Linear relationships in geomagnetic variation studies

The linear properties of Maxwell's equations enable the primary and secondary fields of geomagnetic variations to be related together by an induction tensor. Variations of total field which are confined on or near a plane, as described first by Parkinson, can occur formally only under certain conditions on either the induction tensor (that it have a simple degeneracy), or on the primary variation field components (that they consistently obey the same linear relationship over all time). The second condition is implausible for typical transient variations observed on earth, and examination of the first condition demonstrates that for variations with no consistent correlation of the horizontal components, the existence of a well-determined Parkinson vector means that observed vertical variations are secondary fields, induced by observed horizontal variations. This conclusion has important implications for the theoretical explanation of the geomagnetic “coast effect”.That primary fields be spatially uniform is a tacit condition of much theoretical work on geomagnetic variations, though the condition can in fact be relaxed to require spatial uniformity of the primary fields just within some “induction region”. If however the primary fields are not uniform over the induction region a poor Parkinson-vector determination may result. This may be most noticeable at sites which have their induction regions greatly extended by a process such as current channelling.     

Interglacial vegetation succession: A view from southern Europe

Factors influencing interglacial vegetation development in southern Europe are considered in a series of comparisons of the vegetation and climatic signatures of selected periods. Multivariate analysis provides a method for standardizing comparison of interglacial vegetation successions, and insolation values and geological evidence supply information on the climatic character of individual periods. Application of this comparative approach to a long pollen record from northwest Greece presents an opportunity to examine a series of interglacial successions under constant background site characteristics, secure chronostratigraphical positions and minimal differences in species' immigration rates. The record of four interglacial period equivalent to marine oxygen isotopic substages 5e, 7c, 9c and 11c is examined. The comparison shows that the two earliest periods are characterized by similar vegetation development despite differences in climatic regimes. Dependence on initial conditions is one of the emergent aspects of the comparisons, suggesting that the nature of surviving populations during a cold stage may be critical in determining the course of interglacial succession.     

Generalized inversion of a global numerical weather prediction model

Summary We construct the generalized inverse of a global numerical weather prediction (NWP) model, in order to prepare initial conditions for the model at time t=0 hrs. The inverse finds a weighted, least-squares best-fit to the dynamics for –24<t<0, to the previous initial condition att=–24, and to data att=–24,t=–18,t=–12 andt=0. That is, the inverse is a weak-constraint, four-dimensional variational assimilation scheme. The best-fit is found by solving the nonlinear Euler-Lagrange (EL) equations which determine the local extrema of a penalty functional. The latter is quadratic in the dynamical, initial and data residuals. The EL equations are solved using iterated representer expansions. The technique yields optimal conditioning of the very large minimization problem, which has 10⁹ hydrodynamical and thermodynamical variables defined on a 4-dimensional, space-time grid.In addition to introducing the inverse NWP model, we demonstrate it on a medium-sized problem, namely, a study of the impact of reprocessed cloud track wind observations (RCTWO) from the 1990 Tropical Cyclone Motion Experiment (TCM-90). The impact is assessed in terms of the improvement of forecasts in the South China Sea att=+48 hours. The calculation shows that the computations are manageable, the iteration scheme converges, and that the RCTWO have a beneficial impact.     

Comptel analysis of GRB 940217

COMPTEL on board CGRO has observed a very strong (S[> 0.3 MeV] = 2.03 × 10^–4 erg cm^–2), complex, and long lasting (162 s) gamma-ray burst on February 17, 1994 (GRB 940217). Temporal fluctuations occur on timescales as short as 100 ms. Hard-to-soft spectral evolution has been observed during the burst emission and also within individual peaks. The photon spectra obtained within the 6 peaks can be modelled by single power law spectra and by broken power laws with break energies at around 1 MeV. The best-fit power law slopes vary between 1.1 and 3.5 throughout the event. The burst is located at [ ₂₀₀₀, ₂₀₀₀] = [29.5°, 3.8°] with a 3 error radius of 0.9°. COMPTEL does not detect any significant post-burst emission (as reported by EGRET) at low energies (< 30 MeV), and our upper limits are marginally consistent with the EGRET detections. Using high energy spectral and temporal information, distance limits to GRB 940217 have been derived.     

Spectral characterisation of gamma-ray bursts with COMPTEL and BATSE

Although the earliest observed gamma-ray burst spectra were well described by thermal bremsstrahlung models, subsequent observations above 1 MeV showed the existence of high energy power law tails in 60% of events. In order to accurately characterise burst spectra, both the low energy turnover and the high energy tail must be accounted for. We have addressed this issue by jointly deconvolving spectra obtained by BATSE and COMPTEL onboard theCompton Observatory. We present preliminary results obtained by application of this method to the gamma-ray burst of February 17, 1994.     

Measurement of partition coefficients of phenol and cresols in gas-charged crude oil/water systems

An instrument has been constructed for monitoring the partition coefficients of phenol and cresols between crude oil and water under sub-surface conditions. The device has the capacity for introducing methane gas into crude oil, thereby allowing measurements under live oil (solution gas-containing) conditions. The partition coefficients of phenol and cresols have been measured in crude oil: water substrates under “live” oil and “dead” oil (without solution gas) conditions over a temperature range 25–150 °C. Over the range investigated it is seen that the introduction of gas (crude oil saturated at 100 bar with methane) into the system resulted in an approximate doubling of partition coefficients compared to the equivalent dead oil: brine systems. The partition coefficient data obtained using the device may be employed in a number of petroleum exploration and production activities such as the determination of residual oil saturation of a water-flooded petroleum reservoir. Partition coefficient measurements may help in predicting toxic organic solute loadings in oilfield discharge waters.     

Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system

We describe the development and preliminary application of the inverse Regional Ocean Modeling System (ROMS), a four dimensional variational (4DVAR) data assimilation system for high-resolution basin-wide and coastal oceanic flows. Inverse ROMS makes use of the recently developed perturbation tangent linear (TL), representer tangent linear (RP) and adjoint (AD) models to implement an indirect representer-based generalized inverse modeling system. This modeling framework is modular. The TL, RP and AD models are used as stand-alone sub-models within the Inverse Ocean Modeling (IOM) system described in [Chua, B.S., Bennett, A.F., 2001. An inverse ocean modeling system. Ocean Modell. 3, 137–165.]. The system allows the assimilation of a wide range of observation types and uses an iterative algorithm to solve nonlinear assimilation problems. The assimilation is performed either under the perfect model assumption (strong constraint) or by also allowing for errors in the model dynamics (weak constraints). For the weak constraint case the TL and RP models are modified to include additional forcing terms on the right hand side of the model equations. These terms are needed to account for errors in the model dynamics.Inverse ROMS is tested in a realistic 3D baroclinic upwelling system with complex bottom topography, characterized by strong mesoscale eddy variability. We assimilate synthetic data for upper ocean (0–450 m) temperatures and currents over a period of 10 days using both a high resolution and a spatially and temporally aliased sampling array. During the assimilation period the flow field undergoes substantial changes from the initial state. This allows the inverse solution to extract the dynamically active information from the synthetic observations and improve the trajectory of the model state beyond the assimilation window. Both the strong and weak constraint assimilation experiments show forecast skill greater than persistence and climatology during the 10–20 days after the last observation is assimilated.Further investigation in the functional form of the model error covariance and in the use of the representer tangent linear model may lead to improvement in the forecast skill.     

Euler–Lagrange equations for the spectral element shallow water system

We present the derivation of the discrete Euler–Lagrange equations for an inverse spectral element ocean model based on the shallow water equations. We show that the discrete Euler–Lagrange equations can be obtained from the continuous Euler–Lagrange equations by using a correct combination of the weak and the strong forms of derivatives in the Galerkin integrals, and by changing the order with which elemental assembly and mass averaging are applied in the forward and in the adjoint systems. Our derivation can be extended to obtain an adjoint for any Galerkin finite element and spectral element system.We begin the derivations using a linear wave equation in one dimension. We then apply our technique to a two-dimensional shallow water ocean model and test it on a classic double-gyre problem. The spectral element forward and adjoint ocean models can be used in a variety of inverse applications, ranging from traditional data assimilation and parameter estimation, to the less traditional model sensitivity and stability analyses, and ensemble prediction. Here the Euler–Lagrange equations are solved by an indirect representer algorithm.     

Comparative Study of Sand Porosity and a Technique for Determining Porosity of Undisturbed Marine Sediment

Porosity is a fundamental property of marine sediment from which wet bulk density can be easily determined and used in a variety of geoacoustic, geotechnical, and sedimentological studies, analyses, and models. However, methods of sampling marine sands suffer from the common problem of core disturbance making the in situ porosity difficult to obtain. Embedding the sediment within an epoxy resin matrix will minimize the disturbance to the microfabric and preserve the in situ sedimentary structure for subsequent study. Image analysis can then be used on thin sections to study the microfabric and porometry. A comprehensive review and analysis of published data on the porosity of predominantly clean sands has been completed and a simple, accurate, and nondestructive technique is described for preparing and measuring the porosity of marine sediment (siliciclastic sand) that has been infiltrated aboard ship immediately upon sample collection and chemically fixed and infiltrated with epoxy shortly thereafter. The average porosity of 36 samples of marine sand collected offshore Fort Walton Beach, Florida, and embedded with resin was determined to be 41.30%. From the review of published data the average porosity of sand was determined to be 37.7%, 42.3%, and 46.3% for packed, natural (in situ), and loose packing conditions, respectively, for a range of sorting coefficients and grain sizes.