Wash watermelon and slice into 2 inch slices.  Remove rind from all slices.  Trim slices into triangular pieces that will fit nicely on a salad plate.  Season each slice with salt.  Brush one side of each slice with olive oil.  Heat a large skillet over medium-high heat.  When hot, place watermelon slices, oiled side down, on the hot skillet an grill until browned.  With a large spatula or tongs, remove the slices and place heated side up on a chilled plate.  Put the reserved watermelon in a sieve over a bowl and squeeze watermelon pieces with your hands, collecting juice in a bowl below.  Measure out 1 cup of juice.  In a saucepan, combine vinegar and watermelon juice and bring to a boil over medium heat.  Reduce heat and simmer uncovered for about fifteen minutes or until reduce to about 1/4 cup.  Pour the reduced juice into a serving bowl and whisk in the remaining olive oil.  Season to taste with salt and pepper.  Add the arugula, almonds, scallions and radishes and toss well.  Gently mound the salad over melon slices and serve.