Landmark Communications Inc., the Norfolk newspaper, broadcasting and cable television concern, today announced plans to spend more than $20 million to develop a 24-hour, all-weather cable TV network.

The cable channel will be run by a unit of Landmark, which has hired John Coleman, weatherman for American Broadcasting Co.'s "Good Morning America," to be the subsidiary's chairman and president. Coleman will appear on both shows beginning in September 1982.

The project will be known as "The Weather Channel," which Landmark Chairman Frank Batten said at a press conference here would be on the air next spring, joining 24-hour sports and news networks on cable television systems.

Explaining the market for the service and quoting studies done for the company, Batten said that about half the population seeks weather information twice a day, while a third looks for a weather forecast five times a day. Coleman said the studies indicate viewers will spend an average of six minutes watching the network.

"We will save lives, and when times get tough we will be there," Coleman said. "We will improve the quality of American life. If it's going to rain on your parade, we don't want it to be a surprise." Batten predicted the new, advertiser-supported network would be "the most popular channel on cable TV."

The service will be both national and local, with local forecast appearing in text and other forms during the programming and will have a staff of 21 meteorologists.

Two weeks ago, Landmark announced the $10.5 million purchase of transmission space on an RCA satellite, Satcom I, from Premiere, a joint venture involving movie companies and Getty Oil Co.