 Hi everyone. I am here today to talk to you about accumulated degree hours. My name is Cameron Cockman. I have a Bachelor's of Science in Mathematics from NC State and I'm kind of a math guy, so that's what I'm here to talk about. So let's go ahead and jump into it. So we are talking about accumulated degree hours, or sometimes accumulated degree days. The degree hour is a unit of heat time. So what is heat time? It's kind of a weird thing. Heat time is a measurement of area. So think about it as if you are measuring a piece of wood laid out on the floor. But instead of putting length and width, we use temperature and time. So let's look at an application that everybody can understand. Make it simple. Cooking. If we want to bake a potato and we put it in the oven for an hour and it's 400 degrees, that will probably cook it. So here's a graph of the temperature and the time on two axes showing in a rectangle. And that's going to cook the potato. But what if we tried it another way? What if we set the potato outside in the sun where it's 100 degrees for four hours? But wait a second. Those graphs have the same area. Is that going to cook a baked potato sitting outside in the heat for four hours? Probably not. So why not? The difference between the two are thresholds. At a certain temperature, baked potatoes or potatoes in general will start cooking in an oven. But sitting outside in a hot summer day, they're not going to get to that threshold temperature to begin the process of cooking. So just for fun, what if we take this example one step further and put the potato on the surface of the sun? What's going to happen to the potato? Well, it's going to burn very quickly. So there's another threshold too, the threshold between cooking and immediately burning and disintegrating. So that's something to consider as well. So how does this apply to entomology and bugs and that sort of thing? Well, bugs like a potato cook essentially. They, in their growth stages, will need a certain threshold temperature in order to grow into the next larval stage and advance on to adulthood and things. All right, so here we have a graph of a typical two week period. And you can see the rise and fall of the temperatures and those are day and night cycles. So when a bug grows, it has to deal with these changing in temperatures. So we're going to zoom in and look at a typical day where it starts off cool, getting cooler as it gets in the early morning. Then the sun comes up, it gets warmer, and then the sun starts going down and it starts cooling off again. That is a typical day. So what we now have to examine is these bugs have a threshold temperature at which point their growth becomes possible. So if you know that threshold, they won't grow. So we look at a typical day and we say, okay, well, it's going to pass above that threshold. The threshold here is marked as 66 degrees and drawn with the red line. So the threshold here is we need to know how much area is above this curve. And if you've taken calculus, you know it's possible to calculate this. But it's unwieldy and typically temperatures jump around a lot more than this smooth curve in this example. So we need to know, we need to estimate the area of this space on a typical day. So what we do is we just estimate it. We throw in an average temperature. We subtract out the threshold value that we know for bugs that's given to us in most cases. And then we multiply that by the time to calculate the area above that curve. So we can do this for days, we can do this for hours, whatever time we need to do it for, we're just trying to calculate the area of a box. It's as simple as that. So let's move on to the first example. Let's imagine a bug. It doesn't matter what bug it is, we're just doing it as a test case. And we know this bug has a threshold temperature of 58 degrees. Below 58 degrees, the bug just won't have any growth, it won't advance in its larval stages, it won't be active at all. But above 58 degrees, it'll grow, it'll advance in its larval stages, that sort of thing. We know that its eggs were left outside on a day where the high was 68 degrees and the low was 54. So we have that passing through that threshold temperature. So we know that it's going to be sometime above that temperature, sometimes below it. So how many degree hours did this bug receive on the first day? Well, we just plug it into the formula that we're given. So it's 68 degrees minus 54 degrees, excuse me, divided by 2 to find the average temperature. Simple as that, which is 61. Our threshold is given to us is 58. So we subtract those two and multiply by 24 to give 72 degree hours or 3 degree days. It doesn't really matter, they're both the same. You multiply 3 degree days by 21 or 24, then you're given 72 degree hours. Simple as that. So the second day, it was warmer with an average temperature of 64 degrees. So we do the exact same thing as before to get that it was 144 degree hours on the second day. But that's not the accumulated degree hours. So we need to accumulate those two values, so we add them together. 72 plus 144 equals 216 accumulated degree hours at the end of the second day. So that's the method we calculate when we know what bug we have to deal with and how many degree hours it's taking to do things and how many degree hours it's getting. Unfortunately, a lot of the time we won't know that exact data. We don't know the time, we're given the bug, we know the threshold temperature and we know the temperature of the conditions it was in, but we don't know how long the bug has been there. So we need to do this process in reverse. So forensic entomologists typically will be given the information of a certain stage of growth, weather information and the threshold temperatures, which have been tested in a lab. So let's look at example two. A body is found with a specific maggot on and around it in the second instar stage and that is simply its second stage of growth. The body was indoors at a constant 72 degrees Fahrenheit. Well that's convenient. We don't have to worry about taking an average temperature or worrying about highs and lows. And we know the bug's threshold temperature was at 64 degrees. It is also known that it takes at least 320 accumulated degree hours for the bug to reach its second instar stage and 480 accumulated degree hours to reach the third instar stage. So then we can ask the question, how long has the body been there? So once again we just plug into our equation. This time we leave time as a variable and we're given the accumulated degree hours and the temperatures and we solve for time. But since we have to deal with this range of values that could be time, we end up with a range as our answer. As you can see on this slide here we have somewhere between 40 and 60 hours our body has been decomposing and having bugs grown on it based on those. Typically forensic entomologists will look at not just one type of bug but several types and they can narrow this range down a lot more than just this 20 hour period that the body could have been first found dead in the situation or killed in the situation. And that's all for accumulated degree hours. I hope this has been helpful. Thank you very much.