bayesian estimation of uncertainty in runoff prediction and the value of data an application of the glue approach this paper addresses the problem of evaluating the predictive uncertainty of topmodel using the bayesian generalised likelihood uncertainty estimation glue methodology in an application to the small ringelbach research catchment in the vosges france the wide range of parameter sets giving acceptable simulations is demonstrated and uncertainty bands are presented based on different likelihood measures it is shown how the distributions of predicted discharges are non gaussian and vary in shape through time and with discharge updating of the likelihood weights using bayes equation is demonstrated after each year of record and it is shown how the additional data can be evaluated in terms of the way they constrain the uncertainty bands

the bochner schoenberg eberlein property for commutative banach algebras especially fourier and fourier stieltjes algebras the classical bochner schoenberg eberlein theorem characterizes the continuous functions on the dual group of a locally compact abelian group g which arise as fourier stieltjes transforms of elements of the measure algebra m g of g this has led to the study of the algebra of bse functions on the spectrum of an arbitrary commutative banach algebra and of the concept of a bse algebra as introduced by takahasi and hatori since then bse algebras have been studied by several authors in this paper we investigate bse algebras in the general context on the one hand and on the other hand we specialize to fourier and fourier stieltjes algebras of locally compact groups

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

reproducibility of soil moisture ensembles when representing soil parameter uncertainty using a latin hypercube based approach with correlation control 1 representation of model input uncertainty is critical in ensemble based data assimilation monte carlo sampling of model inputs produces uncertainty in the hydrologic state through the model dynamics small monte carlo ensemble sizes are desirable because of model complexity and dimensionality but potentially lead to sampling errors and correspondingly poor representation of probabilistic structure of the hydrologic state we compare two techniques to sample soil hydraulic and thermal properties shtps 1 latin hypercube lh based sampling with correlation control and 2 random sampling from shtp marginal distributions a hydrology model is used to project shtp uncertainty onto the soil moisture state for given forcings for statistical comparison we generate 20 ensembles for 7 ensemble sizes variance in ensemble moment estimates decreases with increasing ensemble size the lh based approach yields less variance in the estimate of ensemble moments at all ensemble sizes an advantage greatest with small ensembles implications for hydrologic uncertainty assessment data assimilation and parameter estimation are discussed

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

uniqueness and observability of conceptual rainfall runoff model parameters the percolation process examined many researchers have expressed concerns regarding the uniqueness of parameter estimates for conceptual rainfall runoff r r models obtained through calibration recent studies sorooshian et al this issue sorooshian and gupta this issue have revealed that even though stochastic parameter estimation techniques can help the problems are not all due to inefficiencies in the calibration techniques used but are caused by the manner in which the model is structurally formulated thus even when calibrated under ideal conditions simulation studies it is often impossible to obtain unique estimates for the parameters it is possible to resolve this problem at least in part by appropriate reparameterizations of the pertinent model equations in this paper the percolation equation of the soil moisture accounting model of the national weather service river forecast system sma nwsrfs will be discussed it is shown that a logical reparameterization of this equation can result in conditions that improve the chances of obtaining unique parameter estimates it is believed that these results have implications for other conceptual r r models in which similar approaches are used in the representation of the percolation infiltration process

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 hybrid model for point rainfall modeling a hybrid point rainfall model a product of two random processes is presented the model uses a jitter model a general technique for improving the fit of any point process based model we use the nonrandomized bartlett lewis rectangular pulse and an autoregressive model as a jitter first the five parameters of the bartlett lewis model are estimated by the method of moments using the mean of one aggregation level and the dry probabilities of all aggregation levels considered second the parameters of the autoregressive model are derived from the moments of the historical data and those given by the bartlett lewis model without additional cost in terms of parameter calibration using 15 min point rainfall data of capella central queensland australia as a test case the results of the hybrid model were better than the best results given by the randomized bartlett lewis model on its own the nonrandomized bartlett lewis model produced very poor results

evaluation of maximum likelihood parameter estimation techniques for conceptual rainfall runoff models influence of calibration data variability and length on model credibility the success of an automatic calibration procedure is highly dependent on the choice of the objective function and the nature quantity and quality of the data used the objective function should be selected on the basis of the stochastic properties of the errors present in the data and in the model also the data should be chosen so as to contain as much valuable information about the process as possible in this paper we compare the performance of two maximum likelihood estimators the amle which assumes the presence of first lag autocorrelated homogeneous variance errors and the hmle which assumes the presence of uncorrelated inhomogeneous variance errors to the commonly used simple least squares criterion sls the model calibrated was the soil moisture accounting model of the u s national weather service s river forecast system sma nwsrfs the results indicate that a properly chosen objective function can enhance the possibility of obtaining unique and conceptually realistic parameter estimates furthermore the sensitivity of the estimation results to various characteristics of the calibration data such as hydrologic variability and length are substantially reduced

model smoothing strategies to remove microscale discontinuities and spurious secondary optima in objective functions in hydrological calibration 1 environmental processes frequently exhibit threshold type behavior e g the initiation of fluxes such as snowmelt recharge and quick flow incorporating such thresholds into hydrological models introduces discontinuities into the objective functions used in model calibration making parameter estimation unnecessarily more difficult moreover this study shows that model thresholds can produce spurious multimodality in least squares objective functions even if the underlying model is near linear in its parameters in contrast smoothing the model with respect to its parameters and inputs yields differentiable objective functions and in some cases can also improve its macroscale characteristics by removing spurious secondary optima this simplifies model calibration and sensitivity analysis by reducing the complexity of objective functions and permitting the use of powerful derivative based analysis methods such as newton type optimization and hessian based uncertainty assessment this paper details smoothing strategies for several classes of thresholds and discontinuities commonly found in hydrological models including step and angle discontinuities in the constitutive functions and flux constraints arising from conservation laws in the governing differential equations the smoothing algorithms and their parameters are selected to ensure infinite differentiability of the model and its objective functions while preserving the macroscale behavior of the original governing equations the improvements in the structure of the model and its objective functions are illustrated empirically for a degree day based snow model the smoothing techniques are general and can be applied to other models with thresholds

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

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

comparison of newton type and direct search algorithms for calibration of conceptual rainfall runoff models an examination of the calibration aspect of conceptual rainfall runoff models was undertaken using the sacramento soil moisture accounting model and a study comparing the performance of a newton type optimization algorithm with that of a direct search algorithm results indicate that the direct search algorithm is the more robust of the two because the newton type algorithm is more susceptible to poor conditioning of the response surface graphical studies of the response surface of the model s parameter space confirmed the presence of discontinuities and a rough textured surface particularly in the derivatives

reply to comment by chu et al on high dimensional posterior exploration of hydrologic models using multiple try dream zs and high performance computing publications water resources research commentary 10 1002 2013wr014425 this article is a reply to chu et al 2014 doi 10 1002 2012wr013341 reply to comment by chu et al on high dimensional posterior exploration of hydrologic models using multiple try dream zs and high performance computing jasper a vrugt 1 2 3 and eric laloy 4 correspondence to j a vrugt jasper uci edu citation vrugt j a and e laloy 2014 reply to comment chu et al on high dimensional posterior exploration of hydrologic models using multiple try dream zs and high performance computing water resour res 50 2781 2786 doi 10 1002 2013wr014425 received 15 july 2013 accepted 8 feb 2014 accepted article online 15 feb 2014 published online 21 mar 2014 department of civil and environmental engineering university of california irvine california usa 2 department of earth system science university of california irvine california usa 3 institute for biodiversity and ecosystems dynamics university of amsterdam amsterdam netherlands 4 institute for environment health and safety belgian nuclear research centre mol belgium 1 introduction the comment of chu et al 2014 hereafter referred to as cyg raises questions about some of the results presented in our paper laloy and vrugt 2012 hereinafter lv which is not to be confused with las vegas although appropriate concerning the subject of this work on monte carlo simulation as a preamble we would like to remark that the work presented in chu et al 2010 and lv 2012 concern two different elds of study cyg view the model calibration as an optimization problem and use common concepts to ef ciently nd a single realization of the parameter values that minimizes or maximizes if appropriate some user de ned objective function our work on the contrary uses bayesian principles coupled with mcmc simulation to derive a distribution of parameter values that honor the observed data this distribution summarizes parameter and model predictive simulation uncertainty a requirement for probabilistic analysis operational forecasting disentangling error sources and decision making the maxi mum a posteriori density map parameter values derived with mcmc simulation should reside in close vicinity of the best solution found with an optimization algorithm if the exact same data set prior distribu tion and likelihood objective function are used in this reply we assume that cyg used a correct imple mentation of the mt dream zs algorithm and similar data set prior and likelihood function as lv otherwise the comparative analysis is meaningless we emphasize this for three reasons first the results presented herein contradict cyg and are similar to those reported in lv but now with more trials plotted second contributions in physics horowitz et al 2012 toyli et al 2012 yale et al 2013 and geophysics linde and vrugt 2013 laloy et al 2012 rosas carbajal et al 2014 t lochbuehler et al summary statistics from training images as model constraints in probabilistic inversion geophysical journal international in review 2014 demonstrate proper convergence behavior of mt dream zs on complex and high dimensional targets involving hundreds of parameters third to justify their sp uci algorithm the original paper of chu et al 2010 portrays misleading results of the predecessor of dream called scem ua section 4 of this reply will address this latter issue in more detail we now respond to the comments of cyg we use different sections with numbering corresponding to cyg 2 computational time unit cyg nd the computational time unit ctu diagnostic to be a poor indicator of the performance of mt dream zs they suggest using the number of function evaluations or clock time instead the cpu time s scales linearly with ctu or cpu 5 actu where a s denotes the average time it takes to complete a sin gle function model evaluation as a is dependent on the processor speed hardware lv purposely reported the ctu values note that we neglect the actual run time of mt dream zs in the determination of a which is appropriate given the intended application of this algorithm to cpu intensive forward models we purposely do not use the number of function evaluations as performance diagnostic this metric does not properly convey the cpu time ctu of parallel algorithms such as dream zs or mt dream zs these vrugt and laloy c 2014 american geophysical union all rights reserved v

hydrologic consistency as a basis for assessing complexity of monthly water balance models for the continental united states methods to select parsimonious and hydrologically consistent model structures are useful for evaluating dominance of hydrologic processes and representativeness of data while information criteria appropriately constrained to obey underlying statistical assumptions can provide a basis for evaluating appropriate model complexity it is not sufficient to rely upon the principle of maximum likelihood ml alone we suggest that one must also call upon a principle of hydrologic consistency meaning that selected ml structures and parameter estimates must be constrained as well as possible to reproduce desired hydrological characteristics of the processes under investigation this argument is demonstrated in the context of evaluating the suitability of candidate model structures for lumped water balance modeling across the continental united states using data from 307 snow free catchments the models are constrained to satisfy several tests of hydrologic consistency a flow space transformation is used to ensure better consistency with underlying statistical assumptions and information criteria are used to evaluate model complexity relative to the data the results clearly demonstrate that the principle of consistency provides a sensible basis for guiding selection of model structures and indicate strong spatial persistence of certain model structures across the continental united states further work to untangle reasons for model structure predominance can help to relate conceptual model structures to physical characteristics of the catchments facilitating the task of prediction in ungaged basins

generalised f algebras as predual algebras of jbw triples and characterisations of the fourier algebras on locally compact groups abstract we introduce the notion of a generalised f algebra as a banach algebra a whose banach space dual is a j b w triple with a certain additional condition on a distinguished character of a this generalises the well known notion of f algebras which in turn includes as special cases many important classes of banach algebras on locally compact groups and semigroups our main use of this new notion is to give some axiomatic characterisations of the fourier algebras on locally compact groups strengthening our previous work 37 but we also quickly review some well known results in f algebras that can be extended to the context of generalised f algebras

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

on hydrological model complexity its geometrical interpretations and prediction uncertainty knowledge of hydrological model complexity can aid selection of an optimal prediction model out of a set of available models optimal model selection is formalized as selection of the least complex model out of a subset of models that have lower empirical risk this may be considered equivalent to minimizing an upper bound on prediction error defined here as the mathematical expectation of empirical risk in this paper we derive an upper bound that is free from assumptions on data and underlying process distribution as well as on independence of model predictions over time we demonstrate that hydrological model complexity as defined in the presented theoretical framework plays an important role in determining the upper bound the model complexity also acts as a stabilizer to a hydrological model selection problem if it is deemed ill posed we provide an algorithm for computing complexity of any arbitrary hydrological model we also demonstrate that hydrological model complexity has a geometric interpretation as the size of model output space the presented theory is applied to quantify complexities of two hydrological model structures sac sma and sixpar it detects that sac sma is indeed more complex than sixpar we also develop an algorithm to estimate the upper bound on prediction error which is applied on five different rainfall runoff model structures that vary in complexity we show that a model selection problem is stabilized by regularizing it with model complexity complexity regularized model selection yields models that are robust in predicting future but yet unseen data

characterisations of fourier and fourier stieltjes algebras on locally compact groups abstract motivated by the beautiful work of m a rieffel 1965 and of m e walter 1974 we obtain characterisations of the fourier algebra a g of a locally compact group g in terms of the class of f algebras i e a banach algebra a such that its dual a is a w algebra whose identity is multiplicative on a for example we show that the fourier algebras are precisely those commutative semisimple f algebras that are tauberian contain a nonzero real element and possess a dual semigroup that acts transitively on their spectrums our characterisations fall into three flavours where the first one will be the basis of the other two the first flavour also implies a simple characterisation of when the predual of a hopf von neumann algebra is the fourier algebra of a locally compact group we also obtain similar characterisations of the fourier stieltjes algebras of g en route we prove some new results on the problem of when a subalgebra of a g is the whole algebra and on representations of discrete groups

the c algebra generated by operators with compact support on a locally compact group abstract let g be a locally compact group and vn g be the von neumann algebra generated by the left regular representation of g let ucb denote the c subalgebra generated by operators in vn g with compact support when g is abelian ucb corresponds to the space of bounded uniformly continuous functions on the dual group of g in this paper we prove among other things that for a large class of locally compact groups which include the heisenberg group the ax b group and the motion group the centre of the banach algebra ucb is the fourier stieltjes algebra b g

bayesian inference of uncertainties in precipitation streamflow modeling in a snow affected catchment 1 bayesian inference is used to study the effect of precipitation and model structural uncertainty on estimates of model parameters and confidence limits of predictive variables in a conceptual rainfall runoff model in the snow fed rudback catchment 142 ha in southern finland the ihacres model is coupled with a simple degree day model to account for snow accumulation and melt the posterior probability distribution of the model parameters is sampled by using the differential evolution adaptive metropolis dream zs algorithm and the generalized likelihood function precipitation uncertainty is taken into account by introducing additional latent variables that were used as multipliers for individual storm events results suggest that occasional snow water equivalent swe observations together with daily streamflow observations do not contain enough information to simultaneously identify model parameters precipitation uncertainty and model structural uncertainty in the rudback catchment the addition of an autoregressive component to account for model structure error and latent variables having uniform priors to account for input uncertainty lead to dubious posterior distributions of model parameters thus our hypothesis that informative priors for latent variables could be replaced by additional swe data could not be confirmed the model was found to work adequately in 1 day ahead simulation mode but the results were poor in the simulation batch mode this was caused by the interaction of parameters that were used to describe different sources of uncertainty the findings may have lessons for other cases where parameterizations are similarly high in relation to available prior information

harvest scheduling subject to maximum area restrictions exploring exact approaches we consider a spatial problem arising in forest harvesting for regulatory reasons blocks harvested should not exceed a certain total area typically 49 hectares traditionally this problem called the adjacency problem has been approached by forming a priori blocks from basic cells of 5 to 25 hectares and solving the resulting mixed integer program superior solutions can be obtained by including the construction of blocks in the decision process the resulting problem is far more complex combinatorially we present an exact algorithmic approach that has yielded good results in computational tests this solution approach is based on determining a strong formulation of the linear programming problem through a clique representation of a projected problem

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

fourier stieltjes algebra of a topological group abstract this paper is an invitation to the study of the fourier stieltjes algebra b g the linear span of the continuous positive definite complex valued functions on a topological group g we study b g when g has a host algebra or a group c algebra the analogue of the group c algebra of a locally compact group our main challenge is that a topological group g cannot have a positive regular borel measure which is left translation invariant unless g is locally compact

calibration of a conceptual rainfall runoff model for flood frequency estimation by continuous simulation an approach is described to the calibration of a conceptual rainfall runoff model the probability distributed model pdm for estimating flood frequencies at gauged sites by continuous flow simulation a first step was the estimation of routing store parameters by recession curve analysis uniform random sampling was then used to search for parameter sets that produced simulations achieving the best fit to observed hourly flow data over a 2 year period goodness of fit was expressed in terms of four objective functions designed to give different degrees of weight to peaks in flow flood frequency results were improved if necessary by manual adjustment of parameters with reference to peaks extracted from the entire hourly flow record although the primary aim was to reproduce observed peaks consideration was also given to finding parameter sets capable of generating a realistic overall characterization of the flow regime examples are shown where the calibrated model generated simulations that reproduced well the magnitude and frequency distribution of peak flows factors affecting the acceptability of these simulations are discussed for an example catchment a sensitivity analysis shows that there may be more than one set of parameter values well suited to the simulation of peak flows