Time mean and variability of the scale-decomposed ......Time mean and variability of the...

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


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


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


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


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


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)


the summer season (June, July

and August)


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


the summer season


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


the summer season


the summer season


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


the summer season


the summer season


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


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.


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


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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