# latitude bounds derivations

1. latitude ranges from midpoints

symbol

description

unit

variable name

$$\phi(i)$$

latitude

$$degN$$

latitude {:,latitude}

$$\phi^{B}(i,l)$$

latitude boundaries ($$l \in \{1,2\}$$)

$$degN$$

latitude_bounds {:,latitude,2}

The pattern : for the dimensions can represent {time}, or no dimension at all.

\begin{eqnarray} \phi^{B}(1,1) & = & \frac{3\phi(1) - \phi(2)}{2} \\ \phi^{B}(i,1) & = & \frac{\phi(i-1) + \phi(i)}{2}, 1 < i \leq N \\ \phi^{B}(i,2) & = & \phi^{B}(i+1,1), 1 \leq i < N \\ \phi^{B}(N,2) & = & \frac{3\phi(N) - \phi(N-1)}{2} \end{eqnarray}

This formula applies if the harp option regrid_out_of_bounds is set to nan or to extrapolate. If the option is set to edge then the first and last boundary value are set to the midpoints ($$\phi^{B}(1,1) = \phi(1)$$, $$\phi^{B}(N,2) = \phi(N)$$).

Note that all latitude values will always be clamped to the range $$[-90,90]$$.