 Scale analysis is very important because it tells us which terms in any equation are the most important and which terms we can ignore. In scale analysis, you do not need to know the exact values for the variables, but instead, you need only know the order of magnitude. The process is straightforward. First, determine the phenomena of interest, whether it be cyclone, front, hurricane, tornado, synoptic scale, winter weather. Determine the characteristic that is typical lengths and times of which the phenomenon occurs. Determine the range of fluctuations of equation variables in space and time during the phenomenon. Approximate derivatives, that is, the partial of p with respect to x would become delta p over delta x, where they are roughly estimate. Prepare the magnitudes of terms in the equation, and then keep only the relatively large terms, say the top two orders of magnitude, and neglect the much smaller terms. Let's look at this example of the experimental equation for mid-latitude synoptic scale flow. So in this case, it's mid-latitude synoptic scale flow. The length is about 1,000 kilometers, which is 10 to the 6 meters. The height is about 10 kilometers, which is 10 to the 4 meters. And if we were in the boundary layer only, we would find that the friction drag coefficient is 10 to the minus 2, and the height of the boundary layer is about 1,000 meters. Now, we know that u is about 10 meters a second, roughly. It could be a lot less and a lot more, but it's that order of magnitude. Delta p is about 10 millibar over the length of interest. We see that the time then is equal to the length, the scale of the synoptic scale flow divided by the velocity, which is 10 to the 6 divided by 10, or 10 to the 5 seconds, which is about a day. And we see that the Coriolis parameter is about 10 to the minus 4 per second, and we can estimate other factors such as the w velocity, which is height divided by time, so that's about 10 to the minus 1 meters per second, and so on. We continue on looking at derivatives in other terms. And so, for instance, the acceleration in the u direction is about 10 meters per second divided by 10 to the 5, which is about 10 to the minus 4, and so that's the size of that term. We see that the Coriolis term is about 10 to the minus 3. We see that other apparent terms are 10 to the minus 5 to 10 to the minus 7. They're quite a bit smaller. The pressure gradient force we see is 1 over the density, which is about 1 kilogram per meter cubed times the pressure difference, which is about 10 to the 3 pascals divided by the distance, which is 10 to the 6 meters, so it's about 10 to the minus 3. And we see that if we were in the boundary layer, that the aerodynamic drag, which causes friction, is acting as friction, is about 10 to the minus 3. So in the boundary layer, we would need to consider this term because it's the same order of magnitude as the pressure gradient term, more of the larger terms. When we're not in the boundary layer, then C sub D is actually very, very small, and this term is very small. We can ignore it. The last term is viscosity, which is true friction, and we can see that for the case of viscosity, it's tiny, and therefore we can always ignore it for synoptic scale flow. So when we look at the terms we have, we see that we have, away from the boundary layer, we have two terms that count. That is, we have the Coriolis term and we have the pressure gradient term, and those are the only two terms that we need to keep.