Part 3: How well does the ETKF predict the signal variance evolution?

To see how well the ETKF is able to predict the signal variance due to targeted observations, I compared the ETKF signal variance(SigVar) evolution from the WSR flight on January 20, 2005 to the NCEP signal evolution. I compared the SigVar to both the surface pressure and kinetic energy signals. This particular flight date was chosen because the actual signal appeared to propagate not only into the verification region at the verification time but also propagated across the Atlantic into eastern Europe. The targeted verification region was 82W, 37N and the verification time was 00z on January 23. The purpose of this flight was to improve the forecast of a snowstorm that was predicted to impact the eastern United States on or about January 23^rd. Flight path number 37 was determined to be the optimal path for targeted observations. The actual flight track was extended to the northeast in order to contain 40N 135W. The flow regime for this time period was quite “wavy” with troughs centered at latitudes 140E, 160W and 70W and ridges centered at 160E, 110W and 25W at the observation time.

The ETKF signal variance maximum at the observation time was located at 38N, 135W and 40N, 160 W. These areas are on the northeast and northwest edges of the flight path on the leading edge of an upper-level trough to the east and along the trough axis to the west. The signal variance extends along the downstream side of the trough ahead of the maximum SigVar and over the ridge downstream, following the height contours. The SigVar in this region is not only around the sondes but in the dynamically connected region just downstream. There is a secondary SigVar maximum in a smaller region centered at 25N, 115W downstream of the southernmost sonde. This location coincides with the eddy that was discussed earlier in part 1. There is no obvious dynamical connection between this area and the sonde region so it is possible that this signal is spurious and simply due to large ensemble spread in this region however it is also reasonable to assume that the location of the trough in the sonde region would influence the intensity of this feature in the analysis. There is one more small region of signal variance off the coast of Maine. This region is sufficiently far away from the dropsonde region to assume that this is a spurious signal.

The actual signal in the surface pressure at the observation time has two maximums centered on the east and west extremes of the flight path at about the central latitude of the path. This makes sense because the largest difference between the analysis with and without the observations would be expected in the vicinity of the sondes. There are also a minor, seemingly random surface pressure signal in the tropical latitudes, mostly over the oceans. It is not clear what the explanation for this phenomena might be. The kinetic energy signal is more localized around the sondes with maximum values on the eastern edge of the flight track. The KE signal maximum is in good agreement with the ETKF SigVar maximum at 135W both in location and relative strength.

The ETKF SigVar maximum propagates eastward at a speed of about 20 degrees per day( covering greater longitude when it propagates further north ) approximately following the same height contours. The signal variance in the Baja region is stationary for the first 36 hours and then propagates in the same manner. The signal variance maximum spreads out in latitude to incorporate the signal in the Baja region. Starting at 24 hours there is also a small area of SigVar off the coast of Japan. This area seems to propagate slowly eastward, and spread out until it is connected with the sonde region. The signal off Maine propagates propagates eastward as well following the height contours. After 49 hours there appears to be some westward propagation as well but to a much lesser degree. The SigVar spreads out in longitude until all there is a continuous SV connecting all the initial SigVar regions following the height contours. The SigVar blows up 60 hours or so after the observation time so that there is a SigVar practically everywhere, but the initial maximum remains coherent as it propagates from the western pacific to the eastern boundary of the north Atlantic. According to the ETKF signal variance, the effect of the observations can be expected to propagate into Europe by 132 hours.

The propagation of the surface pressure signal is at about the same rate as the ETKF signal variance (approximately 20 degrees per day). The SP signal weakens then amplifies greatly in the verification region at the verification time. A coherent signal propagates across the Atlantic moving into more northerly regions towards Greenland and then Europe. In addition to the propagating signal a strong SP signal remains in the observation region 84 hours after the observation time before it decays. As the signal propagates there is a lingering signal in it's wake that decays within about 36 hours. There is no SP signal in the two regions indicated by the ETKF SigVarthat were upstream off the eastern coast of Asia and downstream off the coast of Maine. This would suggest that the SigVar in these regions was a result of spurious correlations. There is no SP signal in the Baja region either however this signal is apparent in the KE. Unlike the ETKF SigVar, the SP signal does not spread out over the region surrounding the areas of maximum values. However the general location of the SP signal and the ETKF SigVar maximum are very similar. Although the ETKF SigVar does not incorporate surface pressure the signals would be expected to propagate in a similar manner as illustrated in this comparison. It also seems reasonable that the SP signal would linger for 24 hours or so before current observations would become more influential than the targeted observations.

The kinetic energy signal initially propagates at about the same speed as the ETKF SigVar and the SP signal at about 20 degrees per day towards the east. Once the signal reaches the verification region the maximum signal spreads out along the trough axis. The signal continues to propagate into the same region of the northern Atlantic, north of eastern Europe . A KE signal remains in the sonde region up to 60 hours after the observation time. Like the SP signal this signal is concentrated in the northernmost portion of the flight track. It is interesting to note that from about 60 hours onward there is a KE signal to the south of the initial KE signal which is in approximately the same region as the ETKF predicted signal from the Baja region. This would indicate that this SigVar was not due to a spurious correlation. There is no KE signal in the upstream or downstream regions (off Maine and Japan) indicated by the ETKF SV which would seem to confirm that these are indeed spurious correlations. The KE signal is to the south and west of thev erification region at the verification time. KE signal is very similar in structure to the ETKF SigVar maximum. It propagates at approximately the same speed, has maximum values in the same regions, and has a similar orientation with respect to the height contours.

The good agreement between the SP signal and the predicted SigVar from the ETKF is encouraging not only because the maximum effect is in the verification region at the verification time but because the actual and predicted signals are in agreement out to 132 hours past the observation time. In general the KE signal maximum is co-located with the ETKF signal maximum while the SP signal max tends to lag the ETKF signal max with a smaller signal in the region of the ETKF signal max.

Since the ETFK predicted signal variance and the realized SP and KE signals remain coherent out to 144hrs I decided to run the ETKF for a verification region in the area of Northern Europe at a verification time of 144hrs. For this verification region and time the ETKF indicated that flight path 56 would be the optimal location for targeted observations. This track is is narrower in longitude, along the same latitudes as the extended track 37 used in this WSR case. This flight track is oriented in a more south to north direction while track 37 is oriented south to northeast. I then evaluated the ETKF signal evolution for this flight track and compared it to the one for the actual flight track. The two SV evolution maps are almost exactly alike. The most significant difference is that at 72 hours the strongest signal is near Greenland for a 144 hour verification time and less strong in the initial verification region for a 72 hour verification time. By 96 hours the ETKF predicted signal variance for both tracks are almost identical. This would indicate that the majority of the variance is contained in a smaller region that is encompassed by both of the flight tracks. A possible way to test this theory is to design smaller flight tracks that are encompassed by the initial flight tracks.