ERA5 Bounding Box Area Computation
Bounding box format (NWSE):
[9.34, 123.25, 9.26, 123.32]
This follows the North–West–South–East convention:
- North = $9.34^\circ$ latitude
- West = $123.25^\circ$ longitude
- South = $9.26^\circ$ latitude
- East = $123.32^\circ$ longitude
1. Angular Extent
Latitude span:
$$
\Delta \phi = 9.34 - 9.26 = 0.08^\circ
$$
Longitude span:
$$
\Delta \lambda = 123.32 - 123.25 = 0.07^\circ
$$
2. Degree-to-Distance Conversion
At latitude $\phi \approx 9.3^\circ$ (Philippines):
- $1^\circ$ latitude $\approx 111\ \text{km}$
- $1^\circ$ longitude $\approx 111 \cos \phi\ \text{km}$
$$
1^\circ \text{ longitude} \approx 111 \cos(9.3^\circ) \approx 109.7\ \text{km}
$$
North–South distance:
$$
L_{NS} = 0.08 \times 111 \approx 8.88\ \text{km}
$$
East–West distance:
$$
L_{EW} = 0.07 \times 109.7 \approx 7.68\ \text{km}
$$
3. Area Calculation
$$
A = L_{NS} \times L_{EW}
$$
$$
A \approx 8.88 \times 7.68 \approx 68.2\ \text{km}^2
$$
4. Conversion to Hectares
Recall:
$$
1\ \text{km}^2 = 100\ \text{hectares}
$$
$$
A = 68.2 \times 100 = \boxed{6,\!820\ \text{hectares}}
$$
5. Interpretation
- Area ≈ 6,820 hectares
- Comparable to a medium-sized city or municipality
- Much smaller than a native ERA5 grid cell (~31 km × 31 km)
- Appropriate for station-centered ERA5 extraction and interpolation