Place the watermelon turnip slices in the jar. Peel the hard skin from the broccoli stalks and discard skin. Thinly slice the stalks on a diagonal and place in the jar.
Combine the water and ume vinegar and pour over the vegetables. Place a piece of cheesecloth over the mouth of the jar and secure with the jar's o-ring, an elastic band, or string.
Let sit on the counter overnight. Remove cheesecloth, place the cap on and refrigerate. Remove 2 or 3 pieces daily and serve with meals as desired. Keep for 1 month refrigerated.
Per serving - 4 calories, 0 g fat (8% calories from fat), 0 g protein, 1 g carbohydrate, 1 g fiber, 0 mg cholesterol, 418 mg sodium