Quantile regression ensemble for summer temperatures

Quantile regression ensemblefor summer temperatures

and its impact on built environment studies

Manuel Herrera – University of Bath, UKMatthew Eames – University of Exeter, UK

Chunde Liu – University of Bath, UKAlfonso Ramallo-Gonzalez – University of Bath, UK

David A. Coley – University of Bath, UK

iEMSs 2016 - Toulouse, France

Outline

1 IntroBuilt environment and weather conditionsUnderstanding heatwaves

2 Quantile methods for summer temperaturesQuantile regressionQuantile regression ensemble

3 50 summers in London: 1961-2010

4 Conclusions and further work

Built environment

Buildings and weather conditions• Climate change will have a significant

impact on global building design andenergy use in the near and distant future

• Temperature changes will make somebuildings become uncomfortable or evenfail certain regulations

• Objectives: typical weather and extremeconditions: heatwaves and cold snaps

• Heatwaves are related to ventilation,overheating, and thermal comfort issues

Heatwave of 2003More than 70,000 people died across Europe during the extreme heatwave of2003. The cause was not just the weather, but building design not being resilientenough to cope and protect occupants from external conditions.

Built environment

Understanding heatwavesHeatwave definition?Short distances between upper and lower quantiles are of key importance inestablishing criteria regarding the existence of heatwave events, conditioned tosteadily higher minimum temperatures

Open questionA heatwave event is an extreme weather eventbut is it really extreme data?

• Pattern extraction at lower and upperquantiles of the temperature time series

• How do affect meteorological variables tothe temperature at different quantiles?Are similar results to those found at themean? Quantile Regression

Outline





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≥x′i β

q|yi − x ′i βq |+N∑

i:yi≤x′i β

(1− q)|yi − x ′i βq | (1)

• Simplex method for moderate data size or Interior Point method for largerdatabases

• Bootstrap standard errors are often used instead of analytic standarderrors

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 tomaintain a suitable uncertainty level

• For regression problems, ensemble integration is done using a linearcombination 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 theensemble, q represents a specified quantile for QR, and hq,i (y |x) are weightedfunctions; i = 1, · · · ,K .

Quantile methods

Quantile regression ensemble (ii)

• In this case, the interest is focused on ensemble regressions with weightsproportional 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 setα′i · [Q50,i (y |x)− Qq,i (y |x)]−1 for q ∈ lower QR set,

(3)

where αi and α′i are normalizing coefficients such that∑

hi (q) = 1. The choiceof these weights aims to increase the importance of critical phases of summertemperatures that contain the highest temperatures during the day coincidingwith warmer nights.

Outline





50 summers in London

A typical summer in London is ...


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 toSeptember are selected to represent thesummer period

• The data available is: wind direction(wdir), wind speed (wspeed), cloud cover(cloud), air pressure (airp), airtemperature (airt), and dew pointtemperature (dpt).


Current results offered by CIBSE

• CIBSE: The Chartered Institution of Building Services Engineers. It is aninternational professional engineering association based in London thatrepresents building services engineers.

• Probabilistic Design Summer Years (pDSYs) is currently proposed asreference of warm summers.

• It is focused on different overheating metrics such as the number of hoursin a building in which the temperature is above a certain threshold whenoccupied.

• 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 2003contains an extreme hot event for a short period.


Quantile regression (i)What CIBSE pDSY doesn’t tellHow do vary the temperature? How are its relationship with other variables? Arewell represented the temperature extremes? Why we should be constrained tocomplete periods of years? Quantile regression

The following Table shows the difference between the coefficients for OLSregression and quantile regression (QR) for quantiles 0.05, 0.5, 0.95; seeEquation (1). Year 1989.

Input OLS QR 0.05 QR 0.50 QR 0.95wdir 0.0036 0.0011 0.0032 0.0038wspeed 0.5862 0.2491 0.6100 0.6536cloud -0.3178 -0.1368 -0.2965 -0.4712airp 0.1646 0.0701 0.1898 0.2201dpt 0.8443 0.9685 0.0161 0.6825


Quantile regression (ii)This Figure shows prediction intervals for every quantile at each explanatoryvariable. In red is the result of the OLS regression based on the mean. We cansee how the relationships in the weather database significantly changedepending on the quantile. Year 1989.

• Wind direction does not seem tohave a contribution

• Cloud cover and dew pointtemperature decrease when QRquantile value increases

• Wind speed and air pressurecoefficients increase as QR hashighest values


Quantile regression (iii)The regression scatter plot for QR and the hourly data for 1989 summer timeseries is represented in the Figure, where QR values for the 0.05 quantile are inred and for 0.95 are in green colour.


Quantile regression ensemble: 1961–2010The ensemble weights are proportional to the distance to the median. As a resultwe have the two regressions, for the quantiles 0.05 and 0.95 as displayed in theFigure below. Each one is an ensemble over the predictors of 50 regressionmodels 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.

Outline





Conclusions

• QR estimates rates of change for functions alongor near the upper or lower boundary of theconditional distribution of temperatures.

• QR models have been seen to be useful tounderstand the rate of changes in extremeevents along with the causes of the mostextreme data.

• An ensemble of QR predictions based on thedistance of the estimated model values with themedian is also proposed.

• A synthetic weather file is proposed instead ofusing a complete summer of observed data.

Further work

• Approaching Quantile Random Forests(ensemble).

• Developing parallelized QR ensembles whichcan be used in applications which otherwisewould involve an intensive computational effort.

• Working with data coming from different weatherscenarios and weather generators

• Investigating the use of synthetic weather filesto be applied in the built environment instead ofusing a complete observed data.

Manuel Herrera et al.B [email protected] bath.ac.uk/ace/research/eden/index.html

Quantile regression ensemble for summer temperatures

Engineering

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