# longitude bounds derivations

1. longitude ranges from midpoints

symbol

description

unit

variable name

$$\lambda(i)$$

longitude

$$degE$$

longitude {:,longitude}

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

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

$$degE$$

longitude_bounds {:,longitude,2}

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

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