Superiority of artificial neural networks over conventional hydrological models in simulating urban catchment runoff

Globally, urban flooding has materialised as a profound environmental crisis, impeding the sustainable and healthy development of nations, primarily driven by the severity of their occurrences, the minuscule temporal window for intervention, and the extensive ramifications imposed upon urban ecosystems (Mosavi et al. 2018; Balacumaresan et al. 2024; Hossain et al. 2024). Against the backdrop of Australia's heightening vulnerability to climate-related challenges and the extensive nationwide urban sprawl, projections from the Intergovernmental Panel on Climate Change (IPCC) Coupled Model Intercomparison Project Phase (CMIP) downscaled climate models, under multiple emissions scenarios, strongly imply with high confidence limits (95%), a substantive intensification of rainfall extremes at 6–7% per °C of warming in short (<24 h) and long duration rainfall extremes and 12–14% per °C of warming for rare, extreme, and localised short duration rainfall events (IPCC 2018, 2022; BoM & CSIRO 2022).

These projected changes are expected to escalate the recurrence of unprecedented extreme rainfall intensity events, distort the variability in localised rainfall patterns, modulate the magnitude and timing of runoff generation, and subsequently perpetuate an incessant residual urban flooding risk. Therefore, comprehending and predicting urban flood occurrences and their potential impacts on urban landscapes to stipulate timely and effective flood warnings is paramount. However, the urban flood prediction process is decidedly complex, pertaining to the intricate topography and inherent non-linearity associated with influential hydrological processes of urban catchments, compounded by varying spatial and temporal resolutions, and constrained by limited data availability (Chapi et al. 2017; Lee et al. 2018; Khosravi et al. 2020; Kim & Han 2020).

In the recent past, numerous hydrological, empirical, and hydrodynamic models have been employed in design flood investigations and urban flood forecasting, primarily to comprehend the response of urban catchments to intense storm events (Teng et al. 2017; Asadi et al. 2019). However, numerous limitations allied with these models, including the adoption of simplified mathematical conceptualisations, approximation of catchment characteristics and governing equations (Hill et al. 2013; Ávila et al. 2022; Atashi et al. 2023; Balacumaresan et al. 2024), the necessity for detailed, high-quality datasets, and numerous catchment-specific parameters for precise model calibration (Kemp 2002; Laurenson et al. 2010; Mohsen & Muskula 2023; Sayed et al. 2023), internal inconsistencies, predictive uncertainties (Renard et al. 2010; Moges et al. 2021; Brown et al. 2022), and computational intensity (Kemp & Daniell 2016; Xie et al. 2021; Kemp & Hewa 2023) momentously impact performance, prediction accuracy, and result reliability, leading to substantial over-/underestimation in flood flow estimates (Kemp & Daniell 2016; Xie et al. 2021; Brown et al. 2023). The October 2022 Maribyrnong River flooding in Victoria highlighted the critical shortcomings of existing conventional modelling practices which led to severe underestimation of flood peaks, resulting in profound repercussions and inciting severe communal outrage against the Victorian Water Industry's modelling practices (Clay & Aubrey 2023; Turner & Sun n.d.). This incident underscores the requirement for enhancing the precision of current flood flow estimation practices, which if left unaddressed, could exacerbate, in lieu of the adverse impacts of climate change.

Focusing on enhancing the hydrological modelling quality and utility, Renard et al. (2010), Moges et al. (2021), and Gupta & Govindaraju (2023), amongst others, highlighted the requirement to address four fundamental sources of coexisting uncertainties – input, output, parametric, and structural, the potentials of mitigating which have been extensively researched, with the most common advocation being the adoption of a systematic approach as suggested by Bennett et al. (2013), Doherty (2015), White et al. (2020), Herrera et al. (2022), and Brown et al. (2022, 2023) to quantify the various uncertainty sources, principally input and parametric. This has been extensively explored, in recent years, such as in the works of Kumari et al. (2019) suggesting the employment of ensemble precipitation estimates addressing spatial variability, Tegegne et al. (2019) recommending investigation of sub-catchments spatial scale to comprehend impact level upon flow quantile reproduction, and Brown et al. (2022, 2023) proposing optimising appropriate loss parameters for pervious surfaces in urban environments and identifying apt flood frequency analysis methods for diverse Annual Exceedance Probability (AEP) scenarios. However, uncertainty quantification in hydrological models continues to present challenges, specifically structural/model uncertainties associated with the lumped and simplified representation of hydrologic processes in hydrologic models, leading to the accumulation of discrepancies in the flow estimation process. Recent research, as seen in the works of Sikorska et al. (2015), Vidyarthi et al. (2020), Vidyarthi & Jain (2023), Moges et al. (2021), Papacharalampous et al. (2020), Gupta & Govindaraju 2023; Liu et al. (2023), and Balacumaresan et al. (2024), have initiated exploration of the potential of various statistical paradigms, data-driven, machine-learning-based and hybrid modelling approaches in addressing these structural uncertainties, with data-driven and machine-learning-based approaches, specifically involving artificial neural networks (ANNs) showcasing commendable progress as a feasible alternative to the conventional modelling approach (Kao et al. 2021; Wang et al. 2023).

Accordingly, ANNs have been widely adopted within the hydrological research community in recent times, for various applications, namely for simulating rainfall–runoff relationship(s) Vidyarthi & Chourasiya 2020; Vidyarthi et al. 2020; Kao et al. 2021), comprehending physical catchment responses to intense storm events (Khoirunisa et al. 2021; Wang 2021; Vidyarthi & Jain 2023) for flood prediction, susceptibility analysis and mapping (Sayers et al. 2014) and in hybrid-modelling for improved prediction accuracy (Ghumman et al. 2011; Vidyarthi & Jain 2023; Iamampai et al. 2024). This is principally due to the countless benefits offered, such as the aptitude to recognise and mimic decidedly complex, non-linear associations coexisting amidst input–output variables (Aziz et al. 2017), requiring limited comprehension surrounding the underlying physical processes, with much of the process-generalisation being based upon the input–output dataset description (Aziz et al. 2017; Balacumaresan et al. 2024), lower computation cost (Sayers et al. 2014), model flexibility and versatility in processing multivariate inputs with different characteristics and limited data availability, higher result accuracy rate, etc., which collectively offset most of the limitations associated with hydrological models. This makes ANN models a highly viable option for consideration in improving the accuracy of the industry's current flood flow estimation practices. Accordingly, the fundamental drive of this research project focuses on enhancing the accuracy of the flood flow estimation process, through the adoption of ANN-based techniques.

Past research work has showcased the ANN model's capability to accurately estimate the expected flood flow and displayed the superiority of ANN model performance and prediction accuracy when comparatively assessed against prominent hydrological models used globally such as the Hydrologic Engineering Centre - Hydrologic Modelling System (HEC-HMS) model (Gunathilake et al. 2021), Hydrological Simulation Program Fortran (HSPF) (Javan et al. 2015), Sacramento soil moisture accounting (SAC-SMA) model (Daliakopoulos & Tsanis 2016), soil water assessment tool (SWAT) (Jimeno-Sáez et al. 2018), identification of unit hydrographs and component flows from rainfall evaporation and streamflow data (IHACRES) model (Ahooghalandari et al. 2015), Australian water balance model (AWBM) (Vidyarthi & Jain 2023), and Génie-Rural-à-4-Paramètres-Journalier (GR4J) model (Humphrey et al. 2016).

The potential of ANN models as an alternative modelling option for accurate streamflow estimation in Australian catchments, although not officially implemented by the Australian Water Industry, is an actively engaging and ongoing research dimension. Current research facets have been primarily centred on various topics such as short-term lead time streamflow forecasting (Joorabchi et al. 2007), studying the vitality and influence of input selection practices on ANN model performance in streamflow forecasting (Asadi et al. 2019), testing-lagged relationships and assessing the effectiveness of climate-indices in rainfall and streamflow forecasting (Abbott & Marohasy 2014; Khastagir et al. 2022; Oad et al. 2023), and in comparatively evaluating the performance of ANN models against other non-linear, linear, and conventional modelling practices such as layered recurrent neural network (LRNN) (Tran et al. 2011), gene expression programming (GEP) [non-linear], and quantile regression technique (QRT) [linear] in regional-flood frequency analysis (RFFA) (Aziz et al. 2017), particle swarm optimisation (PSO) technique in training ANN-based rainfall–runoff model for Jardine River Basin, Queensland (Vidyarthi & Chourasiya 2020), support vector machine (SVM)-based RFFA models in design flood estimations at ungauged catchments (Zalnezhad et al. 2022), the conventional GR4J model and a hybrid of ANN-GR4J model for predicting 1-month ahead streamflow forecasts (Humphrey et al. 2016), and against IHACRES model in simulating daily discharge (Ahooghalandari et al. 2015).

Downscaling the focus to Australian hydrological modelling practices, the Runoff Routing Burroughs (RORB) model is widely employed as the industrial standard practice across Victoria and many other parts of Australia for design flood investigation and flood forecasting/mapping, primarily surrounding the convenience, open-accessibility, local adaptiveness, and consistent maintenance in accordance with the Australian Rainfall and Runoff 2019 (ARR2019) guidelines (Laurenson et al. 2010; Kemp & Alankarage 2023; Balacumaresan et al. 2024; Imteaz 2024). However, RORB has its fair share of limitations, specifically structural/model-based uncertainties such as assumption of a single dominating runoff process, internal inconsistency (dependency on no. of sub-catchments), presumption of a single catchment response time/lag, representation of flow-paths with a single reach, which collectively impact the model performance and the accuracy of the results, leading to over/underestimation of the expected flood flow peaks (Kemp 2002; Laurenson et al. 2010; Kemp & Daniell 2016; Kemp & Hewa 2018; Kemp & Daniell 2020; Kemp & Alankarage 2023). Given how the limitations associated with conventional modelling practices lead to significant underestimation of the expected flood peaks, assessment of the various industrial standard practices being embraced by the Australian Water Authorities is deemed essential. However, to the best of our knowledge, there has been limited to no research focused on comparatively assessing the performance of the RORB model against data-driven or machine-learning-based approaches. Therefore, the novelty aspect of this research addresses the knowledge gap, by performing a comparative evaluation of a deep learning-based ANN model against the Victorian Water Industry standard hydrologic practice, RORB, which serves as the benchmark model. The evaluation focuses on the respective models' performances, prediction accuracy, and result reliability, thereby demonstrating and ascertaining the validity of the developed ANN model's potential as an alternative for improving the current flood flow estimation practices in Victoria. This comparative evaluation will collectively fulfil the primary aim of this study, which was associated with the incorporation of deep learning-based neural network modelling practices in enhancing the accuracy of the hydrological flood flow estimation process, to prepare for counteractive measures to mitigate the potential incessant urban flooding risk, which is expected to intensify in the wake of the adverse impacts of climate change and rapid urbanisation.

The remainder of this paper is structured covering the study materials and methods, including the study area, datasets, and flood flow estimation methods using ANNs and RORB model. This is followed by a comparative evaluation of the results for the selected storm events, culminating with the discussion and conclusion.

The Gardiners Creek catchment, distinguished by pronounced urbanisation and situated in the southeastern suburbs of Melbourne (37°49′S, 145°7′E to 37°50′S, 145°2′E), within the lower reaches of the Yarra Basin, was designated as the case study catchment. Originating at Blackburn Lake, Blackburn North, the creek flows over an approximate length of 30 km (19 miles) and outlets to the Yarra River, approximately 6 km from the Melbourne Central Business District (CBD) at Heyington, encompassing a total catchment area of 111 km². Significant variability is exhibited in the Gardiners Creek catchment's topographic profile, along its entire course, with elevations ranging between 96.21 m at its origin point to 12.3 m at the creek's terminus, relative to Australian Height Datum (AHD). Concerning the prevailing climatic conditions within the catchment extent, the creek experiences an average annual precipitation of 750 mm, while the mean monthly maximum and minimum temperatures vary between 25 and 15.3 °C (in summer) and 15 and 7.6 °C (in winter), respectively, procuring a climate classification of temperate-oceanic (Cfb), based on the Köppen–Geiger classification index.

The degree of urbanisation within the catchment boundary is reflected by an average impervious fraction of 47% (0.47), with a heterogeneous distribution of land use, the predominant allocation being residential zoning at 64%, followed by public use areas at 11%, roads at 9% and other land uses covering the remaining 16%. The Gardiners Creek catchment collectively functions as both a multifaceted urban environment and a noteworthy environmental asset for the East Melbourne region, servicing the local community, in terms of countless aspects, namely through providing accessibility across a multitude of municipalities, specifically Boroondara, Stonnington, Whitehorse, and Monash, as an esteemed recreational hub and a remarkable wildlife corridor thriving within an increasingly urban environment, underscoring its substantiality as an exemplary site for this study.

In this research project, two hydrological variables crucial for any flood investigation study – the observed localised rainfall depth (in mm) and the recorded streamflow (in m³/s) – were acquired from Melbourne Water Corporation. These variables, which were concurrently recorded at 6-min time intervals and aggregated daily, were obtained from the representative streamflow gauging stations situated within the study catchment boundary. The monitoring sites were selected based on the hydrologic data quality (https://www.melbournewater.com.au/water-and-environment/water-management/rainfall-and-river-levels#/), auditability (data completeness), and the station's spatiality upon rainfall distribution within the delineated sub-catchments (using spatial averaging techniques – Thiessen Polygon). The details of the selected monitoring sites have been summarised in Table 1.

The dataset selection phase chiefly employs the classification of independent and dependent variables in the calibration and validation of the developed neural network model. The localised rainfall depth (in mm) and the flow contributions from the upstream catchment (upstream catchment flow) (in m³/s) were selected as the independent variables, based upon the dominancy exhibited over catchment hydrological processes and overall water balance and the cruciality in comprehending accelerated flow dynamics at downstream locations and spatially distributed travel time of runoff, respectively. The inclusion of the upstream catchment flow contributions also serves the purpose of partially replicating the runoff routing procedure in RORB models, capturing some of the temporal and spatial dynamics as observed in the patterns of the historical data provided. The estimated flood flow/runoff, the primary hydrological variable crucial in any flood investigation/flood forecasting application, which is obtained as a function of the collective integration of both the independent variables remains as the dependent variable. Thus, the localised rainfall, upstream catchment flow, and estimated flood flow were, respectively, translated as the input and output variables employed for the neural network model calibration/validation, while also being incorporated in the development of storm files for the calibration of the RORB model.

An event-based modelling approach was embraced for this research context, where the selection of storm events, beyond the consideration of data quality and auditability, further involved a meticulous evaluation of the length of hydrologic data records (both rainfall and flow) and the historical flood records of the study catchments, as documented for the pertinent councils (Victoria State Emergency Services 2022). The storm event selection encompassed a temporal window of 3 days circumscribing each selected event, enabling a nuanced comprehension of the urban study catchment's current hydrological response dynamics. The details of the selected storm events have been summarised in Table 2, where it can be noticed that the highest streamflow recordings were observed at the Great Valley Road at Gardiners Station, primarily owing to its strategic location in proximity to the catchment's terminus.

The data pre-processing phase assessed the vitality of various input variable features, filter outliers, and address noise that could potentially impair the model's performance (Rajaee et al. 2019). Concerning the rainfall duration and intensity, every catchment's response time to rainfall entails an inherent lag-time (T_L), which, nonetheless, transcends the interpretative capability of neural network models, mandating its adjustment to retrospectively synchronise the peak discharge data with the corresponding antecedent peak rainfall magnitudes, prior to model simulation. Given the catchment's urban genus with increased imperviousness influencing overland flow convergence at a significantly accelerated rate, in comparison to previous conditions, this synchronisation is mandatory, to prevent flow over/underestimation (Iowa SUDAS 2019; Sultan et al. 2022). Pertaining to outlier filtering and noise treatment, durations with zero rainfall depth recordings were excluded due to their negligible impact upon rainfall extremes and their controversial origin – either reflecting true zero rainfall on a non-rainy day or false positives from measurement device detection thresholds (Gupta & Gupta 2019).

ANNs comprise a sequence of interconnected artificial neurons continuously receiving, processing, and transmitting signals throughout the network (Haykin 2005; Choudhury et al. 2018). The signals, acquired from the network environment via a learning process, are stored within interneuron connection strengths/synapses which retain the ability to fluctuate signal strength at a connection, forming the basis for generalisation (Haykin 2005), achieved during the training phase. In the training phase, following neuron activation, the signal gets transmitted to the next layer's neurons, and the forward propagation process is continued until the output layer is reached (Haykin 2005; Choudhury et al. 2018). These propagated signals, representing the overall network response, undergo evaluation against the actual target output, in the output layer, determining the prediction error and developing an error signal at the output layer neurons (Haykin 2005; Choudhury et al. 2018). The error signal is transmitted backwards, repeatedly, layer-by-layer, until all the perceptron in the neural network has received the error signal, describing their relevant contribution to the overall error (Choudhury et al. 2018), where based upon the error signal information received, the model training process is undertaken, with consistent adjustments to the synaptic weights, and the cycle of forward/backwards propagation is continued for several iterations until the optimised weight matrix is achieved (Haykin 2005; Choudhury et al. 2018). The optimal weight matrix achievement indicates the presence of minimal error difference between model prediction and target variables.

In addition to obtaining the optimised weight matrix, the inherent non-linearity associated with influential hydrological processes of urban catchments must be offset through the determination of the optimal hidden layer dimensions and hidden layer neuron content within (Choudhury et al. 2018). The number of hidden layers and neurons within must be varied within each layer, and the training incessantly repeated, until the model alleviates at an appropriate complexity level, with properly generalised outputs and minimal incidence of over/(under)fitting transpiration, indicating achievement of optimal hidden layer dimensions (Haykin 2005; Berhanu et al. 2016; Choudhury et al. 2018).

RORB is a hydrological software program that embraces an event-based approach, to simulate runoff and streamflow routing, by deducting losses from rainfall and/or other channel inflow sources to spawn rainfall excess (Laurenson et al. 2010; Kemp & Daniell 2020). This rainfall excess is subsequently routed through the delineated catchment storage, generating runoff hydrographs at specified location(s), within the modelled channel network (Laurenson et al. 2010). The storage routing procedure enables RORB to function as a spatially distributed, non-linear hydrological simulation tool, accounting for both temporal and spatial variations, and enabling comprehensive streamflow modelling at multiple gauging stations within the modelled catchment. Since its inception in 1975 for rural catchments, the RORB model has been extensively refined to support urban and partly rural/urban catchments, incorporate multiple design storm event simulation methods (simple/ensemble/Monte-Carlo), include a graphical user interface (RORB-Graphical Editor (RORB-GE) mode) and GIS extensions (ArcRORB, MIRORB), and align with ARR2019 practices and provide regional prediction equations for most Australian regions (Hill et al. 2013; Kemp & Hewa 2018). The RORB model, with its consistent enhancements and numerous features, has become the most widely accepted and adopted hydrological practice in Australia, especially in Victoria, where RORB serves as the standard for the Water Industry (Laurenson et al. 2010; Hill et al. 2013; Kemp & Daniell 2020).

Some of the most common applications of RORB are in flood flow estimation, specifically in design storm event simulations and for model calibration, by fitting to historical storm event(s) rainfall and runoff data (Laurenson et al. 2010; Hill et al. 2013), while also being employed in flood routing through channel networks and design of certain hydraulic structures (spillways, retarding basins). There are two major inputs that must be provided by the user to run the RORB model, which is a graphical catchment file and a storm file (Hill et al. 2013). The graphical catchment file can either be developed on RORB or imported using available Geographic Information System (GIS) extensions, while the storm file and associated parameters (areal reduction factor (ARF), losses and temporal patterns) can either be imported from Australian Bureau of Meteorology (BoM) IFD2016 and ARR2019 datahubs, respectively (design storm event) or be user-specified (historical storm events) (Kemp & Hewa 2018; Kemp & Daniell 2020). In the case of user-specified model calibration, alongside the above-mentioned parameters, the user is required to specify four supplementary calibration parameters – two routing parameters – variation of stream lag parameter (K_c), non-linearity factor (m), and two loss parameters (initial (IL)/continuing (CL)), for model calibration with the observed data.

In this study, a graphical catchment file of Gardiners Creek catchment was developed using the RORB-GE mode, delineating the catchment into 45 sub-catchments (refer to Figure 1), interconnected by nodes and reaches, based upon an imported catchment backdrop developed using QGIS. The selected storm event datasets were utilised in developing storm files, describing the time increments, spatial and temporal variability, and observed runoff hydrographs. The developed files were used to run the RORB model, following the specification of the four calibration parameters – variation of stream lag parameter (K_c), non-linearity factor (m = 0.8), and losses (IL/CL) (Hill et al. 2013; Kemp & Daniell 2020). The non-linearity factor (m) is retained at a recommended value of 0.8, as per ARR2019 specifications, while the other parameters contribute to the model calibration procedure. The three routing parameters (K_c, IL, and CL) are varied for each interstation area corresponding to the specific gauging stations, under consideration.

The RORB model calibration is performed, primarily focused on obtaining a good fit between the modelled and observed flood hydrographs, in terms of corresponding peak flows and runoff volumes, which is established through tweaking the K_c and losses parameters, until a good fit is achieved, completing the model calibration. This is repeated for all three selected gauging stations, with varied routing parameters per interstation area. The calibrated model results are then used for the comparative assessment and model validation purposes, using the same statistical indices. A sample extract of the calibration parameters used for attaining the hydrograph for the 4th of February 2011 storm event at the Gardiners Creek downstream at High Street Road Ashwood station has been summarised in Table 3.

Ascertaining the validity of the developed ANN-based flood flow estimation model is crucial for real-world application, established through a meticulous evaluation of its respective performance. This is achieved through juxtaposing the ANN model's predictions for three specific storm events which transpired within the last quindecinnial period – 4th of February 2011, 6th of November 2018, and 5th of March 2020, across the three selected streamflow gauging stations (as summarised in Table 1), against the benchmark hydrological model's (RORB) flow hydrograph(s), with regard to performance, prediction precision, and result reliability. The model performances are assessed using the statistical indices – Pearson's coefficient of determination (R²), mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), Nash–Sutcliffe efficiency (NSE), index of agreement (d), and Kling Gupta Efficiency (KGE) (Haykin 2005; Choudhury et al. 2018).

Referring to Figures 3(a)–5(b), an initial comparative assessment of the LM-ANN model against the RORB model, based upon observed streamflow records, suggests superiority in the LM-ANN model's performance, evident from its significantly elevated correlation and enhanced goodness-of-fit achievement with observed records, in both datasets (train/test), respectively. Conversely, the RORB model's performance appears less robust in comparison, as illustrated in the figures. When a meticulous examination of the models' performances, based upon the aforementioned statistical indices is conducted as encapsulated in Table 4, the coefficient of determination (R²) exhibits variability across the three stations, ranging between 89.5 and 96.9%, unequivocally demonstrating attainment of a superior goodness-of-fit, adeptly mirroring the observed streamflow records, with minimal, unbiased deviations, and elucidating between 89.5 and 96.9% of the variance in the streamflow being attributable to the localised rainfall and upstream catchment flow contributions (Singh et al. 2023). In contrast, the R² values for the RORB model across both datasets range between 72.3 and 82.9%, reflecting a moderate goodness-of-fit achievement, and further highlighting that the RORB model demonstrates a moderate efficacy in replicating the observed streamflow records, with only up to 82.9% of the variance in the flow being attributable to the independent variables (localized rainfall and upstream catchment flow contributions) (Kemp & Alankarage 2023, Singh et al. 2023). The Index of Agreement (d) values further corroborate the superior goodness-of-fit achievement of the LM-ANN model, showcasing an exceptional level of agreement between predicted and observed flow, ranging between 0.93 and 0.96, further highlighting the LM-ANN model's robust performance and its capacity to replicate the observed streamflow with minimal deviation. In contrast, the d values for the RORB model reflect a less precise fit, indicating more pronounced discrepancies between observed and modelled flow. In comparison, the LM-ANN model distinctly outperforms the RORB model, in both datasets, demonstrating a superior fit and reaffirming its enhanced capability to faithfully replicate observed records and further substantiating the robustness and reliability of its predictions.

A comparative evaluation of the predictive skill and efficiency of the RORB and ANN models, based upon the Nash–Sutcliffe efficiency (NSE) and Kling–Gupta Efficiency (KGE), reveals distinct disparities in performance. For the RORB model, the NSE and KGE values span from 0.64 to 0.84 and from 0.78 to 0.86, respectively, collectively categorising the model's prediction efficiency as moderate, reflecting its moderate ability to aptly capture the dynamics of the observed streamflow, with some variabilities in terms of accuracy. Conversely, the LM-ANN model exhibits outstanding performance, with NSE values between 0.89 and 0.96, signifying excellent predictive skill and a high degree of efficiency. The KGE values, ranging from 0.92 to 0.96, further reinforce this evaluation, indicating a superior level of agreement between the predicted and observed data and highlighting the model's robustness. The ANN model's R² values, which range from 89.5 to 96.9%, further corroborate these findings, demonstrating a strong concordance with observed data and categorising the simulation results as highly satisfactory and reliable (R² of 0.895 > 0.6 and NSE of 0.89 > 0.5) (Lin et al. 2017).

Finally, the three error metrics – mean absolute error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE) are considered to underscore the pronounced differences in both models' performances. For the RORB model, the MAE, MSE, and RMSE values range from 0.55 to 11.4 m³/s, 0.27 to 75.2 m³/s, and 0.52 to 8.67 m³/s, respectively, indicating a higher degree of error and variability, and further reflecting the RORB model's lower precision and less consistent alignment with observed streamflow. In contrast, the ANN model demonstrates substantially lower error metrics, with the MAE, MSE, and RMSE values spanning between 0.23 and 4.03 m³/s, between 0.14 and 12.8 m³/s, and between 0.38 and 3.58 m³/s, thereby affirming the model's superior prediction accuracy, precision, and overall robustness in replicating observed streamflow data. In summation, the ANN model's substantially lower error metrics unequivocally advocate for its superior performance and result reliability, markedly surpassing the RORB model in streamflow simulation, with minimal deviations from observed data.

Referring to Figures 6(a)–11(b) and Tables 5 and 6, the results clearly emphasise the ANN model has again outperformed the RORB model in both datasets (training and testing) for both modelled storm events. This is evidenced by the stronger positive correlation (d) and higher goodness-of-fit (R²) achieved by the ANN model, with values ranging from 0.91 to 0.96 and from 88 to 96% for the event on February 4th 2011, and from 0.92 to 0.94 and from 91 to 96% for the event on March 5th 2020. In comparison, the RORB model's performance is notably lower, with R² and d values ranging between 0.78 and 0.87 and between 63 and 88% (February 4th 2011), and 0.81 to 0.88 and 71 to 81% (March 5th 2020). The NSE, KGE, and the three error metrics (MAE, MSE, and RMSE) further support this, indicating that the ANN model exhibits much higher and stronger predictive skill. The NSE and KGE values for the ANN model range from 0.86 to 0.96 and 0.87 to 0.96 (February 4th 2011) and from 0.92 to 0.96 and 0.94 to 0.97 (March 5th 2020), with the three error metrics being much lower, varying between 0.44 and 4.88 m³/s (MAE), 0.2 and 16.6 m³/s (MSE), and 0.31 and 4.07 m³/s (RMSE) for the February 4th 2011 event, and between 0.11 and 2.41 m³/s (MAE), 0.34 and 10.3 m³/s (MSE), and 0.58 and 3.21 m³/s (RMSE) for the March 5th 2020 event. These results indicate minimal variance between the ANN model's simulated values and the observed values, confirming its prediction accuracy. In contrast, the RORB model displays significantly lower predictive skills, with NSE and KGE values fluctuating between 0.78 to 0.86 and 0.8 to 0.9 (February 4th 2011), and 0.79 to 0.86 and 0.82 to 0.9 (March 5th 2020). The error metrics for the RORB model are notably higher, varying between 0.66 and 23.3 m³/s (MAE), 0.14 and 49.2 m³/s (MSE), and 0.38 and 7.23 m³/s (RMSE) for the February 4th 2011 event, and between 0.25 and 9.03 m³/s (MAE), 1.21 and 45.6 m³/s (MSE), and 1.35 and 6.75 m³/s (RMSE) for the March 5th 2020 event.

In summary, the ANN model distinctly outperforms the RORB model, in terms of superior performance, higher goodness-of-fit achievement between modelled and observed values, excellent predictive skill, and a much lower minimal error difference. The strong, positive correlation testifies to the model's superior performance, while the higher goodness-of-fit achievement, excellent predictive skills, and much lower generalisation error conform to the model's prediction accuracy and result reliability. The study results are further supported by similar research findings of Rezaeianzadeh et al. (2014), Gunathilake et al. (2021), Javan et al. (2015), Daliakopoulos & Tsanis (2016), Humphrey et al. (2016), and Jimeno-Sáez et al. (2018), where in all cases, the respective developed neural network models displayed better performance, significantly surpassing that of the respective conventional models (HEC-HMS, SWAT, HSPF, GR4J) employed in the studies. Thus, it can be deduced that the developed ANN model has exceptional understanding of Gardiners Creek catchment's characteristics, sharing similarity with the results of Vidyarthi & Jain (2023), showcasing the developed deep learning neural network has adequately captured some of the physics associated with the Gardiners Creek's rainfall–runoff process and is capable of accurately modelling the current catchment response state to present-day storm events, much better than the industrial standard hydrological practice (RORB), as showcased by the results, suggesting its suitability as an alternative option for incorporation in enhancing flood flow estimation practices.

However, the necessity for the adoption of process-based modelling practices cannot be completely disregarded, particularly in design hydrology, i.e., in the estimation of expected flood flow peaks for the management of envisioned land use changes/land subdivision works. Given the rapid urbanisation and population growth being experienced across Australia, leading to extensive urban sprawl across its regional states/territories, an increased demand for effective planning and management strategies to balance infrastructural development with environmental and social considerations is projected to arise. In such a scenario, as part of future research directions, supplementary input variables indicating land-use changes such as land cover types, impervious surface area, relevant vegetation, and topographic indexes (e.g. normalised differential vegetation index (NDVI), topographic wetness index (TWI)) and remote-sensing or GIS-based spatial data, are recommended to be considered alongside the historical storm data, whilst re-calibrating the developed model. Using a robust dataset comprising of various potential land-use change scenarios surrounding the study catchment, utilisation of a scenario/sensitivity-based analysis can greatly assist the neural network model in comprehending the influence of land-use changes on flow predictions, which can then be adopted for future flow predictions, under different conditions and scenarios.

The high complexity and non-linearity associated with the influential hydrological processes of urban catchments, hampers the prediction accuracy of conventional hydrological models, resulting in significant over/(under)estimation of flood flow peaks, as evidenced by the 2022 Maribyrnong River flooding debacle. ANN models have showcased the capacity to offset most of these limitations, namely the ability to recognise complex, non-linear relationships without requiring an in-depth insight of the underlying physical processes. Accordingly, this research proposed a deep learning neural network-based enhanced accuracy flood flow estimation model, for Victorian urban catchments to predict the expected flood flow. The model was trained and tested using multiple storm events, at three selected gauging station locations within the selected study catchment, Gardiners Creek. The performance of the developed neural network model was comparatively assessed against the Victorian Water Industry standard hydrological practice, RORB, as the benchmark model.

The study results demonstrate the ANN model's superior performance, evidenced by a stronger positive correlation and higher goodness-of-fit achievement (R² betwixt 88–96%), in comparison to the RORB model's conspicuously lower performance (R² betwixt 72–88%). The ANN model also exhibits substantially lower error metrics (MAE & RMSE range of 0.26–16.6 m³/s) and higher predictivity skills (NSE and KGE range of 0.86–0.97), markedly surpassing the RORB model, which displayed higher error metrics (MAE and RMSE range of 0.25–23.3 m³/s) and lower predictivity skills (NSE and KGE range of 0.78–0.88). Thus, it can be concluded that the deep learning neural network-based flood flow estimation model remarkably surpasses the RORB model, with superior performance, enhanced goodness-of-fit achievement (higher R² and d), excellent predictive skill (higher NSE and KGE), and a much lower generalisation error (lower MAE and RMSE). This stipulates the ANN-based flood flow estimation model's superior understanding of Gardiners Creek's physical catchment characteristics and its enhanced capability to accurately model the current catchment response state to present-day storm events, surpassing the performance of the industrial standard hydrological practice (RORB). The developed ANN model can be considered as a potential alternative for the Victorian Water Industry, enhancing current flood flow estimation practice and precisely estimating the expected flows in urban catchments, while tackling emerging challenges posed by climate change. Some limitations of this study involve the exclusion of land-use changes and land-subdivision work impacts upon the study catchment area, which is anticipated to undergo significant transformation due to its functionality as a multifaceted urban hub and due to the collective impact of Australia's rapid urbanisation and population growth. Thus, future researchers are recommended to incorporate robust land-use change scenarios, grounded upon spatial data and national records, expected within the respective study catchment, alongside historical storm incidence data. Calibrating the neural network model with these factors will augment its comprehensive capability, model robustness and enhance predictive skill making it ideal for future high-vulnerability flood risk scenarios.

As part of future works, the developed deep learning neural network model will be employed to assess future flood flows under multiple greenhouse gas emissions scenarios across multiple timescales. The assessment will assist in investigating the latent ramifications of climate change-induced rainfall intensification upon urban catchments (gauged/ungauged) throughout Victoria. The findings will apprise the Victorian government and relevant water authorities in formulating effective flood risk mitigation strategies.

We sincerely thank Melbourne Water Corporation for providing the daily rainfall and streamflow records and other essential data (DEM model details, catchment physical data) for the Gardiners Creek catchment, based upon which the case study analysis was conducted.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.