Summer and winter daily heavy precipitation events (events above the 97.5th percentile) are analyzed in regional climate simulations with 36-, 12-, and 4-km horizontal grid spacing over the headwaters of the Colorado River. Multiscale evaluations are useful to understand differences across horizontal scales and to evaluate the effects of upscaling finescale processes to coarser-scale features associated with precipitating systems.
Only the 4-km model is able to correctly simulate precipitation totals of heavy summertime events. For winter events, results from the 4- and 12-km grid models are similar and outperform the 36-km simulation. The main advantages of the 4-km simulation are the improved spatial mesoscale patterns of heavy precipitation (below ~100 km). However, the 4-km simulation also slightly improves larger-scale patterns of heavy precipitation.
Heavy precipitation events have high impacts on the society, economy, and ecology by causing floods, landslides, and avalanches. In the headwater region of the Colorado River (hereafter Colorado Headwaters), the focus area of this study, heavy precipitation is not only a hazardous weather event but also an important part of the hydrological water balance (e.g., Petersen et al. 1999; Serreze et al. 2001; Weaver et al. 2000).
One of the most important processes leading to heavy precipitation events is deep convection. However, convection parameterizations in climate models can introduce large errors in the simulation of precipitation (see, e.g., Molinari and Dudek 1992; Dai et al. 1999; Brockhaus et al. 2008). By decreasing the horizontal grid spacing in regional climate models (RCMs) below ~4 km (Weisman et al. 1997) deep convection starts to be partially resolved and convection parameterizations can be omitted. Furthermore, this high resolution leads to a more realistic representation of orography and surface fields, which is especially important in regions with complex orography like the Colorado Headwaters. However, simulations at this fine resolution demand significant computational resources. Ikeda et al. (2010) and Rasmussen et al. (2011b) demonstrated improvements of simulated snowpack at grid spacings less than 6 km (compared to coarser-resolution simulations) due to the improved representation of mesoscale orographic forcing. Hohenegger et al. (2008) showed improvements for the locations of the maxima and diurnal circle of precipitation in 2.2-km simulations over the European Alps compared to its 25-km parent simulation for one summer convective season.
In this study we use output from 8-yr model simulations, with three different grid spacings of 4, 12, and 36 km. This dataset enables us to investigate a sample of heavy precipitation events, which makes a statistical evaluation of the simulation of these events possible. We are focusing on events in December–February (DJF) and June–August (JJA) because heavy precipitation events in these seasons have typically different synoptic-scale forcing and mesoscale processes. In March–May (MAM) and September–November (SON) a mixture of DJF and JJA types of heavy precipitation events can occur. Analyses from these transitional seasons are briefly described in section 3f.
The main research questions in this study are as follows:
What is the effect of grid spacing on the representation of heavy precipitation events in the Colorado Headwaters?
On which spatial scales do differences occur?
Which grid spacing should be used to simulate heavy precipitation events?
2. Data and methods
a. Model and data
The simulations were performed with the Weather Research and Forecasting model (WRF) version 3.1.1 (Skamarock et al. 2008) for an 8-yr period from 1 January 2001 to 31 December 2008 (plus three months of spinup) by the Colorado Headwaters research group at the National Center for Atmospheric Research (NCAR) (Rasmussen et al. 2011a). Three single domain simulations with horizontal grid spacing of 4 km (WRF4), 12 km (WRF12), and 36 km (WRF36) were performed. The initial conditions and 3-hourly lateral boundary forcing are derived from the 32-km North American Regional Reanalysis (NARR; Mesinger et al. 2006). The domain and model setup are the same as in Ikeda et al. (2010), Rasmussen et al. (2011b), and Liu et al. (2011). While deep convection was parameterized in the 12- and 36-km simulations using the Betts–Miller–Janjić scheme (Betts and Miller 1986; Janjić 1994), no convective parameterization was used in the 4-km simulation because deep convection is partially simulated at this grid spacing (Weisman et al. 1997). Nonetheless, properties such as maximum vertical velocities are underestimated even in simulation with a 4-km grid (Weisman et al. 1997). However, Langhans et al. (2012) demonstrated that in simulations with 4.4-, 2.2-, 1.1-, and 0.55-km horizontal grid spacing bulk flow properties such as heating or moisture tendencies but also precipitation are converging and are nearly resolution independent.
The evaluation of simulated heavy precipitation events is conducted in the Colorado Headwaters region (the area inside the dashed rectangle in Fig. 1) using shielded weighing precipitation gauges at 99 stations within the Snowpack Telemetry (SNOTEL; white dots in Fig. 1) network (Serreze et al. 1999). All 99 stations have a complete record of daily precipitation for the entire period 2001–08. The stations are located in the region with highest snowpack (between 2400 and 3500 m above mean sea level) in forest clearings. The SNOTEL precipitation gauges have a resolution of 2.5 mm. The largest error source of weighing type gauges is the undercatch of snowfall due to wind (Serreze et al. 1999; Yang et al. 1998; Rasmussen et al. 2012). This error might be especially large for heavy precipitation events that typically occur with strong wind. However, the forest clearings in which SNOTEL gauges are typically located reduce the wind speed to less than 2 m s−1, leading to an underestimation of snowfall by only 10%–15% (Rasmussen et al. 2012). For comparisons of SNOTEL observations with model precipitation, the model values at the four nearest grid points around each station are weighted with inverse-distance averaging. In addition to the SNOTEL observations, the Climate Prediction Center (CPC) precipitation dataset (Higgins et al. 2000) and the NARR precipitation are used for comparisons.
In this study, heavy precipitation events are defined as events above the 97.5th percentile of daily domain-averaged total SNOTEL precipitation within the 8-yr period 2001–08. Compared to the 30-yr period 1980–2010 in DJF four of the 10 most extreme events occurred within 2001–08, including the two most extreme events (the 30- and 15-yr events in terms of return level in 1980–2010). In JJA, 2 of the 10 most extreme events occurred in the simulated period, namely the 7.5- and 3.75-yr events in 1980–2010. Selecting events above the 97.5th percentile leads to a sample of heavy precipitation events consisting of the 18 most intense precipitation days in each season within 2001–08. The selection of heavy precipitation events from SNOTEL observations means that only events at high altitude are investigated. A selection based on valley stations may lead to a different set of events.
b. Spectral decomposition of precipitation fields
The discrete cosine transformation (DCT) is used here to decompose heavy precipitation fields in additive components of variance according to different wavelengths. This allows comparisons of the three simulations with each other and observations in spectral space and estimating their effective resolution.
The DCT was first applied for atmospheric spectra analysis by Denis et al. (2002). When applied on regional domains, its advantage to standard (periodic) Fourier transformation is that aliasing of large-scale variance into short scales is limited.
In Eq. (2) is the precipitation value at the grid points , and is the spectral coefficient corresponding to the wavenumbers. In the next step is used to calculate spectral variances according to
c. Analysis of different horizontal scales
The skill of the simulations and the NARR and CPC datasets to accurately reproduce point measurements for different horizontal scales of precipitation systems is evaluated by resampling the data to 31 common grids with different grid spacings starting from those of the 4-km simulation to a 189-km grid. The large range of 4–189 km is selected to investigate the upscaling effect of small-scale features, which are resolved in the 4-km simulation, to larger scales. The upper limit of 189-km grid spacing was chosen to have at least six grid points within the Colorado Headwaters. The resampling technique, applied in this study, does not use any interpolation and is able to spatially conserve precipitation amounts within a region [for details about the method, see Suklitsch et al. (2008)]. On each new grid, precipitation values are calculated at the locations of SNOTEL station as described in section 2a. Those values are then compared to the SNOTEL observations to calculate the spatial correlation coefficients (CCs), spatial standard deviations normalized by the standard deviation of SNOTEL (NSDs), and root-mean-square errors (RMSEs). The resampling approach enables the evaluation of the same spatial scales in all three simulations and in CPC and NARR data and makes it possible to conduct a quantitative analysis of the upscaling effect of small-scale features on larger scales.
d. Spatial similarities and dissimilarities
Correlograms and variograms are frequently used in geostatistics to explore the spatial organization of different phenomena (e.g., Isaaks and Mohan Srivastava 1989). They illustrate how the correlation and variance depends on spatial scale. Therefore, we take simulated/measured precipitation at SNOTEL locations and sample data pairs at different distances. The distance between a given data pair is usually called the “lag” (plus/minus some lag tolerance t; in this study t = 10.000 m). The lag vector consist of I values where and . The lagged versions of the precipitation at locations is . Defining as the number of pairs separated by lag (plus/minus t) the statistics for lag can be computed as
where and are the means of the and values:
and and are the corresponding standard deviations:
Once and are calculated they can be plotted against . The plots are then called correlograms and variograms. In correlograms similarities within a field are measured without accounting for differences in precipitation magnitude whereas variograms give insights in dissimilarities and are sensitive to differences in magnitude.
3. Results and discussion
a. Spatial patterns of mean heavy precipitation events
Figure 2 displays the average of the heavy precipitation sample in the Colorado Headwaters in DJF (Figs. 2a–d) and JJA (Figs. 2e–h). In DJF domain average precipitation measured at SNOTEL stations (Fig. 2a) is more than twice as high as JJA precipitation (Fig. 2e). Also the spatial patters differ. In DJF (Fig. 2a) the precipitation maximum is located in the southwestern part of the Colorado Headwaters because in this season heavy precipitation is typically associated with a southwesterly flow bringing moist air from the Pacific. In JJA, when typically situations with weak synoptic-scale forcing lead to strong precipitation, the heaviest precipitation occurs in the northeastern part of the Colorado Headwaters (the Front Range Mountains; Fig. 2e).
Comparing the simulations, in DJF smaller grid spacings lead to more precipitation whereas in JJA the opposite is true. In DJF there is only ~3% of total precipitation convective induced in the WRF12 and WRF36 simulations, which means that there is only a small amount of precipitation coming from the convection parameterization. In this season the higher precipitation values in simulations with smaller grid spacings are probably due to the improved representation of mesoscale orographic forcing (Ikeda et al. 2010; Rasmussen et al. 2011b). In JJA the convective precipitation amounts for 62% in WRF12 and 69% in the WRF36 simulation (compared to zero in the WRF4 simulation), which contributes to the overestimation of heavy precipitation in this season. A more detailed analysis of differences between observed and simulated precipitation events is given in section 3c.
b. Power spectra
Figure 3a illustrates the median power spectra of the 18 simulated DJF heavy precipitation events, the spectra of the model topography, and those of the CPC and NARR datasets. Most variance can be found in the large scales (high wavelengths). Clearly visible is the strong relationship between the spectra of the simulated events and those of the orography. This shows the strong relationship of precipitation to orographic uplift in the region in DJF. The spectra of the 4- and 12-km simulations start to diverge at wavelengths smaller than ~50 km (clearly for DJF) where the 4-km simulation has higher variability. This spatial scale indicates the effective resolution of the 12-km run, which is approximately 4 times its grid spacing. The same ratio can be seen for the 36-km simulation, and similar results were found for WRF kinetic energy spectra by Skamarock (2004). The CPC spectrum agrees fairly well with the simulated spectra. The NARR spectrum shows a lower variability than the other spectra.
In JJA (Fig. 3b) the relationship between the spectra of the orography and those of the simulated events is much weaker than in DJF. This is because the heaviest DJF precipitation occurs typically near to mountain slopes where strong upslope winds exists whereas heavy JJA precipitation originates from deep convection, which can be induced by upslope winds but is not restricted by the location of mountain slopes. Between ~50 and ~170 km the 12-km run and between ~80 and ~300 km the 36-km simulation has higher variances than the 4-km run, which is probably caused by the convection parameterization in the coarser models. As in DJF, the spectra of the CPC dataset in JJA also fit very well to the simulations whereas the variances in the NARR spectrum are lower.
c. Spatial differences
Relative differences between the averaged 18 events (simulated minus observed) in DJF are depicted in Figs. 4a–c for the 4-, 12-, and 36-km simulations. During this season all simulations tend to overestimate heavy precipitation in the northern part of the domain. The overestimation is also larger at low elevation stations and tends to get smaller above ~3200 m. Precipitation differences increase with resolution but the RMSEs decrease because absolute differences get smaller.
In JJA (Figs. 4d–f), the 4-km simulation is clearly more robust in terms of average difference, RMSE, and spatial patterns compared to the coarser-resolution simulations that tend to overestimate heavy JJA precipitation. Differences of individual events are additionally less spread in the 4-km run, which means that not only the median but also single events are better represented compared to the coarser simulations. There is no clear zonal, meridional, or height dependency in the differences.
d. Scale-dependent analysis
In this section the spatial CCs, NSDs, and RMSEs of the simulated, CPC, and NARR data are evaluated for a range of horizontal scales as described in section 2c.
In DJF the highest median CCs can be found for the 4-km simulation on its original grid (Fig. 5a). At their resolved scales the 12- and 4-km simulations have very similar CCs whereas the 36-km run has slightly lower CCs and larger sample variabilities. The CPC data have higher CCs than the simulations below ~90 km while the NARR dataset has lower values on all scales. Similar results can be found for the NSDs (Fig. 5b). The 4-km simulation has closest values to one at scales below 12 km and very similar values to the 12-km run afterward. The 36-km run has generally higher median NSDs, while the CPC and NARR data show lower values. The smallest RMSEs in the 4-km simulation show robustness especially at scales larger than 50 km (Fig. 5c). All simulations improve the RMSEs of the NARR driving data.
The median CCs in JJA are generally smaller and the sample spread larger compared to DJF (Fig. 5d). This is probably due to the stochastic nature (nonlinear land–atmosphere, cloud–cloud, and/or cloud–radiation interactions that can grow upscale, particularly under generally weak synoptic forcing in JJA) of convective precipitation. At scales from 12 to 60 km, the 12-km run has higher CCs than the 4-km simulation. CPC and NARR have higher CCs below ~120 km. The 4-km simulation has high NSDs below 12 km and similar values to the 12-km simulation and CPC afterward (Fig. 5e). Below 100 km, the 36-km run clearly has higher variability than the finer grid datasets. The sample spread of NSDs is smallest for the 12-km simulation above 20 km. The best RMSEs and smallest sample variability below ~100 km are achieved with the 4-km model (Fig. 5f). The smallest RMSEs can be found in the CPC dataset whereas the NARR RMSEs are similar to the simulations.
e. Spatial similarities and dissimilarities
Figure 6 shows median correlograms and variograms from the WRF simulations, CPS, NARR, and SNOTEL observations. All simulations show median CCs that are larger than SNOTEL at scales below ~70 km in DJF (Fig. 6a). Some of these differences may be due to measurement errors at the SNOTEL sites. Below 70 km the 4-km run is most similar to the SNOTEL sites. At scales larger than ~70 km the correlations of the 4- and 12-km simulations start to match the SNOTEL observations, whereas the 36-km run has too high correlations until ~120 km. The correlation between pairs of stations becomes anticorrelated at ~190 km, which is the typical scale of a mountain range in the Colorado Headwaters (see also the peak in Fig. 3). The CCs of NARR and CPC are similar to those of the WRF12 simulation. The DJF variogram (Fig. 6b) shows weaker variability in all simulations at scales below ~70 km than SNOTEL. The 4-km simulation shows the most realistic spatial variability at all scales while the NARR and CPC data have the lowest variability.
In JJA (Fig. 6c), CCs at small scales are generally lower than in DJF because of the higher spatial variability and smaller size of convective precipitation cells (anticorrelation starts at ~110 km). All simulations have higher CCs than SNOTEL at scales below ~100 km. The 4-km simulation performs best at these scales while above ~100 km all simulations begin to match the SNOTEL observed CCs. For scales above ~260 km all simulations except the 4-km model generate stronger anticorrelations than SNOTEL. The CPC CCs are similar to those of the WRF12 simulation while the NARR CCs fit more to those of the WRF36 run. Variability in all simulations is lower than that of SNOTEL in JJA (Fig. 6d). At scales below ~110 km the 4-km simulation has the closest correspondence with observations, and at larger spatial scales the 36-km run matches the 4-km simulations. As in JJA variances are lowest in the CPC and NARR datasets.
f. Analyses of MAM and SON heavy precipitation
In the transition seasons MAM and SON heavy precipitation can arise from a mixture of DJF (large-scale frontal system) and JJA (airmass thunderstorm) types of storms. The mean precipitation of the SON and MAM heavy precipitation sample (12.3 mm day−1 in MAM and 14.8 mm day−1 in SON) is higher than the mean in JJA but lower than that in DFJ. Also, the convective part of the total precipitation in the WRF12 and WRF36 runs is ~12% in MAM and ~33% in SON, between the percentages in DJF and JJA (see section 3a). The highest observed precipitation values in MAM are in the northeastern part of the domain (similar to JJA) and in SON in the southwestern part (similar to DJF). In both seasons the domain total heavy precipitation increases with decreasing grid spacing (similar to DJF). The lowest RMSEs are found in the WRF4 simulation followed by the WRF12 and WRF36 runs. In MAM and on small scales in SON the WRF4 simulation has higher CCs than the coarser simulations. The correlogram and variogram analyses lead to conclusions similar to those for JJA and DJF. The WRF4 simulation resembles correlations from SNOTEL observations best at scales below ~100 km and has most realistic variances on larger scales.
4. Summary and conclusions
Comparisons of heavy precipitation events, defined as the highest 2.5 percentile, in the Colorado Headwaters between SNOTEL observations and high-resolution simulations with the WRF model show a good agreement in DJF, especially in the 4- and 12-km simulations. JJA heavy precipitation is more difficult to simulate because of the stochastic component of convective precipitation and the generally weaker synoptic-scale forcing. In this season the convection-permitting 4-km run is able to generate a nearly bias-free sample of heavy precipitation events and outperforms the coarser gridded simulations, which generally overestimate precipitation. In DJF a grid spacing of 12 km seems to be sufficient to get patterns of heavy precipitation comparable to the 4-km run.
Most variance and spatial information can be found in the large-scale patterns (above ~100 km). This is the reason why the 4- and 12-km simulations show only small advantages over the 36-km run at these scales. Improvements of large scales due to modeled upscaling of small-scale features (e.g., deep convection, updrafts at mountain slopes) that are resolved in the 4-km run are usually small but do occur in the majority of evaluations. The major advantages of high-resolution simulations are found for small scales. In particular, the 4-km run outperforms coarser-resolution simulations by producing spatially more independent and variable fields at scales below ~100 km that agree well with the SNOTEL observations. In addition, large-scale features such as the domain average JJA total precipitation are also improved in the WRF4 simulation by avoiding error-prone convection parameterization schemes.
A notable result is the significant improvements in the WRF simulations compared to the NARR forcing data. The correlograms and variograms show that all simulations (especially the WRF4 run) were able to improve the spatial variability and interdependencies of the NARR dataset. Furthermore, the spatial correlation coefficients and the root-mean-square errors are improved in all seasons (except JJA), which highlights the downscaling ability of heavy precipitation events with the WRF model.
The choice of horizontal grid spacing for an RCM to simulate heavy precipitation is dependent on the underlying question. If the main interest is accurate representation of large-scale (e.g., Colorado Headwaters) average heavy precipitation, even 36-km grid spacing can be sufficient in SON, DJF, and MAM. This is not true in JJA when the convective part of modeled precipitation is large. In this season heavy precipitation amounts are significantly improved in the 4-km grid spacing simulation. If the model output is used for impact studies that focus, for example, on water catchments, ecology in mountain lakes and rivers, or economic losses from extreme events, the 4-km model has benefits by improving especially mesoscale structures, which can be essential for these applications. In addition, late season runoff is accurately simulated from the 4-km simulation results due to its accurate simulation of the high snowpack values at the highest elevations, which typically melt two months earlier in the coarser-resolution 36-km simulation.
Further work is in progress to study the representation of atmospheric processes in extreme precipitation events in models with parameterized and explicitly resolved convection, including the use of large-eddy simulations. Furthermore, we see great potential in applying convection-permitting simulations in climate studies to analyze possible changes in extreme events. This would have the advantage that errors from convective parameterization schemes can be avoided and uncertainties are reduced.
This work was supported by the National Science Foundation (NSF) under the NCAR Water System Program, through the NSF EASM contract on Assessing High-Impact Weather Response to Climate Variability and Change Utilizing Extreme Value Theory, and by the Austrian Marshall Plan Foundation. We acknowledge high-performance computing support provided by NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation.