barcode tracers

Motivation:

Suppose we have a geographically isolated event (say a particular region of equatorial deep convection) and we want to ask the question "Which regions of weather, say, up to 14 days ago could have contributed to this?". If one kept track of the advecting winds at every time step in the last 14 days, initialize a point-source tracer in the region of interest, and evolve the system backwards in time. Anywhere that had that tracer could concievably have contributed to the weather at the point of interest.

Now, this is prohibitively expensive for the usual reasons. So the question is, if we have a restart file 14 days before the event of interest (say, a set of grid point locations), can we initialize a set of tracers that would back out these dependencies? That is, in data analysis we identify a grid cell of interest and we can back out a "heat map" (which might be a binary mask) of grid cells. Assume the lag time $T$ is fixed and, for the moment, there is only one cell with ID $i_{\textrm{event}}$ for which we want to compute this "inversion".

If I'm allowed to have an entirely different "component" which isn't a bolt-on tracer system, then here's a potential way to do this with particles: At each barcode time step, initialize a particle containing a bit-mask with a bit for each horizontal grid cell. Another design branch here would be to initialize several particles and add an uncertainty parameter $\kappa$ that introduces stochasticity to the advection of these particles. Move forward one (dynamics?) timestep, then take the bitwise or of every particle assigned to a grid cell with the stored "upwind bitmap" for that grid cell. After $n_{\textrm{remap}}$ timesteps, re-initialize the ensembles of particles..

Related idea that's almost already not being done: Partition the equations into a prognostic and a control term, add probability distribution to control term. Use this to do hypothesis testing. [https://www.sciencedirect.com/science/article/pii/S1053811909011999]. Main idea is to do formal hypothesis testing by making ensemble-aware adjustments to the model state in the lead up to an event. Null hypothesis in this case: "modifying this variable at this point does not correlate with the strength of measured signal after lag"

Transformed eulerian mean: store quantity on a node with statistical estimates of variance. Online diagnose: here is a point that significantly increased variance of mean circulation.