Frost Window and Sowing Date on the Northern Adelaide Plains
A 240-hectare mixed farm near Mallala grows wheat and canola in rotation. The manager has three seasons of yield data and local frost records. Sowing before 25 April has averaged 4.1 t/ha wheat but 18% of those crops were hit by a September frost in one of the three years, cutting yield to 1.9 t/ha. Sowing after 20 May has averaged 3.2 t/ha with no frost losses recorded. The long-term median break of season is 12 May, and stored soil moisture at the start of the program is 62 mm, below the 80 mm the manager considers adequate for early sowing. Canola must be sown before mid-May to avoid heat stress at flowering. The farm's fixed costs are high and the bank requires a stable income floor.
1. Recommend a sowing strategy for the coming season and justify it using expected value reasoning rather than best-case yield.
Read the worked answer
The decision is not 'which date yields most' but 'which date gives the best risk-weighted return given the soil moisture and frost exposure'. Compare expected yields:
- Early sowing (before 25 April): in two of three years 4.1 t/ha, in one year 1.9 t/ha. Expected yield = (2 × 4.1 + 1 × 1.9) / 3 = 3.37 t/ha.
- Late sowing (after 20 May): 3.2 t/ha with no recorded frost loss, so expected yield = 3.2 t/ha.
The early option is only marginally better on average (0.17 t/ha) but carries a large downside. That margin is smaller than the error in three years of data, so it is not a reliable advantage.
Two further points decide it. First, stored soil moisture is 62 mm, below the 80 mm threshold the manager associates with successful early sowing, so the 4.1 t/ha figure may not be achievable this year. Second, the bank requires an income floor, and a 1.9 t/ha frost year on 240 ha would threaten that floor. The canola constraint (sow before mid-May to avoid flowering heat stress) means canola should be prioritised into the late-April to early-May window, with wheat following. A defensible answer is: sow canola in the first half of May once moisture is adequate, sow wheat after 20 May unless at least 80 mm of stored moisture is present by 25 April, in which case split the wheat area between early and late sowing to hedge frost risk. The reasoning - expected value, data reliability, moisture threshold and the income floor - matters more than the exact dates chosen.
2. Explain why three seasons of yield data are a weak basis for this decision, and state what records would strengthen it.
Read the worked answer
Three seasons give only three observations, and frost events are rare and irregular. One frost year out of three does not establish an 18% probability; it could reflect a 5% or a 40% long-term risk. The manager is effectively estimating a tail risk from a very small sample, which makes the expected-value calculation fragile.
Other weaknesses: the data are from one paddock sequence, not replicated trials, so soil type, nutrition and disease differ between years and confound the sowing-date comparison. Yields are also whole-farm averages, hiding paddock variation.
To strengthen the basis, the manager should:
- Use long-term frost records (date of last frost and frequency by week) from the nearest weather station rather than farm memory.
- Record sowing date, flowering date and frost damage per paddock each year, so frost exposure is tied to the crop's growth stage, not just the calendar.
- Track stored soil moisture at sowing and rainfall in the following weeks.
- Run small strip trials of early versus late sowing within the same paddock and season to remove confounding.
- Build the record over 8–10 years before treating any probability as reliable.
The examinable point is that a decision under risk needs a probability estimate, and a probability estimated from three years is not trustworthy.