1. A marine well with shallow-water flow monitoring for monitoring marine shallow-water flow from an open hole section of the marine well during marine drilling operations using a drilling rig, wherein the marine well with shallow-water flow monitoring comprises: a. a video feed of the open hole section from a video capture device proximate the open hole section; b. an analysis processor connected to a network and the video feed; c. an analysis data storage, wherein the analysis data storage comprises a non-transitory computer readable medium, connected to the analysis processor; d. computer instructions in the analysis data storage to receive a mud pumps off time from mud pumps on the drilling rig connected to the analysis processor when the mud pumps are turned off and drilling fluid no longer flows to the open hole section of the marine well; e. computer instructions in the analysis data storage to receive and store the video feed in the analysis data storage; f. a discharge category model in the analysis data storage providing a plurality of discharge categories of shallow-water flow for the open hole section of the marine well; g. computer instructions in the analysis data storage for comparing the video feed during a first time period from a first mud pumps off time to the plurality of discharge categories in the discharge category model, identifying a discharge category from the discharge category model that most closely matches the video feed during a first time interval, and designating the discharge category as a baseline discharge category for the open hole section while simultaneously calculating from the video feed and the first mud pumps time off, a quantity of time required to achieve the baseline discharge category; h. computer instructions in the analysis data storage for comparing the video feed during a subsequent time period from a subsequent mud pumps off time to the plurality of discharge categories in the discharge category model, identifying a subsequent discharge category from the discharge category model that most closely matches the video feed during a subsequent time interval, while simultaneously calculating from the video feed and the subsequent mud pumps time off and a quantity of time required to achieve the subsequent discharge category; i. computer instructions in the analysis data storage to compare the subsequent discharge category from the subsequent time period to the baseline discharge category, and if the baseline discharge category is different or if the time period required to achieve the subsequent discharge category is different than the computer instructions designate the subsequent discharge category as the baseline discharge category; j. computer instructions in the analysis data storage to use data feeds from at least one of a seismic profile data feed, a logging while drilling data feed, a measurement while drilling data feed, and a drilling parameters data feed to determine if anticipated changes or changes within acceptable limits have occurred in data parameters of the marine well that are not related to shallow-water flow and to verify that the subsequent discharge category should be designated as the baseline discharge category; k. computer instructions in the analysis data storage to form an alert when the subsequent discharge category differs from the baseline discharge category or if the subsequent time period to achieve the subsequent discharge category is different than the first time period, and no anticipated changes or changes within acceptable limits have occurred in data parameters of the marine well according to at least one: the logging while drilling data feed, the seismic profile data feed, the drilling parameter data feed, and measurement while drilling data feed; and l. computer instructions in the analysis data storage to transmit an alarm to the network and to client devices in communication with the network for immediate action.