Did you try over-writing the 'runs' property of each object? If you said floors[0].runs = [] (or floors[i].runs = [], if you're looping through), then those two empty arrays would no longer show up in your stringify.

Editing my answer, to match the OP edits:

floors.forEach(function(floor){
   var newRuns = [];
   floor.runs.forEach(function(run){
       if (run.length > 0){
           newRuns.push(run);
       }
   })
   floor.runs = newRuns;
})

After I assign your object from the OP into a variable and run my code on it, then stringify the result, I get this as a return:

{"floors":[{"floorName":"Grd Floor","floorNotes":"","floorPlan":"Buckley_Grd.jpg","floorWidth":"57.392","floorHeight":"20.776","runs":[[{"xCoOrd":"37.88235294117647","yCoOrd":"59.307359307359306","drawingType":"node"},{"xCoOrd":"37.88235294117647","yCoOrd":"59.307359307359306","drawingType":"node"},{"xCoOrd":"48.549019607843135","yCoOrd":"50","drawingType":"node"}]]}]}

Is that what you're hoping to see? I used this fiddle to produce that result.

Runs is a property of an object, you can remove items from that array. In your example above floors[0].runs.splice(0,2), should remove both of those arrays I think.

Keeping the same reference

Iterating downwards lets you safely perform operations which decrease the length of an Array by 1 each time

var i, parentArray = obj['floors'][0]['runs'];
for (i = parentArray.length; i >= 0; --i) {
    if (parentArray[i].length === 0) parentArray.splice(i, 1);
}

Making a new reference

Creating a new array without the values you don't want can be achieved using .filter

obj['floors'][0]['runs'] = obj['floors'][0]['runs'].filter(function (x) {
    return x.length > 0;
});

To remove an object completely you have to remove the reference from the parent. To do this what you can do is create a new Array in which you copy only the references to the non-empty arrays.

I have created this function which should remove all empty arrays. I haven't tested it too much, but this should give you an idea:

function clearEmptyArrays(obj) {
   for(var key in obj) {

    var arr = obj[key];

    if(Array.isArray(arr)) {
      // Iterate through all elements and remove empty arrays
      var nonEmptyArr = [];
      for(var i = 0; i < arr.length; ++i) {
        // Recursive call if it's an object inside an array
        if(typeof arr[i] === 'object') clearEmptyArrays(arr);

        // Save all non-empty arrays or objects inside this one
        if((Array.isArray(arr[i]) && arr[i].length > 0) || !Array.isArray(arr[i])) {        
            nonEmptyArr.push(arr[i]);
         }
      }

      obj[key] = nonEmptyArr;
      return;
    }

    // Recursive call if it's an object
    if(typeof arr === 'object') {
        clearEmptyArrays(arr);
    }
  }
}

You can call it like this: clearEmptyArrays(myObj); and will update the Object in-place.

Demo: https://jsfiddle.net/zeo7dauh/