Abstract. We propose a new paradigm to describe the temporal evolution of continental fog layers. This paradigm defines fog as a layer saturated from the surface to a known upper boundary, and whose liquid water path (LWP) exceeds a critical value, the critical liquid water path (CLWP). When the LWP is less than the CLWP the fog water cannot extend all the way to the surface, leading to a surface horizontal visibility greater than 1 km. On the opposite, when the LWP is larger than the CLWP, the fog water extends all the way to the surface, inducing a horizontal visibility less than 1 km. The excess water with respect to the critical value is then defined as the reservoir liquid water path (RLWP). The new fog paradigm is formulated as a conceptual model that relates the liquid water path of adiabatic fog with its thickness and surface liquid water content, and allows the critical and reservoir liquid water paths to be computed. Both variables can be tracked in real time using vertical profiling measurements, enabling a real time diagnostic of fog status. The conceptual model is tested using data from seven years of measurements performed at the SIRTA observatory, combining cloud radar, microwave radiometer, ceilometer, scatterometer and weather station measurements. In this time period we found 80 fog events with reliable measurements, with 56 of these lasting more than three hours. The paper presents the conceptual model and its capability to derive the LWP from the fog CTH and surface horizontal visibility with an RMS uncertainty of 10.5 g m−2. The impact of fog liquid water path and fog top height variations on fog life cycle (formation to dissipation) is presented based on four case studies, and statistics derived from 56 fog events. Our results show in particular that the reservoir liquid water path is consistently positive during the mature phase of the fog and that it starts to decrease quasi monotonously about one hour before dissipation, reaching a near-zero value at the time of dissipation. The reservoir liquid water path and its time derivative could hence be used as an indicator for life cycle stage and support short range forecasting of fog dissipation.
A METHOD OF REAL-TIME NURBS INTERPOLATION WITH CONFINED CHORD ERROR FOR CNC SYSTEMS
