A modified randomized maximum likelihood for improved Bayesian history matching

Randomized maximum likelihood is known in the petroleum reservoir community as a Bayesian history matching technique by means of minimizing a stochastic quadratic objective function. The algorithm is well established and has shown promising results in several applications. For linear models with linear observation operator, the algorithm samples the posterior density accurately. To improve the sampling for nonlinear models, we introduce a generalized version in its simplest form by re-weighting the prior. The weight term is motivated by a sufficiency condition on the expected gradient of the objective function. Recently, an ensemble version of the algorithm was proposed which can be implemented with any simulator. Unfortunately, the method has some practical implementation issues due to computation of low rank pseudo inverse matrices and in practice only the data mismatch part of the objective function is maintained. Here, we take advantage of the fact that the measurement space is often much smaller than the parameter space and project the prior uncertainty from the parameter space to the measurement space to avoid over fitting of data. The proposed algorithms show good performance on synthetic test cases including a 2D reservoir model.     

Introducing top-down methods in assessing compliance with the Kyoto Protocol

Abstract

The Kyoto Protocol has an ambitious reporting and review system to assess Parties' compliance with their emission commitments. It is based on a ‘bottom-up’ approach; that is, each Party is required to submit detailed inventories of emissions and removals. This requires considerable resources and may still not detect all important cases of non-compliance. We consider the case for introducing ‘top-down’ methods; that is, independent inverse modelling methods that calculate probable emissions using measured concentrations of gases in the atmosphere and meteorological models. We argue that the top-down methods are at present too inaccurate, too cumbersome, and politically too problematic to serve as independent alternatives to the reported emission inventories for assessing compliance, although they could be useful in monitoring the global success of the protocol. We conclude that these top-down approaches may supplement the traditional emission inventories, in particular those dealing with fluorinated gases, thereby providing input for improving the emission inventory methods.     

Fault displacement modelling using 3D vector fields

In history matching and sensitivity analysis, flexibility in the structural modelling is of great importance. The ability to easily generate multiple realizations of the model will have impact both on the updating workflow in history matching and uncertainty studies based on Monte Carlo simulations. The main contribution to fault modelling by the work presented in this paper is a new algorithm for calculating a 3D displacement field applicable to a wide range of faults due to a flexible representation. This gives the possibility to apply this field to change the displacement and thereby moving horizons and fault lines. The fault is modelled by a parametric format where the fault has a reference plane defined by a centre point, dip and strike angles. The fault itself is represented as a surface defined by a function z = f(x,y), where x, y and z are coordinates local to the reference plane, with the z-axis being normal to the plane. The displacement associated with the fault outside the fault surface is described by a 3D vector field. The displacement on the fault surface can be found by identifying the intersection lines between horizons and the fault surface (fault lines), and using kriging techniques to fill in values at all points on the surface. Away from the fault surface the displacement field is defined by a monotonic decreasing function which ensures zero displacement at a specified distance from the fault. An algorithm is developed where the displacement can be increased or decreased according to user-defined parameters. This means that the whole displacement field is changed and points on horizons around the fault can be moved accordingly by applying the modified displacement field on them. The interaction between several faults influencing the same points is taken care of by truncation rules and the ordering of the faults. The method is demonstrated on a realistic synthetic case based on a real reservoir.     

Pacific Walker Circulation variability in coupled and uncoupled climate models

There is still considerable uncertainty concerning twentieth century trends in the Pacific Walker Circulation (PWC). In this paper, observational datasets, coupled (CMIP5) and uncoupled (AGCM) model simulations, and additional numerical sensitivity experiments are analyzed to investigate twentieth century changes in the PWC and their physical mechanisms. The PWC weakens over the century in the CMIP5 simulations, but strengthens in the AGCM simulations and also in the observational twentieth century reanalysis (20CR) dataset. It is argued that the weakening in the CMIP5 simulations is not a consequence of a reduced global convective mass flux expected from simple considerations of the global hydrological response to global warming, but is rather due to a weakening of the zonal equatorial Pacific sea surface temperature (SST) gradient. Further clarification is provided by additional uncoupled atmospheric general circulation model simulations in which the ENSO-unrelated and ENSO-related portions of the observed SST changes are prescribed as lower boundary conditions. Both sets of SST forcing fields have a global warming trend, and both sets of simulations produce a weakening of the global convective mass flux. However, consistent with the strong role of the zonal SST gradient, the PWC strengthens in the simulations with the ENSO-unrelated SST forcing, which has a strengthening zonal SST gradient, despite the weakening of the global convective mass flux. Overall, our results suggest that the PWC strengthened during twentieth century global warming, but also that this strengthening was partly masked by a weakening trend associated with ENSO-related PWC variability.     

European VOC Emission Estimates Evaluated by Measurements and Model Calculations

Observations and model calculations of the concentration of hydrocarbonsat five Scandinavian rural sites during March–June 1993are reported.Decreasing concentrations from March to June are observedat all sites. The highest concentrations of hydrocarbons were found in air massescoming in from the southwest to southeast, indicating that long rangetransport fromcontinental Europe and the U.K. is important in pollution episodes. An episode of elevated concentrations of hydrocarbons observed at three of the sites in the middle of Marchis described and discussed in relation to the synoptic situation and thepresenceof other chemical compounds (NO₂, PAN, total nitrate andozone).A Lagrangian numerical model is used to calculate the concentrations of theindividual hydrocarbons at the fivesites and comparison with observations is made.The calculated concentrations for nonmethane hydrocarbons with quite longchemicallifetimes agree well with the observations.For the sum of observed and calculated hydrocarbons the correlationcoefficientsare in the range of 0.65–0.88 for the five sitesand the ratio between calculated and measured concentrations was0.72–0.97, indicating thatthe European VOC emission inventory is quite well estimated.     

Tropospheric Ozone at High Latitudes in Clean and Polluted Air Masses, a Climatological Study

Several years of continuous measurements of surfaceozone at Norwegian monitoring sites are studied in aclimatological way. The monitoring sites are at rurallocations extending from 58°N, a few hundredkilometers from the European continent and into theArctic at 79°N. The ozone observations are sorted intoclasses of integrated NO_x emissions along 96 h backtrajectories. The average seasonal cycles of ozone areestimated for each class separately. The differencesindicate the change from the background air due toanthropogenic emissions. The average seasonal cycle ofozone in the cleanest air masses showed a maximum inspring and a minimum during summer and autumn at allsites, but the spring maximum was more pronounced atthe southernmost locations. Polluted air masses showedan ozone deficit during winter and a surplus duringsummer. The deviation from the background was clearlylinked to the integrated NO_x emission along thetrajectories. In summer the calculations indicate thatthe number of ozone molecules formed per NO_x moleculedrops with increasing emissions. The average seasonalcycle of ozone at Birkenes for different transportsectors indicate that the most pronounced ozoneformation takes place in air masses from E-Europe/Russia.     

Neodymium isotopic study of Baffin Bay water: sources of REE from very old terranes

Water samples were collected from Baffin Bay and surrounding areas in order to evaluate this region as a potential source of Nd from old continental material to Atlantic water. The isotopic data ranged from ε_Nd(0) = −9.0 to −26 with most of the data around ε_Nd(0) = −20 compared with values of North Atlantic Deep Water (NADW) with ε_Nd(0) = −13.5. The concentration of Nd in Baffin Bay waters was as high as 6 × 10⁻¹² g/g compared with 2.5 × 10⁻¹² g/g for NADW. The combination of low ε_Nd and high Nd concentration indicates that Baffin Bay may be a significant source of Nd from very old crustal material. A simple box model was used to evaluate the contribution to the Nd budget of NADW and it was concluded that a substantial fraction of the Nd from ancient crustal sources that is required to maintain the isotopic composition of NADW could be supplied by Baffin Bay outflow.