The National Weather Service

 - Wikipedia entry.

Here's info from the entry's section on its history. It has bounced around from department to department: 

In 1870, the Weather Bureau of the United States was established through a joint resolution of Congress signed by President Ulysses S. Grant with a mission to "provide for taking meteorological observations at the military stations in the interior of the continent and at other points in the States and Territories...and for giving notice on the northern (Great) Lakes and on the seacoast by magnetic telegraph and marine signals, of the approach and force of storms." The agency was placed under the Secretary of War as Congress felt "military discipline would probably secure the greatest promptness, regularity, and accuracy in the required observations." Within the Department of War, it was assigned to the U.S. Army Signal Service under Brigadier General Albert J. Myer. General Myer gave the National Weather Service its first name: The Division of Telegrams and Reports for the Benefit of Commerce.

Cleveland Abbe – who began developing probabilistic forecasts using daily weather data sent by the Cincinnati Chamber of Commerce and Western Union, which he convinced to back the collection of such information in 1869 – was appointed as the Bureau's first chief meteorologist. In his earlier role as the civilian assistant to the chief of the Signal Service, Abbe urged the Department of War to research weather conditions to provide a scientific basis behind the forecasts; he would continue to urge the study of meteorology as a science after becoming Weather Bureau chief. While a debate went on between the Signal Service and Congress over whether the forecasting of weather conditions should be handled by civilian agencies or the Signal Service's existing forecast office, a Congressional committee was formed to oversee the matter, recommending that the office's operations be transferred to the Department of War following a two-year investigation.

The agency first became a civilian enterprise in 1890, when it became part of the Department of Agriculture. Under the oversight of that branch, the Bureau began issuing flood warnings and fire weather forecasts, and issued the first daily national surface weather maps; it also established a network to distribute warnings for tropical cyclones as well as a data exchange service that relayed European weather analysis to the Bureau and vice versa. The first Weather Bureau radiosonde was launched in Massachusetts in 1937, which prompted a switch from routine aircraft observation to radiosondes within two years. The Bureau prohibited the word "tornado" from being used in any of its weather products out of concern for inciting panic (a move contradicted in its intentions by the high death tolls in past tornado outbreaks due to the lack of advanced warning) until 1938, when it began disseminating tornado warnings exclusively to emergency management personnel.