E :: (real(- infinity .. infinity) ~ " m^2 s^-2" field ( x(grid)
, y(grid)
, z(half)
) on
(i = 1 .. nlon + 1 by
j = 1 .. nlat + 1 by
k = 1 .. nlev
)
)
Scalar Form
E := ( 1 / 2
* ( 1 / h_y * ave(h_y * u ^ 2, x)
+ 1 / h_x * ave(h_x * v ^ 2, y)
)
)
Dimensioned
E := ( 1 / 2
* ( 1 / h_y * ave(h_y * u ^ 2, x)
+ 1 / h_x * ave(h_x * v ^ 2, y)
)
)
Discretized
E := ( 1 / 2
* ( 1 / hyt * ave_h(hyu * u ^ 2, x)
+ 1 / hxt * ave_h(hxv * v ^ 2, y)
)
)
CSE Eliminated
E := ( 1 / 4
* ( ( ( varidx(v, [i, j, k]) ^ 2 * varidx(hxv, [i, j])
+ varidx(v, [i, j - 1, k]) ^ 2 * varidx(hxv, [i, j - 1])
)
/ varidx(hxt, [i, j])
)
+ ( ( varidx(u, [i, j, k]) ^ 2 * varidx(hyu, [i, j])
+ varidx(u, [i - 1, j, k]) ^ 2 * varidx(hyu, [i - 1, j])
)
/ varidx(hyt, [i, j])
)
)
)