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Garden with Insight v1.0 Help: Plant next day functions: accumulate heat units and calculate heat unit index

If the plant has entered this part of its next-day routine, it is not a seed. On the day the plant germinates from seed to seedling, it resets its heat units to zero. Heat units then begin to accumulate again towards maturity.

Each day the difference between today's mean air temperature and the minimum (base) temperature for growth is added to the accumulated heat units:

HU = HU + max(0, Ti - Tb) - max(0, Ti -To)

where HU is the accumulated heat units for a particular plant, Ti is the air temperature for day i, Tb is the minimum growth temperature, and To is the optimal growth temperature. The "max" notation means that if either of the two differences is negative, that term is not added or subtracted. Note that we added the second term to bound the heat unit accumulation when the temperature is too hot.

If the "optimal temperature" option for plant growth is turned on, the optimal growth temperature is used instead of the mean air temperature to calculate heat units.

The heat unit index is the number of accumulated heat units divided by the number of heat units expected for this plant when it is at physiological maturity -- the potential heat units. Maturity is defined empirically, as when the plant is usually harvested or as the length of a typical growing season for the plant. On a seed packet the number of days from planting to harvest is analogous to the expected (potential) heat units.

The heat unit index acts as an index of the development of a plant through its growing season and drives many processes in the plant model. It is not unreasonable to use heat units as an index of plant growth, because time to maturity can be predicted fairly well for many plants on the basis of summing temperatures over a base. In fact, this index is so useful that even your gas or electric bill may have a graph of heat units, which are also called heating or cooling days, as an index of how hot or cold the season has been in relation to other years. Because the heat unit index is so important, the choice of potential heat units and the meaning of "maturity" has a large effect on the outcome of the simulation, including estimates of yield.

How a plant's potential heat units are calculated

Because the accumulation of heat units works by addition of daily temperatures, the heat units a plant can be expected to experience in a typical growing season will vary in different climates. In the EPIC model, potential heat units are calculated using the current climate and the planting and harvest dates for a crop. These dates are specified when the crop is planted. However, in the Garden with Insight model we do not know when the plant will be harvested because that date is not specified when the plant is planted. We need another way of estimating potential heat units.

To calculate the heat units required for germination and for maturity, we use several parameters that describe the normal (typical) growing season to calculate a normal heat unit total for the climate. We use planting and harvest dates based on frost dates instead of calendar dates to make plant cultivars flexible in different climates. Most gardening books and seed packets recommend planting dates in reference to frosts (for example, "when all danger of frost is past" or "three weeks after the last frost"). The last spring frost is defined as the last day in which the smoothed mean minimum temperature falls below freezing. The first fall frost is the first day in which this condition occurs.

We start by figuring the normal planting date for the plant. This is done by one of four possible methods:

1. If the heat units are to be calculated from the spring planting date, we add or subtract a number of days from the last spring frost.
2. If the heat units are to be calculated from the fall harvest date, we subtract the number of days it normally takes from planting to maturity from the fall harvest date. We assume the plant is physiologically mature at the harvest date.
3. If the heat units can be calculated either from the spring planting date or the fall planting date, we do either method 1) or method 2) depending on whether the actual planting date is closer to the normal spring planting date or the fall harvest date.
4. If the climate is warm and has no period of the year when the temperature falls below freezing, today's date is used for the normal planting date.

Now having the normal planting date, we simply accumulate heat units in the current climate as if the plant were growing in that climate. First we start at the planting date and accumulate heat units for the number of days from planting to emergence (the end of germination). Then we start at the planting date plus the number of days from planting to emergence and accumulate heat units for the number of days from emergence to maturity.

Finally, we check the calculated heat units against a minimum and maximum number of allowable heat units for the plant, which keep the expected heat units in reasonable bounds for the plant regardless of climate. If the plant is particularly sensitive to temperature, for example, so that the seed packet's 60 days to maturity does not hold in colder climates, these bounds can be used to reflect that sensitivity.

calculation of germination
EPIC Heat unit accumulation
Model contents

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Updated: May 4, 1998. Questions/comments on site to
Copyright © 1998 Paul D. Fernhout & Cynthia F. Kurtz.