Benchmarking observational uncertainties for hydrology: rainfall,river discharge and water quality

This review and commentary sets out the need for authoritative and concise information on the expected error distributions and magnitudes in observational data. We discuss the necessary components of a benchmark of dominant data uncertainties and the recent developments in hydrology which increase the need for such guidance. We initiate the creation of a catalogue of accessible information on characteristics of data uncertainty for the key hydrological variables of rainfall, river discharge and water quality (suspended solids, phosphorus and nitrogen). This includes demonstration of how uncertainties can be quantified, summarizing current knowledge and the standard quantitative results available. In particular, synthesis of results from multiple studies allows conclusions to be drawn on factors which control the magnitude of data uncertainty and hence improves provision of prior guidance on those uncertainties. Rainfall uncertainties were found to be driven by spatial scale, whereas river discharge uncertainty was dominated by flow condition and gauging method. Water quality variables presented a more complex picture with many component errors. For all variables, it was easy to find examples where relative error magnitudes exceeded 40%. We consider how data uncertainties impact on the interpretation of catchment dynamics, model regionalization and model evaluation. In closing the review, we make recommendations for future research priorities in quantifying data uncertainty and highlight the need for an improved ‘culture of engagement’ with observational uncertainties. Copyright © 2012 John Wiley & Sons, Ltd.     

Observational and predictive uncertainties for multiple variables in a spatially distributed hydrological model

In this study, uncertainty in model input data (precipitation) and parameters is propagated through a physically based, spatially distributed hydrological model based on the MIKE SHE code. Precipitation uncertainty is accounted for using an ensemble of daily rainfall fields that incorporate four different sources of uncertainty, whereas parameter uncertainty is considered using Latin hypercube sampling. Model predictive uncertainty is assessed for multiple simulated hydrological variables (discharge, groundwater head, evapotranspiration, and soil moisture). Utilizing an extensive set of observational data, effective observational uncertainties for each hydrological variable are assessed. Considering not only model predictive uncertainty but also effective observational uncertainty leads to a notable increase in the number of instances, for which model simulation and observations are in good agreement (e.g., 47% vs. 91% for discharge and 0% vs. 98% for soil moisture). Effective observational uncertainty is in several cases larger than model predictive uncertainty. We conclude that the use of precipitation uncertainty with a realistic spatio‐temporal correlation structure, analyses of multiple variables with different spatial support, and the consideration of observational uncertainty are crucial for adequately evaluating the performance of physically based, spatially distributed hydrological models.     

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.     

Sensitivity analysis and calibration of the Modified Universal Soil Loss Equation (MUSLE) for the upper Malewa Catchment, Kenya

Simulation models are widely used for studying physical processes such as surface runoff, sediment transport and sediment yield in catchments. Most models need case-specific empirical data for parameterization before being applied especially in regions other than the ones they have been developed. Sensitivity analysis is usually performed to determine the most influential factors of a model so that they can be prioritized for optimization. In this way uncertainties in model outputs can be reduced considerably. This study evaluates the commonly used modified universal soil loss equation (MUSLE) model used for sediment yield simulation for the case of the upper Malewa catchment in Kenya. The conceptual factors of the model are assessed relative to the hydrological factors in the model. Also, the sensitivity of the model to the choice of the objective function in calibration is tested. The Sobol' sensitivity analysis method was used for evaluating the degree of sensitivity of the conceptual and hydrological factors for sediment yield simulations using the MUSLE model. Nash-Sutcliffe Efficiency (NSE) and the modified Nash-Sutcliffe Efficiency (NSEm) are used to test the sensitivity of the model to the choice of the objective function and robustness of model performance with sediment data measured from upper Malewa catchment, Kenya. The results indicate that the conceptual factors are the most sensitive factors of the MUSLE model contributing about 66% of the variability in the output sediment yield. Increased variability of sediment yield output was also observed. This was attributed to interactions of input factors. For the upper Malewa catchment calibration of the MUSLE model indicates that the use of NSEm as an objective function provides stable results, which indicates that the model can satisfactorily be applied for sediment yield simulations.     

Temporal sampling strategies and uncertainty in calibrating a conceptual hydrological model for a small boreal catchment

How much data is needed for calibration of a hydrological catchment model? In this paper we address this question by evaluating the information contained in different subsets of discharge and groundwater time series for multi‐objective calibration of a conceptual hydrological model within the framework of an uncertainty analysis. The study site was a 5·6‐km² catchment within the Forsmark research site in central Sweden along the Baltic coast. Daily time series data were available for discharge and several groundwater wells within the catchment for a continuous 1065‐day period. The hydrological model was a site‐specific modification of the conceptual HBV model. The uncertainty analyses were based on a selective Monte Carlo procedure. Thirteen subsets of the complete time series data were investigated with the idea that these represent realistic intermittent sampling strategies. Data subsets included split‐samples and various combinations of weekly, monthly, and quarterly fixed interval subsets, as well as a 53‐day ‘informed observer’ subset that utilized once per month samples except during March and April—the months containing large and often dominant snow melt events—when sampling was once per week. Several of these subsets, including that of the informed observer, provided very similar constraints on model calibration and parameter identification as the full data record, in terms of credibility bands on simulated time series, posterior parameter distributions, and performance indices calculated to the full dataset. This result suggests that hydrological sampling designs can, at least in some cases, be optimized. Copyright © 2009 John Wiley & Sons, Ltd.     

Modelling the impact of stormwater source control infiltration techniques on catchment baseflow

Stormwater management increasingly recognises the need to emulate, to the maximum extent possible, the flow regime of receiving waters in their pre‐development state. Hydrological models play a central role in assessing the catchment‐scale impacts of alternative stormwater management strategies. However, because of the complexity of physical processes involved in urban hydrology, particularly subsurface flows, the predictive performance of such models is often low. We investigated how the structure of hydrological models influenced the prediction of urbanisation and stormwater management impacts on baseflow. We calibrated three conceptual models of the same reference catchment and compared the modelled flow regime from different stormwater management scenarios, using each of the three model structures. Scenarios were assessed using six metrics, characterising the whole streamflow regime and in particular baseflow. Although the three models of the reference catchment represented the observed hydrograph well, the most complex structure developed using a thorough diagnostic of the catchment behaviour better captured the change in hydrological regime during dry years. Predictions of baseflow changes due to urbanisation varied significantly according to the model structure. Similarly, the models showed distinct responses to the stormwater management scenarios applied, especially for scenarios involving infiltration of stormwater at source. Our results confirm the importance of predicting the consequences of land use changes with conceptual models that are consistent with the hydrological behaviour of the study catchment. Future work should help to quantify the uncertainties due to model structure and thus provide practical guidance to the use of catchment models for assessing stormwater management strategies. Copyright © 2013 John Wiley & Sons, Ltd.     

The exponential decline in saturated hydraulic conductivity with depth: a novel method for exploring its effect on water flow paths and transit time distribution

The strong vertical gradient in soil and subsoil saturated hydraulic conductivity is characteristic feature of the hydrology of catchments. Despite the potential importance of these strong gradients, they have proven difficult to model using robust physically based schemes. This has hampered the testing of hypotheses about the implications of such vertical gradients for subsurface flow paths, residence times and transit time distribution. Here we present a general semi‐analytical solution for the simulation of 2D steady‐state saturated‐unsaturated flow in hillslopes with saturated hydraulic conductivity that declines exponentially with depth. The grid‐free solution satisfies mass balance exactly over the entire saturated and unsaturated zones. The new method provides continuous solutions for head, flow and velocity in both saturated and unsaturated zones without any interpolation process as is common in discrete numerical schemes. This solution efficiently generates flow pathlines and transit time distributions in hillslopes with the assumption of depth‐varying saturated hydraulic conductivity. The model outputs reveal the pronounced effect that changing the strength of the exponential decline in saturated hydraulic conductivity has on the flow pathlines, residence time and transit time distribution. This new steady‐state model may be useful to others for posing hypotheses about how different depth functions for hydraulic conductivity influence catchment hydrological response. Copyright © 2016 John Wiley & Sons, Ltd.     

The assumption of uniform specific discharge: unsafe at any time?

Nearby catchments in the same landscape are often assumed to have similar specific discharge (runoff per unit catchment area). Five years of streamflow from 14 nested catchments in a 68 km² landscape was used to test this assumption, with the hypothesis that the spatial variability in specific discharge is smaller than the uncertainties in the measurement. The median spatial variability of specific discharge, defined as subcatchment deviation from the catchment outlet, was 33% at the daily scale. This declined to 24% at a monthly scale and 19% at an annual scale. These specific discharge differences are on the same order of magnitude as predicted for major land‐use conversions or a century of climate change. Spatial variability remained when considering uncertainties in specific discharge, and systematic seasonal patterns in specific discharge variation further provide confidence that these differences are more than just errors in the analysis of catchment area, rainfall variability or gauging. Assuming similar specific discharge in nearby catchments can thus lead to spurious conclusions about the effects of disturbance on hydrological and biogeochemical processes. Copyright © 2016 John Wiley & Sons, Ltd.     

The importance of aspect for modelling the hydrological response in a glacier catchment in Central Asia

Understanding how explicit consideration of topographic information influences hydrological model performance and upscaling in glacier dominated catchments remains underexplored. In this study, the Urumqi glacier no. 1 catchment in northwest China, with 52% of the area covered by glaciers, was selected as study site. A conceptual glacier‐hydrological model was developed and tested to systematically, simultaneously, and robustly reproduce the hydrograph, separate the discharge into contributions from glacier and nonglacier parts of the catchment, and establish estimates of the annual glacier mass balance, the annual equilibrium line altitude, and the daily catchment snow water equivalent. This was done by extending and adapting a recently proposed landscape‐based semidistributed conceptual hydrological model (FLEX‐Topo) to represent glacier and snowmelt processes. The adapted model, FLEX^G, allows to explicitly account for the influence of topography, that is, elevation and aspect, on the distribution of temperature and precipitation and thus on melt dynamics. It is shown that the model can not only reproduce long‐term runoff observations but also variations in glacier and snow cover. Furthermore, FLEX^G was successfully transferred and up‐scaled to a larger catchment exclusively by adjusting the areal proportions of elevation and aspect without the need for further calibration. This underlines the value of topographic information to meaningfully represent the dominant hydrological processes in the region and is further exacerbated by comparing the model to a model formulation that does not account for differences in aspect (FLEX^G,nA) and which, in spite of satisfactorily reproducing the observed hydrograph, does not capture the influence of spatial variability of snow and ice, which as a consequence reduces model transferability. This highlights the importance of accounting for topography and landscape heterogeneity in conceptual hydrological models in mountainous and snow‐, and glacier‐dominated regions.     

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.     

Investigating the behaviour of a small Mediterranean catchment using three different hydrological models as hypotheses

Mediterranean catchments are characterized by strong nonlinearities in their hydrological behaviour. Properly simulating those nonlinearities still represents a great challenge and, at the same time, an important issue in order to improve our knowledge of their hydrological behaviour. The main aim of this work is find out diverse modelling approaches to reproduce the observed nonlinear hydrological behaviour in a small Mediterranean catchment, Can Vila (Vallcebre, NE Spain). To this end, three hydrological models were considered: two lumped models called LU3 and LU4 of increasing complexity, and a distributed model called TETIS. The structures of these different models were used as hypotheses, which could explain and reproduce the observed nonlinear behaviour at the outlet. Four analyses were carried out: (i) goodness‐of‐fit criteria analysis, (ii) residual errors analysis, (iii) sensitivity analysis and (iv) multicriteria analysis based on the concept of Pareto Optimal. These analyses showed the higher capability and robustness of the distributed model to reproduce the observed complex hydrological behaviour in this catchment. Copyright © 2015 John Wiley & Sons, Ltd.     

Detecting and attributing drought-induced changes in catchment hydrological behaviours in a southeastern Australia catchment using a data assimilation method

It is widely recognized that multi-year drought can induce changes in catchment hydrological behaviours. However, at present, our understanding about multi-year drought-induced changes in catchment hydrological behaviours and its driving factors at the process level is still very limited. This study proposed a new approach using a data assimilation technique with a process-based hydrological model to detect multi-year drought-induced changes in catchment hydrological behaviours and to identify driving factors for the changes in an unimpaired Australian catchment (Wee Jasper) which experienced prolonged drought from 1997 to 2009. Modelling experiments demonstrated that the multi-year drought caused a significant change in the catchment rainfall-runoff relationship, indicated by significant step changes in the estimated time-variant hydrological parameters SC (indicating catchment active water storage capacity) and C (reflecting catchment evapotranspiration dynamics), whose average values increased 23.4% and 10.2%, respectively, due to drought. The change in the rainfall-runoff relationship identified by the data assimilation method is consistent with that arrived at by a statistical examination. The proposed method provides insights about the drivers of the changes in the rainfall-runoff relationship at the processes level. Increasing catchment water storage capacity and decreasing ratio of rainfall to soil moisture for supplying actual evapotranspiration during drought are the main driving factors for the catchment behaviours change in the Wee Jasper catchment in terms of model structure. And they are related to decrease in catchment groundwater level and deep soil moisture. The proposed new method can be used as an effective technique for detecting both the change of hydrological behaviours induced by prolonged drought and its driving factors at the process level.     

Using high‐resolution isotope data and alternative calibration strategies for a tracer‐aided runoff model in a nested catchment

Testing hydrological models over different spatio‐temporal scales is important for both evaluating diagnostics and aiding process understanding. High‐frequency (6‐hr) stable isotope sampling of rainfall and runoff was undertaken during 3‐week periods in summer and winter within 12 months of daily sampling in a 3.2‐km² catchment in the Scottish Highlands. This was used to calibrate and test a tracer‐aided model to assess the (a) information content of high‐resolution data, (b) effect of different calibration strategies on simulations and inferred processes, and (c) model transferability to <1‐km² subcatchment. The 6‐hourly data were successfully incorporated without loss of model performance, improving the temporal resolution of the modelling, and making it more relevant to the time dynamics of the isotope and hydrometric response. However, this added little new information due to old‐water dominance and riparian mixing in this peatland catchment. Time variant results, from differential split sample testing, highlighted the importance of calibrating to a wide range of hydrological conditions. This also provided insights into the nonstationarity of catchment mixing processes, in relation to storage and water ages, which varied markedly depending on the calibration period. Application to the nested subcatchment produced equivalent parameterization and performance, highlighting similarity in dominant processes. The study highlighted the utility of high‐resolution data in combination with tracer‐aided models, applied at multiple spatial scales, as learning tools to enhance process understanding and evaluation of model behaviour across nonstationary conditions. This helps reveal more fully the catchment response in terms of the different mechanistic controls on both wave celerites and particle velocities.     

Multi‐criterial validation of TOPMODEL in a mountainous catchment

The need for powerful validation methods for hydrological models including the evaluation of internal stages and spatially distributed simulations has often been emphasized. In this study a multi‐criterial validation scheme was used for validation of TOPMODEL, a conceptual semi‐distributed rainfall–runoff model. The objective was to test TOPMODEL's capability of adequately representing dominant hydrological processes by simple conceptual approaches. Validation methods differed in the type of data used, in their target and in mode. The model was applied in the humid and mountainous Brugga catchment (40 km²) in south‐west Germany. It was calibrated by a Monte Carlo method based on hourly runoff data. Additional information for validation was derived from a recession analysis, hydrograph separation with environmental tracers and from field surveys, including the mapping of saturated areas. Although runoff simulations were satisfying, inadequacies of the model structure compared with the real situation with regard to hydrological processes in the study area were found. These belong mainly to the concept of variable contributing areas for saturation excess overland flow and their dynamics, which were overestimated by the model. The simple TOPMODEL approach of two flow components was found to be insufficient. The multi‐criterial validation scheme enables not only to demonstrate limitations with regard to process representation, but also to specify where and why these limitations occur. It may serve as a valuable tool for the development of physically sound model modifications. Copyright © 1999 John Wiley & Sons, Ltd.     

Semi‐distributed flood runoff model at the subcontinental scale for southwestern Iran

Rainfall–runoff modelling, as a surface hydrological process, on large‐scale data‐poor basins is currently a major topic of investigation that requires the model parameters be identified by using basin physical characteristics rather than calibration. This paper describes the application of the TOPMODEL framework accompanied by a kinematic wave model to the Karun River sub‐basins in southwestern Iran with just one conceptual parameter for calibration. ISLSCP1, HYDRO1K and Reynolds data sets are presented in a geographical information system and used as data sources for meteorological information, hydrological features and soil characteristics of the study area respectively. The results show that although the model developed can adequately predict flood runoff in the catchment with only one calibrated parameter, it is suggested that the effect of surface reservoirs be considered in the proposed model. Copyright © 2007 John Wiley & Sons, Ltd.     

Modelling of wildfire impacts on catchment hydrology applied to two case studies

We used a conceptual modelling approach on two western Canadian mountainous catchments that were burned in separate wildfires in 2003 to explore the potential of using modelling approaches to generalize post‐wildfire catchment hydrology in cases where pre‐wildfire hydrologic data were present or absent. The Fishtrap Creek case study (McLure fire, British Columbia) had a single gauged catchment with both pre‐fire and post‐fire data, whereas the Lost Creek case study (Lost Ck. fire, Alberta) had several instrumented burned and reference catchments providing streamflows and climate data only for the post‐wildfire period. Wildfire impacts on catchment hydrology were assessed by comparing pre‐wildfire and post‐wildfire model calibrated parameter sets for Fishtrap Creek (Fishtrap Ck.) and the calibrated parameters of two burned (South York Ck. and Lynx Ck.) and two unburned (Star Ck. and North York Ck.) catchments for Lost Ck. Model predicted streamflows for burned catchments were compared with unburned catchments (pre‐fire in the case of Fishtrap Ck. and unburned in the case of the Lost Ck.). Similarly, model predicted streamflows from unburned catchments were compared with burned catchments (post‐fire in the case of Fishtrap Ck. and burned in the case of the Lost Ck.). For Fishtrap Ck., different model parameters and streamflow behaviour were observed for pre‐wildfire and post‐wildfire conditions. However, the burned and unburned model results from the Lost Ck. wildfire did not show differing streamflow responses to the wildfire. We found that this hydrological modelling approach is suitable where pre‐wildfire and post‐wildfire data are available but may provide limited additional insights where pre‐disturbance hydrologic data are unavailable. This may in part be because the conceptual modelling approach does not represent the physical catchment processes, whereas a physically based model may still provide insights into catchment hydrological response in these situations. Copyright © 2015 John Wiley & Sons, Ltd.     

Closing the Gaps in Our Knowledge of the Hydrological Cycle over Land: Conceptual Problems

This paper reviews the conceptual problems limiting our current knowledge of the hydrological cycle over land. We start from the premise that to understand the hydrological cycle we need to make observations and develop dynamic models that encapsulate our understanding. Yet, neither the observations nor the models could give a complete picture of the hydrological cycle. Data assimilation combines observational and model information and adds value to both the model and the observations, yielding increasingly consistent and complete estimates of hydrological components. In this review paper we provide a historical perspective of conceptual problems and discuss state-of-the-art hydrological observing, modelling and data assimilation systems.     

The effect of differences between rainfall measurement techniques on groundwater and discharge simulations in a lowland catchment

Several rainfall measurement techniques are available for hydrological applications, each with its own spatial and temporal resolution and errors. When using these rainfall datasets as input for hydrological models, their errors and uncertainties propagate through the hydrological system. The aim of this study is to investigate the effect of differences between rainfall measurement techniques on groundwater and discharge simulations in a lowland catchment, the 6.5‐km² Hupsel Brook experimental catchment. We used five distinct rainfall data sources: two automatic raingauges (one in the catchment and another one 30 km away), operational (real‐time and unadjusted) and gauge‐adjusted ground‐based C‐band weather radar datasets and finally a novel source of rainfall information for hydrological purposes, namely, microwave link data from a cellular telecommunication network. We used these data as input for the, a recently developed rainfall‐runoff model for lowland catchments, and intercompared the five simulated discharges time series and groundwater time series for a heavy rainfall event and a full year. Three types of rainfall errors were found to play an important role in the hydrological simulations, namely: (1) Biases, found in the unadjusted radar dataset, are amplified when propagated through the hydrological system; (2) Timing errors, found in the nearest automatic raingauge outside the catchment, are attenuated when propagated through the hydrological system; (3) Seasonally varying errors, found in the microwave link data, affect the dynamics of the simulated catchment water balance. We conclude that the hydrological potential of novel rainfall observation techniques should be assessed over a long period, preferably a full year or longer, rather than on an event basis, as is often done. Copyright © 2016 The Authors. Hydrological Processes. Published by John Wiley & Sons Ltd.     

Hydrological field data from a modeller's perspective: Part 1. Diagnostic tests for model structure

Hydrological scientists develop perceptual models of the catchments they study, using field measurements and observations to build an understanding of the dominant processes controlling the hydrological response. However, conceptual and numerical models used to simulate catchment behaviour often fail to take advantage of this knowledge. It is common instead to use a pre‐defined model structure which can only be fitted to the catchment via parameter calibration. In this article, we suggest an alternative approach where different sources of field data are used to build a synthesis of dominant hydrological processes and hence provide recommendations for representing those processes in a time‐stepping simulation model. Using analysis of precipitation, flow and soil moisture data, recommendations are made for a comprehensive set of modelling decisions, including Evapotranspiration (ET) parameterization, vertical drainage threshold and behaviour, depth and water holding capacity of the active soil zone, unsaturated and saturated zone model architecture and deep groundwater flow behaviour. The second article in this two‐part series implements those recommendations and tests the capability of different model sub‐components to represent the observed hydrological processes. Copyright © 2010 John Wiley & Sons, Ltd.