Goswami, B. N.

English

Publications of the IAS Fellows

SERIES ⎜ ARTICLE
8 RESONANCE ⎜ March 1997
Introduction
In the last two parts we  discussed the physical basis for weather
forecasting and the practical and conceptual difficulties
encountered when one tries to forecast the weather.  In this
concluding part, we shall trace the history of weather forecasting
and describe its current status.
Traditional weather forecasting reminds us of meteorologists
sitting with the weather charts spread in front of them and
making forecasts based on their ‘experience’.  This experience is
the knowledge gathered over years of observations and the
background theory on weather.  Given a background condition,
a particular weather pattern, say a low pressure area, tends to
evolve on the average in a certain way.  This may be termed as
mean or ‘climatological’ behaviour.  Also atmospheric
fluctuations have a certain amount of ‘persistency’.  In other
words, once a low pressure is formed, it persists for a while.
Forecasts made by meteorologists based on ‘climatology’ and
‘persistence’ and empirical knowledge about evolution of weather
systems are known as synoptic forecasts.  Before the advent of
computers, this was the only method of weather forecasting.
Upto 12 hours or 24 hours in advance, the meteorologists can
actually  make very good forecasts based on this technique.  But
beyond that  this type of forecast  is not useful.
Even with the approximations that must be made, the motion of
the air is governed by a set of physical laws as described in Part
I of this series.   Therefore, if we knew the initial state and  we
could solve the equations, we could predict the future state.  The
first problem is that these equations are highly nonlinear coupled
The Challenge of Weather Prediction
3. Old and Modern Ways of Weather Forecasting
B N Goswami
B N Goswami  is with the
Centre for   Atmospheric
and Oceanic Sciences at
the Indian  Institute of
Science, Bangalore. After
his PhD in Plasma Physics
he was attracted to this
field by the challenges in
weather  and climate
prediction. His interests
include understanding
variability and
predictability of  all
tropical phenomena
including the monsoon.
The previous articles of this
series were:
1.  The basic driving, November
1996.
2. Difficulties in predicting the
weather, January 1997.
SERIES ⎜ ARTICLE
9RESONANCE ⎜ March 1997
partial differential equations.  It is not possible to arrive at
analytic solutions.  Thus, the only way to predict is using
numerical techniques.  The modern concept of numerical weather
forecasting was born in the fertile mind of the Quaker
mathematician Lewis Fry Richardson (1881–1953)  during World
War – I.  Richardson was attracted by the success of spherical
astronomy where the motion of the planets and the timing of the
solar eclipse could be predicted years in advance.  Although
spherical astronomy deals with simple geometrical relations
whereas meteorology has to struggle with an enormously complex
mechanical and thermodynamical system, Richardson argued
that it should be possible to proceed from an initial state of the
atmosphere to a final state by a purely mathematical process.
Richardson who served with an ambulance unit in France
during   World War I, worked through long nights and developed
a step by step integration method for solving differential
equations and in 1922 published one of the most remarkable
books in meteorology,  Weather Prediction by Numerical Process.
Here he presented a set of equations that he thought described
the physical processes governing the atmospheric phenomena
together with a method for their approximate solution.  Although
the example worked out by Richardson in the book was a
spectacular failure, this was the beginning of numerical weather
forecasting.  Richardson, with immense labour using his hand
calculator, calculated the change of pressure at the surface over
a period of six hours for an area in Europe and obtained an
answer which was in error by at least two orders of magnitude.  It
must have required considerable courage to publish such a
ludicrous result.  We have reason to be thankful to him for this
courage as this example brought to focus some of the intrinsic
difficulties in solving  meteorological equations!
During the next two decades not much progress took place in
numerical weather prediction (NWP).  In the late 40’s Jule
Charney (a pioneer of modern meteorology who was later a
professor at the Massachussetts Institute of Technology) provided
a theoretical basis to overcome the problems faced by Richardson.
Lewis Fry Richardson
made the first attempt at
numerically solving the
atmospheric equations
make a six hour forecast
in 1922 using his hand
calculator!  His attempt,
though  a spectacular
fai lure, showed the
intrinsic problems in
solving the meteoro-
logical equations.
The group led by Jule
Charney at the Institute
for Advanced Study,
Princeton, made the first
successful numerical
weather prediction in
April 1950, using the first
ever bui l t  computer
ENIAC.
SERIES ⎜ ARTICLE
10 RESONANCE ⎜ March 1997
Meanwhile, the first electronic computer ENIAC (Electronic
Numerical Integrator and Computer) was being built at
Princeton.  Professor John Von Neumann at the Institute of
Advanced Studies in  Princeton  recognised the enormous
potential of this machine and organised a group with Jule
Charney, R Fjortoft and a few others to conduct numerical
forecasts of the atmospheric system.  Using the simplified
equations proposed by Charney (known as the   barotropic vorticity
equation) the first successful numerical forecast was produced
with the ENIAC in April, 1950 for a level in the middle
troposphere (500 hPa) supposed to represent the total behaviour
of the atmosphere.  Thus the era of numerical weather prediction
was finally launched.  Although the integration of the barotropic
vorticity equation was made in a relatively small domain in the
middle latitude (about 5000 Km x 5000 Km) only, a forecast of
24 hours took 36 hours of the computer time!
Figure  1   A cartesian grid for
solving the meteorological
equations .
SERIES ⎜ ARTICLE
11RESONANCE ⎜ March 1997
In a modern weather forecasting centre such as the one we have
in New Delhi (National Centre for Medium Range Weather
Forecasts), the basic equations are solved over the entire globe
as shown in  Figure 1.  The method of solving illustrated in this
figure is known as finite difference technique in which the
equations are solved at a set of equi-spaced points.  The other
technique, more commonly used in recent times, is known as
spectral technique.  In this technique the variables are expressed
in terms of a set of orthogonal basis functions (spherical
harmonics) and equations expressing the evolution of the
Figure 2  Generalised flow
diagram of a general
circulation model.
SERIES ⎜ ARTICLE
12 RESONANCE ⎜ March 1997
amplitudes of these basis functions are solved.  The flow chart in
Figure 2 shows how this integration is carried out.  The grid
spacing shown in  Figure  1  and  Figure 2 is somewhat outdated.
Most state of the art models now use 1o x 1o grid spacing or
better.  They divide the atmosphere into 20 layers or more in the
vertical.  This gives us about 1.3 million points for the seven
variables!  In addition the calculation of the forcing functions
such as radiation and cloud formation and release of latent heat
requires very complex calculations.  With all these constraints,
the forecasts for tomorrow and days beyond must be produced
today or else it will not have any value!  This is why the weather
forecasting centres require super computers.
Solving the equations in a super computer is only part of the
story.  A major effort is required to specify the initial state.  The
initial state comes from all those weather observations mentioned
in Part II of the series.  Currently, in addition to about 900 upper
air stations, about 10,000 surface meteorological stations,  7000
merchant ships and 600 drifting buoys send their routine weather
Figure 3  The Global
Teleconnection System (GTS)
(Adopted from WMO
Bulletin, Vol. 45, January
1996).
SERIES ⎜ ARTICLE
13RESONANCE ⎜ March 1997
reports.  These are passed around the globe through ‘hot lines’
called the Global Teleconnection System (GTS) as shown in
Figure 3.  Most NWP centres have facilities to receive these data.
In addition to these, weather observations by several aircrafts
and satellites are also passed on through the GTS.  Since these
are different types of information and at non-uniform space and
time points with relatively large data void regions, a system has
to be evolved to generate data at regular grid points required by
the model.  This,  known as  Objective Analysis Scheme  uses a
certain objective interpolation scheme to fill up the data void
regions.  In principle, this initial condition must exactly satisfy
the governing equations.  However, due to  observational errors
as well as the interpolation over the data void regions, the initial
observations normally do not satisfy the governing equations.
Figure 4   Schematic dia-
gram of an interactive
analysis/forecast/retrieval
system.
INTERACTIVE ANALYSIS/FORECAST/
RETRIEVAL SYSTEM
SERIES ⎜ ARTICLE
14 RESONANCE ⎜ March 1997
This imbalance is seen by the model as an initial error which
grows rapidly with the integration of the model.  To reduce this
initial ‘shock’ a short forecast by the model is used as the first
guess and the differences between the observation and the first
guess are minimised using an objective minimisation technique.
This procedure generates an initial state for the forecasts that is
in approximate balance with the model equations.  Before doing
all this the system must also carry out some quality control
checks on the data.  Similarly, getting the meteorological
parameters from satellite observations requires a set of
calculations called  Satellite Retrieval Scheme.  A schematic
diagram of the interactive analysis/forecast/retrieval system is
shown in  Figure 4.  This procedure is quite involved and
requires almost as much, if not more time on the computer as the
actual numerical integration of the computer model.
NWP has never looked back since  the first numerical forecasts
in April, 1950.  The tremendous advance in computer technology
allows us to solve more complex models over a global domain.
Moreover, specification of initial conditions has steadily
improved through better observation, data collection and
communication techniques and availability of satellite
observations.  In addition, our understanding of the physical
processes responsible for the weather changes has also steadily
improved.  As a result, today, operational NWP centres are
capable of making successful forecasts of the large scale
circulation features in the middle latitude about 6-7 days in
advance.  By large scale circulation features we refer to wind
conditions or temperatures over thousand kilometres or higher
spatial scales.  However, even in middle latitude, prediction of
rainfall is somewhat less successful.  Similarly, if we want the
forecast for a specific small town, it is less skillful.  In the tropics,
the skill of the forecast for even the large scale circulation
features is currently only about 2-3 days while the skill for
precipitation forecasts is even poorer.  This is because in the
middle latitudes, rainfall is rather passive.  The circulation
forces upward motion that condenses the moisture and produces
Due to tremendous
advance in computer
technology, better under-
standing of the physical
processes and better
acquisi t ion of data
(through conventional
means and satellites)
have increased the skill
in the middle latitude
forecasts at least six fold
since 1950.  In contrast,
the tropical forecasts
have improved by only
about two fold since then.
SERIES ⎜ ARTICLE
15RESONANCE ⎜ March 1997
rain.  In the tropics, rain plays a much more active role.  It
actually dictates the  type of circulation we should have.  As a
result, to improve the tropical forecasts we must improve our
knowledge of how the rains form in the tropics and how they
interact with the circulation.  The challenge of the day is
therefore, to push the skill of tropical forecasts from the present
2-3 days to let us say 5-6 days through better understanding and
formulation of the relevant processes.  Every one day
improvement in the averaged forecast skill can save us crores of
rupees !
Before concluding, let me add a few words on climate forecasting.
By climate, we refer to the average state of the atmosphere such
as the monthly or seasonal mean.  Thus, climate forecasts must
be made at least one season in advance.  From the discussion on
the limit to weather forecasts, it is clear that even if we have a
‘perfect’ model and ‘near perfect’ observations, the skill of
weather forecasts will be limited to about two weeks at best.
Does this mean that there is no hope for climate forecasts?
Fortunately, the answer to this question is no.  This is because,
so far we have considered the atmosphere in isolation from the
ocean.  Oceans have large thermal inertia.  On time scales of a
season or longer the oceans can modulate the mean condition of
the atmosphere.  Therefore, even though weather is not
predictable beyond two weeks, the climate may be predictable
beyond a season!  This will be the subject of a future article.
Better understanding of
how clouds are formed
and organised in the
tropics holds the key to
improving the tropical
weather forecasts.
Address for Correspondence
B N Goswami
Centre for Atmospheric and
Oceanic Sciences
Indian Institute of Science
Bangalore  560 012, India
email:
goswamy@cas.iisc.ernet.in
Fax: (080) 334 1683
     Suggested Reading
   Nigel Calder. The Weather Machine. The Viking Press. New York. p 144,   1974.
  John M Wallace and Peter Hobbs. Atmospheric  Sciences: An  Introductory Survey.  Academic Press. San Diego,
California. p 467, 1977.
   Richard A Anthes, John J Cahir, A B Fraser and Hans A Panofsky.  The Atmosphere. (Third Edition) Charles E
Merrill Publishing  Company.     Colombia, Toronto, London, Sydney. p 532, 1981.
   A Miller,  J C Thompson,  R  E  Petterson  and  D R Harayau. Elements of  Meteorology. Charles   E  Merrill Publishing
Company. Colombia,   Toronto, London, Sydney. p 417, 1983.
 J P Peixoto and A H Oort. Physics of Climate. American Institute of  Physics.  p 520, 1992.
 N Kumar . Deterministic Chaos: Complex Chance Out of Simple Necessity. Universities Press (India) Limited.
Hyderabad.  1996.


The challenge of weather prediction: What makes it difficult? 3. Old and new ways of weather prediction

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The challenge of weather prediction: What makes it difficult? 3. Old and new ways of weather prediction

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