A comparison of duality and energy a posteriori estimates for $\mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ in parabolic problems

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.

Just add water and salt: the optimisation of petrogenic hydrocarbon biodegradation in soils from semi-arid Barrow Island, Western Australia

We investigated the potential of soil moisture and nutrient amendments to enhance the biodegradation of oil in the soils from an ecologically unique semi-arid island. This was achieved using a series of controlled laboratory incubations where moisture or nutrient levels were experimentally manipulated. Respired CO2 increased sharply with moisture amendment reflecting the severe moisture limitation of these porous and semi-arid soils. The greatest levels of CO2 respiration were generally obtained with a soil pore water saturation of 50–70%. Biodegradation in these nutrient poor soils was also promoted by the moderate addition of a nitrogen fertiliser. Increased biodegradation was greater at the lowest amendment rate (100 mg N kg−1 soil) than the higher levels (500 or 1,000 mg N kg−1 soil), suggesting the higher application rates may introduce N toxicity. Addition of phosphorous alone had little effect, but a combined 500 mg N and 200 mg P kg−1 soil amendment led to a synergistic increase in CO2 respiration (3.0×), suggesting P can limit the biodegradation of hydrocarbons following exogenous N amendment.

Triple isotope (δD, δ17O, δ18O) study on precipitation, drip water and speleothem fluid inclusions for a central European cave (NW Switzerland)

Deuterium (dD) and oxygen (d18O) isotopes are powerful tracers of the hydrological cycle and have been extensively used for paleoclimate reconstructions as they can provide information on past precipitation, temperature and atmospheric circulation. More recently, the use of 17Oexcess derived from precise measurement of d17O and d18O gives new and additional insights in tracing the hydrological cycle whereas uncertainties surround this proxy. However, 17Oexcess could provide additional information on the atmospheric conditions at the moisture source as well as about fractionations associated with transport and site processes. In this paper we trace water stable isotopes (dD, d17O and d18O) along their path from precipitation to cave drip water and finally to speleothem fluid inclusions for Milandre cave in northwestern Switzerland. A two year-long daily resolved precipitation isotope record close to the cave site is compared to collected cave drip water (3 months average resolution) and fluid inclusions of modern and Holocene stalagmites. Amount weighted mean dD, d18O and d17O are �71.0‰, �9.9‰, �5.2‰ for precipitation, �60.3‰, �8.7‰, �4.6‰ for cave drip water and �61.3‰, �8.3‰, �4.7‰ for recent fluid inclusions respectively. Second order parameters have also been derived in precipitation and drip water and present similar values with 18 per meg for 17Oexcess whereas d-excess is 1.5‰ more negative in drip water. Furthermore, the atmospheric signal is shifted towards enriched values in the drip water and fluid inclusions (D of ~ þ 10‰ for dD). The isotopic composition of cave drip water exhibits a weak seasonal signal which is shifted by around 8e10 months (groundwater residence time) when compared to the precipitation. Moreover, we carried out the first d17O measurement in speleothem fluid inclusions, as well as the first comparison of the d17O behaviour from the meteoric water to the fluid inclusions entrapment in speleothems. This study on precipitation, drip water and fluid inclusions will be used as a speleothem proxy calibration for Milandre cave in order to reconstruct paleotemperatures and moisture source variations for Western Central Europe.

Persistent reduced ecosystem respiration after insect disturbance in high elevation forests

Amid a worldwide increase in tree mortality, mountain pine beetles (Dendroctonus ponderosae Hopkins) have led to the death of billions of trees from Mexico to Alaska since 2000. This is predicted to have important carbon, water and energy balance feedbacks on the Earth system. Counter to current projections, we show that on a decadal scale, tree mortality causes no increase in ecosystem respiration from scales of several square metres up to an 84 km2 valley. Rather, we found comparable declines in both gross primary productivity and respiration suggesting little change in net flux, with a transitory recovery of respiration 6–7 years after mortality associated with increased incorporation of leaf litter C into soil organic matter, followed by further decline in years 8–10. The mechanism of the impact of tree mortality caused by these biotic disturbances is consistent with reduced input rather than increased output of carbon.