Time mean and variability of the scale-decomposed atmosphericwater budget in a 25-year simulation of the Canadian RegionalClimate Model over North America
Soline Bielli Æ Rene Laprise
Received: 20 September 2006 / Accepted: 20 April 2007
� Springer-Verlag 2007
Abstract The scaled-decomposed atmospheric water
budget over North America is investigated through the
analysis of 25 years of simulation by the Canadian
Regional Climate Model (CRCM) driven by the NCEP–
NCAR reanalyses for the period 1975–1999. The time
average and time variability of the atmospheric water
budget for the winter and summer seasons are decomposed
into their large-scale and small-scale components to
identify the added value of the regional model. For the
winter season, the intra-seasonal transient-eddy variance is
the main temporal variability. The large- and small-scale
terms are of the same order of magnitude, and are large
over both coasts and weak over the continent. For the
summer season, the time–mean atmospheric water budget
is rather different to that of winter, with maximum values
over the south-eastern part of the continent. The summer
intra-seasonal variance is about twice stronger than in
winter and also dominates the variability, but the inter-
monthly variance is non-negligible and can be in part
associated to North American Monsoon System. Over the
continent, the intra-seasonal climatological variance is
dominated by the variability of the small scales. The small
scales, that is those scales that are only resolved in the
regional model but not in the reanalyses, contribute to the
added value in a regional climate simulation. In the winter
season, the added value of the CRCM is large and dom-
inated by oceanic forcing, while in summer, it is dominant
(larger than the large scales) and controlled mainly by
convective processes.
1 Introduction
The atmospheric water vapour transport may be used to
diagnose the processes responsible for the maintenance and
variability of the surface water budget. The atmospheric
moisture transport and certain aspects of the water balance
over North America have substantial regional and seasonal
variations, as noted in many studies such as Rasmusson
(1967, 1968), Roads et al. (1994), Rasmusson and Mo
(1996), and Ropelewski and Yarosh (1998), among others.
Over North America the cold season is dominated by the
passage of vigorous mid-latitude synoptic weather systems
associated with baroclinic energy conversion as a result of
intense land–ocean thermal contrasts. The warm season is
of particular interest as it is characterized by a monsoonal
circulation: the North American Monsoon System
(NAMS). The NAMS is characterised by an out-of-phase
relationship between precipitation over the Southwest and
the Great Plains and an in-phase relationship between
precipitation over the Southwest and the East Coast of the
United States (Higgins et al. 1997a). May–June mark the
transition between the cold and the warm seasons, and the
development of the NAMS. During this phase, the synop-
tic-scale transient-eddy activity decreases over the United
States and Mexico, with a migration to the north of the
extra-tropical storm tracks. The magnitude of the diurnal
cycle of precipitation and the occurrence of the low-level
jet (LLJ) increase during this development phase. Changes
in precipitation that follow the onset of the NAMS (from
S. Bielli (&) � R. Laprise
Canadian Network for Regional Climate Modelling
and Diagnostics, Universite du Quebec a Montreal,
OURANOS, 550 rue Sherbrooke Ouest, 19e,
Montreal, QC H3A 1B9, Canada
e-mail: [email protected]
123
Clim Dyn
DOI 10.1007/s00382-007-0266-5
June to July) are characterized in particular by increased
precipitation over the Northern Great Plains (centred over
Kansas and Missouri) and to the North along the Canada–
USA border (Berbery and Fox-Rabinovitz 2003). The
mature phase of the NAMS occurs in July and August and
the dissipation takes place during September–October. The
Great Plains LLJ transports considerable moisture from the
Gulf of Mexico into the central USA, playing a critical role
in the summer precipitation there (Higgins et al. 1997b).
A methodology to decompose the regional-scale atmo-
spheric water budget into different spatial scales was re-
cently proposed by Bielli and Laprise (2006) (hereafter
BL06). This method was applied to a simulation of a single
winter month with the CRCM over North America, through
the examination of the vertically integrated moisture flux
and its monthly-mean component, separating scales only
resolved by the regional climate model (RCM) from those
resolved by large-scale analyses or general circulation
models. Results of this study showed the following. (1) The
added value of the RCM for the moisture budget resides in
the nonlinear interactions between large scales (defined as
the scales larger than 1,000 km and smaller than 6,000 km)
and small scales (scales smaller than 600 km). (2) The
main contribution to small-scale forcing of the wind is
topographic, and therefore occurs only over the continent,
whereas the humidity field presents small-scale structures
over both the oceans and the continent. (3) Examination of
the small-scale time–mean component of the moisture flux
divergence reveals that it is confined in the stationary part
forced by topography, with very little contribution due to
transient eddies.
In this paper, we will take advantage of a recently
completed 25-year simulation with the CRCM, to gener-
alize our previous results to several winter seasons to in-
crease the statistical significance of the results, but to also
investigate the summer season, which is expected to be
rather different due to the more convective nature of the
precipitation. While BL06 focused on the time–mean
atmospheric water budget and its decomposition into sta-
tionary and transient components, this paper goes further
and studies the time variability of each term in the budget,
and analyses the spatial scales into which this variability is
contained. The power spectra of the vertically integrated
moisture flux divergence over North America based on
fields available at six-hourly intervals for one month (e.g.,
BL06 Fig. 15) shows that the variance of the intramonthly
temporal variability is at least one order of magnitude
larger than the variance of the monthly mean; this justifies
the importance of studying the temporal variability of the
water vapour budget. Moreover, this information is of
relevance to climate-change studies that recognize the
importance of changes in extremes, as climate change is
likely to affect the frequency and magnitude of extreme
weather events due to higher temperatures, an intensified
hydrological cycle and possibly more vigorous atmospheric
motions. In this study, the centre of attention will be the
time mean and time variability of atmospheric water bud-
get for 25 winter and 25 summer seasons simulated by the
CRCM driven by reanalyses for the period 1975–1999.
Section 2 briefly describes the CRCM and the configura-
tion used for this study, and it summarizes the diagnostic
methodology. Section 3 presents the results for the winter
and the summer seasons. Finally Sect. 4 contains a sum-
mary and conclusions as well as perspectives for future
work.
2 Experimental design
2.1 The Canadian Regional Climate Model
The CRCM used for this study is a fully elastic non-
hydrostatic limited-area model. It uses a semi-Lagrangian
semi-implicit numerical scheme (more details can be found
in Caya and Laprise 1999). For this experiment, a hori-
zontal grid mesh of 45 km is used on a 192 by 144 grid-
point polar-stereographic computational domain, with a 15-
min time step. In the vertical the model has 29 Gal-Chen
levels and the top of the domain is located at 29-km height.
The lateral boundary conditions are provided through the
one-way nesting method inspired by Davies (1976) and
refined by Robert and Yakimiv (1986) and Yakimiv and
Robert (1990), and nudging of horizontal winds is applied
over a lateral sponge zone of nine points. Figure 1 shows
the model topography over the domain where the diag-
nostics are performed; only 172 by 124 grid points are
considered, a band of 10 points corresponding to the
sponge zone having been removed. The model subgrid-
scale parameterization is similar to that used by Laprise
et al. (2003). The simulation was initialized in January
Fig. 1 Domain where the diagnostics are calculated and topography
(m)
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
1973 and was run for 27 years. The first 23 months of the
simulation are discarded as they represent the spin up of the
model, thus only 25 years are analyzed. The CRCM was
driven by NCEP–NCAR reanalyses with a resolution of 2.5
by 2.5� available every 6 h. The reanalyses were interpo-
lated on the CRCM grid at every time step, to provide
lateral boundary condition. Model-simulated data are ar-
chived every 6 h for diagnostic and are interpolated on 30
pressure levels, 23 of which are below 700 hPa to have a
good vertical resolution in the lower troposphere where
atmospheric water vapour is concentrated, thus decreasing
the truncation errors due to vertical interpolation, espe-
cially near topographic features. As noted by Rasmusson
(1968) and as shown by BL06, high vertical resolution is
needed in the boundary layer to capture properly the de-
tailed structure of the moisture flux. How well the four-
time daily analyses capture the diurnal cycle of moisture
flux especially during summer has yet to be determined
(Trenberth 1991). To answer partly this question, an extra
simulation has been performed for the month of July 1975
with output archived at every time steps. The results are
presented in Appendix.
2.2 Water budget and methodology
We use the same methodology as BL06 where the verti-
cally integrated water budget is defined as (e.g. Peixoto and
Oort 1992):
otq ¼ �r:Qþ E � P ð1Þ
with the overbar representing vertical integration in
pressure
w ¼ 1
g
Zpsfc
ptop
wdp ¼ 1
g
Zp0
ptop
bwdp
with ptop and psfc the lowest and the highest pressure values
in a vertical atmospheric column, respectively. Here p0 is
chosen as a value exceeding the maximum value of psfc in
the domain (1,050 hPa) and the term b represents a mask to
take into account the topography in the lower boundary
(Boer 1982). Q is the horizontal moisture flux ðQ ¼ VqÞ;Vis the horizontal wind vector, q is the specific humidity, E
is the evapotranspiration and P is the precipitation.
Following BL06, each term X of the water budget will
be decomposed into three spatial scales such that X = X0
+ XL + XS. The subscript 0 represents the planetary
scales that are too large to be fully resolved by the RCM
finite-size domain: they are here defined as the domain-
mean value. The subscript L represents large scales (syn-
optic scales) that are resolved by both the RCM and the
NCEP–NCAR reanalyses (scales larger than 1,000 km).
Finally, the subscript S represents small scales that are
only resolved by the CRCM (scales smaller than 600 km).
The scale decomposition between large scales L and small
scales S is performed by using the Discrete Cosine
Transform (DCT, Denis et al. 2002). In between 600 and
1,000 km, a gradual transition is used in the DCT filter
response to avoid an abrupt cutoff and to reduce Gibbs
effects. The response is chosen such that the low-pass
filter preserves all scales larger than 1,000 km and the
high-pass filter preserves all scales smaller than 600 km;
in between the response varies as a cosine square (cf
Fig. 2 of BL06).
The moisture flux divergence, which is a quadratic term,
is handled as follows. The specific humidity q and both
components of the horizontal wind field V = (u,v) are all
decomposed into the 0, L and S components on pressure
levels at each archived time. The vertically integrated
moisture flux is then calculated for each component and the
total flux is obtained as:
Q ¼Xa;b
Vaqb ¼ V0q0 þ V0qL þ V0qS þ VLq0 þ VLqL
þ VLqS þ VSq0 þ VSqL þ VSqS ð2Þ
with (a,b) 2(0,L,S)
The divergence r:Q of each of the nine terms is finally
calculated with finite differences on polar-stereographic
grid. To simplify the visualization of the results, these nine
terms are then recomposed into a large-scale or resolved
term ðr:QÞR and a small-scale or unresolved term ðr:QÞUas:
r:Q ¼ ðr:QÞR þ ðr:QÞU ð3aÞ
with
ðr:QÞR ¼ r:V0q0 þr:V0qL þr:VLq0 þr:VLqL ð3bÞ
ðr:QÞU ¼ r:V0qS þr:VSq0 þr:VLqS
þr:VSqL þr:VSqS
ð3cÞ
The resolved term R regroups all the terms that are both
resolved by the CRCM and the nesting data, while the
unresolved term U regroups all the terms that involve either
the small-scale humidity, or the small-scale wind or both,
and hence are not resolved by large-scale reanalyses or
typical GCMs.
A number of statistics are developed to investigate the
features of the time- and space-decomposed vertically
integrated moisture flux divergence. Let us note the archive
of a variable X as Xj,y where the subscript j is the time step
of the archive within a period (either a month or a season in
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
this study) and y represents the year. Several averages and
variances can be defined as follows:
The period (seasonal or monthly) average for year y is
defined as:
XJy ¼
1
J
XJ
j¼1
Xj;y ð4aÞ
The period climatological average:
XY ;J ¼ 1
J � YXY
y¼1
XJ
j¼1
Xj;y ð4bÞ
The climatological variance of transient perturbations:
r2c ¼
1
Y � JXY
y¼1
XJ
j¼1
ðXj;y � XY ;JÞ2 ð5aÞ
The intra-period climatological variance of transient
perturbations:
r2ipc ¼
1
Y � JXY
y¼1
XJ
j¼1
ðXj;y � XJyÞ
2 ð5bÞ
The inter-annual climatological variance of transient
perturbations:
r2iac ¼
1
Y
XY
y¼1
ðXJy � X
Y ;JÞ2 ð5cÞ
Note that r2c = ripc
2 + r2iac.
In the following, we use J = 356 for the winter season
and J = 388 for the summer season (1 output every 6 h for
3 months), and Y = 25 years.
The time decomposition allows to write X0 ¼ X � Xt
with Xt
representing average of X over some time period
and X¢ representing the deviation thereof, so that r2 ¼ X02t
is the transient-eddy variance. Returning to the spatial
decomposition of a quantity X = XR + XU and combining
with the time decomposition allows to write
X0R ¼ XR � XRt
and X0U ¼ XU � XUt
so that
r2 ¼ X 02t ¼ ðX0R þ X0UÞ
2t
¼ r2R þ r2
U
þ CovU;R with CovU;R ¼ 2X0RX0Ut
ð6Þ
If R represents the large or resolved scales and U rep-
resents the small or unresolved scales, then the total tem-
poral variance is equal to the sum of the temporal variances
of the resolved scales and of the unresolved scales, plus a
cross term that represents the temporal covariance between
unresolved and resolved scales. The added value of
the CRCM in the time variability is contained in the sum
r2U + CovU,R.
3 Results
3.1 Winter season
3.1.1 Mean atmospheric water budget
Before proceeding with the statistical analysis and scale
decomposition of the divergence of the moisture flux, it is
instructive to look at the 25-year (1975–1999) climatology
for winter (December, January and February) of each of the
four terms involved in the water budget equation. Figure 2
presents the climatological values of water vapour ten-
dency, moisture flux divergence, evapotranspiration
(shown with a minus sign) and precipitation. The mean
precipitation field shows two regions of maximum pre-
cipitation: one on the windward side of the mountains on
the West Coast and over the eastern Pacific Ocean, and one
off the East Coast, over the Gulf Stream. This pattern is
very close to that shown by BL06 for the monthly mean
precipitation of February 1990. The moisture flux conver-
gence shows two main regions of convergence over the
West Coast, closely related to the precipitation there, and
another over the Appalachians. Evaporation is largest over
the Pacific and Atlantic Oceans: the maximum over the
Gulf Stream is closely related to the maximum of preci-
pitation there. The time–mean water vapour tendency is
small (note that the scale is multiply by 100 compared to
the other terms) and hence plays a negligible role in the
time–mean water vapour budget. For comparison, Fig. 3
shows the analysis of precipitation as inferred from NCEP–
NCAR reanalyses and CRU observations (over continent
only) for the same period. Both CRU precipitation and
CRCM precipitation fields exhibit a maximum right along
the West Coast. Although the simulated precipitation tends
to be slightly stronger over the Rocky Mountains and
slightly weaker over the Appalachian Mountains, the
overall structure of precipitation is well reproduced by the
CRCM.
3.1.2 Temporal variability
In this section, the time variance of the four terms of the
atmospheric water budget are calculated over the 25 win-
ters, and decomposed into the large-, small-scale and
covariance terms (Fig. 4). Here the moisture flux diver-
gence itself is decomposed using the DCT as opposed to
the next section that will show the moisture flux divergence
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
Fig. 2 Climatological mean
water vapour budget terms
calculated from the CRCM
simulation for the winter season
(December–January–February),
from December 1974 to
February 1999, as simulated by
the CRCM. P precipitation, –Eminus evapotranspiration, r:Qdivergence of the vertically
integrated moisture flux, and otqvertically integrated water
vapour tendency. Note that the
scale for the water vapour
tendency is displayed with a
factor 100 compared to the other
terms. Values are in mm/day
Fig. 3 Mean winter
precipitation from December
1974 to February 1999,
produced by NCEP–NCAR
reanalyses (left panel) and from
analysis of observations over
the continent from CRU (rightpanel). Values are in mm/day
Fig. 4 Climatological standard
deviation of the total, large- and
small-scale parts, and
covariance term between large-
and small-scale terms of
precipitation,
evapotranspiration, vertically
integrated water vapour
tendency and vertically
integrated moisture flux
divergence, for winter from
1975 to 1999, as simulated by
the CRCM
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
calculated from the decomposed wind and humidity fields.
Maximum variability in precipitation occurs where the
mean precipitation is maximum. The variability of the
large-scale part is at least twice stronger than the variability
of the small-scale part, but they both show the same pat-
tern. The covariance between large and small scales is
rather small for the precipitation, except right over the
Rocky Mountains where it contributes to the added value.
The variability of the evapotranspiration is weak and
mainly large scales, and it occurs where the mean evapo-
transpiration is maximum. The small-scale and covariance
contributions are weak except for a very small region right
along Virginia and Georgia coast. The time–mean water
vapour tendency is negligible but its time variability is
quite large. Its variability over the continent is essentially
due to the variability of its large-scale part, whereas over
the ocean the variability of the small scales is also
important. The covariance term for the water vapour ten-
dency is important mainly near the coast and over the
oceans where it contributes to the added value of the
CRCM. The variability of the moisture flux divergence is
very similar to that of the water vapour tendency, indi-
cating the secondary role played by precipitation and
evaporation in the temporal variability.
In summary, the water vapour budget is dominated by
the large scales in winter, with a significant contribution of
the small scales for all terms but the evapotranspiration.
The covariance between large and small scales is large
mainly for the water vapour tendency and the moisture flux
divergence, increasing the added value of the CRCM
mostly near the coasts and over the oceans; it is also non-
negligible for precipitation over the mountains.
3.1.3 Decomposed temporal variability of the moisture
flux divergence
The temporal variability of the atmospheric moisture flux
divergence is now decomposed into its various spatial and
temporal contributions. Figure 5 presents the transient-
eddy climatological standard deviation (Eq. 5a, rc), the
intra-seasonal climatological standard deviation (Eq. 5b,
ripc), and the inter-annual standard deviation (Eq. 5c, riac)
for the 25 winters of the simulation (December 1974–
February 1999). The term rc exhibits two maxima over
regions where most of the meteorological perturbations are
passing through during winter, also corresponding closely
to the maximum climatological precipitation (Fig. 2). The
maximum magnitude of rc around 40 mm/day is about
four to five times larger than the amplitude of the mean
moisture flux divergence over the same region. Two
secondary maxima of variability can be seen over the
Appalachian Mountains and over Oregon and Washington
states with values around 25 mm/day. The term ripc is
almost identical to rc as most of the variability is due to the
intra-seasonal variances. Indeed, the riac accounts overall
for less than 5% of the total standard deviation. For the
winter season, the term riac shows structures mainly over
the oceans and coastal regions.
Before showing the variability of the recomposed
resolved and unresolved terms, it is informative to display
the nine scale-decomposed terms individually to see their
pattern and amplitude. Figure 6 shows the intra-seasonal
standard deviation of the nine decomposed terms of the
moisture flux divergence over the 25 winters. This figure
reveals that the large-scale term with the maximum vari-
ability is r:VLqL while the small-scale term with maxi-
mum variability is r:VLqS: The terms involving the very
large-scale wind V0 tend to have more variability over the
ocean whereas terms involving the small-scale wind VS
tend to have more variability over the mountains. The
terms involving the large-scale wind VL have variability
over both the continent and the ocean. Note that these
variability components do not sum to give the total vari-
ability shown in Fig. 5 as can be shown by the definition
(Eq. 6). The difference between the total variability and the
sum of the variability of the nine terms of Fig. 6 (not
shown) is negligible everywhere except near the West
Coast and along the coast of Greenland where it shows
slightly negative values.
These nine terms are now recomposed following Eq. 3b,
c and Fig. 7 displays the variability of the resolved ðr:QÞRand the unresolved parts of the moisture flux divergence
through the term ripc2 . The unresolved part accounts for the
variance of the recomposed unresolved term r2U plus the
covariance between the recomposed resolved and unre-
solved terms CovU,R, so that r2U + CovU,R represents the
added value of the CRCM. In the west, the variance of the
resolved-scale part of the moisture flux divergence tends to
be stronger away from the coast, decreasing from its
maximum value over the Pacific Ocean towards the West
Coast. On the contrary the variability of the unresolved-
scale part is larger along the West Coast spanning from
Northern California to Southern British Columbia and de-
creases away from the coast. Over the continent, R and U
are of the same magnitude except over the mountains
where R is stronger. On the eastern part of the domain,
right along the coast, resolved-scale term is larger than the
unresolved-scale one; away from the coast, both terms have
about the same magnitude.
Figure 8 shows the inter-annual variance r2iac of the
resolved-scale and unresolved-scale parts of the moisture
flux divergence for the winter. Although it accounts globally
for less than 5% of the total variability, it still shows valuable
information. The inter-annual variability of the moisture
flux divergence over the Pacific Ocean is mainly due to the
variability of the resolved part. This band of maximum
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
variability tends to somewhat vary within the winter season
(not shown). In December it is slightly shifted to the north
with respect to the mean winter position; it is shifted to the
south in January and it is weaker in February. This inter-
annual variability may be related to the Subtropical Pacific
Jet Stream or a portion of the jet called the Pineapple Express
which moves northward from its average position a few
times during the winter season and brings mild and very
rainy weather over the West Coast. Also during winter, the
Pacific anticyclone moves southward along with a south-
ward migration into California of the Polar jet. Thus the
variability can be also related to the inter-annual variation of
the Polar Jet Stream. Over the continent, for the inter-annual
variability, both resolved and unresolved terms have about
the same amplitude. Interestingly enough, negative values
appear along the west coast and the Appalachian Mountains
due to the contribution of the covariance term, that reduce
the variability due to the resolved part there.
Fig. 5 Mean vertically
integrated moisture flux
divergence, seasonal
climatological standard
deviation of transient
perturbations rc, intra-seasonal
standard deviations of transient
perturbations ripc, and inter-
annual standard deviation of
transient perturbations riac, for
winter for the period 1975–
1999, as simulated by the
CRCM. Note that for this figure
the moisture flux divergence is
calculated from pressure-level
data whereas in Fig. 2 it is
calculated on Gal-Chen model
levels during integration of the
model
Fig. 6 Intra-seasonal
climatological standard
deviation (ripc) for the nine
terms of the scale-decomposed
divergence of the vertically
integrated moisture flux, in
winter for the period 1975–
1999, as simulated by the
CRCM. Note that these
variability components do not
sum to give the total variability
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
3.2 Summer season
3.2.1 Mean atmospheric water budget
The mean atmospheric water budget is quite different
during the summer season (June, July and August) com-
pared to the winter season. Figure 9 shows the 25-year
mean of the four terms of the atmospheric water budget in
summer. The maximum of precipitation occurs over the
continent, with large amounts in the south-eastern part of
the USA where precipitation is mainly balanced by
evapotranspiration. Over the Pacific Ocean, precipitation is
mainly balanced by convergence of the moisture flux,
while over the Atlantic Ocean, precipitation is balanced by
evapotranspiration except right along the Coast where
moisture flux convergence dominates. Note also that there
Fig. 7 Intra-seasonal climatological variance (ripc2 ) of the resolved
scales R (left panel) and contribution from unresolved scales rU2 +
CovU,R (right panel) of the divergence of the vertically integrated
moisture flux for the winter season (December, January and February)
from 1975 to 1999, as simulated by the CRCM
Fig. 8 Same as Fig. 6 but for
the inter-annual contributions to
variance (riac)
Fig. 9 Same as Fig. 2 but for
the summer season (June, July
and August)
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
is little evaporation over the Hudson Bay, northern oceans
and Great Lakes; precipitation is balanced by the moisture
flux convergence in these areas. The mean water vapour
tendency is again negligible (note the scale factor of 100
for this field). Figure 10 shows the 1975–1999 summer-
mean precipitation from the NCEP–NCAR reanalyses and
from the CRU data. Precipitations produced by the CRCM
and the reanalyses are in general stronger everywhere
compared to those from CRU data, although the overesti-
mation is less in the CRCM compared to the NCEP–NCAR
reanalyses, but the CRCM fails to reproduce the dry region
in the southwestern part of the domain (North California–
Oregon). It is well documented that the CRCM systemat-
ically overestimates the summer precipitation over the
continent. Sensitivity experiments revealed that the con-
vection scheme itself was not solely responsible for the
overestimation of summer precipitation; Jiao and Caya
(2006) showed that excess moisture accumulation in the
planetary boundary layer as well as in the soil were
responsible for the precipitation overestimation in the
CRCM. In the newly developed 4th-generation CRCM, a
more advanced and more comprehensive land–surface
model, the Canadian Land Surface Scheme (CLASS), has
replaced the original bucket model. A simulation with the
same configuration as the one used for this study is under
progress with this new version. When the results will
become available the same analysis will be repeated to
compare with the one done in this study. Therefore, one
must keep in mind for this present study that precipitations
are overestimated especially over the continent and this
will undoubtedly influence the results. Hence the following
analysis must be taken with care, as it represents mostly a
proof of concept of the methodology.
3.2.2 Temporal variability
The seasonal variability of precipitation, evapotranspira-
tion, water vapour tendency and moisture flux divergence,
and their large- and small-scale parts as well as the
covariance between large- and small-scale terms are shown
on Fig. 11. Precipitation has its maximum variability over
the continent in summer as opposed to the winter vari-
ability that is large over the oceans. The small-scale part
dominates the variability of the precipitation over the
continent. The covariance between the large and the small
scales is modest generally reinforcing the small-scale
variability of the precipitation over the southeastern part of
the domain. Over the North Pacific Ocean, the large-scale
part dominates the variability. The variability of the
evapotranspiration is weak and is mainly due to large-scale
variability. For the water vapour tendency, the variability
of the small-scale part is greater than the variability of the
large-scale part not only over the continent but also over
the Atlantic Ocean, and the covariance between large and
small scales increases the variability almost everywhere.
Over the Pacific Ocean, large-scale variability dominates
the water vapour tendency term. As was the case in winter,
the summer temporal variance of the moisture flux diver-
gence is comparable to that of the water vapour tendency.
The variability of the small scale part of the moisture flux
divergence is comparable to that of the large-scale over the
Atlantic Ocean, greater over the Continent and smaller
over the Pacific Ocean. The covariance between large and
small scale is positive almost everywhere and maximum
over the southeastern convective region as well as over the
Atlantic Ocean, thus increasing the added value of the
CRCM, except over the Rocky Mountains where it is very
weak or slightly negative over the highest elevation points.
Overall the variability of the moisture flux divergence is
weak over the Western mountainous part of the continent.
This was also similar for the winter season.
3.2.3 Decomposed temporal variability of the moisture
flux divergence
Figure 12 shows the climatological mean moisture flux
divergence, and its three standard deviations rc, ripc and
riac for the 25 summers from 1975 to 1999. The variability
of the moisture flux divergence is large over the eastern
part of the United States and off the East Coast over the
Atlantic Ocean. A secondary maximum appears over the
North Pacific Ocean and the Gulf of Alaska. The western
part of North America is the region that shows least
variability during summer. As for the winter season, the
intra-seasonal variability dominates and the inter-annual
standard deviation accounts for less than 5% of the total in
Fig. 10 Same as Fig. 3 but for
the summer season
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
the region of maximum variability. The inter-annual vari-
ance shows structures only where the intra-seasonal stan-
dard deviation is maximum.
Figure 13 shows the nine individual terms of the intra-
seasonal standard deviation. In the east the dominant term
of the decomposition is r:VLqS while over the Pacific
Ocean the term r:VLqL tends to be stronger. Hence, the
dominant summer term, especially over the continent, is a
small-scale term that involves the small-scale humidity and
the large-scale wind; therefore it is not resolved by large-
scale model or reanalyses. All four terms involving either
the small-scale wind or the small-scale humidity have
important contributions to the total divergence of moisture
flux over the continent. Over the Atlantic Ocean, the terms
involving the small-scale humidity have the strongest
variability. For the large-scale terms, the term r:V0qL is
weak for summer, which is different from the situation in
winter; this is probably due to the fact that the mean wind
Fig. 11 Same as Fig. 4 but for
the summer season
Fig. 12 Same as Fig. 5 but for
the summer season
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
is weaker and less dominated by large-scale perturbations
in summer. The difference between the total variability and
the sum of the variability of all terms of Fig. 13 (not
shown) is negative along the coast like the difference for
the winter season, and also over mountainous regions such
as the Rocky and Appalachians Mountains.
Figure 14 displays the intra-seasonal variance of the
resolved-scale and unresolved-scale parts of the moisture
flux divergence. Over the Pacific Ocean, the maximum for
both unresolved-scale and resolved-scale variability is
shifted to the north compared to the winter maximum
position. But similarly to the winter, the maximum of the
resolved-scale part is away from the coast whereas the
maximum of the unresolved-scale variability is right along
the coast. Over the continent where the variability of the
large scales is about three times weaker than the variability
of the small scales, the intra-seasonal variability is domi-
nated by the unresolved scales. This is different from the
winter season where the large scale variability over the
continent is slightly larger than the small-scale variability.
Over the Atlantic Ocean, both large- and small-scale
components have similar structure and amplitude. Note that
the unresolved-scale variability maximum pattern extends
along the East Coast.
The intra-seasonal variance reflects both variations of
the monthly means in the 3 months that compose the sea-
son and the intra-monthly variations. The difference of
intra-monthly variability from one month to another is in
part modulated by the NAMS. Figure 15 shows the intra-
monthly variances of transient perturbations of the large-
scale moisture flux divergence for June, July and August,
from 1975 to 1999. The region of strong variability of the
large-scale moisture flux divergence over the Pacific Ocean
is moving towards the northwest during the summer sea-
son, keeping about the same amplitude. In June, its position
is close to North California and Oregon Coast and, in
August, it is much closer to the coast of Alaska. In the same
time, the region of large variability over the Atlantic Ocean
Fig. 13 Same as Fig. 6 but for
the summer season
Fig. 14 Same as Fig. 7 but for
the summer season
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
is displacing toward the North and is decreasing in inten-
sity and in spatial extension. Over the continent, the inter-
monthly variability is small and no major differences can
be seen from one month to another.
Figure 16 is the same as Fig. 15 but for the unresolved
part of the variability of moisture flux divergence. The
region of strong variability of the small-scale moisture flux
divergence coincides with the pattern of the frequency of
the LLJ. Figure 7 in Higgins et al. (1997) shows a region
of strong jet along the West Coast of the United States
which is located at the same position, with another maxi-
mum of variability over the Pacific Ocean. The Great
Plains LLJ is an important source of moisture for the
United States east of the Rocky Mountains. Over the
Pacific Ocean, the variability of the unresolved part shows,
similarly to the large-scale variability, a displacement to
the northwest accompanied by a slight increase in vari-
ability from June to August. Over the continent, centred on
Illinois and Indiana, the maximum of small-scale vari-
ability increases somewhat from June to July, and then
decreases significantly from July to August. The change
from June to July is coherent with an increased in precip-
itation noted by Berbery and Fox-Rabinovitz (2003),
associated with the mature phase of the NAMS, August
being the end of the mature phase of the NAMS. Over the
Atlantic Ocean, similarly to the large-scale northward
displacement, the small-scale maximum variability is
moving to the north and is decreasing in intensity from
June to August. The monthly inter-annual standard devia-
tion (not shown) is also characterized by a slight increase
of variance from June to July over the southeastern conti-
nent, followed by an important decrease in the same region
in August.
4 Summary and conclusion
This paper describes a methodology for attempting to de-
fine the added value of using a high-resolution climate
model to add ‘‘fine-scale details’’ onto the large-scale
fields used to drive the RCM. This is done in the context of
the atmospheric water budget, given that this deals with
variables such as precipitation in which the impact of
Fig. 15 Intra-monthly climatological variance ripc2 of the resolved or
large-scale part of the moisture flux divergence, for the months of
June, July and August, from 1975 to 1999, as simulated by the CRCM
Fig. 16 Same as Fig. 15 but for the unresolved part of the moisture
flux divergence
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
accrued resolution is most directly felt. In this paper, the
atmospheric water budget in winter and summer over
North America as simulated by the Canadian RCM driven
by reanalyses for 25 years is studied. A decomposition of
the budget into time mean and time variability, as well as in
large scales (that are resolved by reanalyses and coarse-
mesh global models) and small scales (that are only
resolved by fine-mesh regional models), allows to quantify
the added value of a regional climate model. The two
seasons are characterised by rather distinct precipitation
making processes, predominantly stratiform in winter and
convective in summer. This has profound impact in the
scales at which precipitation is produced, and the transports
required to support it.
In summary for the winter season, the climatological
mean atmospheric water budget is rather similar to that
shown by Bielli and Laprise (2006) for a single winter
month. The climatological transient-eddy standard devia-
tion of the moisture flux divergence is four to five times
stronger than the time mean. The intra-seasonal variance
dominates the variability of the flow as the inter-annual
variance account overall for less than 5% of the total var-
iance. On the West Coast, the intra-seasonal variability of
the large-scale moisture flux divergence dominates away
from the coast, while the variability of the small-scale term
gradually dominates near the coast. On the East Coast, it is
somehow the contrary, with the dominance of the vari-
ability of the large-scale part of the moisture flux diver-
gence near the coast; away from the East Coast, both large-
and small-scale variability have the same magnitude. Over
the continent, both large- and small-scale seasonal vari-
abilities are weak. The inter-annual variance is small but
nevertheless shows interesting structures that can be in part
related to the Jet Stream. Variability in precipitation and
water vapour tendency is dominated in winter by the large
scales, with some contributions from the small scales
mainly over the oceans. The variability of evapotranspi-
ration is weak and only due to the large scales.
For the summer season, the time–mean atmospheric
water budget is quite different to that of winter. Maxima of
precipitation and evapotranspiration appear now over the
continent, especially over the southeastern part of the
domain. The climatological standard deviation, particularly
over the continent, is almost eight times larger than the
time–mean divergence of the moisture flux. Analogous to
the winter season, the intra-seasonal climatological vari-
ance dominates the variability, but the inter-monthly vari-
ability is also large in summer. Contrary to the winter
season, the summer intra-seasonal variability over the
continent is largely dominated by the variability of the
small-scale part. Within the intra-seasonal variability,
the intra-monthly climatological standard deviation varies
from June to August coherently with the variation of the
North American Monsoon System over the southeastern
part of the domain, and consistently with the Jet Stream
position over the Pacific Ocean.
The small scales generated by the CRCM, i.e. the added
value produced by the use of a finer resolution, is large in
winter (with magnitude equivalent those of the large
scales) and coherent with the large-scale structures. The
dominant small-scale contribution to the variability of the
moisture flux divergence is located over the oceans and
occurs where both the mean and the variance show maxi-
mum values. Small scales in winter have also a topographic
signature, with non-negligible small-scale variability,
especially over the Rocky Mountains. The added value for
the summer season is quite different to that of the winter
season in terms of pattern and magnitude. Indeed, the
added value of the CRCM in summer is larger than the
large-scale values over the southeastern part of the domain,
where convection often occurs. Therefore, the dominant
contribution of the small scales for the summer season is
convection. The region of large small-scale convection
contribution is coherent with the region of enhanced pre-
cipitation and low-level jet (LLJ) associated with the
NAMS. In conclusion, the added value of the CRCM for
the winter season is large and dominant over ocean regions,
while the added value for the summer season is dominant
(larger than the large-scales) and controlled mainly by the
convection over the continent. The conclusions derived for
summer however are likely affected by the noted tendency
of the CRCM to excessive continental precipitation.
This work aims at quantifying the added value of high-
resolution RCM as a tool for downscaling climate projec-
tions when driven by low-resolution coupled GCMs or
reanalyses. Overall, based on a rather long simulation of
CRCM over 25 years, the results show little change in the
time–mean quantities due to the increased resolution, ex-
cept over locations subject to strong fine-scale forcing such
as mountainous regions or near sharp land–sea contrast.
However the results clearly show enhanced time variability
with increased horizontal resolution. This finding is of
great interest for issues related to changes in extremes
under altered anthropogenic forcing.
Acknowledgments This research was supported by the Canadian
Foundation for Climate and Atmospheric Sciences (CFCAS) and the
Ouranos Consortium. The authors are grateful to the staff of the
CRCM Network and Ouranos Simulation Team for their assistance,
and to Mr. Claude Desrochers for maintaining an efficient local
computing facility.
Appendix
Impact of vertical interpolation and time sampling on the
reliability of the water budget for a summer month.
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
Bielli and Laprise (2006) showed that it is essential to
use enough pressure levels in the lower troposphere when
computing the moisture budget, especially if one wants to
look at the added value of the CRCM. The use of a
6-hourly temporal resolution introduces some approxima-
tions, but overall the vertical resolution is more important.
These conclusions were drawn for a winter month and the
temporal resolution issue might be exacerbated in summer
in order to properly capture the diurnal cycle of moisture
over the continents. In this section, we will evaluate the
impact of vertical interpolation and time sampling on the
reliability of the water budget for a summer month.
An additional simulation has been made for the month
of July 1975 with output archived every time step (15 min).
The output data were then interpolated on two sets of
pressure levels (17 and 30 pressure levels). Figure 17
shows the moisture flux divergence computed for the 4
different configurations: 17 pressure levels and 6-h output
Fig. 17 Monthly mean
vertically integrated moisture
flux divergence for July 1975, as
simulated by the CRCM,
calculated on 17 pressure levels
and 6-h output data (P17-6 h),
on 17 pressure levels and 15-
min output data (P17-15 min),
on 30 pressure levels and 6-h
output data (P30-6 h), and on 30
pressure levels and 15-min
output data (P30-15 min)
Fig. 18 Variance spectra of the
vertically integrated moisture
flux divergence for July 1975, as
simulated by the CRCM,
calculated on Gal-Chen levels
(GC6 h) and on pressure levels
(P17-6 h, P17-15 min, P30-6 h,
P30-15 min). Left panel shows
the time mean and right panelthe transient eddies
S. Bielli and R. Laprise: Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation
123
data (P17-6 h), 17 pressure levels and 15-min output data
(P17-15 min), 30 pressure levels and 6-h output data (P30-
6 h), and 30 pressure levels and 15-min output data (P30-
15 min). Contrary to what was expected, the time sampling
is not a larger source of error in summer than it is in winter
when calculating the mean moisture flux divergence. In-
deed, Fig. 17 shows clearly that the biggest discrepancy in
the mean moisture flux divergence when comparing with
Fig. 9 is due to the lack of vertical resolution in the low
levels near the high topography (P17-6 h and P30-6 h).
The errors due to vertical resolution in the summer are
much larger than in winter, but the errors due to time
sampling are smaller. Figure 18 shows the spectra of the
moisture flux divergence for these four configurations. This
figure confirms that for the time–mean part of the moisture
flux divergence, the errors due to time sampling are small
(purple line vs. cyan or orange lines), and that errors due to
vertical resolution in the low levels are worse (red or green
lines) in summer than in winter shown by Bielli and
Laprise (2006). For the time-fluctuation part of the mois-
ture flux divergence, little differences are noted between
winter and summer. Hence errors due to time sampling are
small and using 17 pressure levels instead of 30 results in
an overestimation of the variance.
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