*Tid:***17 december 2000 kl 1515-1600 **

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Magnus Moglia
**

**Titel:** **
A stochastic model for changes of wind and temperature in the atmosphere
**

*Sammanfattning: *

The background of this report is the problem that for instance the wind deflects bullets which are shot through the atmosphere. That is a problem because the wind and other atmospheric phenomena are not easily predicted.

Measurements are needed to get knowledge about the current weather and weather balloons are sent into the atmosphere to measure winds, temperature et cetera on different altitudes. A number of curves are acquired from these measurements. For instance is the curve with temperature against height important. The problem with measurements is that during the time between the measurement and the shooting the curves are constantly changing.

The model of this report describes the changes of curves from one time to another and it can be used to simulate the change of curves from one time to another.

There are a lot of mechanisms working together in the atmosphere and I have only taken a few of them in consideration. It shouldn't be hard though to build other mechanisms into the model.

I have concentrated on temperature and horizontal winds in this report. Air pressure, vertical winds and the Richardson number are determined from these quantities. The Richardson number is an indicator of turbulence. It is possible to trace the forming of turbulence if the model is a good description of the actual atmosphere.

The model is based on the idea to describe a curve by splitting it into parts which change independently of each other. There are different models for different parts of the curves.

I think of a curve as a line plus the deviations from the line.

The first description of a curve is a line. The changes of the line is described by a linear regression model. The part of the curve which is not described by a line is the deviations from the line. The changes of these are described by a translations process and a moving average process. The translations process is governed by a Markov process. The model parameters has been estimated with a method which is hard to investigate the efficiency of.

My hope is that this model can be used to simulate weather changes so that it is possible to find some kind of strategy when shooting so that the variation due to the lack of knowledge about the atmosphere is minimized.