Forecasting rainfall based on the Southern Oscillation Index phases at longer lead-times in Australia

Additional keywords: El Nino Southern Oscillation, forecast quality, hindcasting, Inter-decadal Pacific Oscillation, pastoralists.

Major drivers of profitability in Australian pastoral agriculture are rainfall and the ability to manage systems that are exposed to high rainfall variability. One of the tools available to help manage high rainfall variability is seasonal climate forecasting, now used by 30–50% of agricultural producers in decision-making (Australian Government Department of Agriculture Fisheries and Forestry 2004; Keogh et al. 2004, 2005). The Southern Oscillation Index (SOI) phase forecasting system (Stone et al. 1996) is one statistical forecasting system used by agricultural producers in the grain (Hammer et al. 1996), peanut (Meinke and Hammer 1997), sugar (Everingham et al. 2003), water (Abawi et al. 2000), and pastoral industries (Cobon 1999; Ash et al. 2000; Johnston et al. 2000; McKeon et al. 2000; Stafford Smith et al. 2000; McIntosh et al. 2005) to reduce climate-related risks. Tailoring decisions based on seasonal forecasts can lead to increased profitability and sustainability of natural resources (Hammer et al. 1996; Cobon and McKeon 2002).

Another statistical forecasting system based on indexes of sea surface temperature is the official operational seasonal forecast run by the Australian Bureau of Meteorology. Both forecasting systems show broad-scale forecast skill in excess of climatology, with the Bureau forecasts performing better in south-western Australia and the SOI phase forecasts performing better in central and eastern Australia, and, in particular, northern Queensland (Fawcett and Stone 2010). The Australian Bureau of Meteorology has developed a dynamical seasonal forecasting system, POAMA (Predictive Ocean-Atmosphere Model for Australia), which is a state-of-the-art, seasonal to inter-annual forecasting system based on a coupled model of the ocean and atmosphere. Assessment of some contemporary seasonal forecast systems in Europe demonstrates that the POAMA2 system is on a par with the other state-of-the-art systems (e.g. ECMWF system 3, UK Met Office Had GEM2-A, and Metro France ARPEGE4.6) (Lim et al. 2012).

Australian rainfall in some seasons and areas is significantly correlated with the SOI in the same or preceding seasons (Pittock 1975; McBride and Nicholls 1983; Chiew et al. 1998). Simultaneous correlations between the SOI and rainfall are strongest in spring (September–November) and weakest in summer (December–February). Lag correlations between the SOI in winter and spring rainfall are stronger than those of the SOI in summer and autumn rainfall, and the SOI in spring and summer rainfall.

A strong auto-correlation between SOI values early in the austral winter with those 3–6 months ahead (Gordon 1986) is sometimes referred to as ‘phase-locking’, which permits the use of seasonal forecasting once the early stages of the El Nino Southern Oscillation (ENSO) cycle have commenced. The SOI phase system was developed using principal components analysis (PCA) and subsequently cluster analysis of pairs of consecutive monthly SOI values. The PCA analysis identifies mean values and the change from one month to the next as the components explaining most of the variability. The PCA algorithms and cluster analysis resulted in five categories or phases of the SOI. The predictor (e.g. SOI phase) is selected on two leading principal components that reflected a 2-month SOI average and a change in SOI over 2 months, not on joint relationships between predictor and predictand (e.g. rainfall). That is, the predictor is derived from selecting principal components because they explain maximal variance, not because they are well correlated with the predictand, which is the primary cause of artificial skill in forecast systems. The SOI phases are then used to quantify future rainfall probabilities based on lag relationships derived from historical SOI patterns and rainfall (Stone et al. 1996). The original forecast system was explicitly developed for a ‘zero’ lead forecast (e.g. January–February SOI is used to predict March–May rainfall). In total, 60 world maps (twelve 3-month rainfall periods × five SOI phases) provide a spatial representation of this analysis showing the probability of exceeding the climatological rainfall median for any 3-month season following each SOI phase (i.e. all with zero lead-time). These maps are used in a range of industries to reduce the risk associated with drier than normal conditions or to take advantage of wetter than normal conditions.

The SOI phase forecast is provided for rainfall, pasture growth, and dryland wheat, e.g. www.longpaddock.qld.gov.au, www.daff.qld.gov.au/26_6256.htm. The rainfall forecast is issued each month for the next 3-month period (i.e. zero lead-time). This rolling 3-month forecast at zero lead-time makes it difficult for agricultural managers in Australia, particularly pastoralists managing large properties, to implement key decisions based on the forecast when the lag between the predictor and predictand is zero. For example, mustering on large, northern beef properties may occur only twice a year, and on both occasions takes months to complete. Adjusting livestock numbers commensurate with a seasonal rainfall forecast requires some months of advanced warning. In addition, decisions related to livestock numbers are made and implemented in the dry season, as access to the properties is limited during the wet season in the austral summer. Several surveys of pastoralists in northern Australian pastoral regions showed that they needed longer lead-times and indicators of forecast quality for the forecasts to be useful (Park et al. 2004; Paull 2004; Keogh et al. 2005). These surveys showed that forecasts for the austral warm season (November–March) issued first in June using the April–May SOI phase and reissued each month for the same forecast period counting down from 5 months to zero lead-time would be most useful for application in management in these regions. These forecasts that target a particular period and are issued with lead-times that count down to the forecast period have been tested using the SOI phase system for application in the north-eastern Australian sugar industry (Everingham et al. 2003). They found that for some regions, an early indication of anomalies in the yields of sugarcane can be produced some 7 months before the commencement of harvest (June), which is useful information for marketers, shipping schedules, and storage requirements. The magnitude and accuracy of the anomaly in yield, however, was not clearly defined for the varying lead-times.

There is considerable scope for improvement, or expansion of seasonal climate prediction (Drosdowsky and Allan 2000). The introduction of different target-season lengths, increased lead-times and prediction of other parameters besides rainfall (Clewett et al. 2003), pasture growth (Carter et al. 2000), and commodities (Potgieter et al. 2002) are areas of possible expansion. Here, we expand the boundaries of an operational statistical forecast system by increasing the target season length (from 3 to 5 months) and increasing lead-time (from 0 to 5 months) and investigate the utility of the ‘expanded SOI phase system’ in agricultural decision-making.

We map probabilities of exceeding the climatological rainfall median for the austral warm season (November–March) for lead-times of 0 to 5 months for the SOI phases. Our aims were to (i) examine the difference (shift) in probability distribution between the unconditional or climatological distribution and the conditional or forecast distribution; (ii) determine whether the shift between the distributions was large enough to be statistically significant and/or practically useful to foster changes in decision-making; and (iii) assess whether the SOI phase system can be used with some confidence at varying lead-times counting down to the November–March forecast period. For this assessment, we use measures of forecast quality including discriminatory ability (Kruskal–Wallis test; Kruskal and Wallis 1952) and skill (Linear Error in Probability Space skill score, in both hindcast and forecast modes; Potts et al. 1996). Probability (P) values are used to objectively evaluate temporal and spatial patterns of forecast quality. In addition we use the percentage of significant (P ≤ 0.1) stations as a measure of temporal coherence in forecast quality, and to compare 3- and 5-month forecast periods at varying lead-times.

The pastoral industry covers ~70% of Australia (Australian State of the Environment Committee 2001) (Fig. 1a), and areas north of ~30°S either have austral warm season dominant rainfall or are in arid regions with low and highly variable annual rainfall (Australian Government Bureau of Meteorology 2013). The pastoral areas occupy major components of the equatorial, tropical, grassland, and desert zones (Fig. 1b) (Köppen 1931; Stern et al. 2000), whereas the wheat–sheep and high-rainfall zones tend to be associated more with the subtropical and temperate classifications of Köppen (1931).

Fig. 1.  (a) Key agriculture regions in Australia and (b) major climate classification groups defined by Köppen (1931) and modified by Stern et al. (2000).

For the hindcast analysis, rainfall data were used from 590 locations across Australia (Fig. 2a). The monthly rainfall data were accessed from the SILO patch point dataset (Jeffrey et al. 2001) with infilled records from all locations used in each analysis starting in January 1889 and finishing in December 2004. For the verification in real time (1991–2010), analysis was completed for locations where a full data record was available. Depending on the length of the forecast period (3 or 5 months) and starting month, a full record was available for 500–527 locations. The November–March forecast period had a full data record for 509 locations (Fig. 2b).

Fig. 2.  Locations where rainfall data were used for this investigation (a) hindcast analysis (590 locations) and (b) November–March linear error in probability space (LEPS) in real time 1991–2010 (509 locations).

The SOI phase forecast system uses pre-determined clusters of the SOI that represent the variability in month-to-month values of the SOI (Stone et al. 1996). The five SOI phases, consisting of consistently negative, consistently positive, rapidly falling, rapidly rising, and near zero, were used to determine the probability of exceeding the climatological median rainfall using the stratified climatology technique. For certain times of the year and for particular regions, rainfall distributions can vary significantly with SOI phases. The magnitudes of these differences are important for decision-makers (Keogh et al. 2004, 2005). The SOI phase system is applied by grouping the years with the same SOI phase (analogue years), calculated using the 2 months preceding the forecasting period (i.e. November–March), and then comparing how the distribution of rainfall changes between each of the other phases and the full climatological record. This configuration of the SOI phases represents zero lead-time, which is defined here as the time between the end of the latest observed period and the beginning of the predictand period. For example, a 1-month lag between the predictor and the forecast period (predictand) is a 1-month lead-time (e.g. January–February SOI phase to predict April–June rainfall) and so on.

The quality of a forecasting system has more than one dimension and can be measured through various statistical approaches. The main attributes contributing to the quality of a forecasting system relate to the reliability of the forecast (i.e. is there any bias in the forecast system?), the discrimination of the forecast relative to a benchmark forecast system (i.e. change in shift and/or change in dispersion of forecast), and the skill of the forecast (i.e. changes in accuracy relative to a benchmark forecast system) (Murphy 1993; Potgieter et al. 2003). The skill of a forecast may be verified in either hindcast or forecast mode. Verification in hindcast mode uses data used to build the forecast system, whereas verification in forecast mode uses data independent of that used to build the forecast system (i.e. independent verification in real-time). Splitting datasets into components used and not used to build the forecast system and using the latter in the analysis of forecast quality is a technique used to remove artificial skill. The analysis of independent data gives a measure of true forecast quality. However, in this study, because the techniques used to develop the SOI phase system were unlikely to produce artificial skill in the dependent data, there is not likely to be any advantage in one dataset over the other from an artificial skill viewpoint. These measures of forecast quality give confidence that the outcomes generated from the forecast not only have discriminative ability and skill but are statistically significant and not purely artificial or due to chance. Probability (P) values (derived from Monte Carlo techniques) were used to help determine the likelihood that a forecast may have artificial skill, although a fixation on statistical significance can be misleading and detract from the more important physical processes or effects (Nicholls 2001). Results that are real and large enough to be practically useful might not be statistically significant because the sample size used was not large enough for the statistical technique to yield significance, whereas results that are statistically significant may not be large enough to be practically useful. The inferential procedures used provide evidence of the likelihood that differences between rainfall distributions might arise by chance. Quantifying the magnitude of the differences in rainfall distribution can be important from a pastoral manager’s point of view.

Although forecast quality is intrinsic in determining how good a forecasting system is, a clear understanding of the causal mechanisms linking ocean, atmosphere, and climate contributes valuable information about the forecasting system and, therefore, should not be ignored in decision-making regimes. A forecast system should not automatically be rejected solely because a P-value does not reach an arbitrary significance level, which is dependent on sample size. The small number of years of rainfall records in most locations in Australia makes it difficult to achieve statistical significance (Clewett et al. 2003). The quality of a forecast in a particular region may be useful and real even if it does not reach an arbitrary significance level of P = 0.01, 0.05, or 0.10. In this paper, actual P-values are reported (Nicholls 2001; Maia et al. 2007).

Here, we assume no bias in the historical rainfall data or SOI phase system, use the Kruskal–Wallis (KW) test statistic as a measure of discrimination, and the linear error in probability space (LEPS) score as a measure of skill. These methods can help provide pastoral managers, considering seasonal forecasts in their management decisions, with a measurable degree of confidence in the quality of the forecast, with potentially greater benefits expected for forecasts of higher quality (Adams et al. 1995).

The global nature of ENSO implies that its patterns of influence cohere in both time and space at scales representing not less than months/seasons and regions/catchments, respectively. A forecast system based on the mechanistic properties of ENSO, such as the SOI phases, should show properties of temporal and spatial coherence. To help assess temporal coherence in forecast quality we used the percentage of locations with P ≤ 0.1 as an indicator. This technique allowed rapid assessment of forecast quality in time. It was calculated for different seasons and lead-times and diagrammatically represented using bubble plots. The interpretation of temporal coherence involves comparison of bubbles on the diagonal of the bubble plot. For each cell in the forecast period (either 3 or 5 months) × lead-time matrix, if the number of significant locations was >20% and the cell diagonally upward from this also matched this criterion, then the forecast was deemed to have temporal coherence over this period. The bubble plots were useful for detecting skilled combinations of lead-time and season, to detect artificial skill, and to compare 3- and 5-month forecast periods at varying lead-times.

Spatial coherence of forecast quality was assessed by the shaded areas on the P-value maps that represented P ≤ 0.01, 0.01 ≤ P ≤ 0.05, 0.05 ≤ P ≤ 0.1, 0.1 ≤ P ≤ 0.2, 0.2 ≤ P ≤ 0.3, and P > 0.3.

The probability of exceeding the climatological median rainfall was calculated for subsets of years corresponding to each of the five SOI phases for each location, and probability of exceedance maps were constructed using kriging methods described later. These maps show the magnitude of shift in percentage chance of exceeding climatological median rainfall associated with each of the five SOI phases.

For every month of the year, probability distributions of rainfall for 3- and 5-month periods were produced for analogue years corresponding to each SOI phase and tested for forecast discrimination and skill. The KW test statistic was used to determine whether at least one of the set of five probability distributions belonged to populations with different medians when compared against the distribution of the other phases (Sheskin 2004). Forecast skill was assessed using the cross-validated LEPS tercile skill score where the forecast error is given a skill score in terms of the probability of it occurring (Wilks 1995).

Since the procedure for calculating the LEPS skill score does not yield a P-value, a Monte-Carlo procedure (Good 1997) using 2000 iterations was used to obtain a P-value for each LEPS skill score. Conversion to P-values provided a means of objectively evaluating and comparing temporal and spatial patterns of forecast quality across lead-times of the SOI phase system (Maia et al. 2007). Independent verification in real time (no SOI data used to build the forecast system are used to give the forecast) was also performed using cross-validated LEPS for the period from 1991 to 2010. The dataset was divided into years where the model was trained (all years before 1991) and years where it was verified (1991–2010). Kriging was used to obtain smoothed maps of percentage chance of exceeding climatological median rainfall and P-values (KW, LEPS) from station data. Kriging is a spatial statistical technique (Legendre and Legendre 1998) that uses the values of a variable at surrounding points in order to determine the value of the variable at a central point. It involved the fitting of the most appropriate model (exponential, spherical, or linear models were used in this case) to the semi-variance of the surrounding points as well as choosing the correct starting parameters for the model. R Statistical software (R Foundation 2004) was used to derive the KW, LEPS, and P-values.

The maps of percentage chance (probability) of exceeding median climatological rainfall show the consistently negative SOI phase at zero, 1-, and 2-month lead-times to be associated with a low probability of exceeding median rainfall in the austral warm season, and the consistently positive SOI to be associated with high probabilities (Fig. 3). The falling SOI phase was generally (but not always) associated with low probabilities and the rising and near-zero SOI phases were generally close to a 50% chance of exceeding median rainfall. These rainfall probability patterns for each SOI phase were similar for 0–2-month lead-times, which indicates a degree of persistence in the SOI phase from July–August through to September–October. These patterns were not as evident in the SOI phase maps for 3–5-month lead-times, indicating a breakdown in SOI persistence at the longer lead-times.

Fig. 3.  Maps of Australia showing the probability of exceeding the climatological rainfall median for the austral warm season (November–March) for lead-times of 0–5 months using the five-phase SOI forecast system. The five phases consist of: phase 1, consistently negative; phase 2, consistently positive; phase 3, falling; phase 4, rising; phase 5, near zero.

The shift in probability from the climatological rainfall median (i.e. shift from 50% probability of exceeding median) for the negative, positive, and falling SOI phases for the 0–2-month lead-time was commonly ±10–30% over large parts of northern and eastern Australia, and in some situations the shift was –40% (Fig. 3). The magnitude of this shift is adequate for many pastoral managers to change decisions based on the forecast of rainfall. In western Queensland, respondents to a survey said that, if given a 68%, on average, probability of exceeding the median rainfall, they might change a decision (Keogh et al. 2004). Similarly in another pastoral region, the Gascoyne Murchison area in Western Australia, forecasts with a probability of exceeding the median of ≥60% would influence respondents to change management decisions (Keogh et al. 2005). For example, pastoralists were prepared to accept the risk if a forecast was correct on 60–70% of occasions. However, feedback received from pastoral managers during the data collection period of these studies (and others) indicates that they would be more confident in changing decisions if the forecast were also associated with a level of ‘accuracy’.

At zero lead-time, the SOI phase system provided temporal coherence in forecast quality when assessed in hindcast mode for 3-month forecast periods starting in the austral winter and ending early in the austral summer (Fig. 4a, b). This supports previous studies showing that the association between SOI and 3-month Australian rainfall follows a ‘predictability barrier’ in autumn, builds in winter, reaches a peak in spring, and dissipates in summer (McBride and Nicholls 1983; Stone et al. 1996; Chiew et al. 1998). A similar temporal pattern of forecast quality was observed for the 5-month forecast period (Fig. 4d, e), although it extended through summer, presumably because of stronger associations between SOI and rainfall in early rather than late summer.

Fig. 4.  Percentage of significant (P < 0.1) rainfall stations for (a, b, c) 3-month and (d, e, f) 5- month forecast periods of the SOI phase system using (a, d) Kruskal–Wallis (KW); (b, e) linear error in probability space (LEPS) hindcast; and (c, f) LEPS in real-time. Elongated circles drawn on the upward diagonal show the temporal coherence associated with the July–August SOI phase with either the (a, b) November–January or (d, e) November–March rainfall periods.

For the November–January (Fig. 4a, b) and November–March (Fig. 4d, e) rainfall periods, there was temporal coherence in forecast quality in hindcast mode for the zero, 1-,and 2-month lead-times. These lead-times were associated with SOI phases in September–October (zero lead-time), August–September (1-month lead-time), and July–August (2- month lead-time). The July–August SOI phase was associated with >20% of locations with P ≤ 0.1 for the rainfall periods September–January, October–February, and November–March (lead-times 0–2 months); the August–September SOI phase for the rainfall periods October–February and November–March (lead-time 0–1 month); and the September–October SOI phase for the November–March (zero lead-time) rainfall period. The level of temporal coherence (as indicated by % of locations with P ≤ 0.1) appeared best in spring and declined as summer months were included in the forecast period. As such, the level of significant locations in the spring and early summer period appeared higher for the 3-month forecast period than the 5-month period. This is again consistent with scientific understanding of ENSO and its influence on Australian rainfall. There was some evidence of real-time temporal coherence in forecast quality for the April–May and May–June SOI phases (Fig. 4c, f).

Spatial forecast quality (hindcast and forecast modes) was evident for the austral warm season (November–March) forecast period in the central Queensland coastal areas for 0–2-month lead-times (Fig. 5). We found P-value maps derived from the hindcast KW and LEPS tests to be similar, a finding supported by Maia et al. (2007), but there were differences between hindcast and forecast modes. Spatial forecast quality in hindcast and forecast modes was evident for large areas of north-eastern Australia (lead-times of 0–5 months) and the Pilbara region in Western Australia (0–3 months). However, the extent of forecast quality was not as evident in forecast compared with hindcast mode (Fig. 5). In forecast mode, areas of forecast quality were evident along central parts of the Queensland coast for 0–5 months. In another study, real-time LEPS verifications of the SOI phase system, forecasting 3-month rainfall from September 1997 to October 2004, shows skill (LEPS score >5.0) in north-eastern Australia (R. Fawcett, pers. comm.). This area is of similar size to the shaded portions of the P-value maps in hindcast mode (Fig. 5, 0–2-month lead-time). Although the timeframe, target period, and overall approach of the analysis was different to the one used here, the results demonstrate that the relationship between SOI phase and Australian rainfall may currently persist despite the apparent reduction of its influence on longer time-scale climate modes during the period of real-time verification in this study.

Fig. 5.  The P-values of hindcast Kruskal–Wallis (KW) (left-hand panels), linear error in probability space LEPS (centre panels), and LEPS in real-time 1991–2010 (right-hand panels) tests for the SOI phase system for November–March rainfall at different lead-times.

The performance of a forecast system in a real-time setting is an important test of its utility in present-day applications. Estimates of forecast quality based on hindcasts, where the forecast system ‘knows’ data that occurred later than the time being forecast, can be biased and overestimate the real quality of the forecast. Although the development of the SOI phase system does not involve training of data forming joint relationships of predictor and predictand, we did complete an analysis of forecast quality using only data not used to construct the forecast system. Since the SOI phase forecast system was developed using SOI data before 1991, only post-1991 data (SOI and rainfall) were used to assess forecast quality in real-time (i.e. independent verification in real time). The disadvantages of this procedure are the short length of records of the data, which is compounded by the low-frequency nature of ENSO, the variation in the relationship between predictor and predictand on decadal to multi-decadal timescales, and permanent changes in the predictor/predictand relationships caused by climate change. For these reasons, the World Meteorological Organization acknowledges that real-time monitoring is neither as rigorous nor as sophisticated as the hindcast verification; nevertheless, it is necessary for forecast production and dissemination (World Meteorological Organisation 2002).

The relationship between SOI and seasonal rain over most of Australia has changed over time (Nicholls et al. 1996, 1997), and the short length of record of the ‘out of sample’ independent data used to assess the quality of the forecast system in real-time may correspond to a period when low frequency climate modes are providing strong (or weak) modulation of the inter-annual ENSO signal (Allan 2000; Power et al. 1999). When the Inter-decadal Pacific Oscillation (IPO; Folland et al. 1998) lowers temperatures in the tropical Pacific Ocean, year-to-year ENSO variability is closely associated with year-to-year variability in rainfall, but no robust relationship exists when the IPO raises temperatures (Power et al. 1999). Variations in rainfall are only significantly correlated with the SOI when the IPO index is negative. For the period in which our independent verification in real-time was completed (1991–2010), the IPO was mostly positive and ‘out of phase’ with ENSO, and this superposition of the two climate modes may help explain the reduced level of real-time forecast quality at this time. This paradigm suggests that the climate system exhibits underlying, predictable, inter-decadal variability that causes inter-decadal changes in ENSO and its impact on Australia.

Alternatively, more recent studies describe indices of the IPO and its northern Pacific partner, the Pacific Decadal Oscillation (PDO; Mantua et al. 1997), as largely unpredictable inter-decadal variability in traditional ENSO indices (Power et al. 2006; Power and Colman 2006). The unpredictability of this inter-decadal variation is likely to be associated with the non-linear relationship between ENSO and Australian rainfall. For example, the curves of best fit of observed SOI v. observed Australian rainfall are non-linear. The slopes are larger in magnitude for a positive SOI and smaller for a negative SOI. This means that if the positive SOI anomaly associated with a La Nina event is large in magnitude, then there is a strong tendency for the rainfall increase to be large. However, a large negative SOI excursion associated with an El Nino event provides a poorer guide to the extent of drying over Australia. Therefore, if the climate system spends more time during a given inter-decadal period on the negative SOI side (e.g. if the period is dominated by El Ninos, as was the case between 1991 and 2010) then the relationship between ENSO and Australian rainfall will appear weak. At the same time, the inter-decadal sea surface temperature (SST) anomaly will be El Nino-like simply because the period is more heavily influenced by El Nino events. The IPO and its index will reflect the dominance of El Nino SST anomalies during the period and tend to be in a positive phase, and by association, the relationship between SOI and Australian rainfall will be weak. The non-linear relationship between ENSO and Australian rainfall (McBride and Nicholls 1983), and the dominance of El Nino-like conditions between 1991 and 2010, help explain the relatively poor independent verification in real-time during the relatively short 20-year period that it was assessed in this study.

Because independent verification in real-time was assessed over a short period (20 years) when the decadal–multi-decadal relationship between predictor and predictand appeared weak, we have placed greater emphasis on the outcome of the longer hindcast analysis in interpreting the results than in the independent verification. Putting more emphasis on the hindcast results could be perceived as a limitation but, because the predictor (e.g. SOI phase) in this forecast system was selected on leading principal components and not on joint relationships between predictor and predictand (e.g. rainfall), the level of artificial skill in this hindcast analysis is likely to be zero (DelSole and Shukla 2009), which provides further justification to place more emphasis on the hindcast results. Better understanding of the processes driving climate variability on decadal and multi-decadal timescales is needed to improve both tactical and strategic decision making in agricultural enterprises.

The tests of forecast quality used here provided information regarding the skill of the overall forecast system. Other tests, such as the Kolmogorov–Smirnov test (Conover 1971), provide information about whether the cumulative probability distribution of an individual phase is different from the combined cumulative probability of the other four phases. This statistic can be important for the decision-maker and is best evaluated for that location at the local level using the expertise of a climate extension officer and climate analysis tools such as RAINMAN (Clewett et al. 2003).

Agricultural producers in northern Australia rely on summer rainfall, and key management decisions can change depending on rainfall. The SOI phases used at 0–2-month lead-time for the November–March period provided a forecast for the key rainfall period in northern Australia over a lead-time period long enough for key decisions to be made and implemented before November. The forecast provided a useful shift in median rainfall probabilities (–40% to +30%), which is important from a viewpoint of systems management.

The SOI phase system provided forecast quality when assessed in hindcast mode for the austral warm season at lead-times of up to 2 months. This represents an increase in the forecast lead-time of 2 months. The majority of locations showing forecast quality were in northern Australia (north of 25°S), predominately in north-eastern Australia (north of 25°S and east of 140°E). Agricultural managers in these areas can be more confident when using these probabilistic forecasts of rainfall because they have passed a variety of forecast quality measures including statistical verification in both hindcast and forecast modes. The forecast verification showed small areas of forecast quality along the central Queensland coast but failed our temporal tests of forecast quality. Possible reasons for forecast quality in hindcast mode being better than in forecast mode have been discussed.

This seasonal forecast which targets the austral warm season at lead times of 0–2 months could be useful to pastoralists, sugarcane growers, water managers, horticulturalists, and aquaculturalists among others operating businesses in north-eastern Australia. The SOI phase forecast system used in ‘target mode’ provides more opportunity for management decisions to be changed and, as a result, can be more useful in agriculture than when issued in ‘rolling mode’ at zero lead-time.