Getting the observations in

Before the model can run, it needs to know where the atmosphere is right now — and that is harder than it sounds.

The problem of now

A numerical weather model does not start from nothing. It starts from a three-dimensional picture of the atmosphere — pressure, temperature, wind, humidity at every grid point from the surface to the stratosphere — and projects that picture forward in time. The question is where that picture comes from. The answer is not "observations alone", because observations are uneven, arrive at different times, and each one measures something slightly different from what the model expects at that location. Stitching them together is a discipline in its own right, called data assimilation.

Think of it as a negotiation. The model has already been running; it has a forecast of what the atmosphere should look like right now, called the background field. A radiosonde ascent lands. A cluster of commercial aircraft reports arrives. Satellites pass overhead. Each new reading disagrees with the background field by some amount. Data assimilation decides, for every disagreement, how much to trust the observation and how much to trust the prior guess — weighting each by an estimate of its own uncertainty.

The mathematics behind that negotiation is called variational assimilation, and it treats the whole problem as an optimisation: find the atmospheric state that is most consistent with both the background and the observations simultaneously, given what is known about the error in each. The European Centre for Medium-Range Weather Forecasts ↗ in Reading, England has used a scheme called 4D-Var — four-dimensional variational assimilation — since 1997, and the technique has since spread to most major centres. The "four dimensions" are the three of space plus time: observations scattered across a six-hour window are all assimilated together, the model itself acting as a bridge between them.

Where the measurements come from

The inputs are bewildering in variety. Radiosondes, launched twice daily from roughly eight hundred land stations worldwide, provide vertical profiles of temperature, humidity and wind. Ships and buoys contribute surface pressure and sea temperature. Commercial aircraft report altitude, temperature and wind automatically, thousands of times a day. Ground-based weather stations — many housing instruments in a Stevenson screen — supply the dense surface layer. And then there are satellites: infrared and microwave sounders that measure radiance, from which temperature and humidity are inferred through retrieval algorithms. Each source has its own bias, its own noise, its own geographic thinning.

Not all of it arrives in time. The assimilation window for an operational model closes at a fixed cut-off; any observation that has not reached the processing system by then is simply not used. The World Meteorological Organization ↗ coordinates the global observing system that underpins this, setting formats and transmission standards precisely so that data from a buoy in the Southern Ocean can arrive at a forecast centre in seconds and be understood without human intervention.

What the background field knows

The background field — that prior guess — is not arbitrary. It is the previous cycle's short-range forecast, verified against what arrived then, and it carries with it a coherent physical structure: fronts in roughly the right place, pressure patterns with the right gradients. A lone dubious surface report cannot easily break that structure; the assimilation will down-weight it automatically. This is a feature, not a condescension toward observations. A single broken barometer should not reroute a depression.

The weakness is the same as the strength: the model's prior can suppress a genuine anomaly if the observing network is thin enough. Over the oceans, where radiosondes are sparse and satellite data must carry most of the weight, the background field's grip is tighter and errors that enter here tend to grow. This is one reason that improving forecast skill over the Southern Hemisphere — historically data-sparse — has tracked the rise of satellite assimilation more closely than any increase in conventional observations. Getting the observations in turns out to mean knowing which ones to believe.