Large-scale length and time scales for use with stochastic convective parameterization

Many numerical models for weather prediction and climate studies are run at resolutions that are too coarse to resolve convection explicitly, but too fine to justify the local equilibrium assumed by conventional convective parameterizations. The Plant-Craig (PC) stochastic convective parameterization scheme, developed in this paper, solves this problem by removing the assumption that a given grid-scale situation must always produce the same sub-grid-scale convective response. Instead, for each timestep and gridpoint, one of the many possible convective responses consistent with the large-scale situation is randomly selected. The scheme requires as input the large-scale state as opposed to the instantaneous grid-scale state, but must nonetheless be able to account for genuine variations in the largescale situation. Here we investigate the behaviour of the PC scheme in three-dimensional simulations of radiative-convective equilibrium, demonstrating in particular that the necessary space-time averaging required to produce a good representation of the input large-scale state is not in conflict with the requirement to capture large-scale variations. The resulting equilibrium profiles agree well with those obtained from established deterministic schemes, and with corresponding cloud-resolving model simulations. Unlike the conventional schemes the statistics for mass flux and rainfall variability from the PC scheme also agree well with relevant theory and vary appropriately with spatial scale. The scheme is further shown to adapt automatically to changes in grid length and in forcing strength.

The precipitation climate of Central Asia: intercomparison of observational and numerical data sources in a remote semiarid region

In this study, we systematically compare a wide range of observational and numerical precipitation datasets for Central Asia. Data considered include two re-analyses, three datasets based on direct observations, and the output of a regional climate model simulation driven by a global re-analysis. These are validated and intercompared with respect to their ability to represent the Central Asian precipitation climate. In each of the datasets, we consider the mean spatial distribution and the seasonal cycle of precipitation, the amplitude of interannual variability, the representation of individual yearly anomalies, the precipitation sensitivity (i.e. the response to wet and dry conditions), and the temporal homogeneity of precipitation. Additionally, we carried out part of these analyses for datasets available in real time. The mutual agreement between the observations is used as an indication of how far these data can be used for validating precipitation data from other sources. In particular, we show that the observations usually agree qualitatively on anomalies in individual years while it is not always possible to use them for the quantitative validation of the amplitude of interannual variability. The regional climate model is capable of improving the spatial distribution of precipitation. At the same time, it strongly underestimates summer precipitation and its variability, while interannual variations are well represented during the other seasons, in particular in the Central Asian mountains during winter and spring

Stochastic parameterization: uncertainties from convection

In 2005, the ECMWF held a workshop on stochastic parameterisation, at which the convection was seen as being a key issue. That much is clear from the working group reports and particularly the statement from working group 1 that “it is clear that a stochastic convection scheme is desirable”. The present note aims to consider our current status in comparison with some of the issues raised and hopes expressed in that working group report.

Easing transition and promoting a positive student experience within an international partnership scheme for British and Chinese teachers

This article investigates the needs and challenges of a group of Chinese secondary school teachers in their transition to postgraduate studies in the UK in the context of a British-Chinese partnership. The strategies and efforts of the host institution, local community and the Chinese students themselves to help ease the transition and promote a positive student experience are discussed. The article highlights the sociological processes of international postgraduate student transition and contributes to our understanding of issues of student support pertinent to international partnership arrangements.

A study of the arrival over the United Kingdom in April 2010 of the Eyjafjallajökull ash cloud using ground-based lidar and numerical simulations

We make a qualitative and quantitative comparison of numericalsimulations of the ashcloud generated by the eruption of Eyjafjallajökull in April2010 with ground-basedlidar measurements at Exeter and Cardington in southern England. The numericalsimulations are performed using the Met Office’s dispersion model, NAME (Numerical Atmospheric-dispersion Modelling Environment). The results show that NAME captures many of the features of the observed ashcloud. The comparison enables us to estimate the fraction of material which survives the near-source fallout processes and enters into the distal plume. A number of simulations are performed which show that both the structure of the ashcloudover southern England and the concentration of ash within it are particularly sensitive to the height of the eruption column (and the consequent estimated mass emission rate), to the shape of the vertical source profile and the level of prescribed ‘turbulent diffusion’ (representing the mixing by the unresolved eddies) in the free troposphere with less sensitivity to the timing of the start of the eruption and the sedimentation of particulates in the distal plume.

Space heating and hot water demand analysis of dwellings connected to district heating scheme in UK

To achieve CO2 emissions reductions the UK Building Regulations require developers of new residential buildings to calculate expected CO2 emissions arising from their energy consumption using a methodology such as Standard Assessment Procedure (SAP 2005) or, more recently SAP 2009. SAP encompasses all domestic heat consumption and a limited proportion of the electricity consumption. However, these calculations are rarely verified with real energy consumption and related CO2 emissions. This paper presents the results of an analysis based on weekly head demand data for more than 200 individual flats. The data is collected from recently built residential development connected to a district heating network. A methodology for separating out the domestic hot water use (DHW) and space heating demand (SH) has been developed and compares measured values to the demand calculated using SAP 2005 and 2009 methodologies. The analysis shows also the variance in DHW and SH consumption between both size of the flats and tenure (privately owned or housing association). Evaluation of the space heating consumption includes also an estimation of the heating degree day (HDD) base temperature for each block of flats and its comparison to the average base temperature calculated using the SAP 2005 methodology.

Implementation of a new urban energy budget scheme into MetUM. Part II: Validation against observations and model intercomparison

In the first part of this article, we introduced a new urban surface scheme, the Met Office – Reading Urban Surface Exchange Scheme (MORUSES), into the Met Office Unified Model (MetUM) and compared its impact on the surface fluxes with respect to the current urban scheme. In this second part, we aim to analyze further the reasons behind the differences. This analysis is conducted by a comparison of the performance of the two schemes against observations and against a third model, the Single Column Reading Urban model (SCRUM). The key differences between the three models lie in how each model incorporates the heat stored in the urban fabric and how the surface-energy balance is coupled to the underlying substrate. The comparison of the models with observations from Mexico City reveals that the performance of MORUSES is improved if roof insulation is included by minimizing the roof thickness. A comparison of MORUSES and SCRUM reveals that, once insulation is included within MORUSES, these two models perform equally well against the observations overall, but that there are differences in the details of the simulations at the roof and canyon level. These differences are attributed to the different representations of the heat-storage term, specifically differences in the dominant frequencies captured by the urban canopy and substrate, between the models. These results strongly suggest a need for an urban model intercomparison exercise. Copyright © 2010 Royal Meteorological Society and Crown Copyright

Implementation of a new urban energy budget scheme in the MetUM. Part I: Description and idealized simulations

This paper describes the formulation of a new urban scheme, MORUSES (Met Office–Reading Urban Surface Exchange Scheme) for use in the Met Office Unified Model. The implementation of the new scheme ensures that (1) the new scheme offers more flexibility in the parametrization of the building properties, and hence provides a more realistic representation of the fluxes; (2) the bulk outputs are in satisfactory agreement with previous observational studies; and (3) the impact of the new scheme on the energy balance fluxes is similar to the impact of the current urban scheme when set up to mimic it. As well as having a better physical basis, MORUSES also gains in flexibility in applications and adaptations to different urban materials as well as urban planning. The new scheme represents the urban area as a composition of two tiles, a canyon and a roof, using a simple 2D geometry. Sensitivity analysis to canyon geometry and thickness of the roof canopy emphasizes the gain in flexibility captured by the new scheme. Copyright © 2010 Royal Meteorological Society and Crown Copyright

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

Producing leisure spaces out of thin air: the case of the Countryside Stewardship Scheme

This paper examines the growing dysfunction between the apparently increasing significance of diverse leisure practices in the countryside and the largely unchanging official response towards them. Although there is recognition in the recent rural White Paper (DOE and MAFF, 1995) that access is essential to enjoying the countryside, the construction of this term is dubious, since paid access agreements, based on producer requirements, are favoured over any form of demand-driven freedom to roam. Using the Countryside Stewardship Scheme (CSS) as an example of the incentive structure developed to promote this policy, the paper applies Plato's simulacrum as a reading of how this process is being utilised to underpin the dominant rights associated with rural property interests. In particular, the paper makes the point that rather than representing the corollary of a market situation, as its supporters claim, the CSS involves government grant for the eclectic provision of short term licences over ground which remains unmapped as anything other than its continued agricultural use. In concluding, the paper asserts that rather than representing an increase in the availability of leisure sites in the countryside, the CSS and other schemes represent a diversion from the wider and deeper socio-cultural process of continued wealth and power redistribution.

Estimation of systematic error in an equatorial ocean model using data assimilation

Assimilation of temperature observations into an ocean model near the equator often results in a dynamically unbalanced state with unrealistic overturning circulations. The way in which these circulations arise from systematic errors in the model or its forcing is discussed. A scheme is proposed, based on the theory of state augmentation, which uses the departures of the model state from the observations to update slowly evolving bias fields. Results are summarized from an experiment applying this bias correction scheme to an ocean general circulation model. They show that the method produces more balanced analyses and a better fit to the temperature observations.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Numerical Methods for Stiff Two-Point Boundary Value Problems

We consider the two-point boundary value problem for stiff systems of ordinary differential equations. For systems that can be transformed to essentially diagonally dominant form with appropriate smoothness conditions, a priori estimates are obtained. Problems with turning points can be treated with this theory, and we discuss this in detail. We give robust difference approximations and present error estimates for these schemes. In particular we give a detailed description of how to transform a general system to essentially diagonally dominant form and then stretch the independent variable so that the system will satisfy the correct smoothness conditions. Numerical examples are presented for both linear and nonlinear problems.