Analysis Weighting Strategy

• 3-D Weighting

  • Successive Correction with Barnes Weighting

  • Distance weight e^-(d/r)2 applied in 3-dimensions

  • Instrument error reflected in observation weight
    • w_o = e^-(d/r)2 / err_o ²
  • Each analysis iteration becomes the background for the next iteration
  • Decreasing Radius of Influence (r) with each iteration

  • Each iteration improves fit and adds finer scale structure

  • Works well with strongly clustered observations

  • Iterations stop when fine scale structure & fit to obs become commensurate with observaton spacing & instrument error

• Smooth Blending with Background First Guess

• Background subtracted to yield observation increments (u_o)
• Background (with zero increment) has weight at each grid point
• Background weight proportional to inverse square of estimated error
• w_b = 1 / err _b ²
• For each iteration, analyzed increment (u) is as follows:
  • u_i,j,k = (u_ow_o) / ((w_o) + w_b)