Urban air quality simulation Vivien Mallet 1 , 2 With contributions - - PowerPoint PPT Presentation

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Urban air quality simulation Vivien Mallet 1 , 2 With contributions - - PowerPoint PPT Presentation

Aug 26, 2023 272 likes •958 views

Urban air quality simulation Vivien Mallet 1 , 2 With contributions by Anne Tilloy 1 , 2 Raphal Prillat 1 , 2 David Poulet 3 Fabien Brocheton 3 Frdric Mah 4 Pierre Pernot 4 Fabrice Joly 4 1 INRIA 2 CEREA, joint laboratory cole des Ponts

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Urban air quality simulation

Vivien Mallet1,2 With contributions by Anne Tilloy1,2 Raphaël Périllat1,2 David Poulet3 Fabien Brocheton3 Frédéric Mahé4 Pierre Pernot4 Fabrice Joly4

1INRIA 2CEREA, joint laboratory École des Ponts ParisTech - EDF R&D, Université Paris-Est 3Numtech 4Airparif

Berkeley–Inria–Stanford Workshop, Stanford University, May 2013

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Quick introduction to urban air quality simulation

Simulation of pollutant concentrations over a city with street resolution.

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Urban air quality simulation: what for?

Objectives

1 Evaluating the air concentrations of NO2, PM10, O3, . . .

Analyzing: exposure of population for one or several past years Forecasting: for the next few days

2 Supporting decision making

Characterizing: emission sources, local versus regional pollution Testing: scenarios of emissions reduction, new roads or industrial facilities

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Simulation tools: numerical models with street resolution

Classical model: ADMS Urban

1 Computing the stationary solution of the reactive transport equation

Every point source creates a plume, with Gaussian shape crosswind Parameterization for the standard deviations depending on meteorological variables Special treatment within the streets

2 Inputs

Time-dependent: spatial distribution of emissions, background pollutant concentrations, meteorological variables (one value for the whole domain) Time-independent: street network

3 High computational costs

∼ 10 min of computations for a single date, i.e., ∼ 4 h for a full day

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Simulation tools: numerical models with street resolution

Output points of ADMS Urban for Paris (east part)

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An important source of information: observations

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Merging model outputs and field observations

Data assimilation classical assumptions

The error on the simulated concentration vector xb has mean 0 and variance B The observation vector y can be compared with Hxb where H is called the observation operator The error on the observation vector y has mean 0 and variance R No correlation between simulation and observational errors

BLUE: best linear unbiased estimator

BLUE is the linear estimator xa = Lxb + Ky whose error has mean 0 and variance A, so that A has minimal trace BLUE reads xa = xb + K(y − Hxb), with K = BH⊤(HBH⊤ + R)−1

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SLIDE 8

Parameterization for the error variances

Observational error

Observational error variance: R = rI

Simulation error

Simulation error covariance: Bij = b exp

  • − dij

Ld

  • exp
  • −|Pi−Pj|

Lp(i,j)

  • dij: distance, along the network, between the projections on the

network of the output points i and j Pi: distance to the road network Ld and Lp(i, j) = Lp + α min (Pi, Pj): decorrelation lengths

Determination of the parameters

Statistical study of y − Hxb, whose variance should be HBH⊤ + R Leave-one-out cross-validation

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Simulation error covariances

With respect to a traffic station

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Simulation error covariances

With respect to a background station

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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SLIDE 20

Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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SLIDE 23

Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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SLIDE 28

Before and after assimilation (preliminary result)

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SLIDE 29

Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

596000 598000 600000 602000 604000 606000 608000 2424000 2426000 2428000 2430000 2432000 2434000 15 30 45 60 75 90 105 120 135 596000 598000 600000 602000 604000 606000 608000 2424000 2426000 2428000 2430000 2432000 2434000 15 30 45 60 75 90 105 120 135

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SLIDE 33

Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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SLIDE 41

Before and after assimilation (preliminary result)

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SLIDE 42

Before and after assimilation (preliminary result)

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SLIDE 43

Before and after assimilation (preliminary result)

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Before and after assimilation (preliminary result)

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SLIDE 45

Before and after assimilation (preliminary result)

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SLIDE 46

Before and after assimilation (preliminary result)

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SLIDE 47

Before and after assimilation (preliminary result)

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SLIDE 48

Before and after assimilation (preliminary result)

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SLIDE 49

Before and after assimilation (preliminary result)

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SLIDE 50

Before and after assimilation (preliminary result)

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SLIDE 51

Before and after assimilation (preliminary result)

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SLIDE 52

Before and after assimilation (preliminary result)

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SLIDE 53

Before and after assimilation (preliminary result)

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SLIDE 54

Before and after assimilation (preliminary result)

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SLIDE 55

Before and after assimilation (preliminary result)

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SLIDE 56

Before and after assimilation (preliminary result)

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SLIDE 57

Before and after assimilation (preliminary result)

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SLIDE 58

Leave-one-out cross-validation (preliminary result)

Station Error change (%) AUB −8 BAGN +15 BASC −44 BONA −45 CELE −33 ELYS −44 ETU6 −44 HAUS −56 IVRY −44 PA12 −50 PA13 −7 PA18 −42 PA4C −49 PERA −51

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SLIDE 59

Standard deviation of the analysis (preliminary result)

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SLIDE 60

Reduction of the standard deviation (preliminary result)

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SLIDE 61

Data assimilation at urban scale

Running operationally since June 2011

See http://votreair.airparif.fr/ Real-time traffic → emission model → ADMS Urban → real-time

  • bservations → data assimilation

Still a prototype, but will be extended to Paris or Paris region by Airparif

Part of Numtech products

For air quality agencies and cities Might need to assimilate new type of observations Need for a better uncertainty estimation.

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SLIDE 62

Reduction strategy

Dimension reduction

Projection of inputs p (when necessary) and outputs x into a reduced subspace E.g., for outputs, application of principal component analysis on

  • utputs of a one-year simulation

99% of total variance explained with just 8 modes x ≃ 8

j=1 αjΨj = Ψα

5 10 15 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Relative part of unexplained variance against number of modes

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SLIDE 63

Projection modes

Example for Clermont-Ferrand

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SLIDE 64

Reduction strategy

Reduced model

Complete model: x = M(p) Reduced model: α = Ψ⊤M(p); note that x ≃ ΨΨ⊤M(p) p ∈ R10 and α ∈ R8 are low-dimensional vectors

Emulation

Components of α show a smooth dependence on the components of p Emulation consists in finding a surrogate function m for Ψ⊤M We can always reconstruct the full output: x ≃ Ψm(p)

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SLIDE 65

Building the emulator

Training values

Let us consider the jth component of Ψ⊤M, and its emulator mj We draw M samples p(i), possibly by latin hypercube sampling We apply the reduced model to constitute the learning set: Ψ⊤

j M(p(i))

Emulator formulation

The emulator is made of two parts: mj(p) =

10

  • k=1

βj,kpk

  • Regression

+

M

  • i=1

wi,j(p, p(1), . . . , p(M))

  • Ψ⊤

j M(p(i)) − 10

  • k=1

βj,kp(i)

k

  • Interpolation of the residuals

Different options for the interpolation of the residuals:

Kriging (particular case of Gaussian processes), which also provides an uncertainty estimation; Interpolation in high dimension with radial basis functions Even the closest neighbor(s)

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Urban air quality simulation May 2013 65 / 67

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SLIDE 66

Model reduction applied to urban simulations

Computational costs: dimension reduction, emulator training and prediction

About 6 months of simulation to determine the reduced subspace spanned by the columns of Ψ M = 2000 samples for the emulator training, i.e, less than 3 months

  • f simulation

Full ADMS Urban cost: ∼ 10 min on 12 cores for one date (i.e, one hour) Emulator prediction cost: 50 ms

  • V. Mallet

Urban air quality simulation May 2013 66 / 67

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SLIDE 67

Summary and perspectives

Data assimilation

Merging model outputs and observations

1

Strongly improves the evaluation of air quality across the city

2

Provides insights on the best locations for the monitoring stations

Requires better uncertainty estimation

Model reduction

Dimension reduction is very efficient on outputs Emulation is possible and is so fast that it dramatically changes the perspectives

A few perspectives

Propagation of inputs PDFs through the emulator Inverse modeling: computing the a posteriori PDFs on the inputs

  • V. Mallet

Urban air quality simulation May 2013 67 / 67