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**CFS Retrospective Forecast Daily Climatology**

**in the EMC/NCEP CFS public server**

**Åke Johansson, Catherine Thiaw and Suranjana Saha**

Environmental Modeling Center, NCEP/NWS/NOAA

Email for correspondence regarding daily climatology:
ake.johansson@noaa.gov

Website for graphs:
<http://www.emc.ncep.noaa.gov/gmb/ajohansson/clim/clim.html>

Email for correspondence regarding CFS in general: cfs@noaa.gov

Revised: February 27, 2007

**1. Introduction**

The new NCEP Climate Forecast System (CFS), which is being run
operationally out to 9 months on a daily basis since August 2004 (Saha
et al. 2006) is regularly used by a large number of users. A ubiquitous
feature of dynamical models of the atmosphere and/or ocean is the
existence of a climate drift which manifests itself in, many cases
appreciable, systematic errors. These errors limit the effectiveness of
the models in almost all its applications. The systematic errors are not
only visible in the ensemble or time-mean fields, but are equally
disturbing for the variability in the models. To increase the usefulness
of the CFS forecasts it is therefore imperative to have access to a
forecast climatology that is available at all forecast lead times. Since
the CFS is used for forecasting on the monthly and seasonal time scales
a monthly mean forecast climatology was prepared and released already at
the start of operational production. However, it has also been
recognized that in many applications there is a need of a daily \[i.e.,
instantaneous values\] climatology that is available at all available
forecast lead times. A smooth daily climatology of the annual cycle has
therefore been prepared. The set of 4320 retrospective forecasts -- the
CFS hindcast data set -- which constitute an integral part of the CFS,
has been used for this purpose. Since the CFS hindcast data set spans
the 24 years from 1981 to 2004, the climatology is based on 24-yrs
instead of the WMO standard of 30-yrs.

In many applications it is also valuable to have access to, in addition
to the forecast climatology, an observed climatology. A daily observed
climatology valid at 00 and 12 UTC, calculated in a corresponding
fashion to the forecast climatology, have therefore been prepared for a
subset of the variables.

**Information on how to access and read the data is given in the
Appendix.**

**2. Variables and spatial and temporal domains**

The climatology is only calculated for a subset of all the variables
produced by the CFS.

The number of atmospheric variables considered is 30 and they are listed
in Table 1. The forecast data are of global extent and given on a
regular 2.5°×2.5° latitude-longitude grid, i.e., at 73×144 = 10,512 grid
points. This is somewhat coarser than the native T62 quadratic reduced
Gaussian grid.

The number of oceanic variables considered is 12 and they are listed in
Table 2. The forecast data are available over the oceans between the
latitudes 74°S and 64°N and are given on a 1°×2° regular
latitude-longitude grid, i.e., at 139×180 = 25,020 grid points. This is
somewhat coarser than the native ocean model grid. Around 2/3 of these
grid points are over the oceans (land points have undefined values).

An additional oceanic variable, the SST field that is used in the
coupling to the atmosphere, is also considered. This field is for
computational reasons given on a denser grid, 1°×1° latitude-longitude
grid, of global extent, i.e., at 180×360 = 64,800 grid points.

[**WARNING**. Oceanic variables at high northern and southern latitudes,
poleward of 50ºN and 65ºS, are of lower quality compared to the interior
of the domain. The reason for this is partly because of the proximity to
the imposed climatological lateral boundary conditions at 64°N and 74°S,
and partly because of the restricted atmosphere-ocean coupling at high
latitudes (for further details see Saha et al. 2006). The daily
climatology that has been produced is therefore likewise of uncertain
quality in these regions.]{.mark}

At each atmospheric grid point the climatologies of each atmospheric
variable are available on all calendar dates in a 366 day year for all
forecast lead times from 24 hours up to 6480 hours (9 months) with an
increment of 12 hours, i.e., at a total of 366×539 = 197,274 time pairs
(calendar date , forecast lead time). The daily climatology is valid at
00 UTC for forecast lead times of 24 hr, 48 hr, ... and at 12 UTC for
forecast lead times of 36 hr, 60 hr, ...

At each oceanic grid point the climatologies of each oceanic variable
are available on all calendar dates in a 366 day year for all forecast
lead times from 24 hours up to 1080 hours (1.5 months) with an increment
of 24 hours, i.e., at a total of 366×45 = 16,470 time pairs (calendar
date , forecast lead time). The daily climatology refers to daily mean
values.

The SST field that is used in the coupling to the atmosphere is
available on all calendar dates in a 366 day year for all forecast lead
times from 24 hours up to 6480 hours (9 months) with an increment of 24
hours, i.e., at a total of 366×270 = 98,820 time pairs (calendar date ,
forecast lead time). The daily climatology refers to daily mean values.

In addition to the climatological annual cycle of the mean for the above
42 variables, a climatology for the standard deviation (SD) around this
smooth climatological annual cycle of the mean is also calculated.

**3. Methodology**

The problem at hand is to extract, for each variable, at each grid point
and at each forecast lead time, an estimate of the true climatological
annual cycle from 24 years of once daily data which are only given at
roughly half of the days in a year. At each calendar date where data is
available, the straight average value, determined from the available 24
values, is in general composed of the following components:

(i) The true climatological annual cycle

(ii) Meteorological noise

(iii) Climatological noise (Low-frequency meteorological noise, i.e.,
      variability on time scales comparable with, and longer than, the
      24-yrs considered here.)

(iv) Model noise

The extraction of (i) is here done by fitting, through the method of
least squares, the annual cycle of the raw average values to a truncated
Fourier series with sine and cosine as basis functions. There is no a
priori reason why the climatological annual cycle should necessarily be
best represented by a low-order Fourier series. However, previous
studies, such as the ones by Trenberth (1985), Epstein (1988) and Schemm
et al. (1998), have shown that this method gives reasonable results. The
method requires a decision on truncation, i.e., how many Fourier
components should be included to give optimum results. Using too few
components -- underfitting -- implies that part of the true
climatological annual cycle is not included in the estimate, while on
the other hand using too many components -- overfitting -- means that
part of the noise is included in the estimate. Epstein (1991) proposed a
method, based on statistical models, to determine the optimum numbers to
use. That work indicated that the optimum number of components is likely
to vary with variable and geographical location. Given the large number
of variables, the global domain and the large number of forecast lead
times in the CFS data the determination of optimum numbers would require
the construction and execution of an objective and automated procedure.
No attempt to devise such a procedure has here been made. Instead, in
accordance with the experience and practice at NCEP (Schemm et al.
1998), a truncation at wave number 4 is used for all variables at all
locations and at all forecast lead times.

Note that no smoothing or filtering in the spatial domain is performed.
The rationale being that many variables have quite localized
geographical characteristics.

A special circumstance here is that the 24 year average values are not
available at all days in a year. This is due to the fact that the CFS
hindcasts do not start from all days in a given year. Initial conditions
are only given at roughly half of the days in a given month, namely at 3
separate sets of 5 consecutive days. The first set consists of day
9-10-11-12-13, the second set of day 19-20-21-22-23 and finally the
third set of the second to last day of the month, the last day of the
month[^1] and day 1-2-3 of the next month (see Fig. 1). For all these 15
days the initial condition is at 00 UTC. For later reference such a set
of 5 consecutive days is denoted a 5-group.

The fact that data are not available on all calendar dates requires a
slight modification to the most common straightforward method of
calculating Fourier coefficients. The specific technique used here is
described in section 4 and is based on the method of least squares.

**4. Calculation of Fourier coefficients**

Let y be a periodic function with period T=365 days. Values of y are
given at N discrete points in time, $t_{j}$, j=1, 2, ..., N, where
N=180. These time points are irregularly spaced as described in the
previous section and graphically depicted in Fig. 1. The periodic
function y can be approximated by a truncated Fourier series

$\overset{\sim}{y}(t_{j\ })\  = \ \sum_{k = - K}^{K}{c_{k}\ e^{\text{ikt}_{j^{'}}}}$
, j = 1, 2, ... , N

where $c_{k}$ are complex Fourier coefficients, K is the maximum wave
number and

$t_{j^{'}}\  = \ {\omega t}_{j}\  = \ \frac{2{\pi t}_{j}}{T}$

is a nondimensional time. From here on the prime is omitted for brevity.
The spectral coefficients are obtained from a minimization of the
quantity

$S\  = \ \sum_{j = 1}^{N}{\ \left\lbrack \ \overset{\sim}{y}(t_{j})\  - \ y(t_{j}) \right\rbrack^{\ 2}} = \ \sum_{j = 1}^{N}{\ \left\lbrack \ \sum_{k = - K}^{K}{c_{k}\ e^{\text{ikt}_{j}}}\  - \ y(t_{j}) \right\rbrack^{\ 2}}$
.

S is thus the sum of the squared difference between the truncated
Fourier series and the actual data. The minimization is obtained by
differentiating S with respect to each complex coefficient, i.e.,

$\frac{\partial S}{\partial c_{l}}\  = \ 2\ \sum_{j = 1}^{N}{\ \left\lbrack \ \sum_{k = - K}^{K}{c_{k}\ e^{\text{ikt}_{j}}}\  - \ y(t_{j}) \right\rbrack\ }e^{\text{ilt}_{j}}\  = \ 0$
,

which is equivalent to

$\sum_{k = - K}^{K}{c_{k}\ }\sum_{j = 1}^{N}e^{i(l + k)t_{j}}\  = \ \sum_{j = 1}^{N}{\ y(t_{j})\ e^{\text{ilt}_{j}}}$
. (1)

By defining

$a_{\text{lk}}\  = \ \frac{1}{N}\sum_{j = 1}^{N}e^{i(l + k)t_{j}}\ ,\ b_{l}\  = \ \frac{1}{N}\sum_{j = 1}^{N}{\ y(t_{j})\ e^{\text{ilt}_{j}}}$

equation (1) can be written as a matrix equation

$\sum_{k = - K}^{K}{c_{k}a_{\text{lk}}\ }\  = \ b_{l}\  \Leftrightarrow \ A\ X\  = \ B$
(2)

where

$$A\  = \ \begin{pmatrix}
1 & \frac{1}{N}\sum_{j = 1}^{N}e^{\text{it}_{j}} & \frac{1}{N}\sum_{j = 1}^{N}e^{2\text{it}_{j}} & & \frac{1}{N}\sum_{j = 1}^{N}e^{i2\text{Kt}_{j}} \\
\frac{1}{N}\sum_{j = 1}^{N}e^{- \text{it}_{j}} & 1 & & & \\
\frac{1}{N}\sum_{j = 1}^{N}e^{- 2\text{it}_{j}} & & & & \\
 & & & & \frac{1}{N}\sum_{j = 1}^{N}e^{\text{it}_{j}} \\
\frac{1}{N}\sum_{j = 1}^{N}e^{- i2\text{Kt}_{j}} & & & \frac{1}{N}\sum_{j = 1}^{N}e^{- \text{it}_{j}} & 1
\end{pmatrix}\ X\  = \ \begin{pmatrix}
c_{- K} \\
 \\
 \\
 \\
c_{0} \\
 \\
 \\
 \\
c_{K}
\end{pmatrix}\ $$

$$B\  = \ \begin{pmatrix}
\frac{1}{N}\sum_{j = 1}^{N}{y(t_{j})e^{\text{iKt}_{j}}} \\
 \\
 \\
\frac{1}{N}\sum_{j = 1}^{N}{y(t_{j})} \\
 \\
 \\
\frac{1}{N}\sum_{j = 1}^{N}{y(t_{j})e^{- \text{iKt}_{j}}}
\end{pmatrix}$$

Note that the matrix **A** is Hermitian. If data are available on a
sufficiently dense equidistant net then the off-diagonal elements are
all zero, implying that the coefficients c~k~ are independent of each
other and can be solved without matrix manipulations. However, in the
present case **A** is a full Hermitian matrix and the coefficients c~k~
are dependent of each other. The complex matrix equation (2) is solved
by using a dense linear algebraic equation subroutine, in which the
matrix **A** is factored using Gaussian elimination with partial
pivoting to compute the LU decomposition of **A**.

A smooth daily climatological annual cycle, c, is defined by only
considering 4 wave numbers, i.e.,

$c(t_{j\ })\  = \ \sum_{k = - 4}^{4}{c_{k}\ e^{\text{ikt}_{j}}}$ , t~j~
= 1 Jan, 2 Jan , ... , 31 Dec (3)

The climatology is thus determined by 9 real coefficients in accordance
with NCEP practice as discussed in section 3. Note that the climatology
is defined on each day in a 365 day year. At 00 UTC for forecast lead
times of 24 hr, 48 hr, ... and at 12 UTC for forecast lead times of 36
hr, 60 hr, ... The methodology to compute (3) is thus performing two
tasks, firstly it performs a smoothing of the raw mean values on the
days where these are available, and secondly it performs an
interpolation to days where raw mean values are not available.

The climatological value for the leap day, 29 February, is defined as
the mean of the values at 28 February and 1 March. Note the
inconsistency that even though the annual cycle has been assigned a
period of 365 days it is defined at 366 days. The root of this
inconsistency is of course that the true period of the annual cycle, the
Tropical Year, is 365.2422 days, i.e, an uneven multiple of a day.

**5. Observed daily climatological annual cycle**

The atmospheric initial conditions used by the CFS hindcasts are from
the NCEP/DOE Atmospheric Model Intercomparison Project (AMIP) II
Reanalysis (R2) (Kanamitsu et al. 2002). NCEP has subsequently made the
R2 atmospheric analysis operational and the real time operational
analysis is called the Climate Data Assimilation System 2 (CDAS2). Since
the variables that are being produced by the parameterization schemes in
the R2 model are strongly dependent on the model formulation and thus
not really "observed" it was decided to only calculate observed
climatologies for instantaneous variables that are strongly influenced
by observed data and therefore the most reliable. Those variables are
marked with bold letters in Table 1. The methodology and calculation of
Fourier coefficients are essentially the same as described in section 3
and 4. The only difference is that the observed data is available on
every day in the 24 year period 1981-2004, i.e., there are no gaps in
the time series and therefore the total amount of data is approximately
twice as large compared to the forecast data. The R2 data is given twice
daily, at 00 and 12 UTC, and therefore two sets of daily climatologies
have been calculated.

Figure 2 is an example of a comparison between observed and forecast
climatology. The left panel is for the 00 UTC observed climatology of
the mean of the geopotential height at 500 hPa at a grid point close to
Washington, DC, while the left panel is the corresponding forecast
climatology at a lead time of 6480 hours (\~ 9 months). Even though the
gross features are similar there is a pronounced systematic error in the
summer-to-winter amplitude, a reduction of the order of 50 gpm. The
magnitude of the systematic error in summer, \~ 30 m, is of the same
order as a typical anomaly (SD \~ 45 m).

To highlight the difference between the 00 and 12 UTC daily
climatologies Fig.3 is presented. The variable is again the 500 hPa
geopotential height and the upper panel shows the geographical
distribution when the difference is at a minimum in the Northern
Hemisphere (late January), while the lower panel displays the
corresponding difference at a maximum (late July). Note the asymmetry
between the hemispheres.

**6. Examples of CFS forecast daily climatological annual cycle**

To demonstrate the characteristics of the CFS forecast daily
climatological annual cycle for a "well behaved" variable in the
Northern Hemisphere extratropics Fig. 4 is presented. With well behaved
is meant a variable that is continuous, always defined, and with a
probability density function (PDF) that is quasi-Gaussian. The variable
shown is 2 m temperature at a forecast lead time of 660 hours (27.5
days) at a grid point close to Washington, DC. The mean climatological
annual cycle (left panel, red curve) possesses a distinct sinusoidal
behavior with an amplitude of approximately 25 ºC. The shape of the
curve clearly indicates the dominance of the first harmonic and the
suitability of using a fit to sine/cosine functions. Compared to the
time series of the raw 24-yr average values (blue discontinuous curve)
the smooth climatological annual cycle (red curve) intuitively looks
more like a true climatological annual cycle. The standard deviation
(SD) around the calculated mean climatological annual cycle is shown in
the right panel. The red curve now displays a form that indicates the
influence from more than just the first harmonic in establishing the SD
climatology. As expected, the variability is out of phase with the mean
annual cycle with a maximum in winter that is almost 8 times as large as
in summer (in terms of variance). A comparison between Figs. 4 and 5
demonstrates the undesirable climate drift in the CFS forecasts. The
left panel of Fig. 5 shows that the climatology after 8.1 months of
integration has undergone a warming during wintertime, on the order of
2-3 ºC, relative to 0.9 months of integration (left panel of Fig. 4).
The corresponding right panels show that the wintertime variability
during the same time has decreased by around 15% (in terms of variance).

Figure 6 shows a corresponding climatological annual cycle for 2 m
temperature in the tropics, here exemplified by an equatorial grid point
in Indonesia. In contrast to the extratropics the mean climatological
annual cycle (left panel) has considerably less amplitude -- on the
order of 1 ºC - and is furthermore dominated by the second harmonic. The
use of a Fourier series seems to be reasonable even in this case. The
standard deviation (right panel) displays a more complex behavior
indicating that all four wave numbers contribute to the final
climatology. The precision of 0.5 ºC in the gribbed[^2] hindcast data is
here clearly evident and may well have a detrimental effect on the
determination of the climatology. However, the visual impression is that
it looks reasonable.

The examples discussed above indicate that the methodology adopted works
satisfactorily for well behaved variables. However, there are also other
variables, with properties that make it difficult to fit their
climatology to a low-order Fourier series. The next sections are devoted
to a discussion of how the procedure described in section 4 is modified
to accommodate for the difficulties that these properties present.

**7. Variables that can not be negative and variables that are zero part
of the year**

Some variables can not have a mean climatological annual cycle with
negative values. Furthermore, the standard deviation (for all
variables), by definition, can not be negative. In most cases this
circumstance does not pose a problem. However, for variables that are
zero, or close to zero, during part of the year, a straightforward
application of the methodology of section 4 will create unphysical
climatologies. This unwanted behavior is due to the Gibbs phenomenon
which can create:

(i) negative values in parts of the year, which is impossible.

(ii) positive values in times of the year when it is "obvious" that the
     climatology is zero.

The methodology of section 4 has therefore been modified by the
following procedure to ensure that a physically reasonable climatology
is calculated:

1.  Denote the 5 consecutive days which have raw mean values defined as
    a 5-group (see Fig. 1).

2.  If there are no raw mean values in a 5-group that are greater than a
    small value $\varepsilon\  = \ \text{10}^{- 6}$, then all days in
    the 5-group are given a climatological value of zero, rather than
    the smooth climatology given by equation (2).

3.  If a day that does not belong to a 5-group is surrounded by 5-groups
    on either side that have been assigned the final climatological
    value of zero, then that day is assigned the climatological value of
    zero as well, rather than the smooth climatology given by equation
    (2).

4.  If there, after steps 1-3 above have been performed, are any
    remaining days with a negative climatological value, then those days
    are assigned a value of zero.

A set of variables with this type of behavior are short wave radiation
fluxes, which are zero at night. These variables are relatively easy to
correct since there are no instances of sudden departure from zero
during the time of the year when they are zero. An example is shown in
Fig. 7, which displays the climatology for the downward short wave
radiation flux at the earth's surface. A slight discontinuity in the
curvature of the smooth curve is seen at the boundary to the zero line.
However, this only occurs for values less than the resolution (1 W/m^2^)
of the input gribbed forecast data (the discontinuous blue curve).

A variable which is considerably more difficult to handle is
precipitation. In arid regions such as the Saharan desert the raw mean
values of precipitation are often zero during an extended part of the
year. However, due to the episodic nature of precipitation, there may be
an occasional day with non-zero precipitation in the middle of such a
dry spell. It has been found to be very difficult to design an algorithm
that will always create a smooth looking climatology for precipitation.
As seen in Fig. 8 there are instances when the final climatology:

-   suddenly departs from a smooth behavior to become zero.

> (See end of August and December in Fig. 8)

-   take no account of a single precipitation event in an otherwise dry
    part of the year.

> (See mid-July in Fig. 8)

The discontinuities that are seen in Fig. 8 are however occurring for
precipitation amounts that are less than the lowest amount measured in
the USA, i.e., 0.01 inches (0.254 mm), which corresponds to a
precipitation rate of 3 · 10 ^-6^ kg/m^2^/s.

The difficulties shown above reflect the non-trivial nature of
constructing a climatology for a variable such as precipitation. It is
not at all clear that a low-order Fourier series is the preferred
approach to use in this case. Note also the occasional large positive
departures that the raw mean values can possess relative to the final
smooth climatology. This is a consequence of the non-Gaussian, skewed
nature of the PDF of precipitation.

Figure 9 demonstrates an additional problem. In order to avoid the
problem (i) of the Gibbs phenomenon, as discussed above, where both the
mean and the standard deviation have been set to zero during an extended
period in summer when it is clear that it ought to be slightly positive.
However, once again, this only occurs for small precipitation amounts
(of the order of the lowest amount measured, i.e., 0.01 inches).

It should be emphasized that the problems discussed above only occur for
grid points with very little precipitation. For the vast majority of
grid points there are no problems of this kind and the calculated
climatology appears reasonable. Figure 10 is provided to illustrate a
typical example to this effect, namely the precipitation climatology for
Washington, DC. In contrast to 2 m temperature (Fig. 4) it is clear that
all four harmonics contribute to the final climatology for
precipitation. The variability of the raw mean values around the smooth
climatology is appreciable, indicating that the sample size may not be
sufficient to establish a stable estimate of the true climate from the
four complex Fourier coefficients.

**8. Variables that are not defined during part of the year**

There are a number of variables, notably oceanographic variables, which
at certain geographical locations are not defined during part of the
year. An example is the variable "depth to the 2.5 ºC isotherm", whose
climatology at a sub-polar location is shown in Fig. 11. The algorithm
used to solve equation (2) does not always produce a correct answer when
there is a small number of days in a year when a variable is defined.
This problem is to a large extent resolved by using double precision in
the calculations (as is the case for the smooth climatology displayed in
Fig. 11). However, there are still a number of instances when the
problem persists. A solution is to calculate a smooth climatology from
equation (2), only when the variable is defined at more than 2/3 of the
maximum available days (i.e., at approximately 2/3 · 365 · 0.5 \~ 120
days). Otherwise the final climatology is defined as:

-   For days when raw mean values are available, use them as the final
    climatology.

-   For days outside of a 5-group which is surrounded by 5-groups on
    either side that have raw mean values available, use linear
    interpolation to the nearest available raw mean values to define the
    final climatology at that date.

This crude remedy was adopted since it was not deemed meaningful to
elaborate on this issue because of the fact that the grid points
affected are normally at high northern and southern latitudes where the
quality of the modeled oceanographic fields are not very reliable (see
discussion in section 2 and in Saha et al. 2006).

**REFERENCES**

Epstein, E. S., 1988: A spectral climatology. *J. Climate*, **1**,
88--107.

Epstein, E. S., 1991: Determining the optimum number of harmonics to
represent normals based on multiyear data. *J. Climate*, **4**,
1047--1051.

Kanamitsu, M., W. Ebisuzaki, J. Woollen, S-K. Yang, J. J. Hnilo, M.
Fiorino and G. L. Potter, 2002: NCEP--DOE AMIP-II Reanalysis (R-2) ,
*Bull. Amer. Meteor. Soc.*, **83**, 1631-1643.

Saha S., S. Nadiga, C. Thiaw, J. Wang, W. Wang, Q. Zhang, H. M. van den
Dool, H.-L. Pan, S. Moorthi, D. Behringer, D. Stokes, M. Peña, S. Lord,
G. White, W. Ebisuzaki, P. Peng, P. Xie, 2006: The NCEP Climate Forecast
System. *J. Climate*. **19**, 3483-3517.

Schemm, J-K. E., H. M. van den Dool, J. Huang, and S. Saha, 1998:
Construction of daily climatology based on the 17-year NCEP-NCAR
reanalysis. *Proceedings of the First WCRP International Conference on
Reanalyses*. Silver Spring, Maryland, USA. 290-293.

Stackpole, J. D., 1993: GRIB - The WMO Format for The Storage of Weather
Product Information and The Exchange of Weather Product Messages in
Gridded Binary Form. NCEP Office Note, No. 388, 79 pp. \[ Available from
NCEP, 5200 Auth Road, Washington, DC 20233\].

Trenberth, K. E., 1985: Persistence of daily geopotential heights over
the Southern Hemisphere. *Mon. Wea. Rev.*, **113**, 38-53.

**APPENDIX - How to download and use the daily forecasts and forecast
climatology**

1.  ***Operational daily CFS forecast data***

Download the data from the following ftp server:

<ftp://ftpprd.ncep.noaa.gov/pub/data1/nccf/com/cfs/prod/forecast.yyyymmdd/daily_grib_memb>

where yyyymmdd is the date of the ***initial condition (IC)*** and memb
is the member. There are two members from each initial time. For example

<ftp://ftpprd.ncep.noaa.gov/pub/data1/nccf/com/cfs/prod/forecast.20060910/daily_grib_01>

is the directory containing the daily CFS operational forecast data from
the first CFS member initialized from the 00 UTC 10 September 2006
initial condition.

This data will remain on this site for only 7 days. Thereafter the data
will be moved to their permanent site on NWS TOC.

The GRIB files in the two directories are named

var.memb.yyyymmdd.daily

where var is the short name pertaining to a specific variable. These
short names for the variables are listed in the last column in Tables 1
and 2. memb is the member and yyyymmdd is the IC date.

As an example consider the 500 hPa geopotential height data from the
first member, which is contained in the GRIB file:

Z500.01.2006091000.daily

This GRIB file contains forecast data of this variable at all available
forecast lead times with an increment of 12 hours. Note that the total
number of forecast lead times for integrations starting from different
initial dates is different. This is because the length of the
integrations is specified to cover nine whole calendar months plus the
partial month of the initial condition.

2.  ***Hindcast daily CFS forecast data***

Access the data by one of the following methods:

1.  Anonymous ftp login into cfs.ncep.noaa.gov, then go to the
    pub/daily/glb directory

2.  Downloading from the URL: http://cfs.ncep.noaa.gov/daily/glb

The data are in sub-directories named

var/mon/yyyy

where var is the short name pertaining to a specific variable. These
short names for the variables are listed in the last column in Tables 1
and 2. mon and yyyy is the month and year of the ***initial condition
(IC)***. For example:

z500/jan/2005

is the directory that contains forecast data for the 500 hPa
geopotential height for the integrations initialized in "January 2005"
(according to the convention used by the CFS (Saha et al. 2006)). There
are 16 GRIB forecast data files (all 15 members plus the ensemble mean)
in the directory which are named:

z500.m01.jan.2005.cfs.data (IC date is 9 December 2004)

z500.m02.jan.2005.cfs.data (IC date is 10 December 2004)

.

.

.

z500.m15.jan.2005.cfs.data (IC date is 3 January 2005)

z500.ensm.jan.2005.cfs.data (IC date is 9 December 2004)

These GRIB files contain forecast data of this variable at all available
forecast lead times with an increment of 12 hours. Note that the total
number of forecast lead times for the different members is different.
This is because the length of the integrations is specified to cover
nine whole calendar months plus the partial month of the initial
condition.

3.  ***Daily CFS forecast climatology data***

Access the data by one of the following methods:

1.  Anonymous ftp login into cfs.ncep.noaa.gov, then go to pub/dailyclim
    directory

2.  Downloading from the URL: http://cfs.ncep.noaa.gov/dailyclim

The data are in sub-directories named

var/dirf

where var is the short name pertaining to a specific variable. These
short names for the variables are listed in the last column in Tables 1
and 2. dirf is either meanf or sdf and is the directories that contain
the daily forecast climatology data for the mean and the standard
deviation, respectively. The GRIB files in the two sub-directories are
named

var.mm.dd.type.clim.daily

where var is the same variable name as in the sub-directory above, mm
and dd is the month and day (as two position numerical values) of the
***initial condition (IC)*** and type is either mean or sd.

Note the following:

1.  There are 366 GRIB files, i.e., there is also one file for the leap
    day, 29 February, as initial condition.

2.  The GRIB file contains data at all forecast lead times from 24 hours
    up to and including 6480 hours with an increment of 12 hours.

3.  The target time for the climatology is obtained by adding the
    forecast lead time to 00 UTC of the month and day of the initial
    condition.

4.  The leap day, 29 February, is included as the target time between 28
    February and 1 March.

The reason for this specific arrangement of the climatology data is that
it makes it convenient when anomalies or standardized anomalies are to
be calculated for a specific forecast integration. It is just to match
the forecast and climatology files pertaining to the same initial
condition month and day. However, it should be pointed out that the
fourth point above implies that for a specific initial condition date a
contiguous time series of forecast climatologies for increasing forecast
lead time can be obtained from one of the single GRIB files mentioned
above ***[only]{.underline}*** if the integration does not cross over
the February-March boundary unless it happens to be in a leap year. For
all other cases it is necessary to skip over the climatology of the leap
day by retrieving the climatology from two files, namely from:

(a) var.mm.dd.type.clim.daily for target times up to and including 28
    February

(b) var.mm1.dd1.type.clim.daily for target times from and beyond 1 March

> (mm1,dd1) is the date after (mm,dd)

4.  ***Daily R2 observed climatology data***

Access the data by one of the following methods:

1.  Anonymous ftp login into cfs.ncep.noaa.gov, then go to
    pub/daily/climatology directory

2.  Downloading from the URL: http://cfs.ncep.noaa.gov/dailyclim

The data are in sub-directories named

var/R2

where var is the short name pertaining to a specific variable. These
short names for the variables are listed in the last column in Tables 1
and 2. Note that the observed climatology is only available for those
variables that are marked bold. The GRIB files in the two
sub-directories are named

var.R2.type.data

where var is the same variable name as in the sub-directory above and
type is either mean or sd, indicating the mean and the standard
deviation climatologies, respectively

Note that the climatologies are given at 00 and 12 UTC on all days in a
366 day year.

[Table 1]{.smallcaps}. List of atmospheric variables for which daily
forecast climatologies have been calculated. Variables for which an
observed dialy climatology also have been calculated is marked bold.

═════════════════════════════════════════════════════════

  ------------------------------- --------------- ------------ ---------------
  **VARIABLE**                    **LEVEL**       **UNIT**     **FILE NAME**

  Temperature                     2 m             K            tmp2m

  Pressure                        Surface         Pa           ps

  **Pressure**                    **Mean sea      **Pa**       **mslp**
                                  level**                      

  Zonal component of momentum     Surface         N/m^2^       wndstr
  flux                                                         

  Meridional component of         Surface         N/m^2^       wndstr
  momentum flux                                                

  Precipitation rate              Surface         kg/m^2^/s    prate

  Precipitable water              Whole           kg/m^2^      pwat
                                  atmosphere                   

  Sensibel heat flux              Surface         W/m^2^       shtfl

  Latent heat flux                Surface         W/m^2^       lhtfl

  Upward long wave radiation flux Top of          W/m^2^       olr
                                  atmosphere                   

  Upward short wave radiation     Top of          W/m^2^       uswtop
  flux                            atmosphere                   

  Upward long wave radiation flux Surface         W/m^2^       ulwsfc

  Downward long wave radiation    Surface         W/m^2^       dlwsfc
  flux                                                         

  Upward short wave radiation     Surface         W/m^2^       uswsfc
  flux                                                         

  Downward short wave radiation   Surface         W/m^2^       dswsfc
  flux                                                         

  **Geopotential height**         **200 hPa**     **m**        **z200**

  **Geopotential height**         **500 hPa**     **m**        **z500**

  **Geopotential height**         **700 hPa**     **m**        **z700**

  **Geopotential height**         **850 hPa**     **m**        **z850**

  **Geopotential height**         **1000 hPa**    **m**        **z1000**

  **Streamfunction**              **200 hPa**     **m^2^/s**   **sfvp200**

  **Streamfunction**              **850 hPa**     **m^2^/s**   **sfvp850**

  **Velocity potential**          **200 hPa**     **m^2^/s**   **sfvp200**

  **Velocity potential**          **850 hPa**     **m^2^/s**   **sfvp850**

  **Zonal velocity**              **200 hPa**     **m/s**      **wnd200**

  **Zonal velocity**              **850 hPa**     **m/s**      **wnd850**

  Zonal velocity                  10 m            m/s          wnd10m

  **Meridional velocity**         **200 hPa**     **m/s**      **wnd200**

  **Meridional velocity**         **850 hPa**     **m/s**      **wnd850**

  Meridional velocity             10 m            m/s          wnd10m
  ------------------------------- --------------- ------------ ---------------

[Table 2]{.smallcaps}. List of oceanic variables for which daily
forecast climatologies have been calculated.

═════════════════════════════════════════════════════════

  ------------------------------- --------------- ---------- ---------------
  **VARIABLE**                    **LEVEL**       **UNIT**   **FILE NAME**

  Depth to the 2.5 °C isotherm    \-              m          dt2.5c

  Depth to the 5 °C isotherm      \-              m          dt5c

  Depth to the 10 °C isotherm     \-              m          dt10c

  Depth to the 15 °C isotherm     \-              m          dt15c

  Depth to the 20 °C isotherm     \-              m          dt20c

  Depth to the 25 °C isotherm     \-              m          dt25c

  Depth to the 28 °C isotherm     \-              m          dt28c

  Ocean temperature               Surface         K          oceansst

  Ocean heat content[^3]          0-300 m         J/m^2^     oceanheat

  Ocean mixed layer depth         \-              m          oceanmld

  Ocean surface isothermal layer  \-              m          oceansild
  depth                                                      

  Ocean tropical cyclone heat     \-              J/m^2^     oceantchp
  potential                                                  

                                                             

  Ocean temperature[^4]           Surface         K          csstf
  ------------------------------- --------------- ---------- ---------------

[Fig. 1.]{.smallcaps} Schematic representation, marked with open
circles, of the availability of forecast data for the atmospheric
variables in the CFS hindcasts. The sloping lines indicate a specific
integration starting at 00 UTC from the date shown on the abscissa. Note
that the forecasts are valid at 00 UTC for forecast lead times of 24 hr,
48 hr, ... , 6480 hr, and at 12 UTC for forecast lead times of 36 hr, 60
hr, ... , 6456 hr. The figure is for a given month, in this case
January. The same configuration applies to all months in the data set.

![](media/image4.png){width="4.0in"
height="5.195669291338582in"}![](media/image5.png){width="4.0in"
height="5.199212598425197in"}

[Fig. 2.]{.smallcaps} The climatological annual cycle of the mean value
of the geopotential height at a grid point close to Washington, DC, is
shown as a smooth red curve. Shown are both the observed climatology
(left panel) and the forecast climatology at a lead of 6480 hours (\~ 9
months) (right panel). The 24-yr mean values as calculated directly from
the data are shown by the blue curves. The reason for the
discontinuities in the right panel is that these values are only
available during roughly half of the days in a year. The time on the
abscissa in the right panel is the initial time of the forecast, not the
actual time when the forecast is valid. In this case this implies an
offset by roughly nine months. Unit is m.

![](media/image6.png){width="5.25in"
height="4.009055118110236in"}![](media/image7.png){width="5.25in"
height="4.00748031496063in"}

[Fig. 3.]{.smallcaps} Maps of the geographical distribution of the
difference between the 00 and 12 UTC daily climatologies of the 500 hPa
geopotential height. The upper panel is at a time when the difference is
at a minimum in the Northern Hemisphere (late January), while the lower
panel displays the corresponding difference at a maximum (late July).
Note the asymmetry between the hemispheres. Unit is m.

![](media/image8.png){width="3.999212598425197in"
height="5.196456692913386in"}![](media/image9.png){width="4.0in"
height="5.204330708661417in"}

[Fig. 4.]{.smallcaps} The climatological annual cycle of 2 m temperature
at a forecast lead time of 660 hours (27.5 days) at a grid point close
to Washington, DC, is shown as a smooth red curve. Shown are both the
mean (left panel) and the standard deviation (right panel). The 24-yr
mean values as calculated directly from the forecast data is shown by
the blue discontinuous curve. The reason for the discontinuities is that
these values are only available during roughly half of the days in a
year. The time on the abscissa is the initial time of the forecast, not
the actual time when the forecast is valid. In this case this implies an
offset by roughly one month. Unit is K.

![](media/image10.png){width="4.040157480314961in"
height="5.193700787401575in"}![](media/image11.png){width="4.040157480314961in"
height="5.193700787401575in"}

[Fig. 5.]{.smallcaps} As in [Fig.]{.smallcaps} 4 but for a forecast lead
time of 5844 hours (8.1 months).

![](media/image12.png){width="4.0in"
height="5.198425196850394in"}![](media/image13.png){width="3.999212598425197in"
height="5.198425196850394in"}

[Fig. 6.]{.smallcaps} As in [Fig.]{.smallcaps} 4 but for a grid point at
the equator in Indonesia.

![](media/image14.png){width="4.040157480314961in"
height="5.195275590551181in"}![](media/image15.png){width="4.040157480314961in"
height="5.195275590551181in"}

[Fig. 7.]{.smallcaps} As in [Fig.]{.smallcaps} 4 but for downward short
wave radiation flux at the earth's surface. Unit is W/m^2^.

![](media/image16.png){width="4.0in"
height="5.2in"}![](media/image17.png){width="4.0in" height="5.2in"}

[Fig. 8.]{.smallcaps} As in [Fig.]{.smallcaps} 4 but for precipitation
rate at a grid point in the eastern part of the Sahara desert. Unit is
kg/m^2^/s.

![](media/image18.png){width="4.040157480314961in"
height="5.195275590551181in"}![](media/image19.png){width="4.040157480314961in"
height="5.195275590551181in"}

[Fig. 9.]{.smallcaps} As in [Fig.]{.smallcaps} 8 but for a grid point in
the central part of the Sahara desert.

![](media/image20.png){width="4.040157480314961in"
height="5.195275590551181in"}![](media/image21.png){width="4.040157480314961in"
height="5.195275590551181in"}

[Fig. 10.]{.smallcaps} As in [Fig.]{.smallcaps} 8 but for a grid point
close to Washington, DC.

![](media/image22.png){width="4.040157480314961in"
height="5.195275590551181in"}![](media/image23.png){width="4.040157480314961in"
height="5.195275590551181in"}

[Fig. 11.]{.smallcaps} As in [Fig]{.smallcaps}. 4 but for the oceanic
variable "depth to the 2.5 ºC isotherm" at a grid point close to
Antarctica at a forecast lead time of 1080 hours (1.5 months). Unit is
m.

[^1]: For the month of February the 24 year average values for the
    second to last day and last day of the month are ascribed to 27 and
    28 February.

[^2]: The CFS data is stored in GRIB (GRIdded Binary) format. GRIB is a
    data storage format that efficiently packs data and thereby saves
    storage space (see NCEP Office Note 388, Stackpole 1993).

[^3]: Only defined when the ocean depth is larger than 300 m.

[^4]: The SST field that is used in the coupling to the atmosphere