*© Fernando Caracena*, 2016

## Preliminaries

This is a continuation of the discussion presented in the post, "The Big Thompson Storm: Weather Patterns I", which showed conditions on the 500 mb pressure surface. This level is the approximate height of the middle atmosphere as measured by pressure, mean sea level pressure being 1013.25 mb (see a Wikipedia discussion here). I generated the areal patterns of analysis depicted in these posts on my personal computer using computer routines, which I have personally written. The process I used is similar to what is called in meteorology "objective analysis".

Objective analysis is defined as the process of interpolating observations from an irregular distributed locations to a fixed grid. What has been done in these analyses however, is not a process that conforms directly to this definition. At NOAA, I had developed a process similar to objective analysis, which I called "analytic approximation" [*Caracena, F. 1987: Analytic approximation of discrete field samples with weighted sums and the gridless computation of derivatives. J. Atmos. Sci., 44, 3753-3768.*]. This method is similar to Kriging which is used in geology.

Basically, analytic approximation is really a spatial-frequency, band-limited fit of irregularly distributed point observations by an analytic function, which can be evaluated anywhere within the analysis domain. The method involves matrix multiplications, which execute very rapidly on the personal computer. This makes it possible for the weather enthusiast or professional on a low budget to be able to analyze weather observations as soon as they are available.

The charts presented in these series represent a "single pass" analytical approximation of the data. If residuals are also approximated analytically and these corrections applied successively, the analysis can be improved. It is possible to compute the result of an infinite series of successive corrections through simple matrix manipulations. However, this must be done with care, because the results are very sensitive to how this method is applied.

## Evolution of the Large-scale Weather Pattern

Anyone staying late at work at APCL on the Friday before the weekend of the storm would have seen some variation of the 500 mb pattern depicted in Fig. 1 . The short wave trough present 12 hours earlier was still located in approximately the same location as it appeared in the morning at 6:00 AM, MDT. This feature must have been propagating very slowly.

Generally, a short wave trough propagates slower than the wind that blows through it. Although the wind blows very close to horizontally on a pressure surface (*the pressure surface slopes only a few tens of meters per horizontal distance of 1,000 km*) there is a weak secondary, vertical current of only a few centimeters per second that cannot be measured directly. Even though this may seem to be an insignificant number, over 12 hours time it can add up to a lot of vertical displacement (.01m/s* 12 h*3600 s/h=432.0 m).

In the extra tropical cyclone track, which is poleward of the equator, a short wave trough propagates by means of air rising ahead of the trough axis and sinking in its wake. (See here for a discussion of atmospheric cyclone waves). Accompanying a short wave trough is also a temperature trough that is out of phase with the trough in the wind and height fields. Note these features appear in the short wave trough in Fig. 1, but the flow across the isotherms (contours of equal temperature) is almost non existent.

The short wave trough that was visible in the 500 mb analysis Thursday and Friday before the storm had progressed slowly northward by Saturday, the morning of the big storm (Fig. 2). Although the flow was weak across the isotherms, it was more noticeable than earlier.

The discussion continues in the next post through a full depth analysis through the of the troposphere.