1. Introduction
As a vital component of Earth’s hydrological and energy cycles, precipitation is of great scientific and practical importance. It is well known that both the instantaneous precipitation rate and the accumulated precipitation amount on various time scales are characterized by an extremely large spatial discrepancy, which is uncommon in other atmospheric fields. The spatial unevenness of precipitation is highly scale dependent. Precipitation heterogeneity on a local scale is the comprehensive embodiment of the high-level nonlinearity of precipitation processes, the complexity of the phase transition of water, and the sensitivity of precipitation to terrain forcing. Greater insight into the local unevenness of precipitation is fundamental for accurate weather and climate prediction on a finer scale. The quantitative recognition of such local unevenness of precipitation is also valuable for hydrological processes and water resource management (Nykanen et al. 2001). Despite its relevance to both research and operation, precipitation unevenness on a local scale has yet to be systematically studied.
Precipitation has been a key metric and ultimate test for the performance of various numerical models (Tapiador et al. 2019). Reproducing precipitation features as accurately as possible is one of the primary goals of both weather and climate models. Because of the continued growth in computational capacity, global storm-resolving simulation has become practical in recent years. A framework for the intercomparison of the global storm-resolving model, the Dynamics of the Atmospheric general circulation Modeled on Nonhydrostatic Domains (DYAMOND), has been set up to explore the performance of the emerging class of atmospheric circulation models (Stevens et al. 2019). In climate applications, global storm-resolving models are expected to ease certain systematic biases that arise from parameterized convection and enhance the understanding of how climate changes with warming (Stevens and Satoh 2021). In weather applications, a major goal of storm-resolving weather prediction is to accurately forecast high-impact storms, including their locations and intensities (Yano et al. 2018). On the storm-resolving scale, more intricate atmospheric processes and more realistic land surface forcing are resolved, which are believed to contribute to the ability to reproduce more details in precipitation patterns (Karki et al. 2017). Therefore, the local unevenness of precipitation can be a natural metric for these high-resolution models, which meets both the scientific demand for atmospheric responses to fine-scale forcings and the social demand for reliable forecasts. This study provides an intuitive method to quantify the local unevenness of precipitation. Focusing on central and eastern China, which feature complex terrain of a wide range of scales, a series of characteristics in local unevenness are revealed, and the variation in local unevenness is discussed, which can be utilized as a whole set of metrics to evaluate storm-resolving models.
This paper proceeds as follows. First, the methods quantifying the local unevenness and data that are used are described in section 2. Next, the features of local unevenness and their relationship with topography are analyzed. Then, the seasonal differences in local unevenness in three types of terrain are discussed. The major results are summarized, and related discussions are given in the last section.
2. Data and methods
The daily rain gauge records during 1961–2020 that were used in this study were obtained from the Daily Meteorological Dataset of Basic Meteorological Elements of the China National Surface Weather Station (V3.0). This dataset, released by the National Meteorological Information Center of the China Meteorological Administration, has undergone strict quality control. A month with qualified values less than 21 days is set as missing. If there is any month missing in a year, the data for the whole year are regarded as missing. To ensure the completeness of records, 1656 stations are used in the study area (17°–43°N, 99°–126°E) (Fig. 1) after removing stations with more than 5% missing years of the whole period. The topography data are derived from the digital elevation model GTOPO30.
Distribution of 1656 stations over central eastern China. The filled color denotes the number of stations within a 100-km radius of each station. The black contours represent topographic heights of 500, 1000, 2000, and 3000 m.
Citation: Journal of Hydrometeorology 24, 11; 10.1175/JHM-D-22-0240.1
The local relief at the ith station is calculated by taking the difference in elevation between the highest station and the lowest station within 100 km of the ith station. The elevation of the station is represented by the mean elevation of the area surrounding it within 5 km. Consistent with the LUI, the local relief is calculated only at stations with no less than 5 neighboring stations.
A local maximum (LM) station of precipitation is defined if the station satisfies the following conditions: its climatological precipitation amount is the largest among all the stations within its 100-km scope and is more than 10% higher than the average precipitation amount of those neighboring stations; the number of its neighboring stations is equal to or greater than 5. The enhancement of precipitation at the LM station is measured by the difference in precipitation between the LM and its neighboring stations within a 100-km scope.
3. Results
a. LUI and topography
The spatial distribution of the LUI, which is calculated from the climatological annual mean precipitation for 1961–2020, is shown in Fig. 2b. The mean LUI of 1546 stations is 0.359, and the standard deviation for the LUI among these stations is 0.189. The overall pattern of the spatial distribution of the LUI is quite similar to that of the local relief (Fig. 2c), and the pattern correlation between them reaches 0.569. Extremely high LUIs (larger than 1.0) are found at 14 stations, all of which are located to the west of 105°E. Three of these stations are on the northeastern edge of the Tibetan Plateau, two of these stations are on the eastern edge of the Tibetan Plateau, and nine stations are on the southern edge of the Yungui Plateau. As shown in Fig. 2c, all three regions feature high local relief. In contrast, both low LUIs and low local relief can be found in the Sichuan basin, adjacent to the eastern Tibetan Plateau. To the east of the 500-m contour line, most high-LUI regions correspond to isolated mountains or small-scale mountain ranges, and most plain areas have low LUIs.
(a) Topography over central eastern China. The shading shows the surface elevation (unit: m). The first, second, and third terrain ladders are separated by the 3000- and 500-m height contours. Important topography and rivers are marked. The distributions of the (b) LUI and (c) local relief (m). The black contours represent the topographic heights at 500, 1000, 2000, and 3000 m.
Citation: Journal of Hydrometeorology 24, 11; 10.1175/JHM-D-22-0240.1
The relationship between the LUI and local relief is regionally dependent. Figure 3a shows the correlation between them in a meridional sliding window of 5° latitude. The correlation coefficients between 28° and 32°N, approximately along the Yangtze River, exceed 0.70. Along the 30°N section (middle panel of Fig. 3b), both the LUI and local relief decrease sharply at approximately 104°E and then fluctuate coherently eastward, with a correlation coefficient as high as 0.893. The consistency between the LUI and local relief decreases rapidly on both the north and south sides (Fig. 3a). For stations to the north (south) of 33°N (28°N), the correlation of the pattern between the LUI and local relief is only 0.478 (0.412). As shown by the two lines on the top of Fig. 3b, the LUI along 36°N does not increase with the local relief between 108° and 114°E. This low LUI value may be affected by the propagation of convective systems from the northwestern mountains to the southeastern plains (Sun et al. 2018), in which the consistency within the system prevails heterogeneity caused by local relief and leads to a relatively even local precipitation distribution. Along the 26°N section (bottom panel of Fig. 3b), the two series have similar general decreasing trends from west to east, while they present distinct phases on a more local scale. The maximum lead–lag correlation coefficient of 0.504 appears when the LUI is 1° longitude eastward of the local relief. This poor consistency indicates the effect of the terrain is relatively weak in this region. There is evidence of the increased frequency of heavy rainfall events in the vicinity of large cities over coastal South China (Wang et al. 2015; Wu et al. 2019), and the urban heat island effects can account for the convective initiation and alter the subsequent regional heavy rainfall distribution (Yin et al. 2020).
(a) Correlation between the LUI and local relief in a 5° latitude sliding window with a step of 1° latitude over 99°–126°E. The x axis presents the correlation values. (b) LUI (black solid lines) and local relief (gray dashed lines) along 26°, 30°, and 36°N. The left y axis presents the LUI values. The right y axis presents the local relief values (m).
Citation: Journal of Hydrometeorology 24, 11; 10.1175/JHM-D-22-0240.1
b. LM and topography
To further quantify and highlight the local inhomogeneity of precipitation, the local maximum (LM) station is defined as described in section 2. Based on the climatological annual precipitation amount for the period of 1961–2020, 59 LM stations are identified in central and eastern China. On average, each LM station has 11.4 neighboring stations. As shown in Fig. 4a, all 59 stations are located on or near high topographic relief. The LM stations to the west of 105°E clearly outline the eastern edge of the Tibetan Plateau. The large-relief belt, which extends from North China to Southwest China and divides the second terrain ladder and the third terrain ladder, is also a zone of LM station concentration. On the third terrain ladder, there is no LM station in the plain area, and most of the LM stations are found in the mountainous area to the south to 33°N. Taking into account the significant differences in the impact of various scales of terrain, the LM stations are classified into three groups: the high-elevation group, the edge group, and the eastern isolated-mountain group (Fig. 4b). Using 30-min-resolution topographic data, the 500-m contour can roughly represent the junction of the second and the third terrain ladder. The edge group contains 10 LM stations, located within 50 m away from the 500-m contour (blue rectangles in Fig. 4b). The remaining LM stations are divided into the high-elevation (the eastern isolated-mountain) group to the west (east) of the 500-m contour. The high-elevation group contains 31 LM stations (black dots in Fig. 4b), and the eastern isolated-mountain group contains 18 LM stations (red triangles in Fig. 4b).
Distribution of LM stations. Shading denotes (a) topographic relief (m) and (b) elevation (m). The black dots in (a) denote all LM stations. The black dots, blue rectangles, and red triangles in (b) denote LM stations in the high-elevation group, the edge group, and the eastern isolated-mountain group, respectively. The black contours represent the topographic heights at 500, 1000, 2000, and 3000 m.
Citation: Journal of Hydrometeorology 24, 11; 10.1175/JHM-D-22-0240.1
Figure 5 shows the topography around the LM stations for each group in descending sequence. The average elevation of the surrounding regions of the high-elevation LM stations (black dashed line) is 1710.0 m, which is higher than the average elevation of the LM stations (black dot, 1515.5 m) in this group. Compared with the black dashed line, the gray dashed line, which presents the elevation of regions around the LM stations in the edge group, is considerably lower. However, the LM stations in the edge group (gray dot) have an ordinal rank that is similar to those in the high-elevation group (black dot). In terms of elevation, the LM stations in the eastern isolated-mountain group (black triangle, 445.0 m) and those in the edge group (gray dot, 441.4 m) are almost the same, whereas the former has a much higher relative position in their surrounding regions. Based on the features shown in Figs. 4 and 5, the high-elevation group can represent the local unevenness on plateaus, the edge group represents the contrast between the elevated second terrain ladder on the west side and the lower plain area on the east side, and the eastern isolated-mountain group features isolated mountains on the plain.
Elevation of LM stations and their surrounding regions for the high-elevation group (black dashed line), the edge group (gray dashed line), and the eastern isolated-mountain group (black solid line). At every LM station, the elevations of all grids (at 10-km resolution) within the 100-km scope are sorted in decreasing order. In each group, a series of elevations is calculated by averaging the sorted series of elevations of all the LM stations in the group and is shown by the line. The black dot, gray dot, and black triangle denote the average elevations of the LM stations in the high-elevation, edge, and eastern isolated-mountain groups, respectively. The x axis is the ordinal rank of grids in LM regions.
Citation: Journal of Hydrometeorology 24, 11; 10.1175/JHM-D-22-0240.1
Focusing on the LM stations and their surrounding stations, the distributions of precipitation amount, frequency, and intensity with height are analyzed in each group. As shown in the left column of Fig. 6, there are generally two precipitation amount peaks (one in the third bin with an average elevation lower than 800 m and the other in the seventh bin with an average elevation at approximately 1900 m) in the high-elevation group. The two peaks can also be reflected by both the frequency and intensity. The minimum frequency is found in the fourth bin (average of approximately 1000 m) between the two peaks. In contrast, the intensity reaches the lowest value at the highest elevation. The topographic influence of this group of stations is complex, including both the large-scale terrain forcing around the boundary of the Tibetan Plateau and the small-scale local terrain forcing in deep valleys embedded in the high-elevation areas (Li 2018). The edge group, which is presented in the center column of Fig. 6, features a single peak. The precipitation amount and frequency reach a peak in the fifth bin (average of approximately 210 m), while the intensity reaches a maximum in the fourth bin (average of approximately 160 m). After reaching the peak, the precipitation frequency decreases gently between the fifth bin (average of approximately 210 m) and the sixth bin (average of approximately 300 m) with increasing height, but the precipitation intensity decreases considerably. In this group, the influence of the northeast–southwest-oriented terrain ladder plays a dominant role in the concentration of precipitation at relatively low levels. The column on the right side of Fig. 6 is for the eastern isolated-mountain group. Both the amount and the frequency of precipitation in the eastern isolated-mountain group reach the maximum in the highest bin (average of approximately 550 m). The frequency is lowest in the second bin (average of approximately 30 m) and then gradually increases with height. In contrast, the highest intensity is found in the lowest bin. The high frequency of weak precipitation around the top of topography is closely related to the effects of small-scale isolated mountains. Overall, the average value, the median value, and the interquartile range consistently show that there are significant differences in the characteristics of precipitation distribution with terrain among the three groups of stations, indicating the distinction in the impact of terrain on precipitation at various scales.
Distributions of (a)–(c) the average annual precipitation amount (mm), (d)–(f) frequency (%), and (g)–(i) intensity (mm day−1) at the LM stations and their neighboring stations plotted against elevation. Precipitation at the LM stations and their neighboring stations is shown for (left) the high-elevation group, (center) the edge group, and (right) the eastern isolated-mountain group. For each group, stations are divided into eight bins according to their elevations from low to high. The number of stations in the first to seventh bin is equal to the integer obtained by dividing the total station number in the group by 8, while the last (the eighth) bin contains the remaining stations. Red lines and blue lines denote the average and median precipitation in each bin, respectively. The light blue shading shows the range between the 25th and 75th percentiles of each bin. The vertical brown line denotes the average elevation of the corresponding bin.
Citation: Journal of Hydrometeorology 24, 11; 10.1175/JHM-D-22-0240.1
c. Seasonal variation
Based on LM stations and their neighboring stations, distinct characteristics of precipitation distributions with altitude in three groups have been identified on an annual time scale. The seasonal variations in these distributions are analyzed in this section.
Figure 7 shows the annual cycle of local precipitation unevenness in the three groups. The LUI in the high-elevation group (the eastern isolated-mountain group) presents a single peak, with the strongest unevenness occurring in the cold (warm) season. The monthly series of the LUI in the edge group features two peaks (one in the cold season and the other in the warm season). The amplitude (defined as the difference between the maximum and minimum of the monthly LUI) of the high-elevation group (0.64) is larger than that of the other two groups (0.36 of the edge group and 0.26 of the eastern isolated-mountain group). In general, precipitation unevenness in the three groups exhibits distinct seasonal variations, with key turning points in May and October. The distributions of precipitation against elevation in the three groups in the warm season (from May to October) and cold season (from November to February) are discussed in the following text.
Seasonal variation of the LUI for the LM stations and their neighboring stations in the high-elevation group (black line and gray shading), the edge group (blue line and light blue shading), and the eastern isolated-mountain group (red line and pink shading). The line denotes the average, and the shading shows the range between the 25th and 75th percentiles of each group.
Citation: Journal of Hydrometeorology 24, 11; 10.1175/JHM-D-22-0240.1
Figure 8 shows the distributions of the precipitation amount, frequency, and intensity plotted against elevation in the three groups in the warm season. The warm-season precipitation amount in the high-elevation group presents a double-peak pattern (Fig. 8a), which is similar to the annual distribution (Fig. 6a). However, the general increase in frequency with altitude (Fig. 8d) is significantly different from the annual pattern (Fig. 6d). In the edge group (the center column of Fig. 8), the warm-season frequency decrease (0.60%) at higher elevations (from the fifth bin to the eighth bin, with an average range of approximately 210–870 m) is much smaller than the annual decrease (10.22%). At lower elevations, the heights of the maximum mean frequency and amount (both in the fourth bin at approximately 160 m) are slightly lower than the annual heights (both in the fifth bin at approximately 210 m). The intensity increase (2.12 mm day−1) at lower elevations (from the first bin to the fourth bin, with an average range of approximately 20–160 m) is larger than the annual increase (0.60 mm day−1). In the eastern isolated-mountain group (the right column of Fig. 8), the warm-season frequency increase (11.62%) at higher altitudes (from the second bin to the eighth bin, with an average range of approximately 30–550 m) is larger than the annual increase (9.05%), which is consistent with the warm-season frequency increase at higher altitudes in the high-elevation group and the edge group.
As in Fig. 6, but for the warm season (May–October).
Citation: Journal of Hydrometeorology 24, 11; 10.1175/JHM-D-22-0240.1
Figure 9 is the same as Fig. 8, except that it shows the cold season. The amount peak at approximately 1900 m in the high-elevation group greatly weakens in the cold season (Fig. 9a). The frequency shows a general decrease with altitude (Fig. 9d), which is the opposite to the warm-season pattern. In the edge group (the center column of Fig. 9), the cold-season amount peak is more prominent, and the cold-season maximum mean amount (in the fifth bin at approximately 210 m) is slightly higher than the warm-season maximum mean height (in the fourth bin at approximately 160 m). The frequency decrease (20.19%) at higher elevations (from the fifth bin to the eighth bin, with an average range of approximately 210–870 m) is much larger than the warm-season decrease (0.60%). At lower elevations, the heights of the maximum mean frequency and intensity (both in the fifth bin at approximately 210 m) are slightly higher than the warm-season heights (both in the fourth bin at approximately 160 m). In the eastern isolated-mountain group (the right column of Fig. 9), the cold-season frequency increase (6.09%) at higher altitudes (from the second bin to the eighth bin, with an average range of approximately 30–550 m) is smaller than the warm-season increase (11.62%), indicating a smaller frequency gap between high and low elevations.
As in Fig. 6, but for the cold season (November–April).
Citation: Journal of Hydrometeorology 24, 11; 10.1175/JHM-D-22-0240.1
4. Summary and discussion
To provide quantitative and systematic insights into the local unevenness of the spatial distribution of precipitation, the LUI and LM are defined and analyzed in this paper. The main findings based on the new methods are summarized as follows:
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Local unevenness of precipitation is dominantly influenced by local topography, and the LUI is significantly related to terrain. High LUIs spatially correspond to high local topographic relief. The correlation between them is regionally dependent, and the highest correlation coefficient appears along the Yangtze River.
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Local maximum stations are identified to represent areas with strong local unevenness. According to different characteristics of topographic influences, LM stations are divided into three groups. Each of them presents a distinct distribution of precipitation with altitude: double peaks in the high-elevation group, a low-altitude peak in the edge group, and a high-altitude peak in the eastern isolated-mountain group.
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Precipitation distributions with altitude in the three groups present seasonal variations. Precipitation tends to occur at higher (lower) elevations in the warm (cold) season. The frequency distribution in the high-elevation group shows a general increasing tendency with altitude in the warm season and a general decreasing tendency in the cold season. The low-altitude frequency peak in the edge group is more prominent in the cold season. The high-altitude frequency peak in the eastern isolated-mountain group is more prominent in the warm season.
The characteristic of relatively more precipitation occurring at higher (lower) elevations in the warm (cold) season may be explained by the increased convective (stratiform) precipitation in the warm (cold) season (not shown). Studies have noted that the mean profile patterns of convective and stratiform precipitation are different (Tao et al. 1993), and convective precipitation corresponds to a higher rain top (Yunfei et al. 2003). The local unevenness analyzed in this paper is calculated from the climatological annual mean and monthly mean precipitation. Considering the complexity of precipitation processes, it is interesting to carry out event-based and refined classification before the assessment of local unevenness. For example, the partitioning of precipitation into short- and long-duration events can distinguish daytime convection and nocturnal stratiform precipitation (Yu et al. 2007), and these two kinds of precipitation can lead to different patterns of local unevenness. Furthermore, the temporal heterogeneity of precipitation is also closely related to the influence of local topography (Gan et al. 2019; Zhang et al. 2021). Synthesizing temporal and spatial unevenness will reinforce understanding of precipitation processes over complex terrain. Both the LUI and LM can successfully indicate the key characteristics of precipitation on a local scale and can be used as quantitative criteria to evaluate the performance of storm-resolving models.
Acknowledgments.
This work was supported by the National Natural Science Foundation of China (42225505, U2142204), S&T Development Fund of CAMS (2022KJ007), and the Jiangsu Collaborative Innovation Center for Climate Change.
Data availability statement.
The rain gauge data used during this study are obtained from the Daily Meteorological Dataset of Basic Meteorological Elements of China National Surface Weather Station (V3.0), which is provided by the National Meteorological Information Center (NMIC) of the CMA (http://data.cma.cn/). The original topography data are downloadable at the official website (https://www.usgs.gov/centers/eros/science/usgs-eros-archive-digital-elevation-global-30-arc-second-elevation-gtopo30).
REFERENCES
Gan, Y., N. Li, and J. Li, 2019: Differences in the rainfall characteristics between Mount Tai and its surrounding areas. J. Meteor. Res., 33, 976–988, https://doi.org/10.1007/s13351-019-9006-0.
Karki, R., S. ul Hasson, L. Gerlitz, U. Schickho, T. Scholten, and J. Bohner, 2017: Quantifying the added value of convection-permitting climate simulations in complex terrain: A systematic evaluation of WRF over the Himalayas. Earth Syst. Dyn., 8, 507–528, https://doi.org/10.5194/esd-8-507-2017.
Li, J., 2018: Hourly station-based precipitation characteristics over the Tibetan Plateau. Int. J. Climatol., 38, 1560–1570, https://doi.org/10.1002/joc.5281.
Nykanen, D. K., E. Foufoula-Georgiou, and W. M. Lapenta, 2001: Impact of small-scale rainfall variability on larger-scale spatial organization of land–atmosphere fluxes. J. Hydrometeor., 2, 105–121, https://doi.org/10.1175/1525-7541(2001)002<0105:IOSSRV>2.0.CO;2.
Stevens, B., and M. Satoh, 2021: Editorial for the special edition on DYAMOND: The DYnamics of the Atmospheric general circulation Modeled on Non-hydrostatic Domains. J. Meteor. Soc. Japan, 99, 1393–1394, https://doi.org/10.2151/jmsj.2021-d.
Stevens, B., and Coauthors, 2019: DYAMOND: The DYnamics of the Atmospheric general circulation Modeled on Non-hydrostatic Domains. Prog. Earth Planet. Sci., 6, 61, https://doi.org/10.1186/s40645-019-0304-z.
Sun, W., J. Li, R. Yu, and W. Yuan, 2018: Circulation structures leading to propagating and non-propagating heavy summer rainfall in central North China. Climate Dyn., 51, 3447–3465, https://doi.org/10.1007/s00382-018-4090-x.
Tao, W.-K., S. Lang, J. Simpson, and R. Adler, 1993: Retrieval algorithms for estimating the vertical profiles of latent heat release: Their applications for TRMM. J. Meteor. Soc. Japan, 71, 685–700, https://doi.org/10.2151/jmsj1965.71.6_685.
Tapiador, F. J., R. Roca, A. Del Genio, B. Dewitte, W. Petersen, and F. Zhang, 2019: Is precipitation a good metric for model performance? Bull. Amer. Meteor. Soc., 100, 223–233, https://doi.org/10.1175/BAMS-D-17-0218.1.
Wang, D., P. Jiang, G. Wang, and D. Wang, 2015: Urban extent enhances extreme precipitation over the Pearl River Delta, China. Atmos. Sci. Lett., 16, 310–317, https://doi.org/10.1002/asl2.559.
Wu, M., Y. Luo, F. Chen, and W. K. Wong, 2019: Observed link of extreme hourly precipitation changes to urbanization over coastal South China. J. Appl. Meteor. Climatol., 58, 1799–1819, https://doi.org/10.1175/JAMC-D-18-0284.1.
Yano, J.-I., and Coauthors, 2018: Scientific challenges of convective-scale numerical weather prediction. Bull. Amer. Meteor. Soc., 99, 699–710, https://doi.org/10.1175/BAMS-D-17-0125.1.
Yin, J., D.-L. Zhang, Y. Luo, and R. Ma, 2020: On the extreme rainfall event of 7 May 2017 over the coastal city of Guangzhou. Part I: Impacts of urbanization and orography. Mon. Wea. Rev., 148, 955–979, https://doi.org/10.1175/MWR-D-19-0212.1.
Yu, R., Y. Xu, T. Zhou, and J. Li, 2007: Relation between rainfall duration and diurnal variation in the warm season precipitation over central eastern China. Geophys. Res. Lett., 34, L13703, https://doi.org/10.1029/2007GL030315.
Yunfei, F., L. Yihua, G. Liu, and Q. Wang, 2003: Seasonal characteristics of precipitation in 1998 over East Asia as derived from TRMM PR. Adv. Atmos. Sci., 20, 511–529, https://doi.org/10.1007/BF02915495.
Zhang, M., J. Li, and N. Li, 2021: Fine-scale characteristics of summer precipitation over Cang Mountain. J. Appl. Meteor. Climatol., 60, 1285–1300, https://doi.org/10.1175/JAMC-D-20-0220.1.