I'll preface this article by saying that it's going to be SUPER NERDY. I'm totally fine with that. I've always been nerdy and I'm sure I always will be. Oh..yeah - there's going to be some math (or "maths" as the British say) - but not too much I promise. OK here goes:
I work for an architecture firm located in the West End of downtown Dallas. We are currently constructing an expansion to our existing building. It's fascinating to watch the progress to say the least. As I was taking a short break from work this afternoon, I found myself looking out the window from my desk watching the flurry of construction activity below. I quickly noticed something which instantly drew my attention away - clouds! It's not like clouds are anything new, BUT we've been under a fairly dry weather pattern lately - so much so that clouds have been few and far between. Some folks love that kind of weather. Call me crazy, but I'm the opposite. Give me clouds! Give me storms! Anytime I can look outside and see clouds, I'm happy. But I wasn't expecting to see clouds today, except maybe a few cirrus here and there. At this point you're thinking - wow! - those must be some cool clouds. Well, no. They weren't cool There were just there. I'm sure they were unnoticed by 99.9% of everyone else. But they were there nonetheless! And I saw them. Here's was my view. See them - waaayyy off in the distance....
Told you it was boring! But it got me thinking - I wonder if I can see these on satellite? You see, since my last post, a new weather satellite called GOES-16 has gone into operation. This satellite is AWESOME - providing very high-resolution images in a much faster time than the previous generation of weather satellites. It also can take 1-minute increment snapshots, giving a whole new way to experience cloud animations. It's an amazing tool to say the least. Pulling up the view for North Texas yielded this.
To the untrained eye, this may not look like much. Here's an annotated version.
As you can see from my vantage point (near "DFW"), the clouds I saw were nearly to the Red River!! This really surprised me. I didn't think they would be that far north. Naturally, that led me to my next question - how far away are they? As you can see from the satellite picture, lakes around the DFW region show up dark - which means they can be very easily identified by their shape. Assuming the clouds I photographed earlier were the same ones I circled above in yellow, then I determined that they were a bit further north of Lake Ray Roberts. Thanks to Google Maps, it made measuring the distance pretty easy.
Based on the satellite view and Google Maps, I estimated that the clouds in the picture were approximately 54 miles away. But that's just in one direction. I wondered if there was a way to calculate their heights? This is where the math (and a little imagination) comes in! Imagine if you will, 3 points in space - me (the observer), a point roughly 54 miles distant, and directly above that a point representing the clouds. In essence what I've just described is a RIGHT TRIANGLE. BINGO! Can't see it? Check this out....
In this view, my unknown value "X" is the height of the clouds. This is what I need to solve for. Given the 3 points I mentioned earlier, we can use trigonometry (more specifically the TANGENT operation) to estimate what the heights would be. However I would still need to estimate one other piece of the equation - the angle of the clouds above the horizon - as seen from my perspective. After looking up some crude ways of measuring degrees using my hands (I must have looked like a real tool holding out my hands toward the window!!!) I came up with my guess of 7 degrees. I now had all I need to work out the problem. Here's what I jotted down.
6.63 miles. This was my guess. Was I right? Beats me!! I had no real way of knowing. But like I was taught in school - go back to make sure your answer makes sense. Ok. Sure. Um..how? Oh yeah - SOUNDINGS!
I won't get into the nitty gritty of soundings here (I've written about them in previous posts) but I will briefly say that soundings are a tool which give a good idea of the vertical make up of the atmosphere by using a weather balloon to measure data like temperature, dewpoint, winds, etc.
A few clicks later yielded this...
Remember that the bigger distance between the red (temperature) and green (dew point) lines, the drier the atmosphere is at that given point. The above sounding indicates very dry air in place - much too dry to support clouds.
BUT
Look here...
This is the area on the entire sounding where the 2 lines are closest - just above the 9 KM line and is the area where clouds would be most likely to be. I switched over to the raw data view to see the numerical values which form the basis of these lines. I was looking for the line which contained the smallest separation between the temperature and dewpoint - something called the dewpoint depression.
And there it is - 286 mb - or 9770 meters above the ground. But how does that tie into my guess of 6.63 miles? For that, it's just a matter of conversion:
My guess of the height of clouds: 6.63 miles = 10669.95 meters
Sounds data indicating likely area of clouds = 9770 meters
Difference? 900 meters. Just under 1 KM! WOW! Not a bad guess overall for just looking out the window.
-Andrew
