Hydrological Frequency Analysis Research Articles

Multi-distribution regula-falsi profile likelihood method for nonstationary hydrological frequency analysis

Multi-distribution regula-falsi profile likelihood method for nonstationary hydrological frequency analysis

Hydrological Frequency Analysis in Changing Environments Based on Empirical Mode Decomposition and Metropolis-Hastings Sampling Bayesian Models

Hydrological Frequency Analysis in Changing Environments Based on Empirical Mode Decomposition and Metropolis-Hastings Sampling Bayesian Models

Optimal Scheduling of Reservoir Flood Control under Non-Stationary Conditions

To improve reservoir flood control and scheduling schemes under changing environmental conditions, we established an adaptive reservoir regulation method integrating hydrological non-stationarity diagnosis, hydrological frequency analysis, design flood calculations, and reservoir flood control optimization scheduling and applied it to the Chengbi River Reservoir. The results showed that the peak annual flood sequence and the variation point of the annual maximum 3-day flood sequence of the Chengbi River Reservoir was in 1979, and the variation point of the annual maximum 1-day flood sequence was in 1980. A mixed distribution model was developed via a simulated annealing algorithm, hydrological frequency analysis was carried out, and a non-stationary design flood considering the variation point was obtained according to the analysis results; the increases in the flood peak compared to the original design were 4.00% and 8.66%, respectively. A maximum peak reduction model for optimal reservoir scheduling using the minimum sum of squares of the downgradient flow as the objective function was established and solved via a particle swarm optimization algorithm. The proposed adaptive scheduling scheme reduced discharge flow to 2661 m3/s under 1000-year flood conditions, and the peak reduction rate reached 60.6%. Furthermore, the discharge flow was reduced to 2661 m3/s under 10,000-year flood conditions, and the peak reduction rate reached 65.9%.

Nonstationary hydrological frequency analysis using the Metastatistical extreme value distribution

The nonstationary hydrological frequency analysis (NS-HFA) aids in assessing the recurrence of hydrological extremes under nonstationarity, but its reliability is often questioned due to relatively limited record lengths. The Metastatistical extreme value (MEV) distribution, which harnesses the ordinary event records along with the extremes, has proven advantageous under stationarity and in instances with limited records. Yet, nonstationary applications of the MEV distribution are lacking, and only modified versions, such as the simplified MEV (SMEV) and block-based MEV (MEVBB) distributions, have been proposed. This paper develops the nonstationary version of the MEV distribution for NS-HFA (called the MEV-based model), which incorporates an explicit nonstationary structure and preserves the stochastic interannual variability of ordinary events. The developed model is assessed using several benchmark models in both simulation studies and real applications for both in-sample fitting and out-of-sample prediction from the perspectives of uncertainty, accuracy, and fitting efficiency. The benchmark models for comparison included the MEVBB as well as the SMEV- and Generalized Extreme Value distribution (GEV)-based models. The results demonstrated that the proposed MEV-based model outperformed the MEVBB regarding overfitting and captured the underlying process more efficiently, accurately, and with less uncertainty. In addition, the MEV-based model was superior to the GEV-based model due to its higher accuracy, equivalent or better fitting efficiency, and lower uncertainty. Furthermore, although the MEV-based model performed overall equivalently to the SMEV-based, the MEV-based model was shown advantageous for adopting nonstationary stochastic physical covariates and facilitating out-of-sample predictions. Overall, these results demonstrated that the proposed MEV-based model has distinct advantages for the NS-HFA, and consequently promotes its implementation.

Nonstationary hydrological frequency analysis in light of model parameters and climate projections uncertainty

Nonstationary hydrological frequency analysis (HFA) has been a commonly used approach for design flood estimation under nonstationary conditions, which underlies deep uncertainty. Most of the previous studies focus on the influence of model parameter (MP) uncertainty on design flood, little is known about quantitative assessment on the commonly-used precipitation projection (PP) uncertainty impact on it. To address this concern, this study proposed an analysis framework to quantify the design flood estimation uncertainty in light of MP uncertainty, PP uncertainty and both of them. Firstly, the equidistant cumulative distribution function method was used to correct the PP provided by twenty-eight GCMs to improve their quality; secondly, the optimal nonstationary distribution model, coupling with the Equivalent Reliability method, was applied to estimate the design flood; then the uncertainty analysis framework composed of Bayesian theory and poor-man ensemble strategy was employed to analyze the impact of the MP uncertainty, PP uncertainty and both of them on the design flood estimation. Moreover, the investigation on which one between MP and PP uncertainty was dominated in the total uncertainty on design flood estimation was conducted based on a case study. Results showed that MP and PP uncertainty has noticeable impacts on the design flood uncertainty. The MP uncertainty impact on the design flood was greater than the PP uncertainty.

Hydrological frequency analysis under nonstationarity using the Metastatistical approach and its simplified version

The implementation of nonstationary hydrological frequency analysis (NS-HFA) has often been hampered by the relatively short datasets and the resulting high uncertainty. Most recently, the non-asymptotic Metastatistical extreme value (MEV) and simplified MEV (SMEV) distributions, which rely on the ordinary events rather than the extremes only, have attracted attention in the HFA of both rainfall and streamflow. Despite their use for trend detection/attribution and producing future projections, their practical implementation for the NS-HFA is absent in the literature. This paper therefore implemented these models (called MEV and SMEV-based models) in the NS-HFA and comprehensively assessed their performance from the perspectives of fitting efficiency, accuracy, and uncertainty for both in-sample fitting and out-of-sample prediction purposes. The asymptotic models based on the generalized extreme value (GEV) distribution were used as the benchmark. The assessment employed synthetic and real rainfall datasets that exhibit stationarity in the number of events per year. All the nonstationary ordinary-event datasets followed the Weibull distribution with linearly changing parameters, while their standardized annual maximum series aligned with the GEV distribution. Thus, the MEV, SMEV- and GEV-based models could be fairly assessed and compared. The regula-falsi profile likelihood method was extended to quantify the uncertainty of the MEV and SMEV-based models. The results demonstrated that the MEV model was not advantageous over other models in terms of all three evaluation perspectives. Whereas the SMEV-based models demonstrated superiority due to their higher accuracy, equivalent or better fitting efficiency, as well as lower uncertainty compared to all other models. Therefore, this paper advocates the use of the SMEV distribution to advance the NS-HFA by harnessing the information from the ordinary events.

Enhanced profile likelihood method for the nonstationary hydrological frequency analysis

In the nonstationary hydrological frequency analysis (NS-HFA), the profile likelihood (PL) method has shown superiority in uncertainty estimation due to its higher accuracy and realistic asymmetric estimates. However, its wide application has been hindered by two issues, namely the high computational burden and the numerical instability problems arising when dealing with short datasets. This paper aimed to solve or mitigate these two issues. To reduce its computational burden, the classical regula-falsi numerical method was incorporated into the PL method (namely, the RF-PL method) for estimating the bounds of the confidence intervals through an explicit analytical expression of the reparametrized log-likelihood function rather than computing the full profile. The generalized maximum likelihood principle, which constrains the distribution shape parameter to a physically/statistically reasonable range, was extended to the proposed RF-PL method (namely, the RF-GPL method) to handle short datasets. The proposed methods were applied to eight annual maximum series of flow and precipitation from North America, which present temporal trends in the mean and/or the standard deviation, to demonstrate their efficiency. The results showed that the RF-PL method substantially reduced the computational time of the PL method by 94–96% without degrading its estimation accuracy. Moreover, the RF-GPL was proven to be effective in avoiding or substantially mitigating the numerical instability issue of the RF-PL method for small sample sizes in addition to reducing the uncertainty in the estimates. As expected, the superiority of the RF-GPL method decreases with the increase of the sample size, which is beneficial in enhancing the estimation of the shape parameter in the RF-PL method. Therefore, the RF-GPL method is advantageous over the RF-PL method for short datasets, whereas its outperformance would be case-dependent for long datasets. These advancements overcome the common hurdles of the PL method and consequently enable its practical implementation more widely in the NS-HFA.

Incorporating decadal climate variability information in the operation and design of water infrastructure

Abstract The high thermal and mechanical inertia of the oceans results in slow changes in sea surface temperatures (SSTs). Changes in SSTs, in turn, can impact atmospheric circulation including water vapor transport, precipitation, and temperatures throughout the world. The Pacific Decadal Oscillation (PDO), the tropical Atlantic SST gradient variability, and the West Pacific Warm Pool are patterns of natural climate variability that tend to persist over decadal time periods. There are current efforts to produce decadal climate predictions, but there is limited understanding if this information can be used in water resources management. Understanding the current state of decadal climate variability (DCV) phenomena and the probability of persisting in that state may be useful information for water managers. This information could improve forecasts that aid operations and short-term planning for reservoir management, domestic and industrial water supplies, flood risk management, energy production, recreation, inland navigation, and irrigation. If conditions indicate a higher likelihood of drought, reservoir managers could reduce flood storage space and increase storage for conservation purposes. Improved forecasts for irrigation could result in greater efficiencies by shifting crops and rotational crop patterns. The potential benefits of using a forecast must be balanced against the risk of damages if the forecast is wrong. Seasonal forecasts using DCV information could also be used to inform drought triggers. If DCV indices indicate that the climate has a higher probability of dry conditions, drought contingency plans could be triggered earlier. Understanding of DCV phenomena could also improve long-range water resources planning. DCV can manifest itself in relatively short-term hydrologic records as linear trends that complicate hydrologic frequency analysis, which has traditionally assumed that hydrologic records are stationary.

Quantitative Relationships between the Tidal Current Limit, Tidal Level Limit and River Discharge in the Changjiang River Estuary

Estuaries are areas where runoff and tide interact. Tidal waves propagate upstream from river mouths and produce tidal currents and tidal level variations along rivers. Based on the hydrological frequency analysis of river discharge in the dry season and flood season at the Datong hydrological station over the past 70 years, a three-dimensional estuary numerical model was used to produce the quantitative relationships between the tidal current limit, tidal level limit and river discharge in the Changjiang River estuary. The positions of tidal current limit and tidal level limit depend not only on river discharge but also on river topography. When river discharge varies from a hydrological frequency of 95% to 5%, the relationship between the tidal current limit and river discharge is y=2×10−13x3+3 × 10−8x2− 0.0074x+359.35 in the flood season, with a variation range of 90 km, and y=−4×10−10x3−1 × 10−5x2−0.1937x − 1232.9 in the dry season, with a variation range of 200 km. The relationship between the tidal level limit and river discharge is y=6×10−8x2−0.0096x+775.94 in the flood season, with a variation range of 127 km, and y=0.3428x2−17.9x+777.55 in the dry season, with a variation range of 83 km, which is located far upstream of the Datong hydrological station.

Open Science Practices for Studies of Event-Related Potentials (ERPs): Reporting ERP Reliability and Data Quality in the Spirit of Transparency

Hydrological frequency analysis (HFA) is commonly used for the assessment of the risk associated to hydrological events. HFA is generally based on the assumptions of homogeneity, independence and stationarity of the hydrological data. Hydrological events are often described through a number of dependent characteristics, such as peak, volume and duration for floods. Unfortunately, in this multivariate setting, the verification of the above assumptions is often neglected. When a shift occurs in a data series, it can affect the stationarity and the homogeneity of the data. The objective of this paper is to study tests for shift detection in multivariate hydrological data. The considered shift tests are mainly based on the notion of depth function, except for one test that is considered for comparison purposes. A simulation study is performed to evaluate and compare the power of all these tests with hydrological constraints. A flood analysis application is also carried out to show the practical aspects of the considered tests. The power of the considered tests is influenced by a number of factors, including the sample size, the shift amplitude, the magnitude of the series and the location of the shift in the series.

Multivariate non-stationary hydrological frequency analysis

To study hydrological events, such as floods and droughts, frequency analysis (FA) techniques are commonly employed. FA relies on some assumptions, especially, the stationarity of the data series. However, the stationarity assumption is not always fulfilled for a variety of reasons such as climate change and human activities. Thus, it is essential to check the stationarity or we should develop models that take into account the non-stationarity in a new risk assessment framework. On the other hand, a majority of hydrological phenomena are described by a number of correlated characteristics. To model the dependence structure between these hydrological variables, copulas are the most employed tool. Generally in the literature, the multivariate model is assumed to be the same over time even though multivariate stationarity is required. Considering the non-stationarity in the dependence structure is important because when the copula parameter changes, the multivariate quantile curve changes accordingly. Different scenarios can be considered when choosing a multivariate non-stationary model since several variables and a dependence structure are involved. The objective of the present study is to construct a model that integrates simultaneously multivariate and non-stationarity aspects along with hypothesis testing. For the copula part, we consider versions called Dynamic copulas and series of association measures are obtained through rolling windows of the corresponding series. Adapted versions of the AIC criterion are employed to select the final model (margins and copula). The procedure is applied to a flood volume and peak dataset from Iran. The obtained model constitutes of a lognormal distribution for the margins with linear trend in the peak series, stationary for the volume series and a quadratic trend in the logistic Gumbel copula parameter for the dependence structure.

Hydrological frequency analysis of large-ensemble climate simulation data using control density as a statistical control

Hydrological frequency analysis of large-ensemble climate simulation data using control density as a statistical control

Regional hydrological frequency analysis at ungauged sites with random forest regression

Flood quantile estimation at sites with little or no data is important for the adequate planning and management of water resources. Regional Hydrological Frequency Analysis (RFA) deals with the estimation of hydrological variables at ungauged sites. Random Forest (RF) is an ensemble learning technique which uses multiple Classification and Regression Trees (CART) for classification, regression, and other tasks. The RF technique is gaining popularity in a number of fields because of its powerful non-linear and non-parametric nature. In the present study, we investigate the use of Random Forest Regression (RFR) in the estimation step of RFA based on a case study represented by data collected from 151 hydrometric stations from the province of Quebec, Canada. RFR is applied to the whole data set and to homogeneous regions of stations delineated by canonical correlation analysis (CCA). Using the Out-of-bag error rate feature of RF, the optimal number of trees for the dataset is calculated. The results of the application of the CCA based RFR model (CCA-RFR) are compared to results obtained with a number of other linear and non-linear RFA models. CCA-RFR leads to the best performance in terms of root mean squared error. The use of CCA to delineate neighborhoods improves considerably the performance of RFR. RFR is found to be simple to apply and more efficient than more complex models such as Artificial Neural Network-based models.

Stationary hydrological frequency analysis coupled with uncertainty assessment under nonstationary scenarios

The use of the nonstationary hydrological frequency analysis (HFA) has been prompted when nonstationarity is diagnosed in hydrometeorological data. However, the inconclusive identification of the physical process(es) and driver(s) behind the nonstationarity challenges the identification of an appropriate model structure, and consequently might hinder its reliable implementation. To date, no solid consensus on whether the nonstationary HFA is always superior to the stationary HFA has been reached. Therefore, this paper aimed to advance the understanding of the stationary and nonstationary HFAs under nonstationary scenarios by illustratively comparing their performance in real applications, and examining the effects of the nonstationarity on the stationary HFA through a simulation study, especially from the perspective of the uncertainty. The investigation of the effects of the nonstationarity on the stationary HFA was conducted in two fundamental nonstationary scenarios, namely temporal trends in the mean and variance, in which the degree of nonstationarity was quantifiable and known a priori. The HFAs were conducted using the Particle Filter, a Bayesian filtering technique which was recently employed in the stationary HFA and was further extended for the nonstationary HFA in this paper. The illustrative comparison did not demonstrate a consistent superiority of either HFA approach in terms of both fitting efficiency and uncertainty. This result thus implied that the stationarity HFA could outperform the nonstationary HFA in some cases. Besides, the simulation investigation of the stationary HFA revealed that the increase of nonstationarity degree would lead to the deterioration in the analysis accuracy and the elevation of uncertainty. The uncertainty in the stationary HFA was found to primarily originate from the nonstationarity, while the distribution selection would be the other but secondary source of uncertainty. The results from both the illustrative comparison and the simulation investigation suggested that whether the stationary or nonstationary HFA outperforms the other could be associated with the degree and pattern of nonstationarity. Therefore, it is recommended to consider them when developing a strategic framework to select an appropriate approach to deal with nonstationary hydrometeorological data.

Introduction of Confidence Interval Based on Probability Limit Method Test into Non-Stationary Hydrological Frequency Analysis

Nonstationarity in hydrological variables has been identified throughout Japan in recent years. As a result, the reliability of designs derived from using method based on the assumption of stationary might deteriorate. Non-stationary hydrological frequency analysis is among the measures to counter this possibility. Using this method, time variations in the probable hydrological quantity can be estimated using a non-stationary extreme value distribution model with time as an explanatory variable. In this study, we build a new method for constructing the confidence interval regarding the non-stationary extreme value distribution by applying a theory of probability limit method test. Furthermore, by introducing a confidence interval based on probability limit method test into the non-stationary hydrological frequency analysis, uncertainty in design rainfall because of lack of observation information was quantified, and it is shown that assessment pertaining to both the occurrence risk of extremely heavy rainfall and changes in the trend of extreme rainfall accompanied with climate change is possible.

Uncertainty Evaluation in Hydrological Frequency Analysis Based on Confidence Interval and Prediction Interval

The shortage of extreme rainfall data gives substantial uncertainty to design rainfalls and causes predictions for torrential rainfall to deviate strongly from adopted probability distributions used in river planning. These torrential rainfalls are treated as outliers which existing studies do not evaluate. However, probability limit method test which its acceptance region expresses with high accuracy the range where observed ith order statistics could realize. Confidence interval which quantifies uncertainty of adopted distributions can be constructed by assuming that these critical values in both sides of the adopted region follow the same function form applied to actual observed data. Furthermore, its validity is proved through comparison of confidence interval derived from ensemble downscaling calculations. In addition, these critical values are almost in accordance with outliers in samples from the ensemble downscaling calculations. Therefore, prediction interval which expresses the range that an unknown observed datum can take is constructed by extrapolating the critical values for limit estimation of a future datum. In this paper, quantification method of uncertainty of design rainfall and occurrence risk of outliers in the traditional framework, using the proposed confidence interval and prediction interval, is shown. Moreover, their application to future climate by using Bayesian statistics is explained.

Estimating the design flood under the influence of check dams by removing nonstationarity from the flood peak discharge series

Abstract The construction of check dams in northwestern China has resulted in nonstationary changes in flood peak discharge series; the stationary assumption of the conventional hydrological frequency analysis is no longer satisfied. According to the characteristics of the construction and operation of check dams, the nonstationarity of flood peak discharge series are largely induced by changes in the effective runoff generation area (i.e., the basin area minus the area controlled by check dams). Knowing the power function relationship between the flood peak discharge and the basin area, we can remove the influence of the effective runoff generation area and convert the original nonstationary series into a stationary series. This de-nonstationarity method can achieve stationarity in the first and second moments simultaneously. Therefore, we can calculate the design value of the reconstructed series using the conventional frequency analysis method. According to the effective runoff generation area under design conditions, we can then obtain the corresponding design flood of the original series. We applied this method to the Mahuyu River basin to obtain the design flood under nonstationarity. Due to the consideration of the deterministic influence of check dams during the de-nonstationarity process, the uncertainty analyzed by the bootstrap method is obviously small.

Probability Distribution and Characterization of Daily Precipitation Related to Tropical Cyclones over the Korean Peninsula

Rainfall events are known to be driven by various synoptic disturbances or dominant processes in the atmosphere. In spite of the diverse atmospheric contributions, the assumption of homogeneity is commonly adopted when a hydrological frequency analysis is conducted. This study examines how the dominant processes, particularly the landfalling tropical cyclones (TCs) and non-TC events, have various effects to the characteristics of rainfall in South Korea. With rainfall data from the fifty-nine weather stations spread across the country, the multiple contributions of the TC and non-TC rainfall to the relative amount of rainfall, duration, intensity and maximum rainfall, on a seasonal and monthly scale, are first explored in this study. For the second objective, suitable probability distributions for the TC and non-TC time series are identified potentially for a synthetic analysis. Our results indicate that TCs cause a heterogeneous spatial distribution in the rainfall characteristics over the gauge networks particularly in the southern and eastern coastal areas. Some gauges in these areas attribute a significant portion of their amount and annual maximum rainfall to landfalling TCs. The results also show that the Pearson Type III distribution best represents the non-TC wet-day series, while the TC wet-day series can be represented by various distributions including the Weibull and Gamma distributions. From the analysis, we present how the characteristics of TCs differ from non-TCs with the emphasis on the need to consider their individual effects when conducting synthetic analyses.

Uncertainty quantification using the particle filter for non-stationary hydrological frequency analysis

Recent changes in climate, anthropogenic activities and land-use patterns have significantly altered the hydrological cycle and thus led to the presence of non-stationarity in hydrological data series. Existing conventional approaches for hydrological frequency analysis (HFA) have commonly overlooked non-stationarity and consequently they might produce false estimates of hydrological design events. Assessing the effect of non-stationarity through uncertainty quantification is a potentially feasible approach for HFA. This paper proposed to incorporate the particle filter (PF) into HFA (here flood frequency analysis (FFA) was exemplified) (named PF-FFA) for quantifying prediction uncertainty in flood quantile estimates. The feasibility of the PF-FFA was verified through comparison with the conventional L-moment based FFA (LM-FFA) as well as the random sampling based FFA (RS-FFA) in terms of both accuracy and precision respectively using several selected evaluation indices. Furthermore, the comparison of the use of constant and varying shape parameter in the PF-FFA demonstrated that the use of constant shape parameter would deteriorate the performance in both accuracy and precision, especially for datasets showing a high-level degree of non-stationarity. Through these elaborate investigations, the PF-FFA was shown to be an effective approach when dealing with non-stationary datasets as it successfully captured the effect of non-stationarity compared to the LM-FFA and RS-FFA.

Assessing the Regional Concept with Sub-Sampling Approach to Identify Probability Distribution for at-Site Hydrological Frequency Analysis

The framework of regional analysis allows superior discrimination as well as better identification of the shape of a population distribution in a hydrological frequency analysis. The aim of this study is to incorporate the better of regional concept while performing an at-site frequency analysis. The study proposes a new method in the form of sub-sampling technique with the aid of a regional distribution selection procedure to choose an appropriate probability distribution function for frequency analysis. The technique is evaluated against common distribution selection methods: a widely used goodness-of-fit method in Anderson–Darling (AD) and a popular graphical assessment tool in L-moment ratio diagram (LMRD). The performance is evaluated by applying the technique to gauged annual maximum daily precipitation data series of 24 stations located across China. It is found that the technique accomplished a better performance in discriminating among distributions which or else may not be achievable only by the AD or LMRD test. In general, all results indicate that the proposed technique can be an attractive means in discriminating as well as identifying the best distribution for at-site frequency analysis.