorems for the metropolis algorithm converse results showing non geometric convergence rates for chains where the rejection rate is not bounded away from unity are also given these show that the negative definiteness property is not redundant

dynamic averaging of rainfall runoff model simulations from complementary model parameterizations 1 in this paper we analyze how our evaluation of the capacity of a rainfall runoff model to represent low or high flows depends on the objective function used during the calibration process we present a method to combine models to produce a more satisfactory streamflow simulation on the basis of two different parameterizations of the same model where we previously had to choose between a more efficient simulation for either high flows or low flows but inevitably less efficient in the other range we show that a balanced simulation can be obtained by using a seasonal index to weigh the two simulations providing good efficiency in both low and high flows

ensemble evaluation of hydrological model hypotheses it is demonstrated for the first time how model parameter structural and data uncertainties can be accounted for explicitly and simultaneously within the generalized likelihood uncertainty estimation glue methodology as an example application 72 variants of a single soil moisture accounting store are tested as simplified hypotheses of runoff generation at six experimental grassland field scale lysimeters through model rejection and a novel diagnostic scheme the fields designed as replicates exhibit different hydrological behaviors which yield different model performances for fields with low initial discharge levels at the beginning of events the conceptual stores considered reach their limit of applicability conversely one of the fields yielding more discharge than the others but having larger data gaps allows for greater flexibility in the choice of model structures as a model learning exercise the study points to a leaking of the fields not evident from previous field experiments it is discussed how understanding observational uncertainties and incorporating these into model diagnostics can help appreciate the scale of model structural error

a shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters author s vrugt ja gupta hv bouten w sorooshian s abstract markov chain monte carlo mcmc methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models however mcmc methods require the a priori definition of a proposal or sampling distribution which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the markov chain and its rate of convergence in this paper we present an mcmc sampler entitled the shuffled complex evolution metropolis algorithm scem ua which is well suited to infer the posterior distribution of hydrologic model parameters the scem ua algorithm is a modified version of the original sce ua global optimization algorithm developed by duan et al 1992 the scem ua algorithm operates by merging the strengths of the metropolis algorithm controlled random search competitive evolution and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution three case studies demonstrate that the adaptive capability of the scem ua algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional metropolis hastings samplers

calibration of rainfall runoff models application of global optimization to the sacramento soil moisture accounting model conceptual rainfall runoff models are difficult to calibrate by means of automatic methods one major reason for this is the inability of conventional procedures to locate the globally optimal set of parameters this paper investigates the consistency with which two global optimization methods the shuffled complex evolution sce ua method developed by the authors and the multistart simplex msx method are able to find the optimal parameter set during calibration of the sacramento soil moisture accounting model sac sma of the national weather service river forecast system nwsrfs in the first phase of this study error free synthetic data are used to conduct a comparative evaluation of the algorithms under ideal conditions in 10 independent trials of each algorithm in which 13 parameters of the sac sma model were optimized simultaneously the sce ua method achieved a 100 success rate in locating the precise global optimum i e the true parameter values while the msx method failed in all trials even with more than twice the number of function evaluations in the second phase historical data from the leaf river watershed are used to conduct a comparative evaluation of the algorithms under real conditions using two different estimation criteria drms and hmle the sce ua algorithm obtained consistently lower function values and more closely grouped parameter estimates while using one third fewer function evaluations than the msx algorithm

adaptive markov chain monte carlo through regeneration abstract markov chain monte carlo mcmc is used for evaluating expectations of functions of interest under a target distribution this is done by calculating averages over the sample path of a markov chain having as its stationary distribution for computational efficiency the markov chain should be rapidly mixing this sometimes can be achieved only by careful design of the transition kernel of the chain on the basis of a detailed preliminary exploratory analysis of an alternative approach might be to allow the transition kernel to adapt whenever new features of are encountered during the mcmc run however if such adaptation occurs infinitely often then the stationary distribution of the chain may be disturbed we describe a framework based on the concept of markov chain regeneration which allows adaptation to occur infinitely often but does not disturb the stationary distribution of the chain or the consistency of sample path averages

a new selection metric for multiobjective hydrologic model calibration a novel selection metric called convex hull contribution chc is introduced for solving multiobjective mo optimization problems with pareto fronts that can be accurately approximated by a convex curve the hydrologic model calibration literature shows that many biobjective calibration problems with a proper setup result in such pareto fronts the chc selection approach identifies a subset of archived nondominated solutions whose map in the objective space forms convex approximation of the pareto front the optimization algorithm can sample solely from these solutions to more accurately approximate the convex shape of the pareto front it is empirically demonstrated that chc improves the performance of pareto archived dynamically dimensioned search pa dds when solving mo problems with convex pareto fronts this conclusion is based on the results of several benchmark mathematical problems and several hydrologic model calibration problems with two or three objective functions the impact of chc on pa dds performance is most evident when the computational budget is somewhat limited it is also demonstrated that 1 000 solution evaluations limited budget in this study is sufficient for pa dds with chc based selection to achieve very high quality calibration results relative to the results achieved after 10 000 solution evaluations

combining multiobjective optimization and bayesian model averaging to calibrate forecast ensembles of soil hydraulic models 1 most studies in vadose zone hydrology use a single conceptual model for predictive inference and analysis focusing on the outcome of a single model is prone to statistical bias and underestimation of uncertainty in this study we combine multiobjective optimization and bayesian model averaging bma to generate forecast ensembles of soil hydraulic models to illustrate our method we use observed tensiometric pressure head data at three different depths in a layered vadose zone of volcanic origin in new zealand a set of seven different soil hydraulic models is calibrated using a multiobjective formulation with three different objective functions that each measure the mismatch between observed and predicted soil water pressure head at one specific depth the pareto solution space corresponding to these three objectives is estimated with amalgam and used to generate four different model ensembles these ensembles are postprocessed with bma and used for predictive analysis and uncertainty estimation our most important conclusions for the vadose zone under consideration are 1 the mean bma forecast exhibits similar predictive capabilities as the best individual performing soil hydraulic model 2 the size of the bma uncertainty ranges increase with increasing depth and dryness in the soil profile 3 the best performing ensemble corresponds to the compromise or balanced solution of the three objective pareto surface and 4 the combined multiobjective optimization and bma framework proposed in this paper is very useful to generate forecast ensembles of soil hydraulic models

a gibbs sampler for inequality constrained geostatistical interpolation and inverse modeling 1 interpolation and inverse modeling problems are ubiquitous in environmental sciences in many applications the parameters being estimated or mapped have physical constraints such as nonnegativity e g concentration hydraulic conductivity solubility limits censored data e g due to dry wells or detection limits and other physical boundaries or missing data geostatistical interpolation and inverse modeling techniques have often been applied for estimating such parameters but these methods typically cannot enforce physical constraints this paper describes a statistically rigorous and computationally efficient gibbs sampler a markov chain monte carlo technique based on an a priori truncated gaussian distribution model which allows for multiple and variable physical constraints to be enforced within a geostatistical framework sample interpolation and inverse modeling applications confirm that estimates uncertainty bounds and conditional simulations reflect the specified constraints leading to conclusions that are more consistent with the underlying conceptual model and provide a more accurate measure of the posterior uncertainty of the parameters being estimated in addition especially in inverse modeling applications a posteriori confidence bounds are narrower even in areas where constraints are not imposed the method is applicable in multiple dimensions for data with or without measurement error and with any variogram model

ancient numerical daemons of conceptual hydrological modeling 2 impact of time stepping schemes on model analysis and prediction 1 despite the widespread use of conceptual hydrological models in environmental research and operations they remain frequently implemented using numerically unreliable methods this paper considers the impact of the time stepping scheme on model analysis sensitivity analysis parameter optimization and markov chain monte carlo based uncertainty estimation and prediction it builds on the companion paper clark and kavetski 2010 which focused on numerical accuracy fidelity and computational efficiency empirical and theoretical analysis of eight distinct time stepping schemes for six different hydrological models in 13 diverse basins demonstrates several critical conclusions 1 unreliable time stepping schemes in particular fixed step explicit methods suffer from troublesome numerical artifacts that severely deform the objective function of the model these deformations are not rare isolated instances but can arise in any model structure in any catchment and under common hydroclimatic conditions 2 sensitivity analysis can be severely contaminated by numerical errors often to the extent that it becomes dominated by the sensitivity of truncation errors rather than the model equations 3 robust time stepping schemes generally produce better behaved objective functions free of spurious local optima and with sufficient numerical continuity to permit parameter optimization using efficient quasi newton methods when implemented within a multistart framework modern newton type optimizers are robust even when started far from the optima and provide valuable diagnostic insights not directly available from evolutionary global optimizers 4 unreliable time stepping schemes lead to inconsistent and biased inferences of the model parameters and internal states 5 even when interactions between hydrological parameters and numerical errors provide the right result for the wrong reason and the calibrated model performance appears adequate unreliable time stepping schemes make the model unnecessarily fragile in predictive mode undermining validation assessments and operational use erroneous or misleading conclusions of model analysis and prediction arising from numerical artifacts in hydrological models are intolerable especially given that robust numerics are accepted as mainstream in other areas of science and engineering we hope that the vivid empirical findings will encourage the conceptual hydrological community to close its pandora s box of numerical problems paving the way for more meaningful model application and interpretation

parameter identification for a runoff model for forest roads rainfall simulation is a commonly used approach for studying runoff and erosion from forest roads and a method is needed to estimate infiltration parameters from these experiments we used two algorithms the simplex and shuffled complex evolution to estimate parameters for a physically based infiltration and overland flow model each algorithm was tested by estimating parameters for 92 field measured hydrographs from forest roads nine of the field measured hydrographs allowed us to further test whether estimated parameters could be extended to other antecedent conditions and plot sizes the results demonstrate 1 the physically based model is able to estimate hydrographs from forest roads 2 the two algorithms find unique parameter sets in spite of an error surface that suggests identifiability problems between the hydraulic conductivity and pressure parameters 3 the two algorithms converged to the same parameter values and 4 that parameters estimated for one antecedent condition and plot size can be extended to others with reasonably small error

bayesian analysis for uncertainty estimation of a canopy transpiration model 1 a bayesian approach was used to fit a conceptual transpiration model to half hourly transpiration rates for a sugar maple acer saccharum stand collected over a 5 month period and probabilistically estimate its parameter and prediction uncertainties the model used the penman monteith equation with the jarvis model for canopy conductance this deterministic model was extended by adding a normally distributed error term this extension enabled using markov chain monte carlo simulations to sample the posterior parameter distributions the residuals revealed approximate conformance to the assumption of normally distributed errors however minor systematic structures in the residuals at fine timescales suggested model changes that would potentially improve the modeling of transpiration results also indicated considerable uncertainties in the parameter and transpiration estimates this simple methodology of uncertainty analysis would facilitate the deductive step during the development cycle of deterministic conceptual models by accounting for these uncertainties while drawing inferences from data

bayesian inversion of mualem van genuchten parameters in a multilayer soil profile a data driven assumption free likelihood function this paper introduces a hierarchical simulation and modeling framework that allows for inference and validation of the likelihood function in bayesian inversion of vadose zone hydraulic properties the likelihood function or its analogs objective functions and likelihood measures are commonly assumed to be multivariate gaussian in form however this assumption is not possible to verify without a hierarchical simulation and modeling framework in this paper we present the necessary statistical mechanisms for utilizing the hierarchical framework we apply the hierarchical framework to the inversion of the vadose zone hydraulic properties within a multilayer soil profile conditioned on moisture content observations collected in the uppermost four layers the key result of our work is that the goodness of fit validated likelihood function form provides empirical justification for the assumption of multivariate gaussian likelihood functions in past and future inversions at similar sites as an alternative the likelihood function need not be assumed to follow a parametric statistical distribution and can be computed directly using nonparametric methods the nonparametric methods are considerably more computationally demanding and to demonstrate this approach we present a smaller dimension synthetic case study of evaporation from a soil column the main drawback of our work is the increased computational expense of the inversion

on the existence of global integral forms on supermanifolds it is shown that the berezin approach to integration on supermanifolds can be applied to cases where the supermanifold is a twisted extension of a real manifold this is done by showing that supermanifolds admit a subatlas of coordinate charts with transition functions of a quite restricted kind

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

a maximum likelihood criterion for use with data collected at unequal time intervals a new maximum likelihood nmle criterion suitable for model calibration using data which are recorded at unequal time intervals and contain autocorrelated errors is derived validation of the nmle criterion has been carried out both on a simple two parameter reservoir model using synthetically generated data and on a more complicated hillslope model using real data from the pukeiti catchment in new zealand comparison between the nmle criterion and the simple least squares criterion reveals the superiority of the former over the latter comparison between the nmle criterion and the maximum likelihood criterion for the autocorrelated case proposed by sorooshian 1978 has shown that both criteria would yield results with no practical difference if equal time interval data were used however the nmle criterion can work on variable time interval data which provide more information than equal time interval data and therefore produce better visual results in hydrologic simulations

improved parameter inference in catchment models 2 combining different kinds of hydrologic data and testing their compatibility often some of the parameters of catchment models fitted to runoff data are poorly determined thereby making the task of developing useful regionalization relationships more difficult the bayesian methodology developed in part 1 is extended to utilize several kinds of hydrologic data in parameter inference the goal being to improve the precision of poorly determined parameters the concept of compatibility is developed using statistical hypothesis tests different kinds of data are said to be compatible if differences between their fitted parameters are not statistically significant the pooling of incompatible data may undermine the model s ability to predict runoff and also induce bias in the parameters a hierarchy of three levels of information is introduced to enable systematic checking for compatibility finally a case study is presented using data on runoff soil moisture and interception it is shown that substantial reductions in parameter uncertainty can be realized also the importance of compatibility testing is demonstrated

a partitioned update scheme for state parameter estimation of distributed hydrologic models based on the ensemble kalman filter 1 sequential data assimilation methods such as the ensemble kalman filter enkf provide a general framework to account for various uncertainties in hydrologic modeling simultaneously estimating dynamic states and model parameters with a state augmentation technique but this technique suffers from spurious correlation for impulse responses such as the rainfall runoff process especially in the case of high dimensional state spaces containing various parameters this paper presents a partitioned forecast update scheme based on the enkf to reduce the degree of freedom of the high dimensional state space and to correctly capture covariances between states and parameters in this update scheme the parameter set is partitioned into several types according to their sensitivities and each type of sensitive parameter is estimated in an individual loop by repeated forecast and assimilation we test this scheme with a synthetic case and a distributed hydrologic model concerning the real case of the zhanghe river basin in china the results from the synthetic experiments show that this new scheme can retrieve optimal parameter values and represent the correlations in a more stable manner when compared with the standard state augmentation technique the real case further demonstrates the robustness of the partitioned update scheme for state and parameter estimation owing to the low estimation errors of streamflow in the assimilation and the prediction periods

cohomology of supermanifolds the aim of this chapter is to unfold a basic cohomological theory for supermanifolds which will be exploited in the next chapter to study the structure of superbundles in particular to build a theory of characteristic classes this cohomology theory does not embody only trivial extensions of results valid for differentiable manifolds for instance the natural analogue of the de rham theorem does not hold in general and similarly in the case of complex supermanifolds there is generally speaking no analogue of the dolbeault theorem these features are consequences of the fact that the structure sheaf of a supermanifold does not need to be cohomologically trivial related to this is also the fact that the cohomology of the complex of global graded differential forms on a g supermanifold m a i e the super de rham cohomology of m a depends on the g supermanifold structure of m a so that homeomorphic and even smoothly diffeomorphic g supermanifolds may have a different super de rham cohomology that is super de rham cohomology is a fine invariant of the supermanifold structure

on the use of spatial regularization strategies to improve calibration of distributed watershed models 1 hydrologic models require the specification of unknown model parameters via calibration to historical input output data for spatially distributed models the large number of unknowns makes the calibration problem poorly conditioned spatial regularization can help to stabilize the problem by facilitating inclusion of additional information while a common regularization approach is to apply a scalar multiplier to the prior estimate of each parameter field this can cause problems by simultaneously changing both the mean and the variance of the distribution this paper explores a multiple criteria regularization approach that facilitates adjustment of the mean variance and shape of the parameter distribution using prior information to constrain the problem while providing sufficient degrees of freedom to enable model performance improvements we also test simple squashing functions to help in maintaining conceptually reasonable parameter values throughout the spatial domain we apply the method to three basins in the context of the distributed model intercomparison project dmip2 obtaining considerable performance improvements at the basin outlet however the prior parameter estimates are found to give much better performance at the interior points treated as ungauged suggesting that the spatial information has not been properly exploited the results also suggest that basin outlet hydrographs may not be particularly sensitive to spatial parameter variability and that an overall basin mean value may be sufficient for flow forecasting at the outlet although not at the interior points we discuss weaknesses in our study approach and suggest diagnostically more powerful strategies to be pursued

supergroups factorizations through matrix realization using a matrix realization generic elements of the supergroups u m n and osp m 2n are obtained through the exponentiation of the corresponding super lie algebra elements the emphasis is put on the contribution of the odd part the application to the factorization problem is given and the relationship with nonlinear differential superequations is clarified

efficient posterior exploration of a high dimensional groundwater model from two stage markov chain monte carlo simulation and polynomial chaos expansion 1 this study reports on two strategies for accelerating posterior inference of a highly parameterized and cpu demanding groundwater flow model our method builds on previous stochastic collocation approaches e g marzouk and xiu 2009 and marzouk and najm 2009 and uses generalized polynomial chaos gpc theory and dimensionality reduction to emulate the output of a large scale groundwater flow model the resulting surrogate model is cpu efficient and serves to explore the posterior distribution at a much lower computational cost using two stage mcmc simulation the case study reported in this paper demonstrates a two to five times speed up in sampling efficiency

on lfp spectrum and τ quasi einstein metric abstract in this paper we study l f p spectrum estimates for some smooth potential function f on complete noncompact riemannian manifolds via the bakry emery curvature as its applications we give the upper bound estimate of the l f 2 spectrum for the complete noncompact quasi einstein metric we give an example to show the sharpness of our estimate we also get a lower bound estimate when 0 1 and 0

effective and efficient algorithm for multiobjective optimization of hydrologic models 1 practical experience with the calibration of hydrologic models suggests that any single objective function no matter how carefully chosen is often inadequate to properly measure all of the characteristics of the observed data deemed to be important one strategy to circumvent this problem is to define several optimization criteria objective functions that measure different complementary aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated efficient or pareto optimal solutions in this paper we present an efficient and effective markov chain monte carlo sampler entitled the multiobjective shuffled complex evolution metropolis moscem algorithm which is capable of solving the multiobjective optimization problem for hydrologic models moscem is an improvement over the shuffled complex evolution metropolis scem ua global optimization algorithm using the concept of pareto dominance rather than direct single objective function evaluation to evolve the initial population of points toward a set of solutions stemming from a stable distribution pareto set the efficacy of the moscem ua algorithm is compared with the original mocom ua algorithm for three hydrologic modeling case studies of increasing complexity

keller osserman type conditions for differential inequalities with gradient terms on the heisenberg group abstract we study the qualitative behavior of non negative entire solutions of differential inequalities with gradient terms on the heisenberg group we focus on two classes of inequalities u f u l u and u f u h u g u where f l h g are non negative continuous functions satisfying certain monotonicity properties the operator called the laplacian generalizes the p laplace operator considered by various authors in this setting we prove some liouville theorems introducing two new keller osserman type conditions both extending the classical one which appeared long ago in the study of the prototype differential inequality u f u in r m we show sharpness of our conditions when we specialize to the p laplacian while proving these results we obtain a strong maximum principle for which to the best of our knowledge seems to be new our results continue to hold with the obvious minor modifications also for euclidean space

quantitative comparison of canopy conductance models using a bayesian approach 1 a quantitative model comparison methodology based on deviance information criterion a bayesian measure of the trade off between model complexity and goodness of fit is developed and demonstrated by comparing semiempirical transpiration models this methodology accounts for parameter and prediction uncertainties associated with such models and facilitates objective selection of the simplest model out of available alternatives which does not significantly compromise the ability to accurately model observations we use this methodology to compare various jarvis canopy conductance model configurations embedded within a larger transpiration model against canopy transpiration measured by sap flux the results indicate that descriptions of the dependence of stomatal conductance on vapor pressure deficit photosynthetic radiation and temperature as well as the gradual variation in canopy conductance through the season are essential in the transpiration model use of soil moisture was moderately significant but only when used with a hyperbolic vapor pressure deficit relationship subtle differences in model quality could be clearly associated with small structural changes through the use of this methodology the results also indicate that increments in model complexity are not always accompanied by improvements in model quality and that such improvements are conditional on model structure possible application of this methodology to compare complex semiempirical models of natural systems in general is also discussed

calibrating hydrologic models in flow corrected time 1 modeling streamflow hydrographs can be a highly complex problem particularly due to difficulties caused by multiple dominant streamflow states switching of dominant streamflow generation mechanisms temporally and dynamic catchment responses to precipitation inputs based on antecedent conditions because of these complexities and the extreme heterogeneity that can exist within a single catchment model calibration techniques are generally required to obtain reasonable estimates of the model parameters models are typically calibrated such that a best fit is determined over the entire period of simulation in this way each time step explicitly carries equal weight during the calibration process data transformations e g logarithmic or square root are a common way of modifying the calibration process by scaling the magnitude of the observations here we consider a data transformation that is focused on the time domain rather than the data domain this approach previously employed in transit time modeling literature conceptually stretches time during high streamflows and compresses it during low streamflow periods dynamically weighting streamflows in the time domain the transformation known as flow corrected time is designed to provide greater weight to time periods with larger hydrologic flux here the flow corrected time transformation is compared to a baseline untransformed case and the commonly employed logarithmic transformation considering both visual and numerical nash sutcliffe efficiency assessments we demonstrate that over the time periods that dominate hydrologic flux the flow corrected time transformation resulted in improved fits to the observed hydrograph

automatic calibration of conceptual rainfall runoff models optimization algorithms catchment conditions and model structure from 32 crr catchment cases combinations from four conceptual rainfall runoff models crr and eight catchments calibrated with either two or three optimization methods 1 the shuffle complex evolution method sce ua 2 the multiple start simplex msx and 3 the local simplex it seems that all three methods produced parameter sets of comparable local optimum quality even with comparable performance among the models some parameter values derived by the three optimization methods for the same crr catchment cases are surprisingly different from each other in addition parameter sets of sce ua or msx which often produce marginally better results than the local simplex at the calibration stage could end up with worse results at the validation stage apparently given the inherent limitations of calibration data model inadequacies and identifiability problems it is impossible to achieve global convergence in the parameter search however other than those for dry catchments such as ihimbu or bird creek the parameter sets obtained are generally feasible both sce ua and the local simplex are viable optimization tools while msx is inefficient computationally sce ua can complete the parameter search in one run while the local simplex often requires multirun operations to get good results

efficient subspace probabilistic parameter optimization for catchment models the estimation of catchment model parameters has proven to be a difficult task for several reasons which include ill posedness and the existence of multiple local optima recent work on global probabilistic search methods has developed robust techniques for locating the global optimum however these methods can be computationally intensive when the search is conducted over a large hypercube moreover specification of the hypercube may be problematic particularly if there is strong parameter interaction this study seeks to reduce the computational effort by confining the search to a subspace within which the global optimum is likely to be found the approach involves locating a local optimum using a local gradient based search it is assumed that the local optimum belongs to a set of optima which cluster about the global optimum a probabilistic search is then conducted within a hyperellipsoid defined by the second order approximation to the response surface around the local optimum a case study involving a five parameter conceptual rainfall runoff model is presented the response surface is shown to be riddled with local optima yet the second order approximation provides a not unreasonable description of parameter uncertainty the subspace search strategy provides a rational means for defining the search space and is shown to be more efficient typically twice but up to 5 times more efficient than a search over a hypercube four probabilistic search algorithms are compared shuffled complex evolution sce genetic algorithm using traditional crossover and multiple random start using either simplex or quasi newton local searches in the case study the sce algorithm was found to be robust and the most efficient the genetic algorithm although displaying initial convergence rates superior to the sce algorithm tended to flounder near the optimum and could not be relied upon to locate the global optimum

intrinsic and extrinsic comparison results for isoperimetric quotients and capacities in weighted manifolds abstract let m g be a complete non compact riemannian manifold together with a function e h which weights the hausdorff measures associated to the riemannian metric in this work we assume lower or upper radial bounds on some weighted or unweighted curvatures of m to deduce comparisons for the weighted isoperimetric quotient and the weighted capacity of metric balls in m centered at a point o m as a consequence we obtain parabolicity and hyperbolicity criteria for weighted manifolds generalizing previous ones a basic tool in our study is the analysis of the weighted laplacian of the distance function from o the technique extends to non compact submanifolds properly immersed in m under certain control on their weighted mean curvature

estimating epistemic and aleatory uncertainties during hydrologic modeling an information theoretic approach 1 with growing interest in understanding the magnitudes and sources of uncertainty in hydrological modeling the difficult problem of characterizing model structure adequacy is now attracting considerable attention here we examine this problem via a model structureindependent approach based in information theory in particular we a discuss how to assess and compute the information content in multivariate hydrological data b present practical methods for quantifying the uncertainty and shared information in data while accounting for heteroscedasticity c show how these tools can be used to estimate the best achievable predictive performance of a model for a system given the available data and d show how model adequacy can be characterized in terms of the magnitude and nature of its aleatory uncertainty that cannot be diminished and is resolvable only up to specification of its density and its epistemic uncertainty that can in principle be suitably resolved by improving the model an illustrative modeling example is provided using catchment scale data from three river basins the leaf and chunky river basins in the united states and the chuzhou basin in china our analysis shows that the aleatory uncertainty associated with making catchment simulations using this data set is significant 50 further estimated epistemic uncertainties of the hymod sac sma and xinanjiang model hypotheses indicate that considerable room for model structural improvements remain

some examples of compact supermanifolds with non abelian fundamental group a detailed construction is given of a supermanifold which is compact and has far from trivial topology higher dimensional examples are also described the grassmann algebra from which the supermanifolds are constructed may have finite or infinite dimension

using discharge data to reduce structural deficits in a hydrological model with a bayesian inference approach and the implications for the prediction of critical source areas 1 a distributed hydrological model was used to simulate the distribution of fast runoff formation as a proxy for critical source areas for herbicide pollution in a small agricultural catchment in switzerland we tested to what degree predictions based on prior knowledge without local measurements could be improved upon relying on observed discharge this learning process consisted of five steps for the prior prediction step 1 knowledge of the model parameters was coarse and predictions were fairly uncertain in the second step discharge data were used to update the prior parameter distribution effects of uncertainty in input data and model structure were accounted for by an autoregressive error model this step decreased the width of the marginal distributions of parameters describing the lower boundary percolation rates but hardly affected soil hydraulic parameters residual analysis step 3 revealed model structure deficits we modified the model and in the subsequent bayesian updating step 4 the widths of the posterior marginal distributions were reduced for most parameters compared to those of the prior this incremental procedure led to a strong reduction in the uncertainty of the spatial prediction thus despite only using spatially integrated data discharge the spatially distributed effect of the improved model structure can be expected to improve the spatially distributed predictions also the fifth step consisted of a test with independent spatial data on herbicide losses and revealed ambiguous results the comparison depended critically on the ratio of event to preevent water that was discharged this ratio cannot be estimated from hydrological data only the results demonstrate that the value of local data is strongly dependent on a correct model structure an iterative procedure of bayesian updating model testing and model modification is suggested

ensemble based assimilation of discharge into rainfall runoff models a comparison of approaches to mapping observational information to state space 1 the optimization of hydrologic models using the ensemble kalman filter has received increasing attention during the last decade the application of this algorithm is straightforward when the relationship between the state variables and the observations is linear in other words when the observations can be directly mapped onto the state space however when this relationship is nonlinear a number of methods can be derived in order to perform this transfer up till now it has not been demonstrated which of these methods is recommended for discharge assimilation with the ensemble kalman filter the objective of this paper is to analyze these methods for conceptual rainfall runoff models in a small scale catchment the study has been performed in the bellebeek catchment 86 36 km2 in belgium using two time series models and one conceptual rainfall runoff model a first analysis of the algorithms has been performed using the one time step ahead discharge predictions the results indicate that linearization of the storage discharge relationship the observation system should be avoided if discharge data are assimilated using the ensemble kalman filter further assimilating discharge data into conceptual rainfall runoff models for small catchments does not work well when a unit hydrograph is used for runoff routing this can be explained by the stronger impact of the model error caused by errors in the forcings model structure and parameters accumulated over the duration of the unit hydrograph as compared to the impact of erroneous initial conditions a second analysis using longer lead times has led to the conclusion that for the type of catchment and model used in this study the accuracy of the meteorological forcings is more important than an accurate estimation of the model initial conditions through data assimilation

a note on the meaning of covariant derivatives in supersymmetry we analyze in this paper the group theoretical meaning of the covariant derivatives and show that they are horizontal left invariant vector fields on superspace obtained from a super lie group which at the same time exhibits the structure of a principal bundle with a canonical connection the geometrical construction is general and not restricted to the super poincare group

a formal likelihood function for parameter and predictive inference of hydrologic models with correlated heteroscedastic and non gaussian errors estimation of parameter and predictive uncertainty of hydrologic models has traditionally relied on several simplifying assumptions residual errors are often assumed to be independent and to be adequately described by a gaussian probability distribution with a mean of zero and a constant variance here we investigate to what extent estimates of parameter and predictive uncertainty are affected when these assumptions are relaxed a formal generalized likelihood function is presented which extends the applicability of previously used likelihood functions to situations where residual errors are correlated heteroscedastic and non gaussian with varying degrees of kurtosis and skewness the approach focuses on a correct statistical description of the data and the total model residuals without separating out various error sources application to bayesian uncertainty analysis of a conceptual rainfall runoff model simultaneously identifies the hydrologic model parameters and the appropriate statistical distribution of the residual errors when applied to daily rainfall runoff data from a humid basin we find that 1 residual errors are much better described by a heteroscedastic first order auto correlated error model with a laplacian distribution function characterized by heavier tails than a gaussian distribution and 2 compared to a standard least squares approach proper representation of the statistical distribution of residual errors yields tighter predictive uncertainty bands and different parameter uncertainty estimates that are less sensitive to the particular time period used for inference application to daily rainfall runoff data from a semiarid basin with more significant residual errors and systematic underprediction of peak flows shows that 1 multiplicative bias factors can be used to compensate for some of the largest errors and 2 a skewed error distribution yields improved estimates of predictive uncertainty in this semiarid basin with near zero flows we conclude that the presented methodology provides improved estimates of parameter and total prediction uncertainty and should be useful for handling complex residual errors in other hydrologic regression models as well

a multistart weight adaptive recursive parameter estimation method 1 the determination of the parameters for hydrologic models has been the subject of a large number of studies during the last 3 decades a multitude of methods have been developed for this purpose generally the mismatch between the model simulations and the observations is lumped into an objective function which is then is optimized by these methods this can lead to parameter values that result in a good model performance under certain e g low flow conditions but not under other e g high flow conditions the objective of this paper is to demonstrate a calibration algorithm which leads to a good model performance under all boundary conditions this algorithm is referred to as multistart weight adaptive recursive parameter estimation mwarpe for this purpose the equations of the extended kalman filter ekf have been used recursively in a monte carlo approach strongly increasing the chance that a globally optimal parameter set is obtained instead of a local optimum the method has been applied to a rainfall runoff model for the zwalm catchment in belgium using a 1 year a 2 year and a 3 year calibration period the results have been compared to the shuffled complex evolution sce ua method a synthetic study revealed that for narrow parameter limits the sce ua algorithm outperformed mwarpe while for broad parameter limits the opposite occurred for the test case using in situ observed data the sce ua method resulted in slightly lower rmse values than mwarpe but mwarpe performed better outside the calibration period it has been found that mwarpe can bypass local optima in the determination of the final parameter set also the best initial parameter sets with the lowest rmse do not lead to the best final parameter values to apply the method only four parameters need to be specified more specifically the number of starting points the number of iterations per starting point one parameter used to initialize the model error covariance matrix and the observation error for this reason the method could be a simple alternative to more complex methods if model parameters have to be determined when time and or computational power are limited

lattices supersymmetry and kahler fermions it is shown that a graded extension of the space group of a generalised simple cubic lattice exists in any space dimension d the fermionic variables which arise admit a kahlerian interpretation each graded space group is a subgroup of a graded extension of the appropriate euclidean group e d the relevance of this to the construction of lattice theories is discussed

baker campbell hausdorff relations for the super poincare group baker campbell hausdorff relations are obtained for the connected supergroup associated with the super poincare algebra iosp 1 4

supersymmetry and supercoherent states of a nonrelativistic free particle coordinate atypical representation of the orthosymplectic superalgebra osp 2 2 in a hilbert superspace of square integrable functions constructed in a special way is given the quantum nonrelativistic free particle hamiltonian is an element of this superalgebra which turns out to be a dynamical superalgebra for this system the supercoherent states defined by means of a supergroup displacement operator are explicitly constructed these are the coordinate representation of the known atypical abstract super group osp 2 2 coherent states we interpret obtained results from the classical mechanics viewpoint as a model of classical particle which is immovable in the even sector of the phase superspace and is in rectilinear movement in the appropriate coordinate system in its odd sector

estimating information entropy for hydrological data one dimensional case there has been a recent resurgence of interest in the application of information theory to problems of system identification in the earth and environmental sciences while the concept of entropy has found increased application little attention has yet been given to the practical problems of estimating entropy when dealing with the unique characteristics of two commonly used kinds of hydrologic data rainfall and runoff in this paper we discuss four important issues of practical relevance that can bias the computation of entropy if not properly handled the first zero effect arises when precipitation and ephemeral streamflow data must be viewed as arising from a discrete continuous hybrid distribution due to the occurrence of many zero values e g days with no rain no runoff second in the widely used bin counting method for estimation of pdf s significant error can be introduced if the bin width is not carefully selected the third measurement effect arises due to the fact that continuously varying hydrologic variables can typically only be observed discretely to some degree of precision the fourth skewness effect arises when the distribution of a variable is significantly skewed here we present an approach that can deal with all four of these issues and test them with artificially generated and real hydrological data the results indicate that the method is accurate and robust