Annual forecasting of the Australian macadamia crop - integrating tree census data with statistical climate-adjustment models

To facilitate marketing and export, the Australian macadamia industry requires accurate crop forecasts. Each year, two levels of crop predictions are produced for this industry. The first is an overall longer-term forecast based on tree census data of growers in the Australian Macadamia Society (AMS). This data set currently accounts for around 70% of total production, and is supplemented by our best estimates of non-AMS orchards. Given these total tree numbers, average yields per tree are needed to complete the long-term forecasts. Yields from regional variety trials were initially used, but were found to be consistently higher than the average yields that growers were obtaining. Hence, a statistical model was developed using growers' historical yields, also taken from the AMS database. This model accounted for the effects of tree age, variety, year, region and tree spacing, and explained 65% of the total variation in the yield per tree data. The second level of crop prediction is an annual climate adjustment of these overall long-term estimates, taking into account the expected effects on production of the previous year's climate. This adjustment is based on relative historical yields, measured as the percentage deviance between expected and actual production. The dominant climatic variables are observed temperature, evaporation, solar radiation and modelled water stress. Initially, a number of alternate statistical models showed good agreement within the historical data, with jack-knife cross-validation R2 values of 96% or better. However, forecasts varied quite widely between these alternate models. Exploratory multivariate analyses and nearest-neighbour methods were used to investigate these differences. For 2001-2003, the overall forecasts were in the right direction (when compared with the long-term expected values), but were over-estimates. In 2004 the forecast was well under the observed production, and in 2005 the revised models produced a forecast within 5.1% of the actual production. Over the first five years of forecasting, the absolute deviance for the climate-adjustment models averaged 10.1%, just outside the targeted objective of 10%.

Statistical methods for analysis of multi-harvest data from perennial pasture variety selection trials

Variety selection in perennial pasture crops involves identifying best varieties from data collected from multiple harvest times in field trials. For accurate selection, the statistical methods for analysing such data need to account for the spatial and temporal correlation typically present. This paper provides an approach for analysing multi-harvest data from variety selection trials in which there may be a large number of harvest times. Methods are presented for modelling the variety by harvest effects while accounting for the spatial and temporal correlation between observations. These methods provide an improvement in model fit compared to separate analyses for each harvest, and provide insight into variety by harvest interactions. The approach is illustrated using two traits from a lucerne variety selection trial. The proposed method provides variety predictions allowing for the natural sources of variation and correlation in multi-harvest data.

Statistical forecasting of the Australian macadamia crop

Three types of forecasts of the total Australian production of macadamia nuts (t nut-in-shell) have been produced early each year since 2001. The first is a long-term forecast, based on the expected production from the tree census data held by the Australian Macadamia Society, suitably scaled up for missing data and assumed new plantings each year. These long-term forecasts range out to 10 years in the future, and form a basis for industry and market planning. Secondly, a statistical adjustment (termed the climate-adjusted forecast) is made annually for the coming crop. As the name suggests, climatic influences are the dominant factors in this adjustment process, however, other terms such as bienniality of bearing, prices and orchard aging are also incorporated. Thirdly, industry personnel are surveyed early each year, with their estimates integrated into a growers and pest-scouts forecast. Initially conducted on a 'whole-country' basis, these models are now constructed separately for the six main production regions of Australia, with these being combined for national totals. Ensembles or suites of step-forward regression models using biologically-relevant variables have been the major statistical method adopted, however, developing methodologies such as nearest-neighbour techniques, general additive models and random forests are continually being evaluated in parallel. The overall error rates average 14% for the climate forecasts, and 12% for the growers' forecasts. These compare with 7.8% for USDA almond forecasts (based on extensive early-crop sampling) and 6.8% for coconut forecasts in Sri Lanka. However, our somewhatdisappointing results were mainly due to a series of poor crops attributed to human reasons, which have now been factored into the models. Notably, the 2012 and 2013 forecasts averaged 7.8 and 4.9% errors, respectively. Future models should also show continuing improvement, as more data-years become available.