Data Assimilation

Data Assimilation Andrew Collard

Overview • Introduction to Atmospheric Data Assimilation • Control Variables • Observations • Background Error Covariance • Summary NEMS/GFS Modeling Summer School

Introduction to Atmospheric Data Assimilation • The data assimilation step of the GFS system provides the initial conditions (“the analysis”) for a GFS forecast model run. • The analysis is obtained by optimally combining our best a priori knowledge of the atmosphere (through a short-range forecast) and a wide variety of observations of the atmospheric state. • This talk will focus on the operational hybrid EnKF/3DVar system. NEMS/GFS Modeling Summer School

Data Assimilation as part of the GFS Suite (1) NEMS/GFS Modeling Summer School

Data Assimilation as part of the GFS Suite (2) NEMS/GFS Modeling Summer School

The Cost Function J : Penalty (Fit to background + Fit to observations + Constraints) x’ : Analysis increment (xa – xb) ; where xb is a background Bvar: Background error covariance H : Observations (forward) operator R : Observation error covariance (Instrument + representativeness) yo’ : Observation innovations Jc : Constraints (physical quantities, balance/noise, etc.) 7

Overview • Introduction to Atmospheric Data Assimilation • Control Variables • Observations • Background Error Covariance • Constraints and Balance • Summary NEMS/GFS Modeling Summer School

Analysis variables • The analysis variables are • Streamfunction (Ψ) • Unbalanced Velocity Potential (χunbalanced) • Unbalanced Temperature (Tunbalanced) • Unbalanced Surface Pressure (Psunbalanced) • Ozone – Clouds – etc. • Satellite bias correction coefficients DTC – Summer Tutorial

Analysis variables • χ = χunbalanced + A Ψ • T = Tunbalanced + B Ψ • Ps = Psunbalanced + C Ψ • Streamfunction is a key variable defining a large percentage T and Ps (especially away from equator). Contribution to χ is small except near the surface and tropopause. DTC – Summer Tutorial

Analysis variables • A, B and C matrices can involve 2 components • A pre-specified statistical balance relationship – part of the background error statistics file • Optionally a incremental normal model balance • Not working well for regional problem DTC – Summer Tutorial

Observations The observation yo is compared with the model state x after the latter is transformed into observation space. For many direct “conventional” observations such as temperature or wind speed this observation operator comprise a transform from the analysis variables and an interpolation to the observation’s time and position. For other data sources, such as radiance observations, this operator is far more complex. NEMS/GFS Modeling Summer School

Radiosondes Pibal winds Synthetic tropical cyclone winds wind profilers conventional aircraft reports ASDAR aircraft reports MDCARS aircraft reports Dropsondes Doppler radial velocities Surface land observations Surface ship and buoy observation VAD (NEXRAD) winds Input data – Conventional currently used DTC – Summer Tutorial

Radiosondes

Radiosonde Data Coverage NEMS/GFS Modeling Summer School

Atmospheric Motion Vectors MODIS IR and water vapor winds GMS, JMA, METEOSAT and GOES cloud drift IR and visible winds GOES water vapor cloud top winds Wind speeds from ocean surface state SSM/I wind speeds QuikScat and ASCAT wind speed and direction SSM/I and TRMM TMI precipitation estimates GPS Radio occultation refractivity and bending angle profiles SBUV ozone profiles and OMI total ozone Satellite Derived Products currently used in Global Model DTC – Summer Tutorial

Cloud Tracked Winds

Infrared Sounders: GOES-15 Sounder: Channels 1-15, Ocean Only Aqua AIRS: 148 Channels MetOp-A IASI: 165 Channels MetOp-A HIRS: Channels 2-15 Microwave Sounders: AMSU-A on: NOAA-15 Channels 1-10, 12-13, 15 NOAA-18 Channels 1-8, 10-13, 15 NOAA-19 Channels 1-7, 9-13, 15 METOP-A Channels 1-6, 8-13, 15 AQUA Channels 6, 8-13 NPP ATMS: Channels 1-14,16-22 MHS on: NOAA-18 Channels 1-5 NOAA-19 Channels 1-5 METOP-A Channels 1-5 Satellite Radiances currently used in Global Model DTC – Summer Tutorial

Meterological Satellite Constellation (from WMO) Currently operationally Assimilate radiances at NCEP

Typical Satellite Data Coverage NEMS/GFS Modeling Summer School

Shortwave window (with solar contribution) Longwave window H2O CO2 Brightness Temperature (K) O3 Q-branch CO2 Wavelength (μm) An Infrared (IASI) Spectrum

Observation Operators for Infrared Radiances 100 hPa HIRS-4 HIRS-5 Selected AIRS Channels: 82(blue)-914(yellow) HIRS-6 HIRS-7 HIRS-8 1000 hPa

Satellite Radiance Observation Operator • The observation operator for radiance assimilation needs to accurately model the observed radiance • The calculations are complex comprise a significant fraction of the total data assimilation run time • For certain situations the first-guess fields and/or the radiance calculation is not accurate enough (e.g., clouds) • Quality control in these situations is very important. • Even after quality control biases remain in the observed-calculated differences and sophisticated bias control algorithms are used to remove these. NEMS/GFS Modeling Summer School

Variational Data Assimilation J : Penalty (Fit to background + Fit to observations + Constraints) x’ : Analysis increment (xa – xb) ; where xb is a background Bvar: Background error covariance H : Observations (forward) operator R : Observation error covariance (Instrument + representativeness) yo’ : Observation innovations Jc : Constraints (physical quantities, balance/noise, etc.) B is typically static and estimated a-priori/offline 26

Kalman Filter in Var Setting Forecast Step Extended Kalman Filter Analysis • Analysis step in variational framework (cost function) • BKF: Time evolving background error covariance • AKF: Inverse [Hessian of JKF(x’)]

Motivation from KF • Problem: dimensions of AKF and BKF are huge, making this practically impossible for large systems (GFS for example). • Solution: sample and update using an ensemble instead of evolving AKF/BKF explicitly Forecast Step: Ensemble Perturbations Analysis Step:

What does Be gain us? Temperature observation near warm front Bf Be 29

Single Temperature Observation 3DVAR bf-1=0.0 bf-1=0.5

Summary • The analysis is produced through an optimal combination of information from the model forecast and the observations • Observations come from a large number of sources, each with different strengths and weaknesses • Accurate simulation of observed values is very important, particularly for radiance observations. • Quality control and bias correction are crucial. • The use of background information from an EnKF system greatly improves our ability to spread the information supplied by the observations is a realistic manner.

Data Assimilation