**2. Data, method, and a first study**

this potential [3]. Machine learning has close relationships with artificial intelligence, pattern recognition and data mining. Data mining focuses on the discovery of previously unknown properties embedded in data [4], whereas machine learning focuses on prediction based on known properties learned from exposure to data sets during a process known as "training". A principle objective of the learning process is to construct a model that can generalize from experience [5]. Subsequently, the performance of the trained model can be tested using data not utilized in the training set. Performance of the model in testing gives confidence, but not

Artificial neural networks (ANNs), a form or machine learning, provide several important advantages over simple statistical models. ANNs can accommodate non-linear relationships, and test multiple inputs, and this is particularly important when the influence of climate indi-

Rather than progressing from simple statistical models to artificial neural networks, however, meteorological agencies around the world now tend to rely almost exclusively on general circulation modeling for rainfall forecasting. These are physical models, that attempt to simulate real-world oceanic and atmospheric circulation patterns. For example, the Australian Bureau of Meteorology uses the Predictive Oceanic Atmospheric Model for Australia (POAMA) as its operational model for forecasting daily rainfall, and also as the basis of its monthly and seasonal forecasts. The skill of the forecasts from ANNs can be compared with POAMA (and other general circulation models) through a comparison of root mean square errors (RMSE), mean absolute errors (MAE) and correlation coefficients – with such comparisons a focus of this chapter. RMSE is commonly applied to compare skill between different rainfall forecasting models, as it gives a simple, transparent, quantitative measure of difference between input and target and is easily understood across disciplines [7]. RMSE is more sensitive than MAE to the occasional large error (the squaring process gives higher proportionate weight to the large errors), and is therefore arguably more useful when skill at forecasting floods is particularly relevant. Given the importance of skillful monthly rainfall forecasts for most inhabited regions, for activities as diverse as crop harvesting, mine scheduling, and dam management, it is surprising that there are so few comparative studies and so little discussion about how advances in machine learning might aid medium-term rainfall forecasting – including the forecasting of flood events. Queensland is a state in the north-east of Australia, facing the South Pacific. Brisbane is the fast-growing capital of Queensland, and is located in the south-east. Brisbane has a long history of flooding and the Wivenhoe dam was built specifically for flood mitigation following

The flooding of Brisbane in January 2011 has been termed a "dam release flood" [8] with the sudden release of water from the Wivenhoe storage a principal cause of flooding. The extent of the rainfall in 2010/2011 was *not* unprecedented relative to historical records that extend back to 1864; but the heavy rainfall was not forecast [9]. Because the heavy rain in December 2010 and January 2011 followed a long period of drought, and was not forecast, the Wivenhoe dam was not properly managed for flood mitigation – the purpose for which it was originally built. Because of the extent of the economic losses the flood event has led to a class action lawsuit against the dam operator SEQEB and the State of Queensland, with the trial expected to commence in late

certainty, that the model would provide reliable forecasts if deployed operationally.

ces may vary geographically and temporarily in poorly understood ways [6].

34 Engineering and Mathematical Topics in Rainfall

a flood in 1974.

2017 [10].

Monthly data were obtained from the Bureau's Climate Data Online. Data was downloaded for all 62 sites in south eastern Queensland that are considered in this chapter. The sites were chosen on the basis of their geographic spread and also the quality of the data: that is the desirability of long data series with few missing values.

South-eastern Queensland is defined very broadly in this chapter, and does not correspond with the administrative region of South East Queensland.

This chapter is a review of various studies undertaken since 2012 focused on this general area, with specific information on data and methodology in the published technical papers that are referenced [11–21]. However, in this first section, the method used in an early study [17] is provided in more detail, by way of background into how an ANN can be practically deployed to generate a rainfall forecast.

Many neural network applications incorporate multilayer perceptrons (MLPs) as fundamental processing elements (PEs) trained with a standard backpropagation algorithm. These neural networks can perform well in solving static problems but are limited in solving temporal problems, ones where the previous value of the input affects the current output. Recurrent networks, such as Jordan networks, extend the basic MLP architecture by also including context units, PEs that remember past activity. In the Jordan network, the output of the network is copied to the context unit.

In addition, the context units are locally recurrent, that is, they feedback onto themselves. The local recurrence decreases the values by a multiplicative time constant (τ) as they are fed back. This constant determines the memory depth, that is, how long a given value fed to the context unit will be "remembered". The context unit acts as a simple lowpass filter, creating an output (*y*(*n*)), calculated as a weighted average value of some of its more recent past inputs. In the case of the Jordan context unit, the output is obtained by summing the past values multiplied by the scalar τ*n*, where:

$$\mathbf{y(n) = \sum x(n)\pi n} \tag{1}$$

Genetic optimization provides an efficient way of selecting those inputs that are significant in determining target rainfall and eliminating those inputs with very low information content. Essentially, genetic optimization enables elimination of inputs that carry mainly noise rather than useful signal, so that the number of input considered in the optimized model might typically be reduced from over 40 to less than 10.

In the early study [17] forecasts were made for Lowood and two other sites within the Brisbane catchments (upstream of the Wivenhoe dam) using the Jordan network with optimization. The initial forecasts were made using only lagged input parameters – that is any variable measured in the past. The initial focus was on:


**iii.** Determining the capacity of the ANN to deal with unary, binary and ternary data sets, that is, with an increasing number of input variables;

**3. Progressing to automation and single-month optimization**

quently applied with all the data input sets.

which ANN model and set of inputs is optimal.

tions along the Queensland coast [20].

A wide range of ANN architectures have been applied in forecasting rainfall [11, 13, 25–27]. The selection of an ANN architecture is commonly achieved through a trial and error process [11–13]. This can, however, be very time-consuming: that is choosing network topology, and architecture based on trial and error – with the selected model with lowest error score, subse-

Forecasting of Medium-term Rainfall Using Artificial Neural Networks: Case Studies…

http://dx.doi.org/10.5772/intechopen.72619

37

In contrast, with the Neurosolutions Infinity software that we used since 2015 [19–21] the selection of network architecture and configuration was automated. This offered a great advantage in terms of arriving at an optimum forecast model for each data set of interest without prohibitive time outlay. The Infinity program uses a pre-set formula incorporating RMSE, MAE and correlation coefficient values to evaluate the accuracy for each ANN model and a corresponding set of selected inputs. Based on this formula, the program determines

In the early study using the Jordan ANN model (Lowood example), and also subsequently with the Infinity software automating the process of selection of network architecture, the default was for optimization of "all-months" within each calendar year at the same time. That is, it was assumed that the same climate indices would be important for each of the months of the year. This did not prove valid. Indeed, it is well known within the climate science literature, that the magnitude of the linear correlation between SOI and annual rainfall are highly variable both temporarily and geographically particularly for Australia [24, 28] has shown that other 'remote drivers' of Australian rainfall dominant at different times of the year. Furthermore, this temporal variability has been a reason why forecasting beyond autumn in the southern hemisphere, and spring in the northern Hemisphere spring has been considered particularly problematic [29–31]. In a study published in 2015 [15] we showed for the first time that the prominent rainfall peak in December 2010 for the location of Harrisville, which is near Lowood, could be much more skillfully forecast using a single-month optimization technique. Further, the very heavy rainfall could be forecast at the long-lead times of at least 12 months, as shown in **Table 1**. We have since extended the method of single month optimization to show its relevance to loca-

The process is much more time consuming as 12 optimizations are carried out to produce monthly rainfall forecasts for the entire year. Improved skill, however, is generally achieved

While single-month optimization clearly gives a lower RMSE and MAE than all-month optimization and therefore is a preferred forecast method, it should be noted that both methods of ANN optimization provided a superior forecast to climatology and POAMA as shown in **Table 1**.

The results shown in **Table 1** where achieved from a general regression neural network (GRNN). This same ANN architecture was used to generate forecasts for Bingera, which is in a coastal catchment to the north of Brisbane. Both single-month and all-month optimization

as demonstrated by reduced MAE and RMSE and increased correlation coefficient r.

methods gave skillful forecasts for Bingera, as shown in **Figure 2**.


**Figure 1** shows the skill of this forecast, as an orange line, relative to observed rainfall, blue line. Clearly the ANN was able to forecast that December 2011 was likely to be unusually wet at Lowood. The rainfall of over 600 mm for the month of December contributed to the flooding of Brisbane in early January 2011.

In this early study [17], several climate indices were also successfully forecast and then inputted as lead variables. A 'lead', also known as a forecast value, are un-measurable from the reference point of the current period, but potentially predictable in a forecast model.

Variations in rainfall in many parts of the world, including south-eastern Queensland, are associated with large-scale climate phenomena which can be described by climate indices typically measuring changes in temperatures and pressures across oceans [22–24]. ENSO, a Pacific Ocean phenomenon, can be represented by both the Southern Oscillation Index (SOI) and a combination of four different Niño values (Niño 4, Niño 3.4, Niño 3, Niño 1.2). The Interdecadal Pacific Oscillation (IPO) also measures pressure and temperature changes in the Pacific Ocean. The Indian Ocean Dipole measured by the Dipole Mode Index (DMI), is a measure of pressure and temperature changes in the Indian Ocean.

These large-scale climate indices were used as input data, together with local data for each site specifically rainfall, and temperatures. This data was always divided into training (75%), evaluation (15%) and testing sets (10%) – with absolutely no overlap.

**Figure 1.** Rainfall at Lowood, south-eastern Queensland, as observed and forecast by the ANN [17].
