Conditional resampling of hydrologic time series using multiple predictor variables: A K-nearest neighbour approach

Unlike parametric alternatives for time series generation, non-parametric approaches generate new values by conditionally resampling past observations using a probability rationale. Observations lying ‘close’ to the conditioning vector are resampled with higher probability, ‘closeness’ is defined using a Euclidean or Mahalanobis distance formulation. A common problem with these approaches is the difficulty in distinguishing the importance of each predictor in the estimation of the distance. As a consequence, the conditional probability and hence the resampled series, can offer a biased representation of the true population it aims to simulate. This paper presents a variation of the K-nearest neighbour resampler designed for use with multiple predictor variables. In the modification proposed, an influence weight is assigned to each predictor in the conditioning set with the aim of identifying nearest neighbours that represent the conditional dependence in an improved manner. The workability of the proposed modification is tested using synthetic data from known linear and non-linear models and its applicability is illustrated through an example where daily rainfall is downscaled over 15 stations near Sydney, Australia using a predictor set consisting of selected large-scale atmospheric circulation variables.     

A hidden Markov model segmentation procedure for hydrological and environmental time series

In this paper we present a procedure for the segmentation of hydrological and enviromental time series. We consider the segmentation problem from a purely computational point of view which involves the minimization of Huberts segmentation cost; in addition this least squares segmentation is equivalent to Maximum Likelihood segmentation. Our segmentation procedure maximizes Likelihood and minimizes Huberts least squares criterion using a hidden Markov model (HMM) segmentation algorithm. This algorithm is guaranteed to achieve a local maximum of the Likelihood. We evaluate the segmentation procedure with numerical experiments which involve artificial, temperature and river discharge time series. In all experiments, the procedure actually achieves the global minimum of the Likelihood; furthermore execution time is only a few seconds, even for time series with over a thousand terms.     

A theoretically based Wakeby distribution for annual flood series

Abstract

The exact distribution of the ratio of any magnitude to the sum of all magnitudes in an annual flood series satisfying the usual distribution-free assumptions of independence and identical distribution, and the additional parametric assumption of exponential tail behaviour with truncation, is shown to be a beta distribution of the first kind. A two-parameter linear transformation of the beta distribution completes the derivation and yields a Wakeby distribution which has the number of members in a series as a given parameter. The Wakeby distribution is developed to illustrate how, in principle, some perceived deficiencies in current flood frequency analysis may be met: more complex parametric assumptions should lead to distributions of wider application. In particular, the distribution has a secure theoretical basis and is hydrologically more realistic because it bounds the variate and requires the definition of a temporally finite annual series. Analytical expressions are obtained for estimating the two distribution parameters; the quantite standard error and a plotting rule. An example is given of the application of the distribution to the design flood problem and an annual flood series is modelled. It is further suggested that a suitable design value for the largest flood to be withstood by a protection work is a statistic of the largest flood occurring during its lifetime. For the derived Wakeby distribution this criterion specifies risk and probability of non-exceedance of the design flood once a lifetime is selected.     

On the annual maximum distribution in dependent partial duration series

As a basis for development of the annual maximum distribution the so-called partial duration series with Poissonian occurrence times and exponentially distributed peak exceedance values has been selected. The model is generalized by allowing for a Markov dependence between succeeding peak values. Correlation values from p=0 to p=1 can be accounted for by introducing the Marshall-Olkin bivariate exponential distribution, which is presented in detail. The developed distribution function for the annual maximum is throughly analysed and a variety of distribution forms depending on the value of the correlation coefficient and the intensity in the Poisson process is hereby recognized. To a certain extent this might be considered as parallel to the scattering of hydrological regions with different generating mechanisms for the annual maxima.     

Matched block bootstrap for resampling multiseason hydrologic time series

A nonparametric method for resampling multiseason hydrologic time series is presented. It is based on the idea of rank matching, for simulating univariate time series with strong and/or long‐range dependence. The rank matching rule suggests concatenating with higher likelihood those blocks that match at their ends. In the proposed method, termed ‘multiseason matched block bootstrap’, nonoverlapping within‐year blocks of hydrologic data (formed from the observed time series) are conditionally resampled using the rank matching rule. The effectiveness of the method in recovering various statistical attributes, including the dependence structure from finite samples generated from a known population, is demonstrated through a two‐level hypothetical Monte Carlo simulation experiment. The method offers enough flexibility to the modeller and is shown to be appropriate for modelling hydrologic data that display strong dependence, nonlinearity and/or multimodality in the time series depicting the hydrologic process. The method is shown to be more efficient than the nonparametric ‘k‐nearest neighbor bootstrap’ method in simulating the monthly streamflows that exhibit a complex dependence structure and bimodal marginal probability density. Even with short block sizes, this bootstrap method is able to predict the drought characteristics reasonably accurately. Copyright © 2005 John Wiley & Sons, Ltd.     

Application of Markovian models for non-ergodic and non-stationary earthquake times series for the identification of seismic patterns and future projections*

The current earthquake forecast algorithms are not free of shortcomings due to inherent limitations. Especially, the requirement of stationarity in the evaluation of earthquake time series as a prerequisite, significantly limits the use of forecast algorithms to areas where stationary data is not available. Another shortcoming of forecast algorithms is the ergodicity assumption, which states that certain characteristics of seismicity are spatially invariant. In this study, a new earthquake forecast approach is introduced for the locations where stationary data are not available. For this purpose, the spatial activity rate density for each spatial unit is evaluated as a parameter of a Markov chain. The temporal pattern is identified by setting the states at certain spatial activity rate densities. By using the transition patterns between the states, 1- and 5-year forecasts were computed. The method is suggested as an alternative and complementary to the existing methods by proposing a solution to the issues of ergodicity and stationarity assumptions at the same time.     

A simple method for effective multi-site generation of stochastic hydrologic time series

This paper presents an algorithm for generating stationary stochastic hydrologic time series at multiple sites. The ideas in this paper constitute a radical departure from commonly accepted methodologies. The approach relies on the recent advances in statistical science for simulating random variables with arbitrary marginal distributions and a given covariance structure, and on an algorithm for re-ordering the generated sub-sets of each synthetic year of data such that the annual auto-correlation of desired lag is maintained, along with the autocorrelations between the end of the preceding year and the beginning of the current year. The main features of the proposed algorithm are simplicity and ease of implementation. A numerical test is presented containing the generation of 1000 years of weekly stochastic series for four sites based on the 84 years of historical natural weekly flows from Southern Alberta in Canada.     

地下流体学科月、年评比数据报送软件

为了更好地完成向中国地震局地下流体学科技术管理组报送数字化月、年评比数据的工作,研制了地下流体学科月、年评比数据报送软件,实现了从天津预处理前兆数据库PDB_TJ中读取数字化数据,写入Excel生成附件文件,对数据个数进行检验,自动发送邮件等功能,使用起来方便快捷.     

A precipitation occurrence model

 An imbedded renewal process as a model of precipitation occurrence is fairly well known. Data permitting verification of assumptions determining such a model, for example independence and distribution of sojourn times, are available rather rarely, however, due to problems with definition of a precipitation. An operational definition of a precipitation is obtained by associating the precipitation occurrence with an opening sojourn time of a precipitation collector. This paper describes identification of the renewal model using such definition and applies the model to compare several different precipitation collectors.     

地倾斜年变形态改变分析

2006年在清理核实云南省地震前兆观测数据过程中,发现澄江地震局水平摆仪2002年的观测数据与前后两年的差异较大,经过逐一落实,找出差异大的原因,揭示数据处理的重要性。     

A gis-based distributed parameter hydrologic model for urban areas

A hydrologic model for urban areas has been developed which incorporates distributed parameter modelling concepts and functions in the context of a geographic information system. In the proposed model, the watershed is represented as a cascade of grid cells, whose size can be specified by the user. Preliminary processing includes the determination of overland flow directions for each cell. An automated procedure is used to establish the cell-to-cell connectivity scheme, which is used to order the computations within each time step. Infiltration is computed using the Green-Ampt equation, while runoff rates are computed using a coupling of the continuity equation and Manning's equation for turbulent flow. Storm sewer flows are routed using time-shift routing. The model is capable of simulating flow through streets and offers the possibility of predicting the downstream movement of sewer system overflows. In preliminary testing on a small residential watershed, the model was able to reproduce measured hydrographs.     

A practical method for outlier detection in autoregressive time series modelling

A practical method is developed for outlier detection in autoregressive modelling. It has the interpretation of a Mahalanobis distance function and requires minimal additional computation once a model is fitted. It can be of use to detect both innovation outliers and additive outliers. Both simulated data and real data re used for illustration, including one data set from water resources.     

Impulse response of the kinematic diffusion model as a probability distribution of hydrologic samples with zero values

It is hypothesized that the unit impulse response of a linearized kinematic diffusion (KD) model is a probability distribution suitable for frequency analysis of hydrologic samples with zero values. Such samples may include data on monthly precipitation in dry seasons, annual low flow, and annual maximum peak discharge observed in arid and semiarid regions. The hypothesized probability distribution has two parameters, which are estimated using the methods of moments (MOM) and maximum likelihood (MLM). Also estimated are errors in quantiles for MOM and MLM. The distribution shows an equivalency of MOM and MLM with respect to the mean value—an important property for ML-estimation in the case of the unknown true distribution function. The hypothesized KD distribution is tested on 44 discharge data series and compared with the Muskingum-like (M-like) probability distribution function. A comparison of empirical distribution with KD and M-like distributions shows that MOM better reproduces the upper tail of the distribution, while MLM is more robust for higher sample values and more conditioned on the value of the probability of the zero value event. The KD-model is suitable for frequency analysis of short samples with zero values and it is more universal than the M-like model as its modal value cannot be only equaled to zero value but also to any positive value.     

An improved time series model for monthly stream flows

This study aims to develop an improved time series model to overcome difficulties in modeling monthly short term stream flows. The periodic, serial dependent and independent components of the classical time series models are improved separately by information transfer from a surrounding long term gauging station to the considered flow section having short term records. Eventually, an improved model preserving the mathematical model structure of the classical time series model, while improving general and monthly statistics of the monthly stream flows, is derived by using the improved components instead of the short term model components in the time series modeling. The correlative relationships between the current short term and surrounding long term stations are used to improve periodic and serial dependent behaviors of monthly flows. Independent components (residuals) are improved via the parameters defining their theoretical probability distribution. The improved model approach is tested by using 50 year records of Göksu-Himmetli (1801) and Göksu-Gökdere (1805) flow monitoring stations located on the Ceyhan river basin, in south of Turkey. After 50 year records of the station 1801 are separated into five 10 year sub series, their improved and classical time series models are computed and compared with the real long-term (50 year) time series model of this station to reveal efficiencies of the improved models for each subseries (sub terms with 10 year observation). The comparisons are realized based on the model components, model estimates and general/monthly statistics of model estimates. Finally, some evaluations are made on the results compared to the regression method classically applied in the literature.     

Flood probability analysis for un-gauged watersheds by means of a simple distributed hydrologic model

A methodology is proposed for the inference, at the regional and local scales, of flood magnitude and associated probability. Once properly set-up, this methodology is able to provide flood frequencies distributions at gauged and un-gauged river sections pertaining to the same homogeneous region, using information extracted from rainfall observations. A proper flood frequency distribution can be therefore predicted even in un-gauged watersheds, for which no discharge time series is available.     

A multivariate gamma distribution arising from a Markov model

A Markov chain{X _t }, which has been useful for modelling in hydrology, can be specified by the Laplace transform (LT) of the conditional p.d.f. ofX _t+1 givenX _t =x _t , which is assumed to be of the exponential formH()exp{-G()x _t }. For appropriate choice ofH andG the marginal distribution ofX _t is the (univariate) gamma distribution. In this case, the joint p.d.f. ofX _t +1,...,X _t+n and its LT, are obtained, and this is extended to a seasonal version of the chain. A simple method of generating observations from these multivariate gamma distributions is noted, and the joint LT is applied to the problem of determining moments of weighted sums of such variables.     

Observed advantage for negative binomial over Poisson distribution in partial duration series

The goodness of fit of the negative binomial and the Poisson distributions to partial duration series of runoff events is tested. The data have been recorded by eight hydrometric stations located on ephemeral rivers in Isreal. For each station, a number of threshold discharges are considered, by that series of nested subsamples are formed. Owing to size limitations, a Chi-square test is conducted on samples associated with low to moderate threshold discharges. Positive results, at a 5% significance level, are obtained in 30 out of the 53 tests of the Poisson distribution, and in 22 out of the 28 tests of the negative binomial distribution. The fit of the Poisson distribution to samples of conventionally recommended sizes (of 2 to 3 events per year) is found positive for five rivers and negative for the three other rivers The fit of the negative binomial distribution to these samples is found positive for six rivers, inconclusive for one river and short of data for the eighth river. Mixed results are obtained as the threshold level is raised. Therefore, no direct extrapolation is possible to samples associated with high thresholds.An indirect extrapolation is drawn through a comparison of the actual properties of the samples with those expected under a perfect fit of the distribution functions. Ranges of such properties are defined with respect to the properties of the tested samples and to the test results. The actual properties of nine of the eleven samples associated with high thresholds (i.e. mean number of events <-0.1year ^–1) are found within these ranges. This provides a hint for a probable good fit of either distribution, and particularly the negative binomial, to the occurrence frequency of high events.     

Observed advantage for negative binomial over Poisson distribution in partial duration series

The goodness of fit of the negative binomial and the Poisson distributions to partial duration series of runoff events is tested. The data have been recorded by eight hydrometric stations located on ephemeral rivers in Isreal. For each station, a number of threshold discharges are considered, by that series of nested subsamples are formed. Owing to size limitations, a Chi-square test is conducted on samples associated with low to moderate threshold discharges. Positive results, at a 5% significance level, are obtained in 30 out of the 53 tests of the Poisson distribution, and in 22 out of the 28 tests of the negative binomial distribution. The fit of the Poisson distribution to samples of conventionally recommended sizes (of 2 to 3 events per year) is found positive for five rivers and negative for the three other rivers The fit of the negative binomial distribution to these samples is found positive for six rivers, inconclusive for one river and short of data for the eighth river. Mixed results are obtained as the threshold level is raised. Therefore, no direct extrapolation is possible to samples associated with high thresholds.An indirect extrapolation is drawn through a comparison of the actual properties of the samples with those expected under a perfect fit of the distribution functions. Ranges of such properties are defined with respect to the properties of the tested samples and to the test results. The actual properties of nine of the eleven samples associated with high thresholds (i.e. mean number of events <-0.1year ^–1) are found within these ranges. This provides a hint for a probable good fit of either distribution, and particularly the negative binomial, to the occurrence frequency of high events.     

A nonlinear data‐driven model for synthetic generation of annual streamflows

A hybrid model that blends two non‐linear data‐driven models, i.e. an artificial neural network (ANN) and a moving block bootstrap (MBB), is proposed for modelling annual streamflows of rivers that exhibit complex dependence. In the proposed model, the annual streamflows are modelled initially using a radial basis function ANN model. The residuals extracted from the neural network model are resampled using the non‐parametric resampling technique MBB to obtain innovations, which are then added back to the ANN‐modelled flows to generate synthetic replicates. The model has been applied to three annual streamflow records with variable record length, selected from different geographic regions, namely Africa, USA and former USSR. The performance of the proposed ANN‐based non‐linear hybrid model has been compared with that of the linear parametric hybrid model. The results from the case studies indicate that the proposed ANN‐based hybrid model (ANNHM) is able to reproduce the skewness present in the streamflows better compared to the linear parametric‐based hybrid model (LPHM), owing to the effective capturing of the non‐linearities. Moreover, the ANNHM, being a completely data‐driven model, reproduces the features of the marginal distribution more closely than the LPHM, but offers less smoothing and no extrapolation value. It is observed that even though the preservation of the linear dependence structure by the ANNHM is inferior to the LPHM, the effective blending of the two non‐linear models helps the ANNHM to predict the drought and the storage characteristics efficiently. Copyright © 2007 John Wiley & Sons, Ltd.     

Periodicities in the time series of annual minimum temperatures for the United States Gulf Coast region

The minimum winter temperature series for the United States Gulf Coast for 1799–1988 (190 values) was subjected to Maximum Entropy Spectral Analysis. Significant periodicities in the QBO region (T-2–3 years) and atT=3.7, 4.5, 5.5, 6.5, 7.5, 12.9, 15.5 and 22 years were detected. Some of these were present in the first half only (1799–1893) while others in the latter half only (1894–1988), indicating a transient nature. Also, more than 50% of the variance was random. Many of the significant periodicities are seen in other geophysical parameters. Some may be harmonics of the 11-year sunspot cycle and the 22-year Hale magnetic sunspot cycle.