1. Introduction
Regional climate models (RCMs) have been deployed over the last two decades to improve our understanding of regional climate and the study of impacts of climate change (Giorgi and Mearns 1999 and references therein). With current horizontal resolution at about 50 km it is this finer-scale information that is mostly asked for in climate change impact studies and for the development of regional adaptation strategies (Giorgi 2008). While running a global model at RCM’s resolution requires computer resources that are still not available, dynamical downscaling using RCMs reduces substantially the computational cost for regional-scale simulations (Laprise 2008; Lucas-Picher et al. 2008). Nevertheless, an RCM simulation over a domain covering North America has a similar number of 3D grid cells as a global model and therefore requires more computation power than a global climate model simulation because of the reduced time step. Typical RCM simulation over North America currently requires about 1 month of supercomputer CPU time per 10 years of integration time.
The simulation of the dynamic and thermodynamic nonlinear atmospheric processes in both global and regional models reproduces the chaotic nature of the climate system. This makes climate simulations sensitive to small perturbations in any component of the climate modeling system configuration, including small changes in the initial state of a simulation. It means that slight changes in the modeling setup will produce different realizations of climate when repeating the experiment. This characteristic is termed internal variability (IV; Seth and Giorgi 1998; Giorgi and Bi 2000). The overall variability of the real climate system is linked to (i) external forcings (e.g., solar cycles and volcanic eruptions) and (ii) drivers within the climate system itself (e.g., ENSO). This latter variability is unforced and results from the chaotic nature of the climate system. Throughout this article we ignore the first type and thus will consider only the variability that is intrinsic to the climate system, thus excluding variability due to external forcings. This unforced variability can be associated with a global climate model’s internal variability. Internal variability in a “perfect” global climate model (GCM) should then be equal to the unforced natural variability of the real climate system since the model is completely free to develop alternative circulations that are in accordance with unmodified external forcings applied to the system in repeated simulations (e.g., orbital parameters, solar output, greenhouse gas concentrations, etc.). J. M. Murphy et al. (2009, 26–27) report that GCMs “[…] provide realistic simulations of a number of key aspects of natural internal variability in the observed climate.” Therefore, the best estimate we can have of the natural variability is obtained through GCMs’ IV (J. M. Murphy et al. 2009). Internal variability in RCMs is usually thought to be smaller than in GCMs because the freedom of the RCM to develop alternate atmospheric flows is limited by the driving data imposed at the lateral boundaries of the RCM domain (Christensen et al. 2001). To avoid confusion, the RCM’s IV will be referred to here as “internal variability,” while “natural variability” is used to address the unforced variability in the real climate system as estimated through GCM’s IV.
In order for RCMs to be valued as tools of higher precision through the downscaling of GCM simulations (note that the term precision is used here in the sense of refinements in the calculations and specifications of the physiographical properties and not in the sense of accuracy), the study of RCM internal variability has followed in various studies (e.g., Jacob and Podzun 1997; Giorgi and Bi 2000; Christensen et al. 2001; Caya and Biner 2004: Rinke et al. 2004: de Elía et al. 2008; Lucas-Picher et al. 2008; Frigon et al. 2010) to estimate the regional uncertainty associated with regional climate projections. Numerous regional climate simulations have been generated in international projects [Prediction of Regional Scenarios and Uncertainties for Defining European Climate Change Risks and Effects (PRUDENCE; Christensen et al. 2002); Project to Intercompare Regional Climate Simulations (PIRCS; Takle et al. 1999); North American Regional Climate Change Assessment Program (NARCCAP; Mearns et al. 2009); Regional Climate Model Intercomparison Project (RMIP; Fu et al. 2005); Ensemble-Based Predictions of Climate Changes and Their Impacts (ENSEMBLES; van der Linden and Mitchell 2009)] and a variety of issues of IV have been addressed in recent studies, including the change of IV with respect to different perturbations, domain location and size, seasons, as well as time scale. A comprehensive overview of recent studies can be found in Alexandru et al. (2007). The studies to date mainly investigate IV using time series of several months to a year in current climate and at the domain scale from a perspective of model theory and meteorology. De Elía et al. (2008) and Lucas-Picher et al. (2008) extended the study of IV to multiyear simulations.
Recently, Musíc and Caya (2009) presented a study on IV in RCM simulations from a hydrological perspective, analyzing the modeled water cycle of three of the largest watersheds in North America (St. Lawrence, Mississippi, and Mackenzie). In the present study, we focus on RCM internal variability at a smaller scale, investigating hydroclimatic variables at the level of watershed areas below 200 000 km2. Most water users operate at basins of this size and have an increasing stake in utilizing climate change information along with the related uncertainties. It is our objective to investigate the range of IV for a set of watersheds by analyzing pairs of 30-yr CRCM simulations in order to provide estimates of uncertainty required for hydrological impact studies. This work is intended to serve the impact and adaptation (I&A) community, who are increasingly using RCM data in their assessment work. The increase in available simulations to address this data-intensive analysis is the result of the continuous effort of the Ouranos Climate Simulation Team in generating ensembles of simulations using the Canadian RCM to better serve the I&A community.
Following this introduction, a short description of the Canadian Regional Climate Model (CRCM) is provided and the experimental setup is presented. Section 3 presents the results of the study followed by a discussion of these results in section 4. Finally, the conclusions are presented in section 5.
2. Experimental setup
The present study was carried out using the Canadian Regional Climate Model (CRCM). The design of the experiment is described by an overview of the simulations, the watersheds over which the analysis is made, and by the indicators and statistics used in the investigation.
a. Description of the CRCM
All simulations for the study were realized using version 4.2.0 of the CRCM (Caya and Laprise 1999; Musíc and Caya 2007; Brochu and Laprise 2007). Version 4 of the CRCM underwent major improvements in the radiative scheme (Puckrin et al. 2004), in the treatment of cloud cover (Paquin and Harvey 2003), of atmospheric boundary mixing scheme (Jiao and Caya 2006), and in the land surface processes (Verseghy 1991; Verseghy et al. 1993). The CRCM is driven by reanalysis and GCM data to specify the lateral atmospheric boundary conditions. In the CRCM’s usual configuration, a weak large-scale spectral nudging of the horizontal wind is implemented following Riette and Caya (2002) and is used within the regional domain in order to prevent the CRCM’s large-scale flow from decoupling from that of the driving data. Spectral nudging can be turned off to operate the CRCM in a more “conventional” configuration. The application of weak spectral nudging can be considered a good compromise between too much divergence from the driving field and too much forcing (Alexandru et al. 2009). This is particularly the case for the CRCM North American domain, which is about four times larger than typical European domains used in the PRUDENCE or ENSEMBLES projects.
b. Experiment design
The CRCM runs for this internal variability study consist of pairs of simulations performed over the two regional domains presented in Fig. 1. One domain covers North America (NA) with 201 × 193 grid points while the other covers eastern Canada centered over Québec (QC) with 112 × 88 grid points. Note that the size of the QC domain is close to RCM domains used in European projects like PRUDENCE and ENSEMBLES, while the size of the NA domain is typical of RCM domains used in NARCCAP over North America and in the Coordinated Regional Climate Downscaling Experiment (CORDEX) over all continents (Giorgi et al. 2009). Both domains were configured with a horizontal resolution of 45 km (true at 60°N). Table 1 summarizes the twin experiments. Pairs of simulations were performed over each domain—a pair consisting of a reference simulation and its “twin.” The twin runs are identical in setup to the reference simulation with the sole difference of a 1-month offset in initial conditions to trigger internal variability (see Table 1). Over each domain, pairs of simulations were performed for present climate conditions (1961–90) and for future climate (2041–70). A 3-yr spinup period (1958–60 or 2038–40) is used in all simulations to allow the simulated climate system to reach equilibrium (Paquin et al. 2006).
Domains used for the CRCM simulations. The large domain covers NA and the small domain covers eastern Canada, centered over QC. Numbers indicate the dimension of the 45-km resolution grids. The basins of interest are located within the dashed rectangle.
Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-051.1
Experiment configuration of the pairs of simulations with the CRCM v4.2.
Lateral boundary driving data were taken from the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) global reanalysis atmospheric fields (Uppala et al. 2005) at a 2.5° × 2.5° resolution, and from atmospheric fields from the fourth and fifth members of the Canadian Coupled Global Climate Model ensemble (CGCM3; Scinocca et al. 2008; Flato and Boer 2001). The future climate simulations follow the Intergovernmental Panel on Climate Change (IPCC)’s Special Report on Emissions Scenarios (SRES) A2 emission scenario (Nakicenovic and Swart 2000). In the global climate model–driven simulations, daily sea surface temperature and sea ice were taken from the driving data itself, while ERA-40-driven runs used the Atmospheric Model Intercomparison Project (AMIP II; Fiorino 2005) monthly ocean data. For all but one pair of simulations, an altitude-dependent large-scale nudging was applied to horizontal winds of wavelengths longer than 1400 km, from zero (infinite relaxation time) just above 500 hPa to a relaxation time of 10 h at the model top (~10 hPa). As shown by de Elía et al. (2008), the large-scale nudging affects CRCM’s internal variability. To be able to quantify the influence of spectral nudging on the CRCM internal variability, the spectral nudging was switched off in one of the ERA-40-driven pairs of simulations. Natural variability (excluding external forcings such as solar cycles and volcanoes) is assessed by comparing CRCM simulations driven by members 4 and 5 of the CGCM3. In the area investigated, it was found that the CRCM driven by these two members covers almost the full range of variability observed in the five-member CGCM3 driving experiment (Frigon et al. 2010). Note that the latter are not CRCM twin simulations.
The analysis of the CRCM-simulated hydrological variables was performed over 30-yr periods for the 21 basins with drainage areas varying from 13 000 to 177 000 km2. The map of Fig. 2 shows the studied basins located in Québec and partly in Ontario and Newfoundland/Labrador. On the CRCM’s 45-km grid, the drainage areas are represented by a number of grid cells varying from 9 for the smallest to 91 for the largest watersheds. Results of the analysis are presented as time- and basin-averaged values of annual precipitation, runoff, evapotranspiration, and annual daily maximum of snow water equivalent (SWE). Note that the maximum SWE value is not an extreme value but a measure of the maximum in annual snow cover on the ground. SWE is provided in mm, while all other variables are given in mm day−1. To provide an overview of ERA-40-driven simulated hydroclimatic conditions over the basins of interest for the 1961–90 time window, Fig. 2 presents values of annual means, surrounded by their 10% and 90% quantiles (Q10 and Q90) for precipitation (green), runoff (blue), and evapotranspiration (red) from CRCM’s spectrally nudged simulation (over the NA domain; run acw in Table 1).
QC and Labrador drainage basin names and location. Number of CRCM 45-km grid cells used for the basin analysis are given in parentheses next to basin’s three-letter names. Bar charts and labels provide a hydroclimatic reference with 30-yr values for mean annual precipitation and runoff (mm day−1) taken from the spectrally nudged ERA-40-driven CRCM simulation over the NA domain.
Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-051.1
In this study, deviations of 
3. Results
The effect of CRCM internal variability is illustrated in Fig. 3 with time series of annual precipitation for one basin of this study, taken from the spectrally nudged ERA-40-driven CRCM twin simulations over the NA domain. In this illustrative example, the first 15 yr of the twin simulations appear to agree quite well in the precipitation over the basin as well as in the interannual trend. After about 1975, however, the situation changes and large differences in the simulated annual precipitation occur with highest deviations in 1980 and 1986. During this period, the tendencies from year to year often have opposite signs, although the lateral boundary conditions (LBC) of the twin simulations are identical. Toward the end of the simulated period, the two realizations show very similar evolution of their annual means again. The black line illustrates the 30-yr means of the two time series that differ by only 0.006 mm day−1 or less than 1%. It must be noted that this temporal distribution of agreement and disagreement in the annual time series is a random process and is not controlled by the LBC. Other examples may show larger deviations at the start of the simulation period and more similar values at other times. Neither of the two realizations of the 30-yr period can be considered more realistic than the other. The time series simply illustrate the difference of possible pathways for the evolution of the individual weather systems within the interior domain of the model. The following sections present an investigation of these differences in the pairs of twin simulations of the 30-yr-averaged hydroclimate over the 21 basins. The IV analysis keeps a focus on simulations over the large NA domain. Specificities of the Quebec domain are emphasized where appropriate.
Thirty years of mean annual precipitation in the Arnaud River basin simulated by a pair of spectrally nudged ERA-40-driven CRCM twin runs over the NA domain (acx–acw). The difference between the two 30-yr means of about 0.006 mm day−1 does not show at the scale of the graph (black line). Note that the dotted lines between symbols only help to clarify the difference between simulations but have no physical meaning for annual precipitation.
Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-051.1
a. Analysis of means and centered RMSD
The relative differences of 
Relative differences 
Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-051.1
Summary of the analysis of CRCM’s IV of hydrological variables at the basin scale, comparing the effect of the two domains NA and QC. Values were derived from all 21 basins’ IV and all twin simulations performed over each domain. Values of 
Magnitudes of internal variability (relative difference in 
The scatterplots of Fig. 4 confirm the impact of domain size on the magnitude of internal variability developed in RCM simulations as described in previous research (e.g., Jacob and Podzun 1997; Seth and Giorgi 1998; Vannitsem and Chomé 2005; Alexandru et al. 2007; de Elía et al. 2008). For each domain, the IV estimates of the watersheds form a cluster of values, revealing the domain-specific magnitude of deviations between the examined twin runs (clustering by symbols in Fig. 4). As a rule of thumb, basin internal variability differs by about one order of magnitude between the domains NA (TXT) and QC (dots). The larger internal variability over the larger domain is attributable to the higher freedom in the development of characteristic circulation in a simulation and to the larger distance of the investigated watersheds to the western inflow boundary (Lucas-Picher et al. 2008). However, to some extent, IV in the present study is constrained by the weak spectral nudging that is routinely employed in the configuration of CRCM runs. A totally efficient spectral nudging would constrain the CRCM atmospheric circulation to follow that of the driving data, generating an IV that would be independent of the size of the domain and be very close to zero. The large difference in basin IV over the two domains used in the present study reveals the rather limited control of the spectral nudging, allowing the CRCM to generate its own smaller-scale features.
To assess the influence of spectral nudging on the CRCM’s IV, the ERA-40-driven pair of twin simulations over the NA domain was repeated without spectral nudging. Figure 5 presents the relative differences of 
Panels and axes as in Fig. 4 but data are for the NA domain only. Colors identify pairs of twin runs driven by ERA-40 (1961–90) spectrally nudged (blue) and nonnudged (black) and natural variability experiments driven by members 4 and 5 of the CGCM3 for 1961–90 (red) and 2041–70/A2 (green).
Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-051.1
The analyses for the other variables in Fig. 5 show a similar behavior, with an important increase in the range of relative differences in 
The amplitude of CRCM IV with and without spectral nudging needs to be viewed in relation to the natural climate variability that is intrinsic to the climate system (excluding external forcings such as solar cycles or volcanic eruptions). The IV in a GCM can be considered a best estimate of the natural variability in the climate system and can be estimated by running GCMs several times with small perturbations to the initial conditions (D. M. Murphy et al. 2009), which define the various GCM members. These perturbations to the initial conditions trigger the IV, causing simulations to produce different sequences of weather events and even somewhat different climate statistics, although the differences in the climate means are expected to decrease as the length of the simulation increases (de Elía et al. 2008). The representation of the physical processes as well as the external forcings applied is very similar in both RCMs and GCMs. Therefore, the difference in IV between RCMs and GCMs results from the lateral boundary conditions imposed on the RCMs.
Values of relative differences in 
Similarities between the different configurations of the CRCM (domain and spectral nudging) can be found when comparing the relative magnitudes of basin IV, as shown in Tables 2 and 3. Generally, values of IV measured as relative differences in 
Summary of the analysis of CRCM’s internal variability of hydrological variables at the basin scale, comparing simulations with and without spectral nudging. Values were derived from all 21 basins’ IV values for the ERA-40-driven twin simulations. Values of 
It must be noted that the distance of the watersheds from the inflow boundary of the RCM domain has an influence on the amplitude of IV. As shown by Lucas-Picher et al. (2008), the IV in RCM simulations without spectral nudging has its minimum value near the inflow boundary and increases as the weather systems travel toward the outflow boundary. Therefore, the values of IV presented above for the Quebec watersheds, located in the northeast of North America are probably close to the area of maximum IV in the NA domain (Fig. 1).
b. Analysis of correlation and variation
To determine the year-to-year agreement of CRCM twin simulations, the correlation coefficients (R2) of the 30-yr time series were analyzed. Just as the centered RMSD and the difference between 30-yr climate means of simulations, correlation coefficients also show different characteristics depending on the domain configuration and the way the boundary conditions are applied to the CRCM. The ranges of R2 are provided in Table 2 for the simulations over different domains and in Table 3 for the simulations with and without spectral nudging. From Table 2, we see that for the small QC domain of twin runs R2 is rarely lower than 0.97, indicating almost identical annual evolution of annual basin means of atmospheric and land surface components of the water cycle. Over the larger NA domain, the larger IV in atmospheric flow reduces the coefficients of determination to a range starting as low as 0.2 but commonly reaching values between 0.6 and 0.9. Thus, the greater freedom over the larger domain can result in uncorrelated time series for some basins as well as highly correlated annual statistics for others—a fact related to the above discussion of Fig. 3. When spectral nudging is deactivated, the values of the coefficient of determination are commonly much lower at around 0.2 and rarely exceed 0.5 (Table 3). Thus, without spectral nudging, the annual time series of twin simulations cannot be expected to be correlated at the watershed scale.
In a second step, the differences in the interannual variability of the hydrologic variables in the twin experiments were investigated. The coefficient of variation was used in order to assess the differences in the annual fluctuations of the variables. The nature of the coefficient of variation (CV) allows for the intercomparison of variables with different means so that results from different variables and domains can be compared. The values of the differences of CV (CVdiff) from the twin simulations are shown for the NA domain on the ordinates in Fig. 6. The range of CVdiff is the largest for runoff and SWE. The large interannual variability of runoff can be attributed to its dependence on the variability of precipitation and evapotranspiration. The large range of the variability of maximum SWE is due to outlier basins in the future climate simulation. A range of ±0.04 will encompass most values for runoff and SWE, while the threshold is smaller for precipitation at ±0.02 and smallest for evapotranspiration at ±0.01. This smaller internal variability for evapotranspiration again is attributable to the stronger constraining influence of the land surface scheme driving the process.
Absolute differences 
Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-051.1
In the ERA-40-driven twin simulations performed without spectral nudging, we find that CVdiff is larger than in the twin pair with spectral nudging (Table 3). However, CVdiff in the nonnudged ERA-40-driven simulation (Table 3) is within the ranges of CVdiff derived from all twins with spectral nudging (Table 2), including the global climate model–forced simulations. This indicates a rather weak influence of the spectral nudging on the interannual variance in the simulations. The graphs for the QC domain exhibit similar behavior in their values of CVdiff but about one order of magnitude smaller than over the NA domain (not shown). Just as for the relative differences in 
In the investigation of the differences in the twin pairs of CRCM simulations, the relation of the variances of the time series was also addressed. The results for the NA domain show that in the comparison of variances for a given watershed, the variance of one twin can be up to twice as large as the other’s. Common values for this relation, however, range between almost equal variance of twin members 
c. Analysis of extreme values
Extremes in hydrology are of particular interest in the attempts to assess the future changes of climate and their impacts on watershed management. Therefore, the internal variability in the highest and lowest annual values observed in the hydroclimatic variables modeled by CRCM is of major interest. To address this issue, the 10% and 90% quantiles (Q10 and Q90) were taken from the 30 annual basin values and analyzed in a similar fashion as the mean values. The resulting relative differences of Q10 and Q90 in the twin simulations over the NA domain are shown in Fig. 7. For both annual extremes, internal variability is more pronounced than for the overall means shown in Fig. 4. Maximal relative differences of 8%–10% are found for a small number of the studied basins. The majority of basins deviate by less than about ±5% in precipitation and evapotranspiration, and by less than about ±8% in runoff and maximum snow water equivalent (see Tables 2 and 3 for a summary of full ranges). In the extremes of maximum snow, some values exceed this upper boundary and exhibit values up to 15% in terms of relative difference. In absolute terms, the factor of increase of IV in the extreme values, compared to IV in the means, is raised to about 3–5, depending on the variable addressed (see Table 2). As in all previous analyses, internal variability of Q10 and Q90 for the NA domain is larger than for the QC domain, where relative differences range around ±3%. The results give some indication that for precipitation and runoff, the increase of internal variability from the small QC domain to the large NA domain runs is larger for the Q90 (a factor of about 5) than for the Q10 (a factor of about 3). This relation is increased up to a factor of 10 for the extremes of maximum snow water equivalent (Table 2).
Relative differences of the quantiles Q10 and Q90 (%) from 3 twin CRCM simulations (colors) for 21 basins over the NA domain; panels as in Fig. 6.
Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-051.1
In summary, relative IV in Q10 and Q90 compared to the IV of the means is roughly doubled over the NA domain and tripled over the QC domain. In the simulations without spectral nudging over the NA domain, the IV in the extreme values is also roughly twice as large as the IV in the mean values (Table 3). Thus, the use of spectral nudging leaves the relation of the IV in means and extreme values unaffected, while the change of domain size has an impact on the relation between extremes of IV and means of IV.
4. Discussion
The plots of Figs. 4–7 show the results from the CRCM simulations using three different driving data on two different domains analyzed for 21 watersheds. For the NA domain, the clusters of points describing various measures of IV from a variety of CRCM simulations overlap largely (i.e., the symbols on the figures show little grouping by color), spanning quite similar ranges of values for reanalysis- and GCM-driven simulations for both current and future climates. To determine the significance of the differences between the clusters (i.e., differencing the groups of points of the same color) it would be necessary to apply statistical tests to the data. This, however, is particularly difficult for our data since the 21 values were collected from differently sized samples (based on the watershed size) and furthermore they are spatially correlated. This may lead to erroneous results from statistical tests (Wilks 2006). We therefore must rely on the interpretation of the information presented above. Some differences and particularities in the scatterplots that require special attention are discussed below.
Outlier points belonging to adjacent or close by watersheds suggest a geographical and/or simulation dependence of IV. Examples are the basins exhibiting some of the largest values of relative centered RMSD in annual runoff (Fig. 4b). They belong to the NA-CGCM3#4 present simulation (red) and are all located in the far north of Quebec (ARN, BAL, PYR, MEL, and FEU; for 3-letter basin codes see Fig. 2). Note that the upper-end outliers of the same simulation on the QC domain also belong to that same group (red dots in Fig. 4b, unlabeled). What unites these basins is the low mean runoff in the region (the denominator in 
Another example of outlier points is the four eastern watersheds (ROM, MOI, NAT, and CHU) in Figs. 4d and 6d that exhibit quite pronounced differences in their coefficients of variation in the annual daily maximum SWE, along with large differences in their means. These high values for the four basins belong to the CGCM3#4-A2 future simulation (green) based on the A2 greenhouse gas emissions scenario. This might suggest that these outliers are related to specific conditions in the future simulation that would enhance internal variability. However, 
In Fig. 8, the relation of IV to the size of the basins is shown for precipitation in the simulations over the North American domain (Figs. 8a,b) and the Quebec domain (Figs. 8c,d). As can be seen from the graphs, the IV tends to be lower for larger basins where more CRCM grid cells were used in the calculation in both the (positive) absolute difference of means 
Assessment of internal variability of precipitation (mm day−1) from twin simulations for 21 basins over the (a),(b) NA and (c),(d) QC domain compared to the number of CRCM gridpoint samples used per basin: (a) Absolute differences 
Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-051.1
In general, Fig. 8 suggests that large values of IV tend to occur on small basins. Over a small basin not only the smaller sample may increase the differences between the twins but a small shift in the transient eddies may also arbitrarily relocate mean precipitation to or away from the basins, meaning that they are more likely to be dominated by grid cells with the same sign in the patchy spatial pattern of IV. Therefore the spatial clustering of larger IV in the northern, southeastern, or western part of the study area cannot be attributed to geographical location but to groups of basins with a small sample size (see Fig. 2). The differences in the IV estimates obtained from the three simulations per basin vary greatly. The range of these differences may be larger for a large basin than for a small basin (e.g., CHU and RDO in Fig. 8a) and vice versa (e.g., ARN and BOM in Fig. 8c). At the same time, a large basin may yield higher IV than a smaller basin (e.g., ARN and CHU in red in Fig. 8b). This puts in perspective the results from Vanvyve et al. (2008), who concluded that IV and region size are inversely proportional. The results for other variables are similarly ambiguous in regard of a dependency on time period and on the nature of the driving data.
In their assessment of IV in 1-yr simulations, Giorgi and Bi (2000) and Rinke et al. (2004) both concluded that RCM IV is insensitive to the kind and magnitude of perturbations in the lateral boundary conditions. From the analysis of our 30-yr simulations, no clear dependency of IV on LBC in terms of time period (past versus future climate) and source of driving data (reanalysis versus GCM climate simulation) can be found. This suggests independence of IV from climate change. Although we see some differences between the results from our twin experiments (more so in E′ than in 
The uncertainty level in climate change (CC) signal detection due to CRCM internal variability is illustrated in Fig. 9 for annual precipitation, runoff, and maximum snow water equivalent. For the 21 basins, the CC signal was computed as the difference between the corresponding future (CGCM3#4-A2; simulations adk and aec) and present (CGCM3#4; simulations adj and aeb) 30-yr time periods of the twin experiments (Table 1). The CC signal differences between twins are generally small (distance from 1:1 line), while the differences between basins are more substantial. Even if good agreement of two assessments increases the confidence in the CC signal, this does not confirm a clear CC signal. In Fig. 9, the blue square box, centered at (0, 0), indicates the range of uncertainty for each variable. The range is computed as 
Mean climate change signal from NA domain simulations for 21 basins computed from the reference period (1961–90) and the future period (2041–70 A2) for (a) annual precipitation (mm day−1), (b) annual runoff (mm day−1), and (c) annual maximum SWE (mm). Results from two twin simulations are compared (adk–adj and aec–aeb). Ranges of internal variability for the basins are indicated for each variable by the blue box centered at (0, 0).
Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-051.1
The above examples demonstrate how IV and its assessment for individual variables play an important role in the interpretation of a CC signal projected by RCM simulations. In practice, the assessment of the uncertainty of a climate change signal would also need to take into account the natural variability of the climate system. In that case, boxes similar to those in Fig. 9 would need to be derived from GCM’s IV. To do this at the regional scale, multiple members from a global model ensemble would need to be downscaled in RCM simulations. The variability between the downscaled members, however, would be a combination of the driving GCM’s and the RCM’s IV. To isolate the natural variability as the irreducible uncertainty in the climate change signal, the RCM’s IV needs to be removed from the combined variability. Thus, although the IV of the GCM is dominating the variability in climate simulations, the RCM’s internal variability still needs to be assessed and cannot be neglected.
Regional climate models are often run using reanalysis data as their lateral boundary conditions. Such simulations are used in the validation of the models to conduct sensitivity experiments or as intelligent interpolations to produce “perfect” regional 4D climate observation series. In this case, the RCM represents the single source of internal variability. Leaving aside the errors in the production of reanalysis datasets and in climate variable measurements, the IV of the RCM is an irreducible source of uncertainty and must be addressed and quantified as such. The like applies to the model’s sensitivity to changes in the model or the parameterization. Its significance can only be determined when the internal variability of the RCM is known.
5. Conclusions
The impact of internal variability on hydroclimatic variables was investigated with pairs of simulations (twins) performed with the Canadian Regional Climate Model (CRCM) at a 45-km resolution. The twin simulations differ only by an offset of one month in the starting date of the integrations in order to trigger internal variability (IV). The data of twin 30-yr simulations over the 1961–90 and 2041–70 periods were analyzed for 21 watersheds in Quebec and Labrador. IV was studied with simulations performed over two domains: the larger covers North America (NA) while the smaller covers Québec and eastern Canada (QC). Since the standard configuration of the CRCM uses a weak spectral nudging, results were also compared to a pair of twin simulations without spectral nudging. Internal variability was assessed from time series of annual values of precipitation, runoff, evapotranspiration, and the annual daily maximum snow water equivalent (SWE) on the ground by comparing time–spatial averages over each of the 21 watersheds.
The experiment reinforced the notion from earlier studies that internal variability is sensitive to the location of the analyzed region with respect to the external forcing at the inflow boundary of the RCM through the choice of domain size and location. For all variables examined, smaller basin IV is found in simulations over smaller domains. It is worth noting that the small domain resembles the extent of the domains used in European RCM projects (ENSEMBLES and PRUDENCE) while the large domain is similar to the extent of North American projects domains (NARCCAP) and most of the CORDEX domains (Giorgi et al. 2009). Basin internal variability from the large North American domain runs is approximately one order of magnitude larger than from the smaller Quebec domain. The smaller IV is linked to higher temporal correlation of twin runs in the smaller domain.
Absolute values of IV for the larger NA domain are smallest for evapotranspiration, intermediate for precipitation and runoff, and largest for annual maximum SWE. In relative terms, the highest IV was observed for runoff over the large domain with very similar ranges of relative IV for SWE. Ranges of relative IV are similar in magnitude for precipitation and evapotranspiration, but about half as large as those for runoff and SWE. These relative magnitudes amongst the variables are quite stable across our two domains and in the simulations with and without spectral nudging. We therefore conclude that they can be expected to be similar for other RCMs and domains. In both simulation domains, internal variability in extreme annual values (Q10 and Q90) is larger than in the mean values by a factor of 2–5. The internal variability of the investigated 21 watersheds (representing a relatively small region within the domain) was found to be unaffected by the geographical location of the basins. However, the size of the watershed has an impact on IV. Although IV for a large watershed may occasionally be much larger than the one for a small basin, larger IV was found more frequently for the smaller watersheds.
The weak spectral nudging routinely applied in the CRCM has a profound impact on simulations made over a large domain such as the one covering NA. When the weak spectral nudging is not applied in twin runs over NA, the range of relative basin IV of all four studied variables almost doubles to reach values close to the ranges obtained between two CRCM simulations driven by two different members of the CGCM3. This means that when spectral nudging is not activated over the NA domain, the CRCM’s IV reaches values close to the natural variability of the climate system (excluding the variability because of external forcings such as solar cycles and volcanoes). IV close to the natural variability strongly impairs the ability of a reanalysis-driven regional model to reproduce the observed year-to-year chronology. This conclusion is supported by the important reduction in the coefficient of determination from the spectrally nudged twins (~0.6) to the nonnudged twins (~0.2). Therefore, reanalysis-driven RCM simulations without a form of spectral nudging cannot be expected to reproduce the observed sequence of weather events nor the extremes observed during the simulated period. This inability is a consequence of internal variability alone, leaving aside model imperfections. The validation of such simulations should be limited to comparing climate statistics in a similar way that GCMs are validated. Similar behavior can be expected for other large domains dominated by large-scale inflow and outflow as the NA domain used in this study. It might even lead to unstable situations at the outflow boundary if the RCM generates features too different from those of the driving model.
From the analysis of CRCM’s internal variability it can be concluded that the uncertainty produced by internal variability in 30-yr climate simulations over large domains cannot be neglected in validation of model results. This was found despite the fact that internal variability decreases with length of the integration. Even with the use of spectral nudging, the intrinsic noise of the model at the watershed scale reaches 5% for the 30-yr mean and up to 15% for the extreme annual values (Q10 and Q90). This is critical information when assessing the model’s skill by comparing simulations to real-world climate observations. It is also important to be aware of the model’s level of IV when addressing the sensitivity of the model to changes in configuration and to external forcing.
Therefore, the assessment of RCM internal variability is also required in the analysis of a regional climate change signal. The dynamical downscaling of GCM climate simulations with an RCM is performed in a model chain that yields uncertainties due to internal variability from both the driving GCM simulation and that of the integration with the driven RCM. Although the magnitude of the GCM’s internal variability generally surpasses that of the RCM, the RCM’s internal variability must not be neglected since it can locally be larger than the CC signal. This is especially true when RCMs are used over large domains without nudging of large-scale circulation. In climate change studies, multiple members of a GCM simulation ensemble are usually employed to address the uncertainty from the natural variability of the climate system, where a GCM’s IV is used as a surrogate to evaluate that uncertainty. When these members are downscaled with an RCM, the regionalized results are affected by the sum of the driving GCM’s IV and the RCM’s own IV. This means that the uncertainty from natural variability can only be isolated if the RCM’s IV is known. Consequently, sound regional climate change assessment must factor in the internal variability of both models, driving GCM and driven RCM.
Our analysis of seven twins of CRCM simulations showed no systematic dependency of IV on the integration horizon (current versus future climate) or on the driving data (reanalysis driven versus GCM driven). However, a clear dependency on model configuration in terms of domain and spectral nudging was found. We conclude that in order to assess the IV of a given RCM configuration, the time- and resource-consuming effort of our approach of producing multiple pairs of 30-yr simulations can be greatly reduced. Our experiment of sampling 21 watersheds for hydrological studies in Quebec proved adequate to obtain useful estimates of the model’s noise contained in the climatologic values of regional hydrometeorological variables. When comparing different model configurations, the differences in the order of magnitude of IV in annual climate means was clearly detectable, while the repetition of the twin experiment over the same domain with alternate boundary conditions revealed only small changes in results. Thus, a reasonable estimate of the IV for a particular RCM configuration can be obtained from a single pair (or triplet) of 30-yr simulations with perturbed initial conditions. This requires only the effort of one (or two) additional simulation to create a twin instead of the five additional simulations per domain that were analyzed for this study. However, in our approach of increasing the sample size by looking at actual watersheds of different extent, the number of CRCM grid cells averaged per basin showed to have an important impact on the basin-scale IV. Therefore, in the application of regional climate simulation in climate change impact studies the size of sites should be accounted for. Similar to our watershed-based experiment, this could be achieved by analyzing a number of arbitrary samples of a size comparable to that of the target area in order to derive the IV at that scale.
The presented results are valid for our midlatitude domains with strong inflow and outflow in the northern westerlies. Comparing simulations with and without spectral nudging showed the effect of that technology on a large domain. Different models, configurations, and domains can be expected to require the investigation of the specific IV in the RCM’s simulations. Unfortunately, to date, the various publications that study RCM internal variability allow for little direct comparison of results from different models. The differences of the studies appear mainly in the lengths of the simulations analyzed, the statistics used to measure IV, and the time frame to which they are applied. Although some comparative studies exist, the intermodel differences or similarities in internal variability remain to be explored. Particularly, we find that the IV in nonnudged simulations performed over large domains can reach amplitudes comparable to natural climate variability. This high level of IV in an RCM without spectral nudging may lead to false assumptions about the intrinsic part of natural climate variability when different members of a GCM experiment are dynamically downscaled. The IV of the RCM itself needs to be removed from the variability introduced by the use of driving data from different GCM members.
Finally, the low correlation between the time series of annual means from a pair of RCM twin simulations without spectral nudging over large domains strongly limits the use of the RCM as an intelligent interpolator. Because of this large IV, a validation of the reanalysis-driven runs without spectral nudging may be hard to accomplish. This of course can be different for watersheds closer to the inflow boundary of the RCM and will be investigated in future work.
Acknowledgments
The authors thank Dr. Biljana Musíc for her generously devoted effort put into the processing of the tremendous amounts of original CRCM model output into manageable time series used for the analysis. Her work and support in the production of this manuscript is greatly acknowledged. The comments of three anonymous reviewers helped substantially in improving the manuscript. Their effort and input is greatly appreciated. This work was financially supported by and carried out as part of the research program of the Canadian Network for Regional Climate Modeling and Diagnostics (CRCMD), the Pacific Climate Impacts Consortium (PCIC), and the Ouranos Consortium. The CRCM data has been generated and supplied by the Ouranos Climate Simulation Team; we also thank the Canadian Center for Climate Modelling and Analysis (CCCma) for kindly providing the CGCM3 archives. ECMWF ERA-40 data used in this study have been provided by ECMWF.
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