Maximum principles for vectorial approximate minimisers on non-convex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property. The primary advance compared to results already existing in the literature is that we have dropped the quasiconvexity assumption of the integrand in the gradient term. The lack of weak Lower semicontinuity is compensated by introducing a nonlinear convergence technique, based on the approximation of the projection onto a convex set by reflections and on the invariance of the integrand in the gradient term under the Orthogonal Group. Maximum Principles are implied for the relaxed solution in the case of non-existence of minimizers and for minimizing solutions of the Euler–Lagrange system of PDE.

Large inert carbon pool in the terrestrial biosphere at the Last Glacial Maximum

During each of the late Pleistocene glacial–interglacial transitions, atmospheric carbon dioxide concentrations rose by almost 100 ppm. The sources of this carbon are unclear, and efforts to identify them are hampered by uncertainties in the magnitude of carbon reservoirs and fluxes under glacial conditions. Here we use oxygen isotope measurements from air trapped in ice cores and ocean carbon-cycle modelling to estimate terrestrial and oceanic gross primary productivity during the Last Glacial Maximum. We find that the rate of gross terrestrial primary production during the Last Glacial Maximum was about 40±10 Pg C yr−1, half that of the pre-industrial Holocene. Despite the low levels of photosynthesis, we estimate that the late glacial terrestrial biosphere contained only 330 Pg less carbon than pre-industrial levels. We infer that the area covered by carbon-rich but unproductive biomes such as tundra and cold steppes was significantly larger during the Last Glacial Maximum, consistent with palaeoecological data. Our data also indicate the presence of an inert carbon pool of 2,300 Pg C, about 700 Pg larger than the inert carbon locked in permafrost today. We suggest that the disappearance of this carbon pool at the end of the Last Glacial Maximum may have contributed to the deglacial rise in atmospheric carbon dioxide concentrations.

Cloud optical and microphysical properties derived from ground-based and satellite sensors over a site in the Yangtze Delta region

Comprehensive surface-based retrievals of cloud optical and microphysical properties were made at Taihu, a highly polluted site in the central Yangtze Delta region, during a research campaign from May 2008 to December 2009. Cloud optical depth (COD), effective radius (Re), and liquid water path (LWP) were retrieved from measurements made with a suite of ground-based and spaceborne instruments, including an Analytical Spectral Devices spectroradiometer, a multi␣lter rotating shadowband radiometer, a multichannel microwave radiometer profiler, and the Moderate Resolution Imaging Spectroradiometer (MODIS) on Terra and Aqua satellites. Retrievals from zenith radiance measurements capture better the temporal variation of cloud properties than do retrievals from hemispherical fluxes. Annual mean LWP, COD, and Re are 115.8 ± 90.8 g/m2, 28.5 ± 19.2, and 6.9 ± 4.2 microns. Over 90% of LWP values are less than 250 g/m2. Most of the COD values (>90%) fall between 5 and 60, and ~80% of Re values are less than 10 microns. Maximum (minimum) values of LWP and Re occur in summer (winter); COD is highest in winter and spring. Raining and nonraining clouds have signi␣cant differences in LWP, COD, and Re. Rainfall frequency is best correlated with LWP, followed by COD and Re. Cloud properties retrieved from multiple ground-based instruments are also compared with those from satellite retrievals. On average, relative to surface retrievals, mean differences of satellite retrievals in cloud LWP, COD, and Re were -33.6 g/m2 (-26.4%), -5.8 (-31.4%), and 2.9 ␣m (29.3%) for 11 MODIS-Terra overpasses and -43.3 g/m2 (-22.3%), -3.0 (-10.0%), and -1.3 ␣m (-12.0%) for 8 MODIS-Aqua overpasses, respectively. These discrepancies indicate that MODIS cloud products still suffer from large uncertainties in this region.

Quantifying the roles of ocean circulation and biogeochemistry in governing ocean carbon-13 and atmospheric carbon dioxide at the last glacial maximum

We use a state-of-the-art ocean general circulation and biogeochemistry model to examine the impact of changes in ocean circulation and biogeochemistry in governing the change in ocean carbon-13 and atmospheric CO2 at the last glacial maximum (LGM). We examine 5 different realisations of the ocean's overturning circulation produced by a fully coupled atmosphere-ocean model under LGM forcing and suggested changes in the atmospheric deposition of iron and phytoplankton physiology at the LGM. Measured changes in carbon-13 and carbon-14, as well as a qualitative reconstruction of the change in ocean carbon export are used to evaluate the results. Overall, we find that while a reduction in ocean ventilation at the LGM is necessary to reproduce carbon-13 and carbon-14 observations, this circulation results in a low net sink for atmospheric CO2. In contrast, while biogeochemical processes contribute little to carbon isotopes, we propose that most of the change in atmospheric CO2 was due to such factors. However, the lesser role for circulation means that when all plausible factors are accounted for, most of the necessary CO2 change remains to be explained. This presents a serious challenge to our understanding of the mechanisms behind changes in the global carbon cycle during the geologic past.

Climatic impacts of fresh water hosing under Last Glacial Maximum conditions: a multi-model study

Fresh water hosing simulations, in which a fresh water flux is imposed in the North Atlantic to force fluctuations of the Atlantic Meridional Overturning Circulation, have been routinely performed, first to study the climatic signature of different states of this circulation, then, under present or future conditions, to investigate the potential impact of a partial melting of the Greenland ice sheet. The most compelling examples of climatic changes potentially related to AMOC abrupt variations, however, are found in high resolution palaeo-records from around the globe for the last glacial period. To study those more specifically, more and more fresh water hosing experiments have been performed under glacial conditions in the recent years. Here we compare an ensemble constituted by 11 such simulations run with 6 different climate models. All simulations follow a slightly different design, but are sufficiently close in their design to be compared. They all study the impact of a fresh water hosing imposed in the extra-tropical North Atlantic. Common features in the model responses to hosing are the cooling over the North Atlantic, extending along the sub-tropical gyre in the tropical North Atlantic, the southward shift of the Atlantic ITCZ and the weakening of the African and Indian monsoons. On the other hand, the expression of the bipolar see-saw, i.e., warming in the Southern Hemisphere, differs from model to model, with some restricting it to the South Atlantic and specific regions of the southern ocean while others simulate a widespread southern ocean warming. The relationships between the features common to most models, i.e., climate changes over the north and tropical Atlantic, African and Asian monsoon regions, are further quantified. These suggest a tight correlation between the temperature and precipitation changes over the extra-tropical North Atlantic, but different pathways for the teleconnections between the AMOC/North Atlantic region and the African and Indian monsoon regions.

Asymmetric forcing from stratospheric aerosols impacts Sahelian rainfall

The Sahelian drought of the 1970s–1990s was one of the largest humanitarian disasters of the past 50 years, causing up to 250,000 deaths and creating 10 million refugees1. It has been attributed to natural variability2–5, overgrazing6 and the impact of industrial emissions of sulphur dioxide7,8. Each mechanism can influence the Atlantic sea surface temperature gradient, which is strongly coupled to Sahelian precipitation2,3. We suggest that sporadic volcanic eruptions in the Northern Hemisphere also strongly influence this gradient and cause Sahelian drought. Using de-trended observations from 1900 to 2010, we show that three of the four driest Sahelian summers were preceded by substantial Northern Hemisphere volcanic eruptions. We use a state-ofthe- art coupled global atmosphere–ocean model to simulate both episodic volcanic eruptions and geoengineering by continuous deliberate injection into the stratosphere. In either case, large asymmetric stratospheric aerosol loadings concentrated in the Northern Hemisphere are a harbinger of Sahelian drought whereas those concentrated in the Southern Hemisphere induce a greening of the Sahel. Further studies of the detailed regional impacts on the Sahel and other vulnerable areas are required to inform policymakers in developing careful consensual global governance before any practical solar radiation management geoengineering scheme is implemented.

Recent climatic trends and linkages to river discharge in Central Vietnam

In this study, change in rainfall, temperature and river discharge are analysed over the last three decades in Central Vietnam. Trends and rainfall indices are evaluated using non-parametric tests at different temporal levels. To overcome the sparse locally available network, the high resolution APHRODITE gridded dataset is used in addition to the existing rain gauges. Finally, existing linkages between discharge changes and trends in rainfall and temperature are explored. Results are indicative of an intensification of rainfall (+15%/decade), with more extreme and longer events. A significant increase in winter rainfall and a decrease in consecutive dry days provides strong evidence for a lengthening wet season in Central Vietnam. In addition, trends based on APHRODITE suggest a strong orographic signal in winter and annual trends. These results underline the local variability in the impacts of climatic change at the global scale. Consequently, it is important that change detection investigations are conducted at the local scale. A very weak signal is detected in the trend of minimum temperature (+0.2°C/decade). River discharge trends show an increase in mean discharge (31 to 35%/decade) over the last decades. Between 54 and 74% of this increase is explained by the increase in precipitation. The maximum discharge also responds significantly to precipitation changes leading to a lengthened wet season and an increase in extreme rainfall events. Such trends can be linked with a likely increase in floods in Central Vietnam, which is important for future adaptation planning and management and flood preparedness in the region. Copyright © 2012 John Wiley & Sons, Ltd.

Comparison of TAMSAT and CPC rainfall estimates with raingauges, for southern Africa

Two different TAMSAT (Tropical Applications of Meteorological Satellites) methods of rainfall estimation were developed for northern and southern Africa, based on Meteosat images. These two methods were used to make rainfall estimates for the southern rainy season from October 1995 to April 1996. Estimates produced by both TAMSAT methods and estimates produced by the CPC (Climate Prediction Center) method were then compared with kriged data from over 800 raingauges in southern Africa. This shows that operational TAMSAT estimates are better over plateau regions, with 59% of estimates within one standard error (s.e.) of the kriged rainfall. Over mountainous regions the CPC approach is generally better, although all methods underestimate and give only 40% of estimates within 1 s.e. The two TAMSAT methods show little difference across a whole season, but when looked at in detail the northern method gives unsatisfactory calibrations. The CPC method does have significant overall improvements by building in real-time raingauge data, but only where sufficient raingauges are available.

Dynamic hydrological modeling in drylands with TRMM based rainfall

This paper introduces and evaluates DryMOD, a dynamic water balance model of the key hydrological process in drylands that is based on free, public-domain datasets. The rainfall model of DryMOD makes optimal use of spatially disaggregated Tropical Rainfall Measuring Mission (TRMM) datasets to simulate hourly rainfall intensities at a spatial resolution of 1-km. Regional-scale applications of the model in seasonal catchments in Tunisia and Senegal characterize runoff and soil moisture distribution and dynamics in response to varying rainfall data inputs and soil properties. The results highlight the need for hourly-based rainfall simulation and for correcting TRMM 3B42 rainfall intensities for the fractional cover of rainfall (FCR). Without FCR correction and disaggregation to 1 km, TRMM 3B42 based rainfall intensities are too low to generate surface runoff and to induce substantial changes to soil moisture storage. The outcomes from the sensitivity analysis show that topsoil porosity is the most important soil property for simulation of runoff and soil moisture. Thus, we demonstrate the benefit of hydrological investigations at a scale, for which reliable information on soil profile characteristics exists and which is sufficiently fine to account for the heterogeneities of these. Where such information is available, application of DryMOD can assist in the spatial and temporal planning of water harvesting according to runoff-generating areas and the runoff ratio, as well as in the optimization of agricultural activities based on realistic representation of soil moisture conditions.

Reducing inconsistencies in point observations of maximum flood inundation level

Flood simulation models and hazard maps are only as good as the underlying data against which they are calibrated and tested. However, extreme flood events are by definition rare, so the observational data of flood inundation extent are limited in both quality and quantity. The relative importance of these observational uncertainties has increased now that computing power and accurate lidar scans make it possible to run high-resolution 2D models to simulate floods in urban areas. However, the value of these simulations is limited by the uncertainty in the true extent of the flood. This paper addresses that challenge by analyzing a point dataset of maximum water extent from a flood event on the River Eden at Carlisle, United Kingdom, in January 2005. The observation dataset is based on a collection of wrack and water marks from two postevent surveys. A smoothing algorithm for identifying, quantifying, and reducing localized inconsistencies in the dataset is proposed and evaluated showing positive results. The proposed smoothing algorithm can be applied in order to improve flood inundation modeling assessment and the determination of risk zones on the floodplain.

Pollen, plant macrofossil and charcoal records for palaeovegetation reconstruction in the Mediterranean-Black Sea Corridor since the Last Glacial Maximum

New reconstructions of changing vegetation patterns in the Mediterranean-Black Sea Corridor since the Last Glacial Maximum are being produced by an improved biomisation scheme that uses both pollen and plant macrofossil data, in conjunction. Changes in fire regimes over the same interval will also be reconstructed using both microscopic and macroscopic charcoal remains. These reconstructions will allow a diagnosis of the interactions between climate, fire and vegetation on millennial timescales, and will also help to clarify the role of coastline and other geomorphic changes, salinity and impacts of human activities in this region. These new data sets are being produced as a result of collaboration between the Palynology Working Group (WG-2) within the IGCP-521 project and the international Palaeovegetation Mapping Project (BIOME 6000). The main objective of this paper is to present the goals of this cooperation, methodology, including limitations and planned improvements, and to show the initial results of some applications.

Results of PMIP2 coupled simulations of the mid-Holocene and Last Glacial Maximum, Part 2: feedbacks with emphasis on the location of the ITCZ and mid- and high latitudes heat budget

A set of coupled ocean-atmosphere(-vegetation) simulations using state of the art climate models is now available for the Last Glacial Maximum (LGM) and the Mid-Holocene (MH) through the second phase of the Paleoclimate Modeling Intercomparison Project (PMIP2). Here we quantify the latitudinal shift of the location of the Intertropical Convergence Zone (ITCZ) in the tropical regions during boreal summer and the change in precipitation in the northern part of the ITCZ. For both periods the shift is more pronounced over the continents and East Asia. The maritime continent is the region where the largest spread is found between models. We also clearly establish that the larger the increase in the meridional temperature gradient in the tropical Atlantic during summer at the MH, the larger the change in precipitation over West Africa. The vegetation feedback is however not as large as found in previous studies, probably due to model differences in the control simulation. Finally, we show that the feedback from snow and sea-ice at mid and high latitudes contributes for half of the cooling in the Northern Hemisphere for the LGM, with the remaining being achieved by the reduced CO2 and water vapour in the atmosphere. For the MH the snow and albedo feedbacks strengthen the spring cooling and enhance the boreal summer warming, whereas water vapour reinforces the late summer warming. These feedbacks are modest in the Southern Hemisphere. For the LGM most of the surface cooling is due to CO2 and water vapour.