As is well known, a complete stochastic solution of the stochastic differential equation governing saturated groundwater flow leads to an infinite hierarchy of equations in terms of higher-order moments. Perturbation techniques are commonly used to close this hierarchy, using power-series expansions. These methods are applied by truncating the series after a finite number of terms, and products of random gradients of conductivity and head potential are neglected. Uncertainty regarding the number or terms required to yield a sufficiently accurate result is a significant drawback with the application of power series-based perturbation methods for such problems. Low-order series truncation may be incapable of representing fundamental characteristics of flow and can lead to physically unreasonable and inaccurate solutions of the stochastic flow equation. To support this argument, one-dimensional, steady-state, saturated groundwater flow is examined, for the case of a spatially distributed hydraulic conductivity field. An ordinary power-series perturbation method is used to approximate the mean head, using second-order statistics to characterize the conductivity field. Then an interactive perturbation approach is introduced, which yields improved results compared to low-order, power-series perturbation methods for situations where strong interactions exist between terms in such approximations. The interactive perturbation concept is further developed using Feynman-type diagrams and graph theory, which reduce the original stochastic flow problem to a closed set of equations for the mean and the covariance functions. Both theoretical and practical advantages of diagrammatic solutions are discussed; these include the study of bounded domains and large fluctuations. 相似文献
Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of Hamiltonian ordinary differential equations bound together by integral transport laws. In particular, we show that this parcel Hamiltonian structure is compatible with the stacking of layers under isentropic or isothermal constraints. The appeal of the parcel formulation is the simplification of various calculations, in particular the derivation of the continuum Poisson bracket and the proof of the Jacobi identity. A comparison and connection is made between the Hamiltonian dynamics of fluid parcels and the Hamiltonian system of partial differential equations. The parcel formulation can be seen as a precursor and tool for the study of Hamiltonian numerical schemes. 相似文献
Intraseasonal variability of the tropical Indo-Pacific ocean is strongly related to the Madden–Julian Oscillation (MJO). Shallow seas in this region, such as the Gulf of Thailand, act as amplifiers of the direct ocean response to surface wind forcing by efficient setup of sea level. Intraseasonal ocean variability in the Gulf of Thailand region is examined using statistical analysis of local tide gauge observations and surface winds. The tide gauges detect variability on intraseasonal time scales that is related to the MJO through its effect on local wind. The relationship between the MJO and the surface wind is strongly seasonal, being most vigorous during the monsoon, and direction-dependent. The observations are then supplemented with simulations of sea level and circulation from a fully nonlinear barotropic numerical ocean model (Princeton Ocean Model). The numerical model reproduces well the intraseasonal sea level variability in the Gulf of Thailand and its seasonal modulations. The model is then used to map the wind-driven response of sea level and circulation in the entire Gulf of Thailand. Finally, the predictability of the setup and setdown signal is discussed by relating it to the, potentially predictable, MJO index. 相似文献
As Arctic sea ice declines in response to climate change, a shift from thick multiyear ice to a thinner ice cover is occurring. With this transition, ice thicknesses approach a threshold below which ice no longer insulates the atmosphere from oceanic surface fluxes. While this is well known, there are no estimates of the magnitude of this threshold, nor of the proportion of sea ice area that is below this threshold as ice thins. We determine this threshold by simulating the atmospheric response to varying thicknesses, ranging from 0.0 to 2.0 m and determine that threshold to be 0.40–0.50 m. The resulting “effective” ice area is 4–14% lower than reported total ice area, as 0.39–0.97 × 106 km2 of the total ice area falls below the threshold throughout the twentieth century, including during notable ice minima. The atmosphere above large non-insulating ice-covered regions is susceptible to more than 2 °C of warming despite ice presence. Observed mean Arctic Ocean ice thickness is projected to fall below this threshold as early as the mid-2020s. Studies on ocean–atmosphere interactions in relation to sea ice area should focus on this insulating sea ice area, where ice is at least 0.40–0.50 m thick, and treat ice regions below 0.40–0.50 m thickness with caution.
The equations of motion applying to the wind field in a forest canopy are simplified to a balance between the shearing stress gradient and either the form-drag of the leaves in the upper dense canopy, or the overall horizontal pressure gradient in the more open space beneath. The equations imply that, in descending through the forest, the stress and wind vectors turn through an angle which depends on the forest characteristics and on the stability and the speed of the airflow above the forest. The turning is roughly confirmed by an overall average measured on a very flat site near Thetford, Norfolk, covered by an extensive uniform pine forest. 相似文献
In principle, many climate policymakers have accepted that large-scale carbon dioxide removal (CDR) is necessary to meet the Paris Agreement’s mitigation targets, but they have avoided proposing by whom CDR might be delivered. Given its role in international climate policy, the European Union (EU) might be expected to lead the way. But among EU climate policymakers so far there is little talk on CDR, let alone action. Here we assess how best to ‘target’ CDR to motivate EU policymakers exploring which CDR target strategy may work best to start dealing with CDR on a meaningful scale. A comprehensive CDR approach would focus on delivering the CDR volumes required from the EU by 2100, approximately at least 50 Gigatonnes (Gt) CO2, according to global model simulations aiming to keep warming below 2°C. A limited CDR approach would focus on an intermediate target to deliver the CDR needed to reach ‘net zero emissions’ (i.e. the gross negative emissions needed to offset residual positive emissions that are too expensive or even impossible to mitigate). We argue that a comprehensive CDR approach may be too intimidating for EU policymakers. A limited CDR approach that only addresses the necessary steps to reach the (intermediate) target of ‘net zero emissions’ is arguably more achievable, since it is a better match to the existing policy paradigm and would allow for a pragmatic phase-in of CDR while avoiding outright resistance by environmental NGOs and the broader public.
Key policy insights
Making CDR an integral part of EU climate policy has the potential to significantly reshape the policy landscape.
Burden sharing considerations would probably play a major role, with comprehensive CDR prolonging the disparity and tensions between progressives and laggards.
Introducing limited CDR in the context of ‘net zero’ pathways would retain a visible primary focus on decarbonization but acknowledge the need for a significant enhancement of removals via ‘natural’ and/or ‘engineered’ sinks.
A decarbonization approach that intends to lead to a low level of ‘residual emissions’ (to be tackled by a pragmatic phase-in of CDR) should be the priority of EU climate policy.
The Cambridge 2-D Eulerian model has been used to study the potential atmospheric distributions and lifetimes of a number of CFC replacement compounds and their degradation products. The study has focused on HFC 134a and HCFCs 123, 141b and 142b and the major products formed by their atmospheric degradation. The loss of these compounds and their products by hydroxyl radical attack, photolysis and in-cloud hydrolysis have been investigated. The study has shown that HCFCs 141b and 142b have sufficiently long lifetimes to enter the stratosphere in significant quantities, where degradation leads to an increase in the total stratospheric chlorine concentration. The study has also highlighted areas where further experimental work would be valuable, in particular characterisation of the product channels for the degradation reactions and determination of the removal rates of the products in the aqueous phase. 相似文献
Observations are presented of large-amplitude internal waves (LAIWs) generated by the steepening of the internal tide on the Australian North West Shelf (NWS) over a 4-month period extending from strongly stratified summer conditions to weakly stratified winter conditions. The observations are from a site in water depth of 124 m where current and temperature measurements were made from a fixed vertical mooring and a benthic L-shaped spatial array. The observations show the LAIWs at this site to be characterized by strong seasonal variability, with energetic LAIWs of depression being dominant during summer and weaker LAIWs of elevation being dominant during the winter months as the stratification weakens, the upper mixed layer deepens, and the thermocline is close to the bottom. Waves were also seen to propagate from a range of directions towards the observation site. Modeling using the Regional Ocean Modeling System (ROMS v2.1) revealed that internal tide generation in the area occurred at water depths of between 400 and 600 m along an arc of approximately 120 km in length, some 70 km to the northwest of our experimental site. The results demonstrate both the 3D nature as well as the seasonal variation of the LAIW field. 相似文献
Hydrothermal emission of mantle helium appears to be directly related to magma production rate, but other processes can generate methane and hydrogen on mid-ocean ridges. In an on-going effort to characterize these processes in the South Atlantic, the flux and distribution of these gases were investigated in the vicinity of a powerful black smoker recently discovered at 8°17.9' S, 13°30.4' W. The vent lies on the shoulder of an oblique offset in the Mid-Atlantic Ridge and discharges high concentrations of methane and hydrogen. Measurements during expeditions in 2004 and 2006 show that the ratio of CH4 to 3He in the neutrally buoyant plume is quite high, 4 × 108. The CTD stations were accompanied by velocity measurements with lowered acoustic Doppler current profilers (LADCP), and from these data we estimate the methane transport to have been 0.5 mol s− 1 in a WSW-trending plume that seems to develop during the ebb tidal phase. This transport is an order of magnitude greater than the source of CH4 calculated from its concentration in the vent fluid and the rise height of the plume. From this range of methane fluxes, the source of 3He is estimated to be between 0.14 and 1.2 nmol s− 1. In either case, the 3He source is significantly lower than expected from the spreading rate of the Mid-Atlantic Ridge. From the inventory of methane in the rift valley adjacent to the vent, it appears that the average specific rate of oxidation is 2.6 to 23 yr− 1, corresponding to a turnover time between 140 and 16 days. Vertical profiles of methane in the surrounding region often exhibited Gaussian-like distributions, and the variances appear to increase with distance from the vent. Using a Gaussian plume model, we obtained a range of vertical eddy diffusivities between 0.009 and 0.08 m2m2 s− 1. These high values may be due to tidally driven internal waves across the promontory on which the vent is located. 相似文献
We carried out a magnetotelluric field campaign in the South–East Lower Saxony Basin, Germany, with the main goal of testing this method for imaging regional Posidonia black shale sediments. Two‐dimensional inversion results of the magnetotelluric data show a series of conductive structures correlating with brine‐saturated sediments but also with deeper, anthracitic Westphalian/Namurian coals. None of these structures can be directly related with the Posidonia black shale, which appears to be generally resistive and therefore difficult to resolve with the magnetotelluric method. This assumption is supported by measurements of electrical resistivity on a set of Posidonia shale samples from the Hils syncline in the Lower Saxony basin. These rock samples were collected in shallow boreholes and show immature (0.53% Ro), oil (0.88% Ro), and gas (1.45% Ro) window thermal maturities. None of the black shale samples showed low electrical resistivity, particularly those with oil window maturity show resistivity exceeding 104 Ωm. Moreover, we could not observe a direct correlation between maturity and electrical resistivity; the Harderode samples showed the highest resistivity, whereas the Haddessen samples showed the lowest. A similar trend has been seen for coals in different states of thermal maturation. Saturation of the samples with distilled and saline water solutions led to decreasing electrical resistivity. Moreover, a positive correlation of electrical resistivity with porosity is observed for the Wickensen and Harderode samples, which suggests that the electrical resistivity of the Posidonia black shale is mainly controlled by porosity. 相似文献