How to Catch a Rare Downpour ✎

Original: "A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes"
· Hongwei Shang, Jun Yan, Xuebin Zhang
arXiv:1204.0286 · 2012-04-02 · arXiv non-exclusive · independent analysis · 1 min
Weather stations record rain every day, but flood forecasts used to rely on just one day per year. A new approach puts all those records to work.

Imagine you have 55 old photo albums, one for each year. Each album holds 365 snapshots of rain, but in the past you only looked at the single wettest shot from every album. The other 364 snapshots gathered dust in a box. The new method pulls out every snapshot and lays them all out in order.

First, each weather station is tuned individually, like a piano tuner before a concert. You take all the days when rain crossed a certain threshold and build a curve from those days. The curve shows how likely an extreme downpour is. Before, that curve had only 55 points; now it has hundreds, so it comes out smoother.

The key trick: clean each signal separately first, and only then adjust the connections between stations. That way, one station's error doesn't corrupt the big picture.

Then the stations learn to listen to each other. If rain in two neighboring towns almost always starts at the same time, they likely share a common cause, such as a large atmospheric front. This connection is measured using the strongest rains of each year. Once the connections are tuned, the risk map comes into focus. For California, the new method detected El Niño's influence at 22 stations, while the old one found it at only 14. And the corridor of possible error narrowed by about a third.

The joint 50-year return level for the station pair Napa and Winters at a Southern Oscillation Index value of -1 was about 10–15 cm of precipitation per day, depending on the estimation method.

G(z) = \exp\left\{-\left[1 + \xi\left(\frac{z-\mu}{\sigma}\right)\right]^{-1/\xi}\right\}
Distribution of block maxima, where μ is the location parameter, σ the scale, and ξ the shape.
\Pr\{Z(x_1) \le z, \ldots, Z(x_p) \le z\} = \exp(-\zeta/z)
Measure of extremal dependence: ζ=1 for complete dependence, ζ=p for independence.
Concepts
Multivariate ENSO Index NOAA CPC maximum likelihood Oceanic Niño index ERSST Niño 1+2 probabilistic forecast ENSO precipitation anomaly relative ONI ensemble forecast bayesian evidence zebiak cane model likelihood ratio test spring predictability barrier probabilistic model nested sampling Monte Carlo methods Analogue forecast parameter estimation