Lisø PhD Dissertation Manuscript - NTNU

770 Nordvik and Lisø
climate change? First, we have to define a general
approach to potential impacts of climate change on the
building stock: Let s = h represent the same climate in
period 2 as the climate that prevailed in period 1. The
difference between the net present value of the building
under a constant climate and under climate uncertainty
D a is:
a c
D = ENV ( ) −NV
= { v ( W, zˆ ) −c ( W,
zˆ ) −mˆ
1 1 1 1 1
S
Â
2s 2 2s 2s 2s 2s 2s 3 3
+ p
d { v ( W, zˆ ) −c ( W,
zˆ ) − mˆ + d T }
s=
1
1 1 1 1 1
−v ( W, z˜ ) −c ( W,
z˜ ) −m˜
+ d { v ( W, z˜ ) −c ( W,
z˜ ) − m˜ + d T
2 2h 2 2h 2 2 3 3
(8)
Variables with a hat (as zˆ) are the optimal values of the
variables under a particular climate change scenario,
and variables with a tilde (as z˜) are optimal values under
a given set of historic weather data.
The cost consists of changed performance of the
building enclosure, changed operating costs and of
changed effort. Note that changed performance in
period 1 as a result of the effect a given climate change
scenario has on period 1 effort, enters the cost of climate
change. In this paper, we will not go any further into
discussions of the expressions for the cost of climate
change on future building maintenance and operation.
Anyway, the purpose of including Equation 8 is twofold:
firstly it is an illustration of which kind of results
that can be derived from the model; and secondly, it
shows that the cost of climate change is not only determined
by the interaction between climatic impact and
the technical state of a building. It is also affected by the
possible implications of climate change on the behaviour
of the decision makers. Behaviour, in this context,
should be interpreted as strategies for adaptation.
To illustrate the second point made above: The BRE
study (Graves and Phillipson, 2000) is important in so
far as it represents an attempt to handle the technical
implications of climate change on the built environment.
However, their approaches can be seen as a measurement
of the expected impacts and costs, given that
the decision makers do not adapt. It can be shown that
estimates like this can be interpreted as an upper bound
for the expected impact or cost of climate change. A
more constructive, or political, interpretation is that it is
a warning of what might happen if nothing is done.
The model analysed above is somewhat restricted.
The only option open to the owner of the building is to
continue the use of it. The performance of the building
enclosure, and the operating costs, are affected by the
effort put into maintenance.
Conversions, scrapping and climate change
General approach
A more realistic approach is to allow for additional
elements in the action sets. In addition to maintaining
the building, we will here introduce two more possible
actions. First, the building can be abandoned or
scrapped, either in the first or in the second period. If a
building is not scrapped during one of the two first
periods, it will be terminated in period 3. We will also
allow for conversions of the buildings. By a conversion
we mean an action, which alters the fixed component
(W) in the description of the building.
To handle this analytically, some new symbols need
to be defined:
• T1 is the termination value of period 1;
• T2s is the termination value of state s in period 2;
• Wˆ is the starting value of the fixed part of the
building; and
• C(Wˆ,W) is the cost of converting the fixed part of
the building from Wˆ to W.
In the optimization problem that arises out of this, the
optimal period 2 reaction to information that arrives in
period 2 enters the period 1 decision problem. Furthermore,
this choice involves choosing between discrete
alternatives. Consequently standard static optimization
tools are not suitable, and the problem should be
analysed using backward induction.
Instead of spelling out the whole optimization problem,
we start by characterizing the choices made in
period 2. There are three possible actions in period 2.
Start by defining some subsets of the state space S:
• S Ci is the state space consisting of all states where
the optimal choice will be to convert the building,
given that an ex ante optimally designed
strategy i is chosen in period 1, i = M, C.
• S Ti is the state space consisting of all states where
the optimal choice will be to terminate the building,
given that an ex ante optimally designed
strategy i is chosen in period 1, i = M, C.
• S Mi is the state space consisting of all states where
the optimal choice will be to keep the building
without any conversions, given that an ex ante
optimally designed strategy i is chosen in period
1, i = M, C.
The state dependent optimal values of the building
under each of the three possible actions are given in
Equations 9a–c:
2s 2s2 2 2s 2 2 2
V ( C) = v ( W , z ) −c( W , z ) −C(
W, W )
3
d 3
Ci
+ T all s∈S 2
d
(9a)