Atmospheric Modeling, Data Assimilation and Predictability

Introduction

In Chapter 2 we derived the equations that govern the evolution of the atmosphere, and in Chapter 3 we discussed the numerical discretizations that allow the numerical integration of those equations on a computer. The discretization of the continuous governing equation is limited by the model resolution, i.e., by the size of the smallest resolvable scale. We have seen that in a finite difference scheme, the smallest scales of motion that can be (poorly) resolved are those which have a wavelength of two grid sizes. In spectral models, the motion of the smallest wave present in the solution is more accurately computed, but for these and for any type of numerical discretization there is always a minimum resolvable scale. Current climate models typically have a horizontal resolution of the order of several hundred kilometers, global weather forecast models have resolutions of 50–100 km, and regional mesoscale models of 10–50 km. Storm-scale models have even higher resolution, with grid sizes of the order of 1–10 km. In the vertical direction, model resolution and vertical extent have also been increased substantially, with current models having typically between 10 and 50 vertical levels, and extending from the surface to the stratosphere or even the mesosphere. As computer power continues to increase, so does the resolution of atmospheric models.

Despite the continued increase of horizontal and vertical resolution, it is obvious that there are many important processes and scales of motion in the atmosphere that cannot be explicitly resolved with present or future models.