The theory that forms the basis of TOPMODEL was first outlined by Mike Kirkby some 45 years ago. This paper recalls some of the early developments: the rejection of the first journal paper, the early days of digital terrain analysis, model calibration and validation, the various criticisms of the simplifying assumptions, and the relaxation of those assumptions in the dynamic forms of TOPMODEL, and it considers what we might do now with the benefit of hindsight.

The concept of time of concentration in the analysis of catchment responses dates back over 150 years. It is normally discussed in terms of the velocity of flow of a water particle from the furthest part of a catchment to the outlet. This is also the basis for the definition in the International Glossary of Hydrology, but this is in conflict with the way in which it is commonly used. This paper provides a clarification of the concept and its correct useage.

This paper discusses how uncertainties resulting from lack of knowledge are considered in a number of different natural hazard areas including floods, landslides and debris flows, dam safety, droughts, earthquakes, tsunamis, volcanic ash clouds and pyroclastic flows, and wind storms. As every analysis is necessarily conditional on the assumptions made about the nature of sources of such uncertainties it is also important to follow the guidelines for good practice suggested in Part 2.

Part 1 of this paper discussed the uncertainties arising from gaps in knowledge or limited understanding of the processes involved in different natural hazard areas. These are the epistemic uncertainties that can be difficult to constrain, especially in terms of event or scenario probabilities. A conceptual framework for good practice in dealing with epistemic uncertainties is outlined and implications of applying the principles to natural hazard science are discussed.

Flooding is a significant hazard and extreme events in recent years have focused attention on effective means of reducing its risk. An approach known as natural flood management (NFM) seeks to increase flood resilience by a range of measures that work with natural processes. The paper develops a modelling approach to assess one type NFM of intervention – distributed additional hillslope storage features – and demonstrates that more strategic placement is required than has hitherto been applied.

The theme of the paper is exploration of the potential for seasonal flow forecasting for large lakes using a range of stochastic transfer function techniques with additional insights gained from simple analytical approximations. The methods were evaluated using records for two of the largest lakes in the world. The paper concludes with a discussion of the relevance of the results to operational flow forecasting systems for other large lakes.

This paper describes simple models of phosphorus load which are identified for three catchments in the UK. The models use new hourly observations of phosphorus load, which capture the dynamics of phosphorus transfer in small catchments that are often missed by models with a longer time step. Unlike more complex, process-based models, very few parameters are required, leading to low parameter uncertainty. Interpretation of the dominant phosphorus transfer modes is made based solely on the data.

Reproduction of past floods requires information on discharge and flood extent, commonly unavailable or uncertain during extreme events. We explored the possibility of reproducing an extreme flood disaster using rainfall and post-event hydrometric information by combining a rainfall-runoff and hydraulic modelling tool within an uncertainty analysis framework. Considering the uncertainty in post–event data, it was possible to reasonably reproduce the extreme event.

We developed a parsimonious topography-based hydrologic model coupled with a soil biogeochemistry sub-model in order to improve understanding and prediction of soluble reactive phosphorus (SRP) transfer in agricultural headwater catchments. The modelling approach includes an analysis of the information contained in the calibration data and propagation of uncertainty in model predictions using a GLUE "limits of acceptability" framework.

Uncertainties in natural hazard risk assessment are generally dominated by the sources arising from lack of knowledge or understanding of the processes involved. This is Part 2 of 2 papers reviewing these epistemic uncertainties and covers different areas of natural hazards including landslides and debris flows, dam safety, droughts, earthquakes, tsunamis, volcanic ash clouds and pyroclastic flows, and wind storms. It is based on the work of the UK CREDIBLE research consortium.

Uncertainties in natural hazard risk assessment are generally dominated by the sources arising from lack of knowledge or understanding of the processes involved. This is Part 1 of 2 papers reviewing these epistemic uncertainties that can be difficult to constrain, especially in terms of event or scenario probabilities. It is based on the work of the CREDIBLE research consortium on Risk and Uncertainty in Natural Hazards.