Quantifying drought risk through rainfall modelling and simulation
Hydrological droughts are a considerable risk to society. These occur when water supply becomes low, and are usually a result of meteorological droughts – defined as periods of below-average rainfall.
Having accurate models of rainfall is therefore crucial to understanding the likelihood of extreme drought behaviour. Statistical modelling of rainfall is challenging though, because of the complex temporal structure in both the occurrence of rainfall and its intensity. While many statistical rainfall modelling approaches have been proposed in the past, few deal with high temporal resolution such as hourly rainfall totals (in mm). This is a particular problem for hydrological models – used in the water industry for quantifying drought risk – as they require high resolution rainfall data as input.
Dr Oliver Stoner and Dr Theo Economou (Department of Mathematics) have developed an advanced yet highly interpretable statistical data model (Stoner and Economou, 2020) for capturing the behaviour of high resolution rainfall time series. This compartmental model describes rainfall in terms of latent dry, wet and wetter “states”, effectively discretising time into periods where there is either low, moderate or high amounts of rainfall. The word “amount” is used loosely to describe a range of ways that rainfall can accumulate, from short bursts of heavy rainfall to long periods of constant drizzle. The model also includes diurnal, seasonal and other, potentially unobserved, temporal structures to capture the complex behaviour of rainfall in time. In particular, the modelling framework is very well suited in capturing extreme rainfall intensity (such as the observable maximum amount of hourly rainfall) while retaining physical plausibility through prior constraints, as well as extreme periods of little/no rainfall – which is crucial for drought characterisation. With respect to input to hydrological models, the proposed approach offers an objective way of characterising a different probability distribution for rainfall depending on the state, offering a consistent model for both drought and flood risk.
Dr Laura Dawkins and Dr Joe Osborne at the Met Office, in collaboration with Dr Theo Economou (joint Met Office – University of Exeter lecturer) have built on this work to apply, adapt and further develop the model for application to a customer, Anglian Water. The model was adapted to accurately model daily rainfall data at 39 locations in Eastern England, but also extended to include climate indices, such as the North Atlantic Oscillation, to more accurately explain rainfall behaviour. The data were obtained from the freely available HadUK-Grid (HadUK). The project was commissioned by Anglian Water, and the goal was to provide more accurate daily rainfall simulations for the region, compared to a previous approach where the rainfall time scale was monthly and a bias correction was necessary to realistically simulate the most extreme droughts. Daily rainfall simulations were obtained from the statistical model, which were then converted to the Deficit Drought Index or DDI (a measure of drought intensity). Figure 1 shows observed (blue line) and simulated (grey lines) time series of the DDI at four of the 39 locations, illustrating how the statistical model describes the data very well (the mean of the simulations shown by the black line closely matches the blue line), but is also able to produce alternative but plausible data sets. In particular, the simulations include droughts as intense but also more extreme compared than the most extreme in the observed record, e.g. 1920s and 1930s events in Ipswich (site V38).
These simulated data sets are then used to quantify extremes, and better inform hydrological models. The framework was further extended by the Met Office to intelligently interpolate the simulated time series for the 39 locations coherently in space. The interpolation took into account the terrain structure and resulted in an extended (simulated) data set with a high spatial resolution, as illustrated in Figure 2 (note these are not observed values, they are stochastic simulations). Anglian Water is currently using these simulations to plan for the future in terms of infrastructure development, in order to ensure there are adequate water resources to meet demand.
Figure 1: A comparison of the DDI time series from observed rainfall and from simulated rainfall for four sites in Eastern UK: V38, V16, V20 and V07. The observed DDI is shown in blue, while the 1000 simulations and the mean of the simulations are shown in grey/black respectively. [Figure from Dawkins and Osborne (2020)]
Figure 2: Gridded rainfall simulations in the Eastern UK region, for 3 consecutive days in January 2018. [Figure adapted from Dawkins and Osborne (2020b)]
Dawkins L and Osborne J. 2020. Extreme Drought Explorer: Exploration and Development (commercial consultancy report provided to Anglian Water)
Dawkins L and Osborne J. 2020(b). Extreme Drought Explorer: Creating a Gridded Stochastic Dataset (commercial consultancy report provided to Anglian Water)
HadUK. Info at website https://www.metoffice.gov.uk/research/climate/maps-and-data/data/haduk-grid/haduk-grid.
Stoner O and Economou T. 2020. An Advanced Hidden Markov Model for Hourly Rainfall Time Series. Computational Statistics and Data Analysis. DOI:10.1016/j.csda.2020.107045.
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