Application of Probability Density Function Matching Method for Visibility Forecasting in Xinjiang of China

Application of Probability Density Function Matching Method for Visibility Forecasting in Xinjiang of China | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Application of Probability Density Function Matching Method for Visibility Forecasting in Xinjiang of China Chao Liu, Junan Xiao, Xiaoqin Rao, Cong Hua, Chao Xie, DaWei An This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8583058/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Visibility greatly impacts people's daily activites, such as transportation. However, numerical models often exhibit substantial errors in visibility forecasting. The objective of this study is to reduce the systematic errors in visibility forecasting products from the European Center for Medium-Range Weather Forecasts (ECMWF), thereby enhancing the forecasting performance. Taking the visibility observations from 105 national meteorological stations in Xinjiang of China as an objective criteria, the visibility forecasts from model products of the ECMWF within the 72-hour forecast period from November 2022 to March 2023 are corrected using the probability density function (PDF) matching method. On this basis, an objectively-corrected forecasting product with an interval of 3-h is established for the next three days in Xinjiang through a rolling modeling approach, and the visibility forecasts before and after correction are further evaluated and analyzed. The results show that the visibility in ECMWF forecasts is overestimated under low-visibility conditions in most areas of Xinjiang. The PDF matching method can effectively reduce these errors, with all evaluation metrics being obviously improved after the correction. The forecasted visibility within the 72-hour forecast period before correction is 3.3–3.8 km higher than the observation, while it is 1.4–2.1 km lower than the observation after correction, with the mean absolute error being reduced by over 20%. For forecasts of visibility below 1 km, the threat score increases from 0.05 to 0.09 after correction. Spatially, 88 stations across Xinjiang exhibit positive improvement with varying degrees, mainly concentrated in the urban agglomerations on the northern slope of Tianshan Mountains (with the improvement exceeding 70%) and in most areas of southern Xinjiang (with the improvement ranging from 50% to 70%). Additionally, the analysis of typical fog-haze and sand-dust weather processes further reveals that the visibility corrected using the PDF matching method becomes much closer to the observations, providing more accurate references for visibility forecasting of Xinjiang meteorological departments. Probability density function matching method Visibility Corrected forecast Xinjiang Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction As is known, visibility indicates the atmospheric transparency. Low-visibility events frequently impact people's daily activities such as the transportation, causing increased traffic accidents and flight delays that bring substantial inconvenience and harm to people's daily life (Hu et al. 2021; Yang et al. 2021). However, the factors affecting visibility are multifaceted. Especially for the low-visibility weather, its occurrence and development are not only interconnected with weather patterns and atmospheric circulation, but also affected by the underlying surface, climatic environment and human activities, posing challenges to accurate forecasting. In early studies, visibility forecasts were mainly based on synoptic diagnosis. The formation conditions of visibility were firstly diagnosed, and forecasts were further made through the combination with forecaster's experience and extrapolation from the real-time observation (Husar et al. 1981; Watson et al. 2002). With the development of numerical forecasting technology, numerical forecast products from domestic and abroad have become the primary references for forecasters. Visibility in numerical models often relies on the diagnostic analyses of various physical quantities, including cloud water content, relative humidity, and precipitation (Gultepe and Milbrandt. 2010). Herman and Schumacher (2016) identified fog-haze and heavy precipitation as the primary factors leading to the reduction of visibility, consequently limiting the accuracy of visibility forecasts in numerical models. It is worth noting that the incompleteness of parameterization schemes in numerical model will lead to systematic errors in the forecasts of specific elements. Additionally, owing to the differences in designing the dynamical frameworks and physical parameterization schemes among numerical models, the systematic errors vary with different models. Utilizing statistical methods to construct forecasting models based on hindcasts of numerical models and observations can eliminate systematic errors to a certain extent, thereby correcting the forecasts of numerical models. Research from the American Meteorological Development Laboratory has indicated that the forecast performance of model output statistics derived from the global forecast system significantly surpasses the original model results (Dallavalle et al. 2004; Zhao et al. 2022). Currently, researchers mostly use statistical methods such as multiple linear regression and stepwise regression to correct the model results. In multivariate linear modeling, a specific method is utilized to construct a forecasting model to predict the visibility variations, where the selected forecasting factors have clear physical significance. Using 40,000 sets of visibility data, Afan and Bayu. (2021) discovered that the stepwise regression method yields visibility forecasts with a smaller root mean square error (RMSE) and higher correlation coefficient with observations. Ni et al. (2015) employed a mathematical modeling method to forecast the visibility in the North China region and found a stable forecasting ability in predicting the visibility variation trend in Beijing. Similarly, numerous studies have established linear relationships between visibility and various meteorological factors and pollutants. Visibility forecasts with various degrees of effectiveness have been achieved and extensively applied. Nevertheless, there are still numerous nonlinear relationships between visibility and diverse meteorological elements. To address these nonlinear issues, neural networks, a computational science that has experienced a resurgence and rapid development in recent years, have been widely applied in the field of meteorology especially in visibility forecasting, with the back propagation neural network (BPNN) as the main component (Gao et al. 2022; Chen et al. 2023). Based on a five-year data series gathered from 238 weather monitoring stations in and around North Carolina, Duddu et al. (2020) developed and validated the ability of the BPNN model in visibility forecasting, and observed that the BPNN exhibits superior forecasting capability for fog relative to dense fog. Lu et al. (2020) employed a neural network approach to develop a visibility forecasting model in Taiyuan area. This model responds well to various performance indicators and provides a significant reference value for local visibility forecasting. With the advances in computer technology and artificial intelligence (AI), AI methods such as machine learning have seen widespread adoption, with beneficial attempt in visibility forecasting (Kim et al. 2022). Liang et al. (2023) employed three methods of support vector machine, multilayer perceptron (MLP), and extreme gradient boosting (XGBoost) to predict the visibility in various regions of Taiwan. They found that the MLP is more suitable for hilly regions, while the XGBoost is more effective in basins and plains. This indicates that different methods should be taken to get optimal visibility forecasts in different regions. Based on extensive historical datasets, Luz et al. (2023) developed five distinct machine learning models (including convolutional neural networks, long short-term memory networks, and multi-method coupling) for visibility forecasting and conducted comparative analysis and examinations at two weather observation stations in Florida, USA. However, for operational visibility forecasts, the forecasting effectiveness and degree of operationalization are not satisfactory using whether traditional statistical methods, interpreted numerical forecast products, or AI techniques like deep learning. There remains an obvious gap between the forecasts and the actual demand of forecasting services, which is mainly reflected in the following aspects. Firstly, visibility modeling necessitates consideration of multiple elements. Atmospheric visibility is closely linked to water vapor and aerosol contents in the air, and it is influenced by local wind speed, wind direction, precipitation, and particulate matter concentrations (Gao et al. 2017; Peng et al. 2020). Considering the inherently localized nature of visibility, current research has mainly focused on single station or specific region, where only the meteorological factors that affect the local visibility are selected. This poses a challenge in establishing unified visibility forecasting models. Secondly, the parameterization schemes of visibility vary in different numerical models. Existing numerical weather forecasting models, including the mainstream models in the European Center for Medium-Range Weather Forecasts (ECMWF), only consider the impacts of precipitation, humidity, and low clouds on visibility, while neglecting the influence of aerosols. This oversight is particularly noticeable during fog-haze events, when visibility is often overestimated, especially in the urban agglomerations on the northern slope of Tianshan Mountains in Xinjiang (Gultepe et al. 2006; Physics et al. 2009). Thirdly, the AI technique manifests a high level of sophistication, and its data-driven nature lacks clear physical mechanisms. Although the AI technique has rapidly advanced in recent years and found extensive application in meteorology, it operates as a black box. If all relevant data are simply inputted without considering the intrinsic physical relationships between independent and dependent variables, the complex mapping relationship acquired through sample learning can lead to poor interpretability, thereby impact the modeling speed and forecasting accuracy. In comparison, as a method directly targeting the forecast elements, the PDF matching method corrects the model's systematic errors by adjusting the model forecasts of meteorological elements so as to be consistent with the observation in terms of their probability density distributions. The PDF method is known for its simplicity in computation and its effective correction of systematic errors, without the need to analyze the complex sources of systematic errors in the model. As a result, it is now widely applied in satellite-retrieved precipitation(Xie, 2011), precipitation forecasting(Hamill et al. 2012), wind speed forecasting(Qian, 2019), etc. However, there is a scarcity of research utilizing this method for the correction of visibility. To date, only Huang et al. (2019) has applied this method to correct low visibility forecasting in the Sichuan Basin, and achieving satisfactory forecasting results. Currently, the majority of studies on the visibility in Xinjiang focus on the spatio-temporal distributions, variation trends, and influencing factors (Zhu and Zhu. 2012; Fei et al. 2019 Zhang et al. 2021). While few study on visibility forecasting has been reported, except Zhu (2011), who combined the Weather Research and Forecasting model with the support vector machine method to establish a visibility forecasting model for Urumqi Diwopu International Airport. This indicates significant research gaps in visibility forecasting in Xinjiang, with previous studies primarily concentrating on single-point experiments. Therefore, this study utilizes the PDF matching method to objectively correct the visibility forecast products of the ECMWF model through a rolling modeling approach. Our results can enhance the level of refined service for low-visibility weather in Xinjiang, and provide robust weather service and technical support for meteorological disaster prevention and mitigation and for the advancement of the "One Belt, One Road" strategy. The remainder of this paper is organized as follows. Section 2 presents the data and methods used in this study. Section 3 offers the corrected results and evaluates of the forecast products before and after the correction. Section 4 further analyzes the performance of the corrected forecasts in two different types of low-visibility cases in Xinjiang. Finally, the main conclusions are provided in section 5 . 2. Data and methods 2.1. Data Due to the consistent forecasting quality and high accuracy, the ECMWF high-resolution model products are widely used in daily operational forecasts. In this study, the visibility forecast products of the ECMWF model spanning from November 1, 2022, to March 31, 2023 are used. The model provides 72-hour forecasts initiated at 0800 and 2000 Beijing Time (BT) every day, with a spatial resolution of 0.1° × 0.1° and a temporal resolution of 3 hours. Besides, the hourly visibility observations from 105 national meteorological stations across Xinjiang during the same period are also collected. Located in the hinterland of the Eurasian continent, Xinjiang is characterized by a typical continental temperate arid climate and covers a vast area of 1,660,000 km 2 with diverse terrain, including the Altai Mountains in the north, the Tianshan Mountains in the center, and the Kunlun Mountains in the south. The region also includes the Gurbantunggut Desert and the Taklamakan Desert, the second-largest desert in the world. This natural topography, often referred to as “three mountains and two basins”, greatly contributes to the unique weather and climate in Xinjiang. Furthermore, the meteorological observation stations in Xinjiang are sparsely and unevenly distributed, with a higher concentration in the north and lower in the south, as shown in Fig. 1 . To mitigate the influence of topography, the bilinear interpolation method was applied to interpolate the gridded visibility forecasts onto the observation stations, and then the corrected visibility forecasts at stations were obtained and evaluated by observations. 2.2. Probability density function matching method The PDF matching method corrects the systemic errors of model through adjusting the model results to align with the observations in their probability density distributions. This method involves the following steps. Firstly, the observed and forecasted visibility values are divided by 9 threshold values, namely 0.05 km, 0.2 km, 0.5 km, 1.0 km, 3.0 km, 5.0 km, 10.0 km, 15.0 km, and 25.0 km. Secondly, the frequencies of observed visibility within different intervals are computed, and the PDF for the observed visibility values and frequencies is constructed, denoted by f(x). In the third step, the frequencies of model forecasted visibility in different intervals are calculated and brought into f(x) to obtain the corrected values of visibility forecasts. In particular, due to the complex and varying topography of Xinjiang and its significant impact on the visibility distribution, the PDF is established on a station-by-station basis rather than establishing a unified function across the entire region. Additionally, in order to fully consider the variations in the model performance at different forecast leading times, we employed a rolling modeling approach to establish the PDFs based on the observations in 20 days prior to the forecast initial time. The frequencies of the visibility within different threshold intervals for observations and model forecasts are calculated through the following equation. \(\:{P}_{i}=\frac{{A}_{i}}{B}\) (1), where \(\:{A}_{i}\) is the number of the visibility samples within a certain threshold interval, \(\:B\) is the total number of visibility samples, and \(\:{P}_{i}\) is the corresponding frequency. 2.3. Evaluation methods To evaluate the correction effectiveness of the PDF matching method on visibility forecasts, the following metrics are used in this study. \(\:ME=\frac{1}{n}\sum\:_{i=1}^{n}\left({F}_{i}-{O}_{i}\right)\) (2), \(\:RMSE=\frac{1}{n}\sum\:_{i=1}^{n}{\left({F}_{i}-{O}_{i}\right)}^{2}\) (3), \(\:{MAE}_{{F}_{i}}=\frac{1}{n}\sum\:_{i=1}^{n}\left|\left.{F}_{i}-{O}_{i}\right|\right.\) (4), \(\:{MAE}_{{C}_{i}}=\frac{1}{n}\sum\:_{i=1}^{n}\left|\left.{C}_{i}-{O}_{i}\right|\right.\) (5), \(\:IP=\frac{{MAE}_{{C}_{i}}-{MAE}_{{F}_{i}}}{{MAE}_{{F}_{i}}}\times\:100\%\) (6), \(\:TS=\frac{Na}{Na+Nb+Nc}\) (7), \(\:MR=\frac{Nb}{Na+Nb}\) (8), \(\:FAR=\frac{Nc}{Na+Nc}\) (9), where the ME, MAE, RMSE, and TS represent the mean error, mean absolute error, root mean square error, and threat score, respectively. The variable \(\:n\) denotes the sample number, while \(\:{F}_{i}\) , \(\:{C}_{i}\) , and \(\:{O}_{i}\) stand for the visibility forecast value, corrected value, and observed value at a specific station \(\:i\) . Additionally, IP indicates the improvement percentage of the corrected results relative to the original model results. \(\:Na\) , \(\:Nb\) , and \(\:Nc\) measure the numbers of hits, misses and false alarms. The value of TS ranges between 0 and 1, indicating the forecast accuracy, while MR and FAR represent the missing ratio and false alarm ratio, respectively. 3. Results 3.1. Error analysis of visibility forecasts In this study, the performance of the ECMWF model visibility forecasts are analyzed in terms of the spatial distributions and magnitudes compared with the observations. 3.1.1. Spatial distributions For visibility products of the ECMWF model within the forecast leading time of 72-hour, the forecast errors are analyzed, with the spatial distributions shown in Fig. 2 . It can be seen that the ECMWF model tends to overestimate the visibility in most areas of Xinjiang, with positive biases of 3–6 km in the urban agglomerations on the north slope of Tianshan Mountains, 4–8 km at most stations in southern Xinjiang, and over 10 km in the Aksu region. Meanwhile, the model underestimates the visibility by 1–3km in Altay and Tacheng of northern Xinjiang at most of the forecast leading times. The factors affecting visibility are different between the southern and northern Xinjiang, where the particulate matter with particle size below 10 microns (PM 10 ) carried by sand and dust makes the major contribution in southern Xinjiang (An et al. 2012; Sun and Gao. 2022). However, research has also found that due to the dense population and high industrial emissions, the visibility in Urumqi, the capital of Xinjiang, is mainly affected by the particulate matter with particle size below 2.5 microns (PM 2.5 ). A decreasing trend is also observed over the years (Li and Wang. 2012; Wang et al. 2022), which makes Urumqi become the city with the poorest performance of ECMWF visibility forecasts across northern Xinjiang (with an RMSE of 10.9 km). In addition, despite the generally good air quality in the Altay region throughout the year, the average RMSE still reaches 10.7 km during the seasons of fall and winter due to the impact of snowfall weather, especially the wind-blowing snow weather. 3.1.2. Magnitudes To further analyze the forecasting performance of the ECMWF model at different visibility levels, this study divides the visibility into five levels, with the values between 0–0.2 km, 0.2–0.5 km, 0.5–1.0 km, 1–10 km, and greater than 10 km. The frequencies of the observed and forecasted visibility at these levels are calculated using Eq. (1). The ECMWF model obviously overestimates the frequency of visibility greater than 10 km, with the forecasted frequency (85%) being obviously higher than the observed frequency (56%). Conversely, for visibility below 10 km, the ECMWF model underestimates the frequencies at all levels. For instance, the observed frequencies are respectively 35% and 6% for visibility within 1.0–10 km and 0.5–1.0 km, while the forecasted frequencies are only 9% and 3%. In general, the ECMWF model exhibits an overestimation of the visibility, while it tends to underestimate (overestimate) the visibility under high-visibility (low-visibility) conditions. Therefore, using the PDF matching method to adjust the visibility forecasts of the ECMWF model based on the frequencies at different visibility levels, in particular, to mitigate the errors of overestimating low visibility, is of great importance to meet operational needs and improve the accuracy of visibility forecasts. 3.2. Evaluation of forecasting performance after correction To further evaluate the effectiveness of the PDF matching method on the visibility forecasting in Xinjiang, we establish different PDFs for different stations at different forecast leading times, forecast initial times and visibility threshold levels. These PDFs are then used to correct the visibility forecasts from the ECMWF model, and then the corrected forecasts are quantitatively evaluated with various metrics. 3.2.1. Evaluation metrics This study evaluates the corrected forecasts for specific forecast leading times (12-hour, 24-hour, 36-hour, 48-hour, 60-hour, and 72-hour) using the metrics of ME, MAE, RMSE (Table 1 ). The results demonstrate an obvious improvement in the visibility forecasts after correction. Before the correction, the ECMWF model overestimates the visibility by 3.3–3.8 km at the forecast leading time of 72- hour, whereas it underestimates the visibility by 1.4–2.1 km after correction, aligning more closely with the observation. Furthermore, Compared to Afan and Bayu (2021), who reduced the RMSE of visibility prediction by 15% using the ARIMA model, the MAEs of forecasts at all forecast leading times decrease by over 20% compared with the original forecasts after the correction, and the RMSEs also decrease from 10.3–10.6 km to less than 10 km. In particular, the RMSEs for forecasts at the leading times of 12-hour and 24-hour drop to less than 9 km. In addition, when comparing the effectiveness of correction on visibility forecasts at different levels, the TS for visibility below 10 km has been improved from 0.23 to 0.34.Furthermore, in low-visibility scenarios (< 1 km), the TS value increased by 80% (from 0.05 to 0.09), significantly outperforming the fog prediction based on BP neural networks by Duddu et al. (2020) (TS = 0.07). This indicates that the PDF method exhibits superior forecast performance in systematic error correction, especially suitable for the needs of site-by-site modeling in Xinjiang's complex terrain.Meanwhile, both the false alarm ratio and the missing ratio exhibit decreasing trends of varying degrees. It illustrates that employing the PDF matching method can effectively mitigate the overestimation in visibility forecasts by the ECMWF model, and reduce the false alarm ratio and missing ratio to some extent. Table 1 Mean error (ME), mean absolute error (MAE) and root mean square error (RMSE) of visibility forecasts at different forecast leading times by the ECMWF model before and after correction. Forecast leading time ME MAE RMSE 12 3.3 (− 1.4) 8.6 (6.5) 10.3 (8.7) 24 3.5 (− 1.4) 8.7 (6.6) 10.4 (8.9) 36 3.6 (− 1.5) 8.8 (6.7) 10.5 (9.0) 48 3.6 (− 1.8) 8.8 (6.7) 10.5 (9.1) 60 3.7 (− 2.0) 8.9 (6.9) 10.6 (9.1) 72 3.8 (− 2.1) 8.9 (6.9) 10.6 (9.2) Note: Original values of metrics outside parentheses, corrected values in parentheses (unit: km). 3.2.2. Spatial distribution of correction effects Figure 3 illustrates the spatial distributions of the forecast errors at different forecast leading times for various stations in Xinjiang after the correction by the PDF matching method. It is evident that the corrected forecasts at most stations are closer to the observation, with the errors predominantly falling within the range between − 1 km and − 3 km. Compared with the pre-corrected visibility forecasts (Fig. 2 ), the most obvious improvement is observed in the urban agglomerations on the north slope of Tianshan Mountains and in southern Xinjiang. The forecast errors in these two regions are in the range of 3–6 km and 4–8 km before correction. After the correction, the errors have been reduced obviously and the stability at different forecast leading times has been enhanced, which greatly improves the systematic overestimation of the visibility forecasts before the correction. However, for forecasts in high mountain areas (e.g., Tianchi station, Xiaoquzi station) along the Tianshan Mountains, no obvious improvement is observed, with the mean errors remaining around − 12 km before and after the correction. Overall, the forecast errors after correction exhibit a uniform spatial distribution, which are not affected by topography or latitude. The distribution of IP for corrected visibility forecasts is presented in Fig. 4 . The results show that positive improvement is found at most stations in Xinjiang. In particular, the forecasts at stations in the urban agglomerations on the northern slope of Tianshan Mountains are obviously improved by more than 70%, while those at stations in the southern Xinjiang are improved by 50%–70%. Conversely, the forecasts at stations in Yili and Tacheng exhibit relatively small or no improvement, while some negative improvement are found at stations in Altay and other areas. The correction effects within different IP intervals are further analyzed, as shown in Fig. 5 . It is found that the corrected visibility forecasts at 88 stations in Xinjiang exhibit positive improvement with varying degrees. Among them, the improvement effect at 57 stations exceeds 60%, accounting for 54.2% of the total number of stations in Xinjiang. It is worth noting that the improvement effect at nearly one-third of the stations in Xinjiang (34 stations) exceeds 80%. On the other hand, the visibility forecasts at 17 stations in Xinjiang show negative improvement, possibly due to the complex underlying surface or high-altitude terrain. Overall, the correction has led to obvious improvement in visibility forecasts at most stations, which can meet the requirements of meteorological departments in operational forecasting. 4. Case study The unique underlying surface and terrain conditions in Xinjiang result in great differences in climate between its northern and southern regions. To validate the correction effectiveness of the PDF matching method in various weather processes, a typical fog-haze event and a dust event are selected for comprehensive analysis and evaluation. 4.1. Fog-haze event From December 25, 2022, to January 5, 2023, the northern slope of the Tianshan Mountains in Xinjiang was impacted by a warm high-pressure ridge in the upper layer and a weak-pressure field at surface. Meanwhile, low-level southerly winds from the back of Mongolian high pressure promotes the formation of strong temperature inversions within the boundary layer over these areas, resulting in poor vertical diffusion capacity that is conducive to the formation of foggy weather. Consequently, the visibility in Urumqi, Changji and Shihezi maintained at a relatively lower level for a long time. Most stations of the Tianshan Mountains experienced the visibility of less than 500 meters, with Urumqi City recording the lowest visibility of less than 100 meters. By January 5, the influence of cold air led to a gradual improvement in regional atmospheric dispersion conditions, bringing an end to this process. During this fog-hazy weather process, the forecast errors of visibility by the ECMWF model at most stations are within the range of 8–12 km (Fig. 6 a- 1 ). After applying the PDF matching method, the forecast errors have been reduced to 2–4 km (Fig. 6 a- 2 ). The MAEs have also decreased from 6–12 km (Fig. 6 b- 1 ) to 3–6 km (Fig. 6 b- 2 ) after the correction, with an improvement of over 60% at most stations. This indicates that the PDF method effectively reduces the ME and MAE. However, limited correction effectiveness was observed at certain high-altitude mountainous stations, such as “Xibaiyanggou” and “Tianchi” (blue markers in Fig. 6 a- 1 ), located at elevations of 1930 m and 1942.5 m, respectively. For instance, at the“Tianchi”station, the ME remained at -12.3 km after correction, compared to -12.7 km prior to correction, with similarly marginal improvements in MAE. This discrepancy is likely attributed to the complex underlying surface conditions in high-altitude regions. Although studies on visibility correction forecasts across different underlying surfaces are scarce, analogous challenges in achieving optimal corrections at high-altitude stations have been reported in previous research, such as Qian et al. (2019) ’s work on wind speed correction in plains versus mountainous areas. These findings underscore the need for further investigation into terrain-specific correction methodologies to enhance model accuracy in topographically complex environments. 4.2. Sand-dust event From March 19 to March 24, 2023, a sand-dust weather process occurred in most regions of North China due to the combined effect of Mongolian cyclone and surface cold front. Persistent sand-blowing or dust-floating weather was also observed in most areas of southern and eastern Xinjiang, with strong sandstorms occurred in local area. Figure 7 illustrates the spatial distributions for the forecast errors and MAEs of visibility from the ECMWF model forecasts and the results corrected by the PDF matching method during this weather process. The results reveal an obvious overestimation of visibility forecasted by the ECMWF model at most stations in southern Xinjiang, with the forecast errors reaching 6–10 km and the MAEs exceeding 12 km (Figs. 7 a- 1 and 7 b- 1 ), even reaching 20 km at individual stations. After the correction by the PDF matching method, the above two evaluation metrics are improved obviously, as shown in Figs. 7 a- 2 and 7 b- 2 , where the MAEs in most areas have been reduced to less than 6 km. In addition, the Aral City is taken as an example to evaluate the correction effect. The visibility forecasts with the forecast leading time of 30 h initiated at 0800 BT from March 18 to 21, 2023 and corresponding correction results are compared (Fig. 8 ). It is demonstrated that the forecasts corrected by the PDF matching method are closer to the observations, with the forecast errors below 2 km. Especially at 1400 BT on March 21, 2023, when the visibility at Aral station decreased to 2.2 km, the corrected visibility is 4.3 km, while the forecasted visibility before the correction reaches 11.1 km. This further confirms the obvious correction effect over the original ECMWF forecasts using the PDF matching method. 5. Conclusions Based on the visibility observations from 105 national meteorological stations in Xinjiang, the visibility forecast products of the ECMWF model within the 72-hour forecast leading time from November 2022 to March 2023 are evaluated in terms of the forecast errors. On this basis, an objectively corrected forecast product of visibility for the next three days with an interval of 3 hours in Xinjiang is established based on the PDF matching method through a rolling modeling approach. The visibility forecast results before and after correction are further evaluated and analyzed. The main conclusions are as follows. The ECMWF model tends to overestimate the visibility in most areas of Xinjiang. Specifically, the forecast errors are in the range of 3–6 km in the urban agglomerations on the northern slope of the Tianshan Mountains, and within 4–8 km at most stations in southern Xinjiang, with the errors even exceeding 10 km in Aksu area. The visibility frequencies within different ranges show that the observed frequencies for visibility within 1.0–10 km and 0.5–1.0 km are 35% and 6%, respectively, while the forecasted frequencies from the ECMWF model are only 9% and 3%. This indicates that the model forecast exhibits a characteristic of overestimation of low visibility. The PDF matching method can effectively reduce the visibility forecast errors of the ECMWF model, leading to an obvious improvement in evaluation metrics. For instance, within the 72-hour forecast period, the ECMWF model overestimates the visibility by 3.3–3.8 km, while the corrected results are 1.4–2.1 km lower than the observations, with the MAE reduced by over 20%. Furthermore, the TS value also increases from 0.05 to 0.09 for visibility less than 1 km after the correction. In terms of the spatial distribution of correction effectiveness, there are 88 stations in Xinjiang exhibiting positive improvement with varying degrees. These stations are primarily located in the urban agglomerations on the northern slope of the Tianshan Mountains (with improvement exceeding 70%) and in most of southern Xinjiang (with the improvement ranging from 50% to 70%). Finally, the case study demonstrates the obvious improvement in visibility forecasts during a fog-haze event in northern Xinjiang and a sand-dust event in southern Xinjiang after applying the PDF matching method, where the corrected visibility forecast aligns more closely with the observations. Declarations Competing interests The authors declare that they have no conflict of interest. Author Contribution Chao.Liu. and Hua. Cong. wrote the main manuscript text and Junan.Xiao. prepared figures 1-4 and all Tables. Xiaoqin. Rao. prepared figures 5-8 and Chao. Xie. checked all data.Dawei. An. prepared the references. All authors reviewed the manuscript. Acknowledgement This research was supported by National Key R&D Program Pilot of China(2022YFC3701205). The authors are grateful to the anonymous reviewers for their insightful comments. Data Availability The measurement data involved in this study are available upon request. 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Monthly Weather Review.145(9),3441-3463. Herman G R, Schumacher R S. 2016. Using reforecasts to improve forecasting of fog and visibility for aviation[J]. Wea Forecasting,31(2),467-482. Hu S.Y., Zhao, G., Tan, T.Y., et al. 2021. Current challenges of improving visibility due to increasing nitrate fraction in PM 2.5 during the haze days in Beijing, China. Environmental Pollution. 290. Huang C.H., Wang B.Y., Chen Z.P., et al. 2019. Analysis of Temporal and Spatial Distribution Characteristics of Low Visibility over the Last Ten Years in Sichuan Basin, China and Correction Methods for Model Forecasts. Plateau and mountain meteorology research.39(4):67-73. Husar R B, Holloway J M, Patterson D E, et al. 1981. Spatial and temporal pattern of eastern U.S. haziness: a summary. Atmos.environ., 15(10/11),1919-1928. Li, X., Wang, S.L. 2012. Variation Characteristics in Atmospheric Visibility and Their Effective Factors in Xinjiang during 1980-2007. Desert and Oasis Meteorology,6(3),14-20 (in Chinese). Liang, C.W., Chang, C.C., Hsiao, C.Y., et al. 2023. prediction and analysis of atmospheric visibility in five terrain types with artificial intelligence. Heliyon.e19281. Lu, S.D., Chen, L.J., Zhao, G.X., et al. 2020. Analysis of Main Influence Factors of visibility in Taiyuan and the prediction of visibility. Desert and Oasis Meteorology,14(4),105-112 (in Chinese). Luz, C.O., Luis, D.O., Mitchell, S. 2023.Deep Learning Models for Visibility Forecasting Using Climatological Data. International Journal of Forecasting, 39(2),992-1004. Kim J., Kim, S.H., Seo, H.W., et al. 2022. Meteorological characteristics of fog events in Korean smart cities and machine learning based visibility estimation. Atmospheric Research. 275,106239. Ni, J.B., Li, W.C., Shang, K.G. et al. 2015. Automatic Identification and Prediction of Low Visibility Weather in North China. .Journal of Arid Meteorology, 33(1),174-179 (in Chinese). Peng, Y., Wang, H., Hou, M.L., et al. 2020. Improved method of visibility parameterization focusing on high humidity and aerosol concentrations during fog-haze events: Application in the GRAPES_CUACE model in Jing-Jin-Ji, China. Atmospheric Environment. 222,117139. Physics C, Weather S. Branch T, et al. 2009. Probabilistic Parameterizations of Visibility Using Observations of Rain Precipitation Rate, Relative Humidity and Visibility. Journal of Applied Meteorology and Climatology,1999,36-46. Qian L, Qiu, X.X., Zheng, L.L., 2019. Error Correction of WRF Model Gust Speed Based on Probability Function Matching Method[J].Meteorological Science and Technology.47(6),916-926. Sun, W.T., Gao, X. 2022. Geomorphology of Sand Dunes in the Taklamakan Desert based on ERA5 reanalysis data. Journal of Arid Environmental. 207,104848. Wang, J.M., Zhou, X.L., Hua, Z.Y., et al. 2023. Concentration Level, Health Risk Assessment and Source Apportionment of Nitrosamines in PM 2.5 in Urumqi during Winter Time. Atmospheric Pollution Research. 14,101756. Watson J G. Visbility: science and regulation. 2002. Journal of the Air & Waste Management Association, 52(6),628-713. Xie P.P., Xiong A.Y. 2011. A conceptual model for constructing high-resolution gauge-satellite merged precipitation analyses. Journal of Geophysical Research,116,D21. Yang Y.C., Ge, B.Z., Chen X.S, et al. 2021. Impact of Water Vapor Content on Visibility: Fog-haze Conversion and its Implications to Pollution Control. Atmospheric research.256. Zhang, X.X., Ding, X., Talifu, D., et al. 2021. Humidity and PM 2.5 Composition Determine Atmospheric Light Extinction in the Arid Region of Northwest China. Journal of Environmental Sciences. 100,279-286. Zhao, C.G., Zhao, S.R., Lin, J., et al. 2022. Visibility Forecast and Influence Factor Analysis Based on Regional Modeling. Meteorological monthly. 48(6),773-782 (in Chinese). Zhu,G.D. 2011.Multi-factor Forecast in Urumqi International Airport Based on SVM Method. Desert and Oasis Meteorology,5(4),40-43(in Chinese). Zhu, L., Zhu,G.D. 2012. Analysis on the Climatic Characteristics of Low Visibility in 30 Years at Urumqi Airport. Journal of Civil Aviation Flight University of China,23(5),27-30(in Chinese). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 13 Mar, 2026 Reviews received at journal 13 Mar, 2026 Reviewers agreed at journal 27 Feb, 2026 Reviews received at journal 02 Feb, 2026 Reviewers agreed at journal 01 Feb, 2026 Reviewers invited by journal 30 Jan, 2026 Editor assigned by journal 12 Jan, 2026 Submission checks completed at journal 12 Jan, 2026 First submitted to journal 12 Jan, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8583058","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":583938693,"identity":"564fe3b0-face-464e-bebb-98a6581f9ab4","order_by":0,"name":"Chao Liu","email":"","orcid":"","institution":"National Meteorological Centre","correspondingAuthor":false,"prefix":"","firstName":"Chao","middleName":"","lastName":"Liu","suffix":""},{"id":583938694,"identity":"931055e2-02e8-4b66-8d9f-a15d6a9a1314","order_by":1,"name":"Junan Xiao","email":"","orcid":"","institution":"Xinjiang Meteorological Observatory","correspondingAuthor":false,"prefix":"","firstName":"Junan","middleName":"","lastName":"Xiao","suffix":""},{"id":583938695,"identity":"d78c2e18-8b36-4fb2-9c0c-df665ef6fdcd","order_by":2,"name":"Xiaoqin Rao","email":"","orcid":"","institution":"National Meteorological Centre","correspondingAuthor":false,"prefix":"","firstName":"Xiaoqin","middleName":"","lastName":"Rao","suffix":""},{"id":583938696,"identity":"f0abe2a4-a3a5-4efc-bc40-0aa858a63d43","order_by":3,"name":"Cong Hua","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyElEQVRIiWNgGAWjYBACAygtR7oWY9K1JDYQrcVcIvnhh487atP7px1+wPil4jAD/2wCui1npBlLzjxzPHfG7TQDZpkzhxkk7hwg4LAbCWbMvG3HcjdIJxgwS7alMRhIJBDSkv4NpCXdQDr9A7FackC21CQYSOcYMH5ssyFCy5k3xZIz2w4YzridU3CY4YwNj8QNQlqOp2/88LGtTp5/dvrGhz8qJOT4ZxDQAgWHISQPAwMPUeqBoA5MMv4gVv0oGAWjYBSMKAAAVHtCORgHwHoAAAAASUVORK5CYII=","orcid":"","institution":"National Meteorological 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14:53:45","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8583058/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8583058/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101754298,"identity":"a197713f-c08c-4152-99c4-27acc0fb45b9","added_by":"auto","created_at":"2026-02-03 10:42:11","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":115401,"visible":true,"origin":"","legend":"\u003cp\u003eLocations of 105 national meteorological stations across Xinjiang.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8583058/v1/1754a8c1bb8a3eb568220435.jpg"},{"id":101697616,"identity":"59cd19c3-3497-4c50-a95c-f98b66f064fe","added_by":"auto","created_at":"2026-02-02 17:18:00","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":244058,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial distributions of visibility forecast errors from the European Center for Medium-Range Weather Forecasts (ECMWF) model at different forecast leading times.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8583058/v1/d9f2ba8911851b75a575f29d.jpg"},{"id":101753092,"identity":"c095e024-f5b4-4ac5-9b15-43dd283b35a2","added_by":"auto","created_at":"2026-02-03 10:39:13","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":241441,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial distributions of the forecast errors at different forecast leading times after the correction by the probability density function (PDF) matching method.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8583058/v1/22b9e7e872d674704014ce0c.jpg"},{"id":101697618,"identity":"494d829d-62ee-45cd-a4a7-f6c09ec70636","added_by":"auto","created_at":"2026-02-02 17:18:00","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":95306,"visible":true,"origin":"","legend":"\u003cp\u003eThe distribution of improvement percentage (IP) for visibility forecasts after the correction by the PDF matching method.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8583058/v1/7812aa42a8f4ab5a014b1797.jpg"},{"id":101697620,"identity":"3d262307-18f9-4cbb-be22-1fff70ec5b1c","added_by":"auto","created_at":"2026-02-02 17:18:00","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":44390,"visible":true,"origin":"","legend":"\u003cp\u003eStatistic of station numbers within different IP intervals.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8583058/v1/00c2aa3e4c0e416abb5fd4c9.jpg"},{"id":101753401,"identity":"98a8d115-6a6a-46b9-894b-c4e132bdecc0","added_by":"auto","created_at":"2026-02-03 10:39:59","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":143932,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial distributions for the forecast errors (left column) and mean absolute errors (MAEs; right column) of visibility between the ECMWF model forecasts and the results corrected by the PDF matching method at the stations on the northern slope of Tianshan Mountains in Xinjiang.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8583058/v1/6a1433c2df1bdc1f70b8d92b.jpg"},{"id":101697622,"identity":"9c92fe85-5bb4-43be-8b09-dea46854e2ef","added_by":"auto","created_at":"2026-02-02 17:18:00","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":158648,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial distributions for the (a) forecast errors and (b) MAEs of visibility from the ECMWF model forecasts and the results corrected by the PDF matching method in southern Xinjiang.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8583058/v1/743c78fba28f1ccc51079034.jpg"},{"id":101753519,"identity":"71f12d4c-15a9-4b14-a160-5dc9bcd611f0","added_by":"auto","created_at":"2026-02-03 10:40:11","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":46244,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the visibility forecasts at the forecast leading time of 30 h initiated at 0800 BT from March 18 to 21, 2023 in Aral, Xinjiang before and after correction.\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-8583058/v1/a8c1ef8eddffd0bb3acb348a.jpg"},{"id":101755782,"identity":"a36d91e9-aca5-4265-a3f6-64324d48f804","added_by":"auto","created_at":"2026-02-03 10:54:45","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1776063,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8583058/v1/362a466e-1e32-47b6-8d86-9e230866fe45.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Application of Probability Density Function Matching Method for Visibility Forecasting in Xinjiang of China","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eAs is known, visibility indicates the atmospheric transparency. Low-visibility events frequently impact people's daily activities such as the transportation, causing increased traffic accidents and flight delays that bring substantial inconvenience and harm to people's daily life (Hu et al. 2021; Yang et al. 2021). However, the factors affecting visibility are multifaceted. Especially for the low-visibility weather, its occurrence and development are not only interconnected with weather patterns and atmospheric circulation, but also affected by the underlying surface, climatic environment and human activities, posing challenges to accurate forecasting.\u003c/p\u003e \u003cp\u003eIn early studies, visibility forecasts were mainly based on synoptic diagnosis. The formation conditions of visibility were firstly diagnosed, and forecasts were further made through the combination with forecaster's experience and extrapolation from the real-time observation (Husar et al. 1981; Watson et al. 2002). With the development of numerical forecasting technology, numerical forecast products from domestic and abroad have become the primary references for forecasters. Visibility in numerical models often relies on the diagnostic analyses of various physical quantities, including cloud water content, relative humidity, and precipitation (Gultepe and Milbrandt. 2010). Herman and Schumacher (2016) identified fog-haze and heavy precipitation as the primary factors leading to the reduction of visibility, consequently limiting the accuracy of visibility forecasts in numerical models. It is worth noting that the incompleteness of parameterization schemes in numerical model will lead to systematic errors in the forecasts of specific elements. Additionally, owing to the differences in designing the dynamical frameworks and physical parameterization schemes among numerical models, the systematic errors vary with different models. Utilizing statistical methods to construct forecasting models based on hindcasts of numerical models and observations can eliminate systematic errors to a certain extent, thereby correcting the forecasts of numerical models. Research from the American Meteorological Development Laboratory has indicated that the forecast performance of model output statistics derived from the global forecast system significantly surpasses the original model results (Dallavalle et al. 2004; Zhao et al. 2022). Currently, researchers mostly use statistical methods such as multiple linear regression and stepwise regression to correct the model results. In multivariate linear modeling, a specific method is utilized to construct a forecasting model to predict the visibility variations, where the selected forecasting factors have clear physical significance. Using 40,000 sets of visibility data, Afan and Bayu. (2021) discovered that the stepwise regression method yields visibility forecasts with a smaller root mean square error (RMSE) and higher correlation coefficient with observations. Ni et al. (2015) employed a mathematical modeling method to forecast the visibility in the North China region and found a stable forecasting ability in predicting the visibility variation trend in Beijing. Similarly, numerous studies have established linear relationships between visibility and various meteorological factors and pollutants. Visibility forecasts with various degrees of effectiveness have been achieved and extensively applied. Nevertheless, there are still numerous nonlinear relationships between visibility and diverse meteorological elements.\u003c/p\u003e \u003cp\u003eTo address these nonlinear issues, neural networks, a computational science that has experienced a resurgence and rapid development in recent years, have been widely applied in the field of meteorology especially in visibility forecasting, with the back propagation neural network (BPNN) as the main component (Gao et al. 2022; Chen et al. 2023). Based on a five-year data series gathered from 238 weather monitoring stations in and around North Carolina, Duddu et al. (2020) developed and validated the ability of the BPNN model in visibility forecasting, and observed that the BPNN exhibits superior forecasting capability for fog relative to dense fog. Lu et al. (2020) employed a neural network approach to develop a visibility forecasting model in Taiyuan area. This model responds well to various performance indicators and provides a significant reference value for local visibility forecasting. With the advances in computer technology and artificial intelligence (AI), AI methods such as machine learning have seen widespread adoption, with beneficial attempt in visibility forecasting (Kim et al. 2022). Liang et al. (2023) employed three methods of support vector machine, multilayer perceptron (MLP), and extreme gradient boosting (XGBoost) to predict the visibility in various regions of Taiwan. They found that the MLP is more suitable for hilly regions, while the XGBoost is more effective in basins and plains. This indicates that different methods should be taken to get optimal visibility forecasts in different regions. Based on extensive historical datasets, Luz et al. (2023) developed five distinct machine learning models (including convolutional neural networks, long short-term memory networks, and multi-method coupling) for visibility forecasting and conducted comparative analysis and examinations at two weather observation stations in Florida, USA.\u003c/p\u003e \u003cp\u003eHowever, for operational visibility forecasts, the forecasting effectiveness and degree of operationalization are not satisfactory using whether traditional statistical methods, interpreted numerical forecast products, or AI techniques like deep learning. There remains an obvious gap between the forecasts and the actual demand of forecasting services, which is mainly reflected in the following aspects. Firstly, visibility modeling necessitates consideration of multiple elements. Atmospheric visibility is closely linked to water vapor and aerosol contents in the air, and it is influenced by local wind speed, wind direction, precipitation, and particulate matter concentrations (Gao et al. 2017; Peng et al. 2020). Considering the inherently localized nature of visibility, current research has mainly focused on single station or specific region, where only the meteorological factors that affect the local visibility are selected. This poses a challenge in establishing unified visibility forecasting models. Secondly, the parameterization schemes of visibility vary in different numerical models. Existing numerical weather forecasting models, including the mainstream models in the European Center for Medium-Range Weather Forecasts (ECMWF), only consider the impacts of precipitation, humidity, and low clouds on visibility, while neglecting the influence of aerosols. This oversight is particularly noticeable during fog-haze events, when visibility is often overestimated, especially in the urban agglomerations on the northern slope of Tianshan Mountains in Xinjiang (Gultepe et al. 2006; Physics et al. 2009). Thirdly, the AI technique manifests a high level of sophistication, and its data-driven nature lacks clear physical mechanisms. Although the AI technique has rapidly advanced in recent years and found extensive application in meteorology, it operates as a black box. If all relevant data are simply inputted without considering the intrinsic physical relationships between independent and dependent variables, the complex mapping relationship acquired through sample learning can lead to poor interpretability, thereby impact the modeling speed and forecasting accuracy. In comparison, as a method directly targeting the forecast elements, the PDF matching method corrects the model's systematic errors by adjusting the model forecasts of meteorological elements so as to be consistent with the observation in terms of their probability density distributions. The PDF method is known for its simplicity in computation and its effective correction of systematic errors, without the need to analyze the complex sources of systematic errors in the model. As a result, it is now widely applied in satellite-retrieved precipitation(Xie, 2011), precipitation forecasting(Hamill et al. 2012), wind speed forecasting(Qian, 2019), etc. However, there is a scarcity of research utilizing this method for the correction of visibility. To date, only Huang et al. (2019) has applied this method to correct low visibility forecasting in the Sichuan Basin, and achieving satisfactory forecasting results. Currently, the majority of studies on the visibility in Xinjiang focus on the spatio-temporal distributions, variation trends, and influencing factors (Zhu and Zhu. 2012; Fei et al. 2019 Zhang et al. 2021). While few study on visibility forecasting has been reported, except Zhu (2011), who combined the Weather Research and Forecasting model with the support vector machine method to establish a visibility forecasting model for Urumqi Diwopu International Airport. This indicates significant research gaps in visibility forecasting in Xinjiang, with previous studies primarily concentrating on single-point experiments. Therefore, this study utilizes the PDF matching method to objectively correct the visibility forecast products of the ECMWF model through a rolling modeling approach. Our results can enhance the level of refined service for low-visibility weather in Xinjiang, and provide robust weather service and technical support for meteorological disaster prevention and mitigation and for the advancement of the \"One Belt, One Road\" strategy.\u003c/p\u003e \u003cp\u003eThe remainder of this paper is organized as follows. Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the data and methods used in this study. Section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e3\u003c/span\u003e offers the corrected results and evaluates of the forecast products before and after the correction. Section \u003cspan refid=\"Sec13\" class=\"InternalRef\"\u003e4\u003c/span\u003e further analyzes the performance of the corrected forecasts in two different types of low-visibility cases in Xinjiang. Finally, the main conclusions are provided in section \u003cspan refid=\"Sec16\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e"},{"header":"2. Data and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Data\u003c/h2\u003e \u003cp\u003eDue to the consistent forecasting quality and high accuracy, the ECMWF high-resolution model products are widely used in daily operational forecasts. In this study, the visibility forecast products of the ECMWF model spanning from November 1, 2022, to March 31, 2023 are used. The model provides 72-hour forecasts initiated at 0800 and 2000 Beijing Time (BT) every day, with a spatial resolution of 0.1\u0026deg; \u0026times; 0.1\u0026deg; and a temporal resolution of 3 hours. Besides, the hourly visibility observations from 105 national meteorological stations across Xinjiang during the same period are also collected. Located in the hinterland of the Eurasian continent, Xinjiang is characterized by a typical continental temperate arid climate and covers a vast area of 1,660,000 km\u003csup\u003e2\u003c/sup\u003e with diverse terrain, including the Altai Mountains in the north, the Tianshan Mountains in the center, and the Kunlun Mountains in the south. The region also includes the Gurbantunggut Desert and the Taklamakan Desert, the second-largest desert in the world. This natural topography, often referred to as \u0026ldquo;three mountains and two basins\u0026rdquo;, greatly contributes to the unique weather and climate in Xinjiang. Furthermore, the meteorological observation stations in Xinjiang are sparsely and unevenly distributed, with a higher concentration in the north and lower in the south, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. To mitigate the influence of topography, the bilinear interpolation method was applied to interpolate the gridded visibility forecasts onto the observation stations, and then the corrected visibility forecasts at stations were obtained and evaluated by observations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Probability density function matching method\u003c/h2\u003e \u003cp\u003eThe PDF matching method corrects the systemic errors of model through adjusting the model results to align with the observations in their probability density distributions. This method involves the following steps. Firstly, the observed and forecasted visibility values are divided by 9 threshold values, namely 0.05 km, 0.2 km, 0.5 km, 1.0 km, 3.0 km, 5.0 km, 10.0 km, 15.0 km, and 25.0 km. Secondly, the frequencies of observed visibility within different intervals are computed, and the PDF for the observed visibility values and frequencies is constructed, denoted by f(x). In the third step, the frequencies of model forecasted visibility in different intervals are calculated and brought into f(x) to obtain the corrected values of visibility forecasts. In particular, due to the complex and varying topography of Xinjiang and its significant impact on the visibility distribution, the PDF is established on a station-by-station basis rather than establishing a unified function across the entire region. Additionally, in order to fully consider the variations in the model performance at different forecast leading times, we employed a rolling modeling approach to establish the PDFs based on the observations in 20 days prior to the forecast initial time.\u003c/p\u003e \u003cp\u003eThe frequencies of the visibility within different threshold intervals for observations and model forecasts are calculated through the following equation.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{i}=\\frac{{A}_{i}}{B}\\)\u003c/span\u003e \u003c/span\u003e (1),\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the number of the visibility samples within a certain threshold interval, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:B\\)\u003c/span\u003e\u003c/span\u003e is the total number of visibility samples, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{P}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the corresponding frequency.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Evaluation methods\u003c/h2\u003e \u003cp\u003eTo evaluate the correction effectiveness of the PDF matching method on visibility forecasts, the following metrics are used in this study.\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:ME=\\frac{1}{n}\\sum\\:_{i=1}^{n}\\left({F}_{i}-{O}_{i}\\right)\\)\u003c/span\u003e \u003c/span\u003e (2),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:RMSE=\\frac{1}{n}\\sum\\:_{i=1}^{n}{\\left({F}_{i}-{O}_{i}\\right)}^{2}\\)\u003c/span\u003e \u003c/span\u003e (3),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{MAE}_{{F}_{i}}=\\frac{1}{n}\\sum\\:_{i=1}^{n}\\left|\\left.{F}_{i}-{O}_{i}\\right|\\right.\\)\u003c/span\u003e \u003c/span\u003e (4),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{MAE}_{{C}_{i}}=\\frac{1}{n}\\sum\\:_{i=1}^{n}\\left|\\left.{C}_{i}-{O}_{i}\\right|\\right.\\)\u003c/span\u003e \u003c/span\u003e (5),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:IP=\\frac{{MAE}_{{C}_{i}}-{MAE}_{{F}_{i}}}{{MAE}_{{F}_{i}}}\\times\\:100\\%\\)\u003c/span\u003e \u003c/span\u003e (6),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:TS=\\frac{Na}{Na+Nb+Nc}\\)\u003c/span\u003e \u003c/span\u003e (7),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:MR=\\frac{Nb}{Na+Nb}\\)\u003c/span\u003e \u003c/span\u003e (8),\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:FAR=\\frac{Nc}{Na+Nc}\\)\u003c/span\u003e \u003c/span\u003e (9),\u003c/p\u003e \u003cp\u003ewhere the ME, MAE, RMSE, and TS represent the mean error, mean absolute error, root mean square error, and threat score, respectively. The variable \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e denotes the sample number, while \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{i}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{C}_{i}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{O}_{i}\\)\u003c/span\u003e\u003c/span\u003e stand for the visibility forecast value, corrected value, and observed value at a specific station \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e. Additionally, IP indicates the improvement percentage of the corrected results relative to the original model results. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Na\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Nb\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Nc\\)\u003c/span\u003e\u003c/span\u003e measure the numbers of hits, misses and false alarms. The value of TS ranges between 0 and 1, indicating the forecast accuracy, while MR and FAR represent the missing ratio and false alarm ratio, respectively.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Error analysis of visibility forecasts\u003c/h2\u003e \u003cp\u003eIn this study, the performance of the ECMWF model visibility forecasts are analyzed in terms of the spatial distributions and magnitudes compared with the observations.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.1.1. Spatial distributions\u003c/h2\u003e \u003cp\u003eFor visibility products of the ECMWF model within the forecast leading time of 72-hour, the forecast errors are analyzed, with the spatial distributions shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. It can be seen that the ECMWF model tends to overestimate the visibility in most areas of Xinjiang, with positive biases of 3\u0026ndash;6 km in the urban agglomerations on the north slope of Tianshan Mountains, 4\u0026ndash;8 km at most stations in southern Xinjiang, and over 10 km in the Aksu region. Meanwhile, the model underestimates the visibility by 1\u0026ndash;3km in Altay and Tacheng of northern Xinjiang at most of the forecast leading times. The factors affecting visibility are different between the southern and northern Xinjiang, where the particulate matter with particle size below 10 microns (PM\u003csub\u003e10\u003c/sub\u003e) carried by sand and dust makes the major contribution in southern Xinjiang (An et al. 2012; Sun and Gao. 2022). However, research has also found that due to the dense population and high industrial emissions, the visibility in Urumqi, the capital of Xinjiang, is mainly affected by the particulate matter with particle size below 2.5 microns (PM\u003csub\u003e2.5\u003c/sub\u003e). A decreasing trend is also observed over the years (Li and Wang. 2012; Wang et al. 2022), which makes Urumqi become the city with the poorest performance of ECMWF visibility forecasts across northern Xinjiang (with an RMSE of 10.9 km). In addition, despite the generally good air quality in the Altay region throughout the year, the average RMSE still reaches 10.7 km during the seasons of fall and winter due to the impact of snowfall weather, especially the wind-blowing snow weather.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e3.1.2. Magnitudes\u003c/h2\u003e \u003cp\u003eTo further analyze the forecasting performance of the ECMWF model at different visibility levels, this study divides the visibility into five levels, with the values between 0\u0026ndash;0.2 km, 0.2\u0026ndash;0.5 km, 0.5\u0026ndash;1.0 km, 1\u0026ndash;10 km, and greater than 10 km. The frequencies of the observed and forecasted visibility at these levels are calculated using Eq.\u0026nbsp;(1). The ECMWF model obviously overestimates the frequency of visibility greater than 10 km, with the forecasted frequency (85%) being obviously higher than the observed frequency (56%). Conversely, for visibility below 10 km, the ECMWF model underestimates the frequencies at all levels. For instance, the observed frequencies are respectively 35% and 6% for visibility within 1.0\u0026ndash;10 km and 0.5\u0026ndash;1.0 km, while the forecasted frequencies are only 9% and 3%. In general, the ECMWF model exhibits an overestimation of the visibility, while it tends to underestimate (overestimate) the visibility under high-visibility (low-visibility) conditions. Therefore, using the PDF matching method to adjust the visibility forecasts of the ECMWF model based on the frequencies at different visibility levels, in particular, to mitigate the errors of overestimating low visibility, is of great importance to meet operational needs and improve the accuracy of visibility forecasts.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Evaluation of forecasting performance after correction\u003c/h2\u003e \u003cp\u003eTo further evaluate the effectiveness of the PDF matching method on the visibility forecasting in Xinjiang, we establish different PDFs for different stations at different forecast leading times, forecast initial times and visibility threshold levels. These PDFs are then used to correct the visibility forecasts from the ECMWF model, and then the corrected forecasts are quantitatively evaluated with various metrics.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1. Evaluation metrics\u003c/h2\u003e \u003cp\u003eThis study evaluates the corrected forecasts for specific forecast leading times (12-hour, 24-hour, 36-hour, 48-hour, 60-hour, and 72-hour) using the metrics of ME, MAE, RMSE (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The results demonstrate an obvious improvement in the visibility forecasts after correction. Before the correction, the ECMWF model overestimates the visibility by 3.3\u0026ndash;3.8 km at the forecast leading time of 72- hour, whereas it underestimates the visibility by 1.4\u0026ndash;2.1 km after correction, aligning more closely with the observation. Furthermore, Compared to Afan and Bayu (2021), who reduced the RMSE of visibility prediction by 15% using the ARIMA model, the MAEs of forecasts at all forecast leading times decrease by over 20% compared with the original forecasts after the correction, and the RMSEs also decrease from 10.3\u0026ndash;10.6 km to less than 10 km. In particular, the RMSEs for forecasts at the leading times of 12-hour and 24-hour drop to less than 9 km. In addition, when comparing the effectiveness of correction on visibility forecasts at different levels, the TS for visibility below 10 km has been improved from 0.23 to 0.34.Furthermore, in low-visibility scenarios (\u0026lt;\u0026thinsp;1 km), the TS value increased by 80% (from 0.05 to 0.09), significantly outperforming the fog prediction based on BP neural networks by Duddu et al. (2020) (TS\u0026thinsp;=\u0026thinsp;0.07). This indicates that the PDF method exhibits superior forecast performance in systematic error correction, especially suitable for the needs of site-by-site modeling in Xinjiang's complex terrain.Meanwhile, both the false alarm ratio and the missing ratio exhibit decreasing trends of varying degrees. It illustrates that employing the PDF matching method can effectively mitigate the overestimation in visibility forecasts by the ECMWF model, and reduce the false alarm ratio and missing ratio to some extent.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eMean error (ME), mean absolute error (MAE) and root mean square error (RMSE) of visibility forecasts at different forecast leading times by the ECMWF model before and after correction.\u003c/b\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eForecast leading time\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eME\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e3.3 (\u0026minus;\u0026thinsp;1.4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.6 (6.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.3 (8.7)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e3.5 (\u0026minus;\u0026thinsp;1.4)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.7 (6.6)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.4 (8.9)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e3.6 (\u0026minus;\u0026thinsp;1.5)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.8 (6.7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.5 (9.0)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e3.6 (\u0026minus;\u0026thinsp;1.8)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.8 (6.7)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.5 (9.1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e3.7 (\u0026minus;\u0026thinsp;2.0)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.9 (6.9)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.6 (9.1)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026minus;\" colname=\"c2\"\u003e \u003cp\u003e3.8 (\u0026minus;\u0026thinsp;2.1)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8.9 (6.9)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.6 (9.2)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003eNote: Original values of metrics outside parentheses, corrected values in parentheses (unit: km).\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2. Spatial distribution of correction effects\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the spatial distributions of the forecast errors at different forecast leading times for various stations in Xinjiang after the correction by the PDF matching method. It is evident that the corrected forecasts at most stations are closer to the observation, with the errors predominantly falling within the range between \u0026minus;\u0026thinsp;1 km and \u0026minus;\u0026thinsp;3 km. Compared with the pre-corrected visibility forecasts (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), the most obvious improvement is observed in the urban agglomerations on the north slope of Tianshan Mountains and in southern Xinjiang. The forecast errors in these two regions are in the range of 3\u0026ndash;6 km and 4\u0026ndash;8 km before correction. After the correction, the errors have been reduced obviously and the stability at different forecast leading times has been enhanced, which greatly improves the systematic overestimation of the visibility forecasts before the correction. However, for forecasts in high mountain areas (e.g., Tianchi station, Xiaoquzi station) along the Tianshan Mountains, no obvious improvement is observed, with the mean errors remaining around \u0026minus;\u0026thinsp;12 km before and after the correction. Overall, the forecast errors after correction exhibit a uniform spatial distribution, which are not affected by topography or latitude.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe distribution of IP for corrected visibility forecasts is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The results show that positive improvement is found at most stations in Xinjiang. In particular, the forecasts at stations in the urban agglomerations on the northern slope of Tianshan Mountains are obviously improved by more than 70%, while those at stations in the southern Xinjiang are improved by 50%\u0026ndash;70%. Conversely, the forecasts at stations in Yili and Tacheng exhibit relatively small or no improvement, while some negative improvement are found at stations in Altay and other areas. The correction effects within different IP intervals are further analyzed, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. It is found that the corrected visibility forecasts at 88 stations in Xinjiang exhibit positive improvement with varying degrees. Among them, the improvement effect at 57 stations exceeds 60%, accounting for 54.2% of the total number of stations in Xinjiang. It is worth noting that the improvement effect at nearly one-third of the stations in Xinjiang (34 stations) exceeds 80%. On the other hand, the visibility forecasts at 17 stations in Xinjiang show negative improvement, possibly due to the complex underlying surface or high-altitude terrain. Overall, the correction has led to obvious improvement in visibility forecasts at most stations, which can meet the requirements of meteorological departments in operational forecasting.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Case study","content":"\u003cp\u003eThe unique underlying surface and terrain conditions in Xinjiang result in great differences in climate between its northern and southern regions. To validate the correction effectiveness of the PDF matching method in various weather processes, a typical fog-haze event and a dust event are selected for comprehensive analysis and evaluation.\u003c/p\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Fog-haze event\u003c/h2\u003e \u003cp\u003eFrom December 25, 2022, to January 5, 2023, the northern slope of the Tianshan Mountains in Xinjiang was impacted by a warm high-pressure ridge in the upper layer and a weak-pressure field at surface. Meanwhile, low-level southerly winds from the back of Mongolian high pressure promotes the formation of strong temperature inversions within the boundary layer over these areas, resulting in poor vertical diffusion capacity that is conducive to the formation of foggy weather. Consequently, the visibility in Urumqi, Changji and Shihezi maintained at a relatively lower level for a long time. Most stations of the Tianshan Mountains experienced the visibility of less than 500 meters, with Urumqi City recording the lowest visibility of less than 100 meters. By January 5, the influence of cold air led to a gradual improvement in regional atmospheric dispersion conditions, bringing an end to this process.\u003c/p\u003e \u003cp\u003eDuring this fog-hazy weather process, the forecast errors of visibility by the ECMWF model at most stations are within the range of 8\u0026ndash;12 km (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea-\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). After applying the PDF matching method, the forecast errors have been reduced to 2\u0026ndash;4 km (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea-\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The MAEs have also decreased from 6\u0026ndash;12 km (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb-\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) to 3\u0026ndash;6 km (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb-\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) after the correction, with an improvement of over 60% at most stations. This indicates that the PDF method effectively reduces the ME and MAE. However, limited correction effectiveness was observed at certain high-altitude mountainous stations, such as \u0026ldquo;Xibaiyanggou\u0026rdquo; and \u0026ldquo;Tianchi\u0026rdquo; (blue markers in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea-\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), located at elevations of 1930 m and 1942.5 m, respectively. For instance, at the\u0026ldquo;Tianchi\u0026rdquo;station, the ME remained at -12.3 km after correction, compared to -12.7 km prior to correction, with similarly marginal improvements in MAE. This discrepancy is likely attributed to the complex underlying surface conditions in high-altitude regions. Although studies on visibility correction forecasts across different underlying surfaces are scarce, analogous challenges in achieving optimal corrections at high-altitude stations have been reported in previous research, such as Qian et al. (2019) \u0026rsquo;s work on wind speed correction in plains versus mountainous areas. These findings underscore the need for further investigation into terrain-specific correction methodologies to enhance model accuracy in topographically complex environments.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Sand-dust event\u003c/h2\u003e \u003cp\u003eFrom March 19 to March 24, 2023, a sand-dust weather process occurred in most regions of North China due to the combined effect of Mongolian cyclone and surface cold front. Persistent sand-blowing or dust-floating weather was also observed in most areas of southern and eastern Xinjiang, with strong sandstorms occurred in local area. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e illustrates the spatial distributions for the forecast errors and MAEs of visibility from the ECMWF model forecasts and the results corrected by the PDF matching method during this weather process. The results reveal an obvious overestimation of visibility forecasted by the ECMWF model at most stations in southern Xinjiang, with the forecast errors reaching 6\u0026ndash;10 km and the MAEs exceeding 12 km (Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea-\u0026lt;link rid=\"fig1\"\u0026gt;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u0026lt;/link\u0026gt;\u003c/span\u003e and \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb-\u0026lt;link rid=\"fig1\"\u0026gt;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u0026lt;/link\u0026gt;\u003c/span\u003e), even reaching 20 km at individual stations. After the correction by the PDF matching method, the above two evaluation metrics are improved obviously, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea-\u0026lt;link rid=\"fig2\"\u0026gt;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u0026lt;/link\u0026gt;\u003c/span\u003e and \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb-\u0026lt;link rid=\"fig2\"\u0026gt;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u0026lt;/link\u0026gt;\u003c/span\u003e, where the MAEs in most areas have been reduced to less than 6 km. In addition, the Aral City is taken as an example to evaluate the correction effect. The visibility forecasts with the forecast leading time of 30 h initiated at 0800 BT from March 18 to 21, 2023 and corresponding correction results are compared (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e). It is demonstrated that the forecasts corrected by the PDF matching method are closer to the observations, with the forecast errors below 2 km. Especially at 1400 BT on March 21, 2023, when the visibility at Aral station decreased to 2.2 km, the corrected visibility is 4.3 km, while the forecasted visibility before the correction reaches 11.1 km. This further confirms the obvious correction effect over the original ECMWF forecasts using the PDF matching method.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eBased on the visibility observations from 105 national meteorological stations in Xinjiang, the visibility forecast products of the ECMWF model within the 72-hour forecast leading time from November 2022 to March 2023 are evaluated in terms of the forecast errors. On this basis, an objectively corrected forecast product of visibility for the next three days with an interval of 3 hours in Xinjiang is established based on the PDF matching method through a rolling modeling approach. The visibility forecast results before and after correction are further evaluated and analyzed. The main conclusions are as follows.\u003c/p\u003e \u003cp\u003eThe ECMWF model tends to overestimate the visibility in most areas of Xinjiang. Specifically, the forecast errors are in the range of 3\u0026ndash;6 km in the urban agglomerations on the northern slope of the Tianshan Mountains, and within 4\u0026ndash;8 km at most stations in southern Xinjiang, with the errors even exceeding 10 km in Aksu area.\u003c/p\u003e \u003cp\u003eThe visibility frequencies within different ranges show that the observed frequencies for visibility within 1.0\u0026ndash;10 km and 0.5\u0026ndash;1.0 km are 35% and 6%, respectively, while the forecasted frequencies from the ECMWF model are only 9% and 3%. This indicates that the model forecast exhibits a characteristic of overestimation of low visibility.\u003c/p\u003e \u003cp\u003eThe PDF matching method can effectively reduce the visibility forecast errors of the ECMWF model, leading to an obvious improvement in evaluation metrics. For instance, within the 72-hour forecast period, the ECMWF model overestimates the visibility by 3.3\u0026ndash;3.8 km, while the corrected results are 1.4\u0026ndash;2.1 km lower than the observations, with the MAE reduced by over 20%. Furthermore, the TS value also increases from 0.05 to 0.09 for visibility less than 1 km after the correction.\u003c/p\u003e \u003cp\u003eIn terms of the spatial distribution of correction effectiveness, there are 88 stations in Xinjiang exhibiting positive improvement with varying degrees. These stations are primarily located in the urban agglomerations on the northern slope of the Tianshan Mountains (with improvement exceeding 70%) and in most of southern Xinjiang (with the improvement ranging from 50% to 70%).\u003c/p\u003e \u003cp\u003eFinally, the case study demonstrates the obvious improvement in visibility forecasts during a fog-haze event in northern Xinjiang and a sand-dust event in southern Xinjiang after applying the PDF matching method, where the corrected visibility forecast aligns more closely with the observations.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no conflict of interest.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eChao.Liu. and Hua. Cong. wrote the main manuscript text and Junan.Xiao. prepared figures 1-4 and all Tables. Xiaoqin. Rao. prepared figures 5-8 and Chao. Xie. checked all data.Dawei. An. prepared the references. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis research was supported by National Key R\u0026amp;D Program Pilot of China(2022YFC3701205). The authors are grateful to the anonymous reviewers for their insightful comments.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe measurement data involved in this study are available upon request.\u003c/p\u003e"},{"header":"References","content":"\u003cp\u003eAfan, G.S., Bayu K. 2021 Visibility Forecasting Using Autoregressive Integrated Moving Average(ARIMA) Models. Procedia Computer Science. 179,252-259.\u003c/p\u003e\n\u003cp\u003eAn, J.Q., Liu, H.B., Wang, X.M., et al.2022. Oxidative Potential of Size-segregated Particulate Matter in the Dust-storm Impacted Hotan, Northwest China. Atmospheric Environment. 280,119142.\u003c/p\u003e\n\u003cp\u003eChen, J., Liu, Z.X., Yin, Z.T., et al. 2023. 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Geomorphology of Sand Dunes in the Taklamakan Desert based on ERA5 reanalysis data. Journal of Arid Environmental. 207,104848. \u003c/p\u003e\n\u003cp\u003eWang, J.M., Zhou, X.L., Hua, Z.Y., et al. 2023. Concentration Level, Health Risk Assessment and Source Apportionment of Nitrosamines in PM\u003csub\u003e2.5\u003c/sub\u003e in Urumqi during Winter Time. Atmospheric Pollution Research. 14,101756.\u003c/p\u003e\n\u003cp\u003eWatson J G. Visbility: science and regulation. 2002. Journal of the Air \u0026amp; Waste Management Association, 52(6),628-713.\u003c/p\u003e\n\u003cp\u003eXie P.P., Xiong A.Y. 2011. A conceptual model for constructing high-resolution gauge-satellite merged precipitation analyses. Journal of Geophysical Research,116,D21.\u003c/p\u003e\n\u003cp\u003eYang Y.C., Ge, B.Z., Chen X.S, et al. 2021. Impact of Water Vapor Content on Visibility: Fog-haze Conversion and its Implications to Pollution Control. Atmospheric research.256.\u003c/p\u003e\n\u003cp\u003eZhang, X.X., Ding, X., Talifu, D., et al. 2021. Humidity and PM\u003csub\u003e2.5\u003c/sub\u003e Composition Determine Atmospheric Light Extinction in the Arid Region of Northwest China. Journal of Environmental Sciences. 100,279-286.\u003c/p\u003e\n\u003cp\u003eZhao, C.G., Zhao, S.R., Lin, J., et al. 2022. Visibility Forecast and Influence Factor Analysis Based on Regional Modeling. Meteorological monthly. 48(6),773-782 (in Chinese).\u003c/p\u003e\n\u003cp\u003eZhu,G.D. 2011.Multi-factor Forecast in Urumqi International Airport Based on SVM Method. Desert and Oasis Meteorology,5(4),40-43(in Chinese).\u003c/p\u003e\n\u003cp\u003eZhu, L., Zhu,G.D. 2012. Analysis on the Climatic Characteristics of Low Visibility in 30 Years at Urumqi Airport. Journal of Civil Aviation Flight University of China,23(5),27-30(in Chinese).\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":false,"email":"","identity":"aerosol-and-air-quality-research","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Aerosol and Air Quality Research","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"VoR Journals","inReviewEnabled":false,"inReviewRevisionsEnabled":false},"keywords":"Probability density function matching method, Visibility, Corrected forecast, Xinjiang","lastPublishedDoi":"10.21203/rs.3.rs-8583058/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8583058/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eVisibility greatly impacts people's daily activites, such as transportation. However, numerical models often exhibit substantial errors in visibility forecasting. The objective of this study is to reduce the systematic errors in visibility forecasting products from the European Center for Medium-Range Weather Forecasts (ECMWF), thereby enhancing the forecasting performance. Taking the visibility observations from 105 national meteorological stations in Xinjiang of China as an objective criteria, the visibility forecasts from model products of the ECMWF within the 72-hour forecast period from November 2022 to March 2023 are corrected using the probability density function (PDF) matching method. On this basis, an objectively-corrected forecasting product with an interval of 3-h is established for the next three days in Xinjiang through a rolling modeling approach, and the visibility forecasts before and after correction are further evaluated and analyzed. The results show that the visibility in ECMWF forecasts is overestimated under low-visibility conditions in most areas of Xinjiang. The PDF matching method can effectively reduce these errors, with all evaluation metrics being obviously improved after the correction. The forecasted visibility within the 72-hour forecast period before correction is 3.3\u0026ndash;3.8 km higher than the observation, while it is 1.4\u0026ndash;2.1 km lower than the observation after correction, with the mean absolute error being reduced by over 20%. For forecasts of visibility below 1 km, the threat score increases from 0.05 to 0.09 after correction. Spatially, 88 stations across Xinjiang exhibit positive improvement with varying degrees, mainly concentrated in the urban agglomerations on the northern slope of Tianshan Mountains (with the improvement exceeding 70%) and in most areas of southern Xinjiang (with the improvement ranging from 50% to 70%). Additionally, the analysis of typical fog-haze and sand-dust weather processes further reveals that the visibility corrected using the PDF matching method becomes much closer to the observations, providing more accurate references for visibility forecasting of Xinjiang meteorological departments.\u003c/p\u003e","manuscriptTitle":"Application of Probability Density Function Matching Method for Visibility Forecasting in Xinjiang of China","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-02 17:17:55","doi":"10.21203/rs.3.rs-8583058/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-14T00:44:41+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-13T09:35:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"321363010241214787367594711515577270323","date":"2026-02-28T03:23:44+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-03T03:54:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"80622978492953361031324906398464911160","date":"2026-02-01T19:44:40+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-30T16:53:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-13T04:26:44+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-13T04:26:41+00:00","index":"","fulltext":""},{"type":"submitted","content":"Aerosol and Air Quality Research","date":"2026-01-12T14:43:22+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":false,"email":"","identity":"aerosol-and-air-quality-research","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Aerosol and Air Quality Research","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"VoR Journals","inReviewEnabled":false,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"6a657af3-5c5f-4299-8d73-05c2af4aec12","owner":[],"postedDate":"February 2nd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-17T04:53:32+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-02 17:17:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8583058","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8583058","identity":"rs-8583058","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}