For any stationary solution of the potential vorticity equation, the streamfunction Ψ and the potential vorticity Q are functionally related, i.e., Q=F (Ψ). For analytical modons which are considered as one of the models of atmospheric blocking, the functional form of Q=F (Ψ) is assumed to be linear and therefore the modon boundary is assumed to be circular. Modons with boundaries other than a circle have been numerically investigated by several authors. Boyd and Ma (1990) calculated numerically the functional form of Q=F (Ψ) for elliptical modons elongated in the basic flow direction on an ƒ plane. In this note, the functional form of Q=F (Ψ) is calculated analytically for modons with an elliptical boundary slightly different from a circle. For modons elongated in the basic flow direction, the result agrees qualitatively with the above-mentioned numerical one. On the other hand, for modons elongated in the direction perpendicular to the basic flow, the functional form of Q=F (Ψ) is shown to be qualitatively different from that for modons elongated in the basic flow.
Impedance tensors for periods of 5.3 to 1920 minutes were estimated by making use of the stable data of the geoelectric field over a long range of time and the geomagnetic variations due to a large-scale magnetic storm. The wavelength of geomagnetic variations used as the inducing field in applying the magnetotelluric method is very long. Multiple coherencies between each component of the geoelectric field and both N-S and E-W components of the geomagnetic field are high; coherencies between the two horizontal components of the geomagnetic field are low. Therefore, estimated impedance tensors are reliable. Since skewnesses are not so high, the subterranean resistivity structure beneath the observation area can be regarded to be two-dimensional and coordinate transformation was performed referring to the principal axes calculated from impedance tensors. Apparent resistivities obtained from transformed data for both H- and E-polarizations are different by a factor of about 100.
Numerical experiments of tropical cyclone motion are performed with the use of a triply-nested grid model which has been developed primarily for the study of tropical cyclones. One of the features of the model is that the mixing ratios of cloud water and rainwater are taken to be predicted variables because evaporation of rainwater and convective downdraft are considered to be important. Cumulus parameterization and other aspects of the model are basically the same as those described in Yamasaki (1986, 1987) except for the use of the longitude-latitude coordinates, inclusion of topography, finer vertical resolution (ten-layer model) and so on. The grid sizes of the coarse, intermediate and fine grid areas are taken to be 15/4, 5/4 and 5/12 degrees, respectively. Several typhoons in August and September 1990 (SPECTRUM period) are chosen for the numerical experiments. The initial condition is taken from the objectively analyzed global data of JMA. An axially symmetric vortex is superimposed on this data. The objective of this study is to see to what degree the model can predict typhoon motion and what are the primary causes of prediction errors. It is found that while the model appears to show somewhat good performance for the prediction of typhoon motion, the primary causes of prediction errors are poor prediction of the behavior of the subtropical high and the initial fields of wind and conditional instability.