waterfill

var calculate = function( arr ) {
    var air_sum = 0;
    var ground_sum = 0;

    var last = arr.length - 1;
    var left_max  = arr[0];
    var right_max = arr[last];

    for ( var i = 0; i <= last; i++ ) {
        var el = arr[ i ];
        if ( left_max < el ) {
            air_sum += ( el - left_max ) * i;
            left_max = el;
        }

        el = arr[ last - i ];
        if ( right_max < el ) {
            air_sum += ( el - right_max ) * i;
            right_max = el;
        }

        ground_sum += el;
    }

    var full_sum = left_max * arr.length;

    return full_sum - air_sum - ground_sum;
};

// testing
[
    [[0,0,0,10,0,0,0,0,0],0],
    [[0,1,0,10,0,0,0,0,0],1],
    [[1,0,1], 1],
    [[5,0,5], 5],
    [[0,1,0,1,0], 1],
    [[1,0,1,0,1,0,1,0], 3],
    [[1,0,1,0], 1],
    [[1,0,1,2,0,2], 3],
    [[2,5,1,2,3,4,7,7,6], 10],
    [[5,1,0,1], 1],
    [[2,5,1,2,3,4,7,7,6,3,5], 12]
].forEach(function( el ) {
    if( calculate( el[0] ) !== el[1] ) throw( el );
});