Typhoon Tracking and Axisymmetric Analysis

Typhoon Tracking and Axisymmetric Analysis#

This document demonstrates the process of tracking a typhoon’s center and performing axisymmetric analysis using mean sea level pressure (MSL), temperature, and precipitation data. The provided functions in easyclimate, implement the core algorithms for cyclone tracking and axisymmetric decomposition.

import numpy as np
import xarray as xr
import pandas as pd
import matplotlib.pyplot as plt
import cartopy.crs as ccrs
import easyclimate as ecl

loads meteorological reanalysis datasets (ERA5) for a typhoon. The datasets include:

Temperature (t_data): A multi-level atmospheric temperature field.
Mean Sea Level Pressure (slp_time, slp_data): MSL pressure data with time, latitude, and longitude dimensions. A single time slice (slp_data) is extracted for initial analysis.
Precipitation (tp_data): Total precipitation data, converted from its original units (m/h) to millimeters per hour (mm/h) by multiplying by 1000 and updating the units attribute.

t_data = xr.open_dataset("test_t_typhoon_201919.nc").t

slp_time = xr.open_dataset("test_slp_typhoon_201919.nc").msl
slp_data = slp_time.isel(time = 0)

tp_data = xr.open_dataset("test_pr_typhoon_201919.nc").tp *1000
tp_data.attrs["units"] = "mm/h"

Tracking#

We uses the easyclimate.field.typhoon.track_cyclone_center_msl_only function to locate the typhoon center at a single time step using MSL pressure data. The function takes the following inputs:

slp_data: A 2D xarray.DataArray containing MSL pressure with latitude and longitude dimensions.
sample_point: An initial guess for the cyclone center, like (longitude=140°, latitude=20°).

The function identifies local minima in the MSL pressure field using a 3x3 minimum filter (scipy.ndimage.minimum_filter) with nearest boundary conditions to account for the grid edges. This ensures robust detection of low-pressure centers, which are characteristic of cyclones.

To be specific, the function computes the great-circle distance between the provided sample_point and all detected minima using the formula:

\[\cos \alpha = \sin \theta_0 \sin \theta + \cos \theta_0 \cos \theta \cos (\lambda - \lambda_0)\]

where \(\alpha\) is the central angle, and the closest minimum is selected as the cyclone center.

To refine the cyclone center beyond the grid resolution, the function applies biquadratic interpolation around the identified minimum. It constructs a quadratic function:

\[f(x, y) = c_0 + c_1x + c_2y + c_3xy + c_4x^2 + c_5y^2 + c_6x^2y + c_7xy^2 + c_8x^2y^2\]

and solves for the extremum by setting the gradient to zero (i.e., \(\\nabla f = 0\)). The solution involves computing the inverse of the Hessian matrix:

\[\begin{split}\mathbf{A}^{-1} = \frac{1}{d} \begin{pmatrix} f_{yy} & -f_{xy} \\ -f_{xy} & f_{xx} \end{pmatrix}, \quad d = f_{xx}f_{yy} - f_{xy}^2\end{split}\]

to determine the offsets \(\Delta x\) and \(\Delta y\). If the determinant \(d = 0\), the grid-based minimum is used instead.

df_track = ecl.field.typhoon.track_cyclone_center_msl_only(slp_data, (140, 20))
df_track

	lon	lat	slp_min
0	140.197533	19.766941	96263.759953

Here, we extends the tracking to multiple time steps by iterating over the time dimension of the slp_time dataset. For each time step:

The easyclimate.field.typhoon.track_cyclone_center_msl_only function is called with the MSL data slice at time_item, the same initial guess (140, 20), and an index_value set to the current time index.
Results are stored in a list (track_list) and concatenated into a single pandas.DataFrame (result) with columns lon, lat, and slp_min, indexed by time.

track_list = []

for time_item in np.arange(len(slp_time.time)):
    tmp = ecl.field.typhoon.track_cyclone_center_msl_only(slp_time.isel(time = time_item), (140, 20), index_value = [time_item])
    track_list.append(tmp)

result = pd.concat(track_list)
result

	lon	lat	slp_min
0	140.197533	19.766941	96263.759953
1	140.033467	20.215966	95901.328523

Here, we visualizes the MSL pressure field and the tracked typhoon center on a map.

fig, ax = ecl.plot.quick_draw_spatial_basemap(central_longitude=120)
ax.set_extent([120, 150, 5, 30], crs = ccrs.PlateCarree())


c = (slp_data/100).plot.contour(
    levels = 11,
    transform=ccrs.PlateCarree(),
    zorder = 1
)
ax.clabel(c)

ax.scatter(
    df_track["lon"][0], df_track['lat'][0],
    c="red",
    transform=ccrs.PlateCarree(),
    zorder = 2
)

<matplotlib.collections.PathCollection object at 0x7fa8c76f21a0>

Typhoon Tracking and Axisymmetric Analysis

Contents

Typhoon Tracking and Axisymmetric Analysis#

Tracking#

Axisymmetric Analysis#

Temperature (multi-level variable)#

Precipitation (single level variable)#