Vertically Integrated Mass, Moisture, Heat, and Energy Budget Products Derived from the NCEP/NCAR Reanalysis

March 2003

Climate Analysis Section, CGD, NCAR

Contact:

David Stepaniak
davestep@ucar.edu

My home page

Contents
Accessing the Data
Three-panel figure shows diabatic minus frictional heating Q1- Qf (top), latent heating Q2 (middle), and Q1-Qf-Q2 (bottom) which is roughly equivalent to divergence of vertically integrated total energy transport, . The fields represent an annual mean in W m-2 for the period 1979-2001 at T31 spectral truncation. Further details are provided below.
GOES-11 image of a portion of the Intertropical Convergence Zone (ITCZ) in the eastern Pacific Ocean and the upward branch of the Hadley Circulation, a region of intense latent heating (see Q2 in the second panel in the figure immediately above). Image courtesy of GOES Project Science Office.

Contents

Introduction

We report here a newly completed (March 2003) recomputation and updating of vertically integrated monthly mean mass, moisture, heat, and energy budget products derived from the NCEP/NCAR reanalysis. This new archive spans January 1979 to December 2001 (23 years), and incorporates TOVS (TIROS Operational Vertical Sounder) reruns in addition to grid corrections implemented by NCEP for reanalysis data covering the period March 1997 through October 2001.

Our monthly mean budget products are derived from 6-hourly model () level data which the Data Support Section (DSS) at NCAR makes available in the form of `grbsanl' grib files on the MSS. The DSS web page ` ds090.0 HOME PAGE: NCEP/NCAR Global Reanalysis Products, 6-hrly, monthly ' provides extensive documentation and useful background. For an overview of the NCEP/NCAR reanalysis project see Kalnay and others, 1996.

We note that the spectral truncation of the fields in the grbsanl files is T62 on a 192x94 grid (longitude by latitude), which we subsequently regrid to 192x96 with T63 truncation, the resolution at which we carry out all our budget computations. However, spatial spectra (power as a function of total wavenumber n) shows that in certain derived fields a considerable amount of extraneous power may exist beyond n=42 or so, and thus the final spectral truncation of our products is T42 on a 128 x 64 Gaussian grid ¹.

We make a total of 36 budget products available in both netCDF and Fortran direct access binary files via email requests (see the section Accessing the Data). The description of these products and their derivation is outlined in the following sections, in which product names are highlighted in capital red letters in the tables and text of each section (see especially entries under `Product Name' in tables). The reader is referred to Trenberth (1991, 1997) for derivations and details of the budget equations we employ.

¹ Our regridding and truncation, as well as the two-dimensional operators for divergence , inverse Laplacian , and gradient are carried out in spectral space via a Fortran 90 interface and static library created for Spherepack 3.0. (An NCAR Technical Note and web page by Adams and Swarztrauber, 1997, provides a detailed description of the Spherepack 3.0 package.)

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Physical Constants

We employ the following constants, consistent with those used in the NCAR Community Climate Model 2, i.e. CCM2 (see Hack and others, 1993), and later generations of the CCM (and CCSM).

Constant Symbol Value Units
Specific Heat Capacity of Dry Air at Constant Pressure Cp 1004.64 J kg-1 K-1
Acceleration Due to Gravity g 9.80616 m s-2
Latent Heat of Vaporization of Water L 2.5104x106 J kg-1
Gas Constant for Dry Air Rd 287.04 J kg-1 K-1
Ratio of Molecular Weight of Water Vapor to that of Dry Air 0.622 Dimensionless
Radius of Earth a 6.37122x106 m
Density of Liquid Water H2O 1.0x103 kg m-3

Contents

Basic Fields at 6-hourly Resolution Available from NCEP

In model level (i.e. ) coordinates we utilize u, v, T, and q at 6-hourly temporal resolution on 28 levels. (The levels are 0.0027, 0.0101, 0.0183, 0.0288, 0.0418, 0.0580, 0.0782, 0.1028, 0.1326, 0.1682, 0.2101, 0.2582, 0.3125, 0.3720, 0.4357, 0.5017, 0.5681, 0.6329, 0.6943, 0.7508, 0.8014, 0.8458, 0.8838, 0.9159, 0.9425, 0.9644, 0.9821, and 0.9950, where pressure in the vertical is given by pi = iPs.) In addition, we employ the surface fields Ps and s at 6-hourly temporal resolution.

Basic Variable Symbol Units Level(s) Working Spectral Truncation Times
Zonal (eastward component) wind u m s-1 28 T63 6-hourly
Meridional (northward component) wind v m s-1 28 T63 6-hourly
Temperature T K (Kelvin) 28 T63 6-hourly
Specific Humidity q kg kg-1 28 T63 6-hourly
Surface pressure Ps Pa Surface T63 6-hourly
Surface geopotential s m2 s-2 Surface T63 6-hourly

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Derived Fields at 6-hourly Resolution

Fields not available in coordinates in the NCEP reanalysis which must be derived at 6-hourly resolution and for all levels in the vertical include the kinetic energy, K = (u2+v2)/2, and the geopotential height, z = s /g + (Rd /g) H Tv, where H is the CCM hydrostatic matrix, and Tv the virtual temperature which is computed as Tv = T(1 + q). The hydrostatic matrix H is a function of the surface pressure Ps (see Hack and others, 1993, p. 27, for details, and our subroutine ccm2_hydrostatic_matrix). In addition, we compute the products uT, vT, uz, vz, uq, vq, uK, and vK, at 6-hourly temporal resolution for all levels.

Derived Variable Symbol Units Levels Working Spectral Truncation Times
Kinetic energy K J kg-1 28 T63 6-hourly
Geopotential height z m (gpm - geopotential meters) 28 T63 6-hourly
Zonal temperature flux uT m K s-1 28 T63 6-hourly
Meridional temperature flux vT m K s-1 28 T63 6-hourly
Zonal geopotential height flux uz m2 s-1 28 T63 6-hourly
Meridional geopotential height flux vz m2 s-1 28 T63 6-hourly
Zonal moisture flux uq m s-1 28 T63 6-hourly
Meridional moisture flux vq m s-1 28 T63 6-hourly
Zonal kinetic energy flux uK J m kg-1 s-1 28 T63 6-hourly
Meridional kinetic energy flux vK J m kg-1 s-1 28 T63 6-hourly

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Monthly Means

We compute monthly means of the basic and derived variables from the 6-hourly data. The monthly mean spans 00Z of the first day of a month to 18Z of the last day of a month, and incorporates a 29th day in February of the leap years 1980, 1984, 1988, 1992, 1996, and 2000. From this first batch of monthly means it is the monthly mean surface pressure s that we make available as a budget product.
Vertically Integrated Monthly Mean Variable Symbol Product Name Units Level Final Spectral Truncation Times
Monthly mean surface pressure s PS Pa Surface T42 Monthly

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Vertical Integrals of Monthly Means

We define the vertical integral of a monthly mean field as a mass-weighted sum corresponding to   ( )dp/ g   where ( ) in the vertical integral is the monthly mean operator, and s the monthly mean surface pressure. We note that monthly means are computed before any vertical integration is performed. Trenberth and others (2002) discuss differences that arise (up to order ±10 W m-2) in the divergence of total energy () if the vertical integral is performed at 6-hourly resolution, then the monthly mean taken, in the ERA-15 eta () archive for January of 1989.

In practice, the integral is obtained by computing pi = is at the model layer interfaces given by i = 0.0000, 0.0066, 0.0139, 0.0231, 0.0347, 0.0492, 0.0672, 0.0894, 0.1165, 0.1492, 0.1878, 0.2329, 0.2842, 0.3414, 0.4033, 0.4686, 0.5353, 0.6013, 0.6648, 0.7240, 0.7777, 0.8253, 0.8664, 0.9013, 0.9305, 0.9546, 0.9742, 0.9900, and 1.0000, where = 0.0000 is the top of the atmosphere, and = 1.0000 is the surface of the Earth. (In the -coordinate such as for ERA-15, pi = ai + bi s for ai and bi at model layer interfaces.) Then, dp for a given layer is computed as the difference between the pressure of the lower interface bounding the model layer, and the pressure of the upper interface bounding the model layer.

Since the units of dp/g, Pa/(m s-2), reduce to kg m-2, the term 'mass weighted' is used in association with the vertical integral. We also note that the flux quantities appearing in the following table are not mass-corrected. The mass correction and mass corrected fluxes are described in subsequent sections (see Mass Correction and Mass Corrected Vertically Integrated Monthly Mean Fluxes).

Vertically Integrated Monthly Mean Variable Symbol Product Name Units Level Spectral Truncation Times
Vertically integrated zonal velocity (u)dp/ g U kg m-1 s-1 Total column T42, Final Monthly
Vertically integrated meridional velocity (v)dp/ g V kg m-1 s-1 Total column T42, Final Monthly
Vertically integrated temperature (T)dp/ g T K kg m-2 Total column T42, Final Monthly
Vertically integrated specific humidity
(Precipitable water)		 (q)dp/ g PW kg m-2 Total column T42, Final Monthly
Vertically integrated geopotential height (z)dp/ g Z kg m-1 Total column T42, Final Monthly
Vertically integrated kinetic energy (K)dp/ g KE J m-2 Total column T42, Final Monthly
Vertically integrated zonal temperature flux (uT)dp/ g - kg K m-1 s-1 Total column T63, Working Monthly
Vertically integrated meridional temperature flux (vT)dp/ g - kg K m-1 s-1 Total column T63, Working Monthly
Vertically integrated zonal geopotential height flux (uz)dp/ g - kg s-1 Total column T63, Working Monthly
Vertically integrated meridional geopotential height flux (vz)dp/ g - kg s-1 Total column T63, Working Monthly
Vertically integrated zonal moisture flux (uq)dp/ g - kg m-1 s-1 Total column T63, Working Monthly
Vertically integrated meridional moisture flux (vq)dp/ g - kg m-1 s-1 Total column T63, Working Monthly
Vertically integrated zonal kinetic energy flux (uK)dp/ g - J m-1 s-1 Total column T63, Working Monthly
Vertically integrated meridional kinetic energy flux (vK)dp/ g - J m-1 s-1 Total column T63, Working Monthly

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Monthly Tendencies

To compute tendencies for a given month we utilize basic and derived variables, here generally denoted by A, at 18Z of the last day of the previous month (ldpm), A18Z, ldpm, 00Z of the first day of the given month (fdgm), A00Z, fdgm, 18Z of the last day of the given month (ldgm), A18Z, ldgm, and 00Z of the first day of the following month (fdfm), A00Z, fdfm. Where required we also compute vertical integrals, denoted by Ã, at the same times, thus forming

Ã18Z, ldpm = A18Z, ldpmdp/g,

Ã00Z, fdgm = A00Z, fdgmdp/g,

Ã18Z, ldgm = A18Z, ldgmdp/g,

and

Ã00Z, fdfm = A00Z, fdfmdp/g.

Averages are then computed from these quantities for the beginning of the month (bom), and the end of the month (eom):

Abom = ½(A18Z, ldpm + A00Z, fdgm),

Aeom = ½(A18Z, ldgm + A00Z, fdfm),

and

Ãbom = ½(Ã18Z, ldpm + Ã00Z, fdgm),

Ãeom = ½(Ã18Z, ldgm + Ã00Z, fdfm).

Finally, a monthly tendency is defined as

ðA/ðt = (Aeom - Abom)/(N x 86400),

or, for a vertically integrated quantity,

ðÃ/ðt = (Ãeom - Ãbom)/(N x 86400)

where ð/ðt is the time derivative operator, N the number of days in a month, and 86400 the number of seconds in a day.

Monthly Tendency Symbol Product Name Units Level Final Spectral Truncation Times
Precipitable water tendency ð( qdp/ g)/ðt QTEN kg m-2 s-1 Total column T42 Monthly
Internal energy tendency ð( CpTdp/ g)/ðt ITEN W m-2 Total column T42 Monthly
Kinetic energy tendency ð( Kdp/ g)/ðt KTEN W m-2 Total column T42 Monthly
Latent energy tendency ð( Lqdp/ g)/ðt LETEN W m-2 Total column T42 Monthly
Geopotential tendency ð( sdp/ g)/ðt
=
ð(sPs/ g)/ðt		 PHISTEN W m-2 Total column T42 Monthly
Total energy tendency ð(CpTdp/ g + Kdp/ g +
Lqdp/ g + sPs/ g)/ðt
=
ð(CpTdp/ g)/ðt + ð(Kdp/ g)/ðt +
ð(Lqdp/ g)/ðt + ð(sPs/ g)/ðt 		TETEN W m-2 Total column T42 Monthly
Surface pressure tendency ðPs/ðt PSTEN Pa s-1 Surface T42 Monthly

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Moisture Budget and Evaporation minus Precipitation

The moisture budget involves the precipitable water tendency, ð(qdp/ g)/ðt, and the vertically integrated moisture flux ( (uq)dp/ g, (vq)dp/ g), from which we derive evaporation minus precipitation E-P:

E-P = ð(qdp/ g)/ðt + ( (uq)dp/ g, (vq)dp/ g)

or, in terms of budget and intermediate products

EP = QTEN + ( (uq)dp/ g, (vq)dp/ g)

where is the divergence operator.

Residual Monthly Mean Variable Symbol Product Name Units Level Final Spectral Truncation Times
Evaporation minus precipitation E-P EP kg m-2 s-1
(mm day-1 in archive)		 Total column T42 Monthly

To convert a variable with units kg m-2 s-1 to mm day-1 multiply by (103mm m-1 x 86400 s day-1) and divide by H2O. Similarly, to convert a variable with units mm day-1 to W m-2 multiply by (H2O x L) and divide by (103mm m-1 x 86400 s day-1).

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Mass Budget and Mass Budget Residual

The mass budget involves the surface pressure tendency ðPs/ðt, the vertically integrated mass flux ( (u)dp/ g, (v)dp/ g), and E-P, from which we can derive the mass budget residual, R, an estimate of the degree of atmospheric mass balance (or lack thereof):

R = ðPs/ðt + g ( (u)dp/ g, (v)dp/ g) - g (E-P)

or, in terms of budget and intermediate products

MRES = PSTEN + g ( (u)dp/ g, (v)dp/ g) - g EP

where

Residual Monthly Mean Variable Symbol Product Name Units Level Final Spectral Truncation Times
Mass budget residual R MRES Pa s-1 Total column T42 Monthly

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Mass Correction

In association with the mass budget residual R we define a potential function such that = R and thus

= R.

In principle, a mass correction which minimizes the mass budget residual may be obtained by subtracting a barotropic correction (uc, vc) from (, ), i.e. (-uc, - vc), at each level, where (, ) is the three-dimensional monthly mean horizontal wind. Combining the vertically integrated mass and moisture budget equations, substituting (-uc, - vc) for (, ), and solving for (uc, vc) yields

(uc, vc) = / (s - g (q)dp/ g - t).

Here t is the monthly mean pressure at the top of the atmosphere, this being uniformly 0. In terms of budget and intermediate products

= MRES

(UC, VC) = / (PS - g PW)

where

Residual Monthly Mean Variable Symbol Product Name Units Level Final Spectral Truncation Times
Barotropic correction
to
zonal wind		 uc UC m s-1 Total column T42 Monthly
Barotropic correction
to
meridional wind		 vc VC m s-1 Total column T42 Monthly

In practice, the mass correction is applied to the vertically integrated monthly mean flux quantities, as described in the next section.

Contents

Mass Corrected Vertically Integrated Monthly Mean Fluxes

Given a generalized variable A, the mass corrected vertically integrated monthly mean flux of this variable is defined as

(uA)dp/ g - uc (A)dp/ g
or
(uA)dp/ g - UC x A

and

(vA)dp/ g - vc (A)dp/ g
or
(vA)dp/ g - VC x A

Vertically Integrated Monthly Mean Flux
(Mass Corrected)		 Symbol Product Name Units Level Final Spectral Truncation Times
Vertically integrated zonal temperature flux (uT)dp/ g - uc (T)dp/ g
or
(uT)dp/ g - UC x T		 UT kg K m-1 s-1 Total column T42 Monthly
Vertically integrated meridional temperature flux (vT)dp/ g - vc (T)dp/ g
or
(vT)dp/ g - VC x T		 VT kg K m-1 s-1 Total column T42 Monthly
Vertically integrated zonal geopotential height flux (uz)dp/ g - uc (z)dp/ g
or
(uz)dp/ g - UC x Z		 UZ kg s-1 Total column T42 Monthly
Vertically integrated meridional geopotential height flux (vz)dp/ g - vc (z)dp/ g
or
(vz)dp/ g - VC x Z		 VZ kg s-1 Total column T42 Monthly
Vertically integrated zonal moisture flux (uq)dp/ g - uc (q)dp/ g
or
(uq)dp/ g - UC x PW		 UQ kg m-1 s-1 Total column T42 Monthly
Vertically integrated meridional moisture flux (vq)dp/ g - vc (q)dp/ g
or
(vq)dp/ g - VC x PW		 VQ kg m-1 s-1 Total column T42 Monthly
Vertically integrated zonal kinetic energy flux (uK)dp/ g - uc (K)dp/ g
or
(uK)dp/ g - UC x KE		 UK J m-1 s-1 Total column T42 Monthly
Vertically integrated meridional kinetic energy flux (vK)dp/ g - vc (K)dp/ g
or
(vK)dp/ g - VC x KE		 VK J m-1 s-1 Total column T42 Monthly

We note that Cp(UT,VT), g(UZ,VZ), L(UQ,VQ), and (UK,VK) all have units of J m-1 s-1. Taking the horizontal divergence, , of any of these, or any sum of these, gives rise to divergences of energy with units W m-2.

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Divergences of Energy

We compute divergences of energy from the mass corrected vertically integrated monthly mean fluxes. In terms of archived budget products the divergences of energy are

TEDIV = (CpUT+ gUZ+LUQ+ UK, CpVT+ gVZ+LVQ+ VK)

DSEDIV = (CpUT+ gUZ, CpVT+ gVZ)

LEDIV = (LUQ, LVQ)

KEDIV = (UK, VK)

Divergence of Energy Symbol Product Name Units Level Final Spectral Truncation Times
Divergence of total energy TEDIV
or
 TEDIV W m-2 Total column T42 Monthly
Divergence of dry static energy DSEDIV DSEDIV W m-2 Total column T42 Monthly
Divergence of latent energy LEDIV LEDIV W m-2 Total column T42 Monthly
Divergence of kinetic energy KEDIV KEDIV W m-2 Total column T42 Monthly

where FA is the total atmospheric energy transport (CpUT+ gUZ+LUQ+ UK, CpVT+ gVZ+LVQ+ VK) with units J m-1 s-1. Strictly speaking, `divergence of energy' here refers to `divergence of energy transport'. In addition, we define the zonal mean poleward atmospheric energy transport PAET as

PAET() = [ CpVT(, ) + gVZ(, ) + LVQ(, ) + VK(, )] a cos() d

where is longitude, latitude, and a the radius of the Earth. The units of PAET are W which we normally convert to PW (i.e. 1015W) by dividing PAET by (1015W PW-1). Note that at present we do not include PAET as a budget product for this particular archive.

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Diabatic minus Frictional Heating (Heat and Energy Budget)

We compute diabatic minus frictional heating, Q1- Qf, as a residual of the energy budget. In terms of archived budget products Q1-Qf is given by

Q1-Qf = TETEN+TEDIV - LEP

where –LEP = Q2, the latent heating.

Residual Monthly Mean Variable Symbol Product Name Units Level Final Spectral Truncation Times
Diabatic minus frictional heating Q1-Qf Q1QF W m-2 Total column T42 Monthly

In general, the estimated frictional heating Qf is less than a few W m-2 on an annual mean basis (see Peixoto and Oort, 1992, p. 383) and can be safely disregarded compared to the diabatic heating Q1. Thus, Q1-Qf Q1.

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Vertically Averaged Total Energy

As a final diagnostic, we compute vertically averaged total energy TE where the vertical average is simply (g / s) ()dp/ g. In practice TE is computed as the sum

TE = (g / s) [ Cp (T)dp/ g + g (z)dp/ g + L (q)dp/ g + (K)dp/ g ],

or, in terms of archived budget products

TE = (g / PS) [ CpT + gZ + LPW + KE ].

Vertically Averaged Monthly Mean Variable Symbol Product Name Units Level Final Spectral Truncation Times
Vertically Averaged Total Energy TE TE J kg-1 Total column T42 Monthly

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ERBE Period (February 1985 – April 1989) Radiation Products and Net Upward Surface Flux

Our budget product offerings would not be complete without an estimate of the net upward surface flux Fs for the ERBE period February 1985 – April 1989. We compute Fs as

Fs = TETEN + TEDIV - RT

where RT is the net downward radiation through the top-of-the-atmosphere (TOA), and

RT = AT - OT

where AT and OT are the absorbed solar (shortwave) radiation and outgoing longwave radiation, respectively, at the TOA. In terms of archived budget products this reads

FS = TETEN + TEDIV - NET

and

NET = ASR - OLR.

An annual mean net upward surface flux Fs for the ERBE period is shown below. Three-panel figure shows TOA annual mean absorbed solar (shortwave) radiation AT (top), outgoing longwave radiation OT (middle), and net radiation RT (bottom) which is given by RT = AT - OT. The units in all three panels is W m-2 at T31 spectral truncation. The annual mean is in fact an annualized mean over the ERBE period February 1985 – April 1989.

Radiation Product or Net Surface Flux Symbol Product Name Units Level Final Spectral Truncation Times
Absorbed solar radiation AT ASR W m-2,
> 0 downward through TOA		 TOA T42 Monthly,
February 1985 – April 1989 only
Outgoing longwave radiation OT OLR W m-2,
> 0 upward through TOA		 TOA T42 Monthly,
February 1985 – April 1989 only
Net downward radiation RT NET W m-2,
> 0 downward through TOA		 TOA T42 Monthly,
February 1985 – April 1989 only
Net upward surface flux Fs FS W m-2,
> 0 upward through surface into atmosphere		 surface T42 Monthly,
February 1985 – April 1989 only
Figure (above) shows an annualized mean net upward surface flux Fs for the ERBE period (February 1985 – April 1989) in W m-2 at T42 spectral truncation. Negative (blue) regions in equatorial and Tropical oceans represent a net flux of energy from the atmosphere into the oceans on an annual mean basis. Other noteworthy features are the significant net fluxes of energy from the Kuroshio, the Gulf Stream, and the Aghulas Current into the atmosphere. (Note that we have masked land areas in this figure – ideally, Fs should be roughly 0 over land areas. We also show both masked and unmasked versions of this figure.)

Contents

Accessing the Data

The products are available in both netCDF and Fortran direct access binary files with one variable archived as 276 monthly mean 128 x 64 grids per file (51 monthly mean grids in the case of ERBE period AT, OT, RT, and Fs). The Fortran direct access files were written on a big-endian machine (SGI Origin 2000), and thus be aware that if you attempt to read the direct access files on a little-endian machine (for example a Pentium-based PC running Linux), the bytes of a data element (in this case 4 bytes for a 32 bit REAL) will be in reverse to that for a big-endian machine. (We supply a subroutine for converting between and big- and little-endian 32 bit REAL data elements. See native_4byte_real.)

The file naming convention for 32 of the 36 products is 

T42t_PRODUCTNAME_1979-2001_MM.EXT

where T42t signifies T42 spectral truncation with `tapering' (see Sardeshmukh and Hoskins, 1984), PRODUCTNAME is the name of a budget product highlighted in red in the previous sections or in the summary table shown below, MM refers to `monthly mean', and EXT is either `nc' for netCDF or `Fda' for Fortran direct access. Users need only specify PRODUCTNAME and EXT. Note that in the case of AT, OT, RT, and Fs, the file naming convention is 

T42t_PRODUCTNAME_198502-198904_MM.EXT

for the ERBE period radiation products and net upward surface flux.

The size of a file is 9043968 bytes (.Fda) to roughly 9047300 bytes (.nc) each – for AT, OT, RT, and Fs, the size of a file is 1671168 bytes (.Fda) to roughly 1673300 bytes (.nc) each.

The files may be obtained via email requests.

The metadata of the netCDF files may be viewed with ncdump, for example, ncdump -h T42t_TEDIV_1979-2001_MM.nc.

The coordinate variables (time, lat, lon) and the coordinate variable values are listed for convenience on a separate web page.

A short Fortran program, `READ_FDA', for reading the Fortran direct access (.Fda) version of the files may be viewed separately. Or, simply download PROG_READ_FDA.f90 using your browser. We also make available a Fortran 90 subroutine, ccm2_hydrostatic_matrix, for computing the hydrostatic matrix H (see the section Derived Fields at 6-hourly Resolution above).

For convenience we include an ocean depth and land elevation data set at 128x64 (i.e. `T42 Gaussian') resolution with longitudes and latitudes identical to those in the netCDF and Fortran direct access budget product files. For more information, see T42b_ELEVATION.nc and T42b_ELEVATION.Fda, which are now available via request only. We routinely use this ocean depth and land elevation data file as a land-sea mask, where ELEVATION < 0 represents oceans and seas, and ELEVATION 0 represents land. Sea ice is not represented in this data set. An image of the 128x64 ocean depth and land elevation data set is provided. (This link also includes further details about the construction of the data set).

Contents

Summary Table of all Products

As a summary we reassemble all 36 budget product descriptions in the following table (refer to the previous sections for more specific details).

Variable Symbol Product Name Units Level Final Spectral Truncation Times
Monthly mean surface pressure s PS Pa Surface T42 Monthly
Vertically integrated zonal velocity (u)dp/ g U kg m-1 s-1 Total column T42 Monthly
Vertically integrated meridional velocity (v)dp/ g V kg m-1 s-1 Total column T42 Monthly
Vertically integrated temperature (T)dp/ g T K kg m-2 Total column T42 Monthly
Precipitable water (q)dp/ g PW kg m-2 Total column T42 Monthly
Vertically integrated geopotential height (z)dp/ g Z kg m-1 Total column T42 Monthly
Vertically integrated kinetic energy (K)dp/ g KE J m-2 Total column T42 Monthly
Precipitable water tendency ð( qdp/ g)/ðt QTEN kg m-2 s-1 Total column T42 Monthly
Internal energy tendency ð( CpTdp/ g)/ðt ITEN W m-2 Total column T42 Monthly
Kinetic energy tendency ð( Kdp/ g)/ðt KTEN W m-2 Total column T42 Monthly
Latent energy tendency ð( Lqdp/ g)/ðt LETEN W m-2 Total column T42 Monthly
Geopotential tendency ð( sdp/ g)/ðt
=
ð(sPs/ g)/ðt		 PHISTEN W m-2 Total column T42 Monthly
Total energy tendency ð(CpTdp/ g + Kdp/ g +
Lqdp/ g + sPs/ g)/ðt
=
ð(CpTdp/ g)/ðt + ð(Kdp/ g)/ðt +
ð(Lqdp/ g)/ðt + ð(sPs/ g)/ðt 		TETEN W m-2 Total column T42 Monthly
Surface pressure tendency ðPs/ðt PSTEN Pa s-1 Surface T42 Monthly
Evaporation minus precipitation E-P EP mm day-1 Total column T42 Monthly
Mass budget residual R MRES Pa s-1 Total column T42 Monthly
Barotropic correction
to
zonal wind		 uc UC m s-1 Total column T42 Monthly
Barotropic correction
to
meridional wind		 vc VC m s-1 Total column T42 Monthly
Vertically integrated zonal temperature flux²;
(Mass Corrected)		 (uT)dp/ g - uc (T)dp/ g UT kg K m-1 s-1 Total column T42 Monthly
Vertically integrated meridional temperature flux²
(Mass Corrected)		 (vT)dp/ g - vc (T)dp/ g VT kg K m-1 s-1 Total column T42 Monthly
Vertically integrated zonal geopotential height flux ²
(Mass Corrected)		 (uz)dp/ g - uc (z)dp/ g UZ kg s-1 Total column T42 Monthly
Vertically integrated meridional geopotential height flux²
(Mass Corrected)		 (vz)dp/ g - vc (z)dp/ g VZ kg s-1 Total column T42 Monthly
Vertically integrated zonal moisture flux²
(Mass Corrected)		 (uq)dp/ g - uc (q)dp/ g UQ kg m-1 s-1 Total column T42 Monthly
Vertically integrated meridional moisture flux²
(Mass Corrected)		 (vq)dp/ g - vc (q)dp/ g VQ kg m-1 s-1 Total column T42 Monthly
Vertically integrated zonal kinetic energy flux²
(Mass Corrected)		 (uK)dp/ g - uc (K)dp/ g UK J m-1 s-1 Total column T42 Monthly
Vertically integrated meridional kinetic energy flux²
(Mass Corrected)		 (vK)dp/ g - vc (K)dp/ g VK J m-1 s-1 Total column T42 Monthly
Divergence of total energy TEDIV
or
 TEDIV W m-2 Total column T42 Monthly
Divergence of dry static energy DSEDIV DSEDIV W m-2 Total column T42 Monthly
Divergence of latent energy LEDIV LEDIV W m-2 Total column T42 Monthly
Divergence of kinetic energy KEDIV KEDIV W m-2 Total column T42 Monthly
Diabatic minus frictional heating Q1-Qf Q1QF W m-2 Total column T42 Monthly
Vertically Averaged Total Energy TE TE J kg-1 Total column T42 Monthly
Absorbed solar radiation AT ASR W m-2,
> 0 downward through TOA		 TOA T42 Monthly,
February 1985 – April 1989 only
Outgoing longwave radiation OT OLR W m-2,
> 0 upward through TOA		 TOA T42 Monthly,
February 1985 – April 1989 only
Net downward radiation RT NET W m-2,
> 0 downward through TOA		 TOA T42 Monthly,
February 1985 – April 1989 only
Net upward surface flux Fs FS W m-2,
> 0 upward through surface into atmosphere		 surface T42 Monthly,
February 1985 – April 1989 only

² In the netCDF files, the term `transport' rather than `flux' is used in the long_name attribute of the variables UT, VT, UZ, VZ, UQ, VQ, UK, and VK.

Contents

References

Adams, J. C., and P. N. Swarztrauber, 1997: SPHEREPACK 2.0: A model development facility. NCAR Technical Note NCAR/TN-436-STR, 59 pp. (See especially http://www.scd.ucar.edu/css/software/spherepack/ and documentation therein for Spherepack 3.0.)

Hack, J. J., B. A. Boville, B. P. Briegleb, J. T. Kiehl, P. J. Rasch, and D. L. Williamson, 1993: Description of the NCAR Community Climate Model (CCM2). NCAR Technical Note NCAR/TN-382+STR, 108 pp.

Kalnay, E., M. Kanamitsu, R. Kistler, W. Collins, D. Deaven, L. Gandin, M. Iredell, S. Saha, G. White, J. Woollen, Y. Zhu, M. Chelliah, W. Ebisuzaki, W.Higgins, J. Janowiak, K. C. Mo, C. Ropelewski, J. Wang, A. Leetmaa, R. Reynolds, R. Jenne, and D. Joseph, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437-471.

Piexoto, J. P., and A. H. Oort, 1992: Physics of Climate. New York, American Institute of Physics, 520 pp.

Sardeshmukh, P. D. and B. J. Hoskins, 1984: Spatial smoothing on the sphere. Month. Wea. Rev., 112, 2524 -2529.

Trenberth, K. E., 1991: Climate diagnostics from global analyses: conservation of mass in ECMWF analyses. J. Climate, 4, 707-722.

Trenberth, K. E., 1997: Using atmospheric budgets as a constraint on surface fluxes. J. Climate, 10, 2796-2809.

Trenberth, K. E., D. P. Stepaniak, and J. M. Caron, 2002: Accuracy of atmospheric energy budgets. J. Climate, 15, 3343-3360.

Contents

Extended Bibliography

The majority of the references listed here are Climate Analysis Section publications based solely or in part on atmospheric mass, moisture, heat and energy budget products derived from reanalyses – the NCEP/NCAR reanalysis to a larger degree, and ERA-15 (and ECMWF operational global analyses) to a lesser degree³. Other publications are listed for technical reference and further background.

Trenberth, K. E., and D. P. Stepaniak, 2004: Inferred annual cycle of equivalent ocean heat content. Geophys. Res. Lett., submitted.

Trenberth, K. E., D. P. Stepaniak, and L. Smith, 2004: Interannual variability of the mass of the atmosphere. J. Climate, submitted³.

Trenberth, K. E., and L. Smith, 2004: The mass of the atmosphere — A constraint on global analyses. J. Climate, submitted³.

Trenberth, K. E., and D. P. Stepaniak, 2003: Seamless poleward atmospheric energy transports and implications for the Hadley Circulation. J. Climate, 16, 3705-3721.

Trenberth, K. E., and D. P. Stepaniak, 2003: Co-variability of components of poleward atmospheric energy transports on seasonal and interannual timescales. J. Climate, 16, 3690-3704.

Trenberth, K. E., D. P. Stepaniak, and J. M. Caron, 2002: Accuracy of atmospheric energy budgets. J. Climate, 15, 3343-3360.

Trenberth, K. E., D. P. Stepaniak, and J. M. Caron, 2002: Interannual variations in the atmospheric heat budget. J. Geophys. Res., 107, D8, 10.1029/2000JD000297.

Trenberth, K. E., J. M. Caron, D. P. Stepaniak, and S. Worley, 2002: The evolution of ENSO and global atmospheric temperatures. J. Geophys. Res., 107, D8, 10.1029/2000JD000298.

Trenberth, K. E., and D. P. Stepaniak, 2002: A pathological problem with NCEP reanalyses in the stratosphere. J. Climate, 15, 690-695.

Trenberth, K. E., and J. M. Caron, 2001: Estimates of meridional atmosphere and ocean heat transports. J. Climate, 14, 3433-3443.

Trenberth, K. E., D. P. Stepaniak, J. W. Hurrell, and M. Fiorino, 2001: Quality of reanalyses in the tropics. J. Climate, 14, 1499-1510.

Trenberth, K. E., J. M. Caron, and D. P. Stepaniak, 2001: The atmospheric energy budget and implications for surface fluxes and ocean heat transports. Climate Dyn., 17, 259-276.

Trenberth, K. E., D. P. Stepaniak, and J. M. Caron, 2000: The global monsoon as seen through the divergent atmospheric circulation. J. Climate, 13, 3969-3993.

Trenberth, K. E., and C. J. Guillemot, 1998: Evaluation of the atmospheric moisture and hydrological cycle in the NCEP/NCAR reanalyses. Climate Dyn., 14, 213-231.

Trenberth, K. E., 1997: Using atmospheric budgets as a constraint on surface fluxes. J. Climate, 10, 2796-2809.

Trenberth, K. E., and C. J. Guillemot, 1996: Evaluation of the Atmospheric Moisture and Hydrological Cycle in the NCEP Reanalyses. NCAR Technical Note NCAR/TN-430+STR, 308 pp.

Trenberth, K. E., and C. J. Guillemot, 1995: Evaluation of the global atmospheric moisture budget as seen from analyses. J. Climate, 8, 2255-2272.

Trenberth, K. E., J. W. Hurrell, and A. Solomon, 1995: Conservation of mass in three dimensions. J. Climate, 8, 692-708.

Trenberth, K. E., and A. Solomon, 1994: The global heat balance: heat transports in the atmosphere and ocean. Climate Dyn., 10, 107-134.

Trenberth, K. E., J. C. Berry, and L. E. Buja, 1993: Vertical Interpolation and Truncation of Model-Coordinate Data. NCAR Technical Note TN-396+STR, 54 pp.

Trenberth, K. E., and A. Solomon, 1993: Implications of global atmospheric spatial spectra for processing and displaying data. J. Climate, 6, 531-545.

Trenberth, K. E., 1992: Global Analyses from ECMWF and Atlas of 1000 to 10 mb Circulation Statistics. NCAR Technical Note TN-373+STR, 191 pp.

Trenberth, K. E., 1991: Climate diagnostics from global analyses: conservation of mass in ECMWF analyses. J. Climate, 4, 707-722.

³ With the advent and availability of ERA-40 from ECMWF in 2003, our focus and publications will begin to incorporate budget products derived from this new 40 year reanalysis.

Contents

Web page written and maintained by
David Stepaniak davestep@ucar.edu
My home page
Last modified 3rd February 2006.

CAS, the Climate Analysis Section in CGD at NCAR.

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