In a large saucepan, bring the water to a boil. Remove from the heat. In a food processor, puree the ginger with 1 tablespoon of the hot water. Add the pureed ginger to the remaining hot water and let stand for 1 hour. Pour through a fine strainer into a glass jar. Add the lime juice and light brown sugar and stir well. Cover and refrigerate for up to 3 weeks.