LT Urban
The energy modelling of urban form
CARLO RATTI, DARREN ROBINSON#, NICK BAKER AND KOEN STEEMERS
The Martin Centre, Cambridge University, 6 Chaucer Road, Cambridge, CB2 2EB, UK.

Tel: 01223 331714. E-mail: dr203@cam.ac.uk
Abstract
This paper describes one aspect of a large three year EU funded project on the theme of urban
environmental analysis, called PRECis – assessing the Potential for Renewable Energy in Cities. One
objective of PRECis is to develop a tool to predict building energy consumption within urban
neighbourhoods (small, say 1km2, parts of a city) and use this tool to explore the relationships between
urban form and building energy use. LT, an established tool for estimating energy consumption in nondomestic buildings, has been modified to work at the urban scale; while input parameters which describe the
building fabric (orientation of facades, angles of obstruction of the sky, etc.) are derived by imageprocessing urban Digital Elevation Models (DEMs). This paper describes the method and discusses some
preliminary results for three case studies in London, Toulouse and Berlin.
INTRODUCTION
Building energy performance is conventionally
understood to be dependent upon (1): (i) building design,
(ii) services design and performance, and (iii) occupant
behaviour. To this list we would add urban form. Although
often not a design variable, the urban environment directly
affects the availability of daylight and solar radiation, with
consequent implications for heating, lighting and cooling
energy use. The potential for natural ventilation as a
function of noise and pollution is also indirectly affected by
urban form.
Most building energy and environmental modelling
software concentrate on building and systems design.
Occupant behaviour is presently ill understood and urban
form is generally neglected. Our approach in this work is
the reverse. By assuming standard building, systems,
behavioural and climatic parameters we are able to assess
the effects of urban texture on energy consumption. The aim
of the work is not primarily diagnostic – i.e. to provide
absolute energy consumption predictions – but comparative.
In this paper we describe the method and some
preliminary results for three 400m2 urban sites in London,
Toulouse and Berlin. More generally, the work aims to
produce urban planning guidelines, related to building
energy performance.
CONTEXT
As noted above, overshadowing from adjacent buildings
can significantly affect building energy use. Figure 1 for
example depicts the proportionate change in energy
consumption of a UK office for two urban horizon angles
(mean angle of skyline above the mid height of a window).
In winter the south facade is deprived of useful direct and
diffuse solar gains thus increasing the heating load with
increased obstruction. The north facade is only marginally
affected, as only diffuse solar gains are reduced. In summer
there is an energy saving for cooling, though this is small
because high altitude direct solar gain is largely unaffected.
Both orientations show a marked increase in lighting energy
demand.
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Lighting N
Lighting S
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Cooling S
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Figure 1. Relative energy consumption for North and South
orientations as a function of urban horizon angle (obtained
using the LT model)
Despite the apparently clear the relationship between
urban form and building energy use, it is a relatively
neglected area of applied research.
A number of studies in the 1970s suggested building
volume to surface area ratio as an important parameter, this
being analogous to heat loss. March (2) for instance proved
that the optimal parallelepiped shape for a building, to
minimise heat loss, is a half cube. While Owens (3) reports
on a study by BRE where different typologies of buildings
were analysed and ranked in terms of surface to volume
ratios and consequent heat losses.
Fortunately, understanding of building performance has
matured greatly over the past 30 years. It is now commonly
understood that a building is an integrated entity;
structurally, functionally and environmentally. As such,
heat losses or surface to volume ratios are a poor indicator
of building energy demand. Rather, an integrated analysis is
required, which considers the relationship between urban
form and energy use for lighting, ventilating and cooling as
well as heating. To this end, the LT model seemed to be a
natural candidate for urban-scale energy analysis.
LT MODEL
Before embarking upon a description of the Lighting and
Thermal (LT) energy model, it is perhaps useful to draw a
distinction between the LT Model and the now widely
known LT Method (1). The LT Method is a procedure for
predicting the energy consumption of non-domestic
buildings at the concept design stage. A series of charts that
depict energy consumption versus glazing ratio have been
produced using the LT Model. The user consults the
appropriate chart as defined by location, building use,
internal heat gains, design illuminance and orientation.
Specific energy consumption (MWh/m2) for each end use
(heating, lighting, ventilating and cooling) can then be read
off from the curves for the relevant glazing ratio.
Multiplying by the relevant zone area gives total annual
energy consumption (MWh). If the building façade is
adjacent to urban obstructions, pre-computed urban horizon
factors (UHFs) are used to adjust this predicted energy
consumption. A separate program ‘Atrium’ has been used to
pre-compute the thermal savings arising from the use of
glazed buffer spaces. The attractiveness of the LT Method
then, lies with the rapidity and ease with which it may be
deployed to predict building energy consumption. It also
requires a minimal input description. For these reasons, LT
appears to be a suitable medium for studying the
dependency of building energy use upon urban form – a
computationally intensive task. Before accepting this, let us
first consider the theoretical basis of the foundation stone of
the LT Method – the LT Model.
LT Model Description
LT is an integrated energy model. It predicts the heating,
lighting, ventilating and cooling energy use of a 9m by 6m
by 3m module with one exposed glazed wall (Figure 2).
Previously spreadsheet based (4), the model has been
redeveloped for this project, in the form of a standalone
computer model.
Figure 2. Energy flows in the LT model
Lighting
Daylight factors are calculated at two reference points on
the working plane, within the front and rear halves of the
LT module. The sky component is calculated using the
method due to Hopkinson et al (5) and the externally
reflected component using an empirical equation derived by
Steemers from physical modelling (6). Both use the CIE
standard overcast sky luminance distribution. The internally
reflected component is based on the split flux method, with
front-back correction factors to normalise for location (5).
The concept of ‘urban horizon angle’ was introduced into
LT by Steemers (6) for the externally reflected component
calculation. This is the altitude angle subtended from the
mid-point of the module window to the mean roof height of
the adjacent buildings. This can then be projected back into
the module to derive sky and obstruction view factors for
each daylighting reference point. The same principal is
applied to define the ‘obstruction sky view’ angle. This is
used to calculate obstruction luminance as a function of the
view of the sky that is seen by the obstructing façade as well
as reflected diffuse solar radiation
An hourly diffuse irradiance profile is calculated from
daily total diffuse irradiation, using the method due to Liu
and Jordan (7). This is applied to vertical irradiation, to
implicitly account for the effects of circumsolar and horizon
brightening. A standard luminous efficacy converts this into
vertical illuminance, which is then projected onto the
horizontal plane, using Littlefair’s ratio of vertical to
horizontal illuminance (8). Multiplying the daylight factor
by the external illuminance gives the orientation-dependent
internal illuminance. If this is below the design illuminance
level then artificial lighting is switched on. Electrical energy
is consumed and heat gains are emitted.
Thermal
Heating and cooling energy use are predicted on the basis
of an energy balance for the middle day of each month.
The total heat loss rate is determined from the product of
fabric and ventilation conductance and a 24-hour mean air
temperature difference. The mean internal temperature is
defined by adjusting a temperature setpoint with IHVE
heating intermittency correction factors (9), which vary with
occupied duration and thermal mass. The mean outdoor
temperature is defined in the climate file. Results are scaled,
according to the number of occupied days within a given
month. Equipment, metabolic, lighting and solar gains are
subtracted from this to give nett heating load.
Equipment and metabolic gains are user defined as a
lumped casual heat gain. Lighting gains are based on hours
of artificial lighting use (above), luminous efficacy and
design illuminance. Solar gain is the sum of direct and
diffuse sky and diffuse wall and ground reflected daily total
irradiation. An hourly shading coefficient calculation
accounts for shading due to adjacent buildings.
Furthermore, if there is a cooling load blinds are
automatically employed to reduce/omit direct gain to mimic
good occupant behaviour and adaptive opportunity. Finally,
a solar utilisation factor (10) accounts for the proportion of
solar gain that is useful in offsetting heating demands.
A similar procedure, though using a separate setpoint, is
used to calculate cooling loads. Heating and cooling loads
are translated into delivered energy using either a boiler
efficiency or a cooling coefficient of performance.
Energy consumption
The thermal and lighting routines predict heating,
lighting and cooling energy demand. A further, separate
routine determines ventilation energy use by multiplying a
constant fan power by the number of occupied hours.
Primary energy and CO2 conversion factors account for
distribution and power station thermodynamic efficiency
losses as well as consequent emissions.
Urban-scale energy modelling presupposes that the
model will be applied to at least every building within the
area being covered, if not to every floor. It therefore seems
appropriate to apply a model, which captures the principal
energy flows with reasonable accuracy without entailing the
computational demands of full dynamic simulation. For this
reason the LT model described above seems well suited to
the task at hand.
representing central London, Toulouse and Berlin are
shown in Figures 4a to 4c. They can be viewed in
axonometric or perspective projection (Figure 5).
APPLICATION TO URBAN-SCALE MODELLING
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Although the LT model has numerous variables, many of
these have been fixed with sensible default values in the
past, to minimise user-input demands. Since our aim in this
project is to highlight the effects of urban form upon
building energy consumption, it is appropriate to apply this
principal to urban-scale modelling. The remaining variables
relate to urban obstructions to sun and light penetration,
façade orientation, and zone area (Figure 3).
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Building 1
Building 2
.
.
.
Building n
Orientation | UHA | OSV
Zone type
Floor 1 Passive
Floor 2 Non-passive
.
.
.
UHA above refers to urban
Floor n
horizon angle and OSV to
obstruction sky view.
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Figure 3 . LT Urban input requirements
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Façade glazing ratio is presently fixed at 30% for passive
and 0% for non-passive zones. Likewise, external
obstruction reflectances are fixed, but these may vary
between cities if there is a clear location-dependence.
Finally, the climate is also fixed (at Kew, UK) to ensure that
differences in energy consumption are due solely to
variations in urban texture.
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DERIVING LT PARAMETERS BY IMAGE
PROCESSING
The question now arises how to calculate the above
parameters on extensive portions of cities. Existing
architectural software cannot easily be adapted to this
purpose. Its extension to the urban scale fails because of
problems in constructing precise geometric models and the
difficulties of processing them, as the time is likely to
depend on the square of the number of geometric elements
being modelled. These difficulties, coupled with the
associated computational demands, have contributed to the
scarcity of tools for energy assessment at the urban scale
thus far.
Our approach is based on deriving the parameters needed
by LT using very simple digital models of urban form. By
borrowing techniques from image processing and the geosciences (cf. (11) and (12)), algorithms have been developed
to derive the necessary urban form parameters in a way
which is independent of geometric complexity and relates
linearly to the size of the image under investigation.
The inputs of these algorithms are Digital Elevation
Models (DEM). A DEM is an image in which each pixel
(elementary square unit on the image) has a grey-scale
proportional to the height of the urban surface. 256 levels of
grey are usually employed, with zero representing street
level.
DEMs in urban areas can be obtained easily, as they are a
by-product of the production of orthographs; three examples
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Figure 4 . Digital Elevation Model of a) London [upper], b)
Toulouse [middle] and c) Berlin [lower]
DEMs can be analysed with image processing
techniques. Richens (13) and Ratti and Richens (14) have
used this approach to derive environmental parameters, such
as shadowing distribution, daylight availability, sky view
factor and so on. Similar techniques have been used within
the present project to derive the morphological parameters
required by LT. The Image Processing Toolbox within the
Matlab (Matrix Laboratory) environment has been used for
this purpose.
0<d≤6), see Figure 7. Non passive zones (where the
distance of each pixel is greater than 6 meters d>6) can be
detected by subtraction.
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Figure 5 . Perspective view of the London DEM
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Figure 7 . Passive zones, 15m above ground level
Converting volumes into floor surfaces
Orientation of façades.
LT requires data on a floor-by-floor basis. Therefore, the
three dimensional information of the DEM needs to be
converted into floor surfaces. If a standard floor height
value is assumed (i.e. 3 metres), it becomes possible to slice
the city at different levels. This slicing process can be easily
performed on the DEM with a simple image processing
operation based on subtraction. Figure 6 shows the London
DEM sliced at 15 meters.
Filters have been developed in image processing to
detect edges. In particular, ‘Sobel’ filters construct x and y
derivatives on a DEM. By filtering the DEM it is possible to
classify each façade pixel according to its orientation.
Values are grouped in classes of approx. 22.5 degrees, as
presented in Figure 8.
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Figure 6 . Built space at 15m above ground level
On each slice (corresponding to a building floor) and
indeed at each pixel, LT needs the following parameters:
whether the space is passive and the corresponding glazing
ratio or non-passive, facade orientation, UHA and OSV.
Their derivation is described below.
Identification of passive and non-passive zones
Passive zones are defined as being within two floor-toceiling heights of a façade, in this case 6 metres. From an
image processing viewpoint the problem can be stated as
follows: given an image consisting of black (built) and
white (unbuilt) pixels, assign to each black pixel a value
corresponding to its distance from the nearest white pixel.
The solution to this problem can be obtained using
algorithms developed for distance transformations in digital
images. (see Borgefors (15) for a review). Applying the
Euclidian distance transform to the image of Figure 6 with
thresholding (detecting all the pixels within a certain range),
it is possible to define the extent of passive zones (where
the distance of each pixel is between 0 and 6 metres,
Figure 8. Zone orientation (degrees clockwise from North),
15m above ground
Determining the Urban Horizon Angle, UHA
As noted earlier the UHA is used by LT to determine the
effects of overshadowing due to adjacent buildings. In a
uniform urban canyon, its computation would be
straightforward from the height ‘H’ of the opposite
buildings divided by the canyon width ‘W’
(H/W=tan(UHA)). However, with complex textures, the
computation of UHA is considerably more involved.
Our central algorithm assigns to each pixel the value of
the maximum obstruction angle in a given direction based
on the following steps: 1) define the direction of view, 2)
compute the components of an opposite vector, scaled so
that the larger of the x and y components is just 1 pixel, 3)
create another image ‘newimage’ where the DEM is
translated by the x and y components, 4) subtract from
‘newimage’ the previous DEM image and divide the results
by the magnitude of the translation δs=√x2 + y2 5) apply the
arctan function to determine the UHA in degrees.
The above operations give the obstruction angle
produced by buildings at a distance δs. The procedure
should then be repeated for increasing δs until ‘newimage’
has been completely shifted. At each iteration the maximum
value of the obstruction angle should be taken. This process
results with the maximum obstruction angle value on each
pixel for a given direction.
processing
Matlab image
processing toolbox
LT Model
input
Digital elevation
model
+22.5
+45°
°
0°
+67.5
°
-45°
-67.5°
-22.5°
output
Figure 10. LT Urban – data exchange
With this approach, the energy analysis is complete, with
results overlaid onto a DEM, in a few seconds. Results from
this energy modelling for the 15m high slices of London,
Toulouse and Berlin are shown in Figures 11a to 11c below.
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Figure 9 . Maximum obstruction angle in the range ±67.5 o
at intervals of 22.5o.
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Should the urban canyon have a regular profile, it would
be enough to assign to each façade a value corresponding to
the maximum obstruction angle in the perpendicular
direction. Unfortunately, urban textures often present more
complex patterns. Therefore, on each façade we decided to
scan the city in several directions. The value in the direction
perpendicular to the façade was averaged with 6 other
values, taken in the range [±67.5o] at regularly spaced
intervals of 22.5o (figure 9).
Contributions from directions away from the façade
normal have less impact on obstructing solar radiation, in
proportion to the cosine of the angle between them and the
façade normal. This is accounted for in our derivation of
mean UHA.
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Determining the Obstruction Sky View, OSV
The OSV can be derived from the above UHA by
averaging on each façade values taken from the opposite
facades. Seven directions in the range [±67.5 o] at regularly
spaced intervals of 22.5o are considered, weighted again
with a cosine correction.
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RESULTS AND DISCUSSION
With the geometric parameters outlined above, it is
possible to proceed with the energy modelling. This has
been achieved in two ways. Firstly, the geometric
parameters were parsed from Matlab to the LT model on a
per pixel basis (Figure 10). However, this requires several
minutes per slice (or floor). The alternative has been to
generate a 3-dimensional matrix of pre-computed values
from the LT Model (using the same data exchange method
depicted in Figure 10), for the range of urban parameters
being investigated (i.e. 10 increments of UHA and OSV for
each of 16 orientations for passive zones and a non-passive
zone). The 3-dimensional matrix is analogous to the precomputed LT charts, which the LT method is based on.
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Figure 11. Predicted annual energy consumption (MWhm 2 -1
y ) for a) London, b) Toulouse and c) Berlin.
In the London case (average energy consumption:
0.141MWhm-2), with the 30% glazing ratio selected, there
are several rather inefficient courtyards. This is due to their
high aspect ratio (H/W) which limits useful daylight and
solar transmission. There are also several deep plan
buildings and significant overshadowing in parts. Berlin
follows a similar trend, but with more deep plan and lower
aspect ratio courts (average energy consumption:
0.144MWhm-2). The Toulouse case study site is
characterised by narrow plan buildings and minimal
overshadowing
(average
energy
consumption:
0.134MWhm-2). It is comforting therefore, to note that the
results from this analysis are the reverse of those from the
total built surface area to volume ratio, also derived from
image processing. The latter suggests Berlin to be the most
efficient (built volume to surface area ratio: 5.93m) and
Toulouse the least (built volume to surface area ratio:
4.04m), whereas the integrated energy modelling predicts
Toulouse to be the most efficient and Berlin the least.
CONCLUSIONS AND FUTURE WORK
As part of an EU funded project on urban environmental
analysis, a new tool has been developed to support urbanscale building energy modelling. This has been achieved by
interfacing a simplified energy model with image
processing techniques. The latter is used to derive geometric
parameters that describe building and adjacent urban form
from digital elevation models. These data are parsed to the
energy model and the results used to create a new image of
annual energy consumption for heating, lighting, ventilating
and cooling for each built pixel. This tool, called LT Urban,
has been used to study the relationship between urban form
and building energy consumption for three case study sites London, Toulouse and Berlin - with encouraging results.
Further work is planned, with current version of LT
Urban, to predict energy consumption for different generic
urban forms, such as those proposed by Martin and March
(2). From this, it may be possible to identify urban energy
planning guidelines. For these forms, as well as for several
case study sites, existing and potential energy consumption
will also be predicted. The latter will be based on an
adaptive façade: the glazing ratio that corresponds to the
minima on an LT curve (of total energy consumption versus
glazing ratio) can be identified for each built pixel. In this
way, for example, the effects of increasing glazed areas on
lower south facing floors in built-up areas on energy
consumption can be evaluated. It is also planned to evaluate
different city forms with and without their local climate.
This will help to identify whether optimal city forms have
evolved, consciously or otherwise, in response to climate.
From a modelling perspective, it is planned to extend the
image-processing role to include aspects of urban
microclimate modelling that relate to energy prediction. For
example, the Cluster Thermal Time Constant model (16)
may be embedded to generate canyon temperatures that can
be referenced at run-time by the energy model. Likewise,
the real urban profile should be used as the basis for
determining the solar shading coefficients that are used by
LT to adjust direct solar gain due to urban obstructions.
Regarding the energy model, some progress has been
made to extend the applicability of LT to the predominantly
clear sky climates of Southern Europe. Thus far, this has
involved developing a daylighting model for sunny skies.
As such the model considers direct and diffuse illumination,
the latter for an hourly clear sky luminance distribution.
Contributions from sun and diffuse lit obstructing buildings
and ground are also considered. A more detailed description
is beyond the remit of this paper and will be reserved for a
future publication.
Simplified active solar water heating and photovoltaic
(PV) models have also been incorporated into LT. The
former is based upon an annual model presented in
B.S.5918 (17). This has been adapted into a monthly model
in a similar fashion to that described by Gadsden et al (18).
The PV model is an adaptation of a simplified model
described by Duffie and Beckman (19).
It is anticipated that these new features will be used in
the next stage of development of LT Urban. The PV and
solar water heater models will contribute to the prediction
of renewable energy potential for each case study site.
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