Pooling Groups Research Articles

A formal statistical model for pooled analysis of extreme floods

This paper describes a formal statistical model underlying the region-of-influence method routinely used in regional frequency analysis of hydrological extremes, and is an improvement to the existing Flood Estimation Handbook (FEH) method for pooled frequency analysis of annual maximum flows in the UK. Specification of a pooling-group method requires three issues to be resolved: how to define hydrological similarity, the size of pooling groups and calculation of the pooled L-moment ratios. Because these issues are interrelated, an exploratory and iterative study has been undertaken before arriving at the final version of the method. Improvements provided by the model are: (1) that it allows an increased weight to be given to a gauged catchment when it is itself the target location and (2) it does not require identification of a homogeneous region, since the expected differences between the L-moment ratios within a pooling group are explicitly accounted for. Using annual maximum series from 602 gauged rural catchments, a comparison of candidate methods shows that the new method performs better than these others, including the FEH method. While the numerical comparison suggests that the improvement is 4%, and thus only minor, arguments are given for why this is a misleading conclusion.

Effects of intersite dependence of nested catchment structures on probabilistic regional envelope curves

Abstract. This study analyses the intersite dependence of nested catchment structures by modelling cross-correlations for pairs of nested and unnested catchments separately. Probabilistic regional envelope curves are utilised to derive regional flood quantiles for 89 catchments located in Saxony, in the Southeast of Germany. The study area has a nested structure and the intersite correlation is much stronger for nested pairs of catchments than for unnested ones. Pooling groups of sites (regions) are constructed based on several candidate sets of catchment descriptors using the Region of Influence method. Probabilistic regional envelope curves are derived on the basis of flood flows observed within the pooling groups. Their estimated recurrence intervals are based on the number of effective sample years of data (i.e. equivalent number of uncorrelated data). The evaluation of the effective sample years of data requires the modelling of intersite dependence. We perform this globally, using a cross-correlation function for the whole study area as well as by using two different cross-correlation functions, one for nested pairs and another for unnested pairs. In the majority of the cases, these two modelling approaches yield significantly different estimates for the effective sample years of data, and therefore also for the recurrence intervals. The reduction of the recurrence interval when using two different cross-correlation functions is larger for larger pooling groups and for pooling groups with a higher fraction of nested catchments. A separation into nested and unnested pairs of catchments gives a more realistic representation of the characteristic river network structure and improves the estimation of regional information content. Hence, applying two different cross-correlation functions is recommended.

Region-of-influence approach to a frequency analysis of heavy precipitation in Slovakia

Abstract. The paper compares different approaches to regional frequency analysis with the main focus on the implementation of the region-of-influence (ROI) technique for the modelling of probabilities of heavy precipitation amounts in the area of the Western Carpathians. Unlike the conventional regional frequency analysis where the at-site design values are estimated within a fixed pooling group (region), the ROI approach as a specific alternative to focused pooling techniques makes use of flexible pooling groups, i.e. each target site has its own group of sufficiently similar sites. In this paper, various ROI pooling schemes are constructed as combinations of different alternatives of sites' similarity (pooling groups defined according to climatological characteristics and geographical proximity of sites, respectively) and pooled weighting factors. The performance of the ROI pooling schemes and statistical models of conventional (regional and at-site) frequency analysis is assessed by means of Monte Carlo simulation studies for precipitation annual maxima for the 1-day and 5-day durations in Slovakia. It is demonstrated that a) all the frequency models based on the ROI method yield estimates of growth curves that are superior to the standard regional and at-site estimates at most individual sites, and b) the selection of a suitable ROI pooling scheme should be adjusted to the dominant character of the formation of heavy precipitation.

Usefulness of the reversible jump Markov chain Monte Carlo model in regional flood frequency analysis

Regional flood frequency analysis is a convenient way to reduce estimation uncertainty when few data are available at the gauging site. In this work, a model that allows a non‐null probability to a regional fixed shape parameter is presented. This methodology is integrated within a Bayesian framework and uses reversible jump techniques. The performance on stochastic data of this new estimator is compared to two other models: a conventional Bayesian analysis and the index flood approach. Results show that the proposed estimator is absolutely suited to regional estimation when only a few data are available at the target site. Moreover, unlike the index flood estimator, target site index flood error estimation seems to have less impact on Bayesian estimators. Some suggestions about configurations of the pooling groups are also presented to increase the performance of each estimator.

An investigation of site-similarity approaches to generalisation of a rainfall–runoff model

Abstract. This paper investigates a new approach to spatial generalisation of rainfall–runoff model parameters – site-similarity with pooling groups – for use in flood frequency estimation at ungauged sites using continuous simulation. The method is developed for the generalisation of a simple conceptual model, the Probability Distributed Model, with four parameters which require specific estimation. The study is based on a relatively large sample of catchments in Great Britain. Various options are investigated within the approach. In the final version, the pooling group comprises the 10 calibrated catchments closest, in catchment property space, to the target site, where the catchment properties used to define the space differ for each parameter of the model. An analysis that, explicitly, takes account of calibration uncertainty as a source of error enables the uncertainty associated with generalised parameter values to be reduced, justifiably. The approach uses calibration uncertainty estimated through jack-knifing and employs a weighting scheme within pooling groups that uses weights which vary both with distance in the catchment property space and with the calibration uncertainty. Models using generalised values from this approach perform relatively well compared with direct calibration. Although performance appears to be better in some areas of the country than others, there are no obvious relationships between catchment properties and performance.

Prediction uncertainty in a median‐based index flood method using L moments

The standard for conducting flood frequency analysis in the UK, as set out in the Flood Estimation Handbook, is based on the index flood method, using the median of the annual maximum flood as the index flood. For a given target site, a region‐of‐influence approach is used, involving the creation of a collection of hydrologically similar catchments (pooling group). This paper examines the sampling uncertainty of quantile estimates on the basis of pooling groups and using the median as the index flood for both gauged and ungauged sites. Analytical approximations for the variance of the quantile estimates were derived, on the basis of asymptotic theory, and were used to calculate approximate confidence intervals for flood frequency curves obtained using both single‐site and pooled analysis at gauged and ungauged sites. A series of bootstrap experiments were conducted to quantify the intersite dependence and to develop generalized expressions to be included in the analysis. It is shown that the pooled analysis yields narrower confidence intervals than the single‐site analysis and that the presence of intersite correlations increases the sampling uncertainty. The method was extended to encompass estimation at ungauged sites in the UK on the basis of a regression model for the index flood, which significantly increases the prediction uncertainty compared with using an estimate of the index flood derived from observations at the target site.

Switching the pooling similarity distances: Mahalanobis for Euclidean

In recent years, catchment similarity measures based on flood seasonality have become popular alternatives for identifying hydrologically homogeneous pooling groups used in regional flood frequency analysis. Generally, flood seasonality pooling measures are less prone to errors and are more robust than measures based on flood magnitude data. However, they are also subject to estimation uncertainty resulting from sampling variability. Because of sampling variability, catchment similarity in flood seasonality can significantly deviate from the true similarity. Therefore sampling variability should be directly incorporated in the pooling algorithm to decrease the level of pooling uncertainty. This paper develops a new pooling approach that takes into consideration the sampling variability of flood seasonality measures used as pooling variables. A nonparametric resampling technique is used to estimate the sampling variability for the target site, as well as for every site that is a potential member of the pooling group for the target site. The variability is quantified by Mahalanobis distance ellipses. The similarity between the target site and the potential site is then assessed by finding the minimum confidence interval at which their Mahalanobis ellipses intersect. The confidence intervals can be related to regional homogeneity, which allows the target degree of regional homogeneity to be set in advance. The approach is applied to a large set of catchments from Great Britain, and its performance is compared with the performance of a previously used pooling technique based on the Euclidean distance. The results demonstrate that the proposed approach outperforms the previously used approach in terms of the overall homogeneity of delineated pooling groups in the study area.

A comparison of three approaches to spatial generalization of rainfall–runoff models

The generalization of the parameters of rainfall-runoff models, to enable application at ungauged sites, is an important and ongoing area of research. This paper compares the performance of three alternative methods of generalization, for two parameter-sparse conceptual models (PDM and TATE), specifically for use in flood frequency estimation using continuous simulation. Two of the methods are based on fitting regression relationships between catchment properties and calibrated parameter values, using weighted or sequential regression (with weights based on estimates of calibration uncertainty), and the third is based on the use of pooling groups, defined through measures of site-similarity based on catchment properties. The study uses a relatively large sample of catchments in Britain. For the PDM, the site-similarity method performs best, but not greatly better than either regression method, so there may be cases where the use of regression would be preferable. For the TATE model, weighted regression performs best (with a very similar level of performance to that of the PDM with site-similarity), whereas site-similarity performs worst (due to poor performance for catchments with higher baseflow), indicating that the choice of model and generalization method should not be separated. The use of sequential regression, which was developed to try to allow for parameter interdependence, shows no clear advantage for either model. Other than the poor performance of the TATE model with site-similarity for catchments with a higher baseflow index, there are no clear relationships between performance of any model/method and catchment type.

Site-focused nonparametric test of regional homogeneity based on flood regime

In regional flood frequency analysis, the proper identification of homogeneous pooling groups is a key factor for reliable quantile estimation. A new test of regional homogeneity based on flood regime is proposed in this paper. In contrast to other tests, this test does not use flood magnitude data and is focused on a site of interest and a target return period. The test relies on a nonparametric comparison of the regional variability of local flood regimes within a given pooling group with the variability that could be expected in a theoretically homogeneous group with the same hydrological properties as the original group. The performance of the test in the detection of regional heterogeneity is evaluated in a set of simulation experiments, each with different pooling group size, record length, and degree of regional heterogeneity. The test is then applied to a large set of real data, and the pooling measures and quantile errors are compared with the results obtained from the Hosking and Wallis's (HW) homogeneity test included in the same pooling algorithm. The simulation results demonstrated that the power of the test rapidly improves as the record length, pooling size, and degree of regional heterogeneity increase. In our study area the new test rejected fewer similar sites and led to similar quantile errors in comparison with the approach based on the HW test. The test is a sound alternative to the existing tests of regional homogeneity and is particularly convenient for site-focused pooling algorithms that require homogeneity testing at each step of the pooling.

Homogeneous pooling group delineation for flood frequency analysis using a fuzzy expert system with genetic enhancement

Pooled flood frequency analysis has been widely used to improve flood quantile estimation at sites that have short streamflow gauging records. When conducting pooled frequency analysis, it is necessary to delineate homogeneous pooling groups. A basic requirement for a pooling group is that the catchments in a pooling group should have sufficient similarity in hydrological response to provide a basis for information transfer. In this paper, methods using fuzzy expert systems (FES) are developed to derive an objective similarity measure between catchments. The steps for building the FES are explained in detail. The performance of the FES is improved by tuning of the membership functions of the fuzzy sets using a genetic algorithm. The proposed methods are applied to flood data from Great Britain and compared with results obtained from two other methods. The results indicate that the proposed FES methods have the capability of utilizing inputs from different categories of catchment characteristics and producing similarity measures that have high reliability.

Spatial patterns of homogeneous pooling groups for flood frequency analysis

Several methods for the exploration and modelling of spatial point patterns are introduced to study the spatial patterns of homogeneous pooling groups for flood frequency analysis. The study is based on selected catchments in Great Britain, where a high density of gauging stations has been established. Initial pooling groups are formed using the K-means clustering algorithm with appropriately selected similarity measures. The pooling groups are subsequently revised to improve the homogeneity in the hydrological response. Spatial patterns of the initial and final pooling groups are explored in terms of intensity and dependence of the spatial distribution of the catchments. A test against a spatial point process is used to confirm or reject the initial impression of spatial clustering. Changes in the spatial patterns from the initial to the final pooling groups are examined using two comparison methods. The spatial pattern analysis described above can be used to answer the following questions: whether homogeneous catchments tend to exist in the vicinity of each other; whether the improvement in homogeneity tends to form more clustered pooling groups; and how the spatial patterns observed can be used to direct the selection of pooling variables.

EFFECTIVENESS OF STOCK TRANSSHIPMENT UNDER VARIOUS DEMAND DISTRIBUTIONS AND NONNEGLIGIBLE TRANSSHIPMENT TIMES*

This paper investigates the operational characteristics of a pooling group consisting of two stocking locations, supplied periodically by a central warehouse. The two locations may collaborate by moving inventory between them. The lateral transshipment times are shorter than the regular replenishment lead times, but they are not negligible. Several alternative types of ordering and transshipment policies are examined. Extensive experimentation by simulation leads to the conclusion that the benefits of risk pooling are substantial only when demand is highly variable. Moreover, the type and variability of the demand distributions are key determinants of the appropriate transshipment policy and pooling groups design.

Analysis of the linkage between rain and flood regime and its application to regional flood frequency estimation

Improving techniques of flood frequency estimation at ungauged sites is one of the foremost goals of contemporary hydrology. River flood regime is a resultant reflection of a composite catchment hydrologic response to flood producing processes. In this sense the process of identifying homogeneous pooling groups can be plausibly based on catchment similarity in flood regime. Unfortunately the application of any pooling approach that is based on flood regime is restricted to gauged sites. Because flood regime can be markedly determined by rainfall regime, catchment similarity in rainfall regime can be an alternative option for identifying flood frequency pooling groups. An advantage of such a pooling approach is that rainfall data are usually spatially and temporary more abundant than flood data and the approach can also be applied at ungauged sites. Therefore in this study we have quantified the linkage between rainfall and flood regime and explored the appropriateness of substituting rainfall regime for flood regime in regional pooling schemes. Two different approaches to describing rainfall regime similarity using tools of directional statistics have been tested and used for evaluation of the potential of rainfall regime for identification of hydrologically homogeneous pooling groups. The outputs were compared to an existing pooling framework adopted in the Flood Estimation Handbook. The results demonstrate that regional pooling based on rainfall regime information leads to a high number of initially homogeneous groups and seems to be a sound pooling alternative for catchments with a close linkage between rain and flood regimes.

The use of flood regime information in regional flood frequency analysis

Understanding the hydro-climatological controls on floods is fundamental for estimating flood frequency. The river flood regime is a reflection of a complex catchment hydrological response to flood producing processes. Hence, the catchment similarity in a flood regime is a feasible basis for identifying flood frequency pooling groups used in regional estimation of design events. This study describes a focused pooling approach that is based on flood regime information. A flood regime descriptor that is sensitive to the modality of the underlying temporal distribution of flood occurrences, and depicts both flood seasonal pattern and flood regularity, was developed and tested. The approach was applied to peaks-over-threshold data from a number of essentially rural sites using a site-focused pooling framework. The relative performance of this approach was evaluated and compared with the performance of a pooling approach based on a previously used flood seasonality measure, using a regional bootstrap resampling technique. The regional bootstrap model was further used for quantifying the sensitivity of the proposed flood regime descriptor to the record length and the length of overlapping period. The results demonstrate that pooling based on the regime index proposed in this study out-performed the pooling based on the previously used seasonality measure in terms of both bias and RMSE of estimated flow quantiles. A detailed description of flood regime captured in the proposed index provides sufficient information for effective regional estimation of extreme flow quantiles for the study area.

Assessing the effectiveness of hydrological similarity measures for flood frequency analysis

This paper evaluates the relative performance of four hydrological similarity measures that are used to form homogeneous pooling groups for regional frequency analysis. One pair of similarity measures is based on seasonality indexes that reflect the timing of extreme events. A further pair of measures considers a characterisation, at the basin scale, of the frequency distribution of rainfall extremes and the extent of the impervious portion of the catchment. The measures are applied to a case study encompassing a large area in Northern-Central Italy. The similarity measures are examined in the context of a pooling scheme that is designed to identify hierarchical, focused pooling groups. The performance of the similarity measures is quantified using a Monte Carlo experiment. The results demonstrate that similarity measures based on seasonality indexes are effective for estimating extreme flow quantiles for the study area. For ungauged catchments, a similarity measure incorporating both rainfall statistics and permeability information is most effective.

Pooling in multi-location periodic inventory distribution systems

Risk pooling through lateral transshipment in inventory distribution systems is an effective means of improving customer service and reducing total system costs. The objective of this paper is to study the performance of an inventory system with one central warehouse and multiple retail outlets, collaborating in the case of imminent shortage by moving inventory between them. The analysis concentrates on the case of three outlets (stocking locations), which captures most of the characteristics and tradeoffs of multi-location systems with complete pooling. In addition to determining order-up-to quantities for the stocking locations, the decision maker must also specify the details of the transshipment policy when one or two locations face shortages. Simulation with a wide choice of model parameters leads to some very interesting and practically useful conclusions, including the following: (a) the benefits of risk pooling through transshipment are substantial and increase with the number of pooled locations; (b) the type of transshipment policy in case of shortages does not affect significantly the system's performance; and (c) it is preferable to form “balanced” pooling groups, consisting of locations that face similar demand.

Factor Analyses of Pooled Hand Questionnaire Data are of Questionable Value

A number of researches have used factor analyses and principal components analyses on handedness questionnaire data in order to learn something about handedness. However, these researchers have analyzed pooled data from righthanders and lefthanders. The practice of pooling groups that are known in advance to be heterogeneous is highly questionable because it is not possible to disentangle the sources of variance that are contributed by within group differences from those that arise from between group differences. The factor structure and item loadings that result from pooled data are misleading and cannot inform meaningfully about the relation of hand preference to handedness. Similar problems can be anticipated in other neuroPsYchologIcal applications of factor analysis, where data from heterogeneous groups is pooled.

Rural risk pooling groups in California and Nevada

Perspectives in Healthcare Risk ManagementVolume 10, Issue 4 p. 29-31 Article Rural risk pooling groups in California and Nevada Catherine Carlson R.N. M.S., Catherine Carlson R.N. M.S. Director Risk management and quality assurance, CHD Development Corporation, San Francisco, Reno NVSearch for more papers by this authorSandra Mahon Vice-President B.S.N., Sandra Mahon Vice-President B.S.N. Risk management and quality assurance, CHD Development Corporation, San Francisco, Reno NVSearch for more papers by this author Catherine Carlson R.N. M.S., Catherine Carlson R.N. M.S. Director Risk management and quality assurance, CHD Development Corporation, San Francisco, Reno NVSearch for more papers by this authorSandra Mahon Vice-President B.S.N., Sandra Mahon Vice-President B.S.N. Risk management and quality assurance, CHD Development Corporation, San Francisco, Reno NVSearch for more papers by this author First published: Autumn (Fall) 1990 https://doi.org/10.1002/jhrm.5600100410AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volume10, Issue4Autumn (Fall) 1990Pages 29-31 RelatedInformation