TP-03: External Conditions | HEM Reference

Overview

External conditions define the boundary temperatures and wind environment that drive the heat balance at each timestep. The ExternalConditions module supplies hourly air temperature, derives sky and ground temperatures for longwave radiation and ground floor heat loss, adjusts meteorological wind speed for local terrain roughness and altitude, and calculates operative temperature within thermal zones.

This page covers the temperature and wind processing within the ExternalConditions scope. Weather file parsing and simulation time indexing are documented in TP-01: Overview and Climate Data. Solar geometry and irradiance calculations are documented in TP-08: Solar Gains and Shading.

Inputs

Parameter	Symbol	Unit	Description
External air temperature	$T_{ai r}$	°C	Hourly time series from weather file (EPW)
Wind speed	$u_{10}$	m/s	Meteorological wind speed at 10 m height
Wind direction	$θ_{w in d}$	degrees	Direction from which wind blows (0° = North, clockwise)
Site altitude	$h_{a l t}$	m	Altitude of the building site above sea level
Terrain class	—	—	One of: OpenWater, OpenField, Suburban, Urban
Zone base height	$z_{ba se}$	m	Height of the base of the ventilation zone above ground
Zone height	$H_{z o n e}$	m	Height of the ventilation zone
Thermal resistance of unconditioned space	$R_{u}$	m²K/W	Effective thermal resistance of an adjacent unheated space
Sky-air temperature difference	$Δ T_{s k y}$	K	Difference between external air and sky temperatures
Element pitch	—	degrees	Tilt of the building element from horizontal
Element area	$A$	m²	Gross area of each building element in the zone

Calculation

Air Temperature

The external air temperature at each timestep is read directly from the hourly weather data series:

$T_{ai r} (t) = T_{ai r, d a t a} [t]$

The model also derives several temporal averages used by other calculations.

Annual mean air temperature. The arithmetic mean over all 8760 hourly values in the weather file:

$\overset{ˉ}{T}_{ai r, ann u a l} = \frac{1}{8760} \sum_{t = 0}^{8759} T_{ai r} (t)$

Monthly mean air temperature. The arithmetic mean of the hourly temperatures within the current calendar month:

$\overset{ˉ}{T}_{ai r, m o n t h} = \frac{1}{n _{m o n t h}} \sum_{t = t_{s t a r t}}^{t_{e n d}} T_{ai r} (t)$

where $n_{m o n t h}$ is the number of hours in the month and $t_{s t a r t}$ , $t_{e n d}$ are the bounding hour indices.

Minimum daily average temperature. The lowest of the 365 daily mean temperatures across the year. Each daily mean is computed over 24 consecutive hourly values. This value is used in ground floor heat loss calculations (see TP-05: Fabric Heat Loss).

Sky Temperature

The sky temperature is not modelled as an explicit time series. Instead, the thermal radiation exchange between an external surface and the sky is represented as an additional heat loss term per unit area at the external surface node.

Following BS EN ISO 52016-1:2017, section 6.5.13.3, the extra thermal radiation to sky per unit area of building element is:

$Φ_{s k y} = F_{s k y} \cdot h_{r e} \cdot Δ T_{s k y}$

where:

$F_{s k y}$ is the longwave sky view factor for the element
$h_{r e} = 4.14$ W/(m²K) is the external radiative heat transfer coefficient (BS EN ISO 13789:2017, Table 8)
$Δ T_{s k y} = 11.0$ K is the default difference between air and sky temperature for an intermediate climatic region (BS EN ISO 52016-1:2017, Table B.19)

The sky view factor depends on the element pitch $β$ (in degrees, where 0° is a horizontal ceiling and 90° is a vertical wall):

$F_{s k y} = \frac{1 + c o s β}{2}$

This gives $F_{s k y} = 1.0$ for a horizontal roof, $F_{s k y} = 0.5$ for a vertical wall, and $F_{s k y} = 0.0$ for a floor. The term $Φ_{s k y}$ enters the external node heat balance equation as described in TP-04: Space Heating Demand.

Ground Temperature for Ground Floor Elements

Ground floor elements do not use the external air temperature directly. Instead, a virtual ground temperature is calculated at each timestep using the periodic heat transfer method from BS EN ISO 13370:2017, Annex C.

The monthly heat flow through the ground floor is (BS EN ISO 13370:2017, Eqn C.4):

$Φ_{g r o u n d, m o n t h} = U \cdot A \cdot (\overset{ˉ}{T}_{in t, ann u a l} - \overset{ˉ}{T}_{ai r, ann u a l}) + P \cdot ψ_{w a l l - f l oor} \cdot (T_{in t, m o n t h} - T_{ai r, m o n t h}) - H_{p i} \cdot (\overset{ˉ}{T}_{in t, ann u a l} - T_{in t, m o n t h}) + H_{p e} \cdot (\overset{ˉ}{T}_{ai r, ann u a l} - T_{ai r, m o n t h})$

where:

$U$ is the ground floor steady-state U-value W/(m²K)
$A$ is the total floor area m²
$P$ is the exposed perimeter m
$ψ_{w a l l - f l oor}$ is the wall-floor junction linear thermal transmittance W/(mK)
$\overset{ˉ}{T}_{in t, ann u a l}$ is the annual mean internal temperature °C
$T_{in t, m o n t h}$ , $T_{ai r, m o n t h}$ are monthly mean internal and external air temperatures °C
$H_{p i}$ , $H_{p e}$ are internal and external periodic heat transfer coefficients W/K

The virtual ground temperature is then derived (BS EN ISO 13370:2017, Eqn F.2):

$T_{g r o u n d, v i r t u a l} = T_{in t, m o n t h} - \frac{Φ _{g r o u n d, m o n t h} - P \cdot ψ _{w a l l - f l oor} \cdot ( T ˉ _{in t, ann u a l} - T ˉ _{ai r, ann u a l} )}{A \cdot U}$

This virtual temperature replaces $T_{ai r}$ at the external node of the ground floor element in the heat balance matrix, capturing the combined steady-state and periodic ground heat transfer.

Wind Speed Adjustment

Meteorological wind speed data is measured at a standard height of 10 m at a weather station whose terrain may differ from the building site. Two adjustments are applied: terrain roughness correction and air density correction for altitude.

Terrain Roughness Coefficient

The roughness coefficient $C_{R}$ corrects for the aerodynamic roughness of the terrain surrounding the building, following BS EN 1991-1-4 (Eurocode 1). Each terrain class is characterised by three parameters: the terrain factor $K_{R}$ , the roughness length $z_{0}$ m, and the minimum height $z_{min}$ m.

Terrain class	Description	$K_{R}$	$z_{0}$ (m)	$z_{min}$ (m)
OpenWater	Rough open sea, lake shore	0.17	0.01	2
OpenField	Farmland, small structures	0.19	0.05	4
Suburban	Suburban or industrial areas	0.22	0.3	8
Urban	Dense urban, tall buildings	0.24	1.0	16

The roughness coefficient at height $z$ is:

$C_{R} (z) = K_{R} \cdot ln (\frac{z}{z _{0}})$

where $z = max (z_{a c t u a l}, z_{min})$ and $z_{a c t u a l}$ is the height of the airflow path above ground. For ventilation calculations, this height is typically the mid-height of the ventilation zone:

$z_{a c t u a l} = z_{ba se} + \frac{H _{z o n e}}{2}$

Wind Speed at Zone Level

The meteorological wind speed is corrected from weather station conditions to building site conditions using the ratio of roughness and topography coefficients:

$u_{s i t e} = \frac{C _{R, s i t e} \cdot C _{T, s i t e}}{C _{R, m e t} \cdot C _{T, m e t}} \cdot u_{10}$

where:

$C_{R, s i t e}$ is the roughness coefficient at the building site at zone mid-height
$C_{T, s i t e}$ is the topography coefficient at the building site (default 1.0)
$C_{R, m e t}$ is the roughness coefficient at the weather station at 10 m (default 1.0)
$C_{T, m e t}$ is the topography coefficient at the weather station (default 1.0)

The default values of 1.0 for the meteorological coefficients assume the weather data is already representative of open terrain at 10 m, which is the standard condition for EPW files.

Air Density Adjustment for Altitude

Air density decreases with altitude, affecting infiltration and ventilation flow rates. The reference air density $ρ_{a, r e f}$ is adjusted for the site altitude $h_{a l t}$ above sea level:

$ρ_{a, a l t} = ρ_{a, r e f} \cdot (1 - \frac{0.00651 \cdot h _{a l t}}{293})^{4.255}$

This altitude-adjusted density is then further corrected for the current external air temperature when converting between volume and mass flow rates (see TP-06: Ventilation and Infiltration):

$ρ_{a} (T) = \frac{T _{e, r e f}}{T} \cdot ρ_{a, a l t}$

where $T_{e, r e f} = 293.15$ K (20 °C) and $T$ is the air temperature in kelvin.

Operative Temperature

The operative temperature within a thermal zone determines whether heating or cooling demand exists at each timestep. It is calculated per BS EN ISO 52016-1:2017, section 6.5.5.3, as the arithmetic mean of the internal air temperature and the mean radiant temperature:

$T_{o p} = \frac{T _{in t, ai r} + T ˉ _{m r}}{2}$

The mean radiant temperature is the area-weighted average of the internal surface temperatures across all building elements in the zone:

$\overset{ˉ}{T}_{m r} = \frac{\sum _{i = 1}^{n} A _{i} \cdot T _{s, in t, i}}{\sum _{i = 1}^{n} A _{i}}$

where:

$T_{in t, ai r}$ is the zone internal air node temperature °C, taken from the heat balance solution vector
$A_{i}$ is the area of building element $i$ m²
$T_{s, in t, i}$ is the internal surface node temperature of element $i$ °C

The operative temperature is used in the space heating and cooling demand calculation (see TP-04: Space Heating Demand) to determine whether the zone is below the heating setpoint or above the cooling setpoint. A free-floating operative temperature (with zero heating/cooling input) is first computed; if it falls outside the setpoint deadband, the model iterates to find the required heating or cooling load.

Adjacent Unconditioned Space (ZTU) Temperature

Building elements separating a conditioned zone from an adjacent unconditioned space (e.g. an unheated garage, attic, or corridor) use a simplified treatment. Rather than modelling the unconditioned space as a separate thermal zone, the additional thermal resistance of the unheated space is incorporated into the external surface heat transfer coefficient.

The standard external surface heat transfer coefficient $h_{se}$ and its corresponding resistance $R_{se}$ are:

$h_{se} = h_{ce} + h_{r e} = 20.0 + 4.14 = 24.14 W/(m²K)$

$R_{se} = \frac{1}{h _{se}} = 0.0414 m²K/W$

For a ZTU element, the effective external surface resistance is increased by the thermal resistance of the unconditioned space:

$R_{se, e f f} = R_{se} + R_{u}$

The effective external heat transfer coefficient is then:

$h_{se, e f f} = \frac{1}{R _{se, e f f}}$

This effective coefficient is assigned entirely to the convective component ( $h_{ce, e f f} = h_{se, e f f}$ , $h_{r e, e f f} = 0$ ). The split between convective and radiative components does not affect the heat balance result because the external node temperature for a ZTU element is the outdoor air temperature, and the longwave radiation to sky is zero (the element does not see the sky). Solar absorption at the external surface is also set to zero, as the element faces an unconditioned interior rather than the outdoor environment.

The external temperature for a ZTU element remains the outdoor air temperature $T_{ai r} (t)$ . The effect of the unconditioned buffer space is captured entirely through the increased surface resistance, which reduces the rate of heat transfer between the conditioned zone and the exterior.

Outputs

Quantity	Symbol	Unit	Description
External air temperature	$T_{ai r}$	°C	Hourly value from weather data
Annual mean air temperature	$\overset{ˉ}{T}_{ai r, ann u a l}$	°C	Mean over all 8760 hours
Monthly mean air temperature	$\overset{ˉ}{T}_{ai r, m o n t h}$	°C	Mean for current calendar month
Minimum daily average temperature	$T_{ai r, d ai l y, min}$	°C	Lowest daily mean across the year
Thermal radiation to sky	$Φ_{s k y}$	W/m²	Extra heat loss per unit area at external surface
Virtual ground temperature	$T_{g r o u n d, v i r t u a l}$	°C	Effective external temperature for ground floor elements
Site wind speed	$u_{s i t e}$	m/s	Wind speed corrected for terrain and height
Altitude-adjusted air density	$ρ_{a, a l t}$	kg/m³	Reference air density corrected for site altitude
Operative temperature	$T_{o p}$	°C	Mean of air temperature and mean radiant temperature
ZTU effective surface coefficient	$h_{se, e f f}$	W/(m²K)	Reduced external heat transfer coefficient for ZTU elements

Assumptions

The sky-air temperature difference is constant at $Δ T_{s k y} = 11.0$ K, the default for an intermediate climatic region per BS EN ISO 52016-1:2017, Table B.19. No adjustment is made for cloud cover, humidity, or season.
The sky view factor is calculated from element pitch alone. Shading from surrounding buildings or terrain does not reduce the longwave view factor (though it does reduce solar diffuse irradiance).
Wind data in the EPW file is assumed to represent open-terrain conditions at 10 m height. The default meteorological roughness and topography coefficients are both 1.0.
The topography coefficient $C_{T}$ is 1.0 at both the weather station and the building site. No correction is applied for hilltops, valleys, or escarpments.
Air density at standard conditions uses a reference temperature of 293.15 K (20 °C).
The operative temperature is a simple average of air and mean radiant temperature, with equal weighting. This is appropriate for air velocities below approximately 0.2 m/s, which is typical of domestic rooms.
Adjacent unconditioned space (ZTU) elements use the outdoor air temperature at the external node. The buffering effect of the unheated space is represented solely by the additional thermal resistance $R_{u}$ , with no separate thermal capacity or heat balance for the unconditioned zone.
The annual mean internal temperature used in the ground floor periodic heat transfer calculation is a fixed profile derived from SAP 10 notional building runs, not from the dynamic simulation itself.

Cross-references

TP-01: Overview and Climate Data: weather file parsing, simulation time indexing, and climate data structure
TP-04: Space Heating Demand: operative temperature drives the heating/cooling demand calculation; external node heat balance receives $Φ_{s k y}$
TP-05: Fabric Heat Loss: surface heat transfer coefficients, ZTU element resistance, ground floor U-value
TP-06: Ventilation and Infiltration: wind speed at zone level drives infiltration pressure differences; altitude-adjusted air density converts volume to mass flow rates
TP-07: Thermal Mass: internal surface temperatures used in mean radiant temperature calculation
TP-08: Solar Gains and Shading: solar geometry and irradiance calculations from the same ExternalConditions module