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z!z>U(yCKQ=b6`ee<0~TrAwnxwLqbc_YYrp2Mjh?kcZ(=O;!ES}?> zW^l@@r*w1P9V?JOH@7s?^ui6PxHMa%BBvw?{IGuC#Y`Lnyu8*cN^v#6X|};=WEoo( zn|T~iJu*kPIMj?EyjJ8PB69f-UA^a`{bM6MAPUN?-RmVd8+w)E^XM zfjhib8bhz*L+^gUR5%+i)ixK4$@H{!A(g6AF+W$(C!PtwXy6++R_hsH%YDONyiHGp zqW-#fSBK6lZBdpb+(T7b=+!kI9`L6#)rf$pCyY$8d}VU z4qKm6!QHNZ+;=j%uPb5l(n&nH4purAcg;!3kRb)wNNEz&%Fr%x43`e-+NU>fo0OIZ z>6|K!9^gEnVH{aFevcYrG!nt;>{&FYJ~AJE1CiR1Z2)4`j6t=O%_Z4b$6v6G_PeX` zJvaJdZ0;vKNmB@v0^#m!6uybNqOml%VXnjPQvZ(AF*t$IV)NOZ8~RI%`~<*E_ur|i z6j(cHrnSrTI)6Y-bqg2uhw;NdHuENbPVdnRac7X29RN87(K(`+BpBt5?nPfs6V3SM z@R3#35%}>0Np$4>m${P{np<9G7ar0_fd+{2b&v;$lc6@*Uzm_i_PbLRE?MiFKaNX^ zonqFldMWOX!J+Qm?5W2niCQt8nfZtxp&srV0].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() \ No newline at end of file +# 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() \ No newline at end of file