The impact of observation spatial and temporal densification in an - - PowerPoint PPT Presentation

The impact of observation spatial and temporal densification in an ensemble Kalman Filter

Isabelle Mirouze1, Sophie Ricci1, Nicole Goutal2

1: CERFACS / CNRS UMR 5318, 2: LNHE-EDF / LHSV TUC 2019, Toulouse, France

www.cerfacs.fr

Outline

◮ Current observational network ◮ Framework and configuration ◮ Twin experiments ◮ Conclusions

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In situ observations

Limnimetric in situ stations at bidos, Brazil (Paris, 2015) Global Runoff Data Center (GRDC) 12/08/2019:

• 1919-1979 • 1980-1989 • 1990-1999 • 2000-2009 • 2010-2017

https://www.bafg.de/GRDC/EN/Home/homepage node.html

Mainly for water height. Few observations of discharge. Network is sparse and number of available data is decreasing. Accessing the observations can be difficult (charges, not shared). Drones deployed punctually for a particular event.

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Spatial altimetry for water height

JASON-2 altimeter tracks over the Amazon basin Surface Water and Ocean Topography Mission

Current satellites: incomplete and low resolution spatial coverage, adapted to only major lakes and rivers. SWOT: scheduled for a launch in 2021, will provide a global and high resolution coverage, adapted to river with width > 50 m product example: reach average every 10 km with 10 cm accuracy

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Test case for Mascaret

Source: A. Besnard and N. Goutal, simHydro, 2010

Input parameters: Ks1 Tonneins - Mas d’Agenais Ks2 Mas d’Agenais - Marmande Water height observations: Ks3 Marmande - La R´ eole In situ: Marmande, 1 hour Qup Time series at Tonneins Swot-like: every 10 km, 1-3 day

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(Extended) Kalman Filter

Propagation: xb,(k)= Mxa,(k−1) Analysis: xa,(k)=xb,(k)+K (yo,(k)−Hxb,(k) ) xa: analysis vector xb: background vector Hxb: in obs. space yo:

• bs. vector

K = Bxy (Byy + R)−1: Kalman gain R: Observation error covariance matrix Byy: Background error covariance matrix in observation space Bxy: Covariance matrix for background error in model/obs. space

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From Kalman Filter to Ensemble Kalman Filter

Issues for the Kalman Filter: Compute yb = Hxb with H complex and non-linear Compute Byy, Bxy To use an Ensemble of Kalman Filters Monte Carlo sampling with Ne members

Source: S. Ricci TUC 2019, Toulouse, France 7

Ensemble Kalman Filter

Generate the ensemble with perturbations δi for each member i xa,(k−1)

i

= xa,(k−1) + δi Integrate the model to obtain xb,(k)

i

= Mxa,(k−1)

i

yb,(k)

i

= HMxa,(k−1)

i

Calculate stochastically (exponent (k) has been dropped) Byy = 1 Ne − 1

Ne

• i=1
• yb

i − yb

yb

i − yb

T Calculate stochastically (exponent (k) has been dropped) Bxy = 1 Ne − 1

Ne

• i=1
• xb

i − xb

yb

i − yb

T

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Twin experiments

Experiment Ks1 Ks2 Ks3 Qup In situ Swot ”Truth” Ref 40 32 33

• riginal

No No ”Real life” Ctl 30 40 40 modified No No ”Now” Ais 30 40 40 modified Hourly No A3d 30 40 40 modified No 3 days ”Future” A1d 30 40 40 modified No 1 day Ais3d 30 40 40 modified Hourly 3 days Ais1d 30 40 40 modified Hourly 1 day Initial conditions: identical for all experiments Spinup: 2 days to allow the experiments to diverge from Ref Assessment period: 50 days from 01/05 to 20/06 Forecast: 24 hours Water level observations generated from Ref + δ ∼ N(0, 10cm)

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Ensemble generation and cycling

◮ Ksj ∼ U[Ksj − 5, Ksj + 5] ◮ Qup: Qup+Gaussian Process

◮ Choose the kernel of the GP and apply a PCA ◮ Truncate the components according to threshold → c1, c2, c3 ◮ c1, c2, c3 ∼ N(0, σ)

◮ Control vector: x = (Ks1, Ks2, Ks3, c1, c2, c3)T

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Size of the ensemble

Ais with Ne = 50 Ais with Ne = 100

Water height drift upstream of Marmande when Ne = 50 ⇒ Run Ais with Ne = 100 but keep other experiments with Ne = 50

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Size of the ensemble

A3d with Ne = 50 Ais3d with Ne = 50 A1d with Ne = 50 Ais1d with Ne = 50 TUC 2019, Toulouse, France 12

Mean and RMS error wrt Ref for water height

Experiment Global (mm) Marmande (mm) Mean RMS Mean RMS Ctl

• 696

854

• 844

904 Ais100

• 161

312 69 Ais 337 907 9 70 A3d

• 104

363

• 119

373 Ais3d 8 418 5 73 A1d

• 29

199

• 16

200 Ais1d

• 16

157 2 69 * All assimilation experiments improve statistics. * Assimilating hourly in situ observations at Marmande:

• cancels out the bias;
• reduces the rmse down to the observation accuracy (10 cm).

* Assimilating daily Swot-like data only cancels out the bias.

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Mean and RMS error wrt Ref for water height

Experiment Global (mm) Marmande (mm) Mean RMS Mean RMS Ctl

• 696

854

• 844

904 Ais100

• 161

312 69 Ais 337 907 9 70 A3d

• 104

363

• 119

373 Ais3d 8 418 5 73 A1d

• 29

199

• 16

200 Ais1d

• 16

157 2 69 * Assimilation experiments (except Ais) improve statistics. * Assimilating daily Swot-like observations:

• cancels out the bias;
• reduces significantly the rmse.

* Assimilating 3-day Swot-like + in situ data cancels out the bias.

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Mean and RMS error wrt Ref for water height

* Swot-like data → cancels out the bias at any location * Ais3d ”bad” rmse → adjustment upstream Marmande for the first high flow * A3d, A1d → constant rmse, the more frequent data the better

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Correction of the upstream discharge

The upstream discharge is not well corrected by any of the experiments → difficulties to correct upstream of the observations

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Correction of the Strickler coefficients

* Ks1: the more Swot observations, the faster the convergence towards the true value * Ks2: the more Swot observations, the smaller the oscillations around the true value * Ks3: well corrected for all exp.

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Forecast mean and RMS error wrt Ref for water height

* The bias stays stable during the forecast * Ais (in situ data only with Ne = 50) performs worse than Ctl * The reanalysis rmse improvement holds for 12 hours * Compared to Ctl, the rmse is still improved at a 24 hour lead time (extrapolation ∼ 30 hours)

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Conclusions

◮ Assimilating observations at Marmande only

◮ fails at correcting the water height upstream of Marmande ◮ fails at calibrating the Ks (equifinality)

◮ Observations regularly distributed (spatial densification) allow

◮ the reduction of the ensemble size for the same rmse ◮ the Strickler coefficients to be better calibrated (equifinality) ◮ cancelling the reanalysis bias ◮ reducing the reanalysis rmse

◮ Increasing the frequency of the Swot-like observations

(temporal densification) allows

◮ a decrease in the rmse ◮ a faster convergence towards the true values of the Strickler

coefficients

◮ The reanalysis improvement holds for the first 12 hours

forecast

This study has been carried out thanks to the TOSCA-SWOT funding from CNES TUC 2019, Toulouse, France 18