The impact of internal atmospheric variability on the North Pacific SST variability

Abstract

The impact of internal atmospheric variability on North Pacific sea surface temperature (SST) variability is examined based on three coupled general circulation model simulations. The three simulations differ only in the level of atmospheric noise occuring over the ocean at the air-sea interface. The amplitude of atmospheric noise is controlled by use of the interactive ensemble technique. This technique simultaneously couples multiple realizations of a single atmospheric model to a single realization of an ocean model. The atmospheric component models all experience the same SST, but the ocean component is forced by the ensemble averaged fluxes thereby reducing the impact of internal atmospheric dynamics at the air-sea interface. The ensemble averaging is only applied at the air-sea interface so that the internal atmospheric dynamics (i.e., transients) of each atmospheric ensemble member is unaffected. This interactive ensemble technique significantly reduces the SST variance throughout the North Pacific. The reduction in SST variance is proportional to the number of ensemble members indicating that most of the variability can simply be explained as the response to atmospheric stochastic forcing. In addition, the impact of the internal atmospheric dynamics at the air-sea interface masks out much of the tropical-midlatitude SST teleconnections on interannual time scales. Once this interference is reduced (i.e., applying the interactive ensemble technique), tropical-midlatitude SST teleconnections are easily detected.

Appendix

The traditional “null hypothesis” for low frequency climate variability in the mid-latitude oceans is due to Hasselmann (1976). Hasselmann’s hypothesis postulates that the atmosphere, which is modeled as stochastic noise forcing, generates low-frequency SST variability via a red noise oceanic response. In this Appendix we describe what would be expected in comparing the variances from the interactive ensemble and the standard coupled model under the condition that the null hypothesis is valid. In this null hypothesis, the atmosphere is viewed as a stochastic weather noise generator and the ocean is a red noise filter. Coupled air-sea interactions are modeled as stable feedbacks. The simplest form of this model can be written as

$$ \begin{aligned} A^{n} & = \alpha O^{{n - 1}} + N^{n} \\ O^{n} & = \beta A^{{n - 1}} + P^{n} \\ \end{aligned} $$

(1)

where A is the atmospheric flux, O is the SST, α and β are the coupling parameters, and N and P represent Gaussian white noise forcing. The coupling parameters are stable (0 < α, β < 1). With these assumptions the SST variance (σ _o ²) can be written as

$$ \sigma ^{2}_{o} = \frac{{\beta ^{2} \sigma ^{2}_{N} + \sigma ^{2}_{P} }} {{1 - \alpha ^{2} \beta ^{2} }} $$

(2)

where the respective noise variances of the atmosphere and the ocean are denoted by σ _N ² and σ _P ². In a similar fashion, we can write the null hypothesis version of the interactive ensemble as

$$ \begin{aligned} A^{n}_{1} & = \alpha O^{{n - 1}} + N^{n}_{1} \\ & \ldots \\ A^{n}_{M} & = \alpha O^{{n - 1}} + N^{n}_{M} \\ O^{n} & = \beta \frac{1} {M} {\sum\limits_{m = 1}^M {A^{{n - 1}}_{m} } } + P^{n} \\ \end{aligned} $$

(3)

where each of the atmospheric noise realizations are drawn from the same population. The SST variance in the interactive ensemble (σ _oo ²) is given by

$$ \sigma ^{2}_{{oo}} = \frac{{\frac{{\beta ^{2} }} {M}\sigma ^{2}_{N} + \sigma ^{2}_{P} }} {{1 - \alpha ^{2} \beta ^{2} }} $$

(4)

and ratio of the variances is given by

$$ \frac{{\sigma ^{2}_{{oo}} }} {{\sigma ^{2}_{o} }} = \frac{{\frac{{\beta ^{2} }} {M}\sigma ^{2}_{N} + \sigma ^{2}_{P} }} {{\beta ^{2} \sigma ^{2}_{N} + \sigma ^{2}_{P} }} \enspace . $$

(5)

There are a few limits to the ratio that are worth noting. First, in the limit of very large ensemble sizes the ratio is given by

$$ \frac{\sigma ^2_{oo}} {\sigma ^2_o} \approx \frac{\sigma ^2_P} {\beta ^2 \sigma ^2_N + \sigma ^2_P} {\enspace}. $$

(6)

If, in addition, we assume that the ocean noise and the atmospheric noise are comparable, then the variance ratio lies somewhere between 0.5 and 1. Second, if we assume that the ocean noise is small compared to the atmospheric noise then A5 implies that the variance ratio is given by

$$ \frac{{\sigma ^{2}_{{oo}} }} {{\sigma ^{2}_{o} }} \approx \frac{1} {M} $$

(7)

Third, if the null hypothesis correct and the ocean noise is relatively small, then the ratio converges to zero for very large ensembles. In this case the variability in the interactive ensemble model goes to zero.

Figure 11 shows the variance ratio (i.e., Eq. 5) for three different values of the coupling parameter β as a function of noise variance ratio (σ _P ²/σ _N ²). The curves plotted in Fig. 11 correspond to assuming six ensemble members for the interactive ensemble. For weak coupling (β = 0.25), the variance ratio becomes relatively large for relatively small values of ocean noise. This is as expected. If the coupling is weak then the ocean noise has a large effect on the total variance. As the coupling strength increases the variance ratio approaches one only with considerably larger values of the oceanic noise. In this case, the coupling is more important and the ocean noise has a smaller impact.

Fig. 11.

The variance ratio for three different values of the coupling parameter β as a function of noise variance ratio (σ _P ²/σ _N ²)

In order to interpret the CGCM results presented, it is useful to consider three ranges of values for the ratio of the variances.

• 1. If the ratio is on the order of 1/M as in A7, we conclude that the null hypothesis is likely to be correct (i.e., the variability is behaving like stochastically forced system with stable coupled feedbacks) and the ocean noise is relatively small.

• 2. if the variance ratio is between 0.5 and 1.0 then either the null hypothesis is correct and the ocean noise is playing a significant role or the null hypothesis is incorrect and there are unstable coupled feedbacks or important non-linearities. In other words, we can make no definitive conclusion.

• 3. If, on the other hand, the ratio exceeds 1.0, then we conclude that the null hypothesis fails and that there are unstable coupled feedbacks and/or important non-linearities.