River flow modelling: comparison of performance and evaluation of uncertainty using data-driven models and conceptual hydrological model

Hydrological and statistical models are playing an increasing role in hydrological forecasting, particularly for river basins with data of different temporal scales. In this study, statistical models, e.g. artificial neural networks, adaptive network-based fuzzy inference system, genetic programming, least squares support vector machine, multiple linear regression, were developed, based on parametric optimization methods such as particle swarm optimization (PSO), genetic algorithm (GA), and data-preprocessing techniques such as wavelet decomposition (WD) for river flow modelling using daily streamflow data from four hydrological stations for a period of 1954–2009. These models were used for 1-, 3- and 5-day streamflow forecasting and the better model was used for uncertainty evaluation using bootstrap resampling method. Meanwhile, a simple conceptual hydrological model GR4J was used to evaluate parametric uncertainty based on generalized likelihood uncertainty estimation method. Results indicated that: (1) GA and PSO did not help improve the forecast performance of the model. However, the hybrid model with WD significantly improved the forecast performance; (2) the hybrid model with WD as a data preprocessing procedure can clarify hydrological effects of water reservoirs and can capture peak high/low flow changes; (3) Forecast accuracy of data-driven models is significantly influenced by the availability of streamflow data. More human interferences from the upper to the lower East River basin can help to introduce greater uncertainty in streamflow forecasts; (4) The structure of GR4J may introduce larger parametric uncertainty at the Longchuan station than at the Boluo station in the East river basin. This study provides a theoretical background for data-driven model-based streamflow forecasting and a comprehensive view about data and parametric uncertainty in data-scarce river basins.     

Quantification of parametric uncertainty of ANN models with GLUE method for different streamflow dynamics

This study describes the parametric uncertainty of artificial neural networks (ANNs) by employing the generalized likelihood uncertainty estimation (GLUE) method. The ANNs are used to forecast daily streamflow for three sub-basins of the Rhine Basin (East Alpine, Main, and Mosel) having different hydrological and climatological characteristics. We have obtained prior parameter distributions from 5000 ANNs in the training period to capture the parametric uncertainty and subsequently 125,000 correlated parameter sets were generated. These parameter sets were used to quantify the uncertainty in the forecasted streamflow in the testing period using three uncertainty measures: percentage of coverage, average relative length, and average asymmetry degree. The results indicated that the highest uncertainty was obtained for the Mosel sub-basin and the lowest for the East Alpine sub-basin mainly due to hydro-climatic differences between these basins. The prediction results and uncertainty estimates of the proposed methodology were compared to the direct ensemble and bootstrap methods. The GLUE method successfully captured the observed discharges with the generated prediction intervals, especially the peak flows. It was also illustrated that uncertainty bands are sensitive to the selection of the threshold value for the Nash–Sutcliffe efficiency measure used in the GLUE method by employing the Wilcoxon–Mann–Whitney test.     

Detection of trends in hydrological extremes for Canadian watersheds

The potential impacts of climate change can alter the risk to critical infrastructure resulting from changes to the frequency and magnitude of extreme events. As well, the natural environment is affected by the hydrologic regime, and changes in high flows or low flows can have negative impacts on ecosystems. This article examines the detection of trends in extreme hydrological events, both high and low flow events, for streamflow gauging stations in Canada. The trend analysis involves the application of the Mann–Kendall non‐parametric test. A bootstrap resampling process has been used to determine the field significance of the trend results. A total of 68 gauging stations having a nominal record length of at least 50 years are analysed for two analysis periods of 50 and 40 years. The database of Canadian rivers investigated represents a diversity of hydrological conditions encompassing different extreme flow generating processes and reflects a national scale analysis of trends. The results reveal more trends than would be expected to occur by chance for most of the measures of extreme flow characteristics. Annual and spring maximum flows show decreasing trends in flow magnitude and decreasing trends in event timing (earlier events). Low flow magnitudes exhibit both decreasing and increasing trends. Copyright © 2010 John Wiley & Sons, Ltd.     

Identification and quantification of streamflow trends on the Canadian Prairies

Abstract

Trend analysis was performed on streamflow data for a collection of stations on the Canadian Prairies, in terms of spring and summer runoff volumes, peak flow rates and peak flow occurrences, as well as an annual volume measure, for analysis periods of 1966–2005, 1971–2005, and 1976–2005. The Mann-Kendall statistical test for trend and bootstrap resampling were used to identify the trends and to determine the field significance of the trends. Partial correlation analysis was used to identify relationships between hydrological variables that exhibit a significant trend and meteorological variables that exhibit a significant trend. Noteworthy results include decreasing trends in the spring snowmelt runoff event volume and peak flow, decreasing trends (earlier occurrence) in the spring snowmelt runoff event peak date and decreasing trends in the seasonal (1 March–31 October) runoff volume. These trends can be attributed to a combination of reductions in snowfall and increases in temperatures during the winter months.     

Seasonal trends in Romanian streamflow

Mean daily streamflow records from 44 river basins in Romania with an undisturbed runoff regime have been analyzed for trends with the nonparametric Mann‐Kendall test for two periods of study: 1961–2009 (25 stations) and 1975–2009 (44 stations). The statistical significance of trends was tested for each station on an annual and seasonal basis, for different streamflow quantiles. In order to account for the presence of serial correlation that might lead to an erroneous rejection of the null hypothesis, a trend‐free prewhitening was applied to the original data series. The regional field significance of trends is tested by a bootstrap procedure. Changes in the streamflow regime in Romania are demonstrated. The main identified trends are an increase in winter and autumn streamflow since 1961 and a decrease in summer flow since 1975. The streamflow trends are well explained by recent changes in temperature and precipitation that occurred in the last 50 years. Copyright © 2013 John Wiley & Sons, Ltd.     

A test for directional-linear independence,with applications to wildfire orientation and size

A nonparametric test for assessing the independence between a directional random variable (circular or spherical, as particular cases) and a linear one is proposed in this paper. The statistic is based on the squared distance between nonparametric kernel density estimates and its calibration is done by a permutation approach. The size and power characteristics of various variants of the test are investigated and compared with those for classical correlation-based tests of independence in an extensive simulation study. Finally, the best-performing variant of the new test is applied in the analysis of the relation between the orientation and size of Portuguese wildfires.     

Simple generalization approach for intensity–duration–frequency relationships

Rainfall intensity–duration–frequency (IDF) relationships describe rainfall intensity as a function of duration and return period, and they are significant for water resources planning, as well as for the design of hydraulic constructions. In this study, the two‐parameter lognormal (LN2) and Gumbel distributions are used as parent distribution functions. Derivation of the IDF relationship by this approach is quite simple, because it only requires an appropriate function of the mean of annual maximum rainfall intensity as a function of rainfall duration. It is shown that the monotonic temporal trend in the mean rainfall intensity can successfully be described by this parametric function which comprises a combination of the parameters of the quantile function a(T) and completely the duration function b(d) of the separable IDF relationship. In the case study of Aegean Region (Turkey), the IDF relationships derived through this simple generalization procedure (SGP) may produce IDF relationships as successfully as does the well‐known robust estimation procedure (REP), which is based on minimization of the nonparametric Kruskal–Wallis test statistic with respect to the parameters θ and η of the duration function. Because the approach proposed herein is based on lower‐order sample statistics, risks and uncertainties arising from sampling errors in higher‐order sample statistics were significantly reduced. The authors recommend to establish the separable IDF relationships by the SGP for a statistically favorable two‐parameter parent distribution, because it uses the same assumptions as the REP does, it maintains the observed temporal trend in the mean additionally, it is easy to handle analytically and requires considerably less computational effort. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparison of linear and nonlinear dimension reduction techniques for automated process monitoring of a decentralized wastewater treatment facility

Multivariate statistical methods for online process monitoring have been widely applied to chemical, biological, and engineered systems. While methods based on principal component analysis (PCA) are popular, more recently kernel PCA (KPCA) and locally linear embedding (LLE) have been utilized to better model nonlinear process data. Additionally, various forms of dynamic and adaptive monitoring schemes have been proposed to address time-varying features in these processes. In this analysis, we extend a common simulation study in order to account for autocorrelation and nonstationarity in process data and comprehensively compare the monitoring performances of static, dynamic, adaptive, and adaptive–dynamic versions of PCA, KPCA, and LLE. Furthermore, we evaluate a nonparametric method to set thresholds for monitoring statistics and compare results with the standard parametric approaches. We then apply these methods to real-world data collected from a decentralized wastewater treatment system during normal and abnormal operations. From the simulation study, adaptive–dynamic versions of all three methods generally improve results when the process is autocorrelated and nonstationary. In the case study, adaptive–dynamic versions of PCA, KPCA, and LLE all flag a strong system fault, but nonparametric thresholds considerably reduce the number of false alarms for all three methods under normal operating conditions.     

Matched block bootstrap for resampling multiseason hydrologic time series

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

A framework for quantifying the impacts of climate change and human activities on hydrological drought in a semiarid basin of Northern China

Climate change and human activities are two major driving forces affecting the hydrologic cycle, which further influence the stationarity of the hydrologic regime. Hydrological drought is a substantial negative deviation from the normal hydrologic conditions affected by these two phenomena. In this study, we propose a framework for quantifying the effects of climate change and human activities on hydrological drought. First, trend analysis and change‐point test are performed to determine variations of hydrological variables. After that, the fixed runoff threshold level method (TLM) and the standardized runoff index (SRI) are used to verify whether the traditional assessment methods for hydrological drought are applicable in a changing environment. Finally, two improved drought assessment methods, the variable TLM and the SRI based on parameter transplantation are employed to quantify the impacts of climate change and human activities on hydrological drought based on the reconstructed natural runoff series obtained using the variable infiltration capacity hydrologic model. The results of a case study on the typical semiarid Laohahe basin in North China show that the stationarity of the hydrological processes in the basin is destroyed by human activities (an obvious change‐point for runoff series is identified in 1979). The traditional hydrological drought assessment methods can no longer be applied to the period of 1980–2015. In contrast, the proposed separation framework is able to quantify the contributions of climate change and human activities to hydrological drought during the above period. Their ranges of contributions to hydrological drought calculated by the variable TLM method are 20.6–41.2% and 58.8–79.4%, and the results determined by the SRI based on parameter transplantation method are 15.3–45.3% and 54.7–84.7%, respectively. It is concluded that human activities have a dominant effect on hydrological drought in the study region. The novelty of the study is twofold. First, the proposed method is demonstrated to be efficient in quantifying the effects of climate change and human activities on hydrological drought. Second, the findings of this study can be used for hydrological drought assessment and water resource management in water‐stressed regions under nonstationary conditions.     

Improvement of overtopping risk evaluations using probabilistic concepts for existing dams

Hydrologic risk analysis for dam safety relies on a series of probabilistic analyses of rainfall-runoff and flow routing models, and their associated inputs. This is a complex problem in that the probability distributions of multiple independent and derived random variables need to be estimated in order to evaluate the probability of dam overtopping. Typically, parametric density estimation methods have been applied in this setting, and the exhaustive Monte Carlo simulation (MCS) of models is used to derive some of the distributions. Often, the distributions used to model some of the random variables are inappropriate relative to the expected behaviour of these variables, and as a result, simulations of the system can lead to unrealistic values of extreme rainfall or water surface levels and hence of the probability of dam overtopping. In this paper, three major innovations are introduced to address this situation. The first is the use of nonparametric probability density estimation methods for selected variables, the second is the use of Latin Hypercube sampling to improve the efficiency of MCS driven by the multiple random variables, and the third is the use of Bootstrap resampling to determine initial water surface level. An application to the Soyang Dam in South Korea illustrates how the traditional parametric approach can lead to potentially unrealistic estimates of dam safety, while the proposed approach provides rather reasonable estimates and an assessment of their sensitivity to key parameters.     

Regional analysis of low flow using L-moments for Dongjiang basin,South China

Abstract

Dongjiang water has been the key source of water supplies for Hong Kong and its neighbouring cities in the Pearl River Delta in South China since the mid-1960s. Rapid economic development and population growth in this region have caused serious concerns over the adequacy of the quantity and quality of water withdrawn from the Dongjiang River in the future. Information on the magnitude and frequency of low flows in the basin is needed for planning of water resources at present and in the near future. The L-moment method is used to analyse the regional frequency of low flows, since recent studies have shown that it is superior to other methods that have been used previously, and is now being adopted by many organizations worldwide. In this study, basin-wide analysis of low flows is conducted for Dongjiang basin using five distributions: generalized logistic, generalized extreme value, lognormal, Pearson type III and generalized Pareto. Each of these has three parameters estimated by the L-moment method. The discordancy index and homogeneity testing show that 14 out of the 16 study sites belong to a homogenous region; these are used for further analysis. Based on the L-moment ratios diagram, the Hosking and Wallis goodness-of-fit statistical criterion and the L-kurtosis criterion, the three-parameter lognormal distribution is identified as the most appropriate distribution for the homogeneous study region. The regional low-flow estimates for each return period are obtained using the index flood procedure. Examination of the observed and simulated low flows by regional frequency analysis shows a good agreement in general, and the results may satisfy practical application. Furthermore, the regional low-flow relationship between mean annual 7-day low flows and basin area is developed using linear regression, providing a simple and effective method for estimation of low flows of desired return periods for ungauged catchments.     

Evaluation of the water quality at Tahtali dam watershed in Izmir-Turkey by means of statistical methodology

Sustaining the human ecological benefits of surface water requires carefully planned strategies for reducing the cumulative risks posed by diverse human activities. Municipal governments in Izmir City play a key role in developing solutions to surface water management and protection. Therefore, several methodologies are carried out to develop new solutions for protecting available water resources. In the present study, the major chemical loads of surface water at the Tahtal? dam reservoir were evaluated statistically by using monthly averaged values of the measured parameters. Here, the SPSS and NCSS statistical programs were applied during the statistical analyses. Analyses were carried out in two stages. In the first part of the statistical analyses, the mean, median, minimum, maximum, 25th and 75th quartiles were calculated. In second part, the data were investigated by using statistical median test, normality test, parametric and non-parametric correlation and regression analyses. These methods were performed on water quality data taken from four sample sites representing the recharge and discharge areas at the Tahtal? dam. The Median test is applied to check if medians of water quality data from four sample sites (Derebo?az?, Bulgurca, Menderes and Gölcükler) are equal or not. Commonly a non-parametric test (distribution-free test) is used to compare two independent groups of sampled data. Since there are more than two groups in independent group comparison, Kruskal–Wallis test is applied instead of Mann–Whitney U test. Finally, the main objective of using statistical analyses in third research is to estimate the types of pollution sources, the level of pollution and its environmental impacts on the Tahtal? dam reservoir by means of statistical methodology.     

Development of an operational low-flow index for hydrological drought monitoring over Europe

Near real-time monitoring of hydrological drought requires the implementation of an index capable of capturing the dynamic nature of the phenomenon. Starting from a dataset of modelled daily streamflow data, a low-flow index was developed based on the total water deficit of the discharge values below a certain threshold. In order to account for a range of hydrological regimes, a daily 95th percentile threshold was adopted, which was computed by means of a 31-day moving window. The observed historical total water deficits were statistically fitted by means of the exponential distribution and the corresponding probability values were used as a measure of hydrological drought severity. This approach has the advantage that it directly exploits daily streamflow values, as well as allowing a near real-time update of the index at regular time steps (i.e. 10 days, or dekad). The proposed approach was implemented on discharge data simulated by the LISFLOOD model over Europe during the period 1995–2015; its reliability was tested on four case studies found within the European drought reference database, as well as against the most recent summer drought observed in Central Europe in 2015. These validations, even if only qualitative, highlighted the ability of the index to capture the timing (starting date and duration) of the main historical hydrological drought events, and its good performance in comparison with the commonly used standardized runoff index (SRI). Additionally, the spatial evolution of the most recent event was captured well in a simulated near real-time test case, suggesting the suitability of the index for operational implementation within the European Drought Observatory.     

波阻抗反演中的不确定性分析

在波阻抗反演中引入一种新的计算机统计分析方法,通过实际地震资料作Ｂｏｏｔａｔｚａｐ试验,用重采样的方法获取大量的地震数据集,对数据集中所有地震剖面的反演结果作统计分析,获取反演结果的均值,方差,量信区间等统计结果,分析波阻抗反演的不确定性。     

Comparison of bootstrap confidence intervals for an ANN model of a karstic aquifer response

Following many applications artificial neural networks (ANNs) have found in hydrology, a question has been rising for quantification of the output uncertainty. A pre‐optimized ANN simulated the hydraulic head change at two observation wells, having as input hydrological and meteorological parameters. In order to calculate confidence intervals (CI) for the ANN output two bootstrap methods were examined namely bootstrap percentile and BCa (Bias‐Corrected and accelerated). The actual coverage of the CI was compared to the theoretical coverage for different certainty levels as a means of examining the method's reliability. The results of this work support the idea that the bootstrap methods provide a simple tool for confidence interval computation of ANNs. Comparing the two methods, the percentile requires fewer calculations and yields narrower intervals with similar actual coverage to that of BCa. Overall, the actual coverage was proved lower than desired when not modeled points were present in the data subset. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimates of changes in design rainfall values for Canada

Annual maximum rainfall data from 51 stations in Canada were analyzed for trends and changes by using the Mann–Kendall trend test and a bootstrap resampling approach, respectively. Rainfall data were analyzed for nine durations ranging from 5 min to 24 h. The data analyzed are typically used in the development of intensity‐duration‐frequency (IDF) curves, which are used for estimating design rainfall values that form an input for the design of critical water infrastructure. The results reveal more increasing than decreasing trends and changes in the data with more increasing changes and larger changes, noted for the longer rainfall durations. The results also indicate that a traditional trend test may not be sufficient when the interest is in identifying changes in design rainfall quantiles. Copyright © 2012 John Wiley & Sons, Ltd.