A method of estimating imperviousness for the catchment modelling of urban environments

The world is experiencing rapid urbanisation with the growth of the urban population and the expansion of urban areas (Andersen 2013). According to a prediction published in the Economist, by the middle of the 21st century, the proportion of people living in urban areas will reach 64 and 86% for developing and developed countries, respectively (Grimond 2007). To meet the urbanisation demand, natural vegetated lands are continually replaced by impervious surfaces such as asphalt roads, buildings and parking lots (Jensen & Cowen 1999), interrupting water infiltration and weakening the flood resilience of the natural catchment. In urban environments, impervious surfaces are dominant runoff producers under very frequent and frequent rainfall events due to the minor depression storage, interception and infiltration losses, where the runoff flow rate and volume are significantly higher than the same-size rural catchments (Ball et al. 2019). The impervious runoff examination for 763 rainfall events in 26 urban catchments showed that the average initial loss of 70% of study catchments was equal to or less than 1 mm (Boyd et al. 1993), which corroborated the dominant role of impervious surfaces in the runoff generation of urban catchments. However, the expansion of urban impervious surfaces will inevitably lead to water issues in those urban environments. Urban flooding caused by frequent rainfall is a common phenomenon worldwide and is getting severe due to objective factors like unscientific development, rapid urbanisation and climate change (Jamali et al. 2018; Huang et al. 2021). Therefore, urban impervious surfaces and their impact on flood resilience have become a unified theme that a scientifically planned impervious fraction must be considered during urbanisation (Weng 2012).

Limited by the current hydrologic data monitoring and measurement techniques, catchment modelling is one of the most popular approaches to simulating catchment rainfall–runoff process (Beven 2012), where most catchment modelling systems adopt impervious fractions as the input parameter to quantify runoff generation. Spatial variability, like changes in land use land cover (LULC), is strongly correlated with the hydrological and hydraulic response of the catchment. Therefore, the spatial variability of LULC is an innegligible issue when modelling an urban catchment. However, the existing catchment imperviousness estimation approaches provide a challenge for the development of reproducible and efficient workflows in the provision of estimates of impervious fraction values.

Estimation of the catchment response will be based on the available data. However, for potential future development within a catchment, details of the LULC are not available until the development has been undertaken. This is where the problem for catchment managers is generated: this is further complicated by an inability to reverse development once it has occurred. Therefore, there is a need for a catchment manager to estimate future catchment responses for development conditions that have not yet occurred. This is possible with the novel and innovative approach proposed herein.

Urban planning is a crucial phase of urbanisation that sets the tone and provides scientific advice for the city's future development, where land zoning is one of the most commonly used urban planning schemas to determine development patterns, environmental protection strategies and social and economic activities. In urban environments, the catchment impervious fraction is closely tied to the functional land zone to which it belongs. For example, the latest version of the Australia New South Wales (NSW) local environmental plan (LEP) making guideline proposes seven urban land use categories to standardise urban planning and development. These categories are residential zones, commercial zones, industrial zones, special purpose zones, recreation zones and environment protection zones (NSW Government 2021). Similarly, the American Planning Association (ASA) employed the optimum land use patterns theory to classify urban land uses as social, economic, functional and environmental (Duranton & Puga 2015). The Organisation for Economic Cooperation and Development (OECD) of the United Kingdom outlined a long-term vision of land development for the next 30 years in the national planning framework (NPF) and the regional development strategy, which support all levels of government to make spatial-related strategies under the framework and provide essential information (e.g. impervious rate) for all stakeholders interested in local development (OECD 2017).

The acquisition methods of impervious data for catchment modelling purposes can be summarised into two categories: manual and automatic. The manual method refers to delineating and extracting geometric elements of impervious features using geographic information system (GIS) tools through human cognition of impervious areas from remote sensing imagery (Slonecker et al. 2001). The manual method is more accurate than the automatic method, when combined with a field survey. Nevertheless, this accuracy sorely relies on the subjectivity and experience of the modeller and is usually accompanied by a massive data acquisition and interpretation workload, which limits the scope of its application, such as in large urban catchments (Mohapatra & Wu 2010; Weng 2012).

In recent years, the automatic impervious data acquisition method has sparked heated discussion in both academia and industry, as a result of the growing demand for large-area catchment models and an increasing heterogeneity of land use land cover (LULC) in urban catchments. The availability of remote sensing data is the core of the automatic acquisition method that extracts the spatial geometry of impervious features by analysing the spectral and texture features of LULC in remote sensing images. Remote sensors with sensitive spectral resolution can automatically distinguish the reflected spectral wavelengths of LULCs from the entire radiation spectrum and render the different LULCs to extract impervious features in post-image processing (Slonecker et al. 2001). For example, while the spectrum-based impervious features extraction approaches for pixel and object of remote sensing imagery have been proposed and achieved excellent performance in various application fields (Flanagan & Civco 2001; Yang et al. 2003; Yuan et al. 2008; Van de Voorde et al. 2009), but still require to invest many human resources in data interpretation at the feature extraction stage (Wu & Murray 2003). In the recent decade, urban impervious feature classification and extraction have entered a new era with the development of remote sensing databases and machine learning (ML) algorithms. The convolutional neural network (CNN)-based ML models resolved the drawbacks (e.g. salt-pepper noise) of spectrum-based classification approaches and achieved high precision and automaticity in classifying and segmenting remote sensing images, especially when dealing with some areas with high heterogeneous LULC. For example, Li et al. (2019) used an ML-based approach to distinguish the types of urban built-up areas with an overall accuracy of 95%. Xu et al. (2018) utilised the Res-Unet model to extract buildings' footprints from the high-resolution remote sensing imagery of Vaihingen and Potsdam. Zhang et al. (2018) developed an integrated approach of the multilayer perceptron (MLP) and CNN to classify LULC of urban remote sensing imagery and obtained an outstanding precision (classification accuracy of 90.93%) and robust performance (Kappa coefficient of 3.68) compared with the other tested approaches.

Catchment modelling parameter sets can be classified as measured or inferred, with the catchment impervious fraction belonging to the measured parameter set and playing a crucial role in deducing dimensionless inferred parameters such as depression storage and Manning's value (Choi & Ball 2002). The extracted impervious data can be interpreted and transported to the catchment model as input parameters to simulate the catchment rainfall–runoff process, identify the flood risks under existing catchment conditions and further guide urban development. However, there is a specific information hysteresis in guiding urban development or flood mitigation by modelling the existing catchment scenarios as urban is a dynamic system with the changing of LULC every day (Chen et al. 2009). A prospective catchment model can predict catchment hydrology in the post-development scenarios and enhance the hydrologic evaluation capacity of city planners in defining functional zones for pre-developed catchments if we can build the prospective model with scientifically estimated imperviousness before it is urbanised. In addition, determining the impervious fraction of different functional land zoning categories is a grand challenge to catchment modellers, especially when dealing with large urban catchments and heterogeneous LULC (Salvadore et al. 2015). A reliable zone-based impervious fraction estimation approach can not only initialise catchment models but also support building harmony between land use, water and environments, such as legislative constraints on land use, building size and population density based on the natural characteristics of a land lot (National Research Council 2009; Byrne et al. 2014). Therefore, the research on the impervious features of different land zones has considerable significance for enhancing catchment modelling capacity, guiding urban planning and assessing the flood risks of catchment urbanisation.

This paper proposes a prior probability approach to analyse the impervious fraction of five representative functional urban land zones in Australia, including low- to medium-density residential, high-density and commercial residential, industrial, urban green land and urban road. Five urban catchments within the Greater Sydney area are selected as the database to extract impervious surfaces for evaluating the distribution of the impervious fraction of the five functional land zones. The section ‘Methodology’ first describes the study catchment conditions and adopted datasets in this study, followed by the workflow of LULC classification, impervious features extraction, samples' probability-fitting and the outputs stability study. The ‘Results and discussion’ section demonstrates the predicted LULC maps, occurrence likelihood distribution of impervious fraction and information entropy (IE) distribution under different land zoning categories. The key findings and research prospects are involved in the ‘Conclusion’.

The proposed methodology consists of four components: image classification, impervious feature extraction, probability-fitting study and data stability analysis. Firstly, the approach proposed by Gong et al. (2022) was duplicated to conduct the imagery classification and segmentation. This study inherited the MeanShift algorithm to preliminary segment image objects by clustering pixel spectral information. In the deep learning (DL) module, the DeepLabV3+ (Chen et al. 2017) substituted Unet (Zhou et al. 2018) to classify the LULC information from the high-resolution imagery due to its better stability and consistency in predicting big datasets, as verified by Gong et al. (2022) and Yurtkulu et al. (2019). Then, the GIS spatial fusion approach was utilised to integrate the simplified land zoning and classified LULC maps (Tripp Corbin 2015). Secondly, a fishnet sampling GIS grid layer was created to adapt the format of the fundamental dataset, extract LULC features from the study catchment imagery and then export the statistical database for impervious and pervious samples. Finally, the computed distribution curves of the impervious feature were translated to IE for output stability analysis.

The datasets used for this study include remote sensing imagery and land zoning maps. The spatial resolution of remote sensing imagery has experienced a significant evolution, from 80 m (Landsat-7), 30 m (Landsat-TM) and 10 m (SPOT) to 1.0 m (IKONOS) and 0.3 m (QuickBird) with global, multi-temporal and high-geometric resolution image sequences after decades of rapid development, which become the essential geospatial dataset for urban planning, resource development, ecological protection, catchment modelling and disaster prevention and mitigation (Chevrel et al. 1981; Johnston & Barson 1993; Toutin & Cheng 2002; Dial et al. 2003; Williams et al. 2006; Ball et al. 2019). The term spatial resolution implies the most acceptable object size that the remote sensor will detect on the ground, which does not translate into object recognition capacity but represents the information coverage area of one single pixel on the ground (Atkinson & Curran 1997). As the fundamental data, the high-resolution imagery is indispensable for generating the DL training set, classifying ground LULC and extracting impervious features. Selecting the appropriate spatial resolution and associated imagery product is the critical step in data preparation, where the pixel size must cover the majority of LULC features without overloading the training process.

The adopted remote sensing dataset of the study is the standard RGB (three bands: Red, Green and Blue) imagery fused by multiple metadata, including AAM, Jacobs Group Ausimage and Landsat, which was rendered and released by the Spatial Service Department of the NSW State Government (NSW Spatial Service 2021). The selected spatial resolution is 0.29 m per pixel width, referring to the minimum size of study catchments' LULC objects. According to Li et al. (2019), Weih & Riggan (2010) and Xu et al. (2018), less than 0.5 m pixel width has sufficient capacity to delineate textural features of LULC (e.g. single dwelling, plants) without losing their spectral information.

Functional land zoning is one of the most welcome urban planning approaches used in countries with abundant experience in city management, which plays a critical role in regulating the built markets and creating functional urban living spaces (Caves 2004; Mason 2012). Many municipalities and similar levels of government divide the urban areas into different sections and permit the construction of particular structures on the associated land zones to achieve the planned functional zoning purpose or a planned environmental friendly development. In practice, land zoning maps are usually drafted by local governments in response to delineating particular zones for various land use purposes, which play an essential role in promoting scientific, regulated and sustainable urban development (Gurran et al. 2015). In this study, land zoning maps occurred from the official database of local governments, including the City of Sydney (City of Sydney Council 2012), Willoughby (City of Willoughby Council 2012), Ryde (City of Ryde Council 2014), City of Parramatta (City of Parramatta Council 2011) and Strathfield (City of Strathfield Council 2012). Local deviations were found between the land zoning maps and actual land covers during the on-catchments investigation, which are caused by the lagging development and changing land zones. For example, the remote sensing image shows the factory building complex zoned as a residential area on its land zoning map since the development of the relevant residence has not yet been completed. Also, some attributes of land zoning maps with similar impervious fractions are uniformly considered in this study. For example, development in City of Sydney land zoning map, zone R5 (larger lots residential) and zone B3 (commercial core) are usually presented as residential–commercial mix buildings and have no significant differences in impervious fractions.

In summary, appropriate adjustment and correction for the official land zoning maps by referring to the actual ground cover of remote sensing imagery are essential to ensure the consistency and stability of the subsequent samples. This study merges the original land zoning subdivisions into five representative land zoning categories: high-density residential and commercial, low- to medium-density residential, industrial, urban roads and urban landscaping. This simplified land zoning pattern groups land subdivisions with similar impervious features without sacrificing their functional discrimination from the perspective of urban planning. The simplified land zoning maps are shown in Figure 5.

The dominant surface that generates runoff in an urban catchment is the impervious area under all kinds of rainfall events (from frequent to rare). In this study, the DeepLabV3+ DNN has classified the ground features of remote sensing imagery into the seven defined LULC classes, where railways, impervious ground, roads and roofs are grouped as impervious features due to their rapid rainfall response in urban environments. In contrast, trees and pervious land are treated as pervious features.

A fishnet sampling approach is proposed to extract impervious features from the predicated LULC maps of study catchments. Firstly, we created a mesh layer with a grid size of 100 × 100 m² to rasterise the entire area of the study catchments. The fishnet grid size is determined to be consistent with the average size of the large structures (e.g. factories and warehouses) in the study catchments so that one grid could cover homogeneous ground objects to the greatest extent without losing the samples' textural information and zonal diversity.

The probability-fitting method is a numerical calculation method guided by probability and statistics theory that helps people deal with uncertainty in complex situations (Malz 1997). Establishing a probability model or stochastic process with a large number of random variables is the kernel of the probability-fitting method, assuming its parameters or numerical characteristics are equal to the solution of the problem by creating a joint distribution of possible outcomes resulting from the combination of the related variables (Tokuda et al. 2002). These parameters or numerical features will be translated to specified values or ranges as a final approximation of realistic scenarios (Metropolis & Ulam 1949). In catchment modelling, the determination of the model parameters is driven by probability to some extent instead of physical state since the continuous dynamic changing of the catchment, such as change of LULC, that is, the parameters take values from a range rather than a fixed number (Kuczera & Parent 1998).

In this study, the probability-fitting method was utilised as a quantitative probabilistic analysis tool to generate the likelihood and accumulated likelihood distribution of impervious fractions of each land zoning category.

• Firstly, determine the variables that represent the source of uncertainty. The land zoning attribute is defined as the study variable that groups study samples into five zoning categories: high-density residential and commercial zone, low- to medium residential zone, urban green land zone, industrial zone and urban road zone.

• Secondly, assume a distribution for each variable. In this case, the skewness distribution was assumed to conform to the samples' distribution as the constraint of the boundary condition.

• Thirdly, generate some iterations with possible realisations of each variable. As the study sample, the grid impervious fraction was transferred to the input side of the assumed distribution equations to realise iteration, where the whole impervious fraction domain (0–100%) was split into 20 fraction ranges with an increment of 5%.

• Finally, substitute all samples into the iteration to generate a joint likelihood distribution.

Considering a proportion of the area (no land zoning data) is erased during sample impervious feature extraction and resulting in the reduction of sample area compared with the preset sample area (1 ha), this study adopted the area reduction ratio of the sample area and the preset sample area as the quantity to count the number of samples.

Essentially, land zoning information has positive feedback for estimating the imperviousness of a plot; that is, the confidence range of the imperviousness of a plot can be further narrowed by knowing its land zoning information. The quantisation of land zoning information and its contribution to the impervious fraction distribution have significant meaning in exploring the validity of the probability-fitting model results.

In the 1940s, inspired by the theory of thermodynamics, Claude Elwood Shannon (1916–2001) invented the concept of IE by excluding redundancy from the average amount of information. IE resolves the question of information quantisation and clarifies the relationship between probability and information redundancy in the mathematic language (Núñez et al. 1996).

The imagery processing outputs consist of two components: classified LULC maps and simplified land zoning maps. LULC maps describe the spatial distribution of ground features with detailed representative land cover classes in the study catchments. While the simplified land zoning maps eliminate the information unrelated to catchment imperviousness (e.g. administration and cadastre) from the original dataset by merging subdivisions that belong to the same land zoning attribute. As the inputs of the probability-fitting study, a high accuracy standard was considered to evaluate the LULC prediction performance of the DeepLabV3+. The two indicators, overall accuracy and Kappa coefficient, are applied to measure the prediction accuracy and reliability through the randomly distributed 500 checking points among the study catchments (Sim & Wright 2005). The Kappa coefficient (Stehman 1996), an index that can punish the ‘bias’ of the model, is adopted to assess prediction consistency. The prediction error within impervious LULC classes (roof, road, impervious land and railway) is ignored as they are unified during impervious feature extraction. Figure 5 shows the catchment's raw remote sensing imagery, simplified land zoning maps and the corresponding LULC prediction.

The accuracy assessment of LULC classification is presented in Table 2 by using the confusion matrix to compare the ground truth and DNN prediction. The overall prediction accuracy is 0.9073, where the impervious features, pervious land and trees achieved the prediction accuracy of 0.9634, 0.7422 and 0.8611, respectively. A robust LULC prediction model developed by Rwanga & Ndambuki (2017) was also assessed by using the confusion matrix and got a Kappa coefficient of 0.722. In this study, the Kappa coefficient (0.8217) qualifies as considerable, indicating that the proposed DL approach has consistent prediction performance among the defined LULC classes of the selected study catchments. The acceptable level of prediction accuracy varies depending on the available conditions, and most DL models consider 75% accuracy as the lowest boundary of excellent prediction (Li et al. 2019; He et al. 2020; Kiran 2020). In this study, the 0.9634 prediction accuracy of impervious features is sufficient to estimate parameters for simulating the rainfall–runoff process in urban catchments. Therefore, the outputs of impervious feature extraction are acceptably conveyed to the sampling process as the inputs of the probability-fitting study.

The LULC maps and simplified land zoning maps were transmitted to the fishnet sampling procedure to prepare the dataset for the probability-fitting study. The workflow is shown in Figure 3 and the governing equations for computing samples' impervious fractions are presented in Equations (3) and (5). The amount of fishnet samples is proportional to the area of different land zoning categories in the study catchment, which aligns with the theory of stratified random sampling for avoiding the ‘bias’ caused by the larger area land zoning category (e.g. low- to medium-density residential) (Vries 1986). Table 3 illustrates the number of raw and downscaled fishnet samples (after applying the area reduction ratio).

In catchment modelling, a distributed impervious fraction parameter set can be estimated using the functional polynomial fitting curves for any pre-developed urban catchment. For example, in urban planning, an area of the pre-developed catchment will not only be zoned for specified land use but also be divided into a number of land lots. These land zone-attributed lots can be mapped to the corresponding distribution curve as inputs to generate their impervious fraction numbers at the output side. These outputs are capable of better representing the imperviousness of the catchment after development with the increase of the input amount. This prior likelihood approach provides a new pattern to estimate the parameter of catchment impervious fraction for modelling catchment hydrology to guide the planning and development of urban catchments more effectively.

In this study, the polynomial fitting curves are used to generate the polynomial function of each land zoning category and translate them into probability functions for the IE formulas (6) and (7) in Section 2.7 to compute their values of conditional entropy and the IG. Table 4 lists the polynomial probability function of the gross dataset and five land zoning categories, where their R² values reflect the high goodness-of-fit of the polynomial function to the sample distribution. R² can take any value between 0 and 1, standing for the goodness-of-fit from low to high.

Table 4

Polynomial probability functions

Category .	Polynomial probability functions .	R2 .
Gross dataset		0.9992
High-density residential and commercial		0.9995
Low- to medium-density residential		0.9998
Industrial		0.9993
Urban green land		0.9993
Urban road		0.9996

Category .	Polynomial probability functions .	R2 .
Gross dataset		0.9992
High-density residential and commercial		0.9995
Low- to medium-density residential		0.9998
Industrial		0.9993
Urban green land		0.9993
Urban road		0.9996

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The results in Section 3.2 demonstrate the distinctive distribution patterns of impervious fraction likelihood under different land zoning categories, which has verified the selectivity enhancement spectrum of land zoning to the impervious fraction from the perspective of statistics. In this section, land zoning is informationised to quantify its contribution to different impervious fraction intervals using IE, conditional entropy and IG. The information amount of knowing one event's probability by measuring its IE, that the higher the probability, the lower the IE (Núñez et al. 1996; Volkenstein 2009). IE could be 0 when we know that an event will definitely happen (e.g. the sun rising from the east) because the amount of information required to judge the probability of this event is zero. When a new condition is involved in judging one event's occurrence, the enhancement degree of the event probability by the new condition is also different depending on its provided information amount, hence requiring the condition IE to measure it.

This study presented an integrated data-driven approach to estimate the impervious fractions for selected five urban catchments in Sydney under five predefined land zoning categories and a designed stability testing procedure with IE theory. Remote sensing imagery and land zoning maps were obtained and preprocessed for DL-based image classification and land zoning-based impervious feature extraction. The clustering algorithm MeanShift and DNNs DeepLabV3+ were utilised to reduce pixel textural/spectral complexity and classify the LULC of the remote sensing imagery with an overall impervious features prediction accuracy of 0.9634. Then, the predicted LULC maps and preprocessed land zoning maps were spatially fused and transported to the first proposed ‘fishnet’ sampling layer to extract impervious features based on the spatial relation between LULC and associated land zoning categories. After that, for the probability-fitting study, the extracted impervious samples were grouped by different land zoning categories and optimised by two computational items: the area reduction factor and the LAI. Three elements, likelihood distribution, accumulated likelihood distribution and corresponding polynomial fitting curves of impervious fractions, were computed using the gross sample set and land zoning sample set under the probability-fitting study, demonstrating various intervals of centralised distribution and occurrence likelihood. Finally, the IE theory was introduced to evaluate the prediction stability and verify the contribution of land zoning to estimate particular impervious fraction ranges by quantifying their IE, condition IE and IG, where land zoning shows robust information enhancement power in reducing the IE of particular impervious ranges.

In the probability-fitting study, the occurrence likelihood distributions of impervious fractions are different due to the specified LULC characteristics of different land zoning categories, which means urban planning has a decisive effect on the imperviousness of a land lot. Therefore, given the environmental or development plan of a pre-developed catchment, the impervious fraction of a specific area within the catchment can be estimated using the proposed workflow in this study and then translated to parameters of catchment modelling systems for simulating the rainfall–runoff process of the catchment. This approach can also improve the scientific estimation of the impact of urbanisation. These impacts guide urban managers to reduce or avoid the corresponding flood risk in the functional subdivision of urban areas. Due to the mechanism of DL, the DNNs-based LULC classification and segmentation may be more or less affected by seasonal or phenological variations within the remote sensing imagery (Yuan et al. 2008). For example, the LAI was involved in this study to reduce the obstruction of the tree canopy while extracting underlying impervious features. The statistical relationship between land zoning categories and impervious fraction was built on the Australian regional database. The global land zoning scheme has not yet been assessed due to the limitation of data availability. In addition, the approach's robustness can be gradually improved with the increase of study samples based on the construction method of the probability-fitting study. In this study, the proposed approach has been evaluated from the perspective of DL and statistics. Nevertheless, hydrological validation, such as hydrograph prediction and model calibration, has not been considered in this study, as the focus of this study was the development of reproducible parameter values for a catchment model. Further research should focus on resolving the seasonal or phenological influence on LULC classification, examining more urban catchments to increase the approach's robustness and hydrological validation of the parameter values derived using the approach outlined herein. Furthermore, the IG from the land zoning dataset to urban imperviousness estimation should be explored further using the database with different land zoning schemes. In summary, the efficacy and overall accuracy of the impervious fraction estimation approach are determined by both LULC prediction accuracy and sample amount, as well as the knowledge and experience of the modeller for applicable scenario selection. Although it is impossible to explore the comprehensive urban environment in one paper, this study clarifies the differences in estimating urban catchment impervious fraction under different land zoning categories.

The support of the City of Sydney Council, Sydney, Australia, is gratefully acknowledged. The remote sensing imagery and land zoning map are provided by NSW Spatial Service and Environmental Data Portal of Australia NSW Government.

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

The authors declare there is no conflict.