1. Introduction
Despite increases in computer power, most atmospheric general circulation model (GCM) simulations still use coarse resolution with the horizontal resolution being about 200–500 km. Therefore, they only produce large- and synoptic-scale atmospheric features. Because of the resolution limitation, which could be crucial for land–atmosphere interaction studies with highly heterogeneous land surface conditions and steep orography, regional climate models (RCMs) have been developed and applied for dynamically downscaling GCM simulations or reanalyses at regional or local scales (e.g., Dickinson et al. 1989; Kida et al. 1991; Giorgi et al. 1993; Juang and Kanamitsu 1994; Paegle et al. 1997; Bosilovich and Sun 1999; Leung and Ghan 1999; Laprise et al. 2000; Fennessy and Shukla 2000; Liang et al. 2001; Xue et al. 2001; Zhang et al. 2003; Castro et al. 2005; De Sales and Xue 2006; and many others). In these types of approaches, RCMs are forced by surface boundary conditions from specification or prediction by a coupled ocean and/or land surface model, as well as by lateral boundary conditions (LBCs) from a GCM or reanalysis at regular temporal intervals. In this paper, we will refer to this lateral nesting approach as the dynamic downscaling method (DDM).
There are a number of issues concerning the use of the DDM (Laprise et al. 2000; Denis et al. 2002). The most important issue is whether, and if so under what conditions, the DDM is really capable of improving/adding more climate information at different scales compared to the GCM or reanalysis that imposes LBC to the RCMs, especially when RCMs run for a long time. At least, the RCM should, in most circumstances, produce the large-scale behavior of those GCMs or reanalyses with the same characteristics. This is a fundamental question about the DDM and the assumption “yes” to this question should be the motivation for using the DDM for regional climate study in the first place.
Many issues related to the capability of the DDM have caused skepticism in the climate modeling community. For example, Van Tuyl and Errico (1989) found that, using a limited area model (LAM)—the predecessor of the RCM, the self-interaction of large scales does not contribute significantly to small scales. Laprise et al. (2000) found ‘‘no evidence for extended predictability of scales that are not forced through the lateral boundary conditions.’’ For a particular case considered by Castro et al. (2005), their DDM does not even retain the value of the large scale, which exists in the laterally imposed global reanalysis. A number of studies have shown that the results from the DDM were sensitive to different parameters, especially domain size, horizontal resolution, topography, convective scheme, and vegetation and soil conditions (i.e., Anthes et al. 1989; Zeng and Pielke 1993; Jones et al. 1995; Seth and Giorgi 1998; Hong and Pan 2000; Liang et al. 2001, 2004; Xue et al. 2001; Denis et al. 2002; Castro et al. 2005). All of these studies indicate the necessity for more investigation of the DDM with different RCMs.
In this study, we conduct a number of tests of the North American regional climate using the Eta/SSiB (simplified simple biosphere model: Xue et al. 1991) to investigate the sensitivity of the Eta/SSiB simulation to domain size and location, sources of LBC, horizontal resolution, and initial soil moisture and surface temperature conditions; most of these factors have been listed as the primary factors in previous studies affecting downscaling ability. It has been demonstrated that the simulation error growth in LAMs is very distinct from that of global forecast models (e.g., Anthes et al. 1989; Paegle et al. 1997; Laprise et al. 2000). To more comprehensively evaluate the model results, especially for precipitation, in addition to simulation errors, temporal and spatial analyses as well as spectral analyses were conducted to quantitatively evaluate the model’s ability in simulating regional climate features at different scales. Furthermore, we also tested the necessity of using the ensemble approach. Although studies (e.g., Laprise et al. 2000) have indicated that slightly different initial conditions might not yield very different results in the LAM simulation when the RCM’s domain becomes large the model internal variability increases. We believe a careful evaluation is necessary.
Part of the difficulty in exploring this issue is rooted in the lack of validation data for small-scale features. Validation of the RCM’s small scales using low-resolution GCM output or global reanalyses as climate reference is impossible because the small scales generated by the RCM are absent in the GCM and global reanalyses (Denis et al. 2002). Because of this, Denis et al. (2002) adopted the “Big Brother” approach in which a large-domain regional high-resolution model was used to produce a high-resolution reference dataset for evaluation as well as a low-resolution dataset driving a nested RCM with the same dynamics and physics over a small domain. They found that during one-month simulations, the high-resolution RCM over eastern North America, which was driven by a large domain and low-resolution dataset, was capable of reproducing the time mean and variability of finescale features in sea level pressure, 975-hPa temperature, and precipitation. The shortcoming in this type of experiment is that the nested RCM only produces the features in the driving model with the same dynamic and physical processes, which does not necessarily represent the real world.
In this study, we will use 1) observed precipitation data, 2) National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) Global Reanalysis (NNGR: Kalnay et al. 1996; Kistler et al. 2001), and 3) NCEP North American Regional Reanalysis (NARR: Mesinger et al. 2006) to investigate the coupled regional Eta/SSiB model’s downscaling ability. The NCEP Eta Model and its Data Assimilation System (at 32-km/45-layer resolution with 3-hourly output) were used for NARR. The NCEP NARR is a high frequency, dynamically consistent meteorological and land surface hydrology dataset for the 25-yr period 1979–2003. We will use this dataset to test the sensitivity of the RCM to the LBC and to evaluate the RCM’s ability in reproducing the NARR small-scale as well as synoptic-scale features as a function of domain size, boundary location, horizontal resolution, etc.
In this paper, we will first present the Eta/SSiB RCM and experimental design. Then we will discuss the results from a series of numerical experiments, including examination of differences from observations and global and regional analyses and comparison of their spectra.
2. Description of the Eta/SSiB RCM and experimental design
The Eta Model has been used as the primary short-range weather forecasting tool at NCEP and at other national weather services and research institutions. [Please see the Eta Model development papers (e.g., Janjic 1984, 1990, 1994; Mesinger 1984; Mesinger et al. 1988; and many others) for full references.] The performances of the Eta Model and its components have been extensively investigated (e.g., Betts et al. 1997; Mesinger et al. 1988; Berbery et al. 2003). The version of the NCEP Eta Model used in this study was the operational version obtained in 2000. We have run the model using 38 vertical layers and a grid-mesh size of 80 km. A test with horizontal resolution 32 km was also conducted. A biophysical model known as SSiB is coupled with the Eta Model for this study (Xue et al. 2001). When reinitialized every two days, this Eta/SSiB Model produced realistic monthly mean precipitation over the United States and the flood areas in the simulation for June, July, and August 1993, a summer of heavy flooding in the central United States (Xue et al. 2001).
A considerable effort has been devoted to the development of the Eta Model from a 48-h weather forecast model to a regional climate model. The purpose of the development was to identify the sensitivity of hydrometeorological prediction at seasonal time scales to terrestrial hydrologic–atmospheric coupling processes. This effort did not simply extend the length of simulations but involved a substantial amount of model development. In a 48-h forecast, surface boundary conditions, such as sea surface temperature (SST) and sea ice, were fixed as initial conditions. Our development included updating SST and sea ice, the distance between the sun and earth, and vegetation parameters (such as leaf area index). Additionally, we developed a scheme to simulate the water and energy exchange over sea ice. We refer to this regional climate model as the Eta/SSiB RCM in this paper.
In the model runs, the NNGR (Kalnay et al. 1996; Kistler et al. 2001), hereafter denoted “Reanalysis 1” in this paper, was the primary source used as the initial conditions (for atmosphere, SSiB soil moisture and soil temperature, and snow depth), LBCs, and SST for most of the Eta Model runs in this study. Other Eta simulations using other global reanalyses or NARR were also conducted and will be discussed.
The coupling of an RCM and the imposed GCM/reanalysis forcing is through the RCM’s lateral boundaries. In the Eta Model, only the atmospheric variables in the outermost row of grid points (“outer boundary”) are updated by the lateral boundary conditions. In our experiments, LBCs were updated at 6-h intervals, with linear interpolation in between.
The values of temperature, specific humidity, and zonal and meridional winds are prescribed at these points, except for the tangential velocity components at the outflow points that are linearly extrapolated from the interior of the domain. The values of atmospheric variables along the first interior row of grid points (“inner boundary”) are defined as horizontal four-point averages, thus being an average of the prescribed or extrapolated values on the outermost line and values on the second outermost line of points, which are fully predicted. In addition, a semi-Lagrangian scheme is used in three rows along the boundaries starting from the third interior row. Thus, the Eta LBC scheme does not have a relaxation zone in which model variables are less and less forced by the driving model data until some distance from the boundary. This study does not investigate the impact of different numerical techniques for LBC coupling on the model simulation. The location of the lateral boundaries and the domain size, however, are the major points of this study.
Most simulations were conducted from 1 May through 31 July 1998. There was no reinitialization of any fields during the entire integration. The year 1998 was an El Niño–Southern Oscillation (ENSO) year with a substantial amount of precipitation over the areas to the south of the Great Lakes in June and drought in Texas/Oklahoma. The 1998 Eta/SSiB RCM tests in this study are listed in Table 1. To confirm the results from the 1998 simulation, the years of 1993 and 1995 were also selected for comparison (section 7).
3. Observational and reanalyses precipitation for summer 1998
The observed rainfall was derived from the gauge-only dataset obtained from the NCEP Climate Prediction Center containing about 7000 rain gauge stations daily, mostly over the United States. June 1998 was a very wet month south of the Great Lakes, forming a crescent-shaped rainfall band (Fig. 1b). This rainfall band formed in May (Fig. 1a) with strong intensification in June. In July, the heavy rainfall band moved to the south, forming a southeast–northwest rainfall band (Fig. 1c). Farther southwest, a drought in Texas/Oklahoma emerged and intensified during these three months. The time series of the area-averaged 5-day running mean precipitation from observations is shown in Fig. 2. The domain for the time series covered the area between 30° and 50°N, 120° and 80°W, which includes most of the continental United States and will be referred to as the “Test Area” in this paper. We also calculated the precipitation statistics for a smaller interior area with more precipitation concentration (35°–45°N, 105°–80°W), where the results were very consistent with those in the Test Area; these results will not be discussed, for conciseness of the paper.
The NNGR precipitation is shown in Figs. 2a and 1d–f. Within the United States, NNGR precipitation had similar spatial distribution patterns and temporal variations compared to observations. Despite the clear wet bias, the temporal correlation coefficient of daily mean precipitation, 0.65, over the Test Area was very high (Table 2a), and the spatial correlation, which was calculated based on monthly mean precipitation at each grid, was 0.7 (Table 3), indicating that the NNGR properly simulated the variability of precipitation. Outside the United States, NNGR spatial distribution patterns were similar to the Climate Prediction Center Merged Analysis of Precipitation (CMAP: Xie and Arkin 1997). However, the May rain in northwest Canada (north of 55°N and west of 100°W) did not exist in CMAP, and June and July rainfall over that region was too strong. For the Canadian eastern coast, the reanalysis rainfall also showed a wet bias compared with CMAP.
The NARR has successfully assimilated high-quality and detailed precipitation observations into the atmospheric analysis following the assimilation technique described in Mesinger et al. (2006). NARR precipitation in May–July (MJJ) 1998 was very similar to the observation (Fig. 2a; Table 2) with 0.74 correlation. The spatial distributions of NARR monthly mean daily precipitation were also very similar to observations within the United States, shown in Figs. 1a–c. The spatial correlations with observations over the test area were very high (Table 3). Outside the United States, it was similar to CMAP but the intensity was slightly weak.
4. Precipitation downscaling experiments
a. Domain size and location
It has been established that the domain location can affect an RCM’s numerical performance. For example, Giorgi et al. (1996) placed the left boundary over U.S. Pacific coastal waters to avoid complex topography within the boundary zone. Liang et al. (2001) used the locations of the upper-level jet stream and low-level jet to determine the positions of the northern and southern boundaries. The first domain tested in this study was the Eta operational forecast domain (Case 1, Table 1; Domain I, Fig. 3), including the continental United States, all of Canada and Central America, and a substantial portion of the surrounding oceans. Hereafter, we designate this domain as the “Big Domain” for easy identification.
To investigate the Eta RCM’s internal variability within the Big Domain, an ensemble of five runs with initial conditions from 1 to 5 May 1998 was executed. The ensemble mean was only able to produce the observed daily precipitation averaged over the Test Area well during the first 15 days (Fig. 2b). In addition, the simulated time series of precipitation failed to capture the major weather events during the 3-month simulation. The correlation of area-averaged daily precipitation with observations was negative with a large standard deviation (Table 2a). In fact, the correlation for May was 0.43, but June and July had large negative correlations. The root-mean-square (rms) errors of monthly mean precipitation were large (Table 2b). The model internal variability was also very large with this domain size, especially for daily precipitation (Fig. 2b, Table 2a), indicating the necessity for using an ensemble approach. The spatial distribution of the first month’s precipitation simulation within the United States was similar to observations (not shown) with a spatial correlation about 0.47 (Table 3). The intensity was stronger (Table 2a). After the first month, a substantial low precipitation bias was persistent during the entire June (Fig. 4a) and July period. The areas to the south of the Great Lakes were quite dry. The spatial correlation of monthly mean precipitation deteriorated dramatically during June and July (Table 3).
To test whether the disappointing simulation in Case 1 was caused by the domain size, we selected a second domain (Case 2, Table 1; Domain II, Fig. 3), which reduced coverage over the ocean but still included the entire Gulf of Mexico in the southern boundary. Because the southern Great Plains (SGP) low-level jet (LLJ) plays an important role in moisture transport for the U.S. continental summer precipitation, it is ideal to include the LLJ and its moisture source area within the model domain. The Case 2 domain is referred to as the “South Domain” in this paper. Meanwhile, the northern boundary included the upper-level jet and the western boundary covered the North American Pacific coastal waters. Similar to Case 1, Case 2 only properly simulated the first weather event (Fig. 2c, Table 2a). Unlike Case 1, however, Case 2 did simulate the proper number of major weather events, but the phases were 5–10 days earlier than observations in most events and with a substantial dry bias, especially during June and July. The rms error was also reduced compared with Case 1, but still large. Moreover, the internal variability was much smaller compared with Case 1 (Fig. 2c, Table 2a). It should be noted that the internal variability was mainly manifested in the amplitude of the precipitation intensity, not in the timing of weather events. It seems that the latter was mainly controlled by LBCs. The simulation divergence of different initial conditions did not grow during the three-month integration, consistent with previous LAM studies. The correlation of daily precipitation between Case 2 and observation was 33%, better than Case 1 but still quite low. With this domain, the spatial correlation of monthly mean precipitation improved substantially, especially in June (Table 3). However, the dry bias in June and July still existed (Table 2a). Figure 4b shows that Case 2 properly simulated precipitation areas in June. However, after June the major precipitation shifted to the north and to the east of the Great Lakes, as in Case 1.
Since moisture transport from the Gulf of Mexico is crucial for the SGP LLJ and summer precipitation, it was suspected that inappropriate LBC or improper boundary condition transport might be the main cause for the simulation problem in Case 2 and Case 1. We conducted several experiments to test the impact of the boundary position on the simulation. It was found that the position of the southern boundary had the most significant influence on simulations. Therefore, we selected another domain (Case 3, Table 1; Domain III, Fig. 3), in which the southern boundary was shifted to the north. This domain is referred to as the “Medium Domain” in this paper. Compared with Case 2, the improvements in area-averaged monthly means (Table 2a), time series (Fig. 2d), and spatial maps of monthly means (Figs. 5a–c) were dramatic. Unlike Cases 1 and 2, Case 3 simulated most weather systems with time lags for some events. The correlation coefficient is high (Table 2a) and the rms errors in June and July were reduced (Table 2b). The spatial correlations with the observations in both June and July were higher than in Case 2 (Table 3). Case 3 also simulated rainfall bands along the areas to the south of the Great Lakes and another precipitation center in the northwestern United States, as well as a dry Texas in May; but the precipitation in Indiana and Illinois was weak (Fig. 5a). Figure 5b shows that Case 3 simulates the June mean reasonably well, but with the position of the maximum precipitation slightly shifted to the south. The precipitation areas in July were simulated (Fig. 5c), but July precipitation over the central United States was weak and the light rain over Arizona was not simulated. This case shows the importance of the southern boundary condition and is consistent with another study with the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5; Liang et al. 2001). It was found that MM5 performance deteriorated substantially when the southern buffer zone was extended to the Tropics, where large forcing uncertainty was identified.
The ensemble mean and standard deviation for Case 3 is shown in Fig. 2d. Because both Case 2 (Domain II) and Case 3 (Domain III) had small standard variations and each member was consistent with the ensemble mean, in the following discussions we only applied one simulation for the experiment with the domain sizes equal to or smaller than the size in Case 2, as was done in most previous RCM studies.
To further test the domain size effect, we selected a relatively small domain, which mainly covered the continental United States (Case 4, Table 1; Domain IV, Fig. 3). Case 4, referred to as the “Small Domain” in this paper, simulated the major weather systems during the three months, although the first precipitation event was too strong and the fourth event was weak. The second event’s timing was about 5 days earlier than observed (Fig. 2a). The monthly means of precipitation over the Test Area were close to observation (Table 2), with the correlation of daily precipitation being 0.51. The precipitation band to the south of the Great Lakes in May and its intensification in June was properly simulated (Figs. 5d,e; Table 3). However, the rain to the southwest of the Great Lakes in June was slightly weak. The precipitation in July was concentrated along the east coast rather than along a southeast–northwest band from Florida to Nebraska as shown in Fig. 1c. Heavy precipitation in July appeared in the northeastern corner of the domain (Fig. 5f). The CMAP showed a precipitation area, but there was only about 3–5 mm day−1 between 45° and 57°N, 80° and 60°W in July 1998. By and large, the spatial and temporal correlations with observations in Case 4 were similar to Case 3 (Tables 2, 3). The precipitation intensity over eastern Canada and Florida in July was worse than in Case 3. It seems that the problem in these two areas in Case 4 was that they were too close to the boundary. The Case 4 results confirm that the simulated problem in Cases 1 and 2 seems to be related to the domain size and/or locations of the boundary position. A number of studies with other RCMs have indicated similar deterioration of simulation quality with increased domain size (i.e., Jones et al. 1995; Seth and Giorgi 1998). However, comparing Case 3 and Case 4, it seems that it is not necessarily the smaller the domain size, the better the results. There may be an optimal domain size for a specific RCM under a certain climate condition.
b. LBCs
The discussion in the last section indicated that the position of the southern LBC may play a crucial role in the RCM’s downscaling. To further investigate whether this finding is valid if we use other global reanalyses for LBC forcing, we conducted a number of experiments to test the sensitivity of the Eta/SSiB to the LBCs. In previous discussions, global Reanalysis 1 was used for LBCs. We have used global Reanalysis 2 (Kanamitsu et al. 2002) as well as ECMWF global reanalysis (Simmons and Gibson 2000) as LBC for the Eta Model. Although these global reanalyses yielded some improvements in the model simulations of spatial distribution of monthly mean precipitation, they did not produce significantly different results from those using global Reanalysis 1 as LBC.
In further testing, the NARR data were used. When we used the NARR as LBC (i.e., initializing the RCM 80-km run with the NARR 32-km data), the RCM preprocessing code picked up the closest 4 surrounding 32-km grid points and bilinearly interpolated to the new 80-km grid. Comparison between the NARR dataset and the Eta/SSiB simulation should be able to validate the Eta/SSiB’s small-scale features and whether it caused the aliasing problem. The analysis of this comparison will be discussed in section 6. While using NARR for LBC, we still used NNGR initial land surface conditions for these next model runs for better association with the previous runs of section 4.
Three cases were selected for tests: Case 5 (Table 1; Domain III, Medium Domain; Fig. 3), Case 6 (Domain II, South Domain), and Case 7 (Domain I, Big Domain). Please note that the Case 7 domain is one to two lines less than the Big Domain at each side of the domain depending on the NARR’s domain size. Case 5 improved temporal variation and spatial distribution of precipitation in July (Figs. 2e, 6c; Table 3). The southeast–northwest precipitation band from Florida to Nebraska was clearly simulated, while Case 3 was relatively dry in the central United States. The correlation of daily precipitation was 0.62, close to the NNGR. Although the amount of improvement was not that large, it was quite consistent in every other year’s similar cases (see section 7). The late June and July precipitation simulations, however, were overestimated (Figs. 2e, 6b). It was rather wet in Texas and Oklahoma in July.
Unlike Case 2, Case 6 had no dry bias in June and had much less dry bias in July (Table 2a; Fig. 2e). The correlation of daily precipitation was only reduced from 0.62 in Case 5 (Median Domain) to 0.55, equal to the Case 4 results. The simulated spatial distribution of June was substantially improved compared to Case 2 (Fig. 4c; Table 3), especially over the southeastern United States. However, the precipitation band to the north of the Great Lakes was too strong (Fig. 4c). In Case 7, although the correlation coefficient was still negative and a dry bias still persisted in June and July (Table 2a), the monthly mean errors were much smaller than in Case 1 and compatible with other cases (Table 2b). Since this one run still showed negative correlation, no ensemble run was conducted. By and large, all three cases had clear improvements in the July (the third month) simulation (Tables 2 and 3).
c. Model grid spacing
Model resolution has also been identified as the major factor affecting the RCM’s simulation (e.g., Castro et al. 2005). Seth and Giorgi (1998) found that resolution has a negligible effect on the model precipitation results in the range between 40 and 60 km. We conducted one experiment with 48-km resolution, and the Big Domain and did not find substantial improvement in model simulation (not shown). To further test this effect, we conducted another two experiments with 32-km resolution as well as global NNGR LBC and initial land surface conditions. The Medium (Case 8, Domain III) and South Domains (Case 9, Domain II) were selected. Case 8 (Case 9) is the 32-km counterpart of Case 3 (Case 2).
Compared with the simulations using the same domain size and LBCs but coarse resolution, the most substantial improvement was in the July simulation for Case 8 and in the June and July simulations for Case 9 (Fig. 2f, Tables 2b and 3). There was no dry bias in June and July. The patterns of the spatial distribution in Case 8 were consistent with observation (Figs. 6d–f). The July simulation was better than Case 3, which had a clear dry bias, and Case 5, which had a wet bias. The heavy narrow rainfall band from Florida to Colorado as well as a dry Texas were clearly simulated in Case 8 (Fig. 6f) and Case 9 (not shown). Although both Case 8 and Case 9 correctly simulated the number of weather events during the time period, the shifting of the timing was very evident in a number of events (Fig. 2f), which might be related to higher internal variability and affected the correlation coefficients in Table 2a. The improvement in correlation coefficients in Case 9 was not substantial compared with the same domain size but 80-km resolution; compared to Case 8, the correlation coefficient for Case 9 is still relatively low (Table 2a). The improvement from grid resolution seems to be partially compensated by the overprediction along the eastern coastline. Although the precipitation problem along the sea/land boundary appeared in previous simulations, the sea/land contrast likely caused more problems in the high-resolution case. A further analysis of the Case 8 results will be discussed in section 6.
d. Land surface initialization
As indicated earlier, in the above NARR LBC tests, the NNGR land surface conditions were used as initial conditions, which were produced by a two-layer soil model in the reanalysis system. NARR introduced the Noah land surface scheme (Ek et al. 2003; Mesinger et al. 2006), which had different structures and presentation of the biophysical process than SSiB, such as water holding capacity, soil depth, soil property, vegetation biophysical processes, etc. We conducted another experiment (Case 10, Table 1; Domain III, Fig. 3), in which the same domain and LBC (NARR) as Case 5 were used but with NARR soil moisture and surface temperature as initial land surface conditions.
This test shows that initial soil moisture affected the three-month precipitation simulation. The correlation of daily precipitation with observations (0.55) in Case 10 was lower than in Case 5 (0.62) but close to the Case 4 results (Table 2a). Compared with Case 5, the correlation coefficients in Case 10 were lower by 0.05 and 0.17 in May and July, respectively. The spatial correlation coefficients in Case 10 were also slightly lower in June and July (Table 3). In addition, Case 5 and Case 10 produced different precipitation intensity (Table 2a). With the complex structure of the biophysical model, the direct transfer of soil moisture produced by one biophysical model might not yield the optimal results when they are applied to another biophysical model. However, the differences caused by these two initial soil moisture datasets were not as substantial when compared with those produced by the effects of domain size, LBC, and grid spacing discussed earlier.
5. Effect of the DDM on circulation and other atmospheric variables
In the previous two sections, we discussed the impact of different factors on the precipitation simulation. It is also important to know which atmospheric processes were affected by those LBCs and contributed to the simulated precipitation differences. We checked atmospheric variables at different atmospheric levels. The Eta Model simulated some variables, such as 2-m atmospheric temperatures, quite well regardless of the domain size, as discovered by Vannitsem and Chomé (2005) in a European climate study. The differences between simulated daily mean and NNGR and NARR reanalyses were generally smaller than 1°, and the correlation coefficients were mostly higher than 90%. Even in the worst case, such as Case 1, the correlations at 500 and 850 hPa were 0.92 and 0.75, respectively. Although it is expected that the correlation of variables with red spectra is higher than those with white spectra (e.g., precipitation) since white spectra variables have less variance in the driven large scales, the high correlations described above nevertheless validate the Eta’s ability in simulating the large-scale fields. However, we found substantial differences in correlation coefficients between simulated and reanalysis relative humidity and meridional wind at 850 hPa, as well as 200-hPa zonal wind among different cases (Table 4).
In the experiments with the Big Domain (Cases 1 and 7), the correlation coefficients for all three of these variables were significantly lower than in other cases, regardless of whether the NNGR or NARR LBC was used (Table 4). In Case 2 (South Domain), the correlation for the 200-hPa zonal wind with NNGR/NARR was not that different from Case 3, but the correlation coefficient of 850-hPa relative humidity with NNGR/NARR was only 0.45/0.27 in Case 2, significantly lower than that of 0.62/0.52 in Case 3. The correlation coefficients of relative humidity with NARR were lower than NNGR, indicating that relative humidity might have high spatial and temporal variability. While the NARR LBC was used, the correlation of relative humidity with NNGR in Case 6 (also South Domain) was increased to 0.75, consistent with the improvement in the precipitation simulation (Table 2).
The June zonal wind at 200 hPa from NARR and several simulations is shown in Fig. 7. The magnitude and large-scale patterns of the NARR fields are similar to those in NNGR but with more detailed structures in low atmospheric layers. In June 1998, there was a very strong jet located to the south of the Great Lakes where the observed heavy precipitation band was located (Fig. 7a). Although the global NNGR precipitation had a serious wet bias, the location of the heavy precipitation in June was correctly simulated (Fig. 1e), consistent with the jet position. Case 1 with the Big Domain simulated a weak 200-hPa jet with the core of the jet located to the north of the Great Lakes (Fig. 7b), also consistent with the location of its precipitation band. Both Cases 2 and 3 simulated the 200-hPa jet well in terms of its location and intensity (Figs. 7c and 7d), although Case 3 was slightly better. But the wind over northern Canada was weaker than that in the reanalysis. Case 2 had a high correlation coefficient, 0.89, though it was lower than in Case 3 (0.96). The results of Cases 5, 6, 8, and 9 were very similar to Cases 2 and 3 (Table 4). It seems that the NARR LBC had less impact on the simulation at upper atmospheric levels.
The effect of NARR LBC on humidity at lower atmospheric levels, however, was substantial (Table 4, Fig. 8). Figure 8a shows that June relative humidity at 850 hPa in NARR has a southwest–northeast gradient with a dry area over northern Mexico and southern California. The southeastern United States was relatively wet compared with other areas at the same latitude. The global NNGR had a very similar pattern. Case 1 generally simulated this spatial distribution (Fig. 8b). But the relative humidity was very high over the high latitudes and the correlation coefficient with NNGR was very low (Table 4). In Case 2, the dry area from southern California expanded to the east, producing a south–north gradient in the relative humidity distribution (Fig. 8c). The southeast United States became dry, consistent with the low precipitation in Case 2. Case 3 largely corrected the dry bias in Case 2 over that area (Fig. 8d). The June relative humidity over the southeastern United States (30°–35N°, 100°–75°W) for NARR and Cases 2, 3, 5, and 8 were 0.60, 0.43, 0, 54, 0.56, and 0.55, respectively. With the NARR LBC, the relative humidity at 850 hPa in Case 5 was properly simulated (Fig. 8e, Table 4), especially in the southeastern United States.
The SGP LLJ plays an important role in transporting the moisture from the Gulf of Mexico to the continental United States (Bonner et al. 1968; Mo et al. 1995). Convective activity and jet strength normally correlated strongly. NARR showed that the strong major moisture transport was confined to the south of the Great Lakes in June (Fig. 9a). In Case 1, the moisture transport was rather weak (Fig. 9b). On the other hand, the area covered by this moisture transport extended too far to the north compared with the reanalysis, consistent with its simulated precipitation. In addition, the Case 1 correlation with NNGR for the 850-hPa meridional wind was very low (Table 4). Case 2 had relatively weak moisture transport compared with NARR and Case 3 (Figs. 9c,d), which was consistent with its lower relative humidity (Fig. 8c) and lower precipitation. In Case 3 (Fig. 9d) and Cases 5, 6, 8, and 9 (not shown), the moisture transport was properly simulated. The June vertical integrated moisture flux convergences over the area between 30° and 45°N, 95° and 80°W were −1.83, −1.93, −0.12, 1.32, and 1.34 mm day−1 for Cases 1, 2, 3, 5, and 8, respectively, consistent with the differences in SGP LLJ and precipitation among these cases. These results confirm that the U.S. summer precipitation simulation was very sensitive to moisture transport by the LLJ.
6. Spectral analysis
Discussions in previous sections mainly focus on the model’s ability to simulate large-scale features. To have a more objective and comprehensive analysis of the results, in this section we use spectral analysis to quantitatively examine the Eta RCM downscaling ability (i.e., its ability to produce small-scale information based on the enforced LBC). In this study, we compare the Eta/SSiB’s performance with NARR to examine the RCM’s downscaling ability. Thus far, NARR is the best available data that we have for model evaluation at a small scale. Although it is possible that the similar models used for this study and NARR may produce a bias for the results, this study is nevertheless more demanding than the Big Brother approach (Denis et al. 2002). Both the presence of scales and the simulation correlation to the real world are examined in this study.
Since integrated kinetic energy is mainly a function of large-scale winds at upper levels and should be relatively insensitive to surface forcing, we also conducted another analysis of precipitation that is the end product of multiple physical and dynamical processes in the RCM and is more sensitive to land surface forcing (Xue et al. 2001). For the precipitation, we compared the model results and NNGR with NARR since the CMAP resolution is too coarse and the NCEP station data cover only a limited area. A number of studies (e.g., Ruiz-Barradas and Nigam 2006) have shown that NARR precipitation is very close to the NCEP station data where they are available and consistent with CMAP outside the United States.
Figures 10a and 10b show the June mean ΔS(k)frac for precipitation and kinetic energy, respectively. Wavenumber is presented on a logarithmic scale. For convenience, the wavelength is also listed in the figure. Since the minimum resolved wavelength in a discrete model is 2Δx, or even 4Δx, the ΔS(k)frac for wavelengths smaller than Δx is not shown in the figure. The solid and dashed vertical lines indicate wavelengths at 500 and 160 km, respectively. Since June 1998 had the most weather activity, and the results for June and the other two months were consistent, we only discuss the June results. We consider NARR as more close to the “real” world, especially in high wavenumbers. Therefore, if ΔS(k)frac is close to zero, it indicates a better simulation. In the following discussions based on Figs. 10a and 10b, we expect NNGR data to show more spectral power at low frequencies and Case 9 (32-km resolution) to retain more variability at high frequencies.
NNGR precipitation had more (less) spectral power than NARR precipitation for wavelengths larger (smaller) than about 900 km (about 4Δx). It was consistent with the horizontal resolution in these two reanalyses. Considering that the NARR precipitation is very close to the real one, NNGR may have too much spectral power at large wavelengths (low frequencies), consistent with its overprediction of the precipitation field. It was very unlikely that the NARR precipitation underestimated the spectral power at low frequencies by such a magnitude. Case 8 (with 32-km resolution) showed larger (about the same) variability than NARR for wavelengths larger (smaller) than about 900 km, lying between NARR and NNGR. However, since it used NNGR as the LBC, Case 8 did not retain S(k) in the large wavelengths but added more S(k) at small wavelengths to the imposed NNGR LBC. Both changes may indicate an improvement to the imposed LBC since Case 8 was closer to NARR over the entire spectrum than NNGR. Case 5 (80-km resolution with NARR as LBC) retained the variability for wavelengths larger than about 500 km and underestimated spectral power for wavelengths smaller than about 500 km. Compared to NNGR, it had more spectral power for wavelengths less than 1000 km. Comparing Case 8 and Case 5, it seems that resolution played a more important role in retaining the high-frequency spectral power than the LBC. Case 3 (80-km resolution with NNGR LBC) had lower spectral power compared with NNGR. The spectral power preserved for wavelengths less than 500 km was rather low. Case 1 and Case 2 poorly retained the spectral power in NNGR, consistent with the discussions of precipitation in previous sections. The results here demonstrate the characteristic response in ΔS(k)frac due to grid spacing, domain size, and LBC. By and large, only Case 8 may be capable of producing better spectral power distribution than the imposed LBC, and Case 5 can retain spectral power for wavelengths longer than 500 km.
For kinetic energy, NNGR had close spectral power with the NARR for wavelengths longer than about 1000 km, with a slightly positive/negative ΔS(k)frac for wavelengths longer/shorter than about 2500 km. It lost spectral power rapidly for wavelengths less than 1000 km. Case 8 consisted of higher spectral power than NNGR for most wavelengths less than about 2500 km. It was close to NARR for wavelengths longer than about 250 km with relatively large oscillations since the ratio emphasized small differences between two spectra at small scales. It then lost spectral power rather dramatically. Case 5 also generally produced slightly higher ΔS(k)fra for wavelengths longer than about 750 km and had rather high spectral power between wavelengths of 500 and 160 km, indicating more variability within this spectral range. Case 1 again had the worst performance. Unlike the precipitation case, Case 2 had much better spectral power distribution in kinetic energy, which was consistent with its proper 200-hPa jet simulation (Fig. 7c). The Case 2 and Case 3 results were similar. They added more spectral power compared to the imposed NNGR LBC for wavelengths less than about 1000 km and were similar to Case 8 for small scales (300–160 km).
It should be pointed out that this is a preliminary spectral analysis due to the caveat in the RCM spectral analysis scheme and the uncertainty in reanalyses data. As pointed out by Laprise (2003), the justification for applying spectral analysis in the regional model for approximate evaluation was mostly based on the relatively successful application of empirical methods, not based on purely mathematical grounds. More studies with different decomposition methods, RCMs, and validation datasets are necessary to continue exploring this issue.
7. Simulations for other years
Thus far, we have focused our analysis on the 1998 case. In this section, we only briefly present those analyses from the 1993 and 1995 cases for domain size and LBC experiments (Table 5). These two years had quite different climate features from the 1998 case. In 1995, the majority of precipitation occurred in May and it gradually became drier during June and July (Table 6). Two simulations were conducted for the 1995 case, with the Medium Domain and NNGR and NARR as LBC (Table 5). Because heavy precipitation occurred in May 1995 and it was gradually drying out during the remaining months in sync with the Eta/SSiB RCM trend in precipitation simulation shown in the 1998 case, it was not surprising to see a high correlation between daily observed and simulated precipitation. However, Case 11 still showed a persistent dry bias in June and July (Table 6). Only the NARR LBC in Case 12 overcame the dry bias in the June and July simulations (Table 6).
The 1993 flood in the midwestern United States developed in June and peaked in July (Xue et al. 2001). The 1993 case might be expected to be a difficult one for the Eta/SSiB since the third month presented the heaviest precipitation, while in the previous experiments the simulation in the third month tended to have a dry bias. The simulation with the Medium Domain and NNGR LBC (Case 13, Table 5) captured the variability of precipitation during that time period (not shown). However, a substantial dry bias developed in June and the correlation coefficient was low (Table 6). In the third month, the simulated precipitation in the Test Area was more than 25% less than observed (Table 6). With the NARR LBC (Case 14), the correlation coefficients improved substantially and the dry bias in June and July were substantially reduced (Table 6).
8. Conclusions
This study investigates the ability of the DDM to simulate the North American regional climate, mainly precipitation, using the Eta/SSiB RCM. The main objective is to understand whether the Eta/SSiB RCM is capable of simulating North American regional climate features at different scales under imposed LBC. The downscaling ability was examined by considering the spectral behavior of the Eta/SSiB RCM solution in regards to several factors. The domain size and location, LBCs, grid spacing, and land surface initial conditions were selected for tests for May–July of 1998, 1995, and 1993. The year 1998 was the main focus for evaluation.
The simulation results indicated that domain size, LBCs, and grid spacing were crucial for the model’s downscaling ability. In general, the Eta/SSiB had satisfactory simulations for the first month (May). The simulation problems appeared in the second and especially the third month (June and July). With inappropriate resolution, LBC, or southern boundary positions, the atmosphere over the southeastern United States was gradually drying out during the second- and/or third-month simulation, depending on the climate situation in a specific year. Several tests with different domain sizes indicated that the Eta/SSiB model in the North American climate simulation was particularly sensitive to its southern boundary position because of the importance of the moisture transport by the LLJ in summer precipitation. The model simulation was very sensitive to the intensity and position of the LLJ. In the 1998 cases, only the Eta/SSiB with 80-km resolution and NARR LBC (Case 5) or with 32-km resolution and NNGR as LBC (Case 8), both in conjunction with appropriate domain sizes that were determined after numerical testing, were able to properly simulate all three-month precipitation and other atmospheric variables, especially humidity, over the southeastern United States. The fact that the better simulation strongly depended on high resolution or the LBC associated with high-frequency information indicated that there might be strong high-frequency atmospheric variability over the Gulf of Mexico and the southeastern United States, probably associated with sharpness of LLJ. Furthermore, the spectral analysis showed that only Case 8 may be able to produce better spectral power distribution than the imposed LBC, that is, adding more variability at small scales and retaining spectral power at large scales. Case 5 retained spectral power for large wavelengths but lost spectral power for precipitation and may add too much spectral power for kinetic energy at small scales. These results suggest that the Eta/SSiB RCM with high resolution or using the LBCs containing high frequency components was able to produce better North American seasonal simulations; in particular, the simulated monthly mean precipitation could be better than that in the NNGR, which was imposed as LBC. The LBCs from different global reanalyses could only yield marginal differences in the Eta/SSiB simulation. Meanwhile, the model tests also revealed that, when the model domain was larger than the South Domain (Case 2), the model internal variability was quite large and an ensemble approach was necessary.
Acknowledgments
The authors thank Drs. Chris Castro and Roger Pielke of Colorado State University as well as Dr. Xin-Zong Liang of the Illinois State Water Survey for helpful discussions. We also appreciate Dr. Castro’s providing of the spectral analysis code for this study, and Drs. Hyun-Suk Kang and Fernando De Sales of UCLA for helping conduct the spectral analysis. Special thanks go to reviewer A for his(her) substantial and constructive comments and suggestions. Research funds were provided by NOAA NA16GP1581, NA05OAR4310010, and NSF ATM-0097260. The model runs were carried out on the NCAR supercomputers.
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APPENDIX
Spectral Analysis Method
Despite the popularity of spectral analysis in GCM studies, there is no strictly correct method of implementing Fourier decomposition in RCM analysis because of the nonperiodic RCM domain. Several methods have been proposed to provide reasonable estimates of the scale decomposition of variances (e.g., Errico 1985; Tatsumi 1986; Chen and Kuo 1992; Denis et al. 2002). Some of these methods are obtained by removing some “trend” across the regional domain to make fields “periodic” (Laprise 2003). We used the Errico (1985) method, which included a double Fourier series after removing a linear trend in each horizontal dimension across the domain.
Monthly mean precipitation (mm day−1): (a) May, (b) June, and (c) July observation (United States only); (d) May, (e) June, and (f) July NNGR.
Citation: Journal of Climate 20, 16; 10.1175/JCLI4239.1
Five-day running means for the Test Area for MJJ 1998 precipitation (mm day−1): (a) NNGR, NARR, Case 2, (b) Case 1, (c) Case 3, (d) Case 4, (e) Cases 5 and 6, and (f) Cases 8 and 9. Bold lines indicate observations. The dotted lines in (b), (c), (d) indicate the standard deviation.
Citation: Journal of Climate 20, 16; 10.1175/JCLI4239.1
Eta domains for model sensitivity experiments: (I) Large Domain, (II) South Domain, (III) Medium Domain, (IV) Small Domain, and (V) Land Domain. See text for domain definition. Dashed lines indicate the Test Area.
Citation: Journal of Climate 20, 16; 10.1175/JCLI4239.1
June precipitation (mm day−1): (a) Case 1, (b) Case 2, and (c) Case 6.
Citation: Journal of Climate 20, 16; 10.1175/JCLI4239.1
Monthly mean precipitation (mm day−1): (a)–(c) Case 3 and (d)–(f) Case 4.
Citation: Journal of Climate 20, 16; 10.1175/JCLI4239.1
Monthly mean precipitation (mm day−1): (a)–(c) Case 5 and (d)–(f) Case 8.
Citation: Journal of Climate 20, 16; 10.1175/JCLI4239.1
June 200-hPa wind (m s−1): (a) NARR, (b) Case 1, (c) Case 2, and (d) Case 3.
Citation: Journal of Climate 20, 16; 10.1175/JCLI4239.1
June 850-hPa relative humidity: (a) NARR, (b) Case 1, (c) Case 2, (d) Case 3, and (e) Case 5.
Citation: Journal of Climate 20, 16; 10.1175/JCLI4239.1
June 850-mb wind streamlines and moisture transport (g g−1 m s−1): (a) NARR, (b) Case 1, (c) Case 2, and (d) Case 3.
Citation: Journal of Climate 20, 16; 10.1175/JCLI4239.1
Fractional change in spectral power vs log10(k) and wavelength for (a) precipitation and (b) column-average total KE. The solid and dashed vertical lines indicate wavelength at 500 and 160 km, respectively. Wavelength in units of m.
Citation: Journal of Climate 20, 16; 10.1175/JCLI4239.1
Initial and boundary conditions for the 1998 cases.
Table 2a. Precipitation (mm day−1) and correlations between observation and simulation for the 1998 cases over the Test Area. Standard deviations for ensemble runs are in parentheses. (Note: NARR in this table indicates the NARR LBC; otherwise NNGR LBC is used. Similar notations are also used for the following tables)
Table 2b. Rms errors (mm day−1) for the 1998 cases over the Test Area.
Spatial correlation (%) of precipitation between observation and simulation for the 1998 cases. Standard deviations for ensemble runs are in parentheses.
Correlations (%) of atmospheric variables between simulation and NNGR/NARR for the 1998 cases over the Test Area.
Initial and boundary conditions for the 1995 and 1993 cases.
Precipitation (mm day−1) and correlations between observation and simulation over the Test Area for the (a) 1995 and (b) 1993 case.
