3 Digital Computing
3.1 Growing Degree-Days
Growing Degree-Days is a measure of temperature duration. Specifically it is the persistence of temperature in excess of a threshold amount that is necessary for daily biological processes such as insect development to begin. It is also the amount of average temperature over the threshold, which influences the speed of development. The threshold can be peculiar to a species of interest although most insect species have closely equivalent thresholds. Growing Degree-Days is calculated in such a way that, at any point in the year, its cumulative sum is proportional to development of insects up to that point in the year. Growing Degree-Days is capped by a temperature ceiling (the cutoff temperature), too, above which the amount of daily development does not depend on temperature but only on duration.
The terminology is confusing. The term "Growing Degree-Days" as applied to phenology of insects (in this paper) is distinct from the terms "degree-days" and "cooling degree-days" common in meteorological contexts and "heating degree-days" common in heating, ventilation, and air-conditioning (HVAC) contexts. "Degree-days" accounts for day-to-day differences in energy consumption for heating and cooling buildings, but the terms "degree-days" and "Growing Degree-Days" are used interchangeably in biological contexts, too. Please be aware that academic papers may and frequently do use their own terminology.
In 1969, Baskerville and Emin published refinements to the calculation of Growing Degree-Days based on high-speed digital computing, which adhere more closely to models of insect development than conventional cooling degree-days does. Theirs are the calculations that produce Growing Degree-Day tables used to control various species of insects.
3.2 Growing Degree-Day Table
Here is such a table for codling moth:
Growing Degree-Day (°F) Table For Codling Moth (Cydia pomonella) Threshold = 50°F Cutoff = 88°F Method: gdd_single_sine_horizontal_cutoff \ Min Daily Temp Max 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 48 0 0 0 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 50 0 0 0 0 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 52 0 1 1 1 2 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 54 1 1 2 2 3 4 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 56 2 2 2 3 4 5 6 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 58 3 3 3 4 5 6 7 8 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 60 4 4 4 5 6 7 8 9 10 *** *** *** *** *** *** *** *** *** *** *** *** *** *** *** 62 5 5 5 6 7 8 9 10 11 12 *** *** *** *** *** *** *** *** *** *** *** *** *** *** 64 5 6 6 7 8 9 10 11 12 13 14 *** *** *** *** *** *** *** *** *** *** *** *** *** 66 6 7 7 8 9 10 11 12 13 14 15 16 *** *** *** *** *** *** *** *** *** *** *** *** 68 7 8 8 9 10 11 12 13 14 15 16 17 18 *** *** *** *** *** *** *** *** *** *** *** 70 8 9 9 10 11 12 13 14 15 16 17 18 19 20 *** *** *** *** *** *** *** *** *** *** 72 9 10 10 11 12 13 14 15 16 17 18 19 20 21 22 *** *** *** *** *** *** *** *** *** 74 10 11 11 12 13 14 15 16 17 18 19 20 21 22 23 24 *** *** *** *** *** *** *** *** 76 11 12 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 *** *** *** *** *** *** *** 78 12 13 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 *** *** *** *** *** *** 80 13 14 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 *** *** *** *** *** 82 14 15 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 *** *** *** *** 84 15 16 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 *** *** *** 86 16 17 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 *** *** 88 17 18 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 *** 90 18 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 36 37 38 38 92 18 19 20 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 37 38 38 94 19 20 20 21 22 23 24 25 26 27 28 29 30 31 32 33 33 34 35 36 37 38 38 38 96 20 20 21 22 23 23 24 25 26 27 28 29 30 31 32 33 34 35 35 36 37 38 38 38 98 20 21 21 22 23 24 25 26 27 28 29 30 30 31 32 33 34 35 36 36 37 38 38 38 100 20 21 22 22 23 24 25 26 27 28 29 30 31 32 32 33 34 35 36 36 37 38 38 38 102 21 21 22 23 24 25 26 27 27 28 29 30 31 32 33 34 34 35 36 37 37 38 38 38 104 21 22 22 23 24 25 26 27 28 29 30 30 31 32 33 34 34 35 36 37 37 38 38 38 106 22 22 23 24 24 25 26 27 28 29 30 31 31 32 33 34 35 35 36 37 37 38 38 38 108 22 22 23 24 25 26 27 27 28 29 30 31 32 32 33 34 35 35 36 37 37 38 38 38 110 22 23 23 24 25 26 27 28 28 29 30 31 32 33 33 34 35 36 36 37 37 38 38 38 112 22 23 24 24 25 26 27 28 29 30 30 31 32 33 34 34 35 36 36 37 37 38 38 38 114 23 23 24 25 26 26 27 28 29 30 31 31 32 33 34 34 35 36 36 37 37 38 38 38 116 23 24 24 25 26 27 27 28 29 30 31 31 32 33 34 34 35 36 36 37 37 38 38 38 118 23 24 24 25 26 27 28 28 29 30 31 32 32 33 34 35 35 36 36 37 37 38 38 38
The asterisks fill cells representing the nonsense situation where minimum temperature would exceed the maximum.
Using the paper table requires a paper calendar. Each morning, the minimum and maximum temperature of the preceding day are recorded. The minimum temperature is located along the top of the table, the maximum temperature is located along the side, and the Growing Degree-Days where the column and row intersect are transcribed to yesterday's cell on the calendar. Cumulative Growing Degree-Days for today is the sum of Growing Degree-Days from all the previous cells on the calendar. Using the paper table is fairly simple even though the calculations that produce the table are arcane.
Predicting the developmental stage of an insect is then a straightforward matter of comparing today's cumulative Growing Degree-Days with published Growing Degree-Day requirements for each developmental stage of the species of interest.
The published Growing Degree-Day requirements for various species have been experimentally verified.
U. C. Agriculture and Natural Resources has a list of insect "Research Models" and the papers that purport to validate them, but see also Coop's "Library of Degree-Day Models."
Looking at the summaries of these papers, it is obvious that methods of approximating the actual Growing Degree-Days vary as do recommended threshold and cutoff temperatures for each species. The marvel is that insect-development models function well enough to be of real-world value in pest treatment, so do not be seduced by the precision of all the figures. It is not possible to practice the concepts without adopting one or another of the thresholds and cutoffs and explicit methods, of course; nevertheless, you should still feel free to make your own choices from the range of options that the research presents.