Stock dynamics for forecasting material flows—Case study for housing in The Netherlands

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a v a i l a b l e a t w w w. s c i e n c e d i r e c t . c o m

w w w. e l s e v i e r. c o m / l o c a t e / e c o l e c o n

METHODS

Stock dynamics for forecasting material flows—Case study for housing in The Netherlands Daniel B. Müller ⁎ Center for Industrial Ecology, School of Forestry and Environmental Studies, Yale University, New Haven, CT 06511, USA

AR TIC LE I N FO

ABS TR ACT

Article history:

This article discusses the role of lifestyle in physical material accounting and introduces a

Received 23 September 2004

new method for simultaneously determining national or regional resource demand and

Received in revised form

waste generation through estimations of the population and its lifestyle, which is

21 April 2005

manifested in the stocks of service providing goods, their composition and lifetimes.

Accepted 29 September 2005

Improving our comprehension of the stocks in use is essential for environmental policy

Available online 2 December 2005

making because (1) they are becoming the most important resource providers, (2) they are important drivers for resource and energy consumption as well as waste and emission

Keywords:

generation, and (3) their magnitudes and dynamics are the parts of the material cycles that

Material flow analysis

is usually least understood.

Dynamic modelling

A generic dynamic material flow analysis model is presented and applied for the diffusion

Prospects for resource demand

of concrete in the Dutch dwelling stock for the period of 1900–2100. Simulation results are

Waste management

illustrated for a standard scenario and a parameter variation. The results show that (1)

Vintage effects

construction and demolition flows follow a cyclical behaviour, (2) the cycles of construction

Diffusion processes

and demolition flows are phase displaced in the first half of the 21st century, with decreasing construction and increasing demolition, and (3) growth of the dwelling stock is becoming increasingly more material intensive as a growing amount of material is used for replacements. The presented stock dynamics approach can principally be applied for any anthropogenic material stock; however, it is most useful for the examination of metabolic consequences of diffusion processes of durable and fixed capital stocks. © 2005 Elsevier B.V. All rights reserved.

1.

Introduction

Human activities make use of an increasing variety of services provided by stocks of capital and consumer goods. Producing, operating, maintaining, and disposing of these stocks causes material and energy flows that interact with the environment. One of the most challenging tasks in resource management is assessing long-term changes in these flows. Appraisals of future material flows are useful for early recognition of environmental problems, for investment planning in mining, pro-

duction, and waste management infrastructures, and for government policy formulation, such as land policy, environmental policy, R&D funding emphasis, or strategic stockpile objectives. At least four techniques are used to forecast pre-use (upstream) material flows: intensity of use (IU) technique (e.g., Tilton, 1990), demand function (e.g., Fisher et al., 1972), production function (e.g., Kopp and Smith, 1980), and input–output analysis (IOA) (e.g., Leontief et al., 1983; Myers, 1986). These methods have their strengths, shortcomings, and specific field

⁎ Tel.: +1 203 432 2510; fax: +1 203 432 5556. E-mail address: [email protected]. 0921-8009/$ - see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2005.09.025

EC O L O G IC A L E C O N O M IC S 5 9 ( 2 0 06 ) 14 2 –1 56

of application (Tilton, 1990). For the purpose of this study, which is concerned with long-term changes of entire material flow cycles, these approaches have several limitations: (1) They all focus on a particular part of the system, neglecting important relationships among processes of entire material cycles, such as the availability of secondary resources for substitution of primary resources.1 (2) They all focus on flows, while ignoring time-dependent effects of stocks. (3) Parameter estimation for the determination of long-term future flows is very difficult, as it is exclusively based on extrapolating the determinants to the future, leading to high uncertainties if these determinants do not follow characteristic long-term patterns. For example, Moore et al. (1996) found that the intensity of use for construction materials shows a completely different pattern for the United States and the United Kingdom. On the post-use (down-stream) side, waste flows can be calculated using historic data of input flows into use and estimations of lifetime distributions (Baccini and Bader, 1996; Zeltner et al., 1999; Kleijn et al., 2000; Van der Voet et al., 2002; Spatari et al., 2005; Elshkaki et al., 2005). This inputlifetime approach leads to somewhat more reliable results for durable goods, because one determinant of the waste flows is the historic input into use, which can be measured and does not need to be estimated. However, the long-term waste flows depend not only on historic inputs but also on future inputs, which these approaches need to assume. Theoretically, economic upstream approaches could be combined with input-lifetime approaches in order to determine input, output, and stocks in use. Another approach to determine both resource demand and waste generation is to use the material stocks in use and the lifetime as determinants (Binder et al., 2001). This approach makes use of historic data of material stocks–which can be observed or calculated using the input-lifetime approach–for combined upstream and downstream calculations. The difficulty with this approach lies in estimating future material stocks in use, particularly when substitution effects occur. In order to diminish these shortcomings, Real (1998), Müller (1998), Müller and Bader (2004) relate the material stocks in use to services. It is assumed that users are not primarily interested in certain material stocks, but in the services they provide. A certain service can be provided using different combinations of materials. In this article, the service concept is further elaborated and applied for a case study of concrete in dwellings. The present study is based on the hypothesis that stocks in use play an important role for understanding the long-term changes of material cycles. This hypothesis is based on the following reasoning: 1. Research by Bergbäck and Lohm (1997), Zeltner et al. (1999), Hendriks et al. (2000), Sörme et al. (2001), Lifset et al. (2002),

1 The IU technique focuses on apparent consumption of final products (input flows into use), while demand and production functions are performed either for production or fabrication and manufacturing (excluding indirect metal trade). IOA uses wider system boundaries, which include flows in all industrial sectors (in Fig. 1, production and fabrication and management) with possibilities for extensions; however, its flow focus limits the range of application to systems without stocks.

143

Gordon et al. (2004), Graedel et al. (2004) and others indicate that considerable amounts of the materials mined in the 20th century are incorporated in products that are still in use. For most engineering materials, the input into use is still several times larger than the output of waste streams, which results in a growth of the overall material stocks. 2. These findings suggest an exploration of the anthropogenic material stocks as sources of secondary raw materials. Compared with the exploration of primary resources, however, there is little knowledge about the reservoirs of materials in products in use. 3. Mining anthropogenic material stocks differs significantly from traditional mining, as the amounts of waste streams are not primarily determined by demand (pull), but mainly by user's decisions to discard or demolish products in use (push). In other words, the price elasticity of scrap supply is usually very low compared to the price elasticity of virgin raw materials. In order to understand the temporal development of mining activities for anthropogenic material stocks, it is therefore not sufficient to investigate markets and industry activities. In addition, we need to understand the structure and functions of products in use, and how they interact with decisions about lifestyles. The principal goal of this article is to introduce the stock dynamics approach as an alternative method for simultaneously forecasting resource demand and waste generation. Instead of using prices or GDP as main drivers, this method is based on physical accounting. The central driving forces are the population and its lifestyle, which are manifested in service providing stocks of products in use. The provision of these services can be realized by different stocks of goods in use, with different material composition, and with different lifetimes. The stock in use forms the physical link between resource demand (input) and waste generation (output). Its omission– which is the case for most economic models–not only violates the principle of mass balance of in use stocks, but it reduces questions of lifestyle to questions of acquisition of new products, which leads to a confusion of means and ends. This confusion of means and ends distracts us from grappling with the more important problem of choosing well among means. In the next section, the stock dynamics model is described in generic terms. In Section 3, the model is applied for a case study of concrete in Dutch residential building stock. Model simulations are carried out for a standard scenario and a parameter variation for all determinants. Section 4 discusses the results from a more theoretical level, introducing the question whether stocks follow flows or vice versa. Furthermore, it discusses reasons why further research into stock dynamics is relevant for environmental policy making.

2.

Model

For didactic reasons, the model is limited to a description of stocks in use, their inputs, outputs, and determinants; however, it is built in such a way that it can be used as a module for material flow analysis (MFA) models describing entire anthropogenic material cycles.

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The system illustrated in Fig. 1 involves three types of processes, illustrated with rectangles: population within the region of interest (p), service units in use (s), and their associated material stocks in use (m). All processes have a state , K(m)) and a derivative, which is the net stock variable K(p), K(s)
ðpÞ dK dKðsÞ dKðmÞ accumulation ; ; . Each process has an input (I(p), dt dt dt (s) (m) I , I ) and an output flow (O(p), O(s), O(m)), represented with straight-line arrows and ovals. Stocks and flows are shaped by determinants (hexagons), which are lifestyle (service units per (m) capita K(s) c ), materials intensity per service unit (Ms ), and lifetime (L). Influences between different variables are indicated with dashed line arrows. The overall stock of service units in use is driven by population and lifestyle. The demand for service units in use determines, in conjunction with the lifetime, how many units need to be added, and how many units are retiring. The input of new service units determines, depending on the technology, how much material is needed. This material input is used, together with the lifetime, to calculate the material stock accumulation and output. The stock dynamics model describes stocks and flows exclusively in dependence on physical determinants. These physical determinants could be explained with economic variables, such as prices, income, or elasticity. For example, the lifestyle variable could be explained with a per capita or household income distribution; or, the material intensity to produce a service unit could be described with the relative

prices of different materials that can substitute each other. Such an economic extension, however, would not change the structure of the model presented in Fig. 1. For the following, population (K(p)) is considered an external variable, and disregard births and immigration (I(p)) as well as deaths and emigration (O(p)). The system in Fig. 1 is then determined with six equations. The first two equations are balance equations for the service unit and the material stocks. dKs ðtÞ ¼ IðsÞ ðtÞ−OðsÞ ðtÞ dt Balance equations for the service units dKm ðtÞ ¼ IðmÞ ðtÞ−OðmÞ ðtÞ dt

Balance equation for materials

ð1Þ ð2Þ

The balance equations involve the assumption of mass and service unit conservation. While the conservation of materials is trivial, the conservation of service units needs explanation. From an economic perspective, the value of a product in use is depreciating over time, an attribute that would not be captured with a balance equation. Eq. (1), however, assumes that the service derived from a product is constant over its entire lifetime. This assumption is adequate for most durable goods. However, it is important to be aware that this definition of service does not include the concept of product value. The remaining four equations form the model approach. The stock of service units is defined by the population (K(p)(t)) and a service unit stock per capita (K(s) c (t)), each of which is time dependent. ðsÞ

KðsÞ ðtÞ ¼ KðpÞ ðtÞTKc ðtÞ

ð3Þ

The service units per capita can be defined directly, or, as illustrated in the case study in Section 3, through different parameters representing social structure and lifestyle. The service units can have different lifetimes, and are represented by a lifetime distribution (L(s)(t, t′)). The lifetime distribution is the probability that a unit is discarded at time t if it entered use at time t′. The lifetime distribution links the input and output of service providing structures: Z t LðsÞ ðt; tVÞIðsÞ ðtVÞdtV: ð4Þ OðsÞ ðtÞ ¼ t0

Eq. (5) links the two sub-systems of service units and materials: The inputs of material m and service s are coupled through the material intensity per service unit produced M(m) s (t). ðmÞ

IðmÞ ðtÞ ¼ IðsÞ ðtÞTMs ðtÞ

Fig. 1 – Extended MFA system for the stock dynamics model. Rectangles represent processes, ovals depict flows, and hexagons illustrate determinants or drivers. Note: this model can be extended in various ways, for example to include economic or further physical variables as determinants, as is done in the application for the Dutch dwelling stock, which describes lifestyle (square meters per capita) in terms of average household size and average dwelling size.

ð5Þ

This equation can be used to investigate effects of substitution among different materials, however, in order to explain substitution effects, the material intensity would need to be considered as a dependent on economic variables, such as relative prices of alternative materials. The last equation assumes that the materials also follow a certain pattern of lifetime distribution, in an analogous way as for the service units in formula (4). Z t LðmÞ ðt; tVÞIðmÞ ðtVÞdt V ð6Þ OðmÞ ðtÞ ¼ t0

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If we assume that no materials are replaced during the lifetime of the service units, we can set LðmÞ ðt; tVÞ ¼ LðsÞ ðt; tVÞ ¼ Lðt; tVÞ:

ð6aÞ

The model then uses the following four drivers or determinants as external parameter functions: K(p)(t) K(s) c (t) L(t, t′) M(m) s (t)

Population Service stock per capita (lifestyle) Lifetime distribution Material intensity per service unit.

3.

Concrete in the Dutch dwelling stock

3.1.

Background

The Netherlands has experienced a vast expansion of the settlement areas over the past few decades, which led to high demands for construction materials. In the case of gravel, sand, and clay, the resource supply is almost exclusively based on domestic sources, which, in the Dutch landscape, often causes significant, irreversible changes in land use, such as turning agricultural land into lakes. As the mineral resources are unevenly distributed over the country2, an increasing number of affected communities started opposing mining activities in their neighbourhoods. These political problems have increasingly endangered mineral resource supply security. In 2001, the Ministry of Transport, Public Works, and Water Management, which is responsible for minerals supply, sponsored a preliminary research project to clarify the use of MFA as a tool for resource management (Müller, 2001). This project involved a combined investigation of gravel, sand, and clay (here summarized as minerals), and timber in the Netherlands. Fig. 2 shows the stocks and flows of these materials for the year 1997. Calculations and data sources are documented in Müller (2001). Dutch constructions incorporate a mineral stock of 500 metric tons per capita (t/cap) and a timber stock of 3 t/cap. Both stocks are increasing, the timber stock by about 1% per year and the minerals stock by about 2% per year, because the demolition rate is lower than the construction rate. The timber stock in the buildings is larger than the timber stock in the forests (1.6 t/cap). This number includes only the stock of managed forests, and excludes natural forests that are not aimed at wood production. Moreover, as annual timber harvest is lower than growth, the managed forest timber stock also increases with a rate of about 1.8% per year. Although the stocks of the in-ground geological resources are not quantified, one can estimate based on geological maps that they are orders of magnitude larger than current stocks in use. The input to the geological inventory of 0.2 t/(cap year) represents annual river depositions.

The flows of minerals are, in general, about two orders of magnitude higher than the flows of timber. Compared to many other countries, The Netherlands does not have a strong tradition of timber construction, which is also reflected in the fact that most of the timber used in The Netherlands is imported (0.5 t/(cap year), while only about 6% (0.03 t/(cap year)) stem from domestic production. Timber recycling is almost negligible, whereas mineral recycling is well established. 96% of the minerals in construction and demolition waste are recycled—or down-cycled, as it is almost exclusively used as filling materials in infrastructures, and only about 4% is stored in landfills (0.04 t/(cap year)). The input of timber into the construction inventory (actual use of timber in construction: 0.13 t/(cap year)) is higher than the output (used wood: 0.1 t/(cap year)). This relation is even stronger for minerals: The input (10.8 t/(cap year)) is an order of magnitude higher than the output (1.2 t/(cap year)). This has significant implications for the future waste generation and resource demands for possible replacements. In order to understand long-term changes of resource demand and waste generation, this static analysis needs to be extended with a dynamic approach that describes the mechanism of changes. This is illustrated in the following section, in which the model introduced in Section 2 is applied to concrete in dwellings.

3.2.

For example, gravel is only available in the province of Limburg. Sand and clay are more evenly distributed among the provinces, however, there are still disparities among parts of the provinces.

Application of the model

The model is applied for concrete in the Dutch dwelling stock, which represents an important part of the overall construction inventory. Not included is the non-domestic building stock (e.g., commercial and public buildings), and infrastructures (e.g., roads, water and energy supply systems, water and waste disposal systems, and dikes). All of these systems could be modelled using the same approach as described here for dwellings. The adaptation of the generic model to the Dutch dwelling stock is illustrated with Fig. 3.

3.2.1.

Population

This dwelling model uses population as an external variable, which is not generated by a population sub-model. Input and output of population are therefore neglected here.

3.2.2.

Service unit and lifestyle

The service unit is expressed here as useful floor area (UFA). This is the floor area of a building measured within the external walls, excluding cellars, non-habitable attics and, in multiple dwellings, all communal areas. Consequently, the lifestyle variable represents the UFA per capita. ) corresponds with the floor area The UFA per capita (K(UFA) c per person3, an indicator frequently used as a social indicator for sustainable development in general and for housing quality in particular. It measures the adequacy of living space in 3

2

145

The UFA per capita in this model is an average, while the indicator used by the United Nations (UN/ESA, 2004a) uses the median. The difference between average and median can become significant in countries with high disparities of housing conditions.

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Fig. 2 – Timber and minerals cycle of the Dutch construction economy in 1997. Stocks: [t/cap], flows: [t/(cap*a)].

dwellings, or the adequacy of the basic human need for shelter. A low value for the indicator is a sign of overcrowding. In low-income settlements, reduced space per person can be associated with certain categories of health risks (UN/ESA, 2004a). There are no time series of the overall UFA in The Netherlands, nor are there time series of the UFA per capita. The dwelling model therefore disaggregates the UFA per capita into two components. ðsÞ

ðUFAÞ

Kc ðtÞ ¼ Kc

ðUFAÞ

ðtÞ ¼

Kd

ðtÞ

ðpÞ Kd ðtÞ

ð7Þ

(t) denotes the average UFA per dwelling, measured K(UFA) d on the entire dwelling stock, and K(p) d (t) is the number of per-

sons per dwelling. Even though Eq. (7) is an identity, it is used because the determinants of K(UFA) offer more explanatory c power than simply using the K(UFA) trend description alone. c The average UFA per dwelling reflects changes in dwelling construction, while the average number of person per dwelling is an indicator of change in the social structure of households. The average number of persons per dwelling corresponds to the average number of persons per household or household size. The household size is used by the UN Department for Economic and Social Affairs as an indicator for production and consumption patterns. Household size affects the pattern of consumption of goods and services, which are shared among household members. For example, in industrialized countries decreasing household size is one of the factors causing an increase in per capita and aggregate energy use in residential buildings, including lighting, heating, and fuel for cooking. Other goods and services, which may be affected by household size, include water supply, solid waste disposal and household appliances (UN/ESA, 2004b). The occupancy of dwellings could theoretically be further differentiated to include effects of generational dynamics (Büttner and Grübler, 1995). An inclusion of generational factors could allow us to simulate effects of cohort or gender specific patterns of sharing households. For example, widows or parents with grown up children tend to stay in large apartments.

3.2.3.

Fig. 3 – Stock dynamics model applied for the dwelling stock.

Material stock and material intensity

The application of the model is illustrated for concrete. The material intensity is therefore expressed as the concrete use per square meter of UFA. The same model could be used for any construction material, however, for didactic reasons the model is illustrated here only for concrete, which constitutes in The Netherlands one of the largest fractions of the construction materials and the construction and demolition waste. Choosing concrete for the illustration of the model has the additional advantage that it allows us to describe the diffusion of an innovation in the observed time frame, as the use of concrete in dwellings started just around 1900.

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Population

6 25 x 10

Lifetime distribution dwellings

0.03

(a)

0.025

20

3

(b)

2.5

0.02

2

0.015

1.5

0.01

1

0.005

0.5

Concrete use per UFA

t/m 2

(c)

15 10 5 0 1900

140 120

m2

1950

2000 Year

2050

2100

UFA per dwelling (stock)

0 0

50 100 150 Years after dwelling entering use

Persons per dwelling

6

(d)

5

100

200

0 1900

70

(e)

60

1950

m2

2000 Year

2050

2100

UFA per capita

(f)

50

4

40

80 3

30

60 2

40 20 0 1900

20

1

1950

2000 Year

2050

2100

0 1900

10 1950

2000 Year

2050

2100

0 1900

1950

2000 Year

2050

2100

Fig. 4 – Estimation of parameters functions for variants low (light grey), medium (dark grey), and high (black).

3.3.

Calibration

The dwelling model is run here for a period from 1900 to 2100. This is a time span that is roughly two building generations. The calibration is executed with historic data from 1900 until about 2003, and, with different assumptions, from the period 2003 until 2100 (see Figs. 4 and 5). Each parameter is estimated for a low, a medium, and a high variant for the future period. The differences of these future assumptions allow us (1) to cover a wide range of possible development paths, and (2) to compare the influence of changes in a single parameter on the entire system (see Section 3.5).

3.3.1.

Population

Historic population data are available for all years from the Dutch census. The three variants for the future represent the high, medium, and low variants of the World Population Prospects, revision 2002, by the United Nations (UN Population Division, 2004). Data for 2005–2050 are available for 5-year steps. The UN Population Division further developed these variants until the year 2300, indicating 100-year steps (UN Population Division, 2003). The three variants differ only in assumptions about fertility, and they all assume the same increase in life expectancy. Both the lower and the medium variants show a saturation in population at the beginning of the 21st century, and a continuous decrease thereafter. The high variant results in a further increase similar to the population growth of the 20th century (Fig. 4a).

3.3.2.

Useful floor area per dwelling

The data for the average UFA per dwelling are assembled from several historic Annual Bulletins of Housing and Building Sta-

tistics for Europe and North America, which is published by the UN Economic Commission for Europe (UN/ECE). For The Netherlands, data are only available for the years 1995 and 2000. However, the same reports have sporadic information about the UFA per new dwelling (available for the years 1966, 1980, and 1998), and, for the years 1962–1974, data about the living floor space4 per new dwelling. For the year 1966, data are available for both living floor space and UFA, the latter being 1.6 times larger than the former. This number was used as a conversion factor for all years. Data before 1962 are estimated using the difference of average UFA and UFA in new dwellings of the known years, and indications of numbers of rooms per dwelling. The resulting estimation of the average UFA per dwelling shows a steady increase over the entire 20th century, with a slight flattening towards the end of the century. The overall average UFA per dwelling has almost doubled within this period. The medium variant assumes a moderate increase in UFA per dwelling, the low variant a decrease, and the high variant a strong increase (Fig. 4d).

3.3.3.

Persons per dwelling

The number of persons per dwelling was calculated by dividing the population by the dwelling stock. Dwelling stock data (Fig. 5a) are taken from Statistics Netherlands (CBS, 2001). 4 The living floor space is the total space within habitable rooms, which are defined as having an individual size of not less than 4 m2 with a height over the major area of the ceiling of at least 2 m. Excluded from computation under this second definition are kitchenettes (which are not defined so as to be distinguishable from kitchens but are presumably taken to be rooms of less than 4 m2 by 2 m), bathrooms, toilets, corridors, lobbies and verandas.

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x 106 10 9

Dwelling stock

4

16 x 10 /a

(a)

14

8

(b)

12

7 6

10

5

8

4

6

3

4

2

2

1 0 1900 6

x 10 t/a 6 5

Completed new dwellings

1950

2000

2050

0 2100 1900 2

Apparent cement use

6

t/m

2000

2050

2100

Total concrete use per UFA dwellings

(d)

(c)

5

4

4

3

3

2

2

1

1

0 1900

1950

1950

2000

2050

0 2100 1900

1950

2000

2050

2100

Fig. 5 – Data used for calibration.

Data are available for the years 1899, 1909, 1920, 1930, and 1947–present for each year. Data between these measuring points were either filled up with data of historic reports of Statistics Netherlands (Statistical Yearbook of The Netherlands and its predecessors, the “Jaarcijfers voor Nederland”), or by interpolation. The values obtained this way for the persons per dwelling do not reflect precisely the occupancy of the dwellings, which is calculated by dividing population and occupied dwelling stock. However, the difference is very small, as the vacant dwellings make up only about 2–3% of the entire dwelling stock. In The Netherlands, the number of persons per dwelling since 1950 has decreased from 4.6 to 2.3. These numbers reflect changes in the social structure, such as couples having fewer children, young adults postponing marriage, divorced or separated persons living alone, and an increasing number of elderly persons living alone. The medium variant assumes a stabilization slightly below the present level, the high variant is calculated with a further decrease, and the low variant with a re-increase in persons per dwelling (Fig. 4e).

3.3.4.

Useful floor area per capita

The UFA per capita (Fig. 4f) was calculated through the UFA per dwelling (Fig. 4d) and the persons per dwelling (Fig. 4e) using formula (7). The combined effects of decreasing number of persons per dwelling and increasing UFA per dwelling resulted in more than a doubling of the UFA per capita since the 1950s (Fig. 4f).

3.3.5.

Lifetime distribution of dwellings

Data about the lifetime of dwellings are generally poor. In the literature, lifetime distributions are therefore often approximated with different functions, such as Weibull, Winfrey, Normal, and Log-normal distributions (OECD, 2001). Due to

the absence of empirical data, there is no clear indication as to which of these approaches is most accurate. For reasons of simplicity, a normal distribution is used in this work. − 1 Lðt; tVÞ ¼ pffiffiffiffiffiffi Te r 2p

ðt−tV−sÞ2 2r2

ð8Þ

The term L(t, t′) represents the probability that the input at time t′ b t is transferred into an output at time t, provided that the lifetime of products follows a normal distribution with mean lifetime τ and standard deviation σ. This function is normalized so that its integral over time equals 1 for any combinations of τ and σ. However, as the lifetime cannot be negative (t N t′), there is a cut off of a fraction of the curve, which can result in integrals that are less than 1 in the defined area, meaning that an input is never transferred entirely to an output; however, this cut off effect is marginal if 2σ ≤ τ. It is assumed that the lifetime of the dwellings is independent of the dwelling vintages. There are good reasons to question this assumption, as in many city centres, buildings are often much older than the average lifetime would suggest; however, the observed data does not allow us to quantify such changes. In the Netherlands, the “Statistiek Kapitaalgoederenvoorraad” (Statistics on Capital Stock) and the “Desinvesteringsenquete” (Questionnaire on Disinvestments) provide directly observed data on service lives of different types of assets for a number of industries (Verbiest and van den Ven, 1997). Verbiest and van den Ven use an average service life of dwellings of 100 years, and for non-residential buildings 20–55 years. As some dwellings are linked with non-residential buildings, overall dwellings are estimated here with an average of 90 years, a high of 120 years, and a low variant of 60 years (Fig. 4b). All variants assume a standard deviation of 20 years.

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3.3.6.

Concrete intensity per useful floor area

Concrete is a composite material made up of cement, water, gravel, and sand. Reinforcing bars are not included here, as this study is concerned with the flow of minerals. There are no direct data available for the average material composition in different dwelling vintages. Estimations can be made in two different ways, which have been characterized as bottom-up and top-down approaches (Kohler et al., 1999), and which were applied here in combination. The bottom-up approach divides dwelling vintages into different categories, such as detached single-family houses, attached single-family houses, and multi-family houses. For each category and vintage class, a typical representative is chosen for an in-depth analysis of the material composition in different building elements (such as foundation, external walls, internal walls, windows, doors, ceilings, roof). The information about the category composition of the dwelling stock (building typology) and the material composition of the categories and their elements can be aggregated to data about the material composition of the entire dwelling stock (Fig. 4c and circles in Fig. 5d). This approach was applied, among others, by Gruhler et al. (2002) for Eastern Germany, by Kohler et al. (1999) in Germany, and by TNO (1999) in the Netherlands. Spengler et al. (1997) compare demolition waste from complete selective dismantling of the domestic buildings in different communities in Alsace (France) and Baden (Germany). The top-down approach uses information about the annual consumption of construction materials used for new dwelling construction, divided by the annually produced UFA. In the case of concrete, the annual consumption used for new dwellings can be calculated on the basis of overall concrete production data and estimates of the share that is used for dwelling construction. Overall concrete production can be computed by the apparent use of cement (Fig. 5c) and the average cement content in concrete (here assumed to be 11%). The apparent use of cement is obtained directly from statistics (UN/ECE bulletin of housing and building statistics of various years), and calculated as production (data from CBS, 2001) plus import minus export (both derived from the UN Comtrade database). Fig. 5d shows a graph with the total concrete production per dwelling UFA and the estimated effective concrete use per dwelling UFA. The share of concrete used for dwelling construction seems to be fairly constant around one third of the overall concrete production. A top-down approach for concrete in dwellings was earlier applied by Redle (1999) for a Swiss Lowland region. The obtained results for this Swiss Lowland region and the Netherlands are very similar. The diffusion of concrete in dwellings can be disaggregated into two parallel diffusion processes: the diffusion of dwellings and the diffusion of the concrete technology in dwelling construction. In the phase from about 1950–1970, both dwelling construction and concrete use per UFA were increasing, contributing to the strong growth in cement use. From the 1970s to the end of the 20th century, dwelling construction decreased by a factor of two, while concrete density in dwellings was still increasing, leading to stagnation in cement use. The very recent and strong decrease of cement use is not yet reflected in the concrete density of the vintage class 1990– 2000, but might well become significant in the longer term,

149

which is assessed with the parameter variation (Section 3.5). As experiences with diffusion processes (e.g., lead in water pipelines) show, new developments might eventually rule out concrete use by substituting it with new materials, or these can decrease the concrete density. For the 21st century, the medium variant assumes a saturation of concrete density on a level of 2.1 t/m2 UFA, the low variant assumes a decrease, and the high variant a further increase of the concrete use per new dwelling UFA (Fig. 4c). A decrease in concrete use per UFA could result from enhanced material performance (material efficiency), consumer preferences (style), or from relative prices of substitutable raw materials5.

3.4.

Simulation of the standard scenario

Eqs. (1)–(8) were programmed on MATLAB Simulink, using the Dormand-Prince solver with variable steps. In order to produce reasonable initial conditions, the model was run for an extended period from 1850 to 2100, although only the period of 1900–2100 is illustrated here. The simulation results for the standard scenario, which represents the medium variant for all parameter functions, are illustrated in Fig. 6. The graphs show input, output, and stock of service units (dwelling UFA) and materials.

3.4.1.

Useful floor area

The input of UFA peaks in the 1970s and then steadily falls to about 30% of this peak in the mid of the 21st century, and has a second, lower peak in the second half of the 21st century. The output of UFA progressively increases, with a peak that coincides with the second input peak. Input and output of UFA work in the 21st century in opposite direction. This can be explained with a coincidence of two factors: (1) the saturation of the UFA causes a reduced input, and (2) the lifetime of the dwellings is long enough to push the output wave to coincide with the reduced input. This has significant implications for resource management, as is shown later on. The stock change of UFA is calculated as input minus output. In the 20th century, the stock change is very similar to the input curve, because the output is not yet significant. However, in the 21st century the net addition to the stock is falling much faster than the input, and stabilizes near zero around 2040. In other words, in the 20th century the input of new dwellings leads to a net addition of the stock (growth), while in the 21st century the input of new dwellings is increasingly used up for replacement of retired dwellings. The overall UFA stock is the integral of the stock change, which in this scenario assumed to reach saturation in the first half of the 21st century.

5 For example, a carbon dioxide tax of 25 per ton CO2 would lead to increases in cement prices of roughly 20%, rising concrete prices by about 2–3%. Considering that potential substitutes for concrete like brick or steel are also energy intensive, carbon taxes are unlikely to be the dominant factor for substitution in this case.

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Input and output of UFA 6 2 18 x 10 m /a 16 (a) 14 12 new UFA 10 8 6 4 2 retired UFA 0 1900 1950 2000 2050 2100 6 25 x 10 t/a

20

Input and output concrete

(d)

Stock change UFA 2 6 16 x 10 m /a 14 (b) 12 10 8 6 4 2 0 -2 1900 1950 2000 2050 6 25x 10 t/a

Construction

20

6 2 Stock UFA 1000 x 10 m 900 (c) 800 700 600 500 400 300 200 100 0 2100 1900 1950 2000 2050

Stock change concrete

x 106 t 1500

(e)

(f)

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Stock concrete

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10 10 500

5 5 Demolition 0 1900

1950

2000

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0 -5 1900

1950

2000

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0 1900

1950

2000

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Fig. 6 – Simulation result for the medium variant.

3.4.2.

Concrete

The simulation results for concrete show a behaviour that is similar to the UFA results. However, the increasing use of concrete, which coincides with the construction boom in the second half of the 20th century, further amplifies the increase in input. The peak is therefore delayed in the 1980s, and the decrease to about 40% of the peak is to some extent absorbed by the increasing concrete use per UFA. The stock change for materials is an indicator of the use of primary resources. The output of demolition waste can theoretically be used as a secondary resource. In the case of concrete, there are technologies to crush the used concrete and use it as an aggregate. If all end of life concrete was recycled within the dwelling system, the (net) stock change would equal the input of primary concrete aggregates6. The stock change of concrete decreases more smoothly than the stock change of UFA, and reaches zero at the end of the 21st century. The overall stock of concrete in dwellings is further increasing in the 21st century, and saturates only at the end of the 21st century.

3.5.

Parameter variation

The model simulations of the previous section are based on the medium variant for all parameter functions. As there are significant uncertainties regarding how these determinants will behave in the future, it is important to understand their influence on the system. In this section, the affect of each

6 Crushed concrete can be used for other purposes than dwellings. A more realistic indication of the primary aggregate consumption would require a wider system boundary that includes the entire lifecycle of aggregates, including quantifications of all use segments (such as non-residential buildings, infrastructures, etc.).

(m) determinant (K(s) c , Ms , L) is tested individually for all combinations of low, medium, and high variants (Figs. 7–9). Not all combinations lead to realistic scenarios: The combination of “UFA low” and “lifetime high” (graphs on the bottom of Fig. 7) is physically impossible, because the shrinking UFA cannot be achieved with the long lifetimes assumed, which results in negative construction activities. The widespread of parameter assumptions is chosen to capture a large range of possible scenarios. The medium variant for all determinants (here the middle graph in Fig. 8) is considered as the most likely; however, this involves a personal judgement that can be challenged. By making the assumptions and their effects explicit, the reader has the chance to build up his or her own judgement and to see the consequences of these assumptions. The results are illustrated only for concrete input (construction) and concrete output (demolition). The result is a 3dimensional matrix with three elements in each direction. Fig. 7 shows all combinations for the low variant of UFA (shrinking dwelling stock), Fig. 8 for the medium variant of UFA (saturation of dwelling stock), and Fig. 9 for the high variant of UFA (increasing dwelling stock). The influence of the average lifetime can be tested by comparing the graphs in columns, the impact of concrete density by looking at the graphs in the same row, and the effect of UFA by observing the differences among corresponding graphs in Figs. 7–9.

3.5.1.

Influence of the average lifetime

The lifetime has an impact on the delay of the demolition flow compared to the peak of construction. It also delays the second construction peak, caused by replacements. And thirdly, it has an effect on the height of both the demolition and the second construction peaks. The first construction peak is little affected by the lifetime; the role of the lifetime becomes dominant only in the 21st century.

x 108 m2

16 14 12 10 8 6 4 2 0 1900

UFA low

1950

2000

t/m2 3

2050

Lifetime short 0.03

0.01

0 0

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100

150

200

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0.02

0.01

0 0

50

100

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200

2.5 2

2

1.5

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0.02

0.01

00

50

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1

1

1

0.5

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0.5

1950

2000

2050

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2100

C. density high

t/m2 3

2

1950

2000

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2000

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7 4.5 x 10 t/a 4 3.5 3 Construction 2.5 2 1.5 1 0.5 0 1900 7 1950 2000 4.5 x 10 t/a

7 4.5 x 10 t/a 4 3.5 3 Construction 2.5 Demolition 2 1.5 1 0.5 0 2050 2100 1900 7 1950 2000 4.5 x 10 t/a

7 4.5 x 10 t/a 4 3.5 3 Construction 2.5 Demolition 2 1.5 1 Demolition 0.5 0 2050 2100 1900 7 1950 2000 2050 2100 4.5 x 10 t/a

4 3.5 3 Construction 2.5 2 1.5 1 0.5 0 1900 1950 2000

4 3.5 3 Construction 2.5 2 Demolition 1.5 1 0.5 0 2050 2100 1900 1950 2000

4 3.5 3 Construction 2.5 2 Demolition 1.5 1 0.5 0 2050 2100 1900 1950 2000

7 4.5 x 10 t/a

0.03

C. density medium

4 3.5 3 2.5 2 1.5 1 0.5 0 1900

7 4.5 x 10 t/a

4 3.5 3 Construction 2.5 2 1.5 Demolition 1 0.5 0 1950 2000 2050 2100 1900

le

Im

p

ib s s o

Demolition

2050

2100

7 4.5 x 10 t/a

4 3.5 3 Construction 2.5 2 1.5 Demolition 1 0.5 0 1950 2000 2050 2100 1900

le

Im

p

ib s s o

p

1950

le

ib oss

Construction

Im

EC O L O G IC A L E C O N O M IC S 5 9 ( 2 0 06 ) 14 2 –1 56

0.02

t/m2 3

2.5

0 1900

2100

C. density low

2000

Demolition

2050

2100

151

Fig. 7 – Concrete input (construction) and output (demolition) in tons per year, as influenced by lifetime and concrete density variations, for a “UFA low” scenario (shrinking dwelling stock).

152

x 108 m2

16 14 12 10 8 6 4 2 0 1900

UFA medium

t/m2 3

2000

2050

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0.02

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00

50

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x 10 7 4.5 4 3.5 Construction 3 2.5 2 1.5 1 Demolition 0.5 0 1950 2000 2050 2100 1900 t/a x 10 7 4.5 4 3.5 3 Construction 2.5 2 1.5 1 0.5 Demolition 0 1950 2000 2050 2100 1900

t/a

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1

0 1900

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2000

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Construction

Demolition 1950

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2100

x 10 7 4.5 4 3.5 Construction 3 2.5 2 1.5 1 Demolition 0.5 0 1950 2000 2050 2100 1900 t/a x 10 7 4.5 4 3.5 3 Construction 2.5 2 1.5 1 0.5 Demolition 0 1950 2000 2050 2100 1900

t/a

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2100

t/a

Construction

Demolition 1950 t/a

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Construction

Demolition 1950

2000

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2100

x 10 7 t/a

x 10 7 t/a

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 2100 1900

C. density high

Construction

Demolition 1950

2000

2050

4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 2100 1900

Construction

Demolition 1950

2000

2050

2100

Fig. 8 – Concrete input (construction) and output (demolition) in tons per year, as influenced by lifetime and concrete density variations, for a “UFA medium” scenario (stabilizing dwelling stock).

EC O LO GIC A L E CO N O M ICS 5 9 ( 2 00 6 ) 1 4 2 –1 56

0.02

0.03

2.5

2100

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t/m2 3

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1

1950

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C. density low

x 108 m2 UFA high 16 14 12 10 8 6 4 2 01900 1950 2000 2050

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4.5 x 10 4 3.5 3 2.5 2 1.5 1 0.5 0 1900 7 4.5 x 10 4 3.5 3 2.5 2 1.5 1 0.5 0 1900

1950

2000

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0.02

0.01

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50

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t/a

9 x 10 8 7 Construction 6 5 4 3 2 Demolition 1 0 1950 2000 2050 2100 1900 7 t/a 4.5 x 10 4 3.5 3 Construction 2.5 2 1.5 1 0.5 Demolition 0 1950 2000 2050 2100 1900

1950

2000

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Demolition 1950

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4 3.5 3 2.5 2 1.5 1 0.5 0 2100 1900

0 1900

2100

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7 9 x 10 t/a 8 7 6 5 4 Construction Construction 3 2 1 Demolition Demolition 0 1950 2000 2050 2100 1950 2000 2050 2100 1900 7 t/a 9 x 10 t/a

t/a

Construction

1950

2000

8 7 6 5 4 3 2 1 Demolition 0 2050 2100 1900

7 4.5 x 10 t/a

7 4.5 x 10 t/a

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C. density high

Construction Demolition

1950

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7 9 x 10 t/a

Construction

Demolition 1950

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8 7 6 5 4 3 2 1 0 2100 1900

EC O L O G IC A L E C O N O M IC S 5 9 ( 2 0 06 ) 14 2 –1 56

0.02

t/m2 3

2

7

Lifetime short

density medium

2.5

2100

0.03

t/m2 C. 3

C. density low

Construction Demolition 1950

2000

2050

2100

153

Fig. 9 – Concrete input (construction) and output (demolition) in tons per year, as influenced by lifetime and concrete density variations, for a “UFA high” scenario (growing dwelling stock).

154 3.5.2.

EC O LO GIC A L E CO N O M ICS 5 9 ( 2 00 6 ) 1 4 2 –1 56

Influence of concrete density

The effect of changing concrete densities lies in an amplification of the general trend of the construction and demolition curves. However, the effect on the demolition is delayed by the lifetime. A decreasing concrete density can cause a surplus of demolition waste compared to the needs for construction.

3.5.3.

Influence of UFA

The shape of the UFA stock determines the general shape of the construction and demolition curves. The more accentuated the saturation of the UFA, the stronger is the wave phenomenon of construction and demolition. Furthermore, a shrinking UFA causes significant demolition waste flows that can surpass construction needs.

3.5.4.

Commonalities

Although these calculations show a wide variety of combinations, there are some important commonalities. 1. Construction and demolition curves show a wave characteristic. Both construction and demolition flows follow a longterm fluctuation. The cyclical behaviour is even observable in the case of a further growth of the UFA. The reason for this wave phenomenon lies in the long average lifetime of dwellings and the relatively short time span of the diffusion of a large part of the dwelling stock in the 20th century. In other words, due to the long lifetime of dwellings, demolition waste was low through the entire period of dwelling stock growth in the second half of the 20th century, and will pick up only in the first half of the 21st century. 2. Construction and demolition are phase displaced at the beginning of the 21st century. For almost all combinations, construction has a peak at the end of the 20th century and decreases in the first half of the 21st century, while demolition is insignificant in the 20th century and progressively increases in the first half of the 21st century. This has significant consequences for waste management, recycling technologies, and primary raw material mining. The reason for the phase displacement lies in a coincidence of two factors: the saturation of the dwelling stock causes a decrease in the amount of concrete and other raw materials used, while the lifetime of the dwellings is long enough to delay demolition so that it occurs at a time of decreasing construction. In the second half of the 21st century, most combinations of parameters show a transition to a more parallel course of construction and demolition. 3. Growth is becoming more expensive. For almost all scenarios, demolition is increasing in the first half of the 21st century. In order to maintain a constant stock of UFA, all demolished buildings need to be replaced. The increasing replacement needs use up an increasing amount of the input. A continuation of the current growth rate of the UFA (“UFA high”) would cause progressively higher concrete demands even if the concrete use per UFA remains constant (assuming an average lifetime of 90 years, concrete demand would double until 2070). The increase in material demand is caused by the increasing resource demand for replacement.

4.

Discussion and conclusions

4.1.

Stocks: driving flows or driven by flows?

The results endorse the initial hypothesis that stocks in use play a prominent role in understanding long-term changes of societal metabolism. In contrast to most economic methods, which focus on flows and implicitly assume that stocks are driven by flows, the stock dynamics approach presented here uses the stock of service units in use as one of the drivers for material flows, switching cause and effect. This switch is motivated by the presumptions that the stocks in use reflect better quality of life than the input flows into use, and that they provide in many cases a better basis for the analysis of saturation and substitution effects. The relation between stocks and services made here for buildings needs to be critically questioned for applications with other goods such as energy carriers or food, as their services (for example ensuring homeostasis of a constant room or body temperature) depends on a continuous flow. The question as to whether stocks drive flows or vice versa is thus not always easy to answer, and might also depend on whether the focus of the question is short- or long-term. In nature, the rocks shape the water in the short-term, but in the long-term, it is the water that shapes the rocks.

4.2.

Do stocks follow long-term patterns?

Stocks are essentially integrals of flows, meaning that relatively small changes in stocks have significant consequences for the flows. As the model presented uses stocks of service units in use to determine flows, and precise estimations of the development of stocks are impossible, this model approach has significant shortcomings with respect to determining short-term changes. In the long-term, however, there are indications that stocks of service units follow certain patterns. Grübler and Nakićenović (1996) investigated long-term patterns of transport infrastructures in the context of long-wave theory. They showed that economic long-term cycles are linked with the diffusion of innovations, which they exemplified with infrastructures measured in terms of length of canals, railways, and roads in use, parameters that correspond to the concept of stocks of service units. They further observed that the diffusion of these infrastructure service unit stocks follows a characteristic pattern of emergence, growth, and saturation. These findings cannot be transferred directly to dwellings, as buildings as such are not new innovations, and their emergence lies for most areas far back in time7. For the quantity of overall material flows, however, emergence is less relevant than the question as to whether or not saturation occurs, and on what level possible saturation takes place.

7 Innovations of building technology are not related to the service units provided (UFA), but to the use of materials, which is related to share of the material flows related to the yearly produced building UFA, and is flow related.

EC O L O G IC A L E C O N O M IC S 5 9 ( 2 0 06 ) 14 2 –1 56

Although it is practically impossible to determine the exact level of saturation in advance, it is important from a resource management perspective to understand that saturation and substitution can occur, with corresponding implications for material cycles. The stock dynamics approach can be used as a bridge between diffusion scenarios and their metabolic implications.

4.3.

Implications for stock dynamics research

The stock dynamics approach presented here integrates the concept of services into a dynamic material flow model. By using the population and its lifestyle as the central driving forces of material cycles, it regards the demand for end products not as an end in itself, but as a mean to acquire and maintain a stock in use that fulfils the changing needs for services. From a physical perspective, the lifestyle manifests itself in a stock of goods, which is maintained and renewed by acquiring new products and by disposing of undesired or used products. Further research is required to analyse the qualitative and quantitative relationships between lifestyles, services, and stocks in use. Further research into the analysis of anthropogenic stocks should be a priority for environmental policy for the following reasons: 1. Anthropogenic stocks are becoming the most relevant resource providers. While primary resources are getting increasingly scarce, require increasing amounts of energy for their extraction, or their mining faces political opposition, the stocks built up in the latter half of the 20th century are reaching end of life and are becoming available as potential secondary resources. Decreasing our dependence on primary resources requires efficient recycling, which involves reliable knowledge of the stocks in use. 2. Anthropogenic stocks are important drivers for resource and energy demand as well as waste and emission generation. Scenarios based on stock models can be used by policy makers to assess environmental implications of demands for in use stocks, such as housing and infrastructures, and to find a balance between the needs for services and their environmental consequences. 3. Anthropogenic stocks are the parts of the material cycles that are usually least understood, both in terms of quantities and their dynamics. Compared with the exploration of primary resources, there is very little systematic knowledge about the genesis, the locations, and the forms of secondary resources.

Acknowledgement For critical comments and many fruitful discussions I would like to thank Helge Brattebø, Robert Gordon, Thomas Graedel, Arnulf Grübler, Reid Lifset, and Barbara Reck. The conceptual development of this project was developed by the first author at the Interfaculty Research Program “Design and Management of Infrastructures” at the TU Delft, for which I wish to thank Margot Weijnen for her support.

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