Modelling and inversion of electromagnetic data using an approximate plate model

This paper presents a computational method for the interpretation of electromagnetic (EM) profile data in the frequency domain using a thin plate model within a two-layer earth. The modelling method is based on an integral equation formulation, where the conductor is represented by a lattice structure composed of two-dimensional surface elements. Several approximations are used to simplify the theoretical basis and to decrease the computation time. The simple parametric model allows efficient use of optimization methods. We employ a linearized inversion scheme based on singular value decomposition and adaptive damping. The new forward computation method and the parameter optimization are combined in the computer program, emplates . The modelling examples demonstrate that the approximate method is capable of describing the characteristic behaviour of the EM response of a thin plate-like conductor in conductive surroundings. The efficacy of the inversion is demonstrated using both synthetic and field data. An optional depth compensation method is used to improve the interpreted values of the depth of burial. The results show that the method is cost effective and suitable for interactive interpretation of EM data.     

An applied model for the height of the daytime mixed layer and the entrainment zone

A model is presented for the height of the mixed layer and the depth of the entrainment zone under near-neutral and unstable atmospheric conditions. It is based on the zero-order mixed-layer height model of Batchvarova and Gryning (1991) and the parameterization of the entrainment zone depth proposed by Gryning and Batchvarova (1994). However, most zero-order slab type models of mixed-layer height may be applied. The use of the model requires only information on those meteorological parameters that are needed in operational applications of ordinary zero-order slab type models of mixed-layer height: friction velocity, kinematic heat flux near the ground and potential temperature gradient in the free atmosphere above the entrainment zone. When information is available on the horizontal divergence of the large-scale flow field, the model also takes into account the effect of subsidence, although this is usually neglected in operational models of mixed-layer height owing to lack of data. Model performance is tested using data from the CIRCE experiment.     

Energy Balance Of A Sparse Coniferous High-Latitude Forest Under Winter Conditions

Measurements carried out in Northern Finland on radiation and turbulent fluxes over a sparse, sub-arctic boreal forest with snow covered ground were analysed. The measurements represent late winter conditions characterised by low solar elevation angles. During the experiment (12–24 March 1997) day and night were about equally long. At low solar elevation angles the forest shades most of the snow surface. Therefore an important part of the radiation never reaches the snow surface but is absorbed by the forest. The sensible heat flux above the forest was fairly large, reaching more than 100 W m^-2. The measurements of sensible heat flux within and above the forest revealed that the sensible heat flux from the snow surface is negligible and the sensible heat flux above the forest stems from warming of the trees. A simple model for the surface energy balance of a sparse forest is presented. The model treats the diffuse and direct shortwave (solar) radiation separately. It introduces a factor that accounts for the shading of the ground at low solar elevation angles, and a parameter that deals with the partial transparency of the forest.Input to the model are the direct and diffuse incoming shortwave radiation.Measurements of the global radiation (direct plus diffuse incoming shortwaveradiation) above the forest revealed a considerable attenuation of the globalradiation at low solar elevation. A relation for the atmospheric turbidity asfunction of the solar elevation angle is suggested. The global radiation wassimulated for a three month period. For conditions with a cloud cover of lessthan 7 oktas good agreement between model predictions and measurementswere found. For cloud cover 7 and 8 oktas a considerable spread can beobserved. To apply the proposed energy balance model, the global radiationmust be separated into its diffuse and direct components. We propose a simpleempirical relationship between diffuse shortwave and global radiation asfunction of cloud cover.     

Long-Term Mean Wind Profiles Based on Similarity Theory

We provide general forms for long-term mean wind profiles from similarity-based wind profiles, beginning with a probabilistic adaptation of Monin–Obukhov similarity theory. We develop an analytical formulation for the stability distributions prevailing in the atmospheric surface layer, which in turn facilitates the derivation of a long-term mean wind profile based on Monin–Obukhov similarity theory. The modelled stability distributions exhibit good agreement with measurements from sites having different local conditions. The long-term wind profile formulation is further extended to include the influence of the depth of the atmospheric boundary layer (h), which becomes relevant for heights above h/3, and the resultant long-term ‘tall’ profile form also matches observations.     

Nomogram for the Height of the Daytime Mixed Layer

A method to construct a nomogram of the daytime mixed-layer-height evolution is presented. The nomogram will be specific for a given location and land surface type and is intended to be an easy tool to achieve a general understanding of mixed-layer behaviour. Also it is a pedagogical graphical one-pager that displays the bulk of data that controls the evolution of the mixed layer. Nomograms from northern, central and southern Europe are presented and discussed. Comparison with data from two sites shows good agreement although the nomograms overestimated the mixing height when it was low.     

Comparing mixing-length models of the diabatic wind profile over homogeneous terrain

Models of the diabatic wind profile over homogeneous terrain for the entire atmospheric boundary layer are developed using mixing-length theory and are compared to wind speed observations up to 300 m at the National Test Station for Wind Turbines at Høvsøre, Denmark. The measurements are performed within a wide range of atmospheric stability conditions, which allows a comparison of the models with the average wind profile computed in seven stability classes, showing a better agreement than compared to the traditional surface-layer wind profile. The wind profile is measured by combining cup anemometer and lidar observations, showing good agreement at the overlapping heights. The height of the boundary layer, a parameter required for the wind profile models, is estimated under neutral and stable conditions using surface-layer turbulence measurements, and under unstable conditions based on the aerosol backscatter profile from ceilometer observations.     

Remanence correction in magnetic interpretation with the infinitely deep plate model

Summary Conditions are given under which two thick plates, differing in dip, apparent susceptibility, and remanence, will produce similar magnetic anomalies. From these conditions correction formulae are developed. Using these formulae the dip and susceptibility of a plate with remanent magnetization can be obtained from those of non-remanent plate. An interpretation procedure is suggested where the magnetic anomaly is first interpreted by means of a plate without remanence, dip and apparent susceptibility are then estimated by using the correction formulae developed. Thickness, position and depth of the plate are unaffected by the remanence correction procedure. The procedure is independent of the field component measured.     

Regional EM studies in the 80's

The review describes in broad terms the development of regional EM studies during the last five-six years. Large simultaneous magnetometer arrays, broadband and dense profiling with five component instruments, the use of remote reference techniques and in-field data processing have increased both the number and the quality of EM surveys. The increase has been strong all over the world.An extensive list of references, divided geographically, is presented. Selected examples of regional resisitivity-versus-depth curves are shown for Africa, the Baikal region, the Baltic Shield, the Canadian Shield, the Carpathian regions, the Central Andes, Iceland, India, the Juan de Fuca Plate, the Münsterland Basin, the Rio Grande rift, the Scottish Caledonides, the Tasman Sea, and for the United States in general. Because of the influence of tectonic settings and the metamorphic grade of rocks, only qualitative aspects of the results are relevant.Classical array studies, especially in Australia, in the Carpathian regions, in India, in North Germany and in Scotland have been reinterpreted and completed with more accurate 2D modelling and dense MT profiling. In the USA and Canada also new regions have been surveyed extensively. New regional EM work has been conducted extensively on the Baltic Shield and in Central and North Africa, Siberia, China, in the areas around the Caspian and Black Seas and in South America.The newest studies are supported by or compared with other geophysical data, which also are used in extrapolating for missing EM data density. There are several successful large-scale projects in operation: the European Geotraverse (EGT), the KAPG International Geotraverses and the EMSLAB project (with its first preliminary results). Regional EM studies have been increasingly applied to geothermal, hydrocarbon and mineral prospecting as well as local structural studies, e.g. studies of sites for nuclear waste disposal.     

Mixing Height Over Water And Its Role On The Correlation Between Temperature And Humidity Fluctuations In The Unstable Surface Layer

Results from an experimental investigation of themixing height over inner Danish waters carriedout from September 1990 to October 1992, are discussed.The statistical analysis of the mixed-layer height (z_i)over the sea does not exhibit the dailyvariation that is characteristic of the mixed layerover land, but it is nearly constant over a24-hour cycle. During summer, the mixed layer ishigher than during winter. A second inversionwas often observed.A case study of the development of the mixed layerover the sea under near-neutral and unstableatmospheric conditions during six consecutivedays is presented. A zero-order mixed-layer heightmodel is applied. In addition to momentum and heatfluxes the effect of subsidence was found to be importantfor the evolution of the mixed layer over the sea. Themodelled evolution of z_i compared successfullywith measurements.We have investigated the influence of themixed-layer height on the correlation coefficient R_qTbetween temperature and humidity fluctuations usingthe values obtained with the model.We found that the evolution of R_qT follows theevolution of the mixing height. An empirical modellinking the surface values of R_qT to z_i and the Obukhov scaling length L has been suggested. The modelreproduces the experimental features.