Input selection and optimisation for monthly rainfall forecasting in Queensland, Australia, using artificial neural networks

Atmospheric Research 138 (2014) 166–178

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Input selection and optimisation for monthly rainfall forecasting in Queensland, Australia, using artificial neural networks John Abbot 1, Jennifer Marohasy ⁎ School of Medical & Applied Sciences, Central Queensland University, Bruce Highway, Rockhampton, QLD 4702, Australia

a r t i c l e

i n f o

Article history: Received 20 August 2013 Received in revised form 21 October 2013 Accepted 1 November 2013 Keywords: Rainfall Climatology ENSO Statistical forecast Seasonal forecast

a b s t r a c t There have been many theoretical studies of the nature of concurrent relationships between climate indices and rainfall for Queensland, but relatively few of these studies have rigorously tested the lagged relationships (the relationships important for forecasting), particularly within a forecast model. Through the use of artificial neural networks (ANNs) we evaluate the utility of climate indices in terms of their ability to forecast rainfall as a continuous variable. Results using ANNs highlight the value of the Inter-decadal Pacific Oscillation, an index never used in the official seasonal forecasts for Queensland that, until recently, were based on statistical models. Forecasts using the ANN for sites in 3 geographically distinct regions within Queensland are shown to be superior, with lower Root Mean Square Errors (RMSE), Mean Absolute Error (MAE) and Correlation Coefficients (r) compared to forecasts from the Predictive Ocean Atmosphere Model for Australia (POAMA), which is the General Circulation Model currently used to produce the official seasonal rainfall forecasts. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Until recently, the two government-based seasonal rainfallforecasting programs for Queensland, Australia, used statistical models to provide the public with official forecasts (Fawcett and Stone, 2010). The first, produced by the Australian Bureau of Meteorology (BOM), commenced in 1989. The second, produced by the Queensland Government (QG) through the Department of Environment and Resource Management, commenced in 1994. Both programs issued seasonal (three-month) rainfall forecasts, in the format of the probability of exceeding the climatological seasonal median rainfall, and both were based on

⁎ Corresponding author. Tel.: +61 7 4930 9622, +61 41 88 73 222 (Mobile); fax: +61 7 4930 9255. E-mail addresses: [email protected] (J. Abbot), [email protected] (J. Marohasy). 1 Tel.: +61 7 4930 9622, +61 41 88 73 222 (Mobile); fax: +61 7 4930 9255. 0169-8095/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.atmosres.2013.11.002

classification systems using climate indices representing broad scale atmospheric and oceanic circulation patterns. In June 2013, the BOM moved to a new system based exclusively on The Predictive Ocean Atmosphere Model for Australia, POAMA, which is considered by the BOM to be a state-of-the-art seasonal to inter-annual seasonal forecast system based on a coupled ocean/atmosphere model and ocean/ atmosphere/land observation assimilation systems (Australian Bureau of Meteorology, 2013). While POAMA generates quantitative seasonal and monthly rainfall predictions, the BOM chooses to continue to present its official forecasts simply as the probability of exceeding the long-term average value. A major limitation of such forecasts is that they provide no information about the magnitude of the expected deviation from the median rainfall value within the defined forecast period. For many practical purposes, such as management of water infrastructure or scheduling mine operations, the distribution of rainfall within the three-month period is more important than an averaged seasonal value (Sharma et al.,

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2012). Furthermore, these programs failed to adequately forecast the exceptional wet summer of 2010 to 2011, with significant economic and social consequences (van den Honert and McAneney, 2011). Researchers at the BOM acknowledge that there is presently a gap in rainfall prediction capability beyond 1 week and shorter than a season (Hudson et al., 2011). After about the first week the forecast system has typically lost most of the information from the atmospheric initial conditions, which are the basis for weather forecasts, while in the first month the ocean state probably has not changed much since the start of the forecast: hence it is difficult to beat persistence as a forecast (Vitart, 2004). Fawcett and Stone (2010) have reviewed the two major governmental statistical models used to forecast seasonal rainfall in Queensland, concluding that the skill level demonstrated for seasonal rainfall by both government agencies was “only moderate, although better than climatological and randomly guessed forecasts”. While official BOM seasonal forecasts are now based on POAMA, there is no evidence to suggest that this General Circulation Model (GCM) produces a more skilful forecast than the statistical system historically used. In fact results so far for POAMA have been disappointing (Hendon et al., 2012), and a review of 27 GCMs producing rainfall simulations for Queensland under the Intergovernmental Panel on Climate Change's Coupled Model Intercomparison Project Phase 5 produce widely divergent forecasts (Irving et al., 2012). Artificial Neural Networks (ANNs) have been investigated for rainfall forecasting in many parts of the world including Greece (e.g. Nastos et al., 2013), China (e.g. Wu et al., 2001) and India (e.g. Venkatesan et al., 1997; Guhathakurta et al., 1999; Philip and Joseph, 2003; Chattopadhyay and Chattopadhyay, 2008; Shukla et al., 2011), but have been rarely applied in Australia (Mekanik et al., 2013), and are not used to generate the official forecasts (Abbot and Marohasy, 2012). The present study applies an ANN model with the objective of generating a more practical and skillful medium-term rainfall forecast for localities in Queensland than both the historical forecasts based on simple statistical models or the new method using the GCM, POAMA. 2. Theory 2.1. Artificial neural networks and rainfall forecasting ANNs are powerful and versatile data-modelling tools that are able to capture and represent complex input and output relationships (ASCE Task Committee on Application of Artificial Neural Networks in Hydrology, 2000; Iseri et al., 2005). ANNs acquire knowledge through learning from multiple exemplars, storing that knowledge within inter-neuron connection strengths known as synaptic weights (Chakraverty and Gupta, 2008). A major advantage of neural networks lies in their ability to represent both linear and non-linear relationships and in their ability to learn these relationships directly from the data being modelled. Traditional linear models are simply inadequate for modelling data that contains non-linear characteristics. The simplest types of neural network are based on multilayer perceptrons (MLPs), creating static models, where the input– output map depends only on the present input. However, if we want to process temporal data, each time sample has to be fed to

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a different input, requiring very large networks. With temporal problems, such as rainfall forecasting, the previous value of the input can potentially influence the current output. Jordan and Elman networks (Elman, 1990; Ding et al., 2013) can solve temporal problems by processing information over time using recurrent connections by incorporating context units. The context unit remembers the past of its inputs using a factor the unit forgets the past with an exponential decay. This means that events that just happened are stronger than the ones that have occurred further in the past. Other neural models, such as Time Lagged Recurrent Networks can also solve temporal problems by using memory units and are a type of dynamic neural network (ASCE Task Committee on Application of Artificial Neural Networks in Hydrology, 2000). It is impossible to know in advance with any certainty which type of network architecture will give the best results for a particular problem. In the present investigation, through a process of trial and error it was found that Jordan and Elman networks generally gave superior results compared to other configurations tested. The context unit controls the ‘forgetting factor’ through a time constant set between 0 and 1. On the other extreme, a value of zero means that only the present time is factored in (i.e. there is no self-recurrent connection). The closer the value is to 1, the longer the memory depth and the slower the ‘forgetting’ factor. Based on experimentation, a Jordan network with one hidden layer and a time constant of 0.8 was selected for rainfall forecasts described in this study. 2.2. Input Variables, including Climate Indices ANNs, like other statistical models, require a set of input predictor data. There are an infinite number of input variables potentially relevant to medium-term rainfall forecasting. In practice however, we are limited to inputs that have been measured and, in particular, high-quality numerical values that extend back in time for a period long enough to enable pattern detection. In this study we considered relationships between lagged values for temperature, atmospheric pressure and rainfall as well as climate indices. Climate indices describe recurrent patterns in sea surface temperatures (SST) and air pressures. The dominant concurrent phenomenon affecting Queensland rainfall is the El Niño– Southern Oscillation (ENSO) spanning the Pacific Ocean (Risbey et al., 2009). The Southern Oscillation Index (SOI) is a quantitative estimate of ENSO, defined as the normalised atmospheric pressure difference between Tahiti and Darwin. The simple statistical QG seasonal rainfall forecast model is based on the SOI, in particular a statistical technique of ‘stratified climatology’, employing five phases, or categories, derived from pairs of consecutive monthly values of the SOI (Stone and Auliciems, 1992; Stone et al., 1996). Because relationships between rainfall and the SOI are weak throughout the year over the western third of Australia and during the late southern summer and autumn period over eastern Australia, the BOM historically chose to use climate indices based on sea surface temperature (SST) anomalies that span the Pacific and also Indian Oceans, designated as SST1 and SST2 (Drosdowsky and Chambers, 2001). The dominant mode of SST variability over the Indian–Pacific Ocean, SST1, strongly correlates with the SOI. Its skill as a predictor of seasonal rainfall with 1-month lag is comparable to that of the SOI with

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no lag (Drosdowsky and Chambers, 2001). SST2 coincides with the geographic area used to calculate another well-known climate index, the Dipole Mode Index, DMI. The DMI is a measure of the Indian Ocean Dipole, IOD, which is a coupled ocean and atmosphere phenomenon in the equatorial Indian Ocean that affects the climate of Australia and other countries that surround the Indian Ocean basin (Saji et al., 1999). The seasonal and spatial variation of skill of SST2 is similar to that of the DMI (Drosdowsky and Chambers, 2001). While use of the climate indices, SOI, SST1 and SST2, to generate the official seasonal forecasts did not change significantly in two decades (Fawcett and Stone, 2010), there were many studies over this same period attempting to better understand relationships between these and other climate indices and Australian rainfall (Klingaman et al., 2012). Risbey et al. (2009) examined concurrent relationships between seasonal rainfall over Australia with individual ENSO-related drivers additional to SOI, including the Modokai Index, EMI, Niño 3, Niño 3.4 and Niño 4, which are all measures of SST difference in the equatorial Pacific. Other non-ENSO indices considered in the Risby et al. study were the DMI, the Southern Annular Mode, SAM, and the Madden-Jullian Oscillation, MJO. Risby acknowledged that analysis based on linear correlations between rainfall and individual drivers could only produce crude indications of the relative importance of individual climate indices, and the approach did not account for possible interactions. Their results nevertheless indicate which individual driver might be most significant for determination of seasonal rainfall throughout Australia. Of the indices considered, SOI was most the influential in northern parts of Queensland. For South East Queensland, the identity of the dominant driver was more variable, depending on the season, including influences of SOI. Many other studies have explored the relationships of ENSO-related indices to rainfall in Queensland, including Chowdhury and Beecham (2010) and Power and Smith (2007). Cai et al. (2001) examined relationships between SOI and Queensland annual rainfall over the period 1889–1998 on a decadal basis. This study shows that the magnitude of linear correlation coefficients between SOI and annual rainfall are highly variable on a temporal basis, and also geographically. Murphy and Ribbe (2004) examined linear correlations between rainfall and SOI for South East Queensland before and after 1946. The reported correlations were very weak in the earlier period (0.06) but very strong in the later period (0.72). Cai et al. (2010) described the non-linearity, or asymmetry, of relationships between ENSO phenomena and Australian rainfall, focussing on the SOI with particular reference to South East Queensland. Their analysis showed a significant correlation exists during La Niño conditions with summer rainfall increasing in South East Queensland as the La Niña amplitude increases. Such an ENSO–rainfall teleconnection is not evident during El Niño conditions. Although rainfall tends to decrease, the influence is not statistically significant (correlation of − 0.08). There is some evidence that the relationship between ENSO and rainfall is modulated by phases of the Inter-decadal Pacific Oscillation, IPO (Cai et al., 2010; Power et al., 1999, 2006). When the IPO is in a negative phase, the impact of ENSO on Queensland rainfall is enhanced (Verdon and Franks, 2006).

A strong concurrent relationship does not necessarily translate into a strong lagged relationship (Schepen et al., 2012). It is lagged relationships that are essential for forecasting. Chiew et al. (1998) examined linear correlations between rainfall and ENSO indices (SOI and SSTs) for the Queensland region, including lagged relationships. The strongest linear correlations, r above 0.4, were found for spring rainfall, particularly in the North East, including Cairns. The geographical coverage and intensity of the strongest correlations declined as lags were progressively increased from 0 to 1, 2 and 3 months. Correlations with summer rainfall were less expansive geographically, and these also diminished with lag time. Kirono et al. (2010) investigated linear correlations between 12 individual climate indices, lagged for 1 or 2 months, and seasonal rainfall across Australia including SOI, Niño 3, Niño 4, DMI, SAM, SST1 and SST2. Results for South East Queensland exhibited sporadic influence of individual lagged climate indicators. For North East Australia, strong relationships are most evident in spring and summer. The strongest relationships for rainfall in spring were Niño 4, and for summer rainfall, Niño 4, DMI, SOI, and SST1. Schepen et al. (2012) estimated the influence of 13 individual lagged climate indices on seasonal rainfall for geographical grid areas across Australia. The indices studied included SOI, Niño 3, Niño 3.4, Niño 4, DMI, EMI, and also the Indian Ocean East Pole index, EPI, at lag periods of 1, 2 and 3 months. The variability in the strengths of relationships between lagged climate indices and rainfall were calculated by using the pseudo-Bayes factor that can accommodate non-linear relationships. This factor is probably more useful in providing a measure of the strength of rainfall–input relationships than the Pearson correlation coefficient (r). However, evaluations using the pseudo-Bayes factor are still potentially limited in that they evaluate each rainfall–input relationship in isolation from the effect of other inputs. This may not give a true indication of a specific input's influence when introduced in combinations with other inputs. It can be concluded that a range of lagged climate indices potentially convey valuable predictive information for mediumterm rainfall forecasting and have potential as input variables. The strength of individual associations between a given index and future rainfall are highly variable geographically, change throughout the annual cycle, and with the lag period. 2.3. Measures of forecast skill There are many different ways to compare the skill of rainfall forecasts (Al-Salihi et al., 2013; Wu and Chau, 2013). In this study, the Root Mean Square Error (RMSE) was the primary statistic used. The Mean Absolute Error (MAE), Pearson correlation coefficient (r), and Weighted Non-dimensional Index (WNDI) (Abbot and Marohasy, 2012) were also applied in specific instances and to compare the skill of output from the ANN model with POAMA. RMSE are commonly applied to compare skill between different rainfall forecast models and gives a simple, transparent, quantitative measure of difference between input and target and is easily understood across disciplines (Singh and Borah, 2013; Acharya et al., 2012). There is an extensive literature evaluating the merits of using RMSE relative to MAE (e.g. Saigal and Mehrotra, 2012; Willmott and Matsuura, 2005)

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and concluding that the RMSE is more sensitive to the occasional large error (the squaring process gives higher proportionate weight to large errors). In fact, on this basis it is arguable that there are advantages in using RMSE over MAE when comparing the skill of Queensland rainfall forecasts because period of very high rainfall are of particular significance, potentially having profound economic and social impacts. When comparing skill across sites with very different average monthly rainfalls, WNDI provides a method for normalizing values (Johns et al., 2006; Abbot and Marohasy, 2012). Correlation coefficients are widely used in rainfall forecasting (e.g. Mekanik et al., 2013), but results can be potentially misleading if the set of predicted values is consistently a constant multiple of the target value.

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The input datasets used in this study can be considered as three types: 1. Local variables, specifically rainfall, maximum and minimum temperature and atmospheric pressure, that we considered potentially most important, and for which long data series were available; 2. The climate indices (SOI, SST1 and SST2) used in the official forecasts; and 3. Additional climate indices (e.g. Niño 3.4, SAM, DMI, and IPO) that are likely to be influential by representing the broad scale atmospheric and oceanic phenomena thought to affect Queensland rainfall, based on a review of the literature (see Section 2.2). 3.2. Local input variables

3. Data and methods 3.1. Artificial neural networks For preliminary screening of input variables (see Section 3.4) Synapse (Peltarion, Stockholm, Sweden) ANN software was used with a static Elman network (Elman, 1990), without genetic optimisation. Although the results from this configuration did not generally achieve RMSE values as low as subsequently obtained with genetic optimisation, the processing time was much shorter (approximately 20 min per forecast run, versus 5– 12 h). ANN software, NeuroSolutions 6 for Excel (NeuroDimensions, Florida, USA), also with an Elman network incorporating genetic optimisation (Ding et al., 2013), was used for subsequent optimisation of a more limited set of input variables, and for comparing rainfall forecasts with output from a general circulation model and climatology. For each input data set, the ANN model was optimised for 3000 epochs using a genetic optimisation algorithm for 10, 15 or 20 generations. The historical rainfall record for Queensland is limited to about 120 years, and this includes periods of at least 10 years of drought followed by shorter periods characterised by flooding. It is desirable to ensure testing sets include both extended periods of relative drought and also heavy rainfall. On the other hand, experience showed that reducing the training set to 60% of the available data impaired training results. For these reasons, training sets comprised approximately 85% of the total data, with the remainder used for testing. The desired target output was assigned as the observed monthly rainfall with a lead-time of 1 month, 2 months or 3 months in advance of the current month. There is a danger in overtraining a neural network when the network parameters are overly tuned to the training data set. When this occurs, in addition to the inherent relationship, the network attempts to fit the noise component of the data. As a result, the network can perform very well over the dataset used for training, but it may exhibit poor predictive capabilities when presented with new data (Wang and Sheng, 2010). To avoid the problem of overtraining, we stopped training when the RMSE in the testing set was minimised. Both Synapse and NeuroSolutions software enable continuous monitoring of the errors in both training and testing sets during training, and this feature was utilised in this study.

Local input data series are specific to particular localities. Three different broadly defined regions of Queensland were selected for investigation, Fig. 1: 1. The tropical North East coast, including the sites of Cairns, Townsville and Pleystowe; 2. The central interior, including the sites of Richmond, Ayrshire Downs, Barcaldine and Isisford; and 3. The South East, including the sites of Brisbane, Pittsworth, Gatton and Harrisville. Monthly rainfall data was obtained from the Australian BOM's High Quality Climate Database for Cairns, Harrisville and Ayrshire Downs. These sites were chosen on the basis of their geographic spread and also the quality of data, that is, long series with few missing values. Each site selected had between zero and four missing monthly rainfall values over their entire ranges. It was necessary to use temperature data from the nearby site of Richmond (030045), beginning in 1893, in conjunction with the rainfall data for Ayrshire Downs, Fig. 1. The closest site to Harrisville that has a long temperature data series is Brisbane (the capital of Queensland), but to obtain a long data series it was necessary to compile maximum and minimum temperature records using data from three sites in Brisbane: the Brisbane Regional Office (40214), Brisbane Aero (40223) and Brisbane (40913). This combination provided a data series extending from January 1887 to the present. Continuous monthly minimum and maximum temperature records exist for Cairns (031011) over the period from 1910 to the present, and this was used as input in conjunction with rainfall data for Cairns. Other sites shown in Fig. 1, Pittsworth (041082) and Gatton (040082) in the south–east region and Barcaldine (036007) and Isisford (036026) in the central interior region, were not used as sites for neural network rainfall forecasts, but were used for comparative forecasts with the BOM preferred general circulation model known as the Predictive Ocean Atmosphere Model for Australia, POAMA. Pressure values were obtained from the BOM, for Cairns stations (031010 and 031011) extending back to 1889. Pressure data is given as readings taken several times during a day, generally increasing in frequency to the present. These values were first converted to average daily pressure, then to a monthly average pressure.

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Fig. 1. Map of Queensland with high-quality rainfall sites.

3.3. Climate indices Some of the data series for the climate indices used in this study are available as monthly values from at least 1890 to the present at the Royal Netherlands Meteorological Institute (KNMI) Climate Explorer—a web application that is part of the World Meteorological Organisation. Data downloaded from this website was obtained as monthly values for SOI, Niño 3.4, and DMI corresponding to the historical records of rainfall data used for Cairns, Harrisville and Ayrshire Downs. Monthly values for the IPO from January 1871 until November 2012 were obtained from Chris Folland, Met Office, Hadley Centre, UK. We used SAM values based on Fan and Wang (2004), specifically the data series jisaoSLP available at http://jisao. washington.edu/data/aao/slp. SST1 and SST2 data series are available on the BoM website but have only been computed from 1949 because of concerns about the quality of the data before this time, http:// www.bom.gov.au/climate/ahead/sst_data_table.html. The raw

sea surface temperature dataset used by the BOM for constructing the model are the GISST1.1 set.

3.4. Pre-screening of input variables With any statistical model, including ANNs, it is generally preferable to train and test with historical data sets extending as far back as possible. Restricting training to sets with reduced length generally gives inferior results, as a more limited set of exemplars are presented to the network to enable mapping of inputs to target outputs. In particular, embedded patterns that are only manifested over relatively long time scales (e.g. decades) may not be adequately incorporated into the optimised model if the available training sets are not of sufficiently long duration. Considering multiple potential input data sets, and a target output set, the overall constraint on input/output data will correspond to the set with the shortest available historical record. As rainfall records for the sites considered in this study extend back for about 120 years,

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it is preferable, if possible, to use corresponding input sets that extend back at least over this period. In some cases, however, shorter length input data sets may convey useful forecast information not necessarily available in the longer input sets. The selection of a preferred set of inputs may therefore involve a compromise between the length of data sets, and the diversity of relevant information presented. Where both shorter and longer sets are available that are likely to impart similar information for forecasting, preference is given to the longer set. To assist in input selection, potential input sets (with longer and shorter data series) were pre-screened using an ANN implemented with Peltarion Synapse software, without genetic optimisation, Appendix A. The skill of the forecast has been measured in terms of the RMSE (mm) for forecasts of Cairns monthly rainfall, with 1-month lead-time, using combined training and testing data sets extending from 1950 to 2010. This procedure produced some indication of the likely usefulness of a range of input sets for optimised forecasting within a neural network, and is considered a superior approach to assessments of input utility based on examining individual correlations between inputs and rainfall. The RMSE values generated from ANN forecasts using Niño 3.4 and DMI as inputs are generally comparable to, or lower, than corresponding forecasts using SST1 and SST2 respectively, Appendix A. SST1 and SST2 are only available as data series from 1949. For subsequent forecasts, using genetic optimisation, Niño 3.4 and DMI were thus used as preferred inputs, rather than SST1 and SST2, as this enabled much longer time series to be investigated. Further justification for the choice of particular indices following pre-screening follows. The two climate indices used in the official BoM forecasts based on sea surface temperature anomalies, SST1 and SST2, gave RMSE values comparable to Niño 3.4 and DMI, respectively, Appendix A. This is consistent with the findings of Drosdowsky and Chambers (2001) that SST1 is strongly correlated with Niño 3 (r = 0.81), and SST2 is strongly related to sea surface temperatures in the Indian Ocean, which are measured by the DMI. SAM has been shown to be much more influential in determining rainfall over the southern part of the Australian continent than the northern regions (Meneghini et al., 2007; Risbey et al., 2009). Various approaches have been taken to calculation of SAM, each covering different specific time periods (Ho et al., 2012). The SAM index used in this study extended from 1949 to 2011. Given the RMSE was in the higher range and therefore less skilful at forecasting rainfall, Appendix A, and that the SAM series considered extended back only to 1949, this index was not included in further investigations using genetic optimisations. The indices Niño 3, Niño 3.4 and Niño 4 each correspond to SST anomalies in the Pacific Ocean, but refer to different geographical regions. All three indices are available from 1880 to present. Schepen et al. (2012) reported that there is stronger evidence for using lagged Niño 3.4 and Niño 4 to forecast Australian seasonal rainfall than lagged Niño 3. The Niño 3.4 data series was used for input in this investigation and is abbreviated to ‘Nino’ in the tables. The availability of atmospheric pressure data over extended periods at the site of interest is also a constraint, so

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that this local variable was also excluded from further investigations where genetic optimisations were used. Monthly time series for IPO, maximum temperature (MaxT) and minimum temperature (MinT) are available over historical periods to match the available historical rainfall records and these input sets were retained for subsequent investigations with genetic optimisation. As a result of pre-screening assessments, the input variables used in forecasting with a NeuroDimension ANN implementing genetic optimisation were rainfall (Rain), MaxT, MinT, SOI, IPO, DMI and Niño 3.4 (Nino). 3.5. Combinations of input variables tested Using the ANN model with genetic optimisation we compare and contrast the relationships between rainfall at the three localities of Ayrshire Downs, Cairns and Harrisville. Seven unary input data sets were constructed corresponding to monthly values of the input variables Rain, SOI, IPO, Nino, DMI, MaxT, and MinT. A unary data set was defined as the current monthly value of one of these input parameters, plus the twelve corresponding lagged values for the previous twelve months, comprising a total of 13 input columns to the neural network. Binary, ternary and quaternary combinations of these unary sets were also used as inputs. A binary data set was defined as a combination of two unary data sets. For example, the combination of 26 input data columns for SOI and MaxT comprises a binary set. Similarly, ternary combinations of the unary sets consist of 39 input data columns, as for example the combination of SOI, MaxT and Rain. 3.6. Comparing ANN Model output with output from POAMA POAMA version 1.5 (POAMA-1.5), replaced POAMA version 1 as the BOM's operational dynamical seasonal prediction system in September 2007 and was used until 2011 when it was superseded by a newer version, POAMA-2. In December 2011 we were provided with output from version POAMA-1.5 to facilitate comparisons with our forecasts using ANNs. Monthly average rainfall forecasts with 1, 2 and 3-month lead times were provided as anomalies and simple bilinear interpolations of surrounding grid points undertaken. This interpolation was necessary because POAMA forecasts for 250-km2 grid boxes. From these values, we calculated monthly rainfall and also RMSE for Harrisville and Ayrshire Downs. We do not have equivalent computed output from POAMA-1.5 for Cairns. It is possible, however, to determine the linear correlation corresponding to the monthly rainfall for Cairns, Harrisville and Ayrshire Downs for POAMA 2 from an interactive program (POAMA-2 Seasonal System Australian Temperature/Rainfall Skill) at the BOM website (2013). Using the displayed charts we determined Pearson Correlation Coefficients as r values for POAMA-2. 4. Results 4.1. Correlations between lagged data inputs and target rainfall Where complex, poorly understood relationships exist between a target output and many potential input variables,

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determining the most appropriate set of inputs to provide to a forecast model can be difficult. A useful preliminary step can be to first examine individual relationships between potential input variables and the target output, in this case rainfall. Considering results derived from Schepen et al. (2012) it is apparent that for the sites of interest in this study (Cairns, Harrisville and Ayrshire Downs), a different climate index is most influential for each season, Appendix B. Again with reference to results derived from Schepen et al. (2012) and considering just two of these indices, SOI and Nino, for the sites of interest, it is evident that the strength of influence on rainfall fluctuates between “little” and “very strong” with the seasons, Appendices C and D. 4.2. Input selection and optimisation Tables 1, 2 and 3 present results for monthly rainfall forecasts with 1, 2 and 3 months lead for Cairns (June 1998 to November 2010), Harrisville (July 1997 to November 2010) and Ayrshire Downs (July 1997 to November 2010) for unary and binary input data sets. For each geographical site, the two lowest values of RMSE have been underlined to emphasise the most skilled rainfall forecasts. Generally, the lowest values of RMSE correspond to binary combinations of inputs sets, rather than a unary set. Of the 18 underlined values, there is only one instance corresponding to a unary input set, Table 3. The underlined RMSE values, computed from binary input sets, are dominated by combinations of a local atmospheric temperature or rainfall, with a climate index. Of the 17 underlined values resulting from binary inputs (Tables 1, 2 Table 1 Accuracy of ANN model forecast for Cairns measured as RMSE (mm) using unary and binary input sets for 1, 2 and 3 months lead times. June 1998– November 2010, lowest two RMSE values underlined. RMSE = 150.6 mm for climatology. Unary

Binary Rain

Cairns, Rain MaxT MinT SOI IPO DMI Nino

Lead 1-month 164.6 139.8 135.5 158.9 158.4 219.5 153.4 219.5 172.8 225.9 169.3 199.4 166.3

Cairns, Rain MaxT MinT SOI IPO DMI Nino

Lead 2-months 140.2 122.4 159.0 160.7 163.4 216.2 191.4 207.2 160.9 228.5 172.8 193.5 156.1

Cairns, Rain MaxT MinT SOI IPO DMI Nino

Lead 3-months 176.2 161.6 166.8 170.6 173.7 248.6 172.9 156.3 231.3 236.3 169.9 233.6 174.1

Binary MaxT

128.2 123.1 118.4 141.2 149.0

158.9 144.4 138.8 163.9 121.6

176.2 165.9 157.1 168.7 159.3

Binary MinT

164.4 168.4 158.5 157.2

158.1 163.9 161.5 162.0

157.5 162.9 165.0 171.7

Binary SOI

224.0 219.9 196.2

219.1 180.7 239.7

216.2 233.1 200.4

Binary IPO

215.7 200.1

212.2 188.7

235.3 211.7

Binary DMI

Table 2 Accuracy of ANN model forecast for Harrisville measured as RMSE (mm) using unary and binary input sets for 1, 2 and 3 months lead times. July 1997– November 2010, lowest two RMSE values underlined. RMSE = 53.1 mm for climatology. Unary

Binary Rain

Binary MaxT

Binary MinT

Binary SOI

Binary IPO

Binary DMI

48.1 47.4 50.9 49.1 47.6

47.7 46.0 47.7 46.7

51.0 55.9 51.8

55.7 49.4

54.1

Harrisville, Lead 2-months Rain 51.7 MaxT 59.7 65.1 MinT 47.9 48.2 49.1 SOI 54.7 50.1 47.0 46.4 47.9 IPO 50.8 DMI 108.3 106.6 48.7 Nino 52.3 51.7 52.1

47.2 45.7 48.0 49.0

50.7 57.9 56.9

52.1 54.7

55.4

Harrisville, Lead 3-months Rain 50.8 MaxT 50.1 49.5 47.1 48.4 MinT 49.7 SOI 55.4 49.2 49.3 IPO 52.0 50.6 49.6 DMI 56.2 77.7 48.7 Nino 51.9 48.9 46.4

48.2 47.7 48.2 48.5

54.7 56.8 55.4

56.0 53.5

55.7

Harrisville, Lead 1-month Rain 49.4 MaxT 49.2 49.5 MinT 47.4 47.8 SOI 51.3 48.2 IPO 57.0 47.9 DMI 55.8 50.8 Nino 48.5 48.3

and 3), 15 fall into this category. There are no examples of underlined RMSE values resulting from binary combinations of two inputs comprising only climate indices. Table 3 Accuracy of ANN Model forecast for Ayrshire Downs measured as RMSE (mm) using unary and binary input sets for 1, 2 and 3 months lead times. June 1997– November 2010, lowest 2 RMSE values underlined. RMSE = 44.7 mm for climatology. Unary

Binary Rain

Binary MaxT

Lead 1-month

203.5

Ayrshire Downs, Rain 50.4 MaxT 50.3 MinT 60.7 SOI 54.5 IPO 53.9 DMI 57.9 44.4 Nino

Lead 2-months

200.8

Ayrshire Downs, Rain 50.5 MaxT 48.6 MinT 59.0 SOI 56.4 IPO 57.3 DMI 58.1 Nino 50.3

Lead 3-months

210.4

Ayrshire Downs, Rain 52.1 MaxT 49.7 MinT 58.8 SOI 56.7 IPO 55.3 DMI 72.5 Nino 53.1

63.9 56.6 53.9 46.3 51.6 48.2

48.6 56.3 53.2 53.4 54.3 51.0

50.5 54.4 52.9 51.6 53.5 53.1

49.6 48.5 46.3 50.6 45.9

50.5 49.2 45.8 48.4 48.7

49.8 50.1 47.5 87.7 49.3

Binary MinT

Binary SOI

Binary IPO

Binary DMI

58.2 56.9 59.3 56.0

57.7 58.2 50.6

55.9 51.4

52.8

56.8 54.9 55.4 58.5

55.9 57.0 57.5

55.9 57.5

59.3

54.8 58.6 57.2 59.7

53.6 58.1 61.6

59.4 52.0

58.4

J. Abbot, J. Marohasy / Atmospheric Research 138 (2014) 166–178

The ANN rainfall forecasts derived only from unary sets as input generally produces forecasts poorer than climatology, Tables 1, 2 and 3. The frequencies of occurrence of individual climate indices, corresponding to underlined RMSE values in Tables 1, 2 and 3, in decreasing order of skill of forecast are: IPO (9), Nino (5), SOI (1) and DMI (1). This suggests that the IPO unary input dataset carries the most useful rainfall forecast input information, and DMI the least useful information, when applied in combination as a binary input set for the sites under consideration. The ANN model was used to compute RMSE values for 35 different quaternary forecasts for each site, corresponding to all possible combinations of the 7 selected unary input sets, each unary input set contributing information to 20 individual forecasts, Appendix E. The most skilled forecast for Cairns had Rain, MaxT, MinT and SOI as inputs; for Harrisville it was rain, MinT, IPO and SOI; while for Ayrshire Downs the best combination was rain, MaxT, SOI and Nino, Appendix E. This suggests that superior forecasts are associated with input combinations comprising rainfall, a local atmospheric temperature, and at least one climate index.

173

differences in annual average rainfall (2035.1 mm, 800.5 mm and 503.0 mm respectively). Therefore, in order to compare model skill across sites it is necessary to apply a weighted non-dimensional index (WNDI), Table 4. Considering each of the measures of model skill (RMSE, WNDI, r and MAE) the ANN models, for every combination shown in Table 4, can provide a better forecast than climatology at all three sites, Table 4. The statistical measures MAE, WNDI and r varied in unison with the RMSE. Direct comparisons with POAMA-1.5 were only available for Harrisville and Ayreshire Downs. At these sites, for all skill measures POAMA produced a forecast worse than climatology, that is, worse than a forecast based simply on the long term mean rainfall, Table 4. The ANN also provided a more skilled forecast than climatology for Ayrshire Downs at 2-month and 3-month lead-times, (POAMA 1.5, RMSE = 50.4 and RMSE = 52.1, respectively) compared to climatology (RMSE = 44.7). Similar sequences of results for forecast skill were found for the sites of Barcaldine and Isisford, also located in the central interior of Queensland, as illustrated in Fig. 1. POAMA 1.5 RMSE values were consistently above climatology (RMSE = 49.5 and RMSE = 47.7) respectively) for forecasts with lead times of 1, 2 and 3 months for Barcaldine (RMSE = 56.6, RMSE = 57.2, RMSE = 58.0, respectively) and Isisford (RMSE = 53.1, RMSE = 53.6, and 53.8, respectively). The ANN model can give a better forecast than climatology (RMSE = 53.1) even when only using the binary inputs (RSME = 47.4), Table 4. The best forecast is obtained with IPO, Rain, MinT and SOI as inputs (RMSE = 43.8), Table 4. POAMA-1.5 again gives the forecast with the least skill (RMSE = 74.6), Table 4. This sequence of forecast skill, based on RMSE, using different methods was again evident for 2 and 3 month lead times for Harrisville (POAMA-1.5, RMSE = 69.1 and RMSE = 64.5; respectively), and also for

4.3. Comparisons of forecast skill between different models Because the statistical models historically used by the BOM to generate the official seasonal forecasts, and also the QG model, do not generate rainfall forecasts as time series data, it is not possible to directly compare their forecast skill with output from the ANN model. It is possible, however, to compare output from the ANN models developed in this study with climatology, and also output from POAMA, Table 4. For each particular site (Cairns, Harrisville and Ayrshire Downs) it is valid to consider RMSE, r and MAE as measures of the skill of the forecast. The three sites (Cairns, Harrisville and Ayrshire Downs) are located in climatically distinct regions of Queensland, with large

Table 4 Comparison of forecasts from ANN model with climatology and POAMA for Cairns, Harrisville and Ayrshire Downs 1-month lead. RMSE

WNDI

r

MAE

Cairns (annual rainfall 2035.1 mm) ANN quarternary IPO/SOI/MaxT/MinT ANN binary IPO/MaxT ANN ternary Rain/IPO/MaxT ANN ternary IPO/MaxT/SOI AAN binary MaxT/SOI ANN unary MaxT Climatology POAMA-2

Inputs

118.2 118.4 120.6 126.2 123.0 137.7 150. 6 –

0.697 0.698 0.711 0.744 0.726 0.811 0.888 –

0.86 0.86 0.86 0.85 0.85 0.80 0.73 0.3–0.4

74.4 78.4 73.7 74.6 79.4 80.2 95.2 –

Harrisville (annual rainfall 800.5 mm) ANN quaternary Rain/IPO/MaxT/MinT ANN ternary Rain/MaxT/IPO ANN quaternary IPO/Rain/MinT/DMI ANN binary IPO/MinT ANN binary MaxT/SOI Climatology POAMA-1.5

39.5 43.2 43.9 45.9 47.4 53.1 74.6

0.592 0.648 0.658 0.688 0.711 0.796 1.118

0.65 0.55 0.63 0.62 0.55 0.36 0.34

30.4 33.6 33.8 35.9 34.8 36.0 58.5

Ayrshire Downs (annual rainfall 503.0 mm) ANN quaternary MaxT/Rain/Nino/SOI ANN quaternary Rain/MaxT/IPO/Nino ANN ternary MaxT/Nino/DMI Climatology POAMA-1.5 POAMA-2

38.8 40.7 40.8 44.7 52.6 –

0.926 0.970 0.973 1.066 1.254 –

0.75 0.71 0.71 0.54 0.46 0.4–0.5

25.8 25.7 28.1 28.0 33.5 –

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the locations of UQ Gatton (POAMA-1.5: RMSE = 70.2 and RMSE = 64.4; respectively) and Pittsworth (POAMA-1.5, 62.4 and RMSE 58.9 respectively), also located in South East Queensland, Fig. 1. 4.4. Visual comparison of forecast skills by way of time-series plots Output from General Circulation Models such as POAMA is often presented as maps showing areas delineated according to various levels of correlation coefficients (Hendon et al., 2012, Hudson et al., 2011). When comparing observed rainfall with forecasts at specific sites in a region, it can also be very informative to examine time series plots, Fig. 2. Inspection of the results as a time dependant signals can be particularly useful in identifying the relative strengths and weaknesses of different forecast methods (Abbot and Marohasy, 2012). Output from the ANN Model with quaternary input (Rain, MaxT, SOI, Nino) is compared visually with POAMA-1.5 and climatology for Ayrshire Downs for the period August 1997 to December 2010 I by way of time series plots, Fig. 2. During this period two summers were exceptionally wet, 1999–2000 and 2008–2009, Fig. 2. POAMA-1.5 did not forecast the periods of extreme rainfall. The ANN model provided some indication that the summer of 1999–2000 would be wet, and forecast the wet summer of 2008–2009, Fig. 2. A visual comparison of the three forecasts (climatology, POAMA1.5 and output from the ANN with ternary input SOI, MinT, Nino) for Harrisville shows the POAMA forecasts to be much noisier both underestimating and overestimating monthly rainfall for the period August 1997 to December 2010, Fig. 2. The BOM did not make time series data for POAMA available for Cairns. At this site, the ANN model forecast with ternary input (Rain, IPO, MaxT) was able to forecast the drier summers of 2001–2002 and 2002–2003, accurately forecast the wetter summers of 2007–2008 and 2008–2009, but did not forecast the considerably wetter summers of 1999–2000 and 2003–2004, Fig. 2. 5. Discussion and conclusions Much of the present research effort by government institutions in Australia, which is focused on monthly and seasonal rainfall forecasts, is limited to the application of general circulation models, in particular, POAMA. However, results so far have been disappointing with medium-term monthly forecasts consistently about equivalent to, or worse than, climatology, Table 4. Nevertheless in June 2013, POAMA was adopted as the system for generating the BOM's official seasonal forecasts. ANNs are not currently used in Australia for official rainfall forecasting. After pre-screening, we used an ANN model with genetic optimisation to test relationships between the lagged values available as long data series and rainfall for geographically distant sites in Queensland. Results indicate that of the climate indices investigated, the IPO unary input dataset carries the most useful forecast information when applied in combination with other input sets, Tables 1, 2 and 3. The results reported in this paper confirm the usefulness of climate indices for rainfall forecasting in Queensland and show that an ANN model, when input selection has been optimised,

can provide a more skilled forecast than climatology, Table 4. The preferred climate index, however, varies considerably with the geographic region. This is not surprising in view of the high variability previously reported in relationships between climate indices and rainfall spatially and temporally (Schepen et al., 2012). It follows that an optimal forecast for geographically distant localities across Australia will not be achieved by restricting inputs to only two or a limited number of pre-defined climate indices as was the case when statistical models were used for the official BOM seasonal forecasts. Using an ANN to forecast, it is relatively easy to use different input sets according to geographical location, but this is likely to be inherently more difficult using a categorisation approach (as once used with the simple statistical models by the BOM) because the number of discrete categories becomes unmanageable as the number of potential input variables is extended. Selected quaternary sets, Appendix E, gave the lowest RMSE of any combinations (unary, binary, ternary or quaternary), for Cairns, Ayrshire Downs and Harrisville. However, again no unique set of input variables was identified as optimal for all three sites. The ANN model can give a more skilled forecast than the best available general circulation model, POAMA-2, Table 4. Both POAMA-1.5 and POAMA-2 produce monthly rainfall forecasts either close to, or worse than climatology, Table 4. POAMA-1.5 gives particularly poor results when forecasting rainfall over northern parts of Queensland during the monsoonal season (December, January and February) with Hendon et al. (2012) reporting r values in the range −0.2 to +0.2 for the Cairns region. In contrast, considering only these 3 months for Cairns, the best ANN model gave an r value of 0.85. For the site of Harrisville, in south east Queensland, a time series plot showed that POAMA produced a very noisy forecast, Fig. 2. For the central Queensland site of Ayrshire Downs, POAMA-1.5 did not forecast the exceptionally wet summers of 1999–2000 and 2008–2009, while the ANN model provided some indication that the summer of 1999–2000 would be wet, and forecast the wet summer of 2008–2009, Fig. 2. In a recent study, using an ANN model to forecast rainfall for the site of Nebo, also in central Queensland, Abbot and Marohasy (2013) show that through the inclusion of IPO as an input, it was possible to predict the very heavy rainfall during the summer of 2010–2011. In conclusion, this study suggests three practical ways in which medium-term rainfall forecasts for Queensland can be improved: 1. Through the use of more sophisticated statistical modelling techniques than historically used by the BOM, in particular ANNs; 2. Deployment of a model that produces forecast rainfall as a continuous function, rather than as a small number of discrete categories with an assigned probability; and 3. Development of a model that can easily be adapted to test and incorporate additional input data series, as climatic knowledge develops.

Acknowledgements This work was funded by the B. Macfie Family Foundation.

J. Abbot, J. Marohasy / Atmospheric Research 138 (2014) 166–178

Fig. 2. Comparing observed rainfall (mm) versus the forecast rainfall (mm) for Ayrshire Downs, Harrisville and Cairns using climatology, POAMA general circulation model and the ANN model.

175

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Appendix A. Pre-screening of input variables through comparison of RMSE (mm). Forecast for Cairns with a Peltarion Synapse ANN Model using unary and binary input sets, 1-month lead, November 2001–November 2010. Combined training and testing data sets extended from 1950 to 2010

Unary

Binary

MaxT

130.0

MaxT

Rain

SOI

SST1

SAM

SST2

DMI

MinT

IPO

Pressure

Rain SOI SST1 SAM SST2 DMI MinT IPO Pressure Niño 3.4

161.3 211.7 214.0 217.3 225.1 214.1 149.9 207.8 162.5 178.4

154.8 145.2 146.7 154.2 146.7 151.1 153.6 147.6 150.5 136.6

155.1 152.0 156.1 158.1 155.3 155.4 163.8 161.3 154.7

213.3 235.3 226.4 215.7 144.1 195.4 163.9 195.6

243.8 226.5 221.3 153.9 206.4 160.6 187.1

220.0 231.3 159.1 228.7 161.7 219.2

212.5 150.6 227.1 159.9 208.0

157.8 216.7 167.4 182.7

152.6 150.3 145.3

165.2 191.6

163.5

Appendix B. Influence of lagged climate indices on seasonal rainfall for grid areas corresponding to Cairns, Harrisville and Ayrshire Downs derived from Schepen et al. (2012). Lag period in months

Cairns Season SON DJF MAM JJA

Climate index Niño 4 SOI EMI EPI

Lag period 3 1 2 3

Strength Very Strong Positive Positive Little

Climate index EMI Niño 3 EMI Niño 4

Lag period 1 2 3 1

Strength Positive Strong Little Positive

Climate index Niño 4 SOI Niño 4 Niño 3.4

Lag period 1 1 2 1

Strength Very Strong Positive Little Little

Harrisville Season SON DJF MAM JJA Ayrshire Downs Season SON DJF MAM JJA

Appendix C. Influence of 1-month lagged climate indices SOI on seasonal rainfall for Cairns, Harrisville and Ayrshire Downs derived from Schepen et al. (2012)

Season

Cairns

Ayrshire Downs

Harrisville

JFM FMA MAM AMJ MJJ JJA JAS ASO SON OND NDJ DJF

Positive Little Little Little Little Little Little Little Very Strong Very Strong Strong Strong

Little Little Little Little Little Little Strong Very Strong Very Strong Positive Little Little

Positive Little Little Little Little Little Little Little Little Little Positive Positive

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Appendix D. Influence of 1-month lagged climate indices Niño 3.4 on seasonal rainfall for Cairns, Harrisville and Ayrshire Downs derived from Schepen et al. (2012)

Season

Cairns

Ayrshire Downs

Harrisville

JFM FMA MAM AMJ MJJ JJA JAS ASO SON OND NDJ DJF

Strong Strong Little Little Little Little Positive Strong Very Strong Very Strong Strong Positive

Little Little Little Little Little Little Strong Very Strong Very Strong Positive Little Little

Strong Little Little Little Little Little Positive Little Little Little Positive Positive

Appendix E. Accuracy of ANN model forecast for Cairns using quaternary input measured by RMSE (mm), 1-month lead times, lowest 3 RMSE (mm) values underlined

Quaternary Input

Cairns

Harrisville

Ayrshire Downs

Climatology Rain/MaxT/MinT/IPO Rain/MaxT/MinT/SOI Rain/MaxT/MinT/Nino Rain/MaxT/MinT/DMI Rain/MaxT/IPO/SOI Rain/MaxT/IPO/Nino Rain/MaxT/IPO/DMI Rain/MaxT/SOI/Nino Rain/MaxT/SOI/DMI Rain/MaxT/Nino/DMI Rain/MinT/IPO/SOI Rain/MinT/IPO/Nino Rain/MinT/IPO/DMI Rain/MinT/SOI/Nino Rain/MinT/SOI/DMI Rain/MinT/Nino/DMI Rain/IPO/SOI/Nino Rain/IPO/SOI/DMI Rain/IPO/Nino/DMI Rain/SOI/Nino/DMI MaxT/MinT/IPO/SOI MaxT/MinT/IPO/Nino MaxT/MinT/IPO/DMI MaxT/MinT/SOI/Nino MaxT/MinT/SOI/DMI MaxT/MinT/Nino/DMI MaxT/IPO/SOI/Nino MaxT/IPO/SOI/DMI MaxT/IPO/Nino/DMI MaxT/SOI/Nino/DMI MinT/IPO/SOI/Nino MinT/IPO/SOI/DMI MinT/IPO/Nino/DMI MinT/SOI/Nino/DMI IPO/SOI/Nino/DMI

150.6 128.3 113.1 131.7 141.9 148.9 126.0 129.7 156.8 128.4 136.7 162.5 154.5 155.3 154.4 169.9 159.8 164.7 166.9 179.2 241.6 118.2 141.5 140.8 131.9 132.3 128.7 132.3 135.3 138.0 128.7 157.5 154.7 159.9 169.1 219.0

53.1 50.2 48.5 49.8 50.3 45.9 50.6 50.2 49.0 48.3 46.6 43.8 50.3 43.9 48.8 51.5 54.1 46.7 50.5 48.7 51.7 47.9 44.7 44.3 48.4 47.9 49.7 48.0 49.5 46.9 49.9 46.7 50.4 47.2 49.2 54.6

44.7 47.9 50.4 48.0 49.7 46.6 40.7 48.3 39.2 49.2 49.1 54.8 48.9 54.6 52.6 54.6 54.1 46.9 53.3 53.3 53.4 49.7 50.0 49.3 50.3 50.6 51.7 48.8 47.3 50.9 49.7 59.6 56.0 58.6 55.9 54.1

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Professor John Abbot has been involved in research understanding kinetic and mechanistic behaviour associated with complex chemical and physical system for thirty years and has over 100 papers published in international journals. He has a BSc from Imperial College, London and a PhD from McGill University, Montreal. Professor Abbot has been involved in basic research associated with pulp and paper manufacture in Canada and Australia, and the refining of crude oil working at the Caltex oil refinery in Brisbane, Australia. It was the flooding of Brisbane in January 2011 that motivated his initial interest in seasonal weather forecasting using artificial neural networks.

Dr. Jennifer Marohasy has a BSc and PhD from the University of Queensland, Brisbane. She worked as a research entomologist for 12 years before making a career change to management and policy where she headed the environmental unit at Queensland Canegrowers Ltd, and later at the Melbourne-based Institute of Public Affairs. In both of these positions water management was a focus and Dr. Marohasy became particularly interested in the limitations of seasonal weather forecasting. Since 2011 she has been an adjunct research fellow at Central Queensland University working with Professor Abbot on seasonal forecasting using artificial neural networks.