Dachamatics

Frost threshold and critical bud temperatures

The temperature below which the coming night is called dangerous for a particular planting. The threshold comes from one of three sources, and the source is stated alongside the value.

Quantities

SymbolQuantityUnit
T_minforecast daily minimum air temperature°C
T_limthreshold below which a night is called a frost°C
T₁₀temperature killing 10% of buds at the named stage°C
T₉₀temperature killing 90% of buds at the named stage°C
T_ecocropkilling temperature during early growth°C
τtime elapsed since the bud stage was markeddays
τ_maxperiod for which a stage mark is counteddays

Formulas

Source scale conversion

T_C = (T_F − 32) · 5 / 9

The critical bud temperature table is printed in degrees Fahrenheit and stored in them. The result is given to one decimal place: rounding to whole degrees would merge 24 and 25 °F into one value, that is, two distinct source rows.

Threshold selection

T_lim = T₁₀,         if a stage is marked and τ < τ_max
        T_ecocrop,   if the registry has a record
        0 °C         otherwise

The steps replace one another and are not summed. The value τ_max = 14 days is set by the application and is stated on screen.

Warning condition

T_min < T_lim

The inequality is strict: a night whose minimum equals the threshold is not called a frost. The next two forecast days are examined, and the first one satisfying the condition is named.

Three sources of the threshold

Zero degrees is the definition of the word frost and carries no statement about the plant. The killing temperature during early growth is taken from FAO ECOCROP and is filled in for twenty of the forty catalogue crops; the spread is substantial — pear −9 °C, garlic −5 °C, cabbage −1 °C. The bud killing temperature applies to a fruit tree at a named stage of development and is taken from the MSU Extension table, which derives from Washington State University bulletins and, for tart cherry, from MSU research.

Definition of the tabulated values

T₁₀ and T₉₀ are the temperatures at which, after thirty minutes of exposure, 10% and 90% of buds are killed respectively. The threshold is set by T₁₀; T₉₀ is shown alongside and takes no part in the comparison. The proportion of bud loss that costs the crop differs by species: the source states that cherries require well over half the buds to survive, while apples, pears and peaches need 10–15%.

The stage is entered by hand

The bud stage cannot be derived from the available data. Annotated iNaturalist observations give a monthly histogram over two phases, whereas the path from the first stage to full bloom takes three to five weeks and has nine stages. A growing degree day calculation would require the number of degree days to each stage, which is absent from every registry in use.

How long a mark counts

A mark is counted for 14 days, after which the threshold returns to the previous step. The value is set by the application. Early stages are hardier than late ones (apple: 15 °F against 28 °F), so a stale mark lowers the threshold and suppresses the warning, whereas no mark at all restores the previous behaviour.

Coverage

The table covers all six fruit trees in the catalogue: apple (9 stages), pear (8), apricot (8), sweet cherry (9), tart cherry (8) and plum (8). The figures are transcribed from the MSU edition and checked row by row against the USU Extension edition (IPM-012-11): matched by stage name, every value agreed except one — 90% bud kill for tart cherry at full bloom, where the editions differ by 1 °F.

Applicability and limitations

Sources

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