# Data Assimilation Andrew Collard. Overview Introduction to Atmospheric Data Assimilation Control Variables Observations Background Error Covariance Summary.

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Data Assimilation Andrew Collard

Overview Introduction to Atmospheric Data Assimilation Control Variables Observations Background Error Covariance Summary NEMS/GFS Modeling Summer School 2

Overview Introduction to Atmospheric Data Assimilation Control Variables Observations Background Error Covariance Summary NEMS/GFS Modeling Summer School 3

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 4

Data Assimilation as part of the GFS Suite (1) NEMS/GFS Modeling Summer School 5

Data Assimilation as part of the GFS Suite (2) NEMS/GFS Modeling Summer School 6

The Cost Function J : Penalty (Fit to background + Fit to observations + Constraints) x’ : Analysis increment (x a – x b ) ; where x b is a background B var : Background error covariance H : Observations (forward) operator R : Observation error covariance (Instrument + representativeness) y o ’ : Observation innovations J c : 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 8

4 August 2013DTC – Summer Tutorial Analysis variables The analysis variables are Streamfunction (Ψ) Unbalanced Velocity Potential (χ unbalanced ) Unbalanced Temperature (T unbalanced ) Unbalanced Surface Pressure (Ps unbalanced ) Ozone – Clouds – etc. Satellite bias correction coefficients

4 August 2013DTC – Summer Tutorial Analysis variables χ = χ unbalanced + A Ψ T = T unbalanced + B Ψ Ps = Ps unbalanced + C Ψ Streamfunction is a key variable defining a large percentage T and P s (especially away from equator). Contribution to χ is small except near the surface and tropopause.

4 August 2013DTC – 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

Overview Introduction to Atmospheric Data Assimilation Control Variables Observations Background Error Covariance Summary NEMS/GFS Modeling Summer School 12

Observations NEMS/GFS Modeling Summer School 13 The observation y o 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.

4 August 2013DTC – Summer Tutorial Input data – Conventional currently used 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

Radiosonde Data Coverage NEMS/GFS Modeling Summer School 16

4 August 2013DTC – Summer Tutorial Satellite Derived Products currently used in Global Model 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

Cloud Tracked Winds Winds derived using full disk 15-minute Meteosat-8 10.8µm SEVIRI data for 12 UTC on 01 February 2007. These winds are derived from tracking cloud features using the 10.8µm channel. High level (100-400 hPa) winds are shown in violet; mid-level (400-700 hPa) are shown in cyan; and low levels (below 700 hPa) are shown in yellow.

4 August 2013DTC – Summer Tutorial Satellite Radiances currently used in Global Model 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-19Channels 1-5 METOP-AChannels 1-5

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

Typical Satellite Data Coverage NEMS/GFS Modeling Summer School 21

An Infrared (IASI) Spectrum O3O3 CO 2 H2OH2O Wavelength (μm) Brightness Temperature (K) Q-branch Longwave window Shortwave window (with solar contribution)

Observation Operators for Infrared Radiances HIRS-4 HIRS-5 HIRS-6 HIRS-7 HIRS-8 Selected AIRS Channels: 82(blue)-914(yellow) 1000 hPa 100 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 24

Overview Introduction to Atmospheric Data Assimilation Control Variables Observations Background Error Covariance Summary NEMS/GFS Modeling Summer School 25

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

27 Kalman Filter in Var Setting Forecast Step Analysis Analysis step in variational framework (cost function) Extended Kalman Filter B KF : Time evolving background error covariance A KF : Inverse [Hessian of J KF (x’)]

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

What does B e gain us? Temperature observation near warm front 29 BfBf BeBe

Single Temperature Observation 30 3DVAR  f -1 =0.0  f -1 =0.5

Summary 31 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.

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