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1.
A new approach for streamflow simulation using nonparametric methods was described in a recent publication (Sharma et al.
1997). Use of nonparametric methods has the advantage that they avoid the issue of selecting a probability distribution and
can represent nonlinear features, such as asymmetry and bimodality that hitherto were difficult to represent, in the probability
structure of hydrologic variables such as streamflow and precipitation. The nonparametric method used was kernel density estimation,
which requires the selection of bandwidth (smoothing) parameters. This study documents some of the tests that were conduced
to evaluate the performance of bandwidth estimation methods for kernel density estimation. Issues related to selection of
optimal smoothing parameters for kernel density estimation with small samples (200 or fewer data points) are examined. Both
reference to a Gaussian density and data based specifications are applied to estimate bandwidths for samples from bivariate
normal mixture densities. The three data based methods studied are Maximum Likelihood Cross Validation (MLCV), Least Square
Cross Validation (LSCV) and Biased Cross Validation (BCV2). Modifications for estimating optimal local bandwidths using MLCV
and LSCV are also examined. We found that the use of local bandwidths does not necessarily improve the density estimate with
small samples. Of the global bandwidth estimators compared, we found that MLCV and LSCV are better because they show lower
variability and higher accuracy while Biased Cross Validation suffers from multiple optimal bandwidths for samples from strongly
bimodal densities. These results, of particular interest in stochastic hydrology where small samples are common, may have
importance in other applications of nonparametric density estimation methods with similar sample sizes and distribution shapes.
Received: November 12, 1997 相似文献
2.
T. I. Harrold A. Sharma S. Sheather 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(4):310-324
Mutual information is a generalised measure of dependence between any two variables. It can be used to quantify non-linear
as well as linear dependence between any two variables. This makes mutual information an attractive alternative to the use
of the correlation coefficient, which can only quantify the linear dependence pattern. Mutual information is especially suited
for application to hydrological problems, because the dependence between any two hydrologic variables is seldom linear in
nature. Calculation of the mutual information score involves estimation of the marginal and joint probability density functions
of the two variables. This paper uses nonparametric kernel density estimation methods to estimate the probability density
functions. Accurate estimation of the mutual information score using kernel methods requires selection of appropriate smoothing
parameters (bandwidths) for use with the kernels. The aim of this paper is to obtain a practical method for bandwidth selection
for calculation of the mutual information score. In this paper, the lag-one dependence structures of several autocorrelated
time series are analysed using mutual information (note that this produces the lag-one auto-MI score, the analog of the lag-one
autocorrelation). Empirical trials are used to select appropriate bandwidths for a range of underlying autoregressive and
autoregressive-moving average models with normal or near-normal parent distributions. Expressions for reasonable bandwidth
choices under these conditions are proposed. 相似文献
3.
The key problem in nonparametric frequency analysis of flood and droughts is the estimation of the bandwidth parameter which defines the degree of smoothing. Most of the proposed bandwidth estimators have been based on the density function rather than the cumulative distribution function or the quantile that are the primary interest in frequency analysis. We propose a new bandwidth estimator derived from properties of quantile estimators. The estimator builds on work by Altman and Léger (1995). The estimator is compared to the well-known method of least squares cross-validation (LSCV) using synthetic data generated from various parametric distributions used in hydrologic frequency analysis. Simulations suggest that our estimator performs at least as well as, and in many cases better than, the method of LSCV. In particular, the use of the proposed plug-in estimator reduces bias in the estimation as compared to LSCV. When applied to data sets containing observations with identical values, typically the result of rounding or truncation, the LSCV and most other techniques generally underestimates the bandwidth. The proposed technique performs very well in such situations. 相似文献
4.
There are two basic approaches for estimating flood quantiles: a parametric and a nonparametric method. In this study, the comparisons of parametric and nonparametric models for annual maximum flood data of Goan gauging station in Korea were performed based on Monte Carlo simulation. In order to consider uncertainties that can arise from model and data errors, kernel density estimation for fitting the sampling distributions was chosen to determine safety factors (SFs) that depend on the probability model used to fit the real data. The relative biases of Sheater and Jones plug-in (SJ) are the smallest in most cases among seven bandwidth selectors applied. The relative root mean square errors (RRMSEs) of the Gumbel (GUM) are smaller than those of any other models regardless of parent models considered. When the Weibull-2 is assumed as a parent model, the RRMSEs of kernel density estimation are relatively small, while those of kernel density estimation are much bigger than those of parametric methods for other parent models. However, the RRMSEs of kernel density estimation within interpolation range are much smaller than those for extrapolation range in comparison with those of parametric methods. Among the applied distributions, the GUM model has the smallest SFs for all parent models, and the general extreme value model has the largest values for all parent models considered. 相似文献
5.
Hakan Karaca 《Acta Geophysica》2018,66(4):633-642
As a relatively recent development, spatial smoothing methods have been introduced to identify seismic patterns. Among the methods developed to model the spatial variation, methods based on utilization of 3-D Gaussian isotropic kernels have a wide reception. The most important question remaining to be answered in the application of these methods is the determination of the optimum kernel bandwidth. At the present, researchers’ efforts to clarify the subject have still not yet finalized, this study aims to provide insightful knowledge for future efforts. In this study, for the region bounded by 27°–33° longitudes and 39°–41° latitudes, where the western section of the famous Northern Anatolian fault lies, smoothing techniques are implemented to determine the optimum smoothing kernel bandwidth for point sources. The influence of the modeling of seismicity through the computation of the optimum smoothing kernel bandwidth is examined. In addition, the sensitivity of each smoothing technique to the seismic patterns, whether densely clustered or scarcely populated, is investigated. In the end, the smoothing method based on optimum neighbor number is identified as highly sensitive to the density of seismicity and seismic clusters, and better in modeling high seismicity compared to the model based on single optimum smoothing distance used for the entire region of interest. 相似文献
6.
F. J. Rodríguez-Cortés J. Mateu 《Stochastic Environmental Research and Risk Assessment (SERRA)》2015,29(1):295-308
We consider kernel-based non-parametric estimation of second-order product densities of spatial point patterns. We present a new family of optimal and positive kernels that shows less variance and more flexibility than optimal kernels. This family generalises most of the classical and widely used kernel functions, such as Box or Epanechnikov kernels. We propose an alternative asymptotically unbiased estimator for the second-order product density function, and compare the performance of the estimator for several members of the family of optimal and positive kernels through MISE and relative efficiency. We present a simulation study to analyse the behaviour of such kernel functions, for three different spatial structures, for which we know the exact analytical form of the product density, and under small sample sizes. Some known datasets are revisited, and we also analyse the IMD dataset in the Rhineland Regional Council in Germany. 相似文献
7.
Balaji Rajagopalan Upmanu Lall David G. Tarboton 《Stochastic Hydrology and Hydraulics》1997,11(6):523-547
Kernel density estimators are useful building blocks for empirical statistical modeling of precipitation and other hydroclimatic
variables. Data driven estimates of the marginal probability density function of these variables (which may have discrete
or continuous arguments) provide a useful basis for Monte Carlo resampling and are also useful for posing and testing hypotheses
(e.g bimodality) as to the frequency distributions of the variable. In this paper, some issues related to the selection and
design of univariate kernel density estimators are reviewed. Some strategies for bandwidth and kernel selection are discussed
in an applied context and recommendations for parameter selection are offered. This paper complements the nonparametric wet/dry
spell resampling methodology presented in Lall et al. (1996). 相似文献
8.
Balaji Rajagopalan Upmanu Lall David G. Tarboton 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(6):523-547
Kernel density estimators are useful building blocks for empirical statistical modeling of precipitation and other hydroclimatic
variables. Data driven estimates of the marginal probability density function of these variables (which may have discrete
or continuous arguments) provide a useful basis for Monte Carlo resampling and are also useful for posing and testing hypotheses
(e.g bimodality) as to the frequency distributions of the variable. In this paper, some issues related to the selection and
design of univariate kernel density estimators are reviewed. Some strategies for bandwidth and kernel selection are discussed
in an applied context and recommendations for parameter selection are offered. This paper complements the nonparametric wet/dry
spell resampling methodology presented in Lall et al. (1996). 相似文献
9.
Exploratory analysis of statistical post‐processing methods for hydrological ensemble forecasts 
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下载免费PDF全文 Despite many recent improvements, ensemble forecast systems for streamflow often produce under‐dispersed predictive distributions. This situation is problematic for their operational use in water resources management. Many options exist for post‐processing of raw forecasts. However, most of these have been developed using meteorological variables such as temperature, which displays characteristics very different from streamflow. In addition, streamflow data series are often very short or contain numerous gaps, thus compromising the estimation of post‐processing statistical parameters. For operational use, a post‐processing method has to be effective while remaining as simple as possible. We compared existing post‐processing methods using normally distributed and gamma‐distributed synthetic datasets. To reflect situations encountered with ensemble forecasts of daily streamflow, four normal distribution parameterizations and six gamma distribution parameterizations were used. Three kernel‐based approaches were tested, namely, the ‘best member’ method and two improvements thereof, and one regression‐based approach. Additional tests were performed to assess the ability of post‐processing methods to cope with short calibration series, missing values or small numbers of ensemble members. We thus found that over‐dispersion is best corrected by the regression method, while under‐dispersion is best corrected by kernel‐based methods. This work also shows key limitations associated with short data series, missing values, asymmetry and bias. One of the improved best member methods required longer series for the estimation of post‐processing parameters, but if provided with adequate information, yielded the best improvement of the continuous ranked probability score. These results suggest guidelines for future studies involving real operational datasets. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
10.
Conventional method of probabilistic seismic hazard analysis (PSHA) using the Cornell–McGuire approach requires identification of homogeneous source zones as the first step. This criterion brings along many issues and, hence, several alternative methods to hazard estimation have come up in the last few years. Methods such as zoneless or zone-free methods, modelling of earth’s crust using numerical methods with finite element analysis, have been proposed. Delineating a homogeneous source zone in regions of distributed seismicity and/or diffused seismicity is rather a difficult task. In this study, the zone-free method using the adaptive kernel technique to hazard estimation is explored for regions having distributed and diffused seismicity. Chennai city is in such a region with low to moderate seismicity so it has been used as a case study. The adaptive kernel technique is statistically superior to the fixed kernel technique primarily because the bandwidth of the kernel is varied spatially depending on the clustering or sparseness of the epicentres. Although the fixed kernel technique has proven to work well in general density estimation cases, it fails to perform in the case of multimodal and long tail distributions. In such situations, the adaptive kernel technique serves the purpose and is more relevant in earthquake engineering as the activity rate probability density surface is multimodal in nature. The peak ground acceleration (PGA) obtained from all the three approaches (i.e., the Cornell–McGuire approach, fixed kernel and adaptive kernel techniques) for 10% probability of exceedance in 50?years is around 0.087?g. The uniform hazard spectra (UHS) are also provided for different structural periods. 相似文献
11.
B. Rajagopalan U. Lall D. G. Tarboton D. S. Bowles 《Stochastic Environmental Research and Risk Assessment (SERRA)》1997,11(1):65-93
A nonparametric resampling technique for generating daily weather variables at a site is presented. The method samples the
original data with replacement while smoothing the empirical conditional distribution function. The technique can be thought
of as a smoothed conditional Bootstrap and is equivalent to simulation from a kernel density estimate of the multivariate
conditional probability density function. This improves on the classical Bootstrap technique by generating values that have
not occurred exactly in the original sample and by alleviating the reproduction of fine spurious details in the data. Precipitation
is generated from the nonparametric wet/dry spell model as described in Lall et al. [1995]. A vector of other variables (solar
radiation, maximum temperature, minimum temperature, average dew point temperature, and average wind speed) is then simulated
by conditioning on the vector of these variables on the preceding day and the precipitation amount on the day of interest.
An application of the resampling scheme with 30 years of daily weather data at Salt Lake City, Utah, USA, is provided. 相似文献
12.
A p‐order multivariate kernel density model based on kernel density theory has been developed for synthetic generation of multivariate variables. It belongs to a kind of data‐driven approach and is able to avoid prior assumptions as to the form of probability distribution (normal or Pearson III) and the form of dependence (linear or non‐linear). The p‐order multivariate kernel density model is a non‐parametric method for synthesis of streamflow. The model is more flexible than conventional parametric models used in stochastic hydrology. The effectiveness and satisfactoriness of this model are illustrated through its application to the simultaneous synthetic generation of daily streamflow from Pingshan station and Yibin‐Pingshan region (Yi‐Ping region) of the Jinsha River in China. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
13.
A novel approach to infer streamflow signals for ungauged basins 总被引：1，自引：0，他引：1
In this paper, we present a novel paradigm for inference of streamflow for ungauged basins. Our innovative procedure fuses concepts from both kernel methods and data assimilation. Based on the modularity and flexibility of kernel techniques and the strengths of the variational Bayesian Kalman filter and smoother, we can infer streamflow for ungauged basins whose hydrological and system properties and/or behavior are non-linear and non-Gaussian. We apply the proposed approach to two watersheds, one in California and one in West Virginia. The inferred streamflow signals for the two watersheds appear promising. These preliminary and encouraging validations demonstrate that our new paradigm is capable of providing accurate conditional estimates of streamflow for ungauged basins with unknown and non-linear dynamics. 相似文献
14.
Low streamflow statistic estimators at ungauged river sites generally have large errors and uncertainties. This can be due to many reasons, including lack of data, complex hydrologic processes, and the inadequate or improper characterization of watershed hydrogeology. One potential solution is to take a small number of streamflow measurements at an ungauged site to either estimate hydrogeologic indices or transfer information from a nearby site using concurrent streamflow measurements. An analysis of four low streamflow estimation techniques, regional regression, regional plus hydrogeologic indices, baseflow correlation, and scaling, was performed within the Apalachicola–Chattahoochee–Flint watershed, a U.S. Geological Survey WaterSMART region in the south‐eastern United States. The latter three methods employ a nominal number of spot measurements at the ungauged site to improve low streamflow estimation. Results indicate that baseflow correlation and scaling methods, which transfer information from a donor site, can produce improved low streamflow estimators when spot measurements are available. Estimation of hydrogeologic indices from spot measurements improves regional regression models, with the baseflow recession constant having more explanatory power than the aquifer time constant, but these models are generally outperformed by baseflow correlation and scaling. 相似文献
15.
《水文科学杂志》2013,58(4):613-625
Abstract Estimates of rainfall elasticity of streamflow in 219 catchments across Australia are presented. The rainfall elasticity of streamflow is defined here as the proportional change in mean annual streamflow divided by the proportional change in mean annual rainfall. The elasticity is therefore a simple estimate of the sensitivity of long-term streamflow to changes in long-term rainfall, and is particularly useful as an initial estimate of climate change impact in land and water resources projects. The rainfall elasticity of streamflow is estimated here using a hydrological modelling approach and a nonparametric estimator. The results indicate that the rainfall elasticity of streamflow (? P ) in Australia is about 2.0–3.5 (observed in about 70% of the catchments), that is, a 1% change in mean annual rainfall results in a 2.0–3.5% change in mean annual streamflow. The rainfall elasticity of streamflow is strongly correlated to runoff coefficient and mean annual rainfall and streamflow, where streamflow is more sensitive to rainfall in drier catchments, and those with low runoff coefficients. There is a clear relation-ship between the ? P values estimated using the hydrological modelling approach and those estimated using the nonparametric estimator for the 219 catchments, although the values estimated by the hydrological modelling approach are, on average, slightly higher. The modelling approach is useful where a detailed study is required and where there are sufficient data to reliably develop and calibrate a hydrological model. The nonparametric estimator is useful where consistent estimates of the sensitivity of long-term streamflow to climate are required, because it is simple to use and estimates the elasticity directly from the historical data. The nonparametric method, being model independent, can also be easily applied in comparative studies to data sets from many catchments across large regions. 相似文献
16.
A. Ian McLeod K. W. Hipel 《Stochastic Environmental Research and Risk Assessment (SERRA)》1995,9(3):171-205
Current methods of estimation of the univariate spectral density are reviewed and some improvements are made. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data analysis (EDA) tool which complements, rather than competes with, the popular ARMA model building approach. A new diagnostic check for ARMA model adequacy based on the nonparametric spectral density is introduced. Additionally, two new algorithms for fast computation of the autoregressive spectral density function are presented. For improving interpretation of results, a new style of plotting the spectral density function is suggested. Exploratory spectral analyses of a number of hydrological time series are performed and some interesting periodicities are suggested for further investigation. The application of spectral analysis to determine the possible existence of long memory in natural time series is discussed with respect to long riverflow, treering and mud varve series. Moreover, a comparison of the estimated spectral densities suggests the ARMA models fitted previously to these datasets adequately describe the low frequency component. Finally, the software and data used in this paper are available by anonymous ftp from fisher.stats.uwo.ca. 相似文献
17.
This work develops a top‐down modelling approach for storm‐event rainfall–runoff model calibration at unmeasured sites in Taiwan. Twenty‐six storm events occurring in seven sub‐catchments in the Kao‐Ping River provided the analytical data set. Regional formulas for three important features of a streamflow hydrograph, i.e. time to peak, peak flow, and total runoff volume, were developed via the characteristics of storm event and catchment using multivariate regression analysis. Validation of the regional formulas demonstrates that they reasonably predict the three features of a streamflow hydrograph at ungauged sites. All of the sub‐catchments in the study area were then adopted as ungauged areas, and the three streamflow hydrograph features were calculated by the regional formulas and substituted into the fuzzy multi‐objective function for rainfall–runoff model calibration. Calibration results show that the proposed approach can effectively simulate the streamflow hydrographs at the ungauged sites. The simulated hydrographs more closely resemble observed hydrographs than hydrographs synthesized using the Soil Conservation Service (SCS) dimensionless unit hydrograph method, a conventional method for hydrograph estimation at ungauged sites in Taiwan. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
18.
19.
《Advances in water resources》2005,28(7):711-728
Many recent studies have been devoted to the investigation of the nonlinear dynamics of rainfall or streamflow series based on methods of dynamical systems theory. Although finding evidence for the existence of a low-dimensional deterministic component in rainfall or streamflow is of much interest, not much attention has been given to the nonlinear dependencies of the two and especially on how the spatio-temporal distribution of rainfall affects the nonlinear dynamics of streamflow at flood time scales. In this paper, a methodology is presented which simultaneously considers streamflow series, spatio-temporal structure of precipitation and catchment geomorphology into a nonlinear analysis of streamflow dynamics. The proposed framework is based on “hydrologically-relevant” rainfall-runoff phase-space reconstruction acknowledging the fact that rainfall-runoff is a stochastic spatially extended system rather than a deterministic multivariate one. The methodology is applied to two basins in Central North America using 6-hour streamflow data and radar images for a period of 5 years. The proposed methodology is used to: (a) quantify the nonlinear dependencies between streamflow dynamics and the spatio-temporal dynamics of precipitation; (b) study how streamflow predictability is affected by the trade-offs between the level of detail necessary to explain the spatial variability of rainfall and the reduction of complexity due to the smoothing effect of the basin; and (c) explore the possibility of incorporating process-specific information (in terms of catchment geomorphology and an a priori chosen uncertainty model) into nonlinear prediction. Preliminary results are encouraging and indicate the potential of using the proposed methodology to understand via nonlinear analysis of observations (i.e., not based on a particular rainfall-runoff model) streamflow predictability and limits to prediction as a function of the complexity of spatio-temporal forcing relative to basin geomorphology. 相似文献