Effect of different filtering strategies

Here a series of runs are compared where the details of the filtering strategy are changed. All runs were performed with the Aug 2 2024 (99698724377) master branch code, but the behavior of the filter was changed using simple hacks. The test case is the New Zealand Deepwave case using 4 km horizontal spacing and 1 km vertical. The entire duration of the forcing is 2 hours and the simulation time is shifted by 8 hours in order to match with UTC time from the observations.

The movie below shows a comparison of the vertical velocity for three cases: (1) The stock code where the filter weights are variable in both space and time. The stock values of the filter weight adjustment in time are also used and these more or less prevent the weights from decreasing in time. (2) A hacked version where the filter weights do not very in space, but do vary in time. The filter weight adjustment parameters were also changed so that the weights can decrease in time. (3) A hacked version where the filter weights are constrained to be fixed in both space and time. This case should mimic the old filtering strategy. The constant filter weight was set at 0.20, which is close to the stability bound (the code will run with a weight of 0.175, but visible oscillations are present in the solution).



In the following discussion, the case with fully variable weights will be referred to as the fully-variable case, the case with variable weights in time only as the fixed-in-space case, and the case with weights fixed in space and time as the fully-fixed case.

The solutions are nearly indistinguishable from the start to about 8.2 UTC, when a few oscillations develop in the fixed-in-space case. The oscillations only persist for a few minutes, however, and then the solutions go back to being nearly identical until about 9.0 UTC. At this time, acoustic waves appear near the top of the domain in fully-variable case. Also the fully-fixed case starts to look over-filtered around this time. Around 9.7 UTC, acoustic noise also appears in the fixed-in-space case. The wave pattern in the lower portion of the domain for this case is visibly stronger, and looks more realistic, as compared to the other two cases at this time as well. The acoustic noise in the fixed-in-time case increases somewhat as we approach 10.0 UTC, but remains smaller than the fully-variable case. An odd planar acoustic wave appears in the fixed-in-time case just prior to 10.0 UTC. This defect is unexpected since the forcing scheme is still active and thus the waves must be generated by a mechanism other than the forcing endpoint in time. Around 10.10 UTC an acoustic blast is observed in the fully-variable case, whereas there does not appear to be any additional noise in the fixed-in-space case. By about 10.30 UTC most of the blast junk has dissipated and the solutions go back to a situation where the fixed-in-space case has the strongest, most realistic-looking wave pattern at lower altitudes, the fully-fixed case looks over-filtered, and both the fully-variable and fixed-in-space cases show acoustic noise near the top of the domain. Then from about 10.5 to 11.2 UTC the acoustic noise in the fixed-in-space case increases and exceeds that present in the fully-variable case. From about 11.2 UTC to the end of the simulation the noise level in the upper portion of the domain is reasonably similar between the fully-variable and fixed-in-space cases.

Some of the behavior noted above can be correlated with the filter statistics shown below. Starting with the filter weight time histories, we see that the weights in the fully-variable case are effectively constrained to only increase in time, whereas the weights in the fixed-in-space case can both increase and decrease. It is also apparent that the rate of decrease is greater than the rate of increase for the fixed-in-space case (but this could be corrected with the filt_dec input). When the weights can decrease in time, we see a fairly strong trend towards smaller filter weights. In fact, the only weight that exceeds 0.18 is for w in z, and most of the weights are near or below 0.10. This finding suggests that even the fully-variable case is probably over-filtered, and the results do show smaller solution amplitudes compared to the fixed-in-space case.

Filter Weights

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Moving on the the average oscillation excess plots, we see that the oscillation levels are universally higher in the fixed-in-space case as compared to the other two. The most likely explanation for this is that, by allowing decreases in the filter weights, the oscillation levels come into a reasonable equilibrium as intended by the filter weight control scheme. If the weights can only increase in time, then they most likely over-filter the solution most of the time. The spike in the oscillation excesses in the z direction around 8.2 UTC is due to the starting acoustic transient as it passes through the upper portion of the domain, and we saw a clear depiction of these oscillations in the movie above. Since the filter weights were dropping in time prior to 8.2 UTC, the scheme is caught off guard as the acoustic blast enters the upper portion of the domain. The filter weights increase in response to the threat and the oscillations are controlled.

Oscillation Excess

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The behavior of the percentage of points over the oscillation target is similar to the oscillation excess, at least for the x and y directions. In these directions, the percentages are similar for the fully-variable and fully-fixed cases, but significantly greater for the fixed-in-space case. Again the likely reason for this is the ability for the filter weights to decrease in the fixed-in-space case. The behavior for the oscillation percentages in the z direction are somewhat more similar for the three cases. In all of these, the oscillations in w are highly widespread (60-70% of the points) for at least a half hour period during the simulation. The oscillations peak close to 9.5 UTC for the fully-variable and fully-fixed cases, but occur after 10.0 UTC for the fixed-in-space case. The rapid rise in the oscillation level for this case starting prior to 10.0 UTC correlates with the planar waves seen in the movie above. There is also a suspicious periodic behavior in the percentage plots for this case from about 10.0-11.25 UTC, and this also correlates with the time period when acoustic noise is seen in the upper portion of the domain.

Percentage of Points Exceeding the 2% Oscillation Target

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