Jacopo Riboldi

Jacopo Riboldi

PostDoctoral Researcher

Space/time spectral analysis of atmospheric blocking

Rationale

Wavenumber/phase speed spectral analysis provides a compact representation of the Rossby waves populating the Northern Hemisphere in a given period. When applied to atmospheric blocking, this spectral fingerprinting approach reveals the harmonics associated with the blocking as well as the ones of the Rossby wave packets interacting with it. Although disentangling the two is not completely possible, the spectral signature of blocking is likely evident on harmonics with low zonal wavenumbers ($n=$2-5) and near-zero or slightly negative phase speed. Although this approach cannot provide the exact timing and location of single blocking events, the method is based only on upper-level meridional wind anomalies and is directly related to the stationarity of the hemispheric-scale flow over a given period of time.

Get the poster PDF here

Methodology

Decorrelation time $\tau$ is estimated from an exponential fit of the autocorrelation function A, computed for each wavenumber/phase speed harmonic during the 90 DJF days in each winter. Approximating the decay of A as exponential,

$A=A_0 e^{-\frac{t}{\tau}}$

here $\tau$ corresponds the time needed for the autocorrelation function to drop from 1 to $1/e$. A was computed between lag 0 ($A_0$=1) and lag +5 days, meaning that 6 points are employed to fit $\tau$. If A becomes negative before lag +5, only the available positive values are used to fit the exponential.

Mean decorrelation times were estimated for each winter season and then averaged to obtain the plot in the poster. A broad range of $\tau$ values was obtained across the considered winters, indicating different persistence scales of the same harmonic across different seasons.

Spectral analysis

Focusing on a latitude $\phi$, an Hovmoeller diagram of meridional wind anomalies V' at 250 hPa is built over a time period of two months (61 days). Zonal wavenumbers are obtained from spectral decomposition along the longitude dimension, while frequencies are obtained from V' variability along the time dimension. Interpolation to the phase speed is possible using the Rossby wave dispersion relationship $c_p=\omega/k$, as in Randel and Held (1991). This procedure is repeated for each latitude circle between 35°N and 75°N: the obtained spectra are then averaged to obtain one representative spectrum for the whole mid- to high latitudes. Caveat: blocking tends to occur at high latitudes and is quite broad in scale: this implies that it projects preferentially on harmonics with low wavenumbers ($n$=2,3) traditionally associated with so-called planetary waves. However, high power at these wavenumbers might be simply indicative of strong wind anomalies over a restricted portion of the NH high latitudes, rather than to the presence of a planetary wave spanning the hemisphere. Averaging several spectra from different latitudes can attenuate this deformation.

This same procedure is also repeated for every two-month time window centered on each day between the 1st of February 1979 and the 30th of November 2018: results of this work only use spectra obtained during boreal winter days (DJF).

For a more detailed explanation of the spectral analysis, see the Data and Methods section of our WCD paper.

Event extraction

The area-weighted fraction of grid points occupied by atmospheric blocking in the Northern Hemisphere is computed for each winter day between December 1979 and February 2018. Blocking is defined following the Schwierz et al. (2004) anomaly-based approach.

The days corresponding to the top and bottom 10% of blocked area are selected separately for each season: this leads to the selection of 9+9 days per season, for a total of 351 days in each subset. The corresponding anomalies in spectral power with respect to the DJF mean are averaged to build composites. In case more than 9 days in a season did not feature any blocking, a subset of nine of is chosen at random.

Spectral signature: North Pacific vs North Atlantic blocking

Do North Pacific and North Atlantic blocks have a different spectral signature? Is it possible to distinguish between them?

Two averaging boxes around climatological maxima of blocking frequency at the end of the North Atlantic (80°W-0°E,40°N-70°N) and North Pacific (180°W-120°W,40°N-70°N) storm tracks. Events of large blocked area over the whole Northern Hemisphere feature blocking at the end of the two storm tracks (Fig. 1a). Selecting for single storm tracks isolates the blocking frequency anomalies over the chosen sector: days of high blocked area over the North Atlantic are associated with an average blocking activity over the North Pacific (Figs. 1b,e), and vice versa (Figs. 1c,f). This allows, in principle, for the identification of blocking's spectral characteristics in a single storm track, with minimum contamination coming from blocking activity in the other one.

Fig. 1 pdf: Composite of (top) blocking frequencies and (bottom) blocking frequency anomalies for events in the top 10% of blocked area over (a,d) the whole NH, (b,e) the North Atlantic and (c,f) the North Pacific averaging boxes (marked in dotted blue contours) during boreal winter. Anomalies in blocking frequency are obtained by removing the DJF mean (black contours) from the composites.

Blocking over the North Atlantic has a relatively similar signature to NH blocking events, with anomalous power in westward propagating $n=$2,3 harmonics and (slowly) eastward propagating $n=$3-5 harmonics. Blocking over the North Pacific has a less nitid spectral signature than blocking over the Atlantic. It projects on relatively higher wavenumbers, between 4 and 5, and almost equally between eastward- and westward-propagating harmonics.

While the wavenumbers of the involved harmonics slighty differ, near-zero phase speed are always involved.

Fig. 2 pdf: Composites of spectral power anomalies in days with top 10% of blocked area over (a) the whole NH (b) the North Atlantic and (c) the North Pacific averaging box.

Spectral signature: Sensitivity to blocking diagnostics

How does the spectral signature of blocking change when employing different blocking identification methods?

Three blocking metrics are compared: the Schwierz et al. (2004) (S04) PV anomaly-based diagnostics the Davini et al. (2012) (D12) wave-breaking based diagnostic, and the Woolings et al. (2018) (W18) geopotential anomaly-based diagnostic. One should bear in mind the vertical level (500 hPa) employed by D12 and W18 to diagnose blocking, which is lower than the one chosen for spectral analysis (250hPa). This leads to a non exact correspodence between the circulation patterns associated with blocking and their spectral fingerprint, that is diagnosed at a higher level. In this regard, the equivalent barotropic structure of blocking in the vertical should limit the differences.

The main differences (Fig. 3) are:

  • Anomalies in spectral power are overall weaker for the blocked and non-blocked subsets if the D12 and W18 are employed.
  • Anomalies in spectral power are restricted to fewer ($n,c_p$) harmonics in D12 and W18 than in S04: in general, no wavenumbers above 4 are involved and anomalies are even more "squeezed" next to the $c_p$=0$,$m$,$s$^{-1}$ line. This can in principle pinpoint the involved harmonics more precisely.
  • Differences between the blocked and non-blocked subsets are more significant for the S04 diagnostic than for the other two (Figs. 3c,f,j).

Fig. 3 pdf: Composites of spectral power anomalies on days with top 10% and bottom 10% of blocked area over the whole NH, as well as the difference between these two subsets, for different atmospheric blocking diagnostics. (a-c) Schwierz et al. (2004), (d-f) Davini et al. (2012), (g-j) Woolings et al. (2018). Significant differences are assessed with respect to a 2500-times reshuffling of the members of each composite, as in Riboldi et al. (2018).