5. TLM Validation

Before we proceed to the sensitivity computation, we validate the TLM solutions computed by the ADIFOR-generated code, which describe the linear evolution of perturbations. The validation is carried out by comparison with the nonlinear perturbation (NLP) fields; the difference fields computed between the nonlinear control run and another nonlinear run whose initial state is slightly perturbed from it.

Figure 2 shows the TLM and NLP fields of vorticity at 40 min for a 1% perturbation (bias-type) in water vapor over the whole model domain except for the lateral, top, and bottom boundaries. They are plotted on an x-y plane at z = 4.0 km.

 

Figure 2: x-y slices (at z = 4.0 km) of (a) tangent linear perturbation and (b) nonlinear perturbation in vorticity at t = 40 min for a 1 % perturbation in initial water vapor (in

)

The two fields agree quite well in both magnitude and location. However, after about 55 min, the solutions begin to diverge. That is, in reality, the perturbations and (time-evolving) nonlinear base state interact to a significant extent, and the absence of this interaction in the TLM leads to erroneous results. The correlation drops rapidly below 0.9 after about 45 min. In a case without subgrid-scale turbulent mixing, which is a highly nonlinear process, the time over which the two fields agree increases.