Patrick Sunday is a character only involved in the first Endless Ocean game. However, he does not make an appearance in person and is only mentioned by NPCs.
[WARNING: This article contains spoilers relevant to the main story in Endless Ocean.]
Patrick Sunday was a marine biologist enamored with the legends of the White Mother (Ancient Mother in the American version), an ancient whale-being said to swim the waters of the Manoa Lai Sea (Manaurai Sea in the European release). He dedicated his life to finding this whale-god, despite the ridicule he endured from other scientists who did not believe in the legends told of the White Mother, and unfortunately died without ever fulfilling his dream of proving the White Mother's existence to the scientific community, and indeed the world itself.
Katherine Sunday (Catherine Sunday in the European version) is the only known surviving relative of Patrick. Katharine is Patrick's daughter, and she was hit hard with the news of her father's death. She then decided to continue in her father's footsteps, making it her goal to prove the White Mother's existence to be true and thus validating all of her father's struggles, ensuring that his death while searching for the White Mother wouldn't be in vain. She eventually succeeds and, with the help of the player, finally realizes her dream, and Patrick's before her.
Although it is not directly stated, it is highly suggested that, while searching for signs of the White Mother in the perilous Green Garden, he became entangled in the death trap that is the kelp population that gives the Garden its name. Katherine only states that he dove in the Green Garden one day and never came back, insinuating that this dive to the Garden was Patrick's last. (The player also narrowly escapes this fate when they are planting the devices used to help detect the White Mother. They become entangled in several fronds of kelp, but they escape with the help of their dolphin partners, and Katherine berates the player for not being more careful, supposedly because she did not want to lose another friend or family member to the Garden.)
This theory is further cemented when the player, late in the storyline, travels to to the Green Garden on the advice of a fellow diver who had noticed that Katherine was acting strangely and suggested that she had a connection to the Garden, prompting the player's investigation. The player then finds Patrick's Pocket Watch, which prompts Katherine to open up more about her past and the loss of her father, and why it is her dream to find the White Mother in the first place.