December 2008

NASA/TM–2008–104606, Vol. 27

Technical Report Series on Global Modeling and Data Assimilation, Volume 27

Max J. Suarez, Editor

The GEOS-5 Data Assimilation System—

Documentation of Versions 5.0.1, 5.1.0, and 5.2.0

M.M. Rienecker, M.J. Suarez, R. Todling, J. Bacmeister, L. Takacs, H.-C. Liu, W. Gu, M. Sienkiewicz, 

R.D. Koster, R. Gelaro, I. Stajner, and J.E. Nielsen
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December 2008

NASA/TM–2008–104606, Vol. 27

Technical Report Series on Global Modeling and Data Assimilation, Volume 27

Max J. Suarez, Editor

The GEOS-5 Data Assimilation System—

Documentation of Versions 5.0.1, 5.1.0, and 5.2.0

M.M. Rienecker and M.J. Suarez

NASA Goddard Space Flight Center, Greenbelt, Maryland

R. Todling

Science Applications International Corporation, Beltsville, Maryland

J. Bacmeister

University of Maryland, Baltimore County, Baltimore, Maryland

L. Takacs, H.-C. Liu, W. Gu, and M. Sienkiewicz

Science Applications International Corporation, Beltsville, Maryland

R.D. Koster and R. Gelaro

NASA Goddard Space Flight Center, Greenbelt, Maryland

I. Stajner

 (former employee) Science Applications International Corporation, Beltsville, Maryland

J.E. Nielsen

Science Systems and Applications, Inc., Lanham, Maryland
Available from:

NASA Center for AeroSpace Information National Technical Information Service

7115 Standard Drive 5285 Port Royal Road

Hanover, MD 21076-1320 Springfield, VA 22161
iii

Abstract

This report documents the GEOS-5 global atmospheric model and data assimilation system (DAS),

including the versions 5.0.1, 5.1.0, and 5.2.0, which have been implemented in products distributed for 

use by various NASA instrument team algorithms and ultimately for the Modern Era Retrospectiveanalysis for Research and Applications (MERRA). The DAS is the integration of the GEOS-5

atmospheric model with the Gridpoint Statistical Interpolation (GSI) Analysis, a joint analysis system

developed by the NOAA/National Centers for Environmental Prediction and the NASA/Global Modeling

and Assimilation Office. The primary performance drivers for the GEOS DAS are temperature and

moisture fields suitable for the EOS instrument teams, wind fields for the transport studies of the

stratospheric and tropospheric chemistry communities, and climate-quality analyses to support studies of 

the hydrological cycle through MERRA.

The GEOS-5 atmospheric model has been approved for open source release and is available from:

http://opensource.gsfc.nasa.gov/projects/GEOS-5/GEOS-5.php.
iv
v

Contents

List of Figures ...................................................................................................................................................vii

List of Tables...................................................................................................................................................... xi

1. INTRODUCTION ......................................................................................................................................................... 1

2. THE GEOS-5 ATMOSPHERIC GENERAL CIRCULATION MODEL ........................................................... 2

2.1 HYDRODYNAMICS ...................................................................................................................................................... 2

2.2 PHYSICS ...................................................................................................................................................................... 2

2.2.1 Moist Physics Parameterizations..................................................................................................................... 2

2.2.2 Radiation............................................................................................................................................................ 9

2.2.3 Turbulent Mixing............................................................................................................................................. 12

2.2.4 Chemical Species............................................................................................................................................. 13

2.2.5 Surface Processes............................................................................................................................................ 14

2.2.6 The Catchment Land Surface Model.............................................................................................................. 14

2.3 SPECIFIC IMPLEMENTATION FOR GEOS-5.0.1, GEOS-5.1.0, AND GEOS-5.2.0. ................................................. 16

2.3.1 Ancillary Initial and Boundary Data ............................................................................................................. 17

2.3.2 The Model Grid ............................................................................................................................................... 17

3. THE GEOS-5 ANALYSIS ......................................................................................................................................... 18

3.1 THE GSI SOLVER ..................................................................................................................................................... 18

3.2 THE TREATMENT OF SATELLITE RADIANCE DATA................................................................................................. 20

3.2.1 Data Thinning.................................................................................................................................................. 20

3.2.2 Satellite Data Bias Correction ....................................................................................................................... 21

3.2.3 Ozone Channels............................................................................................................................................... 24

3.3 OTHER ASSIMILATION COMPONENTS ..................................................................................................................... 24

3.3.1 The Precipitation Assimilation ....................................................................................................................... 24

3.3.2 The Surface Temperature Analysis ................................................................................................................ 24

3.4 SPECIFICATION OF BACKGROUND ERROR STATISTICS ........................................................................................... 24

3.4.1 State Variables................................................................................................................................................. 25

3.4.2 The Mass-Wind Balance Constraint .............................................................................................................. 28

3.5 THE OBSERVING SYSTEM AND THE OBSERVATION ERROR STATISTICS................................................................ 43

3.5.1 Conventional In-situ Upper-Air Data ........................................................................................................... 44

3.5.2 Satellite Radiance Data .................................................................................................................................. 48

3.5.3 Satellite Retrievals........................................................................................................................................... 52

3.5.4 Land Surface Observations............................................................................................................................. 54

3.5.5 Ocean Surface Observations .......................................................................................................................... 55

3.6 QUALITY CONTROL.................................................................................................................................................. 55

3.6.1 Conventional Data .......................................................................................................................................... 55

3.6.2 Satellite Radiance Data .................................................................................................................................. 56

3.6.3 Precipitation Data........................................................................................................................................... 57

3.7 THE RADIATIVE TRANSFER MODEL........................................................................................................................ 58

3.8 ANALYSIS DETAILS FOR GEOS-5.0.1, GEOS-5.1.0, AND GEOS-5.2.0................................................................ 60

3.8.1 GEOS-5 Analysis Grid .................................................................................................................................... 60

3.8.2 Data Sources................................................................................................................................................... 60

3.8.3 Radiosonde Corrections for MERRA............................................................................................................ 60

4. THE GEOS-5 DATA ASSIMILATION SYSTEM ................................................................................................ 62

4.1 MODEL – ANALYSIS INTERFACE ............................................................................................................................. 62

4.2 THE INCREMENTAL ANALYSIS UPDATE (IAU)....................................................................................................... 62

4.3 BALANCING VERTICALLY INTEGRATED MASS DIVERGENCE FROM ANALYSIS INCREMENTS.............................. 63

4.3.1 The Minimization Algorithm........................................................................................................................... 66

4.3.2 Wind Adjustment Algorithm............................................................................................................................ 67

4.3.3 Results.............................................................................................................................................................. 68
vi

5. GEOS-5 DEVELOPMENT AND PRODUCT VERSION HISTORY................................................................ 72

5.1 THE VERSIONS.......................................................................................................................................................... 72

5.2 THE UPDATES........................................................................................................................................................... 72

5.3 THE IMPACTS............................................................................................................................................................ 76

6. REFERENCES ............................................................................................................................................................ 82

APPENDIX A. AIRS 281 CHANNEL SUBSET LIST.............................................................................................. 88

APPENDIX B. OBSERVATIONAL ERROR VARIANCES FOR SATELLITE RADIANCES ...................... 92

APPENDIX C. ACRONYMS ........................................................................................................................................ 94

APPENDIX D. ACKNOWLEDGMENTS................................................................................................................... 97
vii

List of Figures

Figure 2.2.1: Schematic of Moist processes in GEOS-5. ................................................................................. 4

Figure 2.2.2: Schematic diagram of the implicit bi-modal PDF structure in the GEOS5_Moist cloud

scheme. The current scheme consists of a boxcar PDF in non-anvil regions added to a δ-function

containing contributions from detraining convection. In the symbols above, overbars refer to

gridbox mean values. ................................................................................................................................... 6

Figure 2.2.3: “Sundqvist-factor” controlling low-temperature autoconversion. ........................................... 7

Figure 2.2.4: Schematic diagram of geometry assumed in rain re-evaporation calculation. ......................... 9

Figure 2.2.5: Separation of the catchment area into hydrological regimes................................................... 15

Figure 2.3.1: Lagrangian control volume and state variables for the GEOS-5 AGCM. .............................. 17

Figure 3.1.1: The explained variance of the balanced part of temperature (red curve) and velocity

potential (green curve) at 60°N used in GEOS-5.0.1 (left) and GEOS-5.1.0 (right). The balanced

velocity potential is largest at the surface to include a surface friction effect. ...................................... 19

Figure 3.1.2: The explained variance of the balanced surface pressure as a function of latitude................ 20

Figure 3.2.1: (a) The difference between the observed (without bias correction) and the calculated

brightness temperature from the NWP model background (O-F), and (b) the normalized

weighting function for AIRS moisture channel 1756.............................................................................. 22

Figure 3.2.2 Examples of AMSU-A mean (upper panels) and standard deviation (lower panel)s of OF values across the scan angles for (a) NOAA-15 and (b) Aqua. The red curve indicates O-F

values before bias correction and the green curve shows O-F values after bias correction. The

blue curve is the difference between observed and the calculated brightness temperature from the

analysis........................................................................................................................................................ 22

Figure 3.2.3: O-F maps for Aqua AMSU-A channel 8 data (a) before bias correction, and (b) after

bias correction. ........................................................................................................................................... 23

Figure 3.2.4: Global mean and standard deviation of O-F values before (left panels) and after (right

panels) bias correction for each channel are shown for (a) Aqua AMSU-A and (b) NOAA-17

HIRS3. ........................................................................................................................................................ 23

Figure 3.2.5: (a) Example of coefficients used in the variational bias correction and (b) the

contributions to the bias correction for AQUA EOS AMSU-A channel 12. ......................................... 23

Figure 3.4.1: Example of estimated background error statistics for ψ. Top: error standard deviation

as a function of latitude and sigma level (in m

2

s

-1

); middle: horizontal scales of covariance (in

km); bottom: vertical scale factor of covariance. Left hand panels are the statistics used for

GEOS-5.0.1; right-hand panels for GEOS-5.1.0..................................................................................... 25

Figure 3.4.2: Example of the vertical correlation at different levels, given a constant vertical scale

factor of 1.0. This structure is generated by the recursive filter to model the vertical correlation

for all variables........................................................................................................................................... 26

Figure 3.4.3: Example of estimated background error statistics for pseudo-relative humidity. Top:

error standard deviation as a function of latitude and sigma level; middle: horizontal scales of

covariance (in km); bottom: vertical scale factors for covariance. ........................................................ 26

Figure 3.4.4: u (left) and v (right) increments (xa–xb), at sigma level 0.267, from a 1 m/s westerly

wind observational residual (yo – h(xb)) at 50°N and 330°E at 250 hPa. ............................................... 27
viii

Figure 3.4.5: The vertical cross-section of u and T increments for the observation used for Figure

3.4.4............................................................................................................................................................. 27

Figure 3.4.6: The profiles of 

!

< "#,$2"% >

(dashed line) and

!

< "#,$ % (f $"#) >

(solid line) at eight

selected latitudes with δψ being at σ = 0.5. These profiles are calculated from the balance

projection coefficients estimated according to the original GSI implementation, and values have

been multiplied by 103. .............................................................................................................................. 31

Figure 3.4.7: The standard deviation profiles of balanced temperature as a function of sigma at eight

selected latitudes. The red curves are the estimates from the original GSI implementation, while

the other curves are from the new approach. The green (yellow) curve shows the statistics used

in GEOS-5.0.1 (GEOS-5.1.0).................................................................................................................... 36

Figure 3.4.8: As in Figure 3.4.7, but for the correlation profiles at σ = 0.5.................................................. 37

Figure 3.4.9: As in Figure 3.4.7, but for the correlation profiles at σ = 0.2.................................................. 38

Figure 3.4.10: As in Figure 3.4.9, but for the cross-correlation profiles between the balanced

temperature and balanced surface pressure. ............................................................................................. 39

Figure 3.4.11a: As in Figure 3.4.6, but from the balanced projections estimated with the new

approach used for GEOS.5.0.1.................................................................................................................. 40

Figure 3.4.11b: As in Figure 3.4.11a, but for statistics used for GEOS.5.1.0 and only for 10oS and

10oN, there being little change at higher latitudes. .................................................................................. 40

Figure 3.4.12: Zonal averages of 

!

| L" |#| $2%" |

(top),

!

| R" |#| $ % (f $&") |

(middle). LΦ and Rψ are 

calculated based on the analysis increments which only includes the wind-mass balance

projections with the new approach. All the values in the top and middle have been multiplied by

1010. The bottom panel displays the ratio of top field to the middle, the contours of 0.5, 0.75, 0.9,

1.0, 1.1, 1.25, 1.5, 2.0, 4.0, 6.0 are plotted. Left-hand panels are for GEOS-5.0.1; right-hand

panels are for GEOS-5.1.0......................................................................................................................... 41

Figure 3.4.13: The distributions of geopotential height increments and vectors of the rotational wind

from the wind-mass balanced projections estimated with the new approach with σ=0.5 (top) and

σ=0.1 (bottom). The left-hand panels are for GEOS-5.0.1; right-hand panels for GEOS-5.1.0........... 42

Figure 3.5.1: AIRS observed brightness temperatures for all 2378 channels are shown in light blue.

The spectral location (blue diamond), instrument noise (red cross), and the assigned observation

errors (green asterisk) in GSI for the 281-channel subset are also shown. ............................................ 50

Figure 4.1.1: The D-grid layout in the GEOS-5 GCM; φ-points denote mass locations. ........................... 62

Figure 4.2.1: A schematic of the IAU implementation. ................................................................................ 63

Figure 4.3.1: The vertically integrated mass-divergence (in arbitrary units) on 1 August, 2006 for the

background (top), the analysis state (middle) and from the difference, or analysis increment

(bottom). ..................................................................................................................................................... 64

Figure 4.3.2: Surface pressure for the background and analysis states (upper panels). Also shown are

the vertically integrated mass-divergence (arbitrary units) of the background (left-hand lower

panel) and the (analysis-background) difference (right-hand lower panel). .......................................... 65

Figure 4.3.3: Surface pressure tendency of the background (left-hand upper panel) and analysis states

(right-hand upper panel), and the resulting surface pressure after 15 minutes of model integration

from the background without analysis (left-hand lower panel) and from the analysis (right-hand

lower panel). ............................................................................................................................................... 65
ix

Figure 4.3.4: Zonal mean of the absolute value of the vertically integrated mass divergence analysis

increment. ................................................................................................................................................... 69

Figure 4.3.5: The zonal mean horizontal wind divergence (plotted on constant pressure surfaces) of

the background state (from the model first guess) and the corresponding results from the analysis

states............................................................................................................................................................ 69

Figure 4.3.6: The zonal mean of the analysis increment of divergence. ....................................................... 70

Figure 4.3.7: The zonal mean of the adjustment made to the control analysis of horizontal

divergence................................................................................................................................................... 70

Figure 4.3.8: Surface pressure after 15 minutes of model integration, initialized from the background

and analysis states (Control, Case 2, and Case 3). ................................................................................... 71

Figure 5.3.1: Mean sea-level pressure for January 2006. The left-hand figure shows GEOS-5.1.0

(upper panel), 5.0.1 (middle panel) and the difference (5.1.0 minus 5.0.1). The mean difference

is 0.05 hPa, the standard deviation of the difference is 0.40 hPa. The right-hand figure shows

GEOS-5.2.0 (upper panel), 5.1.0 (middle panel) and the difference (5.2.0 minus 5.1.0). The

mean difference is 0.05 hPa, the standard deviation of the difference is 0.35 hPa................................ 76

Figure 5.3.2: As in Figure 5.3.1, but for 500-hPa height. The mean difference is between 5.1.0 and

5.0.1 is 3.2 hPa, and the standard deviation of the difference is 6.2 hPa. The mean difference is

between 5.2.0 and 5.1.0 is 2.9 hPa, and the standard deviation of the difference is 3.3 hPa. ............... 77

Figure 5.3.3: Mean difference in precipitation for January 2006 (upper panels) and July 2004 (lower

panels) in mm/day. The left-hand panels show GEOS-5.1.0 minus GEOS-5.0.1. The right-hand

panels show GEOS-5.2.0 minus GEOS-5.1.0. ......................................................................................... 78

Figure 5.3.4: Zonal mean temperature (K) for January 2006. The left-hand figure shows GEOS-5.1.0

(upper panel), 5.0.1 (middle panel) and the difference (5.1.0 minus 5.0.1, lower panel). The

right-hand figure shows GEOS-5.2.0 (upper panel), 5.1.0 (middle panel) and the difference

(5.2.0 minus 5.1.0, lower panel)................................................................................................................ 79

Figure 5.3.5: As in Figure 5.3.4, but zonal mean specific humidity (g/kg). ................................................. 80

Figure 5.3.6: As in Figure 5.3.4, but zonal mean zonal wind (m s

-1

). ........................................................... 81
x
xi

List of Tables

Table 2.2.1: Principal quantities appearing in the GEOS5_Moist physics package.. .................................... 3

Table 2.2.2: Spectral bands, gaseous absorption and Rayleigh scattering in the broadband shortwave

radiation parameterization. Clouds and aerosols are included in all bands............................................ 10

Table 2.2.3: Spectral bands, absorbers, and transmittance parameterizations. ............................................. 12

Table 3.2.1: The sizes of the observation thinning box used in the GSI for different instrument types..... 21

Table 3.5.1: Input observation data sources and parameters.......................................................................... 43

Table 3.5.2: Observation errors for Radiosonde/Dropsonde ‘mass’ reports................................................. 45

Table 3.5.3: Observation errors for radiosonde, profiler and VAD wind (m/s). .......................................... 46

Table 3.5.4: Observation errors for aircraft observations............................................................................... 47

Table 3.5.5: Summary of TOVS/ATOVS observing system. ........................................................................ 49

Table 3.5.6: Summary of GOES satellite operation. ...................................................................................... 51

Table 3.5.7: Summary of DSMP satellite availability.................................................................................... 51

Table 3.5.8: SBUV Observation errors. .......................................................................................................... 52

Table 3.5.9: Observation errors for cloud-tracked winds (m s

-1

).................................................................. 53

Table 3.5.10: Observation errors for surface pressure (hPa)......................................................................... 54

Table 3.5.11: Observation errors for surface temperature and specific humidity......................................... 55

Table 3.7.1: Surface types included in the IR emissivity database................................................................ 60

Table B1: TOVS ............................................................................................................................................... 92

Table B2: GOES ............................................................................................................................................... 93
xii
1

1. Introduction

The assimilation system described in this document is a major new version of the Goddard Earth

Observing System Data Assimilation System (GEOS DAS). The GEOS-5 DAS is based on the GEOS-5

Atmospheric General Circulation Model (AGCM) integrated with the Gridpoint Statistical Interpolation

(GSI) Analysis. This represents a radical evolution of the GEOS system, with the adoption of the GSI

analysis jointly developed with the National Centers for Environmental Prediction (NCEP) and a new set

of physics packages for the AGCM. The first choice allows the Global Modeling and Assimilation Office

(GMAO) to take advantage of the developments, especially that of radiance assimilation, at NCEP and

the Joint Center for Satellite Data Assimilation (JCSDA), and facilitates our own contributions to the 

operational system. The second choice allows us to tune the system for both weather and climate

applications, taking advantage of satellite observations in the assimilation context as we do so.

The GEOS-5 AGCM maintains the finite-volume dynamics (Lin, 2004) used for GEOS-4 (e.g., Bloom et

al., 2005) and found to be so effective especially for transport in the stratosphere (e.g., Pawson et al.,

2007). This dynamical core is integrated with various physics packages (e.g., Bacmeister et al., 2006)

under the Earth System Modeling Framework (ESMF) (e.g., Collins et al., 2005) including the Catchment

Land Surface Model (CLSM) (e.g., Koster et al., 2000). The GSI analysis is a new three-dimensional

variational (3DVar) analysis applied in grid-point space to facilitate the implementation of anisotropic,

inhomogeneous covariances (e.g., Wu et al., 2002; Derber et al., 2003; Purser et al., 2003a, b). GMAO

scientists have contributed to GSI development since 2004.

During implementation in GEOS-5, this system has continued along its development path. One result of 

this was the need to address shocks introduced by imbalances in the mass-wind analysis increments.

Although balance constraints are under development, in order to meet the GMAO’s production schedule

requirements, the decision was made to re-introduce (from GEOS-3) the incremental analysis update 

(IAU) procedure (Bloom et al., 1996) and this has proven very effective.

The primary performance drivers of the GEOS DAS products are temperature and moisture fields suitable 

for the EOS instrument teams, wind fields for the transport studies of the stratospheric and tropospheric 

chemistry communities, and climate-quality analyses to support studies of the hydrological cycle through

the Modern Era Retrospective-analysis for Research Applications (MERRA, e.g., Bosilovich et al., 2006).

Other significant drivers for the GEOS DAS have involved the provision of near real-time mission

support for a number of atmospheric chemistry mission field campaigns.

This report documents Version 0.1 of GEOS-5, also referred to as GEOS-5.0.1, the interim release used to

meet the production timeline requirements of the EOS instrument teams. Upgrades implemented for

Version 1.0, referred to as GEOS-5.1.0, address some of the deficiencies noted by the instrument teams

and in our tuning of the DAS for MERRA. These are documented, as are those for Version 2.0, referred

to as GEOS-5.2.0, which address some additional deficiencies noted by the CERES science team and

some final model tuning and analysis upgrades for MERRA.

This system documentation is organized as follows: The main characteristics of the atmospheric model

are described in Chapter 2. The analysis system is described in Chapter 3. The assimilation system and

observing system details are described in Chapter 4. The specific upgrades from GEOS-5.0.1 to GEOS5.2.0 are documented in Chapter 5.
2

2. The GEOS-5 Atmospheric General Circulation Model

The GEOS-5 atmospheric model is a weather-and-climate capable model being used for atmospheric

analyses, weather forecasts, uncoupled and coupled climate simulations and predictions, and for coupled

chemistry-climate simulations. Applications have used model configurations from 2° to 1/4° resolutions,

with 72 layers to 0.01 hPa, resolving both the troposphere and the stratosphere. The AGCM relies heavily

on ESMF, both superstructure and infrastructure, for its internal architecture (e.g., Collins et al., 2005).

Parallelization is primarily implemented through MPI, although some key parts of the code, such as the

model dynamics, also have Open-MP capability. The model runs on a 2-D decomposition, transposing

internally between horizontal and vertical layouts. Some of the physics such as the solar radiation, which

at any given time is active over only half the globe, is load balanced. The code scales well across compute

nodes and scalability increases linearly with problem size.

Developments of GEOS-5 were guided by a realistic representation of tracer transports and stratospheric

dynamics. The ozone analysis of the DAS is input to the radiation package along with an aerosol

climatology. GEOS-5 is coupled to a catchment-based hydrologic model (Koster et al., 2000) and a

sophisticated multi-layer snow model (Stieglitz et al., 2001) that is coupled to the catchment hydrology.

2.1 Hydrodynamics

The finite-volume dynamical core has an extensive documentation in the open literature (e.g., Lin, 2004,

and references therein). The different implementation in GEOS-5 compared with GEOS-4 is merely a

technical computational issue of layout on processing elements. GEOS-5 uses a 2-D horizontal

decomposition.

2.2 Physics

The physics package includes four major groups of physical processes: moist processes, radiation,

turbulent mixing, and surface processes. Each of these in turn is subdivided into various components. The

radiation module includes longwave and shortwave radiation submodules. The turbulent mixing consists

of the vertical diffusion, planetary boundary layer parameterization, and gravity wave drag. The surface

processes provide surface fluxes obtained from land, ocean and sea ice models.

2.2.1 Moist Physics Parameterizations

In developing GEOS-5, attention has focused on the representation of moist processes. GEOS5_Moist

considers liquid and ice phases of cloud condensate. Two separate cloud “types” are also recognized

explicitly, with separate fraction and condensate variables kept for each type. The cloud types are

distinguished by their source. One type, which will be denoted “anvil” cloud, originates in detraining

convection. The second type, which is referred to as large-scale cloud, originates in a probability

distribution function (PDF) based condensation calculation. Once created, condensate and fraction from

the anvil and large-scale cloud types experience the same loss processes: evaporation, autoconversion,

sedimentation and accretion. Parameter settings may vary by type, but identical formulations are used.

Clouds associated with updraft cores are not treated prognostically, but rainfall from convective cores is

disposed of within GEOS5_Moist.
3

Table 2.2.1: Principal quantities appearing in the GEOS5_Moist physics package. Quantities labeled “input/output”

are AGCM prognostic fields that incur modifications due to moist processes. These fields are normally also

modified by other model processes, e.g., advection. Those labeled “internal” are not modified by processes outside

of GEOS5_Moist, and normally are not prognostic, that is, they are generated and disposed of within a single call to

GEOS5_Moist. These fields are important in the internal dynamics of GEOS5_Moist but are normally not required

by other model processes. Fields labeled “output” are products of GEOS5_Moist for other GEOS5 processes. These

are used but may not be modified by other processes.

Variable Description Status

u Zonal wind Input/output

v Meridional wind Input/output

T Air temperature Input/output

q Specific humidity Input/output

ql,ls Liquid cloud condensate large scale source (LS) Input/output

qi,ls Frozen cloud condensate (LS) Input/output

ql,an Liquid cloud condensate anvil source (AN) Input/output

qi,an Frozen cloud condensate (AN) Input/output

fls Cloud fraction (LS) Input/output

fan Cloud fraction (AN) Input/output

qp,l,ls Liquid precipitating condensate (LS) Internal

qp,i,ls Frozen precipitating condensate (LS) Internal

qp,l,an Liquid precipitating condensate (AN) Internal

qp,i,an Frozen precipitating condensate (AN) Internal

qc,cu Total (ice+liquid) cloud condensate in cumulus updrafts (CU) Internal

qp,c,cu Total precipitating condensate (CU) Internal

qp,l,cu Liquid precipitating condensate (CU) Internal

qp,i,cu Frozen precipitating condensate (CU) Internal

fcu Areal fraction of cumulus updrafts Internal

φcu Mass flux in cumulus updrafts Internal

Pcu

Pan

Pls

Surface flux of precipitation from cumulus updrafts

Surface flux of precipitation from anvils

Surface flux of precipitation from large scale clouds

Output

Output

Output

The basic sequence of events in GEOS5_Moist is as follows. First, the convective parameterization,

Relaxed Arakawa-Schubert, or RAS (Moorthi and Suarez, 1992) is called. RAS estimates convective

mass fluxes for a sequence of idealized convective plumes. Each plume produces detraining fluxes of 

mass and cloud condensate, as well as profiles of precipitating condensate. Adjustments to the

environmental profiles of u, v, T and q are also calculated sequentially by each plume.

Next, the large-scale cloud condensate scheme (PrognoCloud) is called. PrognoCloud first takes the

detraining mass and condensate fluxes from RAS, if any exist, and adds them to the existing condensate 

and fraction of the anvil cloud type. Next, large-scale condensation is estimated using a simple assumed

PDF of qtotal. This step produces a new fraction and condensate for the large-scale cloud type. Freezing of

existing cloud condensate and partitioning of the new cloud condensate are also performed for both cloud

types.

After all sources of cloud condensate have been taken into account, four loss mechanisms are invoked: 1)

evaporation of condensate and fraction, 2) autoconversion of liquid or mixed phase condensate, 3)

sedimentation of frozen condensate, and 4) accretion of condensate by falling precipitation. Each of these

losses is applied to both anvil and statistical cloud types. The formulation of these terms is detailed below.
4

In addition to producing and disposing of condensate, PrognoCloud handles the fallout of autoconverted

(precipitating) condensate. Precipitating condensate is accumulated from the top down. In each model

layer a typical drop size, fall speed, and residence time is estimated. These parameters are used to

estimate re-evaporation of falling precipitation. The calculations are done separately for precipitation

originating from each of the two cloud types, as well as for convective core precipitation. A profile of

autoconverted condensate averaged over the grid-box within convective updrafts is one of the outputs of 

RAS.

A schematic diagram of GEOS5_Moist is shown in Figure 2.2.1. Each process within GEOS5_Moist is

discussed in greater detail below.

Figure 2.2.1: Schematic of Moist processes in GEOS-5.

2.2.1.1 Convection

GEOS5_Moist uses a modified version of the scheme described by Moorthi and Suarez (1992). As in

Moorthi and Suarez a sequence of linearly entraining plumes is considered with mass flux profiles given

by

!

"k (z) ="0k (1+ #kz).

The entrainment parameter for the k-th plume, λk, is determined by the choice of cloud base and cloud

detrainment level. The GEOS-5 implementation is flexible in this respect. The default is to take an

average of the two lowest model layers as the cloud-base layer. In GEOS-5 each model layer is tested,

starting from the model level near 100 hPa and moving down to the level above cloud base. A random

selection of plumes is also possible. However, this choice does not appear to have a major impact on

model behavior as long as roughly similar numbers of plumes are invoked.
5

Once cloud base, detrainment level, and λk have been chosen, a series of calculations is made for the

plume. A modified CAPE-based closure is used to determine the cloud base mass flux, φ0k. In addition to

determining φ0k and λk a steady-state profile of vertical velocity, wk, is determined for each plume as first

suggested by Sud and Walker (1999). The calculation of wk in GEOS-5 is simpler than that of Sud and

Walker: the buoyancy force is vertically integrated from cloud base to detrainment level to obtain a

velocity profile which is multiplied by an empirical tuning parameter:

!

wk ="w,cu g

Tk #T0

T0 zB

$

zD dz.

This approximate approach is employed because of the severe limitations inherent in the plume/parcel

view of convection, including the neglect of pressure forces on the parcel.

Autoconversion of convective condensate, qc,cu, to precipitating condensate, qp,c,cu, is also treated

following Sud and Walker (1999). Once an updraft velocity profile wk(z) is estimated for each plume, it

is used to derive time-scales Δzk/wk for parcels rising through the plume. These time-scales are then

employed in simple temperature-dependent, Sundqvist-type expressions (Sundqvist, 1978) for

autoconversion:

!

"qp,c,cu,k = #"qc,cu,k $ C0,cu f(T) 1 - exp

#qc,cu,k

2

qc,crit

2 / f(T)2

%

&

'

'

'

(

)

*

*

*

+

,

-

.

-

/

0

-

1

-

qc,cu,k

2zk

wk

.

Here, C0,cu is a base autoconversion rate for condensate in convective plumes. It is multiplied by a 

temperature dependent function f(T) specified below. The present model for the updraft velocity is much

simpler than that employed by Sud and Walker: the buoyancy force is integrated in the vertical and scaled

by a tunable parameter.

Each plume modifies the environmental θ and q profiles. These modifications are felt by all subsequent

plumes invoked during the call. In addition to the modification of the background thermodynamic state,

the plumes detrain mass and condensate into the environment, so that net effects,

!

DM = Dk

k

" and DC = Dk qcc,k

k

" ,

are obtained. DM and DC, the mass and condensate effects, respectively, are passed to PrognoCloud to

serve as sources for anvil cloud fraction and anvil cloud condensate. A net profile of precipitating

convective condensate,

!

PRAS = "qpc,k

k

# ,

is also passed to PrognoCloud. Finally, an estimate of updraft areal fractions is made using the total mass

flux through each layer along with the local vertical velocity estimate.

2.2.1.2 Large-Scale Cloud Scheme

Source Terms for Cloud. As described earlier, the scheme distinguishes two types of cloud, that

produced by detraining convection and that produced by large-scale condensation. The first type will be 

referred to as anvil cloud here and denoted by the subscript an. The second type, statistical or large-scale

clouds, will be denoted by the subscript ls.

Anvil Cloud. Anvil cloud condensate, qc,an, and anvil cloud fraction, fan, are updated straightforwardly

using DM and DC from RAS:
6

!

"fan = DM

#$z

and "qc,an = DC

#$z

.

Large-Scale Condensation. Condensation is based on a PDF of total water as in Smith (1990) or

Rotstayn (1997). However, GEOS5_Moist uses a boxcar with a spread determined by the local saturation

humidity, qsat.

The current cloud scheme can be interpreted as a prognostic PDF scheme with a bi-modal structure as

shown in Figure 2.2.2.

Figure 2.2.2: Schematic diagram of the implicit bi-modal PDF structure in the GEOS5_Moist cloud scheme. The

current scheme consists of a boxcar PDF in non-anvil regions added to a δ-function containing contributions from

detraining convection. In the symbols above, overbars refer to gridbox mean values.

Freezing and Melting of Cloud Condensate

Fresh (new) cloud condensate is partitioned initially according to temperature using,

!

f

ice(T) =

0 T > Tice

T "Tice

Tallice "Tice

#

$

%

&

'

(

4

Tice > T > Tallice

1.0 T < Tallice

)

*

+

+

,

+

+

.

However, freezing progresses as long as the condensate remains in subfreezing temperatures. This

freezing is parameterized as a temperature-dependent linear loss term for liquid condensate,

!

qtot =(1" fan )qtot,x

*

+ fanqtot,an

*

q

tot,an

*

=q

sat(T)+qc,an

*

; qc,an= f

anqc,an

*

!

fan"(q 

#

$ qtot,an

* )

!

fk

"

!

" = #qsat
7

!

q

•

l,{ls,an}FRZ = "ql{ls,an}

f

ice(T)

# FRZ

$

%

&

'

(

).

Whenever T exceeds Tice melting of condensate is assumed to occur instantly and completely. A single

ramped temperature-dependent saturation function is used for all calculations of saturation specific 

humidities.

2.2.1.3 Destruction of Cloud

Destruction of cloud occurs in four ways: 1) evaporation “cloud munching”, 2) autoconversion of cloud

condensate to precipitating condensate, 3) sedimentation of and 4) accretion of cloud condensate onto

falling precipitation.

Evaporation Cloud (Ec) “Munching”

This mechanism is meant to represent destruction of cloud along edges in contact with cloud-free air. This

process is parameterized using a microphysical expression from Del Genio et al. (1996),

where U is an environmental relative humidity, qc is the cloud condensate mixing ratio, rc is the cloud

droplet radius derived from an assumed number density, and A and B are temperature-dependent

microphysical parameters. In GEOS-5 this loss is applied only to the anvil type.

Autoconversion of Liquid and Mixed Phase Cloud (Ac)

This is parameterized using the same Sundqvist-type formulation as used in the convective

parameterization:

!

Ac{ls,an} = C0,{ls,an} f(T) 1 - exp

"ql,{ls,an}

2

qc,crit

2 / f(T)2

#

$

%

%

%

&

'

(

(

(

)

*

+

,

+

-

.

+

/

+

ql,{ls,an} .

Figure 2.2.3: “Sundqvist-factor” controlling low-temperature autoconversion.

The same temperature-dependent factor f(T) is used for ls and an clouds. The behavior of f (T) is shown

in Figure 2.2.3. The increase below 273K represents accelerated production of precipitation in mixed-

!

Ec = "CE, c

1"U

#w(A + B)rc

2 qc ,
8

phase clouds. The choice of this function is largely empirical. Destruction of cloud fraction by

autoconversion is not considered.

Rapid conversion or fallout of frozen ice crystals is handled explicitly using the sedimentation

formulation described next.

Sedimentation of Ice Cloud (Sc)

This is parameterized using cirrus ice fall speeds given by Lawrence and Crutzen (1998). However,

instead using their regime division based on latitude, their expression for tropical cirrus is assigned to

anvil clouds, and their mid-latitude form is assigned to large-scale clouds:

 

!

WF,i,an =128.6+53.2log10(qc,i,an )+5.5[log10(qc,i,an )]2

WF,i,ls =106 (qc,i,ls)

0.16 .

A simple one-way advection is used to represent the transition of ice cloud particles to sedimenting

particles - the “fall through” approximation (e.g., Le Treut et al., 1994):

!

Sc = "CS{ls,an} qi,{ls, an}

WF,i{ls,an}

#z

with empirically tuned parameters CS{ls,an}. This approximation is known to overestimate production of

frozen precipitation in other models (Rotstayn, 1997).

Fallout and Re-evaporation of Precipitation and Accretion of Cloud Condensate

All precipitation, including that produced within convective plumes, is finally disposed of in

PrognoCloud. Three streams of precipitation, each with two phases, are considered: liquid and frozen

precipitating condensate from ls clouds - qp,i,ls and qp,l,ls; liquid and frozen precipitating condensate from

an clouds - qp,i,an and qp,l,an, and liquid and frozen precipitating condensate from convective plumes (cu) -

qp,i,cu and qp,l,cu.

The inputs to the subroutine are mixing ratios of precipitating condensate. The precipitating condensate in

each stream and phase is accumulated from the top assuming complete fallout to obtain the downward

flux of precipitation at level k, P↓

box (k). To account for subgridscale variability in precipitation this flux is

scaled by a “shower area factor”, As defined below, P↓

S = P↓box − AX

-1

. This scaled flux is then used to

estimate a typical drop size rp using the Marshall-Palmer distribution. The quantity rp is used to estimate

precipitation fall velocities WF,p and ventilation factors Ve for the precipitation. These are now used along

with the vertical thickness of layer k to estimate the fractional re-evaporation of precipitating condensate 

during its passage through the layer.

The shower area factor As is calculated slightly differently for convective and non-convective

precipitation. For convective precipitation a weighted vertical mean of the updraft areal fraction is used.

For non-convective precipitation, qp,an and qp,ls, a similar weighted mean is calculated using the

corresponding cloud fraction in place of updraft area fraction. The parameter Ef, the “exposed fraction”,

represents the fraction of precipitation exposed to grid-box mean values of relative humidity, as opposed

to the shielded fraction Sf = 1-Ef which falls through a saturated cloudy environment (Figure 2.2.4). For

non-convective precipitation we assume Ef=1. For convective precipitation a shear-dependent exposure is

assumed.
9

Figure 2.2.4: Schematic diagram of geometry assumed in rain re-evaporation calculation.

The change in precipitating condensate calculated within the re-evaporation subroutine is given by:

!

"qp = #CE,pVe 1#U

$w(A + B)rp

2 qp

%z

WF,p

&

'

(

(

)

*

+

+

.

Accretion is parameterized simply using a Sundqvist-style expression as in Del Genio et al. (1996) or Sud

and Walker (1999).

2.2.2 Radiation

The radiative transfer model used in GEOS-5 is one developed at the Goddard Climate and Radiation

Branch. It has been integrated into various atmospheric models including the GEOS-5 AGCM, a

mesoscale model, and a cloud ensemble model (Tao et al., 1996).

2.2.2.2 The Shortwave Spectrum

The solar radiation model is documented in Chou and Suarez (1999). It includes the absorption due to

water vapor, O3, O2, CO2, clouds, and aerosols. Interactions among the absorption and scattering by

clouds, aerosols, molecules (Rayleigh scattering), and the surface are fully taken into account. Fluxes are

integrated over almost the entire spectrum, from 0.175 μm to 10 μm.

Depending upon the nature of absorption, different approaches are applied to different absorbers. Table

2.2.2 shows the spectral bands of the solar radiation model. There are eight bands in the ultraviolet and

visible region (ν > 14280 cm-1) and three bands in the infrared region (ν < 14280 cm-1). Also shown in the 

table are the absorbers and scatterers included in the calculation of solar fluxes in each band. The first

eight bands involve the O3 absorption and Rayleigh scattering. Band 8 also includes the weak absorption

due to water vapor. Single values of the O3 absorption coefficient, the water vapor absorption coefficient,

and Rayleigh scattering coefficient are used in each of the 8 bands. Bands 9-11 include the water vapor

absorption and Rayleigh scattering. Water vapor absorption in these bands is significant, and the kdistribution method is used. Band 9 also includes the weak O3 absorption. The O3 absorption in this band

is folded into the absorption in Band 8. The absorption due to O2 and CO2 is of secondary importance but

!

As=

" p # (z)A(z)dz

" p # (z)dz

A(z)v= cloud fraction or

updraft areal fraction

ρp = density of precipitation 

condensate

Ef “exposed fraction”
10

occurs in wide spectral ranges. Different approaches which compute only the reduction in fluxes are used.

Clouds and aerosols are included in all bands.

Table 2.2.2: Spectral bands, gaseous absorption and Rayleigh scattering in the broadband shortwave radiation

parameterization. Clouds and aerosols are included in all bands.

Spectral Range Band (cm-1) μm

Absorber/Scatterer

1 44440-57140 0.175-0.225 O3

Rayleigh

2 40820-44440

35700-38460

0.225-0.245

0.260-0.280

O3

Rayleigh

3 38460-40820 0.245-0.260 O3

Rayleigh

4 33900-35700 0.280-0.295 O3

Rayleigh

5 32260-33900 0.295-0.310 O3

Rayleigh

6 31250-32260 0.310-0.320 O3

Rayleigh

7 25000-31250 0.320-0.400 O3

Rayleigh

8 14280-25000 0.400-0.700 O3, H2O

Rayleigh

9 8200-14280 0.70-1.22

H2O

O3*

Rayleigh

10 4400-8200 1.22-2.27 H2O

Rayleigh

11 1000-4400 2.27-10.0 H2O

Total Spectrum

O2

CO2

* O3 absorption is folded into Band 8.

Reflection and transmission of a cloud and aerosol-laden layer are computed using the δ-Eddington

approximation. Fluxes are then computed using the two-stream adding approximation. For a cloud layer,

the optical thickness is parameterized as a function of cloud water/ice amount and the effective particle

size, whereas the single-scattering albedo and asymmetry factor are parameterized as a function of the 

effective particle size. Parameterizations are applied separately to water and ice particles. A maximumrandom approximation, a combination of maximum and random cloud overlapping schemes, is adopted

for the overlapping of clouds at different heights.

Aerosol optical properties are specified input parameters, as is the surface albedo which is specified

separately for the UV and PAR region and the infrared. It is also separately specified for direct and

diffuse fluxes. Hence, a set of four surface albedos must be specified as input to the radiation routine.

A special feature of this model is that absorption due to a number of minor absorption bands is included.

Individually the absorption in those minor bands is small, but collectively the effect is large, about 10%
11

of the atmospheric heating. Integrated over all spectral bands and all absorbers, the surface heating is

computed accurately to within a few watts per meter squared of high spectral-resolution calculations, and

the atmospheric heating rate between 0.01 hPa and the surface is accurate to within 5%.

2.2.2.2 The Thermal Infrared Spectrum

The longwave radiation model is documented in Chou et al. (2001). The parameterization includes the

absorption due to major gaseous absorption (water vapor, CO2, O3) and most of the minor trace gases

(N2O, CH4, CFC's), as well as clouds and aerosols with optical properties specified as input parameters.

The thermal infrared spectrum is divided into nine bands and a sub-band. Table 2.2.3 shows the spectral

ranges for these 10 bands, together with the absorbers involved in each band. The water vapor line

absorption covers the entire IR spectrum, while the water vapor continuum absorption is included in the

540-1380 cm-1spectral region. The absorption due to CO2 is included in the 540-800 cm-1region, and the 

absorption due to O3 is included in the 980-1100 cm-1region. The minor absorption due to CH4, N2O,

CFC's, and CO2 is scattered between 800 cm-1and 1380 cm-1region in Bands 4-7. The absorption due to

N2O in the 17μm region is included in sub-band 3a and is identified as Band 10.

Chou et al. (2001) approximates the band-integrated downward and upward longwave fluxes as:

!

Fi

"( p) = 0 Bi p # (%$)

&Ti( p, p $)

&p $

dp $,

!

Fi

"( p) =# iBi($s)Ti( p, ps) + 0 Bi p % ($&)

'Ti( p, p &)

'p &

dp &+(1(# i)Fi

)( ps)Ti( p, ps),

where

!

Ti( p, p ") #

1

Bi($0)

'&% i

B% ($0)T% ( p, p ")d%,

!

B" (#)

is the Planck flux,

!

T" ( p, p #)

is the flux transmittance for isotropic radiation,

!

Bi(") = B# (") $# i % ,

!

"i

is the surface emissivity,

!

ps

is the surface pressure,

!

"s

is the Earth’s surface skin temperature, and

!

"0

is a typical value of the atmospheric temperature, set to 250K. The spectrally integrated Planck fluxes

were pre-computed for each band and then fit with a fifth-degree polynomial in temperature. When

integrated over all bands, errors in this regression are negligible (< 0.1%) for 150K < θ< 350K. The

regression coefficients are given in Chou et al. (2001).

The polynomial approximation is used to calculate sensitivity of the upward fluxes to the surface

temperature. Since the longwave radiation parameterization is called less often than the boundary layer

and land surface parameterizations, all fluxes are linearized about the surface temperature at the

beginning of the radiation interval, and radiative heating rates are recomputed based on this linearization

at each time step.

To achieve a high degree of accuracy and speed, various approaches of computing the transmission

function are applied to different spectral bands and gases. The gaseous transmission function is computed

either using the k-distribution method or the table look-up method. Table 2.2.3 shows the bands, the

absorbers, and the method used to compute transmission in each band.

To include the effect of scattering due to clouds and aerosols, the optical thickness is scaled by the singlescattering albedo and asymmetry factor. The optical thickness, the single-scattering albedo, and the

asymmetry factor of clouds are parameterized as functions of the ice and water content and the particle

size. The aerosol amounts are specified input parameters together with a function that computes optical
12

thickness, single-scattering albedo, and asymmetry factor for each aerosol and each of the 10 bands at

every atmospheric layer. The aerosols used in GEOS-5 correspond to the 15 species of dust, carbon,

sulfate, and sea-salt currently used in the Goddard Chemistry Aerosol, Radiation, and Transport

(GOCART) aerosol model (Chin et al., 2002). These can be produced by the GOCART model or read in

as specified 4-dimensional distributions. The parameterization can accurately compute fluxes to within

1% of the high spectral-resolution line-by-line calculations. The cooling rate can be accurately computed

in the region extending from the surface to the 0.01-hPa level.

Table 2.2.3: Spectral bands, absorbers, and transmittance parameterizations.

Band Spectral Range

(cm-1) Absorber

Transmittance

Parameterization 

Method

1 0-340 H2O line T

2 340-540 H2O line T

3a 540-620

3b 620-720

3c 720-800

H2O, CO2 line

H2O continuum

T

C

4 800-980

H2O line

H2O continuum

CO2, F11, F12, F22

K

C

K

5 980-1100

H2O line, CO2, F11

H2O continuum

O3

K

C

T

6 1100-1215

H2O line

H2O continuum

H2O, CH4, F12, F22

K

C

K

7 1215-1380 H2O line, N2O, CH4

H2O continuum

K

C

8 1380-1900 H2O line T

9 1900-3000 H2O line H

10 540-620 H2O line, CO2, N2O

H2O continuum

K

C

K: k-distribution method with linear pressure scaling.

T: Table look-up with temperature and pressure scaling.

C: One-parameter temperature scaling for water vapor continuum absorption.

In GEOS-5 cloud properties and amounts are predicted at each model layer. In the radiation code, the

layer clouds are grouped into three height ranges: high, middle and low, separated approximately by 400

hPa and 700 hPa pressure levels. Clouds in layers within each height group are assumed maximally

overlapped, and clouds among the three height groups are assumed randomly overlapped. Different types

of aerosols are allowed to co-exist in a layer. The total effective optical thickness, single-scattering

albedo, and asymmetry factor of a layer are computed similarly to those of clouds.

2.2.3 Turbulent Mixing

The free atmospheric turbulent diffusivities are based on the gradient Richardson number.

Two atmospheric boundary-layer turbulent mixing schemes are used. The Louis et al. (1982) scheme is

used in stable situations with no or weakly-cooling planetary boundary layer (PBL) cloud. The Lock et

al. (2000) scheme is used for unstable or cloud-topped PBLs. The latter scheme includes a representation
13

of non-local mixing (driven by both surface fluxes and cloud-top processes) in unstable layers, either

coupled to or decoupled from the surface, and an explicit entrainment parameterization. The scheme is

formulated in the moist conserved variables θl, the liquid–frozen water potential temperature, and qt, the

specific total water content, so that it can treat both dry and cloudy layers. In GEOS-5, the scheme is

extended so that unstable surface parcel calculations include moist heating and entrainment.

GEOS-5 incorporates two gravity wave drag parameterizations, an orographic gravity wave drag

formulation based on McFarlane (1987), and a formulation for non-orographic waves based on Garcia

and Boville (1994).

The mountain waves are forced by the sub-grid orographic variability, h' = sqrt ( avg( [ h- avg(h) ]

2

) ),

where avg() denotes an average over the scale of gridbox. The terrain data, h(x,y), is from the GTOPO30

data (http://edc.usgs.gov/products/elevation/gtopo30/gtopo30.html), with approximately 1 km resolution.

The smallest scales (< 10km) are not used to force gravity waves, but enter into an orographic form drag

used in the turbulence. The nominal gravity amplitude at the surface is given by MIN(h', U/N), where U is

the surface wind speed and N is the low level stratification frequency.

The non-orographic waves, important in the stratosphere and mesosphere, are launched at 100 hPa.

GEOS-5 uses an 8 wave-spectrum, with waves at phase speeds of 10, 20, 30 and 40 ms-1 in both

directions with respect to the wind at launch level. Their amplitude depends on their phase speed in a

Gaussian way, ~ exp( ( -c / 30)

2 ). The amplitude is modified according to latitude, ranging from full

amplitude in both polar regions (90-45 latitude bands) and dropping to 0.2 of the base amplitude in the

tropics (20°S-20°N). The base amplitude, i.e., a wave with c approaching 0 near the poles, is 6.4e

-3 N m-2

.

2.2.4 Chemical Species

2.2.4.1 The Ozone Model

Rather than transporting ozone (O3), the GEOS-5 model transports the odd-oxygen family:

Ox = O3 + O(

3

P) + O(

1

D).

The chemical change in Ox is computed by

Ox(t + dt) = (Ox* + P dt ) / ( 1 + L dt ),

where t is time, P is the Ox production rate, L is the Ox loss frequency, and Ox* is the intermediate Ox

field that includes effects of transport and turbulent processes. Zonally-invariant and monthly-averaged

coefficients P and L are used, as generated by the Goddard two-dimensional chemistry and transport

model with surface source gas boundary conditions for the year 2000 (Fleming et al., 2001).

Ozone is derived from Ox. O3 is specified to be equal to Ox for pressure higher than 1 hPa. At pressures

lower than 1 hPa, O3 is specified as equal to Ox during the nighttime and as

O3 = Ox exp[-1.5(log10 p)

2

],

in the daytime, where p is pressure in hPa. This relation is an empirical fit to equatorial daytime O3/Ox

ratios in a simulation that utilized a complete stratosphere-mesosphere chemistry mechanism. The diurnal

ozone variation is due to fast ozone photolysis and subsequent recombination during nighttime in the

mesosphere.

To avoid development of a low ozone bias in the upper stratosphere in GEOS-5, Ox production rates are

adjusted following Stajner et al. (2004). The Ox production rates are modified so that the ozone chemical
14

balance (which is P/L in the stratosphere) agrees with ozone climatologies from the Upper Atmosphere

Research Satellite data (http://hyperion.gsfc.nasa.gov/Public/Analysis/UARS/urap/home.html) and SBUV

data (Langematz, 2000).

2.2.4.2 Other Constituents

The other radiatively active species, methane (CH4), nitrous oxide (N2O), chlorofluorocarbons (CFC-11,

CFC-12), hydrochlorofluorocarbon (HCFC-22), and stratospheric water vapor (H2O) are specified from

the steady-state climatology of the Goddard two-dimensional chemistry and transport model, which

employed surface source gas boundary conditions from 2000.

2.2.5 Surface Processes

The surface exchange of heat, moisture and momentum between the atmosphere and land, ocean or sea

ice surfaces are treated with a bulk exchange formulation based on Monin-Obukhov similarity theory.

GEOS-5 employs specified distributions of sea surface temperatures and sea ice, either from an observed

weekly/monthly mean time series or annually repeating climatological mean. The sea ice distribution is

prescribed.

2.2.6 The Catchment Land Surface Model

GEOS-5 is coupled to a catchment-based hydrologic model (Koster et al., 2000) and a sophisticated

multi-layer snow model (Stieglitz et al., 2001).

2.2.6.1 Overview

The one-dimensional "layered" framework used by traditional land surface models (LSMs) is arguably

not amenable to an adequate treatment of runoff generation or subsurface soil moisture movement, since

both processes in nature are largely controlled by spatial heterogeneity in soil moisture. The development

of the GMAO Catchment LSM (Koster et al., 2000, Ducharne et al., 2000) is an attempt to improve 

treatment of the subgrid horizontal structure of land surface hydrological processes. In this LSM, subgrid

heterogeneity in surface moisture state is treated statistically, since computational constraints (now and in

the foreseeable future) prevent its explicit resolution. Nevertheless, the applied distributions are related

sensibly to the topography, which exerts a major control over much of the subgrid variability.

2.2.6.2 Modeling Approach

The approach is illustrated in Figure 2.2.5, which shows three different levels of the (shallow) water table

and the associated partitioning of the surface into three regions: (1) a saturated region, from which

evaporation occurs with no water stress and over which rainfall is immediately converted to surface

runoff, (2) a subsaturated region, from which transpiration occurs with limited water stress and over

which rainwater infiltrates the soil, and (3) a “wilting” region, in which the water stress shuts down the

transpiration completely. The relative areas of these regions, which vary in time, are unique functions of

the local topography and the values of the Catchment LSM's three water prognostic variables. By

continually partitioning the catchment into hydrologically distinct regimes and then applying different

runoff and evaporation physics in the different regimes, the Catchment LSM should, at least in principle,

produce a more realistic simulation of areally-averaged surface energy and water processes.
15

Figure 2.2.5: Separation of the catchment area into hydrological regimes.

The soil water prognostic variables used by the Catchment LSM are “non-traditional” in that they are not

strictly associated with soil layers. The main variable, the “catchment deficit”, describes the equilibrium 

water table distribution and the associated distribution of the equilibrium soil moisture profiles in the 

overlying vadose zone. The second variable describes the degree to which the root zone is out of 

equilibrium with the catchment deficit, and the third describes the degree to which the near-surface

moisture is out of equilibrium with the other two variables. The water transfer between the three variables

and the baseflow flux out of the system are controlled in part by the local topography.

The model's other prognostic variables include an interception reservoir water content, a surface

temperature, and the heat contents of six subsurface soil layers, from which time-varying vertical profiles

of soil temperature over several meters can be derived. The model allows explicit vegetation control over 

the computed surface energy and water balances, with environmental stresses (high temperatures, dry soil,

etc.) acting to increase canopy resistance and thus decrease transpiration. Six fundamentally different

types of vegetation are considered in the current version of the Catchment LSM: broadleaf evergreen

trees, broadleaf deciduous trees, needleleaf trees, grassland, shrubs, and tundra vegetation. Bare soil

evaporation, transpiration, and interception loss occur in parallel. The energy balance formulations in the

model (again, applied separately in each hydrological regime) were derived in large part from the Mosaic

land surface model (Koster and Suarez, 1996), which in turn borrowed heavily from the SiB model of

Sellers et al. (1986) for the transpiration calculation.

Snow is modeled using three prognostic variables (heat content, snow water equivalent, and snow depth)

in each of three layers (Stieglitz et al., 2001). The melting and refreezing of snow, snow compaction,

liquid water retention, and the impact of snow density on thermal conductivity and albedo are explicitly

treated.

M1

M2

M3

Saturated fraction

equals zero; part of

catchment now below

wilting point.

Lower water table

leads to smaller

saturated fraction

Significant saturated

fraction leads to high

surface runoff

PLAN VIEW: M1 PLAN VIEW: M2 PLAN VIEW: M3

ground surface

water table height
16

2.2.6.3 Implementation in GEOS-5

The Catchment LSM's implementation into the GEOS-5 system involves the “tiling” of a surface grid cell

into a number of independent and irregularly shaped hydrological “catchment” elements. The catchment

boundaries are derived from a 30-arc-second resolution (approximately 1 km) digital elevation model

(DEM) provided by the U.S. Geological Survey. The delineation procedure considers network topology

and drainage area (Verdin and Jenson, 1996; Verdin and Verdin, 1999) along with the application of 

ordering rules associated with a catchment coding system. For computational efficiency, and to take

advantage of resolved heterogeneity in atmospheric forcing, catchments that straddle adjacent grid cells

are separated into independent adjoining catchments, one in each grid cell. Runoffs produced by these

artificially separated catchments can be combined into a single runoff that can then be routed across the

continent.

Global distributions are needed for a number of model parameters. The global HYDRO1K data set

produced by the U.S. Geological Survey provided the distributions of compound topographic index

needed to compute, within each catchment element, the parameters that control the shape of the shallow

water table (using a TOPMODEL-type construct). Global soil texture information is derived from a 5-

minute data set assembled by Reynolds et al. (1999). Global seasonal climatologies of leaf area index and

greenness fraction are taken from AVHRR-based data generated at the University of Wales and compiled

by the Global Soil Wetness Project (Dirmeyer et al., 2006). Global distributions of vegetation type are

taken from http://edcsns17.cr.usgs.gov/glcc/globdoc2_0.html, the Earth Resources Observation and

Science website. GEOS-5 uses a two-stream approximation that lets snow-free albedo (for the visible and

near-infrared bands) vary with solar incidence angle, but the values so produced are scaled so that they

are consistent, on the monthly time scale, with the snow-free albedos produced by Moody et al. (2005) 

from MODIS data. Global surface emissivity data are taken from Wilbur et al. (1999).

2.2.6.4 Testing of the Catchment LSM

Various incarnations of the Catchment LSM have been evaluated extensively against observations

through participation in the PILPS-2e project (Bowling et al., 2003), the Rhone-AGG project (Boone et

al., 2006), and the second phase of the Global Soil Wetness Project (Dirmeyer et al., 2006). In addition,

the Catchment LSM has proven to be an effective host for a soil moisture data assimilation system 

(Reichle and Koster, 2005; Reichle et al., 2007).

2.3 Specific Implementation for GEOS-5.0.1, GEOS-5.1.0, and GEOS-5.2.0.

The GCM used in GEOS-5.0.1 has a 0.5° latitude by 0.625° longitude horizontal resolution, with the

prognostic variables discretized on a staggered D-grid (Figure 2.3.1). There are 72 vertical layers from the

surface to 0.01 hPa. This system has an effective time step of 30 minutes, which is the time step of its

physics parameterization (although the dynamics time step is considerably shorter). The primary variables

are: wind components (u,v); scaled virtual potential temperature (θ*=Tv/pκ); pressure thickness (of the

Lagrangian control volume, p); and specific humidity (q).
17

Figure 2.3.1: Lagrangian control volume and state variables for the GEOS-5 AGCM.

2.3.1 Ancillary Initial and Boundary Data

A climatological aerosol distribution is used (Colarco et al., 2008). The model uses either a climatological

ozone distribution or (in DAS mode) the ozone analysis generated from the DAS. The surface orography

and its sub-grid scale standard deviation were derived from the 30-second US Geological Survey Global

Topographic Data (GTOPO30). An area-preserving algorithm is used to map the high-resolution

GTOPO30 data set to model resolutions. The sea surface temperature and sea ice concentrations are

derived from the weekly 1° Reynolds sea surface temperature (ERSST) version 2 (Reynolds et al., 2002).

They are updated every time step using linear interpolation in time. GEOS-5 also employs an option to

nudge the stratospheric water vapor to the zonal mean climatological HALOE (Halogen Occultation

Experiment) (Randel et al., 1998) and MLS (Microwave Limb Sounder) water vapor data.

2.3.2 The Model Grid 

The GEOS-5 terrain-following Lagrangian control volume (lcv) coordinates are similar to an eta 

coordinate system. The model output and many of the GEOS-5.0.1 products are lcv products. The

products include the full three-dimensional pressure variables at both layer centers (PLijl) and layer edges

(PLEijl). The pressures reported are on a hybrid-sigma coordinate. Indexing in the vertical starts at the top,

i.e., lcv layer 1 is the layer at the top of the atmosphere, lcv layer 72 is adjacent to the earth’s surface.
18

3. The GEOS-5 Analysis

At the heart of the DAS is the analysis itself. The analysis combines information from irregularly

distributed observations with a model state in such a way as to minimize a specified cost function. The

model state (the background used for the analysis first guess) is obtained from a forecast initialized from a 

previous analysis. The weights assigned to each contribution to this combination depend on the specified

error (or uncertainty) statistics for each of the observations and the model background. The GEOS-5 DAS

uses the GSI analysis solver developed at NCEP. Other essential components are the quality-control

software and the Radiative Transfer Model (RTM) needed for the radiance assimilation. The GSI is

coupled to the Community Radiative Transfer Model (CRTM) developed through the JCSDA. For the

stratospheric sounding unit (SSU) data used in MERRA, the GSI has been coupled to the GLATOVS

RTM.

Some details of the GSI are presented in Section 3.1. The background (model forecast) error statistics are 

discussed in Section 3.2. The observation streams and their error characteristics are presented in Section

3.3. The RTMs are presented in Section 3.4. Information pertaining to the implementation of the analysis

for versions 5.0.1 and 5.1.0/5.2.0 of GEOS-5 is given in section 3.2.5.

3.1 The GSI Solver

The GSI solver was developed at NCEP to support their unified 3D-Var analysis system for global and

regional models. The GSI builds upon the Spectral Statistical Interpolation (SSI) analysis which is

documented at http://www.emc.ncep.noaa.gov/gmb/gdas/. The analysis variables are defined in grid space 

and recursive filters are the basic building blocks used to create background error covariance structures

(Derber et al., 2003). The implementation uses the recursive filters to produce approximately Gaussian

smoothing kernels and isotropic correlation functions (Wu et al., 2002). By superposition of Gaussian

kernels with different length scales it is possible to generate non-Gaussian shapes, and generally to

implement a large class of flow-dependent inhomogeneous background error covariance models (Purser

et al., 2003a,b).

The variational analysis, xa, is obtained by minimizing the scalar cost function

!

J(x) = (x " xb)

T B"1

(x " xb) + [y " h(x)] T [E + F]

"1 [y " h(x)] + JC

with respect to the control vector, x. The background, xb, represents a prior estimate of x and B is its

expected error covariance. The vector y contains the available observations, the operator (also called the

forward model) h(x) simulates these observations from x, and E+F=R contains the expected observation

error covariances, including both instrument and representativeness errors. JC represents additional

constraints that can be imposed, such as mass-wind balance and moisture constraints.

The control vector or set of analysis variables, x, represents the atmospheric state at the central point in a 

6-hour time window as well as predictor coefficients used for radiance bias correction (Derber and Wu,

1998; Dee, 2004, 2005) and surface temperatures used to correct model deficiencies at radiance data

locations (Simmons, 2000). The forward model h(x) transforms the model variables into pseudoobservations. The pseudo-observation value at the observation time is obtained by linear interpolation

using background states provided at the analysis time and 3 hours before or after the analysis time. The

forward model can be as simple as interpolation from model grid point to the observation location, or as

complex as a radiative transfer model for satellite observations.
19

To accommodate nonlinear operators h (e.g., precipitation, wind speed, penalties on q for supersaturation

and negative values), J(x) is minimized using an incremental strategy (Courtier et al., 1994) in which the

problem is repeatedly linearized about an updated current solution (the outer loop). In the first outer loop

iteration, the current solution is the 6-hour forecast. In later iterations, the current solution is the result

from the previous iteration. Currently, only two outer loops are performed due to computational

considerations.

A pre-conditioned conjugate gradient algorithm (the inner loop) is used to minimize the resulting

quadratic cost function for the increments. The conjugate gradient algorithm requires the gradient of J

with respect to the analysis variables. The gradient is evaluated using the adjoint of the transformation of

the analysis variables into the observation variables.

The control variables, x, are:

ψ: stream function contribution to wind

χunbal: unbalanced velocity potential function

Tunbal: unbalanced temperature

Punbal: unbalanced surface pressure

q: moisture

cw: cloud water

O3: ozone 

and coefficients for the bias correction of the satellite radiance data.

The balanced part of the temperature is defined by Tbal = Gψ, where G is an empirical matrix that projects

increments of stream function at one level to a vertical profile of the balanced part of the temperature

increments. G is latitude dependent. The balanced part of the velocity potential is defined as χbal = c ψ,

where the coefficient c is function of latitude and height. The explained variance for balanced temperature

and velocity potential as a function of height at 60°N is shown in Figure 3.1.1. The balanced part of the 

surface pressure increment is defined as Pbal = Wψ, where the vector W integrates the appropriate

contribution of the stream function from each level. The explained variance of the balanced surface

pressure calculated in this manner is shown as a function of latitude in Figure 3.1.2.

Figure 3.1.1: The explained variance of the balanced part of temperature (red curve) and velocity potential (green

curve) at 60°N used in GEOS-5.0.1 (left) and GEOS-5.1.0 (right). The balanced velocity potential is largest at the

surface to include a surface friction effect.
20

Figure 3.1.2: The explained variance of the balanced surface pressure as a function of latitude.

The updated (analyzed) fields are: zonal and meridional wind components (u,v), temperature (T),

moisture (q), cloud water (cw), ozone (O3), surface pressure (ps), surface temperature (Tskin). The analyzed

wind components are calculated from the stream function and velocity potential.

3.2 The Treatment of Satellite Radiance Data

Satellite data have become an essential part of the observing system. They represent by far the largest

volume of data ingested into operational NWP assimilation systems and their use in these systems has a

measurable positive impact on forecast skill scores, especially in the Southern Hemisphere.

The analysis procedures for satellite radiance data are presented in Derber and Wu (1998) and McNally et

al. (2000). As input to the surface emissivity calculation and the radiative transfer calculation of h(x), the

background profiles of temperature, moisture (mixing ratio) and ozone (mixing ratio), and the surface

temperature and 10-m wind speed are interpolated to the observation location and the pressure levels used

by the radiative transfer scheme. Based on this information and the surface type, the radiative transfer

code generates a pseudo-observation of brightness temperature and the Jacobian matrix needed for the

minimization.

3.2.1 Data Thinning

The large volume of satellite data and the expense of including them in analyses forces a subsetting or 

thinning of these observations prior to assimilation. In addition, the errors implied by the combined

observation and radiative-transfer error covariance matrix should be correlated both between adjacent

observations and between channels of the same sounding. In practice, it is difficult to estimate these

correlations; therefore, the observation errors are assumed to be un-correlated and this matrix is diagonal.

In the GSI, the thinning strategy is defined by a specified resolution for each instrument type, the

likelihood of the observation passing a quality control (QC) window check, the underlying surface

properties, the difference between the observation time and the analysis time, and the distance between

the observation location and the center of the analysis grid box. The size of the thinning box for each

instrument type is summarized in Table 3.2.1.
21

Table 3.2.1: The sizes of the observation thinning box used in the GSI for different instrument types.

Instrument

Type

AMSU-A AMSU-B/MHS HIRS/AIRS

GOES Sounder/Imager

SSM/I SSU

Thinning

Box Size

145 km 240 km 180 km 160 km 200 km

3.2.2 Satellite Data Bias Correction

Substantial biases are evident when satellite data are compared to the pseudo-observations derived from

the background model [e.g., Eyre et al., 1993]. These biases may be due to bias in the background fields,

or to errors in ground processing or in the forward processing (e.g., radiative transfer), residual

contamination of the observations from cloud, instrument calibration errors, or inaccurate specification of 

instrument spectral response filters. Derber and Wu (1998) ascribe the dominant sources of these biases to

ground processing errors and uncertainties in the radiative transfer calculation.

The biases vary spatially and depend on other satellite parameters such as the local zenith angle. For

many channels, the mean value of the bias (calculated as the difference between the observed radiance

(O) and that (F) calculated from the model background) is large relative to the instrument noise. It is

therefore necessary to apply corrections either before the radiances are used in the assimilation or during

the assimilation procedure. The latter approach, termed adaptive bias correction, has the advantage that

the system automatically adjusts the bias estimate for the satellite data so as to maintain consistency with

all available information, i.e., both the model background and all other observations. One of the

disadvantages of this method is the possibility that the model bias will become incorporated in the

coefficients and feed back into the system and amplify the model bias.

Dee (2005) describes the bias estimation procedure as follows. Bias parameters are estimated along with

the model state in a variational analysis by augmenting the control vector with those bias parameters. To

be explicit, the cost function of Section 3.1 can be written as

!

J(x) = (x " xb)

T B"1

(x " xb) +(b"bb )

T B#"1

(b"bb )+ [y " h(x)" b(x,b)] T R"1 [y " h(x)" b(x,b)] + JC .

The errors in the background estimate for the predictor coefficients, βb, are generally correlated with

the errors in the state estimate because they depend on the same data, however, because of lack of

information, the cross-covariance in the GSI implementation is assumed to be zero giving the form of

the cost function above.

The implementation in the GSI relies on linear predictor models so that the bias model included in the

forward model is

!

b(x,b) = "i pi(x)

i=0

N p

# ,

where b is the bias model and the pi are the predictors. Only a few predictors are used in order not to overfit the biases, but the predictor coefficients for each channel and each sensor are allowed to be different.

In the GSI, p0 is a constant and the other predictors are: scan angle, lapse rate, lapse rate squared and (for

microwave instruments) cloud liquid water. The predictors are scaled so that the same background error

variance is used for each coefficient. A bias estimate is made for each scan position (for GOES it is for 

each integer local zenith angle). The total number of radiance bias parameters included in the system is

roughly N = Np ×Ns × Nc, where Np is the number of predictors used, Ns is the number of sensors being

assimilated, and Nc is the number of channels per sensor.
22

(a) (b)

The background estimate for β is the estimate obtained from the previous analysis. The bias estimates

spin up to a stable estimate fairly quickly, viz., a few days. In GEOS-5, new satellite data are only

introduced after a two-week passive assimilation used to estimate the bias parameters.

Figure 3.2.1a gives an example of the observation minus forecast calculation of the brightness

temperature (i.e., O-F) for AIRS channel 1756 (wavenumber 1524.35cm-1) without bias correction. This

channel is sensitive to upper tropospheric humidity and the bias has large variation globally. The

associated weighting function for this channel is also shown (Figure 3.2.1b). The bias in radiance data

also varies with scan angle. The bias across scan angle is commonly detected in AMSU-A data. Figure

3.2.2 shows such bias for Channel 12 (57.3GHz) of AMSU-A on NOAA-15 and EOS/Aqua respectively.

Figure 3.2.1: (a) The difference between the observed (without bias correction) and the calculated brightness

temperature from the NWP model background (O-F), and (b) the normalized weighting function for AIRS moisture

channel 1756.

Figure 3.2.2 Examples of AMSU-A mean (upper panels) and standard deviation (lower panel)s of O-F values across

the scan angles for (a) NOAA-15 and (b) Aqua. The red curve indicates O-F values before bias correction and the

green curve shows O-F values after bias correction. The blue curve is the difference between observed and the

calculated brightness temperature from the analysis.

(a) (b)
23

(a) (b)

(a) (b)

(a) (b)

Figure 3.2.3: O-F maps for Aqua AMSU-A channel 8 data (a) before bias correction, and (b) after bias correction.

Figure 3.2.4: Global mean and standard deviation of O-F values before (left panels) and after (right panels) bias

correction for each channel are shown for (a) Aqua AMSU-A and (b) NOAA-17 HIRS3.

Figure 3.2.5: (a) Example of coefficients used in the variational bias correction and (b) the contributions to the bias

correction for AQUA EOS AMSU-A channel 12.
24

Examples of the O-F values for channel 8 from EOS AMSU-A on board Aqua before and after the bias

correction are show in Figure 3.2.3. Global averaged O-F values for each channel on EOS AMSU-A

before and after the bias correction are shown in Figure 3.2.4. These examples indicate that the biases

were eliminated by the variation bias correction scheme effectively. Any systematic components of the OFs that are not explained by these predictors are left in the data and are assumed to be systematic forecast

model error. Examples of the bias correction coefficients for NOAA-15 AMSU-A channel 15 are shown

in Figure 3.2.5a, and each term contributing to the bias correction in Figure 3.2.5b.

3.2.3 Ozone Channels

AIRS ozone channels around 9.6 μm are not actively assimilated. Ozone increments generated from the

assimilation of other radiance data are not used in GEOS-5. This choice was made to avoid systematic

ozone analysis increments from radiance data. Experience was that use of these increments led to

unrealistic ozone profiles in the polar night because of accumulation of ozone in the lower stratosphere

and excessive ozone reduction in the upper stratosphere. The impact of radiance data became more

pronounced after the introduction of the IAU with its reduced noise in ozone transport. A part of the

detrimental radiance impact on ozone is believed to be due to polar stratospheric clouds (PSCs). The

semitransparent PSCs are not represented in the GCM or in the forward model for the radiances. The

cloud detection scheme does not exclude radiances affected by such thin clouds even though some 

radiances (such as the AIRS “upper tropospheric moisture” channel at 6.79 μm) are sensitive to ice PSCs

(Stajner et al., 2007).

3.3 Other Assimilation Components

3.3.1 The Precipitation Assimilation

The assimilation system includes instantaneous rain rate estimates from SSM/I and the TRMM

Microwave Imager (TMI). Details are provided in Treadon et al. (2002). The assimilated precipitation

observation is ln(1+rain_rate). The forward model, h(x), is a simplified Arakawa-Schubert cumulus

parameterization that includes cumulus momentum mixing and random selection of the convective cloud

top from a range of values bounded by the sounding profile. The large scale precipitation model is based

on Zhao and Carr (1997). Input to the forward model consists of surface pressure, temperature, specific

humidity, cloud condensate (cw), zonal wind, and meridional wind:

rain_ratetot = rain_ratenv(T,u,v,q,ps) + rain_rategs(T,q,cw,ps).

Only surface pressure is not included as a control variable in the tangent linear (TLM) and adjoint

models. The simulated surface rain rates are most sensitive to the moisture and cloud condensate.

3.3.2 The Surface Temperature Analysis

Accurate specification of the (apparent) surface skin temperature is extremely important in the estimation

of pseudo-observations of satellite brightness temperatures for channels which have a significant

contribution from the surface. Hence this variable is included in the control vector, x. However, the

resulting analysis is not used to update the skin temperature used by the forecast model. The rationale for

this approach is provided by Derber and Wu (1998).

3.4 Specification of Background Error Statistics

A crucial part of the implementation of the any analysis is the specification of the background error

covariance, B, and the observation error covariance, R. Each component of x has its own partition of the 

background error matrix B. The error statistics are estimated in grid space with the ‘NMC’ method

(Parrish and Derber, 1992; Rabier et al., 1998), i.e., by calculating the variances and covariances from the
25

differences between 24-hour and 48-hour forecasts, forecasts initialized 24 hours apart, verifying at the

same time.

3.4.1 State Variables

3.4.1.1 Stream function, u, v, humidity

The variance statistics of ψ are shown in Figure 3.4.1 as a function of latitude and sigma level. The error

variance (m4s

-2

) is larger in mid-latitudes than in the tropics and larger in the southern hemisphere than in

the northern. The horizontal scales are larger in the tropics, and increase with height. The vertical scale

factors are larger in the mid-latitude, and decrease with height. The vertical scale factors depicted in the 

figures below represent inputs to the recursive filters used to create the covariance functions. They are

such that the vertical correlation generated from the recursive filter fits the scales estimated from the

training data sets. The resulting vertical scale of the covariance function varies with height, becoming

broader toward the top of the model. For example, see Figure 3.4.2 which shows the vertical correlation

for pseudo-relative humidity at different levels, given a constant vertical scale factor of 1.0. The error

variances and vertical scales for humidity are shown in Figure 3.4.3.

Figure 3.4.1: Example of estimated background error statistics for ψ. Top: error standard deviation as a function of

latitude and sigma level (in m2s

-1

); middle: horizontal scales of covariance (in km); bottom: vertical scale factor of

covariance. Left hand panels are the statistics used for GEOS-5.0.1; right-hand panels for GEOS-5.1.0.
26

Figure 3.4.2: Example of the vertical correlation at different levels, given a constant vertical scale factor of 1.0. This

structure is generated by the recursive filter to model the vertical correlation for all variables.

Figure 3.4.3: Example of estimated background error statistics for pseudo-relative humidity. Top: error standard

deviation as a function of latitude and sigma level; middle: horizontal scales of covariance (in km); bottom: vertical

scale factors for covariance.
27

Other elements of B can be seen through the marginal gain, i.e., the increment from a single observation,

as shown in Figures 3.4.4 and 3.4.5.

Figure 3.4.4: u (left) and v (right) increments (xa–xb), at sigma level 0.267, from a 1 m/s westerly wind observational

residual (yo – h(xb)) at 50°N and 330°E at 250 hPa.

Figure 3.4.5: The vertical cross-section of u and T increments for the observation used for Figure 3.4.4.

3.4.1.2 Ozone

The background error for ozone is assumed independent from that for the other analysis variables. The

background error standard deviation varies with model level: it is specified as about 4% of the global

mean ozone on each level. The background error standard deviation is horizontally invariant. Horizontal

background error correlations use length scales of about 400 km throughout the troposphere and

stratosphere, increasing to about 800 km at the top analysis level. Vertical correlations are specified using

a common length scale of 0.8.
28

3.4.1.3 Satellite Bias Correction Coefficients

Since the satellite bias correction coefficients are analysis variables, it is necessary to specify the

background error variances. These background error variances have been specified in a simple manner by

scaling the predictors so that the variances of the various predictors are approximately equal (except the

constant predictor) and then applying a constant diagonal matrix for the background errors. The constant

used in the background errors gives fairly large weight to the values from the previous analysis.

3.4.2 The Mass-Wind Balance Constraint

The specification of the background error covariance matrix is extremely important in any data

assimilation system since it is primarily the background error covariance matrix that determines the

spreading of information from observations. Despite its importance, the way in which the background

error covariance matrix is modeled in any practical assimilation system is dominated by the compromises

that must be made in order to produce a viable computational algorithm.

Despite the advantages of the GSI in terms of the flexibility in representing the covariance structures, the

modeling of the linear mass-wind balance through a linear balance constraint is not straightforward. In the

GSI, to avoid the heavy computational burden of solving a Poisson equation at each assimilating level and

at each iteration step, balance projections are introduced to link the balanced part of temperature and

surface pressure directly with the stream function. The corresponding balance coefficients are estimated

together with other background error statistics using the NMC method. This approach is indeed

computationally-efficient, however, to ensure good wind-mass coupling, the balance coefficients have to

be estimated in such a way to ensure the balanced geopotential height increments, which can be expressed

from the balanced temperature and balanced surface pressure, are in good linear balance with the

rotational wind increments from the GSI analysis. Otherwise, the balance projections will lead to

inappropriate wind-mass coupling in which the information about the mass field will be extracted

incorrectly from the wind observations, and vice versa.

Since the linear balance equation was not used in the tuning process for the original approach of

estimating the balance coefficients, it was found that the resultant balance projections did not adequately

model the linear wind-mass balance constraint. A new approach was developed that employs the linear

balance equation and hydrostatic relationship to connect the balanced part of the temperature with the 

stream function, so that the covariance between the stream function and balanced temperature can be

derived from the stream function related covariances. The balance coefficients estimated with this new

approach ensure the wind-mass balance projections are equivalent to directly applying a linear balance

constraint inside the GSI.

3.4.2.1 Linear Mass-Wind Balance Projections in the GSI

3.4.2.1.1 Wind-Mass Balance Projection Coefficients

The control variables of the GSI are stream function increments (δψ), unbalanced velocity potential

increments (δχunbal), unbalanced virtual temperature increments (δTunbal), unbalanced surface pressure

increments (δPunbal) and pseudo-relative humidity increments (δq). Typically the background error

statistics for these control variables are estimated from a set of 24/48-hour forecast differences by the

NMC method, and in the original implementation of the GSI the balance projection coefficients were

estimated from the same set of forecast differences. The linear balance constraint to be satisfied so that

the balanced geopotential heights are in good linear balance with the rotational winds is:

!

"2#$= " %(f "#&),

where 

!

f is the Coriolis parameter and

!

"#

is the geopotential height that can be expressed as
29

!

"#= R"Td ln$ +

RTs

ps

$

1

% "P

(3.4.1)

from the integration over the hydrostatic equation in σ coordinates. In (3.4.1),

!

R

is the gas constant,

!

ps

and

!

Ts

are standard surface pressure and surface temperature, respectively.

The balance projections are introduced in the GSI to avoid the time-consuming process of solving the

linear balance equation directly. The projections define the balanced part of temperature (δTbal) and

surface pressure (δPbal) directly from δψ by assuming

!

"Tbalk= # kl"$l

l=1

N

% ,

"Pbal = μl

l=1

N

% "$l ,

where νkl are the balance coefficients for δTbal and μl the balance coefficients for δPbal, and N is the

number of assimilating levels. The vertical cross-covariance between the stream function at level m and

temperature at level k can be constructed as

!

"#m, "Tk = "#m, "Tbalk +"Tunbalk .

(3.4.2)

If we assume that there are no correlations between δψ and the unbalanced part of temperature,

!

"Tunbalk , then equation (3.4.2) becomes

!

"#m,"Tk = $ kl

l=1

N

% "#m,"#l for m =1,...,N and k =1,...,N.

Thus, we have the following linear system of equations for balanced temperature coefficients

 

!

" k # " k1," k2 ( ,L," kN )

T

:

!

C"# k =$k ,

(3.4.3)

where 

!

C" # (<$"m,$"l >), l =1,K,N, m =1,K,N

is the vertical covariance matrix of δψ, and

 

!

"k # (<$%1,$Tk >,<$%2,$Tk >,L,<$%N ,$Tk >)

T

the vertical cross-covariance vector between δψ and

δT. The matrix (

!

" k , k=1,...,N) forms an N × N coefficient matrix which is latitude dependent. Derived in

the same way, the balance coefficients for surface pressure, 

!

μ " μ1,μ2 ( ,L,μN )

T , can be estimated from 

the following linear system of equations:

!

C"μ = #,

(3.4.4)

where 

!

" # (<$%1,$P >,<$%2,$P >,L,<$%N ,$P >)

T

.

The covariance matrix

!

C"

and vectors

!

"k

and

!

"

are functions of latitude and are usually estimated by the NMC method. Practically,

!

C"

is a singular 

matrix or a matrix very close to singular. Instead of solving equation (3.4.3) or (3.4.4) directly,

!

" k

and

!

μ

are estimated by finding the pseudo-inverse matrix

!

C"

+

of 

!

C".

3.4.2.1.2 Off-line Background Error Covariance Modeling

The relation between the mass and the wind through the wind-mass balance projections, are examined

through

!

L"

and

!

R", the left-hand and right-hand sides of the linear balance equation, respectively:
30

!

L" = #2$",

R% = # &(f #$%).

Using the discrete form of (3.4.1), the covariance between δψ and

!

L"

can be related to the balanced

temperature and balanced surface pressure by

!

"#m, L$k= % bnn "#m,&2"Tbaln+ bnn+1 "#m,&2"Tbaln+1

'

(

) *

+

,

n=1

k%1

- +

RTs

ps

"#m,&2"Pbal ,

(3.4.5)

where 

!

bnn " c p(# ̃ n+1 $# ̃ n ) /2# ̃ n ,

!

bnn+1 " c p(# ̃ n+1 $# ̃ n ) /2# ̃ n+1,

!

" ̃ #" n

R /c p ,

!

" n

is the 

!

"

at the nth

interface of the 

!

"

layers (

!

"1 =1), cp is the specific heat at constant pressure. All the analysis variables are

defined at the mid-point of each layer.

If we substitute the projections for 

!

"Tbaln

and

!

"Pbal

into (3.4.5), then we can see that the GSI

representation of 

!

<"#m,L$ >

depends on the mass-wind balance coefficients and the representation of 

!

<"#,$2"# >. Both

!

<"#,$2"# >

and

!

<"#m,R# >

are the stream function related covariances that are

modeled in the GSI by the recursive filters from the background error statistics for δψ. If δTbal and δPbal

satisfy the linear balance equation with δψ, then we have

!

"#m, L$k= "#m, R#k ,

(3.4.6)

and the balance projection scheme introduced in the GSI is equivalent to using the linear balance equation

inside the analysis. The balance coefficients should be estimated in such a way as to ensure (3.4.6) is

satisfied in the analysis. Otherwise, the balance projections will provide an incorrect wind-mass coupling

with information about the mass field extracted incorrectly from wind observations, and vice versa.

The linear mass-wind balance is a good first-order approximation in the wind-mass balance modeling,

which can be examined by diagnosing

!

<"#m, R# >

and

!

<"#m, L$ >

directly from the same set of

forecast differences (not shown).

3.4.2.1.3 The Performance of the Original GSI Implementation

The wind-mass balance coefficients estimated with the current approach from equations (3.4.3) and

(3.4.4) cannot ensure 

!

<"#m, L$ >

and

!

<"#m, R# >

be close enough to have the correct wind-mass

coupling in the analysis. Figure 3.4.6 shows the profiles of 

!

<"#m, R# >

(solid curves) and

!

<"#m, L$ >

(dashed curves) using equation (3.4.5) from the stream function's background error statistics and the 

balance coefficients estimated with the original approach with m=23 (σ = 0.5) and at the selected

latitudes. We can see that

!

<"#m, L$ >

and

!

<"#m, R# >

are quite different, especially in the tropics. In

the mid- and high-latitudes and at the certain levels (for example, σ = 0.2), the difference is relatively

small (not shown). However, typically there are relatively large differences from 30°S to 30°N no matter

which levels are selected. These differences will surely cause incorrect wind-mass coupling in the GSI

analysis. This was confirmed by looking at the analysis increments generated exclusively from the windmass balance projections. Plots of 

!

R"

and

!

L"

and their ratio (not shown) indicated that the balance

coefficients tuned with the original GSI implementation do not satisfy the linear balance constraint except

in parts of the mid-latitude troposphere. The differences between

!

R"

and

!

L"

are relatively large in the 

region from 40°S to about 40°N and from 200 hPa to levels in the stratosphere.
31

Figure 3.4.6: The profiles of

!

< "#,$2"% >

(dashed line) and

!

< "#,$ % (f $"#) >

(solid line) at eight selected

latitudes with δψ being at σ = 0.5. These profiles are calculated from the balance projection coefficients estimated

according to the original GSI implementation, and values have been multiplied by 103.

3.4.2.2 A new approach for estimating the Linear Mass-Wind Balance Projections

A new estimation approach was developed which makes use of the linear balance constraint and the

stream function related covariances to ensure that the wind-mass balance projections in the GSI satisfy

the linear balance equation.

3.4.2.2.1 Formulation

From equation (3.4.5), we have

!

"#m, L$k% L$k+1= bkk "#m,&2"Tbalk + bkk+1 "#m,&2"Tbalk+1 ,

(3.4.7)
32

where m=1,...,N and k=1,...,N-1. On the other hand, integration of (3.4.1) from the top (σ=0) to the

bottom (σ=1) leads to

!

"#d$ = R"Td$ +

RTs

ps

0

1

% 0

1

% "P.

Applying the ∇2operator to each term in the above equation and then discretizing yields

!

L"

j=1

N

# $ j = R %2

j=1

N

# $Tj$ j +

RTs

ps

%2$P,

where 

!

" j =# j $# j+1. Constructing covariances using the above equation yields

!

"#m, L$ j j=1

N

% " j = R "#m,&2

"Tbal j j=1

N

% " j +

RTs

ps

"#m,&2"Pbal .

(3.4.8)

Equations (3.4.7) and (3.4.8) form a linear system with N equations but having N+1 unknown covariances

!

<"#m,$2"Tbal j>

and

!

<"#m,$2"Pbal >. The linear system can be expressed as

!

B"m = A#m,

(3.4.9)

where 

 

!

" m = #m, L$1 , #m, L$2 ,L, #m, L$N

%

&

' (

)

*

T

,

+m = #m,,2-Tbal1 , #m,,2-Tbal2 ,L, #m,,2-TbalN , #m,,2-Pbal %

&

' (

)

*

T

,

 

!

A =

1 "1 0 L 0 0

0 1 "1 L 0 0

O

0 0 0 L 1 "1

#1 #2 #3 L #N"1 #N

$

%

&

&

&

&

&

&

'

(

)

)

)

)

)

)

N*N

,

and

 

!

B =

b11 b12 0 L 0 0 0

0 b22 b23 L 0 0 0

O

0 0 0 L b(N"1)(N"1) b(N"1)N 0

R#1 R#2 R#3 L R#N"1 R#N

RTs

ps

$

%

&

&

&

&

&

&

&

'

(

)

)

)

)

)

)

)

N*(N+1)

.

A and B are constant matrixes depending on the layer structure of the vertical coordinate, the reference

surface pressure and the reference temperature. The covariance vector α m can be rewritten through the 

linear balance constraint (3.4.6) as

 

!

"m = #m,R#1 , #m,R#2 ,L, #m,R#N

$

%

& '

(

)

T

,
33

which are stream function related covariances that can be estimated from the training data sets or replaced

by their representation in the GSI through the recursive filters from the stream function's background

error statistics. From A, B and α m, the unknown vector β m, which represents the covariance structures

between the stream function and balanced part of temperature and surface pressure, can be estimated by

!

"m = B+A# m,

(3.4.10)

where B+ represents the pseudo-inverse matrix of B. One of differences between the new approach and

the approach described in the section 3.4.2.1 is that ηk in (3.4.3) needs to be estimated independently

from the training data sets, while in the new approach, β m is derived from the stream function related

covariances.

Once we have the covariances

!

<"#m,$2"Tbalk>

and

!

<"#m,$2"Pbal >

for all m and k, the balanced

temperature coefficients vector νk and surface pressure coefficients μ can be estimated from the following

linear equations:

!

C ˆ 

"# k =$ˆ k ,

C ˆ 

"μ = %ˆ ,

(3.4.11)

which can be derived in the same way as the equations (3.4.3) and (3.4.4).

!

C ˆ 

"

is the N × N covariance

matrix defined as

!

<"#m,$2"#l >. It is another stream function related covariance matrix that needs to

be estimated from the training data sets or approximated by the appropriate GSI representation. The

vectors in the right sides of equations (3.4.11) are formed from the components of β m in (3.4.10), that is,

 

!

"ˆ k # $%1,&2$Tbalk , $%2,&2$Tbalk ,L, $%N ,&2$Tbalk

'

(

) *

+

,

T

and 

 

!

"ˆ # $%1,&2$Pbal , $%2,&2$Pbal ,L, $%N ,&2$Pbal '

(

) *

+

,

T

.

3.4.2.2.2 Estimation of α m and

!

C ˆ 

"

From the above formulations, it is clear that the wind-mass balance coefficients from the new estimation

approach are dependent on two vertical covariance matrixes, i.e., (α1, α2, ..., α N) and

!

C ˆ 

". These two

matrixes can be estimated either directly from the training data sets or indirectly from the stream function

background error statistics through the GSI background error covariance modeling. The GSI

representations of α m and

!

C ˆ 

"

are different from their direct diagnostics from the training data sets. The

representation of vertical correlation for the stream function is a near-Gaussian function generated by two

self-adjoint recursive filters, and the horizontal correlation is approximated by the superposition of three

near-Gaussian kernels with different length scales. Compared with the corresponding direct diagnostics,

the GSI representations are smooth and have no remote correlations.

To ensure the balance projection scheme is equivalent to using the linear balance constraint inside the

GSI, α m and

!

C ˆ 

"

should be estimated from the stream function background error statistics. If α m and

!

C ˆ 

"

are estimated from the training data sets, then the estimated coefficients with the new approach will make

the balanced geopotential height satisfy the linear balance equation with the diagnostic stream function

error rather than the corresponding GSI representation since these two are quite different. So the 

estimation of these new balance coefficients involves the following steps: firstly, tuning the stream

function background error statistics from the training data sets, then using an off-line code to calculate α m
34

and

!

C ˆ 

"

from those modeled stream function error statistics, and, finally, estimating the β m, νk and μ from

(3.4.10) and (3.4.11).

3.4.2.3 Evaluations of the New Wind-Mass Balance Projections

The wind-mass balance coefficients estimated with the new approach are different from those from the

original approach described above. Since these coefficients have no clear physical meaning, we will

instead compare the resultant balanced temperature and surface pressure. The vertical covariances for the

balanced temperature and the surface temperature can be written as

!

"Tbalk ,"Tball=# k

T C$# l ,

"Pbal ,"Pbal = μ

T C$μ.

The vertical cross-covariance between these two balanced fields can be expressed as

!

"Pbal ,"Tbalk= μ

T C#$ l .

Since 

!

C"

is an independent matrix, the differences in these covariances only reflect the differences in the 

balance coefficients. If we replace 

!

C"

with its corresponding GSI modeling, then we have the GSI

representation of these covariances.

Figure 3.4.7 shows the profiles of the standard deviation of the background balanced temperature error at

selected latitudes used in GEOS-5.0.1 and 5.1.0. The resultant balanced temperature error in the upper

levels is much smoother in either of the new balance projections (green curves) than in the original

projections (red curves). In the tropics, the more balanced temperature can be explained from the stream

function in the new projections. While in the original projection, the balanced temperature error at the

high latitudes near σ = 0.001 is much larger in the southern hemisphere than in the northern hemisphere.

The GSI representation of vertical correlations from the original and the new balance projections are also

quite different. Figure 3.4.8 shows the profiles of balanced temperature correlation at σ = 0.5 and at the 

same latitudes as Figure 3.4.7. With the new balance projections (green curves), the GSI representation of

the correlation is much smoother and sharper especially at the low-latitudes, and has no remote

correlation. The correlations resulting from the new balance projections have the typical two-sided

negative lobes, which is different from those (red curves) from the original projections. The upper

negative lobe in the extratropics is stronger than the lower negative lobe, except if σ is at 0.2, when the

lower negative lobe is stronger than upper negative lobe (Figure 3.4.9). All of these are typical correlation

features found in the temperature field. Figure 3.4.10 shows the profiles of the cross-correlations between

the balanced temperature and balanced surface pressure. Again, the new cross-correlation curves (green

and yellow curves) are much smoother and retain the major features shown in the red curves.

The new wind-mass balance projections are equivalent to using the linear balance constraint inside the 

GSI. As a parallel to Figure 3.4.6, Figure 3.4.11 shows the profiles of covariances

!

<"#m, L$ >

(dashed

curves) and

!

<"#m, R# >

(solid curves) with m = 21 (σ = 0.5) based on the new balanced coefficients. In

Figure 3.4.11, the differences between

!

<"#m, L$ >

and

!

<"#m, R# >

are reduced significantly

compared to Figure 3.4.6. The slight differences, especially at the tropical latitudes, are due to poor

conditioning of the matrix

!

C ˆ 

"

in which some of small singular values have to be removed before the

estimation procedure. Figure 3.4.12 shows the zonal averages of absolute value of 

!

L"

(top panel) and

!

R"

(middle panel) in the northern hemisphere, computed from the related analysis increments with the 

new wind-mass balance projections. The bottom panel shows that the balance constraint is satisfied over 

most of the globe. Although the ratio near the equator is slightly larger than 1, it is much reduced from the
35

original implementation; and since the dominant error near the equator is unbalanced, the balance

modeling near the equator is not a critical issue. The wind-mass balance from the new projections can

also be seen in Figure 3.4.13 which shows the distribution of geopotential height and rotational wind

increments. The rotational wind vectors follow the geopotential height lines, and the center of the mass

matches the center of the wind very well.
36

Figure 3.4.7: The standard deviation profiles of balanced temperature as a function of sigma at eight selected

latitudes. The red curves are the estimates from the original GSI implementation, while the other curves are from the

new approach. The green (yellow) curve shows the statistics used in GEOS-5.0.1 (GEOS-5.1.0).
37

Figure 3.4.8: As in Figure 3.4.7, but for the correlation profiles at σ = 0.5.
38

Figure 3.4.9: As in Figure 3.4.7, but for the correlation profiles at σ = 0.2.
39

Figure 3.4.10: As in Figure 3.4.9, but for the cross-correlation profiles between the balanced temperature and

balanced surface pressure.
40

Figure 3.4.11a: As in Figure 3.4.6, but from the balanced projections estimated with the new approach used for

GEOS.5.0.1.

Figure 3.4.11b: As in Figure 3.4.11a,

but for statistics used for GEOS.5.1.0

and only for 10oS and 10oN, there

being little change at higher latitudes.
41

Figure 3.4.12: Zonal averages of

!

| L" |#| $2%" |

(top),

!

| R" |#| $ % (f $&") |

(middle). LΦ and Rψ are calculated

based on the analysis increments which only includes the wind-mass balance projections with the new approach. All

the values in the top and middle have been multiplied by 1010. The bottom panel displays the ratio of top field to the

middle, the contours of 0.5, 0.75, 0.9, 1.0, 1.1, 1.25, 1.5, 2.0, 4.0, 6.0 are plotted. Left-hand panels are for GEOS5.0.1; right-hand panels are for GEOS-5.1.0.
42

Figure 3.4.13: The distributions of geopotential height increments and vectors of the rotational wind from the windmass balanced projections estimated with the new approach with σ=0.5 (top) and σ=0.1 (bottom). The left-hand

panels are for GEOS-5.0.1; right-hand panels for GEOS-5.1.0.
43

3.5 The Observing System and the Observation Error Statistics

The data streams currently assimilated by the GEOS-5 DAS are shown in Table 3.5.1. The observation

error covariances are all univariate and the auto-covariance terms are delta-functions so that the

corresponding entries in the matrix R are diagonal. Global constants (usually varying by level) for the

observation error standard deviations used in GEOS-5 are given below in the discussion of each

observation.

Table 3.5.1: Input observation data sources and parameters.

Conventional Data

Radiosondes u, v, T, q, Ps

PIBAL winds u, v

Wind profiles u, v

Conventional, ASDAR, and MDCRS aircraft reports u, v, T

NEXRAD radar winds u, v

Dropsondes u, v, T, Ps

PAOB Ps

GMS, Meteosat, cloud drift IR and visible winds u, v

MODIS clear sky and water vapor winds u, v

GOES cloud drift IR winds u, v

GOES water vapor cloud top winds u, v

Surface land observations Ps

Surface ship and buoy observations u, v, T, q, Ps

SSM/I Rain rate, wind speed

TMI Rain rate

QuikSCAT u, v

Satellite Data

TOVS 1b Radiances AMSU-A: N15, N16, N18

AMSU-B: N15, N16, N17

MHS: N18

HIRS2: TIROS-N, N6, N7, N8, N9,

N10, N11, N12, N14

HIRS3: N16, N17

HIRS4: N18

MSU: TIROS-N, N6, N7, N8, N9,

N10, N11, N12, N14

SSU: TIROS-N, N6, N7, N8, N9,

N10, N11, N14

EOS/Aqua Level 1b Radiances AIRS (150 channels), AMSU-A

SSM/I radiances DMSP-8, DMSP-10, DMSP-11,

DMSP-13, DMSP-14, DMSP-15 (7

channels)

GOES sounder TB GOES-08, GOES-10, GOES-12

Channels 1-18

SBUV2 ozone (Version 8 retrievals) Nimbus 7, NOAA 9, 11, 14, 16, 17
44

3.5.1 Conventional In-situ Upper-Air Data

3.5.1.1 Radiosondes, Dropsondes and Pibals

Radiosondes are the predominant source of conventional upper-air data in GEOS-5. They provide

temperature, wind and moisture information at mandatory and “significant” levels. The temperature

information is assimilated as virtual temperature by the GSI. While radiosonde data are quite valuable,

providing profiles of mass and wind information, they are inhomogeneously distributed, favoring land

over ocean and the Northern Hemisphere over the Southern Hemisphere. There are also temporal

variations in radiosonde soundings, with the majority of observations at 00 and 12 UTC; and only a few

locations launching soundings at the other synoptic times. The GEOS-5 analysis uses data from both

mandatory and “significant” levels; the observation error is increased for profile observations closely

spaced in the vertical.

The radiosonde network is augmented to a limited degree by dropsondes (from aircraft) and pilot balloons

(which provide low-level wind profiles of lesser accuracy). Dropsondes are instrument packages similar

to radiosondes that are dropped from aircraft. The dropsonde transmits information about temperature and

humidity to the aircraft, and wind observations can be inferred from the horizontal motion of the 

dropsonde during its descent.

For pilot balloon (PIBAL) observations, a balloon is tracked with an optical theodolite and the elevation

and azimuth observations are used with a predetermined ascent rate to calculate winds aloft. The NCEP

processing also assigns the PIBAL report type to radiosonde wind reports that are not accompanied by a

mass (height/temperature) report.

3.5.1.2 Aircraft Observations

Aircraft are another significant source of conventional upper-air temperature and wind observations.

These data are also highly inhomogeneous. Although in the vicinity of airports ascent and descent profiles

are available, the data are primarily single level observations. Humidity data are collected on a few

flights but are not yet used in the assimilation system. Aircraft observations are obtained from manual

(AIREP and PIREP) and automated (MDCRS and ASDAR) reports. The automated reports are more

accurate and thus are assigned a smaller observation error.

3.5.1.3 Wind Profilers

Wind profilers are vertically pointing clear-air Doppler radars that produce wind profiles in the vertical

from measurements of energy backscattered by refractive index fluctuations (Hogg et al., 1983). The GSI

currently assimilates wind profiler measurements from the NOAA Profiler Network (NPN) in the central

U.S. and from a few other profiler sites (primarily in the tropical Pacific) that transmit PIBAL format

wind reports over the GTS. Pacific stations have been reporting since about 1990, NPN since May 1992.

3.5.1.4 NEXRAD VAD Winds

Doppler radars measure mean radial velocity versus azimuth angle in 360 degree scans around the radar.

Wind velocity at various heights are derived from a best-fit sine wave to the radial wind components at

given distances from the radar (Klazura and Imy, 1993). Hence, the observation represents the mean wind

in a volume about the radar site. These observations are primarily low and mid-level winds and are

generated at U.S. NEXRAD (WSR-88D) radar locations.
45

3.5.1.6 Synthetic (BOGUS) Tropical Cyclone winds

In the NCEP GDAS processing, if the tropical cyclone vortex relocation program encounters “weak”

vortices which could not be used to update the global sigma first guess, the locations of these storms are

passed to a subsequent program which then generates synthetic (bogus) wind mandatory level profile 

reports (throughout the depth of the storm) in the vicinity of the storm(s) to better define tropical systems

for the analysis. The GEOS-5 system does not run the program that generates these synthetic wind

profiles, but the synthetic observations will be assimilated if they are present in the operational

PREPBUFR data received from NCEP.

Table 3.5.2: Observation errors for Radiosonde/Dropsonde ‘mass’ reports.

Pressure Temperature (K) Specific Humidity (g/kg)

(hPa) Radiosonde Dropsonde Radiosonde Dropsonde

> 1000 1.30 1.50 0.90 1.10

1000 1.10 1.30 0.80 1.00

950 0.90 1.10 0.80 1.00

900 0.70 0.90 0.80 1.00

850 0.60 0.80 1.00 1.20

800 0.60 0.80 1.10 1.30

750 0.60 0.80 1.30 1.40

700 0.60 0.80 1.30 1.50

650 0.55 0.75 1.30 1.50

600 0.50 0.70 1.30 1.50

550 0.50 0.70 1.30 1.50

500 0.50 0.70 1.30 1.50

450 0.50 0.70 1.30 1.50

400 0.50 0.70 1.30 1.50

350 0.55 0.75 1.30 1.50

300 0.65 0.85 1.30 1.50

250 1.10 1.30 – –

200 1.20 1.50 – –

150 1.20 1.50 – –

100 1.20 1.50 – –

75 1.20 1.50 – –

50 1.20 1.50 – –

40 1.40 – – –

30 1.60 – – –

20 1.85 – – –

10 2.00 – – –

5 2.00 – – –

4 2.00 – – –

3 2.00 – – –

2 2.00 – – –

1 2.00 – – –

< 1 2.50 – – –
46

Table 3.5.3: Observation errors for radiosonde, profiler and VAD wind (m/s).

Pressure

(hPa) Radiosonde PIBAL Dropsonde

Profiler from

PIBAL rpt NPN Profiler VAD wind

> 1000 1.5 1.5 1.5 1.4 2.0 2.0

1000 1.5 1.5 1.5 1.4 2.0 2.0

950 1.5 1.5 1.5 1.5 2.0 2.0

900 1.5 1.5 1.5 1.5 2.0 2.0

850 1.5 1.5 1.5 1.5 2.0 2.0

800 1.5 1.5 1.5 1.6 2.0 2.0

750 1.6 1.6 1.6 1.6 2.0 2.0

700 1.7 1.7 1.7 1.6 2.0 2.0

650 1.8 1.8 1.8 1.8 2.0 2.0

600 1.9 1.9 1.9 1.9 2.0 2.0

550 2.0 2.0 2.0 2.0 2.0 2.0

500 2.1 2.1 2.1 2.1 2.1 2.1

450 2.2 2.2 2.2 2.3 2.3 2.3

400 2.2 2.2 2.2 2.6 2.6 2.6

350 2.3 2.3 2.3 2.8 2.8 2.8

300 2.3 2.3 2.3 3.0 3.0 3.0

250 2.4 2.4 2.4 3.2 3.2 3.2

200 2.4 2.4 2.4 2.7 2.7 2.7

150 2.4 2.4 2.4 2.4 2.4 2.4

100 2.4 2.4 2.4 2.4 2.1 2.1

75 2.4 2.4 2.4 2.4 2.1 2.1

50 2.4 2.4 2.4 2.4 2.1 2.1

40 2.4 2.4 2.4 2.4 2.1 2.1

30 2.5 2.5 2.5 2.4 2.1 2.1

20 2.7 2.7 2.7 2.4 2.1 2.1

10 2.9 2.9 2.9 2.4 2.1 2.1

5 3.1 3.1 3.1 2.5 2.1 2.1

4 3.3 3.3 3.3 2.6 2.1 2.1

3 3.5 3.5 3.5 2.7 2.1 2.1

2 3.7 3.7 3.7 2.8 2.1 2.1

1 3.9 3.9 3.9 2.9 2.1 2.1

< 1 4.1 4.1 4.1 3.0 2.1 2.1
47

Table 3.5.4: Observation errors for aircraft observations.

Pressure Temperature (K) Wind (m/s)

(hPa) AIREP AMDAR MDCRS AIREP AMDAR MDCRS

> 1000 2.5 1.3 1.3 6.6 2.3 2.3

1000 2.5 1.3 1.3 6.6 2.3 2.3

950 2.3 1.2 1.2 6.6 2.3 2.3

900 2.1 1.1 1.1 6.6 2.3 2.3

850 1.9 0.9 0.9 6.6 2.4 2.4

800 1.7 0.9 0.9 6.6 2.4 2.4

750 1.5 0.9 0.9 6.1 2.4 2.4

700 1.3 0.9 0.9 5.6 2.4 2.4

650 1.2 0.8 0.8 5.1 2.4 2.4

600 1.2 0.8 0.8 4.6 2.4 2.4

550 1.2 0.8 0.8 4.1 2.5 2.5

500 1.2 0.8 0.8 3.6 2.5 2.5

450 1.2 0.8 0.8 3.6 2.5 2.5

400 1.2 0.7 0.7 3.6 2.5 2.5

350 1.2 0.8 0.8 3.6 2.5 2.5

300 1.3 0.8 0.8 3.6 2.5 2.5

250 1.3 0.8 0.8 3.6 3.0 3.0

200 1.3 0.9 0.9 3.6 3.0 3.0

150 1.4 0.9 0.9 3.6 3.0 3.0

100 1.7 0.9 0.9 3.6 3.0 3.0

75 1.7 1.0 1.0 3.6 3.0 3.0

50 – 1.0 1.0 3.6 3.0 3.0

40 – 1.0 1.0 3.6 3.0 3.0

30 – 1.1 1.1 3.6 3.0 3.0

20 – 1.1 1.1 3.6 3.0 3.0

10 – 1.0 1.0 3.6 3.0 3.0

5 – 1.0 1.0 3.6 3.0 3.0

4 – 1.0 1.0 – 3.0 3.0

3 – 1.0 1.0 – 3.0 3.0

2 – 1.0 1.0 – 3.0 3.0

1 – 1.0 1.0 – 3.0 3.0

< 1 – 1.0 1.0 – 3.0 3.0
48

3.5.2 Satellite Radiance Data

Remotely sensed information from satellites typically offers much greater and more isotropic coverage

than that from conventional in situ sources. In contrast to GEOS-4, GEOS-5 primarily assimilates satellite 

level-1b (raw) radiances rather than retrievals. However, single level cloud motion vector winds obtained

from geostationary satellite images, precipitation and surface wind speed estimates from microwave

sensors, surface wind estimates from scatterometer radar, and column ozone obtained from the SBUV and

SBUV/2 instruments are assimilated as retrievals.

For level-1b radiance data, the observation-minus-forecast departure statistics (both mean and standard

deviation) provide an upper bound of the observation errors as they represent the summed contribution of

errors in radiative transfer model, cloud detection, and errors in the background estimate of the 

atmospheric state. The fit of the GEOS-5 background profiles to the observed radiance for some

instrument channels were found smaller than the current assigned values in GSI suggests that the weight

currently give to these level-1b radiance data in GSI could be slightly increased. However, it is safer to be 

conservative and leave the observation error unchanged from the current assigned values. The assigned

observation error variances in GSI for each instrument types are listed Appendix A.

3.5.2.1 TOVS/ATOVS

The TIROS Operational Vertical Sounder (TOVS) consists of three separate sounding instruments: the

High-resolution Infrared Radiation Sounder 2 (HIRS2), later HIRS3 and HIRS4 for advanced TOVS

(ATOVS); the Microwave Sounding Unit (MSU), later the Advanced Microwave Sounding Unit

(AMSU), and the Microwave Humidity Sounder (MHS); the Stratospheric Sounding Unit (SSU), also

replaced by AMSU. The TOVS instruments measure the radiance from Earth passively in different

spectral regions specific to each type of remote sensing:

• in CO2 or O2 absorption zones to retrieve the vertical temperature profile,

• in water vapor or ozone absorption zones to determine the profiles and total concentrations of water

or ozone,

• in zones of low absorption to determine surface parameters.

The measured radiance includes thermal emission in the microwave and infrared channels and reflected

solar radiation in the visible and shorter-wavelength infrared channels. Radiance is commonly expressed

in terms of equivalent blackbody temperature (brightness temperature), as brightness temperature behaves

more linearly with atmospheric temperature and other parameters than does the radiance.

TOVS has flown on the TIROS-N satellite and on NOAA operational polar-orbiting environmental

satellites (POES) 6-12 and 14. NOAA 10 and 12 did not have an SSU instrument. The Advanced TOVS

instrument (ATOVS), consisting of HIRS3 and AMSU, has been launched on the recent series of NOAA

satellites; NOAA-15, 16 and 17, and HIRS4, AMSU-A and MHS on the latest, NOAA-18.

HIRS2 has one visible channel (0.69 μm), seven shortwave IR channels (3.7 to 4.6 μm), and 12 longwave

IR channels (6.5 to 15 μm). The nominal spatial resolution at nadir is 17.4 km. Details of the instrument

and data can be found at http://www2.ncdc.noaa.gov/docs/podug/html/c4/sec4-1.htm. The HIRS/3

instrument has one visible channel (0.69 μm), seven shortwave IR channels (3.7 to 4.6 μm), and 12

longwave IR channels (6.5 to 15 μm). The nominal spatial resolution at nadir is 20.3 km in the visible and

shortwave IR and 18.9 km in the longwave IR. The HIRS/3 instrument was flown on NOAA-KLM and

instrument details are available at http://goespoes.gsfc.nasa.gov/poes/instruments/hirs3.html. HIRS/4

improves on the resolution of HIRS3, with a nominal spatial resolution of 10 km at nadir. Details of the

instrument are available at http://goespoes.gsfc.nasa.gov/poes/instruments/hirs4.html.

MSU has 4 channels centered near the 57 GHz oxygen cluster. The nominal resolution is 110 km at nadir.

For details of the instrument and data go to http://www2.ncdc.noaa.gov/docs/podug/html/c4/sec4-3.htm.
49

The AMSU-A is divided into two physically separate modules: Module A-1 contains 13 channels and

Module A-2 contains two channels. AMSU-A1 consists of 12 V-band channels (3 through 14) and one

W-band channel (15). AMSU-A2 contains the two lower frequencies (K-band channel 1 and Ka-band

channel 2) The nominal resolution is 48 km at nadir. The AMSU-B provides information on water vapor

profiles from the Earth’s surface to an altitude of about 200-mb. The highest channels, 18, 19 and 20,

span the strongly opaque water vapor absorption line at 183 GHz and provide atmospheric humidity data.

Channels 16 and 17, at 89 GHz and 150 GHz, respectively, enable deeper penetration through the

atmosphere to the Earth's surface. The spatial resolution at nadir is nominally 16 km. Further details can

be found at http://www2.ncdc.noaa.gov/docs/klm/index.htm.

The MHS is a five-channel microwave instrument intended primarily to measure profiles of atmospheric

humidity. It is also sensitive to liquid water in clouds and measures cloud liquid water content. Because

of the high variability of atmospheric water, the MHS has a higher resolution than the AMSU-A, with a

nominal resolution of 16 km at nadir. MHS has four humidity channels in the 157 GHz to 190 GHz range.

As with AMSU-A, it has a surface-viewing window channel at 89 GHz, partly to ensure cross-registration

of the two sounding instruments. See http://goespoes.gsfc.nasa.gov/poes/instruments/mhs.html for further

details.

The stratospheric sounding unit (SSU) provided by the U.K. Meteorological Office were flown on several

NOAA operational meteorological satellites. SSU employs the pressure modulation technique to measure

stratospheric emission in 3 channels of the 15 μm CO2 band. The nominal resolution is 147 km at nadir.

It is designed to retrieve temperatures in the stratosphere. The SSU has three channels with weighting

functions which have peak response at pressure levels of 15, 6, and 2 mb respectively. Details of the

instrument and data can be found at http://www2.ncdc.noaa.gov/docs/podug/html/c4/sec4-2.htm.

The TOVS/ATOVS observing system is summarized in Table 3.5.5.

Table 3.5.5: Summary of TOVS/ATOVS observing system.

Satellite Pre-launch ID Instruments Orbit Operational Data Coverage

TIROS-N TN HIRS/2, MSU, SSU PM 1978/10/30 --- 1980/06/01

NOAA-06 NA HIRS/2, MSU, SSU AM 1979/07/02 --- 1980/04/17

1985/04/08 --- 1986/11/17

NOAA-07 NC HIRS/2, MSU, SSU PM 1981/07/11 --- 1985/02/19

NOAA-08 NE HIRS/2, MSU, SSU AM 1983/04/26 --- 1984/06/20

1985/07/02 --- 1985/10/14

NOAA-09 NF HIRS/2, MSU, SSU PM 1985/01/02 --- 1988/11/01

NOAA-10 NG HIRS/2, MSU AM 1986/11/25 --- 1991/09/01

NOAA-11 NH HIRS/2, MSU, SSU PM 1988/10/12 --- 1994/12/31

1997/07/15 --- 1999/02/25

NOAA-12 ND HIRS/2, MSU AM 1991/08/18 --- 1997/07/14

NOAA-14 NJ HIRS/2, MSU, SSU AM 1995/01/19 --- 2007/05/22

NOAA-15 NK HIRS/3, AMSU-A, AMSU-B AM 1998/07/02 --- current date

NOAA-16 NL HIRS/3, AMSU-A, AMSU-B PM 2001/01/01 --- current date

NOAA-17 NM HIRS/3, AMSU-A, AMSU-B AM 2002/07/15 --- current date

NOAA-18 NN HIRS/4, AMSU-A, HMS PM 2005/10/01 --- current date
50

3.5.2.2 EOS/Aqua

The NASA EOS Aqua spacecraft, launched in May 2002, carries a sounding suite consists of three 

instruments: the Atmospheric Infrared Sounder (AIRS), the Advanced Microwave Sounding Unit

(AMSU) and the Humidity Sounder for Brazil (HSB). All three instruments are cross-track scanners.

AIRS is a 2382-channel high-spectral-resolution grating spectrometer, with 2378 channels measuring

infrared radiation from 3.7-15.4 μm and four visible channels and near-infrared radiation measuring from

0.4-0.94 μm. AIRS obtains atmospheric temperature and humidity profiles from the surface to an altitude 

of 40 km. Its infrared measurements have a horizontal spatial resolution of 13.5km at nadir, and its visible 

and near-infrared measurements have a horizontal spatial resolution of 2.3km at nadir. AIRS is capable of

providing high-resolution measurements in the vertical: 1-km layers in the troposphere and 3-5-km layers

in the stratosphere. Details of AIRS can be found at http://aqua.nasa.gov/about/instrument_airs.php.

AMSU-A on board Aqua, is a 15-channel sounder consisting of two physically separate units AMSU-A1

and AMSU-A2. The A1 module contains 13 channels, and the A2 module has 3 channels. Twelve of

AMSU-A’s channels, with frequencies between 50 and 60 GHz, are used predominantly for temperature

sounding, whereas the other three channels, at frequencies of 23.8, 31.4, and 89 GHz, are used

predominantly for water vapor and precipitation measurements. The horizontal resolution of the AMSUA data at nadir is 40.5 km, three times as coarse as the AIRS data. The AMSU instrument is particularly

valuable for providing sounding information below clouds, except for regions with heavy precipitation

and optically thick clouds. Details can be found at http://aqua.nasa.gov/about/instrument_amsu.php.

Figure 3.5.1: AIRS observed brightness temperatures for all 2378 channels are shown in light blue. The spectral

location (blue diamond), instrument noise (red cross), and the assigned observation errors (green asterisk) in GSI for

the 281-channel subset are also shown.
51

HSB is a microwave humidity sounder. It has four channels, one at 150 GHz and the other three

measuring at spectral bands centered on a strong water vapor absorption line at 183.31 GHz. HSB is

particularly important for accurate humidity profiles under overcast conditions. The horizontal resolution

of HSB at nadir is 13.5km. See http://aqua.nasa.gov/about/instrument_hsb.php for more details.

Level-1b radiances from AIRS and AMSU-A are used in GEOS-5. The full spectral resolution (2378

channels) AIRS data is too large for the global data assimilation model to digest the information.

Therefore, a subset containing 281 channels from the original full spectral resolution set was selected for

the NWP centers. This channel selection is listed in Appendix A. The observation errors assigned in the

GSI for AIRS along with the instrument noise from the instrument team and their spectral locations are

shown in Figure 3.5.1.

3.5.2.3 GOES Sounder Data

GOES satellites are in a geosynchronous orbit. Normally, there are two GEOS satellites in operation:

GOES-East stationed at 75°W, and GOES-West at 135°W, providing coverage of most of the Western

Hemisphere. GOES satellites carry both sounder and imager. Currently, only GOES sounder data are used

in GEOS-5 (Table 3.5.6). The GOES sounder instrument has 18 thermal infrared bands plus a lowresolution visible band. The field of view is 8 km and is sampled every 10 km. The GOES sounder

spectral selection is very similar to the HIRS instruments carried on the NOAA polar-orbiting satellites.

It has six bands in the 15 micron band, two window channels, three mid-tropospheric water vapor bands,

one ozone band, and five 4 near infrared band, and a visible band. Details of the instrument can be found

at http://goespoes.gsfc.nasa.gov/goes/instruments/i_m_sounder.html.

Table 3.5.6: Summary of GOES satellite operation.

Satellite Launch Date Current Status

GOES-08 (I) 1994/04/13 Stand-by mode

GOES-10 (K) 1997/04/25 Operational GOES-West at 135°W

GOES-12 (M) 2001/06/23 Operational GOES-East at 75°W

3.5.2.4 SSM/I Radiances

The Special Sensor Microwave/Imager (SSM/I) is a passive microwave sensor on the Defense

Meteorological Satellite Program (DMSP) satellite series. It has 7 microwave channels at 4 frequencies

(19.35 GHz, 22.235 GHz, 37 GHz, and 85.5 GHz), each with dual (vertical and horizontal) polarization

(except for the 22 GHz channel). This dual polarization allows the detection of surface properties. The

SSM/I has a swath width of about 1400 km with a footprint resolution of 40 km at a spacing of 25 km.

The SSM/I radiance data used in GEOS-5 is summarized in Table 3.5.7. Additional information for the

instrument is available at http://www.class.noaa.gov/release/data_available/dmsp/index.htm.

Table 3.5.7: Summary of DSMP satellite availability.

Satellite Operational Data Coverage

DMSP-08 (F08) July 1987 --- December 1991

DMSP-10 (F10) December 1990 --- November 1997

DMSP-11 (F11) December 1991 --- May 2000

DMSP-13 (F13) May 1995 --- Current

DMSP-14 (F14) May 1997 --- Current

DMSP-15 (F15) December 1999 --- August 2006
52

3.5.3 Satellite Retrievals

3.5.3.1 SBUV and SBUV/2

The Solar Backscatter Ultraviolet Instrument (SBUV) on Nimbus-7 and updated SBUV/2 instruments on

NOAA POES series of satellites measure Solar irradiance and Earth radiance (from backscattered solar

radiation) in the near ultraviolet spectrum. The measurements are taken from sun-synchronous orbits at

nadir using 160 km wide field of view over the sunlit part of the Earth. Using ratios of backscattered

radiances and Solar irradiances at 12 wavelengths total ozone columns and ozone profiles are retrieved.

Version 6 retrievals (Bhartia et al., 1996) were used in GEOS-5.0.1. Version 8 retrievals are used in

GEOS-5.1.0 and GEOS-5.2.0. Version 8 retrievals (Bhartia et al., 2004) use a priori profiles from the

ozone climatology of McPeters et al. (2007) to remove any artificial trends arising from the a priori

guess. The vertical resolution of Version 8 retrievals is 6-8 km in the upper stratosphere. Comparison of

SBUV/2 Version 8 data with the Stratospheric Aerosol and Gas Experiment II (SAGE II) data shows that

most biases are within ±10%, except for larger negative biases near 50 hPa in the Tropics (Terao and

Logan, 2007).

Table 3.5.8: SBUV Observation errors.

Level

Layer bounds

(hPa) Obs error (Du)

1 0.00-0.24 1.000

2 0.24-0.50 1.000

3 0.50-0.99 1.000

4 0.99-1.98 1.000

5 1.98-3.95 1.000

6 3.95-7.90 1.414

7 7.90-15.81 1.225

8 15.81-31.41 1.225

9 31.41-62.82 1.871

10 62.82-126.66 1.871

11 126.66-253.31 1.732

12 253.31-1013.24 1.414

Total

ozone 2.236

3.5.3.2 Cloud-track Winds

Cloud-track winds (CTW, also known as cloud-drift winds or atmospheric motion vectors, AMV) are

observations derived from sequences of images observed by satellites. The winds are calculated by an

objective procedure that selects targets, assigns pressure altitude, and calculates atmospheric motion from 

the motion of the selected targets in successive images.

The GEOS-5 DAS uses cloud-track winds from geostationary satellites produced by NESDIS, JMA, and

EUMETSAT; data from these sources provides near global coverage of CTWs equatorward of 60

degrees. CTW from MODIS on the EOS/Terra and Aqua platforms, also produced by NESDIS, provides

data primarily in the polar regions.
53

Although the cloud track wind data are not thinned, the ‘prepdata’ processing at NCEP applies data

selection based on the value of the quality index assigned to the wind by the data producer. For NESDIS

GOES hi-density winds, the quality marker (QM) is based on a recursive filter flag (RFF) value:

RFF ≤ 49 QM = 13 (exclude)

49 < RFF ≤ 55 QM = 3 (suspect - GSI inflates the observation error by a factor of 1.2)

55 < RFF ≤ 84 QM = 2 (normal)

RFF > 84 QM = 1 (‘keep’ flag, treat as normal).

For EUMETSAT BUFR winds, the QM is based on the quality indicator (QI) value, with the QI

calculated using forecast background:

QI ≤ 0.8 QM = 13 (exclude)

QI > 0.8 QM = 2 (normal).

The EUMETSAT BUFR winds are produced every 90 minutes. The NCEP processing applies a time

window so that only the set of winds produced closest to the synoptic time is retained for use by the 

assimilation. The EUMETSAT ELW BUFR winds have been included in NCEP operational system since 

24 April, 2001. Prior to that NCEP, processed 'SATOB' winds from the GTS and applied similar

restrictions with respect to the quality indicator and time window.

The observation errors used in the GSI for cloud-tracked winds are provided in Table 3.5.9.

Table 3.5.9: Observation errors for cloud-tracked winds (m s

-1

).

Pressure

(hPa)

NESDIS

picture triplet

NESDIS

IR

NESDIS WV

cloud top

JMA

IR/VIS

EUMETSAT

IR/VIS MODIS IR MODIS WV

1000 1.8 3.4 6.0 1.8 1.8 3.8 –

950 1.8 3.0 6.0 1.8 1.8 3.8 –

900 1.8 2.7 6.0 1.8 1.8 3.8 –

850 1.8 2.5 6.0 1.8 1.8 3.8 –

800 1.8 2.7 6.0 2.4 1.8 3.8 –

750 1.8 2.8 6.0 2.4 1.8 3.8 –

700 1.9 3.1 6.0 2.4 2.1 3.9 –

650 1.9 3.3 5.5 2.5 2.1 3.9 –

600 2.0 3.4 5.5 3.0 2.1 4.0 –

550 2.0 3.6 5.0 3.5 2.3 4.0 4.0

500 2.1 3.8 5.0 4.0 2.5 4.1 4.1

450 3.0 4.0 5.0 4.5 3.0 5.0 5.0

400 4.0 4.2 5.0 5.0 4.2 6.0 6.0

350 4.3 4.4 5.0 5.0 4.5 6.3 6.3

300 4.6 4.6 5.0 5.0 4.7 6.6 6.6

250 5.0 4.8 5.0 5.0 5.0 7.0 7.0

200 5.0 5.0 5.0 5.0 5.0 7.0 7.0

150 5.0 5.5 5.0 5.0 5.0 7.0 7.0

100 5.0 6.0 5.0 5.0 5.0 7.0 7.0

75 5.0 6.5 6.0 5.0 5.0 7.0 7.0

50 5.0 7.0 7.0 5.0 5.0 7.0 7.0
54

3.5.3.3 Precipitation Estimates

SSM/I and TMI yield precipitation estimates over the oceans. These data are subsetted by generating a 1°

grid of super-observations. The observational error variance is defined as 1.0 + 0.25× rain_rate.

3.5.3.4 Surface Wind Estimates

The GEOS-5 near-real-time product uses the NCEP GDAS data stream. The NCEP GDAS operational

processing takes SSM/I wind speed generated by the Neural Net 3 algorithm and superobs them onto a 1°

latitude/longitude grid. The QuikSCAT scatterometer data are quality-controlled and then superobed onto

a 0.5° grid.

For the MERRA system, SSM/I wind speed retrievals are obtained from Remote Sensing Systems (RSS,

http://www.ssmi.com/). RSS SSM/I wind speed retrievals are superobed to a 0.5° latitude/longitude grid.

The QuikSCAT scatterometer data for the MERRA system are processed as in the GEOS-4 system,

selecting data only from the ‘sweet spot’ on each side of the swath and thinning by selecting winds from

every other scan position.

The observation errors specified for surface winds varies according to the source:

SSM/I wind speed 2.0 m/s

QuikSCAT winds 2.5 m/s

ERS1/2 winds 2.5 m/s

Atlas buoy winds 2.2 m/s

Surface marine winds 2.5 m/s.

Surface marine observations are provided by ships and moored buoys.

3.5.4 Land Surface Observations

The GEOS-5 GSI assimilates surface pressure observations from land surface stations. For METAR

observations without a surface pressure report, the altimeter setting is used to obtain a surface pressure

value. Other land surface observations (temperature, moisture, wind) are kept as passive.

Table 3.5.10: Observation errors for surface pressure (hPa).

Pressure

(hPa) Surface marine Surface land Dropsonde METAR

> 1000 1.0 1.0 1.0 1.0

1000 1.0 1.0 1.0 1.0

950 1.0 1.0 1.0 1.0

900 1.0 1.0 1.0 1.0

850 1.0 1.0 1.0 1.0

800 1.0 1.0 1.0 1.0

750 1.0 1.0 1.3 1.3

700 1.1 1.0 1.6 1.6

650 1.2 1.2 – –

600 1.2 1.2 – –
55

3.5.5 Ocean Surface Observations

GEOS-5 assimilates surface pressure, temperature, moisture, and wind observations from ships and

buoys. The GSI also uses sea surface temperature in the analysis. Surface marine observations are

provided by ships, moored buoys, tide gauges and the Coastal-Marine Automated Network (C-MAN, see

http://www.ndbc.noaa.gov/cman.php).

The MERRA system includes PAOBs, which are synthetic surface pressure observations derived from

manual analyses of surface pressure, produced by the Australian Bureau of Meteorology (Seaman and

Hart, 2003).

Table 3.5.11: Observation errors for surface temperature and specific humidity.

Pressure Temperature (K) Specific Humidity (g/kg)

(hPa) Surface ship Dropsonde Surface ship Dropsonde

> 1000 1.8 1.5 1.2 1.0

1000 1.8 1.5 1.2 1.0

950 1.8 1.5 1.2 1.0

900 1.8 1.5 1.2 1.0

850 1.8 1.5 1.2 1.0

800 1.8 1.5 1.2 1.0

750 2.0 1.5 1.5 1.0

700 2.3 1.5 1.5 1.0

3.6 Quality Control

The Quality Control (QC) procedures employed prior to assimilation are summarized at

http://www.emc.ncep.noaa.gov/mmb/data_processing/data_processing/. Conventional data are QC’d by a

sequence of programs prior to being passed to the analysis code. The Level 1b satellite radiance data from

RTOVS (HIRS-2, MSU), ATOVS (HIRS-3, HIRS-4, AMSU-A, AMSU-B, MHS), and EOS/Aqua

(AIRS, AMSU-A) as well as SBUV data are processed into BUFR files and passed directly into the GSI

which undertakes QC for the satellite data.

3.6.1 Conventional Data

NCEP’s CQCBUFR program is used to perform complex quality control on rawinsonde height and

temperature data to identify or correct erroneous observations that arise from location, transcription or

communications errors. The CQCBUFR includes a number of checks based upon differences from the

background, including a hydrostatic check, an increment check, horizontal and vertical interpolation

checks, and a lapse rate check. A baseline check is used to determine errors and/or changes in station

location. The program also applies inter-sonde (radiation) corrections to the quality-controlled rawinsonde

height and temperature data. The degree of correction is a function of the rawinsonde instrument type, the

sun angle and the vertical pressure level.

PROFCQC and CQCVAD programs perform complex quality control on wind profiler data and on

NEXRAD or Vertical Azimuth Display (VAD) wind data from WSR-88D radars, respectively. The

checks used are: increment, vertical statistical, temporal statistical, and combined vertical-temporal and

are based upon differences from the background. The CQCVAD program includes an algorithm to

account for the seasonal migration of birds.
56

The PREPACQC program performs quality control on conventional AIREP, PIREP and AMDAR

(Aircraft Report, Pilot Report, Aircraft Meteorological Data Relay) aircraft wind and temperature data.

The flight tracks are checked, with bad reports flagged and duplicate reports removed. AIREP and PIREP

reports are further quality controlled by comparing isolated reports to the background and flagging

outliers flagged and then inter-comparing groups of reports in close geographical proximity using both a

vertical wind shear check and a temperature lapse check.

The ACARSQC program performs quality control on MDCRS and ACARS aircraft wind and temperature

data. Currently only simple data bounds checks are performed.

The last program to execute QC before the data are passed to the GSI is OIQCBUFR. It performs an

optimum interpolation based quality control on the complete set of observations in the PREPBUFR file.

A number of independent checks (horizontal, vertical, geostrophic) are performed using all admitted

observations. Each observation is subjected to the optimum interpolation formalism using all observations

except itself in each check. A final quality decision (keep, toss, or reduced confidence weight) is made

based on the results from all prior platform-specific quality checks and from any manual quality marks

attached to the data.

For the GEOS-5 real-time forward processing system, the preprocessing QC is performed at NCEP prior

to receipt of the data at Goddard. For the MERRA system, the preprocessing QC is conducted at

Goddard.

3.6.2 Satellite Radiance Data

Quality control procedures depend on the observation type. For the quality control of satellite radiance

data, see http://www.emc.ncep.noaa.gov/gmb/treadon/gsi/documents/presentations/1st_gsi_orientation/.

HIRS, GOES, AIRS: High frequencies are eliminated during the day for reflected solar radiation

contamination. Only cloud-free data are used. Screening is also conducted for the surface window to limit

the magnitude of the necessary change in surface emissivity.

AMSU-A: Data are screened according to cloud liquid water, the scattering index, and according to the

magnitude of the necessary change in surface emissivity.

AMSU-B: Data are screened according to the ability to simulate quasi-window channels.

MSU: Data are screened according to the ability to simulate channel 1 (for channels 1 and 2).

GOES imager: Data are screened according to the clear sky fraction and the brightness temperature

standard deviation.

SSM/I Radiances: Okamoto and Derber (2006) describe the methodology used for assimilation of SSM/I

radiances in the GSI. SSM/I radiances are only assimilated over ocean; observations over land or ice are

excluded. The QC of the SSM/I 1b radiances is based on the scattering index, si85, the difference between

an estimate of the 85V brightness temperature from the other channels with the observed temperature

(Ferraro, 1997). Over the ocean, the scattering index is:

si85 = [-174.4 + 0.715 Tb19V + 2.439 Tb22V – 0.00504 (Tb22V)

2 ] – Tb85V

and over the land:

si85 = [451.9 - 0.44 Tb19V - 1.775 Tb22V + 0.00574 (Tb22V)

2] - Tb85V.
57

Rain is detected if si85 > 10 and this information is used for data thinning and QC. Other checks are

based on cloud liquid water (clw), a range check ( 70 < Tb < 320, for each channel), and a polarization

check that (Vpol – Hpol) < -2 for each channel. The clw checks use a clw retrieval (after Weng et al.,

1997) from the 85 GHz channels as the first priority, from the 19 GHz channels as the next priority, and

then from the 37 GHz channel if the others are not available. For example,

clw85 = -0.44 [ log(290.-Tb85H) + 1.11 – 1.26 (log(290. – Tb22V)].

Cloud liquid water estimates are used in data selection/thinning when si85 is not available. The SSM/I

radiances are also subject to a gross check on the observation increment, rejecting those with absolute

value greater than 3σo.

Common procedures: The quality control procedure common to all satellite data types is performed by a

combination of two tests, a gross check and a check against the predicted values from nearby observations

(a buddy check).

Gross check: For each observation location, an observation quality parameter is set based on the expected

observational error variance for that channel. This quality control parameter is modified by the position

across the track of the scan, whether it is over land, sea, snow, sea ice or a transition region, the elevation,

the difference between the model and the real orography, and the latitude (the criterion is made tighter in

the tropics). For the HIRS channels, the criterion is stricter if the observation is designated partly cloudy

by NESDIS, if the differences between selected window channel observations or the simulated window

channels are too large, and for the shortwave channels if the solar zenith angle is small. Some of the

modifications are designed to eliminate observations that are contaminated, and some to eliminate

situations where the simulated observations are deficient. The observation quality parameter is then

compared to the difference between the true and simulated observations. The observation is rejected if the

difference from the simulated observation is greater than three times the observation quality parameter.

The buddy check: At the same time, the observation is compared to a simple interpolation of nearby

observational increments to the observation location. The observation is if the difference from the

simulated observation and the difference between the interpolated increments and the observation

increment are both greater than the observation quality parameter. To minimize the number of

observations that are rejected due to errors in nearby observations, the checking is repeated three times

with only the observations that have passed the previous time through the quality control check being

used for the interpolation of increments. This procedure allows the re-acceptance of some observations

that were rejected in the previous passes through the data.

Note that the data rejections are performed independently for each channel. Thus, the rejection of one

lower tropospheric HIRS channel because of possible cloud contamination does not necessarily result in

the rejection of other tropospheric HIRS channels at the same location. This quality control procedure has

some known deficiencies and probably rejects some good data in order to ensure the removal of all the

bad data.

3.6.3 Precipitation Data

The quality control procedures for precipitation observations are outlined in Treadon et al. (2002).

Because of the large boundary layer sensitivity of the convective scheme, a smoothness check is added to

the data pre-processing. Those observations for which the vertical derivative of the sensitivity profile 

exceeds a given tolerance are not assimilated. The check flags about 5% of the SSM/I data and 4% of the

TMI data.

A time screening is also applied to the observations. As the analysis relative time of the observation

increases, the quality control error bounds smoothly decrease to zero. The quality control bounds also
58

decrease to zero for observations poleward of 45° latitude. Observations are not used over snow-covered

land, ice covered water, and poleward of 60° latitude. These surface type and latitude checks screen out

15.6% of the SSM/I data (0.6% for TMI). Finally, those observations which deviate from the background

rain rate by more than three times the estimated observation error are not assimilated.

3.7 The Radiative Transfer Model

GEOS-5 versions to GEOS-5.2.0 uses the prototype version of the Community Radiative Transfer Model

(pCRTM) for all satellite radiance data except for the historical SSU data stream input for MERRA. The

GLATOVS radiative transfer model (Susskind et al., 1983) is used for the SSU.

The CRTM, developed under the auspices of the JCSDA, is integrated with the GSI. It is documented at

http://www.orbit.nesdis.noaa.gov/smcd/spb/CRTM/ and in Han et al. (2006). The CRTM is comprised

of various components involved in simulating satellite radiances. The four main components are:

• Atmospheric gaseous absorption

• Scattering and absorption by cloud and aerosols

• Surface optics – emissivity and reflectivity

• The radiative transfer solution.

3.7.1.1 The Gaseous Absorption Model

The operational gaseous absorption model used is Compact OPTRAN. The channel or spectral-response

function convolved transmittance is modeled as

!

Tch = Tch,wTch,o

*

Tch,d

*

where 

!

Tch,w

is the water vapor transmittance, and

!

Tch,o

*

and

!

Tch,d

*

are the effective transmittances of

ozone and dry gas (McMillan et al., 1995), respectively. The transmittance component on the right hand

side of the above equation is calculated as

!

Tch,g (Ag ) = exp(" k

ch,g (A #

g )

0

Ai

$ dA #

g ),

where 

!

Ag

is the integrated amount of water vapor, ozone, or dry gas, and

!

kch,g

is the channel absorption

coefficient of water vapor, ozone, or dry gas.

!

kch,g

is predicted as

!

ln(kch,g (Ag )) = cg,0(Ag ) + cg, j

j=1

6

" (Ag )xg, j(Ag );

cg, j(Ag ) = ag, j,n

n=0

N

" ln(Ag )

n

,

where the

!

xg, j

are predictors such as temperature and pressure and the 

!

ag, j,n

are constants obtained

through regression.

Minor gases that are generally well mixed such as CO2, CO, N2O, CH4, CFCs, N2, O2, are not included as

state variables but are fixed. Water vapor and ozone are generally not well-mixed and are included as

variable gases.

3.7.1.2 The Cloud Absorption and Scattering Model

Currently, cloud and precipitation optical parameters are calculated with general Mie theory using a 

modified gamma distribution function. Several types of hydrometers including cloud ice, cloud liquid
59

water, snow, graupel, hail and rain water are included. Parameters such as extinction coefficients, single

scattering albedo and phase matrix elements are pre-calculated and stored in a lookup table. This table is

searched with particle mean size and cloud water content.

Absorption and scattering by aerosols are under development.

3.7.1.3 Surface Emissivity and Reflectivity Models

The CRTM employs a suite of microwave (MW) and infra-red (IR) surface emissivity and reflectivity

models for land, ocean, ice and snow-covered surfaces.

Microwave:

• The MW land emissivity model (LandEM) computes land surface emissivity for various surface

types, including snow, deserts and vegetation using the two-stream radiative approximation

(Weng et al., 2001). The model takes satellite zenith angle, microwave frequency, soil moisture

content, vegetation fraction, soil temperature, land surface temperature and snow depth as inputs

and computes surface emissivity at vertical (V) and horizontal (H) polarizations.

• The empirical snow and ice emissivity models compute the emissivity via a combination of

satellite window channel observations and emissivity databases collected from ground-based MW

instruments (Yan et al., 2004). The emissivity databases contain sets of emissivity spectral data 

measured at a zenith view angle of 50 degrees for various surface types. The window channel

observations are used to identify the snow or ice surface type that best describes the surface

condition observed. After a spectrum is identified, it is adjusted for the requested zenith angle.

• The MW emissivity over the ocean surface is computed using FASTEM-1 (English and Hewison,

1998). It takes the satellite zenith angle, water temperature, surface wind speed, and frequency as

model inputs and computes surface emissivity at V and H polarizations.

Infrared:

• Over the ocean the Infra-Red Sea surface Emissivity (IRSSE) model (van Delst and Wu, 2000) 

utilizes a lookup table of sea surface emissivities derived from the emissivity model for a windroughened sea surface (Wu and Smith, 1997). The lookup table variables are zenith angle (67

entries from nadir to 66.5°), frequency (153 entries from 600 to 3000 cm-1), and wind speed (23

entries from 0 to 15 m/s). Linear interpolation is performed between the lookup table values.

• Over land surfaces, a look-up table is used for the 24 surface types in Table 3.7.1 using the 

emissivity database of Carter et al. (2002). The database contains surface reflectance 

measurements as a function of wavelength in both visible and IR spectral regions for these 

surface types. The emissivity is calculated from the reflectance under the assumption of a 

Lambertian surface in the IR spectral region.

3.7.1.4 The Radiative Transfer Solver

The radiative transfer (RT) solver module solves the RT equation for given atmospheric optical depth

profile, surface emissivity and reflectivity, cloud optical parameters and source functions. The clear and

cloudy cases are treated with different methods, allowing a simple and efficient solution under the clearsky condition. For cloudy cases, the radiative transfer is solved with the advanced doubling-adding

method (Liu and Weng, 2006), in which fast algorithms are applied to compute layer source function and

vertical radiative transfer integration.

The CRTM includes the forward and Jacobian models, as well as the Tangent-linear and Adjoint

models. The forward model simulates satellite observed radiances. The Jacobian model

computes radiance derivatives with respect to the input state variables.
60

Table 3.7.1: Surface types included in the IR emissivity database.

Surface Type

Compacted soil Grass scrub

Tilled soil Oil grass

Sand Urban concrete

Rock Pine brush

Irrigated low vegetation Broadleaf brush

Meadow grass Wet soil

Scrub Scrub soil

Broadleaf forest Broadleaf(70)/Pine(30)

Pine forest Water

Tundra Old snow

Grass soil Fresh snow

Broadleaf/Pine forest New ice

3.8 Analysis Details for GEOS-5.0.1, GEOS-5.1.0, and GEOS-5.2.0

3.8.1 GEOS-5 Analysis Grid

In contrast to the Gaussian grid implementation at NCEP, the GEOS-5 analysis is conducted on the

model’s native grid, both horizontal and vertical.

3.8.2 Data Sources

The sources for the historical data streams for MERRA are given in the MERRA file specification

document, available online at http://gmao.gsfc.nasa.gov/merra. The near-real-time GEOS-5 products and

the corresponding historical product stream re-processed for the NASA instrument teams use the nearreal-time streams utilized by NCEP in their Global Data Assimilation System (GDAS). The exception to

this is the SBUV version 8 stream used in GEOS-5.1.0. The historical stream is obtained from the

Goddard Atmospheric Chemistry and Dynamics Branch. NCEP transitioned to the version 8 retrieval in

January 2008. From that time, GEOS-5 has used the data stream from NCEP in forward processing.

3.8.3 Radiosonde Corrections for MERRA

The radiosonde temperature observations undergo up to three adjustments to remove or reduce biases.

The first removes the unrealistically large 00/12 UTC time-mean temperature differences from NWS

radiosonde observing stations that launch Vaisala RS-80 radiosondes. As shown in Redder et al. (2004),

the differences, which occur primarily in the stratosphere, are a result of a coding error in the postprocessing software at the observing stations. Software implementing the scheme to reverse this effect has

been developed and applied offline to the data set used for MERRA.

Second, the radiosonde temperature data at each station, worldwide, is adjusted using a text data file 

generated from the homogenization scheme (i.e. the removal of artificial changes in time-series) as

described in Haimberger (2007a). This data file contains the temperature adjustments stratified by

observing station, pressure level, synoptic hour (00 or 12 UTC) and detected artificial changes for the

period from 1957 to 2006. The adjustments were generated using the data set of Durre et al. (2006), that

were re-corrected to reverse the effects of the software coding error at NWS stations as discussed

previously (see Haimberger, 2007b).
61

Finally, the radiosonde temperatures are further adjusted to account for the effects of seasonal changes in

the sun's elevation angle and, therefore, radiation bias of the thermistor. The annual average effects of the

solar radiation are assumed to be implicitly accounted for in the adjustments generated by the

homogenization scheme. The seasonal departures are estimated first by calculating the solar elevation

angle at a given station location and observation time on the given date and on the date of the vernal (or 

autumnal) equinox. The radiation biases are then computed using the most recent version of the table

generated at NCEP, and the difference is taken as an estimate of the seasonal departure.
62

4. The GEOS-5 Data Assimilation System

4.1 Model – Analysis Interface

A number of steps is required to move between the state variables of the GEOS-5 GCM and the GEOS-5

analysis. Some are relatively minor, such as interpolating wind components back and forth from the GCM 

D-grid (Figure 4.1.1) to the analysis A-grid (essentially the “φ” points in Figure 4.1.1).

Figure 4.1.1: The D-grid layout in the GEOS-5 GCM; φ-points denote mass locations.

The major elements of the interface between the model and the analysis are:

• the use of an incremental analysis update method to apply the analysis;

• an after-analysis imposition of a constraint on the vertically-integrated divergence; and

• the calculation of a scaling factor to generate surface (2-m, 10-m) variables from the state variables in

the model’s lowest layer.

Although the GEOS-5 DAS uses the same effective grid for the model and the analysis, the grid

employed for the analysis for the 1/2° system is slightly different from the model grid because of a

recursive filter related constraint within the GSI for the number of grid-points to be a multiple of 8.

Hence there is some additional interpolation required beyond the transform from D-grid to A-grid. The

analysis itself is interpolated back to the native model grid prior to the calculation of the increments.

4.2 The Incremental Analysis Update (IAU)

To minimize the spurious periodic perturbations of the analysis, the DAS uses the Incremental Analysis

Update (IAU) technique developed by Bloom et al. (1996). The IAU provides an effective filtering of the

analysis increments found to be essential for the transport of ozone and trace gases within the GEOS-5

system. The implementation used for the GEOS-5 DAS is summarized in Figure 4.2.1. Every six hours, at

the synoptic times, an analysis is performed using backgrounds at that time, three hours earlier, and three

hours later, and observations during the six-hour period spanned by the three backgrounds. The analysis

increments (i.e., the difference between the analysis and the corresponding synoptic background) are then

divided by a time scale (6 hours) to produce an “analysis tendency.” The model is then “backed-up”,

restarting it from its state three hours before the analysis time, and run for six hours, adding in the timeinvariant “analysis tendency” in addition to its normal physics tendencies. At that point a restart is created

that will be used next time the model is backed-up, and the first background for the next analysis cycle is
63

saved. This first 6-hour run is referred to as the “corrector” segment of the IAU. The run is then continued

without an analysis tendency for another six hours, saving the other two backgrounds needed by the next

analysis – one at the next synoptic time and another at the end of the six hours. This 6-hour run is referred

to as the “predictor” segment of the IAU. The entire cycle is then repeated for subsequent synoptic times.

Note that during each of the four daily analysis cycles the model is run for 12 hours.

Figure 4.2.1: A schematic of the IAU implementation.

Except for the analyses themselves, all products from GEOS-5 are produced as model histories during the 

corrector run segment. The sequence of corrector segments (follow the green line in the figure) is a 

continuous model run, with the extra forcing term from the analysis tendencies. The analysis tendencies

do change abruptly every six hours, but state variables are continuous (within the model’s time step) 

solutions of the equations of motion, albeit with the extra forcing term.

4.3 Balancing Vertically Integrated Mass Divergence from Analysis Increments

At each analysis time the DAS produces both a background state and an analysis state of the prognostic

wind v and pressure p fields. Defining the mass- or pressure-weighted variables

!

v* = v"p

D = # • v *

where Δp is the pressure thickness of the model layer, we can define the analysis increment of massdivergence as

!

"D = DA# DB .

Here the subscripts A and B refer to the analysis and background states, respectively.

The mass-divergence vertically integrated from the model surface to the model top is equal to the time 

tendency of the model's surface pressure. While the surface pressure time tendency of the background

state is usually small (due to the inherent dynamical balancing properties of the model integration), the

implied tendency from the analysis may be significantly large due to errors arising from uncertainties in

the observations and error statistics as well as compromises made within the analysis algorithm.
64

Figure 4.3.1: The vertically integrated mass-divergence (in arbitrary units) on 1 August, 2006 for the background

(top), the analysis state (middle) and from the difference, or analysis increment (bottom).
65

Figure 4.3.2: Surface pressure for the background and analysis states (upper panels). Also shown are the vertically

integrated mass-divergence (arbitrary units) of the background (left-hand lower panel) and the (analysisbackground) difference (right-hand lower panel).

Figure 4.3.3: Surface pressure tendency of the background (left-hand upper panel) and analysis states (right-hand

upper panel), and the resulting surface pressure after 15 minutes of model integration from the background without

analysis (left-hand lower panel) and from the analysis (right-hand lower panel).
66

In the vertically integrated mass-divergence for a typical background state, the largest tendencies occur

near high topography, as expected, while the ocean values are quite small (Figure 4.3.1). The vertically

integrated mass-divergence from the analysis state exhibits large coherent values covering the entire

globe. These imbalances produce surface pressure tendencies on the order of 100 hPa per 6-hours in the 

first few timesteps, giving rise to large-scale pressure oscillations and wind adjustments.

Figure 4.3.2 shows the surface pressure for the background and analysis states, and the corresponding

vertically integrated mass divergence for the area near Cuba and the Caribbean Islands on 1 August, 2006.

Of particular interest is the low pressure center associated with Tropical Storm Chris. While the analysis

was able to enhance and strengthen the initial condition associated with Chris, it left behind a state that

contains very strong large-scale imbalances as evidenced by the vertically integrated mass divergence

increment.

Figure 4.3.3 shows the surface pressure time tendency (calculated from the model's first time-step), in

addition to the surface pressure after 15 minutes of model integration. The surface pressure time tendency

is consistent with the vertically integrated mass divergence shown previously, and results in the low

pressure center completely disappearing after the 15 minutes of integration. Thus, the analysis in this case 

produced an atmospheric state that was unsustainable by the model dynamics.

4.3.1 The Minimization Algorithm

To inhibit this computational adjustment due to the imbalances within the analysis state, we wish to find

the smallest change to the analysis increment of mass-divergence (in a least-squares sense) such that the

vertically integrated mass-divergence increment vanishes. In doing so, we will only make adjustments to

the analysis wind field. Noting that:

!

"D # "Do = (DA # DB) #(DAo# DB)

= (DA # DAo ),

where the subscript o refers to the initial guess, we may define the functional F as

 

!

F =

1

2 l=1

LM

"

DAl# DAol

$

%

&

'

(

)

*

2

+ + (DAl

l=1

NM

" # DBl

).

Here 

!

(DAl" DAol ) /#

is the penalty function of the analyzed mass-divergence that we want to minimize,

λ is a Lagrange multiplier used to enforce the strong constraint of vanishing vertically integrated massdivergence increment, LM is the total number of model levels, and α is an arbitrary scaling parameter.

Taking the first variation of F yields

 

!

"F =

1

2 l=1

LM

#

DAl$ DAol

%l

&

'

( )

*

+

"DA

%l

+", (DAl

l=1

NM

# $ DBl

) + , DAl

l=1

NM

#

or, combining terms,

 

!

"F =

1

2 l=1

LM

#

DAl$ DAol

% l

2 + &

'

(

)

)

*

+

,

,

"DA +"& (DAl

l=1

NM

# $ DBl

). Since δDA and δλ are arbitrary, minimization occurs when their coefficients are equal to zero:

!

DAl" DAol

# l

2 + $

%

&

'

'

(

)

*

*

= 0,
67

and

!

(DAl

l=1

NM

" # DBl ) = 0.

Solving the above equations, we find:

!

DA = DAo" #$2,

# =

DAo % "% DB

$2 %

.

4.3.1.1 Case 1: α = 1

With no scaling, the adjustment made is simply a constant applied uniformly in height:

!

DA = DAo" #,

# =

DAo $ "$ DB

LM

.

However, since adjustments will be made through the winds only, large wind changes are possible near

the top of the model where the pressure thickness is very small.

4.3.1.2 Case 1: α = Δp

Here we normalize the penalty term by the pressure thickness, yielding:

!

DA = DAo" #($p)

2

,

# =

DAo % "% DB

($p)

2 %

.

We see that the adjustment is applied with a pressure scaling, resulting in small increments near the top of 

the model.

4.3.1.3 Case 1:

!

" = DAo# DB

Here we normalize the penalty term by the initial mass-divergence increment, yielding:

!

DA = DAo" #(DAo" DB)

2

,

# =

DAo $ "$ DB

(DAo" DB)

2 $

.

Here the magnitude of the adjustment is proportional to the local analysis increment of mass-divergence.

Therefore, if the analysis made no local adjustment to the mass-divergence, the updated value will remain

unchanged.

4.3.2 Wind Adjustment Algorithm

We may write the updated mass-divergence as:

!

DA = DAo+ "DA,

where, as shown above:
68

!

"DA = #$%2.

Expressing the adjusted mass-divergence as an adjusted mass-weighted velocity potential:

!

"DA = #2"$*,

we can then construct the adjusted mass-weighted divergent wind components as:

!

"u#

*

=

1

a cos$

%

%&

"#*,

"v#

*

=

1

a

%

%$

"# *.

These wind increments are then added to the original mass-weighted analysis winds, and subsequently descaled to arrive at the final winds produced by the balancing algorithm:

!

ufinal = (uA

*

+ "u#

* )/"pA ,

v final = (vA

*

+ "v#

* )/"pA .

4.3.3 Results

In all cases the vertically integrated increment of mass divergence is forced to vanish (within truncation).

Figure 4.3.4 illustrates this by comparing the zonal mean of the absolute value of the vertically integrated

mass divergence increment from the standard analysis with the corresponding analysis after balancing

(Case 3). Case 1 and Case 2 show nearly identical results. However, the manner in which the increment of 

vertically integrated mass divergence is made to vanish is quite different between the various cases.

Plots of the zonal mean horizontal wind divergence (Figure 4.3.5) show that in general that the 

background state (and subsequent analyses) have significant divergence near the model top, and a 

secondary maximum near 200 hPa. Case 1, however, shows a pathological divergence field near model

top due to the inability of Case 1 to scale its adjustments. Case 2 and Case 3 produce divergence fields

quite similar to the standard analysis and background states.

Plots of the zonal mean of the analysis increment of divergence (Figure 4.3.6) again highlight the inherent

problems associated with Case 1, while Case 2 and Case 3 look quite reasonable. Case 3 shows a

substantial impact on the overall divergence pattern around 200 hPa.

Figure 4.3.7 shows the zonal mean of the adjustment made to the control analysis of horizontal

divergence. Case 1 makes extremely large adjustments in the upper levels of the model which, when

mass-weighted, tend to produce the desired vertically integrated result. Cases 2 and 3 tend to produce

changes which are more localized in the troposphere. Case 2 applies small mass-weighted changes

uniformly in the vertical, while Case 3 applies somewhat larger adjustments in regions associated with

large analysis increments.

Finally, the forecasts after 15 minutes of integration using the balanced analysis states corresponding to

Case 2 and Case 3 are shown in Figure 4.3.8, together with the original forecasts from the background

and the control analysis. It should again be noted that the initial condition of the mass field for all the 

analysis states were identical. Only the divergent components of the winds were modified for the analysis

cases 1 and 2. We see that the forecasts initialized from the balanced analysis states were better able to

preserve the low pressure associated with Tropical Storm Chris than the original control analysis.
69

Figure 4.3.4: Zonal mean of the absolute value of the vertically integrated mass divergence analysis increment.

Figure 4.3.5: The zonal mean horizontal wind divergence (plotted on constant pressure surfaces) of the background

state (from the model first guess) and the corresponding results from the analysis states.

Control Analysis

Balanced Analysis
70

Figure 4.3.6: The zonal mean of the analysis increment of divergence.

Figure 4.3.7: The zonal mean of the adjustment made to the control analysis of horizontal divergence.
71

Figure 4.3.8: Surface pressure after 15 minutes of model integration, initialized from the background and analysis

states (Control, Case 2, and Case 3).
72

5. GEOS-5 Development and Product Version History

5.1 The Versions

The versions that have been in production at the time of this document are described below.

GEOS-5.0.1: The interim operational version of the GEOS-5 DAS, used to generate early products for the 

Aura instrument teams.

GEOS-5.1.0: Addressed deficiencies noted in GEOS-5.0.1 as well as tuning and development issues for

the Modern Era Retrospective-analysis for Research Applications (MERRA, e.g., Bosilovich et al., 2006).

This system has undergone a formal validation procedure. The validation results will be documented in a

separate technical report. This system was used to support the EOS Aura science team reprocessing effort.

The changes from GEOS-5.0.1 are documented below.

GEOS-5.2.0: Addressed deficiencies noted in GEOS-5.1.0 in high latitudes. This is the system used for

MERRA, to support the ARCTAS field campaign and the CERES science team. The changes from

GEOS-5.1.0 are documented below.

From 5.0.1 to 5.1.0, substantial changes have been made to both the atmospheric general circulation

model (dynamics and physics modules) and analysis system. These modifications operate in concert to

impact virtually all output product fields. It is therefore impossible to identify or attempt to quantify oneto-one correspondences between individual system changes and the resulting impacts on the fields. It is

clear, however, that the product quality has increased overall, with notable substantial improvements in

several key aspects. These include a significantly reduced easterly bias in the upper tropospheric zonal

wind along the equator, improved distribution and mean values of precipitation in both the tropics and

mid-latitude storm tracks, reduced biases in various land surface quantities, and the elimination of

spurious oscillations in both the mid-tropospheric temperature fields at middle to high latitudes and the 

near-top model level temperature fields near the north pole. The 5.2.0 system addresses a deficiency in

the diurnal cycle in the high latitudes.

5.2 The Updates

5.2.1 The Updates in 5.1.0

Updates to the GCM

Updates to the Dynamics Module

1) Correction for reproducibility of results in the case of the model being run on different processor

layouts.

2) The Polar Filter has been switched to use an FFT poleward from about 45 degrees (rather than an FFT

near the poles and an algebraic version farther away from poles). The new Polar Filter was

implemented to fix a problem encountered if the stratospheric jet crossed the pole during N.

Hemisphere Winter.

3) A new computation of U10M and V10M were implemented to represent 10-meter winds better,

assuming neutral stability.

4) A new calculation of diagnostic OMEGA was implemented to be more consistent with the calculated

rate of change of kinetic and potential energies.
73

Updates to the Physics Modules

1) Corrected ALBEDO boundary conditions, using new albedo data sets.

2) Changed Land-Ice Albedo to 0.75.

3) Reduced re-evaporation over land, so that it is the same as over sea.

4) Placed a lower limit of 0.4 on the Reynolds number

5) Decreased the roughness for heat over bare soil (for values of Leaf Area Index < 0.3)

6) Fixed out-of-bounds array in IR radiation routine.

7) Added protection for LOG(DZ...) in Catchment for thinner levels.

8) Limits on the Reynolds Number over ocean grid points were implemented. The upper limit was

changed from 1000 to 50; the lower limit changed from 0.4 to 0.1.

9) The topography data sets have been modified by multiplicative factors to adjust the global mean value

to 231.5 m (which is the mean of GTOPO30).

10) The MOIST CRF parameter MAX_RI was changed from 110 × 10-6 to 75 × 10-6 to increase the

short/long-wave cloud radiative forcing in the mid-levels in the mid-latitude ice clouds.

11) The RAS relaxation timescale was changed from one time step (20 minutes) to 12 hrs.

12) An upper limit of 2 was imposed on the Richardson Number.

13) Modifications were made to include different heat diffusivities over land and over high topography.

14) The autoconversion rate was increased above 700 hPa.

15) The bounds for the relative humidity ramp for mass flux in RAS were increased from [0.3,0.4] to

[0.6,0.8].

16) The temperature perturbation in convective boundary layers was capped at 2 K.

Updates to the Land Surface Module

1) Updates were implemented to the catchment soil thermal conductivity calculation.

2) The surface layer's heat capacity was reduced outside of tropical forests.

3) A snow energy accounting variable (HSNACC) was added to output diagnostics. HSNACC accounts

for, among other things, the fact that the snowpack (but not the atmosphere) must treat differences in

the energy content of snow falling at different temperatures. (HSNACC is an improved version of the

older variable HCORR, which had, in the older model only, been added to SHFLUX.)

4) The WCHANGE and ECHANGE variables were added to output diagnostics. These variables are,

respectively, the change over the timestep of the total water (in kg/m

2

s) and total energy (in W/m

2

) in

the land surface element.

5) Minor issues related to energy and water budget accounting were corrected.

6) Minor issues were corrected in the snow code (initialization of snowpack during first snowfall, and

re-layering).

7) The snow thickness over glaciers has been fixed at 4 m.

8) The capacity of canopy interception reservoir was increased by a factor of 5.

Updates to the GCM-Analysis Interface

1) Switched from FFT to simple average for D-grid to A-grid transform.

2) Fixed a bug in v-wnd in D-grid to A-grid and A-grid to D-grid transforms.

3) Snow-water-equivalent background file provided for CRTM emissivity calculation in GSI (instead of

snow depth)

4) Changes in the grid point land/water/ice definition needed for the Radiative Transfer Model and for

QC. The grid point is defined as a water grid point if the water fraction of the grid box is > 0.6. The

grid point is defined as sea-ice if it is a water grid point and either the ice fraction is > 0.5 or the

surface temperature is < -1.7 C.

5) Updated output routines to handle double precision value for longitude.
74

Updates to the Analysis

1) Updated to new background error statistics. These new statistics provide an improved mass-wind

balance in the tropics and reduce the background error variance for balanced temperature at the

lowest model levels over the globe.

2) Implemented QC bug fix for MODIS, tightening the tolerance on the gross check quality control to

appropriate values.

3) MODIS deep-layer clear-sky winds added to input observation stream (after 2006).

4) The CQCVAD routine was added to provide quality control checks for Doppler VAD winds.

5) Because of background biases, the following microwave channels, which are sensitive to surface

properties, have been excluded over snow, ice and mixed surface types: AMSU-A channels 1-6 and

15; MSU channels 1 and 2; AMSU-B channels 1, 2 and 5.

6) A bug fix was implemented for EOS-AMSU-A emissivity calculation. The EOS AMSU-A bug was a

logic error which resulted in EOS AMSU-A using a default emissivity calculation instead of the EOS

AMSU-A-specific calculation.

7) The changing temperature lapse rate option is invoked for the satellite bias correction estimation.

8) A vortex re-locator was implemented for tropical cyclones (only). The utility re-positions identified

tropical cyclone vortices in the background (model guess) field, in accordance with their observed

locations as determined by the National Hurricane Center. Only the position of the vortex position,

and not its intensity, is explicitly altered by this utility. The re-positioning improves the use of

appropriate observations in the vicinity of the storm and provides a better initial state for the forecast.

9) The satellite bias angle correction file was updated for data from 2001 forward.

10) The channel selection was updated for AQUA/AIRS and AMSU-B on NOAA-15.

11) The impact of all the radiance data on ozone was excluded.

5.2.1 The Updates in 5.2.0

Updates to the GCM

Updates to the Physics Module

1) A bug in cloudnew.F90 related to the use of the wind shear pdf was corrected.

2) Updates were made in cloudnew.F90 to allow a) thicker cold low-level cloud and b) lower limits on

RH in re-evaporation.

3) The upper limits on RADQL and RADQI were lowered to 1 g/kg from 40 g/kg.

4) A bug in MOIST was fixed to pressure weight DTDTFRIC.

5) TROPP_THERMAL, TROPP_EPV, and TROPP_BLENDED options were implemented for

tropopause pressure.

6) Moved updating of FR in GEOS_CatchGridComp.F90 to AFTER DTS and DQS computations. This

provided consistency with the LSM calculations and prevented excessively large DTS and DQS

values.

7) Budgets computed in catchment.f90 were fixed.

8) Protections against negative values of Q2M, Q10M, SPHU, OX, EKM and EKH were implemented.

9) The bounds for the relative humidity ramp for mass flux in RAS were changed from [0.6,0.8] to

[0.5,0.65].

10) The temperature perturbation in convective boundary layers was capped at 2 K over the ocean and 4

K over the land.

11) Corrections were made to ALBEDO and SLRSFC calculations in GEOS_SolarGridComp.F90 and

sorad.F.

12) The historical CO2 record is used.
75

13) A gravity wave drag heating correction based on energy conversion from waves (rather than mean

flow) was implemented.

14) A bug was fixed in PCHEM for time-interpolation of climatology aerosols.

15) The θ to T conversion in PHYSICS (from MOIST) is done using a P**KAPPA calculation consistent

with that in MOIST.

Updates to the Land Surface Module

1) The LANDICEALBEDO was changed to 0.775 (from 0.8).

2) Modifications were made to thermal capacity of ice to allow a diurnal cycle of surface temperature

over land and sea ice.

Updates to the Analysis

1) The satellite bias correction was turned off for AMSU-A channel 14 and SSU channel 3.

2) The IR channels with sensitivity to surface temperature greater than 0.005 are excluded over nonwater surfaces. The channel selection is dynamic, depending on the meteorological background state.

The CRTM adjoint is used to estimate the sensitivity.

3) CRTM coefficients for AMSU and MSU, all channels for NOAA-8 and SSU channels for NOAA-11

were updated.

4) A bug was fixed in the quality control of Aqua AMSU-A.

5) The re-calibrated MSU Channel 3 data set from NCEP is used.
76

5.3 The Impacts

Some insight into the impacts of the changes are provided below in the average difference fields between

selected products.

Figure 5.3.1: Mean sea-level pressure for January 2006. The left-hand figure shows GEOS-5.1.0 (upper panel), 5.0.1

(middle panel) and the difference (5.1.0 minus 5.0.1). The mean difference is 0.05 hPa, the standard deviation of the

difference is 0.40 hPa. The right-hand figure shows GEOS-5.2.0 (upper panel), 5.1.0 (middle panel) and the

difference (5.2.0 minus 5.1.0). The mean difference is 0.05 hPa, the standard deviation of the difference is 0.35 hPa.
77

Figure 5.3.2: As in Figure 5.3.1, but for 500-hPa height. The mean difference is between 5.1.0 and 5.0.1 is 3.2 hPa,

and the standard deviation of the difference is 6.2 hPa. The mean difference is between 5.2.0 and 5.1.0 is 2.9 hPa,

and the standard deviation of the difference is 3.3 hPa.
78

Figure 5.3.3: Mean difference in precipitation for January 2006 (upper panels) and July 2004 (lower panels) in

mm/day. The left-hand panels show GEOS-5.1.0 minus GEOS-5.0.1. The right-hand panels show GEOS-5.2.0

minus GEOS-5.1.0.
79

Figure 5.3.4: Zonal mean temperature (K) for January 2006. The left-hand figure shows GEOS-5.1.0 (upper panel),

5.0.1 (middle panel) and the difference (5.1.0 minus 5.0.1, lower panel). The right-hand figure shows GEOS-5.2.0

(upper panel), 5.1.0 (middle panel) and the difference (5.2.0 minus 5.1.0, lower panel).
80

Figure 5.3.5: As in Figure 5.3.4, but zonal mean specific humidity (g/kg).
81

Figure 5.3.6: As in Figure 5.3.4, but zonal mean zonal wind (m s

-1

).
82

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Weng, F., B. Yan, and N. Grody, 2001: A microwave land emissivity model, Geophys. Res., 106, 20,115-

20,123.

Wilbur, A. C., D. P. Kratz, and S. K. Gupta, 1999: Surface emissivity maps for use in satellite retrievals

of longwave radiation. NASA Tech. Memo. TP-1999-209362, 30 pp.

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inhomogeneous covariances. Mon. Wea. Rev., 130, 2905-2916.

Wu, X. and Smith W.L. 1997: Emissivity of rough sea surface for 8-13μm: modeling and verification.

Appl. Opt., 36, 2609-2619.

Yan, B., F. Weng, K. Okamoto, 2004: Improved Estimation of Snow Emissivity from 5 to 200 GHz. 8th

Specialist Meeting on Microwave Radiometry and Remote Sensing Applications, 24-27 February, 2004,

Rome, Italy.

Zhao, Q.Y., and F.H. Carr, 1997: A prognostic cloud scheme for operational NWP models. Mon. Wea.

Rev., 125,1931-1953.
88

Appendix A. AIRS 281 Channel Subset List

Assimilation

Channel No.

Instrument

Channel

No.

SRF Centroid

Frequency

(cm-1)

1 1 649.613

2 6 650.807

3 7 651.046

4 10 651.765

5 11 652.005

6 15 652.968

7 16 653.209

8 17 653.450

9 20 654.175

10 21 654.417

11 22 654.659

12 24 655.144

13 27 655.873

14 28 656.116

15 30 656.604

16 36 658.070

17 39 658.806

18 40 659.052

19 42 659.544

20 51 661.767

21 52 662.015

22 54 662.512

23 55 662.761

24 56 663.009

25 59 663.757

26 62 664.507

27 63 664.757

28 68 666.011

29 69 666.262

30 71 666.766

31 72 667.018

32 73 667.270

33 74 667.522

34 75 667.775

35 76 668.028

36 77 668.281

37 78 668.534

38 79 668.787

39 80 669.041

40 82 669.549

41 83 669.803

42 84 670.058

43 86 670.567

44 92 672.100

45 93 672.357

46 98 673.641

47 99 673.899

48 101 674.414

49 104 675.189

50 105 675.448

51 108 676.226

52 110 676.745

53 111 677.005

54 113 677.526

55 116 678.308

56 117 678.570

57 123 680.142

58 124 680.404

59 128 681.457

60 129 681.721

61 138 689.491

62 139 689.762

63 144 691.119

64 145 691.391

65 150 692.755

66 151 693.029

67 156 694.400

68 157 694.674

69 159 695.225

70 162 696.052

71 165 696.881

72 168 697.712

73 169 697.990

74 170 698.267

75 172 698.824

76 173 699.102

77 174 699.381

78 175 699.660

79 177 700.218

80 179 700.777

81 180 701.057

82 182 701.618
89

83185702.461

84186702.742

85190703.870

86192704.436

87198706.137

88201706.991

89204707.847

90207708.706

91210709.566

92215711.005

93216711.293

94221712.739

95226714.191

96227714.482

97232715.941

98252721.838

99253722.135

100256723.029

101257723.328

102261724.524

103262724.824

104267726.326

105272727.834

106295734.150

107299735.382

108300735.690

109305737.236

110310738.789

111321742.227

112325743.485

113333746.014

114338747.603

115355753.057

116362755.325

117375759.574

118453793.171

119475801.099

120484804.386

121497809.180

122528820.834

123587843.913

124672871.289

125787917.306

126791918.747

127843937.908

128870948.184

129914965.431

130950979.128

13110031001.384

13210121005.263

13310191008.300

13410241010.481

13510301013.109

13610381016.635

13710481021.077

13810691030.528

13910791035.089

14010821036.465

14110831036.924

14210881039.227

14310901040.151

14410921041.077

14510951042.468

14611041056.104

14711111059.444

14811151061.361

14911161061.841

15011191063.285

15111201063.767

15211231065.216

15311301068.610

15411381072.515

15511421074.478

15611781092.451

15711991103.199

15812061106.826

15912211114.675

16012371123.162

16112521131.229

16212601135.575

16312631216.974

16412661218.496

16512851228.225

16613011236.539

16713041238.110

16813291251.357

16913711285.475

17013821291.709

17114151310.766

17214241316.058

17314491330.976

17414551334.605

17514661339.687

17614771345.312
90

17715001357.236

17815191367.253

17915381377.426

18015451381.213

18115651392.153

18215741397.135

18315831402.153

18415931407.773

18516141419.726

18616271427.229

18716361432.471

18816441437.164

18916521441.888

19016691468.827

19116741471.910

19216811476.247

19316941484.369

19417081493.215

19517171498.958

19617231502.810

19717401513.832

19817481519.074

19917511521.049

20017561524.352

20117631542.449

20217661544.482

20317711547.882

20417771551.981

20517801554.038

20617831556.101

20717941563.709

20818001567.890

20918031569.989

21018061572.092

21118121576.317

21218261586.259

21318431598.495

21418521605.046

21518652181.495

21618662182.400

21718682184.214

21818692185.122

21918722187.850

22018732188.761

22118762191.498

22218812196.075

22318822196.993

22418832197.911

22519112223.936

22619172229.592

22719182230.537

22819242236.225

22919282240.033

23019372248.648

23119412252.497

23220992378.426

23321002379.395

23421012380.365

23521032382.308

23621042383.280

23721062385.227

23821072386.202

23921082387.178

24021092388.154

24121102389.132

24221112390.110

24321122391.089

24421132392.068

24521142393.049

24621152394.030

24721162395.012

24821172395.995

24921182396.979

25021192397.964

25121202398.949

25221212399.936

25321222400.923

25421232401.911

25521282406.863

25621342412.832

25721412419.835

25821452446.195

25921492450.298

26021532454.414

26121642465.804

26221892492.079

26321972500.602

26422092513.493

26522262531.978

26622342540.769

26722802561.129

26823182600.499

26923212603.660

27023252607.887
91

271 2328 2611.066

272 2333 2616.383

273 2339 2622.792

274 2348 2632.466

275 2353 2637.872

276 2355 2640.041

277 2357 2642.214

278 2363 2648.752

279 2370 2656.423

280 2371 2657.522

281 2377 2664.138
92

Appendix B. Observational Error Variances for Satellite Radiances

The observational (instrument and representativeness) error variance for various radiance channels used

in the GSI analysis system.

Table B1: TOVS

Satellite Instrument/Channel R = instrument +

representativeness

variance (°C)

2

NOAA-14 HIRS channel 2 0.410

HIRS channel 3 0.360

HIRS channel 4 0.250

HIRS channel 5 0.245

HIRS channel 6 0.360

HIRS channel 7 0.470

HIRS channel 8 1.000

HIRS channel 9 1.000

HIRS channel 10 0.500

HIRS channel 11 1.000

HIRS channel 12 1.500

HIRS channel 13 0.464

HIRS channel 14 0.390

HIRS channel 15 0.320

MSU channel 2 0.305

MSU channel 3 0.240

MSU channel 4 0.290

NOAA-15 HIRS channel 2 0.410

HIRS channel 3 0.360

HIRS channel 4 0.250

HIRS channel 5 0.245

HIRS channel 6 0.360

HIRS channel 7 0.470

HIRS channel 8 1.000

HIRS channel 9 1.000

HIRS channel 10 0.500

HIRS channel 11 1.000

HIRS channel 12 1.500

HIRS channel 13 0.464

HIRS channel 14 0.390

HIRS channel 15 0.320

AMSU-A channel 1 4.500

AMSU-A channel 2 4.500

AMSU-A channel 3 4.500

AMSU-A channel 4 0.600

AMSU-A channel 5 0.300
93

AMSU-A channel 6 0.200

AMSU-A channel 7 0.250

AMSU-A channel 8 0.275

AMSU-A channel 9 0.300

AMSU-A channel 10 0.400

Table B2: GOES

Satellite Instrument/Channel R = instrument +

representativeness

variance (°C)

2

GOES-8 HIRS channel 1 4.500

HIRS channel 2 0.410

HIRS channel 3 0.360

HIRS channel 4 0.250

HIRS channel 5 0.245

HIRS channel 6 0.360

HIRS channel 7 0.470

HIRS channel 8 1.000

HIRS channel 9 1.500

HIRS channel 10 0.500

HIRS channel 11 1.000

HIRS channel 12 1.500
94

Appendix C. Acronyms

3DVar Three-dimensional Variational assimilation

AGCM Atmospheric General Circulation Model

AIREP AIRcraft REPort

AIRS Advanced Infrared Sounder (on Aqua)

AMSU Advanced Microwave Sounding Unit (on later TIROS)

AMV Atmospheric Motion Vectors (also called CTW)

AQUA EOS PM satellite

ASDAR Aircraft to Satellite DAta Relay system

ATOVS Advanced TOVS

AURA EOS CHEM satellite

AVHRR Advanced Very High Resolution Radiometer

BUFR Binary Universal Form for the Representation of meteorological data

CAPE Convective Available Potential Energy

CLSM Catchment Land Surface Model

C-MAN Coastal-Marine Automated Network

CRTM Community Radiative Transfer Model

CTW Cloud Track Wind (now called AMV)

DAS Data Assimilation System

DEM Digital Elevation Model

DMSP Defense Meteorological Satellite Program

DU Dobson Unit (Ozone amount in atmospheric column)

ECMWF European Centre for Medium Range Weather Forecasting

ELW Expanded Low-resolution Winds

EOS Earth Observing System

ERS-1,2 Environmental Research Satellite (surface winds obtained using the AMI, Active

Microwave Unit)

ESMF Earth System Modeling Framework

EUMETSAT European Organisation for the Exploitation of Meteorological Satellites

fvGCM Finite-volume General Circulation Model

GCM General Circulation Model (Atmospheric)

GEOS Goddard Earth Observing System

GLATOVS Goddard Laboratory for Atmospheres TOVS (radiative transfer model)

GMAO Global Modeling and Assimilation Office (GSFC)

GMS Geostationary Meteorological Satellite 

GOES Geosynchronous Operational Environmental Satellite

GSFC (NASA) Goddard Space Flight Center

GSI Grid-point Statistical Interpolation

GTOPO30 Global Digital Elevation Model (DEM), 30 arc second resolution

GTS Global Telecommunication System

HALOE Halogen Occultation Experiment

HIRS2,3,4 High-resolution Infrared Spectrometer

HSB Humidity Sounder for Brazil

IAU Incremental Analysis Updating

IR Infra-Red

IRSSE Infra-Red Sea Surface Emissivity

JCSDA Joint Center for Satellite Data Assimilation

JMA Japan Meteorological Agency

LCV Lagrangian Control Volume
95

LSM Land Surface Model

MDCRS Meteorological Data Collection and Reporting System

MERRA Modern Era Retrospective-analysis for Research and Applications

METAR Aviation routine weather report

MHS Microwave Humidity Sounder

MLS Microwave Limb Sounder

MODIS Moderate Resolution Imaging Spectroradiometer

MPI Message Passing Interface

MSU Microwave Sounding Unit (part of TOVS)

MW MicroWave

NASA National Aeronautics and Space Administration

NCEP National Centers for Environmental Prediction

NESDIS National Environmental Satellite, Data, and Information Service

NEXRAD Next generation Radar

NMC National Meteorological Center

NOAA National Oceanic and Atmospheric Administration

NPN NOAA Profiler Network

NWP Numerical Weather Prediction

OMF(O-F) Observation Minus Background (or First Guess)

OSS Optimal Spectral Sampling (radiative transfer method)

PAOBS Synthetic surface Pressure OBS

PAR Photosynthetically Active Radiation

PBL Planetary Boundary Layer

PDF Probability Distribution Function

PIBAL PILot BALloon

PILPS Project for the Intercomparison of Land-surface Parameterization Schemes

PIREP PIlot REPort

POES Polar-Orbiting Environment Satellite

QC Quality Control

QM Quality Marker

RAS Relaxed Arakawa-Schubert

RFF Recursive Filter Flag

RH Relative Humidity

Rhone-AGG Rhone AGGregation Experiment

RSS Remote Sensing Systems

RTM Radiative Transfer Model

SARTA Stand-alone AIRS Radiative Transfer Algorithm

SBUV/2 Solar Backscatter Ultraviolet Spectral Radiometer-2

SQC Statistical Quality Control

SSI Spectral Statistical Interpolation

SSM/I Special Sensor Microwave/Imager (on DMSP satellites)

SSU Stratospheric Sounding Unit (superseded by AMSU)

TERRA EOS AM Satellite

TIROS Television and Infrared Observatory Spacecraft

TLM Tangent Linear Model

TMI TRMM Microwave Imager

TOMS Total Ozone Mapping Spectrometer

TOVS TIROS Operational Vertical Sounder

TPW Total Precipitable Water

TRMM Tropical Rainfall Measurement Mission

UTC Coordinated Universal Time
96

UV Ultra-violet

VAD Velocity Azimuth Display wind

VIS Visible

WMO World Meteorological Organization

WSR-88D Weather Surveillance Radar 88 Doppler

WV Water Vapor
97

Appendix D. Acknowledgments

The Global Modeling and Assimilation Office gratefully acknowledges the help and collaboration from 

our colleagues at NOAA/NCEP, especially John Derber and Russ Treadon, in the development of the 

GEOS-5 atmospheric data assimilation system. Without their guidance in the use of the GSI, the GEOS-5

system would not have emerged so quickly. The contributions from other scientists in the GMAO have

been critical to improving the performance of our implementation. Here we particularly thank Steven

Pawson, Steve Bloom, Austin Conaty, Arlindo da Silva, Ron Errico, Jing Guo, Gary Partyka, Phil Pegion,

Chris Redder, Runhua Yang, Banglin Zhang, and Yanqiu Zhu. The tireless efforts of Gi-Kong Kim, Rob

Lucchesi, Tommy Owens, Joe Stassi, Doug Collins and their support staff in terms of system testing are

also gratefully acknowledged; without their contributions the operational products would not have 

emerged. Al Ruddick has helped to coordinate communications and keep the project on schedule. We

thank the NASA instrument teams, particularly the EOS/Aura teams for their feedback on the GEOS-5

products. Their insight and feedback has helped us improve the system. The NASA Center for

Computational Sciences (NCCS) has helped us in untold ways in getting our systems configured for the 

NCCS environment and vice versa. The Software Integration and Visualization Office (SIVO) has helped

with many software optimization issues. Finally, we gratefully acknowledge the support from NASA/HQ,

both Don Anderson, the Modeling Analysis and Prediction (MAP) project manager, and Tsengdar Lee,

the project manager for high performance computing and for the JCSDA. Their encouragement and

support has been essential to the development of GEOS-5.
98
99

Previous Volumes in This Series

Volume 1

September 1994

Documentation of the Goddard Earth Observing System (GEOS) general

circulation model - Version 1

L.L. Takacs, A. Molod, and T. Wang

Volume 2

October 1994

Direct solution of the implicit formulation of fourth order horizontal

diffusion for gridpoint models on the sphere 

Y. Li, S. Moorthi, and J.R. Bates

Volume 3

December 1994

An efficient thermal infrared radiation parameterization for use in

general circulation models

M.-D. Chou and M.J. Suarez

Volume 4

January 1995

Documentation of the Goddard Earth Observing System (GEOS) Data

Assimilation System - Version 1

James Pfaendtner, Stephen Bloom, David Lamich, Michael

Seablom, Meta Sienkiewicz, James Stobie, and Arlindo da Silva

Volume 5

April 1995

Documentation of the Aries-GEOS dynamical core: Version 2

Max J. Suarez and Lawrence L. Takacs

Volume 6

April 1995

A Multiyear Assimilation with the GEOS-1 System: Overview and

Results

Siegfried Schubert, Chung-Kyu Park, Chung-Yu Wu, Wayne 

Higgins, Yelena Kondratyeva, Andrea Molod, Lawrence Takacs,

Michael Seablom, and Richard Rood

Volume 7

September 1995

Proceedings of the Workshop on the GEOS-1 Five-Year Assimilation

Siegfried D. Schubert and Richard B. Rood

Volume 8

March 1996

Documentation of the Tangent Linear Model and Its Adjoint of the 

Adiabatic Version of the NASA GEOS-1 C-Grid GCM: Version 5.2

Weiyu Yang and I. Michael Navon

Volume 9

March 1996

Energy and Water Balance Calculations in the Mosaic LSM

Randal D. Koster and Max J. Suarez

Volume 10

April 1996

Dynamical Aspects of Climate Simulations Using the GEOS General

Circulation Model

Lawrence L. Takacs and Max J. Suarez

Volume 11

May 1997

Documentation of the Tangent Linear and its Adjoint Models of the 

Relaxed Arakawa-Schubert Moisture Parameterization Package of the 

NASA GEOS-1 GCM (Version 5.2) 

Weiyu Yang, I. Michael Navon, and Ricardo Todling
100

Volume 12

August 1997

Comparison of Satellite Global Rainfall Algorithms

Alfred T.C. Chang and Long S. Chiu

Volume 13

December 1997

Interannual Variability and Potential Predictability in Reanalysis

Products

Wie Ming and Siegfried D. Schubert

Volume 14

August 1998

A Comparison of GEOS Assimilated Data with FIFE Observations

Michael G. Bosilovich and Siegfried D. Schubert

Volume 15

June 1999

A Solar Radiation Parameterization for Atmospheric Studies

Ming-Dah Chou and Max J. Suarez

Volume 16

November 1999

Filtering Techniques on a Stretched Grid General Circulation Model

Lawrence Takacs, William Sawyer, Max J. Suarez, and Michael S.

Fox-Rabinowitz

Volume 17

July 2000

Atlas of Seasonal Means Simulated by the NSIPP-1 Atmospheric GCM 

Julio T. Bacmeister, Philip J. Pegion, Siegfried D. Schubert, and

Max J. Suarez

Volume 18

December 2000

An Assessment of the Predictability of Northern Winter Seasonal Means

with the NSIPP 1 AGCM 

Philip J. Pegion, Siegfried D. Schubert, and Max J. Suarez

Volume 19

July 2001

A Thermal Infrared Radiation Parameterization for Atmospheric Studies

Ming-Dah Chou, Max J. Suarez, Xin-Zhong, Michael M.-H. Yan

Volume 20

August 2001

The Climate of the FVCCM-3 Model

Yehui Chang, Siegfried D. Schubert, Shian-Jiann Lin, Sharon 

Nebuda, Bo-Wen Shen

Volume 21

September 2001

Design and Implementation of a Parallel Multivariate Ensemble Kalman

Filter for the Poseidon Ocean General Circulation Model

Christian L. Keppenne and Michele M. Rienecker

Volume 22

August 2002

Coupled Ocean-Atmosphere Radiative Model for Global Ocean

Biogeochemical Models

Watson W. Gregg

Volume 23

November 2002

Prospects for Improved Forecasts of Weather and Short-term Climate 

Variability on Subseasonal (2-Week to 2-Month) Time Scales

Siegfried D. Schubert, Randall Dole, Huang van den Dool, Max J.

Suarez, and Duane Waliser

Volume 24

July 2003

Temperature Data Assimilation with Salinity Corrections: Validation for

the NSIPP Ocean Data Assimilation System in the Tropical Pacific 

Ocean, 1993–1998

Alberto Troccoli, Michele M. Rienecker, Christian L. Keppenne,

and Gregory C. Johnson
101

Volume 25

December 2003

Modeling, Simulation, and Forecasting of Subseasonal Variability

Duane Waliser, Siegfried D. Schubert, Arun Kumar, Klaus

Weickmann, and Randall Dole

Volume 26

April 2005

Documentation and Validation of the Goddard Earth Observing System

(GEOS) Data Assimilation System – Version 4

Senior Authors: S. Bloom, A. da Silva and D. Dee

Contributing Authors: M. Bosilovich, J-D. Chern, S. Pawson, S.

Schubert, M. Sienkiewicz, I. Stajner, W-W. Tan, and M-L. Wu
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13. SUPPLEMENTARY NOTES 

R. Todling, L. Takacs, H.-C. Liu, W. Gu, M. Sienkiewicz, and I. Stajner (former employee): SAle, Lanham, MD; J. Bacmeister: 

University of Maryland, Baltimore County, Baltimore, MD; and J.E. Nielsen: SSAI, Lanham, MD 

14. ABSTRACT 

This report documents the GEOS-5 global atmospheric model and data assimilation system (DAS), including the versions 5.0.1, 

5.1.0, and 5.2.0, which have been implemented in products distributed for use by various NASA instrument team algorithms and 

ultimately for the Modem Era Retrospective analysis for Research and Applications (MERRA). The DAS is the integration of the 

GEOS-5 atmospheric model with the Gridpoint Statistical Interpolation (GSI) Analysis, ajoint analysis system developed by the 

NOAAlNational Centers for Environmental Prediction and the NASA/Global Modeling and Assimilation Office. The primary 

performance drivers for the GEOS DAS are temperature and moisture fields suitable for the EOS instrument teams, wind fields for 

the transport studies of the stratospheric and tropospheric chemistry communities, and climate-quality analyses to support studies of 

the hydrological cycle through MERRA. The GEOS-5 atmospheric model has been approved for open source release and is 

available from: http://opensource.gsfc.nasa.gov/projects/GEOS-5/GEOS-5.php. 

15. SUBJECT TERMS 

Goddard Earth Observing System Data Assimilation System, GEOS DAS, GEOS-S GEOS-S.O.l GEOS-S.1.0 GEOS-S.2.0 Grid-point 

Statistical Interpolation, GSI, Community Radiative Transfer Model, CRTM, Modem Era Retrospective-analysis for Research and Applications, 

MERRA 

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