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The differentiation is approximated by differences computed on the verification grid:
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e_g = \left ( \left | \frac{\partial}{\partial x}(x_f-x_v)\right | + \left | \frac{\partial}{\partial y}(x_f-x_v)\right | \right ) |
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G_L = max \left ( \left | \frac{\partial x_f}{\partial x}\right | , \left | \frac{\partial x_v}{\partial x}\right | \right) + max \left ( \left | \frac{\partial x_f}{\partial y}\right | , \left | \frac{\partial x_v}{\partial y}\right | \right) |
The weights wi applied at each grid point or observation location are defined as
Verification against analyses:
Mathinline w_i = \cos \theta_i, cosine of laltitude athe the grid point i
Verification against observations:
Mathinline w_i = 1/n
, all observations have equal weight