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

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

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.

The ROMS SCB 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). Outer domain: 20km res, 20 levels. Inner domain: 7-20km res, 20 levels. Derives boundary conditions from the outer domain.

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

Seasonal Circulation April October

Mesoscale Eddy Variability ROMS AVHRR

Ecosystem Circulation Surface P April Average

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.

Sensitivity Analysis  Consider a function  Clearly  But  So

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

Seasonal Circulation Index Regions J SST J KE J 90

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

Indices For,

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

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

Physical Circulation Sensitivities

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

Seasonal Variations in Sensitivities I The change in over the target area required to yield one change in for. The change in Q over the target area required to yield one change in for. The change in v over the target area required to yield one change in for. Low sensitivity High sensitivity

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

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

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

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).

Biological Circulation Sensitivities

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

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

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

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!).

Other Ongoing Applications  Intra-Americas Sea  Monterey Bay

Intra-Americas Sea

Seasonal Sensitivity Dependence, J J 2 SST (K) V (m s -1 ) (N m -2 ) (N m -2 ) (m) (m) Q (W m -2 ) Jan (1.1) Feb (0.8) Mar (0.6) Apr (0.8) May (0.7) Jun (0.9) Jul (0.7) Aug (0.7) Sep (1.0) Oct (1.1) Nov (0.9) Dec (0.6) Mean (0.8) Basic State Mn 10~1~0.1~0.2~100 Rank22132 Rank based on percentage of basic state mean

Seasonal Sensitivity Dependence, J 4 (N) Rank based on percentage of basic state mean NO 3 (mmol Nm -3 ) P (mmol Nm -3 ) Z (mmol Nm -3 ) D (mmol Nm -3 ) (N m -2 ) (N m -2 ) V (m s -1 ) Jan X Feb X Mar X Apr X May X Jun X Jul X Aug X Sep X Oct X Nov X Dec X Mean X Basic State ~10~10~10~1~0.1~1 Rank111212

Seasonal Sensitivity Dependence, J 4 (P) Rank based on percentage of basic state mean NO 3 (mmol Nm -3 ) P (mmol Nm -3 ) Z (mmol Nm -3 ) D (mmol Nm -3 ) (N m -2 ) (N m -2 ) V (m s -1 ) Jan X Feb X Mar X Apr X May X Jun X Jul X Aug X Sep X Oct X Nov X Dec X Mean X Basic State ~10~10~10~1~0.1~1 Rank111321

Seasonal Sensitivity Dependence, J 4 (Z) Rank based on percentage of basic state mean NO 3 (mmol Nm -3 ) P (mmol Nm -3 ) Z (mmol Nm -3 ) D (mmol Nm -3 ) (N m -2 ) (N m -2 ) V (m s -1 ) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Mean Basic State ~10~10~10~1~0.1~1 Rank222312

Seasonal Sensitivity Dependence, J 4 (D) Rank based on percentage of basic state mean NO 3 (mmol Nm -3 ) P (mmol Nm -3 ) Z (mmol Nm -3 ) D (mmol Nm -3 ) (N m -2 ) (N m -2 ) V (m s -1 ) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Mean Basic State ~10~10~10~1~0.1~1 Rank323412

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.

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

Summary for CalCOFI Line90 Indices, J 4  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.

A Reminder…