Ionospheric weather revealed by COSMIC missions with the GSI Ionosphere data assimilation system

Chih-Ting Hsu1, Tomoko Matsuo1, Jann-Yenq Liu2

1 Aerospace Engineering, University of Colorado at Boulder 2 Institute of Space Science, National Central University, Taiwan

What is Ionospheric Data

Assimilation?

(A) Model - Evaluate the role of T-I

coupling on ionospheric NWP

FORMOSAT-3/COSMIC FORMOSAT-7/COSMIC-2

(B) Data – Evaluate the role of RO sTEC on

ionospheric NWP

(C) Ionospheric specification

revealed by GSI Ionosphere

a. Observationb. Modelc. Data assimilation scheme

Time

Observation

Analysis step

Forecast stepForecast step

Analysis step

Thermosphere Ionosphere

𝑁: Plasma density𝑄: production rate (dominated by photoionization)

𝐿: loss rate (dominated by chemical processes in the ionosphere)𝒗: plasma drift velocity

𝑦𝑚𝑜𝑑𝑒𝑙 − 𝑦𝑜𝑏𝑠

𝑖𝑛𝑐𝑟𝑒𝑎𝑚𝑒𝑛𝑡: ∆𝑦

y

Likelihood 𝑦

Prior 𝑦𝑚𝑜𝑑𝑒𝑙

Posterior 𝑦𝑚𝑜𝑑𝑒𝑙

• Basic ideal of deterministic update in the EnKF according to the Bayes’ theorem

• 𝑦𝑚𝑜𝑑𝑒𝑙 = 𝐇(x)

1. Data assimilation cycle

2. Data assimilation scheme

3. Model and Observation

a. Observation: COSMIC EDPb. Model: TIE-GCMc. Data assimilation scheme: EnKF (DART)d. Experiment: Observing System

Simulation Experiment (OSSE) a. Observation: COSMIC & COSMIC-2 RO sTECb. Model: GIP/TIE-GCMc. Data assimilation scheme: EnKF (GSI)d. Experiment: OSSE

a. Observation: COSMIC RO sTECb. Model: GIP/TIE-GCMc. Data assimilation scheme: EnKF (GSI)d. Experiment: Data Assimilation

1. The capability of the GSI Ionosphere to reproducerealistic ionospheric feature has be demonstratedby real FORMOSAT-3/COSMIC RO sTEC dataassimilation.

2. Accumulation of observation information can helpimproving ionospheric monitoring.

3. The GSI Ionosphere can effectively correct themodel state variables globally but has issues withlocal adjustment. These issues can be resolved byincreasing the data volume, implying the greatpotential of improving ionospheric NWP by usingFORMOSAT-7/COSMIC-2 data in the future.

C. Ionospheric specification revealed by GSI Ionosphere (real data assimilation)

AcknowledgmentThis study is supported by NASA award NNX14AI17G, AFOSR grant FA9550-15-1-0308,Taiwan Ministry of Science and Technology grant MOST 105-2119-M-008-020, and NationalSpace Organization grant NSPO-S-104083. We deeply thank to Dr. Wenbin Wang, Dr.Timothy Fuller-Rowell, Dr. Tzu-Wei Fang, Dr. Kayo Ide, Dr. Xinan Yue, Dr. Charles Chien-HungLin, Dr. Chia-Hung Chen, and Dr. Chi-Yen Lin for their valuable commends and suggestions.We also thank to the Institute for Mathematics Applied to Geosciences and COSMIC Officein University Corporation of Atmospheric Research and the Space Weather PredictionCenter in National Oceanic and Atmospheric Administration for their kindly help.

𝐿𝑣 (ln(mb)) 𝐿ℎ (km)

0.5 500

1 1,000

3 5,000

7 10,000

No localization No localization

𝜕𝑁

𝜕t= Q − 𝐿 − 𝛻 ∙ (𝑁𝒗)

LEO

GPS

Tangent Point

𝐿ℎ

𝐿𝑣

ത𝐱ka = ത𝐱k

b + 𝐊k(𝒚ko −𝐇kത𝐱k

b) – update of ensemble mean

𝐱′k,na = 𝐱′k,n

b + ෩𝐊k(−𝐇k𝐱′k,nb ) – update of each member

𝐊k = [𝛒kb ∘ 𝐏k

b𝐇kT ][𝛒k

o ∘ (𝐇k𝐏kb𝐇k

T) + 𝐑k]−1 - Kalman Gain

𝐏kb𝐇k

T~1

(N−1)σ𝑛=1𝑁 (𝐱k,n

b − ത𝐱kb) 𝐇k(𝐱k,n

b − ത𝐱kb)

𝑇

𝐇k𝐏kb𝐇k

T~1

(N − 1)

𝑛=1

𝑁

𝐇k(𝐱k,nb − ത𝐱k

b) 𝐇k(𝐱k,nb − ത𝐱k

b)𝑇

Approximated by model ensemble

• Ensemble Kalman Filter (EnKF)

Model Neutral-Ion coupled model1. TIE-GCM2. GIP/TIE-GCM

A. Evaluate the role of T-I coupling on ionospheric NWP

Observation COSMIC & COSMIC-2 Radio Occultation data1. Electron Density Profile

(EDP)2. Slant Total Electron

Content (sTEC)

B. Evaluate the role of sTEC on ionosphericNWP

Conclusions

𝑅𝑀𝑆𝐷 =σ𝑛=1𝑁 (𝑁𝑒𝑁𝑅 − 𝑁𝑒𝐷𝐴)

2

𝑁

A. A neutral-Ion coupled model can helpimprove ionospheric specification andforecasting.

B. GSI Ionosphere are able to assimilatesTEC and improve ionosphericspecification.

C. The GSI Ionosphere reveals a capabilityof monitoring and predictingionospheric weather by assimilatingreal data.1. By incorporating ion-neutral coupling

into the EnKF, the ionospheric electrondensity specification and forecasting canbe considerably improved.

2. Thermospheric composition is the mostsignificant state variable affecting theionospheric specification and forecasting.

3. Estimation of unobserved thermosphericvariables by the EnKF has a much longerlasting impact on the ionosphericforecast (>24 hours) than estimation ofionospheric variables (2 to 3 hours).

4. In the TIE-GCM, the effect of assimilatingelectron densities is not completelypassed to the forecast step unless thedensities of ion species are estimated.

RMSD

DART/TIEGCM

FORMOSAT-3/COSMIC and FORMOSAT-7/COSMIC-2

GNSS RO data

Thermosphere-ionosphere coupled model

Ionospheric numerical weather prediction

(NWP)

1. The GSI Ionosphere can improve the low- and mid-latitude ionosphericspecification.

2. For FORMOSAT-3/COSMIC RO sTEC, Localizing the impact of observationsaround the tangent points in the horizontal direction with a length scale of10,000 km is effective in improving assimilation analysis quality.

3. For FORMOSAT-7/COSMIC-2 RO sTEC, the horizontal localization length scaleof 5000 km is effective in improving assimilation analysis quality.

Exp. State vector

1 x= [𝑓𝑒−]

2 x= [𝑓𝑒−; 𝑓𝑂+]

3 x= [𝑓𝑒−; 𝑓𝑂+; 𝑓𝑇]

4 x= [𝑓𝑒−; 𝑓𝑂+; 𝑓𝑈; 𝑓𝑉]

5 x= [𝑓𝑒−; 𝑓𝑂+; 𝑓𝑂; 𝑓𝑂2]

6 x= [𝑓𝑒−; 𝑓𝑂+; 𝑓𝑇; 𝑓𝑈; 𝑓𝑉; 𝑓𝑂; 𝑓𝑂2]

7 x= [𝑓𝑒−; 𝑓𝑇; 𝑓𝑈; 𝑓𝑉; 𝑓𝑂; 𝑓𝑂2]

1. Purpose 1. Purpose

2. Experiment Design

2. Experiment Design

3. Result

3. Result

Control(100%)

Nature RunOSSE

(33%)

𝑚−3

GSI Ionosphere

ρ=GC(r) r : normalized distance𝐿ℎ: horizontal localization length scale𝐿𝑣: vertical localization length scale

sTEC – Not local (use tangent point as observation location)

EDP – Local dataNeed to assume electron density distribution is spherical symmetric

ReferenceHsu, C.-T., Matsuo, T., Wang, W. B., & Liu, J. Y. (2014). Effects of inferring unobserved

thermospheric and ionospheric state variables by using an Ensemble Kalman Filter on global ionospheric specification and forecasting. Journal of Geophysical Research-Space Physics, 119(11), 9256-9267. https://doi.org/10.1002/2014ja020390

Hsu, C.-T., Matsuo, T., Yue, X., Fang, T.-W.,Fuller-Rowell, T., Ide, K., & Liu, J.-Y.(2018). Assessment of the impact of FORMOSAT-7/COSMIC-2 GNSS RO observations on midlatitude andlow-latitude ionosphere specification:Observing system simulationexperiments using Ensemble SquareRoot Filter. Journal of Geophysical Research: Space Physics, 123, 2296–2314. https://doi.org/10.1002/2017JA025109

Thermosphere Ionosphere

Weak CouplingUn-updated variables evolve along with updated variables through physical processes in the model

Analysis step

Strong CouplingVariables x are update according to observation information

Increment with EnKF

Increment with EnKF, Localized by GC function

GSI Ionosphere

RMSD during forecast periodRoot Mean Square Difference (RMSD) during data assimilation period

FORMOSAT-3/COSMIC and FORMOSAT-7/COSMIC Coverage in an Hour

Horizontal Localization Horizontal Localization

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