Daniel A. Herms
The development rate of plants and insects is linked directly to temperature. The timing of phenological events, such as emergence of insects and flowering of plants, depends on the weather and can vary by several weeks between years. Recording degree-day accumulation is a valuable tool for quantifying how rapidly heat accumulates and thus for predicting the development of plants and insects.
This report discusses three methods that are commonly used to calculate degree-days from daily maximum and minimum temperatures -- the Average, Modified Average, and Modified Sine Wave Methods. Each of the three gives the same result when the daily minimum temperature remains above the specified base temperature (often 50°F). The Modified Sine Wave method is most accurate when the daily minimum temperature falls below the base temperature (as it does frequently during the spring).
A table of degree-day values calculated using the Modified Sine Wave method is presented to facilitate use of this method. Practical application and limitations of degree-day models are discussed.
We have all observed that plants bloom earlier and grow faster during warm years than during cool years. Insects also emerge earlier in warm years. This is because the development rates of plants and cold-blooded animals, including insects, are link-ed directly to temperature. Unlike warm-blooded animals, they have very limited ability to increase their temperature above that of their immediate environment.
The development of plants and cold-blooded organisms is optimal within a rela-tively narrow range of temperatures and slows rapidly as the temperature approach-es upper or lower limits for development (Figure 1). Development ceases altogether once the upper or lower temperature threshold for development is exceeded. Upper and lower developmental thresholds vary from one species to another, depending on the environmental conditions to which the plant or insect is best adapted.
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| Figure 1. The development rate of plants and cold-blooded animals such as insects is dependent on temperature. Development is most rapid around a narrow range of optimal temperatures and slows quickly at higher and lower temperatures. Development stops altogether when the temperature falls below the lower developmental threshold (TL) or rises above the upper developmental threshold (TU). |
Year-to-year variation in weather patterns often makes calendar-based scheduling of horticultural and pest management practices inaccurate. For example, many plants bloomed and insects emerged three weeks earlier during the warm El Niño spring of 1998 than they did during the cool spring of 1997 (see the following report on plant and insect phenology). Calculation of degree-days provides a valuable tool for quantifying how rapidly heat accumulates and thus for predicting the development of plants and insects.
A degree-day (also referred to as a growing degree-day, heat unit, or thermal unit) is a unit of measure reflecting the amount of heat that accumulates above a specified base temperature during a 24-hour period. One degree-day accumulates for each degree the temperature remains above a specified base-temperature for 24 hours.
It is important to understand that degree-days have no meaning until a base temperature is specified. Ideally, when attempting to predict plant and insect development, the lower temperature threshold for development is used as the base temperature for calculating degree-days. Growth and development stops when the temperature drops below this threshold.
The lower developmental threshold temperature is known only for a few species, but experience has shown that 50°F is a reasonable approximation for many species, and it is commonly used as the base temperature (although other temperatures are commonly used, including 0°F, 32°F, and 42°F). In northern climates including Ohio, the upper temperature threshold for development is not generally exceeded for long enough periods to be an important consideration and is often ignored when calculating degree-days.
Cumulative degree-days refers to the total number of degree-days that have accumulated since a designated starting-date and are calculated simply by adding the number of degree-days that accumulate each day. Any date can be used as the starting-date, but January 1 is most commonly used.
There are a number of ways to calculate degree-days, ranging from quite simple to those so complex that a computer is required. The three methods to be discussed here are the Average Method, the Modified Average Method, and the Modified Sine Wave Method. All three methods calculate degree-days from the daily minimum and maximum temperature and a specified base temperature. During a typical 24-hour day, the minimum temperature is usually reached just before dawn and the maximum temperature during mid-afternoon. Figure 2 depicts the temperature pattern for a hypothetical day in which the minimum and maximum temperatures were 45°F and 65°F, respectively. In this example, we have designated the base temperature as 50°F.
The Average Method is the simplest method for calculating degree-days. Using this method, the number of degree-days for a particular day is calculated by subtracting the base temperature from the average temperature for the day according to this formula:
Degree-days = [(max temp + min temp) / 2] - base temp
Using this method, five degree-days accumulated during the day depicted in Figure 2.
[(65 + 45) / 2] - 50 = 5 degree-days
If the maximum temperature for the day never rises above the base temperature, then no development occurs, and zero degree-days accumulate. (Negative degree-day values are not calculated since the development of organisms does not reverse when it is cold.)
When the daily minimum temperature falls below the base temperature (as it does frequently in the spring), the Average Method can underestimate the number of degree-days actually accumulated by a plant or an insect. This is because development occurs even during the short periods that the temperature is above the base temperature, no matter how cold it may be during the rest of the day. In this situation, the Modified Average Method will calculate a higher number of degree-days and thus can be more accurate.
The Modified Average Method is calculated in the same way as the Average Method, except that the base temperature is substituted for the minimum temperature when the minimum temperature drops below the base temperature (as it does in Figure 2) according to the following formula:
Degree days = [(max temp + base temp / 2] - base temp
Using this method, 7.5 degree-days accumulated during the day depicted in Figure 2, as opposed to five degree-days as calculated using the average method:
[(65 + 50) / 2] - 50 = 7.5 degree-days
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| Figure 2. Variation in temperature over the course of a typical day often
follows a predictable pattern with the minimum temperature generally occurring just before dawn and the maximum temperature occurring in mid-afternoon. The base temperature in this example has been specified as 50°F (which is close to the lower developmental threshold for many plants and insects). The shaded area under the temperature curve and above the base temperature represents the amount of degree-days that accumulated during this hypothetical day and can be calculated using the Modified Sine Wave method. |
The Modified Sine Wave Method (Allen, 1976) is even more accurate when the minimum temperature drops below the base temperature. However, most people find it too complex to calculate without the use of a computer. This method makes use of the fact that daily temperature patterns closely resemble a sine wave function (if you remember your trigonometry) and determines the amount of degree-days by calculating the amount of area under the temperature curve and above the base temperature (shaded portion of Figure 2).
On days when the minimum temperature remains above the base temperature, this method yields the same result as the Average Method. Table 1 can be used to determine the number of degree-days that accumulate on days that the minimum temperature falls below the base temperature.
Degree-day models can be valuable tools for predicting insect development and timing pest management practices. Table 2 outlines the steps to follow. The simplest way to construct a degree-day model is to observe a phenological event from one year to the next (for example, adult emergence of bronze birch borer) and note the number of degree-days that have accumulated since the starting date. In Wooster in 1998, bronze birch borer adult emergence first occurred on May 18, after 519 degree-days had accumulated above a base temperature of 50°F since January 1. (See Table 1 in the following report.)
| Table 1. Daily Degree-Day Accumulation Calculated Using the Modified Sine Wave Method When the Minimum Temperature Falls Below a Base Temperature of 50°F. | |||||||
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| Minimum Temperature | |||||||
| Maximum Temperature | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| 50 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 55 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| 60 | 2 | 2 | 2 | 2 | 2 | 3 | 4 |
| 65 | 3 | 3 | 4 | 4 | 4 | 5 | 6 |
| 70 | 5 | 5 | 5 | 6 | 6 | 7 | 9 |
| 75 | 7 | 7 | 7 | 8 | 9 | 10 | 11 |
| 80 | 9 | 9 | 10 | 10 | 11 | 12 | 14 |
| 85 | 11 | 11 | 12 | 13 | 13 | 15 | 16 |
| 90 | 13 | 13 | 14 | 15 | 16 | 17 | 19 |
| 95 | 15 | 16 | 16 | 17 | 18 | 19 | 21 |
| 100 | 17 | 18 | 19 | 20 | 21 | 22 | 24 |
For reasons that will be discussed shortly, the number of degree-days required for a particular phenological event often varies from one year to the next. For example, emergence of bronze birch borer adults occurred at 475 degree-days in 1997, or about two warm days earlier than the 519 degree-days in 1998. If we average the two years, we conclude that bronze birch borer emergence occurs at approximately 496 degree-days (when we specify a base temperature of 50°F and a starting date of January 1). After data have been collected over three or four years, this method becomes quite accurate for many insects.
Since the lower developmental threshold temperature is only known for a few plants and animals, 50°F is often used as the base temperature (which has proven to be a good approximation for many species). If the lower threshold temperature varies substantially from the selected base temperature, then large differences will occur from year-to-year in the number of degree-days required for a particular event such as insect emergence.
| Table 2. Steps to Follow in the Construction of a Degree-Day Model. |
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Furthermore, January 1 may not be the best starting-date to begin accumulating degree-days. The overwintering stage of many insects does not undergo development until it has been exposed to a cold period. For these species, January 1 is a safe starting-date. However, in some species, the overwintering stage can also undergo significant development in the late summer and fall. In this case, a starting-date from the previous summer or fall will be more accurate.
Highly accurate models can be constructed by evaluating different starting dates and base temperatures over several years to determine the best combination. For example, a three-year study found that adult emergence of bronze birch borer was most accurately predicted in Columbus, Ohio, using a starting date of May 1 and a base temperature of 46°F (Akers and Nielsen, 1984).
There are a number of even more sophisticated methods for modeling insect phenology. However, because of the limitations described in this report, these models are often no more accurate than the simpler methods when applied in the field.
By far, the greatest source of error in degree-day models originates in the temperature data used to calculate degree-days. It is virtually impossible to measure the temperature that insects actually experience. Micro-environments in which insects exist are generally very different from the environment of the thermometer used to collect the temperature data. Furthermore, many insects exert some control over their body temperatures through their behavior. For example, they will move to dark surfaces in the sun when they are too cool and to light surfaces in the shade when they are too warm.
Researchers can develop highly accurate models by recording temperatures directly in the insect's environment (for example, by affixing a microprobe directly to the insect). However, these temperatures will differ so dramatically from ambient that such
models will be of little value when used with data collected from weather
stations. For this reason, practical models are developed from temperature data
collected from the same standardized sources that growers and other users of the
model also have access to, such as weather stations. Experience has shown that
over several years, errors in estimating insect development using standardized
data tend to cancel themselves out, leading to models that are accurate enough
for practical purposes. For his models, the author uses daily maximum and minimum
temperature data from The Ohio State University's Ohio Agricultural Research and
Development Center (OARDC) Weather System. Data from this system are available
for a number of locations throughout Ohio and can be accessed via the World Wide
Web at:
http://www.oardc.ohio-state.edu/weather
There are other sources of error in degree-day models, but they are usually relatively small. For example, the methods used to calculate degree-days assume that the development rates of insects are a linear function of temperature. However, temperature has nonlinear effects, especially as temperatures approach the upper and lower threshold (Figure 1). When the temperature oscillates around the base temperature for long periods of time, as it sometimes does in cool springs, errors in prediction can become fairly substantial.
Degree-day models also assume that development rate is only a function of temperature. However, other factors have important effects on development time -- for example, the quality of host plants for insects and drought stress for plants. The variation that these factors contribute to developmental time are difficult to quantify and are generally not incorporated in degree-day models.
Despite these limitations in using degree-day models for predicting insect and plant development, these models have great practical value when used in the field. Degree-day models are much more accurate than calendar-based schedules for timing horticultural pest-management practices. Useful degree-day models can be constructed by observing plant and insect activity and then calculating cumulative degree-days using the Average Method (or Table 1, when the minimum temperature falls below the base temperature). Experience has shown that for practical application in the field, this method is just as useful as more complex models.
An alternative approach is to let plants do the work for you. Because both plant and insect development is temperature dependent, plants track the same environmental variables that affect insect development. As a result, plant phenological events such as flowering time can be used to predict insect activity. The next report discusses how the sequence of blooming times of plants can be used to track degree-day accumulation and predict insect emergence.
Akers, R. C. and D. G. Nielsen. 1984. Predicting Agrilus anxius adult emergence by heat unit accumulation. Journal of Economic Entomology. 77:1459-1463.
Allen, J. C. 1976. A modified sine wave method for calculating degree-days. Environmental Entomology. 5:388-396.
Arnold, C. Y. 1959. The determination and significance of the base temperature in a linear heat unit system. Proceedings of the American Society of Horticultural Science. 74:430-445.
Arnold, C. Y. 1960. Maximum-minimum temperatures as a basis for computing heat units. Proceedings of the American Society of Horticultural Science. 74:682-692.
Baskerville, G. L. and P. Emin. 1969. Rapid estimation of heat accumulation from maximum and minimum temperatures. Ecology. 50:514-517.
Higley, L. G., L. P. Pedigo, and K. R. Ostlie. 1986. DEGDAY: a program for calculating degree-days, and assumptions behind the degree-day approach. Environmental Entomology. 15:999-1016.
Pruess, K. P. 1983. Day-degree methods for pest management. Environmental Entomology. 12:613-619.
Wilson, L. T. and W. W. Barnett. 1983. Degree-days: an aid in crop and pest management. California Agriculture. 37(1):4-7.