Table Of ContentNUMERICAL
WEATHER
PREDICTION
Venkata Bhaskar Rao Dodla
IMS Fellow
Professor of Meteorology (Retd.)
Andhra University
INDIAN METEOROLOGICAL SOCIETY
Mausam Bhavan Complex, Lodi Road, New Delhi - 110 003.
BS Publications
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A catalogue record for this book is available from the British Library
ISBN: 9781032406251 (hbk)
ISBN: 9781032406268 (pbk)
ISBN: 9781003354017 (ebk)
DOI: 10.4324/9781003354017
Typeset in Times New Roman and Bookman Old Style
by BSP Books, Hyderabad 500 095
Contents
Foreword ........................................................................................................ (v)
Preface .......................................................................................................... (vii)
Acknowledgements ........................................................................................ (xi)
1. Advent of Numerical Weather Prediction ............................................. 1-28
2. Hierarchy of Atmospheric Models ...................................................... 29-66
3. Numerical Methods ........................................................................... 67-124
4. Objective Analysis .......................................................................... 125-160
5. Parameterization of Physical Processes .......................................... 161-188
6. Weather Prediction - Lorenz Chaos Theory –
Nonlinear Dynamics, Ensemble Prediction .................................... 189-206
7. Current Status of NWP in India ...................................................... 207-230
Appendix A: Mathematical Formulation of NWP ................................ 231-238
Appendix B: Sigma Coordinate System ................................................ 239-246
Appendix C: Finite Difference Formulation of Multi-Level Primitive
Equation Model ..................................................................................... 247-250
References ............................................................................................. 251-254
(iii)
Foreword
Indian Meteorological Society is a non profit scientific society established in
1957 for advancement of Meteorological and allied sciences and
dissemination of the knowledge of such sciences both among the scientific
workers and among the public and their application for societal benefits. The
society organizes National and International Symposiums (TROPMET
/INTROMET), Regional Seminars and Workshops and has constituted a
number of awards to promote research in meteorology. The IMS popularizes
meteorology by organizing public lectures, teachers and media workshops
interactive sessions with students, essay, debate and quiz competitions on
popular meteorological topics, During interactions it was felt that books for
general public written in easy to understand format on various advance topics
of meteorology are not available in India. To meet this demand, it is decided
by IMS to bring out popular book series as a part of its Diamond Jubilee
Celebrations.
Weather predictions have shown steady improvement in recent decades
leading to change in public perception about weather forecasts. Today
weather forecasts are helping in saving lives by early warning of extreme
weather like cyclone, heat wave etc and improving productivity by weather
advisories to agriculture, energy, health, aviation, marine and other weather
sensitive sectors. Common people are using weather forecasts in planning
their day to day activities. Numerical Weather Prediction (NWP) techniques
using high power computing and observations from Weather Satellites and
Radars have played key role in improving skill of forecasts. NWP Techniques
are being used in all spatial and temporal scales of forecasts starting from
Nowcasts to seasonal forecasts and climate projections. Somehow,
knowledge about NWP has been confined to NWP Centers and some
academic and research institutes. Books on NWP essentially cater to research
community. Need to have a popular book on Numerical Weather Prediction
was being felt for quite some time. Therefore, IMS decided to berin out
second book in its popular book series on Numerical Weather Prediction.
The book under IMS Popular Book series on ‘Numerical Weather
Prediction’ is authored by Prof D.V. Bhaskar Rao pioneer in Numerical
Weather Prediction Meteorology in the country. He initiated teaching and
research programs in NWP at Andhra University in 1977 and made significant
research contributions on tropical cyclone modelling. With his strong passion
for teaching and research, he encouraged and mentored numerous students of
M.Sc., M.Tech., and Ph.D. programs inducing them to a career in
meteorology and allied disciplines. I am thankful to Prof Bhaskar Rao for
having agreed to IMS request to write the book. The book is written in
(v)
simple, easy to understand format and compressively covers all aspects of
Numerical Weather Prediction. The book covers Numerical Methods,
Hierarchy of Atmospheric Models, Objective Analysis, Parameterisation,
Ensemble Prediction and current status of NWP Models. I am also thankful to
Prof. Someshwar Das of Rajasthan Central University for reviewing the
manuscript.
I am sure readers will find the book interesting and will be better informed
about NWP. The book will also create interest in Numerical Weather
Prediction among the students.
AVM (Dr) Ajit Tyagi
President
Indian Meteorological Society
(vi)
Preface
Weather influences on earth’s humanity finds a reference in ancient Indian
scriptures, such as description of hydrological cycle in “Bhagavad Gita”
(~3000 B.C.) and of the seasonal cycles, cloud and rain processes in
“Brihatsamhita” by Varahamihira (~500 A.D.). A verse from Bhagavad Gita
(Chapter 3, Verse 14) reads as
annad bhavanti bhūtāni
parjanyād anna sambhavaḥ
yajhad bhavati parjanyoyajhah ̣
karma samudbhavah ̣
The gist of this verse is “Living beings are created and find their source in
food, food is created by rainfall, Parjanya (Rain God) gives us the material
blessings of rainfall and thus abundance in the material world by the creation
of food and other crops”.
Weather plays a very important role in the lives of all humanity, due to its
impacts. Mankind is vulnerable to weather extremes such as extremes of
temperature (cold and heat waves), extremes of rainfall (drought and floods),
extremes of wind (storms such as cyclones, thunderstorms, tornadoes etc.).
So awareness to weather changes and need to know of their causes had
prompted human instinct to strive towards understanding the atmospheric
changes and learn to protect from weather perils. Understanding weather as
continuous changes in the atmosphere providing sometime comfort and
sometimes distress seems to have been a part of learning in different parts of
the globe since ancient times as evidenced by the writings in the ancient
scriptures. The quote above taken from “Bhagavad Gita” is supposed to be
given in 3137 BC depict the seasons, cloud, rain and hydrological cycle which
reflect the scientific thought of those times.
Current scientific thought accepts that the earth’s atmosphere system is
driven by energy from Sun, in the form of radiation. In brief, the scientific
processes that contribute for the continuously changing atmosphere are as
follows. Solar radiation heats up the earth-atmosphere system differentially,
corresponding to rotation of earth around its own axis once in 24 hours and
around Sun once in 365.25 days causing day and night and seasons. The
radiation energy passes through the atmosphere and most part of it reaches the
earth surface and the surface of the earth gets heated depending on the type of
surface (basically land, water or ice and land featuring innumerable types)
leading to different temperatures at different places. These horizontally
varying temperatures give rise to pressure variations and the horizontal
pressure differences lead to movement of air from one location to another
(vii)
(generally called as wind). The atmosphere, striving to reach an equilibrium
state as per nature, is in continuous motion in all the three dimensions of
space. Though looks simple, the changes in the atmosphere result from
complex interactions between the land, water and ice surfaces of the earth
with atmosphere above. An attempt to delineate these changes brings out the
simultaneous presence of atmospheric motion at different time and spatial
scales, (i.e.) from the smallest scales of molecular motion, turbulent motion to
synoptic and large scale variations where the smallest spatial scales have
smallest time scales and the time scales tend to be longer as the spatial scales
tend to be larger. The enormous complexity of the presence of innumerable
variations makes the understanding of the atmospheric system very difficult.
But the characteristic behaviour of the various systems could be understood
through observations and theory as they have inherent periodic nature. It is
important to realise that it would be impossible to predict a random behaviour
and the basis of the weather prediction is the deterministic characteristic of the
atmosphere. The basic premise for studying weather should be towards
continuously improving our understanding.
Weather prediction had been the focus of attention ever since the science
of meteorology has been carved out of the science of physics. The first
chapter of this monograph describes the development of weather prediction
since 1900s. Despite the complexity of the weather prediction problem,
profound advancements have been during the last few decades mainly due to
the rapid advancements in the observation systems and computational
resources to support weather prediction using atmospheric models. The
development of the atmospheric models based on fundamental physical laws
and solved using well understood numerical methods have established
numerical weather prediction as the state-of-art methodology. Technological
advancements in Radar and satellite measurements and high performance
computing have helped the orientation of weather prediction from subjective
and qualitative style to objective and quantified mode. The weather
predictions are currently oriented to suit different users from agriculture,
transport, industries, and sports etc. apart from the general public who plan
their daily chores following the weather predictions. In recent times of
looming world energy crisis, when strong efforts are being made towards
harnessing alternate energy such as wind and solar energy, weather prediction
plays an important role to provide quantified data at the required time and
spatial scales to serve the particular demand.
This monograph has been prepared to provide a basic understanding of the
numerical weather prediction to a general reader with knowledge of basic
physics and mathematics. The stream of thought follows a lucid style with
least use of technical nomenclature. Since the entire subject of numerical
weather prediction is based on mathematics and physics, elaboration of
mathematics could not be avoided while describing the formulation of models
(chapter 2) and numerical methods (chapter 3). Information on
(viii)
supplementary topics that aid these two topics is given as appendices. Any
reader who is not keen about the mathematics may skip the mathematical part
of these two topics and follow the general information on the other topics. As
such most of the relevant information has been segregated and presented as
about modeling, numerical methods, objective analysis and data assimilation
methods to generate initial conditions and parameterization of physical
processes. The chaos theory of Lorenz, which originated from his
experiments on weather prediction, has been presented for the benefit of
understanding the deterministic predictions and uncertainties of numerical
weather predictions. Above all, this monograph should help a student and
researcher to understand the intricacies of not only the weather prediction but
also the current problems and strategies. The purpose of this monograph
deems to be fulfilled if the information fills the gap between the available
books and research articles and help find clarifications as needed.
-Author
(ix)
