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The range of visibility largely depends upon the meteorological parameters. A visibility parameter, termed as visibility potential parameter (VPP) is proposed to estimate minimum potential visibility (MPV) during foggy morning. The parameter is defined as the product of two variables, namely temperature, and the inverse of relative humidity. The whole VPP range (0.5-8.5) is divided into sixteen groups from lowest group (0.5-1.0) to highest group (8.1-8.5). The analysis of VPP for the Indira Gandhi International (IGI) Airport, New Delhi (India) shows that all the very dense (visibility:< 50 m) fog cases and 98.8% of dense fog (visibility: 50-199 m) cases occurred in the lowest two groups of VPP (0.5-1.0) and (1.1-1.5). The entire moderate (visibility: 200-499 m) fog cases and 93.5% of shallow (visibility: 500-999 m) fog cases occurred in the lowest three VPP groups. The probabilities of occurrence of fog for the lowest three VPP groups are 61%, 43.5%, and 25.9% respectively. The empirical relationship between VPP and MPV is found to be linear. Rapid update of initial error in statistical post-processing (RUPP) forecast is also proposed for improvement of visibility forecasts. The improvement of error ranged from 20% to 87.7% for forecast update period from 1200 UTC to 0000 UTC. Results of this study show that the MPV could provide useful guidance to forecasters about the possible lowest visibility, and use of recent trend than mean trend of past visibility with respect to VPP and successive removal of error structure in the forecast trajectory can improve the forecasts.