Using low-resolution winds to deduce fine structure in tracers

In a number of applications several numerical modellers have recently used low-resolution GCM or NWP analysis winds to deduce very fine structure in the distribution of chemical species and of potential vorticity. This study aims to measure the error introduced by this mismatch of effective resolutions. By appealing to earlier theoretical work by Batchelor (1959), the approach has been organized around the steepness of the kinetic energy spectrum, E(k). It is found that when the spectrum is steeper than E(k) similar to k(-3) the root mean square error is proportional to the square of the wind truncation scale. By contrast, when E(k) approaches k(-5/3) rms error is approximately proportional to the square root of the wind truncation scale. As a result coarse wind resolution produces remarkably accurate global scalar fields a few after advective timescales in the large spatial scales of the troposphere and in the stratosphere, but this result is not expected to hold at smaller scales or in the mesosphere where the spectrum is more shallow.