This document presents research on using quantile regression and ensembles to model summer temperatures in London from 1961-2010. It finds that quantile regression can better capture relationships between temperature and weather variables like wind speed and cloud cover at extreme quantiles. An ensemble approach is also proposed, combining 50 quantile regression models to generate synthetic weather data for use in built environment studies rather than using complete observed years. Further work would expand these quantile methods and test their use with other weather data.

1. Quantile regression ensemble
for summer temperatures
and its impact on built environment studies
Manuel Herrera – University of Bath, UK
Matthew Eames – University of Exeter, UK
Chunde Liu – University of Bath, UK
Alfonso Ramallo-Gonz´alez – University of Bath, UK
David A. Coley – University of Bath, UK
iEMSs 2016 - Toulouse, France

2. Outline
1 Intro
Built environment and weather conditions
Understanding heatwaves
2 Quantile methods for summer temperatures
Quantile regression
Quantile regression ensemble
3 50 summers in London: 1961-2010
4 Conclusions and further work

3. Outline
1 Intro
Built environment and weather conditions
Understanding heatwaves
2 Quantile methods for summer temperatures
Quantile regression
Quantile regression ensemble
3 50 summers in London: 1961-2010
4 Conclusions and further work

4. Built environment
Buildings and weather conditions
• Climate change will have a significant
impact on global building design and
energy use in the near and distant future
• Temperature changes will make some
buildings become uncomfortable or even
fail certain regulations
• Objectives: typical weather and extreme
conditions: heatwaves and cold snaps
• Heatwaves are related to ventilation,
overheating, and thermal comfort issues
Heatwave of 2003
More than 70,000 people died across Europe during the extreme heatwave of
2003. The cause was not just the weather, but building design not being resilient
enough to cope and protect occupants from external conditions.

5. Built environment
Understanding heatwaves
Heatwave definition?
Short distances between upper and lower quantiles are of key importance in
establishing criteria regarding the existence of heatwave events, conditioned to
steadily higher minimum temperatures
Open question
A heatwave event is an extreme weather event
but is it really extreme data?
• Pattern extraction at lower and upper
quantiles of the temperature time series
• How do affect meteorological variables to
the temperature at different quantiles?
Are similar results to those found at the
mean? Quantile Regression

6. Outline
1 Intro
Built environment and weather conditions
Understanding heatwaves
2 Quantile methods for summer temperatures
Quantile regression
Quantile regression ensemble
3 50 summers in London: 1961-2010
4 Conclusions and further work

7. Quantile methods
Quantile regression
• Similarly to OLS, the conditional median function, Qq(y|x), would be
applied
• The quantile q ∈ (0, 1) for y splits the data into proportions q below and
1 − q above: F(yq) = q and yq = F−1(q).
• QR minimises a sum that gives asymmetric penalties (1 − q)|ei| for
over-prediction and q|ei| for under-prediction
Q(βq) =
N
i:yi ≥xi
β
q|yi − xi βq| +
N
i:yi ≤xi
β
(1 − q)|yi − xi βq| (1)
• Simplex method for moderate data size or Interior Point method for larger
databases
• Bootstrap standard errors are often used instead of analytic standard
errors

8. Quantile methods
Quantile regression ensemble (i)
• Ensemble learning is a process that uses a set of models to study a
common objective
• All of these single models are integrated to obtain a more robust and
accurate approach for temperature predictions, in addition to help to
maintain a suitable uncertainty level
• For regression problems, ensemble integration is done using a linear
combination of the predictions.
QTq(y|x) =
K
i=1
hq,i (y|x) · Qi (y|x) (2)
where K is the number of single quantile regressions (QRs) to make up the
ensemble, q represents a specified quantile for QR, and hq,i (y|x) are weighted
functions; i = 1, · · · , K.

9. Quantile methods
Quantile regression ensemble (ii)
• In this case, the interest is focused on ensemble regressions with weights
proportional to the distance of single QRs to the QR for the median,
Q(q50)
• Thus, hq,i (y|x) is given by the expression of Equation (3),
hq,i (y|x) =
αi · [Qq,i (y|x) − Q50,i (y|x)] for q ∈ upper QR set
αi · [Q50,i (y|x) − Qq,i (y|x)]−1 for q ∈ lower QR set,
(3)
where αi and αi are normalizing coefficients such that hi (q) = 1. The choice
of these weights aims to increase the importance of critical phases of summer
temperatures that contain the highest temperatures during the day coinciding
with warmer nights.

10. Outline
1 Intro
Built environment and weather conditions
Understanding heatwaves
2 Quantile methods for summer temperatures
Quantile regression
Quantile regression ensemble
3 50 summers in London: 1961-2010
4 Conclusions and further work

11. 50 summers in London
A typical summer in London is ...

12. 50 summers in London
Summer data: 1961–2010
• 50 years of hourly data (1961 - 2010)
collected at Heathrow weather station
(London, UK)
• For each year, the months of April to
September are selected to represent the
summer period
• The data available is: wind direction
(wdir), wind speed (wspeed), cloud cover
(cloud), air pressure (airp), air
temperature (airt), and dew point
temperature (dpt).

13. 50 summers in London
Current results offered by CIBSE
• CIBSE: The Chartered Institution of Building Services Engineers. It is an
international professional engineering association based in London that
represents building services engineers.
• Probabilistic Design Summer Years (pDSYs) is currently proposed as
reference of warm summers.
• It is focused on different overheating metrics such as the number of hours
in a building in which the temperature is above a certain threshold when
occupied.
• pDSY is based on the years: 1984–2006
• The year 1989 is the current CIBSE DSY representing a moderately warm
year, year 1976 contains a long period of extreme summer and year 2003
contains an extreme hot event for a short period.

14. 50 summers in London
Quantile regression (i)
What CIBSE pDSY doesn’t tell
How do vary the temperature? How are its relationship with other variables? Are
well represented the temperature extremes? Why we should be constrained to
complete periods of years? Quantile regression
The following Table shows the difference between the coefficients for OLS
regression and quantile regression (QR) for quantiles 0.05, 0.5, 0.95; see
Equation (1). Year 1989.
Input OLS QR 0.05 QR 0.50 QR 0.95
wdir 0.0036 0.0011 0.0032 0.0038
wspeed 0.5862 0.2491 0.6100 0.6536
cloud -0.3178 -0.1368 -0.2965 -0.4712
airp 0.1646 0.0701 0.1898 0.2201
dpt 0.8443 0.9685 0.0161 0.6825

15. 50 summers in London
Quantile regression (ii)
This Figure shows prediction intervals for every quantile at each explanatory
variable. In red is the result of the OLS regression based on the mean. We can
see how the relationships in the weather database significantly change
depending on the quantile. Year 1989.
• Wind direction does not seem to
have a contribution
• Cloud cover and dew point
temperature decrease when QR
quantile value increases
• Wind speed and air pressure
coefficients increase as QR has
highest values

16. 50 summers in London
Quantile regression (iii)
The regression scatter plot for QR and the hourly data for 1989 summer time
series is represented in the Figure, where QR values for the 0.05 quantile are in
red and for 0.95 are in green colour.

17. 50 summers in London
Quantile regression ensemble: 1961–2010
The ensemble weights are proportional to the distance to the median. As a result
we have the two regressions, for the quantiles 0.05 and 0.95 as displayed in the
Figure below. Each one is an ensemble over the predictors of 50 regression
models corresponding to each of the 50 years in the database.
Common weather patterns having an impact on the result of both ensembles are:
wspeed and dpt for the QR(0.05) ensemble and wspeed, dpt, and cloud
(negative relationship) for the QR(0.95) ensemble.

18. Outline
1 Intro
Built environment and weather conditions
Understanding heatwaves
2 Quantile methods for summer temperatures
Quantile regression
Quantile regression ensemble
3 50 summers in London: 1961-2010
4 Conclusions and further work

19. Conclusions
• QR estimates rates of change for functions along
or near the upper or lower boundary of the
conditional distribution of temperatures.
• QR models have been seen to be useful to
understand the rate of changes in extreme
events along with the causes of the most
extreme data.
• An ensemble of QR predictions based on the
distance of the estimated model values with the
median is also proposed.
• A synthetic weather file is proposed instead of
using a complete summer of observed data.

20. Further work
• Approaching Quantile Random Forests
(ensemble).
• Developing parallelized QR ensembles which
can be used in applications which otherwise
would involve an intensive computational effort.
• Working with data coming from different weather
scenarios and weather generators
• Investigating the use of synthetic weather files
to be applied in the built environment instead of
using a complete observed data.

21. Manuel Herrera et al.
amhf20@bath.ac.uk
bath.ac.uk/ace/research/eden/index.html