Purée the watermelon and ginger in a food processor or blender. Push the mixture through a fine sieve into a bowl or jug, using a whisk to force out as much liquid as you can. Add the orange juice, lime juice and sugar to the bowl and whisk to combine and to dissolve the sugar. Half fill glasses with ice cubes and pourin enough watermelon mixture to fill each glass three quarters full. Top up with the soda water and serve.