amy stidworthy - optimising local air quality models with sensor data - dmug17

Amy Stidworthy

DMUG6h April 2017

London

Optimising local air quality models with sensor data: examples from

Cambridge

DMUG, London, 6th April 2017

Acknowledgements

• The work presented here has been done by CERC based on ADMS-Urban modelling of Cambridge following the deployment of AQMesh sensors in Cambridge. Partners include: – Rod Jones & Lekan Popoola, Department of Chemistry, University

of Cambridge– Dan Clarke, Cambridgeshire County Council, Cambridge– Jo Dicks & Anita Lewis, Cambridge City Council, Cambridge– Ian Leslie, Computer Laboratory, University of Cambridge– Amanda Randle, AQMesh


Outline of presentation

• Motivation• Optimisation technique• Preliminary results for Cambridge• Further work


Motivation

• Emissions errors account for a significant proportion of dispersion model error

• Traditionally, dispersion models such as CERC’s ADMS-Urban model are validated against data from reference monitors:– Modellers either use the validation to improve model setup; or– Calculate and apply a model adjustment factor to model results

• New low cost air pollution sensors allow large networks of sensors to be installed across a city

• Accuracy and reliability is generally lower than reference monitors, but larger spatial coverage is possible

• How can we best use these sensor data in modelling?• If the data are not accurate and reliable enough for model

validation, maybe we can use the data in a different way...


Optimisation technique: Overview

• The aim is to develop an inversion technique to use monitoring data from a network of sensors to automatically adjust emissions to improve model predictions

• Basic idea:– Run ADMS-Urban to obtain modelled concentrations at monitor

locations in the normal way– Use these modelled concentrations and their associated

emissions as a ‘first guess’, together with a) monitored concentration datab) information about the error in the monitored data and the proportion

of that error that is systematic across all monitorsc) Information about the error in the emissions data and the proportion

of that error that is systematic across all sources– Use an inversion technique to calculated an adjusted set of

emissions that reduces error in the modelled concentrations


Optimisation technique: Introduction

• There are some conditions that have to be satisfied for such a scheme to work:a) The model concentration must be proportional to the emissions,

which means that complex effects like chemistry have to be ignored

b) Any sources included must affect at least one receptor (monitor)c) Any receptor included must have non-zero concentration

• The technique developed uses a probabilistic approach following work by others, for example as used by the Met Office for estimating volcanic ash source parameters using satellite retrievals [Webster et al, 2016]


Optimisation technique: Cost function

We define a cost function J(x) with two terms: one that describes the error in the modelled concentration (left-hand term) and one that describes the error in the emissions (right-hand term)

The aim is to minimise J to obtain x, a vector of adjusted emissions.

Quantity Definition Dimensions

x Vector of emissions (result) nM Transport matrix relating the source term to the observations n by ky Vector of observations kR Error covariance matrix for the observations k by ke Vector of first guess emissions nB Error covariance matrix for the first guess emissions n by n

exBexyMxRyMxx 11 TTJ


Optimisation technique: Least squares problem

• To solve the cost function minimisation problem, we first convert the problem to a ‘least squares’ problem, which is easier to solve computationally

• A ‘least squares’ problem finds the best solution to the equation Ax=f, where x is a vector of size m, f is a vector of size n and A is a matrix with n rows and m columns.

• The result of solving the least squares problem is the vector x that gives the minimum value of the sum of the squares of the elements of (Ax-f)

• So, we need to write the cost function as

Fast forward through the maths...

fAxfAx TxJ


Optimisation technique: Error covariance matrices

• To solve the problem, we need to construct the matrix A and the vector f, but do we have all the information we need for this? M is the transport matrix: this represents the contribution of every source

to every receptor given a unit emission rate y is the vector of monitored concentrations at each receptor e is the vector of emissions for each source

• What are the matrices T and D? These are the related to the ‘covariance’ matrices R and B that represent

the error in the monitored data and emissions data respectively. The diagonal components of the covariance matrices represent the

variance in the data, which is related to the uncertainty in the data; The off-diagonal components represent how much of the error is ‘co-

varying’, or in other words, systematic.

eDyT

fDMT

AfAxfAxT

T

T

TTxJ and


Optimisation technique: Monitoring data error

• The diagonal components of the monitoring data error covariance matrix R represent the variance σObs

2 of the monitored data, which is the square of the standard deviation σObs:– We assume that the standard deviation σObs is equal to the

uncertainty in the monitoring data expressed as a concentration and is equal to Uobs x O, where Uobs is the uncertainty expressed as a fraction.

• The off-diagonal components represent the error that co-varies between monitors, i.e. systematic error– We say that a given proportion of the uncertainty is due to

systematic error


Optimisation technique: Monitoring data error

• So, for any two monitors labelled i and j, their covariance is defined as

• The factor UfObs represents the fraction of the monitoring data uncertainty that is due to systematic error.

• This raises questions:– How much of monitoring data error is systematic?– Should monitors of different types be treated as independent, with

no co-variance?– Are there any causes of monitoring data error that affect all

monitors, e.g. temperature, humidity?– Is there co-variance between sensors for different pollutants?

jijyUUfiyUUfjiiyU

jiObsObsObsObs

ObsObs

22,


Optimisation technique: Emissions data error

• The diagonal components of the emissions error covariance matrix B represent the variance σEm

2 of the emissions data, which is the square of the standard deviation σEm:– We assume that the standard deviation σEm is equal to the

uncertainty in the emissions data expressed as a concentration and is equal to Uem x E, where Uem is the uncertainty expressed as a percentage.

• The off-diagonal components represent the error that co-varies between sources, i.e. systematic error– We say that a given proportion of the uncertainty is due to

systematic error, for example traffic emissions factors


Optimisation technique: Emissions data error

• So, for any two sources labelled i and j, their covariance is defined as

• The factor UfEm represents the fraction of the emissions data uncertainty that is due to systematic error.

• This also raises questions:– How much of the emissions data error is systematic? For

example, what proportion of road emissions data is due to errors in the emission factors (systematic) and how much is due to traffic counts (non-systematic)

– Is there any co-variance in the emissions data error for different pollutants? PM10 and PM2.5 – yes, but PM10 and NOX?

jijeUUfieUUfjiieU

jiEmEmEmEm

EmEm

22,


Preliminary results: Cambridge

• CERC have been collaborating on a project to study ambient air quality across Cambridge using a large number of sensor nodes and computer modelling.

• 20 AQMesh sensor pods have been placed at key points around Cambridge, measuring air quality in near real time.


Preliminary results: Cambridge

• The aim of the preliminary Cambridge tests presented here is primarily to examine the behaviour of the optimisation scheme and refine the process, i.e.– Does it work?!– Is it practical? If it takes weeks to run then obviously not.– What effect does the choice of uncertainty parameters have on

outcome?– How does the validation at the reference monitors change?– Can we learn anything about emissions?


ADMS-Urban model setup

• One source type: 305 road sources• One pollutant: NOX

• 25 monitors: 20 AQMesh monitors and 5 reference monitors• Time-varying emission factors: diurnal profiles for weekdays,

Saturdays and Sundays• Daylight saving option used to obtain correct emission factors• 3-month period: 30/06/2016 01:00 to 30/09/2016 23:00


Optimisation process

Step 1: Run ADMS-Urban to obtain modelled concentrations at monitoring site locations

Step 2: Form the transport matrix, emissions vector and monitored data vector

Step 3: Run the optimisation scheme

Step 4: Create an hourly factors (.hfc) file from the adjusted emissions data

Step 5: Re-run ADMS-Urban using the adjusted emissions .hfc file


Optimisation parameters

• As described previously, we specify the following parameters in the optimisation:

EUParameter name DescriptionUobs(ref) Observation uncertainty (reference monitors)

Uobs(aqmesh) Observation uncertainty (AQmesh sensors)

Ufobs(ref) Observation uncertainty covariance factor (reference monitors)

Ufobs(aqmesh) Observation uncertainty covariance factor (AQmesh sensors)

Uem Emissions uncertainty

Ufem Emissions uncertainty covariance factor


Optimisation Technique: Effect of uncertainty

Optimisation is working!J is reduced for all uncertainty

values Increasing Ou relaxes the

constraints so J is reduced less


AQMesh sensors: more model error toleratedRef: less model error tolerated

GonvillePlace

NewmarketRoad

ParkerSt

reet

RegentStreet

S-1134

S-1135

S-1136

S-1137

S-1138

S-1139

S-1140

S-1141

S-1142

S-1143

S-1144

S-1145

S-1146

S-1147

S-1148

S-1149

S-1150

S-1151

S-1152

S-1153

050

100150200250300

Observed Model (original emissions)Model (adjusted emissions, all sensor data)

NO

x co

ncen

trati

on (u

g/m

3)Effect of monitor uncertainty on concentrations

• In these inversion calculations:– Reference monitor uncertainty set to 10%– AQMesh sensor uncertainty set to 30%– Covariance between Reference monitors (systematic error) set to 5%– Covariance between AQMesh sensors (systematic error) set to 10%– No covariance between Reference monitors and AQMesh sensors

Example hour: 7am on 5th July


Effect of emissions covariance on adjusted emissions

-100%

-50%

0%

50%

100%

150%

200%

Percentage increase in source emission rate with different emissions error covariance settings

Zero emissions error covariance

75% emissions error covariance

• If emissions error covariance is zero, emissions can change completely independently

• With non-zero emissions error covariance, emissions have to change more consistently across all sources


Cambridge: optimisation parameters used

Parameter name

Description Value

Uobs(ref) Observation uncertainty (reference monitors) 0.1

Uobs(aqmesh) Observation uncertainty (AQmesh sensors) 0.3

Ufobs(ref) Observation uncertainty covariance factor (reference monitors)

0.05

Ufobs(aqmesh) Observation uncertainty covariance factor (AQmesh sensors)

0.1

Uem Emissions uncertainty 0.5

Ufem Emissions uncertainty covariance factor 0.4

All monitoring data are provisional apart from Gonville Place reference monitor; AQMesh data were obtained in real time.


Effect of optimisation on model validation

Statistics 1. 2. 3.

MeanObs 31.2 31.2 31.2

Mod 34.5 29.3 31.3

StDevObs 27.9 27.9 27.9

Mod 31.0 26.0 27.0

MB 3.30 -1.91 0.10

NMSE 0.51 0.05 0.39

R 0.70 0.97 0.75

Fac2 0.71 0.94 0.73

1. Orig_RdsOnlyBase case model output

2. Inv_ReRun_AllSensorsModel output using optimised emissions; optimisation carried out using all sensor data

3. Inv_ReRun_AQMeshSensorsOnlyModel output using optimised emissions; optimisation carried out using AQMesh data only

Validation at Reference sites only

Data points not included in the inversion


Effect of optimisation on diurnal emissions profiles

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Weekday Saturday Sunday

0

0.5

1

1.5

2

2.5

Diurnal emission factor profiles: original and adjusted emissions

Original

Adjusted, all sensors

Adjusted, AQMesh sensors only

Emis

sion

fact

or


Effect of optimisation on mean emission rates

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Optimisation using AQMesh sensor data only

Mean first-guess emission rate

Mea

n ad

just

ed e

mis

sion

rate

(g/k

m/s

)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Optimisation using AQMesh sensor data and reference mon-

itor data

Mean first-guess emission rate

Mea

n ad

just

ed e

mis

sion

rate

(g/k

m/s

)


Effect of optimisation on mean emission rates

-60.0%

-40.0%

-20.0%

0.0%

20.0%

40.0%

60.0%

Average %

change-2.8%

Optimisation using AQMesh sensor data only

Percentage change in mean emission rate per road source

-60.0%

-40.0%

-20.0%

0.0%

20.0%

40.0%

60.0%

Average %

change-3.0%

Optimisation using AQMesh sensor data and reference monitor data

Including reference data causes big changes in just a few sources


Example output at reference monitors: 5th July 2016

Montague Rd

Regent St

Gonville Place

Parker St

Newmarket Rd


7-day average concentration: Adjusted - Original

Example of how the optimisation process affects concentration contours:General reduction, but increase in some areas

+30

-30

NOX ug/m3

0


Discussion and further work• We have developed an optimisation scheme to use data from a

network of sensors to automatically adjust emissions and thereby improve model results

• Tests show that the scheme works and initial results are encouraging, but there is more work to do, for example:– More than 1 pollutant– Other source types

• The optimisation scheme run times are also encouraging: approx 15 minutes to run 3 months of hourly data with 305 sources and 25 receptors, carrying out the optimisation for each individual hour

• The values of uncertainty and covariance factors used so far are largely arbitrary; we need to use realistic values to obtain meaningful results

• After Cambridge, the next step is to run the scheme with sensor data collected at Heathrow during the NERC SNAQ project.


Thank you

• Thanks again to CERC’s partners in this work:– Rod Jones & Lekan Popoola, Department of Chemistry, University

of Cambridge– Dan Clarke, Cambridgeshire County Council, Cambridge– Jo Dicks & Anita Lewis, Cambridge City Council, Cambridge– Ian Leslie, Computer Laboratory, University of Cambridge– Amanda Randle, AQMesh

• For more information about the ADMS-Urban dispersion model, see www.cerc.co.uk/Urban

Thank you for listening!

http://www.cerc.co.uk/Urban

amy stidworthy - optimising local air quality models with sensor data - dmug17

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