The effect of compact implicit differencing in a baroclinic primitive equations model

In an effort to improve forecast accuracy, the horizontal accuracy of gridpoint forecast models at a number of numerical weather prediction (NWP) centers was increased from second order to fourth order. The current GLAS model uses second-order explicit finite-difference formulas in the vertical and fourth-order explicit finite-difference formulas in the horizontal. Experiments are described which indicate the increased forecast accuracy gained by use of compact fourth-order finite differences in a simple baroclinic model. Tables show an increase in forecast accuracy by a factor of 100-150 by use of fourth-order instead of second-order vertical discretization.