Insects Do Not Use Calendars: Degree-Day Models, and Why Structural Pest Control Still Schedules by the Date

1. Introduction: the wrong independent variable

Pest control is sold and scheduled by the calendar. Quarterly service, a spring treatment, an autumn exclusion visit, four visits a year.

The organisms being managed do not respond to dates at all.

1.1 Why this belongs in a Winnipeg journal

Because the gap between a warm spring and a cold one is larger here than almost anywhere, which makes the calendar a worse predictor here than almost anywhere. Section 21 sets out where the method would apply to this trade's actual work.

2. The underlying fact

The biology the whole method rests on.

Insects are exothermic, or cold-blooded, and their body temperature and growth are affected by their surrounding temperature. Degree day values interpret that heat accumulation.¹

The consequence, stated plainly by one source: insects emerge earlier in warm years than in cool ones.⁴

2.1 The word consistent

A consistent amount of heat accumulation.¹ That is the claim the whole method depends on, and it is an empirical finding rather than a definition: the same species needs the same total each year, even though the number of days taken to reach it varies.

2.2 Why that makes a date meaningless

A calendar date encodes the average of past years. In any particular year the development that matters has either already happened or has not started, and the date gives no information about which.

Degree days are described as accurate because insects have a predictable development pattern based on heat accumulation.¹ The prediction is available; the trade is using a worse one.

3. What a degree day is

The definition.

A degree day is a measurement of heat units over time, calculated from daily maximum and minimum temperatures, and degree days are based on the rate of an insect's development at temperatures between upper and lower limits for development.¹

3.1 Why heat units and not days

Because a day is a unit of time and development is not a function of time. Two weeks in April and two weeks in July contain the same number of days and very different quantities of usable heat.

Converting to heat units puts the insect's clock on the axis instead of ours, which is the whole of the idea and the reason the method transfers between climates in a way a calendar cannot.

3.2 It is a quantity, not a rate

One degree above the threshold for a day and two degrees above it for half a day are the same accumulation. That is the assumption that makes the arithmetic work, and it is an approximation, because development rate is not perfectly linear with temperature between the two thresholds.

The method survives that approximation because the error is small across the range where most development happens, and because the target accumulations were derived empirically using the same approximation. The model is internally consistent rather than exact.

4. The lower threshold

The first parameter.

The minimum temperature at which insects first start to develop is called the lower developmental threshold, or baseline.³ It is the temperature below which no development can occur for a particular insect.⁵

4.1 The consequence for a cold climate

Below the base, time passes and nothing accumulates. A long cool spring is not a delayed spring; it is, for the insect, a spring that has not begun. A technician standing in a yard in May, seeing nothing, may be looking at an empty building or at one whose occupants have simply not started yet.

That explains why a calendar-scheduled treatment can miss badly in one direction only. A warm year runs ahead of the date; a cold year does not run behind it in a way that matters, because the insect simply waits.

5. The upper threshold

The second parameter, which matters less often and matters a great deal when it does.

The maximum temperature at which insects stop developing is called the upper developmental threshold, or cutoff,³ above which insect development does not accelerate, but remains at a maximum rate.⁵

It is optional: some insects do not have an upper development threshold.¹

5.1 Why an optional parameter matters

Because omitting it where it exists overcounts every hot day, and including one where the species has none undercounts them.¹

Either error is systematic rather than random, which means it accumulates through the season in one direction, the same failure mode §14.1 describes for a wrong base temperature.

5.2 Why it exists

Because biochemical rates do not rise indefinitely with temperature. Past a point, enzymes are working as fast as they will work, and beyond that they begin to fail.

This journal's thermal disinfestation article dealt with the far end of that curve, where heat stops accelerating development and starts killing. The upper threshold is the beginning of the same physics.

6. Two kinds of cutoff

A distinction the sources make and most summaries omit.

When insects reach their upper threshold, development of some species levels off, a horizontal cutoff, and for other species, stops, a vertical cutoff.¹

6.1 What the two mean arithmetically

Under a horizontal cutoff, heat above the ceiling is counted as if it were at the ceiling: the insect keeps developing at its maximum rate. Under a vertical cutoff, that heat contributes nothing, because development has halted.

The same hot afternoon therefore adds degree days under one rule and none under the other, and choosing the wrong rule for a species will bias every prediction in a hot summer. This paragraph is our reading of the definition.

7. The biofix

The third parameter, and the one that most often goes wrong.

The model will have a biofix, which is a date or event that triggers the start of degree-day accumulation, after which daily degree-day values are accumulated and developmental events are timed to specific accumulations. Biofix dates are usually based on specific biological events such as planting dates, first trap catch, or first occurrence of a pest.⁵

It can be a biological event, such as the date at which moth flight begins, or a calendar date, such as March 1.¹

7.1 Why any starting point is needed at all

Because accumulation from an arbitrary origin is meaningless. Two hundred and twenty degree days counted from January is a different quantity from two hundred and twenty counted from first flight, and only one of them predicts anything.

The biofix is what makes the target accumulation portable between years. It is also the most common way a published model gets misapplied, since the number travels more easily than the convention behind it.

7.2 Why a biological biofix is better

Because it is itself an observation of the population rather than an assumption about it. First trap catch says this population, in this location, has reached that stage.⁵

A calendar biofix reintroduces exactly the problem the method exists to solve, which is why §7.2 matters.

7.3 When a calendar biofix is defensible

One source starts accumulation on March 1, because there is typically no insect development before that time.¹

That is legitimate: a calendar date chosen to sit safely before any accumulation is possible adds nothing and loses nothing. In this province the equivalent date would be later, and the principle would hold more strongly because the certainty of no development is greater.

8. The simple calculation

The arithmetic, which is genuinely simple.

Degree days can be calculated using a simple formula for the average daily temperature, calculated from the daily maximum and minimum temperatures, minus the baseline, being the lower developmental threshold.³

Written out, that is the daily maximum plus the daily minimum, divided by two, minus the base temperature.⁷ When temperatures do not exceed the base, zero degree days have accumulated.⁶

9. Worked examples

Three published calculations, which make the behaviour of the formula concrete.

A day with a high of 72 and a low of 44, base 50, gives 8.⁶³ A day with a high of 72 and a low of 50 gives 11.⁶ And for a day with a maximum of 102 and a low of 70, the maximum is replaced with the upper threshold where known, taken as 88, giving 29.⁶

9.1 What zero days mean

When temperatures do not exceed the base, nothing accumulates.⁶ Not a small amount; nothing.

Which is why a prairie winter is not a slow season for an outdoor insect but a suspended one, and why an accumulation started in March is arithmetically identical to one started in January for any species with a base near fifty.

9.2 What the third example demonstrates

Substituting the upper threshold for the recorded maximum. A day reaching 102 is counted as a day reaching 88, because the insect cannot use the difference.

That is the horizontal cutoff of §6 implemented in the simplest possible way, and it is why the upper threshold has to be known before a hot-climate model can be trusted.

9.3 The middle example is the instructive one

Raising the overnight low from 44 to 50, with the same daytime high, added three degree days. Nearly forty per cent more accumulation from a change in the night temperature alone.

Overnight minima matter as much as afternoon maxima, which is not most people's intuition about what drives insect development. The observation is ours.

10. The sine methods

The better calculation, and what it costs.

The single sine method uses the area under a sine wave, adjusted based on the lower and upper thresholds, which is more complicated to compute but more accurately tracks how temperatures change throughout a day resulting in better estimates of insect development particularly in the early part of the season when daily temperatures are close to the developmental thresholds.⁵

It is based on the assumption that temperatures of a 24-hour day follow a sine wave curve, with the number of degree days being the area under this curve within the lower and upper temperature thresholds. Because of the somewhat complicated calculus involved, the sine wave formula is not shown in the extension material, and values calculated this way are usually determined by a computer.⁶

10.1 Why the daily curve assumption is reasonable

Because the minimum temperature is usually reached just before dawn and the maximum temperature during mid-afternoon, following a predictable pattern.⁴

10.2 Where the improvement is concentrated

Early in the season, when daily temperatures sit near the thresholds.⁵ On a day whose low is below the base and whose high is above it, the simple average treats the whole day as partly effective, while the sine method integrates only the hours actually above the threshold.

That is exactly the situation through a prairie spring, which makes the more complex method more necessary here rather than less. Our inference.

11. Where the methods disagree

A warning that belongs beside any published degree-day figure.

Be aware, however, that a direct calculation method will not always give the same degree-day values as a sine-wave method.²

For the modified sine method, on days when the minimum temperature remains above the base temperature, this method yields the same result as the Average Method.⁴

11.1 Why they converge in warm weather

Because when the whole day sits above the base temperature, the area under the curve and the mean of the endpoints describe the same quantity. The sine method is only doing extra work when part of the day is outside the thresholds.⁴

11.2 The practical consequence

A target accumulation published for a species was derived using some method, and applying it to an accumulation computed by a different method compares two different quantities.²

This journal has made the same point about thermal treatment and about detection: a number is only interpretable alongside the procedure that produced it. Here the procedures agree in warm settled weather and diverge precisely when the season is turning, which is when the answer matters.

12. What the model is used for

The applications, which are broader than treatment timing.

Accumulated degree days are useful in timing scouting events such as when to place traps, when to look for damage, when to sample. Insect models are useful in timing insecticide treatment because the entire life cycle, or certain important events, of the insect is known.⁶

When used to determine treatment timing they are an important component of an Integrated Pest Management program, providing a cost effective tool to reduce insect feeding damage.¹

12.1 The economic claim

Cost effective, and reducing feeding damage.¹ A treatment placed in the window when it works replaces one or more placed when it does not.

This journal's article comparing integrated management with conventional spraying found the same result by a different route: better-targeted intervention reduced total applications rather than adding to them.

12.2 Monitoring before treatment

Note the order. The model first tells you when to go and look, and the looking then tells you whether to treat.

That is the structure this journal's detection article argued for and the insect light trap article found missing: an instrument deployed at a time chosen for a reason, producing information that drives a decision.

13. The codling moth case

The worked example the extension literature returns to.

For this pest it is important to know when 220 degree days after biofix will occur, because this point corresponds to first generation egg hatch, when fruit should begin to be protected.¹ And pheromone monitoring traps are placed in the apple orchard at 100 degree days after March 1 in northern Utah to determine initiation of adult moth flight.⁶

13.1 The two numbers do different jobs

One hundred degree days triggers an observation; two hundred and twenty triggers an intervention.¹⁶ The first is cheap and tells you whether the second applies.

13.2 What makes this model usable

A defined biofix, a validated accumulation, and a specific action attached to a specific number. Two hundred and twenty is not a description of the insect's biology; it is an instruction about when to do something.

13.3 Why egg hatch is the target

Because the larva is vulnerable in the interval between hatching and entering the fruit, which is short. Treating before hatch wastes residual life and treating after it puts the target inside the commodity.

This journal met the identical structure in the flea article, where the pupal window created a period during which treatment could not reach the insect, and in the head lice articles, where a second application is timed to hatching. The narrow window is the thing degree days exist to find.

14. When the thresholds are unknown

The honest admission in the extension literature.

The lower and upper thresholds vary among species, and have been determined for many, but not all, major insect pests. For those whose exact values are unknown, including most landscape insect pests, a baseline temperature of 50 degrees Fahrenheit is used.¹

That default is chosen because it approximates the lower developmental threshold for many plants and insects.⁴

14.1 What using a default costs

A base temperature that is a few degrees wrong biases every day's accumulation in the same direction, and the error compounds across the season rather than averaging out.

So a model with a defaulted base is a rough ordering device rather than a prediction, and it will be least reliable in exactly the cool conditions where the base matters most. Our reasoning.

14.2 How you would know the default is wrong

By the model failing in a consistent direction. If predicted events arrive systematically late in cool years and early in warm ones, the base is too high; the reverse indicates it is too low.

That is a diagnosis available only to somebody recording both the prediction and the outcome, which returns to §19. A model nobody checks cannot correct itself.

14.3 The candour is worth noting

Most of most pests are unmodelled, including most landscape species.¹ A field with a mature method still has thresholds for a minority of the organisms people care about, which is a realistic picture of how far this kind of work has actually got.

15. Validation

A detail in a published table that carries a general lesson.

One extension table lists pests for which thresholds and models exist, noting that those with an asterisk have been validated for that state.⁶

15.1 Why a model would fail to transfer

Photoperiod, which varies with latitude and drives diapause independently of temperature. Local population differences in threshold. And the distance between the weather station supplying the temperatures and the microclimate the insect actually occupies.

The first of those is the one most likely to matter at this latitude, and none of the sources addresses it. Our reasoning.

15.2 What that asterisk concedes

That a model existing is not the same as a model working here. Development thresholds are properties of the species, but populations differ, and the relationship between a weather station and the microclimate an insect occupies differs by place.

Publishing which models have been locally confirmed, and by implication which have not, is the kind of disclosure this journal has repeatedly asked for elsewhere.

16. The alternatives it replaced

What was used before, which is what this trade still uses.

Traditionally the arrival of insect pests would be predicted based on a calendar date, a crop development stage, or the development of certain wild indicator plants such as magnolia, lilac, chicory, and thistle.⁵

16.1 Why crop stage was used

Because the crop and the pest experience the same weather, so the crop's development is a running record of the season. It is the same logic as the indicator plant, applied to something the grower is already watching closely.

16.2 The indicator plant idea is better than it sounds

A plant in the same location is integrating the same heat over the same period, so its development is a biological record of the accumulation. Plants also bloom earlier during warm years.⁴

Using a lilac as a thermometer is a sound method with no equipment, and it fails only where the plant and the insect have different thresholds. That assessment is ours.

17. Why calendars are getting worse

A claim from the sources that we would want examined but which is stated plainly.

Calendar dates in particular have become less reliable recently as the climate trends warmer, pushing the arrival of spring earlier, and resulting in less predictable spring temperatures.⁵

17.1 Why this province is the extreme case

A place whose spring can arrive three weeks apart in successive years has a wider distribution around any chosen date than a place with a mild maritime climate.

The argument for heat units over calendars is proportional to that spread, which means it is stronger here than in any of the jurisdictions whose extension services wrote the sources for this article. Our inference.

17.2 The two effects are separate

A shift in the mean, which makes an old calendar date systematically late. And an increase in variance, which makes any fixed date less reliable in both directions.

The first can be fixed by moving the date. The second cannot be fixed by any date at all, which is the stronger argument for the method.

18. Plant phenology as a proxy

Where the two approaches meet.

Since insect development is temperature dependent, monitoring degree-day accumulation is a valuable tool for predicting pest activity, although monitoring degree-days on a daily basis can be cumbersome.⁴

18.1 Why the cumbersome part is the real barrier

Not the arithmetic, which is one subtraction a day, but doing it every day for a season without missing any, and doing it for several locations.⁴

An accumulation with gaps in it is not an accumulation. That is an administrative problem rather than a scientific one, and it is the kind of problem that gets solved by a device or not at all.

18.2 The instrument answer

Devices exist that calculate degree days every few minutes based on temperatures and are highly accurate, with many brands allowing the target pest's upper and lower thresholds to be entered manually.¹

A logger at the site removes the cumbersome part and removes the distance between the weather station and the building, which §15.1 identified as a source of error. It is the same class of device as the monitors this trade already installs, doing a job that generates a prediction rather than a count.

19. How to build a model from nothing

The method for a species nobody has modelled, which covers most of this trade's subjects.

The easiest way to construct a degree-day model is to monitor a phenological event from one year to the next, for example adult emergence.⁴

19.1 Why this is the right shape of project for this trade

It does not require a laboratory, a rearing colony or a grant. It requires visiting the same buildings repeatedly over years, noticing a repeatable event, and writing down the date.

Repeated visits to the same buildings over years is what a pest control route already is. The observation infrastructure exists and is being used to produce service reports rather than data.

19.2 What that actually requires

Recording the date of a repeatable observable event, and the accumulated degree days at that date, for several years. If the accumulation is consistent across years while the date is not, the accumulation is the model.

It is slow and it needs nothing but a thermometer and a habit of writing things down. Three years is the minimum that would tell you anything and five would be better, which is why nobody with a quarterly reporting cycle has done it.

20. Why this trade does not use it

The obstacles, separated into the real and the merely customary.

20.1 The obstacle that is neither

That the data is unavailable. Daily maxima and minima for any location in this province are published, free, and go back decades, and §18.1 describes instruments that log the accumulation on site for the price of a monitor.

Whatever is stopping this trade from using the method, it is not access to temperature.

20.2 The genuine objection

German cockroaches, bed bugs and pharaoh ants live in heated buildings at temperatures that do not track the weather. Their development is real and temperature-driven, but the ambient record has little to do with it, and this journal's article on indoor thermal refugia set out how far indoor conditions diverge from outdoor ones in this climate.

For those species a degree-day model built on weather station data would be measuring the wrong air.

20.3 The objection that is only habit

That service is sold as a number of visits per year. A quarterly contract is a commercial structure rather than a biological one, and nothing prevents the timing of those visits being set by accumulated heat rather than by the quarter.

The same number of visits, placed better, is not a more expensive service. It is the same service with the dates chosen for a reason, and the reason is stated on the report.

The only thing that changes is that somebody has to be watching the accumulation and willing to move a booking by two weeks in a late spring. That is a scheduling habit rather than a technical capability.

21. Where it would work here

The application, which is narrower than agriculture's and real.

Anything that overwinters outdoors. Cluster flies, boxelder bugs and lady beetles develop on ambient heat and their autumn movement to buildings is temperature driven, which this journal's overwintering article described.

Anything whose season we currently guess. Yellowjacket colony development, ant swarming, tick questing and mosquito generations are all outdoor and all currently timed by recollection of previous years.

Anything where a window closes. Exclusion before entry, treatment before a generation matures, lamp replacement before a season, which §13.2 shows is the classic use.

Anything where we place monitors. Section 12.1 is the point: the model tells you when to look.

And it starts with recording. Section 19 needs nothing but dated observations against accumulated heat, and this trade generates dated observations already.

Start with one species and one event. First cluster fly at a known building, against accumulated heat from a fixed spring date, for three years. That is the whole experiment.

22. Limitations and open questions

The sources are agricultural and horticultural extension. Every source here is written for orchards, field crops or landscape plants, and none addresses structural pest control.¹²³

No thresholds for our species. We did not locate published base temperatures or target accumulations for any of the pests this journal usually covers, which is either a gap in our searching or a gap in the literature, and §14 suggests the latter is plausible.

The examples are in Fahrenheit. The worked calculations and the 50 degree default are as published, and degree days in Celsius are a different number requiring a different target accumulation.⁶

No local validation exists. Section 15 is about a table from another jurisdiction. We know of no Manitoba degree-day work for structural pests at all.

The climate claim is asserted rather than evidenced here. One extension source states that calendar dates have become less reliable as spring arrives earlier and becomes less predictable, and we have not gone behind that statement to the underlying data.⁵

Sections 2.1, 4.1, 6.1, 9.2, 10.2, 11.1, 14.1, 15.1, 16.1, 17.1, 19.1, 20 and 21 are our reasoning. The calendar critique, the cold-climate consequence, the cutoff arithmetic, the overnight minimum observation, the prairie spring argument, the comparability point, the defaulted base cost, the reading of the validation asterisk, the indicator plant assessment, the mean-and-variance separation, the model-building requirement, the obstacle analysis and the application list are ours rather than sourced positions.

23. Conclusion

An insect needs a consistent quantity of accumulated heat above a species-specific threshold to reach each life stage, which is why the same species emerges earlier in a warm year than a cool one.¹⁴ Agriculture has been converting that into scheduled action for decades: a base temperature, an upper threshold, a cutoff rule, a biofix, and a target accumulation at which something specific gets done.⁵

The method is not exotic. The simple form is the mean of the day's high and low minus a base temperature,³ and the harder forms exist because integrating under the daily curve is more accurate early in the season when temperatures sit near the thresholds.⁵ Where thresholds are unknown, which is most species, people use 50 degrees and accept the error.¹

Structural pest control has one real reason for not using this, which is that heated buildings break the link between outdoor heat and indoor development. That reason covers the cockroach and the bed bug. It does not cover the cluster fly, the boxelder bug, the yellowjacket, the tick, the carpenter ant swarm or anything else that spends its year outside and arrives on a schedule the weather sets. For those we are using the calendar, in a province where the calendar is the worst predictor available, and the alternative needs a thermometer and the discipline to write down what happened and when.

References

1. Using Degree Days to Time Treatments for Insect Pests. University extension plant health programme. Principal source. Used for the statements that degree days are accurate because insects have a predictable development pattern based on heat accumulation; that insects are exothermic and their body temperature and growth are affected by their surrounding temperature; that every insect requires a consistent amount of heat accumulation to reach certain life stages such as egg hatch or adult flight, and that degree day values interpret that accumulation; that when used to determine treatment timing they are an important component of an integrated pest management programme, providing a cost effective tool to reduce insect feeding damage; that a degree day is a measurement of heat units over time calculated from daily maximum and minimum temperatures, based on the rate of development between upper and lower limits; that when insects reach their upper threshold development of some species levels off, a horizontal cutoff, and for others stops, a vertical cutoff; that some insects do not have an upper development threshold; that lower and upper thresholds vary among species and have been determined for many but not all major insect pests, with a baseline of 50 degrees Fahrenheit used where exact values are unknown including for most landscape insect pests; that the biofix can be a biological event such as the date moth flight begins or a calendar date such as 1 March, with accumulation started on 1 March in one northern state because there is typically no insect development before that time; that for codling moth it is important to know when 220 degree days after biofix will occur because this corresponds to first generation egg hatch when fruit should begin to be protected; and that biophenometers calculate degree days every few minutes based on temperatures, are highly accurate, and allow the target pest's upper and lower thresholds to be entered manually. https://extension.usu.edu/planthealth/research/degree-days
2. Degree-Day Models. University tree fruit extension programme. Used for the statements that phenology is the study of relationships between the weather and biological processes such as insect development; that phenology models, also known as degree-day models, can help predict the best timing of pest management activities such as pesticide applications; that these models are based on the fact that an insect's growth is closely linked to the temperature where it is found; that phenology models do not operate on a calendar-day basis but on a heat unit or degree-day scale; and for the warning that a direct calculation method will not always give the same degree-day values as a sine-wave method, together with the note that some instruments allow thresholds to be programmed while others require temperature information to be downloaded and analysed. https://treefruit.wsu.edu/crop-protection/opm/dd-models/
3. Degree Days and Insect Models. Regional fruit integrated pest management resource. Used for the statements that entomologists have studied biological development over time, or phenology, of several fruit insect pests, discovering degree day values that correlate to key physiological events such as egg hatch or adult flight, and that this predictive information is known as an insect phenology model; that insect models are useful in timing insecticide treatment because the entire life cycle or key events of the insect is known; for the simple formula in which degree days are calculated from the average daily temperature, being the daily maximum plus minimum divided by two, minus the baseline or lower developmental threshold; for the worked example that a day with a high of 72 and a low of 44 accumulates 8 degree days on a baseline of 50; for the statement that the sine wave method yields a more precise calculation; and for the definitions of the lower developmental threshold or baseline as the minimum temperature at which insects first start to develop and the upper developmental threshold or cutoff as the maximum temperature at which they stop. https://intermountainfruit.org/ipm-methods/treatment-timing
4. Using Degree-Days and Plant Phenology to Predict Pest Activity. University extension publication distributed by an arborist association. Used for the statements that insects emerge earlier in warm years than in cool ones and that plants also bloom earlier during warm years; that since insect development is temperature dependent, monitoring degree-day accumulation is a valuable tool for predicting pest activity, although monitoring degree-days on a daily basis can be cumbersome; that a base of 50 degrees Fahrenheit approximates the lower developmental threshold for many plants and insects; that all three calculation methods work from the daily minimum and maximum temperature and a specified base temperature; that during a typical 24-hour day the minimum temperature is usually reached just before dawn and the maximum during mid-afternoon, following a predictable pattern; that on days when the minimum temperature remains above the base temperature the modified sine wave method yields the same result as the average method; that most people find the modified sine wave method too complex to calculate without a computer; and that the easiest way to construct a degree-day model is to monitor a phenological event from one year to the next, for example adult emergence. https://illinoisarborist.org/wp-content/uploads/2024/09/UMN-DD-Hermes.pdf
5. What is degree-day modeling? University vegetable entomology extension programme. Used for the statements that every degree-day model will have a base temperature below which no development can occur for a particular insect, and optionally an upper threshold above which development does not accelerate but remains at a maximum rate; that the model will have a biofix, a date or event that triggers the start of degree-day accumulation, with daily values accumulated after that point and developmental events timed to specific accumulations, biofix dates usually being based on specific biological events such as planting dates, first trap catch, or first occurrence of a pest; that the simple average method averages the daily minimum and maximum temperatures adjusted for the base and upper thresholds; that the single sine method uses the area under a sine wave adjusted for the thresholds, which is more complicated to compute but more accurately tracks how temperatures change through a day, giving better estimates particularly early in the season when daily temperatures are close to the developmental thresholds; that traditionally the arrival of insect pests would be predicted based on a calendar date, a crop development stage, or the development of certain wild indicator plants such as magnolia, lilac, chicory and thistle; and that calendar dates in particular have become less reliable recently as the climate trends warmer, pushing the arrival of spring earlier and resulting in less predictable spring temperatures. https://vegento.russell.wisc.edu/ipm/degree-day-modeling
6. Degree days fact sheet. University climate centre pest fact sheet series. Used for the worked examples in which a day with a high of 72 and a low of 44 gives 8 degree days on a base of 50, a day with a high of 72 and a low of 50 gives 11, and a day with a maximum of 102 and a low of 70 has the maximum replaced by the upper threshold of 88 to give 29; for the statement that when temperatures do not exceed the base, zero degree days have accumulated; for the description of the sine wave method as using the daily minimum, maximum and baseline temperatures together with the upper threshold, based on the assumption that temperatures of a 24-hour day follow a sine wave curve, with degree days being the area under that curve within the thresholds, the formula not being shown because of the calculus involved and values usually being determined by computer; for the statement that accumulated degree days are useful in timing scouting events such as when to place traps, when to look for damage and when to sample, with codling moth pheromone monitoring traps placed at 100 degree days after 1 March in one northern state to determine initiation of adult moth flight; and for the published table noting that those pests marked with an asterisk have models validated for that state. https://climate.usu.edu/includes/pestFactSheets/degree-days08.pdf
7. Growing degree day explanation. University agricultural weather network. Used for the statement of the simple average method as the daily maximum plus the daily minimum divided by two, minus the base temperature, and for the statement that degree-day models have been developed and tested for many common insect pests and are useful for predicting and monitoring insect development and risk from insect pests. https://legacy.wisconet.wisc.edu/gdd_explanation.html