The impact of lateral boundary data errors on the simulated ... - UQAM

Clim Dyn (2007) 28:333–350 DOI 10.1007/s00382-006-0189-6

The impact of lateral boundary data errors on the simulated climate of a nested regional climate model Emilia Paula Diaconescu Æ Rene´ Laprise Æ Laxmi Sushama

Received: 11 November 2005 / Accepted: 16 August 2006 / Published online: 27 October 2006 Springer-Verlag 2006

Abstract In this study, we investigate the response of a Regional Climate Model (RCM) to errors in the atmospheric data used as lateral boundary conditions (LBCs) using a perfect-model framework nick-named the ‘‘Big-Brother Experiment’’ (BBE). The BBE has been designed to evaluate the errors due to the nesting process excluding other model errors. First, a high-resolution (45 km) RCM simulation is made over a large domain. This simulation, called the Perfect Big Brother (PBB), is driven by the National Centres for Environmental Prediction (NCEP) reanalyses; it serves as reference virtual-reality climate to which other RCM runs will be compared. Next, errors of adjustable magnitude are introduced by performing RCM simulations with increasingly larger domains at lower horizontal resolution (90 km mesh). Such simulations with errors typical of today’s Coupled General Circulation Models (CGCM) are called the Imperfect Big-Brother (IBB) simulations. After removing small scales in order to achieve low-resolution typical of today’s CGCMs, they are used as LBCs for driving smaller domain high-resolution RCM runs; these small-domain high-resolution simulations are called Little-Brother (LB) simulations. The difference between the climate statistics of the IBB and those of PBB simulations mimic errors of the driving model. The comparison of climate statistics of the LB to those of the PBB provides an estimate of the errors resulting solely from nesting

E. P. Diaconescu (&) R. Laprise L. Sushama De´partement des Sciences de la Terre et de l’Atmosphe`re, UQAM - Ouranos, 550, rue Sherbrooke Ouest, 19e e´tage, Tour Ouest, Montreál, QC, Canada H3A 1B9 e-mail: [email protected]

with imperfect LBCs. The simulations are performed over the East Coast of North America using the Canadian RCM, for five consecutive February months (from 1990 to 1994). It is found that the errors contained in the large scales of the IBB driving data are transmitted to and reproduced with little changes by the LB. In general, the LB restores a great part of the IBB small-scale errors, even if they do not take part in the nesting process. The small scales are seen to improve slightly in regions with important orographic forcing due to the finer resolution of the RCM. However, when the large scales of the driving model have errors, the small scales developed by the LB have errors as well, suggesting that the large scales precondition the small scales. In order to obtain correct small scales, it is necessary to provide the accurate large-scale circulation at the lateral boundary of the RCM.

1 Introduction The primary tools to study anticipated climate changes are coupled global and nested regional climate models (RCM). Coupled General Circulation Models (CGCMs) provide a global-scale view of projected climate at typically coarse horizontal mesh (grid spacing between 250 and 600 km) and hence cannot be used directly by most impact studies that require grid scales of 10–100 km or finer. Information at regional scales can be simulated with limited-area, high-resolution RCMs driven by the large-scale information from a CGCM. Compared to CGCM, the RCM’s finer

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resolution enables improved representation of the surface forcings such as topography, coastlines, inland water and land-surface characteristics as well as permitting to resolve small-scale processes. Several earlier studies have investigated the ability of nested RCMs to accurately simulate fine-scale climate features when driven only by large-scale information. Jones et al. (1995) showed that the RCM-simulated large-scale atmospheric circulation, in general, follows that of the driving General Circulation Model (GCM). Therefore, it is the large-scale aspects of the driving GCM that are the controls of RCM circulation, suggesting that circulation errors in the RCM are the result of propagation of the GCM errors from the RCM boundaries to the interior of the domain. Noguer et al. (1998) estimated the contribution of the driving GCM circulation and the internal RCM physics to the total RCM errors; they compared an RCM simulation driven by a standard GCM with another RCM simulation driven by a GCM that was relaxed towards a time series of operational analyses using a data-assimilation technique. The errors in the first simulation can be due to internal RCM physics or from errors in the driving data, while the errors in the second simulation are entirely due to the internal RCM physics and not from the driving circulation. Their results indicate that the errors in the RCM-simulated mean sea level pressure (mslp) were almost entirely due to the driving data. However, the surface air temperature and precipitation over western and central Europe, for the summer season, were more influenced by the RCM internal physics than by the errors in the driving data. In a similar comparison between Canadian RCM (CRCM) simulations driven by the NCEP reanalyses and by the secondgeneration Canadian General Circulation Model (CGCM2), de Elıá et al. (personal communication, October 2005) concluded that, during summer, CRCM is only weakly dependent on the driving fields, while during winter large differences were found between the temperature fields of the two CRCM simulations, suggesting that the driving fields have a greater influence on the CRCM simulation in this season. Denis et al. (2002b) designed an experimental framework, called the Big-Brother Experiment (BBE), to validate the downscaling ability of a one-way nested RCM. This experimental framework was constructed to address the uncertainties regarding the ability of the RCM to reproduce accurate fine-scale features; this is an important issue that has been raised in the reports of the Working Group on Numerical Experimentation (WGNE) of the World Climate Research Programme (WCRP)(CAS WGNE 1998, 1999). Using the BBE framework, Denis et al. (2002b, 2003), Antic et al.

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E. P. Diaconescu et al.: Impact of lateral boundary data errors

(2004) and Dimitrijevic and Laprise (2005) showed that an RCM is able to reproduce well the small-scale climate statistics for the winter and summer seasons over two regions with widely different orographic forcing, the East and West Coast of North America. They found that a nested RCM has a remarkable skill in capturing small-scale processes over regions where local surface forcing is important. The BBE framework was used also by Herceg et al. (2006) to evaluate the downscaling ability of NCEP Regional Spectral Model, for a tropical region in April and a mid-latitude region in February. Their study showed that the dynamical downscaling is much more demanding in the presence of physics dominance, such as moist convection. In the above studies, the BBE provided so-called perfect lateral boundary data for driving the RCM. However, to make climate-change projections, an RCM must be driven by CGCM-simulated data that are not perfect. They contain errors due to model imperfections such as inability to accurately represent fine-scale topography and eddy processes, imperfection in capturing internal variability and difficulty in parameterizing subgrid-scale processes. According to Duffy et al. (2003), the coarse resolution of CGCMs even has an impact on the quality of the large-scale solution. Risbey and Stone (1996), while validating the National Centre for Atmospheric Research Community Climate Model (NCAR CCM) simulations, noted major differences in the mean and interannual variations of the stationary waves, jet streams and storm tracks in the North Pacific–North American region, features that are important in defining the fluxes across RCM lateral boundary; hence these errors could bias the results of nested RCM over North America. The studies presented above suggest the necessity for a detailed investigation of the sensitivity of RCM to the driving data errors. This paper is an extension of the previous studies using the BBE protocol with the aim of evaluating the impact of errors in the lateral boundary conditions (LBC) on the simulated fields of the CRCM. The BBE framework allows to isolate the RCM errors due to the imperfect driving data, independently from the errors due to the rest of the model formulation. By studying the RCM response to varying magnitude LBC errors should help identify the maximum allowable error in the driving data that will produce a tolerable error in the RCM-simulated climate. The paper is organized as follows: Modelling and diagnostics methods section describes the RCM formulation, the experimental configuration and the statistical tools. In Results section, the impact of errors in the LBC on the RCM-simulated precipitation rate, mslp and 850-hPa temperature fields are presented.


The paper ends with a discussion of the results and conclusions in Discussions and conclusions section.

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2.2 Experimental design and configuration 2.2.1 The Big-Brother Experiment

2 Modelling and diagnostics methods 2.1 Model description The model used in this study is the Version 3.6.1 of the CRCM (Laprise et al. 1998; Caya and Laprise 1999). CRCM is a limited-area nested model, based on the fully elastic non-hydrostatic equations solved by a semiimplicit, semi-Lagrangian, three-time level marching scheme (Bergeron et al. 1994; Laprise et al. 1997). LBC are implemented following the one-way nesting method of Davies (1976) (see also Robert and Yakimiw 1986; Yakimiw and Robert 1990). The CRCM is forced at the lateral boundary of the domain by the following driving fields: horizontal velocity, temperature, geopotential height, surface pressure and specific humidity. There is also a buffer zone of nine grid-points near the lateral boundary called the sponge zone, where the CRCMsimulated horizontal winds are relaxed towards the values of the driving data, with a strength varying as a cosine square of the distance from the boundary. The driving data are timely, horizontally and vertically interpolated to the CRCM time step and spatial grid. The simulations used 18 unequally spaced Gal-Chen (Gal-Chen and Sommerville 1975) levels in the vertical. The lowest thermodynamic level was about 110 m above the surface and the rigid lid was located near 29 km. The Big-Brother (BB) model lateral boundaries were defined by interpolating six-hourly pressure-level fields on a 2.5 by 2.5 grid of the NCEP reanalyses (Kalnay et al. 1996). The BB-simulated fields were then interpolated on a non-staggered grid on pressure levels archived at 6-h intervals. The initial conditions (IC) for the land surface (ground temperature, snow depth, solid and liquid soil water fractions) were taken from a monthly mean climatology data-base, and the sea surface temperatures (SST) and the sea-ice cover were prescribed from the Atmospheric Model Intercomparison Project (AMIP) monthly data (Fiorino 1997). The lower boundary conditions over land are only specified at initial time and they evolve during the simulation according to the model formulation for land-surface processes. Owing to the simple bucket land-surface scheme (i.e. with moisture and thermal regime represented through a single-layer scheme) used in CRCM, a 5-day spin-up period was found sufficient for the system to attain a reasonable equilibrium between lateral boundary and internal model forcings; the spin-up period is left out of the analysis.

The BBE framework developed by Denis et al. (2002b) used in this study is briefly summarized here. A highresolution large-domain RCM simulation, driven by the NCEP reanalyses, serves as the reference climate: the Perfect Big Brother (PBB). The large scales of the PBB are then used to drive the same RCM, integrated at the same high resolution but over a smaller domain centred in the PBB domain: the Little Brother (LB). Since the two models (PBB and LB) have the same resolution and use the same approximations, the differences between the two simulations represent the errors due to the nesting process. Denis et al. (2002b, 2003), de Elıá et al. (2002), Antic et al. (2004) and Dimitrijevic and Laprise (2005) used this approach where the large-scale data for driving the LB simulation came from a reference run after filtering the small scales, which represent ‘‘perfect’’ large-scale driving data. 2.2.2 Generation of ‘‘Imperfect’’ lateral boundary conditions Rather than adding arbitrary and potentially unphysical or dynamically unbalanced errors to the LBCs, the BBE framework is expanded here in order to generate realistic errors of controllable magnitude in LBCs. In this study, in addition to driving the LB with ‘‘perfect’’ BB driving data as in earlier BBEs, the LB is also driven by a set of BB simulations performed at lower resolution over increasingly larger domains in order to mimic some of the typical CGCM errors. As the domain size increases, the lateral boundaries exert less constraint on the RCM solution, which may then diverge from its reference solution. Thus, the use of lower horizontal resolution permits to mimic the CGCM inability to accurately represent fine-scale topography, making it more challenging to parameterize the subgrid-scale processes. This setup permits to obtain a set of driving data that contain different levels of errors: these simulations are named the Imperfect Big Brother (IBB). After filtering of the small scales, the resulting large scales are used to drive a set of LB simulations at high resolution (45-km grid size) over a smaller domain centred on the BB domain. Thus, the PBB provides the reference virtual climate, the IBB provides a set of imperfect LBCs data for driving, and the LB simulations are driven by perfect and imperfect LBCs. The schematic of the adopted simulation framework is shown in Fig. 1. The comparison between the statistics of the IBB climate and that of

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Fig. 1 Flowchart of the Imperfect Big-Brother experimental protocol. The initial conditions (IC) and lateral boundary conditions (LBC) for driving the large-domain Big Brother (BB) are obtained from NCEP reanalyses, while those for driving small-domain Little Brother (LB) are obtained by removing the small scales of the BB simulations. Climate diagnostics are calculated over the LB domain, excluding the lateral sponge zone

the PBB climate will highlight the LBC data errors, and the comparison between the statistics of the IBB-driven LB and PBB climates will inform on the errors of the RCM due to its driving with imperfect LBCs. 2.2.3 The experimental configuration The PBB operates on a large domain of 194 · 194 grid points, with a 45-km horizontal grid mesh true at 60, covering eastern North America and part of the Atlantic Ocean. IBB simulations are performed on a 90-km horizontal grid mesh over three larger domains (106 · 106, 150 · 150 and 194 · 194 grid points); these three simulations will be referred to as IBB1, IBB2 and IBB3, respectively. The LB simulations driven by the PBB and IBB simulations were performed with a 45km grid-size mesh, on a 100 · 100 grid-point computational domain centred in the PBB domain. Figure 2 presents the domains and topography used for the simulations and Table 1 summarizes the parameters of the simulations. The simulations were performed for five February months from 1990 to 1994. Each BB experiment was initialized at 00:00 UTC 22 January ending 28 February. Each LB experiment was initialized at 00:00 UTC 27 January ending 28 February. The 5-day difference in the initialization time is used as spin-up period; the analysis period is from 1 to 28 February. In order to retain only the large scales in the BB simulation, a low-pass filter is applied to remove disturbances with length scales smaller than 1,225 km and

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Fig. 2 The computational domains used for the simulations of Perfect Big Brother (PBB), Imperfect Big Brothers (IBB1, IBB2 and IBB3), and Little Brother (LB). Topographic height is also shown for the LB domain

leave unaffected those greater than 2,250 km. The filter is performed using a 2-D Discrete Cosine Transform (DCT); this filtering technique is suitable for nonperiodic data as described by Denis et al. (2002a). 2.3 Statistical analysis tools To facilitate calculation, display and intercomparison between the fields, the simulations are interpolated onto a common 45-km grid mesh 100 · 100 polar stereographic grid. The purpose of the analysis is to evaluate the impact of large-scale errors in the IBB simulations on the LB-simulated climate over the common domain, excluding the sponge zone. A spatial decomposition is applied to separate fields (u1) into their large-scale (uls) and small-scale (uss) components using the same DCT filter mentioned in the previous section: u ¼ uls þ uss :

ð1Þ

A temporal decomposition of fields is also performed to separate stationary ðuÞ and transient (u¢) components: Table 1 Description of the simulations performed and analysed in this paper Characteristics simulations

Horizontal grid spacing (km)

Domain size (km2)

Number of grid points

LB PBB IBB1 IBB2 IBB3

45 45 90 90 90

4,500 · 4,500 8,730 · 8,730 9,540 · 9,540 13,500 · 13,500 17,460 · 17,460

100 194 106 150 194

· · · · ·

100 194 106 150 194


uls ¼ uls þ u0ls ;

ð2Þ

uss ¼ uss þ u0ss :

ð3Þ

The overbar represents the time mean over the five February months, which defines the stationary part of a field. The prime denotes the time deviation thereof and is related to the transient component of a field, including the inter-annual and the intra-monthly variability. The spatial correlation coefficient RXY and the ratio of spatial variances (G*) are used to quantify the IBB-PBB and LB-PBB differences in the stationary components of the fields: X X Y Y RXY ¼ ; ð4Þ rX rY 2 2 E 2 D rX C ¼ ¼ X X ; 2 ; rX rY 2 E 2 D ¼ Y Y rY ;

ð5Þ

where X is the stationary components of the large- or small-scale components of the IBB/LB field, Y is the stationary components of the large- or small-scale 2 components is the spatial variance 2 of PBB field, rX of X; rY is the spatial variance of Y; and the angular brackets represent the horizontal average over the LB domain excluding the nesting zone. The spatial variance normalized with respect to PBB spatial variance (G*) reflects the differences in the amplitude of the spatial variations of the fields, while the spatial correlation coefficient describes how well the pattern of the field is reproduced. The differences between the transient components of IBB/LB and PBBare quantified by the spatial correlation coefficients RIBB; PBB ; RLB; PBB between the

transient-eddy standarddeviation offfi the large- and qffiffiffiffiffiffiffi qffiffiffiffiffiffi 02 uls ; u02 small-scale components ss of IBB/LB and PBB fields, the ratio of spatially averaged temporal hr02X i 0 variances C ¼ r02 of the large- and small-scales h Yi components of IBB/LB (X) and PBB (Y) fields and an equivalent temporal correlation coefficient: D E X 0Y 0 ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi R0e ð6Þ XY ¼ rD ErD Effi : 02 02 X Y These various errors relative to the PBB reference field can be combined using Taylor diagrams (Taylor 2001). The Taylor diagram provides a statistical

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comparison between model-simulated and reference fields by plotting, on the same 2-D graph, the mean square difference, the variance and the correlation coefficient, allowing to estimate the part of errors that comes from poor pattern correlation and that from a difference in variance. There are several variants of Taylor diagram (e.g. Boer and Lambert 2001; Taylor 2001; Denis et al. 2002b); in this study we use the version best adapted to an RCM study, which permits separate analysis of the stationary and transient components of a field (Denis et al. 2002b). Thus, for both large- and small-scale components of the field, two Taylor diagrams are plotted. One corresponds to the errors of the stationary components of the IBB and LB, relative to the spatial variance of the stationary component of PBB, with the axes corresponding to the normalized domain-averaged mean square difference of the deviation from the domain mean, the ratio (G*) of the spatial variances of the stationary components, and the corre spatial lation coefficient over the domain RXY between the stationary components of IBB/LB and PBB. The other diagram corresponds to the errors of the transient components of IBB and LB and PBB, relative to the domain-averaged temporal variance of the PBB field, with the axes corresponding to the normalized spatial and time-averaged mean square difference of the time deviations, the ratio (G¢) of domain-averaged transient-eddy variances, and equivalent temporal e correlation coefficient (R¢XY ) between IBB/LB and PBB. By design the PBB fields fall at the origin of the diagram’s axes.

3 Results In this section, the impact of LBC errors on precipitation, mslp and 850-hPa temperature are presented. As mentioned earlier, the analysis is performed over the LB domain excluding the sponge zone, for five February months from 1990 to 1994. 3.1 Precipitation Precipitation is a field that results from several complex physical and dynamical processes in the RCM, and it is not driven at the lateral boundary as dynamical fields such as pressure and temperature are. Figure 3 shows Taylor diagrams for precipitation simulated by the IBB and LB, using the PBB as reference field. The IBB and LB errors are discussed separately in the two subsections that follow.

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3.1.1 Imperfect Big Brothers In the IBB series, the transient components exhibit the largest errors due to very weak temporal correlation. For the stationary large-scale component, the errors are reflected in the smaller spatial correlation coefficients (e.g. RXY ¼ 89% for IBB2) and differences in spatial variance (e.g. G* = 65% for IBB2). Figure 4a shows that the stationary large-scale precipitation errors in the PBB are characterized by a maximum of precipitation located over the Gulf Stream. Figures 4b–d show that the IBB errors are reflected by differences in amplitude and shifts in the position of the maximum. To verify that such errors are typical of CGCM errors, we have compared them with the precipitation errors of the ensemble of 21 CGCMs used in the fourth Assessment Report of the IPCC (2007). Based on a 20-year average over a region of East North America (25N–50N, 85W–50W), the 5th, 25th, 50th, 75th and 95th percentiles of per cent precipitation errors in winter are established to be – 19, – 3, 17, 25 and 54%, respectively. For IBBs, theper cent precipitation errors IBB PBB PBB averaged over the LB domain, vary from – 14 to +4%, and hence lie well within the distribution of the CGCM errors.

Fig. 3 Taylor diagrams showing the precipitation errors of the PBB and IBB (squares) and LB (circles), for the stationary (left panels) and transient (right panels) parts of the large-scale (top panel) and small-scale (bottom panel) components

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For the stationary small-scale precipitation simulated by the PBB and IBB, Fig. 3c shows the Taylor diagram and Fig. 5 the corresponding precipitation field. In the PBB, the main small-scale maximum over the Atlantic contributes to reinforce the large-scale maximum noted earlier over the Gulf Stream, and makes it narrower by flanking it with negative values on both sides. The PBB shows also three small local maxima of precipitation over the Great Lakes region and another zone of maximum over the Maritimes. The IBB captures well the three elongated extrema over the Atlantic, albeit with slightly different amplitudes and positions. On the other hand the IBB series does a poor job in reproducing the maxima over the Great Lakes and Maritimes, probably due to their coarser resolution. Overall the correlations of IBB with PBB are good (R*IBB/PBB ‡ 73% for all IBB). For the large-scale transient components of precipitation, Fig. 3b shows the Taylor diagram and Figs. 6a – d the standard deviation of transient eddies. For the large scales, the transient eddies standard deviation field, in general, resembles the stationary fields (Figs. 4a, b, c, d). The temporal correlation is rather small, unlike the case in weather forecasting. However, this is not a main concern in climate simu-


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Fig. 4 Stationary large-scale component of precipitation (mm/day) for the PBB and IBBs (left panels) and the LBs (right panels). Spatial correlation coefficients (R*) and ratio of spatial variances (G*) are given in the subtitles for comparing PBB and IBBs, and in the central column for comparing the individual LB with their driving IBB

lations. What matters in climate studies is the variance (a measure of variability) and spatial correlation. For all IBB, R*IBB/PBB ‡ 92% for large-scale transient precipitation. For the small-scale transient component of precipitation, Fig. 3d shows the Taylor diagram and Fig. 7 the corresponding standard deviation fields. It is noteworthy that the pattern of small-scale transient-eddy

standard deviation (Fig. 7) has little in common with the corresponding small-scale stationary pattern (Fig. 5), unlike the case for large scales for which the pattern of transient-eddy standard deviation (Fig. 6) resembled the stationary pattern (Fig. 4); in fact, it resembles more the stationary and transient-eddy large-scale components. The small-scale transient eddies are characterized by a deficit of transient activity,

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Fig. 5 As Fig. 4 but for the stationary small-scale component of precipitation

with G* as low as 53% for IBB2; this is consistent with the reduced resolution of the IBB. The IBB small-scale transient eddies are also characterized by very small temporal correlation with the PBB. As mentioned earlier, the spatial correlation is more relevant in climate studies; for all IBB, R*IBB/PBB ‡ 84% for smallscale transient precipitation.

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3.1.2 Little Brothers Figure 3 also shows the Taylor diagrams for precipitation simulated by the LB driven by the PBB and IBB, using the PBB as reference. In all four components of the statistics, the LB scores follow closely those of the corresponding driving IBBs.


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Fig. 6 Transient-eddy largescale component of precipitation (mm/day) for the PBB and IBBs (left panels) and the LBs (right panels). Spatial correlation coefficients (R*) and ratio of spatial variance of transienteddy standard deviation (G*) are given in the subtitles for comparing PBB and IBBs, and in the central column for comparing the individual LB with their driving IBB

For the large-scale stationary component (Fig. 3a), the LBs have almost the same ratios of spatial variances as the IBBs, but slightly smaller spatial correlation coefficients. Figures 4e–h present the LB-simulated large-scale stationary precipitation fields. The similarity of the LB with the corresponding driving IBB is obvious. The largest differences are located in the southwest corner of the domain where all LBs have

smaller precipitation rate; this corresponds to the region where weather systems enter the domain. Vertical velocity is set to zero at the lateral boundary in CRCM; this results in a delay in the onset of precipitation. The spatial variances of the LB are within 8% of the corresponding IBB ones, and the spatial correlation coefficient R*LB/IBB ‡ 97%. In comparison with the reference PBB, the LB spatial correlations are lower

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Fig. 7 As Fig. 6 but for the transient-eddy small-scale component of precipitation

(R*LB/PBB ‡ 84%) and the differences in spatial variance as large as 35%. Therefore, for the LB domain chosen for this study, most part of the stationary largescale errors of the IBBs are transmitted to and reproduced by the corresponding LBs. For the stationary small scales (Fig. 3c), the LB fields are characterized by spatial correlation coefficients that are similar to the corresponding IBB fields,

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but with a modest increase in the spatial variability as a result of the higher resolution. Figures 5e–h show the stationary small-scale components of the LB precipitation. Over the Atlantic Ocean where small scales are mostly intense, the LB patterns are closer to those of the corresponding IBB than to the PBB reference, irrespective of LBC errors. The spatial correlation coefficients with the driving IBB are larger (R*LB/IBB ‡ 87%)


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than with the reference PBB (R*LB/PBB ‡ 73%). Hence the LB reproduces a great part of the stationary smallscale characteristics of the driving IBB. Over the Great Lakes and the Maritimes, the LBs represent better the small-scale features because of the finer horizontal resolution that permits better representation of the coastline and the orographic features. The correlations between IBB/LB and PBB over this sub-region are presented in Table 2; over this sub-region, the LBs develop a better spatial correlation with the PBB reference than the driving IBB as well as higher ratio of spatial variance; this indicates that the LB corrects some of the IBB errors over this region characterized with important surface forcing. Figure 3b shows the Taylor diagram for the transient large-scale component of precipitation. In general the LBs have similar temporal correlation coefficients to those of the driving IBB, but weaker transient variances. Figures 6e–h show the large-scale transient standard deviation of the LB precipitation. As for the stationary large scales, the precipitation in the southwest region is somewhat weaker than in the driving IBB. The spatial correlation coefficients between the LB and the driving IBB are high (R*LB/IBB ‡ 96%) in all three cases, and closer to the driving IBBs than to the PBB (R*LB/PBB ‡ 85%). Table 3 gives the domainaverage values of temporal correlation coefficients and temporal variance ratios between the LB, their driving IBB, and the PBB. The temporal correlation coeffie cients between LB and IBB are large (R¢LB/IBB ‡ 93%), and the ratios of temporal variances of LB to its driving Table 2 Spatial correlation coefficients (R*) and ratio of spatial variances (G*) for stationary small-scale precipitation, computed for a sub-region covering the Great Lakes and the Maritimes

R* G*

IBB1 (%)

LB1 (%)

IBB2 (%)

LB2 (%)

IBB3 (%)

LB3 (%)

63 43

65 71

43 59

55 69

59 46

78 77

Table 3 Temporal correlation coefficients (R¢ e) and ratio of transient-eddy variances (G¢) for the transient large-scale components of precipitation, 850-hPa temperature and mslp

IBBx stands for IBB1, IBB2 and IBB3 and LBx for LB1, LB2 and LB3

e 81%). This suggests IBB are nearly constant (G¢LB/IBB that the LBs reproduce with fidelity the large-scale transient activity of their driving IBB, with some reduction in the temporal variance due to the spin-up in the inflow region. Figure 3d shows the Taylor diagram for the smallscale transient component of precipitation. The LBs’ skill is similar as their driving IBB. Figure 7e–h show the small-scale transient standard deviation of the LB. The overall pattern of the LBs resembles those of its driving IBBs, with two noticeable differences. One is that the LB simulates stronger maximum values of small-scale transient eddies than their driving IBB; this is due to the finer LB horizontal resolution. The second is that the LB variability is underestimated in the southwest part of the domain, corresponding to the main inflow region, as discussed earlier. These two effects appear to almost cancel one another, so that the LB and IBB domain-averaged temporal variabilities are very similar. The spatial correlations between the LB and IBB are very similar (R*LB/IBB ‡ 91%), reflecting the same mean preferred location for smallscale transient activity. Table 4 presents the equivalent temporal correlation coefficients between the LB, their driving IBB and the PBB. While the LB exhibits very small temporal correlations with the PBB, the temporal correlations with their driving IBB are much larger e (R¢LB/IBB > 56%). This suggests that LBCs play a dominant role in the RCM temporal variability. For the LB domain used in this study, all four components of the LB-simulated precipitation resemble the driving IBB-simulated fields. The large-scale errors of the IBB serving to drive the LB are transmitted and reproduced by the LB. There are some improvements in the small-scale stationary features over regions with strong surface forcing. The LB generally produces more intense small scales (both stationary and transient) than the driving IBB, except near the inflow boundary where spin-up delays the onset of precipitation.

Precipitation rate

850-hPa temperature

mslp

x

1

1

2

1

2

R0e IBBx=PBB (%) R0e LBx=PBB (%) R0e LBx=IBBx (%)

75 20 18 73 18 18 96 93 95 e = 95% R¢PLB/PBB

90 90 99 e R¢PLB/PBB

42 41 99 = 99%

33 34 99

89 89 100 e R¢PLB/PBB

40 35 41 35 99 99 = 99%

C0IBBx=PBB (%) C0LBx=PBB (%) C0LBx=IBBx (%)

98 66 104 79 53 83 81 81 80 G¢PLB/PBB = 75%

93 93 100 G¢PLB/PBB

91 92 101 = 100%

109 108 99

99 96 97 G¢PLB/PBB

90 87 97 = 96%

2

3

3

3

99 95 97

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Table 4 As Table 3 for the small-scale component

Precipitation rate

41 4 2 39 5 2 79 71 75 e R¢PLB/PBB = 76%

42 6 3 40 7 4 86 77 82 e R¢PLB/PBB = 84%

C0IBBx=PBB (%) C0LBx=PBB (%) C0LBx=IBBx (%)

89 61 85 87 60 78 98 98 92 G¢PLB/PBB = 80%

94 86 104 78 72 83 83 83 80 G¢PLB/PBB = 79%

91 89 104 76 75 85 83 84 82 G¢PLB/PBB = 80%

Figure 8a shows that the IBB stationary large-scale errors result from different magnitudes of spatial variability and from small values of spatial correlation. The 15% relative mean square difference for IBB2 comes 5% from spatial variance (G*IBB2/PBB = 62%, Fig. 9c) and 10% from spatial correlation (R*IBB2/PBB =

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1

30 1 0.4 25 1 0.8 71 56 63 e = 66% R¢PLB/PBB

3.2.1 Imperfect Big Brothers

Fig. 8 As Fig. 3 but for mslp errors

1

1

R0e IBBx=PBB (%) R0e LBx=PBB (%) R0e LBx=IBBx (%)

Figure 8 shows the Taylor diagrams for the statistics of mslp, for both IBB and LB, compared with PBB. The next subsections present the errors of IBB and LB simulations.

3

mslp

x

3.2 Mean sea level pressure

2

850-hPa temperature 2

3

2

3

94%, Fig. 9c). Figure 8c shows that the IBB small-scale stationary error stems from a combination of reduced spatial correlation and underestimated spatial variance, as is seen in Fig. 10a–d, the latter being due to the coarser resolution of IBB. The errors of the IBB mslp are largest in the transient components (Fig. 8b, d), mainly as a result of e weak temporal correlation (R¢IBB/PBB ): 35% for the large scales and 3% for the small scales. As discussed in Boer and Lambert (2001), complete loss of temporal correlation is a characteristic of CGCM simulations. In the case of a nested model, the LBCs provide some control on the evolution of the solution; as a result some time correlation is retained, particularly for large scales that are present in the driving fields at the LBCs.


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Fig. 9 As Fig. 4 but for the stationary large-scale component of mslp

Surprisingly some time correlation (though weak) is also noted for small scales despite the fact that these are not present in the LBC. It is speculated that the large-scale information contained in the LBCs might precondition the small-scale variability. The smallscale transient eddy standard deviations of IBB simulations are well correlated with PBB: R*IBB/PBB ‡ 97%

(Table 5), reflecting similar preferred location for small-scale transient activity. 3.2.2 Little Brothers Figures 8a–d show that the LB error in mslp are similar to those of IBB, for all four components. Figure 9

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346


Fig. 10 As Fig. 4 but for the stationary small-scale component of mslp

shows very good agreement between the stationary large-scale component of LB and their driving IBB, with spatial correlation coefficients R*LB/IBB 100%. A similar behaviour is noted in the transient large-scale component (not shown), near perfect spatial correlation coefficients between the transient standard devi-

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ation (R*LB/IBB 100%) as well as temporal correlation e coefficients (R ¢LB/IBB ‡ 99%) (Tables 3, 5). In conclusion, the LB’s transient-eddy large scales stay close to and reproduce the errors of the corresponding IBB, indicating that the LBCs play a dominant role in RCM large-scale variability.

E. P. Diaconescu et al.: Impact of lateral boundary data errors Table 5 Spatial correlation coefficients (R*) and ratio of spatial variances (G*) for the transient-eddy large- and small-scale components of 850-hPa temperature and mslp

IBB x stands for (IBB1, IBB2 and IBB3) and LB x for (LB1, LB2 and LB3)

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850-hPa temperature large scales 2

850-hPa temperature small scales 3

1

RIBBx=PBB (%) RLBx=PBB (%) RLBx=IBBx (%)

99 89 95 99 89 96 100 100 100 R*PLB/PBB = 100%

99 97 98 96 97 98 97 98 98 R*PLB/PBB = 97%

100 93 98 100 93 97 100 100 100 R*PLB/PBB = 100%

98 97 97 97 96 97 99 98 98 R*PLB/PBB = 99%

CIBBx=PBB (%) CLBx=PBB (%) CLBx=IBBx (%)

99 113 159 97 109 152 97 97 96 G*PLB/PBB = 97%

88 90 111 76 78 92 87 87 83 * GPLB/PBB = 79%

96 89 116 88 82 109 92 92 93 G*PLB/PBB = 91%

91 104 105 73 87 85 80 83 82 G*PLB/PBB = 77%

Figure 11 and Tables 3, 4 and 5 summarize the LB statistics of 850-hPa temperature field. In general, all IBBs have good spatial correlation coefficient with the reference field for the large-scale components (R*IBB/PBB ‡ 99% for the stationary components and R*IBB/PBB ‡ 89% for the transient-eddy components); the errors are mainly due to differences in spatial variances (e.g. G*IBB/PBB = 66% for the IBB2 stationary large scales, and G*IBB/PBB = 159% for the transient standard deviations of the IBB3 large scales). The domain-average temperature errors IBB PBB vary between –0.6 and +1.5C, and lie within the distribution of the ensemble of 21 CGCM errors used in the

2

1

1

3.3 850-hPa temperature

1

mslp small scales

X

For the stationary small scales (Fig. 8c), the spatial correlation for all LBs (R*LB/PBB) are slightly smaller than with their driving IBBs (R*IBB/PBB). Figure 10 shows very good agreement between the LB and its driving IBB, with high-spatial correlation coefficients (R*LB/IBB ‡ 95%). For the transient components of the small scales, Fig. 8d shows that the LBs have almost the same temporal correlations with the PBB as their driving IBBs, but somewhat smaller spatial-average transient-eddy standard deviations than the corresponding IBBs. Table 5 indicates large values of the spatial correlation coefficients and the ratio of spatial variances between the transient-eddy standard deviations of LB and their driving IBB (R*LB/IBB ‡ 98%, G*LB/IBB ‡ 80%), and Table 4 shows that the temporal correlation between LB and its IBB is also large e (R¢LB/IBB ‡ 77%), as is the ratio of spatial-average transient-eddy standard deviations (G¢LB/IBB ‡ 82%). All these confirms that the IBB small-scale transient activity is well reproduced by the corresponding LB, despite the fact that small scales are excluded by design in the IBB data serving as LBC to the LB.

3

mslp large scales

2

3

2

3

fourth Assessment Report of the IPCC (2007) for which the 5th, 25th, 50th, 75th and 95th percentiles are estimated to be –4, –2, –1.5, 0.2 and 4.1C, respectively. The LB response to the IBB temperature errors is very similar to those of mslp (all the components of LB stay close to the corresponding IBB), and hence will not be described in detail to save space. The reader is referred to Diaconescu (2006) for more details.

4 Discussions and conclusions The primary aim of this study was to investigate the sensitivity of a nested RCM to errors present in the driving data used as LBC. This is an important issue as CGCM-simulated data are used to drive RCMs for regional climate-change projections, and CGCM simulations are not perfect. The approach employed in this study follows the BBE protocol, which enables to isolate the errors due to driving with imperfect data from the errors due to the rest of the RCM formulation. The method consists in first constructing a reference climate by integrating a high-resolution RCM over a big domain: the PBB. Controlled and dynamically coherent errors in the LBCs are generated with other RCM simulations performed at coarser resolution over increasingly larger domains: the IBBs. The large scales of these simulations, obtained after filtering the small scales, provide the set of imperfect lateral boundary data for a second series of high-resolution RCM simulations integrated over a smaller domain: the LBs. The precipitation rate, mslp and 850-hPa temperature fields for five simulated February months are analysed, using the PBB as verification data. The results of the analysis are summarized in Figs. 12 and 13. Figure 12 shows the domain-averaged large-scale errors of the LBs as a function of those of the IBBs. The correlation deficit (100-R) is used here

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Fig. 11 As Fig. 3 but for 850 hPa-level temperature errors

as error measure. For all three variables studied, and for both stationary and transient eddies, there is a nearly linear dependence between the LB and IBB errors, with the lines lying close to the equal-error black diagonal line. For fields that are driven at the lateral boundary, such as the mslp and 850-hPa temperature, the IBB errors are essentially reproduced by the LB. The LB large-scale precipitation exhibits a non-zero offset value at the origin, due to the difficulty

Fig. 12 Little Brother errors versus IBB errors for largescale components of precipitation, mslp and 850hPa temperature fields. The stationary errors (left panel) are represented by (100-R*) and the transient errors (right panel) are represented by (100-R¢ e), with R in per cent. The PBB is plotted as a zeroerror IBB

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in reproducing the field in the inflow region where the weather systems enter the domain. In the regional climate studies, the particular interest is centred on the small scales developed by the RCM, with emphasis on the transient-eddy component that dominates these scales. On the other hand, the large scales used to drive the RCM are dominated by the stationary components. To summarize the impact of the LBC errors on the small scales developed by the


LB, the LB transient small-scale errors are plotted in Fig. 13 as a function of the IBB mslp stationary largescale errors. The Root Mean Square (RMS) difference is used to represent the errors in the IBB stationary large-scale and LB transient-eddy small-scale components. The errors introduced in the stationary large scales of the IBB mslp field vary between 0 and 2.9 hPa. A 2.9 hPa error in the mslp stationary large scales of IBB induces a 0.15 hPa-error in the mslp small-scale transient-eddy component of LB and 1.4 mm/day in the precipitation small-scale transienteddy component. Due to the fact that the small scales are excluded by design from the driving LBC, the small-scale transient-eddy component of PLB has an error of 0.1 hPa in the mslp field and 0.8 mm/day in the precipitation field. Therefore, with respect to the ‘‘perfect’’ case represented by PLB, a 2.9 hPa-error range for the IBB mslp stationary large scales are associated with a 0.04 hPa-interval of error for the LB mslp small scales and a 0.6 mm/day-interval of error for the LB precipitation small scales. In conclusion, the results of this study reinforce the notion that the quality of lateral boundary data plays a critical role in regional climate modelling, highlighting the need for good LBCs and hence the necessity for a credible CGCM simulation to drive an RCM. For the domain and winter period studied here, an almost perfectly linear dependence between the large-scale errors of the RCM and those of its driving data is noted. The results show neither significant correction nor amplification of the errors present in the large-scale data set used as LBCs. For the domain size used in this study, the RCM large-scale climate follows that of the driving model. Analysis of the precipitation rate, mslp and 850-hPa temperature large-scale fields suggests a

Fig. 13 Little Brother transient small-scale errors versus IBB mslp stationary large-scale errors for precipitation (in blue) and mslp (in red) fields. The errors are represented by RMS difference with the corresponding PBB component. The PBB is plotted as a zero-error IBB

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transfer of the LBC-data errors to the RCM. Hence the initial goal of determining the maximum allowable level of error in LBC for producing tolerable RCM errors remains elusive, as the results do not indicate the existence of any threshold in the magnitude of LBC errors for their impact on the results of an RCM. For the small scales, RCM only corrects the smallscale errors caused by the coarser resolution of the driving model in regions where there is important orographic forcing or land-sea contrast. The rest of the small-scale errors are by-and-large reproduced even though the small scales do not take part in the nesting process. For example, if the driving-model large scales are not well placed in space or time, they will be reproduced almost entirely by the RCM and the small scales will also be poorly placed. This result suggests that the large scales precondition the small scales and therefore it is necessary to provide the correct largescale circulation at the lateral boundary of RCM in order to also obtain the correct small scales. This study focussed on the winter period, with only one LB domain size, over a single region, the East Coast of North America. It will be interesting to extend the study for other regions and seasons as well. For the summer season, we speculate that RCM will be less dependent on the driving data and that LBs’ simulations will be more similar to each other than to the IBBs. There are also several other interesting aspects that need to be further explored. For example, previous studies have shown that RCM-simulated climate is sensitive to the region modelled and to the size of the domain. It would therefore be particularly interesting to study regions with strong orographic forcing, where we speculate that a larger correction of small-scale errors may take place. In a research performed with the operational Eta model at NCEP over a large regional domain (11,500 · 8,500 km2), Mesinger et al. (2002) found that the LAM does improve the large scale provided by the global model during the first three days of integration. This suggests that a largedomain simulation over regions with strong orographic forcing might also allow the RCM to correct part of the errors of the large scales. Acknowledgments This research was done as partial requirement for the MSc. Thesis of the first author, as a project within the CRCM Network, financially supported by the Canadian Foundation for Climate and Atmospheric Sciences (CFCAS) and the Ouranos Consortium on Regional Climatology and Adaptation to Climate Change. The technical help of the Climate Simulations Team of Ouranos is greatly appreciated; we are particularly thankful to Dr. Ramoń de Elıá for the useful discussions and to Mr. Claude Desrochers for maintaining a user-friendly local computing environment.

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