Soline Bielli Æ René Laprise. (larger than the large scales) and controlled mainly by convective processes.

Transcription

1 Clim Dyn DOI /s Time mean and variability of the scale-decomposed atmospheric water budget in a 25-year simulation of the Canadian Regional Climate Model over North America Soline Bielli Æ René Laprise Received: 20 September 2006 / Accepted: 20 April 2007 Ó 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 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 intermonthly 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 dominated by oceanic forcing, while in summer, it is dominant S. Bielli (&) R. Laprise Canadian Network for Regional Climate Modelling and Diagnostics, Université du Québec à Montréal, OURANOS, 550 rue Sherbrooke Ouest, 19e, Montréal, QC H3A 1B9, Canada bielli.soline@uqam.ca (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 synoptic-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

2 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 atmospheric water budget into different spatial scales was recently 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 generalize our previous results to several winter seasons to increase 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 stationary 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 budget for 25 winter and 25 summer seasons simulated by the CRCM driven by reanalyses for the period Section 2 briefly describes the CRCM and the configuration 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 summary 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 nonhydrostatic 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 horizontal grid mesh of 45 km is used on a 192 by 144 gridpoint 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 diagnostics 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 subgridscale 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)

3 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 interpolated on the CRCM grid at every time step, to provide lateral boundary condition. Model-simulated data are archived 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, especially 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 detailed structure of the moisture flux. How well the fourtime 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. 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 ¼ X V a q b ¼ V 0 q 0 þ V 0 q L þ V 0 q S þ V L q 0 þ V L q L a;b 2.2 Water budget and methodology þ V L q S þ V S q 0 þ V S q L þ V S q S ð2þ We use the same methodology as BL06 where the vertically integrated water budget is defined as (e.g. Peixoto and Oort 1992): o t q ¼ r:q þ E P ð1þ with the overbar representing vertical integration in pressure w ¼ 1 g Z p sfc p top 1 wdp ¼ g Z p 0 p top bwdp with p top and p sfc the lowest and the highest pressure values in a vertical atmospheric column, respectively. Here p 0 is chosen as a value exceeding the maximum value of p sfc 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; V is 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 = X 0 + X L + X S. 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 domainmean value. The subscript L represents large scales (synoptic scales) that are resolved by both the RCM and the 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:qþ R and a small-scale or unresolved term ðr:qþ U as: r:q ¼ðr:QÞ R þðr:qþ U with ðr:qþ R ¼r:V 0 q 0 þr:v 0 q L þr:v L q 0 þr:v L q L ðr:qþ U ¼r:V 0 q S þr:v S q 0 þr:v L q S þr:v S q L þr:v S q S ð3aþ ð3bþ 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 X j,y where the subscript j is the time step of the archive within a period (either a month or a season in

4 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: X J y ¼ 1 J X J X j;y j¼1 The period climatological average: X Y;J ¼ 1 X Y X J X j;y J Y y¼1 j¼1 The climatological variance of transient perturbations: r 2 c ¼ 1 X Y X J ðx j;y X Y;J Þ 2 Y J y¼1 j¼1 ð4aþ ð4bþ ð5aþ The intra-period climatological variance of transient perturbations: r 2 ipc ¼ 1 X Y X J ðx j;y X J y Y J Þ2 y¼1 j¼1 ð5bþ The inter-annual climatological variance of transient perturbations: r 2 iac ¼ 1 Y X Y y¼1 ðx J y XY;J Þ 2 ð5cþ Note that r 2 2 c = r ipc + r 2 iac. 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 X 0 ¼ X X t with X t representing average of X over some time period and X representing the deviation thereof, so that r 2 ¼ X 02t is the transient-eddy variance. Returning to the spatial decomposition of a quantity X = X R + X U and combining with the time decomposition allows to write XR 0 ¼ X t R X R and XU 0 ¼ X t U X U so that r 2 ¼ X 0 2 t ¼ ðxr 0 þ X0 U Þ2t ¼ r 2 R þ r2 U þ Cov U;R with Cov U;R ¼ 2XR 0 X0 t U ð6þ If R represents the large or resolved scales and U represents the small or unresolved scales, then the total temporal 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 r 2 U + Cov U,R. 3 Results 3.1 Winter season 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 ( ) 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 tendency, moisture flux divergence, evapotranspiration (shown with a minus sign) and precipitation. The mean precipitation field shows two regions of maximum precipitation: 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 The moisture flux convergence 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 precipitation 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 Temporal variability In this section, the time variance of the four terms of the atmospheric water budget are calculated over the 25 winters, and decomposed into the large-, small-scale and covariance terms (Fig. 4). Here the moisture flux divergence itself is decomposed using the DCT as opposed to the next section that will show the moisture flux divergence

5 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, E minus evapotranspiration, r:q divergence of the vertically integrated moisture flux, and o t q vertically 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 (right panel). Values are in mm/day Fig. 4 Climatological standard deviation of the total, large- and small-scale parts, and covariance term between largeand 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

6 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 pattern. 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 evapotranspiration 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 tendency 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, indicating 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 nonnegligible for precipitation over the mountains 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 transienteddy climatological standard deviation (Eq. 5a, r c ), the intra-seasonal climatological standard deviation (Eq. 5b, r ipc ), and the inter-annual standard deviation (Eq. 5c, r iac ) for the 25 winters of the simulation (December 1974 February 1999). The term r c 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 r c 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 r ipc is almost identical to r c as most of the variability is due to the intra-seasonal variances. Indeed, the r iac accounts overall for less than 5% of the total standard deviation. For the winter season, the term r iac 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 variability is r:v L q L while the small-scale term with maximum variability is r:v L q S : The terms involving the very large-scale wind V 0 tend to have more variability over the ocean whereas terms involving the small-scale wind V S tend to have more variability over the mountains. The terms involving the large-scale wind V L have variability over both the continent and the ocean. Note that these variability components do not sum to give the total variability 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:qþ R and the unresolved parts of the moisture flux divergence through the term r 2 ipc. The unresolved part accounts for the variance of the recomposed unresolved term r 2 U plus the covariance between the recomposed resolved and unresolved terms Cov U,R, so that r 2 U + Cov U,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 unresolvedscale part is larger along the West Coast spanning from Northern California to Southern British Columbia and decreases 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 r 2 iac 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

7 Fig. 5 Mean vertically integrated moisture flux divergence, seasonal climatological standard deviation of transient perturbations r c, intra-seasonal standard deviations of transient perturbations r ipc, and interannual standard deviation of transient perturbations r iac, for winter for the period , 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 (r ipc ) for the nine terms of the scale-decomposed divergence of the vertically integrated moisture flux, in winter for the period , as simulated by the CRCM. Note that these variability components do not sum to give the total variability 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 interannual 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 southward 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.

8 Fig. 7 Intra-seasonal climatological variance (r 2 ipc ) of the resolved scales R (left panel) and contribution from unresolved scales r 2 U + Cov U,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 (r iac ) 3.2 Summer season Mean atmospheric water budget The mean atmospheric water budget is quite different during the summer season (June, July and August) compared 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. 9 Same as Fig. 2 but for the summer season (June, July and August)

9 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 summermean 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 overestimation 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 systematically overestimates the summer precipitation over the continent. Sensitivity experiments revealed that the convection 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 Temporal variability The seasonal variability of precipitation, evapotranspiration, 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 variability 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 divergence 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 Decomposed temporal variability of the moisture flux divergence Figure 12 shows the climatological mean moisture flux divergence, and its three standard deviations r c, r ipc and r iac for the 25 summers from 1975 to 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

10 Fig. 11 Same as Fig. 4 but for the summer season Fig. 12 Same as Fig. 5 but for the summer season the region of maximum variability. The inter-annual variance shows structures only where the intra-seasonal standard deviation is maximum. Figure 13 shows the nine individual terms of the intraseasonal standard deviation. In the east the dominant term of the decomposition is r:v L q S while over the Pacific Ocean the term r:v L q L 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 largescale 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:v 0 q L is weak for summer, which is different from the situation in winter; this is probably due to the fact that the mean wind

11 Fig. 13 Same as Fig. 6 but for the summer season 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 dominated 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 season 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 intramonthly variances of transient perturbations of the largescale moisture flux divergence for June, July and August, from 1975 to The region of strong variability of the large-scale moisture flux divergence over the Pacific Ocean is moving towards the northwest during the summer season, 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. 14 Same as Fig. 7 but for the summer season

12 2 Fig. 15 Intra-monthly climatological variance r ipc 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 is displacing toward the North and is decreasing in intensity and in spatial extension. Over the continent, the intermonthly 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 maximum 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 variability from June to August. Over the continent, centred on Illinois and Indiana, the maximum of small-scale variability increases somewhat from June to July, and then decreases significantly from July to August. The change Fig. 16 Same as Fig. 15 but for the unresolved part of the moisture flux divergence from June to July is coherent with an increased in precipitation 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 deviation (not shown) is also characterized by a slight increase of variance from June to July over the southeastern continent, followed by an important decrease in the same region in August. 4 Summary and conclusion This paper describes a methodology for attempting to define 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

13 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 coarsemesh 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 deviation 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 variance. 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 variability of the large-scale part of the moisture flux divergence near the coast; away from the East Coast, both largeand small-scale variability have the same magnitude. Over the continent, both large- and small-scale seasonal variabilities 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 evapotranspiration 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 variance dominates the variability, but the inter-monthly variability 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 maximum 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 precipitation 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 highresolution RCM as a tool for downscaling climate projections 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, except 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.

14 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) 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 approximations, 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. 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 panel the transient eddies

15 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. Indeed, 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 moisture 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. References Berbery EH, Fox-Rabinovitz MS (2003) Multiscale diagnosis of the North American Monsoon System using a variable-resolution GCM. J Clim 16: Bielli S, Laprise R (2006) A methodology for the regional-scaledecomposed atmospheric water budget: application to a simulation of the Canadian Regional Climate Model nested by NCEP NCAR reanalyses over North America. Mon Weather Rev 134: Boer GJ (1982) Diagnostic equations in isobaric coordinates. Mon Weather Rev 110: Caya D, Laprise R (1999) A semi-implicit semi-lagrangian regional climate model: the Canadian RCM. Mon Weather Rev 127: Davies HC (1976): A lateral boundary formulation for multi-level prediction models. Q J R Meteorol Soc 102: Denis B, Côté J, Laprise R (2002) Spectral decomposition of twodimensional atmospheric fields on limited-area domains using the discrete cosine transforms (DCT). Mon Weather Rev 130: Higgins RW, Yao Y, Wang XL (1997a) Influence of the North American monsoon system on the US summer precipitation regime. J Clim (10) Higgins RW, Yao Y, Yarosh ES, Janowiak JE, Mo KC (1997b) Influence of the Great Plains low-level jet on summertime precipitations and moisture transport over the Central United States. J Clim 10: Jiao Y, Caya D (2006) An investigation of summer precipitation simulated by the Canadian Regional Climate Model. Mon Weather Rev 134: Laprise R, Caya D, Frigon A, Paquin D (2003) Current and perturbed climate as simulated by the second-generation Canadian Regional Climate Model (CRCM-II) over northwestern North America. Clim Dyn 21: Peixoto J, Oort A (1992) Physics of Climate. American Institute of Physics, USA, pp 520 Rasmusson EM (1967) Atmospheric water vapor transport and the water balance of North America. I: Characteristics of the water vapor flux field. Mon Weather Rev 95: Rasmusson EM (1968) Atmospheric water vapor transport and the water balance of North America. II: Large-scale water balance investigations. Mon Weather Rev 96: Rasmusson EM, Mo KC (1996) Large-scale atmospheric moisture cycling as evaluated from NMC global reanalysis and forecast products. J Clim 9: Roads JO, Chen SC, Guetter AK, Georgakakos KP (1994) Largescales aspects of the United States hydrological cycle. Bull Am Meteorol Soc 75: Robert A, Yakimiv E (1986) Identification and elimination of an inflow boundary computational solution in limited are model integration. Atmos Ocean 24: Ropelewski CF, Yarosh ES (1998) The observed mean annual cycle moisture budgets over the central United States ( ). J Clim 11: Trenberth KE (1991) Climate diagnostics from global analyses: conservation of mass in ECMWF analyses. J Clim 4: Yakimiv E, Robert A (1990) Validation experiments for a nested gridpoint regional forecast model. Atmos Ocean 28: