# Presentation: 053679

##  GSI Analysis System

- David Parrish
- NOAA/NWS/NCEP/EMC

## general comments

- GSI analysis code is an evolving system.
- Scientific advances – e.g.,
- situation dependent background errors
- new satellite data
- new analysis variables
- Improved coding – e.g.,
- Bug fixes
- Removal of unnecessary computations, arrays, etc.
- More efficient algorithms
- Generalizations of code to allow use on different compute platforms
- Improved documentation

## general comments

- New versions released approximately every  3 months
- Old versions are not supported
- Developers are expected to keep up with current version
- Code is intended to become Operational
-                 (already operational in NAM—June, 2006)
- must satisfy NCEP coding requirements
- must fit into NCEP infrastructure
- EMC does not have resources to provide high level of support.

## general comments

- A LOT of details skipped over in this presentation
- More detailed information can be found on the GSI web site
-       _[http://www.emc.ncep.noaa.gov/gmb/treadon/gsi/](http://www.emc.ncep.noaa.gov/gmb/treadon/gsi/)_
- Location for outside users to obtain latest code and script updates
- Use at own risk—high level support not provided

## History

- The GSI (_G_ridpoint _S_tatistical _I_nterpolation) system was initially developed as the next generation global analysis system
- Wan-Shu Wu, R. James Purser, David Parrish
*Three-Dimensional Variational Analysis with spatially Inhomogeneous Covariances. Mon. Wea. Rev., 130, 2905-2916.*
- Based on SSI (_S_pectral _S_tatistical _I_nterpolation) analysis system
- Replace spectral definition for background errors with grid point version based on recursive filters

## History

- After development of initial GSI analysis system, desire for single global/regional analysis system expressed by EMC management
- realization that GSI fairly straightforward to modify for both applications
- GMAO collaboration
- Modification to fit into WRF and NCEP infrastructure
- Evolution to ESMF

## History

- Implemented with WRF-NMM into the NAM system in June, 2006
- Preimplementation testing for replacement of SSI in GFS system in March, 2007

## Basic analysis problem

**J = J****b**** + J****o**** + J****c**
**J = (x-x****b****)****T****B****-1****(x-x****b****) + (H(x)-y****0****)****T****(E+F)****-1****(H(x)-y****0****) + J****C**
**J = Fit to background + Fit to observations + constraints**
**x****	****= Analysis**
**x****b****	****= Background**
**B****	****= Background error covariance**
**H****	****= Forward model**
**y****0****	****= Observations**
**E+F****	****= R = Instrument error + Representativeness error**
**J****C****    ****	****= Constraint term**

## GSI Code - General Flow

- User input &
- initializations

- Read in &
- distribute
- observations

- Additional
- initializations

- Outer loop      (2 or 3 iterations)
- (Read/distribute) guess & derived fields
- (Read/distribute) background error
- Set up right hand side of analysis equation
- Call inner loop     (50 to 150 iterations)
- Compute gradient information   (**J****x **– path towards minimum)
- Apply background error             (**Bv **where **v = J****x**)
- Compute search direction       (better path to minimum)
- Compute step size  (how far to move to get max decrease of **J**)
- Update analysis increment

- Write analysis & related output

## Expected Scientific advancements

- Inclusion of new types of data
- COSMIC GPS – radio-occultation
- Radiance data
- SSM/I and SSM/IS radiances
- NASA instruments from AQUA, TERRA, CHEM
- NPOESS and METOP
- Next Generation Geostationary satellite
- Doppler radial velocities and reflectivities
- Precipitation observations
- Cloud observations
- Ozone observations

## Expected Scientific advancements

- Improved specification of observational errors
- Situation dependent representativeness errors
- Increased granularity in specification of obs errors.
- Advanced DA techniques
- Situation dependent background errors
- 4-D var.
- Improved balance constraints

## Expected Scientific advancements

- New analysis variables
- SST
- Clouds
- Aerosols
- Precipitation
- Constituents
- Others

## Background error 

**J****b**** = (x-x****b****)****T****B****-1****(x-x****b****) **
**B  ** background error covariance matrix
**x  **  vector of gridpoint values of
-           u, v, T, q, cw , oz, ps, Tskin
- Length of **x **currently 108 for NAM, so
**B  **is 108 **x** 108 = 1016 !
- Much too big to define directly
- Recursive filter used to define **B** as sequence of
- inexpensive subroutines.  Routines contain small number of parameters.

## Background error

- State variable **x :**
- stream function contribution to wind
- balbalanced potential function contribution to wind
- 	Tbal     balanced temperature
- 	pbal      balanced temperature
- unbalunbalanced potential function contribution to wind
- Tunbal  unbalanced temperature
- punbal  unbalanced temperature
- q       moisture
- cw     cloudwater
- oz     ozone        (GFS only WRF-NAM does not currently
-                                carry prognostic ozone variable)
- Each component of **x** has its own partition of the background error matrix **B**

## Multivariate relations in B

- Balanced part of the temperature is defined by
- 			Tbal = G 
- 	where G is an empirical matrix that projects increments of stream function at one level to a vertical profile of balanced part of temperature increments. G is latitude dependent.
- Balanced part of the velocity potential is defined as
- 			bal = c 
- 	where coefficient c is function of latitude and height.
- Balanced part of the surface pressure increment is defined as
- 			Pbal = W 
- 	where matrix W integrates the appropriate contribution of the stream function from each level.

## Background error parameters

- Error variance (diagonal of **B)**
- Correlation lengths (diagonal dominance of **B**)
- Multivariate coupling (dynamic balance between stream function and divergent wind, temperature, and pressure)

## B visualized with single observation analysis (background error example for GFS from 2 years ago)J = (xa -xb)TB-1(xa -xb) + (Hxa -y0)T(E+F)-1(Hxa -y0) 

- u (left) and v (right) increments (**x****a**** – x****b**) at sigma level 0.267, of a 1 m/s westerly wind observational residual (**y****o** **-** **Hx****b**) at 50N and 330 E at 250 mb.

## B visualized with single observation analysis 

-      vertical cross section of u and T 		coupling of stream function to 					temperature and velocity potential

- Only use surface coupling
-  to get surface friction effect
- (convergence in lows,
- divergence in highs)

- Tbal = G 

- bal = c 

## Error variance (diagonal of B)

- Error statistics are estimated in grid space with the ‘NMC’ method. Stats of  are shown.
- Stats are function of latitude and sigma level.
- The error variance (m4 s-2) is larger in mid-latitudes than in the tropics and larger in the southern hemisphere than in the northern.

## Horizontal/vertical scale lengths (spread of B away from diagonal)

-       horizontal scales in units of 100km	             vertical scale in units of vertical grid
-  The horizontal scales are larger in the tropics, and increase with height.
-  The vertical scales are larger in the mid-latitude, and decrease with height.

## Forward Model H

- Transforms state variable **x** into simulated observation    **y = H(x)**
- Can be linear or nonlinear
- As simple as interpolation from grid to observation location (conventional point observations)
- As complex as radiative transfer model (CRTM) for satellite radiance observations.
- CRTM development crucial for successful assimilation of aerosols and chemical constituents

## Satellite Radiance treatment

- John C. Derber
- NOAA/NWS/NCEP/EMC

## Overview

- Goals
- Extract as much information as possible from data
- Prepare for the new data sources
- Improve NWP guidance
- Dogma
- Use data with minimal processing
- Simplify error structure
- Simplify quality control
- Use only information in observations

## Overview

- Difficulties
- Instrument and Radiative transfer issues
- Surface emissivity
- Instrument characterization
- Scattering from clouds, precipitation and aerosols
- Impact of variations in atmospheric constituents
- Quality control issues
- Large volume of data (very redundant)
- Computational cost
- Nonlinearity
- Model biases

## Radiative transfer

- Radiative transfer being developed and maintained by JCSDA
- _[http://cimss.ssec.wisc.edu/~paulv/Fortran90/CRTM/Prototype/](http://cimss.ssec.wisc.edu/~paulv/Fortran90/CRTM/Prototype/)_
- Library called from GSI
- Improvements under development
- Enhance modular RT system through JCSDA (VanDelst, Yang)
- Inclusion of cloud water and precipitation effects in microwave and IR (Bennartz, Weng, Gasiewski, Liou)
- Improved microwave (Okamoto,Yan and Weng) and IR (VanDelst) oceanic surface emissivity
- Inclusion of aerosol effects (Lu)

## Assimilation of Aerosols

- CRTM is being expanded to include effects of aerosols
- But to get estimates of aerosols or other new atmospheric constituents, they must be predicted quantities in the forecast model
- Example:  ozone is not a predictive quantity in the WRF-NAM.  So satellite channels with strong sensitivity to ozone are not currently used.

## Assimilation of Aerosols

- When a new constituent variable has been added to the forecast model, then it is possible to augment the background error **B **and run retrospective tests to get biases for satellite channels which are sensitive to the new variable.

## Obstacles for regional hi res applications involving aerosols

- Very difficult to put together all pieces using WRF framework.
- Too expensive to do testing over full 12km NAM domain

## Progress

- Matt Pyle has developed a 15km, half domain assimilation system with all required pieces, including extended forecasts and verification.  More practical for the testing required to include new obs types/model variables.
- Ozone, aerosol, chemical constituents in WRF NAM???

## Current GSI work

**J****c**** **term – needed to control gravity wave noise, a serious problem in WRF-NDAS.
- Approximate 4dvar – include time dimension when doing analysis.

## Jc term (for dynamic balance)

- “generic” adiabatic model contained in GSI
- Compute analysis increment tendencies of state variables due to passive advection of constituents and adiabatic dynamics for u, v, T, p.
- Use tangent linear model linearized about analysis estimate from previous outer loop.
- Normal mode initialization ideas being adapted to construct constraints which minimize gravity wave noise added by analysis increment while preserving meteorological signal.

## Control of noise needed for:

- More frequent assimilation (6hrs to 1hr in GFS, 3hrs to 1hr in WRF NDAS)
- Improvement in fit of background to observations
- Use of approximate 4dvar

## Approximate 4dvar

- Forward model **H **is augmented to include linear time extrapolation over time of analysis window (currently +/- 3 hrs for GFS, +/- 1.5 hrs for WRF NDAS)
- Use analysis increment tendency to do the extrapolation
- Forward model **H** now includes tangent linear model used to get analysis increment tendencies
- For passive advected aerosols, the wind field is now coupled, being the principle contribution to tendency of aerosol
- Thus winds indirectly observed from aerosols

## Approximate 4dvar

- Doesn’t work unless gravity wave noise minimized with good **J****c**** **term
- With good **J****c**** **term approximate 4dvar should be even better over shorter assimilation interval, because linear extrapolation has smaller error

## Approximate 4dvar

- Very intensive effort underway to get effective **J****c**** **term and 4dvar.
- Substantial progress has been made with both for use with the GFS.
- Some difficulties still with application to WRF-NDAS, not for 4dvar, but the **J****c**** **term
- Expect to have everything working long before we will be able to do aerosol/ other constituent assimilation experiments (waiting on model).