Cross-spectra analysis of mid-tropospheric thermodynamical variables during Southern Africa biomass season.

Yemi Adebiyi

MPO 524

Motivation In southeast Atlantic (at

~600 hPa), there is a significant correlation of increased zonal winds, with cooling and moistening anomalies during polluted condition (tau>0.2)

… For a biomass season between July-October.

Maximum correlation between δU and δT occurs a day before maximum correlation δU and δQv.

MotivationWith the entire mid-level system moving at about 5-7deg/day westwards, this correlation implies a downstream cooling.

• What is the dynamical relationship?

• Are the associated time series coherent? – Cross-spectra analysis

Previous study: MJO Madden and Julian 1971,

used the cross-spectra analysis to support the detection of oscillation in the zonal winds of the Tropical pacific.

An easterly wind at 850hPa will be accompanied by low surface pressure and a westerly wind at 150hPa at a period between 30-90 days.

This turns out to be Madden-Julian Oscillation.© Madden and Julian, 1971

Suppose we have two time series X(t) and Y(t), t=1,……N,

Then the cross-covariance function:

If X and Y are linearly related: Yt = Xt + nt, then the cross-correlation would be:

Now in the frequency domain, we can take Fourier transform of the cross-covariance, to give the cross-spectrum:

Cross-Spectra Analysis

Since the cross-spectrum is generally a complex function, it can be represented in two ways:

1. It can be decomposed into real and imaginary parts

2. It can be written in polar coordinate:

Cross-Spectra Analysis

Cross-Spectra Analysis

The (squared) coherency spectrum can be defined as:

This is similar to the (squared) correlation coefficient.

Properties:

• For a completely random variable X and Y, κxy = 0

• If Y is a linear function of X (Yt = aXt); or a lag shift of X, then κxy = 1

• If Y is a linear function of X and a random white noise, e.g. Yt = aXt + nt

Then

Data ERA-Interim Reanalysis

(2000 –2012)

T, QV and U at 600hPa averaged within two regions R1 – 15S-5S;5E-15E R2 -- 15S-5S;10W-0E

July and October (Biomass season) Remove the sample means

and trends. Employ tapering to reduce

leakages.

Time Series

Region 1 Region 2

Results: Region 1

Shows that easterly winds are associated with cooler air @600hPa

Coherent periods are between ~10-20 days

Spectra are out-of-phase

U / T @ 600hPa

Results: Region 1U / QV @ 600hPa

Shows that easterly winds are associated with drier air @600hPa

Coherent periods are also between ~10-20 days

Similar results for Region 2

Results: Region 1

U / T @ 600hPa

Averaged between 2000-2012

U / QV @ 600hPa

Results: Reg. 1 & 2

U—R1 / T—R2 @ 600hPa

U—R1 / QV—R2 @ 600hPa

Summary The problem is to use cross-spectra analysis to

understand the relationship between mid-level U, and T/Qv; within the same region (and downstream).

The result shows that, within the same region, easterly winds are associated with cooler and moister air, with periods between 10-20days.

The coherence is higher between U and QV than with T, within the same region.

However, coherence is higher between U and downstream T (Region 2), than with QV.

Cross-spectra analysis of mid-tropospheric thermodynamical variables during southern Africa biomass season.

MPO 524