Simulating Z–LWC Relations in Natural Fogs with Radiative Transfer Calculations for Future Application to a Cloud Radar Profiler

Abstract

The vertical distribution of liquid water content (LWC) in natural fog and low stratus is a crucial variable in many applications, e.g. the development of satellite based retrievals of ground fog. Unfortunately, there is very little data concerning fog LWC-profiles, mainly due to the lack of suitable operational instrumentation. A novel ground-based 94 GHz FMCW cloud radar could fill this gap if radar reflectivity Z could be converted to LWC by using appropriate Z-LWC relations. However, this relation strongly depends on drop size distribution (DSD) and is hardly known for natural fog types. In this sensitivity study, the influence of the DSD on the Z-LWC relation in different types and life cycle stages of natural fogs is analyzed using a radiative transfer code (RTC) and published fog drop size distributions. It could be shown that there is a direct but nonlinear relationship between LWC and radar reflectivity. The proportionality factor of the Z-LWC equation in particular reveals specific ranges for the different life cycle stages. If a proper classification of fog life cycle in the field is possible, the results could be used to properly convert Z to LWC.

The Influence of Drop Size Distributions on the Relationship between Liquid Water Content and Radar Reflectivity in Radiation Fogs

“…On the other hand, the mature stage showed Ω values that rarely exceeded 1.43 × 10 2 g/mm 6 /7.27 × 10 2 g/mm 6 (5 % and 95 % confidence interval), which indicates that most DSDs were characterized by large mode radii and a flat overall curve during this stage. The range of Ω values, which declined from formation (7.00 × 10 2 g/mm 6 to 8.00 × 10 2 g/mm 6 ) through mature fog (4.00 × 10 2 g/mm 6 to 5.00 × 10 2 g/mm 6 ) to dissipation (0.00 g/mm 6 to 1.00 × 10 2 g/mm 6 ), is comparable to the results of Maier et al [4].…”

“…Following former studies related to fog DSD, the MGD is appropriate for reliably representing the various DSDs during the respective development stages of radiation fog events, e.g., Tampieri and Tomasi [48], Tomasi and Tampieri [49] and Maier et al [4]. However, studies related to DSD of raindrops indicated that even the three-parameter MGD shows limitations comparing the modeled to the measured DSDs, e.g., Joss and Gori [50], Ulbrich [51] and Adirosi et al [38].…”

“…Furthermore, it would be difficult to relate the differing Z-LWC relationship directly to the high temporal DSD dynamics during fog development. By using the derived MGD parameters, the comparison with other studies, e.g., Maier et al [4], Harris [40], Tampieri and Tomasi [48], Tomasi and Tampieri [49] and Maier et al [30] is facilitated. Nevertheless, the difference between both procedures should be investigated in future studies, using more continuous DSD measurements during different radiation fog events.…”

“…r α+6 e −br γ dr (A13) which, after integrating over the range of radii (see Equation (A9)), yields in [4]:…”

“…Operational spatio-temporal observation is hampered by the sparse density of existing observation networks, especially in complex terrain [4,5]. To tackle this problem, different methods for operational fog forecasting and nowcasting have been developed in the past (see Gultepe et al [6] for an overview).…”