Introduction

In recent years, with the rapid development of the global economy, the level of infrastructure construction in urban areas has increased significantly. Since urban building complexes, asphalt and concrete roads have greater heat absorption rates and smaller specific heat capacities than suburban soils and vegetation, this has led to generally higher temperatures in urban areas than in the surrounding suburbs. Researchers have summarized this phenomenon as the urban heat island (UHI) effect, which is one of the most significant features of urban climate (Peter 1994; Schneider 1989). The climate phenomena of UHI caused by rapid urbanization had even led to the increase of energy consumption, greenhouse gas emission, and air pollution (Li et al. 2019; Chen and You 2019; Stone 2005). In order to solve these climate deterioration problems compromising human health, the development of urban landscape structures, represented by urban blue–green spaces, has been recognized as an environmentally friendly, and politically acceptable approach to mitigate the UHI effect (Byrne and Yang 2009; Carvalho et al. 2017; Antoszewski et al. 2020; Georgiou et al. 2021; Pielke and Avissar 1990). Therefore, how to regulate and locate the landscape structures in urban regions represented by blue–green spaces to cope with urban heat island and other climate phenomena is the focus of current social concern.

Previous studies have revealed that urban blue–green spaces of water bodies, parks, forests, and grasslands showed a strong effect in cooling the land surface temperature (Murakawa et al. 1991; Du et al. 2016; Yan and Dong 2015; Giridharan et al. 2008). While mitigating the UHI effect, they even lead to the appearance of urban cold island (UCI) (Półrolniczak 2017). The size, shape, and connectivity of urban blue–green spaces are demonstrated to be the main factors influencing the cooling effect (Estoque et al. 2017; Gunawardena et al. 2017; Tan et al. 2021). Moreover, researchers also realized that the cooling effect might change significantly when the area of certain types of blue–green space patches exceed a certain value (Yu et al. 2017). It had also been emphasized that the change-point (TVoE) is significant to obtain the maximum cooling efficiency (Yu et al. 2020).

However, studies related to the cooling effect of blue–green spaces mainly shed light on the potential association between single or certain types of blue–green space patches and the land surface temperature but ignored the influence of the global spatial combination and pattern of different categories of blue–green spaces at city scale (Yu et al. 2020). Besides, the heterogeneity of blue–green spaces’ cooling effect, especially their influence on UCI effect, in various periods and regions only had been conducted in a few empirical analyses, and the mechanism difference behind was rarely clarified, either.

Therefore, considering the great importance to understand the mechanism of the city-level spatial layout of the landscape infrastructure, represented by urban blue–green space, on its cooling efficiency in response to global warming and the gap within the related fields, we summarized two research questions that still remained to be answered. (1) How does the spatial pattern (composition, distribution and shape) of different categories of blue–green space at city scale affect the intensity of urban cold island effect? (2) What is the optimal spatial pattern of blue–green spaces of the maximum cooling efficiency at city scale? To address these questions, the panel regression models and a new Quadratic-Curve-Fitting based threshold effect estimating model will be constructed in this study to investigate the impact of spatial pattern of blue–green space on its holistic cooling intensity at city-level and to estimate the optimal spatial layout of blue–green spaces with maximum cooling efficiency. From the perspective of academic contribution, this study not only quantifies the impact mechanism of the composition and distribution pattern of blue–green spaces within cities on their cooling efficiency from the meso-urban scale, but also provides a new method and quantitative basis for estimating the layout of blue–green spaces under the scenario of maximizing cooling efficiency. This enhances the understanding on the link between ecological land elements and sustainable development of urban ecosystem.

Methodology

Research procedure

To answer the two research questions proposed in the introduction section, the specific design of this study is as follows (Fig. 1).

Fig. 1
figure 1

Flow chart of this study

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Specifically, (1) firstly, through the literature review and the understanding of the trend of the times, we set clarifying the cooling mechanisms of the blue–green spaces from the perspective of composition and distribution and estimating the optimal spatial pattern of blue–green spaces of the maximum cooling efficiency at city-level as the two main objectives of this study. (2) Secondly, the Yangtze River Economic Belt, which had experienced significant environmental deterioration and contained rich blue–green resources, was taken as the case study site. Also, we collected the data related to land cover of blue–green spaces and surface temperature from MCD12Q1, MODIS TERRA and AQUA datasets, respectively, and selected the landscape metrics and SUE algorithm to quantify the spatial pattern of blue–green space as well as the heat / cold island intensity for all cities in the Yangtze River Economic Zone from 2003 to 2018. (3) Thirdly, the panel regression models and a new Quadratic-Curve-Fitting-based threshold effect estimating model were constructed to investigate the impact of spatial pattern of blue–green space on its holistic cooling intensity at city-level and to estimate the optimal spatial layout of blue–green spaces with maximum cooling efficiency. (4) Fourthly, we interpreted the regression results and verified the validity of the threshold estimation model in calculating the optimal blue–green spatial pattern based on the regression and fitting results. (5) Finally, based on the results of the research and discussion, we also put forward targeted views on the construction of blue–green space at the urban scale and related policy recommendations.

Study area

The study area of this work is the Yangtze River Economic Belt (Fig. 2), which had experienced numerous economic and development reforms (Jin et al. 2018). The rapid urbanization of cities in this region has been proved to be one of the most significant driving factors of urban heat island effect and climate warming (Huang and Lu 2015). On the other hand, Yangtze River Economic Belt is rich in various natural and ecological resources, with complex terrain and climate conditions (Xing et al. 2018). In order to cope with the ecological side effects brought by the rapid economic development and maintain the sustainability of the ecological security pattern, the Chinese government has made great efforts to restore the balance of the river, lake, wetland and forest ecosystems in the region and intended to build it into a demonstration zone for the protection and restoration of the ecological environment system (Luo et al. 2019). Therefore, it is representative that this study takes the Yangtze River Economic Belt as an example to research the relationship between the dynamic changes of city-level spatial pattern of urban blue–green spaces and their cooling effect under the background of ecological restoration.

Fig. 2
figure 2

Study area and main datasets

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Data collection and processing

The main datasets used in this study are composed of land use type maps, land surface temperature maps, population distribution maps, and landform type maps (Fig. 2). The spatial scope of all maps is the Yangtze River Economic Belt, including data from 2003 to 2018.Footnote 1 The land cover type maps were downloaded from Land Cover Type (MCD12Q1, 500 m) Version 6 data product, which provides global land cover types at yearly intervals (Friedl and Sulla-Menashe 2019). The land surface temperature maps came from MODIS TERRA and AQUA Land Surface Temperature (LST) data. These maps provide the spatial distribution of urban heat islands and cold islands, which are defined as the difference in LST of the urban pixels and the non-urban pixels within each urban extent, based on the simplified urban-extent (SUE) algorithm (Chakraborty and Lee 2019). In addition, the dataset not only includes the annual average urban heat island/cold island intensity data from 2003 to 2018, but also provides data from different seasons (winter and summer) and periods (daytime and nighttime). The population distribution maps are derived from WorldPop Global Project Population Data, which provided the estimated residential population per 100 × 100 m grid square through machine learning approaches (Gaughan et al. 2013). The landform type maps were collected from the Geomorphological Atlas of the People's Republic of China, in which different types of landforms are represented by integers (Zhou and Cheng 2010).

After data collection, we further clipped the raw raster datasets along the boundary lines of 130 cities within the Yangtze River Economic Belt. The data related to the land use type and urban heat/cold islands was processed with the methods in Chapters 2.3 and 2.4, respectively to obtain the quantitative information reflecting the spatial distribution pattern of urban blue–green spaces and the intensity of urban heat/cold island effect. The remaining parts of the data are processed by calculating the average value of all raster grids in each city to construct the panel dataset of the terrain and population characteristics of 130 cities from 2003 to 2018.

Landscape metrics

In this study, we need to quantify the composition and distribution characteristics of urban blue–green spaces at the first step. Here, we introduced the algorithms of landscape metrics to quantify the spatial distribution pattern of urban blue–green spaces. Specifically, the collected land use type maps were clipped into 130 sections according to the boundary lines of cities in the Yangtze River Economic Belt. Then, according to the definition of blue–green space proposed in previous studies (Du et al. 2019; Dzhambov 2018), the original land use type maps were re-classified into six categories (Table 1). Among them, forest, shrublands, grasslands and water bodies were recognized as urban blue–green spaces in this paper.

Table 1 Re-classification results of land use types
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Finally, three landscape metrics of PLAND, NP and LSI, were utilized to measure the spatial pattern of blue–green spaces at city-level from the perspectives of composition, distribution and shape (Formula 1, 2 and 3).

$$\mathrm{PLAND}=\frac{\sum_{j=1}^{n}{a}_{ij}}{A}$$
(1)
$$\mathrm{NP}={n}_{i}$$
(2)
$$\mathrm{LSI}=\frac{0.25\sum_{k=1}^{n}{e}_{ik}^{*}}{\sqrt{A}}$$
(3)

where PLAND represents the percentage of landscape, which is a fundamental measures of landscape composition; \({a}_{ij}\) denotes the area of landscape patch j in landscape type i; A denotes the total landscape area; NP represents the number of landscape patches of a particular patch type, which is a simple measure of the extent of subdivision or fragmentation of the patch type; \({n}_{i}\) denotes the number of patches of the corresponding patch type i; LSI represents the total landscape boundary and all edge within the boundary divided by the square root of the total landscape area (square meters) and adjusted by a constant (circular standard for vector layers, square standard for raster). The LSI will increase with increasing landscape shape irregularity or increasing amounts of edge within the landscape. The greater the value of LSI, the more complex the shape of the landscape patches; \({e}_{ik}^{*}\) denotes total length of edge in landscape between patch types i and k; includes the entire landscape boundary and some or all background edge segments involving class i (McGarigal 2015).

It is worth mentioning that, in general, the landscape metric of NP is sensitive to area. The corresponding NP values of cities with different areas are often affected by the city scale. In the scene where landscape patches can be accurately identified, NP index has certain limitations. However, in this study, because the accuracy of MCD12Q1 V6 is 500 m, the landscape patches with a scale less than 500 m are not able to be accurately identified. Therefore, compared with the selection of PD and other indicators that are not sensitive to the object scale, the use of NP could more truly reflect the spatial distribution pattern (degree of aggregation and dispersion) of various blue–green space patches in different cities for the existing datasets.

Urban heat/cold island effect intensity

In this study, we mainly investigate the influence of the changes on the spatial pattern of urban blue–green spaces on the urban heat/cold island effect to determine its cooling efficiency. Therefore, we introduced the urban heat/cold island data retrieved based on SUE algorithm and MODIS TERRA and AQUA dataset and quantify the intensity of urban heat/cold island effect by calculating the weighted average value of extreme temperature difference they caused (Chakraborty and Lee 2019). The quantification algorithm is presented in Formula 4.

$$\mathrm{Urban heat}/\mathrm{cold island effect intensity}=\frac{{\sum }_{i=1}^{n}{t}_{i}{a}_{i}}{{\sum }_{i=1}^{n}{a}_{i}}$$
(4)

where \({t}_{i}\) denotes the land surface temperature difference between the urban heat/cold islands and their surrounding spaces; \({a}_{i}\) denotes the area of spaces where the urban heat/cold islands effect being detected. Similarly, we also obtained the data related to the annual average all-day, summer daytime, summer nighttime, winter daytime and winter nighttime intensity of urban heat/cold island for 130 cities in the Yangtze River Economic Zone from 2003 to 2018, respectively.

Panel regression model

Model construction

To clarify the impact mechanism of the spatial pattern of urban blue–green spaces on their cooling efficiency, this study considers a quantitative explanation with the help of regression models. Since we have obtained a balanced panel dataset of 130 cities in the Yangtze River economic belt from 2003 to 2018 (Table 2) through Sects. “Data collection and processing” ~ “Urban heat/cold island effect intensity”, the fixed effect panel regression models are introduced to estimate the relationship between the spatial pattern of urban blue–green spaces and their cooling effect (Formula 5).

$${y}_{it}^{\mathrm{UCI}/\mathrm{UHI}}={\beta }_{1}{x}_{it}^{\mathrm{forests}}+{\beta }_{2}{x}_{it}^{\mathrm{shrublands}}+{\beta }_{3}{x}_{it}^{\mathrm{grasslands}}+{\beta }_{4}{x}_{it}^{\mathrm{water}}+{\beta }_{5}{x}_{it}^{\mathrm{tools}}+{\mu }_{i}+{\varepsilon }_{it}$$
(5)

where the dependent variable \({y}_{it}^{\mathrm{UCI}/\mathrm{UHI}}\) could be the annual average all-day, summer daytime, summer nighttime, winter daytime and winter nighttime intensity of urban heat/cold island effect of year t at city i. \({x}_{it}^{\mathrm{forests}}\), \({x}_{it}^{\mathrm{shrublands}}\), \({x}_{it}^{\mathrm{grasslands}}\) and \({x}_{it}^{\mathrm{water}}\) are vectors consisting of calculating results of landscape metrics related to the composition, shape and distribution of four types of urban blue–green spaces of year t at city i. \({x}_{it}^{\mathrm{tools}}\) is a vector consisting of spatial pattern of urban built-up areas and other lands, urban landform and urban population of year t at city i. \({\mu }_{i}\) denotes the fixed effect term on city i, which varies with the basic natural condition of cities. \({\varepsilon }_{it}\) denotes the error term of year t at city (Yan et al. 2019).

Table 2 Descriptive statistics of variables in panel regression model
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In addition, since the main target of this study is to clarify the relationship between spatial pattern of urban blue–green spaces and their cooling effect with the help of panel regression model, we introduced the F-statistic to estimate the overall validity of the model. Specifically, when running a regression model, the F-statistic provides us with a way for globally testing if any of the independent variables is related to the dependent variables. If the p value associated with the F-statistic is ≥ 0.05: Then there is no relationship between any of the independent variables and dependent variable; if the p value associated with the F-statistic < 0.05: then, at least one independent variable is related to dependent variable (Pope and Webster 1972).

Model pre-estimation

Before running the panel regression model to estimate the relationship between the spatial pattern of urban blue–green spaces and the intensity of urban heat / cold island effect at city level, we need to verify whether the panel dataset constructed in this study meet the input requirements of the model and whether the fixed effect is more suitable for this study scenario.

Stationarity test of variables

In the probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models (Unit root 2021). Therefore, we introduced Levin-Lin-Chu unit root test algorithm to test the stationarity of the original data before panel modeling (Levin et al. 2002). The test results were presented in Appendix 1 and indicated that all time-series data utilized in this study are stationary and could be used for further modeling.

Model selection

When using panel data, it is an important question that whether fixed effect model or random effect model would be selected. In this study, we constructed both random and fixed effect models and introduced Hausmann test to determine the model selection (Hausman 1978). The results of Hausmann test are presented in Appendix 2 and further indicated that the fixed effect models are more suitable for global and local scale models constructed to clarify the relationship between the spatial pattern of urban blue–green spaces and their cooling efficiency.

Quadratic-Curve-Fitting based TVoE estimating model

Previous studies had demonstrated that the cooling effect of blue–green spaces change significantly when the area of certain types of landscape patches exceed a certain value. The threshold value of the cooling efficiency (TVoE) of blue–green space patches is significant to obtain the maximum cooling efficiency (Yu et al. 2018). A Logarithmic-Function-Fitting based TVoE estimation algorithm proposed by Yu et al. (2017) dominated the related research field (Fig. 3). This algorithm based on the marginal effect could obtain the optimal threshold value using logarithmic function to fit the area of landscape patches and its cooling effect. In general, this type of Logarithmic-Function-Fitting based TVoE estimation research is mainly devoted to exploring the optimal cooling efficiency of green patches.

Fig. 3
figure 3

TVoE estimating models

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However, we need to re-consider whether the logarithmic function is the most appropriate approach when estimating the cooling efficiency of urban blue–green spaces at city-level. The increase of total area of one type of blue–green space in city inevitably lead to the decrease of other types. As a result, the cooling efficiency of the blue–green spaces may not increase monotonously with the change of size, shape or spatial distribution. Therefore, a TVoE estimating algorithm based on quadratic curve is proposed in this study (Fig. 3). Specifically, we fit the relationship between the spatial pattern of blue–green spaces and the intensity of urban heat/cold island effect with quadratic function and define the point of local extreme value of quadratic function as TVoE at city level. In general, this type of Quadratic-Curve-Fitting based TVoE estimating model is proposed to calculate the overall composition and distribution pattern of various blue–green spaces in cities with ideal cooling effect at city-level.

Results

Impact mechanism of the spatial pattern of urban blue–green spaces on its cooling efficiency

After the pre-test estimation, the impact of the city-level spatial pattern of urban blue–green spaces on their cooling efficiency was revealed in fixed effect regression models under various scales.

Global scale

Firstly, we constructed fixed effect models which took the annual average all day heat/cold island intensity as the dependent variables to examine the overall relationship between the spatial pattern of urban blue–green spaces and their cooling efficiency at city-level. The results are presented in Table 3.

Table 3 Outputs of global panel regression models
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The output of the models indicated that the proportion and distribution characteristics of forests and shrublands in urban space have significant impacts on the intensity of urban cold island effect. Specifically, the intensity of urban cold island effect can be enhanced by 0.013 ℃ and 6.837 ℃ respectively when the proportion of forests and shrublands increases by 1% (PLAND index increases by 1 unit). At the same time, the more concentrated the distribution of shrublands (NP index decreased by 1 unit), the greater the intensity of urban cold island effect (0.007 ℃).

Besides, this study also found that the cooling effect of urban blue–green space on urban cold island and heat island has significant difference. Specifically, the proportion and distribution of forests and shrublands which showed significant impacts on the intensity of urban cold island effect could not mitigate the urban heat island effect significantly. Grasslands and water bodies are the key factors to deal with urban heat island. The intensity of urban heat island effect can be alleviated by 0.005 ℃ and 0.019 ℃, respectively when the proportion of grasslands and water bodies increases by 1% (PLAND index increases by 1 unit). The more scattered the distribution of shrublands (NP index increased by one unit), the weaker the intensity of urban heat island effect (0.007 ℃).

These results preliminarily proved that the spatial pattern of urban blue–green space at city-level has significant cooling effect. In addition to alleviating the urban heat island effect, which had been illustrated in previous studies, it can also enhance the urban cold island effect. Therefore, this study will move another step to reveal the heterogeneity in the impact mechanisms of urban blue–green spaces on the intensity of urban cold island effect.

Temporal heterogeneity

We constructed four fixed effect models which took the summer daytime, summer nighttime, winter daytime and winter nighttime urban cold island intensity as the dependent variables to reveal the differences within the impacts of city-level spatial pattern of urban blue–green spaces on urban cold islands in various time periods. The results are presented in Table 4.

Table 4 Outputs of local panel regression models (temporal heterogeneity)
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The outputs of the models showed that some spatial pattern attributes of urban blue–green space at city-level, which are not related to the all-day intensity of urban clod islands effect, showed extra significant impacts on that of specific time periods. Specifically, in addition to the size, the city-level distribution and shape of the forest will also affect the daytime urban cold island. The daytime intensity of urban cold island effect in winter and summer can be enhanced by 0.0008 ℃ and 0.0006 ℃, respectively when the distribution of forests gets more concentrated (NP index decreased by 1 unit). Similarly, as the shape of the forests becomes more complex (LSI index increased by 1 unit), the intensity of urban cold island effect in the two seasons can be enhanced by 0.026 ℃ and 0.037 ℃, respectively. Water body has also been proved to be significantly associated with winter urban cold island effect. The larger the area, the more concentrated the distribution, and the more complex the shape of water bodies, the higher the intensity of urban cold island effect. The UCI intensity increased by 0.053 ℃, 0.004 ℃ and 0.059 ℃, respectively for one unit change in PLAND (+), NP (−) and LSI (+) indices of water bodies at city-level.

Moreover, the results from Table 4 also indicated that the city-level spatial pattern of blue–green space is more closely related to urban cold island effect in summer and daytime. Specifically, compared with other seasons and time periods, the spatial patterns of water bodies and forests of urban blue–green spaces at city-level have additional effects on the urban cold island effect in summer and daytime, respectively.

Spatial heterogeneity

As the cooling effect of the blue–green spaces changes with the characteristics of the regional natural environment and the intensity of human activities, in order to eliminate the errors caused by these spatial factors on the regression results, we divided the 130 prefecture level cities in the dataset into 4 sections according to the terrain conditions and the permanent population density.Footnote 2 Each section contains 65 provinces, which represent the regions with large population (POP+), sparse population (POP−), mountain topography (GEO+) and flatland topography (GEO−), respectively. Then, we constructed 4 fixed effect models which took the annual all-day urban cold island intensity as the dependent variables in these four regions to further detect the spatial heterogeneity within the impacts of city-level spatial pattern of urban blue–green spaces on urban cold islands. The results were presented in Table 5.

Table 5 Outputs of local panel regression models (spatial heterogeneity)
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The outputs of the models showed that additional links between the shape of grasslands and urban cold island exist in regions with specific demographic and topographical characteristics. In detail, as the shape of the grasslands at city-level in sparsely populated regions and mountainous regions becomes more complex (LSI index increased by 1 unit), the intensity of urban cold island effect can be enhanced by 0.037 ℃ and 0.020 ℃, respectively.

In addition, the results from Table 5 further demonstrated that the impact of city-level spatial pattern of blue–green spaces on the intensity of urban cold island is more significant in sparsely populated regions and mountainous regions. Specifically, the size, distribution and shape of various types of urban blue–green spaces, such as forests, shrublands and grasslands, significantly affect the urban cold island in sparsely populated (POP-) regions and mountainous (GEO+) regions. On the contrary, there was no statistically significant (p value > 0.1) relationship with the UCI in populated regions and flatland regions.

Threshold effect (TVoE) estimation of the cooling efficiency

After clarifying the impact of city-level spatial pattern of blue–green spaces on urban cold island effect, we turned to investigate the optimal spatial pattern of blue–green spaces with the maximum cooling efficiency at city scale. Specifically, we use the Quadratic-Curve-Fitting based TVoE estimating model proposed in chapter 2.6 to fit the relationship between the PLAND, NP and LSI indexes of the 4 types of blue–green space (forests, shrublands, grasslands, water bodies) and the intensity of urban cold island effect. The results were shown in Fig. 4.

Fig. 4
figure 4

Estimation results of TVoE

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The fitting results showed that, being similar to the logarithmic function, the quadratic function is also suitable for fitting the relationship between the spatial characteristics of blue–green space and its cooling effect. Different from logarithmic fitting, the 12 fitting functions constructed in this study do not show monotonic increasing or decreasing characteristics, and the vertices are identified in the corresponding domains. This further indicated that different perspectives and methods should be utilized to estimate the TVoE in cooling efficiency of blue–green spaces from patch-level and city-level, respectively. As mentioned in chapter 2.6, the cooling effect of blue–green patches always increases with area theoretically. Therefore, when estimating the TVoE at patch-level, we focus on finding the turning point where the increasing rate of cooling efficiency slows down and define it as the threshold point (Yu et al. 2017). However, when re-examining from the perspective of the whole city, it can be found that the city-level blue–green space system will change accordingly when the area, distribution and shape of one type of blue–green space in cities change. Therefore, combined with the present hypothesis and the fitting results in Fig. 4, we supposed that when estimating the TVoE of blue–green spaces at city-level, we should turn to find out the change points regarding four types of urban blue–green spaces where the changing direction of the intensity of urban cold island effect change.

The fitting results indicated that the intensity of urban cold island effect first increased and then decreased with the expand of area and the complex of shape of urban blue–green spaces at city-level. Specifically, on the one hand, the intensity of urban cold island effect reaches the local maximum (1.20 ℃) when the area ratio of forests, shrublands, grasslands and water bodies is about 20%, 0.1%, 42.5% and 15.4%, respectively. On the other hand, when the LSI index of forests, shrublands, grasslands and water bodies at city level reach 38.25, 5.08, 48.25 and 8.54 respectively, the intensity of urban cold island effect reaches another local maximum (1.23 ℃). In contrast, the relationship between the city-level distribution of urban blue–green spaces and urban cooling island showed a different trend. The intensity of urban cold island effect first decreased and then increased with the discretization of urban blue–green spaces at city-level. Specifically, when the NP index of forests, shrublands, grasslands and water bodies at city level reach 1000, 24.25, 450 and 75 respectively, the intensity of urban cold island effect reaches another local minimum (1.08 ℃). This further showed that when the blue–green space in the city presents an extreme aggregation and discrete distribution pattern, it is conducive to play its cooling effect.

In summary, by using the Quadratic-Curve-Fitting based TVoE estimating model designed in this study to fit the cold island effect efficiency of urban blue–green space, it is found that the relationship between cooling efficiency of urban blue–green space and its city-level spatial distribution showed a significant threshold effect. Combined with this TVoE model and landscape pattern indices, the optimal spatial pattern of urban blue–green spaces at city-level (from the aspects of area, shape and distribution) with the best cooling efficiency could be proposed.

Discussions

Combining the calculation results of the panel regression models and the Quadratic-Curve-Fitting based TVoE model constructed in "Results", this study has basically given answers the two research questions raised in the introduction section.

On the one hand, the results evidenced that the proportion and distribution characteristics of forests and shrublands in urban areas improved the intensity of urban cold island effect significantly, while that of grassland and water bodies mitigated urban heat island effect. Moreover, it was demonstrated that the city-level spatial pattern of urban blue–green space has a greater influence on its cooling efficiency at specific time periods (summer and daytime) and regions (mountainous cities with a small population).

On the other hand, it was also estimated that the cooling effect reaches the local maximum (around 1.2 ℃) when the PLAND / LSI index of forests, shrublands, grasslands, and water bodies at city-level is about 20%, 0.1%, 42.5% and 15.4%/38.25, 5.08, 48.25 and 8.54, respectively. Furthermore, when the NP index of forests, shrublands, grasslands and water bodies at city level reach 1000, 24.25, 450 and 75 respectively, the intensity of urban cold island effect reaches another local minimum (1.08 ℃). The results of the above threshold calculations provide an important reference for the optimal spatial pattern of blue–green spaces of the maximum cooling efficiency at city scale.

Therefore, in this section, we further discussed the reasonings for these findings. Specifically, we deeply discussed the explanations on the influence mechanism and the validity of Quadratic-Curve-Fitting based TVoE estimating model. The details contents are as follows.

Explanations on the influence mechanism

Overall relationship between urban blue–green spaces and their cooling efficiency

The results of global models (Table 3) explicitly delineated that the 4 types of urban blue–green spaces (forests, shrublands, grasslands, waterbodies) all have significant cooling effect, which is consistent with previous findings (Yang et al. 2017). However, the four landscape elements have notable different ways to achieve cooling. Specifically, grasslands and water bodies are the main driving factors to alleviate urban heat island intensity, and the intensity of urban cold island effect changes with the spatial pattern of forests and shrubland at city-level.

This might be closely related to the difference of light transmittance in different types of blue–green spaces. Compared with grasslands and water bodies, the canopy of forests and shrublands is closed and the structure is complex, which makes the light intensity in the space decrease significantly. The decrease of light energy input helps to reduce the temperature, which leads to the obvious difference of cooling principle between different types of blue–green spaces (Tang et al. 2009; Chen et al. 2015).

In general, regions with significant vegetation cover, such as forests and shrublands, could effectively improve surface moisture, heat capacity and thermal inertia due to their high latent heat flux. Therefore, the spatial pattern of these two types of blue–green spaces is the key to maintain the efficient operation of urban Cold Island. On the contrary, grasslands and water bodies are more sensitive to heat exchange because they have no vegetation cover, so they have a greater impact on urban heat island. The spatial morphology planning of blue–green infrastructure are also considered as important roles in improving urban resilience and achieving sustainable goals for urban environment.

Spatial–temporal heterogeneity in the impact mechanism

Temporal heterogeneity

The results of local models (Table 4) illustrated that the impact of spatial pattern of blue–green spaces at city-level on the urban cold island effect varies with time, and the urban blue–green space has a greater influence on urban cold island in summer and daytime. Specifically, we took the distribution characteristics of urban cold island of Shanghai (Fig. 5) in different seasons (summer and winter in 2018) and time periods (daytime and nighttime) as examples to try to explain the temporal heterogeneity of the cooling effect of blue–green spaces.

Fig. 5
figure 5

Urban cold island in Shanghai (2018)

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From the distribution of urban cold islands in Shanghai in 2018, it was found that the urban cold islands in summer and daytime have the characteristics of more quantity, wide distribution and small area compared with those in winter and nighttime. The average area of urban cold islands in summer and daytime were only 0.6356 and 0.7311 km2, while the average area of which reach 1.1864 and 1.5282 km2 respectively in winter and nighttime. Similarly, the number of urban cold islands in summer and daytime is 47 (188/141) and 213 (271/58) more than those in winter and nighttime, respectively (Table 6).

Table 6 Attributes of urban cold islands in Shanghai (2018)
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This illustrated that the reasonable spatial pattern of urban blue–green space at city-level (especially forests and water bodies) could effectively promote the cooling effect of evenly distributed and small area urban cold islands but showed no effect on centralized and large area ones.

Spatial heterogeneity

The results of local models (Table 5) further illustrated that the link between the city-level spatial pattern of urban blue–green spaces and urban cold island effect only existed in mountainous cities with a small population (POP− and GEO+). The special natural conditions, urban spatial structure, and traffic mode of such cities may be the factors for urban blue–green space to play the initial role.

Firstly, the climate environment of mountain cities with low population density is significantly affected by mountain-valley breezes (Zeng and Tian 2013). The phenomenon of mountain-valley breezes is considered to be the main reason for the rise of urban temperature and humidity (Cao and Xiao 2013). Therefore, we could infer from the results of the spatial heterogeneity that the change of urban blue–green spatial pattern at city-level might be an important factor affecting mountain-valley breezes. Rational allocation of urban blue–green space (especially shrublands and grasslands) is one of the effective strategies to suppress mountain-valley breezes and improve urban cold island effect.

Secondly, mountainous cities with low population density are restricted by their terrain conditions, and its urban spatial structure mainly developed into ‘group mode’, which is different from that of big cities in plain area (‘core mode’). To a certain extent, the multi-core development model avoids the aggregation of urban resources, economy and industry (Huang 2005). Therefore, we could infer from the results of the spatial heterogeneity that the development mode of uniform allocation of urban resources and optimal urban blue–green space allocation could maximize the cooling effect.

Thirdly, mountainous cities with low population density are subject to the geographical environment, and most of the urban roads follow the terrain and mountains and connect with the main roads in a zigzag way, which makes the vehicles driving difficult. This is the reason why cars need to make sharp turns and accelerate and decelerate more frequently. This kind of transportation mode helps to reduce the total amount of resident’s transportation and increase the utilization of public transportation (Zeng and Tian 2013). Therefore, we could infer from the results of the spatial heterogeneity that it is also an important means to improve the cooling efficiency of urban blue–green spaces by reducing traffic and alleviating vehicle energy consumption and exhaust emissions.

Application of Quadratic-Curve-Fitting based TVoE estimating model

Using the Quadratic-Curve-Fitting based TVoE estimating model proposed in "Quadratic-Curve-Fitting based TVoE estimating model", we fit the relationship between the urban cold island effect and the spatial pattern of urban blue–green spaces and estimate the TVoE and optimal pattern of the urban blue–green spaces at city-level. The results in Sect. 3.3 further delineated that the model has good performance. The global blue–green space pattern with the maximum cooling efficiency could be estimated from three aspects of area, distribution and shape. Specifically, additional focus should be paid on the two following points when utilizing this model:

On the one hand, the Quadratic-Curve-Fitting based TVoE estimating model is specifically designed to estimate the optimal spatial pattern of urban blue–green spaces at city-level. Mainstream Logarithmic-Function-Fitting based TVoE estimating models are mainly used to estimate the size threshold of the cooling efficiency of landscape patches (Peng et al. 2020), that is, to calculate the corresponding area when the cooling efficiency of a single urban green space or water body is the maximum (Fig. 3). In these studies, landscape patches are assumed to exist independently. Therefore, its cooling capacity will increase monotonously with the increase of its area, theoretically. However, when investigating from city-level, the area, distribution and shape of all kinds of urban blue–green spaces will be influenced by other kinds. For example, the increase of the area of one kind of blue–green space will inevitably compress the area of other kinds of spaces in the city. Based on this, the proposed model is designed to estimate the global optimal pattern of a city's blue–green space from an overall perspective.

On the other hand, there are two main forms of the outputs of the Quadratic-Curve-Fitting based TVoE estimating model. In this study, a quadratic function (\(y=a{x}^{2}+bx+c, a\ne 0\)) was utilized to fit the landscape metrics corresponding to the urban blue–green spatial pattern and the intensity of urban cold island effect under the corresponding spatial pattern. Therefore, the fitting functions were classified into two categories (Fig. 6).

Fig. 6
figure 6

Basic forms of Quadratic-Curve-Fitting based TVoE estimating model

Full size image

In cases that the graph of fitted function opens upwards, the overall intensity of urban cold island reaches the highest (local maximum of function) when the landscape metric corresponding to spatial pattern of urban blue–green spaces equals to the vertex value (i.e., the axis of symmetry) of the parabola of the univariate quadratic function. As the landscape metrics are further away from vertex, the intensity of urban Cold Island will gradually decrease. On the contrary, in other cases that the graph of fitted function opens downwards, the overall intensity of urban cold island reaches the lowest (local minimum of function) when the landscape metric corresponding to spatial pattern of urban blue–green spaces equals to the vertex value. As the landscape metrics are further away from vertex, the intensity of urban Cold Island gradually increased. For instance, in the case study of this work, the fitting results of the relationship between area and shape of urban blue–green spaces and urban cold island intensity are, respectively, consistent with the above two scenarios.

In summary, the threshold value of urban blue–green spaces’ cooling effect could be estimated at the vertex of quadratic function by using the model proposed in this study, but the meaning of the threshold value needs to be further discussed with reference to the fitting results (parameter a in the quadratic function).

Conclusions

In this study, we clarified the relationship between the urban blue–green spaces and urban cold island effect from the global scale and investigate the spatial–temporal heterogeneity within it. Then, we also proposed a Quadratic-Curve-Fitting based TVoE estimating model and further estimated the threshold value and optimal spatial pattern of urban blue–green spaces at city-level. From a case study established in the Yangtze River Economic Belt, China, the main conclusions are listed as follows.

First, spatial pattern of urban blue–green spaces at city-level has noticeable cooling effect. The proportion and distribution characteristics of forests and shrublands in urban space have significant impacts on the intensity of urban cold island effect. Specifically, the intensity of urban cold island effect can be enhanced by 0.013 ℃ and 6.837 ℃ respectively when the proportion of forests and shrublands increases by 1% (PLAND index increases by 1 unit). At the same time, the more concentrated the distribution of shrublands (NP index decreased by 1 unit), the greater the intensity of urban cold island effect (0.007 ℃).

Second, the impact of spatial pattern of blue–green spaces at city-level on the urban cold island effect varies with time and space. Specifically, the city-level spatial pattern of blue–green space is more closely related to urban cold island effect in summer and daytime. Moreover, the link between the urban blue–green spaces and urban cold island effect only existed in mountainous cities with a small population.

Third, there is a noticeable threshold effect between spatial pattern of blue–green spaces at city-level and the global urban cold island effect intensity. Specifically, the intensity of urban cold island effect first increased and then decreased with the expand of area and the complex of shape of urban blue–green spaces at city-level. In contrast, it first decreased and then increased with the discretization of urban blue–green spaces. The global average intensity of urban cold island effect reaches the local maximum (1.20~1.23 ℃) when the area ratio/LSI index of forests, shrublands, grasslands, and water bodies is about 20%, 0.1%, 42.5% and 15.4%/38.25, 5.08, 48.25 and 8.54, respectively. Furthermore, when the NP index of forests, shrublands, grasslands and water bodies at city level reach 1000, 24.25, 450 and 75 respectively, the intensity of urban cold island effect reaches another local minimum (1.08 ℃).

Based on the above conclusions, we put forward the following policy implications and suggestions for planning of blue–green infrastructure for the urban heat and cooling island effect. When making urban planning and ecological planning with urban blue–green infrastructure as the main object, it is necessary to coordinate the layout mode of all categories of blue–green spaces from a macro perspective. In addition to combating the negative effects of climate change, ecological lands, represented by blue–green spaces, also have great potential to increase urban resilience. Furthermore, in order to maximize the ecological benefits, the natural geography and social economic characteristics of the target city should be taken into consideration during the planning procedure. In addition, there are significant differences in cooling effect and cooling principle between different categories of urban blue–green space. When using ecological lands to adjust urban micro-climate, we need to combine local climate zone to determine the most optimal blue–green space adjustment scheme to achieve the sustainable development goals for urban environment.

The most important contribution of this paper might be that we clarified the relationship between urban blue–green spaces and urban cold island effect at city-level based on the empirical evidence. To our knowledge, this is the first empirical study to explore the link between the city-wide proportion, distribution and shape characteristics of various types of ecological lands (forests, shrublands, grasslands and water bodies) and the overall intensity of the cold island effect at city-level. The empirical results of this study evidenced that, in addition to the characteristics of patches, the overall spatial pattern of urban blue–green space will also significantly affect its cooling effect. Optimal regulation of urban ecological lands is another key factor to mitigate urban heat island and promote urban Cold Island in the future. Additionally, the Quadratic-Curve-Fitting based TVoE estimating model proposed in this work, which is inspired from the Logarithmic-Function-Fitting based models designed for patch-level research (Yu et al. 2017), could also contribute to estimate the threshold effect and optimal spatial pattern of urban blue–green spaces at city-level.

However, due to the lack of data, the resolution of the original land use data set (MCD12Q1) used to quantify the spatial pattern of urban blue–green space is 500 m, and the accuracy of the quantitative results still have room to improve. This is the main deficiency of this study and the compromise of large-scale spatial research. In the future, the main research direction is to select more accurate data and methods to investigate the mechanisms of the heterogeneity of the impact of urban blue–green spatial pattern on its global cooling efficiency.