The impact of observation spatial and temporal densification in an ensemble Kalman Filter Isabelle Mirouze 1 , Sophie Ricci 1 , Nicole Goutal 2 1: CERFACS / CNRS UMR 5318, 2: LNHE-EDF / LHSV www.cerfacs.fr TUC 2019, Toulouse, France
Outline ◮ Current observational network ◮ Framework and configuration ◮ Twin experiments ◮ Conclusions TUC 2019, Toulouse, France 2
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. TUC 2019, Toulouse, France 3
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 TUC 2019, Toulouse, France 4
Test case for Mascaret Source: A. Besnard and N. Goutal, simHydro, 2010 Input parameters: Ks 1 Tonneins - Mas d’Agenais Ks 2 Mas d’Agenais - Marmande Water height observations: Ks 3 Marmande - La R´ eole In situ: Marmande, 1 hour Q up Time series at Tonneins Swot-like: every 10 km, 1-3 day TUC 2019, Toulouse, France 5
(Extended) Kalman Filter x b, ( k ) = M x a, ( k − 1) Propagation: x a, ( k ) = x b, ( k ) + K ( y o, ( k ) −H x b, ( k ) ) Analysis: x a : analysis vector x b : background vector H x b : in obs. space y o : obs. vector K = B xy ( B yy + R ) − 1 : Kalman gain R : Observation error covariance matrix B yy : Background error covariance matrix in observation space B xy : Covariance matrix for background error in model/obs. space TUC 2019, Toulouse, France 6
From Kalman Filter to Ensemble Kalman Filter Issues for the Kalman Filter: Compute y b = H x b with H complex and non-linear Compute B yy , B xy To use an Ensemble of Kalman Filters Monte Carlo sampling with N e members Source: S. Ricci TUC 2019, Toulouse, France 7
Ensemble Kalman Filter Generate the ensemble with perturbations δ i for each member i x a, ( k − 1) = x a, ( k − 1) + δ i i Integrate the model to obtain x b, ( k ) = M x a, ( k − 1) i i y b, ( k ) = HM x a, ( k − 1) i i Calculate stochastically (exponent ( k ) has been dropped) N e 1 � T � � � � y b y b B yy = i − y b i − y b N e − 1 i =1 Calculate stochastically (exponent ( k ) has been dropped) N e 1 � T � � � � x b y b B xy = i − x b i − y b N e − 1 i =1 TUC 2019, Toulouse, France 8
Twin experiments Experiment Ks 1 Ks 2 Ks 3 Q up In situ Swot ”Truth” Ref 40 32 33 original 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) TUC 2019, Toulouse, France 9
Ensemble generation and cycling ◮ Ks j ∼ U [ Ks j − 5 , Ks j + 5] ◮ Q up : Q up + Gaussian Process ◮ Choose the kernel of the GP and apply a PCA ◮ Truncate the components according to threshold → c 1 , c 2 , c 3 ◮ c 1 , c 2 , c 3 ∼ N (0 , σ ) ◮ Control vector: x = ( Ks 1 , Ks 2 , Ks 3 , c 1 , c 2 , c 3 ) T TUC 2019, Toulouse, France 10
Size of the ensemble Ais with N e = 50 Ais with N e = 100 Water height drift upstream of Marmande when N e = 50 ⇒ Run Ais with N e = 100 but keep other experiments with N e = 50 TUC 2019, Toulouse, France 11
Size of the ensemble A3d with N e = 50 A1d with N e = 50 Ais3d with N e = 50 Ais1d with N e = 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 0 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. TUC 2019, Toulouse, France 13
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 0 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. TUC 2019, Toulouse, France 13
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 TUC 2019, Toulouse, France 14
Correction of the upstream discharge The upstream discharge is not well corrected by any of the experiments → difficulties to correct upstream of the observations TUC 2019, Toulouse, France 15
Correction of the Strickler coefficients * Ks 1 : the more Swot observations, the faster the convergence towards the true value * Ks 2 : the more Swot observations, the smaller the oscillations around the true value * Ks 3 : well corrected for all exp. TUC 2019, Toulouse, France 16
Forecast mean and RMS error wrt Ref for water height * The bias stays stable during the forecast * Ais (in situ data only with N e = 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) TUC 2019, Toulouse, France 17
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
Recommend
More recommend
