Statistical ensemble models to forecast the Australian macadamia crop

Abstract

Australian production of macadamia nuts has generally been increasing over time. This underlying trend, however, features considerable year-to-year variability - for example, the 2011 crop was 28,500 tonnes nut-in-shell, vs. 44,000 tonnes in 2014. This degree of variability is generally attributed to climatic influences, particularly around the key phenology phases of flowering, pollination, nut-set and nut-drop. Of late, some management effects have also tended to become equally important to climatic variation. Accurate crop forecasts for the Australian macadamia industry are required each year, in order to facilitate planning, handling, processing and marketing. A range of statistical and other forecasting methods have been used in agricultural systems. These forecasts have shown quite mixed results. Where the independent variables represent the underlying agronomic processes (or are proxies for these), the forecasts should be reasonably accurate. However some projects have produced quite disappointing results, as the forecasting process is well-known to be fraught with problems. One major issue here concerns the 'changing nature' of the macadamia industry as the orchards age, resulting in recent and current yields being lower than those that have been achieved in past years. In this study, two levels of crop predictions were produced for the Australian macadamia industry for each of the six separate production regions. Firstly, the overall longer-term forecast was based on tree census data from growers in the Australian Macadamia Society (AMS), scaled up to include non-AMS orchards. Expected yields were based on historical data provided by the growers, with a nonlinear regression model incorporating the interacting effects of tree age, variety, year, region and tree spacing. Orchard decline amongst older trees, which has recently become more apparent, was also incorporated into the yield model. Long-term forecasts were made out to about 10 years, after which the effects of (unknown) future plantings, tree removals and rejuvenation of orchards begin to have a major impact. The second level of crop prediction was an annual climate-based adjustment of these overall long-term estimates, taking into account the expected effects of the previous year's climate on production. The dominant climatic variables were observed temperature, rainfall and solar radiation, and modelled water stress. Based on the proven forecasting success of boosted regression trees and 'random forests' statistical methods, the average forecast from an ensemble of general linear regression models was adopted (rather than using a single best-fit model). Exploratory multivariate analyses and nearest-neighbour methods were also used to investigate the annual patterns in the data. In parallel, AMS each year conducts an annual survey of about 20 key industry growers and consultants. Their replies were integrated into a 'growers forecast' for each year, and this is also taken into account when the AMS releases its annual crop forecast. Overall, the success rate from this 15-year project has been less than desirable. This is attributed to a number of reasons, including incomplete base-data, macadamia varietal differences and their interactions with climate, and variable management approaches within the industry. Out of the fourteen years of forecasting, the targeted ±10% maximum error rate was only achieved in seven years for the climate forecasts, and six for the growers forecasts. The first seven years of the project generally saw a period of 'good crops', and here the absolute error rates averaged 8.2% for the climate forecasts and 11.6% for the growers forecasts. The next four years had notably poor crops due to low prices which lead to less-intensive management, and all forecasts were too high. The climate-adjusted forecast models had optimistically assumed 'about the same production patterns as before', but these yields were clearly not being achieved. Following a return to more normal prices, the forecasts for the more recent years have shown average absolute error rates of 8.6% for the climate models and 6.8% for the growers forecasts. These are within the targeted ±10%, and compare quite well with other crop forecasting applications.