Global-scale modelling of glaciers, ice sheets and permafrost : recommendations for Hydro-JULES

This report is part of the Hydro-JULES research programme supported by NERC National Capability funding (grant number: NE/S017380/1) to the UK Centre for Ecology & Hydrology (UKCEH), British Geological Survey (BGS) and National Centre for Atmospheric Science (NCAS). Hydro-JULES will deliver an open-source, three-dimensional community model of the terrestrial water cycle. As part of work package 4, the BGS will develop an enhanced representation of groundwater in Hydro-JULES and link it to land-surface processes, with the aim of implementing the model on a global scale. In cold regions, glaciers, ice sheets and permafrost influence regional groundwater flow and recharge processes. This report aims to facilitate the inclusion of cryosphere–groundwater systems in the Hydro-JULES modelling framework by reviewing potential modelling approaches and then prioritising a set of model developments that should be undertaken as part of the ongoing development of the Hydro-JULES modelling framework. All outputs from the HydroJULES programme (including this report) are open and freely available to ensure transparency and auditability in the development of the scientific approach

A lumped conceptual model to simulate groundwater level time-series

Lumped, conceptual groundwater models can be used to simulate groundwater level time-series quickly and efficiently without the need for comprehensive modelling expertise. A new model of this type, AquiMod, is presented for simulating groundwater level time-series in unconfined aquifers. Its modular design enables users to implement different model structures to gain understanding about controls on aquifer storage and discharge. Five model structures are evaluated for four contrasting aquifers in the United Kingdom. The ability of different model structures and parameterisations to replicate the observed hydrographs is examined. AquiMod simulates the quasi-sinusoidal hydrographs of the relatively uniform Chalk and Sandstone aquifers most efficiently. It is least efficient at capturing the flashy hydrograph of a heterogeneous, fractured Limestone aquifer. The majority of model parameters demonstrate sensitivity and can be related to available field data. The model structure experiments demonstrate the need to represent vertical aquifer heterogeneity to capture the storage-discharge dynamics efficiently

Reconstruction of multi-decadal groundwater level time-series using a lumped conceptual model

Multi-decadal groundwater level records, which provide information about long-term variability and trends, are relatively rare. Whilst a number of studies have sought to reconstruct river flow records, there have been few attempts to reconstruct groundwater level time-series over a number of decades. Using long rainfall and temperature records, we developed and applied a methodology to do this using a lumped conceptual model. We applied the model to six sites in the UK, in four different aquifers: Chalk, limestone, sandstone and Greensand. Acceptable models of observed monthly groundwater levels were generated at four of the sites, with maximum Nash–Sutcliffe Efficiency scores of between 0.84 and 0.93 over the calibration and evaluation periods, respectively. These four models were then used to reconstruct the monthly groundwater level time-series over approximately 60 years back to 1910. Uncertainty in the simulated levels associated with model parameters was assessed using the Generalized Likelihood Uncertainty Estimation method. Known historical droughts and wet period in the UK are clearly identifiable in the reconstructed levels, which were compared using the Standardized Groundwater Level Index. Such reconstructed records provide additional information with which to improve estimates of the frequency, severity and duration of groundwater level extremes and their spatial coherence, which for example is important for the assessment of the yield of boreholes during drought period

The Destruction of Tori in Volume-Preserving Maps

Invariant tori are prominent features of symplectic and volume preserving maps. From the point of view of chaotic transport the most relevant tori are those that are barriers, and thus have codimension one. For an $n$-dimensional volume-preserving map, such tori are prevalent when the map is nearly "integrable," in the sense of having one action and $n-1$ angle variables. As the map is perturbed, numerical studies show that the originally connected image of the frequency map acquires gaps due to resonances and domains of nonconvergence due to chaos. We present examples of a three-dimensional, generalized standard map for which there is a critical perturbation size, $\epsilon_c$, above which there are no tori. Numerical investigations to find the "last invariant torus" reveal some similarities to the behavior found by Greene near a critical invariant circle for area preserving maps: the crossing time through the newly destroyed torus appears to have a power law singularity at $\epsilon_c$, and the local phase space near the critical torus contains many high-order resonances.Comment: laTeX, 16 figure

Homoclinic Bifurcations for the Henon Map

Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. We use this limit to assign global symbols to orbits and use continuation from the limit to study their bifurcations. We find a bound on the parameter range for which the Henon map exhibits a complete binary horseshoe as well as a subshift of finite type. We classify homoclinic bifurcations, and study those for the area preserving case in detail. Simple forcing relations between homoclinic orbits are established. We show that a symmetry of the map gives rise to constraints on certain sequences of homoclinic bifurcations. Our numerical studies also identify the bifurcations that bound intervals on which the topological entropy is apparently constant.Comment: To appear in PhysicaD: 43 Pages, 14 figure

Seasonal forecasting of groundwater levels in principal aquifers of the United Kingdom

To date, the majority of hydrological forecasting studies have focussed on using medium-range (3–15 days) weather forecasts to drive hydrological models and make predictions of future river flows. With recent developments in seasonal (1–3 months) weather forecast skill, such as those from the latest version of the UK Met Office global seasonal forecast system (GloSea5), there is now an opportunity to use similar methodologies to forecast groundwater levels in more slowly responding aquifers on seasonal timescales. This study uses seasonal rainfall forecasts and a lumped groundwater model to simulate groundwater levels at 21 locations in the United Kingdom up to three months into the future. The results indicate that the forecasts have skill; outperforming a persistence forecast and demonstrating reliability, resolution and discrimination. However, there is currently little to gain from using seasonal rainfall forecasts over using site climatology for this type of application. Furthermore, the forecasts are not able to capture extreme groundwater levels, primarily because of inadequacies in the driving rainfall forecasts. The findings also show that the origin of forecast skill, be it from the meteorological input, groundwater model or initial condition, is site specific and related to the groundwater response characteristics to rainfall and antecedent hydro-meteorological conditions

Computing periodic orbits using the anti-integrable limit

Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. Using the Henon map as an example, we obtain a simple analytical bound on the domain of existence of the horseshoe that is equivalent to the well-known bound of Devaney and Nitecki. We also reformulate the popular method for finding periodic orbits introduced by Biham and Wenzel. Near an anti-integrable limit, we show that this method is guaranteed to converge. This formulation puts the choice of symbolic dynamics, required for the algorithm, on a firm foundation.Comment: 11 Pages Latex2e + 1 Figure (eps). Accepted for publication in Physics Lettes

AquiMod 2 User Manual

This user manual describes the second version of AquiMod (AquiMod 2), a simple lumped groundwater level simulation model. It covers all of the existing features of AquiMod and the new features in AquiMod 2. Experienced users will be familiar with much of the content of this user manual and will not need to read it in its entirety. Instead, they may wish to refer to the ‘Release Notes’ and ‘Checklist for moving from AquiMod to AquiMod 2’ sections which can be found at the front of this document, and which include links to the sections of the manual that are relevant to the new features. They may also wish to work through the two additional tutorials in this user manual which cover some of the new features in AquiMod 2 (sections 6.4 and 6.5). As well as the addition of tutorial material and descriptive text for new features, the text covering existing features has also been revised in some cases for the benefit of the reader. This includes, for example, revised mathematical notation to provide consistency across the different module components. All examples shown were undertaken on a computer running Windows 10 (64-bit). Consequently, some aspects of running AquiMod 2 may differ when using a different version of the Windows operating system

An approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom

We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of the transformation on nondegenerate Hamiltonians tend to degenerate ones on the critical surface. As a consequence, isoenergetically degenerate and nondegenerate Hamiltonians belong to the same universality class, and thus the corresponding critical invariant tori have the same type of scaling properties. We numerically investigate the structure of the attracting set on the critical surface and find that it is a strange nonchaotic attractor. We compute exponents that characterize its universality class.Comment: 10 pages typeset using REVTeX, 7 PS figure

Long-range forecasts of UK winter hydrology

Seasonal river flow forecasts are beneficial for planning agricultural activities, river navigation, and for management of reservoirs for public water supply and hydropower generation. In the United Kingdom (UK), skilful seasonal river flow predictions have previously been limited to catchments in lowland (southern and eastern) regions. Here we show that skilful long-range forecasts of winter flows can now be achieved across the whole of the UK. This is due to a remarkable geographical complementarity between the regional geological and meteorological sources of predictability for river flows. Forecast skill derives from the hydrogeological memory of antecedent conditions in southern and eastern parts of the UK and from meteorological predictability in northern and western areas. Specifically, it is the predictions of the atmospheric circulation over the North Atlantic that provides the skill at the seasonal timescale. In addition, significant levels of skill in predicting the frequency of winter high flow events is demonstrated, which has the potential to allow flood adaptation measures to be put in place