what is mathematical modelling. how it is useful to us. future prediction with the help of mathematical modelling

3. 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.

4.  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:-

5. ModelReal world data
Predictions/
Explanations
Mathematical
conclusions
Formulation
Analysis
Interpretation
Test

6.  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

8. Mathematical modeling
in meteorology and
weather forecasting

9. 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.

10. Start
Formulation
Assumptions/Axioms
Solution
Satisfied Stop
Interpretation
Validation
YesNO

11. 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.

12. 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.

13. 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.

14.  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.

15. 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.

16. Prepared By-
MD. SARWAR AZAD
XI-B
23
Thank you