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Forecasters cannot tell you whether it will rain in your town on a particular day three weeks from now. Yet scientists try to forecast how much rain a whole monsoon season will bring before it starts. That sounds like a contradiction. The scientist who did much to explain why it is not is Jagadish Shukla. Here is who he is, the idea he championed, a simple worked example of it, and what a student can take from his way of working.
Who is Jagadish Shukla?
His faculty page at George Mason University lists his education in an unusual way. Primary school, 1953: "Under a banyan tree", in the village of Mirdha in Ballia, Uttar Pradesh. Then a B.Sc. (1962), M.Sc. (1964) and Ph.D. (1971) in geophysics from Banaras Hindu University, and a Sc.D. in meteorology from MIT in 1976.
His curriculum vitae fills in the career. He worked as a junior scientific officer at the Indian Institute of Tropical Meteorology in Pune from 1965 to 1971, then at MIT, Princeton and NASA's Goddard Space Flight Center. He founded the Center for Ocean-Land-Atmosphere Studies (COLA) in 1983. The CV lists the Rossby Medal of the American Meteorological Society (2005), the International Meteorological Organization Prize (2007) and the Padma Shri (2012). It also records that he founded a college for women in a village in India in 1999. George Mason University has since named its earth sciences department after him.
Why can't anyone forecast the weather a month ahead?
In 1963 Edward Lorenz published Deterministic Nonperiodic Flow. He showed that in simple equations for convection, "slightly differing initial states can evolve into considerably different states". The atmosphere behaves the same way. Our measurements of today's winds and temperatures always have small errors, and those errors grow until the forecast for a given day is no better than a guess.
This is called sensitive dependence on initial conditions, one of the signatures of chaos.
What did Shukla show about monthly averages?
Shukla asked a different question: if the exact weather on day 25 is unpredictable, what about the average over a whole month? In Dynamical Predictability of Monthly Means (1981) he ran a global general circulation model of the atmosphere for 60 days from nine starting states. Three were real observed states from 1 January of 1975, 1976 and 1977. Six were the same states with small random errors added, about 3 m/s in the winds, comparable to observation errors.
The test was simple in spirit. If runs started from genuinely different states end up with averages no more different than runs that differ only by small errors, the average is unpredictable. He found that 30-day means over the first month were clearly distinguishable, while means over days 31 to 60 were not. Long waves in the atmosphere stayed predictable for at least a month, possibly 45 days.
The same year he and J. G. Charney published a chapter titled Predictability of monsoons in the book Monsoon Dynamics.
Why does the ocean make the monsoon more predictable?
In his 1998 Science paper, Predictability in the Midst of Chaos, Shukla argued that some regions of the atmosphere are an exception to chaos. Winds and rainfall in parts of the tropics are so strongly set by the temperature of the sea surface below that they do not depend sensitively on the starting state of the atmosphere. So, he wrote, it should be possible to predict large-scale tropical circulation and rainfall "for as long as the ocean temperature can be predicted".
Sea temperature changes far more slowly than the air above it, so a warm or cool patch of ocean keeps nudging the atmosphere in the same direction for a long time. That steady push is the predictable signal; the day-to-day chaos is noise around it.
A worked example: how fast does a small error grow?
Here is a classroom illustration with made-up round numbers, not values from Shukla's papers.
Suppose the error in a wind forecast starts at 0.5 m/s and doubles every 2 days.
After 2 days: 0.5 × 2 = 1 m/s.
After 10 days, five doublings: 0.5 × 2⁵ = 0.5 × 32 = 16 m/s.
After 14 days, seven doublings: 0.5 × 2⁷ = 64 m/s.
By day 10 the error is already larger than many real day-to-day differences in wind, so the forecast for that day has lost its value. Shukla's 1981 abstract gives a sense of scale: the root-mean-square wind difference between the three real starting states was more than 15 m/s.
Now think of an average. If sea temperature adds, say, a steady push towards extra rain every day for three months, that push does not double or vanish. It adds up. Averaging cancels much of the random noise, while the steady part remains.
What can a student take from how Shukla worked?
Change the question. "When will it rain on 14 July?" has no good answer. "Will July be wetter than usual?" might. Reframing a problem is often the breakthrough.
Separate signal from noise. His 1981 test compared differences caused by real changes with differences caused by small errors. You can use the same idea when you check whether a change in your test scores is real or just day-to-day variation.
Use models as experiments. He could not rerun the real atmosphere, so he reran a model many times from slightly different starts.
Start wherever you are. His CV begins under a banyan tree.
For more Indian work on weather, read about Anna Mani and her weather instruments and K. R. Ramanathan's meteorology.
Chaos and averaging are ideas that make more sense when you watch them happen. The Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Next step: redo the error example with a doubling time of 3 days and find the day on which the error first passes 15 m/s.
