Development and evaluation of spectral nudging strategy for the simulation of summer precipitation over the Tibetan Plateau using WRF (v4.0)

. Precipitation is the key component determining the water budget and climate change of the 15 Tibetan Plateau (TP) under a warming climate. This high-latitude region is regarded as “the Third Pole” of the Earth and the “Asian Water Tower” and influences the eco-economy of downstream regions. However, the intensity and diurnal cycle of precipitation are inadequately depicted by current reanalysis products and regional climate models (RCMs). Spectral nudging is an effective dynamical downscaling method used to improve precipitation simulations of RCMs by preventing simulated fields from drifting 20 away from large-scale reference fields, but the most effective manner of applying spectral nudging over the TP is unclear. In this paper, the effects of spectral nudging parameters (e.g., nudging variables, strengths and levels) on summer precipitation simulations and associated meteorological variables were evaluated over the TP. The results show that using a conventional continuous integration method with a single initialization is likely to result in the overforecasting of precipitation events and the 25 overforecasting of horizontal wind speeds over the TP. In particular, model simulations show clear improvements in their representations of downscaled precipitation intensity and its diurnal variations, atmospheric temperature and water vapor when spectral nudging is applied towards from the SNQ_trop39 and SNQ_trop25 experiments, however, simulated had a much higher wet bias than the Control, up to 0.1 mm/ h -1 , over the TP than did the Control. The smallest wet bias of precipitation was found in the SNnoT experiment during the day, which also outperformed other experiments at night, reducing the overforecast of precipitation by 0.03 mm/ h -1 compared with the Control and 0.05 mm/ h -1 290 compared with the SN. Consequentlybased on above analysis, the model simulations should be improved especially for precipitation forecasts during 2-12 UTC (10-20 of the local time) requires urgent improvement in the model, even though the precipitation forecasts of has been greatly improved by the SNnoT greatly improved compared to the Control and SN forecasts. In addition, the precipitation forecasts of SNlowU and SNlowT had diurnal variations and comparable precipitation intensities that were similar to Control. These findings indicate that the SNnoT experiment had considerable improvements in simulating diurnal precipitation over the TP in comparison to the Control and SN experiments.


Introduction
The Tibetan Plateau (TP) is referred to the Third Pole of the Earth and its average elevation is greater than 4,000 m. The TP has a complex topography and is also represented as the "Asian Water Tower". Its powerful thermodynamic and dynamic effects not only significantly influence regional climate patterns 40 and climate change but also have great impacts on the processes of the Asian monsoon system and westerlies (Immerzeel and Bierkens, 2010;Wu et al., 2007). Regional variations of atmospheric heating resources over the TP significantly regulate the summer Asian monsoon and associated precipitation (Zhao and Chen, 2001). Precipitation is an essential meteorological variable to reveal the water cycle and surface energy balance (Palmer and Raisanen, 2002). It is thus imperative to realistically simulate 45 variations of precipitation in both spatial and temporal distribution over the TP, which is also a vital component that can assess the performance of models (Bohner and Lehmkuhl, 2005;Karmacharya et al., 2017).
The major limitations for climate studies over the TP are attributed to the sparse observation datasets in both spatial and temporal coverage. Consequently, atmospheric reanalysis products or global climate 50 model (GCM) output are often used, but they are still too coarse to represent the complex terrain of the TP (Lang and Barros, 2004;Palazzi et al., 2013). In addition, the seasonal-to-interannual prediction of precipitation, especially with respect to extreme precipitation events over the southern and southeastern TP, remains poorly modeled by the GCM (Su et al., 2013;Wang et al., 2016). Regional climate models (RCMs) with higher resolution is thus used to dynamically downscale the coarse output of coupled GCMs 55 or reanalysis datasets (Glisan et al., 2013;Lo et al., 2008;von Storch et al., 2000). RCMs have been widely applied to study monsoon variations, regional climate change and perform well in precipitation predictions (Gao et al., 2015;Jiang et al., 2019). Compared to global reanalysis, RCMs generally produce better annual variation and long-term trends of precipitation over the TP during wet seasons (Gao et al., 2015;Jiang et al., 2016). 60 However, these advantages of RCMs are limited to the time range of simulations. When forecast time is beyond 36 h, models' skill is gradually diminishing (White et al., 1999). This is mainly affected by the continuously accumulated deviations between the RCM's circulation fields and the large-scale driving fields as time progresses (Miguez-Macho et al., 2004;Waldron et al., 1996). As a solution, the nudging method was proposed and applied for RCMs to ensure the simulated field be consistent with the large-65 scale driving fields while eliminating the spurious reflections of large-scale circulations inside the domain (Miguez-Macho et al., 2004;von Storch et al., 2000;Miguez-Macho et al., 2005).
Two forms of nudging technique, including grid nudging and spectral nudging, could be used in the Weather Research and Forecasting (WRF) model. Grid nudging in WRF adds one or more artificial tendency terms to relax the model state toward the observed fields at each grid point, which is based on 70 the differences between the model solution and the observations (Stauffer and Seaman, 1994). The horizontal wind, potential temperature and water vapor mixing ratio can be nudged in grid nudging, and it has been successfully used for regional climate simulations (Bowden et al., 2013;Bowden et al., 2012;Lo et al., 2008). However, grid nudging is spectrally indiscriminate, because it modulates the model solution with the same strength, which neglects the features of the variations of interpolated small-scale 75 for the model fields.
Meanwhile, spectral nudging is scale-discriminated, thus only the wavelength longer than the selected wavenumbers of model fields will be nudged towards the driving fields. Spectral nudging is capable to alleviate the bias while keeping the inner variability for model domain. Besides horizontal wind and potential temperature can be nudged in spectral nudging, spectral nudging is also applied to geopotential. 80 Compared with grid nudging, spectral nudging reduces suspicious reflections at the lateral boundaries and removes the influence of domain size and position of the RCM (Miguez-Macho et al., 2004). These advantages of spectral nudging not only improve the variability of mean or extreme precipitation simulations , but also efficiently improve large-scale atmospheric circulation simulations . By the efforts of Sepro et al. (2014), spectral nudging can be applied 85 toward water vapor mixing ratio and restrict nudging toward potential temperature and water vapor mixing ratio above the tropopause. These modifications to fundamental spectral nudging strategy improve the 2-m temperature, upper-layer cloud cover and precipitation simulation over the North America and the contiguous United States (CONUS). Although various sensitivity experiments have been devoted to examine the effect of spectral nudging on regional climate simulations in RCMs (Tang 90 et al., 2018;Moon et al., 2018), studies on how to identify a most effective nudging strategy for precipitation simulation over the TP are limited. Because optimal nudging strategies of different regions may not be suitable for the TP with sophisticated and high topography. The effects of spectral nudging toward water vapor mixing ratio on precipitation simulation are also needed to be evaluated.
In this study, different spectral nudging strategies were conducted over the TP for the July of 2008. The 95 influences of nudging parameters, including nudging variables, strength and model levels where nudging is applied, on precipitation simulations were explored, with a particular focus on the performance of extreme precipitation events. In the following sections, the WRF model, the spectral nudging technique, experimental design and validated data are described in section 2. Section 3 shows the validation of the various WRF simulations against observation data, . and aAnalysis of the effects of spectral nudging on 100 large-scale atmospheric circulation and nudged variables in model field are discussed in section 4. In the section 5, the conclusions of the research are presented.

WRF model configuration
The WRF model version 4.0 was used in this study. The capability of spectral nudging towards water 105 vapor mixing ratio was added in this version. A two-nested domain used in this study is displayed in Figure 1. The outer domain with 30-km spatial resolution provides the large-scale information from the large-scale processesthat has been resolved by the driving field. The inner domain with 10-km spatial resolution is the main study area and covers the complex terrain of the TP. The terrain of the region varies intensely in a short spatial range, which can exert strong turbulent drag on low-level atmospheric 110 circulation and thus influence water vapor transport. To avoid the influence of regional difference when calculating the mean precipitation over the entire TP, evaluations of precipitation simulations were also conducted on extreme (the highest 5 percentile value of) precipitation events.

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The physical options used in this study are followed to the settings of the High Asia Refined (HAR) data (Maussion et al., 2011;Maussion et al., 2014). Specifically, the Thompson scheme (Thompson et al., 115 2004), the Grell 3D ensemble scheme (Kain, 2004), the Dudhia shortwave radiation scheme (Dudhia, 1989) and Rapid Radiative Transfer model longwave radiation scheme (Mlawer et al., 1997), and the unified Noah Land Surface Model (Chen and Dudhia, 2001) were selected. The Yonsei University scheme (Hong et al., 2006) was used for the PBL scheme. With the exception for the PBL scheme, the Yonsei University scheme (Hong et al., 2006) was used in this study. 120 The initial and lateral boundary conditions were driven by the ERA-Interim reanalysis data (ERAI) with 6-h temporal and 79 km spatial resolution (Dee et al., 2011). The sea surface temperatures were also derived from ERAI. All seven simulations, including one without nudging and six with spectral nudging using various nudging strategies (Table 1), were initialized at 20 June 2008 and integrated continuously for 40 days with first 10 days were set to spin-up time. The results of whole July of 2008 are used for 125 evaluation.

Spectral nudging
Spectral nudging, as a dynamical downscaling technique, is used to retain all the large-scale information from the driving fields, and to add smaller-scale information that the coarse driving fields can not resolve.
By adding a nudging term on the variable of model field, perturbation tendencies (differences between 130 the regional field tendency and the driving field tendency) are dampened by spectral nudging at selected spatial scale, and then the inconsistences between model solution and the driving coarse field are alleviated. Spectral nudging Following the study of Miguez-Macho et al. (2004), spectral nudging equation in WRF model is expressed as: where Q is the prognostic variable to be nudged, L is the model operator, Q o is the variable from the 135 driving fields. Q mn and Q omn represent the spectral coefficients of Q and Q o , respectively. The nudging coefficient K mn can vary with m and n (wave numbers in the x and y direction, respectively) and also with height; k m and k n imply the wave vector and depend on the domain size, D x and D y , which can be expressed as: In spectral nudging simulations, cut-off wave number was set to a wavelength of 1000 km, so that the 140 nudging was applied only to the long waves whose physical wavelength are larger than 1000 km.for which This value of wavelength has been validated to be the most appropriate nudging wavelength to simulate precipitation events in many regions (Gomez and Miguez-Macho, 2017;Yang et al., 2019). Therefore, the wave numbers of X and Y directions were 5 and 4, respectively for the outer domain and 5 / 34

Experimental settings
The physical options used in this study are followed to the settings of the High Asia Refined (HAR) data 150 (Maussion et al., 2011;Maussion et al., 2014). Specifically, the Thompson scheme (Thompson et al., 2004), the Grell 3D ensemble scheme (Kain, 2004), the Dudhia shortwave radiation scheme (Dudhia, 1989) and Rapid Radiative Transfer model longwave radiation scheme (Mlawer et al., 1997), and the unified Noah Land Surface Model (Chen and Dudhia, 2001) were selected, with the exception that the Yonsei University scheme (Hong et al., 2006). 155 The initial and lateral boundary conditions were driven by the ERA-Interim reanalysis data with 6-h temporal and 79 km spatial resolution (Dee et al., 2011). The sea surface temperatures were also derived from ERA-Interim. All seven simulations, including one without nudging and six with spectral nudging using various nudging strategies (Table 1), were initialized at 20 June 2008 and integrated continuously for 40 days with first 10 days were set to spin-up time. The results of whole July of 2008 are used for 160 evaluation.
In spectral nudging simulations, cut-off wave number was set to a wavelength of 1000 km, for which has been validated to be the most appropriate nudging wavelength to simulate precipitation events in many regions (Gomez and Miguez-Macho, 2017;Yang et al., 2019). Therefore, the wavenumbers of X and Y directions were 5 and 4, respectively for the outer domain and 3 and 2, respectively for the inner domain. 165 Each nudging simulation was applied above the planetary boundary layer (PBL) so that allowing the near-surface small-scale processes be freedom to respond to local processes.
The conventional continuous integration without nudging is was designated "Control". Default spectral nudging simulation is was designated "SN". The nudging coefficient is related to the nudging relaxation time, which indicates a predetermined time-scale how often nudging variables are relaxed toward the 170 large-scale driving fields. In SN simulation, nudging coefficients for horizontal wind, potential temperature, and geopotential on both domains are were the default value of 3.0×10 -4 s -1 (relaxation time scale of 50 min). For water vapor mixing ratio, default coefficient is was 0.1×10 -4 s -1 (relaxation time scale of 24 h). An infinitely shorter relaxation time does not result a higher consistence between the simulated small-scale fields with the forcing fields (Alexandru et al., 2009;Omrani et al., 2012). The 175 relaxation time of nudging variables is recommended to be equivalent to the temporal interval of the input driving data (Omrani et al., 2013;Spero et al., 2018). Therefore, a nudging coefficient of 0.45×10 -4 s -1 (relaxation time scale of 6 h) was set for wind (SNlowU) and temperature (SNlowT) on basis of SN, respectively, to evaluate may be appropriate. Following this perspective, the subsequent the sensitivity of model solution to nudging coefficientexperiments were conducted with a weaker nudging coefficient 180 (longer relaxation time) for wind and temperature on basis of SN, such as SNlowU and SNlowT simulations. Sensitivity simulation was not applied to geopotential, because it has been shown a neglectable influence when spectral nudging toward geopotential was nudged with different nudging coefficients (Spero et al., 2018).
In WRF version 4, aA new option "ktrop" has been was added in the released WRF model v4.0 to that 185 allowing spectral nudging can be applied towards water vapor mixing ratio. This option adds a lid for both potential temperature and water vapor mixing ratio fields at a predefined layer (nominally selected to represent the tropopause) above the PBL, while horizontal wind component and geopotential are not affected by the option.
As suggested from a 35-years analysis by using ERAIERA-Interim reanalysis data, the pressure level of 190 tropopause over the TP varies between 93 and 106 hPa, with a mean value of 100 hPa during summer (Zhou et al., 2019). Therefore, In this study, the associated level of tropopause was 39 (namely, ktrop = 39) in this study, and relevant simulation is designated "SNQ_trop39". In this paperSince the tropopause layer over the TP is much higher than other regions, it is important necessary to examine the influence of adding the lid at a different model layer, since the tropopause layer over the TP is much higher than 195 other regions. The simulation that the 'ktrop' was set to the model layer of 25 was designated 'SNQ_trop25'. The layer of 25 represented the index of the middle layer of the model, which was the lower limit for 'ktrop'. Considering the cold bias of atmospheric temperature in ERAI over the TP, the simulation with not nudging towards temperature at all was designated 'SNnoT', in which nudging towards moisture was not applied. 200

4 Validation data for model evaluation and comparison
Model simulated precipitation were evaluated against the merged Climate Prediction Center (CPC) MORPHing technique (CMORPH) precipitation dataset (hereinafter called CMORPH) with a temporal and spatial resolution of 1 h and 0.1°, which is developed by the China Meteorological Administration (CMA). The original CMORPH data with a spatial resolution of 8 km and temporal resolution of 30 min 205 are firstly resampled to the 0.1° and 1 h spatial and temporal resolution. Then its systematic biases are corrected by 2400 rain gauges in China by using probability density function matching method. The corrected CMORPH is subsequently combined with hourly rain gauge analysis from automatic stations to derive the merged hourly precipitation dataset by applying the optimal interpolation methods (Joyce et al., 2004;Xie et al., 2017). Many studies demonstrate the high consistency and an acceptable bias of 210 the CMORPH compared with the observed precipitation (Ou et al., 2020;Wei et al., 2018).
Beside the evaluation of precipitation, assessments of wind fieldswater vapor transport and large-scale atmospheric circulation are also particularly important. , The large-scale atmospheric circulation directly controls the atmospheric water vapor (AWV) transport between the TP and its surrounding area and for which exerts a great influence in the formation of precipitation. Impacts of different spectral nudging 215 strategies on the 500-hPa AWV water vapor transport were compared with the ERAI and the fifthgeneration global reanalysis of ECMWF, ERA5, which has a 31-km spatial resolution and 1-h temporal resolution. The horizontal wind fields of ERA5 over the TP have been verified with observations (He et al., 2019) and show the smallest wind bias compared to ERA-Interim reanalysis and an ensemble data assimilation system. In this study, both ERAI and ERA5 was were interpolated to the 10-km downscaled 220 grid resolution as the same to model output.

Impacts of nudging strategy on mean precipitation simulations
The spatial consistency between simulated results and CMORPH was investigated by the monthly mean (larger than 0.1 mm/ day -1 ) and extreme (the highest 5 percentile value of) precipitation (P95, mm/ day -225 1 ; equals to 5.73 mm/ day -1 in this study). The monthly mean spatial distributions of the CMORPH precipitation fields of July and its difference with WRF simulations over the TP are depicted in Figure 2.
As shown in Figure 2c, extreme precipitation can be observed over the southern and southeastern TP, and all simulations have large wet biases of precipitation compared to the CMORPH, especially along the southern edge of the Himalayas. 230 The overestimation of precipitation over the eastern TP was reduced when using spectral nudging method showed apparent higher RMSEs and MAEs compared to Control, up to 23.10 mm day -1 (RSME) in SNQ_trop39 for extreme precipitation events. The degraded skills of the SNQ_trop25 and SNQ_trop39 experiments in predicting precipitation were contrary to previous studies where adding spectral nudging toward water vapor mixing ratio could largely reduce the wet bias of precipitation intensity (Spero et al., 2014;2018). In this assessment, the best performance was achieved by the SNnoT experiment with the 8 / 34 lowest RMSE and MAE for different precipitation thresholds. In addition, the SNnoT experimentIt showed a clear advantage for the extreme precipitation event, reducing the RMSE by 1.16 mm day -1 compared with the Control and 2.27 mm day -1 compared with the SN.

Evaluation of diurnal precipitation
In addition to error metrics, frequency distributions of precipitation intensity and diurnal cycle of the 265 mean precipitation from WRF simulations were compared with CMORPH ( Figure 5). It is clear that precipitation from WRF simulations were heavily overestimated in the occurrence of precipitation events when precipitation intensity exceeds 3 mm day -1 . With respect to Control and other spectral nudging strategies, the frequency distribution of precipitation intensity simulated by the SNnoT experiment was more comparable to with CMORPH ( Figure 5a). The closer frequency density of high precipitation 270 threshold indicated the advantage of restricting nudging for temperature and water vapor mixing ratio in model may be attributed to decreasinge the overforecasting of extreme precipitation events over the southern TP.
The diurnal cycle of precipitation is an important feature of the monsoon precipitation because it controls the circulation characteristic and affects the precipitation magnitude (Bhatt et al., 2014;Sato et al., 2008). 275 To investigate whether using spectral nudging method can improve the simulation of diurnal cycle of precipitation, the variations of hourly precipitation from the CMORPH observations and model simulations are displayed in Figure 5b. According to the CMORPH observations, the averaged peaks of hourly precipitation mainly occurred in the afternoon and mid-night of the local time (UTC+8 h) and reached 0.2 mm h -1 . The precipitation forecast shows simulations of diurnal variation 280 patternsprecipitation had comparable to those ofpatterns with CMORPH, but the simulated precipitation iswith a remarkably larger intensity during the day, which indicatesindicating that some individual precipitation events may be misrepresented. Compared with the Control, although the precipitation from SN showed an improvement in terms of decreasing night-time precipitation overforecasts (the maximum of average precipitation was reduced by 0.05 mm/ h -1 ), the precipitation simulation of the SN experiment 285 it performed worse than the Control during the day. The precipitation predictions intensity from the SNQ_trop39 and SNQ_trop25 experiments, however, simulated had a much higher wet bias than the Control, up to 0.1 mm/ h -1 , over the TP than did the Control. The smallest wet bias of precipitation was found in the SNnoT experiment during the day, which also outperformed other experiments at night, reducing the overforecast of precipitation by 0.03 mm/ h -1 compared with the Control and 0.05 mm/ h -1 290 compared with the SN. Consequentlybased on above analysis, the model simulations should be improved especially for precipitation forecasts during 2-12 UTC (10-20 of the local time) requires urgent improvement in the model, even though the precipitation forecasts of has been greatly improved by the SNnoT greatly improved compared to the Control and SN forecasts. In addition, the precipitation forecasts of SNlowU and SNlowT had diurnal variations and comparable precipitation intensities that 295 were similar to Control. These findings indicate that the SNnoT experiment had considerable improvements in simulating diurnal precipitation over the TP in comparison to the Control and SN experiments.

Large-scale atmospheric circulation anomalies 300
In summer, precipitation occurred in the TP is mainly controlled by two water vapor channels, one of which is the transported by strong southwesterly under the effect of the Indian summer monsoon. The second channel is transported by the south branch of the mid-latitude westerly. By the influences of both channels, a large amount of AWV water vapor from the Bay of Bengal and surrounding oceans could be transferred transported to the TP (Xu et al., 2008;Xu et al., 2002;Zhou and Li, 2002). 305 The terrain of the Himalayas, featured by a sharp topography gradient, is more than 5,000 m on average and is regarded as a natural barrier for northward atmospheric flow. In summer, large amount of atmospheric water vapor transport, originating from the surrounding oceans, impinge on the Himalayas.
The sufficient high topography strictly limits the upslope water vapor transport, and strong upward motions are consequently formed by the lifting effect of the complex terrain (Dong et al., 2016). 310 However, the complex orography of southern slope of the Himalayas is greatly smoothed in current RCMs. Accordingly, the surface friction and sub-grid orographic drag due to the impact of mesoscale and microscale orography on the airflow are weakened, which in turn reduce the convergence and condensation of water vapor over the southern slope of the Himalayas. Consequently, more water vapor transport could arrive the high-latitude TP, causing more precipitation over the TP. 315 The monthly mean AWV transport fields, averaged for the whole atmospheric layer,Column-integrated northward water vapor transport, eastward water vapor transport, averaged over the study period derived from ERAI, ERA5 and model simulations related to the simulated precipitation are displayed in Figure   6. Large-scale atmospheric circulation forces strong water vapor transport into the southwestern TP, leading to a water vapor transport belt along the southwestern slope of the Himalayas. As represented by 320 ERAI (Figure 6a1 and 6a2), there was an obvious wet bias of water vapor transport over the TP and the central Himalaya. Although ERA5 showed a significant reduction in water vapor transport over the southern TP (Figure 6b1 and 6b2), however, there was still excessive water vapor along the Himalayas, indicating that its coarse resolution was insufficient to resolve the impact of orographic drag on northward flow. 325 ERA5 (Figure 6a), large-scale atmospheric circulation favours strong AWV transport into the southeastern TP, with an AWV transport centre occurring at the windward slope of the southwestern Himalayas. With higher spatial resolution and thus more detailed topography, allAll simulations reproduced such AWV fields over the southern TP but with weaker magnitudes compared to ERAI and ERA5, in which more AWV is transported to the interior of the TP.. Note that not all spectral nudging 330 experiments retained the large-scale characters of water vapor transport. From the Figure 6d1, SN simulated an anomalous weak northward water vapor transport over the western Himalayas, where SN misrepresented the large-scale information that has been resolved by the global reanalysis data assimilation (EARI and ERA5). Althoughreduced the wet bias of water vapor transport. Both SNlowU and SNlowT (Figure 6e1d and 6f1e) showed showed comparable results with those of the Control (Figure  335 6b6c1), eastward water vapor transport of SNlowU and SNlowT were slightly weaker than Control over the western TP (Figure 6e2 and 6f2). which indicated stronger AWV transport over the central and northern TP and overestimated the magnitude of the water vapor transport centre at the Bay of Bengal.
Despite the above three experiments (Figure 6b, 6d and 6e) reducing the AWV transport and causing smaller RMSEs in precipitation forecasts over the southern TP (Figure 4a), their AWV transport fields 340 were greatly misrepresented over the remaining regions of the TP, which could have detrimental effects on water cycle analysis. SNQ_trop25 and SNQ_trop39 (Figure 6h1 and 6i1) simulations with nudging toward moisture (Figure 6g and 6h) showed an analogous performance with smallernorthward water vapor transport over the Bay of Bengal, indicating that the difference between SNQ_trop25 and SNQ_trop39 in precipitation simulations may be attributed to local convection and subsequently 345 processes. With reference to the above, the AWVwater vapor transport obtained in by SNnoT ( Figure   6f6g1 and 6g2) showed the most significant reduction over the TP compared to the other spectral nudging experiments. closely approached to that of ERA5, and the wet bias of AWV transport was reduced compared to the other spectral nudging experiments and only indicated a slight overestimation over the western TP. As anticipated from the precipitation anomalies, such a difference decrease in water vapor 350 transport of SNnoT is obviously related to the smaller wet bias of precipitation.
The TP and its surrounding area have been regarded as a favorable region for convective processes because of its high elevation, by which moister can be transferred to the upper layers during summer monsoon season (Fu et al., 2006;Heath and Fuelberg, 2014). Deep convection favors the process of transporting emissions from the surface into the upper-level atmosphere, through which moisture flux is 355 vertically released into the atmospheric and influences the production of precipitation. SNQ_trop25 and SNQ_trop39 (Figure 6g and 6h) showed an analogous performance with smaller water vapor transport over the Bay of Bengal, indicating that the difference between SNQ_trop25 and SNQ_trop39 in precipitation simulations may be attributed to local convection and subsequently processes.

Vertical structure of the convective process 360
The terrain of the southern Himalayas, which has a sharp altitude gradient, is extremely complex.
Atmospheric water vapor transport is impeded, and a strong upward motion is consequently formed at the windward slope caused by the lifting effect of the complex terrain. However, the complex orography of the Himalayas is greatly smoothed in RCMs, even though high horizontal spatial resolutions (e.g. 3 km) are applied (Wang et al., 2020). Therefore, the impact of a drag force due to the complex orography 365 on the airflow is weakened, as is the convergence of water vapor. Consequently, more water vapor transport will be transferred to the high-latitude TP, causing more precipitation over the TP. The TP and its surrounding area have been regarded as a favorable region for convective process because of its strong topography gradient. Deep convection favors the process of transporting water vapor into the upper-level atmosphere, through which moisture flux can be vertically released into the atmosphere and influences 370 the formation of precipitation during summer monsoon season (Fu et al., 2006;Heath and Fuelberg, 2014). Because the horizontal and vertical variations in moisture and temperature at the upper troposphere have not been sufficiently resolved by global driving datasets (Miguez-Macho et al., 2004). The lid was originally designed to avoid transferring moisture and temperature biases above the tropopause in the reference field to the model-simulated field. The strongest upward motion along the latitude was 380 simulated by the SNQ_trop39 (Figure 7g) over the southern slope of the Himalayas, followed by the SN and SNQ_trop25 (Figure 7b and 7f). In the two SNQ simulations, the upward motion was obviously decreased when the lid was applied at the lower model level (Figure 7f and 7g). From above comparison, it is clear that nudging towards temperature and moisture at the middle troposphere was likely to enhance the atmospheric upward motion over the southern slope of the Himalayas. Therefore, more water vapor 385 could be transferred to the upper troposphere, and was subsequently transported to the interior of the TP through high-level southwestern atmospheric advection, causing more precipitation over the TP. Large amounts of water vapor from the Bay of Bagel were transferred to the upper troposphere by the strong upward motion, which were converted to the interior of the TP through high-level southwestern advection, subsequently causing more precipitation over those regions. Despite the SNlowU and SNlowT 390 experiments (Figure 7c and 7d) simulating smaller upward wind compared to that of the SN, both patterns of the upward motion were similar with that of the Control (Figure 7a).
In this case, nudging towards temperature and moisture was restricted in the entire model layer, assuming that nudging towards horizontal wind components and geopotential height was strong enough to reduce large-scale errors in the wave component of temperature and moisture. As shown in Figure 7e Although the intensity of zonal mean upward motion over the TP is relatively weaker than that of meridional upward motion, a similar discrepancy was also observed in the SNnoT (Figure 8e), which indicated the weakest upward motion compared to the other experiments. Therefore, the convergence of airflow accompanied by water vapor over the central TP was enhanced, leading to a slightly larger 405 precipitation intensity in the SNnoT (Figure 2h and Figure 6f datasets are insufficient to represent the horizontal and vertical variations in moisture and temperature above the tropopause (Miguez-Macho et al., 2004). The lid was originally designed to avoid the transferring moisture and temperature biases above the tropopause in the reference field to the modelsimulated fields. With reference to the above analysis, it is suggested that setting the lid at the tropopause layer in the model is inappropriate when simulating precipitation over the TP. 415

Vertical profile of horizontal wind components, the atmospheric temperature, water vapor mixing ratio and horizontal wind speedspecific humidity
The spectral nudging technique is supposed to alleviate the inconsistence between the regional model field and the driving field (e.g. ERA-Interim). However, previous Dynamical downscaling studies in of WRF simulations centred over the TP that usinge ERA-Interim reanalysis products as the reference 420 driving fields have a ensemble underestimations of atmospheric temperature and overestimationslarge bias of the water vapor mixing ratio in summertransport over the TP (He et al., 2019;Xu et al., 2017). Therefore, the reason why not nudging towards temperature and moisture at all is preventing the external forces on moisture and temperature (from nudging), so that their small-scale dynamical features were not affected. In order to show how the settings of nudging parameters influenced the consistence of 425 nudged variables between model field and the driving field, vertical profiles of nudged variables averaged over the TP for the study period were calculated. The difference between ERA-Interim (ERAI) and seven WRF simulations at each pressure layer is displayed in Figure 9, and relevant statistical error metrics are given in Table 2.
As the SNnoT experiment tends to exhibit smaller water vapor transport and weaker upward wind over 430 the TP, the mean vertical profiles of atmospheric temperature and the water vapor mixing ratio from 100 to 700 hPa, averaged over the TP, were further investigated. The performances of the spectral nudging experiments were examined against the Control experiment and their differences are shown in Figure 9.
Compared to Control simulation, obvious improvements are observed in both eastward and northward wind components when spectral nudging was applied (Figure 9a and 9b). Specifically, most of 435 simulations with spectral nudging showed comparable eastward wind speed with ERAI in the each pressure layer, and reduced the bias of eastward wind speeds by 1.2 m s -1 compared to Control (Table 2).
Similarly, although all simulations produced stronger northward wind speeds than ERAI, but the use of spectral nudging reduced the bias by 0.8 m s -1 against Control simulation (Table 2). In terms of SNnoT (purple line), its consistence in both zonal wind and meridional wind fields was not affected by the 440 influence of restricting nudging towards temperature and moisture, with the RMSE of 0.79 m s -1 of U and RMSE of 1.04 m s -1 of V. However, both SNlowU and SNlowT simulations with decreased nudging coefficient for winds and temperature had similar patterns with Control simulation in terms of horizontal wind speeds and atmospheric temperature (Figure 9c). One possible reason could be their weaker nudging coefficient (0.000045 s -1 ), indicating that the horizontal wind component and temperature of 445 model field were relaxed to the driving field at every 6 h, which equals to the input temporal time interval of ERAI. It may weaken the impact of applying spectral nudging on the nudged variables, and thus simulated similar temperature and horizontal winds with Control.
Generally, An apparent improvement is was observed in several spectral nudging experiments in reducing the cold bias compared to the Control (Figure 9c)., except that the SN and SNQ_trop39 experiments 450 resulted in larger cold biases in the upper troposphere, while the SNnoT and SNQ_trop25 experiments only had slightly smaller temperatures above 150 hPa (Figure 9a). Although the performances of SNlowU and SNlowT are were highly comparable to with the Control, both SNlowU and SNlowT simulated higher temperatures at lower levels and had slightly lower RSMEs. This pattern of SNlowU and SNlowT results is also observed in the comparison of the water vapor mixing ratios; both experiments 13 / 34 simulated a slightly drier water vapor mixing ratio in the low troposphere (Figure 9b). The discrepancy of the SN, SNQ_trop25 and SNQ_trop39 in vertical profiles of the temperature difference fields of the SN, SNQ_trop25 and SNQ_trop39 showed similar variations below was found in pressure layer that was higher than 300 hPa, but where the temperatures temperature in SNQ_trop25 was higher than in SN and SNQ_trop39. The higher temperature of SNQ_trop25 was likely attributed to its higher water vapor 460 within the free troposphere (Figure 9d), which caused wetter atmosphere conditions; thus, more heat flux was released once precipitation began.sharply decreased and became colder than those in the Control at higher layers. The vertical profile of temperature in SNnoT SNQ_trop25, however, was aligned with the SNnoT SNQ_trop25 in the middle upper troposphere but had higher smaller temperature. These comparisons indicated that limiting nudging towards temperature in model produced higher 465 temperature.In terms of the vertical spread of the water vapor mixing ratio (Figure 9b), the higher temperature obtained in SNQ_trop25 is likely attributed to its higher water vapor mixing ratio within the free troposphere, which caused wetter atmosphere conditions; thus, more heat flux was released once precipitation began.
Considering the wet bias of water vapor of ERAI over the TP,Compared to the Control experiment, the 470 best performance in reducing the wet bias of the water vapor mixing ratio in atmospheric layers was achieved by the SNnoT, despite the SN simulateding slightly drier water vapor, with a value of 0.17 k kg -1 at 400 hPa. Both SNQ_trop25 and SNQ_trop39 simulated the wettest atmospheric water vapor contentmixing ratio at 500 hPa, but SNQ_trop25 had higher water vapor than did SNQ_trop39 when spectral nudging towards the water vapor mixing ratio was limited above 300 hPa in the SNQ_trop25 475 experiment. Based on the above results, spectral nudging towards water vapor mixing ratio in more atmospheric layers will reduce the wet bias of water vapor. However, such reduction in simulating atmospheric water vaporthe improvement could not compensate for the wet bias of the driving field (ERAI) negative impact that adding the ability to a model to perform spectral nudging towards water vaporthat has been artificially introduces introduced by applying spectral nudging towards water vapor. 480 extra wet bias due to the overestimation of ERA-Interim, when it is used as the reference field, in representing water vapor over the TP. In Moreover, according to the study of He et al., (2019), the evaluation of atmospheric temperature in ERA-Interim against sounding observations showed an apparent cold bias when pressure layer was higher in ERA-Interim abovethan 400 hPa over the TP. The comparisons between SNnoT, SNQ_trop25 and SNQ_trop39 indicate that the cold bias of ERA-Interim 485 in the upper troposphere had a higher contribution in to the deteriorating model's skill in simulating atmospheric temperatures than those of in the lower and middle troposphere. Therefore, to achieve an optimal strategy for precipitation analysis and further water cycle budget studies without degrading temperature and water vapor simulations, model solutions must balance their accuracy in the lower and middle troposphere layers. In terms of the vertical profile of horizontal wind (Figure 9c), most spectral 490 nudging experiments remarkably decreased the wind speed in the middle troposphere; however, the SNlowU and SNlowT showed consistent with that of Control.
In summary, the inter-comparisons of the ensemble model simulations demonstrated that SNnoT achieved notable improvements over the Control and the remaining spectral nudging experiments. It not only improved the agreement of model wind filed with ERAI, but also reduced the cold bias of 14 / 34 temperature above 400 hPa and the wet bias of moisture within troposphere over the TP. in water vapor transport, atmospheric temperature estimations and subsequent convective process simulations. The combinations of weakened convective upward motion over southern slope of the Himalayas the Himalayan foothills and the weakened smaller horizontal wind speed in the free tropospherewater vapor transport simulated by the SNnoT experiment limited water vapor to be transported to the interior of the 500 TP, which indicated leading less moisture available for precipitation. The improved moisture transport and large-scale circulation will have significant implications for precipitation analysis and water cycle budgets over the TP.

Conclusions 505
In the case of downscaling the coarse-resolution reanalysis, regional climate simulations suffer from the large-scale errors due to the inconsistencies between the model solution and the driving field along the boundaries because of the systematic error of RCM (Miguez-Macho et al., 2004;Waldron et al., 1996).
The spectral nudging technique is thus used to relax the specific spectral scale of variables in model field towards the driving field, in order to alleviate the inconsistencies. In this paper, a set of simulations was 510 evaluated to reveal the impactsinfluence and improvements of applying the spectral nudging technique in the WRF model for simulating precipitation and associated meteorological nudged variables over the TP were evaluated using seven experiments.
Firstly, evaluations against the CMORPH precipitation data indicated that conventional continuous simulation cannot reproduce actual precipitation patterns and largely overestimate precipitation events 515 over the western and northern TP. The use of spectral nudging in the WRF model reduces reduced such overestimations but does did not always overcome all deficiencies when simulating the precipitation intensity and its diurnal cycle. Spectral nudging experiments with decreased nudging coefficients (4.5 × 10 -5 s -1 ) for wind and potential temperature showed comparable results with conventional continuous simulation in terms of precipitation, associated water vapor transporthorizontal wind 520 components and temperature simulations. In addition, allowing spectral nudging towards water vapor mixing ratio in more atmospheric layers within the troposphere can reduce the wet bias of water vapor.
But tThis improvement cannot compensate for the wet bias of the driving field (ERAI) that has been artificially introduced by applying spectral nudging towards water vapor. the artificially introduced extra wet bias when water vapor in the model field is relaxed towards the ERA-Interim reanalysis. Therefore, 525 although the ERA-Interim reanalysis has been widely used as a the large-scale reference driving field for regional climate studies of centred the TP in RCMs, its uncertainties when representingthe cold bias of atmospheric temperature and wet bias of water vapor fields over this region should be strongly considered when in the case of downscaling the ERA-Interim reanalysis. Following this perspective, the evaluation of vertical temperature profiles implies that the simulations of atmospheric temperature in the model are 530 more sensitive to the cold bias of temperature due to ERA-Interim in the upper troposphere than those in the lower and middle troposphere.
To decrease the influence of the such biases and inbalance the accuracy of precipitation simulation, temperature and water vapor simulations, spectral nudging towards potential temperature and the water vapor mixing ratio was restricted in the whole layers, (designated SNnoT) preventing the external forces 535 on moisture and temperature (from nudging) to affect small-scale dynamics. The change to spectral nudging has had clear advantages over conventional continuous simulation and other spectral nudging experiments, and largely improved the simulation of precipitation intensity and forecast as well as the forecast of its diurnal cycle over the TP compared to CMORPH. Based on subsequent analysis, SNnoT reduced the meridional water vapor transport and upward motion at the southern slope of the Himalayas; 540 thus, less water vapor could reach the upper layerstroposphere, which caused causing less precipitation over the southern region and the interior of the TP. Consistently, SNnoT also improved the simulations of atmospheric temperature and the water vapor mixing ratio by collectively alleviating the cold bias of temperature and wet bias of the water vapor.
The evaluation and improvement of the spectral nudging technique in the WRF model in this work not 545 only concentrates on optimizing precipitation forecasts but also aims to increase the reliability of RCM data used to assess the regional climate change without degrading the simulations of temperature and water vapor. The conclusion of this work is also useful for the application of RCMs in dynamical downscaling processes when using different reference fields. Since regional cumulus and land surface processes are also essential in regional climate modelling because of their significant effects 550 on both large-scale and regional atmospheric circulation, improvements in representing such physical processes are required in future studies. with the data processing; all authors helped in writing the paper. Table 1: Nudging coefficients (10 -4 s -1 ) used for spectral simulations. Spectral nudging is indicated by "SN". U, V represent for horizontal wind component, T represents for potential temperature, Q represents for water vapor mixing ratio and represents for geopotential. Nudging is applied to all layers above the PBL; layer 745 39 represents approximately the mean pressure level of tropopause over the TP; layer 25 represents approximately the normally lower limit for "ktrop" that is set to the middle layer in model simulation;