Derive QBO Index from data

[pawelbielski]

Deriving Quasi-Biennial Oscillation from data is needed to later find relationships between it and all geolocations on the earth.

Useful resources:

1. Quasi-Biennial Oscillation (QBO) Zonal Wind Index 1953 - September 2001

2. Defining metrics of the Quasi-Biennial Oscillation in global climate models

Steps:

• [x] Find parameters (latitude range, level) that define QBO Index (can be different for different types of QBO indices) and write them into README.md file

• [x] Write a code that derives QBO from the data of a given period (firstly one year) and plots it.

• [x] Move the logic to a separate file with a name calculations.py. Present the results in a jupyter notebook.

• [x] Find an already derived version of QBO from the Internet to cross check your derived Index.

• [x] Once the whole dataset (for multiple years) is available, derive QBO from it.

• [x] Remove seasonal cycle and normalize data

• [x] For plotting please specify all the different definitions of QBO, so that we can see which is the closest to reference.

[pierretoussing]

In the Index I found on the Internet , they simply took the u wind values from Singapoor for pressure level 70 hPa.

@pawelbielski My problem is that I have not figured out yet how to get the values from the netcdf file for specific geographical coordinates.

[pawelbielski]

The coordinates have 512 longitudes and 256 latitudes. It looks like they are defined by the Gaussian Grid.

The definition of Quasi-Biannual Oscillation I got from our climate experts:

There is a quasi-biannual oscillation (with a period of about 26 months) in the equatorial winds (+-5°north and south of the equator) at an altitude of 50 to 30 hPa (high pressures-low altitudes). This means that the winds there blow around the earth in one direction (e.g. to the west) and then into the other (e.g. to the east). This pattern is therefore also visible in the mean wind u around the longitudes (zonal mean of zonal winds).

This looks already as the example of the situation where we need some flexibility. Apparently QBO can have different definitions, so for now it is a good idea to have them implemented and compared. Please notice, that a QBO index defined in that way is just a 1-dimensional time series (time vs. value). @pierretoussing

[pawelbielski]

Remove seasonal cycle and normalize data:

"To avoid artefacts due to autocorrelation and seasonality, we removed the seasonal cycle and normalized the data. Specifically, we calculate for every month (i.e., separately for all Januaries, Februaries, etc.) the long-term mean and standard deviation. Each data point is then normalized by subtracting the mean and dividing by the standard deviation of the corresponding month at that grid cell. This normalization significantly reduces temporal autocorrelation in the time series" - Nature paper

After this step the QBO should match the reference even more.

[pawelbielski]

• [x] Could you also, derive QBO from the altitude 30 hPa in the equatorial winds (+-5°north and south of the equator)? This is the most concrete definitions I received from our climate scientist.

[pawelbielski]

Good job @pierretoussing. It will be interesting to get feedback on the differences between different QBO definitions.

[pierretoussing]

After #10, the data is now deseasonalized before the QBO is derived.