The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: A comparison study using a nonlinear reduced gravity ocean model

This paper compares contending advanced data assimilation algorithms using the same dynamical model and measurements. Assimilation experiments use the ensemble Kalman filter (EnKF), the ensemble Kalman smoother (EnKS) and the representer method involving a nonlinear model and synthetic measurements of a mesoscale eddy. Twin model experiments provide the “truth” and assimilated state. The difference between truth and assimilation state is a mispositioning of an eddy in the initial state affected by a temporal shift. The systems are constructed to represent the dynamics, error covariances and data density as similarly as possible, though because of the differing assumptions in the system derivations subtle differences do occur. The results reflect some of these differences in the tangent linear assumption made in the representer adjoint and the temporal covariance of the EnKF, which does not correct initial condition errors. These differences are assessed through the accuracy of each method as a function of measurement density. Results indicate that these methods are comparably accurate for sufficiently dense measurement networks; and each is able to correct the position of a purposefully misplaced mesoscale eddy. As measurement density is decreased, the EnKS and the representer method retain accuracy longer than the EnKF. While the representer method is more accurate than the sequential methods within the time period covered by the observations (particularly during the first part of the assimilation time), the representer method is less accurate during later times and during the forecast time period for sparse networks as the tangent linear assumption becomes less accurate. Furthermore, the representer method proves to be significantly more costly (2–4 times) than the EnKS and EnKF even with only a few outer iterations of the iterated indirect representer method.     

Placing constraints on phase equilibria and thermophysical properties in the system MgO-SiO2 by a thermodynamically consistent vibrational method

We use a lattice vibrational technique to derive thermophysical and thermochemical properties and phase equilibria in the system MgO-SiO₂ at pressures and temperatures relevant to Earth’s mantle. The technique is based on an extension of Kieffer’s model to incorporate details of the phonon spectrum, and it includes treatment of intrinsic anharmonicity. We use a least squares inversion technique applied to available experimental data, and show that it results in an accurate representation of thermodynamic properties and sound wave velocities of high-pressure phases in the system MgSiO₃. The vibrational method has been validated against laboratory experimental data in the temperature range between 0 and 2500 K and at pressures between 1 bar and 30 GPa. The technique results in a phase diagram consistent with the majority of thermophysical and thermochemical data. It is shown that intrinsic anharmonicity affects significantly slopes and positions of the phase boundaries. Our analysis indicates inconsistencies in a number of data sets of thermophysical properties for stishovite, majorite and ortho-enstatite necessitating new measurements. For akimotoite elasticity data at high-pressure and high-temperature conditions and 1 bar heat capacity measurements are needed. For stishovite elasticity measurements are necessary to reconcile elasticity data with V-P-T measurements. Additionally V-P-T measurements at pressures higher than 10 GPa are needed, which should be reconciled with V-P-T data at lower pressures. Raman and infrared spectroscopic data are necessary for both clino-enstatite and majorite. Additionally structural data are needed to resolve the discrepancy between values for the degree of disorder in majorite. Volume expansion data for ortho-enstatite are needed and effects causing differences in measured volume expansion should be elucidated.     

Persistence of vinyl chloride in ground water at the Woodlawn landfill Superfund site,northeastern Maryland,USA

Since landfill operations ceased in the early 1980s at the Woodlawn landfill Superfund site in northeastern Maryland, USA, the carcinogen vinyl chloride monomer (VCM) has persisted in the site ground water at concentrations in places greater than 100 ppb. Investigations of VCM concentrations from monitoring well data from 1981 through 1991, which were published in 2001, concluded that concentrations were cyclic and were not dissipating. Data from 1991 to 2000 confirm VCM persistence, showing concentration peaks as late as 1997 in the eastern part of the site. These values are significantly above both drinking water standards (>MCL of 2 ppb) and lifetime excess cancer risk (E-6 risk level) from exposure since birth (>0.024 ppb). Sources for VCM are landfill wastes (PVC-sludge) and effluent from an on-site transfer station. In addition to direct release of VCM from wastes, other chlorinated hydrocarbons, trichloroethene and perchloroethene (TCE and PCE) are also present in the ground water, and these compounds can degrade into VCM. Persistence of VCM concentrations is the result of leachate generation, mostly from multi-source wastes in the vadose zone, with subsequent infiltration into the regional aquifer. Increases in VCM concentrations (new leachate generation) alternated with decreases in VCM concentrations (infiltration without leachate) in a cyclic fashion, during this 20-year period.     

The use of neutrons and monochromatic X-rays for non-destructive testing in geological materials

In the paper we present our results for element sensitive high-energy X-ray tomography and high-speed thermal neutron tomography applied to geological samples. The tuneable monochromatic X-ray beam was used for element sensitive tomography of geological samples containing heavy elements using the K-edge dichromatic scanning technique. This type of NDT (non-destructive testing) allowed us to reveal the quantity and location of uranium, lead and mercury in Oklo samples (natural nuclear reactor) and Cinnabar stones. Fast 3-D thermal neutron imaging of dynamical processes was successfully tested at the high flux neutron tomography station of the ILL. The qualitative investigation of water repellents and consolidants applied on sandstones of Bray and limestones of Maastricht were the first samples to be studied with the new imaging technique.     

Temperature Behavior of a Natural Shallow Water Body during a Summer Period

Summary For many biological processes, the daily and seasonal behavior of the temperature of the water layer close to the water surface is very important. An example is the development of larvas of mosquito species which develop in small still water bodies. An outdoor experiment during a summer period of four months has been executed in a small water body situated within a bog area, in order to obtain insight into the daily and seasonal temperature behavior of this water body. The measurements show that during daytime a strong thermal stratification occurs in the water body and that during nighttime a well mixed layer develops growing from the water surface. In the upper water layer a well developed daily temperature cycle is present. This cycle is strongly reduced by depth. On average, the daily maximum water temperature excursion from the mean agree with the daily maximum air temperature excursion from the mean. The range between maximum and minimum water temperature correlate well with the daily global irradiation. Received February 14, 1996 Revised May 21, 1997     

Variations in the Intensity of the Earth's Magnetic Field

The Earth's main magnetic field can be approximated by an axial, geocentric dipole. The remaining non-dipole field is much smaller and is a regional rather than a global feature – quite large changes can occur in a few ka. This review is concerned with changes in the dipole component of the geomagnetic field, and one of the problems is in separating the non-dipole from the dipole contributions to the field. Unlike the many determinations of the direction of the Earth's magnetic field in the past (which have led to fundamental contributions to our understanding of plate tectonics and shown that the field can on occasion reverse its polarity), estimates of the intensity of the field are comparatively few, especially before the Holocene. This is mainly the result of experimental difficulties in obtaining reliable measurements of the field. These problems are discussed in some detail and are followed by a short account of archaeomagnetic intensities and results from Hawaii where many of the first determinations were obtained. Measurements for the last 100 ka from both lavas and lacustrine and oceanic sediments are reviewed and results from different areas compared. An asymmetric saw-tooth pattern has been observed in some of the records over the last few Ma, and this rather controversial question is discussed. Finally an account is given of the far more limited data on palaeointensities in earlier times.A short discussion is given of the interpretation of coherent short wavelength variations which are observed in many marine magnetic profiles. Although short reversals of the field may be responsible for some of these tiny wiggles, it is more likely that in general they are the result of changes in the strength of the Earth's magnetic field.