Changes to the KPP Vertical Mixing Parameterization

1. Changes to the KPP Vertical Mixing Parameterization • Shallowness of summer-time boundary/mixed layer depths G. Danabasoglu and W. G. Large • Presence of some grid-point noise in boundary /mixed layer depths, particularly in the Tropics • General review of physics and numerics ENERGY INPUT AND DISSIPATION NOT CONSIDERED

2. TEST BED x1 POP forced with QSCAT, NCEP, ISCCP, and MSU / Xie-Arkin data sets for July 1999 – December 2001 The initial conditions are for July 1, 1999, obtained from a 42-year forcing cycle experiment. The results shown are from the last years of 2.5-year experiments. Short-wave heat flux has a diurnal cycle. For simplicity, the internal wave mixing is the only interior mixing allowed.

3. BOUNDARY LAYER DEPTH = HBLT = 0.3 This value of the critical bulk Richardson number is based on some sensitivity studies where comparisons with observed ocean responses during the Ocean Storm Experiment were made. The vertical grid resolution was 1 m. Large et al. (1994)

4. CRITICAL BULK RICHARDSON NUMBER Large et al. (1994) suggests that the critical bulk Ri should somewhat increase as the vertical resolution degrades. Obtained by matching 1-m vertical resolution results

5. = 1.8 This value is chosen to satisfy the empirical rule of pure convection, i.e. the ratio of entrainment flux to surface buoyancy flux should be 0.2. Large et al. (1994) Obtained by satisfying the above rule No dependence on resolution

6. BOUNDARY LAYER DEPTH CONTROL Ri and Cv MODS Jan July

7. TURBULENT VELOCITY SCALES Figure 2 of Large et al. (1994)

8. QUADRATIC INTERPOLATION

9. BOUNDARY LAYER DEPTH CONTROL Quadratic Interpolation MODS Jan July

10. SUMMARY OF CHANGES • Diurnal cycle in short-wave heat flux • Critical bulk Ri as a function of the vertical resolution • Cv as a function of N • Turbulent velocity scale limit in stable regions • Quadratic interpolation for HBLT • Use 4-pt maximum instead of 4-pt average for resolved shear • Modify usage of N in turbulent shear computation • Consider interior convection after HBLT is determined • Correct the Ekman and Monin-Obukhov depth limit computations

11. BOUNDARY LAYER DEPTH CONTROL All Physics MODS Jan July

12. SUMMARY OF CHANGES • Diurnal cycle in short-wave heat flux • Critical bulk Ri as a function of the vertical resolution • Cv as a function of N • Turbulent velocity scale limit in stable regions • Quadratic interpolation for HBLT • Use 4-pt maximum instead of 4-pt average for resolved shear • Modify usage of N in turbulent shear computation • Consider interior convection after HBLT is determined • Correct the Ekman and Monin-Obukhov depth limit computations • Use OLDTIME level data in KPP to eliminate temporal noise • Use a Gaussian filter to smooth HBLT

13. BOUNDARY LAYER DEPTH CONTROL All Physics + Numerical MODS Jan July

14. MIXED LAYER DEPTH CONTROL All Physics + Numerical MODS Jan July

15. EQUATORIAL TEMPERATURE LEVITUS CONTROL All MODS Jan July

16. EQUATORIAL TEMPERATURE LEVITUS CONTROL All MODS PMEL