Facets of uncertainty:epistemic uncertainty, non-stationarity, likelihood, hypothesis testing, and communication

This paper presents a discussion of some of the issues associated with the multiple sources of uncertainty and non-stationarity in the analysis and modelling of hydrological systems. Different forms of aleatory, epistemic, semantic, and ontological uncertainty are defined. The potential for epistemic uncertainties to induce disinformation in calibration data and arbitrary non-stationarities in model error characteristics, and surprises in predicting the future, are discussed in the context of other forms of non-stationarity. It is suggested that a condition tree is used to be explicit about the assumptions that underlie any assessment of uncertainty. This also provides an audit trail for providing evidence to decision makers

On hypothesis testing in hydrology:why falsification of models is still a really good idea

This opinion piece argues that in respect of testing models as hypotheses about how catchments function, there is no existing methodology that adequately deals with the potential for epistemic uncertainties about data and hydrological processes in the modelling processes. A rejectionist framework is suggested as a way ahead, wherein assessments of uncertainties in the input and evaluation data are used to define limits of acceptability prior to any model simulations being made. The limits of acceptability might also depend on the purpose of the modelling so that we can be more rigorous about whether a model is actually fit-for-purpose. Different model structures and parameter sets can be evaluated in this framework, albeit that subjective elements necessarily remain, given the epistemic nature of the uncertainties in the modelling process. One of the most effective ways of reducing the impacts of epistemic uncertainties, and allow more rigorous hypothesis testing, would be to commission better observational methods. Model rejection is a good thing in that it requires us to be better, resulting in advancement of the science

Exploratory studies into the prospects for seasonal forecasting of lake levels and outflows

Some of the largest lakes in the world are in Africa and seasonal forecasts of levels and outflows can potentially help with water supply, irrigation and hydropower operations; in particular regarding the risks from floods or droughts. Some factors which increase the prospects for real-time forecasting include the significant time delays between rainfall and outflows resulting from the huge volumes of water stored, and that many studies have shown possible links between regional rainfall and climate indices for the Indian Ocean and elsewhere. On the other hand, on account of the huge areas covered, catchments can span several climate zones and rainfall and flow monitoring networks are often sparse. Exploratory studies into some of these issues are described based on case studies for two large lakes, including some preliminary findings regarding data assimilation and the complexity of models required. The studies were performed using a range of stochastic signal identification tools and are compared with the findings from an ensemble streamflow prediction approach. Preliminary conclusions are then drawn regarding the relevance of these results to the development of operational forecasting models

Exploratory studies into the prospects for seasonal forecasting of lake levels and outflows

Some of the largest lakes in the world are in Africa and seasonal forecasts of levels and outflows can potentially help with water supply, irrigation and hydropower operations; in particular regarding the risks from floods or droughts. Some factors which increase the prospects for real-time forecasting include the significant time delays between rainfall and outflows resulting from the huge volumes of water stored, and that many studies have shown possible links between regional rainfall and climate indices for the Indian Ocean and elsewhere. On the other hand, on account of the huge areas covered, catchments can span several climate zones and rainfall and flow monitoring networks are often sparse. Exploratory studies into some of these issues are described based on case studies for two large lakes, including some preliminary findings regarding data assimilation and the complexity of models required. The studies were performed using a range of stochastic signal identification tools and are compared with the findings from an ensemble streamflow prediction approach. Preliminary conclusions are then drawn regarding the relevance of these results to the development of operational forecasting models

The seventh facet of uncertainty:wrong assumptions, unknowns and surprises in the dynamics of human–water systems

The scientific literature has focused on uncertainty as randomness, while limited credit has been given to what we call here the “seventh facet of uncertainty”, i.e. lack of knowledge. This paper identifies three types of lack of understanding: (i) known unknowns, which are things we know we don’t know; (ii) unknown unknowns, which are things we don’t know we don’t know; and (iii) wrong assumptions, things we think we know, but we actually don’t know. Here we discuss each of these with reference to the study of the dynamics of human–water systems, which is one of the main topics of Panta Rhei, the current scientific decade of the International Association of Hydrological Sciences (IAHS), focusing on changes in hydrology and society. In the paper, we argue that interdisciplinary studies of socio-hydrological dynamics leading to a better understanding of human–water interactions can help in coping with wrong assumptions and known unknowns. Also, being aware of the existence of unknown unknowns, and their potential capability to generate surprises or black swans, suggests the need to complement top-down approaches, based on quantitative predictions of water-related hazards, with bottom-up approaches, based on societal vulnerabilities and possibilities of failure

Embracing Equifinality with Efficiency:Limits of Acceptability Sampling Using the DREAM(LOA) algorithm

This essay illustrates some recent developments to the DiffeRential Evolution Adaptive Metropolis (DREAM) MATLAB toolbox of Vrugt, 2016 to delineate and sample the behavioural solution space of set-theoretic likelihood functions used within the GLUE (Limits of Acceptability) framework (Beven and Binley, 1992; Beven and Freer, 2001; Beven, 2006 ; Beven et al., 2014). This work builds on the DREAM(ABC) algorithm of Sadegh and Vrugt, 2014 and enhances significantly the accuracy and CPU-efficiency of Bayesian inference with GLUE. In particular it is shown how lack of adequate sampling in the model space might lead to unjustified model rejection

Long-term variations in the net inflow record for Lake Malawi

Lake Malawi is the third largest lake in Africa and plays an important role in water supply, hydropower generation, agriculture and fisheries in the region. Lake level observations started in the 1890s and anecdotal evidence of variations dates back to the early 1800s. A chronology of lake level and outflow variations is presented together with updated estimates for the net inflow to the lake. The inflow series and selected rainfall records were also analysed using an unobserved component approach and, although there was little evidence of long-term trends, there was some indication of increasing interannual variability in recent decades. A weak quasi-periodic behaviour was also noted with a period of approximately 4–8 years. The results provide useful insights into the severity of drought and flood events in the region since the 1890s and the potential for seasonal forecasting of lake levels and outflows

Long-term variations in the net inflow record for Lake Malawi

Lake Malawi is the third largest lake in Africa and plays an important role in water supply, hydropower generation, agriculture and fisheries in the region. Lake level observations started in the 1890s and anecdotal evidence of variations dates back to the early 1800s. A chronology of lake level and outflow variations is presented together with updated estimates for the net inflow to the lake. The inflow series and selected rainfall records were also analysed using an unobserved component approach and, although there was little evidence of long-term trends, there was some indication of increasing interannual variability in recent decades. A weak quasi-periodic behaviour was also noted with a period of approximately 4–8 years. The results provide useful insights into the severity of drought and flood events in the region since the 1890s and the potential for seasonal forecasting of lake levels and outflows

Event and model dependent rainfall adjustments to improve discharge predictions

Most conceptual rainfall–runoff models use as input spatially averaged rainfall fields which are typically associated with significant errors that affect the model outcome. In this study, it is hypothesized that a simple spatially and temporally averaged event–dependent rainfall multiplier can account for errors in the rainfall input. The potentials and limitations of this lumped multiplier approach are explored by evaluating the effects of multipliers on the accuracy and precision of the predictive distributions. Parameter sets found to be behavioural across a range of different flood events were assumed to be a good representation of the catchment dynamics and were used to identify rainfall multipliers for each of the individual events. An effect of the parameter sets on identified multipliers was found, however it was small compared to the differences between events. Accounting for event–dependent multipliers improved the reliability of the predictions. At the cost of a small decrease in precision, the distribution of identified multipliers for past events can be used to account for possible rainfall errors when predicting future events. By using behavioural parameter sets to identify rainfall multipliers, the method offers a simple and computationally efficient way to address rainfall errors in hydrological modelling

Knowledge gaps in our perceptual model of Great Britain’s hydrology

There is a no lack of significant open questions in the field of hydrology. How will hydrological connectivity between freshwater bodies be altered by future human alterations to the hydrological cycle? Where does water go when it rains? Or what is the future space-time variability of flood and drought events? However, the answers to these questions will vary with location due to the specific and often poorly understood local boundary conditions and system properties that control the functional behaviour of a catchment or any other hydrologic control volume. We suggest that an open, shared and evolving perceptual model of a region’s hydrology is critical to tailor our science questions, as it would be for any other study domain from the plot to the continental scale. In this opinion piece, we begin to discuss the elements of and point out some knowledge gaps in the perceptual model of the terrestrial water cycle of Great Britain. We discuss six major knowledge gaps and propose four key ways to reduce them. While the specific knowledge gaps in our perceptual model do not necessarily transfer to other places, we believe that the development of such perceptual models should be at the core of the debate for all hydrologic communities, and we encourage others to have a similar debate for their hydrologic domain