Top-Down: City-Systems (Urban Metabolism)

The Urban Metabolism (UM) module aims to describe the resource flows of a city-system at an aggregated level with the use of input-output tables.

This module aims to provide:

1. A framework for the description of resource flows;
2. A description of macro-level drivers for the changes of these flows; and
3. A description of linkages between different resource flows.

The advantgage of this library module–and of this python library– is that each module can be used independently. The UM module can be run independently from the rest of the library.

The library is structured as two types of functions:

1. A function dedicated to the description of a city and city-data, see city.
2. Resource flow specific classes:
   • Materials & api: Materials
   • Water & api: Water
   • Consumption model: Energy & api: Energy
   • Food & api: Food
   • Waste & api: Waste

For each of these classes a Unified Modeling Language (UML) class diagram has been generated.

The description of the individual functions of this module can be found below under: API: Top-Down (Urban Metabolism).

Consumption model: Energy

Energy Class: Energy Flow

“Energy flow is the ultimate of the urban metabolism. The magnitude of energy flows from heating and cooling are typically related to climate, but other components of urban energy use can be linked back to the shape and form of a city, reflected by its infrastructure systems and hence material stocks. (Kennedy.2012)”

\[I_{E} = I_{E,buildings} + I_{E,transport} + I_{E,industry} + I_{E,construction} + I_{E,water pumping} + I_{E,waste}\]

The total energy demand of a city is expressed as the total sum of all energy demands for the different energy sectors. Each energy sector energy demand is calculated, based on different components that are the cause of energy consumed.

Buildings: For the building sector the total energy consumption is computed based on climatic conditions of the city (\(HDD\) and \(CDD\)) and energy consumption intensities based on building type.

\[I_{E,buildings} = I_{E,heating} + I_{E,cooling} + I_{E,light-and-appl.} + I_{E,water-heating}\]

\[I_{E,heating} = \sum_{building-type} HDD * i_{E,heating} * P * f\]

\[I_{E,cooling} = \sum_{building-type} CDD * i_{E,cooling} * P * f * cp\]

Where:

• \(HDD\) Heating degree days.
• \(CDD\) Cooling degree days.
• \(i_{E,cooling}\) heating intensity.
• \(i_{E,heating}\) cooling intensity.
• \(P\) Population of the urban agglomeration.
• \(f\) Floor space area per capita.
• \(cp\)

Transport: The total energy demand for the transport sector is computed based on the different types of transportation observed within the analyzed system:

\[I_{E,transport} = I_{E,passenger} + I_{E,freight} + I_{E,aviation} + I_{E,marine}\]

When anaylzing a city the first xx (Summand) surface passenger transport will be the most relevant. For this transportation category the energy demand is calculated based on the different types of passenger transport found in the city:

\[I_{E,passenger} = \sum_{mode} \frac{1}{P_p} * P * \rho_i * h * \varepsilon\]

Where:

• \(mode\)
• \(P_p\) Average population density \([km^{-2}]\).
• \(\rho_i\) Density of transportation infrastructure \([km * km^{-2}]\).
• \(h\) utilization intensity of infrastructure \([\text{veh-}km * km^{-2}]\).
• \(\varepsilon\) Fuel efficiency \([J*\text{veh-}km^{-1}]\).

The product of the first four terms within the summation is equivalent to the vehicle-kilometers traveled (VKT):

\[VKT = \frac{1}{P_p} * P * \rho_i * h\]

A widely used city indicator when analyzing sustainability in urban environments.

Energy surface balance (NOT IMPLEMENTED):

\[I_{E,S} + I_{E,F} + I_{E,I} = O_{E,L} + O_{E,G} + O_{E,E}\]

Where:

• \(I_{E,S}\) Rate of arrival of radiant energy from the sun.
• \(I_{E,F}\) Rate of generation of heat due to combustion and dissipation in machinery.
• \(I_{E,I}\) Rate of heat arrival from the earth’s interior.
• \(O_{E,L}\) Rate of loss of heat by evapotranspiration.
• \(O_{E,G}\) Rate of loss of heat by conduction to soil, buildings, roads, etc.
• \(O_{E,E}\) Rate of loss of heat by radiation.

Energy class: Stock

This class defines the existing energy stock by sector.

All energy streams are aggregated by sector.

A data-set with the detail energy stream is generated as a csv file and stored under the /results folder.

The Energy Stock is computed as follows:

Water

Water class: Water Demand

Similar to Energy Flow, Water Demand is computed as the sum of different water consumers. In a city most water is consumed at the building level. Therefore total Water Demand (\(Q_W\)) is determined based on residential and non-residential water demand.

\[Q_W = Q^{hh}_{W,D} + Q^{nr}_{W,D}\]

Where:

• \(Q^{hh}_{W,D}\) Household water consumption.
• \(Q^{nr}_{W,D}\) Non-Residential water consumption.

** Residential Water Demand:** The residential water demand or household demand model is computed as function of the following indicators:

• Demographic characteristics of the household.
• Disposable income of the household.
• Average water price in the city.
• Water saving penetration rate (SP) Yuan, X.-C. et al. (2014).
• Water saving rate (SR) Yuan, X.-C. et al. (2014).

\[Q^{hh}_{W,D} = \beta_0 + \sum^{n}_{i} \beta_i HH_{i} + \beta_y Y_{hh,$} + \beta_p P_{$} + \epsilon\]

Where:

• \(Q^{hh}_{W,D}\) Household water consumption.
• \(HH\) Household characteristic.
• \(Y_{hh,$}\) Household income.
• \(P_{W,$}\) Water price.
• \(\beta_i\)
• \(\epsilon_{err}\) Random error term.

Depending on the water tariff in place the variable \(P_{W,$}\) cannot be modeled as a dependent variable. If the water tariff is computed as a function of consumed volume, the error term cannot be assumed.

The Household characteristics (\(HH\)) are based on data availability and the definitions made within the water consumption.

Efficiency rate:

The water saving penetration (\(SP\)) and water saving rate (\(SR\)) are computed at each simulation step. The water saving rate is an indicator for governmental actions to reduce water consumption. And the penetration rate is the likelihood that a household has adopted the respective the water saving behaviour or technology.

\[\begin{split}Q_{W,D}^{base}(SP_{W,D}, SR_{W,D}) = \begin{cases} Q_{W,D}^{hh} \times (1-SR_{W,D}) & \quad \text{if } rand < SP_{W,D}\\ Q_{W,D}^{hh} & \quad \text{ else}\\ \end{cases}\end{split}\]

Where:

• \(Q^{base}_{W,D}\) Base water consumption.
• \(SP_{W,D}\) Water saving penetration rate.
• \(SR_{W,D}\) Water saving rate.

Non-residential Water Demand: The non-residential water demand model is defined as the sum of (source: DGNB):

• Water consumption by buildings occupants. \(Q^{nr}_{DU}\)
• Water consumption for cleaning. \(Q^{nr}_{DC}\)
• Water consumption by spa facilities. \(Q^{nr}_{DS}\)
• Water consumption by laundering facilities. \(Q^{nr}_{DL}\) (not implemented)

\[Q^{nr}_{W,D} = Q^{nr}_{W,DU} + Q^{nr}_{W,DC} + Q^{nr}_{W,DS} + Q^{nr}_{W,DL}\]

Where:

\[Q^{nr}_{W,DU} = \sum_{i=1}^{n} wb_I\]

\[wb_I = \left(n_{NU} \times f_{I} \times as_{I} \times d/a \right) / 1000\]

Where:

• \(n_{NU}\) Number of users/occupants/employees/visitors/customers
• \(f_I\) Installation factor of equipment (see Tab. W1) \([s/d]\)
• \(as_I\) Equipment water demand factor (see Tab. W2) \([l/u]\)
• \(d\) Occupancy rate in days

Table 1 Tab. W1. Installed equipment factors \(f_I\)

Equipment	Office	Hospital (number of beds (number of beds \(n_{e}\))			Commerce		Hotel (single \(n_{ez}\), double \(n_{dz}\))	Residential
	Employee	Employee	Patient	Visitor	Employee	Customer	Customer	Occupant
\(n_{NU}\)			\(0.8 * n_{e}\)	\(0.5 * 0.8 * n_{e}\)			\((n_{ez} + (n_{DZ} * 1.2)) * 0.65\)
Toilet sink	75	45	135	15	45	15	75	195
WC-Saving	4	1	2	0.5	1	0.3	1	4
WC	1	1	1	0.5	1	0.5	1	1
Urinal	4	1		0.5	1	0.2	1
Shower	30	60	90		30			120
Kitchen sink	20	20			20
Sink-Spa							15
WC-Saving-Spa							1
Shower-Spa							600
Dishwasher								0.5
Washing machine								0.25

Table 2 Tab. W2. Water demand factors

Equipment	Office	Hospital	Commerce	Hotel	Residential
Toilet sink \([l/s]\)	0.15	0.15	0.15	0.15	0.15
WC-Saving \([l/u]\)	4.5	4.5	4.5	4.5	4.5
WC \([l/u]\)	9	9	9	9	9
Urinal \([l/u]\)	3	3
Shower \([l/s]\)	0.25	0.25	0.25	0.25	0.25
Bathtub \([l/u]\)					Capacity
Kitchen sink \([l/s]\)		0.25	0.25
Dishwasher \([l/u]\)					20
Washing machine \([l/u]\)					60

\[Q^{nr}_{W,DC} = \sum_{i = 1}^n \left(A_{R,i} \times wb_{R/A} \right) / 1000\]

\[Q^{nr}_{W,DS} = \sum_{i = 1}^n wb_I\]

\[wb_I = \left( n_{SPA} \times f_I \times as_I \times 360 d/a \right) / 1000\]

\[n_{SPA} = n_{NU} \times 0.25\]

\[Q^{nr}_{W,DL} = \sum_{i = 1}^n wb_I\]

Where:

• \(A_R\) Cleaning floor space \([m^3/a]\)
• \(wb_R\) Water demand per cleaning area (see Tab. W3) \([l/(m^2 \times a)]\)
• \(wb_I\) Specific water demand of spa/laundry installations (see Tab. W1 and Tab. W2) \([m^3/a]\)

Table 3 Tab. W3. Water demand per cleaning area. \(wb_R\) in \([l/m^2a]\)

Type of area	Frequency	Office	Hospital	Commerce	Hotel	Residential
Floor	1 x Month	1.50	1.50	1.50	1.50	1.50
	1 x Week	6.25	6.25	6.25	6.25	6.25
	3 x Week	18.75	18.75	18.75		18.75
	4.5 x Week				28.125
	5 x Week		31.25
	6 x Week		37.50	37.50
	7 x Week		43.75		43.75
Glass surface	2 x Year	0.60				0.60
	4 x Year	1.20	1.20	1.20	1.20	1,20
	6 x Year	1.80				1.80
	12 x Year		3.60	3.60	3.60
	24 x Year			7.20	7.20

Flow

This water flow is balanced as follows:

\[I_{W,percip} + I_{W,pipe} + I_{W,sw} + I_{W,gw} = O_{W,evap} + O_{W,out} + \Delta S_w\]

Where:

• \(I_{W,percip}\) Is natural inflow from precipitation.
• \(I_{W,pipe}\) Is water piped into the city.
• \(I_{W,sw}\) Is the net surface water flow into the city.
• \(I_{W,gw}\) Is the net ground water flow into city aquifers.
• \(O_{W,evap}\) Evapotranspiration.
• \(O_{W,out}\) Water piped out of cities
• \(\Delta S_w\) Change in water storage of urban agglomeration.

Anthropogenic Water Use:

The anthropogenic water consumption is computed as follows:

\[Q_W = Q_{W,D} + Q_{W,L}\]

Where:

• \(Q_{W,D}\) Water demand.
• \(Q_{W,L}\) Water losses.

\[Q_{W,D} = \sum_{hh} Q^{base}_{W,D,hh} + CDD * i^{cooling}_W\]

Where:

• \(Q^{base}_{W,D}\) Base water consumption.
• \(CDD\) Cooling Degree Days.
• \(i^{cooling}_W\) Intensity of water use for cooling.

\[Q_{W,L} + A * p_{ti} * l\]

Where:

• \(Q_{W,L}\) Water losses.
• \(A\) Surface area of urban agglomeration.
• \(p^{ti}\) Density of urban infrastructure.
• \(l\) Annual leakage rate per length of linear infrastructure.

\[Q_{WWT} = Q_{WWE} + Q_{WWF} + Q_{INF}\]

Where:

• \(Q_{WWT}\) Treated waste water.
• \(Q_{WWE}\) Generated waste water.
• \(Q_{WWF}\) Wet weather water flow.
• \(Q_{INF}\) Base infiltration.

Urban Aquifers:

\[\Delta S_{W,gw} = \Delta Q_{W,RO} + Q_{W,ar} + \Delta I_{W,gw} - \Delta Q_{W,DO} - Q_{W,gwpump}\]

Where:

• \(\Delta S_{W,gw}\) Change in ground water storage of urban agglomeration.
• \(\Delta Q_{W,RO}\) Change in natural recharge from virgin conditions.
• \(Q_{W,ar}\) Net anthropogenic urban water recharge rate.
• \(\Delta I_{W,gw}\) Net change on ground-water inflow.
• \(\Delta Q_{W,DO}\) Change in natural discharge from virgin conditions.
• \(Q_{W,gwpump}\) Net pump rate of urban agglomeration.

Internal Renewable Water Resources (IRWR)

\[IRWR = S_{W,sw} + S_{W,gw} - S_{W,overlap}\]

External Renewable Water Resources (ERWR)

\[ERWR = I_{W,sw} - O_{W,sw} + I_{W,gw} - O_{W,gw}\]

Total Renewable Water Resources (TRWR)

\[TRWR = (S_{W,sw} + I_{W,sw} - O_{W,sw}) + (S_{W,gw} + I_{W,gw} - O_{W,gw}) - S_{W,overlap}\]

Where:

• \(S_{W,sw}\) Surface water, produced internally.
• \(S_{W,gw}\) Groudwater, produced internally.
• \(S_{W,overlap}\) Overlap between surface water and groundwater.

Stock

Materials

Flow

Stock

All material streams are aggregated by sector.

A data-set will the detail material stream is generated as a csv file and stored under the /results folder.

The Material Stock is computed as follows:

\[S_M = \sum_s \sum_m S^s_{M,m}\]

The total materials stock of a city is expressed as the total sum of all type of materials \(m\) of all urban structures \(s\).

\[S^{rb}_{M,m} = P * f^{rb} * i^{rb}_{M,m}\]

Where:

• \(S^{rb}_{M,m}\) Material stock of residential buildings.
• \(P\) Population of the urban agglomeration.
• \(f^{rb}\) Per-capita floor space for residential buildings.
• \(i^{rb}_{M,m}\) Material intensity per squared meter.

\[S^{ti}_{M,m} = A * p^{ti} * i^{ti}_{M,m}\]

Where:

• \(S^{ti}_{M,m}\) Material amount in linear transportation infrastructure.
• \(A\) Surface area of urban agglomeration.
• \(p^{ti}\) Density of urban infrastructure.
• \(i^{ti}_{M,m}\) Material intensity per kilometer of urban infrastructure.

Waste

Flow

Stock

Food

Demand

** Residential Food Demand:** The residential food demand or household demand model is computed as function of the following indicators:

• Demographic characteristics of the household.
• Disposable income of the household.

\[Q^{hh}_{F,D} = \beta_0 + \sum^{n}_{i} \beta_i HH_{i} + \beta_y Y_{hh,$} + \epsilon\]

Where:

• \(Q^{hh}_{F,D}\) Household food consumption.
• \(HH\) Household characteristic.
• \(Y_{hh,$}\) Household income.
• \(\beta_i\)
• \(\epsilon_{err}\) Random error term.

The Household characteristics (\(HH\)) are based on data availability and the definitions made within the food consumption.

Flow

\[I_F + P_F + I_{W,Kit} = O_{F,RetFW} + O_{F,ResFW} + O_{F,Met} + O_{F,S}\]

Where:

• \(I_F\) mass of food and packaged drinks imported to the city.
• \(P_F\) mass of food and packaged drinks produced in the city, for internal consumption.
• \(I_{W,Kit}\) mass of kitchen water used during food preparation or drunk during meals.
• \(O_{F,RetFW}\) mass of retail food waste produced by grocery stores and restaurants.
• \(O_{F,ResFW}\) mass of residential food waste going to landfill, compost, or organic waste collection.
• \(O_{F,Met}\) mass of carbon and water lost via respiration and transpiration in residents metabolism.
• \(O_{F,S}\) mass of feces and urine exported to sewerage system.

Stock