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

**iii.** Determining the capacity of the ANN to deal with unary, binary and ternary data sets,

**iv.** Determining if the ANN model could forecast the extreme rainfall of December 2010 and

**v.** A 'best forecast' using only lagged values was constructed to explore the potential to

**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 flood-

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

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 mea-

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%),

reference point of the current period, but potentially predictable in a forecast model.

that is, with an increasing number of input variables;

sure of pressure and temperature changes in the Indian Ocean.

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].

improve forecasts through post-processing, as shown in **Figure 1**.

January 2011 for these sites; and

36 Engineering and Mathematical Topics in Rainfall

ing of Brisbane in early January 2011.

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, subsequently applied with all the data input sets.

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 which ANN model and set of inputs is optimal.

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 locations along the Queensland coast [20].

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

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


**4. Best forecasts from longer datasets**

**Table 2.** Attributes used as input for ANN models.

Our very first paper on forecasting rainfall using ANNs [11] focused on 17 sites, chosen specifically because they had the longest continuous rainfall records for anywhere in Queensland. In that paper, we used a temperature series from the relatively far away destination of Sydney – with the comment that there is no comparable temperature dataset available for any Queensland location. We have since used local temperature series, even if this requires the

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

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

39

In our early work, we also limited the selection of climate indices to those of 'long duration' – specifically ENSO (SOI and the four Ninos), IPO and DMI. These climate indices were downloaded from the Royal Netherlands Meteorological Institute (KNMI) Climate Explorer.

infilling of missing values through interpolation and/or linear regression [32].

**Table 1.** Skill parameters for monthly rainfall forecasting for Gatton and Harrisville on an annual basis for the test period July 2004 to August 2011 [15].

**Figure 2.** Test results for Bingera showing difference between single-month and all-month NN optimizations [20].
