The California Indian Museum is one of 79 institutions across the country that have received grants from the new Frankenthaler Climate Initiative — named for the abstract expressionist Helen Frankenthaler and created by her foundation this year. To be authoritative voices on climate, museums also must build trust by dealing with their own impact. That trust begins with the little things — eco-friendly light fixtures, sustainable waste management — and builds when museums show they will be there when natural disasters strike.