Hydrological extremes and associated flood and drought events threaten the security of water supply, food supply, livelihoods and welfare (Kundzewicz and Matczak, 2015). Managing the impacts of both rainfall excess and deficit on the hydrological system poses a significant challenge for authorities and water resource managers across the globe. These challenges are set to become more acute in future: the latest projections for Europe suggest increasing hydrological variability with more severe extremes (Collet et al., 2018; Guerreiro et al., 2018; Teuling, 2018) and further reductions in low flows in many regions (Wilby and Harris, 2006; Christierson et al., 2012; Prudhomme et al., 2012; Kay et al., 2018; Marx et al., 2018). Increasing demands due to a growing population and socio-economic changes also imply growing pressures on water resources in the future, necessitating considerable investment in long-term strategic water resources planning and adaptation (HM Government, 2017).

Understanding extremes of the past can help us prepare for future extreme events. Drought characteristics of events in the recent past can be used to stress test water supply systems (Mens et al., 2015), a practice that is commonly applied in UK water resource management and drought plans (e.g. Southern Water, 2013; Northumbrian Water, 2017). Similarly, drought severity estimates of past events have been used to investigate the impacts of increased drought frequency on water supply vulnerability (Herman et al., 2016). There is a growing trend towards testing water supply systems against events worse than those experienced, using either scenario-based methods (e.g. Stoelzle et al., 2014; Anderton et al., 2015) or stochastic approaches to generate simulated droughts with credible characteristics (e.g. Atkins, 2016). In addition, short-term water management planning can benefit from seasonal forecasting of reservoirs inflows and streamflow volumes (Prudhomme et al., 2017), so that periods of water deficit can be known in advance and appropriate measures put in place to manage resources and mitigate impacts. However, these methods are all dependent on having a good understanding of past variability and long hydrometric records which are used to train and validate stochastic approaches, and to create tools that enable the simulation of river flows as accurately as possible under a range of varied climate conditions.

Observations of global streamflow are sparse prior to the 1950s, with less than 20 % of stations in the Global Runoff Data Centre (GRDC, 2019) beginning pre-1950. Post-1960, the streamflow network expanded rapidly, a pattern that is mimicked by the UK gauging network, where 100 gauging stations in 1950 have increased to over 1300 today. Qualitative data sources and long rainfall records can identify significant drought events in the pre-instrumentational period (Pfister et al., 2006; Marsh et al., 2007; Brázdil et al., 2016). However, these cannot be used to determine whether these events were more or less severe in hydrological terms than those on the observational record, and there is a need for temporally and spatially coherent flow time series to allow systematic assessment of extreme events.

Meteorological records of rainfall and temperature generally extend further back than hydrological data, often providing data from the turn of the 21st century (New et al., 2000), and occasionally as far back as the mid-20th century. Modelled climate reanalysis data (e.g. Compo et al., 2011) and long-term reconstructed climate datasets (e.g. Casty et al., 2007) have been developed for use in scientific research and can be fed into hydrological models to quantitatively reconstruct river flows beyond the limits of the observational period. In the UK, quantitative reconstructions of river flows using simple hydrological models have previously been conducted, but only for a handful of catchments (e.g. Jones and Lister, 1998; Jones et al., 2006). Regional flow reconstructions have been used to explore the implications of drought events on water resources (e.g. Spraggs et al., 2015). Drought reconstruction has also been conducted in other countries using proxy data (Jones et al., 1984; Cook et al., 2015), precipitation data (Noone et al., 2017, Ireland), soil moisture models (Wu et al., 2011, China), and hydrological models (Caillouet et al., 2017, France). Generally, however, there are few extant studies that use hydrological models to derive plausible historical sequences.

Catchment hydrological models are tools that can generate streamflow time series from meteorological time series data, to provide continuous proxy river flow data that are otherwise not directly available. They can be used to extend flow records, creating very long sequences that extend back beyond the initiation of the observational network. Such long time series can enable thorough analysis of past variability and frequency of severe events (e.g. Caillouet et al., 2017); as vital input to short range and seasonal forecasting (Day, 1985; Harrigan et al., 2018), providing valuable early warnings and help preparedness; or for future projections for long-term planning accounting for possible future non-stationarity, for example due to global warming (e.g. Collet et al., 2018).

Calibrating a hydrological model for multiple purposes, e.g. flow reconstruction and forecasting, for high, low, and average flows, requires careful consideration. Currently, models are typically calibrated to minimise a specific type of error against observations, measured by an “evaluation metric” also known as an “objective function”. Commonly used metrics, such as the Nash–Sutcliffe efficiency (Nash and Sutcliffe, 1970) or root mean squared error, tend to focus on the correct estimation of high flows (Krause et al., 2005; Dawson et al., 2007), whilst more general metrics, such as mean absolute percent error and percent bias are also used to more systematically optimise the flows and the water balance respectively. There are few examples focusing on optimising low flow simulation. Most commonly, a single objective function is used, implemented using automatic algorithms to find a deterministic parameterisation of the model. Such algorithms are commonly categorised as “local” (e.g. PEST, Kim et al., 2007) or “global” (e.g. SCE, Duan et al., 1993), some examples of which have been compared by Wallner et al. (2012). However, seeking a single “optimum” parameter set to describe the observations has been argued to be a misconception with theoretical catchment models (Beven, 2012). The need for calibration techniques to maximise hydrological model performance against multiple elements of the flow regime has, however, been recognised, and multi-objective optimisation methods have been advancing since the turn of the century, though few studies explore more than three objectives (Efstratiadis and Koutsoyiannis, 2010). Multi-objective optimisation commonly involves seeking Pareto-optimal solutions that find a compromise between objective functions (e.g. Shafii and De Smedt, 2009; Kamali et al., 2013; Jung et al., 2017). Multi-objective methods may also be used to optimise more than one hydrological variable (e.g. Mostafaie et al., 2018). In addition, utilising multiple model parameterisations have been advocated to account for “equifinality” – that many different parameterisations may produce equally adequate simulations of past observations (see, for example, Beven and Binley, 1992; Beven, 2006).

Here, we develop a framework to establish a national network of catchment hydrological models and evaluate their application to the reconstruction of hydrological time series, with application to the UK over the period 1891 to 2015. The aims of this research are to

develop a robust method for multi-objective model calibration suitable for use in simulating streamflow with associated uncertainty,

The hydrological model employed in this study (see Sect. 3.1) requires rainfall and potential evapotranspiration data to run, and observed flow data for calibration and validation. Means of access to the datasets used in this study are described in the Data availability section at the end of the paper.

In this section, the nine case study catchments (shown in Fig. 1) are used to examine the performance of both the LHS1 and the LHS500 modelled flows at simulating drought events.

The multi-objective calibration framework presented in this paper has produced modelled flow data with demonstrable high performance across a wide range of available observed records. This framework has been developed to enable nationally and temporally coherent flow simulation that can be applied to a wealth of applications, past, present, and future. In this paper, the calibration framework has been applied to a wide range of catchments across the UK, allowing for a detailed exploration of model performance across different hydrological regimes. Two potentially limiting factors in model performance were highlighted in this study: snowmelt and human influences.

The airGR snowmelt module was not employed in this study as only 15 of the 303 catchments showed snowmelt fractions greater than 0.15 (15 %). These catchments were located along 10 rivers, all in Scotland. Despite the lack of snowmelt processes here, all of the catchments met at least the “softest” evaluation thresholds set out in Sect. 3.2.3, with six, eight, and one catchment meeting the hardest, middle, and softest thresholds respectively. This implies that snowmelt only causes modelling issues for high-altitude Scottish catchments.

Human interactions are a common problem in hydrological modelling that remain largely understudied (Calvin and Bond-Lamberty, 2018). Whilst global scale models have been advancing in socio-hydrology, making use of satellite information and governmental estimates of total water consumption, the data to support such endeavours is lacking (Bierkens, 2015). Small-scale catchment models would need to rely on significant amounts of abstraction and licencing data as well as reservoir operation procedures, the details of which are often sensitive and/or unavailable. The lack of abstraction processes in GR4J is likely to be responsible for some reduced model performance, particularly in the regions of Anglian and southern England. The loss function (parameter X2 “inter-catchment exchange coefficient”) of the GR4J model can account for some systematic losses or gains; however, human influence is often non-stationary (e.g. construction and operation of reservoirs, irrigation, and water transfer schemes). For the Lee at Fieldes Weir and the Thames at Kingston naturalised river flow data, which attempt to remove the impact of human activity on the observed flow, were available. Whilst not included in this paper for consistency with the other 301 catchments, calibration scores were slightly better for the naturalised flow data in these catchments, though both naturalised and observed calibrations easily met the hardest thresholds. An alternative approach is to focus studies on the “near-natural” catchments, which are deemed to have minimal human influence. Of the 303 catchments included in this study, 115 are classified as near-natural and are part of the Low Flows Benchmark Network (Harrigan et al., 2017). Since many of the UK's most significant catchments are heavily influenced, they were not excluded from this study, and the model does successfully manage to implicitly account for human influences in these large rivers. Localised issues in the model's performance, and therefore the quality of the reconstructed flow data, highlight the need for users to take caution when choosing a catchment from this set of 303. Depending on their needs, an alternative nearby catchment where model performance is better may be more suitable if model performance is poor in the initially selected catchment.

The modelling framework developed in this study has explored model parameter uncertainty in order to account for equifinality (Beven, 2006). A total of 500 000 parameter realisations were run, and the best 500 of these were selected for each catchment to allow for uncertainty quantification in applications of these flow data. Here, the uncertainty in the model runs was shown to vary more between catchments than over time (from 1890 to 2015, where long observational records were available). Whilst model parameter uncertainty was considered in this study, further sources of uncertainty can contribute to variations in model performance, including model input data (precipitation and PET), flow data used for model calibration, and the choice of hydrological model (Smith et al., 2018b).

The impact of precipitation uncertainty has been shown to be more significant than PET in hydrological modelling (Paturel et al., 1995; Bastola et al., 2011; Guo et al., 2017). Perry and Hollis (2005) and Legg (2015) state that the accuracy of gridded data is dependent on the density of the rain gauge network, with greater errors associated with sparse coverage. Therefore errors in the reconstructed precipitation data applied in this study will be higher in the early part of the record when the station density was lower. Since the model is calibrated to the more recent period 1982–2014, uncertainty from the rainfall data may propagate through to the flow reconstructions in the early part of the record. However, from the moving window analysis of model performance (see Fig. 6), there does not appear to be significant degradation in the quality of flow simulations in the early part of the record. Tanguy et al. (2018) considered the impact of poorer quality and lower density of temperature data on the derivation of the PET dataset that was employed in this study and concluded that, whilst PET is an important variable for predicting runoff, the influence of degraded PET input that results from low quality temperature data on runoff simulation can be limited by the adequate calibration of hydrological models (Bai et al., 2016; Seiller and Anctil, 2016). Thus, the Tanguy et al. (2018) PET dataset is considered suitable for use in hydrological models, especially if they are calibrated to this dataset.

Uncertainties may also arise from the observational flow data used to calibrate models. Uncertainties from the precision of the instruments that measure the water level (stage) and uncertainties from the derivation of the stage-discharge relationship are both particularly sensitive in the extreme flow ranges. For example, a 10 mm error in stage measurement at the Q95 flow can result in a 20 % error in flow for around a third of the UK's gauging stations (National River Flow Archive, 2019). The dataset used in this study was taken from a reputable source (the NRFA) who, in order to minimise such errors, conduct rigorous quality control procedures using both automatic and manual validation procedures annually (Dixon et al., 2013). Nevertheless, hydrometric data quality does vary across the network and errors tend to cluster in the extreme flow ranges, so hydrometric uncertainty could be influential in some periods in catchments used herein – we recommend users consult the NRFA's extensive station and catchment metadata (available at https://nrfa.ceh.ac.uk/) in conjunction with model performance information (Smith et al., 2018a) when using the flow reconstructions.

Whilst the parameter uncertainty in the model was evaluated here, applying different model types and model structures can also yield dramatically different results. Many multi-model experiments have been conducted to assess the differences between hydrological models (e.g. Warszawski et al., 2014; Vansteenkiste et al., 2014). Similarly, different structures of the same model (e.g. GR4J, GR5J, and GR6J) can influence the results. However, Smith (2016) found that model parameter uncertainty can be as wide as that from using different hydrological models, and initial testing of the GR5J and GR6J models showed significant parameter interactions that resulted in poor simulations in many UK catchments. It was therefore decided that considering the parameter uncertainty of the GR4J model would be sufficient to devise an ensemble of flow reconstructions for this dataset and study. Future work will investigate these simulations against a wider set of model runs using other model structures as part of a follow-up study.

The modelling framework developed here has been shown to be fit-for-purpose for drought reconstruction, across a very wide range of catchment behaviours. The reconstructed series can be used to shed light on historical drought occurrence, characteristics (severity, duration, termination, seasonality), and variability. A first exploration of hydrological drought using the reconstructions is presented in a companion paper by Barker et al. (2019). The data can also be used to support drought and water resources planning activities, whether directly or to provide context for stochastic approaches to drought generation. Ensembles of historical drought events can be used to provide insight into the probabilities of the termination of a current event over a certain time period (e.g. Parry et al., 2018). Knowledge of historic events can also be used to explore statistical correlations with atmospheric drivers of droughts that may help predict the onset of events (e.g. Lavers et al., 2015). In these approaches, extending the hydrological record by ∼70 years significantly increases the sample of historic drought events from which to conduct such research. Furthermore, the modelled data may be used to extend streamflow records used in seasonal hydrological forecasting with a hydrological analogue method (e.g. Svensson, 2016). The model calibrations may be applied to studies of the impacts of climate change on future hydrological extremes in the UK, such as in the Future Flows Hydrology project (Haxton et al., 2012), the outputs of which have been widely applied by water resources managers. The modelling framework developed in this study could extend the Future Flows Hydrology research using the more recent UKCP18 data (Met Office Hadley Centre, 2018). However, as with the Future Flows Hydrology project, users will need to be aware of the implications of the lack of artificial influence processes in the model.

In this paper, a novel multi-objective calibration method was derived and tested for 303 catchments in the UK, and the calibrations were used to reconstruct river flows back to 1891. The GR4J model was applied and calibrated using Latin hypercube sampling (LHS) and six evaluation metrics simultaneously to allow for the evaluation of high, median, and low flows, thus optimising the calibrations for a wide range of potential applications. A best run (LHS1) and 500 model parameterisations (LHS500) were used to assess model uncertainty. Overall, the multi-objective calibration procedure has yielded excellent model results when compared to the observations, with the exception of only a few catchments. The reconstructed flows were appraised over 30-year moving windows, and were shown to provide good simulations of flow in the early parts of the record, where observations were available. Model performance and uncertainty during drought events was explored in nine case study catchments, and varied by catchment. The model simulations were used to derive the Standardised Streamflow Index, which allowed for an assessment of the model's ability to simulate significant deviations from a catchment's “norm”. The results showed that, despite observations regularly sitting outside the range of the LHS500, the peaks and troughs of the time series were well represented. Drought event accumulated deficits were extracted from the SSI data and the results were overall very good, demonstrating that the data from these model calibrations are suitable for the identification and characterisation of hydrological drought events in the UK.

The contributions of this paper are threefold: firstly, the multi-objective model calibration framework applied here has been shown to provide robust model calibrations that can be applied in studies of both general and extreme hydrology. This framework could be applied elsewhere across Europe, and indeed globally, to allow for spatially and temporally consistent simulations of hydrology with far reaching potential applications. Secondly, the model calibrations that have been derived for these 303 catchments in the UK can be used in further research and operational applications, such as for seasonal hydrological forecasting, or for assessing changes in river flows under climate change. Finally, this study has produced a crucial dataset of ∼125 years of seamless flow reconstructions across the UK that will allow for the spatial and temporal investigation and quantification of past drought events, as well as long-term trends in flows, that have never before been possible. These methods and results can provide a valuable step forward in our ability to plan for and forecast the onset, duration, and termination of drought events in the UK, and overseas.