An Adjoint Sensitivity Analysis of the Southern California Current Circulation and Ecosystem

1. An Adjoint Sensitivity Analysis of the Southern California Current Circulation and Ecosystem Andy Moore, Emanuele DiLorenzo, Hernan Arango, Craig Lewis, Zack Powell, Arthur Miller, Bruce Cornuelle

2. Outline • Motivation • Model configuration and circulation • Sensitivity and the adjoint • Indices of interest • Examples of sensitivities • Seasonal variations • Summary

3. Motivation • The California Current System is controlled by a number of different regimes (i.e. upwelling, instability, topographic control). • Sensitivity analysis can help to unravel this complex system. • Test hypotheses about other potentially important processes (i.e. stochastic forcing). • Sensitivity analysis is also an important precursor for data assimilation and predictability analysis.

4. The ROMS SCB Domain Outer domain: 20km res, 20 levels. Inner domain: 7-20km res, 20 levels. Derives boundary conditions from the outer domain. 7-20km resolution; forced by NCEP climatological winds and surface fluxes. ROMS has been used before in the CCS and validated by others (Marchesiello et al, 2003; Powell et al, 2005).

5. A 4-Component Nitrogen-Based Trophic Model N uptake by photosynthetic growth of P (Michaelis-Menten) N Dissolved Nitrogen (Nitrate) Excretion and metabolism Constant SWR P Phototrophic Phytoplankton Z Herbivorous (macro) Zooplankton Grazing on P by Z (saturating) Remineralization of D at constant rate Linear Mortality of P at constant rate D Particulate Nitrogen (Detritus) Linear Mortality of Z at constant rate A variant of the NPZD model of Powell et al. (2005) Sinking 5 m day-1

6. Seasonal Circulation April October

7. Mesoscale Eddy Variability ROMS AVHRR

8. Ecosystem Circulation Surface P April Average

9. Adjoint Approach to Sensitivity • We must first define “sensitivity.” • Consider the model state vector: • Consider a function or index, , defined in terms of space and/or time integrals of . • Small changes in will lead to changes in where: • We will define sensitivity as etc.

10. Sensitivity Analysis • Consider a function • Clearly • But • So

11. Validity of the TL Assumption • TL assumption valid for ~30 days for perts that grow to an amplitude of: |SST|~0.5-1.0C |v|~0.2 m/s These are lower bounds!

12. Seasonal Circulation Index Regions JSST JKE J90

13. Indices For , For , “Eady Index” An index of baroclinic instability

14. Indices For , For ,

15. What Physical Processes are likely to Influence J? Turbulence/ wave breaking Advection Long Rossby Waves Instability Q, P-E+R Short Rossby Waves Note: All processes indicated can be significantly influenced by stochastic forcing. Advection Coastally Trapped Waves & Tides

16. A 4-Component Nitrogen-Based Trophic Model N Dissolved Nitrogen (Nitrate) N uptake by photosynthetic growth of P “Sloppy feeding” and excretion Constant SWR P Phototrophic Phytoplankton Z Herbivorous Zooplankton Grazing on P by Z Remineralization of D at constant rate Linear Mortality of P at constant rate D Particulate Nitrogen (Detritus) Linear Mortality of Z at constant rate A variant of the NPZD model of Powell et al. (2005) Sinking 5 m day-1

17. Physical Circulation Sensitivities

18. The Signature of Advection in Day 10 Day 15 Day 5 Day 20 Day 25 Day 30

19. Seasonal Variations in Sensitivities I The change in over the target area required to yield one change in for . Low sensitivity 0.035 0.01 High sensitivity Low sensitivity 32 The change in Q over the target area required to yield one change in for . 20 High sensitivity The change in v over the target area required to yield one change in for . Low sensitivity 2.3 High sensitivity 0.3

20. Seasonal Variations in Sensitivities II Low sensitivity 0.0045 The change in over the target area required to yield one change in for . 0.002 High sensitivity Low sensitivity The change in over the target area required to yield one change in for . 0.003 High sensitivity 0.0003

21. Seasonal Variations in Sensitivities III Low sensitivity The change in Q over the target area required to yield one change in for . 220 High sensitivity 15 Low sensitivity The change in v over the target area required to yield one change in for . 1 High sensitivity < 0.01

22. Interdependencies: Sensitivity of KE to Baroclinic Instability Low sensitivity Log scale High sensitivity Change in required to yield a one change in when varying only v for . Recall that

23. Summary for Physical Circulation • SST anomaly in coastal upwelling regions equally sensitive to variations in and Q, with v a close second. • Highest (Lowest) sensitivity in Fall (Spring) • KE anomaly most sensitive to variations in and baroclinicity. • Highest (Lowest) sensitivity Summer/Fall (Winter/Spring).

24. Biological Circulation Sensitivities

25. Adjoint Sensitivity for Ecosystem Model Oct: on day 1 Oct: on day 1 Mar: on day 1 Oct: on day 1 Oct: on day 1 Jul: on day 1

26. Seasonal Variations in Sensitivities I Low sensitivity Log scale High sensitivity Change in required to yield a one change in for . Note the log-scale!

27. Seasonal Variations in Sensitivity II Low sensitivity The change in N over the target area required to yield one change in for . High sensitivity Low sensitivity The change in P over the target area required to yield one change in for . High sensitivity Low sensitivity The change in Z over the target area required to yield one change in for . High sensitivity

28. Summary of Biological Circulation • For all NPZD-based indices, variations in are found to be important. • Variations in NPZD equally important (internal interactions important). • NPZD concentrations strongly influenced by the physical environment. • Highest (Lowest) sensitivities in Spring/Summer (Fall/Winter). • Extraordinary sensitivities during some Spring periods suggestive of linear instability (i.e. we are perhaps the TL assumption a little too far!).

29. Other Ongoing Applications • Intra-Americas Sea • Monterey Bay

30. Intra-Americas Sea

31. Seasonal Sensitivity Dependence, J2 Rank based on percentage of basic state mean

32. Seasonal Sensitivity Dependence, J4 (N) Rank based on percentage of basic state mean

33. Seasonal Sensitivity Dependence, J4 (P) Rank based on percentage of basic state mean

34. Seasonal Sensitivity Dependence, J4 (Z) Rank based on percentage of basic state mean

35. Seasonal Sensitivity Dependence, J4 (D) Rank based on percentage of basic state mean

36. The Adjoint Operator • Consider • Perturbations in given by: • Sensitivity given by: • is the adjoint of ROMS. • The adjoint provides the Green’s functions for -functions at all points in space-time.

37. Validity of Tangent Linear Assumption TLM and NLM perturbed by first 10 energy SVs. (|SST|~0.5-1C; ~6cm at day 30)

38. Summary for CalCOFI Line90 Indices, J4 • Most thru least sensitive: N, P, Z, D • N: (1) N,P,Z, wind; (2) D,V • P: (1) N,P,Z,V; (2) wind; (3) D • Z: (1) wind; (2) N,P,Z,V; (3) D • D: (1) wind; (2) P,V; (3) N,Z; (4) D • N,P,Z,D: Extraordinary sensitivity in April • N,P,Z,D: Lowest sensitivity typically during fall and winter.

39. A Reminder…