A moving point approach to model shallow ice sheets: a study case with radially-symmetrical ice sheets

Predicting the evolution of ice sheets requires numerical models able to accurately track the migration of ice sheet continental margins or grounding lines. We introduce a physically based moving point approach for the flow of ice sheets based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly and the waiting time behaviours to be modelled efficiently. A finite difference moving point scheme is derived and applied in a simplified context (continental radially-symmetrical shallow ice approximation). The scheme, which is inexpensive, is validated by comparing the results with moving-margin exact solutions and steady states. In both cases the scheme is able to track the position of the ice sheet margin with high precision.

A joint state and parameter estimation scheme for nonlinear dynamical systems

We present a novel algorithm for concurrent model state and parameter estimation in nonlinear dynamical systems. The new scheme uses ideas from three dimensional variational data assimilation (3D-Var) and the extended Kalman filter (EKF) together with the technique of state augmentation to estimate uncertain model parameters alongside the model state variables in a sequential filtering system. The method is relatively simple to implement and computationally inexpensive to run for large systems with relatively few parameters. We demonstrate the efficacy of the method via a series of identical twin experiments with three simple dynamical system models. The scheme is able to recover the parameter values to a good level of accuracy, even when observational data are noisy. We expect this new technique to be easily transferable to much larger models.

Noether-type discrete conserved quantities arising from a finite element approximation of a variational problem

In this work, we prove a weak Noether-type Theorem for a class of variational problems that admit broken extremals. We use this result to prove discrete Noether-type conservation laws for a conforming finite element discretisation of a model elliptic problem. In addition, we study how well the finite element scheme satisfies the continuous conservation laws arising from the application of Noether’s first theorem (1918). We summarise extensive numerical tests, illustrating the conservation of the discrete Noether law using the p-Laplacian as an example and derive a geometric-based adaptive algorithm where an appropriate Noether quantity is the goal functional.

A moving-point approach to model shallow ice sheets: a study case with radially symmetrical ice sheets

Predicting the evolution of ice sheets requires numerical models able to accurately track the migration of ice sheet continental margins or grounding lines. We introduce a physically based moving-point approach for the flow of ice sheets based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly. Our approach is also well suited to capture waiting-time behaviour efficiently. A finite-difference moving-point scheme is derived and applied in a simplified context (continental radially symmetrical shallow ice approximation). The scheme, which is inexpensive, is verified by comparing the results with steady states obtained from an analytic solution and with exact moving-margin transient solutions. In both cases the scheme is able to track the position of the ice sheet margin with high accuracy.

The impact of a thermodynamic sea-ice module in the COSMO numerical weather prediction model on simulations for the Laptev Sea, Siberian Arctic

Previous versions of the Consortium for Small-scale Modelling (COSMO) numerical weather prediction model have used a constant sea-ice surface temperature, but observations show a high degree of variability on sub-daily timescales. To account for this, we have implemented a thermodynamic sea-ice module in COSMO and performed simulations at a resolution of 15 km and 5 km for the Laptev Sea area in April 2008. Temporal and spatial variability of surface and 2-m air temperature are verified by four automatic weather stations deployed along the edge of the western New Siberian polynya during the Transdrift XIII-2 expedition and by surface temperature charts derived from Moderate Resolution Imaging Spectroradiometer (MODIS) satellite data. A remarkable agreement between the new model results and these observations demonstrates that the implemented sea-ice module can be applied for short-range simulations. Prescribing the polynya areas daily, our COSMO simulations provide a high-resolution and high-quality atmospheric data set for the Laptev Sea for the period 14-30 April 2008. Based on this data set, we derive a mean total sea-ice production rate of 0.53 km3/day for all Laptev Sea polynyas under the assumption that the polynyas are ice-free and a rate of 0.30 km3/day if a 10-cm-thin ice layer is assumed. Our results indicate that ice production in Laptev Sea polynyas has been overestimated in previous studies.

Impact of cyclones on sea ice in the Fram Strait: numerical simulations and observations

The sea ice export from the Arctic is of global importance due to its fresh water which influences the oceanic stratification and, thus, the global thermohaline circulation. This study deals with the effect of cyclones on sea ice and sea ice transport in particular on the basis of observations from two field experiments FRAMZY 1999 and FRAMZY 2002 in April 1999 and March 2002 as well as on the basis of simulations with a numerical sea ice model. The simulations realised by a dynamic-thermodynamic sea ice model are forced with 6-hourly atmospheric ECMWF- analyses (European Centre for Medium-Range Weather Forecasts) and 6-hourly oceanic data of a MPI-OM-simulation (Max-Planck-Institute Ocean Model). Comparing the observed and simulated variability of the sea ice drift and of the position of the ice edge shows that the chosen configuration of the model is appropriate for the performed studies. The seven observed cyclones change the position of the ice edge up to 100 km and cause an extensive decrease of sea ice coverage by 2 % up to more than 10 %. The decrease is only simulated by the model if the ocean current is strongly divergent in the centre of the cyclone. The impact is remarkable of the ocean current on divergence and shear deformation of the ice drift. As shown by sensitivity studies the ocean current at a depth of 6 m – the sea ice model is forced with – is mainly responsible for the ascertained differences between simulation and observation. The simulated sea ice transport shows a strong variability on a time scale from hours to days. Local minima occur in the time series of the ice transport during periods with Fram Strait cyclones. These minima are not caused by the local effect of the cyclone’s wind field, but mainly by the large-scale pattern of surface pressure. A displacement of the areas of strongest cyclone activity in the Nordic Seas would considerably influence the ice transport.

Impacts of parameterized orographic drag on the Northern Hemisphere winter circulation

A recent intercomparison exercise proposed by the Working Group for Numerical Experimentation (WGNE) revealed that the parameterized, or unresolved, surface stress in weather forecast models is highly model-dependent, especially over orography. Models of comparable resolution differ over land by as much as 20% in zonal mean total subgrid surface stress (Ttot). The way Ttot is partitioned between the different parameterizations is also model-dependent. In this study, we simulated in a particular model an increase in Ttot comparable with the spread found in the WGNE intercomparison. This increase was simulated in two ways, namely by increasing independently the contributions to Ttot of the turbulent orographic form drag scheme (TOFD) and of the orographic low-level blocking scheme (BLOCK). Increasing the parameterized orographic drag leads to significant changes in surface pressure, zonal wind and temperature in the Northern Hemisphere during winter both in 10 day weather forecasts and in seasonal integrations. However, the magnitude of these changes in circulation strongly depends on which scheme is modified. In 10 day forecasts, stronger changes are found when the TOFD stress is increased, while on seasonal time scales the effects are of comparable magnitude, although different in detail. At these time scales, the BLOCK scheme affects the lower stratosphere winds through changes in the resolved planetary waves which are associated with surface impacts, while the TOFD effects are mostly limited to the lower troposphere. The partitioning of Ttot between the two schemes appears to play an important role at all time scales.

Pension scheme redesign and wealth redistribution between the members and sponsor: the USS rule change in October 2011

The redesign of defined benefit pension schemes usually results in a substantial redistribution of wealth between age cohorts of members, pensioners, and the sponsor. This is the first study to quantify the redistributive effects of a rule change by a real world scheme (the Universities Superannuation Scheme, USS) where the sponsor underwrites the pension promise. In October 2011 USS closed its final salary scheme to new members, opened a career average revalued earnings (CARE) section, and moved to ‘cap and share’ contribution rates. We find that the pre-October 2011 scheme was not viable in the long run, while the post-October 2011 scheme is probably viable in the long run, but faces medium term problems. In October 2011 future members of USS lost 65% of their pension wealth (or roughly £100,000 per head), equivalent to a reduction of roughly 11% in their total compensation, while those aged over 57 years lost almost nothing. The riskiness of the pension wealth of future members increased by a third, while the riskiness of the present value of the sponsor’s future contributions reduced by 10%. Finally, the sponsor’s wealth increased by about £32.5 billion, equivalent to a reduction of 26% in their pension costs.

Essays on robust portfolio selection and pension finance

This thesis examines three different, but related problems in the broad area of portfolio management for long-term institutional investors, and focuses mainly on the case of pension funds. The first idea (Chapter 3) is the application of a novel numerical technique – robust optimization – to a real-world pension scheme (the Universities Superannuation Scheme, USS) for first time. The corresponding empirical results are supported by many robustness checks and several benchmarks such as the Bayes-Stein and Black-Litterman models that are also applied for first time in a pension ALM framework, the Sharpe and Tint model and the actual USS asset allocations. The second idea presented in Chapter 4 is the investigation of whether the selection of the portfolio construction strategy matters in the SRI industry, an issue of great importance for long term investors. This study applies a variety of optimal and naïve portfolio diversification techniques to the same SRI-screened universe, and gives some answers to the question of which portfolio strategies tend to create superior SRI portfolios. Finally, the third idea (Chapter 5) compares the performance of a real-world pension scheme (USS) before and after the recent major changes in the pension rules under different dynamic asset allocation strategies and the fixed-mix portfolio approach and quantifies the redistributive effects between various stakeholders. Although this study deals with a specific pension scheme, the methodology can be applied by other major pension schemes in countries such as the UK and USA that have changed their rules.

Surface Urban Energy and Water Balance Scheme (SUEWS): development and evaluation at two UK sites

The Surface Urban Energy and Water Balance Scheme (SUEWS) is evaluated at two locations in the UK: a dense urban site in the centre of London and a residential suburban site in Swindon. Eddy covariance observations of the turbulent fluxes are used to assess model performance over a twoyear period (2011-2013). The distinct characteristics of the sites mean their surface energy exchanges differ considerably. The model suggests the largest differences can be attributed to surface cover (notably the proportion of vegetated versus impervious area) and the additional energy supplied by human activities. SUEWS performs better in summer than winter, and better at the suburban site than the dense urban site. One reason for this is the bias towards suburban summer field campaigns in observational data used to parameterise this (and other) model(s). The suitability of model parameters (such as albedo, energy use and water use) for the UK sites is considered and, where appropriate, alternative values are suggested. An alternative parameterisation for the surface conductance is implemented, which permits greater soil moisture deficits before evaporation is restricted at non-irrigated sites. Accounting for seasonal variation in the estimation of storage heat flux is necessary to obtain realistic wintertime fluxes.

Evaluation of the Plant–Craig stochastic convection scheme (v2.0) in the ensemble forecasting system MOGREPS-R (24 km) based on the Unified Model (v7.3)

The Plant–Craig stochastic convection parameterization (version 2.0) is implemented in the Met Office Regional Ensemble Prediction System (MOGREPS-R) and is assessed in comparison with the standard convection scheme with a simple stochastic scheme only, from random parameter variation. A set of 34 ensemble forecasts, each with 24 members, is considered, over the month of July 2009. Deterministic and probabilistic measures of the precipitation forecasts are assessed. The Plant–Craig parameterization is found to improve probabilistic forecast measures, particularly the results for lower precipitation thresholds. The impact on deterministic forecasts at the grid scale is neutral, although the Plant–Craig scheme does deliver improvements when forecasts are made over larger areas. The improvements found are greater in conditions of relatively weak synoptic forcing, for which convective precipitation is likely to be less predictable.

Mobile sink based fault diagnosis scheme for wireless sensor networks

Network diagnosis in Wireless Sensor Networks (WSNs) is a difficult task due to their improvisational nature, invisibility of internal running status, and particularly since the network structure can frequently change due to link failure. To solve this problem, we propose a Mobile Sink (MS) based distributed fault diagnosis algorithm for WSNs. An MS, or mobile fault detector is usually a mobile robot or vehicle equipped with a wireless transceiver that performs the task of a mobile base station while also diagnosing the hardware and software status of deployed network sensors. Our MS mobile fault detector moves through the network area polling each static sensor node to diagnose the hardware and software status of nearby sensor nodes using only single hop communication. Therefore, the fault detection accuracy and functionality of the network is significantly increased. In order to maintain an excellent Quality of Service (QoS), we employ an optimal fault diagnosis tour planning algorithm. In addition to saving energy and time, the tour planning algorithm excludes faulty sensor nodes from the next diagnosis tour. We demonstrate the effectiveness of the proposed algorithms through simulation and real life experimental results.

THE CO-INFLUENCE OF THE SEA BREEZE AND THE COASTAL UPWELLING AT CABO FRIO: A NUMERICAL INVESTIGATION USING COUPLED MODELS

A coupled atmospheric-oceanic model was used to investigate whether there is a positive feedback between the coastal upwelling and the sea breeze at Cabo Frio - RJ (Brazil). Two experiments were performed to ascertain the influence of the sea breeze on the coastal upwelling: the first one used the coupled model forced with synoptic NE winds of 8 m s(-1) and the sign of the sea breeze circulation was set by the atmospheric model; the second experiment used only the oceanic model with constant 8 m s(-1) NE winds. Then, to study the influence of the coastal upwelling on the sea breeze, two more experiments were performed: one using a coastal upwelling representative SST initial field and the other one using a constant and homogeneous SST field of 26 degrees C. Finally, two more experiments were conducted to verify the influence of the topography and the spatial distribution of the sea surface temperature on the previous results. The results showed that the sea breeze can intensify the coastal upwelling, but the coastal upwelling does not intensify the sea breeze circulation, suggesting that there is no positive feedback between these two phenomena at Cabo Frio.

Modeling study of the aspect ratio influence on urban canopy energy fluxes with a modified wall-canyon energy budget scheme

The influence of the aspect ratio (building height/street canyon width) and the mean building height of cities on local energy fluxes and temperatures is studied by means of an Urban Canopy Model (UCM) coupled with a one-dimensional second-order turbulence closure model. The UCM presented is similar to the Town Energy Balance (TEB) model in most of its features but differs in a few important aspects. In particular, the street canyon walls are treated separately which leads to a different budget of radiation within the street canyon walls. The UCM has been calibrated using observations of incoming global and diffuse solar radiation, incoming long-wave radiation and air temperature at a site in So Paulo, Brazil. Sensitivity studies with various aspect ratios have been performed to assess their impact on urban temperatures and energy fluxes at the top of the canopy layer. In these simulations, it is assumed that the anthropogenic heat flux and latent heat fluxes are negligible. Results show that the simulated net radiation and sensible heat fluxes at the top of the canopy decrease and the stored heat increases as the aspect ratio increases. The simulated air temperature follows the behavior of the sensible heat flux. (C) 2010 Elsevier Ltd. All rights reserved.

Formulation of a tropical town energy budget (t-TEB) scheme

This work describes the tropical town energy budget (t-TEB) scheme addressed to simulate the diurnal occurrence of the urban heat island (UHI) as observed in the Metropolitan Area of Rio de Janeiro (MARJ; -22A degrees S; -44A degrees W) in Brazil. Reasoning about the tropical urban climate have guided the scheme implementation, starting from the original equations from Masson (Bound-Lay Meteorol 94:357-397, 2000). The modifications include (a) local scaling approaches for obtaining flux-gradient relationships in the roughness sub-layer, (b) the Monin-Obukhov similarity framework in the inertial sub-layer, (c) increasing aerodynamic conductance toward more unstable conditions, and (d) a modified urban subsurface drainage system to transfer the intercepted rainwater by roofs to the roads. Simulations along 2007 for the MARJ are obtained and compared with the climatology. The t-TEB simulation is consistent with the observations, suggesting that the timing and dynamics of the UHI in tropical cities could vary significantly from the familiar patterns observed in mid-latitude cities-with the peak heat island intensity occurring in the morning than at night. The simulations are suggesting that the thermal phase shift of this tropical diurnal UHI is a response of the surface energy budget to the large amount of solar radiation, intense evapotranspiration, and thermal response of the vegetated surfaces over a very humid soil layer.