## 1 Introduction  
The roadway capacity is one of the most important variables in the dynamics of traffic flow. Determining capacity is critical in dynamic traffic management and control strategies. It also has implications in planning, design, and operations together with other traffic flow variables. It has been widely observed that when oversaturation starts, queues ensue, and vehicles discharge from the bottleneck at a rate lower than the pre-queue flow. This is known as the \"the capacity drop phenomenon\", as defined by the Highway Capacity Manual [1]. The capacity value is often considered constant, which represents the maximum traffic a roadway facility can carry. The Highway Capacity Manual (HCM) is a publication frequently used by researchers, academics, and transportation practitioners to estimate capacity. Freeway segment capacity is defined as \"the maximum flow rate associated with the occurrence of some type of breakdown, which results in lower speeds and higher densities\" [1]. With this, HCM calculates capacity as a function of free flow speed (FFS). Capacities presented in the manual are under base conditions and can be adjusted through capacity adjustment factors (CAF) and speed adjustment factors (SAF). Capacity concepts are directly related to flow, and HCM mentions three types of flow, namely oversaturated flow, undersaturated flow, and queue discharge rate. In the HCM methodology, a breakdown in the bottleneck is \"the sudden drop in speed of at least 25%below the free-flow speed (FFS) for a sustained period of at least 15 min that results in queuing upstream of the bottleneck\" [1]. The bottleneck is considered to have recovered when speeds return to 10% of the pre-queue speed and are sustained for at least 15 min. Over the years, a number of studies have examined the effects of adverse weather conditions on road traffic with a focus on pre-breakdown flow rates and maximum flow rates. It has been found that weather conditions, especially precipitation rates, incur detrimental effects on traffic flow variables. HCM incorporates weather adjustment factors to base capacities. The flow in a highway segment is a function of the speed of the traffic stream and the density. Under bad weather conditions, drivers tend to decrease speed and increase the distance between them and the next vehicle in front. Actions such as these could reduce maximum flow and corresponding traffic intensities. For this reason, it is important to incorporate traffic management strategies and techniques in response to bad weather conditions. While there have been many studies considering the effect of weather on pre-breakdown flows, this has not been considered at all for queue discharge rates. In fact, it was not until the 2016 HCM edition that the queue discharge rates were incorporated in the Highway Capacity Manual based on the paper of [PERSON], [PERSON], and [PERSON] [2]. Once the breakdown occurs and queues begin to form, the flow rates discharging from the queue at the bottleneck are generally lower than the pre-breakdown capacity. This post-breakdown or queue discharge flow rate is defined as the 15 min flow rate during oversaturated conditions. The difference between queue discharge flow rate and pre-breakdown capacity varies considerably in the literature, with an average value of about 7% according to [PERSON], [PERSON], and [PERSON] [2], and this is used in the HCM as a default value for the capacity drop. This reduced capacity is used in the oversaturated analysis procedure to estimate the rate at which queues will form and dissipate once demand exceeds capacity. When the queue is cleared, the segment's original pre-breakdown capacity is restored. [PERSON] [3] was one of the first to suggest the capacity drop phenomenon, but there are earlier papers, such as [PERSON] and [PERSON] [4], who did not mention the phenomenon of the capacity drop but were able to fit a fundamental diagram that has a gap based on the experimental data they have taken in the Lincoln Tunnel in New York City.