Sugarcane is an important agricultural crop grown on the east coast of Australia. The timing and amount of rainfall is critical in determining both the yield of sugar and scheduling of harvesting operations. Rainfall forecasts issued through the Australian Bureau of Meteorology are based on general circulation models (GCMs) and have a poor skill levels. They are also limited in utility to end-users such as farmers as they cover very broad geographical areas and are only issued as probabilities above or below median. This paper presents an alternative approach for forecasting monthly rainfall with up to 12 month lead-time based on machine learning, in particular neural networks. Monthly rainfall forecasts have been developed for the eight locations in Eastern Australia at 3 and 12 month lead-time. The accuracy of the forecasts has been assessed relative to a skill scale with 0% representing climatology (the long term average) and 100% representing a perfect forecast (observation). On this scale, neural network forecasts are typically in the range 39.9–68% for all months using a single month optimization. This compares very favorably with forecasts using GCM from the Bureau that have skill levels only in the range −20% to 20%.

INTRODUCTION

Weather forecasting is vital for many aspects in agriculture (Shukla et al. 2011). Climate is a key driver for sugarcane productivity (Everingham et al. 2003). Everingham et al. reported that early knowledge about the climate could add value to production, harvest and marketing efforts (Everingham et al. 2003). Decision-making based on rainfall forecasts can increase profitability of sugarcane seasons. Delivering accurate seasonal and annual rainfall forecasts in sugarcane industry processes such as plantation, fertilization, irrigation, and harvest lead to larger yields, therefore higher profit. Through the season, there are a number of industry operations carried out that are timed to suit typical rainfall conditions (Everingham et al. 2012). Outputs from long lead forecasting models can be beneficial to industry planning early in the year (Everingham et al. 2007). The ability to predict the time and the amount of precipitation before the start of crop seeds allows growers to set schedules for planting, in addition to avoiding seed damage due to wet or dry weather after plantation.

Sugar cane is a plant that requires water to grow. Usually, based on the seasonal amount of precipitation, growers decide whether to include irrigation. Precise rainfall prediction gives growers the opportunity to effectively manage irrigation where they would buy water, identify the best suitable machines, and sign contracts for maintenance earlier if forecasts showed that the amount of rainfall through the season would not be sufficient. Therefore, growers would avoid additional fees for higher water prices during the season, and permit irrigation companies to be scheduled earlier and not overwhelmed. On the other side, if forecasts revealed a wet season, growers would avoid signing contracts with irrigation companies, and paying extra amounts for season insurance.

Fertilization is the process of adding chemicals and pesticides to sugar areas, in addition to spraying fields at different stages during the season. Growers must be careful before adding fertilizers to the ground. If heavy rainfall were detected after adding these chemicals to the fields, it would be dragged to river water and cause pollution. This may produce disastrous effects on river plants. Spraying time is crucial for growers. If there is heavy rainfall and wind, spraying may not lead to satisfiable consequences. Moreover, if there is a dry season, spraying may burn the plants if there is no irrigation.

In Australia, the sugarcane-harvesting season starts around June and continues up until late September. Information about the start day of harvest should be given no later than March (Clarke et al. 2010). Ability to identify the type and amount of rainfall during this part of the season contributes to managing this process. Growers would take a decision to start early if forecasts indicated a wet season, or to start first with paddocks prone to floods. In addition to these forecasts, encourage growers to sign maintenance contracts and setup transport chains earlier with higher numbers of containers to move crops. In the harvest season, wet yield can cause additional work in the mills to clean it up. Sugarcane is a perennial crop, where harvesting in wet weather may damage the sugarcane crop, therefore reducing its profitability during future seasons (Everingham et al. 2003). Wet conditions in the 1998 harvest season diminished the industry revenue by around 175 million dollars (Everingham et al. 2007). The loss was reported as being due to cane being left unharvested, reduced commercial cane sugar levels, and damage to paddocks from wet weather harvesting. On the other hand, if forecasts designated a dry season, growers would start harvesting the driest areas first to avoid loss of crops at the end of the season.

In addition to seasonal and annual, long decadal rainfall prediction enhances decisions related to investment on irrigation structure. Millers would benefit from data to improve long-term management of bagasse supplies. Furthermore, marketers could utilize this data to help choices related to buying expensive items as storage infrastructure.

Sugarcane is a plant that can regrow for five consecutive seasons before being ploughed out from the ground (Clarke et al. 2010). Australia is the third largest raw sugar supplier in the world. In Australia, 95% of sugarcane grows in Queensland, a state located in the north-east of the continent. Sugarcane areas are located along 2,100 km coastline extending from 16 to 29 °S (Everingham et al. 2003). Australian sugar areas are basically situated along Australia's eastern coastline, from Mossman in far north Queensland to Grafton in northern New South Wales. Sugarcane production in Australia occurs from tropical regions in northern Queensland to the sub-tropical environment of northern New South Wales. Sugar industry generates approximately 1 billion AUD in export earnings (Everingham et al. 2012).

Decision-making in water management is crucial, not only in the sugar industry but also for many different aspects such as dam management. Precipitation contributes in a high degree to water management. In 2010, disastrous floods occurred in Brisbane, the capital city of Queensland. It has been stated that the floods were ‘dam-release’ floods. Release of water from the Wivenhoe dam (located at the Brisbane River in South East Queensland, Australia) was the principle cause of flooding along the mainstream and tributaries of the Brisbane River downstream of the dam over the period 11–12 January 2011 (van den Honert & McAneney 2011). Taking into consideration the effect of rainfall on water level in Brisbane catchment, a different strategy would have been taken (van den Honert & McAneney 2011).

LITERATURE REVIEW

Rainfall forecasts play a key role in water management. Rainfall forecasting models have been developed in an attempt to predict precipitation for a specific location. Operational climate forecasts in Australia have been available for more than a decade (Everingham et al. 2007). Various types of forecasting systems have been developed to improve knowledge and assist with decision-making in the sugar industry. These models predict for various durations of time. Decadal, annual, and seasonal forecasts would be helpful to the industry. The Bureau of Meteorology (BOM) is an executive agency of the Australian Government in charge of giving climate administrations to Australia and encompassing ranges. BOM uses general circulation models (GCMs) to produce official rainfall forecasts across Australia. GCMs are dynamic systems that use computer simulation for rainfall forecasting. These models failed to forecast rainfall variability in different periods of time, especially in 2010 where heavy rainfall occurred along different areas in Queensland. The Australian Bureau of Meteorology has developed a dynamical forecasting system, POAMA (Predictive Ocean-atmosphere model for Australia). A seasonal to inter-annual forecasting system based on a coupled model of the ocean and atmosphere (Cottrill et al. 2012), POAMA has been established to provide seasonal forecasts, and it was introduced officially in 2013. POAMA (version P2.4) is reset at the beginning of each month, and then forecasts are released for that month and the next 8 months (Hawthorne et al. 2013). These forecasts are probabilistic, where probability values are launched across large grid areas (250 km). They are considered insufficient for the sugarcane industry, as they give no indication about the magnitude, time and specific location of precipitation.

Researchers tried different techniques to setup models for rainfall forecasting. Climate indices have been used to build forecasting models. Scientists claim that El-Niño southern oscillation (ENSO) is a contributor to rainfall variability over the world. Clarke et al. developed a model using ENSO to predict weather for the sugar season, earlier before autumn (Clarke et al. 2010). The success of an Australian sugarcane-cropping season depends on rainfall and the ability to forecast it. Authors tried to determine if weather conditions in the second half of the harvest season can be predicted early in the year. This method of prediction is probabilistic, and above or below the median values were computed.

Artificial neural networks (ANNs) are massively parallel distributed processing systems representing a new computational technology built on the analogy to the human information processing system (Shukla et al. 2011). ANNs are computer algorithms that aim to recognise non-linear relationships between inputs. It receives input values and establishes a pattern between these values to release forecasts. ANN mimics the biological neurons inside the human brain. It consists of a number of simple and highly interconnected processing elements called neurons that process information by their dynamic state response to external inputs (Baawain et al. 2005). Neurons have additional parameters (weight, learning rate, momentum, etc.). An ANN has a great capability to learn by making proper adjustments of these parameters, in order to produce the desired output (Singh & Borah 2013). The basic structure of a neural network is formed of: input layer, hidden layer and output layer. Each layer consists of a set of neurons. Neurons are linked to the next layer, where each link has a weight that determines the strength and the relationship between the two connected neurons. Output of the neuron is multiplied by this weight while it is transferred to the neuron of the next layer. Neurons not belonging to the input layer may receive multiple inputs, which would be calculated based on a transfer function to produce output. The dataset is usually subdivided into three different sets: training set, validation set and testing set. ANN is trained using the learning process (Zou et al. 2008). During this process, inputs are given to the model, outputs are calculated and weights are modified to desired values (French et al. 1992). Usually, the weight of the interconnected nodes remains the same after finishing the training process. Indeed, to obtain successful training, a large number of known inputs and outputs are required to be added to the neural network (French et al. 1992). The second set is the validation set, which is used to validate the reliability of the trained network (Abbot & Marohasy 2012). The third set is called the test set and it is used to measure the accuracy of the developed model. It is basically a hind cast of data. If the performance during the testing is adequate, then the model can be used in predicting future data (Shukla et al. 2011).

ANN methods and approaches have been used across the world to forecast rainfall and weather variability (Haupt et al. 2009). Rani et al. have used an ANN model to forecast monthly rainfall for Andhra Pradesh in India (Rani et al. 2014). A teaching learning based optimization (TLBO) neural network that simulates teaching-learning phase in life was used in this study. A modification was applied to the learning phase of this model, in an attempt to enhance results. Monthly rainfall historical data were collected from the Indian Institute of Tropical Meteorology (IITM), where the dataset was composed of 1,692 monthly observations, representing the duration between 1871 and 2011. Three different samples were used: training sample, testing sample and hold out sample. A back propagation algorithm was developed for comparison with this model, and results showed that modified TLBO had better results in terms of root mean square error (RMSE) (Rani et al. 2014). Maqsood et al. used ANNs to forecast hourly rainfall for southern Saskatchewan in Canada (Maqsood et al. 2003). Temperature, wind speed and relative humidity were used as input for the neural network models applied in the study.

Neural networks have not been widely explored for forecasting Australian rainfall (Abbot & Marohasy 2013). Abbot and Marohasy predicted rainfall for the Brisbane catchment using ANNs (Abbot & Marohasy 2013). Historical rainfall and temperature datasets in addition to climate indices have been used as input in their study. Neurosolutions6 for Excel was used as the ANN software, where 85% of data were used for training and the remaining for testing. Output was assigned to 1, 2 and 3 months respectively. Results were compared to POAMA in two locations (Gatton and Harristville), having lower RMSE and WNDI for the ANN approach. Authors showed that climate indices and temperature are enhancing components for rainfall forecasting using ANN.

Abbot and Marohasy used ANN again to forecast rainfall for the Brisbane catchment in Australia for 12 month lead-time. Better forecasts have been recorded with this mechanism where correlation exceeded 0.85 for most of the tested months (Abbot & Marohasy 2015a).

He et al. proposed an approach using historical rainfall data and climate indices to develop a forecasting model for south Australia that is based on the integration of multi-resolution analysis and multi-linear regression model (He et al. 2014). Results were compared to a traditional multi-linear regression model where lower relative absolute error for most of the stations studied has been recorded with their mechanism.

In our study, we developed a rainfall forecasting mechanism that uses ANNs and climate attributes to forecast both seasonal (Lead 3) and annual (Lead 12) forecasts. This paper consists of six sections. The following section describes the dataset that has been used to perform the study. The subsequent two sections present the used methodology, and the results and the comparative analysis. The final section derives a conclusion and future directions.

DATA

Rainfall and temperature

Sugarcane production occurs along 2,100 km of coastline between Mossman in north Queensland and Grafton in northern New South Wales. For this study, monthly rainfall data were collected from the BOM for each of the 8 cities: Bingera, Mossman, Macknade, Plane Creek, Maryborough, Victoria Mill, Fairymead and Kalamia. Those sites were chosen to perform this study for their closeness to sugarcane paddocks and mills, in addition to availability of long historical records in each of these locations. Missing data were replaced by values found in the nearest weather station. Long historical datasets for more than 100 years were composed. Planecreek historical monthly rainfall dataset commenced in January 1909. Macknade, Maryborough, Mossman and Victoria plantation began in 1908. Bingera and Fairymead started in January 1900, while Kalamia holds the largest dataset dating back to the late 19th century, August 1892. Annual average rainfall for each of the following locations is represented in Table 1. Maximum and minimum monthly temperatures were collected from BOM for each site.

Table 1

Annual average rainfall for each of the eight sites used in the study

CityAnnual average (mm)
Bingera 1,023 
Kalamia 1,076 
Fairymead 1,094 
Maryborough 1,141 
Plane Creek 1,764 
Victoria Plantation 2,032 
Macknade 2,151 
Mossman 2,385 
CityAnnual average (mm)
Bingera 1,023 
Kalamia 1,076 
Fairymead 1,094 
Maryborough 1,141 
Plane Creek 1,764 
Victoria Plantation 2,032 
Macknade 2,151 
Mossman 2,385 

Climate indices

Multiple studies have been applied showing evidence that climate indices are potential predictors of seasonal and annual rainfall (Pasini & Langone 2010; Schepen et al. 2012). The ENSO is an important climate phenomenon that affects primarily the atmospheric conditions of the tropical Pacific region including the local climate and weather in Australia (Tularam 2010). The Southern Oscillation Index (SOI) and Nino3.0 are the two most widely used indicators to represent ENSO (Baawain et al. 2005). SOI is the monthly averaged pressure difference between Darwin and Tahiti (Baawain et al. 2005), while the Nino3.0 index represents the sea surface temperature (SST) anomalous averaged over the region bounded by 5°N to 5°S and 90°W to 15°W (Baawain et al. 2005). Climate anomalies are expected to be an effect of ENSO, which may lead to several consequences such as high crop loss. ENSO affects multiple countries of the world and influences agricultural activities in these countries (Schepen et al. 2012). According to Fawcett, ENSO should be taken into account when developing forecasting systems for Australia (Fawcett & Stone 2010). It has been added as an input to our ANN model. Data for the SOI were taken from the BOM, while Nino3.0 values were collected from the Royal Netherlands Meteorological Institute Climate Explorer, a web application that analyses climate data statistically.

Nino3.4 is the average SST anomaly in the region bounded by 5°N to 5°S, from 170°W to 120°W. Small temperature deviation in the Nino3.4 region significantly increases or decreases the chance of rainfall in Australia. This temperature deviation is frequently referred to as the value of the Nino3.4 index (Everingham et al. 2007). Nino3.4 values and additional Nino values (Nino4.0, Nino1.2) that can be used as a measurement for the ENSO phenomena were collected from KNMI climate explorer and added to the dataset.

Indian Ocean Dipole (IOD) is a climate index that recent studies have shown to contribute to rainfall variability across Australia (Risbey et al. 2009). It is an ENSO-like coupled ocean–atmosphere phenomenon in the equatorial Indian Ocean. The Dipole Mode Index (DMI) is a measure of the IOD defined as the difference in SST between the tropical western Indian Ocean and the tropical south-eastern Indian Ocean. DMI based in HadISST1 was used in this study (Abbot & Marohasy 2012). This climate index was collected as daily values from KNMI climate explorer, and converted to monthly representations for each month.

The inter-decadal Pacific Oscillation (IPO) measures pressure and temperature changes in the Pacific Ocean (Abbot & Marohasy 2015a). IPO records were added to datasets. IPO data were collected from the UK Met Office as monthly values.

Sunspots

The sun is the main driver of the Earth's climate (Steinhilber et al. 2009). Sunspot records were used in this study. Monthly values were collected from KNMI climate explorer.

PROPOSED METHOD

Research on seasonal climate forecasts for the Australian sugar industry is steadily on the rise (Jaffres & Everingham 2005). Twelve lagged values were created and added for each of the historical monthly rainfall values, maximum and minimum monthly temperature values, climate indices and sunspots. Data were manipulated so that records begin at the same time as monthly rainfall data values. For each of the eight cities, two types of rainfall forecasting were targeted: seasonal and annual. The first type is to forecast seasonally for the next 3 months (Lead 3), while the second is to forecast rainfall up to a year. Neurosolutions infinity (NeuroDimensions Inc., Florida) was the neural network software used to perform this study. For each type of forecasts, two approaches to rainfall forecasting as described below have been proposed. Figure 1 represents the two proposed approaches.
Figure 1

Two approaches followed, all months and one single month optimizations.

Figure 1

Two approaches followed, all months and one single month optimizations.

All months optimization

The first method uses all the historical data as one dataset and input this set into the neural network. For each of the eight sites, data for all the months were combined and added as an input to the neural network; 75% were used for training, 15% for validation and the remaining 10% were used for testing. For each site, two runs were applied: 3 month lead-time, and 12 month lead-time. The 3 month lead-time is to forecast three values for the next coming 3 months, while 12 month lead-time is to forecast up to 1 year. As a result, 16 runs have been applied for the eight sites. Testing data contained at least 10 years of data.

Single month optimization

A single month optimization is a technique for inputting data into the neural network, where instead of adding all the monthly records as a single set, each month's data (rainfall, temperature, sunspots and climate indices) are added to the neural network as a dataset. The 75% of data were used for training, 15% data were used for validation and 10% data were used for testing. For each of the eight sites, 24 runs have been conducted: 12 to forecast seasonally (Lead 3) and the remaining to forecast annually (Lead 12). Lead 3 means each month forecasts the next third month, e.g. June data forecast September, while Lead 12 is to forecast the amount of rainfall for the same month in the next year, e.g. June values predict one single value of June for next year. Using this approach, 192 runs were conducted. At running single month optimization, 10 records representing the latest 10 years of monthly values were used for testing.

DISCUSSION AND ANALYSIS

To compare the two approaches, testing data were collected from all the runs. RMSE, mean absolute error (MAE) and correlation coefficient (r) are statistical techniques used to compare results of forecasts. These statistical techniques have been deployed in water forecasting (Shukla et al. 2011). RMSE measures the difference between the forecast rainfall and observed rainfall quantitatively (Abbot & Marohasy 2015b). RMSE values are positive, where the closer the number is to zero, the more skilful the forecasts are. To achieve precise comparison, a deconstruction of data was performed. Deconstruction is used to divide the 10% of testing data in the first approach (all month optimization) into 12 datasets where each set contains the values of a specific month across all the years used in testing. MEA, RMSE, and r values were calculated for each month for two sites, Bingera (Table 2) and Mossman (Table 3) using the two approaches.

Table 2

MAE, RMSE and r values for Bingera monthly rainfall forecasts between October 2004 and September 2014, seasonal and annual forecasts using all months optimization and one single month optimization

Type
Seasonal (Lead 3)
Annual (Lead 12)
Approach
All-months
One-month
All-months
One-month
MonthMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)r
January 75.43 94.18 0.883 27.37 38.67 0.980 81.60 127.64 0.886 17.39 22.57 0.995 
February 66.67 83.26 0.806 20.36 27.47 0.977 88.05 109.55 0.508 35.65 44.40 0.961 
March 74.22 85.49 0.771 37.65 56.88 0.925 65.95 83.23 0.824 43.23 49.16 0.959 
April 31.96 41.73 0.113 7.69 9.31 0.977 27.96 41.11 − 0.077 16.46 23.07 0.974 
May 31.92 37.13 0.376 14.23 20.95 0.856 30.99 37.89 0.232 7.02 13.81 0.934 
June 43.17 62.42 0.385 9.88 13.96 0.973 46.89 65.01 0.458 29.26 38.24 0.932 
July 29.34 35.59 0.503 12.16 14.78 0.946 32.85 40.67 0.201 16.51 19.69 0.986 
August 31.72 45.23 0.487 20.60 28.44 0.906 34.83 55.25 − 0.240 10.94 12.53 0.964 
September 28.38 46.38 0.439 9.39 16.10 0.990 23.84 31.85 0.803 9.14 14.33 0.996 
October 46.99 54.14 0.120 23.31 28.33 0.984 28.31 34.59 0.356 18.14 22.40 0.810 
November 35.40 46.58 0.355 6.41 8.27 0.985 28.17 35.71 − 0.165 22.58 23.73 0.975 
December 50.94 73.23 0.938 57.80 105.34 0.988 74.83 124.07 0.842 62.41 110.62 0.997 
Average 45.51 58.78 0.51 20.57 30.71 0.96 47.02 65.55 0.39 24.06 32.88 0.96 
Type
Seasonal (Lead 3)
Annual (Lead 12)
Approach
All-months
One-month
All-months
One-month
MonthMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)r
January 75.43 94.18 0.883 27.37 38.67 0.980 81.60 127.64 0.886 17.39 22.57 0.995 
February 66.67 83.26 0.806 20.36 27.47 0.977 88.05 109.55 0.508 35.65 44.40 0.961 
March 74.22 85.49 0.771 37.65 56.88 0.925 65.95 83.23 0.824 43.23 49.16 0.959 
April 31.96 41.73 0.113 7.69 9.31 0.977 27.96 41.11 − 0.077 16.46 23.07 0.974 
May 31.92 37.13 0.376 14.23 20.95 0.856 30.99 37.89 0.232 7.02 13.81 0.934 
June 43.17 62.42 0.385 9.88 13.96 0.973 46.89 65.01 0.458 29.26 38.24 0.932 
July 29.34 35.59 0.503 12.16 14.78 0.946 32.85 40.67 0.201 16.51 19.69 0.986 
August 31.72 45.23 0.487 20.60 28.44 0.906 34.83 55.25 − 0.240 10.94 12.53 0.964 
September 28.38 46.38 0.439 9.39 16.10 0.990 23.84 31.85 0.803 9.14 14.33 0.996 
October 46.99 54.14 0.120 23.31 28.33 0.984 28.31 34.59 0.356 18.14 22.40 0.810 
November 35.40 46.58 0.355 6.41 8.27 0.985 28.17 35.71 − 0.165 22.58 23.73 0.975 
December 50.94 73.23 0.938 57.80 105.34 0.988 74.83 124.07 0.842 62.41 110.62 0.997 
Average 45.51 58.78 0.51 20.57 30.71 0.96 47.02 65.55 0.39 24.06 32.88 0.96 
Table 3

MAE, RMSE and r values for Mossman monthly rainfall forecasts between October 2004 and September 2014, seasonal and annual forecasts using all months optimization and one single month optimization

Type
Seasonal (Lead 3)
Annual (Lead 12)
Approach
All-months
One-month
All-months
One-month
MonthMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)RMAE (mm)RMSE (mm)r
January 153.16 198.33 0.738 196.27 212.38 0.931 117.22 158.22 0.691 76.86 99.28 0.925 
February 182.64 221.22 0.884 116.42 174.66 0.878 199.88 279.86 0.522 202.63 241.85 0.904 
March 169.72 193.28 0.670 72.06 80.21 0.963 123.37 154.09 0.798 76.26 93.29 0.935 
April 174.53 245.61 − 0.189 39.63 63.06 0.963 99.64 120.61 0.841 57.52 88.35 0.984 
May 65.56 118.57 − 0.042 35.56 59.77 0.986 75.14 125.18 − 0.164 14.17 21.33 0.998 
June 43.93 53.71 0.016 21.78 34.82 0.859 48.88 63.06 − 0.173 11.56 21.16 0.926 
July 21.92 25.77 0.041 9.62 11.67 0.962 29.85 35.83 − 0.076 3.39 4.49 0.989 
August 29.90 32.07 − 0.058 9.35 12.05 0.963 19.72 26.30 0.605 1.70 2.10 0.998 
September 32.42 48.95 0.371 8.98 11.61 0.982 29.29 49.85 0.317 13.05 15.65 0.965 
October 54.12 82.50 0.180 15.04 19.22 0.976 72.22 99.51 0.000 13.90 18.20 0.992 
November 100.53 123.78 − 0.309 52.35 63.23 0.965 84.78 118.53 0.099 39.67 52.48 0.969 
December 91.40 107.58 0.583 76.06 93.78 0.867 72.65 93.42 0.706 44.61 48.76 0.958 
Average 93.32 120.95 0.24 54.43 69.71 0.94 81.05 110.37 0.35 46.28 58.91 0.96 
Type
Seasonal (Lead 3)
Annual (Lead 12)
Approach
All-months
One-month
All-months
One-month
MonthMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)rMAE (mm)RMSE (mm)RMAE (mm)RMSE (mm)r
January 153.16 198.33 0.738 196.27 212.38 0.931 117.22 158.22 0.691 76.86 99.28 0.925 
February 182.64 221.22 0.884 116.42 174.66 0.878 199.88 279.86 0.522 202.63 241.85 0.904 
March 169.72 193.28 0.670 72.06 80.21 0.963 123.37 154.09 0.798 76.26 93.29 0.935 
April 174.53 245.61 − 0.189 39.63 63.06 0.963 99.64 120.61 0.841 57.52 88.35 0.984 
May 65.56 118.57 − 0.042 35.56 59.77 0.986 75.14 125.18 − 0.164 14.17 21.33 0.998 
June 43.93 53.71 0.016 21.78 34.82 0.859 48.88 63.06 − 0.173 11.56 21.16 0.926 
July 21.92 25.77 0.041 9.62 11.67 0.962 29.85 35.83 − 0.076 3.39 4.49 0.989 
August 29.90 32.07 − 0.058 9.35 12.05 0.963 19.72 26.30 0.605 1.70 2.10 0.998 
September 32.42 48.95 0.371 8.98 11.61 0.982 29.29 49.85 0.317 13.05 15.65 0.965 
October 54.12 82.50 0.180 15.04 19.22 0.976 72.22 99.51 0.000 13.90 18.20 0.992 
November 100.53 123.78 − 0.309 52.35 63.23 0.965 84.78 118.53 0.099 39.67 52.48 0.969 
December 91.40 107.58 0.583 76.06 93.78 0.867 72.65 93.42 0.706 44.61 48.76 0.958 
Average 93.32 120.95 0.24 54.43 69.71 0.94 81.05 110.37 0.35 46.28 58.91 0.96 

Negative correlations were obtained for several months in the all months optimization for annual forecasts (Lead 12). Using a single month optimization in both seasonal and annual forecasts revealed high correlations (r > 0.8) for all the months in both locations. A correlation average of 0.96 was reported for both types (Lead 3 and Lead 12) in Bingera using one single month optimization, in addition to Mossman Lead 3. A slightly lower average correlation was found in Mossman Lead 12 using one single month optimization. Lower correlation averages were gained using the all months optimization approach in both seasonal and annual forecasts in Bingera and Mossman. Mossman obtained an average RMSE of 69.71 mms and 58.91 mms for Lead 3 and Lead 12 using a single month optimization. Higher RMSE values were acquired using the all months approach for the two types respectively in most of the months. The same applied for Bingera, where lower RMSEs were obtained using a single month approach. The all months optimization revealed lower RMSE in 2 months in December Bingera Lead 3 and Mossman January Lead 3. Tables clearly verify that a single month approach reveals better forecasts than all months approach in both locations.

For all months optimization, 10% of the data represents the 10 years between October 2004 and September 2014 (before deconstruction). For a single month optimization, 10% of the data represents 1-month values between October 2004 and September 2014. To demonstrate better representation, single month testing data results were combined in each of the two locations Bingera and Mossman. Ten records from each run (12 runs in total for each approach and each type) were merged. The formed dataset represents 10 years of data (October 2004 to September 2014). Figures 2 and 3 show testing data results for two locations Bingera and Mossman from each approach on behalf of two types of forecasts, seasonal (Lead 3) and annual (Lead 12). Using two approaches, ANN had the ability to capture patterns in rainfall, with a difference in terms of accuracy and amount of rainfall. All months optimization was capable of forecasting seasonally December 2010 rainfall, where all months optimization Lead 12, single month Lead 3 and single month Lead 12 failed to predict this variation in terms of rainfall. Although better results were shown with single month in most of the locations as in December 2010, this does not mean that we can only rely on single month. Single month optimization predicted correctly rainfall for Mossman January 2014 with Lead 12, while single month optimization was not able to perform with the same level of accuracy in seasonal forecasts (Lead 3).
Figure 2

Bingera observed and forecasted rainfall representation: (a) all months optimization Lead 3, (b) single month optimization Lead 3, (c) all months optimization Lead 12, (d) single month optimization Lead 12.

Figure 2

Bingera observed and forecasted rainfall representation: (a) all months optimization Lead 3, (b) single month optimization Lead 3, (c) all months optimization Lead 12, (d) single month optimization Lead 12.

Figure 3

Mossman observed and forecasted rainfall representation: (a) all months optimization Lead 3, (b) single month optimization Lead 3, (c) all months optimization Lead 12, (d) single month optimization Lead 12.

Figure 3

Mossman observed and forecasted rainfall representation: (a) all months optimization Lead 3, (b) single month optimization Lead 3, (c) all months optimization Lead 12, (d) single month optimization Lead 12.

Ideal point error (IPE), which is calculated by identifying the ideal point to a multi-dimensional space that each model should be evaluated against (Malamos & Koutsoyiannis 2016), was used to inter-compare the performance of the two approaches. IPE is formed by normalising the statistical measurements so that it ranges between 0 and 1, where zero is the best and 1 is the worst (Domínguez et al. 2011). In this study, the IPE is calculated by up to three statistical measurements MAE, RMSE and determination of coefficient . is simple the square of correlation of coefficient presented in the previous Tables 2 and 3. The IPE formula is represented in the following: 
formula
where i represents a case for each month in each specific approach. The following Table 4 summarizes the IPE values for both Bingera and Mossman. The results show that 1 month optimization revealed lower values in most of the cases leading to higher accuracy.
Table 4

IPE for Bingera and Mossman for the two forecasting approaches

Bingera
Mossman
Type
Seasonal (Lead 3)
Annual (Lead 12)
Seasonal (Lead 3)
Annual (Lead 12)
MonthAll-monthsOne-monthAll-monthsOne-monthAll-monthsOne-monthAll-monthsOne-month
January 0.822 0.355 0.793 0.199 0.718 0.863 0.556 0.553 
February 0.746 0.269 0.870 0.421 0.783 0.799 0.914 0.995 
March 0.805 0.576 0.600 0.492 0.768 0.441 0.519 0.501 
April 0.674 0.133 0.631 0.211 0.969 0.370 0.414 0.284 
May 0.600 0.602 0.607 0.235 0.670 0.328 0.652 0.066 
June 0.706 0.170 0.623 0.399 0.604 0.623 0.589 0.449 
July 0.535 0.268 0.622 0.189 0.581 0.214 0.582 0.069 
August 0.576 0.462 0.640 0.169 0.585 0.212 0.372 0.013 
September 0.589 0.135 0.295 0.113 0.519 0.158 0.533 0.224 
October 0.752 0.286 0.559 0.610 0.613 0.206 0.644 0.077 
November 0.642 0.101 0.613 0.256 0.674 0.381 0.665 0.254 
December 0.596 0.814 0.761 0.812 0.539 0.702 0.404 0.309 
Average 0.670 0.348 0.634 0.342 0.668 0.441 0.570 0.316 
Bingera
Mossman
Type
Seasonal (Lead 3)
Annual (Lead 12)
Seasonal (Lead 3)
Annual (Lead 12)
MonthAll-monthsOne-monthAll-monthsOne-monthAll-monthsOne-monthAll-monthsOne-month
January 0.822 0.355 0.793 0.199 0.718 0.863 0.556 0.553 
February 0.746 0.269 0.870 0.421 0.783 0.799 0.914 0.995 
March 0.805 0.576 0.600 0.492 0.768 0.441 0.519 0.501 
April 0.674 0.133 0.631 0.211 0.969 0.370 0.414 0.284 
May 0.600 0.602 0.607 0.235 0.670 0.328 0.652 0.066 
June 0.706 0.170 0.623 0.399 0.604 0.623 0.589 0.449 
July 0.535 0.268 0.622 0.189 0.581 0.214 0.582 0.069 
August 0.576 0.462 0.640 0.169 0.585 0.212 0.372 0.013 
September 0.589 0.135 0.295 0.113 0.519 0.158 0.533 0.224 
October 0.752 0.286 0.559 0.610 0.613 0.206 0.644 0.077 
November 0.642 0.101 0.613 0.256 0.674 0.381 0.665 0.254 
December 0.596 0.814 0.761 0.812 0.539 0.702 0.404 0.309 
Average 0.670 0.348 0.634 0.342 0.668 0.441 0.570 0.316 
There is a wide range of approaches used to look at the aptitude of precipitation conjectures (Abbot & Marohasy 2014). The skill score of a model is calculated to get an indication about the performance of forecasts for future events. In an attempt to assess the accuracy of forecasts, skill score has been calculated for each month of the eight different sites. Skill score is a technique that is used to demonstrate the accuracy of a specific method in prediction. Skill score assesses the accuracy of a model based on a reference model. Our model was compared and evaluated against climatology. Climatology is a technique for forecasting rainfall based on the average of months, e.g. rainfall forecast for a specific month is the average of the rainfall values collected from the previous same month back to a specific time. Formula of skill score: 
formula
where RMSEref is the RMSE value calculated for the reference forecasts (climatology), and RMSE is related to the model to be assessed (ANNs model). Skill Score can be either positive or negative. A 0 skill-score means that the tested model has no skill in prediction; 100 means perfect forecasts. Skill score values were generated for each approach. Climatology forecasts were collected from BOM. Table 5 represents skill scores for seasonal forecasts with the all months optimization approach, Table 6 represents skill scores for seasonal forecasts with single month optimization, Table 7 represents annual forecasts with all months optimization, and Table 8 represents annual forecasts skill score results for annual forecasts with single month optimization.
Table 5

Skill score results for the eight cities used in this study, all months optimization seasonal forecasts

 City
MonthBingeraFairymeadKalamiaMacknadeMaryboroughMossmanPlane CreekVictoria Plantation
January 49.2 70.1 7.6 56.9 52.2 22.6 −47.8 49.4 
February 32.1 51.0 39.9 33.2 35.8 30.7 11.5 59.9 
March 25.6 43.7 18.1 25.6 13.7 23.2 31.4 19.0 
April −2.0 23.3 −5.8 35.2 11.7 −6.9 −38.5 −13.2 
May 10.9 1.2 −45.3 −29.0 −13.4 −8.1 −11.0 −18.4 
June −2.8 2.9 −31.3 −14.3 −13.5 −2.5 −3.4 12.5 
July 14.9 −1.6 −40.3 −30.3 12.0 −6.5 −64.3 9.0 
August 4.2 −9.7 10.0 −36.5 −4.1 −5.7 −49.0 −1.1 
September 4.6 53.0 0.9 12.9 −19.3 2.1 36.4 −1.7 
October −40.8 −8.6 −22.8 −3.2 −16.9 −1.0 −7.5 −4.9 
November −26.2 −6.1 6.6 −4.1 −24.3 −14.3 12.8 6.8 
December 58.9 66.8 −1.8 38.0 51.6 18.5 22.2 −46.3 
 City
MonthBingeraFairymeadKalamiaMacknadeMaryboroughMossmanPlane CreekVictoria Plantation
January 49.2 70.1 7.6 56.9 52.2 22.6 −47.8 49.4 
February 32.1 51.0 39.9 33.2 35.8 30.7 11.5 59.9 
March 25.6 43.7 18.1 25.6 13.7 23.2 31.4 19.0 
April −2.0 23.3 −5.8 35.2 11.7 −6.9 −38.5 −13.2 
May 10.9 1.2 −45.3 −29.0 −13.4 −8.1 −11.0 −18.4 
June −2.8 2.9 −31.3 −14.3 −13.5 −2.5 −3.4 12.5 
July 14.9 −1.6 −40.3 −30.3 12.0 −6.5 −64.3 9.0 
August 4.2 −9.7 10.0 −36.5 −4.1 −5.7 −49.0 −1.1 
September 4.6 53.0 0.9 12.9 −19.3 2.1 36.4 −1.7 
October −40.8 −8.6 −22.8 −3.2 −16.9 −1.0 −7.5 −4.9 
November −26.2 −6.1 6.6 −4.1 −24.3 −14.3 12.8 6.8 
December 58.9 66.8 −1.8 38.0 51.6 18.5 22.2 −46.3 
Table 6

Skill score results for the eight cities used in this study, one single month optimization seasonal forecasts

 Area
MonthBingeraFairymeadKalamiaMacknadeMaryboroughMossmanPlane CreekVictoria Plantation
January 79.1 18.0 27.8 59.6 56.0 17.14 33.9 27.7 
February 77.6 69.5 55.0 53.0 33.4 45.3 34.1 48.4 
March 50.5 68.9 71.0 50.9 20.9 68.2 41.7 78.7 
April 77.2 40.3 57.9 70.3 35.5 72.5 44.8 38.2 
May 49.7 28.1 34.5 72.9 57.4 45.5 81.5 39.8 
June 77.0 85.5 41.2 70.0 74.0 33.5 57.3 77.7 
July 64.7 42.6 81.8 66.3 52.1 51.8 67.6 38.4 
August 39.8 69.5 72.4 49.6 15.0 60.3 50.4 56.7 
September 66.9 69.8 62.6 72.4 69.2 76.8 52.2 24.6 
October 26.3 60.3 31.9 75.3 51.2 76.5 47.2 83.7 
November 77.6 72.5 46.3 88.7 55.2 41.6 61.1 38.1 
December 40.9 60.0 78.6 71.6 47.5 29.0 50.2 52.8 
 Area
MonthBingeraFairymeadKalamiaMacknadeMaryboroughMossmanPlane CreekVictoria Plantation
January 79.1 18.0 27.8 59.6 56.0 17.14 33.9 27.7 
February 77.6 69.5 55.0 53.0 33.4 45.3 34.1 48.4 
March 50.5 68.9 71.0 50.9 20.9 68.2 41.7 78.7 
April 77.2 40.3 57.9 70.3 35.5 72.5 44.8 38.2 
May 49.7 28.1 34.5 72.9 57.4 45.5 81.5 39.8 
June 77.0 85.5 41.2 70.0 74.0 33.5 57.3 77.7 
July 64.7 42.6 81.8 66.3 52.1 51.8 67.6 38.4 
August 39.8 69.5 72.4 49.6 15.0 60.3 50.4 56.7 
September 66.9 69.8 62.6 72.4 69.2 76.8 52.2 24.6 
October 26.3 60.3 31.9 75.3 51.2 76.5 47.2 83.7 
November 77.6 72.5 46.3 88.7 55.2 41.6 61.1 38.1 
December 40.9 60.0 78.6 71.6 47.5 29.0 50.2 52.8 
Table 7

Skill score results for the eight cities used in this study, all months optimization annual forecasts

 Area
MonthBingeraFairymeadKalamiaMacknadeMaryboroughMossmanPlane creekVictoria Plantation
January 31.2 17.5 53.8 44.9 48.4 36.4 −15.2 12.1 
February 10.7 17.7 62.7 18.3 43.3 10.1 43.1 14.7 
March 27.6 12.1 14.6 4.1 60.7 38.1 18.7 39.3 
April −0.5 10.7 −4.8 −0.3 −0.2 46.7 −4.6 16.5 
May 9.0 5.2 −39.7 −25.7 9.5 −14.9 −24.9 −24.1 
June −7.1 −21.6 −2.2 −4.0 −25.1 −21.0 −9.8 −16.8 
July 2.8 16.7 −19.1 2.7 −4.4 −48.2 −11.0 −2.0 
August −17.0 −5.1 −1.9 29.6 1.5 13.1 −0.6 −27.5 
September 34.5 −12.8 −8.5 11.6 4.6 −0.2 −3.2 −3.8 
October 10.0 30.2 −49.4 −8.9 12.0 −25.8 16.4 −10.4 
November 3.3 −1.4 −8.2 60.3 1.2 −12.2 16.2 1.8 
December 30.4 18.6 45.8 65.8 37.4 22.5 −5.3 2.5 
 Area
MonthBingeraFairymeadKalamiaMacknadeMaryboroughMossmanPlane creekVictoria Plantation
January 31.2 17.5 53.8 44.9 48.4 36.4 −15.2 12.1 
February 10.7 17.7 62.7 18.3 43.3 10.1 43.1 14.7 
March 27.6 12.1 14.6 4.1 60.7 38.1 18.7 39.3 
April −0.5 10.7 −4.8 −0.3 −0.2 46.7 −4.6 16.5 
May 9.0 5.2 −39.7 −25.7 9.5 −14.9 −24.9 −24.1 
June −7.1 −21.6 −2.2 −4.0 −25.1 −21.0 −9.8 −16.8 
July 2.8 16.7 −19.1 2.7 −4.4 −48.2 −11.0 −2.0 
August −17.0 −5.1 −1.9 29.6 1.5 13.1 −0.6 −27.5 
September 34.5 −12.8 −8.5 11.6 4.6 −0.2 −3.2 −3.8 
October 10.0 30.2 −49.4 −8.9 12.0 −25.8 16.4 −10.4 
November 3.3 −1.4 −8.2 60.3 1.2 −12.2 16.2 1.8 
December 30.4 18.6 45.8 65.8 37.4 22.5 −5.3 2.5 
Table 8

Skill score results for the eight cities used in this study, one single month optimization annual forecasts

 Area
MonthBingeraFairymeadKalamiaMacknadeMaryboroughMossmanPlane creekVictoria Plantation
January 87.8 69.6 34.1 42.4 72.0 60.1 42.8 80.5 
February 63.8 91.7 62.1 38.8 46.6 22.3 34.7 87.4 
March 57.2 40.5 86.4 46.0 77.4 62.5 31.2 79.0 
April 43.6 57.9 72.3 60.8 46.6 61.0 73.2 71.4 
May 66.8 48.5 56.0 86.9 74.8 80.4 57.5 57.5 
June 37.1 30.8 67.4 39.1 64.0 59.4 42.7 59.1 
July 53.0 53.1 51.7 33.9 34.6 81.4 53.8 48.2 
August 73.5 47.7 69.0 38.0 23.9 93.1 56.9 74.3 
September 70.5 69.7 47.2 33.8 40.0 68.5 29.3 47.8 
October 41.7 61.9 67.0 62.0 85.2 77.4 92.4 59.1 
November 35.7 60.6 67.8 56.7 53.9 51.0 75.6 69.7 
December 38.0 40.4 58.6 69.7 55.6 62.8 38.7 74.3 
 Area
MonthBingeraFairymeadKalamiaMacknadeMaryboroughMossmanPlane creekVictoria Plantation
January 87.8 69.6 34.1 42.4 72.0 60.1 42.8 80.5 
February 63.8 91.7 62.1 38.8 46.6 22.3 34.7 87.4 
March 57.2 40.5 86.4 46.0 77.4 62.5 31.2 79.0 
April 43.6 57.9 72.3 60.8 46.6 61.0 73.2 71.4 
May 66.8 48.5 56.0 86.9 74.8 80.4 57.5 57.5 
June 37.1 30.8 67.4 39.1 64.0 59.4 42.7 59.1 
July 53.0 53.1 51.7 33.9 34.6 81.4 53.8 48.2 
August 73.5 47.7 69.0 38.0 23.9 93.1 56.9 74.3 
September 70.5 69.7 47.2 33.8 40.0 68.5 29.3 47.8 
October 41.7 61.9 67.0 62.0 85.2 77.4 92.4 59.1 
November 35.7 60.6 67.8 56.7 53.9 51.0 75.6 69.7 
December 38.0 40.4 58.6 69.7 55.6 62.8 38.7 74.3 

Our results confirm that ANNs can be used to perform both seasonal and annual forecasts. In their paper, Hawthorne et al. (Hawthorne et al. 2013) compared their model that is based on GCM to climatology, where skill scores varied between −20 → +20% (Hawthorne et al. 2013). Using a single month optimization revealed higher skill scores when compared to climatology. Skill score values for all months optimization varied between −49 and 65% for both seasonal and annual forecasts. Single month optimization showed a skill score range between 15.0 and 93.1%. Only three values were obtained with a skill score less than 20% (Fairymead January Lead 3, Mossman January Lead 3, and Maryborough August Lead 3). This does not mean that forecasts are always better with a single month optimization. For some of the months, higher skill scores were obtained with all months optimization as in Fairymead Lead 3 forecasts (70.1%). The average skill score for each month in the eight locations using a single month optimization to forecast seasonally (annually) was reported as 55.1 (58.1). Based on those results, growers would be able to trust seasonal and annual forecasts following this approach.

CONCLUSION

In this paper, an ANN for predicting rainfall for sugarcane regions has been investigated. Two approaches have been proposed. The first approach was to forecast using all the datasets and the second was to forecast using a single optimization. Single month optimization delivered accurate forecasts for the two forecasting types being targeted: 3 months and 12 months, and those results correlates with (Abbot & Marohasy 2015a). The results were compared to climatology in terms of skill scores. The analysis showed 39.9%–68% better accuracy than climatology using a single month optimization. Growers can rely on this type of forecasts for water management and decision making related to the sugarcane industry. These results are promising and further explorations are to be deployed. Studies revealed that the variation in the Australian rainfall is linked to several climate indices such as ENSO, IOS, PDO, SAM and STR but its usefulness in rainfall forecasting is still uncertain (He et al. 2014). ENSO has been investigated in this model, but new climate indices can be added and explored in future studies. Input data can be investigated and multiple approaches for missing data replacement is to be studied. In addition, new ANN models are to be developed and compared in terms of accuracy.

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