Abstract. Precipitation measurements exhibit large coldseason biases due to under-catch in windy conditions. These uncertainties affect water balance calculations, snowpack monitoring and calibration of remote sensing algorithms and land surface models. More accurate data would improve the ability to predict future changes in water resources and mountain hazards in snow-dominated regions.In 2010, a comprehensive test site for precipitation measurements was established on a mountain plateau in southern Norway. Automatic precipitation gauge data are compared with data from a precipitation gauge in a Double Fence Intercomparison Reference (DFIR) wind shield construction which serves as the reference. A large number of other sensors are provided supporting data for relevant meteorological parameters.In this paper, data from three winters are used to study and determine the wind-induced under-catch of solid precipitation. Qualitative analyses and Bayesian statistics are used to evaluate and objectively choose the model that best describes the data. A continuous adjustment function and its uncertainty are derived for measurements of all types of winter precipitation (from rain to dry snow). A regression analysis does not reveal any significant misspecifications for the adjustment function, but shows that the chosen model does not describe the regression noise optimally. The adjustment function is operationally usable because it is based only on data available at standard automatic weather stations.The results show a non-linear relationship between undercatch and wind speed during winter precipitation events and there is a clear temperature dependency, mainly reflecting the precipitation type. The results allow, for the first time, derivation of an adjustment function based on measurements above 7 m s −1 . This extended validity of the adjustment function shows a stabilization of the wind-induced precipitation loss for higher wind speeds.

Streamflow time series are commonly derived from stage‐discharge rating curves, but the uncertainty of the rating curve and resulting streamflow series are poorly understood. While different methods to quantify uncertainty in the stage‐discharge relationship exist, there is limited understanding of how uncertainty estimates differ between methods due to different assumptions and methodological choices. We compared uncertainty estimates and stage‐discharge rating curves from seven methods at three river locations of varying hydraulic complexity. Comparison of the estimated uncertainties revealed a wide range of estimates, particularly for high and low flows. At the simplest site on the Isère River (France), full width 95% uncertainties for the different methods ranged from 3 to 17% for median flows. In contrast, uncertainties were much higher and ranged from 41 to 200% for high flows in an extrapolated section of the rating curve at the Mahurangi River (New Zealand) and 28 to 101% for low flows at the Taf River (United Kingdom), where the hydraulic control is unstable at low flows. Differences between methods result from differences in the sources of uncertainty considered, differences in the handling of the time‐varying nature of rating curves, differences in the extent of hydraulic knowledge assumed, and differences in assumptions when extrapolating rating curves above or below the observed gaugings. Ultimately, the selection of an uncertainty method requires a match between user requirements and the assumptions made by the uncertainty method. Given the significant differences in uncertainty estimates between methods, we suggest that a clear statement of uncertainty assumptions be presented alongside streamflow uncertainty estimates.

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 zeroplane 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.

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Abstract. Precipitation measurements exhibit large cold-season biases due to under-catch in windy conditions. These uncertainties affect water balance calculations, snowpack monitoring and calibrations of remote sensing algorithms and land surface models. More accurate data would improve the ability to predict future changes in water resources and mountain hazards in snow-dominated regions. In 2010, an extensive test-site for precipitation measurements was established at a mountain plateau in Southern Norway. Precipitation data of automatic gauges were compared with a precipitation gauge in a Double Fence Intercomparison Reference (DFIR) wind shield construction which served as the reference. Additionally, a large number of sensors were monitoring supportive meteorological parameters. In this paper, data from three winters were used to study and determine the wind-induced under-catch of solid precipitation. Qualitative analyses and Bayesian statistics were used to evaluate and objectively choose the model that is describing the data best. A continuous adjustment function and its uncertainty were derived for measurements of all types of winter precipitation (from rain to dry snow). A regression analysis did not reveal any significant misspecifications for the adjustment function, but showed that the chosen model uncertainty is slightly insufficient and can be further optimized. The adjustment function is operationally usable based only on data available at standard automatic weather stations. Our results show a non-linear relationship between under-catch and wind speed during winter precipitation events and there is a clear temperature dependency, mainly reflecting the precipitation type. The results allowed for the first time to derive an adjustment function with a data-tested validity beyond 7 m s−1 and proved a stabilisation of the wind-induced precipitation loss for higher wind speeds.

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. Key words looped rating curve; hysteresis; Jones formula; nonlinear regression; stage-discharge relationship; streamflow measurement; unsteady channel flow Modélisation des relations hauteur-débit affectées par de l'hystérésis en utilisant la formule de Jones et la régression non-linéaire Résumé Les stations de jaugeage où la relation hauteur-débit est affectée par de l'hystérésis due à de l'écoulement non-stationnaire représentent un défi pour l'hydrométrie. Dans de telles situations, la pratique standard, qui est d'ajuster aux mesures une courbe de tarage bijective entre la hauteur et le débit, n'est plus adaptée. Comme solution à ce problème, cette étude propose une méthode basée sur la formule de Jones et la régression non-linéaire qui n'exige pas de données supplémentaires, vu qu'on dispose soit d'un limnigramme, soit des hauteurs avant et après prise de mesure et de la durée de la mesure. La modélisation par régression de la courbe de tarage par la formule de Jones consiste à appliquer l'approximation de vague levante monoclinale et la loi généralisée de frottement pour l'écoulement uniforme, avec des hypothèses simplificatrices sur les propriétés hydrauliques et géométriques du lit de la rivière associée à la station de jaugeage. Les méthodes d'obtention des courbes de tarage par estimation non-linéaire aux moindres carrées sont discutées, tout en incluant une approximation de l'incertitude. La pertinence et le large champ d'application de la méthode sont démontrés...

Streamflow data are used for important environmental and economic decisions, such as specifying and regulating minimum flows, managing water supplies, and planning for flood hazards. Despite significant uncertainty in most flow data, the flow series for these applications are often communicated and used without uncertainty information. In this commentary, we argue that proper analysis of uncertainty in river flow data can reduce costs and promote robust conclusions in water management applications. We substantiate our argument by providing case studies from Norway and New Zealand where streamflow uncertainty analysis has uncovered economic costs in the hydropower industry, improved public acceptance of a controversial water management policy, and tested the accuracy of water quality trends. We discuss the need for practical uncertainty assessment tools that generate multiple flow series realizations rather than simple error bounds. Although examples of such tools are in development, considerable barriers for uncertainty analysis and communication still exist for practitioners, and future research must aim to provide easier access and usability of uncertainty estimates. We conclude that flow uncertainty analysis is critical for good water management decisions.

Abstract: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.