The Sensitivity of the Predictions of a Roadside Dispersion Model to Meteorological Variables: Evaluation Using Algorithmic Differentiation

Abstract

Dispersion and transformation of air pollution originated from a network of vehicular sources can be evaluated using the CAR-FMI model, combined with a meteorological pre-processor, MPP-FMI. The aim of this study is to analyse the sensitivities of both the meteorological pre-processor and the roadside dispersion model to the variations of model input values, taking especially into account the meteorological variables. Comprehensive and systematic analyses of the sensitivities of atmospheric dispersion models have been scarce in the literature. Such sensitivity analyses can be used in the refinement of both categories of models. The sensitivity analyses have been performed using an algorithmic differentiation (AD) tool called TAPENADE. We present selected illustrative results on the sensitivities of the meteorological pre-processing model MPP-FMI and the roadside dispersion model CAR-FMI on the model input variables. However, the AD method in general could also be applied for analysing the sensitivities of any other atmospheric modelling system.

Questions and Answers

Questioner: Heinke Schluenzen

Question: The approach assumes linear relations which are not true for the real atmosphere. What is the conclusion for modelling based on this analysis?

Answer: The method of algorithmic differentiations (AD) does not assume linear relations. However, in this work, to be able to inter-compare the sensitivity of the output parameters of the model to the input data, the partial derivatives needed to be scaled according to the range of the respective input data; thus assuming a linear relationship. The scaling, which assumes a linear relationship, is not a problem specific for AD. The issue raised can be minimised with confidence using AD by increasing the number of data points. The conclusion concerning this sensitivity study is that the most fundamental input parameter to the model combination of MPP-FMI and CAR-FMI is wind speed (U). The second most important is solar radiation ($R_\mathrm {S}$).

Questioner: Peter Viaene

Question: How difficult was it to apply TAPENADE to your code?

Answer: To apply TAPENADE to the code was not that difficult. The main work was to make the computer programs into a FORTRAN subroutine that takes the independent input variables of interest and outputs the dependent output variables. This subroutine is then the top routine that TAPENADE needs to know and the subsequent code will undergo source transformation. Then TAPENADE is told which are independent and dependent variables of interest. The next step was to write a wrapper subroutine to handle the differentiated code which was used construct all the Jacobians (column by column in the forward mode).

Questioner: Emmanouil Oikonomakis

Question: According to your talk, the 2nd most sensitive parameter on the stability ($L^{-1}$) is solar radiation. Does that mean that a consistent trend in solar radiation have a systematic effect on the stability $L^{-1}$?

Answer: For the meteorological pre-processor (MPP-FMI) that was investigated in this study, an increase in solar radiation ($R_\mathrm {S}$) will always favour unstable conditions. This behaviour of the model is systematic. However, in the study, artificial data was used. When using measured data as model input it is highly likely that the many input parameters are likely to be, at least to some degree, interdependent. This interdependency is not possible to study with MPP-FMI but would have to be studied with a boundary layer dynamics model.