Frank and the Weather Computer: Page IV

Frank eyed the output with caution, but it looked all right. The temperature went up in the morning and down in the evening, just like it ought. Plus, he had forecasts of temperature for all these other levels in the atmosphere. He didn't need them, but hey, they looked impressive. Apparently, the formulas the weather computer used for calculating the vertical mixing and the radiative heating of the ground were accurate, or at least reasonably close to reality.

Buoyed by this success, Frank next decided to try to forecast the air pressure. Again the computer asked him for more information; in this case, the air pressure at the top of his air column, at one mile. How was he to know that? Frank checked the computer screen again: one of the options was to have the weather computer compute the pressure at the top from the pressure at the bottom, using the hydrostatic equation and the temperatures he had already specified. The hydrostatic equation says:

The CHANGE OF PRESSURE with HEIGHT is equal to the weight of the intervening air, which at a given pressure level depends only on TEMPERATURE.

So he got a barometer, measured the surface pressure, gave the information to the computer, and it calculated a pressure at one mile: 837 mb.

Frank did the same thing he did with the temperature: he told the computer to assume that the pressure at one mile stayed constant. So the computer went through its temperature forecast again, except that as it did so, it also calculated the air pressure at all levels using the hydrostatic equation.

Since the hydrostatic equation uses just the temperatures to calculate the pressure, it wasn't like the weather computer had to make a new forecast, or even two separate forecasts. It just did the temperature forecast, and used those temperatures to calculate pressure. Terminology: the equation used to calculate temperature, since it involves stepping forward in time, is called a "prognostic" equation, while the equation used to calculate pressure, which relates instantaneous values to each other, is called a "diagnostic" equation.

That was enough work for one day; Frank finished his round of golf, ate an entire pizza, and went to bed.

Despite the pizza, Frank slept well, not knowing that the pressure forecast was actually much worse than the temperature forecast. Why would that be?