Progress in Cloudy Microwave Satellite Data Assimilation at NCEP Andrew Collard 1, Emily Liu 4, Yanqiu Zhu 1, John Derber 2, Daryl Kleist 3, Rahul Mahajan NOAA/NWS/NCEP 3 Univ. Of Maryland 4 24 February NOAA Satellite Science Week

Outline 3DEnsVar and 4DEnsVar Cloud Information in Ensembles Assimilating Cloudy Microwave Radiances Conclusions 24 February 2015 NOAA Satellite Science Week2

Outline 3DEnsVar and 4DEnsVar Cloud Information in Ensembles Assimilating Cloudy Microwave Radiances Conclusions 24 February 2015 NOAA Satellite Science Week3

 f &  e : weighting coefficients for fixed and ensemble covariance respectively x t ’: (total increment) sum of increment from fixed/static B (x f ’) and ensemble B a k : extended control variable; :ensemble perturbations - analogous to the weights in the LETKF formulation L: correlation matrix [effectively the localization of ensemble perturbations] T: operator mapping from ensemble grid to analysis grid GSI Hybrid [3D] EnVar (ignoring preconditioning for simplicity) Incorporate ensemble perturbations directly into variational cost function through extended control variable –Lorenc (2003), Buehner (2005), Wang et. al. (2007), etc.

Hybrid 4D-Ensemble-Var [H-4DENSV] The 4DENSV cost function can be easily expanded to include a static contribution Where the 4D increment is prescribed exclusively through linear combinations of the 4D ensemble perturbations plus static contribution Here, the static contribution is considered time-invariant (i.e. from 3DVAR- FGAT). Weighting parameters exist just as in the other hybrid variants. Again, no TLM or ADJ (so this is NOT 4DVar)!

Hybrid 4D-Ensemble-Var [H-4DENSV] The 4DENSV cost function can be easily expanded to include a static contribution Where the 4D increment is prescribed exclusively through linear combinations of the 4D ensemble perturbations plus static contribution Here, the static contribution is considered time-invariant (i.e. from 3DVAR- FGAT). Weighting parameters exist just as in the other hybrid variants. Again, no TLM or ADJ (so this is NOT 4DVar)!

3DVar vs 3DHybrid vs 4DHybrid Northern Hemisphere Southern Hemisphere 4DHYB-3DHYB 3DVAR-3DHYB Move from 3D Hybrid (current operations) to Hybrid 4D-EnVar yields improvement that is about 75% in amplitude in comparison from going to 3D Hybrid from 3DVAR. 4DHYB DHYB DVAR DHYB DHYB DVAR ----

Outline 3DEnsVar and 4DEnsVar Cloud Information in Ensembles Assimilating Cloudy Microwave Radiances Conclusions 24 February 2015 NOAA Satellite Science Week8

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11 24 February 2015 NOAA Satellite Science Week

Outline 3DEnsVar and 4DEnsVar Cloud Information in Ensembles Assimilating Cloudy Microwave Radiances Conclusions 24 February 2015NOAA Satellite Science Week 12

Properties of AMSU-A Radiances Ch February 2015 NOAA Satellite Science Week 13 AMSU-A sensors see deep into the clouds, giving iinformation on temperature, moisture and cloud structure. Much less sensitive to ice clouds Large temperature sensitivity where the cloud peaks

Properties of AMSU-A Radiances Ch. 1 We now ensure non-zero cloud Jacobians even where cloud is absent from background 24 February 2015 NOAA Satellite Science Week 14 AMSU-A sensors see deep into the clouds, giving iinformation on temperature, moisture and cloud structure. Much less sensitive to ice clouds Large temperature sensitivity where the cloud peaks

Properties of AMSU-A Radiances Ch. 1 This looks odd: Ask me! We now ensure non-zero cloud Jacobians even where cloud is absent from background Broad Jacobians mean we need good background error information to put increments in the right place in the vertical 24 February 2015 NOAA Satellite Science Week 15 AMSU-A sensors see deep into the clouds, giving iinformation on temperature, moisture and cloud structure. Much less sensitive to ice clouds Large temperature sensitivity where the cloud peaks

Observation Error for AMSU-A under All-sky Conditions  Observation error is assigned as a function of the symmetric cloud amount  Gross check ±3 of the normalized FG departure (accept Gaussian part of the samples) Before QC After QC Error Model Obs. error used in the analysis 16 Non-precipitating Samples Normalized by std. dev. of the OMF in each symmetric CLWP bin Gaussian Un-normalized Normalized

Clear-sky vs. All-sky  Thick clouds that are excluded from clear-sky assimilation are now assimilated under all-sky condition  Rainy spots are excluded from both conditions Clear-sky OMF All-sky OMF 24 February 2015 NOAA Satellite Science Week17

First Guess Analysis First Guess Analysis

Outline 3DEnsVar and 4DEnsVar Cloud Information in Ensembles Assimilating Cloudy Microwave Radiances –Analysis Increments Conclusions 24 February 2015 NOAA Satellite Science Week19

Clear sky increments: Cloud increments come from correlations in the ensembles

All sky increments: Additional cloud increments from cloudy microwave observations.

Outline 3DEnsVar and 4DEnsVar Cloud Information in Ensembles Assimilating Cloudy Microwave Radiances –Retention through the forecast Conclusions 24 February 2015 NOAA Satellite Science Week 22

First Guess

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F02

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Analysis - Guess vs. F00 - Guess 3DEnsVar prexp02e Cloud Water Mixing Ratio

Analysis - Guess

F00 - Guess

Impact – 500hPa Height Clear Sky Cloudy Radiance Clear Sky Cloudy Radiance N. HemisS. Hemis -ve means positive impact 24 February 2015 NOAA Satellite Science Week39

Conclusions Cloud background error information from the 3DEnsVar and 4DEnsVar hybrid systems provides detailed flow-dependent covariances needed for microwave cloudy assimilation. “Spin-down” still occurs in the first model cycle after assimilation. This can be minimized through appropriate bias correction and quality control Assimilation of all-sky microwave radiances is providing small positive impact. 24 February 2015 NOAA Satellite Science Week40

4D EnVar: Way Forward Natural extension to operational EnVar –Uses variational approach in combination with already available 4D ensemble perturbations (covariance estimates) No need for development of maintenance of TLM and ADJ models –Makes use of 4D ensemble to perform 4D analysis –Very attractive, modular, usable across a wide variety of applications and models Highly scalable –And can be improved even further –Aligns with technological/computing advances Computationally inexpensive relative to 4DVAR (with TL/AD) –Estimates of improved efficiency by 10x or more, e.g. at Env. Canada (6x faster than 4DVAR on half as many cpus) Compromises to gain best aspects of (4D) variational and ensemble DA algorithms Other centers pursuing similar path forward for deterministic NWP –Canada (replace 4DVAR), UMKO? (ensemble of 4D Ensemble Var)

Hybrid ensemble-4DVAR [H-4DVAR_AD] Incremental 4DVAR: bin observations throughout window and solve for increment at beginning of window (x 0 ’). Requires linear (M) and adjoint (M T ) models Can be expanded to include hybrid just as in the 3DHYB case With a static and ensemble contribution to the increment at the beginning of the window ADJ TLM

4D-Ensemble-Var [4DENSV] As in Buehner (2010), the H-4DVAR_AD cost function can be modified to solve for the ensemble control variable (without static contribution) Where the 4D increment is prescribed exclusively through linear combinations of the 4D ensemble perturbations Here, the control variables (ensemble weights) are assumed to be valid throughout the assimilation window (analogous to the 4D-LETKF without temporal localization). Note that the need for the computationally expensive linear and adjoint models in the minimization is conveniently avoided.