add Verhoogen fig

geo/cumulative_distribution_function_for_earth_elevation.md

@@ -1,45 +1,82 @@
-https://www.ngdc.noaa.gov/mgg/global/relief/ETOPO2022/data/60s/60s_surface_elev_gtif/ETOPO_2022_v1_60s_N90W180_surface.tif
-
-https://www.ngdc.noaa.gov/mgg/global/relief/ETOPO2022/docs/1.2%20ETOPO%202022%20User%20Guide.pdf
-
-For most purposes,
-EGM2008 is an adequate approximation of mean sea level.
-
-import rasterio
-import rasterio.plot
-import matplotlib.pyplot as plt
-import numpy as np
-from matplotlib.ticker import PercentFormatter
-
-
-data = rasterio.open('ETOPO_2022_v1_60s_N90W180_surface.tif')
-
-rasterio.plot.show(data)
-
-band1 = data.read(1).flatten()
-
-# https://stackoverflow.com/a/51477080
-plt.hist(band1,bins=100,weights=np.ones(len(band1))/len(band1))
-plt.title('Histogram for Earth topography and bathymetry')
-plt.xlabel('meters relative to the Earth Gravitational Model of 2008 (EGM2008) geoid surface')
-plt.ylabel('percentage of Earth surface')
-plt.gca().yaxis.set_major_formatter(PercentFormatter(1))
-plt.show()
-
-# https://stackoverflow.com/a/15419072
-values, base = np.histogram(band1, bins=100)
-cumulative = np.cumsum(values)
-percentage = 100*cumulative/cumulative.max()
-plt.plot(base[:-1], percentage)
-plt.title('Cumulative Distribution Function for Earth topography and bathymetry')
-plt.xlabel('meters relative to the Earth Gravitational Model of 2008 (EGM2008) geoid surface')
-plt.ylabel('cumulative percentage of Earth surface')
-plt.show()
-
-plt.plot(np.flip(percentage),base[:-1])
-plt.axhline(y=band1[band1>0].mean(), color='lightgray', linestyle='--')
-plt.axhline(y=band1[band1<0].mean(), color='lightgray', linestyle='--')
-plt.title("Figure 1.7 in \"Earth's dynamic systems\" by Hamblin and Christiansen\nFig, 1-1 in \"The Earth\" by Verhoogen et al.")
-plt.ylabel('meters relative to EGM2008 geoid surface')
-plt.xlabel('cumulative percentage of Earth surface')
-plt.show()
+# Earth's altimetry/bathymetry cumulative distribution function
+
+This is Figure 1.7 from the book ["Earth's dynamic systems" by Hamblin and Christiansen](https://earthds.info/):
+
+![Figure 1.7 from the book "Earth's dynamic systems" by Hamblin and Christiansen](cdf_earth_elevation-EDS_Figure_1.7.png)
+
+This is Figure 1-1 from the book ["The Earth" by Verhoogen et al.](https://archive.org/details/earthintroductio0000verh/page/4/mode/2up):
+
+![Figure 1-1 from the book "The Earth" by Verhoogen et ali.](cdf_earth_elevation-Verhoogen_Fig_1-1.png)
+
+Note that Hamblin and Christiansen for the horizontal axis label use a vague "Percent of Earth's surface" while Verhoogen et al. use a more accurate "Cumulative percentage of earth's surface".
+
+In order to reproduce it we will use the following data 
+
+> NOAA National Centers for Environmental Information. 2022: ETOPO 2022 15 Arc-Second Global Relief Model. NOAA National Centers for Environmental Information. https://doi.org/10.25921/fd45-gt74 . Accessed 2024-08-27.
+
+and we will use the low resolution [(60 arc-second) GeoTIFF image](https://www.ngdc.noaa.gov/mgg/global/relief/ETOPO2022/data/60s/60s_surface_elev_gtif/ETOPO_2022_v1_60s_N90W180_surface.tif).
+
+Here it is the raw data:
+
+![ETOPO22](cdf_earth_elevation-Figure_1.png)
+
+According to the [ETOPO22 User Guide](https://www.ngdc.noaa.gov/mgg/global/relief/ETOPO2022/docs/1.2%20ETOPO%202022%20User%20Guide.pdf)
+
+> All tiles are in horizontal WGS84 geographic coordinates (EPSG1:4326) and referenced in meters relative to the Earth Gravitational Model of 2008 (EGM2008) geoid surface (EPSG:3855). 
+
+and
+
+> For most purposes, EGM2008 is an adequate approximation of mean sea level.
+
+Firs of all we plot the histogram for the Earth altimetry and bathymetry:
+
+![Histogram of Earth altimetry and bathymetry](cdf_earth_elevation-Figure_2.png)
+
+Then we plot the classic "cumulative distribution function" for the same data:
+
+![Cumulative distribution function for the Earth altimetry and bathymetry](cdf_earth_elevation-Figure_3.png)
+
+And finally we reproduce Figure 1.7 in the book "Earth's dynamic systems" by Hamblin and Christiansen and Fig. 1-1 in the book "The Earth" by Verhoogen et al.
+
+![A reproduction of Figure 1.7 in the book "Earth's dynamic systems" by Hamblin and Christiansen and Fig. 1-1 in the book "The Earth" by Verhoogen et al.](cdf_earth_elevation-Figure_4.png)
+
+The Python script to reproduce the figure is the following:
+
+    import rasterio
+    import rasterio.plot
+    import matplotlib.pyplot as plt
+    import numpy as np
+    from matplotlib.ticker import PercentFormatter
+
+
+    data = rasterio.open('ETOPO_2022_v1_60s_N90W180_surface.tif')
+
+    rasterio.plot.show(data)
+
+    band1 = data.read(1).flatten()
+
+    # https://stackoverflow.com/a/51477080
+    plt.hist(band1,bins=100,weights=np.ones(len(band1))/len(band1))
+    plt.title('Histogram for Earth topography and bathymetry')
+    plt.xlabel('meters relative to the Earth Gravitational Model of 2008 (EGM2008) geoid surface')
+    plt.ylabel('percentage of Earth surface')
+    plt.gca().yaxis.set_major_formatter(PercentFormatter(1))
+    plt.show()
+
+    # https://stackoverflow.com/a/15419072
+    values, base = np.histogram(band1, bins=100)
+    cumulative = np.cumsum(values)
+    percentage = 100*cumulative/cumulative.max()
+    plt.plot(base[:-1], percentage)
+    plt.title('Cumulative Distribution Function for Earth topography and bathymetry')
+    plt.xlabel('meters relative to the Earth Gravitational Model of 2008 (EGM2008) geoid surface')
+    plt.ylabel('cumulative percentage of Earth surface')
+    plt.show()
+
+    plt.plot(np.flip(percentage),base[:-1])
+    plt.axhline(y=band1[band1>0].mean(), color='lightgray', linestyle='--')
+    plt.axhline(y=band1[band1<0].mean(), color='lightgray', linestyle='--')
+    plt.title("Figure 1.7 in \"Earth's dynamic systems\" by Hamblin and Christiansen\nFig, 1-1 in \"The Earth\" by Verhoogen et al.")
+    plt.ylabel('meters relative to EGM2008 geoid surface')
+    plt.xlabel('cumulative percentage of Earth surface')
+    plt.show()