Generalised Dirichelt-to-Neumann map in time dependent domains

We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.

Liquid-vapour homogenisation of fluid inclusions in stalagmites: Evaluation of a new thermometer for paleoclimate research

We present a new approach to determine palaeotemperatures (mean annual surface temperatures) based on measurements of the liquid–vapour homogenisation temperature of fluid inclusions in stalagmites. The aim of this study is to explore the potential and the limitations of this new palaeothermometer and to develop a reliable methodology for routine applications in palaeoclimate research. Therefore, we have investigated recent fluid inclusions from the top part of actively growing stalagmites that have formed at temperatures close to the present-day cave air temperature. A precondition for measuring homogenisation temperatures of originally monophase inclusions is the nucleation of a vapour bubble by means of single ultra-short laser pulses. Based on the observed homogenisation temperatures (Th(obs)) and measurements of the vapour bubble diameter at a known temperature, we calculated stalagmite formation temperatures (Tf) by applying a thermodynamic model that takes into account the effect of surface tension on liquid–vapour homogenisation. Results from recent stalagmite samples demonstrate that calculated stalagmite formation temperatures match the present-day cave air temperature within ± 0.2 °C. To avoid artificially induced changes of the fluid density we defined specific demands on the selection, handling and preparation of the stalagmite samples. Application of the method is restricted to stalagmites that formed at cave temperatures greater than ~ 9–11 °C.

Thomas Heywood: just in time

The scholarly study of the dramatic works and career of Thomas Heywood has increased significantly in the last fifty years but still lags far behind that of his contemporaries Shakespeare and Jonson. Labelled the ‘prose Shakespeare’ by Charles Lamb in the early nineteenth century, Heywood seems to have been considered by scholars and publishers to be a ghostly figure who haunted the early modern theatrical world. In fact, recent research using archival records shows the ways in which Heywood is at the centre of an extensive and highly networked professional industry.

Technical note: how accurate can stalagmite formation temperatures be determined using vapour bubble radius measurements in fluid inclusions?

Stalagmites are natural archives containing detailed information on continental climate variability of the past. Microthermometric measurements of fluid inclusion homogenisation temperatures allow determination of stalagmite formation temperatures by measuring the radius of stable laser-induced vapour bubbles inside the inclusions. A reliable method for precisely measuring the radius of vapour bubbles is presented. The method is applied to stalagmite samples for which the formation temperature is known. An assessment of the bubble radius measurement accuracy and how this error influences the uncertainty in determining the formation temperature is provided. We demonstrate that the nominal homogenisation temperature of a single inclusion can be determined with an accuracy of ±0.25 °C, if the volume of the inclusion is larger than 105 μm3. With this method, we could measure in a proof-of-principle investigation that the formation temperature of 10–20 yr old inclusions in a stalagmite taken from the Milandre cave is 9.87 ± 0.80 °C, while the mean annual surface temperature, that in the case of the Milandre cave correlates well with the cave temperature, was 9.6 ± 0.15 °C, calculated from actual measurements at that time, showing a very good agreement. Formation temperatures of inclusions formed during the last 450 yr are found in a temperature range between 8.4 and 9.6 °C, which corresponds to the calculated average surface temperature. Paleotemperatures can thus be determined within ±1.0 °C.

Ice supersaturation in the ECMWF integrated forecast system

A parametrization for ice supersaturation is introduced into the ECMWF Integrated Forecast System (IFS), compatible with the cloud scheme that allows partial cloud coverage. It is based on the simple, but often justifiable, diagnostic assumption that the ice nucleation and subsequent depositional growth time-scales are short compared to the model time step, thus supersaturation is only permitted in the clear-sky portion of the grid cell. Results from model integrations using the new scheme are presented, which is demonstrated to increase upper-tropospheric humidity, decrease high-level cloud cover and, to a much lesser extent, cloud ice amounts, all as expected from simple arguments. Evaluation of the relative distribution of supersaturated humidity amounts shows good agreement with the observed climatology derived from in situ aircraft observations. With the new scheme, the global distribution of frequency of occurrence of supersaturated regions compares well with remotely sensed microwave limb sounder (MLS) data, with the most marked errors of underprediction occurring in regions where the model is known to underpredict deep convection. Finally, it is also demonstrated that the new scheme leads to improved predictions of permanent contrail cloud over southern England, which indirectly implies upper-tropospheric humidity fields are better represented for this region.

Understanding El Niño in ocean-atmosphere general circulation models: progress and challenges

Determining how El Niño and its impacts may change over the next 10 to 100 years remains a difficult scientific challenge. Ocean–atmosphere coupled general circulation models (CGCMs) are routinely used both to analyze El Niño mechanisms and teleconnections and to predict its evolution on a broad range of time scales, from seasonal to centennial. The ability to simulate El Niño as an emergent property of these models has largely improved over the last few years. Nevertheless, the diversity of model simulations of present-day El Niño indicates current limitations in our ability to model this climate phenomenon and to anticipate changes in its characteristics. A review of the several factors that contribute to this diversity, as well as potential means to improve the simulation of El Niño, is presented.

Mean climate and transience in the tropics of the UGAMP GCM - sensitivity to convective parametrization

The sensitivity of the UK Universities Global Atmospheric Modelling Programme (UGAMP) General Circulation Model (UGCM) to two very different approaches to convective parametrization is described. Comparison is made between a Kuo scheme, which is constrained by large-scale moisture convergence, and a convective-adjustment scheme, which relaxes to observed thermodynamic states. Results from 360-day integrations with perpetual January conditions are used to describe the model's tropical time-mean climate and its variability. Both convection schemes give reasonable simulations of the time-mean climate, but the representation of the main modes of tropical variability is markedly different. The Kuo scheme has much weaker variance, confined to synoptic frequencies near 4 days, and a poor simulation of intraseasonal variability. In contrast, the convective-adjustment scheme has much more transient activity at all time-scales. The various aspects of the two schemes which might explain this difference are discussed. The particular closure on moisture convergence used in this version of the Kuo scheme is identified as being inappropriate.

Tracing pre-eruptive magma degassing using (Pb-210/Ra-226) disequilibria in the volcanic deposits of the 1980-1986 eruption of Mount St. Helens

Disequilibria between Pb-210 and Ra-226 can be used to trace magma degassing, because the intermediate nuclides, particularly Rn-222, are volatile. Products of the 1980-1986 eruptions of Mount St. Helens have been analysed for (Pb-210/Ra-226). Both excesses and deficits of Pb-210 are encountered suggesting rapid gas transfer. The time scale of diffuse, non-eruptive gas escape prior to 1980 as documented by Pb-210 deficits is on the order of a decade using the model developed by Gauthier and Condomines (Earth Planet. Sci. Lett. 172 (1999) 111-126) for a non-renewed magma chamber and efficient Rn removal. The time required to build-up Pb-210 excess is much shorter (months) as can be observed from steady increases of (Pb-210/Ra-226) with time during 1980-1982. The formation of Pb-210 excess requires both rapid gas transport through the magma and periodic blocking of gas escape routes. Superposed on this time trend is the natural variability of (Pb-210/Ra-226) in a single eruption caused by tapping magma from various depths. The two time scales of gas transport, to create both Pb-210 deficits and Pb-210 excesses, cannot be reconciled in a single event. Rather Pb-210 deficits are associated with pre-eruptive diffuse degassing, while Pb-210 excesses document the more vigorous degassing associated with eruption and recharge of the system. (c) 2006 Elsevier B.V. All rights reserved.

Nitrate transport in Chalk catchments: monitoring, modelling and policy implications

Rising nitrate levels have been observed in UK Chalk catchments in recent decades, with concentrations now approaching or exceeding legislated maximum values in many areas. In response, strategies seeking to contain concentrations through appropriate land management are now in place. However, there is an increasing consensus that Chalk systems, a predominant landscape type over England and indeed northwest Europe, can retard decades of prior nitrate loading within their deep unsaturated zones. Current levels may not fully reflect the long-term impact of present-day practices, and stringent land management controls may not be enough to avert further medium-term rises. This paper discusses these issues in the context of the EU Water Framework Directive, drawing on data from recent experimental work and a new model (INCA-Chalk) that allows the impacts of different land use management practices to be explored. Results strongly imply that timelines for water quality improvement demanded by the Water Framework directive are not realistic for the Chalk, and give an indication of time-scales over which improvements might be achieved. However, important unresolved scientific issues remain, and further monitoring and targeted data collection is recommended to reduce prediction uncertainties and allow cost effective strategies for mitigation to be designed and implemented. (C) 2007 Elsevier Ltd. All rights reserved.

Catchment-scale modelling of flow and nutrient transport in the Chalk unsaturated zone

The unsaturated zone exerts a major control on the delivery of nutrients to Chalk streams, yet flow and transport processes in this complex, dual-porosity medium have remained controversial. A major challenge arises in characterising these processes, both at the detailed mechanistic level and at an appropriate level for inclusion within catchment-scale models for nutrient management. The lowland catchment research (LOCAR) programme in the UK has provided a unique set of comprehensively instrumented groundwater-dominated catchments. Of these, the Pang and Lambourn, tributaries of the Thames near Reading, have been a particular focus for research into subsurface processes and surface water-groundwater interactions. Data from LOCAR and other sources, along with a new dual permeability numerical model of the Chalk, have been used to explore the relative roles of matrix and fracture flow within the unsaturated zone and resolve conflicting hypotheses of response. From the improved understanding gained through these explorations, a parsimonious conceptualisation of the general response of flow and transport within the Chalk unsaturated zone was formulated. This paper summarises the modelling and data findings of these explorations, and describes the integration of the new simplified unsaturated zone representation with a catchment-scale model of nutrients (INCA), resulting in a new model for catchment-scale flow and transport within Chalk systems: INCA-Chalk. This model is applied to the Lambourn, and results, including hindcast and forecast simulations, are presented. These clearly illustrate the decadal time-scales that need to be considered in the context of nutrient management and the EU Water Framework Directive. (C) 2007 Elsevier B.V. All rights reserved.

Assessing the sources and magnitude of diurnal nitrate variability in the San Joaquin River (California) with an in-situ optical nitrate sensor and dual nitrate isotopes

We investigated diurnal nitrate (NO3-) concentration variability in the San Joaquin River using an in situ optical NO3- sensor and discrete sampling during a 5-day summer period characterized by high algal productivity. Dual NO3- isotopes (delta N-15(NO3) and delta O-18(NO3)) and dissolved oxygen isotopes (delta O-18(DO)) were measured over 2 days to assess NO3- sources and biogeochemical controls over diurnal time-scales. Concerted temporal patterns of dissolved oxygen (DO) concentrations and delta O-18(DO) were consistent with photosynthesis, respiration and atmospheric O-2 exchange, providing evidence of diurnal biological processes independent of river discharge. Surface water NO3- concentrations varied by up to 22% over a single diurnal cycle and up to 31% over the 5-day study, but did not reveal concerted diurnal patterns at a frequency comparable to DO concentrations. The decoupling of delta N-15(NO3) and delta O-18(NO3) isotopes suggests that algal assimilation and denitrification are not major processes controlling diurnal NO3- variability in the San Joaquin River during the study. The lack of a clear explanation for NO3- variability likely reflects a combination of riverine biological processes and time-varying physical transport of NO3- from upstream agricultural drains to the mainstem San Joaquin River. The application of an in situ optical NO3- sensor along with discrete samples provides a view into the fine temporal structure of hydrochemical data and may allow for greater accuracy in pollution assessment.

Understanding land-sea warming contrast in response to increasing greenhouse gases. Part I: Transient adjustment

Climate model simulations consistently show that surface temperature over land increases more rapidly than over sea in response to greenhouse gas forcing. The enhanced warming over land is not simply a transient effect caused by the land–sea contrast in heat capacities, since it is also present in equilibrium conditions. This paper elucidates the transient adjustment processes over time scales of days to weeks of the surface and tropospheric climate in response to a doubling of CO2 and to changes in sea surface temperature (SST), imposed separately and together, using ensembles of experiments with an atmospheric general circulation model. These adjustment processes can be grouped into three stages: immediate response of the troposphere and surface processes (day 1), fast adjustment of surface processes (days 2–5), and adjustment of the whole troposphere (days 6–20). Some land surface warming in response to doubled CO2 (with unchanged SSTs) occurs immediately because of increased downward longwave radiation. Increased CO2 also leads to reduced plant stomatal resistance and hence restricted evaporation, which increases land surface warming in the first day. Rapid reductions in cloud amount lead in the next few days to increased downward shortwave radiation and further warming, which spreads upward from the surface, and by day 5 the surface and tropospheric response is statistically consistent with the equilibrium value. Land surface warming in response to imposed SST change (with unchanged CO2) is slower. Tropospheric warming is advected inland from the sea, and over land it occurs at all levels together rather than spreading upward from the surface. The atmospheric response to prescribed SST change in about 20 days is statistically consistent with the equilibrium value, and the warming is largest in the upper troposphere over both land and sea. The land surface warming involves reduction of cloud cover and increased downward shortwave radiation, as in the experiment with CO2 change, but in this case it is due to the restriction of moisture supply to the land (indicated by reduced soil moisture), whereas in the CO2 forcing experiment it is due to restricted evaporation despite increased moisture supply (indicated by increased soil moisture). The warming over land in response to SST change is greater than over the sea and is the dominant contribution to the land–sea warming contrast under enhanced CO2 forcing.

Climate predictability in the second year

In this paper, the predictability of climate arising from ocean heat content (OHC) anomalies is investigated in the HadCM3 coupled atmosphere–ocean model. An ensemble of simulations of the twentieth century are used to provide initial conditions for a case study. The case study consists of two ensembles started from initial conditions with large differences in regional OHC in the North Atlantic, the Southern Ocean and parts of the West Pacific. Surface temperatures and precipitation are on average not predictable beyond seasonal time scales, but for certain initial conditions there may be longer predictability. It is shown that, for the case study examined here, some aspects of tropical precipitation, European surface temperatures and North Atlantic sea-level pressure are potentially predictable 2 years ahead. Predictability also exists in the other case studies, but the climate variables and regions, which are potentially predictable, differ. This work was done as part of the Grid for Coupled Ensemble Prediction (GCEP) eScience project.

Evidence for long-term regional changes in precipitation on the East Coast Mountains in Mauritius

Global climate change and its impacts are being increasingly studied and precipitation trends are one of the measures of quantifying climate change especially in the tropics. This study uses daily rainfall data to determine if there are changes in the long-term trends in rainfall variability in the East Coast Mountains of Mauritius during the last few decades, and to investigate the factors influencing the trends in the inter-annual to inter-decadal rainfall variability. Statistical modelling has been used to investigate the trends in total seasonal rainfall, the number of rain days and the mean amount of rain per rainy days and the local, regional and large-scale factors that affect them on inter-annual to inter-decadal time scales. The strongest inter-decadal trend was found in the number of rain days for both rainfall seasons, and the other variables were found to have weak or insignificant trends. Both local factors, such as the surrounding sea surface temperatures and large-scale phenomena such as Indian Monsoon and the El Niño Southern Oscillation were found to influence rainfall patterns.