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Applying a Filter to a Time-Series

This example demonstrates low pass filtering a time-series by applying a weighted running mean over the time dimension.

The time-series used is the Darwin-only Southern Oscillation index (SOI), which is filtered using two different Lanczos filters, one to filter out time-scales of less than two years and one to filter out time-scales of less than 7 years.

References

Duchon C. E. (1979) Lanczos Filtering in One and Two Dimensions. Journal of Applied Meteorology, Vol 18, pp 1016-1022.

Trenberth K. E. (1984) Signal Versus Noise in the Southern Oscillation. Monthly Weather Review, Vol 112, pp 326-332

Southern Oscillation Index (Darwin Only)
import matplotlib.pyplot as plt
import numpy as np

import iris
import iris.plot as iplt


def low_pass_weights(window, cutoff):
    """Calculate weights for a low pass Lanczos filter.

    Args:

    window: int
        The length of the filter window.

    cutoff: float
        The cutoff frequency in inverse time steps.

    """
    order = ((window - 1) // 2) + 1
    nwts = 2 * order + 1
    w = np.zeros([nwts])
    n = nwts // 2
    w[n] = 2 * cutoff
    k = np.arange(1.0, n)
    sigma = np.sin(np.pi * k / n) * n / (np.pi * k)
    firstfactor = np.sin(2.0 * np.pi * cutoff * k) / (np.pi * k)
    w[n - 1 : 0 : -1] = firstfactor * sigma
    w[n + 1 : -1] = firstfactor * sigma
    return w[1:-1]


def main():
    # Load the monthly-valued Southern Oscillation Index (SOI) time-series.
    fname = iris.sample_data_path("SOI_Darwin.nc")
    soi = iris.load_cube(fname)

    # Window length for filters.
    window = 121

    # Construct 2-year (24-month) and 7-year (84-month) low pass filters
    # for the SOI data which is monthly.
    wgts24 = low_pass_weights(window, 1.0 / 24.0)
    wgts84 = low_pass_weights(window, 1.0 / 84.0)

    # Apply each filter using the rolling_window method used with the weights
    # keyword argument. A weighted sum is required because the magnitude of
    # the weights are just as important as their relative sizes.
    soi24 = soi.rolling_window(
        "time", iris.analysis.SUM, len(wgts24), weights=wgts24
    )
    soi84 = soi.rolling_window(
        "time", iris.analysis.SUM, len(wgts84), weights=wgts84
    )

    # Plot the SOI time series and both filtered versions.
    plt.figure(figsize=(9, 4))
    iplt.plot(
        soi,
        color="0.7",
        linewidth=1.0,
        linestyle="-",
        alpha=1.0,
        label="no filter",
    )
    iplt.plot(
        soi24,
        color="b",
        linewidth=2.0,
        linestyle="-",
        alpha=0.7,
        label="2-year filter",
    )
    iplt.plot(
        soi84,
        color="r",
        linewidth=2.0,
        linestyle="-",
        alpha=0.7,
        label="7-year filter",
    )
    plt.ylim([-4, 4])
    plt.title("Southern Oscillation Index (Darwin Only)")
    plt.xlabel("Time")
    plt.ylabel("SOI")
    plt.legend(fontsize=10)
    iplt.show()


if __name__ == "__main__":
    main()

Total running time of the script: ( 0 minutes 0.842 seconds)

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