This document demonstrates, step by step, whether the selected bounding box lies within one or more native ERA5 grid cells of resolution $0.25^\circ \times 0.25^\circ$.
[9.34, 123.25, 9.26, 123.32]
This corresponds to:
Thus, the spatial domain is:
$$ 9.26^\circ \le \phi \le 9.34^\circ $$ $$ 123.25^\circ \le \lambda \le 123.32^\circ $$ERA5 is natively defined on a regular latitude–longitude grid with spacing:
$$ \Delta \phi = \Delta \lambda = 0.25^\circ $$Native grid cell boundaries occur at integer multiples of $0.25^\circ$:
We determine the native latitude cell that contains the interval:
$$ [9.26,\ 9.34] $$Compute the enclosing grid boundaries:
$$ \left\lfloor \frac{9.26}{0.25} \right\rfloor \times 0.25 = 9.25 $$ $$ \left\lceil \frac{9.34}{0.25} \right\rceil \times 0.25 = 9.50 $$Thus, the bounding box lies entirely within the latitude band:
$$ \boxed{9.25^\circ \le \phi \le 9.50^\circ} $$Only one native latitude cell is involved.
Now consider the longitude interval:
$$ [123.25,\ 123.32] $$Compute the enclosing grid boundaries:
$$ \left\lfloor \frac{123.25}{0.25} \right\rfloor \times 0.25 = 123.25 $$ $$ \left\lceil \frac{123.32}{0.25} \right\rceil \times 0.25 = 123.50 $$Thus, the bounding box lies entirely within the longitude band:
$$ \boxed{123.25^\circ \le \lambda \le 123.50^\circ} $$Only one native longitude cell is involved.
Combining the latitude and longitude results, the single native ERA5 grid cell that fully contains the bounding box is:
$$ \boxed{\text{NWSE} = [9.50,\ 123.25,\ 9.25,\ 123.50]} $$Total native ERA5 cells involved:
$$ 1 \times 1 = \boxed{1} $$Although only one native grid cell is involved, CDS still performs spatial interpolation because ERA5 variables are defined at grid-cell centers rather than over arbitrary sub-cell domains.