On the assimilation of total-ozone satellite data

A two-dimensional model for advection and data assimilation of total-ozone data has been developed. The Assimilation Model KNMI (AMK) is a global model describing the transport of the column amounts of ozone, by a wind field at a single pressure level, assuming that total ozone behaves as a passive tracer. In this study, ozone column amounts measured by the TIROS Operational Vertical Sounder (TOVS) instrument on the National Oceanic and Atmospheric Administration (NOAA) polar satellites and wind fields from the Meteorological Archive and Retrieval System (MARS) archives at ECMWF have been used. By means of the AMK, the incomplete space-time distribution of the TOVS measurements is filled in and global total-ozone maps at any given time can be obtained. The choice of wind field to be used for transporting column amounts of ozone is extensively discussed. It is shown that the 200-hPa wind field is the optimal single-pressure-level wind field for advecting total ozone. Assimilated ozone fields are the basic information for research on atmospheric chemistry and dynamics, but are also important for the validation of ozone measurements.

Tooth Position after Orthodontic Extractions: A Follow-up Study after Activator Treatment

The long term result of orthodontic extractions of mandibular second premolars and permanent first molars was investigated by measuring the degree of tooth tipping mesial and distal to the extraction sites in cases with complete and incomplete closure of extraction spaces after treatment and/or at follow-up examination. Tooth inclination was determined from photographs taken of dental casts made after treatment and follow-up examination. The inclination of the teeth was measured in relation to each other and in relation to the occlusal line. The results of the investigation revealed that teeth which were tipped mesial and/or distal to the extraction sites after orthodontic treatment had a tendency to upright in relation to each other and in relation to the occlusal line. Uprighting was pronounced in cases which had extraction spaces remaining after treatment, but which were closed at the time of follow-up examination, and in cases with closed extraction spaces after treatment. However, minimal changes in inclination of the teeth adjacent to the extraction sites were found in cases with incomplete space closure after treatment and at follow-up.

Matrix Transformations in an Incomplete Space

Let X = (X, p) be a seminormed complex linear space with zero θ. Natural definitions of convergent sequence, Cauchy sequence, absolutely convergent series, etc., can be given in terms of the seminorm p. Let us write C = C(X) for the set of all convergent sequences for the set of Cauchy sequences; and L∞ for the set of all bounded sequences.