ALBERT

Description: The Lagrange multiplier theory developed in Part I of this study is applied to complete a relative calibration of a Citation aircraft that is instrumented with six field mill sensors. When side constraints related to average fields are used, the Lagrange multiplier method performs well in computer simulations. For mill measurement errors of 1 V m(sup -1) and a 5 V m(sup -1) error in the mean fair-weather field function, the 3D storm electric field is retrieved to within an error of about 12%. A side constraint that involves estimating the detailed structure of the fair-weather field was also tested using computer simulations. For mill measurement errors of 1 V m(sup -l), the method retrieves the 3D storm field to within an error of about 8% if the fair-weather field estimate is typically within 1 V m(sup -1) of the true fair-weather field. Using this type of side constraint and data from fair-weather field maneuvers taken on 29 June 2001, the Citation aircraft was calibrated. Absolute calibration was completed using the pitch down method developed in Part I, and conventional analyses. The resulting calibration matrices were then used to retrieve storm electric fields during a Citation flight on 2 June 2001. The storm field results are encouraging and agree favorably in many respects with results derived from earlier (iterative) techniques of calibration.

Description: It is by no means a simple task to retrieve storm electric fields from an aircraft instrumented with electric field mill sensors. The presence of the aircraft distorts the ambient field in a complicated way. Before retrievals of the storm field can be made, the field mill measurement system must be "calibrated". In other words, a relationship between impressed (i.e., ambient) electric field and mill output must be established. If this relationship can be determined, it is mathematically inverted so that ambient field can be inferred from the mill outputs. Previous studies have primarily focused on linear theories where the relationship between ambient field and mill output is described by a "calibration matrix" M. Each element of the matrix describes how a particular component of the ambient field is enhanced by the aircraft. For example the product M(sub ix), E(sub x), is the contribution of the E(sub x) field to the i(th) mill output. Similarly, net aircraft charge (described by a "charge field component" E(sub q)) contributes an amount M(sub iq)E(sub q) to the output of the i(th) sensor. The central difficulty in obtaining M stems from the fact that the impressed field (E(sub x), E(sub y), E(sub z), E(sub q) is not known but is instead estimated. Typically, the aircraft is flown through a series of roll and pitch maneuvers in fair weather, and the values of the fair weather field and aircraft charge are estimated at each point along the aircraft trajectory. These initial estimates are often highly inadequate, but several investigators have improved the estimates by implementing various (ad hoc) iterative methods. Unfortunately, none of the iterative methods guarantee absolute convergence to correct values (i.e., absolute convergence to correct values has not been rigorously proven). In this work, the mathematical problem is solved directly by analytic means. For m mills installed on an arbitrary aircraft, it is shown that it is possible to solve for a single 2m-vector that provides all other needed variables (i.e., the unknown fair weather field, the unknown aircraft charge, and the unknown matrix M). Numerical tests of the solution, effects of measurement errors, and studies of solution non-uniqueness are ongoing as of this writing.

Description: No abstract available