.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_gallery/plot_multi_linear_reg.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_gallery_plot_multi_linear_reg.py: Multiple Variable Linear Regression ========================================================================================================= This documentation demonstrates a comprehensive analysis of sea surface temperature (SST) variability explained by two climate indices (AO and Niño 3.4) using multiple linear regression. The analysis covers data preparation, index calculation, regression modeling, and visualization of results. .. math:: y = a_1 x_1 + a_2 x_2 Before proceeding with all the steps, first import some necessary libraries and packages .. GENERATED FROM PYTHON SOURCE LINES 16-20 .. code-block:: Python import xarray as xr import cartopy.crs as ccrs import easyclimate as ecl .. GENERATED FROM PYTHON SOURCE LINES 21-25 Two time ranges are defined to account for seasonal analysis with different base periods - ``time_range``: Primary analysis period (1982-2020) - ``time_range_plus1``: Offset by one year for seasonal calculations .. GENERATED FROM PYTHON SOURCE LINES 25-28 .. code-block:: Python time_range = slice("1982-01-01", "2020-12-31") time_range_plus1 = slice("1983-01-01", "2021-12-31") .. GENERATED FROM PYTHON SOURCE LINES 29-36 The Arctic Oscillation index is calculated using: 1. Sea level pressure (SLP) data from the Northern Hemisphere 2. Seasonal mean calculation for December-January-February (DJF) 3. EOF analysis following Thompson & Wallace (1998) methodology The resulting index is then subset to our analysis period. .. GENERATED FROM PYTHON SOURCE LINES 36-42 .. code-block:: Python slp_data = xr.open_dataset("slp_monmean_NH.nc").slp slp_data_DJF_mean = ecl.calc_seasonal_mean(slp_data, extract_season = 'DJF') index_ao = ecl.field.teleconnection.calc_index_AO_EOF_Thompson_Wallace_1998(slp_data_DJF_mean) index_ao = index_ao.sel(time = time_range) index_ao .. raw:: html 
<xarray.DataArray 'PC' (time: 39)> Size: 312B
    array([-0.99517237, -0.37496718,  1.10574761,  1.04859641,  0.12535887,
            0.10322009, -2.66546857, -1.16177425, -0.662752  , -1.67955732,
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            0.01642609,  0.19134825, -0.25406337,  0.62810255, -1.32004343,
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            0.1642507 , -0.39054768, -2.05494313,  1.3799055 ])
    Coordinates:
      * time     (time) datetime64[ns] 312B 1982-12-01 1983-12-01 ... 2020-12-01
    Attributes: (12/15)
        model:          EOF analysis
        software:       xeofs
        version:        3.0.4
        date:           2025-06-21 03:18:07
        n_modes:        2
        center:         False
        ...             ...
        sample_name:    sample
        feature_name:   feature
        random_state:   None
        compute:        True
        solver:         auto
        solver_kwargs:  {}


.. GENERATED FROM PYTHON SOURCE LINES 43-48 The Nino3.4 index is derived from: 1. Hadley Centre SST dataset 2. Seasonal mean for DJF period 3. Area averaging over the Niño 3.4 region (5°N-5°S, 170°W-120°W) .. GENERATED FROM PYTHON SOURCE LINES 48-53 .. code-block:: Python sst_data = ecl.open_tutorial_dataset("mini_HadISST_sst").sst sst_data_DJF_mean = ecl.calc_seasonal_mean(sst_data, extract_season = 'DJF') index_nino34 = ecl.field.air_sea_interaction.calc_index_nino34(sst_data_DJF_mean).sel(time = time_range) index_nino34 .. raw:: html 
<xarray.DataArray 'Nino34_index' (time: 39)> Size: 156B
    array([ 0.05414302,  0.01795494,  0.24856713, -0.08231278, -0.28434724,
           -0.0455286 ,  0.15132348,  0.2527848 ,  0.1607705 ,  0.51797485,
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            0.19944632,  0.19656877,  0.35891408, -0.1823232 , -0.4064587 ,
           -0.21349731, -0.35575086, -0.64792055, -0.3729663 , -0.262498  ,
           -0.42721397,  0.36359602,  0.47783482,  0.3777843 ,  0.5817891 ,
            0.5604557 , -0.12119712, -0.23322351, -0.25149944], dtype=float32)
    Coordinates:
      * time     (time) datetime64[ns] 312B 1982-12-01 1983-12-01 ... 2020-12-01
        month    (time) int64 312B 12 12 12 12 12 12 12 12 ... 12 12 12 12 12 12 12
    Attributes:
        standard_name:  sea_surface_temperature
        long_name:      sst
        units:          C
        cell_methods:   time: lat: lon: mean


.. GENERATED FROM PYTHON SOURCE LINES 54-58 The dependent variable for our regression is prepared as: - Seasonal mean SST for September-October-November (SON) - Using the offset time range to examine potential lagged relationships .. GENERATED FROM PYTHON SOURCE LINES 58-61 .. code-block:: Python sst_data_SON_mean = ecl.calc_seasonal_mean(sst_data, extract_season = 'SON').sel(time = time_range_plus1) sst_data_SON_mean .. raw:: html 
<xarray.DataArray 'sst' (time: 39, lat: 30, lon: 360)> Size: 2MB
    array([[[27.609848, 27.626818, 27.69435 , ..., 27.638601, 27.64776 ,
             27.637032],
            [27.979582, 27.987864, 28.057   , ..., 28.017029, 28.030457,
             28.020773],
            [28.206915, 28.224077, 28.293734, ..., 28.309912, 28.25866 ,
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            ...,
            [27.851227, 27.814247, 27.795563, ..., 28.03151 , 27.987627,
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            [27.730936, 27.695229, 27.656563, ..., 27.95027 , 27.84813 ,
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            [27.72257 , 27.671392, 27.599901, ..., 27.993307, 27.842398,
             27.749907]],

           [[27.396734, 27.40095 , 27.45458 , ..., 27.41075 , 27.441338,
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            [27.766632, 27.772455, 27.823105, ..., 27.736404, 27.781382,
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            [28.059565, 28.063883, 28.119484, ..., 28.043167, 28.083147,
             28.092148],
    ...
            [28.654837, 28.630167, 28.609818, ..., 28.773338, 28.744364,
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             28.67267 ],
            [28.66854 , 28.645025, 28.609365, ..., 28.700104, 28.689146,
             28.676376]],

           [[28.383835, 28.371572, 28.373255, ..., 28.342772, 28.391098,
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            [28.755556, 28.737017, 28.712332, ..., 28.629898, 28.711897,
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            [29.015615, 29.005974, 28.980433, ..., 28.918898, 28.959196,
             28.99497 ],
            ...,
            [28.526505, 28.477676, 28.350496, ..., 28.564367, 28.53063 ,
             28.516111],
            [28.422213, 28.383987, 28.281607, ..., 28.44673 , 28.415787,
             28.405664],
            [28.376661, 28.32148 , 28.226974, ..., 28.431257, 28.40944 ,
             28.388994]]], shape=(39, 30, 360), dtype=float32)
    Coordinates:
      * lat      (lat) float32 120B -14.5 -13.5 -12.5 -11.5 ... 11.5 12.5 13.5 14.5
      * lon      (lon) float32 1kB -179.5 -178.5 -177.5 -176.5 ... 177.5 178.5 179.5
      * time     (time) datetime64[ns] 312B 1983-09-01 1984-09-01 ... 2021-09-01
    Attributes:
        standard_name:  sea_surface_temperature
        long_name:      sst
        units:          C
        cell_methods:   time: lat: lon: mean


.. GENERATED FROM PYTHON SOURCE LINES 62-75 The core analysis applies multiple linear regression to quantify how: - AO index (first predictor) - Niño 3.4 index (second predictor) jointly explain spatial patterns of SON SST variability. The function returns a dataset containing: - Regression coefficients (slopes) for each predictor - Intercept values - R-squared values (goodness of fit) - Statistical significance (p-values) for each parameter .. GENERATED FROM PYTHON SOURCE LINES 75-78 .. code-block:: Python result = ecl.calc_multiple_linear_regression_spatial(sst_data_SON_mean, [index_ao, index_nino34]) result .. rst-class:: sphx-glr-script-out .. code-block:: none /home/runner/work/easyclimate/easyclimate/src/easyclimate/core/stat.py:433: UserWarning: All variables must have the same time coordinates warnings.warn("All variables must have the same time coordinates") .. raw:: html 
<xarray.Dataset> Size: 606kB
    Dimensions:      (lat: 30, lon: 360, coef: 2)
    Coordinates:
      * lat          (lat) float32 120B -14.5 -13.5 -12.5 -11.5 ... 12.5 13.5 14.5
      * lon          (lon) float32 1kB -179.5 -178.5 -177.5 ... 177.5 178.5 179.5
      * coef         (coef) int64 16B 0 1
    Data variables:
        slopes       (lat, lon, coef) float64 173kB -0.001755 -0.02993 ... 0.4529
        intercept    (lat, lon) float64 86kB 28.06 28.08 28.11 ... 28.58 28.54 28.5
        r_squared    (lat, lon) float64 86kB 0.001115 0.0004253 ... 0.2671 0.2581
        slopes_p     (lat, lon, coef) float64 173kB 0.9731 0.845 ... 0.7543 0.001605
        intercept_p  (lat, lon) float64 86kB 1.168e-71 1.273e-71 ... 5.079e-74


.. GENERATED FROM PYTHON SOURCE LINES 79-89 The final visualization shows: - Top panel: Spatial pattern of AO influence on SON SST: Colors show regression coefficients, and Contours indicate statistically significant areas (p < 0.05) - Bottom panel: Spatial pattern of Niño 3.4 influence: Similar interpretation as top panel, and the central longitude is set to 200° for Pacific-centric viewing. Key interpretation points: - Positive coefficients indicate SST increases with positive phase of the index - Negative coefficients indicate inverse relationships - Non-significant areas suggest no robust statistical relationship .. GENERATED FROM PYTHON SOURCE LINES 89-112 .. code-block:: Python fig, ax = ecl.plot.quick_draw_spatial_basemap(nrows=2 ,figsize = (10, 5), central_longitude=200) result.slopes.sel(coef = 0).plot( ax=ax[0], transform=ccrs.PlateCarree(), cbar_kwargs={"location": "bottom", "pad": 0.2, "aspect": 100, "shrink": 0.8}, ) ecl.plot.draw_significant_area_contourf( result.slopes_p.sel(coef = 0), ax = ax[0], transform=ccrs.PlateCarree() ) result.slopes.sel(coef = 1).plot( ax=ax[1], transform=ccrs.PlateCarree(), cbar_kwargs={"location": "bottom", "pad": 0.2, "aspect": 100, "shrink": 0.8}, ) ecl.plot.draw_significant_area_contourf( result.slopes_p.sel(coef = 1), ax = ax[1], transform=ccrs.PlateCarree() ) .. image-sg:: /auto_gallery/images/sphx_glr_plot_multi_linear_reg_001.png :alt: coef = 0, coef = 1 :srcset: /auto_gallery/images/sphx_glr_plot_multi_linear_reg_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 8.560 seconds) .. _sphx_glr_download_auto_gallery_plot_multi_linear_reg.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_multi_linear_reg.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_multi_linear_reg.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_multi_linear_reg.zip `