Improving impervious surface estimation: an integrated method of classification and regression trees (CART) and linear spectral mixture analysis (LSMA) based on error analysis

Abstract

Classification and regression tree (CART) has been widely implemented to estimate impervious surface, an important indicator of urbanization and environmental quality. Although the CART algorithm gains higher overall accuracy than linear regression models, only very few studies have noticed that reliability of CART is affected by systematic errors. Especially, CART typically overestimates impervious surfaces in low-density urban areas and underestimates them in high-density urban areas. The primary objective of this study is to develop an improved integrated method to estimate impervious surface with higher accuracy by reducing the systematic errors of CART. This improved method was applied to three urban areas, Chicago (United States), Venice (Italy), and Guangzhou (China) to examine its effectiveness. When compared with the conventional CART, overall mean average error (MAE) and root mean square error (RMSE) of improved method are decreased by 22.64% and 20.93%, respectively, and R² rises from 0.9 to 0.96. In high-density impervious surfaces, where intensely developed urban area is located, the MAE and RMSE for the improved method are 0.066 and 0.088, respectively, largely improved from 0.100 to 0.130. Since accurate estimation of high-density impervious surfaces is the fundamental issue for monitoring and understanding the urban environment, the improved method demonstrated in this study is significant.

Keywords:

• impervious surface
• CART
• LSMA
• remote sensing

Introduction

The world has experienced significant population growth in urban areas since the 1990s when approximately 43% (2.3 billion) of the world’s population lived in urban areas. And this number has grown to 54% (4 billion) in 2015 (UNHabitat 2016). Rapid urbanization and urban sprawl bring significant impact to the urban environment (Yang et al. 2003b; Sofia et al. 2017) and much more attention is paid to understanding and monitoring the compositions and processes in urban areas (Stow and Chen 2002; Wu 2004; Xiao et al. 2006). For studying the heterogeneous urban landscapes, identification/description/quantification of land-use and land-cover compositions, rather than simple hard classification, should be applied (Ridd 1995; Mather 1999; Weng 2012). As a quantifiable land-use indicator that correlates closely with urbanization impacts, the impervious surface has long been considered as an indicator of urbanization and environmental quality (Arnold Jr and Gibbons 1996).

Impervious surfaces refer to materials through which water cannot infiltrate. In urban areas, impervious surfaces primarily consist of anthropogenic features such as roads, driveways, sidewalks, parking lots, rooftops, etc. The expansion of impervious surfaces can exert considerable influence on urban environment in many aspects (Weng 2001; Yang et al. 2003a; Yuan and Bauer 2007; Sofia et al. 2016; Zhang and Weng 2016). Impervious surfaces increase urban runoff (Corbett et al. 1997; Dams et al. 2013), which aggravates the burden of draining and flood prevention (Sofia et al. 2017). Due to the increased runoff, fluvial denudation and basal erosion of river channel are intensified (Weng 2012; Prosdocimi et al. 2015). Impervious surfaces can also have crucial repercussions on the hydrologic cycle and furthermore result in the decrease of water quality (Meyer and BL Turner 1994; Beck et al. 2016), especially for non-point source pollution sources including pathogens, nourishing materials, toxic substances, sediment, and so on. As a result, the increase of impervious surfaces altered the environment and biological conditions of watersheds and river systems. Researchers have suggested that the impairment from impervious surfaces becomes remarkable at approximately 10% (Schueler 1994). In addition, the expansion of impervious surfaces altered the thermal capacity of an entire city and strengthened urban heat island effects (Mathew et al. 2016).

Efficient and accurate estimation of impervious surfaces distribution with remote-sensing techniques is fundamental in impervious surfaces studies (Weng 2012). Due to the relatively low cost and suitability for large area mapping, remote-sensing techniques have been widely applied for impervious surface estimation since 2000 (Bauer et al. 2004). Some effective approaches, such as imagery transformation (Cablk and Minor 2003), post-classification analysis (Dougherty et al. 2004), classification decision tree algorithm (Zhang et al. 2014), and normalized index extraction (Piyoosh and Ghosh 2017), were developed for mapping impervious surface in per-pixel level. However, in urban areas, most pixels in medium resolution imagery are mixed and composed of several land-use types (Yang et al. 2003b). To evaluate the proportions of impervious surfaces for each pixel, subpixel methods, including linear spectral mixture analysis (LSMA) and classification and regression tree (CART) are widely employed.

Ridd (1995) suggested that pixels in medium resolution imagery are linearly mixed by impervious surface, vegetation, and soil (V-I-S model) since the land-use and land-cover(LULC) of urban areas can be deemed as a linear combination of them (Ridd 1995). Based on the V-I-S model, LSMA is able to estimate impervious surface at the subpixel level with properly selected end-members (pure pixels). LSMA model has been continuously promoted and widely used due to its effectiveness in dealing with spectral mixture problem (Roberts et al. 1999; Wu and Murray 2003; Weng 2012; Huadong et al. 2014; Fan et al. 2015). Wu (2004) normalized the spectral characteristics of three types of endmembers in the model to overcome the problem associated with the selection of endmembers and within-class spectral variability (Wu 2004). Phinn et al. (2002) overlaid the classification results with the LSMA extraction of impervious surfaces and analyzed the abundance of the V-I-S endmembers in different land-use categories at the subpixel level (Phinn et al. 2002). Wu and Murray (2003) suggested that the endmember of the impervious surface should be considered and divided into two types (high-albedo and low-albedo) instead of one considering the obvious heterogeneity of spectral characteristics (Wu and Murray 2003). Lu and Weng (2006) added land-surface temperatures (LST) data while using four-endmember model (vegetation, high-albedo, low-albedo, and soil) to estimate the impervious surface with ETM imagery (Lu and Weng 2006). To address the endmember variability problem, Li and Wu (2016) varied endmember sets spatially by applying kriging interpolation and developed geostatistical temporal mixture analysis technique (Li and Wu 2016). With these improvements, LSMA has then been further implemented in different study areas (Li et al. 2010; Fan and Deng 2014; Scott et al. 2014; Zhang, Chen, and Lu 2015; Hao et al. 2016). However, some problems can still affect the accuracy of LSMA for the following reasons: (1) the variability of spectral characteristics causes low-albedo impervious surfaces to be confused with water and shadow and high-albedo to be confused with sandy bare soil (Small and Lu 2006); (2) misestimation can occur in areas with complex distribute of small or large amounts of impervious surfaces (Weng 2012).

For estimating impervious surfaces at subpixel level using CART, a rule-based model repeatedly splits each parent node into two child nodes, treating each child node as a potential parent node for further split (Breiman et al. 1984). The rule-based model for predicting continuous variables is recursively produced based on training data. Each rule set defines the conditions under which a multivariate linear regression model is established (Huang and Townshend 2003; Yang et al. 2003a). Huang and Townshend (2003) largely improved Breiman’s algorithm by introducing a linear regression model instead of a single target variable for each subset (Huang and Townshend 2003). Yang et al. (2003a) acquired training data by overlaying impervious surface data extracted from an IKONOS imagery with an ETM+ and TM grid and proposed a CART algorithm to estimate the extent of impervious surfaces at the subpixel level (Yang et al. 2003a). Using finer resolution data for calibration/validation and coarser resolution data for predicting impervious surface area at the regional or continental levels, CART has further been implemented by Xian et al. (2005), Xian et al. (2008), Yang et al. (2009), Im et al. (2012), Shao et al. (2015), and Fu et al. (2016) to develop impervious surface estimation model based on multispectral imagery or Synthetic-aperture radar(SAR) data (Xian and Crane 2005; Xian, Crane, and McMahon 2008; Yang et al. 2009; Im et al. 2012; Shao et al. 2015; Fu et al. 2016). Being able to estimate the non-linear relationship between independent and target variables, the regression tree model is considered to have better accuracy and predictability than that of the linear regression model (Yang et al. 2003a). However, despite all the advantages of CART, it is still worth mentioning that the results of the model are affected by some systematic errors. Substantially, underestimation of high-density impervious surfaces and overestimation of low-density impervious surface evidently appeared in many CART research (Yang et al. 2003b; Jiang et al. 2008, 2009; Gao et al. 2009; Im et al. 2012; She and Li 2013; Shao et al. 2015). Although some efforts were made to improve the performance of CART, such as Random Forests, which adopts a series of different CART algorithms (Breiman 2002), the application of these new approaches to estimate impervious surfaces (Deng and Wu 2013; Bernat and Drzewiecki 2014; Zhang et al. 2014) is relatively narrow. Besides, it is indicated by comparison research that for estimating impervious surfaces based on medium resolution imagery, the improvement of Random Forests was inconspicuous (Deng and Changshan 2013; Bernat and Drzewiecki 2014; Drzewiecki 2016).

Other approaches, such as artificial neural network (ANN) and nighttime light photography (NTL) analysis, have also been applied to estimate subpixel impervious surfaces. Hu and Weng (2009) estimated impervious surfaces from medium spatial resolution imagery using the self-organizing map (SOM) and multi-layer perception (MLP), the two most widely used models of ANN, and concluded that MLP was slightly more accurate (Hu and Weng 2009). ANN modeling is capable of solving non-linear relationships (Weng 2012). However, the drawbacks of ANN should be noted. For MLP, none of the methods for estimating the number of hidden layer nodes is widely accepted (Kavzoglu and Mather 2003). Besides, the accuracy of SOM heavily relies on the size of the feature map and the error increases significantly with too few or too many neurons (Weng 2012). NTL analysis, mainly used to estimate the distribution of impervious surfaces at regional to continental scales, has gained more attention recently. Elvidge, Christopher D., et al. (2007) developed a model to estimate the density of impervious surface in globe range based on the radiance-calibrated NTL and the LandScan population count (Elvidge et al. 2007). Ma, Ting, et al. (2012) estimated the dynamics of the urban impervious surface in China from 1992 to 2009 using the Vegetation Adjusted NTL Urban Index, which combines NTL and Normalized Difference Vegetation Index data to achieve a higher accuracy (Ma et al. 2012). Shao and Liu (2014) generated impervious surfaces results based on a linear-regression model developed between the subpixel impervious surfaces fraction and a multi-source index with the integrated use of DMSP-OLS NTL and MODIS NDVI (Shao and Liu 2014). Kotarba andAleksandrowicz (2016) used high resolution nighttime photography from the International Space Station and provided more reliable estimates of impervious surface in smaller area (Kotarba and Aleksandrowicz 2016). Previous research found a good correlation between the actual extent of urban areas and NTL data. However, since the data sources of higher resolution NTL data are heavily limited, OLS-based maps suffer from the saturation problem and coarse resolution of the NTL sensor (Zhang and Seto 2011; Ma et al. 2012).

As one of the most predominate impervious surfaces estimation methods, CART is considered to be more accurate than linear-regression models (De’ath and Fabricius 2000; Huang and Townshend 2003; Yang et al. 2003a; Shao et al. 2015; Lu et al. 2016). However, the research gap appears with the lack of close analysis of the systematic errors of CART algorithm and reasonable improvement of it. Further improvement of CART is a non-trivial challenge. The primary objective of this study is to develop an integrated approach which is objective, repeatable and automate to improve the impervious surface estimation. To address the above-mentioned misestimation problems, an integrated method specifically analyzing and reducing the systematic errors in different density aided by LSMA and error analysis is proposed. This method is able to produce subpixel impervious surface map with higher accuracy compared with conventional CART or LSMA. With the improved ability of impervious estimation, the method demonstrated in this study can provide reliable basic data for research on heat island, hydrology, and other environmental issues in the urban area.

Materials and methods

Study area and data source

In this study, three study areas locate in Chicago, Venice, Guangzhou, which are one of the largest cities in America, Italy, and China, respectively, were selected to test the applicability of the methods to estimate impervious surfaces from complex urban surfaces all over the world (Figure 1). Each of the study areas covers 258.71 km² and encompasses the center area of the cities, where intensely developed urban area is located. Different types of impervious surfaces, from farmhouse, factory to skyscraper, are all widely distributed in the study areas. These areas are selected also for their complex spatial distribution patterns of non-impervious/impervious surfaces with various densities. Large areas of grassland (Chicago), mountain forest (Guangzhou), farmland, and wetland (Venice) are also included. Therefore, the efficiency of different methods for impervious surface estimation is tested in properly selected study areas.

Figure 1. Location of the study areas in Chicago (America), Venice (Italy), and Guangzhou (China) with training and validation area.

Three cloud-free Landsat8 Oli imageries (path/row: 23/31, 192/28, and 122/44; resolution: 30 m) cover the study areas in Chicago, Venice, and Guangzhou were collected. The imageries were acquiredon 12 September, 2016, 23 September, 2014 and 15 October 2014, respectively. They were registered to the Transverse Mercator Projection System and geometric corrections were processed according to 1:50,000 topographic maps. Radiometric correction was performed using the files released by the USGS EROS Data Center. And FLAASH module was applied to conduct atmosphere correction. To reduce errors, water body was excluded using MNDWI (Han-Qiu 2005). In addition, QuickBird Imageries (resolution: 0.6 m) covers all the study area in Chicago (18 June 2016), Venice (14 March 2014), and Guangzhou (5 October 2014) were collected to produce training and validation data (Figure 1).

CART algorithm estimation of impervious surfaces

CART algorithm produces rule set and tree models to predict target variables. Based on training data, the independent variables are recursively divided into subsets such that the total residual sum square (RSS) of all the subsets is minimized. The RSS of the kth subset is calculated as:

(1) $RS{S}_k=\sum _{i=1}^{N_k}\left(\hat{y}-\bar{y}\right)$(1)

Where, $N_k$ is the quantity of the training data in the kth subset, $\hat{y}$ and $\bar{y}$ the predicted and actual values of the target variable (Breiman et al. 1984). However, this algorithm is less satisfactory because the predicted target variable for each subset is a single value $\hat{y}$, the mean value of all the target variables of training data in that subset. The accuracy of the algorithem can be significantly improved with linear regression functions employed to estimate the predicted target variables in each subset. Least square-regression method is used to determine the linear regression functions for each subset (Huang and Townshend 2003). Huang and Townshend (2003) suggest that while a relationship may not be linear globally, a linearity assumption shall be valid for a small subset of the data. Therefore, the CART algorithm is theoretically applicable to explore the complicated relationships between density of impervious surfaces area (ISA) and remote sensing spectral reflectance.

In this study, the process of impervious surface estimation involves the following steps: (1) developing training data using QuickBird imagery; (2) modeling CART algorithm with training data; (3) estimating ISA in the study area using CART algorithm. In this study, CART algorithm was developed using Cubist® (http://www.rulequest.com). This program is a powerful tool for generating CART algorithm presented by Huang and Townshend (Huang and Townshend 2003).

Figure 2 shows the detailed information for training and validation areas. First, 10 training areas were randomly selected for each of the QuickBird imageries of Chicago, Venice, and Guangzhou (Figures 1 and 2(a)). Each of the training areas covered 0.86 km², corresponding to 961 pixels in Landsat8 Oli imagery. Next, the impervious surface was extracted from QuickBird imagery using object-oriented classification, which is capable of integrating different spatial information such as texture, shape, and context to better discriminate between spectrally similar types of land cover. Compared with pixel-based classification, object-oriented classification is more suitable for high resolution remote sensing (Li et al. 2011). Misclassifications caused by shadow, water, or small spot of vegetation were manually checked and modified with visual interpretation. The classification results were then merged to produce a binary raster imagery of impervious versus non-impervious (Figure 2(b)). Afterward, the classification results were overlaid with grid extracted from Landsat8 Oli imagery (Figure 2(c)) and ISA was calculated for every Landsat8 Oli imagery pixels in training area according to the following equation (Figure 2(d)):

(2) $ISA=\frac{A}{900}$(2)

Figure 2. Process of ISA estimation with CART: (a) one of the training areas in QuickBird imagery (Guangzhou); (b) binary map of impervious surfaces in training area extracted using O-O classifier; (c) grid corresponding to Landsat8 Oli imagery in training areas; (d) density of impervious surfaces in training area (30 m resolution) for training; (e) one of the validation areas in QuickBird imagery (Chicago); (f) density of impervious surfaces in validation area (30 m resolution) for accuracy validation.

where, A is the area of the impervious surfaces in one Oli imagery pixel that covers 900 m². In addition, validation data was also estimated by the similar approach (Figure 2(e) and (f)). Finally, ISA (target variables) and the spectral characteristics (independent variables) of Landsat8 Oli imagery pixels in training area were read as training data to develop a CART algorithm, which was expressed as collections of rules associated with a series of multivariate linear model, to estimate ISA for the all three study areas.

LSMA model estimation of impervious surfaces

LSMA is a linear unmixing model that calculates the abundance of endmembers in mixed pixels, which extensively exist in the imagery produced by medium resolution sensors such as Landsat8 Oli. As each mixed pixel of an imagery can be viewed as a linear combination of the endmembers, the mathematical model of the LSMA can be expressed by the following equation (Roberts et al. 1999):

(3) $R_i=\sum _{k=1}^n{f}_k{R}_{ik}+E_{R_i}$(3)

where, R_i is the spectral reflectance of band i, k the class number of endmembers, f_k is the proportion of endmember k within the pixel, R_ik is the known spectral reflectance of endmember k at band i and $E_{R_i}$ is the error for band i. The following conditions must be satisfied to solve for f_k:

(4) $\sum _{k=1}^n{f}_k=1$(4)

where, $f_k\ge 0$. In this study, four-endmembers-LSMA-model was chosen to estimate ISA after comparing the accuracy. Impervious surface fraction was estimated by analyzing the proportion of low- and high-albedo endmembers, together with endmembers of soil and vegetation in pixels (Wu and Murray 2003).

The following four steps were processed to estimate impervious surfaces in this study: (1) exclusion of bodies of water that primarily consisted of pure pixels; (2) minimum noise fraction (MNF) rotation, which produced a smaller number of components that contain most of the information; (3) calculation of the Pixel Purity Index (PPI) from the MNF component imagery and selection of endmembers; and (4) linear spectral mixing analysis and post-processing.

Error analysis

Four validation areas (each covering 0.13 km²) were randomly selected from each of the study areas in Chicago, Venice, and Guangzhou (Figures 1 and 2(e) and (f)). The validation areas contain 1728 Landsat8 Oli imagery pixels for producing validation data.

In this study, CART algorithm was improved with the LSMA estimation results based on several error analysis methods, including scatter plot, the residual error (RE), the RMSE, and the mean absolute error (MAE).

Scatter plot is widely used for validating the accuracy of estimation of the impervious surface (Wu and Murray 2003; Jiang et al. 2008, 2009; Hu and Weng 2009; She and Xiaoning 2013; Ebrahimian et al. 2016). With actual value on the x-axis and predicted value on the y-axis, scatter plot is a straightforward way to analyze the errors of different impervious surfaces estimation methods. And linear fitting function and $R^2$can be calculated by simple linear regression.

Residual error, which measures the difference between estimated and actual ISA, was calculated for each of the pixels in the validation area:

(5) $RE=\hat{y}-\bar{y}$(5)

where, $\hat{y}$ and $\bar{y}$ are the estimated and actual values, respectively.

RMSE and MAE were calculated based on statistics of RE. RMSE is one of the most widely reported error measures in the climatic and environmental literature. While the RMSE treats variance as it gives errors with larger absolute values more weight than errors with smaller absolute values, MAE gives the same weight to all errors and measures the mean absolute value of each difference (Chai and Draxler 2014). Compared with RMSE, MAE is considered to be a more natural and unambiguous index to estimate errors (Willmott and Matsuura 2005). They are commonly calculated by the following equations:

(6) $RMSE={\left(n^{-1}\sum _{i=1}^n|\hat{y}-\bar{y}{|}^2\right)}^{\frac{1}{2}}$(6)

(7) $MAE=n^{-1}\sum _{i=1}^n\left|\hat{y}-\bar{y}\right|$(7)

where, $n$ is the number of validation data, $\hat{y}$ and $\bar{y}$ the estimated and actual values. In this study, scatter plot was applied to estimate the overall accuracy of CART and LSMA while RSME and MAE were used to evaluate and compare the errors of the above two approaches in surfaces with different ISA.

Improving impervious surface estimation

For further analysis and improvements, we divided the resultant impervious surfaces into 10 categories based on their density: 0.0 ~ 0.1(non-impervious surfaces), 0.1 ~ 0.2, 0.2 ~ 0.3, 0.3 ~ 0.4 (low-density impervious surfaces), 0.4 ~ 0.5, 0.5 ~ 0.6, 0.6 ~ 0.7 (medium-density impervious surfaces), and 0.7 ~ 0.8, 0.8 ~ 0.9, 0.9 ~ 1 (high-density impervious surfaces).

The improved method can be divided into several steps (Figure 3), including (1) estimating residual errors (RE_c) from CART for all validation pixels based on the estimated results (Figures 4 and 5); (2) selecting poorly estimated pixels as the ones with high absolute value (ABS) of RE_c. In order to find out the error source, the amount of poorly estimated pixels in each of the above mentioned 10 categories were quantified and analyzed (Figure 6(c)); (3) calculating the MAE of CART and LSMA (MAE_c & MAE_l) for each of the categories based on the pixels in the validation area (Figure 7); (4) choosing the pixels with MAE_l much less than MAE_c as targeted pre-improved pixels; (5) modifying the CART estimated results by replacing ISA_c with ISA_l for all the targeted pixels in the study area.

Figure 3. Procedure of improved CART algorithm by LSMA and error analysis.

Figure 4. Impervious surfaces estimated by CART and LSMA.

Figure 5. Accuracy assessment scatter plot of (a) CART and (b) LSMA.

Figure 6. (a) Box plot of RE_c, (b) quantity of pixels aggregated by ABS of RE_c, and (c) ISA_c.

Figure 7. MAE of CART and LSMA estimation in different ISA.

The improved method becomes significant if most of the poorly estimated pixels from CART can be corrected with better estimated ISA_l. In this study, the statistics in the validation area show that of all the 171 poorly estimated pixels from CART (Figure 6(a)) (with RE_c higher than 0.15), 113 of them were corrected. More detailed analyses and discussion of the improved results are provided in Chapters 3.3 and 4.

Results and analysis

Results estimated by CART algorithm and LSMA model

Figure 4 shows the results of impervious surfaces in three study areas estimated by CART algorithm and LSMA model. And scatter plot was used to analyze the results of accuracy validation based on all the pixels in validation areas (Figure 5). While both results gained acceptable R², CART algorithm performed slightly better than LSMA with higher overall accuracy and R². Besides, the overall MAE and RMSE of CART algorithm were 0.053 and 0.086, respectively, which was slightly less than that of LSMA (0.054 and 0.093). It is also worth mentioning the CART algorithm got more accurate results than LSMA in medium density impervious areas (ISA ranging 0.4 to 0.7) with lower MAE (0.077 vs. 0.107). However, impervious surfaces with actual ISA greater than 0.9 were underestimated and low density (less than 0.1) were overestimated in many cases. Besides, the fitting curve of CART algorithm was not so reasonable as that of LSMA, while the ideal function should be y = x.

Targeted pre-improved pixel

In order to find out the exact error sources of CART algorithm, the distribution of RE_c of all the 1728 pixels in validation area was analyzed into statistics. The box plot (Figure 6(a)) shows 0.15 is the upper limit of the RE_c and outlier pixels with RE_c greater than 0.15 should be considered as poorly estimated. Figure 6(b) shows that 1557 pixels were adequately estimated by CART with absolute value (ABS) of RE_c less than 0.15 while the other 171 pixels were poorly estimated.

The ISA_c of the 171 poorly estimated pixels were then analyzed into statistics (Figure 6(c)) and it surprisingly showed that the ISA_c of nearly half of the poorly estimated pixels ranged 0.7 ~ 0.9. Most of these pixels were underestimated by CART and their actual ISA should be greater than 0.99. Meanwhile, the poorly estimated pixels with ISA_c ranged 0.1 ~ 0.4 were more likely to be overestimated rather than underestimated. Therefore, the underestimation of the high-density impervious surfaces and overestimation of low-density impervious surfaces should be the main error sources of CART algorithm in this study.

Then it is necessary to reduce the underestimation of high-density impervious surfaces by discerning the targeted poorly estimated pixels from all the pixels with ISA_c ranging 0.1 ~ 0.4 or 0.7 ~ 0.9 in the study areas, where actual ISA is not available. The estimation results from LSMA (Figure 4) were then applied. We compared the MAE of CART and LSMA (MAE_c & MAE_l) in different ISA by dividing it into 10 categories (Figure 7). And some features can be seen: (1) for pixels with ISA_c ranging 0.7 ~ 0.9, the MAE_c was expectedly high; (2) for pixels with ISA_c ranging 0.1 ~ 0.4, MAE_c was relatively high when compared with other pixels. These two problems are subsequently related to underestimation of high-density impervious surfaces and overestimation of low-density impervious surfaces, which also correspond with what the scatter plot shows. Besides, the coefficient of x in the function of the fitting curve for validating CART (y = 0.94x+0.03) was reduced from 1.00 to 0.94 (Figure 5(a)). It is due to the underestimation of high-density impervious surfaces and overestimation of low-density impervious surfaces. Meanwhile, the MAE_l of the pixels with ISA_l ranging 0 ~ 0.1 or 0.9 ~ 1 is low, especially when compared with MAE_c of the pixels with ISA_c ranging 0.1 ~ 0.4 or 0.7 ~ 0.9. Therefore, if a pixel has the ISA_c ranging 0.1 ~ 0.4 and ISA_l less than 0.1, its LSMA-estimated results should be more accurate. Similarly, The LSMA-estimated results should be more accurate in pixels with ISA_c ranging 0.7 ~ 0.9 and ISA_l greater than 0.9. Based on the above analysis, the ISA_c can be corrected with the help of ISA_l addressing at the underestimation and overestimation problems.

First, pixels with ISA_c ranging 0.7 ~ 0.9 and ISA_l greater than 0.8 were selected as targeted pre-improved pixels. It is very likely that ISA_l were more accurate and should become finally improved results instead of ISA_c, since these pixels’ MAE_l were much lower than MAE_c (Figure 7).

Then for the same reason, the pixels with ISA_c ranging 0.1 ~ 0.4 and ISA_l less than 0.1 were selected as targeted pre-improved pixels. The ISA_l for these pixels were used to improve the CART estimated results.

Aided by LSMA, the targeted poorly estimated pixels were discerned and the accuracy of CART algorithm can be improved.

Results of the improved method

Figure 8 shows the final results of impervious surfaces map estimated by the improved method. Compared with conventional CART estimated results, high-density impervious surfaces properly increase. And the complex pattern of medium-density impervious surfaces and tiny patches of low-density impervious surfaces remains, which is much better than conventional LSMA estimated results (Figure 4). Besides, non-impervious surfaces such as aggregately distributed vegetation and water body are clearly and finely delineated.

Figure 8. Improved estimation of impervious surfaces in (a) Chicago, (b) Venice, (c) Guangzhou, and (d) accuracy assessment.

Obvious improvements are also revealed from accuracy validation of different error measurements (Table 1) and scatter plot of accuracy assessment with the fitting curve (Figure 8(d)). Overall MAE and RMSE of improved method are lowered by 22.64% and 20.93%, respectively, and R² rises from 0.95 to 0.96. Besides, the function of the fitting curve in validation/prediction compromised scatter plot (y = 1.02x+0.01) improves from the previous y = 0.94x+0.03. Compared with y = x, the coefficient and constant in the function both become substantially more reasonable.

Table 1. Accuracy of impervious estimation.

Methods	Overall/High-density MAE (%)	Overall/High-density RMSE (%)	Fitting Curve Function	R^2
LSMA	5.4/7.1	9.3/10.5	y = 0.99x−0.01	0.94
CART	5.3/10.0	8.6/13.0	y = 0.94x+0.03	0.95
Improved CART	4.1/6.6	6.8/8.8	y = 1.02x+0.01	0.96

More remarkable improvements appear in high-density impervious surfaces (actual ISA > 0.70) where intensely developed urban area locates with land use of CBD, high-density residential and light industry (Ridd 1995). The MAE and RMSE for the improved method in these areas are 0.066 and 0.088, respectively (Table 1), which are apparently improved when compared with those of conventional CART algorithm (0.100 and 0.130).

Discussion

In recent years, CART algorithm has been widely considered to be more accurate than linear regression models and has been continuously implemented to estimate impervious surfaces (De’ath and Fabricius 2000; Huang and Townshend 2003; Yang et al. 2003a; Im et al. 2012; Shao et al. 2015; Lu et al. 2016). However, the evident appearance of underestimation in high-density and overestimation in low-density impervious surfaces in CART algorithm implemented by many researchers undoubtedly indicates that these errors should be systematic, which were presented by their own accuracy validations (Yang et al. 2003b; Jiang et al. 2008, 2009; Gao et al. 2009; Im et al. 2012; She and Xiaoning 2013; Shao et al. 2015). Meanwhile, the discussions of these systematic errors are far from sufficient, let alone analysis or improvement. Much more attention should have been paid to these errors since they not only cause the major decrease of the accuracy in the poorly estimated pixels, but also affect the reliability of the entire algorithm by producing the imprecise fitting curve. Therefore, reasonable improvements of CART algorithm are non-trivial in consideration of the facts that it has already become one of the most predominant methods for impervious surfaces estimation due to its high accuracy.

In this study, we used conventional CART algorithm to estimate impervious surfaces and achieved acceptable overall accuracy. However, large areas of high-density impervious surfaces were underestimated and low-density impervious surfaces overestimated, similar as relevant research. The results estimated by LSMA model were applied to improve the estimation accuracy of CART is based on error analysis. In this study, LSMA, a widely used model for estimating impervious surfaces, was chosen for its effectiveness and conveniences. Besides, LSMA model was less affected by the underestimation in high-density impervious areas and the overestimation of non-imperviousness, although its overall accuracy was lower than the CART algorithm. With proper selections of the model and endmembers, LSMA could produce sound fitting curve in validation/prediction scatter plots as reported in previous research (Yang et al. 2010, 2012; Weng and Pu 2013; Fan and Deng 2014).

Other approaches such as ANN and Random Forests were also tested in one of the study area (Chicago) and compared with conventional CART in order to find out whether they can be applied to improve impervious surfaces estimation (Table 2). However, in high-density impervious surfaces area, the mean errors (ME) of ANN and Random Forests were −0.038 and −0.044, respectively. Similar as CART algorithm, ANN and Random Forests are both affected by problems of underestimating the high-density impervious surfaces. Besides, the overall accuracy of ANN and Random were both lower than CART. Other comparative research has also shown that Random Forests and ANN could be more seriously impacted by underestimation of high-density impervious surfaces than CART (Bernat and Drzewiecki 2014; Drzewiecki 2016). Indicated by related research (Table 3), although Random Forests and ANN are more elaborate models, especially when compared with linear analysis model, they are not able to create impervious surfaces results more accurate than conventional LSMA or CART algorithm in most cases (Hu and Weng 2009; Deng and Changshan 2013; She and Xiaoning 2013; Bernat and Drzewiecki 2014; Fan et al. 2015; Drzewiecki 2016). Therefore, for reducing the systematic errors of CART, the application of Random Forests and ANN should not be effective.

Table 2. Accuracy assessment comparison of different methods tested in study area of Chicago.

Methods	Overall/High-density MAE (%)	Overall/High-density RMSE (%)	Overall/High-density ME (%)
ANN	7.49/9.08	9.61/12.39	−3.65/−3.76
Random Forests	5.82/9.92	8.81/13.71	−2.74/−4.39
CART	5.09/9.64	7.56/12.41	−2.70/−3.78

Table 3. Accuracy assessment comparison of different methods in related research.

Methods	MAE (%)	RMSE (%)	Location & Time	References
LSMA	8.6	10.0	Guangzhou, China (2009)	Fan et al. (2015)
LSMA	5.4	9.3	/	This study
CART	9.5	11.9	Suzhou, China (2010)	She and Xiaoning (2013)
CART	6.1	10.8	Raba, Poland (2009)	Drzewiecki (2016)
CART	5.3	8.6	/	This study
ANN	8.0	11.8	Indianapolis, US (2001)	Hu and Weng (2009)
ANN	6.8	11.3	Raba, Poland (2009)	Drzewiecki (2016)
Random Forests	5.7	/	Virginia, US (2006)	Deng and Changshan (2013)
Random Forests	6.5	11.2	Raba, Poland (2009)	Drzewiecki (2016)
Improved CART	4.1	6.8	/	This study

Instead, we discerned and modified targeted pixels whose ISA_c were poorly estimated. The 82,612 targeted poorly estimated pixels, which accounted for 9.60% of all three study areas, were improved in this study. With reasonable improvements, the poorly estimated pixels, especially pixels in high-density impervious areas were largely corrected. Compared with conventional CART algorithm, the area of surfaces with impervious density above 0.8 in Chicago, Venice, and Guangzhou increased by 15.23%, 27.90%, and 33.64%, respectively, from 74.45 km² to 85.80 km², 13.87 km² to 17.73 km², and 30.51 km² to 45.97 km². The total area of non-imperviousness also increased from 294.36 km² to 329.12 km². With these improvements, high-density impervious surfaces and non-imperviousness are clearly and properly delineated while the complex pattern of medium-density impervious surfaces and tiny patches of low-density impervious surfaces remains.

A small area covering 1 km² in Guangzhou was chosen for a comparative analysis of the estimation results at a small-scale (Figure 9). Above all, the improved estimation of high-density impervious surfaces became much more accurate than conventional CART. For instance, the congested residential estate in the middle part and the road in the northeast part are accurately estimated as high-density impervious surfaces. Since accurate estimation of high-density impervious surfaces, where intensely developed urban area locates, is the fundamental issue for monitoring and understanding the urban environment, the significance of the improvement is beyond what accuracy validation reveals.

Figure 9. Small-scale comparison of the estimation results of conventional and improved CART in Guangzhou, China.

It also worth mentioning that the application of the proposed improved method will be limited if high resolution imageries do not match well with the multispectral imagery. Besides, the proposed method is more suitable for urban areas where impervious surfaces distribute with high heterogeneity, in which scenarios the conventional CART algorithm is likely to underperform.

Conclusions and future study

In this study, it is found out that the source of systematic errors in conventional CART algorithm for estimating impervious surfaces should be the underestimation of high-density impervious and overestimation in low-density impervious surfaces. An improved method for effectively estimating impervious surfaces was then demonstrated based on error analysis of CART algorithm and LSMA. With these improvements, the pixels poorly estimated by conventional CART were discerned and modified. It is particularly significant to improve impervious surface estimation based on CART algorithm since it is one of the most widely used methods of estimating impervious surfaces with high accuracy. With lower MAE and RMSE, higher R² and more reasonable fitting curve in validation/prediction compromised scatter plot, the improved method is proved to be accurate, objective, and repeatable. Besides, it is indicated by small-scale comparison that the significance of the improvement is beyond what the accuracy validation reveals, because the improvement in the estimation of high-density impervious surfaces, where intensely developed urban area locates, is particularly evident when compared with conventional CART algorithm. And the complex pattern of medium-density impervious surfaces and tiny patches of low-density impervious surfaces remains.

The monitoring and understanding of urban surfaces have long been challenging research issues due to spatial complexity. With the improved ability of impervious estimation, the method demonstrated in this study can provide reliable basic data for research on heat island, hydrology, and other environmental change detection in urban area. In the future study, more improvements are worth trying. It may include in-depth analysis for error sources inside CART algorithm itself and more reasonable methods to reduce the poorly estimated pixels. With these approaches, further improvements may appear.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [41701204]; Guangdong Provincial Science and Technology Planning Project.