CAPITULO II 6 HIPÓTESIS
ANÁLISIS E INTERPRETACIÓN.
10. COMPROBACIÓN DE LA HIPÓTESIS.
Before turning to mechanisms that can drive persistent anomalies, it is worth considering the evidence that such mechanisms are in operation. We begin by considering the month-to-month persistence of the NAO. Figure 3.2 shows the seasonal cycle of 1-month lag autocorrelation of the monthly mean NAO. These monthly means are projections on a rotated empirical orthogonal function of 500 hPa geopotential heights from the NCEP/NCAR reanalysis, obtained from the Climate Prediction Center (http://www.cpc.ncep.noaa.gov/data/teledoc/nao.html).
Is this what we expect from red noise? In some respects it is not. The relatively large values of persistence from January to February and from February to March imply either that the decorrelation time of the NAO is longer than ten days, or that the simple red-noise model is
incomplete. It is readily shown that the correlation of successive averages of time interval T of a
red-noise process with decorrelation time t is given by,
† Cor x t
(
( )
,x t(
+t))
=t
T e-2T/t 1-t
T 1-e -T/t(
)
È Î Í ˘ ˚ ˙ . (1)For a 10-day decorrelation time and consecutive 30-day means, we calculate a lag correlation of 0.22. Thus the wintertime values in Figure 3.2 are larger than expected from the daily red noise model, though it should be kept in mind that these “large” values suggest no more than 10% of the variability of the NAO in one month can be explained by its value in the previous month. The observed negative lag-correlations in spring are also inconsistent with the red-noise model. This springtime loss of persistence is a general feature of the Northern Hemisphere large-scale flow, first noted by (van den Dool and Livezey 1984).
Figure 3.2: Month-to-month autocorrelations of the monthly mean CPC NAO index.
Daily data may also be examined to see if these are consistent with the red-noise hypothesis. Lag correlations for daily values of the NAO index, from the same source as before, are shown in Figure 3.3. In all seasons the correlations decay to values below 1/e in fewer than 10 days. In the winter, and to some extent in the fall, however, there is a “shoulder” in the lag correlations, a deviation from exponential decay such that correlations greater than expected from the red-noise model persist for lags a month or longer.
Thus, it appears something more than red noise is going on, offering hope for predictability on long timescales. A note of caution, however, is that longer records of the NAO based on station barometric records (e.g., Jones (1997)) suggest a weaker mid-winter maximum in persistence, though it is unclear if this results from the differing nature of the surface-based and 500 hPa- based indices, if it suggests that the 50 year CPC record is insufficiently long, or if it indicates a true trend towards increasing persistence in the NAO.
What are possible sources for the shoulder? The long thermal memory of the upper ocean is a prime candidate. Barsugli and Battisti (1998) provide a simple linear model useful for quantifying the role of the upper ocean in enhancing the persistence of atmospheric variability. Their model
of a mode of atmospheric variability, and the second representing the evolution of the ocean
mixed-layer temperature, To, or the amplitude of a pattern of mixed-layer temperature that
interacts with the atmospheric mode. The atmosphere is forced by noise, N(t), associated with
the chaotic variability of synoptic systems. There is dissipation in both fluids, and each influences the other. All dissipation and interactions are assumed linear. The resulting equations are:
†
dT
adt
= -aT
a+bT
o+N t( ),
bdT
odt
=cT
a-dT
o.
(2)With a non-dimensional unit of time equal to about five days, Barsugli and Battisti estimate that appropriate values for the dissipation and interaction parameters are,
d it decays approximately on the atmospheric dissipation time,
†
t
a = 1a. The secondrepresents the quasi-steady atmospheric response to an anomaly in T0,
† Ta To Ê Ë Á ˆ ¯ ˜ ª b a 1 Ê Ë Á ˆ ¯ ˜ , and it
decays approximately on the ocean dissipation time,
†
t
o= bd
. Atmospheric forcing of theocean, the c parameter, causes the first eigenvector, and thus the response to impulsive
atmospheric forcing, to include a small response in the ocean, mixing the two eigenvectors. Two examples of the response to atmospheric impulsive forcing are shown in Figure 3.4. The atmospheric curves also represent the expected lagged autocorrelations for the atmospheric
index. Here the atmospheric damping parameter, a, has been reduced from Barsugli and
Battisti’s value to 0.6. This gives an initial exponential decay of the atmospheric index on a timescale of less than 10 days, consistent with wintertime observations of the NAO. In the case
where there is no ocean feedback on the atmosphere, b=0, the exponential decay continues.
When the ocean feedback is increased to the largest value at which the system remains stable,
b=1.1, there is a “shoulder” in the atmospheric response, and significant persistence to the end
of the month and beyond.
Figure 3.4: Impulse response of the Barsugli and Battisti model in the atmosphere and the ocean for two
different values of the coupling parameter, b.
The shoulder, in the case with strong ocean feedback, gives rise to a significant increase in the
one-month lag correlations of the atmospheric index, from 0.18 when b = 0, to 0.31, when b =
1.1. This greater value for the persistence is close to what is observed for the NAO in the winter. Thus it appears that the thermal memory of the ocean mixed layer could be responsible for the
persistence of the NAO beyond the timescales of atmospheric dissipation. If so, this is “good news” for seasonal to interannual predictability, since it implies that there is a significant two- way interaction between the atmosphere and the ocean. Such an interaction could contribute to interseasonal or interannual predictability, if ocean temperature anomalies are, as suggested by observational and modeling studies, affected by re-emergence. That is, mixed layer temperature anomalies created during one cold season, then preserved beneath the shallow seasonal thermocline in the summertime “re-emerge” during the following cold season
(Alexander and Deser 1995; Alexander et al. 1999).
Unfortunately, there are reasons to suspect that the ocean is not responsible for the NAO shoulder. To obtain a value of the persistence close to what is observed, the parameters must take on values that are probably unrealistic, because they are barely stable, and because they are quite different from the original values chosen by Barsugli and Battisti, based on the integration of a coupled model. Moreover, Bretherton and Battisti (2000) found that these original parameter settings yielded excellent agreement with the results of experiments in which the observed historical evolution of SSTs is used to drive large ensembles of atmospheric models. Secondly, the observed month-to-month variability in NAO persistence is hard to explain in terms of local interactions with the upper ocean, since the basic physics of the toy model should operate throughout the winter. Such month-to-month changes are more readily understood if the shoulder comes from the stratosphere (e.g. Baldwin (2003a), since there are distinct seasonal “windows” for robust stratosphere-troposphere interactions – those months when the stratospheric winds are westerly, but when the flow is sufficiently disturbed to permit strong variability.
Figure 3.5: The standard deviation (left) and leading EOF of late winter (February-March-April) monthly mean, Atlantic sector 500 hPa heights in observations (a and e), in an atmospheric model with climatological SST (b and f) and the same atmospheric model coupled to a 50-meter slab ocean mixed layer (c and g). From Peng et al. (2004).
An atmospheric model, one that realistically reproduces the observed structure and variability of the NAO, does not show any increased persistence in the NAO when it is coupled to an ocean mixed layer. Figure 3.5 shows the leading EOF of 500 hPa heights in the Atlantic sector of a version of the U.S. National Center for Environmental Prediction medium range forecast model
(Peng et al. 2004). The model’s NAO pattern is very similar in the coupled (AGCM-ML) and
uncoupled (AGCM) versions of this model, though the variability of monthly means is slightly stronger in the coupled model. The model greatly underestimates the month-to-persistence in the NAO, however (Figure 3.6), and there is only a small difference in the persistence of the NAO between the coupled and uncoupled models, even though the coupled model does produces a significantly greater variance in the NAO in mid winter. It should be noted that while this model has excellent vertical resolution in the troposphere, it does not have a well-resolved stratosphere. Unlike the GCM, the heuristic model of Barsugli and Battisti predicts that increased coupling will significantly enhance the persistence while only slightly increasing the variance. Bladé (1997), on the other hand, found that coupling with a mixed-layer model did, as expected, enhance the month-to-month persistence of the leading EOF of 500 hPa heights in her model. It is perhaps relevant, however, that her experiment was conducted in a perpetual
January setting, while the Peng et al. model includes the seasonal cycle. It is possible that
subtle month-to-month shifts in the preferred patterns of variability create a mismatch between the SST anomalies created in one month and the leading atmospheric pattern in the next.
Figure 3.6: (a) Month-to-month persistence of the NAO in observations and in models coupled and uncoupled to an ocean mixed layer. (b) Standard deviation of the monthly mean NAO index in the coupled and uncoupled models.