On the existence of extreme waves and the Stokes conjecture with vorticity

This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a corner of 120° or a horizontal tangent at any stagnation point about which it is supposed symmetric. Moreover, the profile necessarily has a corner of 120° if the vorticity is nonnegative near the free surface.

Sting jets in simulations of a real cyclone by two mesoscale models

The existence of sting jets as a potential source of damaging surface winds during the passage of extratropical cyclones has recently been recognized However, there are still very few published studies on the subject Furthermore, although ills known that other models are capable of reproducing sting jets, in the published literature only one numerical model [the Met Office Unified Model (MetUM)] has been used to numerically analyze these phenomena This article alms to improve our understanding of the processes that contribute to the development of sting jets and show that model differences affect the evolution of modeled sting jets A sting jet event during the passage of a cyclone over the United Kingdom on 26 February 2002 has been simulated using two mesoscale models namely the MetUM and the Consortium for Small Scale Modeling (COSMO) model to compare their performance Given the known critical importance of vertical resolution in the simulation of sting jets the vertical resolution of both models has been enhanced with respect to their operational versions Both simulations have been verified against surface measurements of maximum gusts, satellite imagery and Met Office operational synoptic analyses, as well as operational analyses from the ECMWF It is shown that both models are capable of reproducing sting jets with similar, though not identical. features Through the comparison of the results from these two models, the relevance of physical mechanisms, such as evaporative cooling and the release of conditional symmetric instability, in the generation and evolution of sting jets is also discussed

Characterising the variability and extremes of the stratospheric polar vortices using 2D moment analysis

The mean state, variability and extreme variability of the stratospheric polar vortices, with an emphasis on the Northern Hemisphere vortex, are examined using 2-dimensional moment analysis and Extreme Value Theory (EVT). The use of moments as an analysis to ol gives rise to information about the vortex area, centroid latitude, aspect ratio and kurtosis. The application of EVT to these moment derived quantaties allows the extreme variability of the vortex to be assessed. The data used for this study is ECMWF ERA-40 potential vorticity fields on interpolated isentropic surfaces that range from 450K-1450K. Analyses show that the most extreme vortex variability occurs most commonly in late January and early February, consistent with when most planetary wave driving from the troposphere is observed. Composites around sudden stratospheric warming (SSW) events reveal that the moment diagnostics evolve in statistically different ways between vortex splitting events and vortex displacement events, in contrast to the traditional diagnostics. Histograms of the vortex diagnostics on the 850K (∼10hPa) surface over the 1958-2001 period are fitted with parametric distributions, and show that SSW events comprise the majority of data in the tails of the distributions. The distribution of each diagnostic is computed on various surfaces throughout the depth of the stratosphere, and shows that in general the vortex becomes more circular with higher filamentation at the upper levels. The Northern Hemisphere (NH) and Southern Hemisphere (SH) vortices are also compared through the analysis of their respective vortex diagnostics, and confirm that the SH vortex is less variable and lacks extreme events compared to the NH vortex. Finally extreme value theory is used to statistically mo del the vortex diagnostics and make inferences about the underlying dynamics of the polar vortices.

Simulating the impacts of global warming on wheat in China using a large area crop model

Temperature is one of the most prominent environmental factors that determine plant growth, devel- opment, and yield. Cool and moist conditions are most favorable for wheat. Wheat is likely to be highly vulnerable to further warming because currently the temperature is already close to or above optimum. In this study, the impacts of warming and extreme high temperature stress on wheat yield over China were investigated by using the general large area model (GLAM) for annual crops. The results showed that each 1±C rise in daily mean temperature would reduce the average wheat yield in China by about 4.6%{5.7% mainly due to the shorter growth duration, except for a small increase in yield at some grid cells. When the maximum temperature exceeded 30.5±C, the simulated grain-set fraction declined from 1 at 30.5±C to close to 0 at about 36±C. When the total grain-set was lower than the critical fractional grain-set (0.575{0.6), harvest index and potential grain yield were reduced. In order to reduce the negative impacts of warming, it is crucial to take serious actions to adapt to the climate change, for example, by shifting sowing date, adjusting crop distribution and structure, breeding heat-resistant varieties, and improving the monitoring, forecasting, and early warning of extreme climate events.

Influence of dynamics on the changes in tropical cloud radiative forcing during the 1998 El Niño

Satellite measurements of the radiation budget and data from the U.S. National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis are used to investigate the links between anomalous cloud radiative forcing over the tropical west Pacific warm pool and the tropical dynamics and sea surface temperature (SST) distribution during 1998. The ratio, N, of the shortwave cloud forcing (SWCF) to longwave cloud forcing (LWCF) (N = −SWCF/LWCF) is used to infer information on cloud altitude. A higher than average N during 1998 appears to be related to two separate phenomena. First, dynamic regime-dependent changes explain high values of N (associated with low cloud altitude) for small magnitudes of SWCF and LWCF (low cloud fraction), which reflect the unusual occurrence of mean subsiding motion over the tropical west Pacific during 1998, associated with the anomalous SST distribution. Second, Tropics-wide long-term changes in the spatial-mean cloud forcing, independent of dynamic regime, explain the higher values of N during both 1998 and in 1994/95. The changes in dynamic regime and their anomalous structure in 1998 are well simulated by version HadAM3 of the Hadley Centre climate model, forced by the observed SSTs. However, the LWCF and SWCF are poorly simulated, as are the interannual changes in N. It is argued that improved representation of LWCF and SWCF and their dependence on dynamical forcing are required before the cloud feedbacks simulated by climate models can be trusted.

Summer drought in northern midlatitudes in a time-dependent CO2 climate experiment

A time-dependent climate-change experiment with a coupled ocean–atmosphere general circulation model has been used to study changes in the occurrence of drought in summer in southern Europe and central North America. In both regions, precipitation and soil moisture are reduced in a climate of greater atmospheric carbon dioxide. A detailed investigation of the hydrology of the model shows that the drying of the soil comes about through an increase in evaporation in winter and spring, caused by higher temperatures and reduced snow cover, and a decrease in the net input of water in summer. Evaporation is reduced in summer because of the drier soil, but the reduction in precipitation is larger. Three extreme statistics are used to define drought, namely the frequency of low summer precipitation, the occurrence of long dry spells, and the probability of dry soil. The last of these is arguably of the greatest practical importance, but since it is based on soil moisture, of which there are very few observations, the authors’ simulation of it has the least confidence. Furthermore, long time series for daily observed precipitation are not readily available from a sufficient number of stations to enable a thorough evaluation of the model simulation, especially for the frequency of long dry spells, and this increases the systematic uncertainty of the model predictions. All three drought statistics show marked increases owing to the sensitivity of extreme statistics to changes in their distributions. However, the greater likelihood of long dry spells is caused by a tendency in the character of daily rainfall toward fewer events, rather than by the reduction in mean precipitation. The results should not be taken as firm predictions because extreme statistics for small regions cannot be calculated reliably from the output of the current generation of GCMs, but they point to the possibility of large increases in the severity of drought conditions as a consequence of climate change caused by increased CO2.

A comparison of extreme value theory approaches for determining value at risk

This paper compares a number of different extreme value models for determining the value at risk (VaR) of three LIFFE futures contracts. A semi-nonparametric approach is also proposed, where the tail events are modeled using the generalised Pareto distribution, and normal market conditions are captured by the empirical distribution function. The value at risk estimates from this approach are compared with those of standard nonparametric extreme value tail estimation approaches, with a small sample bias-corrected extreme value approach, and with those calculated from bootstrapping the unconditional density and bootstrapping from a GARCH(1,1) model. The results indicate that, for a holdout sample, the proposed semi-nonparametric extreme value approach yields superior results to other methods, but the small sample tail index technique is also accurate.

Origin of the Parry arc

Laboratory experiments to determine the preferred orientation of free-falling hexagonal prisms were performed at Reynolds numbers appropriate to falling ice crystals in the atmosphere. Hexagonal plates orient with their c axis vertical for aspect ratios < 0.9, whilst hexagonal columns fall with their c axis horizontal. A secondary alignment is also observed: regular hexagonal columns fall preferentially with two prism facets aligned vertically and not horizontally – the latter scenario was previously assumed to be responsible for the rare Parry arc. However, if the column is made scalene in its cross-section, it can orient such that a pair of prism facets is horizontal. This finding indicates that the development of scalene crystals may be key to the production of certain ice-crystal optical phenomena

Impact of increasing resolution and a warmer climate on extreme weather from NH extra-tropical cyclones

The effect of a warmer climate on the properties of extra-tropical cyclones is investigated using simulations of the ECHAM5 global climate model at resolutions of T213 (60 km) and T319 (40 km). Two periods representative of the end of the 20th and 21st centuries are investigated using the IPCC A1B scenario. The focus of the paper is on precipitation for the NH summer and winter seasons, however results from vorticity and winds are also presented. Similar number of events are identified at both resolutions. There are, however, a greater number of extreme precipitation events in the higher reso- lution run. The difference between maximum intensity distributions are shown to be statistically significant using a Kolmogorov-Smirnov test. A Generalised Pareto Distribution is used to analyse changes in extreme precipitation and wind events. In both resolutions, there is an increase in the number of ex- treme precipitation events in a warmer climate for all seasons, together with a reduction in return period. This is not associated with any increased verti- cal velocity, or with any increase in wind intensity in the winter and spring. However, there is an increase in wind extremes in the summer and autumn associated with tropical cyclones migrating into the extra-tropics.

A wind-tunnel study of flow distortion at a meteorological sensor on top of the BT Tower, London, UK

High quality wind measurements in cities are needed for numerous applications including wind engineering. Such data-sets are rare and measurement platforms may not be optimal for meteorological observations. Two years' wind data were collected on the BT Tower, London, UK, showing an upward deflection on average for all wind directions. Wind tunnel simulations were performed to investigate flow distortion around two scale models of the Tower. Using a 1:160 scale model it was shown that the Tower causes a small deflection (ca. 0.5°) compared to the lattice on top on which the instruments were placed (ca. 0–4°). These deflections may have been underestimated due to wind tunnel blockage. Using a 1:40 model, the observed flow pattern was consistent with streamwise vortex pairs shed from the upstream lattice edge. Correction factors were derived for different wind directions and reduced deflection in the full-scale data-set by <3°. Instrumental tilt caused a sinusoidal variation in deflection of ca. 2°. The residual deflection (ca. 3°) was attributed to the Tower itself. Correction of the wind-speeds was small (average 1%) therefore it was deduced that flow distortion does not significantly affect the measured wind-speeds and the wind climate statistics are reliable.

An extreme value theory approach to calculating minimum capital risk requirements

This paper investigates the frequency of extreme events for three LIFFE futures contracts for the calculation of minimum capital risk requirements (MCRRs). We propose a semiparametric approach where the tails are modelled by the Generalized Pareto Distribution and smaller risks are captured by the empirical distribution function. We compare the capital requirements form this approach with those calculated from the unconditional density and from a conditional density - a GARCH(1,1) model. Our primary finding is that both in-sample and for a hold-out sample, our extreme value approach yields superior results than either of the other two models which do not explicitly model the tails of the return distribution. Since the use of these internal models will be permitted under the EC-CAD II, they could be widely adopted in the near future for determining capital adequacies. Hence, close scrutiny of competing models is required to avoid a potentially costly misallocation capital resources while at the same time ensuring the safety of the financial system.