Amazing Calculus for 'Weather Forecasting'

Calculus with Complex Variables

Fall 2016

DA-IICT

Gandhinagar

By: Nihal Satbhai

201601159

1 Introduction

Friends, We are going to discuss that how Calculus in form of differential equations are using in "Weather Forecasting".

With the help of:

  • 'Horizontal Momentum'
  • 'Vertical Momentum'
  • 'Thermodynamics'

'Continuity' we will derive the formula for 'Weather Forecasting'.

We will cover the following topics here,


1. History of Calculus in weather

2. Numerical Weather Forecasting: Primitive Equations

3. The main variables

4. Using primitive equations to predict weather

5. Find Analytic solution

6. Vector Calculus

7. Weather prediction in future

2 History of Calculus in Weather

Before many years ago our scientists relied on temperature , pressure as well asown experience.

Physical laws including conservation and thermodynamics can be used for this.

British scientist Lewis Fry Richardson was the firrst person who predict this.

The group of meteorologists at new jersy's institute for advanced study developed

the first computer that was used to complete mathematical equation.

3 Numerical Weather Forecasting:

Primitive Equations

We can use primitive equation to approximate global atmospheric low.

Three set of primitive equations are as below:

1: Conservation of momentum

2: Continuty equation

3: Thermal energy equations

4 The main Variables

  • u is places for the zonal velosity
  • v is places for the meridional velosity
  • T is temperature
  • W is water that can form a precipitates
  • w is vertical velocity



7 Find The Solution

  • We can use analytic expression to make them easy to calculate.

Ronald Averanging is used to simplify the primitive equation into an analytical solution.

8 Forecasting Storms

  • Meteorologist has found this Forwecasting very tricky to predict any thing.

Our Meteorologist are able to make advancement using computer and softwar power including mathematical power.

We can now predict hurricanes, tornadoes,cyclones direction and their intensity by using calculus.



9 Vector Calculus

vector calculus plays very important role in predicting tornadoes:

It displays following things:

  • Wind as Vector feild.
  • pressure and humidity as scalar field .

How it works:

  • This elements conspire ti produce a moist mass of rotating air,which Meteorologist called 'Supercell'.

Basic Vector calculus::

  • vector represents the quantity that both magnitude and direction. E.g. Wind in cyclones.
  • When we graph quantity into magnitude and direction,we should use line segment to display vector.
  • Arrow displays the direction og the wind.


10 How Weather is Predicted Today

  • Meteorologist uses barometer to predict air pressure. Thermometer to predict temperature. Anemometers to know the speed of wind. Weather balloons are very useful to predict all of the above thing in the layer of troposphere. Radar measures precipitation.
  • All of the above data collected and put in the numericals weather prediction computers that use the calculus started to predict the weather.

11 How is our Morden Technology

  • Wind guages, Thermometer are strapped out at the sea.
  • Our satelites photograph the earth's weather from their different orbitals.
  • Monitor balloons scan data over the particular location.
  • All of the insrument that we have developed produce more than i million
  • result foe weather everyday.
  • Super computer calculates milions of calculations in seconds only.

12 How will our Future Technology

  • In 2017 there will be a weather tracker called weather wiz that measures upto 88 percent accurency. but it still needs improvement. improvement in softwar and di erent observing instrument are continued.
  • Meteorologists are developing increasingly complicated models.
  • Super computer are being more and more accurate to predict the sense of weather.
  • The rst compuet which was built by British was named 'ENIAK'.

13 Conclusion

  • Here in the topic we have discussed how we can calculate or measure the weather around us.

But nowadays our scientists have made very much better machine using differntial calculus .

Thus di erential calculus is useful to measure weather by solving the equations.

14 Application

  • The use of this Weather Forecasting technology is to save the human being by natural hazards.
  • We can Forecast the weather that how much ther will be rain fall or what will be the speed of wind.So we can easily predict the surroundings and ensure that people could be safe.


15 References

PDF

Video