Ungauged Sites Research Articles

A Canadian viewpoint on data, information and uncertainty in the context of prediction in ungauged basins

The quality (i.e. the degree of uncertainty that results from the interpretation and analysis) of information dictates its value for decision making. There has been much progress towards improving information on the water budgets of ungauged basins by improving knowledge, tools and techniques during the Prediction in Ungauged Basins (PUB) initiative. These improvements, at least in Canada, have come through efforts in both hydrological process and statistical hydrology research. This paper is a review of some recent Canadian PUB efforts to use data to generate information and reduce uncertainty about the hydrological regimes of ungauged basins. The focus is on the Canadian context and the problems it presents, but the lessons learned are applicable to other countries with similar challenges. With a large land mass that is relatively poorly gauged, novel approaches have had to be developed to extract the most information from the available data. It can be difficult in Canada to find gauged or research basins sufficiently similar to ungauged sites of interest that contain the data required to force either statistical or deterministic models. Many statistical studies have improved information or at least an understanding of the quality of that information, of ungauged basin streamflow regimes using innovative regression-based approaches and pooled frequency analysis. Hydrological process research has reduced knowledge uncertainty, particularly in regard to cold regions processes, and this situation has led to the development of new algorithms that are reducing predictive uncertainty. There remains much to do. Current progress has created an opportunity to better integrate statistical and deterministic models via data assimilation of regionalization model estimates and those from coupled atmospheric-hydrological models. Aspects of such a modelling system could also provide more robust uncertainty analyses than traditional approaches.

Application of Artificial Neural Networks for estimating index floods

Abstract This article presents an application of Artificial Neural Networks (ANNs) and multiple regression models for estimating mean annual maximum discharge (index flood) at ungauged sites. Both approaches were tested for 145 small basins in Slovakia in areas ranging from 20 to 300 km2. Using the objective clustering method, the catchments were divided into ten homogeneous pooling groups; for each pooling group, mutually independent predictors (catchment characteristics) were selected for both models. The neural network was applied as a simple multilayer perceptron with one hidden layer and with a back propagation learning algorithm. Hyperbolic tangents were used as an activation function in the hidden layer. Estimating index floods by the multiple regression models were based on deriving relationships between the index floods and catchment predictors. The efficiencies of both approaches were tested by the Nash-Sutcliffe and a correlation coefficients. The results showed the comparative applicability of both models with slightly better results for the index floods achieved using the ANNs methodology.

Nonparametric methods for drought severity estimation at ungauged sites

The objective in frequency analysis is, given extreme events such as drought severity or duration, to estimate the relationship between that event and the associated return periods at a catchment. Neural networks and other artificial intelligence approaches in function estimation and regression analysis are relatively new techniques in engineering, providing an attractive alternative to traditional statistical models. There are, however, few applications of neural networks and support vector machines in the area of severity quantile estimation for drought frequency analysis. In this paper, we compare three methods for this task: multiple linear regression, radial basis function neural networks, and least squares support vector regression (LS‐SVR). The area selected for this study includes 32 catchments in the Canadian Prairies. From each catchment drought severities are extracted and fitted to a Pearson type III distribution, which act as observed values. For each method‐duration pair, we use a jackknife algorithm to produce estimated values at each site. The results from these three approaches are compared and analyzed, and it is found that LS‐SVR provides the best quantile estimates and extrapolating capacity.

Performance-weighted methods for estimating monthly streamflow at ungauged sites

► We provide a systematic approach to evaluating streamflow record estimators. ► We evaluate three techniques for estimating streamflow records at ungauged sites. ► More advanced methods are shown to be hampered by parameter uncertainty. ► We present a blended technique for more-accurately estimating streamflow records. ► These results highlight the potential value of blended estimators. Records of natural streamflow are essential to nearly all water resources projects. In spite of the wide range of available techniques for estimating monthly streamflow records at ungauged sites, few studies have sought to compare their merits. Precedent has dictated the nearly ubiquitous use of the drainage-area ratio (DAR) technique. We evaluate several monthly streamflow information-transfer methods across nearly 1300 minimally-impacted streamflow gages in the continental US from the Hydroclimatic Data Network (HCDN). The DAR method is shown to be quite robust; however, other methods of standardizing streamflow, such as standardizing flows by means (SM) or normalizing flows with means and standard deviations (SMS), are shown to be superior for a subset (∼42%) of sites. The performance of SM and SMS, relative to DAR is shown to be generally correlated with the at-site aridity ratio. We introduce a performance-weighted transfer method that weights each estimator in proportion to its performance, as predicted by basin descriptors including at-site precipitation, aridity ratio, drainage area and ratios of those descriptors between the ungauged and index site. Our blended estimators showed promising results, exhibiting greater Nash–Sutcliffe efficiencies than DAR at 60% of sites considered. Our national comparative assessment demonstrates the merits and disadvantages of several techniques, including the concept of performance weighting. We also introduce regional hydroclimatic regression equations for estimating the mean and variance of monthly streamflows at ungauged sites in the conterminous US.

Evaluation of classical spatial-analysis schemes of extreme rainfall

Abstract. Extreme rainfall is classically estimated using raingauge data at raingauge locations. An important related issue is to assess return levels of extreme rainfall at ungauged sites. Classical methods consist in interpolating extreme-value models. In this paper, such methods are referred to as regionalization schemes. Our goal is to evaluate three classical regionalization schemes. Each scheme consists of an extreme-value model (block maxima, peaks over threshold) taken from extreme-value theory plus a method to interpolate the parameters of the statistical model throughout the Cévennes-Vivarais region. From the interpolated parameters, the 100-yr quantile level can be estimated over this whole region. A reference regionalization scheme is made of the couple block maxima/kriging, where kriging is an optimal interpolation method. The two other schemes differ from the reference by replacing either the extreme-value model block maxima by peaks over threshold or kriging by a neural network interpolation procedure. Hyper-parameters are selected by cross-validation and the three regionalization schemes are compared by double cross-validation. Our evaluation criteria are based on the ability to interpolate the 100-yr return level both in terms of precision and spatial distribution. It turns out that the best results are obtained by the regionalization scheme combining the peaks-over-threshold method with kriging.

Estimation of annual baseflow at ungauged sites in Indiana USA

Summary This study developed regression models for predicting baseflow and baseflow index (BFI) (baseflow/total streamflow) at ungauged sites by using long-term baseflow data, land use, and watershed physiographic characteristics. Baseflow data were derived from daily streamflow records with a recursive digital filter method for baseflow separation for 22 watersheds in Indiana. Filtered average annual baseflow varies between 150 and 320 mm for the study watersheds. BFI varies between 0.40 to 0.88 with an average of 0.60, suggesting that 60% of long-term streamflow in Indiana is likely supported by ground water discharge and shallow subsurface flow. Three regression equations (one for baseflow and one for BFI) were developed and evaluated in the study watersheds. Results showed that the models reasonably estimate baseflow with relative errors (RE) ranging from 0% to 30%, except in one watershed where the RE was 50% during the validation period. These equations can be used to estimate baseflow and BFI at ungauged sites in Indiana. The present work would have implications for improving the capabilities of simple hydrologic/water quality models, and support planning and management of water resources. The methodology used in this study can be applied in other locations and regions.

Low flows quantification and regionalization in North West Algeria

Low flow hydrological regimes are crucial for an efficient development of water resources management tools, especially in those areas stressed by the combination of a dry climate and an excessive water demand, such as the Mediterranean basins. A lot of effort has been made by the worldwide scientific community toward the prediction of low flows features in ungauged catchments. The aims of the present study are: (1) the quantification of low flows characteristics, in particular with regard to the BFI and (2) the application of a simple regional approach to predict the BFI at ungauged sites. The investigated area is located in North West Algeria and has an extension of about 130,000 km2. The relevant extension and the poorly dense monitoring network, which consist in 24 hydrometric stations, require the identification of homogeneous regions, for further application of simple linear regional regression models. Regions delineation is accomplished through the Principal Component Analysis method (PCA) and the cluster analysis, based on physiographic and climatic data. Three significantly different homogeneous areas have been identified, and comparisons between global and local regional multiple linear regression models indicate a large percentage of BFI explained variance in each area.

Coupling hydrodynamic models and value of information for designing stage monitoring networks

Because the collection of data in water systems is important for making informed decisions, monitoring networks are designed and installed in such systems. Traditionally, the design of hydrometric monitoring networks has been concentrated on measuring streamflow/precipitation at particular key (gauged) sites so that streamflow/precipitation can be estimated accurately at ungauged sites. Although many methods take into account a set of final users of the information, there appears to be no method that explicitly considers them in the mathematical formulation of the decision‐making process. This paper presents a novel approach for designing monitoring networks in a water system using the concept of value of information (VOI). This concept takes into account three main factors: (1) the belief that the decision maker has about the state of the water system before having any information; (2) the consequences associated with the decision of having to choose among several possible management actions given the state of the water system; and (3) the evaluation and update of new information when it becomes available. The methodology uses a water level time series generated by a hydrodynamic model at every computational point, each one being a potential monitor site. The method is tested in a polder system in the Netherlands, where monitoring is required to make informed decisions about the operation of a set of hydraulic structures to reduce flood impacts.

Modelling of tide and surge elevations in the Solent and surrounding waters: The importance of tide–surge interactions

A regional two-dimensional hydrodynamic model using the MIKE-21 software and data from a pre-operational forecasting system of the English Channel is described and applied to the Solent–Southampton Water estuarine system. The regional model was able to predict surge heights with a root mean squared error (RMSE) accuracy of 0.09 m during a three month hindcast in the winter of 2009, comparing closely with accuracy assessments from other independent systems. However, consistent underprediction of tidal harmonic constituent amplitudes was present throughout the region leading to errors in the prediction of the total water level elevations. Despite the complex nature of the Solent tidal regime, interpolation of tidal elevations from harmonic analysis at fixed tide gauge locations was shown to be effective in reducing this uncertainty at gauged and un-gauged sites. The degree to which tide–surge interactions were taking place was examined. Of particular interest was the quantification of the sensitivity of the predicted surge to the levels of uncertainty expected in the prediction of the tide within a complex nearshore region such as the Solent. The tide–surge interaction during three surge events was shown to be greatest in the Western Solent and Southampton Waters regions, where the tidal uncertainty was greatest. Interaction between the tide and surge resulted in a change of up to 0.3 m (11%) in the predicted total peak water level when the surge was added to the harmonic analysis-based tidal prediction. Despite the significant effect of removing the tide–surge interactions, tests indicated that the error in tidal range expected in the regional models tidal prediction altered the prediction of the surge only enough to induce changes in peak total water elevations by up to 0.03 m during an event on 10th March 2008. The findings suggest that the current tidal predictions in complex estuarine systems, such as the Solent, are of high enough quality to reproduce the majority of the tide–surge interactions taking place and that the error in the surge due to uncertainties in the predicted tide are expected to be relatively small.

Regional Taiwan rainfall frequency analysis using principal component analysis, self-organizing maps and L-moments

The objective of this paper is to propose an approach, which consists of principal component analysis (PCA), self-organizing maps (SOM) and the L-moment method, for improving estimation of desired rainfall quantiles of ungauged sites. Firstly, PCA is applied to obtain the principal components. Then SOM is applied to group the rain gauges into specific clusters and the number of clusters can be objectively decided by visual inspection. Moreover, the L-moment based discordancy and heterogeneity are used to test whether clusters may be acceptable as being homogeneous. After the gauges are grouped into specific clusters, the homogeneous regions are then delineated. Finally, goodness-of-fit measure is used to select the regional probability distributions and the design rainfall quantiles with various return periods for each region can be estimated. The proposed approach is applied to analyze and quantify regional rainfalls in Taiwan. The proposed approach is a robust and efficient way for regional rainfall frequency analysis. Moreover, one can easily assign an ungauged site to a previously defined cluster according to a map of homogeneous regions. Therefore, the proposed approach is expected to be useful for providing the design rainfall quantiles with various return periods at ungauged sites.

Estimation of Peak Flood Discharges at Ungauged Sites Across Turkey

The reliable forecasting of the peak flood discharge at river basins is a common problem, and it becomes more complicated when there is inadequate recorded data. The statistical methods commonly used for the estimation of peak flood discharges are generally considered to be inadequate because of the complexity of this problem. Recently, genetic programming (GP) which is a branch of soft computing methods has attracted the attention of the hydrologists. In this study, gene-expression programming (GEP) and linear genetic programming (LGP), which are extensions to GP, in addition to logistic regression (LR) were employed in order to forecast peak flood discharges. The study covered 543 ungauged sites across Turkey. Drainage area, elevation, latitude, longitude, and return period were used as the inputs while the peak flood discharge was the output. Model comparison results revealed that GEP predicted the peak flood discharges with R2 = 57.4 % correlation, LGP with 56 % and LR model with 42.3 %, respectively. The peak flood discharges in all river basins can now be determined using the single equation provided by the GEP model.

Comparing methods for estimating flow duration curves at ungauged sites

Summary Flow duration curves (FDCs) are a useful tool for characterising hydrological regimes and flow variability. FDCs observed at 379 gauging stations located across New Zealand were analysed with the aim of investigate how parameterisation and generalisation combine to influence the accuracy of empirically predicted FDCs at ungauged sites. The appropriateness of four strategies for estimating FDCs was compared: (a) parameterise then generalise; (b) parameterise then regionalise then generalise; (c) parameterise and generalise together; and (d) FDC substitution. These strategies were deployed using various combinations of methods for calculating parameters that describe the shape of FDCs (polynomial expressions and probability distribution functions) and then methods for estimating these parameters at ungauged sites using available catchment characteristics (stepwise linear regression and random forests). A parameterise and generalise together strategy was devised by applying a mixed-effects approach. A jack-knife cross-validation procedure was used to provide an independent test of each method for estimating the FDC at ungauged sites. For parameterise then regionalise strategies, it was found that the combination of parameterisation method and generalisation method together, rather than either in isolation, was important in determining overall performance. Results indicated that predictive capability varied between methods and across exceedence percentiles. The mixed-effects approach provided the most parsimonious method for estimating FDC at ungauged sites. A method using the generalised extreme value probability distribution that was generalised using random forests was the most accurate method of estimating flow duration curves at ungauged sites across New Zealand.

Improved methods for daily streamflow estimates at ungauged sites

In this paper, improved flow duration curve (FDC) and area ratio (AR) based methods are developed to obtain better daily streamflow estimation at ungauged sites. A regression based logarithmic interpolation method which makes no assumption on the distribution or shape of a FDC is introduced in this paper to estimate regional FDCs. The estimated FDC is combined with a spatial interpolation algorithm to obtain daily streamflow estimates. Multiple source sites based AR methods, especially the geographical distance weighted AR (GWAR) method, are introduced in an effort to maximize the use of regional information and improve the standard AR method (SAR). Performances of the proposed approaches are evaluated using a jackknife procedure. The application to 109 stations in the province of Quebec, Canada indicates that the FDC based methods outperform AR based methods in all the summary statistics including Nash, root mean squared error (RMSE), and Bias. The number of sites that show better performances using the FDC based approaches is also significantly larger than the number of sites showing better performances using AR based methods. Using geographical distance weighted multiple sources sites based approaches can improve the performance at the majority of the catchments comparing with using the single source site based approaches.

A spatial neural fuzzy network for estimating pan evaporation at ungauged sites

Abstract. Evaporation is an essential reference to the management of water resources. In this study, a hybrid model that integrates a spatial neural fuzzy network with the kringing method is developed to estimate pan evaporation at ungauged sites. The adaptive network-based fuzzy inference system (ANFIS) can extract the nonlinear relationship of observations, while kriging is an excellent geostatistical interpolator. Three-year daily data collected from nineteen meteorological stations covering the whole of Taiwan are used to train and test the constructed model. The pan evaporation (Epan) at ungauged sites can be obtained through summing up the outputs of the spatially weighted ANFIS and the residuals adjusted by kriging. Results indicate that the proposed AK model (hybriding ANFIS and kriging) can effectively improve the accuracy of Epan estimation as compared with that of empirical formula. This hybrid model demonstrates its reliability in estimating the spatial distribution of Epan and consequently provides precise Epan estimation by taking geographical features into consideration.

Regionalization of Rainfall Using RCDA Cluster Ensemble Algorithm in India

The magnitude and frequency of precipitation is of great significance in the field of hydrologic and hydraulic design and has wide applications in varied areas. However, the availability of precipitation data is limited to a few areas, where the rain gauges are successfully and efficiently installed. The magnitude and frequency of precipitation in ungauged sites can be assessed by grouping areas with similar characteristics. The procedure of grouping of areas having similar behaviour is termed as Regionalization. In this paper, RCDA cluster ensemble algorithm is employed to identify the homogeneous regions of rainfall in India. Cluster ensemble methods are commonly used to enhance the quality of clustering by combining multiple clustering schemes to produce a more robust scheme delivering similar homogeneous regions. The goal is to identify, analyse and describe hydrologically similar regions using RCDA cluster ensemble algorithm. RCDA cluster ensemble algorithm, which is based on discriminant analysis. The algorithm takes H base clustering schemes each with K clusters, obtained by any clustering method, as input and constructs discriminant function for each one of them. Subsequently, all the data tuples are predicted using H discriminant functions for cluster membership. Tuples with consistent predictions are assigned to the clusters, while tuples with inconsistent predictions are analyzed further and either assigned to clusters or declared as noise. RCDA algorithm has been compared with Best of K-means and Clue cluster ensemble of R software using traditional clustering quality measures. Further, domain knowledge based comparison has also been performed. All the results are encouraging and indicate better regionalization of the rainfall in different parts of India.

Development and Application of a Distributed Hydrological Model for Discharge Predictions in Un-gauged Basins: Case Study in Malian River Basin

Information about water resources is generally derived from the discharge or flow measured at gauging stations on river. In fact, gauged stations are relatively sparsely installed, not matching the high density of existing and planning engineering. The situation is extremely unfavourable for construction planning and water resources development. With an aim of making a good hydrological simulation in un-gauged basins, this article presents an approach to simulate the flow series for solving the problem induced by data scarcity at un-gauged hydrological engineering sites. The distributed hydrological model constructed in the article performs well in describing the mechanisms for the hydrological processes. It makes good and physical interpolation of response information from gauged to un-gauged basins, with few parameters to calibrate than other distributed models. To make sure that it is available and useful, the proposed approach is applied to the case study of Malian river basin, which is treated as a s...

Extreme rainstorms: Comparing regional envelope curves to stochastically generated events

The depth‐duration envelope curves (DDECs) are regional upper bounds on observed rainfall maxima for several durations. Recently, a probabilistic interpretation has been proposed in the literature in order to associate a recurrence interval T to the DDECs and, consequently, to retrieve point rainfall quantiles for ungauged sites. Alternatively, extreme rainfall quantiles can be retrieved from long synthetic rainfall series obtained with stochastic rainfall generators calibrated to local time series of rainfall events. While DDECs are sensitive to outliers and data errors, the stochastic rainfall generator performance is affected by the limited record lengths used for calibration. The objective of this study is to assess the reliability of the two alternative methods by verifying if they give consistent results for a wide study region in Austria. Relative to previous studies, we propose some generalizations of the DDEC procedure in order to better represent the Austrian data. The comparison of rainfall quantiles estimated with the two methods for large T shows an excellent agreement for intermediate durations (from 1 to 6 h), while the agreement worsen for very short (15 min) and long (24 h) durations. The results are scrupulously analyzed and discussed in light of the exceptionality of rainfall events that set the regional envelopes and the characteristics of the stochastic generator used. Our study points out that the combined use of these regional and local methods can be very useful for estimating reliable point rainfall quantiles associated with large T within regions where many rain gauges are available, but with limited record lengths.

확률분포 모수선도에 의한 미계측 지점의 확률강우량 산정

The objective of this study is to produce a probability distribution parameter map for evaluation of probable rainfall quantile in ungauged site. The rainfall data used in this study are annual maximum rainfalls at 58 stations during the period of more than 30 years for 12 durations. The 16 probability distributions which have been widely used in hydrologic frequency analysis are applied to the basic data and to determine the representative appropriate distribution. The location, scale, and shape parameters of the representative appropriate distribution for each station and each duration are calculated using L-moments method. These parameters are contoured using spatial interpolation, based on the geostatistical method of Kriging to produce parameter maps that depict the spatial variation and magnitude of each parameter. The results of this study are as followings; (1) The GEV distribution is determined as the representative probability distribution in Korea. (2) The parameters for any location in Korea can be estimated using the parameter maps and the rainfall quantile is obtained from GEV distribution equation using parameter about the selected rainfall duration. (3) Comparative analysis of the results shows that the probable rainfall quantiles by the parameter maps are little different from those existing researches. (4) In the result by probability distribution parameter map, rainfall quantile is better easy to evaluate in ungaged site without restriction of return period.

A Non-Linear Rainfall-Runoff Model with a Sigmoid Gain Factor to Simulate Flow Frequency Distribution Curves for Amazon Catchments

A Non-Linear Rainfall-Runoff Model with a Sigmoid Gain Factor to Simulate Flow Frequency Distribution Curves for Amazon Catchments The objective of this paper is to simulate flow frequency distribution curves for Amazon catchments with the aim of scaling power generation from small hydroelectric power plants. Thus, a simple nonlinear rainfall-runoff model was developed with sigmoid-variable gain factor due to the moisture status of the catchment, which depends on infiltration, and is considered a factor responsible for the nonlinearity of the rainfall-runoff process. Data for a catchment in the Amazon was used to calibrate and validate the model. The performance criteria adopted were the Nash-Sutcliffe coefficient (R2), the RMS, the Q95% frequencyc flow percentage error, and the mean percentage errors ranging from Q5% to Q95%.. Calibration and validation showed that the model satisfactorily simulates the flow frequency distribution curves. In order to find the shortest period of rainfall-runoff data, which is required for applying the model, a sensitivity analysis was performed whereby rainfall and runoff data was successively reduced by 1 year until a 1.5-year model application minimum period was found. This corresponds to one hydrological year plus the 6-month long "memory". This analysis evaluates field work in the ungauged sites of the region.

Design rainfall depth estimation through two regional frequency analysis methods in Hanjiang River Basin, China

Hydrological predictions in ungauged basins are of significant importance for water resources management. In hydrological frequency analysis, regional methods are regarded as useful tools in estimating design rainfall/flood for areas with only little data available. The purpose of this paper is to investigate the performance of two regional methods, namely the Hosking’s approach and the cokriging approach, in hydrological frequency analysis. These two methods are employed to estimate 24-h design rainfall depths in Hanjiang River Basin, one of the largest tributaries of Yangtze River, China. Validation is made through comparing the results to those calculated from the provincial handbook approach which uses hundreds of rainfall gauge stations. Also for validation purpose, five hypothetically ungauged sites from the middle basin are chosen. The final results show that compared to the provincial handbook approach, the Hosking’s approach often overestimated the 24-h design rainfall depths while the cokriging approach most of the time underestimated. Overall, the Hosking’ approach produced more accurate results than the cokriging approach.