Status of radiance assimilation using total moisture variable in NCEP-GSI

1. Status of radiance assimilation using total moisture variable in NCEP-GSI Emily, H. C. Liu1,6,Min-Jeong Kim2,4 & Yanqiu Zhu1,5 John Derber1& Andrew Collard1,5 Will McCarty3 1NOAA/NCEP/EMC, 2NOAA/NESDIS 3NASA/GSFC/GMAO,4CIRA, 5IMSG, 6SRG

2. Outline • Background • Choice of control variable • GFS moist physics • Implementation in GSI • Future work

3. Background advantage • Total water (qT=qv+qc) as control variable • Reduce the dimension ---> computationally efficient • Condensation/evaporation rapidly converts between humidity and cloud water, but total water is more constant in time ---- more linear • Change in total water is spatially more homogeneous than in cloud water ---> has a simpler error characteristics • Need to separate total water increment (dqT) into water vapor increment (dqv) and cloud water increment (dqc) in the minimization • The GSI minimizes a quadratic cost function (J) and requires that background error (B) and observation error (R) are Gaussian + where k is the outer loop index and matrix is the Jacobianof linearized about disadvantage

4. Choice of Control Variables • Find a form of total water (control variable) with its error distribution Gaussian (in practice, closer to Gaussian) • The background errors are directly related to the forecast differences in that if the forecast differences are Gaussian, so are the background errors. • 60 pairs of 24 and 48-hour forecasts from GFS were used to study the error distribution of total water (NMC method) dX(t)=X24-X48 t-24 t-48 t X24: 24 hr forecast valid @ t X48: 48 hr forecast valid @ t

5. Following Elias Holm’s work on the construction of a Gaussian control variable for humidity, a symmetrizing transformation is performed on the total water variable to avoid bias and asymmetry. Choice of Control Variables (2) +

6. Choice of Control Variables (3)

7. Scaled Total Water Choice of Control Variables (4)

8. Water Vapor GFS moist physics Convective Condensation (Cb) Large-scale Condensation (Cg) Cloud Evaporation (Ec) Evaporation of Snow (Ers) Evaporation of Rain (Err) • The tangent-linear (TL) and adjoint (AD) of full GFS moist physics are under development and validation. • Using TL and AD of GFS moist physics for partitioning qtot increment into individual qc and qv increment. Cloud Water Autoconversion (Praut) Autoconversion (Psaut) Aggretation (Psaci) Ice Water Liquid Water Accretion (Pracw) Accretion (Psacw) Melting (Psm1) Rain (Pr) Snow (Ps) Melting (Psm2) Falling out Falling out

9. Increment in control space and Implementation Variable transformation from control to state Add partitioning of into & Adjoint of variable transformation from control to state Add adjoint of partitioning into & Minimization Algorithm (CG) Horizontal interpolation to observation location Updated increments Adjoint of horizontal interpolation to observation location Radiativetransfer ( ) Variable transformation & Partitioning Updated guess Adjoint of radiative transfer Simulated radiances ) Observed radiances

10. Future Work • Study the behavior of Jacobians from the GFS moist physics for various atmospheric conditions • Partitioning of into and using TL & AD of full GFS moist physics • Test total water control variable with AMSU-A for non-precipitating clouds over ocean only using current B (qoption=2 for normalized relative humidity) • Construction of new B for qtot (GMAO) • Validate results in global GFS (convergence in the minimization, the fit of the updated guess profiles to observations, …etc.) • Test and validate results in HWRF

11. Future Work (2) GSI in HWRF