Run2 optimal projection selection

Optimal Projection Selection for Regional Analysis

Installation

pip install geopandas pyproj shapely

Overview

Distance calculations in projected coordinate systems must account for distortion patterns. Different regions require different projections to minimize error.

Projection Selection Guide

Global Analysis

• EPSG:3857 (Web Mercator): Distorts toward poles, OK for equatorial regions
• EPSG:3395 (World Mercator): Similar properties, different formulation
• EPSG:54008 (Sinusoidal): Equal-area, preserves area but distorts shape

Pacific Ocean Region

• EPSG:3832 (Web Mercator Auxiliary Sphere): Web standard but with distortion
• EPSG:3857: Web Mercator (distortion increases away from equator)
• Custom approach: Split analysis by region (North/South Pacific separately)

Better Approach: Use Azimuthal Equidistant

# Azimuthal Equidistant centered on Pacific
# Creates accurate distances from a central point
# For Pacific plate, could use various centers

# Create center point (e.g., Pacific plate centroid)
center_geom = pacific_polygon.centroid
print(f"Pacific plate center: {center_geom}")

Validation: Compare Distance Methods

import geopandas as gpd
from shapely.geometry import Point
import math

# Method 1: Projected CRS (EPSG:3857)
gdf_3857 = gdf.to_crs('EPSG:3857')
dist_3857 = gdf_3857.geometry.distance(boundary_3857).max()

# Method 2: Projected CRS (equal-area)
gdf_equal = gdf.to_crs('EPSG:54008')  # Sinusoidal
dist_equal = gdf_equal.geometry.distance(boundary_equal).max()

# Verify consistency
print(f"Distance (Web Mercator): {dist_3857 / 1000:.2f} km")
print(f"Distance (Equal-area): {dist_equal / 1000:.2f} km")

# If results differ significantly, investigate
if abs(dist_3857 - dist_equal) / max(dist_3857, dist_equal) > 0.1:
    print("WARNING: Significant difference between projections")

Important Considerations

1. Distortion Pattern: Each projection has strengths and weaknesses
2. Distance Consistency: For Pacific-wide analysis, use projection that minimizes global distortion
3. Multiple Validation: Cross-check with different projections for critical results
4. Units: Ensure understanding of output units (usually meters for standard projections)
5. Boundary Geometry: Ensure boundary is also in same projection before calculating distance

Recommended Approach for Pacific

# Use World Mercator (EPSG:3857) as primary
# For verification, also check with Mollweide (EPSG:54009)
earthquakes_proj = earthquakes.to_crs('EPSG:3857')
boundaries_proj = boundaries.to_crs('EPSG:3857')

# Convert distance in meters to kilometers
distance_km = earthquakes_proj.geometry.distance(boundaries_proj).max() / 1000