mathematical modelling and its application in weather forecasting
DESCRIPTION
what is mathematical modelling. how it is useful to us. future prediction with the help of mathematical modellingTRANSCRIPT
MATHS PROJECT WORK
MATHEMATICAL MODELLING
What is mathematical modelling?
Conversion of physical situation into mathematics with some suitable conditions is known as mathematical modeling. Mathematical modeling is nothing but a technique and the pedagogy taken from fine arts and not from the basic sciences.
Describe real-world phenomena Investigate important questions about
the observed world Explain real-world phenomena Test ideas Make predictions about the real world
Mathematical modeling is the use of mathematics to:-
Process of mathematical modelling
ModelReal world data
Predictions/Explanations
Mathematical conclusions
Formulation
An
alysis
Interpretation
Test
Describing a simple model Example: how much space is
inside this cardboard box? We know three measurements:• h (height),• w (width), and• l (length), and (luckily!) the formula for
the volume of a cuboids is:• Volume = h × w × l
Conclusion
So we have a very simple model here through which we are solving a real world problem
Mathematical modeling in meteorology and weather forecasting
How it is done??Weather forecasts are
made by collecting quantitative - numerical - data about the current state of the atmosphere. This data is then put into a mathematical model, which will predict the weather based on current conditions.
Mathematical modelling cycleStart
Formulation
Assumptions/Axioms
Solution
Satisfied
Stop
Interpretation
Validation
YesNO
General formulation Mathematical formulation of atmospheric
models used for weather forecasting is based on the equation of mechanics of a compressible fluid, which stem from three fundamental laws: the laws of the momentum and mass conservation and the first law of thermodynamics. These three laws give rise to equations of motion, equation of continuity, and thermodynamic energy equation respectively.
A mathematical model to predict future
dV = -1 grad p-2ω xv - grad U + D
dt ρ
where v is the velocity vector, d/dt is symbol of the total derivative with respect to time, ρis density, p is pressure, ω is the vector of angular velocity of earth’s rotation, U is potential of the gravity force, and D is the vector representing dissipation force.
How it is processed?In mathematical models, raw
data is entered into a computer. A series of calculations is performed on the raw data on it to determine how it will change over time. Normally, mathematical modeling is done by computers, which can carry out many calculations per second.
In the case of weather models, data such as rain fall, temperature and wind speed are fed into a computer. The computer performs calculations on - models - this data, using equations produced from our scientific understanding of atmospheric processes, such as fluid dynamics and thermodynamic equations. These models allow forecasters to predict how the conditions in the atmosphere will evolve. The more sophisticated and up-to-date your model is, the more accurate your forecast should be. Powerful supercomputers are needed to perform the complex calculations in mathematical weather models.
Conclusion
It's thanks to models that we can process raw weather data into sophisticated and accurate forecasts. The model used to create the unique 1 kilometer radius forecast on Weather Labs is the most sophisticated model available.
Even the most sophisticated model can't be right all the time.
Prepared By-MD. SARWAR AZAD
XI-B23
Thank you