Low-noise projections of complex simulator output: A useful tool when checking for code errors

A natural strategy to check for errors in a complex code, such as a computer simulator of weather or climate, is to make physically meaningful perturbations in the simulator parameters, and compare the results of the simulator runs against intuition. Such a strategy must balance the competing demands for CPU cycles of (i) performing many perturbations, and (ii) using long time-averages to suppress the effect of simulator noise. This paper proposes a mathematical solution which can be use to sharpen the perturbation signal in a given ensemble, namely to project the simulator output onto the column-space of linear combinations that maximise the signal-to-noise ratio. There are more refined approaches, but ours is easy to understand and to compute.