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Every year India waits for one number: how much rain the monsoon will bring. The man who first went looking for that number across the whole planet was Gilbert Walker. He did not find a perfect forecast, but he found something bigger, a pressure seesaw linking oceans thousands of kilometres apart. This post covers what he found, how he found it, a correlation example you can do by hand, and what his way of working teaches.
Who was Gilbert Walker?
The Royal Society's biographical memoir by G. I. Taylor records that Gilbert Thomas Walker was born on 14 June 1868, the eldest son of the borough engineer of Croydon. He showed an early interest in arithmetic and mechanics and was moved to the mathematical side at St Paul's School in London. The Oxford Dictionary of National Biography describes him as an applied mathematician and meteorologist, and his entry in Who Was Who gives his death as 4 November 1958.
He came to India to lead the India Meteorological Department (IMD). A review of the history of Indian monsoon forecasting by Rao and colleagues in Mausam (2019) lists his correlation-based forecasting methods from 1904 to 1924.
Why was he searching the whole world for monsoon clues?
Before Walker, IMD forecasts relied mainly on Himalayan snowfall and local weather, an approach begun by Henry Blanford. Walker widened the search. According to Rao and colleagues, he studied worldwide variations in pressure, rainfall and temperature, looking for anything measured months earlier that moved in step with Indian rainfall.
The tool he used was the correlation coefficient: a number between -1 and +1 that tells you how closely two quantities rise and fall together. Rao and colleagues credit Walker with removing much of the guesswork from forecasting by introducing correlated predictors and regression formulas.
What is the Southern Oscillation?
In sifting through these correlations, Walker identified three large pressure seesaws, which he described in papers in 1918 and 1923: the North Atlantic Oscillation, the North Pacific Oscillation and the Southern Oscillation. In the Southern Oscillation, when surface pressure is higher than usual over one side of the tropical Pacific and Indian Ocean region, it tends to be lower than usual over the other. Rao and colleagues note that while the two northern patterns are regional, the Southern Oscillation turned out to have global influence. Walker added it as a predictor for monsoon forecasts in 1924.
He summarised the global picture in a paper titled World weather (1928) in the Quarterly Journal of the Royal Meteorological Society.
How was the Southern Oscillation linked to El Nino?
In 1969 the meteorologist Jacob Bjerknes published Atmospheric teleconnections from the equatorial Pacific. He showed that unusually warm sea in the eastern and central equatorial Pacific comes with weaker trade winds and weaker upwelling of cold water, and that these changes are "closely tied to the 'Southern Oscillation' of Sir Gilbert Walker". He named the east-west loop of tropical air the Walker Circulation.
A review in Mausam by Ashok and colleagues (2019) calls El Nino-Southern Oscillation the strongest driver of year-to-year changes in Indian monsoon rainfall. It also cites work showing that unusually high pressure at Darwin, in northern Australia, tends to come with lower monsoon rainfall.
Did his forecasts work?
Only partly. A 2025 review by Rajeevan and Pattanaik notes the later judgement that Walker's forecasts failed to flag the extreme monsoon years correctly. The statistician Richard Katz, writing in Statistical Science (2002), says early assessments of Walker's work were "somewhat negative", but argues that with hindsight it should be seen as quite successful. Katz also points out that the "Walker" in the Yule-Walker equations of statistics is the same man, from the same climate research, published as On periodicity in series of related terms (1931).
Worked example: computing a correlation like Walker
Here are five years of made-up sample numbers, not real data. x is the pressure anomaly at a station (hPa above or below normal); y is the monsoon rainfall anomaly (per cent above or below normal).
Year 1: x = +2, y = -6
Year 2: x = +1, y = +2
Year 3: x = 0, y = -1
Year 4: x = -1, y = +3
Year 5: x = -2, y = +2
Both means are 0, so the correlation is r = Σxy / √(Σx² × Σy²).
Σxy = (2)(-6) + (1)(2) + (0)(-1) + (-1)(3) + (-2)(2) = -12 + 2 + 0 - 3 - 4 = -17
Σx² = 4 + 1 + 0 + 1 + 4 = 10
Σy² = 36 + 4 + 1 + 9 + 4 = 54
r = -17 / √540 = -17 / 23.24 ≈ -0.73
The negative sign means high pressure goes with low rainfall in this sample. Walker computed many such coefficients by hand from long records. Two warnings he faced too: five years is far too few to trust, and if you test hundreds of stations, some will correlate by pure chance. Our post on Karl Pearson and the correlation coefficient goes deeper into the formula.
What can a student take from how Walker worked?
Widen the search. He did not assume the answer was near India. He looked at the whole globe.
Measure, then explain. His correlations came first; the physics came decades later from Bjerknes. A pattern found carefully is useful even before you understand it.
Be honest about limits. His forecasts missed extremes, and later reviewers said so. That record is part of why the science improved.
If correlation and regression feel abstract, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can revise the statistics behind Walker's work at your own pace. For the next chapter of the story, read about Jagadish Shukla and the predictability of the monsoon.
Next step: redo the worked example with the signs of y reversed and check that r becomes +0.73.
