1 Introduction

Precipitation is one of the most vital water resources and hydrometeorological variables for terrestrial ecosystems. The simulation and prediction of precipitation are necessary to evaluate the influence of climate change. Accurate precipitation modeling with high spatiotemporal resolution becomes particularly pressing for assessing water resources, hydrological processes, and ecosystems under climate change (Giorgi 2006; Fowler and Wilby 2010). General circulation models (GCMs) are major tools for climate modelling and can provide abundant large-scale climate information. However, GCMs have limited capability to provide a detailed description of regional climate due to their coarse resolutions (e.g., ~ 100 km) and oversimplified model physics (Berg et al. 2013). There is an obvious gap between the scales of GCMs and the scales at which human society and ecosystems are strongly influenced (e.g., flooding and drought) (Pieri et al. 2015). This gap can be filled to a large extent by regional climate models (RCMs) with fine resolutions. Driven by boundary conditions provided by GCMs or reanalysis data, RCMs are able to reproduce regional climate processes over complex terrain and under various land use scenarios (e.g., Gutmann et al. 2012; Silverman et al. 2013; Marteau et al. 2015). Thus, RCMs with high resolution can be applied to simulate key climate variables such as precipitation, which is very unevenly distributed (Rummukainen 2010).

The Loess Plateau (LP) in northwestern China is well known for its limited water resources and severe soil erosion (Shi and Shao 2000). It covers different climate zones from semi-humid to arid (Wang et al. 2011; Zhao et al. 2013). Precipitation is a major water resource and is vital to the well-being of the region, which has a population of 100 million. Rain-fed agriculture accounts for 80% of the cultivated land in this area (Li et al. 2010), and it is greatly affected by the amount of precipitation. In addition, extreme precipitation is closely related to severe soil erosion in the LP. Most soil erosion is caused by a few extreme precipitation events in the LP every year (Zhang et al. 2008). Landslides induced by extreme precipitation in this area amount to one-third of the total landslides in China every year (Zhuang et al. 2017). Thus, accurate precipitation simulation is important to soil and water conservation, agriculture, and the control of geological hazards in the LP.

Satisfactory precipitation simulations over the LP have remained a challenge. Previous studies have used different RCMs to simulate precipitation over the LP (e.g., Yu et al. 2011; Wang and Yu 2013; Yang et al. 2015), but large wet biases are found in the simulated precipitation over the LP in these studies. In particular, Ma et al. (2015) used the WRF model to simulate summer precipitation over China, showing no obvious improvements over the LP. Yu et al. (2010) largely overestimated precipitation over the LP, although WRF showed a great improvement compared to other RCMs. Bao et al. (2015) used WRF with a 30 km resolution to simulate precipitation over China and still generated large overprediction over the LP. The overestimation in precipitation simulations of these studies restricts the capacity of RCMs to provide detailed regional climate information and predict the future climate over the LP.

The simulation ability of RCMs depends mostly on the optimal combination of physical parameterizations (Efstathiou et al. 2013; Li et al. 2014). It is not clear which RCM parameterization schemes the precipitation simulations for the LP are most sensitive to. In previous studies involving precipitation simulations over the LP, the selection of RCM parameterization schemes varies, but there is no detailed information about how and why specific parameterizations were chosen (e.g., Bao et al. 2015; Ma et al. 2015). Assessment of the influence of different parameterization schemes on RCM simulation ability is important to understanding the underlying physical mechanisms of precipitation formation over the LP. Additionally, a high RCM resolution can help reduce model uncertainties, better represent topographic effects, and improve precipitation simulations (Sylla et al. 2010; Cardoso et al. 2013; Warrach-Sagi et al. 2013). Moreover, previous studies involving precipitation simulations over the LP have barely focused on extreme precipitation despite its considerable importance for this area. Thus, a comprehensive assessment is needed to investigate the influence of parameterization schemes and resolution on mean and extreme precipitation modeling for the LP.

The goal of this study is to improve the ability of WRF to simulate mean and extreme precipitation over the LP. The research questions to address include: (1) Does an increase in model horizontal resolution improve the simulation of precipitation over the LP? (2) How sensitive is precipitation simulation over the LP to different physical parameterization schemes? (3) What is the performance of WRF in simulating extreme precipitation events over the LP, and what physical mechanisms contribute to these extremes? In view of these research questions, this paper is structured as follows. In Sect. 2, we introduce the study area, the datasets for simulation and evaluation, the model configurations, and the metrics for model assessment. Section 3 describes the influence of the resolution and parameterization schemes on precipitation simulations over the LP and provides a comprehensive evaluation of precipitation simulations at different spatial and temporal scales. Conclusions are included in Sect. 4.

2 Study area, data, and model

2.1 Study area

WRF simulations were conducted for the LP in this study. The LP is the largest loess area in the world and is known for its severe soil erosion. As shown in Fig. 1a, it is located in the upper and middle reaches of the Yellow River basin in China and covers an area of approximately 640,000 km2 (33.70–41.30° N, 100.84–114.53° E). This region has a very complex topography, including sub-plateaus, basins, hills, and gullies, and its elevation ranges from 86 to 4782 m above sea level (m.a.s.l.) (Zhao et al. 2013). The Qinling Mountains are some of the most unique mountains in this region, located at the southern boundary of the LP and reaching as high as 3900 m.a.s.l. (He et al. 2009). The LP has varying climate, including semi-humid, semi-arid, and arid. The average annual temperature ranges from − 2.8 °C in the northwest to 14.5 °C in the southeast. Precipitation is dominated mainly by the East Asian monsoon during summer. The average annual precipitation varies from 200 mm in the northwest to 750 mm in the southeast (Li et al. 2010). Precipitation in the wet season (May through October) accounts for about 78% of the annual precipitation (Sun et al. 2015). Heavy precipitation in the wet season causes severe soil erosion in the LP, from which 90% of the sediments in the Yellow River are derived. The mean annual soil loss rates in this region are 5000–10,000 t km− 2 year− 1 (Gao et al. 2011). Complex terrain, highly variable precipitation, and severe soil erosion make the LP a unique study area to produce realistic precipitation simulations, especially those related to soil erosion.

Fig. 1
figure 1

a The WRF model domain (red box) and the location of the LP (yellow area), b Elevation of the topography (unit: m.a.s.l.) in the domain at a 10 km horizontal resolution

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2.2 Datasets for model simulation and evaluation

The European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis (Dee et al. 2011) was applied to provide initial and boundary conditions for WRF simulations. The ERA-Interim reanalysis supplied daily surface and pressure level climate variables with a 6-hour interval over the period 1980–2011. The ERA-Interim dataset used in this study had a horizontal resolution of 0.5o and included 27 vertical pressure levels. In addition, the ERA-Interim dataset was also utilized to analyze atmospheric water vapor transport compared with the WRF simulation.

A gridded dataset with high spatiotemporal resolution, called the China Meteorological Forcing Dataset (CMFD) (He et al. 2020), was adopted to evaluate the WRF simulation in this study. The spatial and temporal resolutions of the CMFD are 0.1° and 3 hours, respectively, and it covers the period of 1979–2015. Precipitation in the CMFD is derived from precipitation observations and two advanced precipitation products, including the Tropical Rainfall Measuring Mission (TRMM) precipitation products and the Asian Precipitation-Highly Resolved Observational Data Integration Toward Evaluation of the Water Resources (APHRODITE) precipitation data (Huffman et al. 2007; Yatagai et al. 2009). We selected in situ precipitation observations from nine meteorological stations (see Figure S1 in Supplementary Material) distributed across the LP to verify the quality of the gridded CMFD dataset. The CMFD precipitation data averaged over the four grid boxes surrounding each station were compared with in situ observations from that station (Figure S2), and the R-squared values between these two datasets for the nine stations were almost 1.

Four reanalysis products were used in the diagnostic analysis for mean and extreme precipitation to address the uncertainty of these products. These products included ERA-Interim Reanalysis, the Modern-Era Retrospective Analysis for Research and Applications Version 2 (MERRA-2) (Gelaro et al. 2017), the Japanese 55-year Reanalysis (JRA-55) (Kobayashi et al. 2015), and the National Centers for Environmental Prediction (NCEP) Climate Forecast System Version 2 Reanalysis (CFSv2) (Saha et al. 2014).

2.3 WRF model and experimental design

The RCM applied in this study is WRF version 3.6.1. The WRF model is a completely compressible, non-hydrostatic model (Skamarock et al. 2008). It is a flexible, advanced atmospheric simulation system that has been used extensively in both climate and land surface research (e.g., Heikkilä et al. 2011; Yang et al. 2015). The WRF model provides numerous physics options and can meet various research demands.

Long-term (1980–2011) WRF simulations with a high resolution were performed in this study. We ran WRF for 16 months each year, with a 4-month spin-up time starting in the previous September. The simulations for the remaining 12 months of each run were used for analysis. This design was adopted to avoid possible climatic shifts that may result from long-term continuous simulations (Li et al. 2014). The spatial settings of the WRF model in this study included one domain that was centered at 37° N, 108° E (Fig. 1). This domain had a horizontal resolution of 10 km and covered the entire LP. The domain consisted of 160 × 160 grids with the Lambert conformal conic projection. When setting the boundaries of the domain, we attempted to avoid complex terrain, which might have caused potential computational instability. The number of vertical levels was 30, and the top level was set to 50 hPa. It is worth noting that 10 km was adopted as the horizontal resolution in the WRF model due to its better performance and computational feasibility. We tested the model’s performance at different resolutions, i.e., 5, 10, 20, and 30 km, respectively. As shown in Table 1, the WRF model with a 10 km resolution performed better than it did with the other resolutions. The WRF model with a 5 km resolution also had a similar performance to that with a 10 km resolution, but it had a higher root mean square error (RMSE) and lower R-squared (R2), and it also drastically increased the computational cost.

Table 1 Performance of the WRF model at different resolutions
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The physical parameterization schemes applied in the WRF simulations consisted of the Dudhia shortwave radiation scheme (Dudhia 1989), rapid radiative transfer model (RRTM) longwave radiation scheme (Mlawer et al. 1997), Revised MM5 Monin–Obukhov surface layer scheme (Jiménez et al. 2012), and the community land model (CLM) land surface model (Oleson et al. 2010). The microphysics, planetary boundary layer physics, and cumulus schemes were determined through a series of sensitivity tests aiming to find an optimal combination of parameterizations for reproducing precipitation over the LP. We list the parameterization settings employed in control simulations of the sensitivity experiments in the Supplementary Materials (see Table S1). For example, for the control experiment in group 1, we selected the Lin microphysics scheme (Lin et al. 1983), the Kain–Fritsch cumulus scheme (Kain 2004), and the MYNN3 planetary boundary layer scheme (Nakanishi and Niino 2006). For the sensitivity experiment, the WRF model was initialized on June 1, 2007, and ran through July 31, 2007. The first months of simulations were discarded as spin-up. These two months were selected since the spatiotemporal patterns of precipitation in 2007 were close to those of the precipitation climatology (1980–2011) over the LP (Figures not shown).

2.4 Metrics for model evaluation

We used multiple metrics in this study to compare the WRF simulations with the CMFD dataset. The curvilinear grid in the WRF simulations was first interpolated to the rectilinear grid in the CMFD dataset via a simple weighted squared distance approach (Schwitalla et al. 2008). Normalized Taylor diagrams (Taylor 2001) were applied to evaluate the performance of different parameterization schemes in our sensitivity experiments. These diagrams are widely used to assess a model against observations with normalizations of the quantities (e.g., Warrach-Sagi et al. 2013). Taylor diagrams offer an efficient way to simultaneously display three complementary statistics associated with model performance, including correlation coefficient, standard deviation (SD), and RMSE. In addition, the pattern correlation coefficient (PCC) (Walsh and McGregor 1997) was applied to determine the capacity of WRF to reproduce the spatial pattern of precipitation. The PCC is essentially a standard Pearson’s correlation in terms of space (Argüeso et al. 2012b). Moreover, the deviation of WRF simulations from observations was measured by a percent bias (Cardoso et al. 2013) and RMSE. A probability distribution function (PDF) was applied to evaluate the distribution of the percent bias. Nash–Sutcliffe efficiency (NSE) (Nash and Sutcliffe 1970) and R2 were used to evaluate the ability of WRF to capture the temporal characteristics of precipitation at different time scales, i.e., intra-annual, inter-annual, and seasonal.

The WRF simulation evaluation was conducted in different sub-regions of the LP. The whole LP was divided into three sub-regions (Fig. 2) based on precipitation distribution, intensity of soil erosion, and erosion type. As shown in Fig. 2, the main types of erosion in the LP are water erosion and wind erosion, covering 82.63% and 17.13%, respectively. The A-zone occupies 96.51% of the total wind erosion area in the LP, and its annual precipitation is less than 400 mm year− 1. The B-zone accounts for nearly 86% of the total serious water erosion area, and annual precipitation in this zone is between 400 mm year− 1 and 600 mm year− 1. The C-zone has light water erosion, and its annual precipitation is more than 600 mm year− 1. Assessment of WRF model performance at the sub-regional scale is relevant for soil and water conservation management in the LP.

Fig. 2
figure 2

Soil erosion types over the LP, including water erosion (red) and wind erosion (blue), and erosion intensity (from 1 to 6). The LP was divided into three sub-regions: A-zone, B-zone, and C-zone, based on soil erosion distribution

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We adopted a grid-based definition to define extreme precipitation over the B-zone in this study. Extreme precipitation occurred in the B-zone when at least 38% of the CMFD grids in this zone had precipitation greater than 12 mm day− 1 that occurred simultaneously on the same day (Glisan and Gutowski 2014; Roxy et al. 2017). The 38% threshold was determined based on the exceedance probability analysis (Fig. 3). This threshold was at the 95th percentile based on the data for the summer period of 1980–2011, where a total of 147 extreme precipitation days were retrieved.

Fig. 3
figure 3

Exceedance probability curve using the percentage of the CMFD grid points with precipitation greater than 12 mm day− 1 that occurred simultaneously on the same day. The red point is 38%, which is at the 95th percentile

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3 Results

3.1 Influence of physical parameterization schemes on precipitation simulation

In this study we investigated the influence of parameterization schemes of three physical processes, including microphysics, planetary boundary layer, and cumulus, on precipitation simulation. We conducted sensitivity experiments using 11 microphysics, 8 planetary boundary layer, and 7 cumulus schemes. Taylor diagrams were applied to evaluate the sensitivity of the WRF precipitation simulations to different physical parameterization schemes. At first, a set of tests were conducted to explore the influence of different microphysics schemes. The Kain–Fritsch cumulus scheme and MYNN3 planetary boundary layer scheme remained unchanged in this set of tests.

The selection of the microphysics scheme did not have a remarkable influence on precipitation simulation over the LP. The performance of the WRF model with different microphysics schemes is demonstrated in Fig. 4a. The PCCs gather around 0.65, and the normalized SD is within the range of 1.05 and 1.30. The CAM5.1 (Neale et al. 2010) microphysics scheme has the largest PCC of 0.67 and a relatively lower normalized SD of 1.11, which is close to 1. Thus, the analysis of this set of experiments indicates that there is no significant difference among the microphysics schemes in the WRF model. These microphysics schemes might be sufficient to capture the microphysical processes of summer precipitation in the LP. In the following experiments, the CAM5.1 microphysics scheme was adopted.

Fig. 4
figure 4

Comparison of sensitivity tests for different categories of parameterizations in the WRF model: a microphysics schemes, b planetary boundary layer schemes, c cumulus schemes

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The WRF precipitation simulations over the LP were more sensitive to the planetary boundary layer scheme than to the microphysics scheme. The results from the set of experiments with different planetary boundary layer schemes are shown in Fig. 4b. In this Taylor diagram, the points of different boundary layer schemes are more dispersed compared to those of the microphysics schemes. This large dispersion is mainly a result of the large variation in the PCC, with a range of 0.59–0.72, while the spatial SD clusters near 1. Compared to other simulations, the simulation with the MYNN2.5 (Nakanishi and Niino 2006) planetary boundary layer scheme has the largest PCC of 0.72 and a relatively small SD of 0.96. It is worth noting that the TEMF scheme in WRF (Angevine et al. 2010) also produces a high PCC, but it has the largest standard deviation. Considering these two facts, the MYNN2.5 scheme was selected for the following tests.

The capacity of WRF to reproduce observed precipitation over the LP was most sensitive to the cumulus scheme. The performance of the WRF model with varying cumulus schemes displays a higher degree of discrepancy. As shown in Fig. 4c, the PCC of different cumulus schemes has a wider range of 0.56–0.72, and the normalized SD also has a wider range of 0.88–1.18 compared to the microphysics and planetary boundary layer schemes. In addition, the New Simplified Arakawa–Schubert (Han and Pan 2011) scheme generated the lowest PCC, and the Tiedtke (Tiedtke 1989) scheme generated the largest SD. The result of the Kain–Fritsch scheme is closest to the observations since it has the largest PCC and a relatively lower SD. Thus, our sensitivity tests suggest the significance of cumulus schemes for precipitation simulations over the LP, implying that atmospheric convection may largely control summer precipitation over this region.

The sensitivity experiments in this study provided an optimal combination of physical parameterizations for realistically reproducing the observed precipitation over the LP. Ma et al. (2015) suggested that a suitable cumulus scheme in WRF is important to precipitation simulation over this area. Our sensitivity tests can provide a reference and insights into precipitation simulation over the LP. Through comparisons among three categories of parameterization schemes directly associated with precipitation processes, our results indicate that the combination of the CAM5.1 microphysics, MYNN2.5 planetary boundary layer, and Kain–Fritsch cumulus schemes can capture precipitation in the LP quite well. With this optimal scheme combination, a long-term simulation over the LP was performed. A detailed evaluation is provided in the following sections.

3.2 Spatial distribution of precipitation in the LP

The WRF model simulation in this study agreed very well with observations in terms of spatial distribution. The long-term (1980–2011) precipitation climatology from WRF and observations is shown in Fig. 5. The spatial distribution of the observed precipitation climatology was clearly captured by the WRF model. This agreement is indicated by the high PCC of 0.87 between the WRF output and CMFD observations. WRF additionally represented the precipitation gradient from the southeast to the northwest, indicating that WRF was able to reflect the influence of the topographical features. This precipitation gradient shows that the monsoon weakened from southeast to northwest. In addition, the WRF model realistically replicated the magnitude of the precipitation climatology, which was confirmed by a small RMSE of 0.19 mm day− 1. Nevertheless, the WRF model overpredicted precipitation in the westernmost part and underpredicted precipitation in the southern part of the LP. These areas all have complex terrain with high elevations of more than 2000 m.a.s.l. This indicates that the largest deviations of precipitation were produced by the model over high mountains (Herrera et al. 2010; Heikkilä et al. 2011; Argüeso et al. 2012a), suggesting that WRF at a 10 km resolution may still not capture these topographical features. In general, the WRF model was able to accurately simulate the spatial features of the precipitation climatology over the LP to a very large extent.

Fig. 5
figure 5

Annual precipitation climatology (1980–2011) of a CMFD observations, b WRF simulation, and c WRF annual precipitation climatology percent bias (in percentage)

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The WRF model had an adequate performance over the A-zone and B-zone, but not in the C-zone, which accounts for only 9% of the total area of the LP. As discussed in Sect. 2.4, we divided the LP into three regions (shown in Fig. 2) for more in-depth analysis, because the performance of WRF varies depending on the region considered. The PCCs are 0.86, 0.81, and 0.42 for the A-zone, B-zone, and C-zone, respectively. Precipitation over the A-zone and B-zone is often caused by large-scale atmospheric systems, which are relatively easy for RCMs to capture. In this study, the WRF model also produced very good simulations for these regions. Figure 5c shows the percent biases in precipitation simulation over the LP from WRF. Large parts of the A-zone and B-zone demonstrate small percent biases ranging from − 20 to 20%. In contrast, there are large dry biases in the C-zone, where precipitation is strongly affected by high mountains in the south. Moreover, the PDFs of the percent bias over these three regions are shown in Fig. 6. The percent biases within a range of − 20 to 20% cover 87% and 91% of the PDFs for the A-zone and B-zone, respectively, but only 71% for the C-zone. The analysis for the C-zone indicates that the WRF model underpredicted precipitation in the rain shadow of the Qinling Mountains, where the average elevation is 2,000 m.a.s.l. Fowler et al. (2005) and Caldwell et al. (2009) had similar findings when using RCMs to simulate precipitation over the UK and California, respectively. In summary, WRF realistically reproduced the observed precipitation climatology over most of the LP.

Fig. 6
figure 6

PDFs of percent bias (%) in annual precipitation climatology from WRF for a A-zone, b B-zone (water-erosion area), and c C-zone

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The WRF model in this study also reasonably mirrored the seasonal precipitation climatology. Figure 7 shows the seasonal precipitation climatology (1980–2011) in the LP for the CMFD observations and the WRF simulations for spring (March–May), summer (June–August), fall (September–November), and winter (December–February). WRF replicated summer precipitation well, with a PCC of 0.84, and the percent bias within a range of -20–20% covered 90% of the total area of the LP. Fall precipitation in WRF had the largest PCC of 0.87 when compared to that for the other seasons, although it had a wet bias in the western part of the LP. However, WRF overpredicted winter precipitation in most of the western LP. These large biases were due in large part to the small magnitude of winter precipitation as well as uncertainties in the WRF simulations. Winter precipitation over the LP was only 13 mm and accounted for 2.9% of the annual precipitation over this region. Therefore, the WRF model performed very well in capturing the observed seasonal precipitation climatology over the LP, especially for summer and fall.

Fig. 7
figure 7

Precipitation (mm year− 1) climatology (1980–2011) of CMFD observations (a–d), WRF simulations (e–h), percent bias of WRF (%) compared to CMFD (i–l) for spring, summer, fall, and winter from left to right. PCC between the WRF simulations and the CMFD observations is given in the subtitles

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3.3 Temporal variability

3.3.1 Diurnal cycle

The diurnal cycle of precipitation is deemed to be an important metric for the performance of RCMs due to its close association with convection and boundary layer development (Liang et al. 2004). In the CMFD observations for the period of 1980–2011 (Fig. 8), we can see that the most obvious diurnal feature of precipitation over the LP occurred during the summertime when the monsoon precipitation was strongest (Fig. 7). Meanwhile, the most remarkable diurnal cycle occurred in the C-zone and gradually weakened in the B-zone and A-zone with the decay of the monsoon’s influence (Fig. 8a, c, and e). In this study, we examined the performance of the WRF model in simulating the diurnal variations of precipitation for the three sub-regions and the entire LP averaged over the period of 1980–2011. We can see that the WRF model accurately captured the diurnal variations of precipitation, but slightly underestimated the peak values for all regions, which occurred in the late afternoon (1700 local time). Clearly, the timing of the peak values was associated with the afternoon solar heating in the LP, causing maximum low-level atmospheric instability and strong moist convection (Sorooshian et al. 2002).

Fig. 8
figure 8

Observed (a, c, e, and g) and simulated (b, d, f, and h) seasonal patterns of diurnal evolution of precipitation averaged over the A-zone, B-zone, C-zone, and the entire LP for the period of 1980–2011. The horizontal axis is for local time

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3.3.2 Intra- and inter-annual variability

Temporal variability of observed precipitation at the intra- and inter-annual scales was accurately reproduced by the WRF model in our study. At the monthly time scale, Fig. 9a shows the comparison between precipitation averaged over the LP from WRF and from CMFD. WRF simulated precipitation well at this monthly temporal resolution. The R2 and NSE were 0.94 and 0.94, and the RMSE was 0.28 mm day− 1. The annual time series averaged over the LP from WRF and CMFD are shown in Fig. 9b. The WRF model not only captured the variation of precipitation but also simulated its magnitude well, although it produced large biases in a few years. The R2 and NSE were 0.64 and 0.61, and the RMSE was 0.10 mm day− 1. The seasonal cycle of precipitation is presented in Fig. 9c, showing that the WRF simulations agree very well with CMFD observations. WRF realistically produced a bell-shaped curve with maximum precipitation in July and minimum precipitation in December, even though it underpredicted precipitation in August with a 10% bias. The R2 and NSE were 0.99 and 0.99, and the RMSE was 0.12 mm day− 1. Therefore, the WRF model is highly capable of simulating both the magnitude and variation of precipitation over the LP at different time scales.

Fig. 9
figure 9

a Comparison of the monthly precipitation of CMFD to that of WRF for the period of 1980–2011, b annual precipitation of CMFD and WRF, and c the seasonal cycle of precipitation from CMFD and WRF for the LP averaged over the period of 1980–2011

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3.4 Extreme precipitation

The ability of the WRF model to reproduce extreme precipitation over the LP was examined in this study. As described in Sect. 2.4, our analysis focused on extreme precipitation over the B-zone where the most severe soil erosion often occurs. Based on observations, we identified 147 days with extreme precipitation over the B-zone for the period of 1980–2011. The WRF model captured 108 days (73%) of observed extreme precipitation. The PCC between the simulations and observations was 0.90, and the RMSE was 3.14 mm day− 1 (Fig. 10a and c). Meanwhile, the WRF model failed to capture 39 days (27%) of observed extreme precipitation. The PCC between the simulations and observations was only 0.42, and the RMSE was 4.52 mm day− 1 (Fig. 10b and d). For the uncaptured case, the WRF model displaced the precipitation center to the northeast part of the B-zone (Fig. 10d), while the actual center was located in the central part of this zone (Fig. 10b). A mechanistic analysis of the extreme precipitation simulations with WRF is presented in Sect. 3.5.

Fig. 10
figure 10

Composites of CMDF-observed (top panel) and WRF-simulated (bottom panel) summer extreme precipitation (mm day− 1) over the period of 1980–2011 for: captured extreme precipitation (a and c), and uncaptured extreme precipitation (b and d)

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3.5 Mechanistic analysis

3.5.1 Mechanistic analysis for precipitation climatology

The evaluation of simulated water vapor transport over the LP is important in understanding WRF precipitation simulations. In this section, a diagnostic analysis was conducted by comparing the ERA-Interim moisture flux with the WRF simulations, which was integrated vertically from the surface to the 300 hPa pressure level. Figure 11a, b show the moisture flux climatology over the LP for summer averaged based on the daily data over the period of 1980–2011. In both the reanalysis data and simulations, we can see that most of the moisture flux came from the southwest across the southern boundary of the simulation domain, which was controlled largely by the summer Asian monsoon system. When compared with the ERA-Interim, WRF had an excellent performance in simulating the spatial distribution and magnitude of moisture flux, with a PCC of 0.87. In addition, WRF accurately captured the direction of water vapor transport. We also compared the summer climatologies of the vertically integrated moisture fluxes based on four reanalysis products (Figure S3). The results based on these reanalysis products showed a high consistency in both spatial pattern and magnitude. Thus, the WRF model did well at simulating the spatial distribution, magnitude, and moving path of water vapor over the LP when compared with the reanalysis products. The accurate water vapor transport simulations guarantee the high quality of the WRF precipitation simulations, as shown in the above sections.

Fig. 11
figure 11

a ERA-Interim and b WRF-simulated vertically integrated moisture flux (kg kg− 1 m s− 1) climatology from the surface to the 300 hPa level for summer over the period of 1980–2011. Arrows represent direction, and color represents magnitude

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3.5.2 Mechanistic analysis for extreme precipitation

The composites of both reanalyzed and simulated vertically integrated moisture fluxes of the extreme precipitation captured by WRF were shown in Fig. 12a and c. We can see that WRF reproduced the spatial pattern of the reanalyzed water vapor transport with a PCC of 0.94. The simulated moisture flux averaged over the B-zone was 147 kg kg− 1 m− 1 s− 1, while the reanalyzed was 142 kg kg− 1 m− 1 s− 1. The magnitude of the moisture flux for extreme precipitation was almost three times larger than that of the precipitation climatology (58 kg kg− 1 m− 1 s− 1). At the same time, WRF accurately simulated the wind field and geopotential height at the 700 hPa level when compared to the ERA-Interim data (Fig. 13a and c) for the captured case, with a PCC of 0.89 and an RMSE of 5.68 gpm. The critical system that caused the captured extreme precipitation may be a low pressure that was located in the middle of the LP and was consistent with the position of the precipitation center.

Fig. 12
figure 12

ERA-Interim (top panel) and WRF-simulated (bottom panel) composites of vertically integrated moisture flux (kg kg− 1 m s− 1) from the surface to the 300 hPa level for summer extreme precipitation over the period of 1980–2011: captured case (a and c), and uncaptured case (b and d). Arrows represent direction, and color represents magnitude

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Fig. 13
figure 13

ERA-Interim (top panel) and WRF-simulated (bottom panel) composites of 700 hPa wind field (m s− 1, arrows) and geopotential height (gpm, color) for summer extreme precipitation over the period of 1980–2011: captured case (a and c), and uncaptured case (b and d)

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For the uncaptured case (Fig. 12b and d), the WRF model reproduced the moisture flux for the B-zone (PCC was 0.92), although it slightly overestimated the moisture flux compared to the ERA-Interim (148 kg kg− 1 m− 1 s− 1 vs. 174 kg kg− 1 m− 1 s− 1). Meanwhile, the WRF model accurately simulated the wind field and geopotential height at the 700 hPa level when compared to the ERA-Interim data (Fig. 13b and d), with a PCC of 0.91 and an RMSE of 6.41 gpm. We can see that a deep trough with the ERA-Interim data is located in the center of the LP, and the WRF model accurately represented this circulation pattern, generating a precipitation pattern centered in the northeastern B-zone. However, the observed precipitation pattern was centered in the middle of the B-zone. Additional analysis for the biased precipitation simulations is discussed later in this section.

We further analyzed divergence for the 300 hPa level and vertical motion for the 500 hPa level to explore the dynamic processes of extreme precipitation simulations. A nine-point local average method (Onderlinde and Nolan 2016) was applied to smooth the spotty WRF-simulated divergence caused by the complex terrain in the study area (Fig. 14). The WRF-simulated positive divergence values at the 300 hPa level were very consistent with those of ERA-Interim for both captured and uncaptured cases. This result indicates that an anticyclonic circulation developed in the upper troposphere, corresponding with a cyclonic circulation or a low pressure in the lower troposphere (Fig. 13; Wu et al. 2009). These circulation patterns were clearly associated with upward motion for both captured and uncaptured cases as shown in Fig. 15. These analyses strongly suggest that the WRF model reasonably reproduced the dynamic processes included in ERA-Interim that also provided the lateral boundary conditions of this model.

Fig. 14
figure 14

ERA-Interim (top panel) and WRF-simulated (bottom panel) composites of 300 hPa divergence (10− 6 s− 1, color) for summer extreme precipitation over the period of 1980–2011: captured case (a and c), and uncaptured case (b and d)

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Fig. 15
figure 15

ERA-Interim (top panel) and WRF-simulated (bottom panel) composites of 500 hPa vertical velocity (Pa s− 1, color) for summer extreme precipitation over the period of 1980–2011: captured case (a and c), and uncaptured case (b and d)

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We also examined the WRF-simulated extreme precipitation with the ERA-Interim data (Fig. 16). We can see that the simulated precipitation spatially matched the ERA-Interim data for both captured and uncaptured cases. Thus, we can conclude that the biased precipitation produced with the WRF model most likely resulted from the inaccurate ERA-Interim forcing data for the uncaptured case, since both WRF simulations and ERA-Interim data showed similar dynamic processes.

Fig. 16
figure 16

Composites of ERA-Interim (top panel) and WRF-simulated (bottom panel) summer extreme precipitation (mm day− 1) over the period of 1980–2011 for: captured extreme precipitation (a and c), and uncaptured extreme precipitation (b and d)

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4 Conclusions

In this study, we aimed to simulate the mean and extreme precipitation using the WRF model over the LP, where severe soil erosion and landslides are associated mainly with extreme precipitation events. We first investigated the influence of model resolution on the simulation ability of WRF. When compared with observations, the WRF model produced the best results at a 10 km resolution in simulating precipitation over the LP. To assess the influence of physical parameterizations on the ability of WRF to simulate precipitation over the LP, we conducted a series of sensitivity tests. The modeled precipitation was most sensitive to cumulus schemes, moderately sensitive to planetary boundary layer schemes, and less sensitive to microphysics schemes. We finally found an optimal physical scheme combination for precipitation simulations over this region: the Kain–Fritsch cumulus scheme, the MYNN2.5 planetary boundary layer scheme, and the CAM5.1 microphysics scheme.

With the optimal combination of parameterizations, a long-term simulation was performed with the WRF model. The WRF model realistically captured the spatial pattern of the observed precipitation. The simulated magnitude and variability in precipitation at the diurnal, monthly, seasonal, and inter-annual scales matched well with observations. The WRF model performed better in summer and fall than in spring and winter. Moreover, we assessed the ability of WRF to simulate observed precipitation over three sub-regions in the LP. WRF generally reproduced the observed precipitation over these regions in most parts of the LP, even though there were large dry biases over the mountainous regions. These biases most likely resulted from the unrealistic simulation of rain shadow effects on precipitation caused by the high mountains.

In addition, this study highlighted extreme precipitation simulations over the LP. The WRF model captured 73% of the observed extreme precipitation events and failed to capture 27% of them. This model produced similar dynamic processes to those in the ERA-Interim data. The biased precipitation simulations generated with the WRF model most likely resulted from inaccurate ERA-Interim forcing data. This study provides promising insights into reliable projections of future precipitation and informed water resource and soil erosion management for the LP.