Uncertainty in hydrological signatures

Information about rainfall–runoff processes is essential for hydrological analyses, modelling and water-management applications. A hydrological, or diagnostic, signature quantifies such information from observed data as an index value. Signatures are widely used, e.g. for catchment classification, model calibration and change detection. Uncertainties in the observed data – including measurement inaccuracy and representativeness as well as errors relating to data management – propagate to the signature values and reduce their information content. Subjective choices in the calculation method are a further source of uncertainty. <br><br> We review the uncertainties relevant to different signatures based on rainfall and flow data. We propose a generally applicable method to calculate these uncertainties based on Monte Carlo sampling and demonstrate it in two catchments for common signatures including rainfall–runoff thresholds, recession analysis and basic descriptive signatures of flow distribution and dynamics. Our intention is to contribute to awareness and knowledge of signature uncertainty, including typical sources, magnitude and methods for its assessment. <br><br> We found that the uncertainties were often large (i.e. typical intervals of ±10–40 % relative uncertainty) and highly variable between signatures. There was greater uncertainty in signatures that use high-frequency responses, small data subsets, or subsets prone to measurement errors. There was lower uncertainty in signatures that use spatial or temporal averages. Some signatures were sensitive to particular uncertainty types such as rating-curve form. We found that signatures can be designed to be robust to some uncertainty sources. Signature uncertainties of the magnitudes we found have the potential to change the conclusions of hydrological and ecohydrological analyses, such as cross-catchment comparisons or inferences about dominant processes

Perceptual models of uncertainty for socio-hydrological systems:a flood risk change example

Characterizing, understanding and better estimating uncertainties are key concerns for drawing robust conclusions when analyzing changing socio-hydrological systems. Here we suggest developing a perceptual model of uncertainty that is complementary to the perceptual model of the socio-hydrological system and we provide an example application to flood risk change analysis. Such a perceptual model aims to make all relevant uncertainty sources–and different perceptions thereof–explicit in a structured way. It is a first step to assessing uncertainty in system outcomes that can help to prioritize research efforts and to structure dialogue and communication about uncertainty in interdisciplinary work

Reply to Discussion of "Perceptual models of uncertainty for socio-hydrological systems:a flood risk change example"(*)

Ertsen discusses the representation of reality and uncertainty in our paper, raising three critical points. In response to the first, we agree that discussion of different interpretations of the concept of uncertainty is important when developing perceptual models - making different uncertainty interpretations explicit was a key motivation behind our method. Secondly, we do not, as Ertsen suggests, deny anyone who is not a "certified" scientist to have relevant knowledge. The elicitation of diverse views by discussing perceptual models is a basis for open discussion and decision making. Thirdly, Ertsen suggests that it is not useful to treat socio-hydrological systems as if they exist. We argue that we act as "pragmatic realists" in most practical applications by treating socio-hydrological systems as an external reality that can be known. But the uncertainty that arises from our knowledge limitations needs to be recognized, as it may impact on practical decision making and associated costs

Uncertainty in hydrological signatures for gauged and ungauged catchments

Reliable information about hydrological behavior is needed for water‐resource management and scientific investigations. Hydrological signatures quantify catchment behavior as index values, and can be predicted for ungauged catchments using a regionalization procedure. The prediction reliability is affected by data uncertainties for the gauged catchments used in prediction and by uncertainties in the regionalization procedure. We quantified signature uncertainty stemming from discharge data uncertainty for 43 UK catchments and propagated these uncertainties in signature regionalization, while accounting for regionalization uncertainty with a weighted‐pooling‐group approach. Discharge uncertainty was estimated using Monte Carlo sampling of multiple feasible rating curves. For each sampled rating curve, a discharge time series was calculated and used in deriving the gauged signature uncertainty distribution. We found that the gauged uncertainty varied with signature type, local measurement conditions and catchment behavior, with the highest uncertainties (median relative uncertainty ±30–40% across all catchments) for signatures measuring high‐ and low‐flow magnitude and dynamics. Our regionalization method allowed assessing the role and relative magnitudes of the gauged and regionalized uncertainty sources in shaping the signature uncertainty distributions predicted for catchments treated as ungauged. We found that (1) if the gauged uncertainties were neglected there was a clear risk of overconditioning the regionalization inference, e.g., by attributing catchment differences resulting from gauged uncertainty to differences in catchment behavior, and (2) uncertainty in the regionalization results was lower for signatures measuring flow distribution (e.g., mean flow) than flow dynamics (e.g., autocorrelation), and for average flows (and then high flows) compared to low flows.Key Points:We quantify impact of data uncertainty on signatures and their regionalizationMedian signature uncertainty ±10–40%, and highly variable across catchmentsNeglecting gauging uncertainty causes overconditioning of regionalizationPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137249/1/wrcr21917-sup-0001-2015WR017635-s01.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137249/2/wrcr21917.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137249/3/wrcr21917_am.pd

A Comparison of Methods for Streamflow Uncertainty Estimation

International audienceStreamflow 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

Twenty-three unsolved problems in hydrology (UPH) – a community perspective

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through on-line media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focussed on process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come

Estimating uncertainties in hydraulicallymodelled rating curves for discharge time series assessment

Establishing a reliable stage-discharge (SD) rating curve for calculating discharge at a hydrological gauging station normally takes years of data collection. Estimation of high flows is particularly difficult as they occur rarely and are often difficult to gauge in practice. At a minimum, hydraulicallymodelled rating curves could be derived with as few as two concurrent SD and water-surface slope measurements at different flow conditions. This means that a reliable rating curve can, potentially, be developed much faster via hydraulic modelling than using a traditional rating curve approach based on numerous stage-discharge gaugings. In this study, we use an uncertainty framework based on Bayesian inference and hydraulic modelling for developing SD rating curves and estimating their uncertainties. The framework incorporates information from both the hydraulic configuration (bed slope, roughness, vegetation) using hydraulic modelling and the information available in the SD observation data (gaugings). Discharge time series are estimated by propagating stage records through the posterior rating curve results. Here we apply this novel framework to a Swedish hydrometric station, accounting for uncertainties in the gaugings and the parameters of the hydraulic model. The aim of this study was to assess the impact of using only three gaugings for calibrating the hydraulic model on resultant uncertainty estimations within our framework. The results were compared to prior knowledge, discharge measurements and official discharge estimations and showed the potential of hydraulically-modelled rating curves for assessing uncertainty at high and medium flows, while uncertainty at low flows remained high. Uncertainty results estimated using only three gaugings for the studied site were smaller than ±15% for medium and high flows and reduced the prior uncertainty by a factor of ten on average and were estimated with only 3 gaugings

Estimating uncertainties in hydraulicallymodelled rating curves for discharge time series assessment

Establishing a reliable stage-discharge (SD) rating curve for calculating discharge at a hydrological gauging station normally takes years of data collection. Estimation of high flows is particularly difficult as they occur rarely and are often difficult to gauge in practice. At a minimum, hydraulicallymodelled rating curves could be derived with as few as two concurrent SD and water-surface slope measurements at different flow conditions. This means that a reliable rating curve can, potentially, be developed much faster via hydraulic modelling than using a traditional rating curve approach based on numerous stage-discharge gaugings. In this study, we use an uncertainty framework based on Bayesian inference and hydraulic modelling for developing SD rating curves and estimating their uncertainties. The framework incorporates information from both the hydraulic configuration (bed slope, roughness, vegetation) using hydraulic modelling and the information available in the SD observation data (gaugings). Discharge time series are estimated by propagating stage records through the posterior rating curve results. Here we apply this novel framework to a Swedish hydrometric station, accounting for uncertainties in the gaugings and the parameters of the hydraulic model. The aim of this study was to assess the impact of using only three gaugings for calibrating the hydraulic model on resultant uncertainty estimations within our framework. The results were compared to prior knowledge, discharge measurements and official discharge estimations and showed the potential of hydraulically-modelled rating curves for assessing uncertainty at high and medium flows, while uncertainty at low flows remained high. Uncertainty results estimated using only three gaugings for the studied site were smaller than ±15% for medium and high flows and reduced the prior uncertainty by a factor of ten on average and were estimated with only 3 gaugings