From the journal Environmental Science: Atmospheres Peer review history

06-Jul-2022

Dear Mr Leinonen:

Manuscript ID: EA-ART-05-2022-000048
TITLE: Modeling atmospheric aging of small-scale wood combustion emissions: distinguishing causal effects from non-causal associations

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Reviewer 1

Review of the manuscript “Modeling atmospheric aging of small-scale wood combustion emissions: distinguishing causal effects from non-causal associations” by Ville Leinonen et al.

The manuscript describes the analysis of data from aerosol chamber experiments aimed at studying the atmospheric aging of transformation of residential wood combustion emissions. The experiments and their main results (which were interesting and significant) were described in previous publications (Titta et al., 2016; Hartikainen et al. 2018). In this study, based on the data of these experiments, the authors created an empirical model that includes a system of ordinary differential equations. Several advanced statistical techniques were applied to reduce the dimension of the system, form “interaction variables” and investigate the causal relationships between the selected variables. Most of these techniques (especially those aimed at studying the causality) are not widely used in the atmospheric research, but the manuscript describes them only very briefly. Consequently, it is difficult to read, and the information provided in the manuscript is hardly sufficient to allow a reader to reproduce the analysis. The goals of the analysis are not clearly explained. Apparently, the authors tried to investigate if it is feasible to derive useful information on the aerosol aging from the statistical analysis of the relationships between multiple observed variables. The authors have managed to identify some meaningful causal links between the variables of their empirical model, but the study can hardly be regarded as success, because the very complex analysis did not result in any new knowledge on the atmospheric transformations of wood combustion. Moreover, it is impossible to judge if the established relationships are statistically significant or not: the model coefficients are reported in Table S7 without confidence intervals.

Having said all that, I do not doubt that the study is highly original. The authors have done a lot of work, and I hope that their experience described in this manuscript can be instructive and of interest to other researchers dealing with the analysis of aerosol chamber experiments. Therefore, despite the obvious shortcoming of the manuscript, I think it deserves to be published in Environmental Science: Atmospheres after the authors address my comments given below.

1. Abstract and Sect. 4: The authors say about a stochastic model, but I do not think that they have actually created such a model. I would say they built a multiple regression model for the time differences. Typically, stochastic models estimate probability distributions and this is certainly not the case in this study.
2. Sect. 2.1.2: It would help if the authors provided a mathematical formulation for the smoothed estimates.
3. Eq. (1): Could the authors explain more clearly the purpose of creating a regression model by using a causal discovery algorithm? Is there a definite measure of “goodness” of such a complex model?
4. Sect. 2.2.2: What are the “interaction variables”? Is any of them a product of two simple variables? It would help if the interaction variables were explicitly shown as part of the model equation.
5. Sect. 2.2.4: What are the tuning parameters? Were they varied manually? Within which limits?
6. Sect. 2.2.4: Could the authors explain why they did not split the dataset into the training and validation subsets randomly or just by withdrawing each second data point?
7. I seriously doubt that the confidence intervals estimated for a model created without LASSO are really relevant for a model created with LASSO.
8. Fig. 5: Why the confidence intervals do not cover the difference between the modeled and observed evolution? Is this because they are not evaluated properly (see my previous comment)?
9. Captions for Figs. 5, 7, 9, “for the level”: of what?
10. Could the authors provide mathematical equations (at least, symbolic) of the system which was used to generate the simulated data?
11. Sect 3 is entitled as “results and discussion”, but I do not see any discussion. What are the takeaways from so complex analysis for aerosol scientists?
12. Sect. 4, “We recommend considering the errors in similar studies by filtering data in the future”. Can the filtering be one of the possible reasons for the unrealistically narrow confidence intervals? If so, the authors should perhaps first learn how to deal with this issue before recommending the use of the filtering to others.

Reviewer 2

Leinonen et al. describe the use of a causal discovery approach to determine relationships and model time series data for gas and particle phase pollutants in environmental chamber experiments performed on emissions from wood combustion. While the approach is novel and may provide useful insight on organic aerosol systems from complex mixtures (i.e., wood combustion emissions), the paper, as written, is insufficient and weak for the following reasons: (i) it does not describe the causal discovery method clearly, (ii) I have objections with how the covariates and outcome variables are assigned and used, and (iii) both the input data in the methods section and output data and findings in the results section are not very interpretable. I do not think this work, as presented, will be useful to the atmospheric chemistry community. It also does not move the ball with regards to understanding OA evolution from biomass burning emissions. In addition, recent modeling work has shown that PTR-ToF data can be used to explain bulk OA evolution and SOA formation from biomass burning emissions (e.g., Ahern et al., 2019; Akherati et al., 2020), which places limits on the value of this approach. Based on this assessment (see comments below), I recommend that this paper be declined from publishing in ESA.

Comments (major comments marked with a *):
*1. Sections 2.2 to 2.3: These sections describe how the causal discovery algorithm was applied to these chamber data. I found these sections to be insufficient. They are opaque, inconsistent in terms of terminology, and hard to follow. I wasn’t familiar with causal discovery methods so I read this paper instead: https://www.nature.com/articles/s41598-020-59669-x. The authors should see how well the methods have been described in this Scientific Reports paper for a general audience and try to emulate that.
*2. Terminology: Why are the outcome variables (POA1-2, SOA1-3) also used as interaction variables? In the results, it’s obvious that an outcome variable (say, SOA1) will have a causal relationship with an interaction variable that has the outcome variable itself (in this case, O3*SOA1).
*3. Training and testing: Without robust training and test data, the approach cannot be rigorously evaluated. Perhaps this work should be presented as a methods paper first where causal relationships can be identified on a benchmarked (synthetic?) dataset. See, for example, the case study used in the paper cited in comment #1.
4. Page 3, right column: That OA is enhanced by a factor of 2 to 3 after photooxidation is inconsistent with the broader chamber literature with biomass burning. See, for example, Hennigan et al., 2011; Ortega et al., 2013; Tkacik et al., 2017; Ahern et al., 2019; Akherati et al., 2020. On a related note, how does ‘nighttime’ aging differ from ‘daytime’ aging in OA enhancement?
5. Page 4, both columns (starting with ‘Few attempts…’): The state-of-the-science in representing the physicochemical evolution of organic compounds in models - as it pertains to OA from wood combustion - is very poorly described in these paragraphs. I expect the literature review to be much more insightful and pertinent to the contributions of this work. The literature review around the use of causal models is non-existent.
6. Page 4: what do you mean by ‘stabilization of the sample’?
7. Page 5: What was the point of adding O3 to the chamber during the photooxidation experiments? Were NO3 radicals formed in the nighttime experiments through the presence of NO2 and O3? If yes, how were measurements gathered during injection separated from effects of oxidation chemistry?
8. Page 5: Why was OH only estimated from 30 mins of D9 data when the photooxidation length was longer (4 hours)? A better method – to deal with instrument noise – is to first calculate the OH exposure and fit the OH exposure to determine the OH concentrations.
9. Page 6: The discussion around determining an optimal threshold to decide what tracers to consider is not very clear. I recommend reworking and expanding this since this is an important task. For instance, monoterpenes might be a small fraction of total VOC emissions from wood combustion but they are extremely important as an aerosol precursor if one is interested in developing models to determine SOA formation. One would want to make sure that minor but important SOA precursors are not relegated via this thresholding approach.
*10. Page 6: If all of the emissions are from wood combustion, why is there a need for a hydrocarbon-like OA factor? It seems very strange that the SOA factors cleanly separate out as the SOA formed via the 3 oxidants and that’s how the authors interpreted the factors. Is Figure 1 for the 3 SOA factors?
11. Section 2.1.2: The chosen method to filter the data is unclear and so is it’s description. Why not use a simple moving average?
12. I would recommend adding a Table in Section 2 that lists all the covariates and outcome variables being used to create the causal model.
13. Page 7/8: What is the ‘PC-algorithm’?
14. Figure 7: Since this is a chamber experiment, shouldn’t the losses of all particles be dictated by wall losses?
*15. Page 13: ‘As atmospheric measurement data contain large uncertainties, and our measurements of combustion emissions and their aging are no exception, we studied how these uncertainties affect our model by using simulated data sets.’ I didn’t see any instance where uncertainties in the measurements were systematically accounted for and incorporated in the modeling approach. Similarly, I don’t see evidence for the statement that follows: “Based on the simulations, we filtered the initial time series before applying the model and could reduce the error related to the measurement process, thus making the model and the obtained structure more accurate. We recommend considering the errors in similar studies by filtering data in the future.”.
*16. The manuscript is full of confusing descriptions and extremely generalized statements. Consider, this sentence, from a paragraph from the conclusions section: “…most of the dependencies without causal attribution in the simulated model are correlated with at least some of the correct causalities.” What dependencies? What have they causally attributed to? Correlations with causalities? This makes very little sense. Here is another: “From a theoretical point of view, the model developed using the procedure we have explained here is not strictly a causal model, as the procedure is unable to find the correct causal pathways among all possible dependencies without excessive knowledge about the phenomenon.” What knowledge is missing? Why is the model used in this work not a causal model? What is preventing one from finding the correct causal pathways? Finally, this: “In addition, based on the simulations, the model could process prior information more efficiently, which is a topic for further development of the model.” Where has this been shown? The authors need to be specific and preferably cross-reference the statement to the section/figure/table.

REVIEWER REPORT(S):
Referee: 1

Comments to the Author

Review of the manuscript “Modeling atmospheric aging of small-scale wood combustion emissions: distinguishing causal effects from non-causal associations” by Ville Leinonen et al.

The manuscript describes the analysis of data from aerosol chamber experiments aimed at studying the atmospheric aging of transformation of residential wood combustion emissions. The experiments and their main results (which were interesting and significant) were described in previous publications (Titta et al., 2016; Hartikainen et al. 2018). In this study, based on the data of these experiments, the authors created an empirical model that includes a system of ordinary differential equations. Several advanced statistical techniques were applied to reduce the dimension of the system, form “interaction variables” and investigate the causal relationships between the selected variables. Most of these techniques (especially those aimed at studying the causality) are not widely used in the atmospheric research, but the manuscript describes them only very briefly. Consequently, it is difficult to read, and the information provided in the manuscript is hardly sufficient to allow a reader to reproduce the analysis. The goals of the analysis are not clearly explained. Apparently, the authors tried to investigate if it is feasible to derive useful information on the aerosol aging from the statistical analysis of the relationships between multiple observed variables. The authors have managed to identify some meaningful causal links between the variables of their empirical model, but the study can hardly be regarded as success, because the very complex analysis did not result in any new knowledge on the atmospheric transformations of wood combustion. Moreover, it is impossible to judge if the established relationships are statistically significant or not: the model coefficients are reported in Table S7 without confidence intervals.

Having said all that, I do not doubt that the study is highly original. The authors have done a lot of work, and I hope that their experience described in this manuscript can be instructive and of interest to other researchers dealing with the analysis of aerosol chamber experiments. Therefore, despite the obvious shortcoming of the manuscript, I think it deserves to be published in Environmental Science: Atmospheres after the authors address my comments given below.

A: We thank the reviewer of the kind words and constructive feedback. We have made several modifications and improvements to the manuscript with the helpful comments by the reviewers and some additional modifications to improve the readability.

1. Abstract and Sect. 4: The authors say about a stochastic model, but I do not think that they have actually created such a model. I would say they built a multiple regression model for the time differences. Typically, stochastic models estimate probability distributions and this is certainly not the case in this study.

A: The reviewer is correct that the definition of stochastic model may be strict in some specific applications and thus we changed the term to “statistical model”

2. Sect. 2.1.2: It would help if the authors provided a mathematical formulation for the smoothed estimates.

A: We added a mathematical formulation of the filtering estimate and reformulated the chapter about filtering. Section is reformulated as given below.
”The filtering method was similar to locally estimated scatterplot smoothing (Cleveland, 1979), in which observations are weighted according to the proximity of the measurement y_(k,t1) from the measurement y_(k,t0) which state is estimated.

α_(k,t_0 )= ∑_(t_1=1)^(t_0)▒〖w((t-t_0)/h)(y_(k,t_1 )-β_0-β_1 (t-t_0)〗 (1)
(w(x)= {█((1-|x|^3 )^3,when|x|<1@0,when |x|≥1)┤ (2).

We applied the method separately to every time series. The number of previous measurements used (h = time window) to estimate the current state α_(k,t0) was determined in each individual time series by calculating a weighted linear regression (with coefficients β_0 and β_1 and weights (w(x)) to the time series and choosing a window such that the filtered time series was representative to time series. The time series had different ratios of noise to total variation due to different measurement instruments and time resolutions. Figure 2 shows the effect of filtering for one variable during experiment 2B.”

3. Eq. (1): Could the authors explain more clearly the purpose of creating a regression model by using a causal discovery algorithm? Is there a definite measure of “goodness” of such a complex model?

A: The model constructed here consists not of only one regression model but multiple regression models acting as pathways between the initial state of the process and the outcomes from the photochemistry and other processed involved. Causal discovery algorithm is a tool for finding these multiple different regression models in a manner explaining the highest possible proportion of the variation in the measured data. This has been now clarified more in detail in the beginning section 2.2:

“4. Calculating the modeled evolution using the ordinary differential equation (ODE) system deSolve (Soetaert et al., 2010), using estimated coefficients as reaction coefficients, the first observation from the experiment as the initial state and with multiple values of two parameters which the user needs to define. Select values of those parameters based on the smallest RMSE for the calculated evolution.”
A: We tested the model in simulation studies by using metrics that are directly related to 1) the accuracy of the model to represent the evolution and 2) the accuracy of the model to represent the structure. These metrics were also used to evaluate the effect of filtering, correctness of the structure, fraction of uncertainty in data points, and effect of correct and incorrect prior information to the model.

For wood combustion, we used only RMSE to select the model. As we don’t have information about the correctness of the structure, we couldn’t use those metrics for the structural accuracy to evaluate models for wood combustion.

Below is the text of used metrics in the supplement, which we slightly modified for this revision:

“We measured the performance of the model in simulated data set by two ways. First is the accuracy of the model fit to the simulated data set: how well the model can capture simulated evolution and how well the model can predict the simulated evolution after fitted data set. Second can be called as structural accuracy: how well the underlying causal structure of variables can be returned by the model.
For measuring accuracy of the model fit, we compared the evolution obtained from the model to measurements. Evolution was then compared to true evolution, not including the error added to the simulations, using Root Mean Squared Error (RMSE) for each time series. To equally weight each time series when calculating RMSE, each time series were scaled by dividing those with its standard deviation before calculating RMSE. In further text, we refer to this scaled version as RMSE.
In addition to the accuracy of the model, we also evaluated the predictive accuracy of the model. We used the obtained coefficients from the model to predict further time steps of the evolution of the system. Then we compared the prediction to the same time steps from the real system and evaluate the accuracy of model prediction using RMSE. Prediction length was 30% of the simulated data set used to fit a model.
For measuring structural accuracy, we used adjacency precision (AP), adjacency recall (AR) (Scheines and Ramsey, 2016) and F-score (Singh et al., 2017). AP was defined as a fraction of correct edges in the model of all proposed edges. AR was defined as a fraction of correct edges in the model of all correct edges. F-score was defined based on AP and AR as
F_score= 2*(AP*AR)/(AP+AR) .
In addition to F-score, we wanted to study whether incorrect predictors for variables were close to correct causes and whether the model could find a good replacement for each correct predictor that was not chosen for modeled structure. Correlation was used to measure closeness here. For each correct predictor we calculated correlation between it and each predictor in the model (for sameΔ(x)). The maximum of these correlations was taken as the value for that predictor. This results that if the correct predictor was in the model, correlation was 1. In the results section we have calculated the mean value of correlations for all the predictors.”


4. Sect. 2.2.2: What are the “interaction variables”? Is any of them a product of two simple variables? It would help if the interaction variables were explicitly shown as part of the model equation.
A: We thank the Reviewer for asking this, as it was not stated clearly in the manuscript. Interaction variable is indeed a product of two simple variables. We modified the formula 3 (previously formula 1) to also contain an example of interaction variable to clarify this:

“As the output of the procedure, we learn linear differential equations for each variable of interest x_j,j=1,…,n, Eq. (3):
〖Δ(x_(j,t) )=x〗_(j,t+1)-x_(j,t)=β_0+β_1 x_(1,t)+β_2 x_(2,t)+⋯+β_ik x_(i,t) x_(k,t)+⋯ (3)
These differential equations describe how the difference of variable value between subsequent time points is determined by values of measured variables (x_i:s describe the variables used as itself and x_i x_k variables used as interaction variables) immediately before the time interval.”

5. Sect. 2.2.4: What are the tuning parameters? Were they varied manually? Within which limits?
A: We referred here to the tuning parameters alpha (significance of the dependency, can vary between 0 and 1) and depth (“a number of nodes conditioned in the search”), which are described in section 2.2.1. Those were varied manually. The description is pointed out in the text as “the tuning parameters (see section 2.2.1 for description)”.

6. Sect. 2.2.4: Could the authors explain why they did not split the dataset into the training and validation subsets randomly or just by withdrawing each second data point?
A: The data used in this study was from four experiments, which are further divided into two dark aging and two photochemical experiments due to the differences in oxidation pathways. The number of data points (around 100 / experiment, i.e. around 200 / aging type) is relatively low, especially as the number of variables predicted is quite high (15 for dark and 17 for photochemical experiments).

As the time series has the nature that the observation can be dependent on previous observations, we considered the option to use a certain time period as a test data. Most reasonable selection would be the end of the measurement period as the observations in the beginning would be used to “forecast” the observations in the end. However, due to the relatively small number of observations we decided not to split the data.

7. I seriously doubt that the confidence intervals estimated for a model created without LASSO are really relevant for a model created with LASSO.
8. Fig. 5: Why the confidence intervals do not cover the difference between the modeled and observed evolution? Is this because they are not evaluated properly (see my previous comment)?

A: The reviewer is correct; the confidence intervals are not really good for LASSO.
The problem(s) we faced with bootstrap confidence intervals were that
1) If LASSO is used, LASSO can select different predictor variables and therefore the used structure might be different for each bootstrap sample
2) if LASSO is not used, the penalty term applied in LASSO is not also applied, hence the
coefficients in the model can be different than what LASSO solution would give.

For calculating confidence intervals, we didn't use LASSO, hence the problem 2) was faced.
With this approach we tried to illustrate the potential uncertainty in the estimates, but it might be too confusing. Thus, we have now removed the confidence intervals from the figures.

9. Captions for Figs. 5, 7, 9, “for the level”: of what?
A: Predicted level. Added word “predicted”.

10. Could the authors provide mathematical equations (at least, symbolic) of the system which was used to generate the simulated data?
A: The systems (for smaller and larger dataset used) are now shown as tables in the supplement, similar to what have been provided for wood combustion experiments (Tables S1 and S2 in the revised supplement). We would like to note here that in a smaller data set, differential equations are following the Laws of Mass Action. This is not true for the larger data set we used, where equation A*B -> C doesn’t necessarily mean that A*B -> A and A*B -> B (i.e. the A*B doesn’t consume A and B). Also, even if the names of larger system are from the real experiment, the connections between variables don’t represent reality.

 
11. Sect 3 is entitled as “results and discussion”, but I do not see any discussion. What are the takeaways from so complex analysis for aerosol scientists?
A: The reviewer is correct; the discussion part is rather narrow and thus the section is now renamed as “Results”. Our takeaway for aerosol scientist is, that even though the analysis is complex, it is much simpler than the detailed chemistry models which are often used for similar problems. With this kind of approach, the dependencies between variables can be detected with lower computational cost, which gives new insight on the data itself, and give prior information for more detailed chemical analyses i.e. point towards the right direction. We added the text below to the Summary and conclusions -section.

“With the introduced model, the dependencies between variables can be detected with lower computational cost than the detailed chemistry models would require. The results of the model give new insight on the data itself and give prior information for more detailed chemical analyses.”

12. Sect. 4, “We recommend considering the errors in similar studies by filtering data in the future”. Can the filtering be one of the possible reasons for the unrealistically narrow confidence intervals? If so, the authors should perhaps first learn how to deal with this issue before recommending the use of the filtering to others.
A: The problems with confidence intervals were caused by the OLS fits and, as pointed out by the reviewer, were not suitable here. Filtering itself is a valid method for finding the true evolution path under the highly variating processes. We also tried to clarify the sentence by reordering it to
“We recommend considering the errors in similar future studies by filtering the data.”.

Referee: 2

Comments to the Author
Leinonen et al. describe the use of a causal discovery approach to determine relationships and model time series data for gas and particle phase pollutants in environmental chamber experiments performed on emissions from wood combustion. While the approach is novel and may provide useful insight on organic aerosol systems from complex mixtures (i.e., wood combustion emissions), the paper, as written, is insufficient and weak for the following reasons: (i) it does not describe the causal discovery method clearly, (ii) I have objections with how the covariates and outcome variables are assigned and used, and (iii) both the input data in the methods section and output data and findings in the results section are not very interpretable. I do not think this work, as presented, will be useful to the atmospheric chemistry community. It also does not move the ball with regards to understanding OA evolution from biomass burning emissions. In addition, recent modeling work has shown that PTR-ToF data can be used to explain bulk OA evolution and SOA formation from biomass burning emissions (e.g., Ahern et al., 2019; Akherati et al., 2020), which places limits on the value of this approach. Based on this assessment (see comments below), I recommend that this paper be declined from publishing in ESA.

A: We thank the Reviewer on the constructive feedback on our study. We have now made substantial improvements to the manuscript related to the description of our work and clarified the goals of our study more clearly. We do believe these modifications would address the concerns proposed by the Reviewer.

Comments (major comments marked with a *):
*1. Sections 2.2 to 2.3: These sections describe how the causal discovery algorithm was applied to these chamber data. I found these sections to be insufficient. They are opaque, inconsistent in terms of terminology, and hard to follow. I wasn’t familiar with causal discovery methods so I read this paper instead: https://www.nature.com/articles/s41598-020-59669-x. The authors should see how well the methods have been described in this Scientific Reports paper for a general audience and try to emulate that.

A: We attempted to clarify the concept of causal discovery more in detail, following a paper suggested by a reviewer. In addition, we modified sections 2.2 and 2.2.1. Below is the text we added to the section 2.2.1 to clarify the causal discovery algorithms.
“A causal discovery algorithm (Spirtes et al., 2000) attempts to find the causal structure of variables in a studied system. The causal structure refers to qualitative knowledge on the causal relations. For instance, the algorithm may indicate that X causes Y but gives no information on the strength of the effect. Figure 3 illustrates causal graphs where one-headed arrows, called edges, tell the direction of the causality.
Causal discovery methods can be divided into constraint-based and score-based approaches(Shen et al., 2020; Spirtes et al., 2000). We applied the PC-algorithm (Spirtes et al., 2000) which is a constraint-based method implemented in the R package r-causal (Wongchokprasitti, 2019). In constraint-based methods, a series of tests for (conditional) independence between the variables are carried out. Based on these tests, conclusions on the causal structure can be made. For instance, if X and Y are dependent, Z and Y are dependent, but X and Z are independent when conditioned on Y, it can be concluded that the causal graph has a V-structure X -> Y <- Z. However, without auxiliary information it is possible to construct the causal graph only up to an equivalence class (Spirtes et al., 2000), which in practice means the direction of some arrows may remain unknown.”

*2. Terminology: Why are the outcome variables (POA1-2, SOA1-3) also used as interaction variables? In the results, it’s obvious that an outcome variable (say, SOA1) will have a causal relationship with an interaction variable that has the outcome variable itself (in this case, O3*SOA1).

A: The beauty of this type of model is, that the variables in the model can be act at the same time as outcomes and predictor variables for some other variable. More specifically, the current level of a variable can be predictor for the level at the next time point. e.g. in the example of O3*SOA1, reactions of existing SOA1 with O3 decrease the level of SOA1. If, in turn, SOA1 reacts with NO3, it increases the level of SOA1. This is now discussed with more detail in the text.

“The benefit of this type of model is, that the variables in the model can be act at the same time as outcomes and predictor variables for some other variable. More specifically, the current level of a variable can be predictor for the level at the next time point. e.g. in the example of O3*SOA1, reactions of existing SOA1 with O3 decrease the level of SOA1. If, in turn, SOA1 reacts with NO3, it increases the level of SOA1.“

*3. Training and testing: Without robust training and test data, the approach cannot be rigorously evaluated. Perhaps this work should be presented as a methods paper first where causal relationships can be identified on a benchmarked (synthetic?) dataset. See, for example, the case study used in the paper cited in comment #1.

A: The reviewer is correct, this manuscript is more aimed as methods paper, only that we are using real measured data and supporting it with simulations. We have now highlighted the methodological nature of the work more in the abstract and conclusions.

As pointed out also in the response for reviewer 1, comment 6, we were considering whether to split the data into training and test data. The data used in this study was from four experiments, which are further divided into two dark aging and two photochemical experiments due to the differences in oxidation pathways. The number of data points (around 100 / experiment, i.e. around 200 / aging type) is relatively low, especially as the number of variables predicted is quite high (15 for dark and 17 for photochemical experiments). Therefore, we decided not to split the data into training and test data.

We believe that with simulated dataset results shown in the supplement, we were able to study some of the questions (effect of filtering, correctness of the structure, fraction of uncertainty in data points, effect of correct and incorrect prior information) that are related to the performance of our model.

4. Page 3, right column: That OA is enhanced by a factor of 2 to 3 after photooxidation is inconsistent with the broader chamber literature with biomass burning. See, for example, Hennigan et al., 2011; Ortega et al., 2013; Tkacik et al., 2017; Ahern et al., 2019; Akherati et al., 2020. On a related note, how does ‘nighttime’ aging differ from ‘daytime’ aging in OA enhancement?

A: In Tiitta et al. (2016), enhancement ratios (OA/POA) for dark aging were found to be 1.6 to 2.8, hence not being different from daytime photooxidation.

5. Page 4, both columns (starting with ‘Few attempts…’): The state-of-the-science in representing the physicochemical evolution of organic compounds in models - as it pertains to OA from wood combustion - is very poorly described in these paragraphs. I expect the literature review to be much more insightful and pertinent to the contributions of this work. The literature review around the use of causal models is non-existent.

A: We extended the literature review of wood combustion SOA modeling to include several studies of VBS and SOM approaches. Below is the modified version of that text.

”A few studies have been made to capture the atmospheric evolution of wood combustion emissions in both the gaseous and particulate phases (Ahern et al., 2019; Hartikainen et al., 2018, 2020; Isaacman-Vanwertz et al., 2018; Tkacik et al., 2017).
Models of SOA formation and the evolution of the compounds leading to SOA can be divided into at least two groups. One group of modelling, such as the volatility basis set, aim to describe one or several features of the emission. In the volatility basis set (VBS) approach (Donahue et al., 2006, 2011), the evolution of the constituent phases are modeled based on the volatilities of the compounds, considering the equilibrium concentrations of different compounds in gas and particle phases and how different factors, such as chemical and physical reactions, affect the equilibrium state. This approach with the observational data from smog chamber experiments has been commonly used to estimate the SOA mass produced from combustion emission (Bruns et al., 2016; Ciarelli et al., 2017a; Jathar et al., 2014b, 2014a; Robinson et al., 2007; Zhao et al., 2015) and to estimate the proportional contributions of different SOA precursors to formed SOA (Stefenelli et al., 2019). The VBS scheme have been also applied to model biomass-burning organic aerosol in regional chemical transport model (Ciarelli et al., 2016, 2017b).
Second approach to model SOA, and in particular its precursors in the gas phase, is the family of explicit chemical modeling. There exist several chemical models such as the Master Chemical Mechanism (MCM) (Jenkin et al., 1997; Saunders et al., 2003) and GECKO-A (Aumont et al., 2005), which combine large numbers of chemical reactions and predetermined reaction coefficients to replicate the evolution of the system. MCM has recently been applied to wood-burning emissions by running the model with the most important primary emission species to model the evolution of gas-phase species using a smaller selection of reactions from the entire system (Coggon et al., 2019). These can be used to parametrize SOA production. The Statistical Oxidation Model (SOM) offers an approach somewhere between one-quality models and explicit chemical models. SOM uses several qualities of compounds (such as their volatility and numbers of constituent carbon and oxygen atoms) to predict the SOA mass and atomic O:C ratio (Cappa and Wilson, 2012). SOM have been used to simulate the formation and composition of biomass burning SOA in environmental chamber (Akherati et al., 2020).”

Literature for applying causal model in emission estimation applications is almost negligible, and thus this type of review is difficult to conduct. Thus, we also believe our study can be useful for the community. We have now extended our literature review to neighboring fields of atmospheric science to give better overview on applications of causal models.

“In the field of atmospheric science, causal discovery has been applied in different subfields to both test the usability of the method for a certain kind of datasets, but also to understand the causal pathways of a certain phenomenon. Examples of studies includes exploring causal networks in biosphere-atmosphere interaction (Krich et al., 2020), discovering causality in spatio-temporal dataset of surface pressures in oceans (Runge et al., 2015, 2019), discovering causal pathways among atmospheric disturbances of different spatial scales in geopotential height data (Samarasinghe et al., 2020), and testing causal discovery in synthetic atmospheric dataset of advection and diffusion (Ebert-Uphoff and Deng, 2017).”

6. Page 4: what do you mean by ‘stabilization of the sample’?

A: Stabilization period is a period before the actual experiment, when organic compounds should reach an equilibrium state in the chamber. After stabilization period, oxidants are added into the chamber and the experiment will start. We added an explanation to the text.

“… stabilization (i.e. the period when organic compounds should reach an equilibrium state in the chamber) of the sample”

7. Page 5: What was the point of adding O3 to the chamber during the photooxidation experiments? Were NO3 radicals formed in the nighttime experiments through the presence of NO2 and O3? If yes, how were measurements gathered during injection separated from effects of oxidation chemistry?

A: Ozone was added after the stabilization phase and took approximately 10 min to convert NO into NO2 with a final ozone concentration of about 40ppb, which caused the formation of nitrate radicals according to NO2 + O3  ·NO3 + O2. Measurement of primary wood combustion aerosol was done before ozone injection was started.

8. Page 5: Why was OH only estimated from 30 mins of D9 data when the photooxidation length was longer (4 hours)? A better method – to deal with instrument noise – is to first calculate the OH exposure and fit the OH exposure to determine the OH concentrations.

A: We fitted the slope separately for each time point, using 30 intervals to estimate the slope for the time point. The reason we used only 30 min interval for estimating the OH for each point was that the decrease in d9-butanol level (hence also OH concentration) was varying a lot during the experiment, having steepest decrease right after UV lights were turned on and decreasing was smaller after that. Therefore, the slope estimation using whole time series could have given too small estimates for OH level right after UV lights have been turned on. That have been now clarified also in the text.

“The estimation was based on the d9-butanol tracer method, and the slope was determined separately for each time point from 20 observations (time period of 30 min) around the time at which the OH concentration was estimated. The reason for using only 30 minute interval for estimating the OH at the time was that the decline of d9-butanol (hence the concentration of OH) was highly varying during the experiment. The decline in d9-butanol levels was highest right after UV lights were turned on. The slope estimation (see formula (3) in Barmet et al. (2012)) using whole time series could have given too small estimates for OH level right after UV lights have been turned on.”

9. Page 6: The discussion around determining an optimal threshold to decide what tracers to consider is not very clear. I recommend reworking and expanding this since this is an important task. For instance, monoterpenes might be a small fraction of total VOC emissions from wood combustion but they are extremely important as an aerosol precursor if one is interested in developing models to determine SOA formation. One would want to make sure that minor but important SOA precursors are not relegated via this thresholding approach.

A: We assume the Reviewer means section 2.1.1 and the description therein. To obtain the tracers from PTR-MS data to be used later in the study, EFA was applied as two-step process as described in section 2.1.1. First, EFA is applied with rotation and tracers with very small contribution to any of the factors are remover. Then, EFA is applied again to the reduced data set with rotation and final factors are recovered. Only during the first step tracers are actually removed from the data

One of the advantages of EFA is the fact that it considers the correlations of the tracers instead of raw data (Isokääntä et al., 2020). When using raw data (which is used e.g. in NMF), tracers with very small concentrations or, as Reviewer mentioned, VOCs with a small fraction of total VOCs can remain undetected. This can lead to discarding those tracers from the analysis as insignificant background. However, as mentioned, for EFA used for the PTR-MS data, the concentration of the tracers does not affect the created factorization i.e. which tracer belongs to which factor. The concentrations are considered later when the factor time series are calculated. Thus, even if the monoterpenes would have very small concentration in the experiments, but they do exhibit changes in the concentration (e.g. emissions increase over time, no matter how little) or correlate with other tracers, they likely aren’t removed in our analysis. Please also note that the loading value of 0.3 mentioned is only used when calculating the factor time series. However, in the factor profiles/loadings all values are included as demonstrated in Figure 1, leftmost side. Within the time series, single tracers with very small concentration would not affect the overall temporal behavior of the final factor, but for the interpretation of the profiles, all tracers are considered.

*10. Page 6: If all of the emissions are from wood combustion, why is there a need for a hydrocarbon-like OA factor? It seems very strange that the SOA factors cleanly separate out as the SOA formed via the 3 oxidants and that’s how the authors interpreted the factors. Is Figure 1 for the 3 SOA factors?

A: The factors for POA and SOA are from Tiitta et al. (2016) (https://acp.copernicus.org/articles/16/13251/2016/). The figure 1 is for PTR-MS factors, this is now clarified in the figure caption.

11. Section 2.1.2: The chosen method to filter the data is unclear and so is it’s description. Why not use a simple moving average?

A: Based on the comment from referee 1, we have now added the used formulas to filter the time series. This should clarify the used method more.

To filter the data point y_t, we wanted to use only the observations until the measurement (observations y_1,y_2,…,y_(t-1),y_t). This was selected to emulate the situation where the model would be used to predict the evolution of the system e.g. after the experiment has ended. A simple moving average is a smoothing method, that also uses observations that have been made after the observation that is smoothed (observations y_(t-h),y_(t-h+1,)… ,y_t,…,y_(t+h-1),y_(t+h) to smooth observation y_t, h is the time window used for smoothing). Those observations that are made after the observation that is smoothed are not available for the last observation(s) of the experiment. We attempted to clarify our reasoning for choosing a filtering method in the text.

“The reason for using the filtering instead of smoothing was that if the model would be used to predict the evolution of the system after the end of the measurement, the information is only available until the last observation.”

12. I would recommend adding a Table in Section 2 that lists all the covariates and outcome variables being used to create the causal model.

A: We would like to thank the reviewer for this suggestion. We indeed added a table (Table 1) describing all possible predictor variables for each response variable used in the causal discovery algorithm.

13. Page 7/8: What is the ‘PC-algorithm’?

A: PC-algorithm is a causal discovery algorithm that forms a dependence structure based on testing the conditional independencies of variables given the structure. We hope that text related to causal discovery algorithms and PC-algorithm is now clearer as the section 2.2. and section 2.2.1 of causal discovery algorithm are restructured.

14. Figure 7: Since this is a chamber experiment, shouldn’t the losses of all particles be dictated by wall losses?

A: HR-TOF-AMS and SMPS datasets are wall-loss corrected, which is described more in detail in section 2.3 in Tiitta et al. (2016). This is now clarified in the section 2.1.

Particle wall losses has been calculated using two methods. HR-TOF-AMS data wall loss correction (WLrBC,fix) was calculated from the decay of refractory black carbon (rBC) concentrations measured by the SP-AMS. It was corrected by the decay of elemental carbon concentrations measured by a thermal–optical method. The correction was made because of the increased SP-AMS sensitivity for highly coated particles (Willis et al., 2014). WLSMPS was calculated using the method described in Weitkamp et al., 2007, where measured size distributions are used as the initial condition for the general dynamic equation. The calculated WLrBC,fix values agreed well with WLSMPS.


*15. Page 13: ‘As atmospheric measurement data contain large uncertainties, and our measurements of combustion emissions and their aging are no exception, we studied how these uncertainties affect our model by using simulated data sets.’ I didn’t see any instance where uncertainties in the measurements were systematically accounted for and incorporated in the modeling approach. Similarly, I don’t see evidence for the statement that follows: “Based on the simulations, we filtered the initial time series before applying the model and could reduce the error related to the measurement process, thus making the model and the obtained structure more accurate. We recommend considering the errors in similar studies by filtering data in the future.”.

A: We thank the Referee for noting this, as the material related to these sentences is in the supplement. However, we did not have references pointing there. We have now added the references to the referred paragraph (pointing to supplement results section S2, Tables S4 and S5, and Figure S1).

*16. The manuscript is full of confusing descriptions and extremely generalized statements. Consider, this sentence, from a paragraph from the conclusions section: “…most of the dependencies without causal attribution in the simulated model are correlated with at least some of the correct causalities.” What dependencies? What have they causally attributed to? Correlations with causalities? This makes very little sense. Here is another: “From a theoretical point of view, the model developed using the procedure we have explained here is not strictly a causal model, as the procedure is unable to find the correct causal pathways among all possible dependencies without excessive knowledge about the phenomenon.” What knowledge is missing? Why is the model used in this work not a causal model? What is preventing one from finding the correct causal pathways? Finally, this: “In addition, based on the simulations, the model could process prior information more efficiently, which is a topic for further development of the model.” Where has this been shown? The authors need to be specific and preferably cross-reference the statement to the section/figure/table.

A: We have reformulated the conclusion section and added clarifications for these, and some other sentences. More in detail, we modified the first sentence to be
“Most of the dependencies between the variables without causal attribution in the simulated model are co-varying with at least some of the dependencies assumed as causal by the researchers”.
We deleted the second sentence and wrote additional explanation to the following sentence as
“Due to complex chemistry behind the measured data and great number of compounds and phenomena not measured in our study, the results of the model cannot directly be interpreted as the causal evolution of the combustion emissions in the atmospheric chamber.”.
For the third sentence, we clarified that the simulation results mentioned there can be found in the supplement, especially Tables S6 and S7.
“In addition, based on the simulations (see Supplement and Tables S6 and S7), the model could process prior information more efficiently, which is a topic for further development of the model.”
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06-Oct-2022

Dear Mr Leinonen:

Manuscript ID: EA-ART-05-2022-000048.R1
TITLE: Modeling atmospheric aging of small-scale wood combustion emissions: distinguishing causal effects from non-causal associations

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Reviewer 1

After reading the revised manuscript, I find that the authors have sufficiently addressed my comments. The readability of the manuscript has been much improved, and the confusing points have been clarified. Therefore, I recommend the publication of the manuscript in its present form.