Coordinate Reference Systems and Projections

To perform accurate spatial measurements, we must project coordinates from the curved three-dimensional Earth onto a flat two-dimensional map sheet. In GIS, this is managed using Coordinate Reference Systems (CRS). This section details why CRS selection is critical for hydrological analysis, GCS vs. PCS models, UTM zone selection, and how to avoid coordinate transformation issues.

1. Why CRS Matters in Hydrology

Water flow, routing, and volume estimation are completely dependent on accurate distance, area, and slope calculations:

• Area Calculation: Delineating watershed boundaries and computing catchment areas (\(A\)) is fundamental to predicting peak runoff volume. Under GCS (EPSG:4326), area calculations are heavily distorted because degrees of longitude shrink towards the poles.

• Slope and Flow Routing: Hydrological flow routing (such as the D8 algorithm) calculates flow direction by comparing elevation changes (\(\Delta Z\)) with horizontal distance (\(\Delta X, \Delta Y\)). If the elevation is in meters (\(Z\)) but the horizontal coordinates are in degrees (\(X, Y\)), the slope will be calculated incorrectly, breaking stream networks and watershed boundaries.

• Distance and Buffering: Delineating flood risk zones or riparian buffer corridors (e.g., a \(100\text{ m}\) buffer zone around a river) requires coordinate systems with constant linear units (meters).

2. Geographic Coordinate Reference Systems (GCS)

A GCS represents the Earth as a three-dimensional sphere or ellipsoid. Location is measured in angular units (degrees) relative to the equator and the prime meridian:

• Latitude: Angle north or south of the Equator (varies from \(-90^{\circ}\) to \(+90^{\circ}\)).

• Longitude: Angle east or west of the Prime Meridian (varies from \(-180^{\circ}\) to \(+180^{\circ}\)).

• Datums: Ellipsoids that approximate the shape of the Earth. The global standard datum is WGS 84 (used by GPS systems).

• The Distance Dilemma: Because longitude lines converge at the poles, the physical distance of \(1^{\circ}\) of longitude changes depending on latitude. Near the equator, \(1^{\circ}\) is roughly \(111\text{ km}\), but near the poles, it approaches \(0\text{ km}\).

[!WARNING] Because GCS uses degrees as units, running calculations like buffer distances or slopes directly on a GCS layer will yield incorrect results.

3. Projected Coordinate Reference Systems (PCS)

A PCS projects the curved 3D Earth surface onto a flat 2D plane. It uses linear units (meters or feet) instead of degrees, making it suitable for calculating distances, areas, and slopes.

      3D Ellipsoid (Earth)                 2D Flat Projection
         (Lat / Lon)                           (Meters)
            __--__                              +------+
         /         \     ---Projection--->      |      |
         \  WGS84  /                            | UTM  |
           `--__--'                             +------+

Map Projection Types

• Conformable: Preserves local angles and shapes (ideal for navigation).

• Equal Area: Preserves areas (ideal for mapping watershed boundaries and soil zones).

• Equidistant: Preserves distances along specific lines.

4. Universal Transverse Mercator (UTM)

The most common PCS for regional applications is the UTM system. UTM divides the Earth into 60 vertical zones, each \(6^{\circ}\) of longitude wide.

• Linear Units: Locations are defined as Eastings and Northings measured in meters.

• Zone Selection: Each zone has its own central meridian to minimize distortion within that section.

• UTM Zones for Nepal:

• UTM Zone 44N: Covers Western and Central Nepal (longitude \(78^{\circ}\text{E}\) to \(84^{\circ}\text{E}\)).
• UTM Zone 45N: Covers Eastern Nepal (longitude \(84^{\circ}\text{E}\) to \(90^{\circ}\text{E}\)).

5. EPSG Codes

To simplify database management, the European Petroleum Survey Group (EPSG) compiled a registry of geographic and projected coordinate reference systems, assigning a unique identifier code to each.

6. Choosing the Right CRS

Choosing the appropriate CRS is a critical first step for any hydrological modeling project. Follow these guidelines:

• Prefer Projected Coordinate Reference Systems (PCS): Always use a PCS (such as UTM) for hydrological analysis, as it maintains linear units of measurement (meters), ensuring accurate slope, distance, and area calculations.

• Select the Correct UTM Zone: For regional projects in Nepal:

• UTM Zone 44N (EPSG:32644): If your project area lies west of \(84^{\circ}\text{E}\) longitude (e.g., Karnali or Gandaki basins).

• UTM Zone 45N (EPSG:32645): If your project area lies east of \(84^{\circ}\text{E}\) longitude (e.g., Koshi basin).

• Handle Cross-Zone Basins with Care: If a river basin crosses the boundary meridian (\(84^{\circ}\text{E}\)), selecting either zone 44N or 45N will introduce minor distortion at the basin edges. In such cases, use a customized local projection (like a Transverse Mercator projection centered on the basin's meridian) or choose the zone covering the largest portion of the basin to maintain consistency.

7. Reprojection and CRS Transformations

In QGIS, datasets with different CRS can be loaded into the same map canvas. QGIS handles this automatically using On-the-Fly (OTF) Reprojection, transforming coordinates dynamically to match the project CRS.

• Project CRS vs. Layer CRS: The project CRS determines the coordinate grid of the map canvas. The layer CRS is the coordinate system stored in the source file.

• Permanent Reprojection: While OTF reprojection is useful for visualization, running processing tools (like clipping or buffering) on layers with mismatching coordinate systems can cause errors. You should reproject layers to a common projected coordinate system using the Reproject Layer tool before performing spatial analysis.

8. Common CRS Pitfalls in Projects

• Shifted Layers: If coordinate datasets do not align correctly (e.g., a river layer appears shifted 200 meters to the side of a DEM), it is usually because the layer datum was defined incorrectly in the metadata.

• Incorrect Buffer Units: Attempting to create a \(100\text{ m}\) buffer around a river layer, but the output buffer is so large it covers the entire country. This happens when the input layer is in GCS (EPSG:4326), causing QGIS to interpret the "100" input value as \(100^{\circ}\) instead of \(100\text{ meters}\).