Temperature, Accumulated Degree Days and Degree Hours

For most insects within the range between their lower and upper developmental thresholds, development rate increases in near-linear proportion to temperature. A larva at 25 degrees Celsius develops approximately twice as fast as one at 15 degrees Celsius when the base temperature is 5 degrees Celsius. This linearity makes the model mathematically tractable and experimentally testable.

The key experimental measurement is the thermal constant, also called K: the total ADD or ADH required to complete a developmental stage from egg hatch to moulting, or from oviposition to adult eclosion. Researchers determine K by rearing cohorts of the target species at several constant temperatures and recording the time to complete each stage. Plotting development rate (1/days) against temperature gives a straight line; the x-intercept is the base temperature and the reciprocal of the slope gives K. These constants are published in peer-reviewed literature for the main forensically important species and form the reference database the analyst uses.

ADD sums daily mean temperatures above the base temperature. If the daily mean at a scene on a given day was 20 degrees Celsius and the base temperature for the species is 4 degrees Celsius, that day contributes 16 DD to the cumulative total. The simplicity of ADD makes it attractive when only daily temperature records are available, which is the case for many older meteorological stations and rural locations.

The problem with ADD is that the daily mean smooths out variation that is biologically real. Consider a day with a high of 30 degrees and a low of 10 degrees at a base of 4 degrees. The mean is 20 degrees, giving ADD of 16. But if those temperatures held for equal hours, the 12 nighttime hours at 10 degrees contributed (10 minus 4) times 12 = 72 degree-hours, and the 12 daytime hours at 30 contributed (30 minus 4) times 12 = 312 degree-hours, for a total of 384 ADH, equivalent to 16 ADD. No error so far. But in reality, temperature curves through the day and the hourly breakdown is not symmetric. More critically, when nights fall below the base temperature, those hours contribute zero to development, and averaging them into a daily mean effectively attributes thermal units to periods when no development was occurring.

Modern meteorological networks and in-scene data loggers typically record at hourly or sub-hourly intervals. Where that data is available, ADH is preferred because it excludes sub-base hours directly rather than averaging them away. The difference between ADD and ADH matters most in continental climates with large diurnal temperature swings and in spring or autumn cases when night temperatures regularly fall below the base temperature.

No weather station sits at the crime scene. The analyst must obtain historical temperature records from the nearest available station and use them as a proxy for the temperature the larvae actually experienced. Standard practice in most forensic entomology guidelines requires documenting the station used, its distance from the scene, its elevation relative to the scene, and any known systematic differences in exposure (urban versus rural, coast versus inland).

1. Identify the nearest suitable station
   National meteorological services (for example, the UK Met Office, the US National Weather Service, or India's IMD) maintain archives of hourly or daily station data. Choose the station closest to the scene with uninterrupted records covering the estimated colonisation window, and record the station's coordinates and elevation.
2. Deploy on-scene data loggers
   Place temperature data loggers at the scene at the time of examination, in the shade (to record ambient) and, if the body has not yet been moved, in the larval mass. Allow loggers to record for at least 24 to 48 hours concurrently with station readings.
3. Calculate the correction factor
   Compare logger readings to station readings over the logger's deployment period. Compute the mean difference (scene minus station) for each hour or day. This factor, positive or negative, reflects the systematic bias between the two locations.
4. Apply correction retrospectively
   Add the correction factor to each historical station reading within the estimated colonisation window to obtain a reconstructed scene temperature series. Use this corrected series for ADD or ADH calculations.

Once the analyst has a corrected scene temperature series and a species-specific developmental dataset, the back-calculation is straightforward. Starting from the examination date and working backward through the temperature series, ADD or ADH is accumulated hour by hour or day by day until the cumulative total matches the thermal requirement for the stage found. The date at which the total is reached is the estimated oviposition date, and it defines the floor on the mPMI.

In practice the calculation is performed in a spreadsheet or purpose-built software such as the PAST (Postmortem Arthropod Succession Tool) packages developed in academic laboratories, or the publicly available Estimating Postmortem Interval tool maintained by researchers at several European universities. The analyst inputs the examination date, the corrected temperature series, the base temperature, and the stage-specific thermal constant, and the tool outputs the back-calculated date range.

The result is presented as a date range rather than a single point, for two reasons. First, the developmental data themselves carry experimental variance. Second, the temperature correction introduces uncertainty. Good practice is to run the calculation using the lower and upper bounds of the developmental thermal constant and report the resulting date range with that uncertainty stated explicitly.

The thermal-summation model is well validated but its accuracy depends entirely on the quality of the inputs. The main error sources, in rough order of practical impact, are:

• Species misidentification: Using ADD data for the wrong species is the single largest source of systematic error. A one-degree difference in base temperature compounds across many days and can shift the estimated date by several days. Molecular identification of larvae is now standard good practice in most jurisdictions.
• Larval mass heating: Large masses generate internal temperatures that ambient sensors do not capture. If no core temperature was recorded at the scene, the analyst can only note the potential underestimation of thermal exposure and widen the stated uncertainty range.
• Missing temperature records: Gaps in station data require interpolation or substitution from a secondary station. Each step away from the scene data increases uncertainty and should be documented.
• Sample collection stage uncertainty: Staging larvae from body length measurements rather than morphological characters introduces measurement error. Larvae in motion contract significantly from their maximum stretched length; fixed specimens in ethanol are preferred for measurement.
• Drug effects on development: Cocaine, heroin, and some prescription drugs have been shown in controlled trials to accelerate or retard larval development. Where toxicological results indicate drug exposure, development may not follow the standard thermal constant without correction.