We developed the “REAL-Fog” (R‑Estimated spatiAL Fog) tool to calculate the ground-level fog by means of liquid water content (lwc) at a temporal resolution of 1 hour. The tool is based on a distributed and mainly physical model and requires a digital elevation model (DEM) and hourly observations of temperature and humidity. The tool spatially interpolates the air temperature and derived vapour pressure to determine whether the air at ground level is supersaturated. From the supersaturation result, the lwc is then calculated. Due to errors in the measured humidity time series, preprocessing is additionally recommended. Different sources of errors, such as sensor ageing, calibration and sensor uncertainty, are discussed, and a correction method is proposed. The “REAL-Fog” method was applied in a case study of Germany from 1949 to 2017. The daily updated results of this analysis can be found at www.nebelzentrale.de. Two validation strategies are applied. First, modelled lwc values are compared with measured lwc values at Mt. Brocken (1141 m a.s.l.), which is one of the longest time series of lwc in the world and the longest in Germany. The event-based (fog, no fog) Heidke skill score (HSS) reached 0.8. Second, the event-based performance was calculated for 306 visibility sites in Germany. HSS was found to be 0.54.

中文翻译：

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REAL-Fog：一种计算地面大气中雾的简单方法

我们开发了“ REAL-Fog”（R估计的空间雾）工具，以液态水含量（lwc）在1小时的时间分辨率下计算地面雾。该工具基于分布式且主要是物理模型，并且需要数字高程模型（DEM）以及每小时的温度和湿度观测值。该工具在空间上对空气温度和导出的蒸气压进行插值，以确定地面上的空气是否过饱和。根据过饱和结果，可计算出lwc。由于所测量的湿度时间序列存在误差，因此建议另外进行预处理。讨论了错误的不同来源，例如传感器老化，校准和传感器不确定性，并提出了一种校正方法。1949年至2017年，“ REAL-Fog”方法应用于德国的案例研究。该分析的每日更新结果可在www.nebelzentrale.de上找到。应用了两种验证策略。首先，将模型化的lwc值与Mt处测得的lwc值进行比较。Brocken（1141 m asl），是世界上最长的lwc时间序列之一，也是德国最长的时间序列之一。基于事件（无雾，无雾）的海德克技能得分（HSS）达到0.8。其次，针对德国306个可见性站点计算了基于事件的性能。发现HSS为0.54。基于事件的效果是针对德国306个可见度站点进行计算的。发现HSS为0.54。基于事件的效果是针对德国306个可见度站点进行计算的。发现HSS为0.54。