Due to the hourly measurements GEMS provides over the same region, it is natural to ask whether one can benefit directly from the time resolution itself and not only from the resulting larger size of the dataset. Hence, we propose training a machine learning model φ that predicts surface NO2 at a given location z and time t not only from corresponding tropospheric NO2 VCD and meteorological data at time t, but also from (k-1)∈N0 previous hours (N0 denotes the set of natural numbers including zero). This means the model is a mapping φ:Rpk→R, where p is the number of different features: input(z,t):=troposphericNO2VCD(z,t)⋮troposphericNO2VCD(z,t-k+1)meteorological features(z,t)⋮meteorological features(z,t-k+1)⟼φ(input(z,t))≈surfaceNO2(z,t). Here t - j refers to the time j hours before t, where j∈0,1,…,k-1. In all that follows, k is also referred to as the time contiguity of the input features, as it determines how many times each input feature is included in the whole input vector. Note that k = 1 stands for the case in which only input features at current time t are included. Of course, one could also use features at later times t + j, but for simplicity and better readability, we focus on making predictions based on previous-time features in this work.

Our main aim is to inspect whether the performance of the model in predicting surface NO2 at unseen locations will increase by using inputs with higher time contiguity k. Unseen locations are locations from which the model has not seen any training data. As it turns out, it is indeed beneficial to use larger time contiguity k>1 for the machine learning models considered, namely random forests and linear regressors. To the best of our knowledge, this observation has not been made in the literature yet. Regarding work on non-geostationary satellite data, the usage of time-contiguous tropospheric NO2 VCDs is simply impossible, as only single measurements per day are available. We further carefully design experiments that are suitable for answering our main research question about the benefit of time-contiguous inputs. Last but not least, we inspect the influence of tropospheric NO2 VCDs on the models' ability to predict surface NO2 and their influence on the benefit of using time-contiguous inputs. This is of interest as it addresses the question of how useful and necessary satellite observations of NO2 are for the prediction of surface NO2 concentrations.

In Sect.  we describe the different sources of data included in our study. Furthermore, we describe the construction of the datasets used for training machine learning models in our study and give a mathematical description of these datasets. Afterwards, in Sect.  we describe the experiments that provide clear insights into the research questions, e.g., whether time-contiguous inputs can enhance the quality of surface NO2 predictions. We also discuss different loss functions for measuring the performance of trained models on the test dataset. Section  serves as a quick recap of the machine learning models used in this study. Finally, we present and discuss the results of our experiments in Sect. .

In the following, we explain the spatial and temporal pairing of the data sources. Tropospheric NO2 VCDs and meteorological data possess spatial resolutions, as described in the previous section. Consequently, each data point covers an area (pixel) on the Earth's surface, rather than a single point. Here, we associated the location of an in situ station with the VCD pixel or meteorological pixel, whose center is nearest to the station's location (longitude, latitude). Note that the center of a VCD pixel coincides with the respective center of the GEMS satellite pixel, since no regridding is applied.

Tropospheric NO2 VCDs are based on GEMS observations that have been collected within 30 min starting at a quarter to the respective hour, e.g., from 01:45 to 02:15 UTC. In situ measurements of surface NO2 are available as hourly averages, starting on the hour. Temporally, we matched them with the VCDs using this timestamp and found that these data pairs showed the highest Pearson correlation. For example, VCDs between 01:45 and 02:15 UTC were matched with in situ measurements with a timestamp of 01:00 UTC. Unfortunately, at the end of our project, we learned that this was a misinterpretation of the in situ measuring times by 1 h, as the hourly averages actually start at the hour before the given timestamp instead of at the hour of the timestamp, as we had assumed. This means that the VCDs and surface NO2 were not optimally matched within our experiments. However, the abovementioned correlation tests give us confidence that the conclusions of this study are not affected by this mistake, in particular with respect to the improvements in performance when adding data from other measurement times. To maintain consistency in notation, we continue to use the originally interpreted in situ measuring times, but they should be regarded as occurring 1 h earlier. Most meteorological features are given on the hour, which means at a specific point in time. There is one exception, namely evaporation, which is available as an hourly average starting on the hour, similar to in situ measurements. Since the averages of these data sources are taken over different periods of time, there is not a unique way to pair them temporally. Our approach is the following.

Due to the hourly resolution of all data sources, time t is expressed by t = YYYY/MM/DD/HH throughout this work. For example, t = 2021/01/23/01 refers to 23 January 2021 at 01:00 UTC. We associate the in situ measurements of surface NO2, which started at time t and went on for 1 h, with t. In the example, time t = 2021/01/23/01 refers to surface NO2 that has been averaged from 01:00 UTC until 02:00 UTC. Regarding tropospheric NO2 VCDs, the same t refers to measurements that started 45 min later. Hence, t = 2021/01/23/01 describes the VCDs at a time between 01:45 and 02:15 UTC. Finally, for the meteorological features that are instantaneously on the hour, t stands for the feature's value 1 h later at t + 1. Thereby, it is closest to the corresponding VCD time frame. For example, t = 2021/01/23/01 is associated with the meteorological feature at 02:00 UTC.

To sum up, given a location z of an in situ station and a time t = YYYY/MM/DD/HH, we specified a single data point (f(z,t),s(z,t)) that stores surface NO2 s(z,t) combined with the vector of input features f(z,t), which consists of tropospheric NO2 VCDs and meteorological features. As a data preprocessing step, we exclude data points that violate any of the following conditions: 1.

All features are available at location z and time t (tropospheric NO2 VCDs and surface NO2 might be missing for a given z,t, for example, due to clouds).

In the Introduction, we motivate the use of time-contiguous inputs for machine learning models in order to predict surface NO2. For better clarity, we introduce notations and definitions in a mathematical form.

In this study, we considered 23 different features from which we selected 17 to build the feature vectors used in Eq. () as inputs for the machine learning models. The selected and excluded features are listed in Table  and are used in Experiment 1 and Experiment 2; see Sect. . For the feature selection, we proceeded as follows: on the data basis D1,1, we considered 200 different splits into 90 % training and 10 % test stations. For the training data of each split, we calculated the Pearson correlation (see Sect.  for a definition) between in situ measurements of surface NO2 and the respective feature. We selected features which had an absolute mean correlation larger than 0.1. It is worth mentioning that for all 17 of the aforementioned features, the correlation was in fact larger than 0.1 in 98 % of the splits, whereas this was never the case for the remaining six features. More complex feature selection strategies could be applied in the future. However, during this study we focus on the benefits of time-contiguous inputs and not on the optimal choice of input features.

Recall from Sect.  that ΩN is the set of locations and measuring times (z,t) at which all measurements are also available at (N-1) previous hours. Note that ΩN does not parameterize a single dataset but N different datasets DN,k:ΩN→Rpk×R via DN,k:(z,t)⟼f(z,t)f(z,t-1)⋮f(z,t-k+1),s(z,t), which only differ in the time contiguity k∈{1,2,…,N} of the time-contiguous feature vector (f(z,t),…,f(z,t-k+1))T, defined in Eq. ().

As mentioned in the Introduction, we wish to inspect how well a machine learning model is able to make predictions of surface NO2 at locations from which it has not seen training data. This is why we use multiple (six-times) 10-fold spatial cross-validations in all experiments. This involves splitting the dataset 60 times randomly into 90 % training and 10 % test data based on the locations of the in situ stations; see Fig. b for a visualization of a single split. Performance is measured on all the different test datasets and averaged. Due to the limited number of available in situ stations, significant variance in the model's performance is expected across different splits. Therefore, multiple 10-fold spatial cross-validations provide a more reliable estimate of the model's performance compared to a single 10-fold spatial cross-validation. In all that follows, whenever it is mentioned that a machine learning model is trained or tested on DN,k, it implies that the model is trained or tested solely on those data points in DN,k corresponding to the designated training or test stations. Note that for fixed N, surface NO2 that is to be predicted in DN,k is exactly the same for all the different k. Furthermore, for all models, the same 60 splits into training and test stations are considered for spatial cross-validation, which ensures perfect comparability. For a basic outline of a cross-validation pipeline, see Fig. .

Let us recall from Sect.  that our main research question is whether time-contiguous inputs for machine learning models enable higher accuracy for predicting surface NO2. We propose two experiments to gain insight into this question.  

Experiment 1. Do time-contiguous input features provide additional information?

For fixed N, consider the datasets DN,k for different time-contiguities k = 1,…,N. The chosen machine learning model, such as a random forest regressor, is trained and tested on DN,k for all 60 splits from spatial cross-validation. A comparison is made with respect to different k. Fixing N ensures that, regardless of k, the same ground truth (surface NO2) is predicted for computing the cross-validation scores on the test sets. Additionally, all models are trained with the same number of training data points, eliminating any advantage or disadvantage due to differing dataset sizes. Thus, this experiment provides pure insights into the information gain provided by time-contiguous inputs. We conduct this experiment for all N∈{2,3,4,5}.

In a third experiment, we analyze the influence of some features on the performance of the machine learning models. Since testing all the different combinations of input features for all 15 different training and test cases in Experiment 2 would be out of the scope of this study, we focus only on the influence of the tropospheric NO2 VCDs, surface height, and latitude. Note that longitude has not been included during feature selection due to a low correlation with surface NO2. Tropospheric NO2 VCDs are the main consideration within this third experiment since they represent the feature which shows, among all considered input features, by far the best Pearson correlation with surface measurements of NO2, namely around 0.626; see also Table . Although latitude only has a small variation over South Korea and hence a presumably small impact on predicting surface NO2, we considered it (and also longitude) during feature selection to check whether it provides some helpful information. Other studies have also used spatial coordinates to predict surface NO2, mainly over large regions but also over smaller regions, such as over Switzerland . Using spatial coordinates as inputs for a model, however, carries the risk of spatial overfitting, which could make it more difficult to predict surface NO2 outside of South Korea with the same model. This is why we inspect whether the models perform equally well over South Korea without having latitude and surface height as inputs.  

Experiment 3. What is the influence of tropospheric NO2 VCDs, latitude, and surface height on the performance?

We compare four different settings of input features:  

Setting 1. All features selected in Sect. are included, which is exactly the same setup as for Experiments 1 and 2.

Throughout this section, x† ∈ Rn is a vector consisting of n in situ observations of surface NO2, where each coefficient xi†(ti,zi)=s(ti,zi) corresponds to a measurement that has been taken at a given time ti and location (longitude, latitude) zi of a given in situ station. For the sake of simpler notation, we just write xi†, neglecting the dependence on ti and zi within the notation. Similarly, x∈Rn denotes the predictions for x† made by a machine learning model, such as linear regression or random forests. In the following, we discuss different performance measures that quantify the gap between the model's prediction x for x†, the observed surface concentration of NO2.

As pointed out in the Introduction, spatial cross-validation is considered within this research; i.e., data are split into training and test data station-wise. Since the overall number of in situ stations is relatively small, namely 637, the statistical properties of surface NO2 for different test sets are very likely to differ. In particular, the mean or standard deviation of surface NO2 of different test sets will vary. Hence, in order to compare the quality of surface NO2 predictions on different test sets, it is reasonable to use error measures that are more robust or even insensitive to different data distributions.

In order to ensure better comparability of performances of a model on different test sets, one should not use absolute performance measures such as the mean absolute error or root mean square error, since they depend on the scale of the different test sets.

At first glance, it seems reasonable to consider the mean percentage error: MPEx†,x=∑i=1n|xi†-xi||xi†|. The reason why the mean percentage error enables us to compare performances on different test sets is the following property: for every c∈Rn with ci≠0 it holds that MPEcx†,cx=MPEx†,x, where cx† denotes pointwise multiplication. However, since many in situ measurements xi† are very close to or equal to zero, the mean percentage error becomes unstable. As a trade-off, we consider performance measures Ex†,x that are scale-insensitive; i.e., for every λ∈R∖{0} it holds that Eλx†,λx=Ex†,x.

The normalized mean absolute error (NMAE) can be written as NMAEx†,x=∑i=1n|xi†-xi|∑i=1n|xi†|, so the NMAE is just the mean absolute error divided by the mean absolute value of the ground truth x†. If normalization by the standard deviation of x† instead of its mean were considered, this would lead to a measure similar to the coefficient of determination R2; see Appendix . Note that in contrast to the mean absolute error, NMAE is scale-insensitive. Similarly, we define the normalized mean square error (NMSE) as NMSEx†,x=∑i=1n|xi†-xi|2∑i=1n|xi†|2.

Whenever we talk about the correlation between x† and x, we mean the Pearson correlation coefficient (C), which is defined as Cx†,x=covx†,xσx†σ(x), where covx†,x denotes the covariance between x† and x and σx†, and σ(x) is the standard deviation of x† and x, respectively. It should be noted that this is not a performance measure in the sense that x† = x if and only if Cx†,x = 1. Nevertheless, it quantifies the linear relationship between x and x†. Furthermore, it is frequently used in the literature, which is the reason why we consider it in our work, too.

We considered two further scale-insensitive performance measures, the coefficient of determination (R2) and the index of agreement (IOA), which are defined in Appendix .

Although it has already been shown, e.g., by , that linear regression models are not the best for predicting surface NO2, we consider an ordinary least squared regressor as a reference in our study, mainly because it has no tunable hyperparameters, such as regularization parameters, or architecture parameters like those in neural networks (e.g., number of layers, width of layers, activation functions, skip connections). Thus, it provides a clear view on the question of whether time-contiguous inputs are beneficial for this linear regression model. During this study, we used the ordinary least squares regression model provided by the Python scikit-learn package (version 1.2.2, ). In our case of predicting surface NO2 from time-contiguous inputs, the linear regression model is a parameterized function φθ:Rpk⟶Ry⟼Ay+b, where y = (f(z,t),…f(z,t-k+1))T is a (time-contiguous) feature vector defined in Eq. (), A is a 1×pk matrix, and b∈R is a bias term. Let (yn,sn)n=1N be training data, where yn is a feature vector at location zn and time tn and sn the corresponding in situ measurement of surface NO2 at time tn. Training φθ then means to search for a parameter θ = (A,b) that solves the following minimization problem: min⁡θ∑n|φθ(yn)-sn|2. We choose to minimize the squared error since the computation time is much shorter compared to that of other losses such as the absolute error.

There are two main reasons why random forests, a machine learning model originally proposed by , are considered within this research. First, they have already proven to be powerful for predicting surface NO2 in various studies; see, for example, , , , and on OMI and TROPOMI data and on GEMS data. Second, the studies of suggest that random forests are less tunable compared to other machine learning approaches. “Tunable” is defined as the extent to which the performance of a random forest with typical default hyperparameters can be enhanced by adjusting (tuning) those hyperparameters. As discussed before, this reduces the risk of drawing incorrect conclusions about the benefit of using time-contiguous inputs.

In fact, according to , there are mainly four hyperparameters that empirically determine the performance of a random forest:

The first hyperparameter is the number of randomly drawn features considered at every split of a tree. In the Python scikit-learn software package (version 1.2.2, ) that we use for this study, it is called max_features. However, in several other software packages, it is denoted as mtry.

In Experiment 1, we train linear regression models and random forests on D4,k for different time contiguities k∈{1,…,4} of the input features. The test performances of these models are evaluated via six-times spatial 10-fold cross-validation and are illustrated in Figs. b and b, respectively. Specifically, we show average Pearson correlation, NMSE, and NMAE over all 60 splits into training and test stations. We observe that, on average, both linear regression and random forests benefit from a larger time contiguity k regarding all considered performance measures. For example, the average correlation strictly increases from 0.702 for k = 1 to 0.737 for k = 4 in the case of linear regression, and for random forests, it increases from 0.802 to 0.817. Further, the average NMSE decreases from 0.196 to 0.171 for linear regression and from 0.139 to 0.129 for random forests. Therefore, both models benefit from larger time contiguity, but linear regression shows greater improvement, which is expected as it cannot model non-linear effects. Furthermore, we observe that the larger k, the smaller the improvement compared to the case k - 1, which is to be expected since input features at time t - k presumably have a decreasing impact on surface NO2 at time t for larger k.

Although the visualization of average performances suggests an overall trend, it does not clearly indicate whether larger time contiguities (k > 1) consistently improve performance across all 60 station splits during cross-validation compared to k = 1. However, we found that this improvement holds true for all 60 station splits. The performance curves for individual splits are more or less parallel to the average curve. In Figs. a and a, we illustrate this for exemplary station splits, where only five splits are shown for better visibility. To quantify the gain in performance for individual splits between using time contiguity k = 1 and larger time contiguities k>1, we proceed as follows: for a given test dataset, let Ek be the test performance (e.g., correlation) achieved by the model using time contiguity k for its inputs. We define the performance gain of this model over the case with no time contiguity k = 1 in Experiment 1 as 5E1-EkE1-Eopt, where Eopt is the optimal value of the respective performance measure; e.g., Eopt = 1 for the Pearson correlation or Eopt = 0 for NMSE and NMAE. The average performance gains for the cases k∈{2,3,4} compared to k = 1 are depicted in Figs. c and c for linear regression and random forests, respectively. In both cases and for all performance measures, the highest average performance gain is achieved with k = 4. Specifically, linear regression models achieve average performance gains of 15.2 % in correlation, 13.0 % in NMSE, and 7.7 % in NMAE, whereas random forests achieve gains of around 7.8 %, 7.0 %, and 4.7 %, respectively. It is noteworthy that, for linear regression, the performance gain across all 60 splits is approximately at least 12.0 % in correlation, 10.0 % in NMSE, and 6.1 % in NMAE. On the other hand, random forests achieve performance gains of at least 4.6 %, 4.0 %, and 3.1 %, respectively. Therefore, utilizing a larger time contiguity consistently provided beneficial additional information for both linear regression and random forest models.

Additionally, for k = 1 and the best time contiguity k = 4, we examine for each split the orthogonal regression curve between the models' predictions and ground truth measurements of surface NO2 on the corresponding test dataset. For a fixed split, this is illustrated as a two-dimensional histogram in the first row of Fig.  for linear regression and in Fig.  for random forests. Although the histograms are restricted to surface NO2 and predictions between 0 and 40 µgm-3 for better visibility, all data points are taken into account to determine the orthogonal regression curve. It becomes evident that both the slope and the bias of the orthogonal regression curve improve for k = 4 (panel b) compared to k = 1 (panel a), where improvement means that the slope becomes closer to 1 and the bias closer to 0. In the second row of these figures, we plot the mean orthogonal regression curve, which represents the mean slope and mean bias of all 60 orthogonal regression curves. An upper bound for all these curves is represented by the line with the maximal slope and bias across all splits (note that maximal slope and bias might not occur for the same split). Similarly, a lower bound is obtained, and both bounds are shown within the same plots. Both the mean orthogonal regression curve and the upper and lower bounds improved for k = 4 for both linear regression and random forests. However, the improvement is larger for the linear regression models, which is consistent with the previous discussion on performance measures, such as NMSE.

We want to stress another observation: looking at the upper and lower bounds of the orthogonal regression curves, we see that all slopes are smaller than 1, whereas all biases are positive. Further, there is a noticeable gap towards the identity line. Regarding the latter, one possible explanation could be that spatially splitting the dataset into training and test sets causes a large difference in the statistical properties of the training and test sets. This may simply be because there are overall just 637 different in situ stations available, so the law of large numbers may not yet apply well when sampling 10 % of test stations. However, this does not explain why the slopes and biases are not more symmetrically distributed around slope 1 and bias 0. Studying the impact of the number of available in situ stations and their locations on the slopes and biases of these orthogonal regression curves will be an interesting task for future work.

In Experiment 1, the models were trained and tested on DN,k for fixed N but with a different time contiguity k∈{1,…,N} of their input features. This means that for a fixed station split, the number of training data points was the same for all the different k, since the size of DN,k only depends on N (see Table ). However, for M∈{k,…,N-1}, there would be significantly more data points available in DM,k than in DN,k, which could be used during training. To make a fair conclusion about whether a larger time contiguity (k > 1) in the models' input is more beneficial compared to time contiguity k = 1, we need to consider that for k = 1, one can also train on these larger datasets. It should be noted that we have also considered training on smaller datasets, thus on DM,k with M > N. However, non-competitive results were obtained for random forests in these cases. For linear regression, performances were also worse but with some exceptions regarding the NMAE; see Fig.  in Appendix . This is why we restrict the following discussion to training on larger datasets (M ≤ N) only.

Focusing again on the test case N = 4, we compare the performance on test sets in D4,k of models trained on larger datasets DM,k for all M∈{k,…,4} and all k∈{1,…,4}. Note that for M = 4, this is just the setting of Experiment 1. Altogether, 10 different linear regression models and 10 random forest models are used to make predictions of the same ground truths in the split-dependent test sets DN,k.

Average performance measures from spatial cross-validation are shown in Fig. a for linear regression and in Fig. a for random forests. We observe that when training with time contiguity k = 1, i.e., on DM,1, the best results are obtained for M = 4. In other words, there is no improvement on the test set D4,1 if training is done on the larger datasets (M∈{1,2,3}). There is one exception for random forests with the Pearson correlation, where training on D3,1 yields slightly better results on average compared to training on D4,1. However, this difference is quite small, as shown in Fig. a. Moreover, for all performance measures, the best performance across all 10 different training cases is achieved by the models trained on D4,4 with time contiguity k = 4. Note that this is one of the training settings already considered in Experiment 1.

For individual splits, we consider the performance gains that models with time contiguity k > 1 achieve compared to models with no time contiguity (k = 1). Since, in contrast to Experiment 1, we are now dealing with four different training cases for k = 1, we slightly adapt the definition of performance gains from Eq. (): for a given split into training and test stations and fixed N, let EM,k be the test performance (e.g., correlation) on DN,k achieved by a model trained on DM,k. We define the performance gain achieved by this model in Experiment 2 as 6min⁡EP,1-EM,kEP,1-Eopt:P∈{1,…,5}. In other words, for each split, the performance gain is always computed with respect to the best model trained without time contiguity (k = 1).

Average performance gains are depicted in Figs. b and b, which differ only slightly from those in Experiment 1, as models trained on D4,1 are better, on average, than models trained on DM,1. Linear regression models trained with k = 4 still achieve performance gains of 15.0 % in correlation, 12.8 % in NMSE, and 6.6 % in NMAE, whereas random forests achieve average gains of around 7.3 %, 6.6 %, and 4.7 %, respectively. Again, we observe that improvements over k = 1 are not only true on average, but also for each individual split: Figs. c and c show the minimal performance gains over all 60 splits. It shows that linear regression models for k = 4 always achieve an improvement of at least 11.7 % in correlation, 9.1 % in NMSE, and 4.4 % in NMAE. Random forests achieve gains of at least 2.5 %, 3.0 %, and 3.1 %, respectively. Hence, models with a larger time contiguity k > 1 provide reliable and statistically significant improvements (with respect to the performance measures) compared to models with no time contiguity (k = 1). Similar observations are made for the coefficient of determination and the index of agreement, two further performance measures. Definitions can be found in Appendix  and achieved performances in Tables  and  in Appendix .

So far, we have discussed the test case N = 4 in detail. In the remainder of this section, we briefly summarize our similar observations for general N∈{2,3,4,5}: for all N, we observed that the best test performances on DN,k are achieved when training on DN,N, i.e., with time contiguity k = N. If N = 5, we observe that there is barely any difference between training on D5,5 and training on D4,4, which implies that it is not required to use a larger time contiguity than k = 4. Also, for the general test case N, models trained with time contiguity k > 1 achieve reliable performance gains over models trained with k = 1. Results for the test case D2,k are illustrated in Figs.  and  in Appendix .

Altogether, our findings demonstrate that it is indeed reliably beneficial to use time-contiguous input features for predicting surface NO2, in spite of a smaller available training dataset, which answers our main research question. As a rule of thumb, consider the case where surface NO2 is to be predicted at a given location and time for which input features are also available at j≥1 previous hours. Then use j′ = min⁡{3,j} hours, in addition to the features at the current time, as input for a random forest that has been trained with time contiguity k = j′+1 on a dataset Dk,k. If features are not available at previous hours, use the random forest that has been trained without time contiguity. We have demonstrated within this experiment that time-contiguous models provide valuable support whenever they are applicable. An interesting future task would be to inspect whether a similar rule can be observed for other machine learning approaches.

Within this section, we analyzed the difference between time-contiguous models in terms of prediction accuracy. However, we did not systematically assess other potential differences that may arise when switching between models trained with different time-contiguous features. For practical applications, when combining these models to create surface NO2 concentration maps, it remains an interesting avenue for future work to investigate whether the ensemble of such models yields consistent combined spatial patterns in predicted surface NO2.

In Experiment 3, we compare the outcomes of Experiment 2 in four different settings regarding the input of the models, as described in Sect. :  

Setting 1. All features selected in Sect.  are included as input features, which was the setting in Experiments 1 and 2.

Setting 1 is discussed in the previous section, where the results are illustrated in Fig. . Equally detailed illustrations for the remaining three settings are provided in Appendix . A direct comparison between the four settings is made in Fig. : panel (a) shows the average Pearson correlation, NMSE, and NMAE achieved by random forests within these four settings, while panel (b) displays the corresponding average performance gains. For clarity, we only include the results for the models trained on D4,k for different time contiguities k∈{1,…,4}, excluding the models trained on larger datasets DM,k (similar to Experiment 1).

In Setting 3, where latitude and surface height are excluded, the models achieve similar results to those in the original Setting 1. Results are even slightly better without using these coordinates if k > 1. Moreover, the benefit of using time-contiguous input features is larger in Setting 3: average performance gains, calculated with Eq. (), achieved when training on D4,k are 9.3 % in Pearson correlation, 8.3 % in NMSE, and 5.7 % in NMAE. The minimum gains across all 60 station splits are 5.4 %, 3.7 %, and 3.8 % in correlation, NMSE, and NMAE, respectively (see Fig. ). This implies that, similar to Setting 1, including time-contiguous features also provides a reliable improvement in Setting 3. This observation that coordinates are not required as inputs to make good predictions is promising, since it presumably increases the models' chances to also perform well outside of South Korea. Nevertheless, this hypothesis remains to be investigated within further research.

When excluding the tropospheric NO2 VCDs (Setting 2), all performance measures decline, which is expected because the VCDs correlate the most among all input features with the surface NO2 measurements. Despite this, the performances remain acceptable. For instance, with time contiguity k = 1, the average Pearson correlation in Setting 2 is 0.78, whereas it is about 0.8 in Settings 1 and 3, when VCDs are included. Interestingly, without VCDs in Setting 2, the average performance gains achieved with larger k are significantly lower: in Setting 2, the average performance gain is around 2 %, whereas in Settings 1 and 3, it is 3.5 and 4.5 times larger, respectively. Consequently, for time contiguity k = 4, the difference in performance is larger: models in Setting 2 achieve an average correlation of 0.786, while those in Settings 1 and 3 reach almost 0.82. When tropospheric NO2 VCDs, latitude, and surface height are excluded in Setting 4, not only do performances weaken further, but the performance gains also drop below 1 %. In Setting 4, the average correlation is below 0.765 for all k. Similar trends are observed for NMSE and NMAE. This indicates that spatial coordinates play a more critical role when VCDs are excluded, which presumably leads to models that are less capable of generalizing to locations outside of South Korea. Inspecting the connection between including VCDs and the model's ability to generalize to locations outside of South Korea remains an interesting task for the future.

Furthermore, when tropospheric NO2 VCDs are excluded, in both Setting 2 and Setting 4, the use of time-contiguous inputs no longer provides a reliable improvement. Across the 60 station splits, the performance gain is not always positive, which can be seen in Fig. b. Due to this observation that improvements by time-contiguous inputs are only reliable when including VCDs, the following question arises: how is performance affected if VCDs are treated as the only time-contiguous input feature? The experiments covering this case are illustrated in Fig.  in Appendix . We observe that the average performances and average performance gains are higher if the other features are also considered time contiguous. Therefore, one future task could be to find the optimal choice of time contiguity k for each input feature individually.

At the end of this section, we show in Fig.  an example of how predictions of surface NO2 appear on a map for the four investigated settings. We consider latitudes and longitudes within 32° N, 39° N and 124° E, 132° E, respectively. GEMS tropospheric NO2 VCDs on 7 April 2021 from 01:45 to 02:15 UTC are shown in panel (a). We chose this time and day due to little cloud cover in the area and thus only a few missing satellite observations. Predictions of surface NO2 from 01:00 to 02:00 UTC made by random forests are shown in panel (b) for Settings 1 and 3, whereas panel (c) covers the settings with tropospheric NO2 VCDs excluded. All models have been trained with time contiguity k = 4 on D4,4.

We observe that there is a high similarity between predictions made in Settings 1 and 3, when tropospheric NO2 VCDs are included as input features. This is in agreement with our findings from Fig.  that in both settings similar results are achieved regarding all considered performance measures. This observation is promising, as excluding latitude and surface height reduces the spatial bias of the model, which is to be tested in future studies. Therefore, presumably, the model's chance of making suitable predictions in different parts of the world increases. In Settings 1 and 3, the impact of the tropospheric NO2 VCDs on the prediction of surface NO2 is directly visible, since the hotspots of the VCDs and predictions of surface NO2 are depicted at the same locations. On the other hand, when VCDs are excluded in Settings 2 and 4, these hotspots are less recognizable due to a smaller contrast to their neighborhood; see Fig. c. In Settings 2 and 4, the predicted surface NO2 has a coarser resolution, which is to be expected considering that the resolution of meteorological inputs is 8 times coarser compared to the VCDs. In all four settings, the contrast between the hotspots and the background of predicted surface NO2 is less pronounced compared to the contrast observed in the tropospheric NO2 VCDs shown in panel (a). This effect is even more evident in another example from 27 February 2022, shown in Fig. . Notably, the predicted concentrations of surface NO2 over water are only slightly smaller compared to those over land within all settings, even in regions far from the coast, such as the southeastern parts of the maps. However, emissions over water are not expected, aside from maritime traffic. Furthermore, at some distance from the coast, no contribution from land-based emissions is expected due to the short atmospheric lifetime of NO2. Consequently, both the tropospheric NO2 VCDs and the surface NO2 concentrations should be low in these areas. Given the predicted surface concentrations of approximately 7 µgm-3, it appears that the models have likely overestimated surface NO2 concentrations in these areas over water. This aligns with the observation from Fig. , which shows that the models tend to overestimate low surface NO2 values. A possible explanation for this could be that the models were trained only on data from stations located on land or islands.

In the previous sections, the performance of machine learning models is evaluated using whole-year data, spanning January 2021 to November 2022. In this section, we inspect how prediction quality varies across different seasons and throughout the day. Some variation is expected, as the accuracy of GEMS observations also fluctuates. For example, accuracy tends to be lower in the morning due to the shallow boundary layer . For the remainder of this section, we focus on the best-performing models identified in our earlier analysis. Specifically, we reconsider the random forest models from Setting 3 in Sect. , which do not incorporate spatial coordinates as input features. These models were trained on all respective training datasets DN,k, but for this section, their performance is spatially cross-validated on the test datasets for different seasons and times of the day individually. For simplicity, we restrict our attention to models that were trained on the dataset D4,k. Furthermore, we inspect whether benefits from time-contiguous inputs depend on the season or time of the day.

First, we compare the test performance across different seasons. Each season in South Korea is typically defined as a 3-month period: spring (March–May), summer (June–August), autumn (September–November), and winter (December–February). Table  shows the percentage of data points in D4,k belonging to each season. Notably, summer has the fewest valid data points due to the applied filter for the qa value during data preprocessing. In addition, the Pearson correlation between surface NO2, measured at the in situ stations, and VCDs is the lowest in summer (see Table ). These factors likely contribute to the significantly lower performance of the random forest models in summer compared to other seasons (see Fig. ). In contrast, the model performance is the highest in winter across all performance measures, i.e., for Pearson correlation, NMSE, and NMAE. Moreover, we observe that within each season, incorporating time-contiguous inputs improves prediction quality. The performance gains, calculated using Eq. (), are also shown in Fig. . Notably, the largest gains from time-contiguous inputs occur in winter, exceeding 12 % in Pearson correlation for time contiguity k = 4. The smallest gains are observed in summer, with an improvement of only 5 % in Pearson correlation.

Finally, the performance across different times of the day is illustrated in Fig. . Since we focus on training and testing on D4,k, the earliest time window with available data is 10:00–11:00 Korean standard time (KST). The best performance is achieved around midday, while the performance declines in the morning and afternoon. The worst results occur between 16:00 and 17:00 KST, possibly due to the fact that surface NO2 has the weakest correlation with VCDs at that time (see Table ). Moreover, it should be noted that for datasets DN,k with N ≤ 3, in which data points at times earlier than 10:00 KST occur, the performance is expected to further decrease compared to the later morning hours.

Furthermore, at all times, time-contiguous models consistently outperform models with no time contiguity k = 1, demonstrating a clear benefit from using time-contiguous input features.