BackWaiting for the monsoon
Weather forecasts will never be fully accurate. But they can be made with confidence, and that's in a mathematical sense
Premium
Like many of my fellow country folk, I’m sure, I’ve been staring hopefully at the heavens for several days. The question on our minds: When will the monsoon arrive? The India Meteorological Department (IMD) has been offering a tantalizing stream of news, advice and predictions—it’s hit Kerala, spread over Karnataka, expected to arrive in Goa, stalled south of Goa, two days late, farmers please don’t sow your seeds just yet, so on. Through it all, sunny skies, a few sprinkles dismissed as “pre-monsoon showers" and heat like never before. No rains yet.
It’s easy to point fingers at the IMD for this. But that’s misguided. Let me explain why. In an April column (“The margins for a drought"), I wrote that the IMD predicted a good monsoon this year, and the effect on stock markets. But I also wrote that forecasting “remains an inexact science". And that’s true not just for forecasts made months in advance—like in April—but also for those made now, for the immediate future.
In this column, I want to offer a sense of what weather forecasts actually mean. But first, it’s worth understanding the sheer audacity of trying to forecast the weather. The weather is not like a fan switch—once you turn it on, I can predict with full confidence that a breeze will cool your delicate skin. Weather forecasters have many things to consider: the strength and direction of winds, the lay of the land, air pressure and temperature, currents in oceans and more. And those are just obvious factors. If a plane flies through a rain cloud, does that materially change the chance that rain will fall from that cloud? If a butterfly flaps its wings in Brazil—you’ve heard this one—will that eventually set a cyclone raging off the coast of Odisha?
How do you predict weather with any accuracy or confidence?
I use those words deliberately. Weather forecasts will never be fully accurate; that is, don’t hold your breath expecting a forecast for precisely 25.6mm of rain between 11.23am and 4.56pm tomorrow. But they can be made with confidence, and that’s in a mathematical sense.
To show you what I mean, let’s analyse one sentence from a 2012 Mint report (“The Monsoon Chasers") about the IMD. The monsoon, it says, “is a sea breeze so regular that in 3 out of every 5 years of the 100-odd that meteorologists have maintained actual weather records, the total rainfall has remained within 10% of 88cm".
What is this sentence saying? Very broadly, that the average monsoon brings India 88cm of rainfall. But what about the other language—“3 out of 5", “within 10%"? It might sound like bets being hedged, but it really is a textbook example of how meteorologists express confidence in their statements—in particular, how much confidence they have.
After all, if the annual average is 88cm, in how many of those 100 years would the monsoon have brought India 88cm of rain—no more, no less? I’m looking at the numbers on the government’s site data.gov.in, and here’s the answer that you may have guessed anyway: none. Meteorologists would have zero confidence in claiming that the monsoon brings exactly 88cm of rain. But the numbers observed through that century range from a low of 71cm (1965) to a high of 108cm (1917). So, in contrast, they can state with nearly full confidence that we will get between 70cm and 110cm of rain from the monsoon.
Yet, both those statements are effectively meaningless anyway. Which is why meteorologists appear—but only appear —to hedge their bets. That sentence above says that 60% of the rainfall numbers have been between 79cm and 97cm (i.e. “within 10% of 88cm"). Extrapolating from there, which is a reasonable thing to do when you have 100 years of data, they can state with 60% confidence that rainfall this year will be in that 10% range. If they wanted to offer a narrower and more accurate range, they’d have less confidence in it; a broader and less accurate range, more confidence.
And to me, that’s why that sentence is a good compromise between accuracy and confidence. It’s exactly the same as election-time opinion polls that make predictions with a “margin of error". That margin is the range, and the confidence is usually implied: a 4% margin of error means a 95% confidence level. (More about this in my column from 2012, “Father of polls").
This is the way to consider every meteorological forecast you run into. It helps you appreciate how complex a job weather forecasting is and how hard it is to be accurate. Also, how hard it is to satisfy a population as dependent on the monsoon as we are. Think of that when you are next inclined to point fingers at the IMD.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers explores the joy of mathematics, with occasional forays into other sciences.
Comments are welcome at dilip@livemint.com. To read Dilip D’Souza’s previous columns, go to www.livemint.com/dilipdsouza
Unlock a world of Benefits! From insightful newsletters to real-time stock tracking, breaking news and a personalized newsfeed – it's all here, just a click away! Login Now!
