benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

wall pressure and shear stress spectra from direct simulations of channel flow wall pressure and shear stress spectra from direct numerical simulations of turbulent plane channel flow are presented in this paper simulations have been carried out at a series of reynolds numbers up to re 1440 which corresponds to re 6 92 x 10 4 based on channel width and centerline velocity single point and two point statistics for velocity pressure and their derivatives have been collected including velocity moments up to fourth order the results have been used to study the reynolds number dependence of wall pressure and shear stress spectra it is found that the point spectrum of wall pressure collapses for re 360 under a mixed scaling for frequencies lower than the peak frequency of the frequency weighted spectrum and under viscous scaling for frequencies higher than the peak point spectra of wall shear stress components are found to collapse for re 360 under viscous scaling the normalized mean square wall pressure increases linearly with the logarithm of reynolds number the rms wall shear stresses also increase with reynolds number over the present range but suggest some leveling off at high reynolds number

finite surface discretization for incompressible navier stokes equations and coupled conservation laws abstract we present a new finite surface discretization fsd aiming at the incompressible navier stokes equations nse and other coupled conservation laws this discretization defines the velocities as surfaced averaged values living on the faces of the pressure volumes in which the mass is set to be conserved consequently the calculation of the mass balance on these control volumes is exact which allows more accurate information to be kept in the velocity field and produces a very accurate prediction of the pressure in the next time step the proposed discretization reduces the stencil size of the poisson equation in the projection method compared to the finite volume and finite difference discretizations due to highly accurate mass conservation the compact sixth order approximation of fsd can be used with an explicit fourth order pressure treatment this property greatly reduces the cost and complexity of the implementation we present the discrete evolution equation of the surface averaged velocities together with the enforcement of mass conservation and the solution procedure for the pressure the approximation of the nse under this new discretization uses a combination of finite difference and finite volume methods the proposed method is validated using standard laminar test cases we identify the conditions under which a fourth order pressure treatment can support the sixth order and eighth order approximations of the convection term using fourier analysis the performance of the method is evaluated on turbulent channel flows up to friction reynolds number of 950 the quantitative relationships between the accuracy of the solution and grid size are identified we present two performance indices for comparison with other methods at the error level of 1 per mille the proposed method is 28 times faster than the classic second order scheme

reliability of different depth duration frequency equations for estimating short duration design storms 1 the design storm depth is defined as the rainfall depth that is expected to occur in the considered site for a given probability of occurrence and a given duration of the storm it is generally estimated by using parametric depth duration frequency ddf equations in particular this article considers the frequent case when one needs to estimate the design storm depth for very short durations typically from 5 to 45 min while observed rainfall extremes for calibrating the ddf parameters are only available for longer durations in this case the ddf curves are generally extrapolated below the range of durations that were used for estimating their parameters it is well known that this procedure induces estimation errors that depend on the type of ddf equation that is used the aim of this study is to test the capability of seven different ddf curves characterized by two or three parameters to provide an estimate of the design rainfall for storm durations shorter than 1 hour when their parameterization is performed by using data referred to longer storms the results point out that a proper choice of the ddf curve may improve the reliability of the design storm depth estimation significantly in particular ddf curves with three parameters provide a conservative estimation with an average relative error which never exceeded 20 for all the storm duration considered here

the mathematical structure of rainfall representations 3 some applications of the point process theory to rainfall processes part 3 constitutes the final part of three parts devoted to the mathematical structure of rainfall the objective is to illustrate the scope of the tools developed in part 2 in the mathematical description of rainfall and rainfall driven processes a general overview of the three part series is given in part 1

an adaptive implicit explicit scheme for the dns and les of compressible flows on unstructured grids an adaptive implicit explicit scheme for direct numerical simulation dns and large eddy simulation les of compressible turbulent flows on unstructured grids is developed the method uses a node based finite volume discretization with summation by parts sbp property which in conjunction with simultaneous approximation terms sat for imposing boundary conditions leads to a linearly stable semi discrete scheme the solution is marched in time using an implicit explicit runge kutta imex rk time advancement scheme a novel adaptive algorithm for splitting the system into implicit and explicit sets is developed the method is validated using several canonical laminar and turbulent flows load balance for the new scheme is achieved by a dual constraint domain decomposition algorithm the scalability and computational efficiency of the method is investigated and memory savings compared with a fully implicit method is demonstrated a notable reduction of computational costs compared to both fully implicit and fully explicit schemes is observed

a third order multistep time discretization for a chebyshev tau spectral method a time discretization scheme based on the third order backward difference formula has been embedded into a chebyshev tau spectral method for the navier stokes equations the time discretization is a variant of the second order backward scheme proposed by krasnov et al 2008 3 high resolution direct numerical simulations of turbulent incompressible channel flow have been performed to compare the backward scheme to the runge kutta scheme proposed by spalart et al 1991 2 it is shown that the runge kutta scheme leads to a poor convergence of some third order spatial derivatives in the direct vicinity of the wall derivatives that represent the diffusion of wall tangential vorticity the convergence at the wall is shown to be significantly improved if the backward scheme is applied

compatibility of continuous rainfall occurrence models with discrete rainfall observations inferences about the underlying rainfall generating mechanism made through a model fitted to the sampled rainfall series at a particular time scale are meaningful only if they are invariant under the time scale of measurement at which the fitting of the model is made following the work of i rodriguez iturbe et al 1984 this assertion is tested by examining the compatibility of the neyman scott n s model for the continuous underlying rainfall with sampled realizations taken over intervals ranging from one hour to one day the results suggest that the n s model is inconsistent at different time scales and therefore mathematical descriptions of rainfall using this model are inevitably limited to the time scale of measurement at which a description of rainfall is sought these findings are quite general in that they apply to any model with rainfall deposited instantaneously at times described by a n s process regardless of how the amounts associated with the events are distributed and of the dependence structure of the amounts

a point process model for rainfall further developments a stochastic model for rainfall at a single site is studied in which storms arrive in a poisson process each storm consisting of a cluster of a random number of rain cells each cell having random duration and depth a model studied in an earlier paper is extended to provide a better fit to empirical experience the extension being based on the attachment of a single random variable to each storm to achieve in particular some correlation between the durations of the cells within a single storm the properties of the new model are developed its fitting to two sets of empirical data is described and the examination of adequacy of fit is studied in some detail via properties not used in the fitting procedure finally a theoretical study is made of short term prediction from the model

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

bounded cascade models as nonstationary multifractals we investigate a class of bounded random cascade models which are multiplicative by construction yet additive with respect to some but not all of their properties we assume the multiplicative weights go to unity as the cascade proceeds then the resulting field has upper and lower bounds two largely complementary multifractal statistical methods of analysis are used singular measures and structure functions yielding respectively the exponent hierarchies ital d sub ital q and ital h sub ital q we study in more detail a specific subclass of one dimensional models with weights 1 plus minus 1 minus 2 ital p ital r sub ital n minus 1 sup ital h at relative scale ital r sub ital n 2 sup minus ital n after ital n cascade steps the parameter ital h gt 0 regulates the degree of nonstationarity at ital h 0 stationarity prevails and singular ital p model cascades meneveau and sreenivasan phys rev lett 59 1424 1987 are retrieved our model has at once large scale stationarity and small scale nonstationarity with stationary increments due to the boundedness the ital d sub ital q all converge to unity with increasing ital n the rate of convergence is estimated and the results are discussed in terms of residual multifractality a spurious singularity spectrum due to finite size effects the structure function exponents are moremore interesting ital h sub ital q min l brace ital h 1 ital q r brace in the limit ital n r arrow infinity we further focus on the cases ital q 1 related to the fractal structure of the graph ital q 2 related to the energy spectrum and ital q 1 ital h the critical order beyond which our multiplicative and multiscaling bounded cascade model can be statistically distinguished from fractional brownian motion the corresponding additive and monoscaling model less

evidence of nonlogarithmic behavior of turbulent channel and pipe flow employing data of peak position and peak values of reynolds shear stress provided by canonical channel flow direct numerical simulations and pipe and channel flow experiments three recent theories predicting the mean velocity profile of wall bounded turbulent flows are compared based on that analysis it is verified that the mean velocity profile of such internal flows is logarithmic only to leading order and that the higher order terms are proportional to reciprocal powers of the karman number this finding clearly indicates that higher order effects with respect to the karman number and the wall normal coordinate must be considered furthermore our results show that even the statistics of the flow region closest to the wall are affected by flow phenomena that scale with outer variables

the character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model the likely character of the wavevector frequency spectrum of turbulent wall pressure on a smooth rigid plane is reexamined also modeling is extended for low mach numbers to the acoustic wavenumber domain from the relation of the wavevector frequency amplitude of wall pressure to amplitudes of fluctuating vorticity related velocity products reynolds stresses regarded as its sources the dependence of the wall pressure spectrum at subconvective wavenumbers is seen to depend essentially on the rate of decrease of the source cross spectra with wall distance y and on the identity of the wavenumber coefficient e g v or 1 that scales this profile a model wall pressure spectrum proposed earlier is generalized with respect to this rate of decrease and found to permit a range of possible dependences between k0 and k2 in that part of the subconvective domain where k 1 if a contribution to the source spectrum exists that is roughly independent of wall distance for v y k 1 it may dominate the wall pressure in the subconvective range and lead for k 1 to wavenumber independence of the spectrum in accord with the martin leehey wind tunnel measurement a comprehensive trial model for the wall pressure spectrum based on source models yielding this character is proposed and viewed as potentially satisfactory in all wavenumber domains from the acoustic to the convective for c k 1 it varies as k2 as follows for any source spectral profile that decreases at least as y 4 for y and accords with the phillips kraichnan theorem

probability distribution functions and coherent structures in a turbulent channel with the aid of a direct numerical simulation of an incompressible plane turbulent channel at h 162 we have determined the probability distribution functions pdf s of pressure and of the various velocity components from the wall to the channel center the pressure turns out to be symmetric with exponential tails at the wall as well as at y 2 5 at y 12 where the streamwise streaks intensity is maximum the pressure has become asymmetric this character intensifies with the distance away from the wall and the distribution obtained in the channel center resembles those determined in isotropic turbulence and free shear flows very close to the wall y 2 5 the pdf of u ensuremath is highly skewed with exponential and sub gaussian distributions at high and low values respectively this indicates that the high speed streaks are very intermittent at the wall the reverse occurs close to the channel center where intense negative u ensuremath prevail then we show that the most probable orientation of the fluctuating vorticity vector is perpendicular to the wall in the region 5l y l30 which is basically in the low and high speed regions while it is 45 ifmmode circ else textdegree fi with respect to the wall above

revisiting rainfall clustering and intermittency across different climatic regimes 1 one of the vexing questions in rainfall research is the role of intermittency and its nonuniversal signature in anomalous scaling functions whether this lack of universal behavior is due to the bursting patterns in rainfall intensity or the alternation between long dry periods and highly clustered wet phases or both remains an open issue to progress on a narrower scope of this problem the effects of intermittency originating from rainfall occurrence are first separated from rainfall intermittency induced by intensity variability across five climatic regimes considered here it was shown that the rainfall occurrence process op exhibits 1 a near constant spectral slope 2 a near constant clustering exponent and 3 a probability density function of dry phases displaying a power law behavior with an exponent 1 5 consistent with other studies for timescales commensurate with frontal and storm systems also for the op the scaling exponents of the normalized higher order structure functions reveal an extensive monofractal scaling at all five climatic regimes when taken together these intersite results are suggestive that rainfall intensity modulations are the main cause of the nonuniversal anomalous scaling and not the clustering properties associated with the support the nature of these modulations is markedly different when comparing rainfall to a familiar and often interrelated process such as scalar turbulence in the case of turbulence amplitude variability of scalar dissipation rates appear to mitigate the intermittency effects connected with anomalous scaling while for rainfall series intensity fluctuations seem to amplify them

analysis of sample path optimization sample path optimization is a method for optimizing limit functions occurring in stochastic modeling problems such as steady state functions in discrete event dynamic systems it is closely related to retrospective optimization techniques and to m estimation the method has been computationally tested elsewhere on problems arising in production and in project planning with apparent success in this paper we provide a mathematical justification for sample path optimization by showing that under certain assumptions which hold for the problems just mentioned the method will almost surely find a point that is in a specified sense sufficiently close to the set of optimizers of the limit function

a trust region algorithm with adaptive stochastic collocation for pde optimization under uncertainty the numerical solution of optimization problems governed by partial differential equations pdes with random coefficients is computationally challenging because of the large number of deterministic pde solves required at each optimization iteration this paper introduces an efficient algorithm for solving such problems based on a combination of adaptive sparse grid collocation for the discretization of the pde in the stochastic space and a trust region framework for optimization and fidelity management of the stochastic discretization the overall algorithm adapts the collocation points based on the progress of the optimization algorithm and the impact of the random variables on the solution of the optimization problem it frequently uses few collocation points initially and increases the number of collocation points only as necessary thereby keeping the number of deterministic pde solves low while guaranteeing convergence currently an error indicator is used to estimate gradient errors due to adaptive

an entropic stochastic representation of rainfall intermittency the origin of clustering and persistence 1 the well established physical and mathematical principle of maximum entropy interpreted as maximum uncertainty is used to explain the observed dependence properties of the rainfall occurrence process including the clustering behavior and persistence the conditions used for the maximization of entropy are as simple as possible i e that the rainfall processes is intermittent with dependent occurrences intermittency is quantified by the probability that a time interval is dry and dependence is quantified by the probability that two consecutive intervals are dry these two probabilities are used as constraints in a multiple scale entropy maximization framework which determines any conditional or unconditional probability of any sequence of dry and wet intervals at any timescale thus the rainfall occurrence process including its dependence structure is described by only two parameters this dependence structure appears to be non markovian application of this theoretical framework to the rainfall data set of athens indicates good agreement of theoretical predictions and empirical data at the entire range of scales for which probabilities dry and wet can be estimated from one hour to several months

stochastic daily precipitation models 1 a comparison of occurrence processes a first order markov chain and an alternating renewal process arp with a truncated geometric distribution of wet day intervals and a truncated negative binomial distribution of dry day intervals are compared as models describing the occurrence of sequences of wet and dry days numerical optimization techniques are used to obtain approximate maximum likelihood estimates of the fourier coefficients which describe the seasonal variation of the two markov chain parameters and the three parameters in the alternating renewal process for the four u s stations studied the markov chain model was superior to the arp using the minimum akaike information criterion

the optimization of convergence for chebyshev polynomial methods in an unbounded domain by using the method of steepest descent i have compared the suitability of three different methods for solving problems in a semi infinite or infinite domain using chebyshev polynomials exponential mappings are uniformyly bad domain truncation and algebraic mapping both work well but each is superior for a different category of problems when the solution is an entire function then domain truncation is best it is always simpler to apply than algebraic mapping and always at least as accurate much more accurate for functions which decay very rapidly for singular functions on the other hand algebraic mapping is better because it is less sensitive to the mapping scale factor l permitting a better compromise in resolving both the singularity and the exponential decay for both types of problems i give simple explicit estimates of both the optimum choise of domain size or mapping factor and of the attainable accuracy for the model entire function exp azk on a semi infinite interval 0 the optimum domain size is l 0 896 na 1k and the smallest attainable error is roughly e n 0 896 k where n is the number of chebyshev polynomals used similar formulas for singular functions handled via algebraic mapping are given in 3 41 to 3 45 below

semi implicit runge kutta schemes development and application to compressible channel flow time stepconstraintdueto thefine meshnear thewall the explicitsubschemeis asix stage fourth order low storage runge kutta scheme based on analysis in fourier space and results obtained for propagation test cases the semiimplicitschemesareshowntobeoforder3and forwavesdiscretizedbyanumberofpointsperperiodbetween4and 16 tobeasaccurateas ormoreaccuratethan thestandardexplicitfourth orderrunge kuttaalgorithmintermsof dissipationanddispersion thelarge eddysimulationofacompressibleturbulentchannelflowatafrictionreynolds numberof360andamachnumberof0 1isthencarriedoutwithoneoftheproposedalgorithms thecomputational time is reduced by a factor 1 33 with respect to a large eddy simulation using the explicit subscheme in all directions wall pressure and velocity spectra from the large eddy simulation are presented to give insights into the flow turbulent structures in particular wave number frequency spectra are calculated acoustic components appear to be identified in these spectra

spectral methods for the navier stokes equations with one infinite and two periodic directions abstract two numerical methods were designed to solve the time dependent three dimensional incompressible navier stokes equations in boundary layers method a semi infinite domain and mixing layers or wakes method b fully infinite domain their originality lies in the use of rapidly decaying spectral basis functions to approximate the vertical dependence of the solutions combined with one method a or two method b slowly decaying extra functions for each wave vector that exactly represent the irrotational component of the solution at large distances both methods eliminate the pressure term as part of the formulation thus avoiding fractional step time integration they yield rapid convergence and are free of spurious modes in the orr sommerfeld spectra they are also efficient although the operation count is of order n 2 n is the number of modes in the infinite direction these methods have been used for extensive direct numerical simulations of transition and turbulence a new time integration scheme with low storage requirements and good stability properties is also described

continuous time versus discrete time point process models for rainfall occurrence series several authors have had apparent success in applying continuous time point process models to rainfall occurrence sequences in this paper it is shown that if rainfall occurrences are interpreted as the events of a point process and not as a censored sample the continuous time point process methodology and estimation procedures are not directly applicable since they fail to account for the time discreteness of the sample process this is demonstrated analytically by studying the effects of discretization on selected statistical properties of a poisson process a neyman scott process and a renewal cox process with markovian intensity in general the study of rainfall occurrences under the continuous time point process framework may result in misleading inferences regarding clustering dispersion and consequently incorrect interpretations of the underlying rainfall generating mechanisms for example daily rainfall occurrence structures underdispersed relative to the poisson process are usually overdispersed relative to the bernoulli process the discrete time analogue of the poisson these findings are confirmed by the statistical analysis of six daily rainfall records representative of a range of u s climates two of which are described in detail

surface pressure fluctuations beneath two and three dimensional turbulent boundary layers surface pressure fluctuation measurements were made in two dimensional turbulent boundary layers at two reynolds numbers re 7 3 10 3 and 2 34 104 and pressure driven three dimensional turbulent boundary layers at two reynolds numbers approach re 5 94 x 10 3 and 2 32 104 the collapse of spectral levels at middle and high frequencies and the effects of inner and outer boundary layer scaling variables are shown for a wide range of reynolds numbers 1 4 x 10 3 2 34 104 for the two dimensional flows such scaling parameters do not collapse the pressure spectra beneath three dimensional flows which have a nearly constant or flat midfrequency range and at some measurement stations and spectral levels within the flat and high frequency spectral ranges that significantly raise p additionally dimensional spectral levels within the flat frequency range are independent of reynolds number analysis based on the poisson equation shows that the variation of the high frequency spectral levels is related to the variation in near wall mean velocity gradients and 2 structure due to the spanwise pressure gradient

compact fourth order finite volume method for numerical solutions of navier stokes equations on staggered grids the development of a compact fourth order finite volume method for solutions of the navier stokes equations on staggered grids is presented a special attention is given to the conservation laws on momentum control volumes a higher order divergence free interpolation for convective velocities is developed which ensures a perfect conservation of mass and momentum on momentum control volumes three forms of the nonlinear correction for staggered grids are proposed and studied the accuracy of each approximation is assessed comparatively in fourier space the importance of higher order approximations of pressure is discussed and numerically demonstrated fourth order accuracy of the complete scheme is illustrated by the doubly periodic shear layer and the instability of plane channel flow the efficiency of the scheme is demonstrated by a grid dependency study of turbulent channel flows by means of direct numerical simulations the proposed scheme is highly accurate and efficient at the same level of accuracy the fourth order scheme can be ten times faster than the second order counterpart this gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost

discrete orthogonal function expansions for non uniform grids using the fast fourier transform abstract discrete orthogonal function expansions are obtained for non uniformly spaced data by combined use of mapping functions and the fast fourier transform the result yields alias free differentiation and integration operators the method is applicable to periodic zero or zero derivative boundary conditions or combinations thereof truncation is required to avoid aliasing and or singularity but the truncation error is explicit quantitatively expressible and generally small this approach is demonstrated in an infinite physical domain with application to linear convection and diffusion the resulting errors are orders of magnitude smaller than those generated by standard finite difference methods difficulties arising from image fields are an important phenomena the method of differentiation as well as the boundary conditions imply artificial image fields a vortex pairing problem is presented which shows that image flows can totally alter the solution the new scheme avoids this undesirable effect by keeping image flows infinitely far away

high order accurate solution of the incompressible navier stokes equations on massively parallel computers the emergence of petascale supercomputers requires us to develop today s simulation codes for incompressible flows by codes which are using numerical schemes and methods that are better able to exploit the offered computational power in that spirit we present a massively parallel high order navier stokes solver for large incompressible flow problems in three dimensions the governing equations are discretized with finite differences in space and a semi implicit time integration scheme this discretization leads to a large linear system of equations which is solved with a cascade of iterative solvers the iterative solver for the pressure uses a highly efficient commutation based preconditioner which is robust with respect to grid stretching the efficiency of the implementation is further enhanced by carefully setting the adaptive termination criteria for the different iterative solvers the computational work is distributed to different processing units by a geometric data decomposition in all three dimensions this decomposition scheme ensures a low communication overhead and excellent scaling capabilities the discretization is thoroughly validated first we verify the convergence orders of the spatial and temporal discretizations for a forced channel flow second we analyze the iterative solution technique by investigating the absolute accuracy of the implementation with respect to the different termination criteria third orr sommerfeld and squire eigenmodes for plane poiseuille flow are simulated and compared to analytical results fourth the practical applicability of the implementation is tested for transitional and turbulent channel flow the results are compared to solutions from a pseudospectral solver subsequently the performance of the commutation based preconditioner for the pressure iteration is demonstrated finally the excellent parallel scalability of the proposed method is demonstrated with a weak and a strong scaling test on up to o 10 4 processing units and o 10 1 1 grid points

a nonparametric model for stochastic generation of daily rainfall occurrence 1 this paper presents a nonparametric model for generating single site daily rainfall occurrence the model is formulated to reproduce longer term variability and low frequency features such as drought and sustained wet periods while still reproducing characteristics at daily time scales parsimony is achieved within a markovian framework by using aggregate predictor variables that describe how wet it has been over a period of time the use of a moving window to give a seasonally representative sample at any given time of year ensures an accurate representation of the seasonal variations present in the rainfall time series actual simulation proceeds by resampling from the historical record of rainfall occurrence conditional to the current values of the associated predictors the model is applied using historical daily rainfall occurrence from sydney australia we find that the use of multiple predictors specified at a daily level and at seasonal annual and multiyear aggregation levels leads to sequences that more closely reproduce the longer term variability present in the historic records compared to sequences produced by models incorporating only one or two predictors

multiscaling properties of rainfall and bounded random cascades the connection among different types of exponents characterizing multiscaling properties of rainfall and a criterion for stationarity of random fields are discussed and a new phenomenological model for rainfall time series simulation is proposed the bounded random cascade model presented here is a generalization of the well known model with the multiplicative weights of the generator converging to unity as the cascade proceeds to smaller scales this allows one to directly simulate a multiscaling random field with an energy spectrum exponent 1 which is typical for rainfall time series data but which cannot be produced by a standard model a procedure is proposed for estimating the cascade parameters of this new bounded model from observed data parameters are estimated from two data sets with different degrees of intermittency and different spectral exponents the bounded model simulations using these parameters produced realistic rainfall time series with spectral exponents similar to their observed counterparts

the mathematical structure of rainfall representations 2 a review of the theory of point processes part 2 constitutes the second of three parts devoted to the mathematical structure of rainfall an expository yet current treatment of those features of point process theory which are essential to descriptions of the hydrologic processes is developed a general overview of this three part series is given in part 1

a theoretically consistent stochastic cascade for temporal disaggregation of intermittent rainfall generating fine scale time series of intermittent rainfall that are fully consistent with any given coarse scale totals is a key and open issue in many hydrological problems we propose a stationary disaggregation method that simulates rainfall time series with given dependence structure wet dry probability and marginal distribution at a target finer lower level time scale preserving full consistency with variables at a parent coarser higher level time scale we account for the intermittent character of rainfall at fine time scales by merging a discrete stochastic representation of intermittency and a continuous one of rainfall depths this approach yields a unique and parsimonious mathematical framework providing general analytical formulations of mean variance and autocorrelation function acf for a mixed type stochastic process in terms of mean variance and acfs of both continuous and discrete components respectively to achieve the full consistency between variables at finer and coarser time scales in terms of marginal distribution and coarse scale totals the generated lower level series are adjusted according to a procedure that does not affect the stochastic structure implied by the original model to assess model performance we study rainfall process as intermittent with both independent and dependent occurrences where dependence is quantified by the probability that two consecutive time intervals are dry in either case we provide analytical formulations of main statistics of our mixed type disaggregation model and show their clear accordance with monte carlo simulations an application to rainfall time series from real world is shown as a proof of concept

the mathematical structure of rainfall representations 1 a review of the stochastic rainfall models this is the first of a three part series on the mathematical structure of rainfall models several important attempts at modeling rainfall are reviewed special attention is given to the mathematical structures that arise in the rainfall descriptions a general overview of the three part series is given as preface to this part

highly energy conservative finite difference method for the cylindrical coordinate system a highly energy conservative second order accurate finite difference method for the cylindrical coordinate system is developed it is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used this argument holds not only for an unequally spaced mesh but also for an equally spaced mesh on cylindrical coordinates but not on cartesian coordinates numerical tests are undertaken for an inviscid flow with various schemes and it turns out that the proposed scheme offers a superior energy conservation property and greater stability than the intuitive and previously proposed methods for both equally spaced and unequally spaced meshes

a stochastic cluster model of daily rainfall sequences a two level point stochastic model for the rainfall occurrences at a given rainfall station is constructed in the time dimension the model is a cluster process of the neyman scott type the model has the rainfall generating mechanisms as its primary level and the rainfalls that are generated by these mechanisms as the secondary level it uses infinite superposition of rainfalls and has a very flexible dependence structure the model is fitted to daily rainfall sequences in indiana after these are stationarized by a transformation the fit of the model is then tested in terms of its correlation and marginal probability characteristics the present form of the neyman scott cluster model is time homogeneous therefore the neyman scott process as presented in this paper may be of practical use only for modeling the stationary rainfall occurrences

a nonparametric approach for representing interannual dependence in monthly streamflow sequences 1 the estimation of risks associated with water management plans requires generation of synthetic streamflow sequences the mathematical algorithms used to generate these sequences at monthly timescales are found lacking in two main respects inability in preserving dependence attributes particularly at large seasonal to interannual time lags and a poor representation of observed distributional characteristics in particular representation of strong asymmetry or multimodality in the probability density function proposed here is an alternative that naturally incorporates both observed dependence and distributional attributes in the generated sequences use of a nonparametric framework provides an effective means for representing the observed probability distribution while the use of a variable kernel ensures accurate modeling of streamflow data sets that contain a substantial number of zero flow values a careful selection of prior flows imparts the appropriate short term memory while use of an aggregate flow variable allows representation of interannual dependence the nonparametric simulation model is applied to monthly flows from the beaver river near beaver utah and the burrendong dam inflows new south wales australia

a spectral numerical method for the navier stokes equations with applications to taylor couette flow a new spectral method for solving the incompressible navier stokes equations in a plane channel and between concentric cylinders is presented the method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step in addition the number of dependent variables is reduced resulting in a reduction in computer memory requirements several test problems have been computed for the channel flow and for flow between concentric cylinders including taylor couette flow with axisymmetric taylor vortices and wavy vortices in all cases agreement with available experimental and theoretical results is very good

evaluation of cluster based rectangular pulses point process models for rainfall this technical note presents a comparison of cluster based point rainfall models using the historical hourly rainfall data observed between 1949 and 1976 at denver colorado the denver data are used to analyze the performance of three classes of models namely the bartlett lewis model the geometric neyman scott model and the poisson neyman scott model the original formulation of the structure of each model as well as the modified description developed in order to improve the zero depth probability is considered in this study rodriguez iturbe et al 1987a concluded that it is unlikely that empirical analysis of rainfall data can be used to choose between the bartlett lewis model and the neyman scott model in a subsequent paper rodriguez iturbe et al 1987b argued that the choice of the distribution of the number of cells per storm for the neyman scott model either geometric or poisson has no general bias effect on the stochastic structure some investigators e g burlando and rosso 1991 however reported results contradictory to those of the previous authors in light of these observations this note investigates the performance of the cluster based models for the denver data the geometric neyman scott model yields better results compared to the poisson neyman scott model moreover the bartlett lewis model is shown to be very sensitive to the sets of moment equations used in the parameter estimation this sensitivity is not observed in the neyman scott scheme and is believed to be a drawback for applying the bartlett lewis model in hydrologic simulation studies

inexact objective function evaluations in a trust region algorithm for pde constrained optimization under uncertainty this paper improves the trust region algorithm with adaptive sparse grids introduced in siam j sci comput 35 2013 pp a1847 a1879 for the solution of optimization problems governed by partial differential equations pdes with uncertain coefficients the previous algorithm used adaptive sparse grid discretizations to generate models that are applied in a trust region framework to generate a trial step the decision whether to accept this trial step as the new iterate however required relatively high fidelity adaptive discretizations of the objective function in this paper we extend the algorithm and convergence theory to allow the use of low fidelity adaptive sparse grid models in objective function evaluations this is accomplished by extending conditions on inexact function evaluations used in previous trust region frameworks our algorithm adaptively builds two separate sparse grids one to generate optimization models for the step computation and one to approximate the objective function

probabilistic representation of the temporal rainfall process by a modified neyman scott rectangular pulses model parameter estimation and validation the capability of the neyman scott clustered stochastic point process model of rainfall to preserve various observed statistics is considered randomization of the cell duration parameter from storm to storm is shown to considerably improve the wet dry period joint distribution and extreme value statistics a simple procedure for parameter estimation is introduced and applied

a retrospective trust region method for unconstrained optimization we introduce a new trust region method for unconstrained optimization where the radius update is computed using the model information at the current iterate rather than at the preceding one the update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate global convergence to first and second order critical points is proved under classical assumptions and preliminary numerical experiments on cuter problems indicate that the new method is very competitive

the projection method for the incompressible navier stokes equations the pressure near a no slip wall an explicit staggered projection method for the incompressible navier stokes equations with no slip walls is analyzed and used in simulations to address several issues related to the pressure boundary condition required when the continuity equation is replaced by the standard pressure poisson equation ppe 2 p u u f first it is shown that a ppe system supplemented with a neumann pressure boundary condition derived from the momentum equation can be made consistent with the navier stokes equations if it is extended with the requirement that 2 u 0 is zero near the wall and the solution is sufficiently smooth this implies that it is possible to formulate a boundary condition for the standard ppe without the necessity to resort to green s functions which is interesting for theoretical reasons second the equivalence is shown between the staggered projection method and the staggered discretization of above ppe system the derivation of the equivalence sheds light upon the so called ppe paradox and leads to an approximation of the wall value of p n which is not required but implied by the staggered projection method third the near wall regularity of a solution of the navier stokes equations is numerically analyzed by means of direct numerical simulation of turbulent channel flow performed with the staggered projection method from the numerical inspection of all terms of the momentum equation in the near wall region it is concluded that the three components of the momentum equation are satisfied on the wall for t 0 for short times but also in the turbulent regime in the limit t 0 the pressure gradient is observed to converge to the initial pressure gradient in the l 2 norm which confirms a disputed theoretical result in literature even in the maximum norm the pressure gradient appears to converge to the initial pressure gradient the only discontinuities observed in the simulations are the discontinuities of the tangential viscous terms and the time derivatives of the tangential velocities on the wall at t 0 thus the numerical results indicate that the regularity of the solution for turbulent channel flow is stronger than claimed by existing theory

coupling stochastic models of different timescales a methodology is proposed for coupling stochastic models of hydrologic processes applying to different timescales so that time series generated by the different models be consistent given two multivariate time series generated by two separate unrelated stochastic models of the same hydrologic process each applying to a different timescale a transformation is developed referred to as a coupling transformation that appropriately modifies the time series of the lower level finer timescale so that this series becomes consistent with the time series of the higher level coarser timescale without affecting the second order stochastic structure of the former and also establishes appropriate correlations between the two time series the coupling transformation is based on a developed generalized mathematical proposition which ensures preservation of marginal and joint second order statistics and of linear relationships between lower and higher level processes several specific forms of the coupling transformation are studied from the simplest single variate to the full multivariate in addition techniques for evaluating parameters of the coupling transformation based on second order moments of the lower level process are studied furthermore two methods are proposed to enable preservation of the skewness of the processes in addition to that of second order statistics the overall methodology can be applied to problems involving disaggregation of annual to seasonal and seasonal to subseasonal timescales as well as problems involving finer timescales e g daily to hourly with the only requirement that a specific stochastic model is available for each involved timescale the performance of the methodology is demonstrated by means of a detailed numerical example

the relationship between a continuous time renewal model and a discrete markov chain model of precipitation occurrence a relationship between a continuous wet dry renewal model with gamma distributed dry intervals and a markov chain model for daily rainfall is derived the relationship requires numerical evaluation for the general case but closed form solutions are available for the markov process case in which dry intervals are exponentially distributed the markov process equations are equivalent to those derived by j r green 1964 for first order transition probabilities but are presented in a simplified nonrecursive form the markov process relationships are examined for convergence and accuracy with simulation studies and comparison to observed rainfall records the markov process model is shown to provide a good representation in certain parts of the united states in other areas where the markov property is inappropriate due to event clustering or other phenomena the gamma model provides an improved characterization of the relationship between continuous and discrete rainfall occurrence