NUMERICAL 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 A unit of BSP Books Pvt. Ltd. 4-4-309/316, Giriraj Lane, Sultan Bazar, Hyderabad - 500 095 First published 2023 by CRC Press 4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN and by CRC Press 6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742 © 2023 BSP Books Pvt. Ltd CRC Press is an imprint of Informa UK Limited The right of Venkata Bhaskar Rao Dodla to be identified as author of this work has been asserted in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. For permission to photocopy or use material electronically from this work, access www. copyright.com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. For works that are not available on CCC please contact [email protected] Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Print edition not for sale in South Asia (India, Sri Lanka, Nepal, Bangladesh, Pakistan or Bhutan). British Library Cataloguing-in-Publication Data 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)