1

Xuguang Wang, Bo Huang, Jie Feng, Yongming Wang

Multiscale data Assimilation and Predictability (MAP) LabUniversity of Oklahoma, Norman, OK, USA

xuguang.wang@ou.eduhttp://weather.ou.edu/~map

Daryl Kleist and Ting LeiNOAA/NCEP/EMC, College Park, MD, USA

D

UFS workshop, July, 2020

Recent Development of Simultaneous Multiscale Data Assimilation in Hybrid EnVar for FV3-based

Global Forecast System (GFS) and Convection Allowing Regional Prediction System

Acknowledgement: NOAA/EMC: Fanglin Yang, Vijay TallapragadaNOAA/ESRL: Jeff Whitaker, Curtis Alexander

Multiscale data assimilation (MDA)

https://www.gfdl.noaa.gov/fv3/fv3-applications/fv3-full-physics-cloud-permitting-simulation/

-5/3

• An effective next generation data assimilation system is required to analyze the state and its uncertainty across multiple scales, which hereafter is termed as “multiscale data assimilation (MDA)”

Chipilski and Wang (2020)

Sequential vs simultaneous multiscale DA

Sequential MDA Different obs assigned different influence radii (localization scale) when

sequentially assimilated Neglect each obs. contains useful info on errors at all resolved scales.

Simultaneous MDA Ensemble background error covariance(BEC) needs to be constructed to

properly reflect multiscale errors and their interactions. All obs are assimilated at once.

An example: construction of multiscale ensemble BEC through scale aware localization (e.g. Buehner and Shlyaeva 2015).

Allow to more effectively correct the full range of resolved scales with all available obs.

Simultaneous MDA in EnVar for global and convective scale NWP

4

We implemented simultaneous MDA in GSI 4DEnVar by forming multiscale ensemble BEC with scale aware localization extending from the extended control variable (ECV) approach in GSI EnVar(GSI ECV, Wang 2010)

Outline

o Part I (Huang*, Wang, Kleist and Lei 2020)• Simultaneous MDA w/o cross band correlations for FV3GFS

4DEnVar

o Part II (Feng* and Wang 2020)• Further development of FV3GFS MDA to include vertical

dimension

o Part III (Wang* and Wang 2020)• Simultaneous MDA in EnVar for convective scale prediction

5

Exps HL(e-folding dis.)

VL(scale height, e-folding dis.)

W1-Ope Level-dependent localization length (black curve) 0.5

W1-1000 1000 km for full scales 0.5

W1-300 300 km for full scales 0.5

W2-NoCross 1000/300 km forlarge/small scales 0.5

W2-Cross 1000/300 km forlarge/small scales 0.5

W3-NoCross 1000/650/300 km forlarge/medium/small scales 0.5

W3-Cross 1000/650/300 km forlarge/medium/small scales 0.5

Part I: 5-week Cycled Simultaneous MDA 4DEnVar Experiment for NCEP FV3GFS

-

6

W2 versus W1--- Single observation experiment

W1-1000 W1-300

W2-NoCross W2-Cross

W2-Cross-Uni

Applying the same amount of localization (1000km) at different wavebands in W2-Cross-Uni reproduces the analysis increment pattern in W1-1000, consistent with the theory.

W1-300 shows the most restricted analysis increment pattern.

Compared to W2-NoCross, W2-Cross is able to maintain two increment maxima as W1-1000, due to its inclusion of cross-waveband covariances,

7

Tempat 500 hPa

Among W1 experiments, wider localization length results in larger analysis increment power.

As expected, analysis increment power in W2-NoCross and W2-Cross is closer to W1-1000 (W1-300) at small (large) total wavenumbers.

Windat 500 hPa

W2 versus W1---Analysis Increment Power

8

W2 versus W1--- 6-hour background forecast verification

against rawinsondes

Temp Wind

W1-1000 shows the largest forecast error almost at all model levels, while W1-300 shows comparable or slightly improved background forecasts below 100 hPa in contrast to W1-Ope.

W2 improves the background forecasts over W1-Ope at most model levels.

RMSE difference relative to W1-Ope(negative/positive improvement/degradation relative to W1-Ope)

9

W2 versus W1--- 5-day global forecast verification

against EC reanalysisRMSE difference (blue/red improvement/degradation relative to W1-Ope)

Tem

pW

ind

W1-1000 in general degrades global forecasts compared to W1-Ope. Compared to W1-Ope, W1-300 shows degraded temperature forecasts above 150 hPa over five days, but slightly improved wind forecasts below 50 hPa within two days.

W2 SDL improves global forecasts almost at all pressure levels and lead times compared to W1-Ope.

W1-1000−

W1-Ope

W1-300−

W1-Ope

W2-NoCross−

W1-Ope

W2-Cross−

W1-Ope

10

W2-Cross versus W2-NoCross--- 5-day global forecast verification

against EC reanalysis

RMSE difference between W2-Cross and W2-NoCross(blue/red better/worse forecasts in W2-Cross)

W2-NoCross shows slightly better forecasts than W2-Cross within one day. This may benefit from the spatial averaging of ensemble covariances in SD-NoCross.

Beyond one-day, W2-Cross in general shows more accurate forecasts than W2-NoCross, likely contributed by its higher degrees of retained heterogeneity of ensemble covariances and its more balanced analysis through including cross-waveband covariances.

W2-Cross−

W2-NoCross

Tem

pW

ind

11

Compared to W1-1000 and W1-300 that show limited improvement than W1-Ope at a subset of total wavenumbers, SDL improves over W1-Ope almost at all total wavenumbers, especially when applying SDL-Cross.

Global forecast error power spectra

12

Part II: Further development of MDA with vertical dimension

Corr

Sigm

a le

vel

Corr

Global mean vertical corr of U Vertical corr of U @ hurricane grid

— H(L)V— H(L)V(L)— H(L)V(S)

- - -H(S)V- - -H(S)V(L)- - -H(S)V(S)

4DEnVar MDA code is extended to include vertical dimension

13

Horizontal band

Vertical band

Horizontal localization

Vertical localization

Noloc 1 1

H2V1 2 1 1000; 300 km -0.5; -0.5

H2V2_0.5 2 2 1000; 300 km -0.5; -0.5; -0.5;-0.5

H2V2_2.0 2 2 1000; 300 km -2.0; -2.0; -2.0; -2.0

H2V2_2.0_0.5 2 2 1000; 300 km -2.0; -0.5; -2.0; -0.5

Select two grid pointsA : hurricaneB : Subtropical high

Experimental designof one obs test

obs@850hPa for V

Single obs test

14

One obs analysis increment

• Analysis increment of H2V1-0.5 same as H2V2-0.5, consistent with theory• Analysis increment vertical extent : H2V2-0.5 < H2V2-2.0-0.5 < H2V2-2.0

Hurricane Subtropical High

15

Cycling FV3GFS 4DEnVar MDA experiments

Diff of abs(O-B) of CSDL_H2V2 and from CSDL_H2V12017083000-2017090606

U T

Vertical scale-dependent localization has better 6-hr forecasts.

Scale-dependent Covariance Localization for FV3GDAS 4DEnVar Data Assimilation System to Improve Global and Hurricane Predictions

PI: Xuguang Wang, University of Oklahoma

Summary of delivery, outcome, accomplishments:

• Developed and implemented both the horizontal and vertical simultaneous multiscale DA (MDA) in operational 4DEnVar system

• Cycled DA experiments with FV3GFS demonstrated that horizontal MDA improved global forecasts relative to the operational non-MDA configuration

• MDA including vertical dimension shows promises to further improve global forecast

W2-Cross − W1-Ope

Tem

pW

ind

Part III: Simultaneous MDA in EnVar for convective scale NWP

17

• An isolated supercell case that produced F-4 intensity tornadoes in Moore and Oklahoma City (OKC) during about 2210—2240 UTC.

• Supercell maintained well beyond 2300 until about 0000 UTC.

Path of the May 8, 2003 Moore-South OKC Area Tornado

22:00 UTC 08 Mayhttp://www.srh.noaa.gov

18

Increments of convergence(colors) and wind (vector) @ 1.5 km AGL valid at 2115 UTC 8 May 2003

Enhanced LLJ and convergence near storm

Disorganized convergence and divergence couplets near storm

Non-MDA MDA

Simultaneous MDA in EnVar for convective scale NWPCan radar obs correct both the storm and its embedded

environment?

19

Simultaneous MDA in EnVar for convective scale NWPCan radar obs correct both the storm and its embedded

environment?

Non-MDA MDA

Simultaneous MDA EnVar for storm scale prediction demonstrates the power of the method in correcting multi-scales simultaneously with a single source of data

m/s

20

OU MAP short and long term MDA plan

• Continue experiments to optimize vertical MDA in FV3GFS

• Address multi-scale DA by integration with multi-resolution (Kay and Wang 2020 MWR)

• Develop new multiscale DA algorithms in pure ensemble filter

• Objective methods to determine scale separation and localization

• Application of multiscale DA algorithms for MRW, Hurricane, CAM predictions

References*students and postdocs authors

21

Wang, X., 2010: Incorporating ensemble covariance in the Gridpoint Statistical Interpolation (GSI)variational minimization: a mathematical framework. Mon. Wea. Rev., 138, 2990-2995.

Wang, X., D. Parrish, D. Kleist, and J. Whitaker, 2013: GSI 3DVar-based ensemble-variationalhybrid data assimilation for NCEP Global Forecast System: single resolution experiments. Mon.Wea. Rev., 141, 4098-4117.

Wang, X. and T. Lei*, 2014: GSI-based four dimensional ensemble variational data assimilation (4DEnsVar): formulation and single resolution experiments with real data for NCEP GFS. Mon. Wea. Rev., 142, 3303-3325.

Kay, J.*, X. Wang, 2020: A multi-resolution ensemble hybrid 4DEnVar for global numerical weather prediction. Mon. Wea. Rev., 148, 825-847.

Huang, B.*, X. Wang, D. Kleist and T. Lei, 2020: Simultaneous multi-scalde data assimilation with and without cross band correlations for NCEP FV3GFS 4DEnVar. Mon. Wea. Rev., submitted.

Feng, J.* and X. Wang, 2020: Simultaneous multiscale data assimilation with both horizontal and vertical dimensions. Mon. Wea. Rev., in preparation

Wang, Y.* and X. Wang, 2020: Can radar observations update both the storm and its embedded environment simultaneously? Mon. Wea. Rev., to be submitted

Computational Cost

22

Expts

Wall clock time in minutes in each of the four components in a single 4DEnvar DA cycle Total wall

clock time in

minutes

Total cost ratiorelative to W1EnVar

updateEnKFupdate

Control background

forecast

Ensemble background

forecasts

W1 15

7 3 45

70 1.0

W2 25 80 1.14

W3 35 90 1.28

23

By including the cross-waveband covariances, SDL-Cross is more balanced than SDL-NoCross.

By applying tighter horizontal localization at medium scale, W3 is less balanced than W2.

Analysis balance

24

W3 versus W2--- 5-day global forecast verification

against EC reanalysisRMSE difference (blue/red improvement/degradation relative to W2)

Temp Wind

W3 in general shows worse global forecasts than W2 above 50 hPa.

W3 slightly improves the global forecasts at least to three days below 50 hPa.

Degraded global forecasts of W3-Cross versus W2-Cross below 50 hPa beyond three days may be associated with its less balanced analysis.

W3-

NoC

ross

−W

2-N

oCro

ss

W3-

Cro

ss−

W2-

Cro

ss