Model Parameter Estimation Using Ensemble Data Assimilation

－A Case with the NICAM and GSMaP －

RISDA2017-7thDAWS, March 2, 2017 @ Kobe, Japan

Shunji Kotsuki1, Koji Terasaki1, Hisashi Yashiro1,Hirofumi Tomita1, Masaki Satoh2, and Takemasa Miyoshi1,3

1Data Assimilation Research Team, RIKEN-AICS, Japan2The University of Tokyo, Japan

3University of Maryland, College Park, Maryland, USA

GSMaP: Global Satellite Mapping of Precipitation

Goals

• To improve NWP using satellite-derived precipitation following Lien et al. (2013, 2016a,b)

• To produce a new precipitation product through data assimilation

Improvement achieved with GFS-LETKF(U-wind @ 500 hPa)

Lien et al. (2016)Radiosondes ONLY

Radiosondes+Precip.(No-Transform)

Radiosondes+Precip.(Log-Transform)

Radiosondes+Precip.(Gaussian-Transform)

Goals

• STEP1: State Estimation

• STEP2: Parameter Estimation

Kotsuki S., Miyoshi T., Terasaki K., Lien G.-Y. and Kalnay E. (2017): Assimilating the Global Satellite Mapping of Precipitation Data with the Nonhydrostatic Icosahedral Atmospheric Model NICAM. JGR-Atmospheres

• To improve NWP using satellite-derived precipitation following Lien et al. (2013, 2016a,b)

• To produce a new precipitation product through data assimilation

Experimental Setting

• Numerical Model– NICAM (Satoh and Tomita 2004, Satoh et al. 2008, 2014)

• GL6 (approx. 110 km resolution)

• Observations– CTRL: PREPBUFR: only upper sounding data (ADPUPA)– TEST: ADPUPA + GSMaP_Gauge (Ushio et al. 2009)

• with Gaussian transformation

• Data assimilation– LETKF (Hunt et al. 2007)– NICAM-LETKF (Terasaki et al. 2015) with 36 members

• 3D-LETKF• Localization: 400 km (horizontal) & 0.4 lnp (vertical)• Relaxation to prior perturbation (Zhang et al. 2004; α = 0.7)

Gaussian Transformation

NICAM(orig) GSMaP(orig)

mm/6hr mm/6hr

Gaussian Transformation 1 1G G GF y F y y F F y y F F y

　　 　 　　 　

Forward transform (mm/6hrsigma) Inverse transform (sigmamm/6hr)

()GF()F : CDF of Gaussian distribution: CDF of original variable y : original variable (mm/6hr) y : Transformed variable (sigma)

ー: Modelー: Obs.

PDF

CDF

Original variable Transformed variable Lien et al. (2013, 2016)

Step 0: Obtain PDF & CDF

Step 1: Compute

Step 2: Compute

( )F y

1Gy F F y

Obs ȳ

Model ȳ

CDF

Obs F(y)

Model F(y)

e.g., y =1mm/6hr

Spin-up period Experiment

T=1

① to produce PDF/CDF

② Gaussian-Transformation

③ Data Assimilation

T=330days samples

T=2

PDF/CDF construction

mm/6hr mm/6hr

NICAM(orig) GSMaP(orig)

sigma

NICAM(Gauss)

Transformation(Model CDF)

sigma

GSMaP (Gauss)

Transformation （Obs. CDF)

Gaussian Transformation

average: sigma: skewness: kurtosis:

-0.0150.7290.4180.696

sigma

average: sigma: skewness: kurtosis:

0.0802.8376.37293.91

mm/6hr

w/wo Gaussian Transformation

Obs-Guess(GT)

Obs-Guess(orig)

Sampling period : 2014110100 - 2014110118

wo Gaussian-Transformation w Gaussian-Transformation

More Gaussian

Inverse Transformation 1 1G G GF y F y y F F y y F F y

　　 　 　　 　

Forward transform (mm/6hrsigma) Inverse transform (sigmamm/6hr)

()GF()F : CDF of Gaussian distribution: CDF of original variable y : original variable (mm/6hr) y : Transformed variable (sigma)

ー: Modelー: Obs.

PDF

CDF

Original variable Transformed variable Lien et al. (2013, 2016)

Step 0: Obtain PDF & CDF

Step 1: Compute

Step 2: Compute

( )F y

1Gy F F y

mm/6hr

GSMaP(orig)

mm/6hr

NICAM(orig)

NICAM(Gauss)

Transformation(Model CDF)

Forward/Inverse Transformations

GSMaP-like NICAM

Inverse Transformation(Obs. CDF)

sigma

mm/6hr

NICAM Ensemble Forecast

Observation operator

LETKF,f aX : guess, analysis

(ensemble)

oy : observationH : obs. operator

aX fX

fX

&o fHy X

Assimilation of GSMaP by NICAM-LETKF

NICAM Ensemble Forecast

Observation operator

LETKF

QC & Gaussian Transform.

,f aX : guess, analysis(ensemble)

oy : observationH : obs. operator

GSMaP(NICAM grid)

GSMaP(original)

Pre-process

aX fX

fX

&o fHy X

Assimilation of GSMaP by NICAM-LETKF

Inverse Transformation

Assimilated precipitation

RMSDs relative to ERA Interim (in 2014)

Spin-up period

ー: CTRL: Radiosondes ONLYー: TEST: Radiosondes + GSMaP/Gauge (every 5x5 grids)

Improved!!

MADs relative to ERA Interim (in 2014)

U V

T Q

Improved by GSMaP DA Degraded by GSMaP DA

120 hr Forecasts vs. GSMaP/Gauge

Threat Score ( ≥ 1 mm/6hr )

Precipitation forecasts are improved !!!

Average over 8 ensemble forecasts from different initial dates

ー: Radiosondes ONLYー: Radiosondes + GSMaP/Gauge

Threat Score (≥ 5 mm/6hr )

Improved!! Improved!!

Outline

• STEP1: State Estimation

• STEP2: Parameter Estimation

Parameter Estimation in NICAM-LETKF

Online!

Estimated Parameter (large scale condensation)

Berry’s parameterization (warm rain) : Takemura et al. (2005, 2009), Berry (1967)21

2 3 c

B lP NB Bl

ρ : air density P: precipitation ratel : cloud water mixing ratioNc: total number of cloud droplet

max min1 1 12paramX B B

〇 Maintaining ensemble spread of parameter RTPS with α=1

〇 Avoiding excess of parameter range

paramX : parameter used for ETKF: parameter used for FCST

paramX

1 paramB Xmin1B max1B

1 paramB X

max min1 tanh 1 12 paramX B B

Estimated Parameter (large scale condensation)

Ensemble mean and spread of estimated parameters

paramX

: mean : spread

1 paramB X

Change in precipitation fields (2014/06/16)

CTRL GSMaP Gauge (OBS)

TEST (w/ parameter DA)

mm/6h

6-h precip. FCST improved

BIAS Threat Score (> 10 mm/6h)

Precipitation forecasts are improved !!!

ー: CTRLー: TEST (w/ Parameter Estimation)

Change in BIAS vs. ERA Interim (2014/06-2014/12)

improved improved degradeddegradedK g/kg

T Q

ABS(TEST-ERA) – ABS(CTRL-ERA)

Change in BIAS vs. ERA Interim (Average)

less cloudymore cloudy better worse

OLR was degraded. B1 was estimated to fit to GSMaP

Summary

• Assimilating GSMaP data with NICAM-LETKF– State estimation

• Gaussian Transformation worked well• Analyses and forecasts were improved

– Parameter estimation• Precipitation forecasts were improved• Dry bias in the lower troposphere was improved• But, OLR was degraded

– Future plan• Estimate B1 parameter to fit with different references

Kotsuki S., Miyoshi T., Terasaki K., Lien G.-Y. and Kalnay E. (2017): Assimilating the Global Satellite Mapping of Precipitation Data withthe Nonhydrostatic Icosahedral Atmospheric Model NICAM. JGR-Atmosphere