Joint importance of multistate systems

Importance measures in reliability engineering are used to identify weak areas of a system and signify the roles of components in either causing or contributing to proper functioning of the system. Traditional importance measures for multistate systems mainly concern reliability importance of an individual component and seldom consider the utility performance of the systems. This paper extends the joint importance concepts of two components from the binary system case to the multistate system case. A joint structural importance and a joint reliability importance are defined on the basis of the performance utility of the system. The joint structural importance measures the relationship of two components when the reliabilities of components are not available. The joint reliability importance is inferred when the reliabilities of the components are given. The properties of the importance measures are also investigated. A case study for an offshore electrical power generation system is given.

Decreased frequency of North Atlantic polar lows associated with future climate warming

Every winter, the high-latitude oceans are struck by severe storms that are considerably smaller than the weather-dominating synoptic depressions1. Accompanied by strong winds and heavy precipitation, these often explosively developing mesoscale cyclones—termed polar lows1—constitute a threat to offshore activities such as shipping or oil and gas exploitation. Yet owing to their small scale, polar lows are poorly represented in the observational and global reanalysis data2 often used for climatological investigations of atmospheric features and cannot be assessed in coarse-resolution global simulations of possible future climates. Here we show that in a future anthropogenically warmed climate, the frequency of polar lows is projected to decline. We used a series of regional climate model simulations to downscale a set of global climate change scenarios3 from the Intergovernmental Panel of Climate Change. In this process, we first simulated the formation of polar low systems in the North Atlantic and then counted the individual cases. A previous study4 using NCEP/NCAR re-analysis data5 revealed that polar low frequency from 1948 to 2005 did not systematically change. Now, in projections for the end of the twenty-first century, we found a significantly lower number of polar lows and a northward shift of their mean genesis region in response to elevated atmospheric greenhouse gas concentration. This change can be related to changes in the North Atlantic sea surface temperature and mid-troposphere temperature; the latter is found to rise faster than the former so that the resulting stability is increased, hindering the formation or intensification of polar lows. Our results provide a rare example of a climate change effect in which a type of extreme weather is likely to decrease, rather than increase.

Sea-breeze modification of the growth of a marine internal boundary layer

A numerical mesoscale model is used to make a high-resolution simulation of the marine boundary layer in the Persian Gulf, during conditions of offshore flow from Saudi Arabia. A marine internal boundary layer (MIBL) and a sea-breeze circulation (SBC) are found to co-exist. The sea breeze develops in the mid-afternoon, at which time its front is displaced several tens of kilometres offshore. Between the coast and the sea-breeze system, the MIBL that occurs is consistent with a picture described in the existing literature. However, the MIBL is perturbed by the SBC, the boundary layer deepening significantly seaward of the sea-breeze front. Our analysis suggests that this strong, localized deepening is not a direct consequence of frontal uplift, but rather that the immediate cause is the retardation of the prevailing, low-level offshore wind by the SBC. The simulated boundary-layer development can be accounted for by using a simple 1D Lagrangian model of growth driven by the surface heat flux. This model is obtained as a straightforward modification of an established MIBL analytic growth model.

Renewable energy in the UK countryside: policy and practice

Of the technologies currently available for producing energy from renewable sources in the British climate all except one depend on a single ingredient, namely land. Therefore other than offshore wind generation, which has been slow and expensive to establish, renewables have had to be derived almost entirely from the land, whether as sites for turbines or areas on which to grow feedstocks for biomass and biofuels. Of these, only wind turbines have been developed in any number while economic conditions have until now been unfavourable for biomass and biofuel. The UK is unlikely to meet its present targets under the Kyoto agreement, due to a mixture of limited funding and problems of policy. Peter Prag examines the present position and the potential outlook.

A ‘Boscastle-type’ quasi-stationary convective system over the UK Southwest Peninsula

An investigation is presented of a quasi-stationary convective system (QSCS) which occurred over the UK Southwest Peninsula on 21 July 2010. This system was remarkably similar in its location and structure to one which caused devastating flash flooding in the coastal village of Boscastle, Cornwall on 16 August 2004. However, in the 2010 case rainfall accumulations were around four times smaller and no flooding was recorded. The more extreme nature of the Boscastle case is shown to be related to three factors: (1) higher rain rates, associated with a warmer and moister tropospheric column and deeper convective clouds; (2) a more stationary system, due to slower evolution of the large-scale flow; and (3) distribution of the heaviest precipitation over fewer river catchments. Overall, however, the synoptic setting of the two events was broadly similar, suggesting that such conditions favour the development of QSCSs over the Southwest Peninsula. A numerical simulation of the July 2010 event was performed using a 1.5-km grid length configuration of the Met Office Unified Model. This reveals that convection was repeatedly initiated through lifting of low-level air parcels along a quasi-stationary coastal convergence line. Sensitivity tests are used to show that this convergence line was a sea breeze front which temporarily stalled along the coastline due to the retarding influence of an offshore-directed background wind component. Several deficiencies are noted in the 1.5-km model’s representation of the storm system, including delayed convective initiation; however, significant improvements are observed when the grid length is reduced to 500 m. These result in part from an improved representation of the convergence line, which enhances the associated low-level ascent allowing air parcels to more readily reach their level of free convection. The implications of this finding for forecasting convective precipitation are discussed.

Stable isotope and modelling evidence for CO2 as a driver of glacial–interglacial vegetation shifts in southern Africa

Atmospheric CO2 concentration is hypothesized to influence vegetation distribution via tree–grass competition, with higher CO2 concentrations favouring trees. The stable carbon isotope (δ13C) signature of vegetation is influenced by the relative importance of C4 plants (including most tropical grasses) and C3 plants (including nearly all trees), and the degree of stomatal closure – a response to aridity – in C3 plants. Compound-specific δ13C analyses of leaf-wax biomarkers in sediment cores of an offshore South Atlantic transect are used here as a record of vegetation changes in subequatorial Africa. These data suggest a large increase in C3 relative to C4 plant dominance after the Last Glacial Maximum. Using a process-based biogeography model that explicitly simulates 13C discrimination, it is shown that precipitation and temperature changes cannot explain the observed shift in δ13C values. The physiological effect of increasing CO2 concentration is decisive, altering the C3/C4 balance and bringing the simulated and observed δ13C values into line. It is concluded that CO2 concentration itself was a key agent of vegetation change in tropical southern Africa during the last glacial–interglacial transition. Two additional inferences follow. First, long-term variations in terrestrial δ13Cvalues are not simply a proxy for regional rainfall, as has sometimes been assumed. Although precipitation and temperature changes have had major effects on vegetation in many regions of the world during the period between the Last Glacial Maximum and recent times, CO2 effects must also be taken into account, especially when reconstructing changes in climate between glacial and interglacial states. Second, rising CO2 concentration today is likely to be influencing tree–grass competition in a similar way, and thus contributing to the "woody thickening" observed in savannas worldwide. This second inference points to the importance of experiments to determine how vegetation composition in savannas is likely to be influenced by the continuing rise of CO2 concentration.

A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications

A model for the consolidation of rafted sea ice

Rafting is one of the important deformation mechanisms of sea ice. This process is widespread in the north Caspian Sea, where multiple rafting produces thick sea ice features, which are a hazard to offshore operations. Here we present a one-dimensional, thermal consolidation model for rafted sea ice. We consider the consolidation between the layers of both a two-layer and a three-layer section of rafted sea ice. The rafted ice is assumed to be composed of layers of sea ice of equal thickness, separated by thin layers of ocean water. Results show that the thickness of the liquid layer reduced asymptotically with time, such that there always remained a thin saline liquid layer. We propose that when the liquid layer is equal to the surface roughness the adjacent layers can be considered consolidated. Using parameters representative of the north Caspian, the Arctic, and the Antarctic, our results show that for a choice of standard parameters it took under 15 h for two layers of rafted sea ice to consolidate. Sensitivity studies showed that the consolidation model is highly sensitive to the initial thickness of the liquid layer, the fraction of salt release during freezing, and the height of the surface asperities. We believe that further investigation of these parameters is needed before any concrete conclusions can be drawn about rate of consolidation of rafted sea ice features.

Generation of a buoyancy-driven coastal current by an Antarctic Polynya

Descent and spreading of high salinity water generated by salt rejection during sea ice formation in an Antarctic coastal polynya is studied using a hydrostatic, primitive equation three-dimensional ocean model called the Proudman Oceanographic Laboratory Coastal Ocean Modeling System (POLCOMS). The shape of the polynya is assumed to be a rectangle 100 km long and 30 km wide, and the salinity flux into the polynya at its surface is constant. The model has been run at high horizontal spatial resolution (500 m), and numerical simulations reveal a buoyancy-driven coastal current. The coastal current is a robust feature and appears in a range of simulations designed to investigate the influence of a sloping bottom, variable bottom drag, variable vertical turbulent diffusivities, higher salinity flux, and an offshore position of the polynya. It is shown that bottom drag is the main factor determining the current width. This coastal current has not been produced with other numerical models of polynyas, which may be because these models were run at coarser resolutions. The coastal current becomes unstable upstream of its front when the polynya is adjacent to the coast. When the polynya is situated offshore, an unstable current is produced from its outset owing to the capture of cyclonic eddies. The effect of a coastal protrusion and a canyon on the current motion is investigated. In particular, due to the convex shape of the coastal protrusion, the current sheds a dipolar eddy.

Validity of the ice shelf water plume concept beneath Filchner-Ronne Ice Shelf

In winter, brine rejection from sea ice formation and export in the Weddell Sea, offshore of Filchner-Ronne Ice Shelf (FRIS), leads to the formation of High Salinity Shelf Water (HSSW). This dense water mass enters the cavity beneath FRIS by sinking southward down the sloping continental shelf towards the grounding line. Melting occurs when the HSSW encounters the ice shelf, and the meltwater released cools and freshens the HSSW to form a water mass known as Ice Shelf Water (ISW). If this ISW rises, the ‘ice pump’ is initiated (Lewis and Perkin, 1986), whereby the ascending ISW becomes supercooled and deposits marine ice at shallower locations due to the pressure increase in the in-situ freezing temperature. Sandh¨ager et al. (2004) were able to infer the thickness patterns of marine ice deposits at the base of FRIS (figure 1), so the primary aim of this work is to try to understand the ocean flows that determine these patterns. The plume model we use to investigate ISW flow is described fully by Holland and Feltham (accepted) so only a relatively brief outline is presented here. The plume is simulated by combining a parameterisation of ice shelf basal interaction and a multiplesize- class frazil dynamics model with an unsteady, depth-averaged reduced-gravity plume model. In the model an active region of ISW evolves above and within an expanse of stagnant ambient fluid, which is considered to be ice-free and has fixed profiles of temperature and salinity. The two main assumptions of the model are that there is a well-mixed layer underneath the ice shelf and that the ambient fluid outside the plume is stagnant with fixed properties. The topography of the ice shelf that the plume flows beneath is set to the FRIS ice shelf draft calculated by Sandh¨ager et al. (2004) masked with the grounding line from the Antarctic Digital Database (ADD Consortium, 2002). To initiate the plumes, we assume that the intrusion of dense HSSW initially causes melting at the points on the grounding line where the glaciological tributaries feeding FRIS go afloat.

Mid-Holocene and glacial-maximum vegetation geography of the northern continents and Africa.

BIOME 6000 is an international project to map vegetation globally at mid-Holocene (6000 14C yr bp) and last glacial maximum (LGM, 18,000 14C yr bp), with a view to evaluating coupled climate-biosphere model results. Primary palaeoecological data are assigned to biomes using an explicit algorithm based on plant functional types. This paper introduces the second Special Feature on BIOME 6000. Site-based global biome maps are shown with data from North America, Eurasia (except South and Southeast Asia) and Africa at both time periods. A map based on surface samples shows the method’s skill in reconstructing present-day biomes. Cold and dry conditions at LGM favoured extensive tundra and steppe. These biomes intergraded in northern Eurasia. Northern hemisphere forest biomes were displaced southward. Boreal evergreen forests (taiga) and temperate deciduous forests were fragmented, while European and East Asian steppes were greatly extended. Tropical moist forests (i.e. tropical rain forest and tropical seasonal forest) in Africa were reduced. In south-western North America, desert and steppe were replaced by open conifer woodland, opposite to the general arid trend but consistent with modelled southward displacement of the jet stream. The Arctic forest limit was shifted slighly north at 6000 14C yr bp in some sectors, but not in all. Northern temperate forest zones were generally shifted greater distances north. Warmer winters as well as summers in several regions are required to explain these shifts. Temperate deciduous forests in Europe were greatly extended, into the Mediterranean region as well as to the north. Steppe encroached on forest biomes in interior North America, but not in central Asia. Enhanced monsoons extended forest biomes in China inland and Sahelian vegetation into the Sahara while the African tropical rain forest was also reduced, consistent with a modelled northward shift of the ITCZ and a more seasonal climate in the equatorial zone. Palaeobiome maps show the outcome of separate, independent migrations of plant taxa in response to climate change. The average composition of biomes at LGM was often markedly different from today. Refugia for the temperate deciduous and tropical rain forest biomes may have existed offshore at LGM, but their characteristic taxa also persisted as components of other biomes. Examples include temperate deciduous trees that survived in cool mixed forest in eastern Europe, and tropical evergreen trees that survived in tropical seasonal forest in Africa. The sequence of biome shifts during a glacial-interglacial cycle may help account for some disjunct distributions of plant taxa. For example, the now-arid Saharan mountains may have linked Mediterranean and African tropical montane floras during enhanced monsoon regimes. Major changes in physical land-surface conditions, shown by the palaeobiome data, have implications for the global climate. The data can be used directly to evaluate the output of coupled atmosphere-biosphere models. The data could also be objectively generalized to yield realistic gridded land-surface maps, for use in sensitivity experiments with atmospheric models. Recent analyses of vegetation-climate feedbacks have focused on the hypothesized positive feedback effects of climate-induced vegetation changes in the Sahara/Sahel region and the Arctic during the mid-Holocene. However, a far wider spectrum of interactions potentially exists and could be investigated, using these data, both for 6000 14C yr bp and for the LGM.

A case study of sea breeze blocking regulated by sea surface temperature along the English south coast

The sensitivity of sea breeze structure to sea surface temperature (SST) and coastal orography is investigated in convection-permitting Met Office Unified Model simulations of a case study along the south coast of England. Changes in SST of 1 K are shown to significantly modify the structure of the sea breeze immediately offshore. On the day of the case study, the sea breeze was partially blocked by coastal orography, particularly within Lyme Bay. The extent to which the flow is blocked depends strongly on the static stability of the marine boundary layer. In experiments with colder SST, the marine boundary layer is more stable, and the degree of blocking is more pronounced. Although a colder SST would also imply a larger land–sea temperature contrast and hence a stronger onshore wind – an effect which alone would discourage blocking – the increased static stability exerts a dominant control over whether blocking takes place. The implications of prescribing fixed SST from climatology in numerical weather prediction model forecasts of the sea breeze are discussed.

The Madden-Julian Oscillation and the diurnal cycle over the Maritime Continent: scale interactions and modelling

The Maritime Continent archipelago, situated on the equator at 95-165E, has the strongest land-based precipitation on Earth. The latent heat release associated with the rainfall affects the atmospheric circulation throughout the tropics and into the extra-tropics. The greatest source of variability in precipitation is the diurnal cycle. The archipelago is within the convective region of the Madden-Julian Oscillation (MJO), which provides the greatest variability on intra-seasonal time scales: large-scale (∼10^7 km^2) active and suppressed convective envelopes propagate slowly (∼5 m s^-1) eastwards between the Indian and Pacific Oceans. High-resolution satellite data show that a strong diurnal cycle is triggered to the east of the advancing MJO envelope, leading the active MJO by one-eighth of an MJO cycle (∼6 days). Where the diurnal cycle is strong its modulation accounts for 81% of the variability in MJO precipitation. Over land this determines the structure of the diagnosed MJO. This is consistent with the equatorial wave dynamics in existing theories of MJO propagation. The MJO also affects the speed of gravity waves propagating offshore from the Maritime Continent islands. This is largely consistent with changes in static stability during the MJO cycle. The MJO and its interaction with the diurnal cycle are investigated in HiGEM, a high-resolution coupled model. Unlike many models, HiGEM represents the MJO well with eastward-propagating variability on intra-seasonal time scales at the correct zonal wavenumber, although the inter-tropical convergence zone's precipitation peaks strongly at the wrong time, interrupting the MJO's spatial structure. However, the modelled diurnal cycle is too weak and its phase is too early over land. The modulation of the diurnal amplitude by the MJO is also too weak and accounts for only 51% of the variability in MJO precipitation. Implications for forecasting and possible causes of the model errors are discussed, and further modelling studies are proposed.

Wave height analysis from 10 years of observations in the Norwegian Sea

Large waves pose risks to ships, offshore structures, coastal infrastructure and ecosystems. This paper analyses 10 years of in-situ measurements of significant wave height (Hs) and maximum wave height (Hmax) from the ocean weather ship Polarfront in the Norwegian Sea. During the period 2000 to 2009, surface elevation was recorded every 0.59 s during sampling periods of 30 min. The Hmax observations scale linearly with Hs on average. A widely-used empirical Weibull distribution is found to estimate average values of Hmax/Hs and Hmax better than a Rayleigh distribution, but tends to underestimate both for all but the smallest waves. In this paper we propose a modified Rayleigh distribution which compensates for the heterogeneity of the observed dataset: the distribution is fitted to the whole dataset and improves the estimate of the largest waves. Over the 10-year period, the Weibull distribution approximates the observed Hs and Hmax well, and an exponential function can be used to predict the probability distribution function of the ratio Hmax/Hs. However, the Weibull distribution tends to underestimate the occurrence of extremely large values of Hs and Hmax. The persistence of Hs and Hmax in winter is also examined. Wave fields with Hs>12 m and Hmax>16 m do not last longer than 3 h. Low-to-moderate wave heights that persist for more than 12 h dominate the relationship of the wave field with the winter NAO index over 2000–2009. In contrast, the inter-annual variability of wave fields with Hs>5.5 m or Hmax>8.5 m and wave fields persisting over ~2.5 days is not associated with the winter NAO index.