Nonparametric catchment clustering using the data depth function

ABSTRACT

The clustering of catchments is important for prediction in ungauged basins, model parameterization and watershed development and management. The aim of this study is to explore a new measure of similarity among catchments, using a data depth function and comparing it with catchment clustering indices based on flow and physical characteristics. A cluster analysis was performed for each similarity measure using the affinity propagation clustering algorithm. We evaluated the similarity measure based on depth–depth plots (DD-plots) as a basis for transferring parameter sets of a hydrological model between catchments. A case study was developed with 21 catchments in a diverse New Zealand region. Results show that clustering based on the depth–depth measure is dissimilar to clustering on catchment characteristics, flow, or flow indices. A hydrological model was calibrated for the 21 catchments and the transferability of model parameters among similar catchments was tested within and between clusters defined by each clustering method. The mean model performance for parameters transferred within a group always outperformed those from outside the group. The DD-plot based method was found to produce the best in-group performance and second-highest difference between in-group and out-group performance.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR A. Viglione     

Trends in frequency of precipitation extremes in the Yangtze River basin,China: 1960–2003 / Tendances d'évolution de la fréquence des précipitations extrêmes entre 1960 et 2003 dans le bassin versant du Fleuve Yangtze (Chine)

Abstract

The spatial distribution and trends in the frequency of precipitation extremes over the last 44 years (1960–2003), especially since 1990, have been analysed using daily precipitation data from 147 stations in the Yangtze River basin. The research results are as follows: (1) The 15 mm precipitation isohyet approximately divides the precipitation extremes (corresponding to the 95th percentile) of the stations in the middle and lower Yangtze reaches (higher) from those of the upper Yangtze reaches (lower). Also the starting time of the precipitation extremes in the middle and lower Yangtze reaches is earlier than of those in the upper Yangtze reaches. Precipitation extremes are concentrated mostly in June in the middle and lower Yangtze reaches, and July in the upper Yangtze reaches. (2) During the period 1960–2003, the first two decades had fewer precipitation extremes than the last two decades. There have been significant increasing trends and step changes in frequency of annual total precipitation extremes and precipitation extremes with a 1–5 day gap in the middle and lower Yangtze reaches. Precipitation extremes occur more frequently in shorter periods, separated by a few days. Precipitation extremes are also becoming more concentrated in the month with the highest frequency of extremes (June) in the middle and lower Yangtze reaches. In the upper Yangtze reaches, there is an upward tendency of extreme events in June. Increasing precipitation extremes in June for both the middle and lower, and the upper Yangtze reaches will increase the probability of flooding if the observed trends of the last 40 years continue into the future.     

Statistics of extremes and estimation of extreme rainfall: I. Theoretical investigation / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: I. Recherche théorique

Abstract

Abstract The Gumbel distribution has been the prevailing model for quantifying risk associated with extreme rainfall. Several arguments including theoretical reasoning and empirical evidence are supposed to support the appropriateness of the Gumbel distribution. These arguments are examined thoroughly in this work and are put into question. Specifically, theoretical analyses show that the Gumbel distribution is quite unlikely to apply to hydrological extremes and its application may misjudge the risk, as it underestimates seriously the largest extreme rainfall amounts. Besides, it is shown that hydrological records of typical length (some decades) may display a distorted picture of the actual distribution, suggesting that the Gumbel distribution is an appropriate model for rainfall extremes while it is not. In addition, it is shown that the extreme value distribution of type II (EV2) is a more consistent alternative. Based on the theoretical analysis, in the second part of this study an extensive empirical investigation is performed using a collection of 169 of the longest available rainfall records worldwide, each having 100–154 years of data. This verifies the inappropriateness of the Gumbel distribution and the appropriateness of EV2 distribution for rainfall extremes.     

Hydrological and meteorological extremes derived from taxation records: the estates of Brtnice,Třebíč and Velké Meziříčí, 1706–1849

Abstract

This paper addresses the hydrological and meteorological extremes that may be deduced from the taxation records of the estates of Brtnice, T?ebí? and Velké Mezi?í?í, all in the Moravian-Bohemian Highlands of the Czech Republic, for the years 1706–1849. At that time, damage to agricultural crops constituted grounds for tax remission for individual farmers and landowners. Where it survives, the relevant administrative documentation generally includes a statement from the applicant, a report by the official commission tasked with checking the contents of it, and any decisions made by taxation authorities at regional and “land” level (the Jihlava regional office and the Moravian Land Administration (“Gubernium”) respectively). Data extracted may include the type of event, dating, places of occurrence and damage done. The chronology of hydrological and meteorological extremes (torrential rain, flash flood, flood, hailstorm, lightning, frost) covers the period 1706–1849, but only four events are evident before 1748 and there is a gap in records between 1757 and 1789. Extremes are analysed from a spatio-temporal point of view. A total of 97 extreme events (171 extremes of particular type) were identified for the region studied. Torrential rain, hailstorm and flash flood were the major devastating phenomena, and occurred mainly from May to August. Torrential rain and hailstorm are clearly attributable to thunderstorms with very intense convection. Five outstanding events and their impacts upon individual farmers are described in detail. The results are discussed with respect to uncertainties in the basic data and in the context of the Czech Lands, because only some of the extremes disclosed are known and confirmed by other documentary data.

Editor Z.W. Kundzewicz

Citation Dolák, L., Brázdil, R., and Valá?ek, H., 2013. Hydrological and meteorological extremes derived from taxation records: the estates of Brtnice, T?ebí? and Velké Mezi?í?í, 1706–1849. Hydrological Sciences Journal, 58 (8), 1620–1634.     

Analyse fréquentielle régionale des précipitations journalières maximales annuelles au Québec,Canada / Regional frequency analysis of annual maximum daily precipitation in Quebec,Canada

Abstract

Abstract A complete regional analysis of daily precipitations is carried out in the southern half of the province of Quebec, Canada. The first step of the regional estimation procedure consists of delineating the homogeneous regions within the area of study and testing for homogeneity within each region. The delineation of homogeneous regions is based on using L-moment ratios. A simulation-based testing of statistical homogeneity allows one to verify the inter-site variability. The second step of the procedure deals with the identification of the regional distribution and the estimation of its parameters. The General Extreme Value (GEV) distribution was identified as an appropriate parent distribution. This distribution has already been recommended by several previous research studies for regional frequency analysis of precipitation extremes. The parameters of the GEV distribution are estimated based on the computation of the regional L-CV, L-C_S and the mean of annual maximal daily precipitations. The third step consists of the estimation of precipitation quantiles corresponding to various return periods. The final procedure allows for the estimation of these quantiles at sites where no precipitation information is available. The use of a jack-knife resampling procedure with data from the province of Quebec allows one to demonstrate the robustness and efficiency of the regional estimation procedure. Values of the root mean square error were below 10% for a return period of 20 years, and 20% for a return period of 100 years.     

Intensity–duration–frequency curves exploiting neighbouring extreme precipitation data

ABSTRACT

Records of precipitation extremes are essential for hydrological design. In urban hydrology, intensity–duration–frequency curves are typically estimated from observation records. However, conventional approaches seldom consider the areal extent of events. If they do, duration-dependent area reduction factors are used, but precipitation is measured at only a few locations. Due to the high spatial variability of precipitation, it is relatively unlikely that a gauged observation network will capture the extremes that occur during a precipitation event. Therefore, the area reduction approach cannot be regarded as the reduction of an observed maximum. To investigate precipitation extremes, spatial aspects need to be considered using different approaches. Here, we both address the conventional practice of area reduction and consider a within-area chance of increased precipitation, defined as the maximum precipitation intensity observed in a cluster within a selected domain. The results show that (1) the risk of urban flooding is routinely underestimated in current design practice, and (2) traditional calculations underestimate extremes by as much as 30–50%. We show how they can be revised sensibly.     

Precipitation patterns and associated hydrological extremes in the Yangtze River basin,China, using TRMM/PR data and EOF analysis

Abstract

A decadal-scale study to retrieve the spatio-temporal precipitation patterns of the Yangtze River basin, China, using the Tropical Rain Mapping Mission, Precipitation Radar (TRMM/PR) data is presented. The empirical orthogonal function (EOF) based on monthly TRMM/PR data extracts several leading precipitation patterns, which are largely connected with physical implications at the basin scale. With the aid of gauge station data, the amplitudes of major principal components (PCs) were used to examine the generic relationships between precipitation variations and hydrological extremes (e.g. floods and droughts) during summer seasons over the past decade. The emergence of such major precipitation patterns clearly reveals the possible linkages with hydrological processes, and the oscillations in relation to the amplitude of major PCs are consistent with these observed hydrological extremes. Although the floods in some sections of the Yangtze River were, to some extent, tied to human activities, such as the removal of wetlands, the variations in major precipitation patterns are recognized as the primary driving force of the flow extremes associated with floods and droughts. The research findings indicate that long-distance hydro-meteorological signals of large-scale precipitation variations over such a large river basin can be successfully identified with the aid of EOF analysis. The retrieved precipitation patterns and their low-frequency jumps of amplitude in relation to PCs are valuable tools to help understand the association between the precipitation variations and the occurrence of hydrological extremes. Such a study can certainly aid in disaster mitigation and decision-making in water resource management.

Editor Z.W. Kundzewicz; Associate editor A. Montanari

Citation Sun, Z., Chang, N.-B., Huang, Q., and Opp, C., 2013. Precipitation patterns and associated hydrological extremes in the Yangtze River basin, China, using TRMM/PR data and EOF analysis. Hydrological Sciences Journal, 57 (7), 1315–1324.     

Linear and non‐linear scaling of the Yangtze River flow

Power law correlation properties of sign and magnitude series have been studied based on the series of observation records of flow of the River Yangtze. The results obtained give improved insight into and understanding of the linear and non‐linear processes of the water cycle. With the newly developed Delayed Vector Variance method and the surrogate test, the documented linkage between the sign series and the linear process, and that between the magnitude series and non‐linear process can be verified. The spectra estimated by detrended fluctuation analysis method show different properties of intra‐annual and inter‐annual correlations in both sign and magnitude series. The linear process behaves as an 1/f noise at a time scale less than about 60 days, but shows features of anti‐persistence in terms of long‐term fluctuation. The magnitudes are clustered in three ways mainly caused by non‐linear processes, i.e. periodic clustering, strong short‐term clustering of 1/f noise at time scales less than 20 days, and long‐term clustering with weak persistence. Copyright © 2007 John Wiley & Sons, Ltd.     

Modelling the impacts of land-cover change on streamflow dynamics of a tropical rainforest headwater catchment

Abstract

A modelling experiment is used to examine different land-use scenarios ranging from extreme deforestation (31% forest cover) to pristine (95% forest cover) conditions and related Payment for Ecosystem Services (PES) schemes to assess whether a change in streamflow dynamics, discharge extremes and mean annual water balance of a 73.4-km² tropical headwater catchment in Costa Rica could be detected. A semi-distributed, conceptual rainfall–runoff model was adapted to conceptualize the empirically-based, dominant hydrological processes of the study area and was multi-criteria calibrated using different objective functions and empirical constraints on model simulations in a Monte Carlo framework to account for parameter uncertainty. The results suggest that land-use change had relatively little effect on the overall mean annual water yield (<3%). However, streamflow dynamics proved to be sensitive in terms of frequency, timing and magnitude of discharge extremes. For low flows and peak discharges of return periods greater than one year, land use had a minor influence on the runoff response. Below these thresholds (<1-year return period), forest cover potentially decreased runoff peaks and low flows by as much as 10%, and non-forest cover increased runoff peaks and low flows by up to 15%. The study demonstrated the potential for using hydrological modelling to help identify the impact of protection and reforestation efforts on ecosystem services.

Editor Z.W. Kundzewicz

Citation Birkel, C., Soulsby, C., and Tetzlaff, D., 2012. Modelling the impacts of land-cover change on streamflow dynamics of a tropical rainforest headwater catchment. Hydrological Sciences Journal, 57 (8), 1543–1561.     

Hydrological extremes in a southwestern Ontario river basin under future climate conditions/Extrêmes hydrologiques dans un basin versant du sud-ouest de l'Ontario sous conditions climatiques futures

Abstract

The global climate change may have serious impacts on the frequency, magnitude, location and duration of hydrological extremes. Changed hydrological extremes will have important implications on the design of future hydraulic structures, flood-plain development, and water resource management. This study assesses the potential impact of a changed climate on the timing and magnitude of hydrological extremes in a densely populated and urbanized river basin in southwestern Ontario, Canada. An ensemble of future climate scenarios is developed using a weather generating algorithm, linked with GCM outputs. These climate scenarios are then transformed into basin runoff by a semi-distributed hydrological model of the study area. The results show that future maximum river flows in the study area will be less extreme and more variable in terms of magnitude, and more irregular in terms of seasonal occurrence, than they are at present. Low flows may become less extreme and variable in terms of magnitude, and more irregular in terms of seasonal occurrence. According to the evaluated scenarios, climate change may have favourable impacts on the distribution of hydrological extremes in the study area.     

Long-term rainfall trends and change points in hot and cold arid regions of India

This study examined trends and change points in 100-year annual and seasonal rainfall over hot and cold arid regions of India. Using k-means clustering, 32 stations were classified into two clusters: the coefficient of variation for annual and seasonal rainfall was relatively high for Cluster-II compared to Cluster-I. Short-term and long-term persistence was more dominant in Cluster-II (entirely arid) and Cluster-I (partly arid), respectively. Trend tests revealed prominent increasing trends in annual and wet season rainfall of Cluster-II. Dry season rainfall increased by 1.09 mm year^?1 in the cold arid region. The significant change points in annual and wet season rainfall mostly occurred in the period 1941–1955 (hot and cold), and in the dry season in the period 1973–1975 (hot arid) and in 1949 (cold arid). The findings are useful for managing a surplus or deficiency of rainwater in the Indian arid region.

EDITOR A. Castellarin; ASSOCIATE EDITOR S. Kanae     

The distribution of Kendall's tau for testing the significance of cross-correlation in persistent data

Abstract

Kendall's tau (τ) has been widely used as a distribution-free measure of cross-correlation between two variables. It has been previously shown that persistence in the two involved variables results in the inflation of the variance of τ. In this paper, the full null distribution of Kendall's τ for persistent data with multivariate Gaussian dependence is derived, and an approximation to the full distribution is proposed. The effect of the deviation from the multivariate Gaussian dependence model on the distribution of τ is also investigated. As a demonstration, the temporal consistency and field significance of the cross-correlation between the North Hemisphere (NH) temperature time series in the period 1850–1995 and a set of 784 NH tree-ring width (TRW) proxies in addition to 105 NH tree-ring maximum latewood density (MXD) proxies are studied. When persistence is ignored, the original Mann-Kendall test gives temporally inconsistent results between the early half (1850–1922) and the late half (1923–1995) of the record. These temporal inconsistencies are largely eliminated when persistence is accounted for, indicating the spuriousness of a large portion of the identified cross-correlations. Furthermore, the use of the modified test in combination with a field significance test that is robust to spatial correlation indicates the absence of field significant cross-correlation in both halves of the record. These results have serious implications for the use of tree-ring data as temperature proxies, and emphasize the importance of utilizing the correct distribution of Kendall's τ in order to avoid the overestimation of the significance of cross-correlation between data that exhibit significant persistence.

Citation Hamed, K. H. (2011) The distribution of Kendall's tau for testing the significance of cross-correlation in persistent data. Hydrol. Sci. J. 56(5), 841–853.     

Prediction of hydrological drought durations based on Markov chains: case of the Canadian prairies

Abstract

Hydrological drought durations (lengths) in the Canadian prairies were modelled using the standardized hydrological index (SHI) sequences derived from the streamflow series at annual, monthly and weekly time scales. The rivers chosen for the study present high levels of persistence (as indicated by values exceeding 0.95 for lag-1 autocorrelation in weekly SHI sequences), because they encompass large catchment areas (2210–119 000 km²) and traverse, or originate in, lakes. For such rivers, Markov chain models were found to be simple and efficient tools for predicting the drought duration (year, month, or week) based on annual, monthly and weekly SHI sequences. The prediction of drought durations was accomplished at threshold levels corresponding to median flow (Q50) (drought probability, q?=?0.5) to Q95 (drought probability, q?=?0.05) exceedence levels in the SHI sequences. The first-order Markov chain or the random model was found to be acceptable for the prediction of annual drought lengths, based on the Hazen plotting position formula for exceedence probability, because of the small sample size of annual streamflows. On monthly and weekly time scales, the second-order Markov chain model was found to be satisfactory using the Weibull plotting position formula for exceedence probability. The crucial element in modelling drought lengths is the reliable estimation of parameters (conditional probabilities) of the first- and second-order persistence, which were estimated using the notions implicit in the discrete autoregressive moving average class of models. The variance of drought durations is of particular significance, because it plays a crucial role in the accurate estimation of persistence parameters. Although, the counting method of the estimation of persistence parameters was found to be unsatisfactory, it proved useful in setting the initial values and also in subsequent adjustment of the variance-based estimates of persistence parameters. At low threshold levels corresponding to q < 0.20, even the first-order Markov chain can be construed as a satisfactory model for predicting drought durations based on monthly and weekly SHI sequences.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Sharma, T.C. and Panu, U.S., 2012. Prediction of hydrological drought durations based on Markov chains in the Canadian prairies. Hydrological Sciences Journal, 57 (4), 705–722.     

Forecasting Ability of a Multi-Renewal Seismicity Model

The inter-event time (IET) is sometimes used as a basis for prediction of large earthquakes. It is the case when theoretical analysis of prediction is possible. Quite recently, a specific IET model was suggested for dynamic probabilistic prediction of \( M \ge 5.5 \) events in Italy (http://earthquake.bo.ingv.it). In this study we analyze some aspects of the statistical estimation of the model and its predictive ability. We find that more or less effective prediction is possible within four out of 34 seismotectonic zones where seismicity rate or clustering of events is relatively high. We show that, in the framework of the model, one can suggest a simple zone-independent strategy, which practically optimizes the relative number of non-accidental successes, or the Hanssen-Kuiper (HK) skill score. This quasi-optimal strategy declares alarm in a zone for the first 2.67 years just after the occurrence of each large event in the zone. The optimal HK skill score values are about 26 % for the three most active zones, and 2–10 % for the 26 least active zones. However, the number of false alarm time intervals per one event in each of the zones is unusually high: about 0.7 and 0.8–0.95, respectively. Both these theoretical estimations are important because any prospective testing of the model is unrealistic in most of the zones during a reasonable time. This particular analysis requires a discussion of the following issues of general interest: a specific approach to the analysis of predictions vs. the standard CSEP testing approach; prediction vs. forecasting; HK skill score vs. probability gain; the total forecast error diagram and connected false alarms.     

Trimmed L-moments (1,0) for the generalized Pareto distribution

Abstract

Statistical analysis of extremes is often used for predicting the higher return-period events. In this paper, the trimmed L-moments with one smallest value trimmed—TL-moments (1,0)—are introduced as an alternative way to estimate floods for high return periods. The TL-moments (1,0) have an ability to reduce the undesirable influence that a small value in the statistical sample might have on a large return period. The main objective of this study is to derive the TL-moments (1,0) for the generalized Pareto (GPA) distribution. The performance of the TL-moments (1,0) was compared with L-moments through Monte Carlo simulation based on the streamflow data of northern Peninsular Malaysia. The result shows that, for some cases, the use of TL-moments (1,0) is a better option as compared to L-moments in modelling those series.

Citation Ahmad, U.N., Shabri, A. & Zakaria, Z.A. (2011) Trimmed L-moments (1,0) for the generalized Pareto distribution. Hydrol.Sci. J. 56(6), 1053–1060.     

A simulation study to examine the sensitivity of the Pettitt test to detect abrupt changes in mean

Abstract

The Pettitt test is a non-parametric test that has been used in a number of hydroclimatological studies to detect abrupt changes in the mean of the distribution of the variable of interest. This test is based on the Mann-Whitney two-sample test (rank-based test), and allows the detection of a single shift at an unknown point in time. This test is often used to detect shifts in extremes because of the lack of distributional assumptions. However, the downside of not specifying a distribution is that the Pettitt test may be inefficient in detecting breaks when dealing with extremes. Here we adopt a Monte Carlo approach to examine the sensitivity of the Pettitt test in detecting shifts in the mean under different conditions (location of the break within the series, magnitude of the shift, record length, level of variability in the data, extreme vs non-extreme records, and pre-assigned significance level). These simulation results show that the sensitivity of this test in detecting abrupt changes increases with the increase in the magnitude of the shift and record length. The number of detections is higher when the time series represents the central part of the distribution (e.g. changes in the time series of medians), while the skill decreases as we move toward either low or high extremes (e.g. changes in the time series of maxima). Furthermore, the number of detections decreases as the variability in the data increases. Finally, abrupt changes are more easily detected when they occur toward the center of the time series.

Editor D. Koutsoyiannis Associate editor K. Hamed     

Statistics of extremes and estimation of extreme rainfall: II. Empirical investigation of long rainfall records / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: II. Recherche empirique sur de longues séries de précipitations

Abstract

Abstract In the first part of this study, theoretical analyses showed that the Gumbel distribution is quite unlikely to apply to hydrological extremes and that the extreme value distribution of type II (EV2) is a more consistent choice. Based on these theoretical analyses, an extensive empirical investigation is performed using a collection of 169 of the longest available rainfall records worldwide, each having 100–154 years of data. This verifies the theoretical results. In addition, it shows that the shape parameter of the EV2 distribution is constant for all examined geographical zones (Europe and North America), with value κ = 0.15. This simplifies the fitting and the general mathematical handling of the distribution, which become as simple as those of the Gumbel distribution.     

Missing precipitation data estimation using optimal proximity metric-based imputation,nearest-neighbour classification and cluster-based interpolation methods

Abstract

New optimal proximity-based imputation, K-nearest neighbour (K-NN) classification and K-means clustering methods are proposed and developed for estimation of missing daily precipitation records. Mathematical programming formulations are developed to optimize the weighting, classification and clustering schemes used in these methods. Ten different binary and real-valued distance metrics are used as proximity measures. Two climatic regions, Kentucky and Florida, (temperate and tropical) in the USA, with different gauge density and network structure, are used as case studies to evaluate the new methods. A comprehensive exercise is undertaken to compare the performances of the new methods with those of several deterministic and stochastic spatial interpolation methods. The results from these comparisons indicate that the proposed methods performed better than existing methods. Use of optimal proximity metrics as weights, spatial clustering of observation sites and classification of precipitation data resulted in improvement of missing data estimates.

Editor D. Koutsoyiannis; Associate editor C. Onof     

Estimation of the generalized logistic distribution of extreme events using partial L-moments

Abstract

Statistical analysis of extreme events is often carried out to predict large return period events. In this paper, the use of partial L-moments (PL-moments) for estimating hydrological extremes from censored data is compared to that of simple L-moments. Expressions of parameter estimation are derived to fit the generalized logistic (GLO) distribution based on the PL-moments approach. Monte Carlo analysis is used to examine the sampling properties of PL-moments in fitting the GLO distribution to both GLO and non-GLO samples. Finally, both PL-moments and L-moments are used to fit the GLO distribution to 37 annual maximum rainfall series of raingauge station Kampung Lui (3118102) in Selangor, Malaysia, and it is found that analysis of censored rainfall samples of PL-moments would improve the estimation of large return period events.

Editor D. Koutsoyiannis; Associate editor K. Hamed

Citation Zakaria, Z.A., Shabri, A. and Ahmad, U.N., 2012. Estimation of the generalized logistic distribution of extreme events using partial L-moments. Hydrological Sciences Journal, 57 (3), 424–432.     

Time–frequency analysis to profile hydrological regimes: application to Haiti

Abstract

Comprehensive characterization of its flow rates is prerequisite to a proper understanding and water management of a given hydrological region. Several studies question the soundness of stationarity in time series and suggest the need for a quantification of the events and non-stationary features in flow rate time series. In this study, we combine statistical and time–frequency (TF) analyses to characterize and classify the flow rates of an understudied region, namely Haiti. Wavelet transforms and cyclostationarity analyses were combined with principal component analysis and hierarchical clustering to identify three groups of hydrological regimes in the country, suggesting similar management: (1) relatively stable flow rates with TF behaviour; (2) periodic and strongly seasonal flow rates; and (3) unstable flow rates. We argue that the TF methodology can yield additional information in regard to flow events and multiscale behaviour, even for short records. Flow rate characterization would benefit from the exhaustive approach described here.

EDITOR Z.W. Kundzewicz ASSOCIATE EDITOR E. Toth