The identification and evaluation of “Production-living-ecological” functions is an important prerequisite for scientific delimitation of “Production-living-ecological” space and optimization of land space development. On the basis of previous studies, combined with the “Production-living-ecological” space theory of land space planning, the paper takes the northern metropolitan area of Leshan City as the research object, and will identify and evaluate the production function, living function and ecological function of the metropolitan area space. Based on the comprehensive consideration of the development status of the northern metropolitan area of Leshan City and the scientificity and operability of the selection of evaluation indicator factors, 35 indicators were selected to preliminarily construct the “Production-living-ecological” system coupling and coordination evaluation indicator system, including 10 production function indicators, 12 living function indicators and 13 ecological function indicators (see Table 1 below). The entropy

Note: P represents production function, L represents living function; Or P represents production function, L represents ecological function; Or P for living function, L for ecological function.

method is used to calculate the weight of each index.

1) Production space. According to the “Production-living-ecological” space theory of land space planning, production space refers to the regional space mainly providing agricultural products, industrial products and service products, as the place where people engage in production and business activities. The indicators are selected on the basis of reference to relevant literature research, taking into account the development status of the northern metropolitan area of Leshan City and the operability of data collection. The GDP of the secondary industry, added value of private economy and other indicators are selected to characterize the production space of industry and service products in the northern metropolitan area of Leshan City, which are positive indicators; The actual cultivated land area at the end of the year, the added value of agriculture, forestry, animal husbandry and fishery and other indicators are selected to characterize the agricultural production space in the northern metropolitan area of Leshan City (Liu & Zhou, 2021).

2) Living space is the place used by people in their daily life activities, providing necessary space conditions for people’s living and public activities. It mainly includes urban living space and rural living space (Gonçalves & Ferreira, 2015).

3) Ecological space refers to the regional space that plays an important role in ecological protection and has an important impact on maintaining regional ecological security and sustainable development, and can provide ecological services and products. It is the guarantee of human production and life, an area that must be strictly controlled and maintained, mainly including important ecological space and general ecological space. The LAI, LSI and LVI indexes are calculated by Fragstats4.2. The detailed calculation of the indexes refers to the research results of Zhang Lifang et al., and will not be repeated here (Zhang et al., 2020).

The measurement model of the spatial function coupling coordination degree of “Production-living-ecological” in the northern metropolitan area of Leshan City is constructed. The specific calculation formula is as follows:

C = 3 { P × L × E P + L + E } 1 3 (1)

Among them, C is the coupling degree of the “San Sheng” spatial function subsystem in the northern metropolitan area of Leshan City, with a value range of [0, 1]. The larger the value, the stronger the interaction between subsystems. P, L and E are respectively the comprehensive evaluation values of production function, living function and ecological function in the “Production-living-ecological” spatial function system of the northern metropolitan area of Leshan City (Daunt et al., 2021).

In order to further analyze the interaction between the “Production-Living” function, “Production-Ecology” function and “Living-Ecology” function of the northern metropolitan area of Leshan City, the coupling degree model can evolve as follows:

C 1 = 2 { P i × L i P i + L i } 1 2 (2)

C 2 = 2 { P i × E i P i + E i } 1 2 (3)

C 3 = 2 { L i × E i L i + E i } 1 2 (4)

Although the degree of coupling can reflect the degree of interaction between the functions of Leshan Global Tourism Spatial Collaborative Planning System, it cannot indicate whether the functions promote each other at a high level or restrict each other at a low level. Therefore, the coupling coordination index is introduced to build the functional coupling coordination model of Leshan Global Tourism Spatial Collaborative Planning System. The specific calculation formula is as follows:

D = C × T , T = α P × β L × χ E (5)

In the formula: C coupling degree of the “Production-living-ecological” spatial function subsystem in the northern metropolitan area of Leshan City; D is the coupling and co scheduling of the “Production-living-ecological” spatial function subsystem in the northern metropolitan area of Leshan City; P, L, E are the evaluation values of production, living and ecology of Leshan City respectively; α, β, χ are respectively the undetermined coefficients of production, living and ecology. On the basis of referring to the opinions of relevant experts, the undetermined coefficients are determined as α = 0.4, β = 0.3 and χ = 0.3; Similarly, formula (5) can be used to obtain the coupling and co scheduling between the two functions of Leshan Global Tourism Spatial Collaborative Planning System. The calculation formula is as follows:

D = C × T (6)

Among them, T is: T 1 = α P × β L or T 2 = α P × χ E or T 3 = β L × χ E

The D values corresponding to three different T values can be shown in Table 2 as the synergistic relationship between production and life.

The data required for this study mainly include long-term statistical data, including social economic data and ecological environment index data in 2010, 2015 and 2018. The social economic data are mainly from the Statistical Yearbook of Leshan City and the statistical yearbooks of districts and counties in Leshan City published by China Statistics Press in 2011, 2016 and 2019. The ecological environment data is mainly the land use data of the third period from

Note: P represents production function, L represents living function; Or P represents production function, L represents ecological function; Or P for living function, L for ecological function.

2010 to 2018, which is from the Data Center of Resources and Environment Science, Chinese Academy of Sciences (http://www.webmap.cn/main.do?method=index). According to the research methods of Zhang et al. (2020), Tian et al. (2019), Xu et al. (2018) and others, 6 types of cultivated land, grassland, forest land, water area, construction land and unused land were obtained.