Recent Development of Ocean Data Assimilation Systems and Recent Observing System Evaluation Studies in JMA/MRI

Transcription

1 GOV DA-TT & OSEval TT MT 2017, Oct. 13 th, 2017, La Spezia, Italy Recent Development of Ocean Data Assimilation Systems and Recent Observing System Evaluation Studies in JMA/MRI Yosue Fujii, Norihisa Usui, Nariai Hirose, Taahiro Toyoda, and Tsurane Kuragano (JMA/MRI) 1. Recent development of DA systems in JMA/MRI 2. Evaluation of ARGO networ using space-time correlation scale statistically estimated from SLA data 3. Estimation of Analysis Errors in a 4DVAR system using BFGS formula

2 1. Resent Development of DA Systems in JMA/MRI

3 Operational Systems in JMA MOVE/MRI.COM-G2 Tripolar Grid, 1º 0.5º 3DVAR-FGAT+ Bias Correction Seasonal and ENSO predictions MOVE/MRI.COM-NP/WNP G2 (0.5º 1º, Tripolar Grid) MOVE/MRI.COM-Seto (semi-operation) NP(0.5º 0.5º) WNP-4DVAR (0.1º 0.1º) Seto (2m 2m) Nudged to WNP- 4DVAR by IAU WNP(0.1º 0.1º) 3DVAR Kuroshio/Oyashio Monitoring Ocean Forecasting (1 wee-1 month) Monitoring of Coastal Ocean and abnormal tides Ocean Forecasting (-1 wee)

4 New System for Ocean Forecasting Constituted of analysis and forecast models Analysis Model (North Pacific) 10m resolution (eddy-resolving) Nonlinear 4D-Var assimilation scheme (The model operator in the cost function is not linearized.) 4DVAR optimization starts from 3DVAR results Target: Mesoscale Variability Forecast model (the seas around Japan) High resolution (~2m) coastal model Embedded in the analysis model by two-way nesting Tidal components are also simulated. TS fields are modified using the data-assimilated TS fields in the analysis model through Incremental Analysis Update (IAU). Target: Coastal Phenomena, Abnormal Tides Analysis model (10m) Two-way nesting Forecast model (2m) 4

5 Comparison of SST fields Analysis model (10m, 4DVAR) Forecast model (2m, IAU) Rapid mesoscale variability is well estimated by the 4DVAR scheme. Mesoscale features are well constrained Fine-scale structures can be seen. Satellite-based SST map (MGDSST ~25m) The variation is very slow because of time-smoothing effects of the objective analysis (OI). 5

6 Comparison of SST snapshot with NOAA/AVHRR Satellite SST image (NOAA/AVHRR) /sui/aiyo/detail.htm Analysis model (10m) Forecast model (2m, 5-day IAU) 6

7 Comparison with Tide gages Forecast model JPN-assim (with assimilation) JPN-free (without assimilation) Observation tide gauge data 48 hour tide iller filter (Hanawa and Mitsudera, 1985) Daily mean (2009/1/1~2009/12/31) Hachijojima Kuroshio path is well reproduced Kobe Seto Inland Sea (coastal sea) JPN-assim is mostly better than JPN-free

8 New System for Seasonal Forecasting Constituted of Analysis and Forecasts Models (similar to a inner-model-outer-model system which uses an incremental method) Analysis Model Global, Tripolar, Resolution: 1º º Upgrade from 3DVAR to nonlinear 4DVAR assimilation scheme for the ocean state 4DVAR optimization starts from 3DVAR results Sea Ice 3DVAR scheme is newly introduced Separated from the 4DVAR Surf. Air Temp. is modified. Forecast model Global, Tripolar Resolution: 0.25º 0.25º (1º º for current system) TS fields are modified using TS fields in the analysis model by IAU. Sea Ice 3DVAR scheme 8

9 SST deviations from observational data (28Oct-01Nov, 2012) First Guess (New System) - Obs Pre-3DVAR result (New System) - Obs 4DVAR result (New System)- Obs Operational System - Obs

10 Comparison of Sea Ice Concentration Fields Arctic Region (30Jul-03Aug, 2012) Antarctic Region (30Jul-03Aug, 2012) FG (New System) An (New System) FG FG (New (New System) An An (New (New System) System) An (Old System) Observation An An (Old (Old System) System) Observation Sea Ice data are not assimilated in the current operational system By assimilating Sea Ice concentration data, the distribution of the sea ice field is much improved in the new system. The extension of the sea ice area in red circles becomes much improved. And it is effectively modified in the analysis step. The distribution in the Antarctic Pacific basin (in blue squares) is also effectively improved.

11 2. Evaluation of ARGO networ using space-time correlation scale statistically estimated from SLA data

12 12 Estimation of Space-Time Correlation Scale Space-time correlation feature of Sea Level Anomaly (SLA) data at a grid point (x, y) is represented by three-dimensional Gaussian function: Δx, Δy, Δt : Zonal, meridional and time distances from the reference grid point (x, y). Coefficients a 1, a 2,, a 6 are determined by fitting the function to actual distribution of correlation coefficients of SLA data. Along-trac data of T/P, Jason-1/2, ERS-1/2 and Envisat in are used for the estimation of correlation coefficient (the trend is removed). The correlation function is determined for every global 3 0 x 3 0 grid point E-folding ellipsoid is defined by ) exp( ),,,, ( t y a t x a y x a t a y a x a t y x y x ) exp( e t y a t x a y x a t a y a x a

13 Map of Space-Time Correlation Scale persistence e-folding time scale 1 e Oval: 1/3 of e-folding scale from each staggered grid Color shade: persistent e-folding timescale The ellipsoid is zonally extended in the equatorial region The persistence timescale is generally long in the subtropical region Eddies persist for a relatively long time while propagating. E-folding Ellipsoid 13

14 Evaluation of Argo Networ Examine how many Argo profiles there are in a e-folding ellipsoid. For 1N-139W (Red Line), many Argo profiles are included in the ellipsoid mainly because of the large zonal scale Even with a small static spatial-scale and a small local time-scale, the number of profiles in the ellipsoid can be relatively large because the persistent time-scale can be longer due to the propagation of the signal. Schematic figure of the e-folding ellipsoid at several points with a ideal Argo distribution local time-scale persistent time-scale 14

15 Evaluation of Argo Networ Actual number of Argo Profiles in the e-folding ellipsoid The number of Argo in the ellipsoid are sufficient in the tropical Pacific and Indian Oceans in spite of relatively small density. The number is small in the most part of the North Atlantic in spite of large density of Argo floats. The number is large in the Alasan Bay and south of Japan due to large density and relatively large volume of the ellipsoid. This information can be exploited for the effective Argo deployment. Averaged in the period from 02 Jul to 27 Jun When we estimate SLA using dynamic heights from Argo profiles through spatialtemporal OI, we can obtain anomaly correlation over 0.7 if we have roughly more than 10 profiles (yellow colors) in the e-folding ellipsoid. Volume of the e-folding ellipsoid (10 6 m 2 ) 15

16 3. Estimation of Analysis Errors in a 4DVAR system using BFGS formula

17 17 BFGS Formula used in the quasi-newton Method One of major algorisms used for minimizing the cost function in 4DVAR systems is a quasi- Newton method. In quasi-newton methods, the inverse Hessian of the cost function, which is equal to the analysis error covariance matrix, is approximately calculated by the BFGS formula and used for acceleration of convergence. BFGS Formula ) ( ) (, where ) ( ) ) ( )( ) ( (,,,, b a b a T T T T T T x g x g y x x p p p y p p y y p I y p y p I D If you have several pairs of (p, y ), you can calculate the inverse Hessian approximately by starting from an appropriate matrix as D 0 and updating it by the formula above. In quasi-newton methods, the corrections of x in a single iteration step are used as p, and the identical matrix is used as D 0 in general. However, the analysis error covariance matrix calculated in the quasi-newton method does not have a good accuracy.

18 Estimating the Inverse Hessian using ensemble members Cost function Hessian of J: J ( x) ( B 1 ( x x 2 ( x x The Hessian does not depend on x b and Δy. H 1 T 1 b H) ) T B 1 b ) 1 ( Hx y) 2 ( Hx y) If we have ensemble members of x b and Δy (i.e., perturbed observation and bacground), we can generate multiple new cost functions who have a common Hessian. If we minimize those cost function simultaneously, we can get pairs of (p, y ) from all ensemble members and can use in BFGS formula to estimate the common Hessian (i.e., the analysis error covariance matrix). Perturbed observation, bacground R T T R 1 In practice, we add some modifications to the BFGS formula. 4DVAR 4DVAR 4DVAR 4DVAR BFGS Formula With those modifications, it can be theoretically proven that the inverse Hessian is perfectly estimated if we have the same number of the pairs of (p, y ) as the number of observations. Analysis Error Covariance Matrix 18

19 Example: Estimation in Western North Pac. 4DVAR System. Error Reduction Ratio (ERR)= (Bacground error Analysis error)/bacground error 500m T ERR, Oct1st-10 th, 2010, 20 members, 600 pairs Large impacts can be seen Kuroshio Extension Area where the Kuroshio large meander can develop. Japan Sea (Especially western part) East of Taiwan Central Subarctic Region

20 Dependency on the number of pairs (500m T ERR) 1 member, 41 pairs 7 members, 189 pairs 20 members, 420 pairs 3 members, 96 pairs 12 members, 276 pairs 20 members, 600 pairs ERR is underestimated when the number of the pairs is small. If we have more ensemble members, we can obtain more pairs. Increasing the number of the pairs (ensemble members) is very effective.

21 Impact of a specific type of observation data (500m T) Error reduction ratios are calculated for following 4 cases. 1. ALL: All data is assimilated 2. No-Insitu: In-situ profiles are withheld 3. No-Argo: Argo profiles are withheld. 4. No-Alti: Altimetry data are withheld. Then we tae differences in order to examine the impact of a specific type of observations. Impact of Argo profiles (ALL ERR No-Argo ERR) Impact of In-situ profiles (ALL ERR No-Insitu ERR) Impact of Altimetry data (ALL ERR No-Alti ERR) The impacts of Argo mainly reflects the distribution of the floats. But it is especially large in the Japan Sea. Impacts of ship observations can be seen along the southern and eastern Japan coasts, east of Taiwan, and a part in the central subarctic region. Impact of Altimetry data is broadly distributed, but absent in the Japan sea, near the Japan coast, and east of Taiwan.

22 Summary

23 Summary 1. Recent development of DA systems in JMA/MRI 4DVAR Analysis model + Forecast model (Similar to the increment method) 4DVAR optimization starts from a 3DVAR results Sea Ice Concentration data are assimilated through the sea ice 3DVAR scheme in the new system for the seasonal predictions 2. Evaluation of ARGO networ using space-time correlation scale statistically estimated from SLA data Effectiveness of the Argo networ can be assessed by the number of profiles in the e-folding ellipsoid based on statistics of SLA data See Kuragano et al. 2015, doi: /2015JC Estimation of Analysis Errors in a 4DVAR system using BFGS formula It is possible to estimate analysis error covariance matrix through a quasi- Newton method if we use ensemble information. But the method needs more brush-up. 23

24 Than you

25 Bacups

26 Comparison of 3DVAR and 4DVAR Red: in situ observation by onboard ADCP at 97 m depth. Blue: Current fields in the 4DVAR and 3DVAR reanalyses. The current direction is opposite. The shape of the eddy reproduced by 4DVAR coincides well with observation.

27 Evaluation of currents against observation data the current fields are well improved by 4DVAR particularly in areas where temperature stratification is dominant. Histogram of current speed 4DVAR 3DVAR 4DVAR 3DVAR 27

28 Improvement of Kuroshio variations in 4DVAR 28

29 Southward intrusion of Oyashio at 2005 SST at Mar. 7 th, 2005 MODIS 4DVAR The model reproduces southward intrusion of Oyashio to 37.2ºN observed by MODIS. Kuroshio extension is also well reproduced. From the web page of EORC: The Oyashio area is not so large because the intrusion is narrow 年 29

30 4DVAR と 3DVAR の比較 ( 赤道太平洋 OHC ホフメラー ) 3DVAR 4DVAR 概ね一致している 4DVAR の方がメリハリがある?

31 赤道 - 東経 165 度の TAO の水温との比較 4DVAR の方が短周期の変動の再現性が高く精度が良い

32 Analysis Model Resolution 1º º Forecast Run Forecast Model Resolution 0.25º 0.25º Sea Ice Concentration Sea Ice 3DVAR Forecast Run Temp. Sal. SSH Ocean 3DVAR Ocean 4DVAR TS fields Sea Ice 3DVAR IAU Sea Ice Concentration Assimilation Run Assimilation Run

33 Evaluation of Argo Networ Density of Argo floats ( ) The number of Argo in the ellipsoid is relatively large in the But we should note that what is the target we When we estimate SLA using dynamic heights from Argo profiles through spatialtemporal OI, we can obtain anomaly correlation over 0.7 if we have roughly more than 10 profiles in the e-folding Actual number of Argo Profiles in the e-folding ellipsoid ellipsoid. 33