Comparison of the Different Verification Variables:

a) Summary Maps:

All verification variables and level produce almost identical summary maps. The most noticeable difference is that the sea level pressure and temperature norms produce a much smaller signal (O(10^-2)) compared to the norms that include winds(O(10). The temperature norms produce a smaller relative signal in the Atlantic than the total energy norms and the sea level pressure norm except at th 850mb level. The total energy norms produce a slightly smaller signal than the norms that only include the winds. For the given verification region over Europe and the 48 hours verification time the 250mb total energy norms gives the strongest signal in the target regions that would be most likely to be dynamically connected. The other verification variables and level give too strong a signal in the Pacific, in an area that is too remote to affect the verification region in 48 hours, and too small a signal in the Atlantic where observations would be expected to impact the verification region at the given verification time.

b) Signal Variance Evolution:

To determine the significance of temperature as a verifying norm I first compared the total energy norm with the wind norm. Both norms use the 250, 500 and 850mb winds but the total energy norm includes the temperature at these three levels as well. The initial signal is almost exactly the same for the 2 norms but at 36 hours a difference is apparent in the northeast Atlantic in the vicinity of Maine. The signal variance that includes temperature in the verifying norm appears to be much greater in this region. This difference is significant through 96 hours when the signal variance for each of the verifying norms becomes almost identical again. From 96 hours onward the 2 signal variance maps differ only in the areal extent of the region of strong signal variance in the north Atlantic. The signal variance has the same shape for each of the 2 verifying norms but the one that includes temperature covers a greater area. The signal in this region for either norm is far removed from the observation site and is possibly due to spurious long distance correlations. The maximum signal variance is much greater (33.8) for the wind verifying norm than the norm that includes temperature(20.6). This might be an indication that the two variables are out of phase with each other.

A direct comparison of the vertically averaged temperature and wind norms show an initial difference in the signal variance in the Atlantic. The wind verifying norms shows 3 small areas of signal variance in the Atlantic in trough or low pressure regions while the temperature verifying norm only shows 1 small area in one of these regions in a shortwave trough off the coast of Maine. This area is associated with a temperature anomaly that is most likely associated with local convection. The signal variance in the northeast Atlantic is greater for the temperature verifying norm starting at 60 hours. Another noticeable difference between the signal variance in the 2 verifying norms is that the signal for the temperature verifying norm remains between a narrower range of latitudes. The signal variance for the temperature verifying norm appears to lag that of the wind norm by about 5 degrees as it crosses the United States. If you follow the initial signal this becomes apparent by 36 hours. At 48 hours the signal is on either side of the 100W longitude mark for the 2 verifying norms. The most noticeable difference between the two verifying norms is the magnitude of the signal variance. For the wind verifying norm the maximum value is 33.8 while the maximum is only 8.6 for the temperature norm.

Next I compared the temperature and wind norms at each of the three vertical levels. At the 850mb level the initial temperature signal is on the west side of the sondes in a very small area. There is a larger region of signal variance that is greater in magnitude just inland over the downstream ridge. This signal amplifies more rapidly and has a greater phase speed than the signal in the sonde region. The sonde signal does not appear to propagate out of the Pacific but seems to become trapped in the coastal region between the western U.S. and Alaska. There appears to be both upstream growth and propagation in the 850mb wind signal beginning around 48 hours. The wind signal at the same level is initially all around the sonde region both upstream where it is strongest and extending downstream over the ridge to the east. The strongest signal remains in the Pacific and there is also strong local growth upstream in the west-central Pacific. This local growth is not apparent in the temperature signal where the upstream propagation is in a narrower region to the north over Alaska extending westward, and the local growth is much smaller and over Alaska rather than in the Pacific. Both verification norms produce greatly amplifying signals in the Atlantic. The initial signals differ in the Atlantic and over the Baja. The wind norm includes and initial signal in the Atlantic and no signal over the Baja while the temperature norm has no initial Atlantic signal and a small area of signal variance in the Baja region.

The initial signal for the 500mb temperature is just northwest of the sondes extending in a narrow region over the downstream ridge the initial wind signal is in a similar region but extends further downstream and also includes an area of large signal variance on the western side of the sonde region. Both verification norms have initial signals in the Baja region and in the Atlantic near Maine. The temperature norm also has two very small regions of signal variance on the west side of the trough over the U.S. that grow and distort the signal at later time. The area of signal variance is larger for the wind norm which produces additional signals in the southeast Atlantic. The wind signal covers a much larger area initially and spreads out rapidly both up and downstream while the temperature signal has little upstream propagation and follows as much more narrow path. The westward spread of the signal for the wind norm appears to be from local growth in the central Pacific rather than upstream propagation. Both verification norms show an amplification of the signal variance once it reaches the Atlantic after about 72 hours. If you consider the more eastern signal that is initially over the ridge downstream of the sonde region, it appears that the signal may reach the Atlantic as soon as 48 hours.

At 250 mb the temperature norm produces an initial signal variance all around the sonde region and eastward over the downstream ridge an into the trough to the east. There is also a signal in the Baja region, off Maine and in the southeast Atlantic. The signal in the sonde region amplifies with time but there appears to be little propagation while the signal in the downstream trough both amplifies and propagates. The wind norm produces a strong signal from the northeast side of the sonde region extending eastward over the downstream ridge. The signal over Baja is more localized but nearly equal in magnitude. The wind norm produces similar regions of signal variance in the Atlantic as the temperature norm. The 250mb wind norm produces the clearest signal variance evolution of any of the wind and temperature norms. There is some local growth both in the Pacific and Atlantic but it is weak and can be distinguished from the original signal from the sonde region. There is also little upstream propagation for this norm.

At all levels the temperature signal is generally more localized spanning a narrower band of latitudes. There is also generally less local growth in the Pacific but more upstream propagation with the temperature norm. The exception is at the 250mb level where the temperature norm does produce strong local growth in the Pacific. At all levels both norms produce an amplification of signal variance once the signal reaches the Atlantic sometime between 48 and 72 hours. Both norms produce a signal both around the sondes and downstream. The temperature norm produces an upstream signal at 250mb and possibly at 850mb and the wind norm produces an upstream signal at 850 and 500mb. The downstream signal propagates for all norms at all levels while the upstream signal appears to remain trapped near the northwest coast of N. America for all norms with an initial signal upstream from the sondes. The 250mb wind norm has no upstream signal initially and shows the best propagation(ie. it can be easily tracked). The wind signal in general is much greater in magnitude than the temperature signal and increases with height. The temperature signal however is strongest at the surface.

Since the goal of targeted observations is to improve surface forecasts it is important that we determine whether the strong upper level wind signal and the surface variable signals reach the verification region at the same verification time. Whether the temperature signal at the surface is in phase with the upper level wind signal is subjective. If one were to follow the greatest initial wind and temperature signals, then both would end up at about 90W after 72 hours but the initial temperature signal is about 20-25 degrees downstream of the wind signal and also downstream from the sonde region. The signal from the sonde region tracks to the northwest U.S. coast and appears to remain in this area and grow slightly. The situation is similar for the 850mb wind norm vs the 250mb wind norm. If you track the more eastern signal for the lower level it arrives at about 90W after 72 hours with the upper level wind signal while the more western 850mb signal appears to propagate towards southeast Alaska and decay. A possible explanation is that the lower level signals are unable to propagate west of the mountain ranges that line the Pacific northwest so that only the more eastern signal, if it is not spurious, propagates.

The mean sea level pressure norm produces an extremely small signal variance, perhaps due to a scaling issue. There is not a clear maximum signal that can be traced back to the sonde region. There is initially only a tiny signal on the upstream side of the sondes and a larger signal on the Canadian west coast. As the eastern signal propagates it leaves a residual signal of nearly equal magnitude. There is local growth over the oceans begining at 24 hours and also at the front of the propagating signal between 24 and 36 hours. If you neglect the propagation of the local growth in the Atlantic, the signal appears to propagate equally upstream and downstream. The signal remains in a fairly narrow range of latitudes. The initial signal in Canada reaches approximately the same longitude as the upper level wind signal (90W) by 72 hours. Like the low level temperature signal the mslp signal begins well north and east of the 250mb wind signal. The tiny magnitude of the mslp signal as well as the lack of a clear signal maximum to track makes it less useful as a verification variable since no clear, statistically significant signal can be traced from the observation site to any specific verification region.

My initial conclusion is that the 850mb temperature and 250mb wind norms are the most useful verification norms. These levels produce the greatest signal for the respective verification variables and also produced the cleanest signals of all the variables at all levels. There does not appear to be any difference in phase speed between the surface temperature and upper level wind signal. This would support the theory that both signals would propagate as coherent wave packets at the same group velocity. Further analysis is needed to determine if this is true for the actual forecast since changes in upper level features do not immediately translate down the the surface.

Single Verification Levels vs Vertically Averaged Verification Norms:

The vertically averaged wind and total energy norms are dominated by the upper level winds. Further the upper level wind norm appears to produce better target region and a more coherent signal. The temperature norm appears to be most useful at the 850mb level as it produces more reasonable targets and a clearer signal propagation if one can believe the signal that is produced downstream from the sondes. The 500mb temperature norm produces downstream signals and upstream targets that are likely to be spurious and the 500mb wind norm has upstream as well as downstream propagation as well as a smeared out signal. At 250mb the temperature norm still produces target that are too far upstream to be considered viable and a signal that extends far downstream. The 250mb wind and total energy targets are stronger in the Atlantic where we would expect them to be and produce a clear signal. The 250mb wind and total energy signals also extend fairly far downstream however the actual signal from this flight was more closely confined to the sonde region.