Using IS 4 DVAR Data Assimilation in the

Using IS 4 DVAR Data Assimilation in the near coastal modeling system Ivica Janeković & Brian Powell 1

#ifdef LAYOUT • • Region of interest, domain, bathymetry Forward model setup IS 4 DVAR setup TLM validation Problems on the way Results & discussion Preliminary results – still running, suggestions are welcome 2

Domain • Hawaiian Islands -> challenge for model skill • Complex bathymetry, forcing, boundary… • Hawaiian Ridge – major barotropic to baroclinic tidal conversion site -> Kaena Ridge, Niihau-Maui • Coastal dynamics in shallow/slope region on high resolution model for transport study of ordnance • We used nested approach from 2 model grids above – 4 km Hawaiian Islands Grid – -> 1. 2 km Oahu-Maui Grid – -> 200 - 900 m Western Oahu Grid • Our focus is Western Oahu region & DA • 5 ADCP observations at “nice position” (07/09 -07/10) • SST data from MODIS T/A 3

Kauai Kaena Ridge Niihau 4

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(59, 35) West Oahu Grid 33 km 12 km ADCP 6

Bathymetry transect ADCP 7

Forward model setup • We used hi-res bathymetry + LP smoothing – variable rx 0 smoothing, iterative way, many grids… • 20 vertical levels (on the edge with rx 1(!)) – increased number of levels in surface zone -> Θ_s= 7, Θ _b= 0. 1 – vtransform, vstretching = 2 – variable resolution, in region where we have ADCPs (~200 m) while at boundary ~900 m (outer grid 1. 2 km) • Spin-up from 2004 - 2009 using: – forcing with local MM 5 (1. 5 km), WRF (1. 5 km) – boundary from HIOG (1. 2 km outer model), tides inside • Model setup using: – U 3 for advection, GLS - gen, IS 4 DVAR, small diffusion and viscosity, clamped BC, … • Forward model is doing well with tides – dominantly tidally driven (barotropic/baroclinic) – we want to improve circulation & phase 8

IS 4 DVAR setup • • • in the beginning 40, 30, 20 inner loops, 1 outer loop time window of 3 days (based on init and MTLM) clamped boundary conditions adjust initial filed + atmo. forcing, NO BRY ADJUSTMENT OBS: – ADCPs (1 2 3 4) • discarded at the bottom • model/obs depths doesn’t match, bottom layer? ! • ADCP 2 out of phase – SSH (1 2 3 4) • de-mean, added model mean value, nr. 2 faulty – MODIS T/A SST • not many data, proximity to coast, small domain • small grid (tiles), short time step of 60 s (ncpu? ) • small de-correlation scale (patchy fields) • run experiments with: – using only ADCPs – using ADCPs + SSH + MODIS SST 9

NLM-TLM approximation • In order to check validity of TLM approx: – we made inside domain perturbation (“wrong” SST) – run MTLM (10 inner loops) – used 40 (Modified Gram-Schmidt ortho-normalized) perturbations in init field for all state variables – horizontal de-correlation scale set to 3 km – run TLM and NLM (40 members) – correlation (NLM, TLM) for all state variables – system is OK for 5 days, high correlation (>0. 6) – mixing in the 1 st time step for salt, unstable perturbs – mostly driven by atmo and boundary forcing 10

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Effect of init field inside NLM • we run NLM from day_0 (1 st of Nov 2009) using: – real BC, atmo. forcing and initial field – -> state_0 • we run NLM as before but with: – initial field randomly picked (Jun 2009) and then only “changed” ocean_time = day_0 – -> state_1 • compute correlation btw state_0 & state_1 for all state variables in time • After 2 -3 days information in init field is swept away by BC and atmo forcing, correlation is round 1. • This have us interval how frequent we should assimilate 15

correlation (state_0, state_1) 16

Results/disscusion • If only looking at the ADCPs locations – all seems perfect, high correlation (~0. 7 - 0. 8) • What is really happening? • We do have high dimensionality case with small number of obs -> constraint • We made experiments gradually adding obs to see how it affects solutions and constraints • Did we corrected/destroyed baroclinic tides? • What happened to density filed in whole domain? 17

Exp 1: ADCPs only 18

Exp 1: ADCPs only 19

Exp 1: ADCPs only 20

Exp 1: ADCPs only depth -53. 4 -45. 4 -37. 4 -29. 4 -21. 4 -13. 4 ADCP 1 Correlation/STD U 0 UA V 0 0. 68/0. 17 0. 72/0. 15 -0. 60/0. 15 0. 70/0. 18 0. 75/0. 16 -0. 49/0. 12 0. 70/0. 19 0. 76/0. 16 -0. 38/0. 11 0. 71/0. 19 0. 77/0. 16 -0. 32/0. 11 0. 72/0. 19 0. 78/0. 16 -0. 31/0. 10 0. 71/0. 20 0. 77/0. 17 -0. 25/0. 11 VA -0. 57/0. 15 -0. 44/0. 12 -0. 27/0. 11 -0. 18/0. 10 -0. 17/0. 10 -0. 21/0. 11 ADCP 3 Correlation/STD depth U 0 UA V 0 -9. 9 0. 70/0. 16 0. 78/0. 13 0. 27/0. 04 -8. 4 0. 71/0. 16 0. 78/0. 13 0. 27/0. 04 -6. 9 0. 71/0. 16 0. 79/0. 13 0. 25/0. 04 -5. 4 0. 70/0. 16 0. 79/0. 13 0. 23/0. 04 -4. 2 0. 70/0. 16 0. 78/0. 13 0. 21/0. 04 VA 0. 26/0. 04 0. 25/0. 04 0. 23/0. 05 0. 22/0. 05 ADCP 4 Correlation/STD depth U 0 UA V 0 -5. 9 0. 56/0. 21 0. 64/0. 18 -0. 18/0. 07 -3. 2 0. 56/0. 21 0. 64/0. 19 -0. 09/0. 08 VA -0. 14/0. 08 -0. 12/0. 09 21

Exp 2: ADCPs + SSH 22

Exp 2: ADCPs + SSH 23

Exp 2: ADCPs + SSH 24

Exp 2: ADCPs + SSH depth -53. 4 -45. 4 -37. 4 -29. 4 -21. 4 -13. 4 ADCP 1 Correlation/STD U 0 UA V 0 0. 68/0. 17 0. 72/0. 15 -0. 60/0. 15 0. 69/0. 18 0. 75/0. 16 -0. 49/0. 12 0. 70/0. 19 0. 76/0. 16 -0. 36/0. 11 0. 71/0. 19 0. 77/0. 16 -0. 30/0. 11 0. 71/0. 19 0. 77/0. 16 -0. 29/0. 10 0. 71/0. 20 0. 77/0. 17 -0. 25/0. 11 VA -0. 58/0. 15 -0. 46/0. 13 -0. 30/0. 11 -0. 20/0. 10 -0. 16/0. 10 -0. 13/0. 10 ADCP 3 Correlation/STD depth U 0 UA V 0 -9. 9 0. 71/0. 16 0. 77/0. 14 0. 27/0. 04 -8. 4 0. 71/0. 16 0. 78/0. 13 0. 26/0. 04 -6. 9 0. 71/0. 16 0. 78/0. 13 0. 24/0. 04 -5. 4 0. 71/0. 16 0. 78/0. 13 0. 23/0. 04 -4. 2 0. 70/0. 16 0. 78/0. 14 0. 21/0. 04 VA 0. 27/0. 04 0. 25/0. 04 0. 24/0. 04 0. 23/0. 05 0. 22/0. 05 ADCP 4 Correlation/STD depth U 0 UA V 0 -5. 9 0. 56/0. 21 0. 64/0. 18 -0. 19/0. 07 -3. 2 0. 56/0. 21 0. 64/0. 19 -0. 09/0. 08 VA -0. 17/0. 08 -0. 15/0. 09 25

Exp 3: ADCPs + SSH + SST 26

Exp 3: ADCPs + SSH + SST 27

Exp 3: ADCPs + SSH + SST 28

Exp 3: ADCPs + SSH + SST 29

Exp 3: ADCPs + SSH + SST 30

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Exp 3: ADCPs + SSH + SST depth -53. 4 -45. 4 -37. 4 -29. 4 -21. 4 -13. 4 ADCP 1 Correlation/STD U 0 UA V 0 0. 68/0. 17 0. 71/0. 16 -0. 61/0. 14 0. 69/0. 18 0. 74/0. 16 -0. 50/0. 12 0. 69/0. 19 0. 75/0. 16 -0. 39/0. 11 0. 70/0. 20 0. 76/0. 16 -0. 33/0. 10 0. 71/0. 20 0. 77/0. 17 -0. 32/0. 10 0. 70/0. 20 0. 76/0. 17 -0. 27/0. 11 VA -0. 58/0. 15 -0. 45/0. 12 -0. 29/0. 11 -0. 19/0. 10 -0. 18/0. 10 -0. 17/0. 10 ADCP 3 Correlation/STD depth U 0 UA V 0 -9. 9 0. 70/0. 16 0. 78/0. 13 0. 28/0. 04 -8. 4 0. 71/0. 16 0. 78/0. 13 0. 29/0. 04 -6. 9 0. 71/0. 16 0. 78/0. 14 0. 27/0. 04 -5. 4 0. 70/0. 16 0. 78/0. 14 0. 25/0. 04 -4. 2 0. 70/0. 16 0. 78/0. 14 0. 23/0. 04 VA 0. 31/0. 04 0. 30/0. 04 0. 29/0. 04 0. 26/0. 04 0. 24/0. 05 ADCP 4 Correlation/STD depth U 0 UA V 0 -5. 9 0. 55/0. 21 0. 63/0. 18 -0. 20/0. 07 -3. 2 0. 55/0. 22 0. 63/0. 19 -0. 11/0. 08 VA -0. 15/0. 08 -0. 13/0. 09 Corr(ssh_obs, ssh_nlm_0)=0. 75 Corr(SST_obs, SST_nlm_0)=0. 69 Corr(SST_obs, SST_nlm_1)=0. 70 33

Still work in progress • All indicates that the key is to fix outer model as much as possible (use DA) in order to get right BC • Right now we are only adjusting atmo+initial • We do need to perform observation sensitivity – How sensitive is our system to ADCP obs? – Ek vs Ep inside model • Impact studies • Overlapping could help to avoid shocks • Would W 4 DVAR help? 34