Impacts of uncertain river flow data on rainfall‐runoff model calibration and discharge predictions

In order to quantify total error affecting hydrological models and predictions, we must explicitly recognize errors in input data, model structure, model parameters and validation data. This paper tackles the last of these: errors in discharge measurements used to calibrate a rainfall‐runoff model, caused by stage–discharge rating‐curve uncertainty. This uncertainty may be due to several combined sources, including errors in stage and velocity measurements during individual gaugings, assumptions regarding a particular form of stage–discharge relationship, extrapolation of the stage–discharge relationship beyond the maximum gauging, and cross‐section change due to vegetation growth and/or bed movement. A methodology is presented to systematically assess and quantify the uncertainty in discharge measurements due to all of these sources. For a given stage measurement, a complete PDF of true discharge is estimated. Consequently, new model calibration techniques can be introduced to explicitly account for the discharge error distribution. The method is demonstrated for a gravel‐bed river in New Zealand, where all the above uncertainty sources can be identified, including significant uncertainty in cross‐section form due to scour and re‐deposition of sediment. Results show that rigorous consideration of uncertainty in flow data results in significant improvement of the model's ability to predict the observed flow. Copyright © 2010 John Wiley & Sons, Ltd.     

Bayesian analysis of stage–fall–discharge models for gauging stations affected by variable backwater

Parsimonious stage–fall–discharge rating curve models for gauging stations subject to backwater complications are developed from simple hydraulic theory. The rating curve models are compounded in order to allow for possible shifts in the hydraulics when variable backwater becomes effective. The models provide a prior scientific understanding through the relationship between the rating curve parameters and the hydraulic properties of the channel section under study. This characteristic enables prior distributions for the rating curve parameters to be easily elicited according to site‐specific information and the magnitude of well‐known hydraulic quantities. Posterior results from three Norwegian and one American twin‐gauge stations affected by variable backwater are obtained using Markov chain Monte Carlo simulation techniques. The case studies demonstrate that the proposed Bayesian rating curve assessment is appropriate for developing rating procedures for gauging stations that are subject to variable backwater. Copyright © 2009 John Wiley & Sons, Ltd.     

A method for uncertainty constraint of catchment discharge and phosphorus load estimates

River discharge and nutrient measurements are subject to aleatory and epistemic uncertainties. In this study, we present a novel method for estimating these uncertainties in colocated discharge and phosphorus (P) measurements. The “voting point”‐based method constrains the derived stage‐discharge rating curve both on the fit to available gaugings and to the catchment water balance. This helps reduce the uncertainty beyond the range of available gaugings and during out of bank situations. In the example presented here, for the top 5% of flows, uncertainties are shown to be 139% using a traditional power law fit, compared with 40% when using our updated “voting point” method. Furthermore, the method is extended to in situ and lab analysed nutrient concentration data pairings, with lower uncertainties (81%) shown for high concentrations (top 5%) than when a traditional regression is applied (102%). Overall, for both discharge and nutrient data, the method presented goes some way to accounting for epistemic uncertainties associated with nonstationary physical characteristics of the monitoring site.     

PUBLICATIONS OF THE IAHS

Abstract

Gauging stations where the stage—discharge relationship is affected by hysteresis due to unsteady flow represent a challenge in hydrometry. In such situations, the standard hydrometric practice of fitting a single-valued rating curve to the available stage—discharge measurements is inappropriate. As a solution to this problem, this study provides a method based on the Jones formula and nonlinear regression, which requires no further data beyond the available stage—discharge measurements, given that either the stages before and after each measurement are known along with the duration of each measurement, or a stage hydrograph is available. The regression model based on the Jones formula rating curve is developed by applying the monoclinal rising wave approximation and the generalized friction law for uniform flow, along with simplifying assumptions about the hydraulic and geometric properties of the river channel in conjunction with the gauging station. Methods for obtaining the nonlinear least-squares rating-curve estimates, while factoring in approximated uncertainty, are discussed. The broad practical applicability and appropriateness of the method are demonstrated by applying the model to: (a) an accurate, comprehensive and detailed database from a hydropower-generated highly dynamic flow in the Chattahoochee River, Georgia, USA; and (b) data from gauging stations in two large rivers in the USA affected by hysteresis. It is also shown that the model is especially suitable for post-modelling hydraulic and statistical validation and assessment.     

Bedload yields for sand‐bed streams in the Ngarradj Creek catchment,Northern Territory,Australia

Bedload yields were calculated by 39 methods at the East Tributary gauge, nine methods at Upper Swift Creek gauge and 11 methods at Swift Creek gauge in the Ngarradj Creek catchment in northern Australia. These methods involved combining various significant bedload rating curves determined for a measured bedload data set for a 4‐year period with either the hourly or daily hydrographs or flow duration curves for the same period, 1 September 1998 to 31 August 2002. Bedload ratings were both statistically significant (ρ ≤ 0.05) and explained at least 60% of the variance in bedload flux. Bias corrections were used with all methods based on log₁₀‐transformed ratings. Estimated mean annual bedload yields varied by three orders of magnitude at the East Tributary gauge and by two orders of magnitude at Upper Swift Creek and Swift Creek gauges. Hourly discharges usually produced higher estimated yields than daily discharges. The bedload rating‐flow duration curve technique overestimates yields and bias correction methods always produce even higher yields. Ratings using both immersed bedload weight and adjusted immersed bedload weight always under‐predicted yields because they contain an implicit threshold of motion condition that is at least four times greater than that predicted by Bagnold's threshold equation. Such a result questions the applicability of Bagnold's threshold equation to the Ngarradj Creek catchment. The best estimates of mean annual bedload yield at East Tributary, Upper Swift Creek and Swift Creek gauges are 600 ± 170 (SE), 1065 ± 150 and 1795 ± 270 t/year, respectively. © 2015 Commonwealth of Australia. Hydrological Processes © 2015 John Wiley & Sons Ltd.     

MODELLING RAINFALL-RUNOFF FROM LARGE CATCHMENT TO BASIN SCALE: THE GOULBURN VALLEY,VICTORIA

A lumped parameter dynamic rainfall-runoff model, IHACRES, is applied to the large upland area (more than 4500 km²) of the Goulburn Valley Basin, Victoria, Australia to predict streamflow under different climatic conditions. This paper presents the first evaluation of a rainfall–runoff model at large catchment scale, which is comprehensive in terms of the number of catchments investigated and the number of calibration and simulation periods used. The basin is subdivided into 12 catchments (from 100 to 700 km²), each of which is calibrated separately. High values of model efficiency and low bias are consistently obtained for different calibration sub-periods for all catchments in the basin. Simulation or so-called validation tests are used to select the best models for each catchment. This allows simulation of the water regime during long historical (approximately 90 year) periods when only climatological (rainfall and temperature) data were available. This procedure is extremely important for the estimation of the effect of climate variability and of the possible impact of climate change on the hydrological regime in the region and, in particular, for supporting irrigation management of the basin. Analysis of a composite catchment (2417 km²) and its five separate subcatchments indicates that the information content in the rainfall–streamflow data is independent of catchment size. Dynamic modelling of the daily water balance at the macroscale is limited principally by the adequacy of the precipitation gauging network. When a good estimate of areal precipitation is available for a catchment, it is not necessary to consider subcatchment-scale variability for modelling if the only interest is the daily discharge and evaporation losses from the catchment.     

Regionalisation of hydrological responses under land-use change and variable data quality

ABSTRACT

Estimating river flows at ungauged sites is generally recognised as an important area of research. In countries or regions with rapid land development and sparse hydrological gauging networks, three particular challenges may arise—data scarcity, data quality, and hydrological non-stationarity. Using data from 44 gauged sub-catchments of the upper Ping catchment in northern Thailand from the period 1995–2006, three relevant flow response indices (runoff coefficient, base flow index and seasonal elasticity of flow) were regionalised by regression against available catchment properties. The runoff coefficient was the most successfully regionalised, followed by base flow index and lastly the seasonal elasticity. The non-stationarity (represented by the differences between two 6-year sub-periods) was significant both in the flow response indices and in land use indices; however relationships between the two sets of indices were weak. The regression equations derived from regionalisation were not helpful in predicting the non-stationarity in the flow indices except somewhat for the runoff coefficient. A partly subjective data quality scoring system was devised, and showed the clear influence of rainfall and flow data quality on regionalisation uncertainty. Recommendations towards improving data support for hydrological regionalisation in Thailand include more relevant soils databases, improved records of abstractions and investment in the gauge network. Widening of the regionalisation beyond the upper Ping and renewed efforts at using remotely sensed rainfall data are other possible ways forward.

EDITOR Z.W. Kundzewicz ASSOCIATE EDITOR T. Wagener     

Continuous daily hydrograph simulation using duration curves of a precipitation index

The paper describes a parsimonious approach for generating continuous daily stream‐flow time‐series from observed daily rainfall data in a catchment. The key characteristic in the method is a duration curve. It is used to convert the daily rainfall information from source rain gauges into a continuous daily hydrograph at the destination river site. For each source rain gauge a time‐series of rainfall related ‘current precipitation index’ is generated and its duration curve is established. The current precipitation index reflects the current catchment wetness and is defined as a continuous function of precipitation, which accumulates on rainy days and exponentially decays during the periods of no rainfall. The process of rainfall‐to‐runoff conversion is based on the assumption that daily current precipitation index values at rainfall site(s) in a catchment and the destination site's daily flows correspond to similar probabilities on their respective duration curves. The method is tested in several small catchments in South Africa. The method is designed primarily for application at ungauged sites in data‐poor regions where the use of more complex and information consuming techniques of data generation may not be justified. Copyright © 2000 John Wiley & Sons, Ltd.     

Modelling stream flow for use in ecological studies in a large,arid zone river,central Australia

Australian arid zone ephemeral rivers are typically unregulated and maintain a high level of biodiversity and ecological health. Understanding the ecosystem functions of these rivers requires an understanding of their hydrology. These rivers are typified by highly variable hydrological regimes and a paucity, often a complete absence, of hydrological data to describe these flow regimes. A daily time‐step, grid‐based, conceptual rainfall–runoff model was developed for the previously uninstrumented Neales River in the arid zone of northern South Australia. Hourly, logged stage data provided a record of stream‐flow events in the river system. In conjunction with opportunistic gaugings of stream‐flow events, these data were used in the calibration of the model. The poorly constrained spatial variability of rainfall distribution and catchment characteristics (e.g. storage depths) limited the accuracy of the model in replicating the absolute magnitudes and volumes of stream‐flow events. In particular, small but ecologically important flow events were poorly modelled. Model performance was improved by the application of catchment‐wide processes replicating quick runoff from high intensity rainfall and improving the area inundated versus discharge relationship in the channel sections of the model. Representing areas of high and low soil moisture storage depths in the hillslope areas of the catchment also improved the model performance. The need for some explicit representation of the spatial variability of catchment characteristics (e.g. channel/floodplain, low storage hillslope and high storage hillslope) to effectively model the range of stream‐flow events makes the development of relatively complex rainfall–runoff models necessary for multisite ecological studies in large, ungauged arid zone catchments. Grid‐based conceptual models provide a good balance between providing the capacity to easily define land types with differing rainfall–runoff responses, flexibility in defining data output points and a parsimonious water‐balance–routing model. Copyright © 2004 John Wiley & Sons, Ltd.     

A multiplier-based method of generating stochastic areal rainfall from point rainfalls

Catchment modelling for water resources assessment is still mainly based on rain gauge measurements as these are more easily available and cover longer periods than radar and satellite-based measurements. Rain gauges however measure the rain falling on an extremely small proportion of the catchment and the areal rainfall obtained from these point measurements are consequently substantially uncertain. These uncertainties in areal rainfall estimation are generally ignored and the need to assess their impact on catchment modelling and water resources assessment is therefore imperative. A method that stochastically generates daily areal rainfall from point rainfall using multiplicative perturbations as a means of dealing with these uncertainties is developed and tested on the Berg catchment in the Western Cape of South Africa. The differences in areal rainfall obtained by alternately omitting some of the rain gauges are used to obtain a population of plausible multiplicative perturbations. Upper bounds on the applicable perturbations are set to prevent the generation of unrealistically large rainfall and to obtain unbiased stochastic rainfall. The perturbations within the set bounds are then fitted into probability density functions to stochastically generate the perturbations to impose on areal rainfall. By using 100 randomly-initialized calibrations of the AWBM catchment model and Sequent Peak Analysis, the effects of incorporating areal rainfall uncertainties on storage-yield-reliability analysis are assessed. Incorporating rainfall uncertainty is found to reduce the required storage by up to 20%. Rainfall uncertainty also increases flow-duration variability considerably and reduces the median flow-duration values by an average of about 20%.     

Bayesian methods for estimating multi-segment discharge rating curves

This study explores Bayesian methods for handling compound stage–discharge relationships, a problem which arises in many natural rivers. It is assumed: (1) the stage–discharge relationship in each rating curve segment is a power-law with a location parameter, or zero-plane displacement; (2) the segment transitions are abrupt and continuous; and (3) multiplicative measurement errors are of equal variance. The rating curve fitting procedure is then formulated as a piecewise regression problem where the number of segments and the associated changepoints are assumed unknown. Procedures are developed for describing both global and site-specific prior distributions for all rating curve parameters, including the changepoints. Estimation and uncertainty analysis is evaluated using Markov chain Monte Carlo simulation (MCMC) techniques. The first model explored accounts for parameter and model uncertainties in the interpolated area, i.e. within the range of available stage–discharge measurements. A second model is constructed in an attempt to include the uncertainty in extrapolation, which is necessary when the rating curve is used to estimate discharges beyond the highest or lowest measurement. This is done by assuming that the rate of changepoints both inside and outside the measured area follows a Poisson process. The theory is applied to actual data from Norwegian gauging stations. The MCMC solutions give results that appear sensible and useful for inferential purposes, though the latter model needs further efforts in order to obtain a more efficient simulation scheme.     

Rating curve estimation under epistemic uncertainty

River discharge values, estimated using a rating curve, are subject to both random and epistemic errors. We present a new likelihood function, the ‘Voting Point’ likelihood that accounts for both error types and enables generation of multiple possible multisegment power‐law rating curve samples that aim to represent the total uncertainty. The rating curve samples can be used for subsequent discharge analysis that needs total uncertainty estimation, e.g. regionalisation studies or calculation of hydrological signatures. We demonstrate the method using four catchments with diverse rating curve error characteristics, where epistemic uncertainty sources include weed growth, scour and redeposition of the bed gravels in a braided river, and unconfined high flows. The results show that typically, the posterior rating curve distributions include all of the gauging points and succeed in representing the spread of discharge values caused by epistemic rating errors. We aim to provide a useful method for hydrology practitioners to assess rating curve, and hence discharge, uncertainty that is easily applicable to a wide range of catchments and does not require prior specification of the particular types and causes of epistemic error at the gauged location. Copyright © 2014 John Wiley & Sons, Ltd.     

An analytical method of stage–fall–discharge rating

This paper presents an analytical method for establishing a stage–fall–discharge rating using hydraulic performance graphs (HPG). The rating curves derived from the HPG are used as the basis to establish the functional relation of stage, fall and discharge through regression analysis following the USGS procedure. In doing so, the conventional trial‐and‐error process can be avoided and the associated uncertainties involved may be reduced. For illustration, the proposed analytical method is applied to establish stage–fall–discharge relations for the Keelung River in northern Taiwan to examine its accuracy and applicability in an actual river. Based on the data extracted from the HPG for the Keelung River, one can establish a stage–fall–discharge relation that is more accurate than the one obtained by the conventionally used relation. Furthermore, the discharges obtained from the proposed rating method are verified through backwater analysis for measured high water level events. The results indicate that the analytical stage–fall–discharge rating method is capable of circumventing the shortcomings of those based on single‐station data and, consequently, enhancing the reliability of flood estimation and forecasting. Copyright © 2008 John Wiley & Sons, Ltd.     

Diagnostic evaluation of multiple hypotheses of hydrological behaviour in a limits‐of‐acceptability framework for 24 UK catchments

Testing competing conceptual model hypotheses in hydrology is complicated by uncertainties from a wide range of sources, which result in multiple simulations that explain catchment behaviour. In this study, the limits of acceptability uncertainty analysis approach used to discriminate between 78 competing hypotheses in the Framework for Understanding Structural Errors for 24 catchments in the UK. During model evaluation, we test the model's ability to represent observed catchment dynamics and processes by defining key hydrologic signatures and time step‐based metrics from the observed discharge time series. We explicitly account for uncertainty in the evaluation data by constructing uncertainty bounds from errors in the stage‐discharge rating curve relationship. Our study revealed large differences in model performance both between catchments and depending on the type of diagnostic used to constrain the simulations. Model performance varied with catchment characteristics and was best in wet catchments with a simple rainfall‐runoff relationship. The analysis showed that the value of different diagnostics in constraining catchment response and discriminating between competing conceptual hypotheses varies according to catchment characteristics. The information content held within water balance signatures was found to better capture catchment dynamics in chalk catchments, where catchment behaviour is predominantly controlled by seasonal and annual changes in rainfall, whereas the information content in the flow‐duration curve and time‐step performance metrics was able to better capture the dynamics of rainfall‐driven catchments. We also investigate the effect of model structure on model performance and demonstrate its (in)significance in reproducing catchment dynamics for different catchments. Copyright © 2013 John Wiley & Sons, Ltd.     

POTENTIAL OF EXTENDING THE RAINFALL INTENSITY–DURATION–FREQUENCY RELATIONSHIP TO NON-RECORDING RAIN GAUGES

Maximum rainfall intensity–duration–frequency (IDF) curves are commonly applied to determine the design rainfall in water resource projects. Normally, the IDF relationship is derived from recording rain gauges. As the network of non-recording rain gauges (daily rainfall) in Taiwan has a higher density than recording rain gauges, attempts were made in this study to extend the IDF relationship to non-recording rain gauges. Eighteen recording rain gauges and 99 non-recording rain gauges over the Chi-Nan area in Southern Taiwan provide the data sets. The regional IDF formulae were generated for ungauged areas to estimate rainfall intensity for various return periods and rainfall durations larger than or equal to one hour. For rainfall durations less than one hour, a set of adjustment formulae were applied to modify the regional IDF formulae. The method proposed in this study had reasonable application to non-recording rain gauges, which was concluded from the verification of four additional recording rain gauges. © 1997 John Wiley & Sons, Ltd.     

Simple vs complex rating curves: accounting for measurement uncertainty,slope ratio and sample size

Multiple segmented rating curves have been proposed to better capture the variability of the physical and hydraulic characteristics of river–floodplain systems. We evaluate the accuracy of one- and two-segmented rating curves by exploiting a large and unique database of direct measurements of stage and discharge data in more than 200 Swedish catchments. Such a comparison is made by explicitly accounting for the potential impact of measurement uncertainty. This study shows that two-segmented rating curves did not fit the data significantly better, nor did they generate fewer errors than one-segmented rating curves. Two-segmented rating curves were found to be slightly beneficial for low flow when there were strong indications of segmentation, but predicted the rating relationship worse in cases of weak indication of segmentation. Other factors were found to have a larger impact on rating curve errors, such as the uncertainty of the discharge measurements and the type of regression method.     

Climate models and hydrological parameter uncertainties in climate change impacts on monthly runoff and daily flow duration curve of a Mediterranean catchment

ABSTRACT

Climate models and hydrological parameter uncertainties were quantified and compared while assessing climate change impacts on monthly runoff and daily flow duration curve (FDC) in a Mediterranean catchment. Simulations of the Soil and Water Assessment Tool (SWAT) model using an ensemble of behavioural parameter sets derived from the Generalized Likelihood Uncertainty Estimation (GLUE) method were approximated by feed-forward artificial neural networks (FF-NN). Then, outputs of climate models were used as inputs to the FF-NN models. Subsequently, projected changes in runoff and FDC were calculated and their associated uncertainty was partitioned into climate model and hydrological parameter uncertainties. Runoff and daily discharge of the Chiba catchment were expected to decrease in response to drier and warmer climatic conditions in the 2050s. For both hydrological indicators, uncertainty magnitude increased when moving from dry to wet periods. The decomposition of uncertainty demonstrated that climate model uncertainty dominated hydrological parameter uncertainty in wet periods, whereas in dry periods hydrological parametric uncertainty became more important.

Editor M.C. Acreman; Associate editor S. Kanae     

Uncertainty in stage–discharge rating curves: application to Australian Hydrologic Reference Stations data

The purpose of this paper is to determine uncertainty in the gauged range of the stage–gauged discharge relationship for 622 rating curves from 171 Australian Bureau of Meteorology Hydrologic Reference streamgauging Stations (HRS). Water agencies use many methods to establish rating curves. Here we adopt a consistent method across all stations and develop rating curves based on Chebyshev polynomials, and estimate uncertainties from standard regression errors in which residuals from the polynomials are adjusted to ensure they are homoscedastic and normally distributed. Uncertainty in input water level is also taken into account. The median uncertainties in mean response of the available gauged discharge relationship at median daily discharges for the HRS dataset range from +4.5 to ?4.2% (95% confidence band) and for individual gaugings from +29 to ?22% incorporating a water level uncertainty of ±4 mm. The uncertainties estimated are consistent with values estimated in Australia and elsewhere.     

The channel-geometry method: Guidelines and applications

All river engineering schemes require flood discharge estimates as part of the design and appraisal process. Unfortunately, continuous measurement of flood discharges is limited to those river sites with instrumented gauging stations, which constitute only a small proportion of channel reaches where information is required. Therefore, considerable research effort has been devoted to the development of reliable indirect techniques of flood discharge estimation. Research on the interrelationship of stream channel geometry and river discharge has provided the basis for an indirect method of flood estimation – the channel-geometry method – which employs river channel dimensions alone to estimate discharge characteristics at ungauged river sites. Channel-geometry equations are developed empirically by relating streamflow data from gauging stations and channel dimensions measured from natural river reaches in the vicinity of the gauge, and take the form of power function relations. Once regional channel-geometry equations have been defined, a channel width or channel capacity measurement is the only variable needed to estimate the flood flow characteristics at a specified river site. The method is useful as an alternative to traditional catchment-based approaches or as a rapid reconnaissance technique. In addition to the application for flood discharge prediction, channel-geometry equations could prove helpful in the management of river channels, first, by providing a basis for assessing local deviations in the channel form–discharge relation, deviations which could be employed as indicators of the sensitivity of particular stretches of river channel to change, and secondly, in the computation of natural channel dimensions for use in river channel design and river restoration.     

Geodetic observation of sea-level change and crustal deformation in the Baltic Sea region

Based on tide gauge observations spanning almost 200 years, homogeneous time series of the mean relative sea level were derived for nine sites at the southern coast of the Baltic Sea. Our regionally concentrated data were complemented by long-term relative sea-level records retrieved from the data base of the Permanent Service for Mean Sea Level (PSMSL). From these records relative sea-level change rates were derived at 51 tide gauge stations for the period between 1908 and 2007. A minimum observation time of 60 years is required for the determination of reliable sea-level rates. At present, no anthropogenic acceleration in sea-level rise is detected in the tide gauge observations in the southern Baltic. The spatial variation of the relative sea-level rates reflects the fingerprint of GIA-induced crustal uplift. Time series of extreme sea levels were also inferred from the tide gauge records. They were complemented by water level information from historic storm surge marks preserved along the German Baltic coast. Based on this combined dataset the incidence and spatial variation of extreme sea levels induced by storm surges were analysed yielding important information for hazard assessments. Permanent GPS observations were used to determine recent crustal deformation rates for 44 stations in the Baltic Sea region. The GPS derived height change rates were applied to reduce the relative sea-level changes observed by tide gauges yielding an estimate for the eustatic sea-level change. For 13 tide gauge-GPS colocation sites a mean eustatic sea-level trend of 1.3 mm/a was derived for the last 100 years.