Low-level jet development and the interaction of different scale physical processes

Abstract

Two cases of low-level jet events and the interaction of the involved physical processes are investigated. The vertical distribution of the dominant atmospheric motions is studied, using data from a SODAR-RASS system and in situ instrumentation, at a coastal region of the Eastern Mediterranean (Messogia Plain in Attica—Greece). The first low-level jet (LLJ) case was observed during the cold period, after the passage of a cold front and could be characterized as purely synoptic. Coherent inertial motions were found to follow the frontal surface at both the wind components, with larger amplitudes at the alongfront wind component, a fact consistent with the deformation theory. The contribution of the diurnal cycle was found weak in both the components, due to the cloudiness and the small diurnal temperature range, while the synoptic scale dominated the northerly wind component. The second LLJ case represents two successive summertime large-scale jets. The absence of cloudiness and the increased solar radiation provided a favorable environment for the development of local flows which interacted with the synoptic wind field. This interaction led to a LLJ with an oscillating core and a variable depth. The diurnal cycle had a strong imprint on the wind component along the sea breeze direction (easterly), while the synoptic variations dominated the northerly wind component. Strong amplitudes of a coherent quasi 2-day variation were also found in both the cases.

Appendix

Empirical mode decomposition is consisted by the following steps:

• (1) First, in a given time series X(t), the local maxima and minima are identified and then connected by cubic spline lines to create the upper and lower envelopes that cover all the data between them.

• (2) The mean m ₁(t) of the two envelopes is calculated and removed from the time series:

  $$ X(t) - m_{1} (t) = h_{1} (t), $$

  (4)

  where h ₁(t) may be the first component of the time series. The component h ₁(t) is considered to be an IMF if the number of extrema and the number of zero-crossings in h ₁(t) are identical or differ by, at most, one.

• (3) If h ₁(t) is considered to be an IMF [c ₁(t)], then it is removed from the original time series:

  $$ X(t) - c_{1} (t) = r_{1} (t) $$

  (5)

  and the residual r ₁(t) is processed similarly (steps 1–2) to find successive IMFs. If h ₁(t) does not fulfill the criterion of the IMF, it is treated again as X(t) in Eq. 4: a new m(t) is calculated, the resulting residual is tested against the IMF criterion, and so on. This sifting process is necessary to separate the finest local mode from the data based only on the characteristic timescale.

• (4) The above process is repeated to find several c(t) and r(t) and eventually, at step n, only a linear trend remains. The c _1…n (t)s are considered IMFs.

The Hilbert transform (second step) is applied to each IMF to extract the instantaneous frequencies and amplitudes, as a function of time, of each IMF. The Hilbert transform $\tilde{h}(t)$ of a time series h(t) may be defined as the convolution integral of h(t) and (1/πt), written as:

$$ \tilde{h}(t) = h(t) * (1/\pi t), $$

(6)

Then the complex analytic signal associated with h(t) and $\tilde{h}(t),$ z(t), can be expressed as:

$$ z(t) = h(t) + i\tilde{h}(t) = A(t)\exp [iu(t)], $$

(7)

A(t) is the amplitude, u(t) is the phase which can be differentiated to find the instantaneous frequency, ω:

$$ A(t) = [h^{2} (t) + \tilde{h}^{2} (t)]^{1/2} ,\quad u(t) = { \arctan }\left( {{\frac{{\tilde{h}(t)}}{h(t)}}} \right) $$

(8)

$$ \omega = {\frac{{\rm d}u(t)}{{\rm d}t}} $$

(9)

The instantaneous frequency, calculated by the Hilbert transform, should be understood as the frequency of a sine wave that locally fits the signal, rather than the frequency of a sine wave that is present throughout the entire time series signal. In this way, an energy–frequency–time distribution (known as the Hilbert spectrum) is calculated. This frequency–time distribution of the amplitude is designated as the complete Hilbert amplitude spectrum—H(ω,t), which represents the distribution of energy in timescales corresponding to different physical processes. Compared with the traditional Fourier analysis where the amplitude is only a function of frequency and not both frequency and time, the HHT method preserves the time localities of events and is suitable for non-stationary signal analysis (Li et al. 2005). With the Hilbert Spectrum defined, we can also define the marginal spectrum that offers a measure of the total amplitude contribution from each frequency value:

$$ h(\omega ) = \int_{0}^{T} {H(\omega ,t)} {\rm d}t. $$

(10)