1 Introduction

Convective precipitation is essential for North America hydrology during summer (Laing and Fritsch 1997; Zipser et al. 2006), but deep convection often results in extreme events such as flooding, tornadoes and hail. Although convective extremes have great societal relevance, their proper simulation remains a significant challenge (Wilson and Roberts 2006; Browning et al. 2007; Geerts et al. 2017), particularly when the grid spacing of state-of-art models is too coarse to realistically simulate deep convective processes (Prein et al. 2015).

In this study we investigate the simulation of the warm season precipitation diurnal cycle in southern Canada, the U.S. and northern Mexico with a focus on the convective precipitation forming on the lee side of the North American Rocky Mountains. Convective storms in this region are characterized by a marked diurnal cycle. These storms typically initiate in late afternoon and early evening near the foothills and then propagate eastward towards the Midwest from night to early morning (e.g., Carbone et al. 2002; Carbone and Tuttle 2008).

The simulation of these propagating storms is challenging in climate models due to their coarse horizontal grid spacing, which is typically larger than 12 km for regional climate models (Jacob et al. 2014) and 100 km for global climate models (Taylor et al. 2012). At these resolutions cumulus parameterizations are required, but they are main contributor to errors and uncertainties (Déqué et al. 2007). In addition, the coarse representation of orography (Warrach-Sagi et al. 2013) and the simulation of mesoscale processes such as boundary layer processes or the land–atmosphere interaction also cause model biases.

Several studies have focused on the added value of higher spatial resolution in simulating convective precipitation (Hohenegger et al. 2008 from 25 to 2.2 km; Kendon et al. 2012 from 12 to 1.5 km; Dirmeyer et al. 2012 from 125 to 10 km; Ban et al. 2014 at 12 km and 2.2 km; Rasmussen et al. 2014 at 4 km; Sun et al. 2016 at 25 km and 4 km) and have shown that even models with 10 km grid spacing cannot reliably simulate convective precipitation. However, convection-permitting models (CPM) with at least 4 km horizontal grid spacing have shown substantially improvement on the representation of convective precipitation (Gensini and Mote 2014; Prein et al. 2015). One of the most robust benefits of CPM is their ability to more reliably simulate sub-daily convective precipitation (e.g. Richard et al. 2007; Baldauf et al. 2011; Langhans et al. 2013; Fosser et al. 2014; Rasmussen et al. 2014; Prein et al. 2015; Brisson et al. 2016). Furthermore, CPM also improve the representation of the topography and land surface interactions (Prein et al. 2013; Fosser et al. 2014; Rasmussen et al. 2014).

Various aspects of CPM over North America has been evaluated. Coniglio et al. (2013) showed that different planetary boundary layer parameterizations result in changes to the mixed layer convective available potential energy and thus to the capping inversion strength. Using a set of CPM simulations (Liu et al. 2017), Prein et al. (2016) showed that hourly extreme precipitation is well captured in the current climate models and described the reasons for increases in hourly extremes at the end of the twenty first century. This finding is consistent with those from other studies showing that, hourly precipitation rates are increasing while precipitation frequencies are decreasing (Kendon et al. 2014; Ban et al. 2015; Rasmussen et al. 2017). Additionally, convective hazardous weather is projected to increase in intensity and severity (Trapp et al. 2007, 2011; Mahoney et al. 2013; Gensini and Mote 2015; Hoogewind et al. 2017).

One of the most robust added value of CPM is their ability to better represent the warm season precipitation diurnal cycle compared to simulations that use convection parameterizations (see Prein et al. 2015 for a review). The improved diurnal cycle also results in (1) a more realistic relationship between static stability and convection (e.g. through convective available potential energy), (2) an improved simulation of cloud cover height and feedback to the surface energy balance (Fosser et al. 2014), and (3) an improved simulation of convergence zones across mountainous terrain (Barthlott et al. 2006; Fosser et al. 2014; Rasmussen et al. 2014). However, challenges remain in convection-permitting modeling, such as the representation of shallow convection and boundary layer processes (Brisson et al. 2016) and the treatment of partly under-resolved turbulence (Prein et al. 2015). Furthermore, the high computational cost of CPM makes it challenging to investigate the robustness of their performance and to assess uncertainties in future climate projections (Prein et al. 2015).

The purpose of this study is to investigate if a continental-scale CPM can reproduce the observed properties of the diurnal cycle of convective precipitation in North America, and if so, how a warmer climate would change these properties. We focus on the verification of the magnitude and timing of the diurnal precipitation peak, as well as the hourly precipitation amount, intensity, and frequency in May, June, July and August. Changes in these metrics due to climate change are also presented.

2 Data

2.1 Numerical simulation

The Advanced Research Weather Research and Forecasting Model version 3.4.1 (ARW-WRF, Skamarock et al. 2008) was used over a North American domain (Fig. 1) with 4 km horizontal grid spacing (1360 × 1016 horizontal grid points and 51 stretched vertical levels). The description of the model configuration is presented in Liu et al. (2017). The main model physics are: Thompson and Eidhammer (2014) microphysics scheme, the Noah Multi-Physics Land-surface model (Niu et al. 2011), the planetary boundary layer scheme from Yonsei University (YSU, Hong et al. 2006) and the Rapid Radiative Transfer Model (RRTMG, Iacono et al. 2008) for long and short-wave radiation.

Fig. 1
figure 1

WRF computational domain. The colors represent topography (in m asl) and the station locations are shown in purple dots for the U.S. dataset (from TD3240 and DSI-3240), and orange dots for the Canadian dataset (ECCC network). The red box is the region used in Fig. 6 (latitude: 35°–55°N, longitude: 90°–120°W)

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The initial and lateral boundary conditions for the historical simulation are from the ERA-Interim reanalysis (Dee et al. 2011) from October 2000 to September 2013 (WRF-CTR, hereafter). Spectral nudging was applied above the planetary boundary on air temperature, geopotential, and horizontal wind (moisture was not nudged), to scales larger than 2000 km every 6 h. The spectral nudging helped to improve the model performance (Liu et al. 2017) and only constrains the synoptic scales, leaving the mesoscale free to evolve with the model. This allows small-scale phenomena that dominate the diurnal cycle of precipitation during summer to evolve with only minor influences from the lateral boundary conditions.

The future climate simulation was performed by using the pseudo global warming approach (PGW; WRF-PGW, hereafter). The PGW consists of applying the monthly mean climate perturbations to the 6-hourly ERA-Interim to provide boundary conditions of three-dimensional temperature, moisture, wind, geopotential height, and sea surface temperature. When the simulations are performed, the perturbed 6-hourly data are interpolated at every time step and applied to lateral boundaries. The perturbation corresponds to the average end-of-century (2071–2100 minus 1976–2005) climate change signal of 19 Global Climate Models (GCM) from the Climate Model Intercomparison Project (CMIP5; Taylor et al. 2012) under a high-end emission scenario, which is characterized by the representative concentration pathway RCP8.5 (Riahi et al. 2011). A list of the selected GCM is presented in Liu et al. (2017).

The PGW approach was originally proposed by Schär et al. (1996) and has been successfully applied in case study experiments (Lackmann 2015; Trapp and Hoogewind 2016) and in climate change analyses (Hara et al. 2008; Rasmussen et al. 2014; Liu et al. 2017). The PGW approach minimizes the effects of climate internal variability on the results since it assumes that the weather of the current climate reoccurs at the end of the century under warmer conditions. However, the PGW approach is not able to account for sub-monthly or smaller weather changes and approximates the climate change perturbation to monthly means on the lateral boundaries. An analysis with three members from GCM used in CONUS I, shows that the average amplitude of the climate change perturbations on the diurnal cycle are 0.45 °C for temperature and 0.2 g kg–1 for specific humidity. These differences are 10% of the absolute temperature climate change signal and 7.3% for humidity. (c.f. ESM1). The simulated precipitation diurnal cycle can be influenced by not considering this sub-daily variation on the climate change perturbation. This impact should be quantified in future studies.

2.2 Observations

Observed hourly precipitation data were selected to evaluate the performance of WRF-CTR (Fig. 1), from weather stations (OBS) and the Stage IV gridded precipitation product (hereafter sIV, Lin and Mitchell 2005). The OBS dataset is a combination of two weather station networks; one from the U.S. and the other one from Canada. The 2509 stations in the contiguous U.S. (CONUS) are from the TD3240 product (Hammer and Steurer 2000) from 2001 to 2011 and the DSI-3240 product covering 2012–2013 (they are equivalent datasets until 2011). The Canadian network is operated by Environment and Climate Change Canada (ECCC, previously known as Environment Canada) with 394 stations. We only consider weather stations with five or more years of continuous records within the period from 2001 to 2013.

The sIV integrates surface radar and gauge measurements to produce a 4 km spatially-gridded multi-sensor analysis of hourly precipitation covering the CONUS region. We use sIV data from 2002 to 2013, since data in 2001 has major quality issues (Lin and Mitchell 2005).

3 Method

3.1 Datasets standardization

All the datasets (OBS, sIV, WRF-CTR and WRF-PGW) were converted to Local Solar Time (LST) and to the measurement accuracy of the majority (78%) of the TD3240 gauges, which is a bucket size of 2.54 mm. An algorithm was applied to accumulate hourly precipitation over time to stations with smaller bucket sizes (0.245 mm) and to the sIV, WRF-CTR and WRF-PGW datasets. The precipitation is accumulated over time until it exceeds 2.54 mm or a multiple thereof, which is then recorded as a new precipitation record. Any precipitation exceeding 2.54 mm or its multiples is then added to the next hour of the precipitation timeseries. If any missing value is found in the original data, the accumulated value that has not reached 2.54 mm is set to zero and the previous time-steps are also set to zero. The 2.54 mm bucket size is suitable to measure high-intensity precipitation; Mooney et al. (2017) show that the coarser resolution of the minimum bucket size does not affect the characteristics of the diurnal precipitation cycle. However, the intensity and frequency of weak precipitation (less than 2.54 mm h−1) can be affected by this standardization (Mooney et al. 2017). For instance, 10 h long precipitation events with 0.254 mm h−1 intensity will be recorded as single events of 2.54 mm. Similar adjustments to observational records have been used in previous studies (e.g. Groisman et al. 2012; Barbero et al. 2017; Mooney et al. 2017).

The observational network is composed of different gauge types (e.g. tipping-bucket and weighting-bucket) and each gauge has different recording errors (e.g. Duchon and Essenberg 2001; Parker 2016). For instance, uncertainties arise from the electric signal accuracy, the conversion to a physical-meaningful value, bias associated with wind-induced under-catch, trace amounts, and wetting and evaporation losses (e.g. Yang et al. 1998; Rasmussen et al. 2012; Scaff et al. 2015; Pan et al. 2016). In addition, errors associated with the gauge maintenance and operation over long periods of time are frequently present. The TD3240 dataset accounts for 87% of the OBS was analyzed in detail to ensure the consistency and quality of the data (Hammer and Steurer 2000, p. 16). For the sIV, the dataset were processed using an algorithm, which also includes quality-control processes to produce precipitation (WSR-88, Fulton et al. 1998). At the seasonal timescale, the bias of WRF-CTR was within the observational uncertainty comparing with different gridded observational datasets, but WRF-CTR has a systematic warm and dry bias during late summer in the central U.S. (Liu et al. 2017).

3.2 Diurnal cycle characteristics

Harmonic functions are used to estimate the timing and the magnitude of the diurnal precipitation peak. Diurnal and semi-diurnal components are calculated for the analysis (i.e. the 24 h and 12 h harmonic functions of the diurnal cycle). This method allows us to summarize the diurnal cycle in two distinctive characteristics and eliminates noise from the data (Li et al. 2009; Li and Smith 2010a). The harmonic analysis approximates the diurnal cycle of precipitation using a combination of sine and cosine functions, considering the first two harmonics. In Eq. (1) the precipitation (Pt) at time t is defined by the linear sum of the mean precipitation P in 24 h (first term at the right-hand side), and the sine and cosine function for a 24- and 12-h cycle. The cycles are adjusted by the coefficients A1 and B1 for the first harmonic (second and third term at the right-hand side) and adjusted by the coefficients A2 and B2 for the second harmonic (the last two term at the right-hand side) (Wilks 2011, p. 432).

$$P_{t} = P + A_{1} \cdot \cos \left( {\frac{2\pi t}{24}} \right) + B_{1} \cdot \sin \left( {\frac{2\pi t}{24}} \right) + A_{2} \cdot \cos \left( {\frac{4\pi t}{24}} \right) + B_{2} \cdot \sin \left( {\frac{4\pi t}{24}} \right).$$
(1)

Equation (1) is fitted to all datasets on monthly mean hourly precipitation rates in each month between May and August. This calculation was performed for each station in OBS and for each grid point in sIV, WRF-CTR and WRF-PGW. Some examples are shown in Figs. 2 and 3.

Fig. 2
figure 2

Timing of the diurnal precipitation peak (in hours at Local Solar Time) in June, derived from the harmonic analysis. a, b Show bservations (OBS) and stage IV (sIV). c Is the WRF historical runs (WRF-CTR). d, e Show the differences between OBS and WRF-CTR, and between sIV and WRF-CTR, respectively

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Fig. 3
figure 3

Magnitude (in mm) of the diurnal precipitation peak in June. a, b Show observations (OBS) and stage IV (sIV) data. c Shows the WRF historical runs (WRF-CTR). d, e Show the differences between OBS and WRF-CTR, and between sIV and WRF-CTR, respectively

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The precipitation amount, intensity and frequency are analyzed in this study. The precipitation amount is the average precipitation for the entire time series for each month and each hour (in units of mm h−1). The intensity is calculated as the nonzero-average of hourly precipitation for each month (in units of mm h−1). The precipitation frequency is the number of hours with nonzero precipitation (in units of number of occurrences).

The eastern propagation of precipitation is analyzed in the central U.S. considering four sub-regions with similar time of maximum precipitation for the diurnal cycle in June. June was chosen because of the high frequency of mesoscales convective systems. The data in each sub-region are clustered into 6-h bins; from 15 to 20 h (afternoon), from 21 to 02 h (night), from 03 to 08 h (early morning), and from 09 to 14 h (late morning) in LST.

To quantify the performance of the WRF-CTR, the bias is calculated as the difference between the WRF-CTR and OBS, and WRF-CTR and sIV. The bias is derived by comparing each model grid cell with the closest grid cell in sIV and with rain gauge observations if there are any within the grid cell area. The statistical significance of the climate change signal between the WRF-CTR and WRF-PGW is assessed using the non-parametric Mann–Whitney rank sum test at a significance level of 5% (Wilks 2011, p. 159).

4 Results

4.1 Timing of the diurnal precipitation peak

The spatial patterns of the diurnal cycle precipitation peak timing in OBS and sIV are well simulated by WRF-CTR (Fig. 2a–c and ESM2 Figs. S1–S3). The transition is well captured from afternoon peaks over the lee-side of the central Rocky Mountains to night peaks in the Great Plains. The night to early morning transition (east of 100°W) is less pronounced in WRF-CTR than in the OBS and sIV. In July a northward expansion of the eastward propagating signature is present from the Great Plains towards the Canadian Prairies. This signature reaches its northernmost extend in August, which is well captured in WRF-CTR (ESM2 Figs. S2 and S3).

WRF-CTR also simulates the observed (from sIV) sharp land-sea contrast of the diurnal precipitation peak along the Atlantic and Pacific coastlines and near the Great Lakes (Fig. 2b, c). The thermal contrast along the coastal boundary, leads to the development of convergence lines (and thus a solenoidal circulation) that helps trigger convective precipitation near the coast. This coastal effect on the precipitation timing, has been studied in the tropics and on islands (Carbone et al. 2000; Keenan and Carbone 2008; Li and Carbone 2015).

The largest model biases are found in the central U.S. east of 100°W (Fig. 2d, e), with a improperly simulated early morning peaks. Compared to OBS, the largest bias in domain averaged peak timing occurs in June (− 0.7 h), whereas when is compared to sIV it occurs in May (− 4 h, domain average).

4.2 Magnitude of the diurnal precipitation peak

The dominant spatial patterns of the diurnal precipitation magnitude are captured in WRF-CTR (Fig. 3). The simulated and observed magnitude increases to the southeast and shows a relative maximum in the central U.S. The model overestimates the magnitude around the Florida peninsula (approximately 0.7 mm higher in WRF-CTR than sIV in June, not shown) and northward, along the east coast (Fig. 3d, e). Compared to the OBS, the largest monthly mean bias occurs in June (44%; 14% compared to sIV). The Midwest shows a low bias in WRF-CTR (approx. 0.15 mm in Fig. 3), which is consistent with the low precipitation bias reported in Liu et al. (2017) and Prein et al. (2017). The dry-bias in the midwest and part of central CONUS (Liu et al. 2017) is likely associated with the model’s limited capability in simulating organized convective storms under weakly forced synoptic conditions (Prein et al. 2017). A difficulty in simulation in current climate models is the storms that develop under weak large-scale forcing heavily depend on local scale processes (e.g., cold pools, moisture gradients). The soil moisture and its role on the water cycle can be another possible feedback to argue about the systematic bias. Soil moisture affects the latent and sensible heat exchange between the land surface and the atmosphere, which in turn affect the surface air temperature, the atmospheric moisture and precipitation characteristics. The impact of soil moisture on precipitation and its diurnal cycle needs further investigation.

4.3 Propagation of organized convection

The simulation of eastward propagating convection is analyzed by investigating the transition on four sub-regions (top panels in Fig. 4). The afternoon and night peak sub-regions are well captured in WRF-CTR (Fig. 4a, b), with a maximum bias of 22%. The simulated early morning peak sub-region shows an underestimation at night and in the early morning (Fig. 4c). When the model is compared to the sIV data, an overestimation in the afternoon is present (around ± 0.05 mm h−1). This is consistent with the underestimation of the frequency of eastward propagating storms that leads to an underestimation of early morning precipitation in WRF-CTR (Prein et al. 2017). In the early morning peak sub-region, the magnitude of the simulated diurnal precipitation is underestimated compared to sIV (Fig. 5, triangles), consistent with Fig. 3d, e. The simulated magnitude for the late morning and afternoon peak sub-regions varies from a slight overestimation compared to OBS, to an underestimation when compared to sIV (Fig. 5, and ESM2 Figs. S7–S9). The averaged timing of the diurnal precipitation peak is well simulated in most of the regions (Fig. 5, lower panels), with the lowest skill in the early morning peak sub-region (green in Fig. 5, and ESM2 Figs. S1–S3). The early morning peak sub-region shows a delayed peak time in WRF-CTR compared to OBS and sIV. The peak in the sub-regions with late morning and afternoon peaks occurs slightly earlier compared to the OBS and sIV with biases ranging from − 1 to − 34% (up to 4 h), while the precipitation peak timing in the night peak sub-region show a small delay with biases ranging from 7 to 12% (up to 3 h). The average precipitation intensity shows a maximum bias of − 12% (Fig. 4e–h). The average precipitation frequency is typically overestimated in the afternoon and night peak sub-regions in May with bias up to 90% (ESM2 Fig. S7i, j) and in June with bias up to 133% (Fig. 4i, j). In July and August, precipitation frequency is better simulated (Fig. 4i–l, bias up to 49%).

Fig. 4
figure 4

Precipitation diurnal cycle from observations (OBS, thin solid line), Stage IV data (sIV, bold solid line), WRF-CTR (dotted line) and WRF-PGW (dashed line) in June. The sub-regions are defined by clustering stations with similar precipitation peak timing in June. Only stations (dots in maps at the top) with a peak precipitation magnitude greater than 0.1 mm h−1 are considered. The shaded area in the time-series shows the inter-annual variability (of 13 years for OBS, WRF-CTR and WRF-PGW, and 12 years for sIV)

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Fig. 5
figure 5

The comparison of the magnitude of the precipitation peak (in mm) and the timing (in hours at LST) from a two-harmonic fit of the diurnal cycle between the OBS (crosses) and sIV (triangles) corresponding to the horizontal axis and WRF-CTR to the vertical axis. Panel shows results for individual months. The horizontal and vertical error-bars at each point represent the 25th and the 75th percentile of spatial variability. The four colors represent four sub-regions defined in Fig. 4. The WRF-CTR biases (as percentages) are shown in gray boxes

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The eastward propagation of precipitation (Fig. 6) shows a consistent preferential region between 105° and 95°W amongst datasets. The propagation of precipitation varies through months and latitudes. The sIV shows larger precipitation amounts (dots size in Fig. 6) than OBS, especially between 45° and 50°N (Fig. 6a–h). The propagation speed in OBS and sIV is approximately 12 m s−1, consistent with Li and Smith (2010b). In all months, the simulated propagation is slightly faster (approximately 14 m s−1) than the OBS and sIV. The magnitude of the precipitation peak shows a strong decay in the model during late night and early morning (0–6 h LST) between 40° and 45°N in July and August, from 100°W eastward. This result is also highlighted by Prein et al. (2017), who related the dissipation of the storms to model deficiencies in simulating the propagation of organized convective systems under weak synoptic scale forcing conditions, which typically occur in July and August.

Fig. 6
figure 6

The timing of the diurnal precipitation peak in hours at Local Solar Time vs. longitude. Different latitudinal bands are shown in different colors. The dot size represents the relative magnitude of the diurnal precipitation peak with values greater than 0.1 mm h−1. The analyzed region is highlighted by a red box in Fig. 1. The red solid lines show a propagation speed of 12 m s−1 from Li and Smith (2010b). The black dashed lines show a propagation speeds of 10 m s−1 and 14 m s−1

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4.4 Climate change impact on the precipitation diurnal cycle

The diurnal cycle shows no substantial change in the precipitation amount in WRF-PGW (Fig. 4) compared to WRF-CTR. However, the WRF-PGW simulation shows a clear increase in hourly precipitation intensities compared to WRF-CTR in all sub-regions (Fig. 4e–h). At the same time the precipitation frequency is decreasing in WRF-PGW (Fig. 4i–l), so this decrease in frequency and the increase in intensity compensate each other, resulting in similar precipitation amount.

Changes in the timing of the diurnal precipitation peak are not systematic and are non-significant in May (Fig. 7a), consistent with the remaining summer months. The magnitude of the diurnal precipitation peak shows an increase throughout the domain in WRF-PGW (Fig. 7b), with statistically significant increase (black circles) in May over the northern region. In July and August, the magnitude of the diurnal precipitation peak significantly decreased in South Dakota, Nebraska, Kansas, Missouri and Michigan (ESM2 Fig. S10).

Fig. 7
figure 7

Difference between WRF-PGW and WRF-CTR in May, for: a timing of the diurnal precipitation peak in hours at local solar time, b the magnitude of the diurnal precipitation peak (relative change in %), c average precipitation intensity (mm h−1) and d average precipitation frequency (# of events). The spatial grid is reduced to one filled circle every 25 model grid cells to enhance the visibility of the results (circle distance ~ 100 km). Circles with black outlines indicate that at least 20% of the 25 × 25 grid cells show statistically significant changes (5% level using the Mann–Whitney rank sum test)

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The increase in precipitation intensity (Fig. 7c and ESM2 Fig. S11) is present over the entire domain and all months. A statistically significant change occurs in the northern and eastern part of the domain, however the largest increase, but not significant, occurs in the southern part of the domain. The frequency (Fig. 7d) shows an increase in May in south of Canada and a decrease in the southeast U.S. The region with decreasing frequencies is extended to the central U.S. and southern Canada during mid-summer. A statistically significant frequency decrease is present in July and August over the western U.S. including Nevada, Idaho and Wyoming (ESM2 Fig. S11).

5 Summary and conclusions

This study investigates if a North American scale convection-permitting model at 4 km horizontal grid spacing can reproduce the observed diurnal cycle of precipitation during the warm season. The evaluation of the climate change impact on the precipitation diurnal cycle is presented.

We use hourly precipitation datasets—a station-based dataset and a gridded dataset which merges station and radar data—to assess the impact of observational uncertainties for the model evaluation. Results show that the simulated timing of the diurnal precipitation peak agrees with observational datasets in areas with afternoon to night peaks. The accurate simulation of the transition from evening to night-time peaks, over the leeside of the Rocky Mountains, related to propagating mesoscale convective systems, is especially encouraging. The observed movement speed of these storms (approx. 12–14 m s−1 as Li and Smith 2010b) is also captured by the model. These results represent an improvement of the diurnal cycle simulation compared with previous simulations at coarser horizontal grid spacing, which use cumulus parameterizations (e.g., Mooney et al. 2017). Also, the hourly precipitation intensity and frequency is improved compared to coarser resolution models (Fosser et al. 2014; Mooney et al. 2017). However, there are still significant biases in the simulation which include:

  • An overestimation in the magnitude of the diurnal precipitation peak over Florida (around 0.7 mm), which is consistent with the overestimation of precipitation reported by Liu et al. (2017). Since there is a significant warm bias along the coast (see Fig. 12 in Liu et al. 2017), we hypothesize that WRF overestimate the sea breeze effect, which should be further investigated.

  • In July and August, the diurnal cycle of precipitation intensity is underestimated over the central U.S., which is consistent with a dry bias described by Liu et al. (2017). The modeled precipitation frequency is overestimated in early summer and improves later in the warm season. We are currently working on reducing the dry biases by improving the representation of the land surface, radiation, and turbulence schemes.

  • The largest biases simulating the timing of the diurnal precipitation peak are found in the central CONUS with observed precipitation peaks in the early morning. This is related to an underestimation of the frequency of propagating convective systems, which agrees with the results presented by Prein et al. (2017) and Haberlie and Ashley (2019). The moisture flux within the low-level jet zone is properly represented in the model when compared to the ERA-Interim reanalysis (Rasmussen et al. 2017). More detailed analyses of the low-level jet, cold pools, potential vorticity anomalies as well as other atmospheric processes are needed to better understand the origin of these biases.

The most consistent climate change signal is an increase in precipitation intensity throughout the summer, also consistent with previous studies (e.g. Stone et al. 2000; Prein et al. 2016). This increase, along with a significant decrease in the precipitation frequency, indicates more frequent precipitation events with high rain rates followed by longer dry periods, which agrees with Rasmussen et al. (2017). This will have impacts on the agricultural sector and will alter future flooding risk.

Regional climate models on a CPM configuration are robust tools to study climate change impacts on precipitation, as has also been demonstrated in previous studies (Kendon et al. 2014, 2017). Future studies should further explore the causes and implications of the central U.S. warmer bias in the historical simulation and how they affect the simulation of future climates. Finally, a more thorough assessment of the model’s quality outside of the U.S., i.e., in Canada and Mexico, will be beneficial.