AtlantOS OSSE planning meeting, Toulouse17-18 Dec 2015

Ensemble-based array performance assessmentin (coastal) ocean models

P. De Mey1, G. Charria2, J. Lamouroux3, M. Le Hénaff4, M. Iskandarani4

1LEGOS, Toulouse, France, pierre.de-mey@legos.obs-mip.fr2IFREMER, Brest, France

3NOVELTIS, Toulouse, France4University of Miami, Miami, USA

Array design approaches at LEGOS

• Some previous array design approaches

– Classic OSSEs (e.g. Lamouroux et al., 2007, Jordà et al., 2007)

– EnKF-based Ensemble variance reduction studies (e.g. Mourre et al., 2005; 2006; Ayoub et al., 2010)

– Representer Matrix analysis (RMSpectrum: Le Hénaff et al., 2009; ArM: De Mey, 2010) EU projects SANGOMA, JERICO.

• Objective of ArM (“Array Modes”)

– Set up a simple, quantitative criterion to quantify trade-offs & options in the design of observing systems & arrays

– Use Ensembles to estimate prior uncertainties (before measurements are made/used)

– Use DA theoretical framework (but no DA involved).

TAO array assessment: RM analysis (Bennett, 199x)

• Pre-Ensembles era!

• Tropical Pacific, TAO array: SST, D20, surface winds

• The RM summarizes how the observational array “sees” the model error

• By comparing its spectrum to the assumed level of measurement errors, one can infer how many and which d.o.f.s of the background error are effectively constrained by the array (here about 800)

• Two cases linearized around El Niño/La Niña situations -- very similar assessment could have been carried out before from composite.

The ArM toolbox in SANGOMA

• WP2: ArM tools are included in the SANGOMA “diagnostics” toolbox:

– Tool 1 (ArM): array performance criterion

– Tool 2 (ArM-CA): Ensemble consistency criterion.

– https://sourceforge.net/p/sangoma/code/HEAD/tree/tools

• Common features:

– No dependency on an assimilation scheme.

– The tools work in space/time and across variables.

– The observational errors can be correlated.

– The observational operator can be…an operator.

• WP5: Comparison of ArM (LEGOS) with tr(HK) (LGGE).

The ArM toolbox: objective criteria

• Array performance with sangoma_arm()

• Ensemble consistency with sangoma_armca()

Count singular values of S larger than 1:

f

mYRS

2/1

1

1

Count array-space ranks k for

which

1)(var

11

ok

k

Δ

with = tolerance

ArM analysis in practice

• Paradigm: A good array (regardless of its cost) is an array that candetect (and help correct) model state errors

• ArM requires an Ensemble representing prior uncertainties

• Assumptions on prior state error sources and perturbation strategy come back to prioritizing what the array is to be designed for– E.g. perturb wind stress, surface pressure, thermocline, bathymetry, river

runoff, mesoscale, mixing, vorticity balance, etc.

• RM eigenvalues above 1 are associated with array modes detectable above observational noise floor just count them

• Explore array modes & modal representers to get physical insight into the error subspace physical processes which are detectable (constrainable)

• Controllability cannot be tested (no DA involved).

Uses and publication

• The ArM tool has been used in particular in the JERICO EU project(fishing net sensors, gliders, etc.) and will be used in JERICO Next (HF radars) in a LEGOS/Ifremer/Noveltis collaboration.

• The ArMCA tool is intended to be used in a response to CMEMS 21-SE-Call1.

• Two publications so far (in addition to LH2009):– Lamouroux, J., G. Charria, P. De Mey, S. Raynaud, C. Heyraud, P. Craneguy, F.

Dumas, M. Le Hénaff, 2015: Assessment of RECOPESCA network contribution for the monitoring of 3D coastal model errors in the Bay of Biscay and the English Channel. Ocean Dynamics, submitted. (joint SANGOMA/JERICO paper)

– Charria, G., J. Lamouroux, and P. De Mey, 2015: Optimizing observationalnetworks combining gliders, 1 moored buoys and FerryBox in the Bay of Biscayand English Channel. J. Marine Sys., submitted. (JERICO paper)

Wide-swath vs. nadir altimeter, ArM analysis

• SYMPHONIE 3D, summer 2004, wind errors

• Uses V. Enjolras (CNES) PhD thesis correlated KaRin error model

• SWOT detects additional meso/HF d.o.f.s above observational noise floor

Jason 1 SWOT (Jason orbit)

Jason 1

SWOT (Jason orbit)

RM spectra Array Modes (SLA)

Slosh Meso1 Meso2+HF

Le Hénaff, De Mey, O.Dyn. 2009

timecm

Coastal tide gauges

• BoB 3D configuration, Gaussian wind errors, Summer 2004, detided samples

• Assess existing tide gauges (hourly data)

• Array modes contain the array’s view of Kelvin waves propagating Eastward in the model’s error subspace

SLA component of mode 1 modal representerArray modes (SLA) with KW propagation

BoB (Le Hénaff & De Mey, 2008)

(time slice, August 23, 2004, 0000Z)

JERICO: Roscoff-Plymouth Ferrybox vs. Glider, ArM analysis

• Model uncertainty from MARS3D ensemble (50 members; Craneguy, Heyraud, Raynaud @ Actimar)

• Higher repeat cycle of ferrybox needed here, despite being surface only, in part because of HF model errors (linked to tidal front displacements)

Charria, Lamouroux, De Mey, O.Dyn. COSS-TT Topical Collection, 2015

-- Ferrybox-- GliderDT3H-- Combination

JERICO: RECOPESCA fishing net array

• Vertical profilers on fishing nets – 3 scenarii: year 2008, year 2010, 2006-2011

• Observation error: 0.3°C

• Model uncertainty from MARS3D ensemble (50 members; Craneguy, Heyraud, Raynaud @ Actimar)

11

2008 reference SC1 : based on 2010 SC2 : cumulated 2006-2011

Charria (Ifremer), Lamouroux (Noveltis), De Mey (LEGOS) et al.

JERICO: RECOPESCA array mode eigenspectra

• Performance: larger number of observations (SC2) lead to errors being better sampled

• Performance/cost: geographical distribution more important than number of profiles: REFmore efficient (higher ratio) than SC1

Array ev>1 Profiles Ratio

REF 29 126 0.23

SC1 48 265 0.18

SC2 >49 843 >0.05

Charria (Ifremer), Lamouroux (Noveltis), De Mey (LEGOS) et al.

Monte Carlo vs. Polynomial Chaos, ArM analysis

• Small Ensembles canmisrepresent model statistics

• PC (e.g. Xiu, 2010) aims to model stochastic processes by means of polynomials – computationallysuperior to MC methods

• HYCOM, 49 members, i.c. errors

• One more ev with PC

• More tests needed with differentmodel state error sources

Le Hénaff & Iskandarani, U. MiamiIn: Oke et al., 2015 (2013 GOV Symposium paper).

Summary

• Paradigm: A good array (regardless of its cost) is an array that candetect (and help correct) model state errors

• ArM provides a criterion for whole array, not individual observations

– Simple criterion – just count eigenvalues above 1

– Refine array impact assessment by looking at modal representers

– Multiparametric, space+time

– Better fit for targeted arrays than for full, multi-purpose OS

• No data assimilation involved – independent of DA scheme

• Need good, validated estimates of obs. error covariances (all methods)

• Use with systems not generating Ensembles: Multi-model Ensembles

– Work on model-to-model differences instead of errors

– Which observations would help discriminate between the variousmodelling paths?

• To be used in JERICO Next (talk tomorrow)• Not in AtlantOS (at the moment) but open to collaboration