China material stocks and flows account for 1978–2018

System boundary

A PMSF (Provincial Material Stocks and Flows) model, which combines a bottom-up, stocks-drive-flows, and mass-balanced dynamic model, is constructed for material stocks and flows estimates at the provincial level. This combined model can evaluate material inputs, stocks accumulation, and end-of-life outflows. Considering the availability of intensity data and the wide application in society, 13 types of materials, including steel (Fe), aluminium (Al), copper (Cu), rubber, plastic, glass, lime, asphalt, sand, gravel, brick, cement, and wood, are considered in this study. Drawing on a comprehensive provincial product database, annual provincial material uses and flows are estimated. The time horizon is from 1978 to 2018 and all computations are performed in time-discrete steps of one year. The spatial scope covers 31 provinces in mainland China. The workflow is shown in Fig. 1 and is described in detail in the following sections.

Material stocks

The bottom-up accounting method, which starts from counting every piece of material-containing products, then investigates the material intensity for each product, and finally adds up material contained in all product categories, could complement the top-down method by revealing greater details of technologies and identifying geographical locations of material stocks²³. Since the physical data of product stocks are becoming available on provincial scale, the bottom-up approach is appropriately adopted to estimate the material stocks ((Sleft(tright))).

A list of 103 commodities, which are divided into five end-use sectors (including buildings, infrastructure, transportation facilities, machinery, and domestic appliances), is identified and revised based on our earlier study¹⁹ (Online-only Table 1). Unlike our previous research, we have primarily adjusted the commodities identified in the end-use sectors of buildings and infrastructure. For example, we have added different types of highways, power stations, and cable users in the infrastructure, while removing different structures of residential buildings. The material stocks (({S}_{bar{C}})) in each end-use sector ((bar{C})) at the time t are then calculated as the sum of material stocks of related products (Eq. 1).

where ({N}_{i}left(tright)) is the amount of product i in active use in the end-use sector (bar{C}) at time t and ({I}_{i}(t)) is the material intensity of product i.

The number of product ({N}_{i}) quantified by per-household, absolute, or per-capita (Online-only Table 1) is extracted from various official statistical reports, yearbooks, and socio-economic databases (including https://data.stats.gov.cn and http://www.data.ac.cn) for each province during 1979–2019 (see ref. ¹⁹ for detail). Owing to limited data availability for the individual years, linear interpolation has been used to estimate the missing data between consecutively recorded values³².

The material intensity is sourced from various references and estimated based on expert judgements^{10,20,23,24,30,33}, which are also provided in our datasets.

The total material stocks (Sleft(tright)) are calculated as the sum over the five end-use sectors at the time t (Eq. 2).

Residential and non-residential buildings (including buildings of public and industry) are considered when calculating the material stocks in buildings. Unlike residential buildings, the floor space of non-residential buildings is not officially reported in each province. Instead, the floor space of public (({f}_{p})) and industrial buildings (({f}_{i})) in towns and townships in each province are recorded by China Urban-Rural Construction Statistical Yearbook for years (http://www.mohurd.gov.cn/xytj/tjzljsxytjgb/jstjnj/index.html)³⁴. Hence, we estimate the material stocks in non-residential buildings by assuming that the ratio between non-residential and residential buildings in towns (or townships) applies to the urban (or rural) in each province (Eqs. 3–4).

where (R(t)) is the proportion of floor space of non-residential buildings to residential buildings in urban (or rural) at time t, ({f}_{p}(t)) and ({f}_{i}(t)) are the floor space of public and industrial buildings in town (or township) for each province at time t, ({f}_{r}(t)) is the floor space of residential buildings in town (or township) for each province at time t, ({A}_{CR}(t)) is the per-capita floor space of residential buildings in (or rural), and (P(t)) is the urban (or rural) population at time t. For the period 1978–2001, ({f}_{p}(t)), ({f}_{i}(t)) and ({f}_{r}(t)) are held constant at the level of 2002, since these data are unavailable before 2002.

In addition, due to limited official reporting data for (large, medium, small, and micro) passenger cars and (heavy, medium, light, and micro) trucks in each province before 2001, we use the proportion of the different sizes of passenger cars and trucks in 2002 to extrapolate the numbers during 1978–2001. Meanwhile, it is difficult to identify the amount of machines used in diverse industries. We evaluate the metal stocks in industrial machinery by supposing that there is a directly proportional relationship between power consumption and the amount of industrial machines, which is recommended by Zhang et al.²⁹ and Liu et al.³².

Material flows

The material outflow at the time t is defined as the scrap generated from stocks from the end-use sector (bar{C}) of material m, and material inflow at the time t is defined as inputs to stocks of material m. The dynamic stocks-drive-flows model is applied to estimate the material inflows and outflows during 1978–2018 on a sector scale. The annual outflows are determined from stocks using the lifetime model, and the annual inflows are determined from mass balance with outflows and stocks change (Eq. 5):

The lifetime distribution expresses the probability of each end-use sector to reach the end-of-life at the time t. According to previous studies^15,31, we assume a normally distributed lifetime (lambda left(t,t{prime} ,L,sigma right)) ((t{prime} ) = 1949) with end-use sectors dependent mean L and standard deviation σ (Eq. 6), which determines the outflow ({F}_{out}) from stocks and inflows ({F}_{in}) (Eqs. 6–8):

Since material quality requirements are different between buildings, cars, machines, laptops, and other products, the lifetime can vary greatly. However, it is hard to get a specific lifetime of each product in different regions, we assume that the lifetime of products in the same end-use sector keeps unchanged. The mean lifetime and standard deviation for each end-use sector are given in Table 1. According to Eqs. (6–8), when the net stocks (({S}_{left(tright)}-{S}_{left(t-1right)})) less than zero, the ({F}_{in}(t)) will be negative. Hence, to elaborate the negative data of inflow, we will artificially set ({F}_{in}(t)) into zero. The ({F}_{out}(t)) will be equal to the net stocks.

When estimating the inflows and outflows from the year 1978, the stocks and the resulting inflows and outflows before 1978 must be taken into account. These approximations of initial stocks and flows are necessary to make the estimation for the period of 1978–2018 more accurate⁴. Hence, a spin-up period has been implemented, and the length of this spin-up period begins in 1949 when the People’s Republic of China was founded. Due to limited official reporting data that existed in each province before 1978, we use the power function revealed by previous studies³⁵ to extrapolate the material stocks during 1949–1977 (Eq. 9).

where ({S}_{p}left({t}_{0}right)) is the material stocks at the time ({t}_{0}) in province p (during 1949–1977), ({K}_{p1}) and ({K}_{p2}) are coefficients of the fitting model in each province.