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  • View in gallery
    Fig. 1.

    Altitude and distribution of ground-based observation stations in Southwest China.

  • View in gallery
    Fig. 2.

    The key components and interconnections of the existing LCBH estimation algorithms.

  • View in gallery
    Fig. 3.

    (a) The distribution of relative humidity thresholds of SU algorithm with the change of pressure at different stations, where the dotted line represents the minimum and maximum relative humidity thresholds of the ZHA10LRnew algorithm. (b) The ranges of maximum RH threshold (Max_RH) in the RHs-CCL algorithm at the four stations.

  • View in gallery
    Fig. 4.

    The process of the RHs-CCL algorithm.

  • View in gallery
    Fig. 5.

    (top) The joint and (bottom) marginal probability density distribution characteristics of the LCBH between the algorithms, ERA5, and ground observation at Chengdu station [the color bar represents probability density distribution (%)].

  • View in gallery
    Fig. 6.

    As in Fig. 5, but for Chongqing station.

  • View in gallery
    Fig. 7.

    As in Fig. 5, but for Guiyang station.

  • View in gallery
    Fig. 8.

    As in Fig. 5, but for Kunming station.

  • View in gallery
    Fig. 9.

    Taylor diagrams of the LCBH at ground-based observation stations calculated by the algorithms. REF represents the location of the true value, the radius corresponding to the circle formed by REF as the center represents the standard deviation of the true value, the distance from the point of algorithms to the center of a great circle represents the standard deviation of algorithms, the distance from the point to the REF represents the RMSE of algorithms, and the cosine of the angle between the point and the center of a great circle represents the correlation coefficient.

  • View in gallery
    Fig. 10.

    (a) Statistical distribution of algorithms and ERA5 error and (b) statistical distribution of classification accuracy of the algorithms (the values on the columns represent the mean values).

  • View in gallery
    Fig. 11.

    The seasonal feature of diurnal variations of K index averaged at the ground-based observation stations.

  • View in gallery
    Fig. 12.

    (a) Diurnal and (b) monthly variations of low cloud occurrence frequency averaged at ground-based observation stations.

  • View in gallery
    Fig. 13.

    The MAE characteristics of diurnal variations of LCBH of all the algorithms at ground-based observation stations during summer.

  • View in gallery
    Fig. 14.

    As in Fig. 13, but for low cloud occurrence frequency of all the algorithms at ground-based observation stations during summer.

  • View in gallery
    Fig. 15.

    The error partitioning of the SU, ZHA10LRnew, RHs, and RHs-CCL algorithms. The blue-shaded area represents the error, the yellow dashed line represents the error boundary of the RHs algorithm, and the yellow and red dashed lines represent the error boundary of the RHs-CCL algorithm.

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A New Algorithm for Estimating Low Cloud-Base Height in Southwest China

Rongjiang WangaSchool of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, China

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Renjun ZhouaSchool of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, China

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Shuping YangaSchool of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, China

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Rui LiaSchool of Earth and Space Sciences, University of Science and Technology of China, Hefei, Anhui, China

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Jiangping PubKey Laboratory for Cloud Physics of China Meteorological Administration, Beijing, China

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Kaiyu LiucGuizhou Air Traffic Management Bureau of CAAC, Guiyang, Guizhou, China

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Yi DengdSchool of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia

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Abstract

The prevalence of low clouds significantly affects flight safety in Southwest China. However, relevant cloud parameters, especially low cloud-base height (LCBH), lack accurate forecasts. Based on the hourly atmospheric vertical profiles of ERA5 from 2008 to 2019, we developed a new algorithm for estimating LCBH by combining relative humidity (RH) threshold methods with convective condensation level (CCL) (RHs-CCL). To evaluate the performance of RHs-CCL, we use it to estimate the hourly LCBH of airports in Southwest China and compare the results with those based on the ground-based observations and the ERA5 CBH data. Using the observations as a ground truth, we compare the RHs-CCL algorithm with several existing algorithms with the following findings: 1) The correlation coefficient between RHs-CCL and observations reaches 0.5 on average, and the error of RHs-CCL is smaller than those of existing algorithms, with the minimum mean absolute error and root-mean-square error at the four airports studies being able to reach 243 and 321 m. 2) The bias score of RHs-CCL is 0.97 on average, and low clouds classification utilizing RHs-CCL attains the highest accuracy, up to 86%. 3) The errors of ERA5 CBH are the largest when compared with the others. 4) By implementing convective cloud occurrence condition and CCL, RHs-CCL has better applicability in regions of enhanced convective activity. These results suggest the potential of RHs-CCL as an algorithm moving forward for improvement of the LCBH estimates based upon high-resolution reanalysis products and for better predictions of the LCBH utilizing outputs from numerical weather prediction models.

Significance Statement

The new algorithm developed in this study can accurately estimate low cloud-base heights from vertical profiles of atmospheric variables. It provides us a much more computationally efficient approach for predicting low cloud-base height relative to running cloud models, which is critical for weather forecasting at locations lacking computational resources and/or cloud modeling capability. In areas such as Southwest China, low clouds are very common, and they pose major threats to aviation safety. The new algorithm has been successfully integrated into the daily operation at Guiyang Airport in Southwest China and demonstrated excellent skills in estimating cloud-base heights. The implementation of the algorithm in aviation forecasting over a broader region is on the horizon.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Renjun Zhou, zrj@ustc.edu.cn

Abstract

The prevalence of low clouds significantly affects flight safety in Southwest China. However, relevant cloud parameters, especially low cloud-base height (LCBH), lack accurate forecasts. Based on the hourly atmospheric vertical profiles of ERA5 from 2008 to 2019, we developed a new algorithm for estimating LCBH by combining relative humidity (RH) threshold methods with convective condensation level (CCL) (RHs-CCL). To evaluate the performance of RHs-CCL, we use it to estimate the hourly LCBH of airports in Southwest China and compare the results with those based on the ground-based observations and the ERA5 CBH data. Using the observations as a ground truth, we compare the RHs-CCL algorithm with several existing algorithms with the following findings: 1) The correlation coefficient between RHs-CCL and observations reaches 0.5 on average, and the error of RHs-CCL is smaller than those of existing algorithms, with the minimum mean absolute error and root-mean-square error at the four airports studies being able to reach 243 and 321 m. 2) The bias score of RHs-CCL is 0.97 on average, and low clouds classification utilizing RHs-CCL attains the highest accuracy, up to 86%. 3) The errors of ERA5 CBH are the largest when compared with the others. 4) By implementing convective cloud occurrence condition and CCL, RHs-CCL has better applicability in regions of enhanced convective activity. These results suggest the potential of RHs-CCL as an algorithm moving forward for improvement of the LCBH estimates based upon high-resolution reanalysis products and for better predictions of the LCBH utilizing outputs from numerical weather prediction models.

Significance Statement

The new algorithm developed in this study can accurately estimate low cloud-base heights from vertical profiles of atmospheric variables. It provides us a much more computationally efficient approach for predicting low cloud-base height relative to running cloud models, which is critical for weather forecasting at locations lacking computational resources and/or cloud modeling capability. In areas such as Southwest China, low clouds are very common, and they pose major threats to aviation safety. The new algorithm has been successfully integrated into the daily operation at Guiyang Airport in Southwest China and demonstrated excellent skills in estimating cloud-base heights. The implementation of the algorithm in aviation forecasting over a broader region is on the horizon.

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Corresponding author: Renjun Zhou, zrj@ustc.edu.cn

1. Introduction

Clouds can significantly change surface energy and water balance by affecting atmospheric radiation transfer processes and forming precipitation playing an important role in Earth’s climate system (e.g., Webster and Stephens 1984; Li et al. 1995; Chen et al. 2000; Stephens 2005; Dong et al. 2006). There are large uncertainties in the observation of the macro and micro parameters of clouds (e.g., Martucci et al. 2010; Zhang et al. 2017; Mülmenstädt et al. 2018), especially the cloud-base height (CBH; e.g., Stephens and Kummerow 2007). Accurate estimates of the CBH are important for two reasons. On one hand, the CBH has a great influence on the energy exchange between the surface and clouds and stands out as a key variable in affecting regional weather and climate (e.g., Zelinka and Hartmann 2010; Gbobaniyi et al. 2011; Wild 2012; Viúdez-Mora et al. 2015). On the other hand, the CBH is a key indicator of the positioning of cloud layers, which is important for ensuring flight safety (e.g., Leyton and Fritsch 2004; Inoue et al. 2015).

The CBH is in general obtained by satellite or ground-based observations (e.g., Forsythe et al. 2000; Naud 2003; Noh 2017). Satellite observation is usually divided into passive remote sensing and active remote sensing. Passive remote sensing has difficulty capturing information of the cloud interior and cloud base and requires many assumptions to obtain the CBH (e.g., Noh 2017; Liang et al. 2017). Active remote sensing overcomes this difficulty through the use of cloud profile microwave radars to effectively obtain the CBH (e.g., Wielicki et al. 1996; Stephens et al. 2002; Winker et al. 2010). However, such active remote sensing instruments are usually carried by low-orbit satellites and cannot continuously monitor the characteristics of clouds over a fixed region. Ground-based observations thus remain the main approach for obtaining the evolving CBH over time in a given location (e.g., Borg et al. 2011; Costa-Surós et al. 2013; Sharma et al. 2016). The associated monitoring tools include ground-based lidar, radiosonde, ceilometer, all-sky imager, and digital camera. The monitoring results are widely used in cloud, weather, and climate research (e.g., Mahesh 2005; Feister et al. 2010; Janeiro et al. 2010; Varikoden et al. 2011; Zhang 2020).

In addition to direct observations because clouds are the visible aggregation of small water droplets, supercooled water droplets, and ice crystals or their mixtures suspended in the atmosphere at the bottom that do not touch the ground, the CBH can also be obtained indirectly utilizing a set of atmospheric state parameters that is directly measured or from reanalysis products and model forecasts (e.g., Costa-Surós et al. 2014). The methods of estimating the CBH based on atmospheric state parameters are generally divided into three types. The first type is a single-level threshold screening based on the physical properties of clouds. Taking the relative humidity as an example, one method is to examine the observed statistical distribution of relative humidity at the base of clouds and select certain percentile (such as 85th) as the threshold. When the relative humidity at certain height exceeds the threshold, the height is considered the CBH. For example, Decker et al. (1978) used 95% relative humidity threshold to estimate the CBH. In addition to selecting thresholds from percentiles of statistical distributions, one may also express the threshold as a function of altitude and pressure through statistical fitting or physical relationship. For example, Geleyn (1981) designed a humidity threshold function in the Sigma pressure coordinate system to estimate the CBH, which was later adopted by the ECMWF model. Yuan et al. (2016) designed a water vapor pressure threshold function to estimate the CBH. The second type of CBH estimating from atmospheric state parameters is to find the CBH according to the cloud vertical structure (CVS). For example, Chernykh and Eskridge (1996) and Minnis et al. (2005) estimated the CBH using the variation characteristics of relative humidity and temperature in the CVS. Wang and Rossow (1995) and Zhang et al. (2010, 2012) estimated the CBH from the threshold of relative humidity at each layer of the CVS. The first two types of relative humidity threshold algorithms depend on the selection of the relative humidity threshold, and it is related to the altitude and the type of data used. In general, the higher the altitude, the lower the relative humidity threshold. If the relative humidity data used is high resolution (e.g., radiosonde soundings data), then the relative humidity threshold chosen is usually large (close to 100%) and varies little case to case. For low-resolution input data (e.g., reanalysis data), to account for data gaps and greater uncertainties, the overall relative humidity threshold is small and varies significantly case to case. The third type is based on an air parcel model, taking the height where a surface parcel rising dry adiabatically reaches saturation, that is, the lifting condensation level (LCL) as the CBH (e.g., Craven et al. 2002; Manzato and Morgan 2003; Gbobaniyi et al. 2011; Nuijens et al. 2014). In addition, cloud radiation and wind profiles are also used to estimate the CBH (e.g., Grimsdell and Angevine 1998; Pan and Lü 2013). It is noted that algorithms based on the relative humidity threshold and LCL only need atmospheric vertical profiles for estimating the CBH and are relatively easy to implement in forecasting with outputs from numerical models (Costa-Surós et al. 2014). Uncertainties in estimating the CBH using the above methods often come from the selection of threshold values, the impact of vertical resolution of data in the first and second type, and the conditions for the adiabatic rise of an air parcel in the third type. For example, the CBH estimates based on reanalysis data with low vertical resolution often have large error. An et al. (2020) evaluated the CBH of the North American Reanalysis Data (NARR) using ceilometer observations, and found that there is an average error of 600 m. To overcome these uncertainties, one must resort to high-resolution data when using the first and second type of methods, and at the same time strengthen the physical connections between the threshold values and the vertical structures of clouds. The convective nature of clouds must be confirmed when adopting the third type of method.

Because of the unique climate condition in Southwest China, low clouds with large spatial extent and low height occur very frequently (e.g., Zhang et al. 2017; Li et al. 2018; Chen et al. 2018; Liu et al. 2019). Satellite and ground-based observations show that the CBH of these low clouds is typically less than 2000 m, and in extreme cases, less than 50 m. Being so close to the ground, these low clouds significantly affect the take-off and landing of aircraft and pose a threat to aviation safety. Currently, there is a lack of accurate prediction of low cloud-base height (LCBH), and therefore it is necessary to evaluate and compare the LCBH estimation algorithms that are based upon outputs from numerical models.

Low clouds can be divided into two types: stratus clouds and convective clouds. Stratus clouds and large-scale convective clouds are usually generated by large-scale dynamical processes and the area is often large, making them easily captured by the relative humidity threshold algorithm in the numerical model or sounding. However, because of the limitation of convective parameterization, small-scale convective clouds in the real atmosphere cannot be predicted satisfactorily by numerical models. The relative humidity threshold algorithms often miss or misreport small-scale convective clouds. The specific objective of our study is to develop a more accurate algorithm of low cloud-base height estimation based on atmospheric vertical profiles from numerical models or reanalysis products. The long-term goal is to improve numerical models that forecast cloud cover by providing a more accurate estimate of already formed cloud bases to validate the model forecast. In this paper, a new algorithm for estimating the LCBH based on reanalysis data is developed, and its performance is evaluated by comparing the estimates with ground-based observations. Specifically, the new algorithm, which combines relative humidity (RH) threshold methods with convective condensation level (CCL) (RHs-CCL), adds to the cloud vertical structure detection algorithm (ZHA10LRnew) of Costa-Surós et al. (2014) a new humidity threshold algorithm (SU) and also makes use of the CCL. With the ERA5 atmospheric vertical profiles as input, we used the RHs-CCL to estimate the LCBH at four weather stations in Southwest China (Chengdu, Chongqing, Guiyang, and Kunming) for the period 2008 to 2019, and compared the estimates with the LCBH observed at ground stations, as well as the CBH archived by the ERA5. The possible causes of the estimation errors are discussed.

2. Data description

a. Ground-based observations of the LCBH

The ground-based observations of the LCBH comes from the ground weather reports regularly produced by airports around the world and can be downloaded from the website of the Department of Atmospheric Sciences, University of Wyoming (http://weather.uwyo.edu/surface/meteorogram/seasia.shtml). The ground weather report is based on the aviation routine weather reports (METARs), which includes the CBH data. The CBH is mainly detected by ceilometer with a vertical resolution of 30 m and a maximum temporal resolution of 20 min. This dataset has been widely used in data assimilation, cloud climatology, and cloud vertical structure research (e.g., Benjamin 2016; An et al. 2017; Mülmenstädt et al. 2018).

Four provincial capitals in Southwest China were selected as locations for algorithm evaluation in this study: Chengdu (airport code: ZUUU; altitude: 512 m), Chongqing (airport code: ZUCK; altitude: 416 m), Guiyang (airport code: ZUGY; altitude: 1139 m), and Kunming (airport code: ZPPP; altitude: 1892 m) (Fig. 1). As can be seen from Fig. 1. Chengdu and Chongqing are located on the edge of the basin, and their elevations are lower; Guiyang and Kunming are located on the plateau-valley terrain with an average elevation of only 2000 m in the southeastern Qinghai–Tibet Plateau. The data for Chengdu, Chongqing, and Guiyang cover the period 2008–19. Kunming Airport was newly built in July 2012, and the data only span the period 2013–19 with a temporal resolution of 1 h and a vertical resolution of 30 m, consisting of three layers. The ceilometers at the four stations are all CL31 ceilometers manufactured by Vaisala, Inc. (https://www.vaisala.com/). This instrument uses pulsed diode laser lidar technology to measure CBH, which can detect three cloud layers. If cloud bases are obscured by precipitation or fog close to the ground, the CL31 reports vertical visibility. The principle of the CL31 ceilometer to measure the CBH or vertical visibility is based on the lidar formula:
P(z)=E0c2Az2β(z)e20xσ(z)dz.
Fig. 1.
Fig. 1.

Altitude and distribution of ground-based observation stations in Southwest China.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

In Eq. (1), P(z) is the backscattered echo intensity received by the ceilometer at distance z, E0 is the laser pulse output energy, c is the speed of light, A is the receiver aperture, β(z) is the backscattering coefficient at distance z, and σ(z′) is the atmospheric extinction coefficient at z′. After the echo intensity P(z) is obtained, the distance-corrected echo intensity P′(z) of each level can be obtained as a P′(z) = z2P(z) profile; the atmospheric extinction coefficient σ profile can also be inverted under specific conditions. According to the principle that there are many water molecules inside the cloud, the echo power will abruptly increase when the ceilometer receives the echoes that encounter these water molecules (e.g., Morris 2016). A certain algorithm is adopted to sample and extract the height at which the echo power abruptly increases and treats that height as the cloud-base height (e.g., Martucci et al. 2010; Kotthaus et al. 2016). Based upon the detection principle of the ceilometer, its measurement uncertainty mainly comes from the interferences by haze, fog, light fog, rain flags, and precipitation (e.g., Kotthaus et al. 2016). We have removed samples affected by these factors from the data to increase the robustness of the results. We define low clouds as those with the CBH less than 2000 m and the cloud cover more than 20%. Table 1 shows the distribution of the data.

Table 1

The number and proportion of low clouds observed by ground-based observation stations.

Table 1

b. ERA5 atmospheric vertical profile

The ERA5 atmospheric vertical profiles (including the ERA5 CBH) are obtained from ECMWF (https://cds.climate.copernicus.eu). ERA5 is the fifth major global reanalysis produced by ECMWF. In comparison with the ERA-Interim product, ERA5’s main advantages are increased horizontal resolution to 31 km and improved adaptability of tropospheric temperature, wind, and relative humidity (e.g., Hersbach et al. 2020). The dataset is widely used in weather and climate change studies. In this study, the ERA5 data from 2008 to 2019 were used. The temporal resolution is hourly, and the vertical resolution is 25 or 50 hPa. Atmospheric pressure level variables analyzed include geopotential height, relative humidity, and temperature, and surface variables used are 2-m temperature, 2-m relative humidity, and the CBH.

The CBH archived in the ERA5 is defined as the height at which the cloud cover viewed from the ground is greater than 1% or the cloud water mixing ratio is greater than 10−6 kg kg−1. In addition, when the atmospheric state parameters meet the development conditions of convective clouds, the CBH of convective clouds is taken as the CBH. The cloud cover threshold (1%) adopted in the ERA5 is much lower than in our definition of the observed CBH (20%), making the CBH of ERA5 likely lower than the observed counterparts.

3. Description of ZHA10LRnew and SU algorithm

a. ZHA10LRnew estimation algorithm for LCBH

The ZHA10LRnew algorithm originated from ZHA10 cloud vertical structure detection algorithm proposed by Zhang et al. (2010, 2012). ZHA10 represents the one proposed in Zhang et al. (2010). In 2014, Costa-Surós et al. (2014) compared this algorithm with other cloud vertical structure detection algorithms and found that ZHA10 had the best performance. They thus proceeded to develop the ZHA10LRnew algorithm that is applicable to low-resolution input (such as reanalysis data). LRnew stands for low-resolution new, a new version proposed by Costa-Surós et al. on the basis of ZHA10 for low-resolution data detection of CVS, and therefore it was named ZHA10LRnew by Costa-Surós et al. There the CBH is determined as the lowest pressure level in a continuous moist atmospheric layer where the minimum humidity threshold of 90% at cloud base and the maximum humidity threshold of 91.5% inside the cloud are satisfied. In our analysis of the LCBH, the algorithm of ZHA10LRnew is modified with the altitude of the pressure layer obtained by transforming the potential height through the Hobbs formula (e.g., McIntosh 1978).

Although the ZHA10LRnew algorithm can be used to estimate the LCBH at vertical resolution of reanalysis data, many problems remain. The most outstanding one is that the CBH is determined by extending the cloud base to the height that meets the minimum humidity threshold where the maximum humidity threshold must also be satisfied. The difference between the minimum humidity threshold (90%) and the maximum humidity threshold (91.5%) is only 1.5%, and both of them are taken as constants. When low-resolution atmospheric profiles are used as input, it is thus difficult to distinguish between the two thresholds, and often only the maximum humidity threshold takes effect leading to a higher bias in the CBH estimates. Additionally, the algorithm has yet to be tested using reanalysis data.

b. SU estimation algorithm for LCBH

The Salonen and Uppala (SU) algorithm originated from the cloud cover parameterization based on the relative humidity threshold proposed by Geleyn (1981), which was mainly used in the early ECMWF model and in models studying air–sea interactions (e.g., Terray 1998). Salonen and Uppala began to apply it to estimate CBH in 1991. Yuan et al. (2016) found that the algorithm performed well in the estimation of CBH in subtropical regions and named the algorithm SU after Salonen and Uppala. In this scheme, the relative humidity thresholds are expressed as functions of the vertical pressure coordinate σ as follows:
RHc=1ασ(1σ)[1+β(σ0.5)],
where σ = P(i)/P(0), P(i) presents the pressure level, P(0) presents the surface pressure, α = 2, and β = 31/2. The selection of parameters is based on the criteria to reproduce the estimated global mean cloud cover and vertical distribution of radiative cooling as closely as possible (e.g., Geleyn 1981). Salonen and Uppala (1991) used this function to calculate the CBH in studying the attenuation of electromagnetic wave signals caused by clouds and found that the performance was the best when the parameter α = 1. In 2012, the International Telecommunication Union adopted this algorithm to calculate the CBH (e.g., Mandeep and Hassan 2008) and the algorithm was called SU thereafter (e.g., Yuan et al. 2016).

c. LCL/CCL indicators for LCBH

Early studies have shown that LCL and CCL (convective condensation level) can be used to estimate the CBH (e.g., Decker et al. 1978; Li et al. 2017; Zhan et al. 2021). LCL is the height when the air parcel rises to saturation through a dry adiabatic path and is often regarded as the CBH of convective clouds. The formula for calculating the lifting condensation pressure is from Bolton (1980) and Stull (1988), and the calculated pressure of the LCL is then converted to sea level height by the Laplace pressure formula:
LCLT=11TMPK55log(RHz/100)2840+55,
LCLP=PRES(LCLT/TMPK)3.5, and
LCLZ=18400[1+(LCLT273.15)+(TMPK273.15)546.3]×log10(PRESLCLP),
where RHz represents surface relative humidity (%), LCLT represents lifting condensation level temperature (K), TMPK represents surface temperature (K), PRES represents surface pressure (hPa), LCLP represents lifting condensation level pressure (hPa), and LCLZ represents lifting condensation level height (m). The CCL is the altitude where the saturation specific humidity profile and the surface relative humidity profile intersect. CCL can be considered as the base height of thermally driven cumulus clouds.

4. RHs-CCL estimation algorithm for the LCBH

In this study, a new algorithm is developed on the basis of ZHA10LRnew and avoids the problem of ZHA10LRnew by combining SU. Figure 2 shows how ZHA10LRnew uses cloud vertical structure condition to identify CBH. The moist layers we define here are the continuous layers with relative humidity exceed the minimum relative humidity threshold, and they are considered as potential cloud layers. Only the relative humidity of these moist layers meets the maximum relative humidity threshold, the moist layers can be considered as true cloud layers; so, the role of minimum relative humidity threshold is to help identify the potential cloud layers. The maximum relative humidity threshold ensures that these potential cloud layers are true clouds. ZHA10LRnew algorithm determines the possible range of cloud layers by identifying first the moist layers requiring RH (RH profile) to exceed the minimum relative humidity threshold (90%) and be continuous, and then requires the RH to exceed the maximum relative humidity threshold (91.5%) to detect the presence of the cloud. The CBH is determined to be the lowest of these moist layers. When there is only one moist layer and its RH is greater than the maximum relative humidity threshold, CBH is taken to be the height of this layer. Figure 3 shows the humidity thresholds at different pressures and altitudes near the four stations calculated by SU algorithm, as well as the maximum and minimum humidity thresholds defined by ZHA10LRnew. When the minimum relative humidity threshold in the ZHA10LRnew algorithm is replaced by the relative humidity threshold of the SU, the minimum relative humidity threshold corresponding to the pressure level closest to the ground of each station reaches 95% and is greater than 91.5% of the maximum humidity threshold and inactivate cloud vertical structure condition and affect CBH judgment. Furthermore, the maximum relative humidity threshold in the pressure level closest to the ground is equal to that of the SU, while the maximum humidity threshold in the upper layer is still 91.5%. Figure 3 also shows the change in the maximum humidity threshold at the four stations. At this time, ZHA10LRnew algorithm will be completely replaced by SU algorithm. The higher minimum relative humidity threshold is beneficial to the screening of saturated moist thin cloud in the adjacent ground layer and reduces the error of taking the unsaturated moist layer caused by temperature inversion and turbulence as cloud layer. However, the minimum relative humidity threshold provided by SU algorithm decreases from 95% to about 75% with the decrease of pressure and is significantly lower than 90% defined by ZHA10LRnew algorithm. Obviously, this avoids the over estimation problem of ZHA10LRnew on low-resolution data due to the close difference between the minimum humidity threshold and the maximum humidity threshold and enables the new algorithm to output the CBH calculated by SU algorithm on the basis of ensuring the cloud vertical structure of ZHA10LRnew algorithm.

Fig. 2.
Fig. 2.

The key components and interconnections of the existing LCBH estimation algorithms.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

Fig. 3.
Fig. 3.

(a) The distribution of relative humidity thresholds of SU algorithm with the change of pressure at different stations, where the dotted line represents the minimum and maximum relative humidity thresholds of the ZHA10LRnew algorithm. (b) The ranges of maximum RH threshold (Max_RH) in the RHs-CCL algorithm at the four stations.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

Numerical models typically better predict large-scale dynamical processes, and the algorithm can reasonably capture a wide range of stratus clouds and some shallow convective clouds using just the humidity threshold. Humidity thresholds alone, however, may miss many small-scale convective clouds. It is thus desirable to have indicators judging whether convective clouds are present before the estimation of the CBH. Since convective clouds are often produced in a conditionally unstable atmosphere, standard instability indices including the convective available potential energy (CAPE), convective inhibition (CIN), and K index may be adopted (e.g., Livingston et al. 1996; Haklander and Van Delden 2003; Mitra et al. 2012). In our analysis, CAPE > 0 and CIN = 0 or K > 35 were used as the condition for development of convective clouds in an environment lack of distinct mechanical forcing (e.g., frontal and orographic lifting). More specifically, the CBH of convective clouds is likely greater than the LCL with mechanical forcing and is close to the CCL without forcing (e.g., Li et al. 2017). In practice, it is difficult to decide the presence of mechanical lifting of air parcels with an atmospheric vertical profile at a single location. However, the four stations evaluated here are located in tropical and subtropical regions and development of convective clouds without distinct mechanical forcing (e.g., from fronts) may be much more common in reality. Some studies also pointed out that the LCL is always lower than the observed CBH (e.g., Grimsdell and Angevine 1998; Nuijens et al. 2014) while the CCL tends to be greater than or equal to the LCL. Therefore, in our new algorithm, CCL is taken as the CBH of convective clouds. Figure 4 provides a flowchart showing the complete process of LCBH estimation using the new algorithm (RHs-CCL). For the convenience of comparison, the algorithm without convective clouds discrimination and the use of CCL is called RHs. RH stands for relative humidity. The letter “s” indicates the combination of multiple relative humidity threshold algorithms (ZHA10LRnew+SU). For ease of presentation, we name the algorithm RHs. It further considers the mechanism of convection initiation and the CBH of convective clouds on the basis of RHs. Since we estimate the CBH of convective clouds by CCL, we name the new algorithm RHs-CCL. Table 2 summarize the essential features of existing LCBH estimation algorithms, it mainly shows the methods, the relative humidity threshold setting and the advantages and disadvantages of the algorithm.

Fig. 4.
Fig. 4.

The process of the RHs-CCL algorithm.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

Table 2

Essential features of existing LCBH estimation algorithms.

Table 2

5. Results

The hourly vertical profiles (temperature, relative humidity, and geopotential height) at the ERA5 grid points are first mapped to the location of the ground-based observation stations. If ground-based observations indicate presence of clouds, the LCBH estimates are produced by applying the five algorithms (ZHA10LRnew, SU, LCL, RHs, and RHs-CCL) to the corresponding ERA5 vertical profiles. Ground-based observation stations in Chengdu, Chongqing, Guiyang, and Kunming are used as the standards to quantify and compare the performances of these algorithms. Metrics used in the evaluation include Pearson correlation coefficient (CORR), root-mean-square error (RMSE), mean absolute error (MAE), low cloud detection (POLCD), probability of no low cloud detection(PONLCD), bias score (BS), and accuracy (Accuracy).

a. Evaluation of the performance of the LCBH estimation algorithms

Figures 58 show the joint (top panels) and marginal (bottom panels) probability density distributions of the hourly LCBH from the algorithms, ERA5 and ground-based observations at the 4 stations (Chengdu, Chongqing, Guiyang, and Kunming) for the period 2008–19. A 24-h averaging is used to remove diurnal variations of the LCBH. The Pearson CORR, RMSE, and MAE are provided in the scatterplots, and they are defined as follows:
CORR=i=1n(xix¯)(yiy¯)i=1n(xix¯)2i=1n(yiy¯)2,
RMSE=i=1n(xiyi)2n, and
MAE=i=1n|xiyi|n,
where x represents the observed LCBH, n is the number of samples, y represents LCBH estimated by the algorithms, and x¯ and y¯ represent means observed values and means of algorithm estimates, respectively.
Fig. 5.
Fig. 5.

(top) The joint and (bottom) marginal probability density distribution characteristics of the LCBH between the algorithms, ERA5, and ground observation at Chengdu station [the color bar represents probability density distribution (%)].

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

Fig. 6.
Fig. 6.

As in Fig. 5, but for Chongqing station.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

Fig. 7.
Fig. 7.

As in Fig. 5, but for Guiyang station.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

Fig. 8.
Fig. 8.

As in Fig. 5, but for Kunming station.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

The average CORR of the RHs-CCL algorithm is only about 0.5, not the highest among the algorithms evaluated; however, its error index is the smallest at Chengdu, Chongqing, and Guiyang stations with the smallest RMSE and MAE at 205 and 161 m, respectively. It is noted that the error of the RHs-CCL algorithm is not much different from that of the RHs algorithm. On one hand, it shows that the adoption of CCL does not significantly improve the estimation accuracy. On the other hand, it also demonstrates that using CCL is reasonable since the CCL algorithm maintains at least the same accuracy as the humidity threshold algorithm. The error of ZHA10LRnew algorithm is smaller than that of RHs-CCL, but the difference between the two is small in Kunming station. Based on the marginal distributions, the RHs-CCL estimates are most consistent with the ground-based observations at all 4 sites. When compared with ZHA10LRnew and SU algorithms, the RHs-CCL algorithm fits less accurately to high clouds that are above ∼900 m and more accurately to low clouds that are below ∼900 m. The reason is that the SU algorithm reduces the minimum humidity threshold pointing to the cloud base so that a lower level is selected as the cloud base under the same conditions, consistent with the expectation of the algorithm. The comparison with SU also shows that it is reasonable to introduce the humidity threshold condition of cloud vertical structure into SU. The estimates based on the LCL algorithm were obviously biased low, but the correlation with ground observation is good with the highest CORR of 0.77 found at Guiyang. Except for Guiyang and Chongqing stations, the CORR of the ERA5 CBH is very low and the bias index of the ERA5 is the largest among all estimates with the RMSE and MAE in Chengdu reaching the highest values of 1362 and 918 m, respectively.

The Taylor diagram (Taylor 2001) is often used to evaluate the accuracy of a model. It is constructed using the trigonometric cosine relationship between the true value and the test value, which can reflect the correlation coefficient, error and distribution characteristics between the model estimates and the true values. As seen from Fig. 9, except for Kunming station, the average correlation coefficient of the algorithm is about 0.5, and the average error is about 1 times the standard deviation. Among all the algorithms, RHs-CCL has the smallest error and a distribution closest to the observed one.

Fig. 9.
Fig. 9.

Taylor diagrams of the LCBH at ground-based observation stations calculated by the algorithms. REF represents the location of the true value, the radius corresponding to the circle formed by REF as the center represents the standard deviation of the true value, the distance from the point of algorithms to the center of a great circle represents the standard deviation of algorithms, the distance from the point to the REF represents the RMSE of algorithms, and the cosine of the angle between the point and the center of a great circle represents the correlation coefficient.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

In summary, in comparison with other algorithms, the RHs-CCL algorithm has the best LCBH estimation accuracy. The error of the CBH provided by the ERA5 is distinctly higher than those of the other algorithms, which may be associated with issues of cloud parameterizations in the model. One possibility is that the model directly overestimates the height of low clouds in the situation of a single cloud layer. The other possibility is that the model has difficulty handling the situation of multiple layers of clouds. For example, when large-scale stratus clouds are present at high altitudes, small-scale cumulus clouds or newborn clouds may be present at low altitudes. If the small-scale cumulus clouds or newborn clouds are missing from the column, the model will treat the height of the higher stratus clouds as the CBH. The second possibility causes the largest error. In this case, the error of the relative humidity threshold algorithm is significantly smaller than that of the model. This may indicate that although the model can provide relative humidity feedback at low altitudes, it cannot generate small-scale cumulus clouds or other cloud at low altitudes through cloud physical processes; so, the model needs to further improve related cloud physical processes. Of course, the above speculation needs to be verified in a follow-up study.

b. Evaluation of low cloud classification

We may also evaluate the performance of different algorithms in terms of its classification of low clouds versus no low cloud situations. No low clouds mean clear sky or the CBH above 2000 m. The indices used to measure the classification performance are POLCD, PONLCD, BS, and accuracy. They are defined as follows:
POLCD=TPTP+FP×100,
PONLCD=TNTN+FN×100,
BS=TP+FPTP+FN×100, and
accuracy=TP+TNTP+TN+FP+FN×100,
where TP represents the number of true positives, TN is the number of true negatives, FN is the number of false negatives, and FP is the number of false positives.

Tables 36 show the classification results based on the algorithm estimates. When compared with other algorithms, RHs-CCL algorithm shows the most obvious improvement in POLCD at all stations, and the maximum improvement is 27% at Kunming station, which is associated with the introduction of the convective cloud discriminant algorithm and the use of CCL. The atmosphere appears unstable more often at Kunming station, hinting that the convective cloud discriminant algorithm and CCL may maximize their effects there. While POLCD is improved with RHs-CCL, PONLCD is decreased, about 10% lower than that of the ZHA10LRnew algorithm. This is caused by the increase in the number of false positives, indicating that the convective cloud discriminant algorithm and CCL may increase the number of false positives. The increase in false positives caused by the CCL is an important reason why CCL does not significantly improve the accuracy. As can be seen from the classification performance shown in Table 7, CCL causes a significant increase in TP and also an increase in FP. At some stations such as Chongqing, the increase in FP even exceeds that of TP, resulting in a small increase in TN+TP, which eventually causes the accuracy improvement being insignificant. The CCL represents a necessary condition for spontaneous convection initiation. Since other factors such as local terrain, inversion and mechanical forcing of divergence/convergence may limit convection initiation, low cloud detection based upon convective temperature threshold represents thus the upper limit of convection occurrence. This explains why CCL may increase false positives. This also explains why CCL works better at regions with elevated convective activities as shown in shown in Table 7. In terms of BS, except for Chongqing station, RHs-CCL shows a tendency of missing report at all the other stations. The missing report rate was only about 10%. When compared with ZHA10LRnew and RHs, RHs-CCL showed a significant improvement, consistent with the increase of POLCD. In terms of Accuracy, the RHs-CCL and SU are the best with an average score of about 75%. However, these two algorithms do not stand out too much at Chongqing station due to the low proportion of low clouds (∼57%) and weak convective activity there. This limitation suggests the regional applicability of the algorithms. For example, the RHs-CCL algorithm is more suitable for use in tropical and subtropical regions with enhanced convective activities. According to MAE, the error of RHs-CCL and RHs is the smallest with the lowest error value of 240 m found at Guiyang. Therefore, the RHs-CCL algorithm performs generally well in terms of both classification and error indices.

Table 3

The classification performance of the algorithms in Chengdu station.

Table 3
Table 4

The classification performance of the algorithms in Chongqing station.

Table 4
Table 5

The classification performance of the algorithms in Guiyang station.

Table 5
Table 6

The classification performance of the algorithms in Kunming station.

Table 6
Table 7

The difference of classification performance (TP, FP, TN+TP, and Accuracy) between RHs-CCL and RHs at the four stations.

Table 7

Figure 10 summarizes the statistical characteristics of error and classification indices for all the algorithm estimates and the ERA5 CBH. It is clear that RHs and RHs-CCL have the most stable performance, and their RMSE and MAE are respectively 72 and 43 m lower than those of the ZHA10LRnew, and 980 and 441 m lower than those of the ERA5 CBH. The BS and Accuracy of classification show that SU and RHs-CCL are close to each other and have the best performance. When compared with RHs, in terms of POLCD, the RHs-CCL is 18% more likely to reduce the possibility of false positives and 8% more accurate. Moreover, the RHs-CCL is less prone to false positives and 18% more accurate than the ERA5. Based on these comparisons, the RHs-CCL performs the best among all the algorithms by keeping the error very close to that of the RHs algorithm and improving the accuracy at the same time. This is particularly true at regions with active convection. Figure 11 indicates that the K index often exceeds 35 all the stations in summer. In other seasons, only the K index of Kunming station often exceeds 35. The seasonal characteristics of the K index at these sites are therefore consistent with their surface thermal properties and the level of convective activity present at each site.

Fig. 10.
Fig. 10.

(a) Statistical distribution of algorithms and ERA5 error and (b) statistical distribution of classification accuracy of the algorithms (the values on the columns represent the mean values).

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

Fig. 11.
Fig. 11.

The seasonal feature of diurnal variations of K index averaged at the ground-based observation stations.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

To understand the difference between LCL and CCL, we also compared RHs-LCL and RHs-CCL. It is found that the errors of using CCL are all smaller than those of using LCL. Kunming shows the largest improvement with the use of CCL, followed by Chengdu, Chongqing, and Guiyang. These differences may be caused by the differences in the mechanisms of convective cloud occurrence at the ground-based observation stations. In an environment lacking mechanical lifting, convective clouds are generated only when the surface temperature exceeds the convective temperature and the cloud base is found at the CCL. Figure 12a shows the diurnal and monthly variation characteristics of low cloud occurrence frequency at the site; it can be seen that, in terms of diurnal variations, the low cloud occurrence rate in Kunming, Chongqing, and Guiyang is consistent with the ground temperature change in the daytime, whereas the low cloud occurrence frequency in Chengdu is consistent with the ground temperature change in the whole day. The low cloud occurrence frequency increases with ground temperature rise are due to the enhanced atmospheric convection activity on the ground. On monthly variations, only the low cloud occurrence frequency in Kunming and Chengdu is clearly consistent with monthly ground temperature changes, Guiyang is not obvious, and Chongqing is the opposite (Figs. 12b). This shows that the low clouds in Guiyang and Chongqing have more complicated causes on the climatic scale. So these differences explain why CCL performed better than LCL in Kunming and Chengdu. Figures 13 and 14 show the MAE characteristics of diurnal variations of the LCBH and low cloud occurrence frequency of all the algorithms tested at all stations in summer. The error of the RHs-CCL algorithm is in general smallest among all the algorithms, especially during afternoon hours (16–20) and for low cloud occurrence detection. When the absolute value is removed from Figs. 13 and 14, RHs-CCL slightly overestimates the LCBH, especially during afternoon hours (16–20). In addition, RHs-CCL estimates low cloud occurrence frequency more accurately, but overestimates at night. These findings suggest that heating of the surface to reach convective temperature in summer afternoon indeed accounts for a significant portion of shallow convective clouds development at the four stations. The time and locations where RHs-CCL exhibit significant errors are likely due to convection initiation and low cloud development related to other factors such as the strength of surface thermal effects and mesoscale/large-scale lifting associated with terrain forcing and/or atmospheric fronts.

Fig. 12.
Fig. 12.

(a) Diurnal and (b) monthly variations of low cloud occurrence frequency averaged at ground-based observation stations.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

Fig. 13.
Fig. 13.

The MAE characteristics of diurnal variations of LCBH of all the algorithms at ground-based observation stations during summer.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

Fig. 14.
Fig. 14.

As in Fig. 13, but for low cloud occurrence frequency of all the algorithms at ground-based observation stations during summer.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

6. Discussion and conclusions

In this study, a new low cloud-base height estimation algorithm (RHs-CCL) was developed by combining relative humidity threshold methods with the use of convective condensation level. Specifically, we apply the parameterization scheme (SU) used for cloud cover estimation in numerical models to improve the cloud vertical structure detection algorithm (ZHA10LRnew) proposed by M. Zhang et al. that is based on the idea of relative humidity threshold. This gives us an updated algorithm (RHs) for estimating the low cloud-base height. Then the convective cloud discriminant algorithm and CCL is introduced to the RHs to address the problem that relative humidity threshold algorithms often miss convective clouds. The use of CCL finally gives us the new algorithm RHs-CCL. With the ERA5 atmospheric vertical profiles as input, we estimated the hourly low cloud base-height of four provincial capital airports (Chengdu, Chongqing, Guiyang, and Kunming) in Southwest China from 2008 to 2019 using this new algorithm and other existing algorithms. The estimates were compared with the hourly ground-based observations of cloud-base height and also the CBH of the ERA5. The joint and marginal probability density distributions of the estimates and observations were valuated and compared. Also analyzed were metrics such as root-mean-square error, mean absolute error, and classification indices, including probability of low cloud detection, probability of no low cloud detection, bias score, and accuracy. The main findings are as follows:

  1. With the diurnal cycle removed, the joint distribution of the RHs-CCL estimates and the ground-based observations is obviously linear except for Kunming station, with an average correlation coefficient of 0.5. In terms of the marginal distributions, the RHs-CCL fits most closely with the observation. When compared with the ZHA10LRnew and SU, the RHs-CCL fits less accurately to high clouds and more accurately to low clouds. The LCL estimates are significantly lower than ground-based observations. The CBH provided by the ERA5 is biased high with a Pearson correlation coefficient ranging between 0.07 and 0.32, the MAE ranging between 402 and 918 m, and the RMSE being up to 1362 m.

  2. From the perspective of bias and classification indices, without filtering, the RMSE and MAE of RHs and RHs-CCL at all sites are lower than those of other algorithms and the ERA5 CBH. Their RMSE and MAE were respectively 339 and 335 m on average, 76 and 48 m lower than those of ZHA10LRnew, and 125 and 79 m lower when compared with those of the LCL. In terms of classification index, the RHs-CCL and SU have the best classification effect. Their POLCD, PONLCD, BS, and accuracy are respectively 84%, 67%, 101%, and 79%. When compared with RHs, RHs-CCL increased POLCD by 18% and accuracy by 8%. It is clear by observing differences among the stations that the RHs-CCL algorithm is more suitable for use in tropical, and subtropical regions with enhanced convective activities.

  3. The main reason for the improvement of the RHs-CCL algorithm is the addition of cloud vertical structure condition and CCL. Figure 15 shows the basic composition and improvement of the error of the RHs-CCL algorithm. First, by adding the cloud vertical structure condition of the ZHA10LRnew algorithm to SU algorithm, the robustness of the new RHs algorithm is increased and the low clouds detected by the RHs algorithm are thicker clouds. Such clouds are more likely to be associated with significant weather processes making the algorithm more accurate in estimating CBH; therefore, the SU’s margin of error narrows down to RHs (see Fig. 15). However, the problem with RHs is that it tends to ignore thinner clouds, resulting in a drop in classification accuracy. These clouds are mostly small-scale shallow convective clouds. By further introducing the convective cloud occurrence conditions and CCL in the new RHs-CCL algorithm, we incorporate more shallow convective clouds. This brings some additional errors associated with convection initiation (red dotted line) but removes some errors of RHs (blank area in Fig. 15) with error reduction being greater than that of additional error. The area enclosed by the yellow dotted line and the red dotted line excluding the blank area represents the error of RHs-CCL, which is smaller than those of the SU, ZHA10LRnew, and RHs algorithms.

Fig. 15.
Fig. 15.

The error partitioning of the SU, ZHA10LRnew, RHs, and RHs-CCL algorithms. The blue-shaded area represents the error, the yellow dashed line represents the error boundary of the RHs algorithm, and the yellow and red dashed lines represent the error boundary of the RHs-CCL algorithm.

Citation: Journal of Applied Meteorology and Climatology 61, 9; 10.1175/JAMC-D-21-0221.1

The RHs-CCL has a minimum average error of 320 m and the highest classification accuracy of 79%. However, at different stations, such as Guiyang station, the results can improve to 243 m and 86%, while at Chengdu station, the results are reduced to 366 m and 72%. These differences may be associated with the distribution characteristics of the LCBH at the two stations. The average LCBH of Chengdu station is about 300 m more than that of Guiyang station, reaching 1000 m. Because the observation error increases with altitude, the error at Chengdu station is in general greater than that of Guiyang station. In addition to the performance differences caused by different altitudes of stations, the overall error caused by the ERA5 relative humidity error cannot be ignored. In comparing ERA5 relative humidity with radiosonde soundings, it can be found that ERA5 has an error of about 9%. The reason for ERA5 relative humidity error is related to the underestimation of the intensity of the temperature inversion layer by ERA5. Although the ERA5 has a large relative humidity error, the error of the actual algorithm is obviously smaller, indicating that the impact of the ERA5 RH error is limited. We believe that there are two main reasons: 1) When the ERA5 RH is high, it mainly causes false positives. The situation where the error is about 90 mb will likely to be mistaken for no cloud heights as the LCBH, and the true LCBH are ignored or taken as cloud top. This situation requires low RH and high altitude where the true cloud is present. Fortunately, the LCBH of the low clouds at the four stations we used was low, which reduced the occurrence of this situation. 2) The cloud vertical structure constraint in the algorithm enhances the reliability of the algorithm estimates of LCBH. Therefore, the ERA5 relative humidity error contributes little to the algorithm error but may be an important reason for the degradation of the algorithm’s classification performance.

The error of CBH provided by the ERA5 is large partly due to the inaccuracy of new cloud occurrence in the model. After going through the model technical documents provided by the ECMWF, we found that in the ECMWF model, the change of clouds is equal to the change of old cloud plus the occurrence of new clouds, where the new clouds are generated indirectly by using the relative humidity threshold. Large errors in the ERA5 CBH thus suggest potential problems in the relative humidity threshold used by the model.

In conclusion, this study develops a new algorithm for estimating LCBH and evaluates the performance of the new algorithm together with existing algorithms in estimating the LCBH in Southwest China using the ERA5 vertical profiles data as input. While the newly developed algorithm (RHs-CCL) shows the best overall performance, significant errors are found in the CBH provided by the ERA5. This study is limited by the small number of stations used in the analysis and the omission of comparisons with cloud model simulations. Future work will expand the algorithm evaluation to mid–high-latitude locations and further constrain parameters used in the algorithms with observations and cloud model simulations.

Acknowledgments.

This work was supported by the National Key Research and Development Program of China (Grant 2017YFC1501402) and the Research fund for weather modification ability construction project of Northwest China (Grant ZQC-R18169/RYSY201904). We thank the University of Wyoming, Department of Atmospheric Sciences for the ground-based observation CBH data. We also thank the European Centre for Medium-Range Weather Forecasts (ECMWF) for providing the ERA5 atmospheric vertical profile and CBH data.

Data availability statement.

The CBH data from ground-based observations at four airports can be downloaded from the Internet (http://weather.uwyo.edu/surface/meteorogram/seasia.shtml), as can the ERA5 vertical atmospheric profile data and CBH data (https://cds.climate.copernicus.eu).

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