# Mapping Yearly Fine Resolution Global Surface Ozone through the Bayesian Maximum Entropy Data Fusion of Observations and Model Output for 1990–2017

Marissa Delang, Jacob Becker, Kai-Lan Chang, Marc Serre, Owen Cooper, Martin Schultz, Sabine Schröder, Xiao Lu, Lin Zhang, Makoto Deushi, et al.

► To cite this version:

Marissa Delang, Jacob Becker, Kai-Lan Chang, Marc Serre, Owen Cooper, et al. Mapping Yearly Fine Resolution Global Surface Ozone through the Bayesian Maximum Entropy Data Fusion of Observations and Model Output for 1990–2017. Environmental Science and Technology, 2021, 55 (8), pp.4389-4398. 10.1021/acs.est.0c07742. hal-03382635

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https://hal.science/hal-03382635v1

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<figure><img src="image_1.png" /></figure>
1 Mapping yearly fine resolution global surface ozone

2 through the Bayesian Maximum Entropy data fusion

3 of observations and model output for 1990–2017

4 Marissa N. DeLang¹, Jacob S. Becker¹, Kai-Lan Chang²,³, Marc L. Serre¹, Owen R. Cooper²,³,

5 Martin G. Schultz⁴, Sabine Schröder⁴, Xiao Lu⁵, Lin Zhang⁵, Makoto Deushi⁶, Beatrice Josse⁷,

6 Christoph A. Keller⁸,⁹, Jean-François Lamarque¹⁰, Meiyun Lin¹¹,¹², Junhua Liu⁸,⁹, Virginie

7 Marécal⁷, Sarah A. Strode⁸,⁹, Kengo Sudo¹³,¹⁴, Simone Tilmes¹⁰, Li Zhang¹¹,¹²,¹⁵, Stephanie E.

8 Cleland¹, Elyssa L. Collins¹, Michael Brauer¹⁶,¹⁷, J. Jason West*

9 ¹Department of Environmental Sciences and Engineering, University of North Carolina at Chapel Hill, Chapel Hill,

10 NC, USA

11 ²Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO, USA

12 ³NOAA Chemical Sciences Laboratory, Boulder, CO, USA

13 ⁴Jülich Supercomputing Centre (JSC), Forschungszentrum Jülich, Jülich, Germany

14 ⁵Laboratory for Climate and Ocean-Atmosphere Studies, Department of Atmospheric and Oceanic Sciences, School

15 of Physics, Peking University, Beijing, China

16 ⁶Meteorological Research Institute (MRI), Tsukuba, Japan

17 ⁷Centre National de Recherches Météorologiques, Université de Toulouse, Météo-France, CNRS, Toulouse, France

18 ⁸NASA Goddard Space Flight Center, Greenbelt, MD, USA

19 ⁹Universities Space Research Association, Columbia, MD, USA

20 ¹⁰National Center for Atmospheric Research, Boulder, CO, USA

21 ¹¹NOAA Geophysical Fluid Dynamics Laboratory, Princeton, NJ, USA

22 ¹²Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ, USA

23 ¹³Graduate School of Environmental Studies, Nagoya University, Nagoya, Japan
<table>
   <tr>
    <td>24</td>
    <td><sup>14</sup>Japan Agency for Marine-Earth Science and Technology (JAMSTEC), Yokosuka, Japan</td>
   </tr>
   <tr>
    <td>25</td>
    <td><sup>15</sup>Department of Meteorology and Atmospheric Science, Pennsylvania State University, University Park, PA. USA</td>
   </tr>
   <tr>
    <td>26</td>
    <td><sup>16</sup>Institute for Health Metrics and Evaluation, University of Washington, Seattle, Washington, USA</td>
   </tr>
   <tr>
    <td>27</td>
    <td><sup>17</sup>School of Population and Public Health, University of British Columbia, Vancouver, British Columbia, Canada</td>
   </tr>
  </table>
<figure><img src="image_2.png" /></figure>

29

30 ABSTRACT

31 Estimates of ground-level ozone concentrations are necessary to determine the human
32 health burden of ozone. To support the Global Burden of Disease Study, we produce yearly fine
33 resolution global surface ozone estimates from 1990 to 2017 through a data fusion of
34 observations and models. As ozone observations are sparse in many populated regions, we use a
35 novel combination of the M³Fusion and Bayesian Maximum Entropy (BME) methods. With
36 M³Fusion, we create a multi-model composite by bias-correcting and weighting nine global
37 atmospheric chemistry models based on their ability to predict observations (8,834 sites globally)
38 in each region and year. BME is then used to integrate observations, such that estimates match
39 observations at each monitoring site with the observational influence decreasing smoothly across
40 space and time until the output matches the multi-model composite. After estimating at 0.5°
41 resolution using BME, we add fine spatial detail from an additional model, yielding estimates at
42 0.1° resolution. Observed ozone is predicted more accurately (R²=0.81 at test point, 0.63 at 0.1°,
43 0.62 at 0.5°) than the multi-model mean (R²=0.28 at 0.5°). Global ozone exposure is estimated to
44 be increasing, driven by highly populated regions of Asia and Africa, despite decreases in the
45 United States and Russia.
46

46
47 INTRODUCTION

48 Tropospheric ozone is harmful to human health through respiratory and cardiovascular
49 health effects associated with short and long term exposure. ¹⁻³ Additionally, tropospheric ozone
50 influences climate³ and damages plant growth.⁵,⁶ Surface ozone estimates at fine spatial
51 resolution, which are required to determine the human health burden of ozone exposure, are
52 typically based on two sources: monitoring networks and atmospheric chemistry models.
53 Monitoring networks provide high spatial coverage of surface ozone observations in North
54 America, Europe, Japan, South Korea, and recently China; however, stations are scarce
55 elsewhere.⁷ Global atmospheric models provide concentration estimates across many years and
56 cover all world regions; however, models have biases.⁸

57 The Global Burden of Disease (GBD) Study conducts a comparative risk assessment that
58 estimates the health burden caused by specific risk factors from 1990 to present day, updated
59 regularly. Two ambient air pollution risk factors are analyzed: fine particulate matter (PM<sub>2.5</sub>) and
60 ozone.⁹,¹⁰ GBD PM<sub>2.5</sub> estimates are generated through a combination of satellite retrievals and
61 land use information with a single atmospheric model calibrated to surface observations with a
62 Bayesian hierarchical model.¹¹,¹² In contrast, global ozone estimates prior to GBD 2017¹³ were
63 provided by a single model with no bias correction to observations.¹⁴ Satellite measurements
64 provide PM<sub>2.5</sub> estimates at fine resolution, but do not accurately detect surface ozone.¹⁴,¹⁵

65 The recent Tropospheric Ozone Assessment Report (TOAR) collected ozone
66 observations from thousands of sites around the world, which made it possible to incorporate
67 surface observations into GBD estimates.⁷,¹⁶ For GBD 2017, TOAR observations were combined
68 with six atmospheric models from phase one of the Chemistry-Climate Model Initiative
69 (CCMI)¹⁷ using the M³Fusion method for the average of 2008 to 2014.¹⁸ In M³Fusion, the
models were bias corrected and combined by finding the optimal linear combination of models in each world region, weighted based on their performance with respect to observations. Within two degrees of a monitoring station, the multi-model composite was then replaced with a spatial interpolation of observations. The 2008–2014 ozone distribution was extended backwards (1990–2008) by scaling with cubic splines relative to prior GBD ozone estimates and forwards (2014–2017) by extending the annual rate of change from 2012, for use in GBD 2017.¹³

While the M³Fusion method significantly improved upon previous GBD ozone estimates, we identify a potential for further improvements. In particular, the correction within two degrees of an observation can create discontinuities, which could be improved by using advanced geostatistical techniques that combine model output with observations using smooth weighting across space. Here we use a novel combination of the M³Fusion and Bayesian Maximum Entropy (BME) methods,¹⁹⁻²² which is uniquely suited to the challenges of mapping global ozone concentrations, as only observations and models provide useful information and observations are sparse in some world regions. The regional “large-scale” bias correction and weighting of models in the M³Fusion multi-model composite provides the best estimate of ozone far from observations. Then BME provides a local “small-scale” correction, by smoothly integrating observations in both space and time such that estimates match observations at the measurement site, and the influence of those observations decreases with distance according to the spatiotemporal covariance. Since ozone monitoring is inconsistent, allowing observations to affect predictions across time could provide more accurate estimates. Near observation locations, therefore, ozone estimates will be strongly influenced by observations. BME has previously been used to fuse ozone observations with models on state and national scales,²³⁻²⁵ but it has not been used previously globally, and apart from Chang et al.,¹⁸ we are not aware of any global data
93 fusion of ozone observations and models.

94 We aim to estimate global fine resolution (0.1°) surface ozone for each year from 1990 to
95 2017 to support the GBD 2019 Study by combining surface observations with multiple global
96 atmospheric models by first using M³Fusion to create multi-model composites, and then
97 applying BME to smoothly fuse multi-model composites with observations in space and time.

98 We improve upon the single 7-year mean ozone fields produced for GBD 2017¹⁸ by producing
99 yearly output for 1990-2017, including additional observations and model output, smoothly
100 weighting observations across space and time, and applying fine spatial structure based on fine
101 resolution model output. To add fine spatial resolution for GBD, we apply the fine-scale spatial
102 patterns from a global fine resolution model simulation.²⁶ Our annual global ozone maps were
103 used by GBD 2019, which extrapolated to 2019 using log-linear trends based on our 2008-2017
104 estimates, and estimated 365,000 (95% CI: 175,000-564,000) premature chronic obstructive
105 pulmonary disease deaths globally, or 6.21 (2.99-9.63) million disability adjusted life years, from
106 ambient ozone exposure in 2019.²⁷

107 MATERIALS AND METHODS

108 M³Fusion and BME are used in sequence to estimate global surface ozone
109 concentrations. Other methods have been applied on smaller scales, such as neural networks
110 using meteorological and emission variables to predict ozone,²⁸,²⁹ but those relationships may not
111 apply elsewhere, and those methods are inappropriate where there are no observations.

112 GBD's ozone metric for quantifying health outcomes from long term ozone exposure is
113 the ozone season daily maximum 8-hour mixing ratio (OSDMA8).² OSDMA8 is calculated as
114 the annual maximum of the six-month running mean of the monthly average daily maximum 8-
115 hour mixing ratio, including months through March of the following year to contain the Southern
116 Hemisphere summer. All observations, model output, and estimates are reported here as
117 OSDMA8.

118 **Surface Ozone Observations.** We include surface ozone observations from TOAR and the
119 Chinese National Environmental Monitoring Center (CNEMC) Network (Figure 1). TOAR is the
120 world's largest collection of in-situ hourly surface ozone observations covering 1970-2015.<sup>16,30</sup>
121 The database contains dense observations in North America, Europe, Japan, and South Korea,
122 and sparse observations elsewhere.<sup>7</sup> The database was updated for this project to include readily-
123 available datasets for the years 2015–2017, but measurements were not updated for all nations
124 previously included. CNEMC includes surface ozone observations for 2013–2017 in China,<sup>31</sup>
125 which were quality-controlled using the same algorithm that TOAR applies elsewhere. The total
126 observations ranged from a minimum of 1,199 in 1990 to a maximum of 4,999 in 2015. The
127 incomplete TOAR update in 2016 and 2017 yielded fewer observation sites than 2015.
<figure><img src="image_3.png" /><figcaption>**Figure 1.** (a) TOAR and CNEMC monitoring locations with at least one valid yearly OSDMA8 observation over 1990–2017. In total, there are 8,834 monitoring stations, 7,269 from TOAR and 1,565 from CNEMC. (b) Surface observations as OSDMA8 in 2005, with an average of 45.5 ppb and maximum of 82.2 ppb in Mexico City, Mexico. (c) Surface observations as OSDMA8 in 2015, with an average of 46.2 ppb and maximum of 80.9 ppb in Zibo, China.</figcaption></figure>

*Atmospheric Chemistry Model Simulations*. We incorporate modeled ozone from nine atmospheric chemistry model simulations (Table 1). The models, mostly from CCMI,¹⁷ report output for 1990–2010 from the specified dynamics REF-C1SD experiment,¹⁷,³² which uses
annual MACCity emissions.33,34 Three models, MOCAGE, MERRA2-GMI, and GFDL-AM3, were extended past 2010. To increase models after 2010, we include output from the specified dynamics experiments of MRI-ESM2.0 and GFDL-AM4, for modified Coupled Model Intercomparison Project Phase 6 (CMIP6)35 experiments. Hourly ozone mixing ratios were processed to OSDMA8, using the same algorithm as for observations.

<table><caption>**Table 1.** Nine atmospheric chemistry models used in this study.</caption><thead><tr><td>Model</td><td>Years</td><td>Resolution</td><td>Experiment</td><td>Reference</td></tr></thead><tbody><tr><td>CESM1 CAM4-Chem</td><td>1990–2010</td><td>1.9° × 2.5°</td><td>CCMI REF-C1SD</td><td>36</td></tr><tr><td>CESM1 WACCM</td><td>1990–2010</td><td>1.9° × 2.5°</td><td>CCMI REF-C1SD</td><td>37,38</td></tr><tr><td>CHASER</td><td>1990–2010</td><td>2.8° × 2.8°</td><td>CCMI REF-C1SD</td><td>39-41</td></tr><tr><td>GFDL AM3</td><td>1990–2014</td><td>2° × 2.5°</td><td>CCMI REF-C1SD</td><td>42-44</td></tr><tr><td>GFDL AM4</td><td>2010–2016</td><td>1° × 1.25°</td><td>CMIP6 nudged to NCEP winds<sup>a</sup></td><td>45,46</td></tr><tr><td>MERRA2-GMI</td><td>1990–2017</td><td>0.5° × 0.625°</td><td>MACCity and GFED-4s emissions<sup>b</sup></td><td>47,48</td></tr><tr><td>MOCAGE</td><td>1990–2016</td><td>2° × 2°</td><td>CCMI REF-C1SD</td><td>49,50</td></tr><tr><td>MRI-ESM1r1</td><td>1990–2010</td><td>2.8° × 2.8°</td><td>CCMI REF-C1SD</td><td>51</td></tr><tr><td>MRI-ESM2.0</td><td>2011–2017</td><td>2.8° × 2.8°</td><td>CMIP6 historical and ssp370<sup>c</sup></td><td>452</td></tr></tbody></table>

a Nudged to observed meteorology similar to GFDL-AM3 and uses anthropogenic emissions modified from CMIP6 to reflect recent NOₓ trends in China and the United States⁴⁵

b MACCity anthropogenic emissions with biomass burning emissions from Global Fire Emissions Dataset version 4s⁴⁷,⁴⁸

c Emissions from the CMIP6 historical (2011–2014) and ssp370 (2015–2017) experiments⁵²

**Multi-model Composite.** We use M³Fusion to create multi-model composites of the models available in each year from 1990–2017.¹⁸ This method corrects for model bias and finds the
linear combination of models in each region and year that minimizes the mean square error as compared to observations. Since model resolution varies, we use bilinear interpolation to smooth yearly OSDMA8 to a 0.5° × 0.5° grid. We interpolate yearly observations from irregular monitoring station locations to the 0.5° grid using the stochastic partial differential equation approach.⁵³ In each of eight geographical regions (Figure S1) and each year, we weight each model to minimize the difference between the multi-model average and spatially interpolated observations based on a constrained least squares approach:

$$ \begin{array}{l} \underset{\{\alpha_r, \beta_{rk}; k = 1, \dots, n\}}{\text{minimize}} \sum_{s_g \in \text{Regionr}} (\hat{y}(s_g) - \alpha_r - \sum_{k=1}^{n} \beta_{rk} \eta_k(s_g))^2, \quad (1) \\ \text{subject to } \sum_{k=1}^{n} \beta_{rk} = 1 \text{ and } \beta_{rk} \ge 0 \end{array} $$

where $s_g$ is the grid cell at 0.5°resolution, $\hat{y}(s_g)$ is the spatially interpolated observations, $\{\eta_k(s_g); k=1,...,n\}$ is the model output on the same grid from the n models available, $\alpha_r$ is a constant that corrects overall bias in each region, and $\beta_{rk}$ is an optimal weight for the k-th model in region r. All model weights are constrained to be positive and sum to 1. The constant offset $\alpha_r$ guarantees that the residuals from this optimization have a zero mean, through which the mean model bias is corrected in each region.¹⁸

Since M³Fusion relies on spatially interpolated observations to determine model weights, we modify the method for data sparse regions and years. In North America and Europe, we use weights based on each individual year's models and observation values. For all other regions, we calculate individual year weights for 2000–2010, and apply weights from the aggregated 2000–2010 period to 1990–1999. For 2011–2017, East Asia uses individual year weights, while South America, Africa, South-Central Asia, Russia, and Oceania use weights from the aggregated
171 2011–2014 period, for which the TOAR dataset was complete.

172 **Bayesian Maximum Entropy Methodology.** BME is a geostatistical method that incorporates
173 multiple forms of knowledge to predict an estimate of a homogenous, stationary, space-time
174 random field.¹⁹⁻²² Using BME, we combine surface observations and annual multi-model
175 composites to calculate an ozone estimate that matches observations at each monitoring station
176 and the observational influence gradually diminishes across space and time until it matches the
177 multi-model composite. BME has been described previously, including in the fusion of ozone
178 observations with model output at state and national scales¹²⁰⁻²⁴,⁵⁴. We model the offset-
179 removed, homogeneous space-time random field (S/TRF) X(p) at the space-time coordinate
180 p=(s,t).²⁴ In BME, there are two forms of knowledge: site-specific and general. Site-specific
181 knowledge can consist of hard data, with no assumed uncertainty, and soft, probabilistic data.
182 Here we only have hard data, which is the linear limiting case of the BME data integration
183 framework.²⁴ We remove the offset, the multi-model composite at monitoring stations (o<sub>z</sub>(p<sub>0</sub>)),
184 from OSDMA8 observations (z<sub>0</sub>) at monitoring station locations p<sub>0</sub> to obtain hard data x<sub>0</sub>:

$$
185 \qquad \mathbf{x}_0 = \mathbf{z}_0 - o_z(\mathbf{p}_0) \tag{2}
$$

186 The general knowledge base of X(p) includes the mean function m<sub>x</sub>(p) = E[X], which is assumed
187 to be zero, and the covariance function c<sub>x</sub>(p,p') = E[X(p)-m(p)](X(p)-m(p')), which is
188 determined by the experimental covariance of x<sub>0</sub>:

$$
189 \qquad \hat{c}_X(r, \tau) \approx \frac{1}{N(r, \tau)} \sum_{i=1}^{N(r, \tau)} x_{\text{head},i} x_{\text{tail},i} - m_X^2 \qquad (3)
$$

190 where N(r, τ) is the number of pairs of points with values (x<sub>head</sub>, x<sub>tail</sub>) separated by a distance r
191 and time τ, and m<sub>x</sub> is the mean of x<sub>0</sub>. For the S/TRF X(p), we use an exponential covariance
model to best fit the experimental covariance:

$$c_X(r, \tau) = C \left[ \gamma \exp\left(\frac{-3r}{a_{r1}}\right) \exp\left(\frac{-3\tau}{a_{t1}}\right) + \lambda \exp\left(\frac{-3r}{a_{r2}}\right) \exp\left(\frac{-3\tau}{a_{t2}}\right) + (1 - \gamma - \lambda) \exp\left(\frac{-3r}{a_{r3}}\right) \exp\left(\frac{-3\tau}{a_{t3}}\right) \right] \quad (4)$$

with parameters in the supporting information. The BME estimation process involves using general knowledge to obtain the maximum entropy prior probability density function (PDF) of $f_G$, updating $f_G$ by integrating site-specific knowledge to obtain the epistemic Bayesian posterior PDF $f_K$, which provides a complete stochastic description of $X_k=X(p_k)$ at the estimation point $p_k$, and computing space-time estimates based on $f_K$. The posterior PDF is defined as:

$$f_K(x_k) = \left( \frac{f_G(x_0, x_k)}{f_G(x_0)} \right) \qquad (5)$$

where $x_k$ is the offset-removed estimate at points $p_k$. We define the ozone space-time random field (S/TRF), $Z(p)$, as the sum of $X(p)$ and the offset (multi-model composite):

$$Z(p) = X(p) + o_z(p) \qquad (6)$$

We obtain the estimated OSDMA8 $z_k$ at $p_k$ by obtaining the BME estimate $x_k$ for the S/TRF $X(p)$ at $p_k$, and adding back $o_z(p_k)$.

**Fine Resolution Addition.** We calculate ozone BME estimates at 0.5° resolution; however, a finer resolution is desirable for GBD to reduce spatial misalignment with population. Since neither the observations nor the models represent ozone at fine resolution, except where observations are dense, we use the spatial distribution of a fine resolution model. We use output from a NASA G5NR-Chem model²⁶ simulation from July 2013 to June 2014 at 0.125° resolution, which we regrid to 0.1° resolution, to provide the fine spatial structure within each 0.5° grid cell for each year 1990-2017. While we do not expect the modeled 2013–2014 ozone to
be accurate for every year, we use the modeled spatial distribution to inform the fine-scale spatial pattern for each year. In doing so, we assume that the fine spatial patterns of OSMDA8 do not change over time, as these reflect the spatial distributions of emissions and land use, as well as influences like topography and land/water interfaces. For each 0.5° grid cell, we subtract the average of NASA G5NR-Chem grid cells from the BME estimate, and add this difference to each NASA G5NR-Chem grid cell at 0.1° to obtain our BME estimate at 0.1°. Consequently, the sub-grid variability of the output matches the G5NR-Chem model, and the average of each 0.5° grid cell remains the same as the BME estimate (Figures S2-3).

## 220 RESULTS

**Multi-model Composite.** We determine weights for each model in each region and year (Table S1). In most regions and years, the multi-model mean ozone (the simple average of all models) is biased high, as models generally overpredict ozone.⁸,¹⁸ Therefore, the M³Fusion multi-model composite (Figure 2) tends to decrease average ozone compared to the multi-model mean.

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Multi-model composite as OSDMA8 in 2005 (a) and 2015 (b).</figcaption></figure>

**BME Coarse Resolution Output.** We obtain yearly ozone output at 0.5° resolution, with an
associated variance at each estimation point (Figure 3; Figures S4-31). The ozone output matches an observation at its space-time location, and the observation's influence decreases in space and time according to the derived spatiotemporal covariance (Equation S3). In regions with high observational coverage, there is greater spatial variation in our output, whereas less monitored regions are smoother. Across the years, areas of low estimated ozone include the Amazon, Oceania, and southeastern Africa; while high ozone is estimated in East Asia, South-Central Asia, western North America, and central Africa. The Amazon and central Africa are unmonitored; therefore, their respective low and high ozone estimates are based on model output reflecting ozone chemical destruction and dry deposition over the Amazon⁵⁵ and biomass burning in Africa.⁵⁶

In BME, observations are treated as hard data with no variance; therefore, regions with the highest number of observations have the lowest variance, such as North America, Europe, and Japan in 2005 and additionally eastern China in 2015. Away from observations, the output is equal to the multi-model composite and the variance reaches a maximum of 60 ppb², equal to the variance of the offset removed observations. To visualize how BME adjusted the multi-model composite using observations, we subtract the multi-model composite from our BME estimate (Figure 3). In unmonitored regions, there is no difference between our BME output and the multi-model composite. When adding fine resolution in the final step, differences on the global scale are unnoticeable (Figures S4-31).
<figure><img src="image_5.png" /><figcaption>**Figure 3.** BME estimate as OSDMA8 for 2005 (a) and 2015 (b). BME variance for 2005 (c) and 2015 (d). Effect of BME fusion of observations (BME estimate minus multi-model composite)</figcaption></figure>

247

248

249
for 2005 (e) and 2015 (f). Positive values occur where our estimate is higher than the multi-model composite, negative values where our estimate is lower.

**Influence of Observations through Time.** The ability of an observation to influence other years is an important component of our method, since observational coverage changes, generally with more stations being added. The extent of an observation's influence on other years depends on the number of nearby stations in space and time, with more remote stations having a longer temporal influence. In addition to the space-time BME estimates above, we also perform “space-only” BME, in which observations only influence ozone estimates across space in a single year.

By taking the difference between space-time and space-only results, we evaluate how observations influence other years. Since the CNEMC observations started in 2013, analyzing 2012 highlights their temporal influence (Figure 4). On the global scale, the differences between the space-time and space-only methods are difficult to distinguish, but the major differences occur across China. Most of the non-zero differences occur in areas where CNEMC observations were added in 2013–2017, showing the influences of those observations (Figure 4). Whereas Figure 4 shows that BME largely decreased ozone estimates over China in 2012, the effect of adding BME differed among years, including increasing ozone in 2015 and 2016 (Figures S29-30).
<figure><img src="image_6.png" /><figcaption>**Figure 4.** (a) Space-only BME result in 2012 as OSDMA8. (b) Space-time BME result in 2012 as OSDMA8. (c) Observation locations in 2012 and 2013–2017. (d) Effect of BME space-time influence of observations (space-time BME minus the space-only BME) for 2012.</figcaption></figure>

**Evaluation.** To evaluate our results, we perform a leave one out cross validation (LOOCV), where one observation is removed and we evaluate our ability to predict this observation, in five scenarios:

- **Multi-model mean**: average of all model output available in a given year.

- **Multi-model composite**: combination of model output using M³Fusion.
276 - **Space-only correction**: BME corrected multi-model composite where observations
277 only influence across space in a single year.

278 - **Space-time correction**: BME corrected multi-model composite where observations
279 influence across space and time.

280 - **Fine resolution**: space-time corrected output with fine resolution from the NASA
281 G5NR-Chem model.

282 LOOCV was performed using two methods: predicting ozone at the test point's grid cell and at
283 the test point's specific space-time location. The grid cell prediction was performed to allow a
284 fair comparison between scenarios, since the fine resolution addition is limited to predicting at
285 the grid cell level, and to evaluate the benefit of increasing output resolution. When predicting at
286 the test point's grid cell, each subsequent scenario improved performance, as shown by the root
287 mean square error (RMSE) (Table 2). The multi-model composite outperforms the multi-model
288 mean across all validation statistics. Correcting the multi-model composite across space using
289 observations improves the results, which is further amplified by correcting across both space and
290 time. Adding fine spatial structure, which gives our final output, slightly improves performance
291 relative to the space-time scenario. All methods overestimate ozone in comparison to
292 observations, as shown by the mean error (Table 2), though our final product is biased high only
293 slightly.
<table><caption>**Table 2.** LOOCV statistics,ª where results are evaluated in the 0.5 or 0.1 grid cells containing the test point, or at the test point's space-time location.</caption><thead><tr><th>Scenario</th><th>Prediction location</th><th>RMSE<br>(ppb)</th><th>ME<br>(ppb)</th><th>R<sup>2</sup></th><th>varE<br>(ppb<sup>2</sup>)</th><th>varZ<br>(ppb<sup>2</sup>)</th></tr></thead><tbody><tr><td>Multi-model Mean</td><td>0.5° grid cell</td><td>13.76</td><td>11.00</td><td>0.28</td><td>68.48</td><td>62.08</td></tr><tr><td>Multi-model Composite</td><td>0.5° grid cell</td><td>7.82</td><td>1.05</td><td>0.30</td><td>60.03</td><td>43.09</td></tr><tr><td>Space-only Correction</td><td>0.5° grid cell</td><td>6.01</td><td>0.42</td><td>0.57</td><td>36.00</td><td>60.14</td></tr><tr><td>Space-time Correction</td><td>0.5° grid cell</td><td>5.62</td><td>0.57</td><td>0.62</td><td>31.30</td><td>62.01</td></tr><tr><td>Fine Resolution</td><td>0.1° grid cell</td><td>5.54</td><td>0.22</td><td>0.63</td><td>30.68</td><td>63.24</td></tr><tr><td>Multi-model Composite</td><td>Test point's location</td><td>7.82</td><td>1.07</td><td>0.30</td><td>60.00</td><td>43.19</td></tr><tr><td>Space-time Correction</td><td>Test point's location</td><td>3.99</td><td>0.01</td><td>0.81</td><td>15.94</td><td>81.26</td></tr></tbody></table>

For comparison with other studies, we include statistics for predicting at the specific space-time location (Table 2). The addition of the space-time correction to the multi-model composite decreased RMSE from 7.82 to 3.99 ppb, a 49% reduction. In comparison, Chang et al.¹⁸ report that the correction to the multi-model composite in that study decreased the RMSE from 5.16 to 3.82 ppb, a 26% reduction. The greater relative reduction in RMSE here is attributed to the incorporation of both spatial and temporal autocorrelation, and shows our improvement relative to Chang et al.¹⁸.

**Population-Weighted Ozone Trends.** With our yearly output, we use global gridded population from GBD 2019 to analyze trends in population-weighted ozone as an indicator of exposure. The

<footnote>ª Root mean square error (RMSE), mean error (ME), R-squared (R²), variance of error (varE), and variance of the estimated ozone (varZ). The mean and variance of observed ozone are mO=45.62 ppb and varO=81.96 ppb², respectively. Statistic definitions are included in Table S2.</footnote>
309 2019 global population is used for all years, meaning that differences in exposure result from
310 changes in ozone, not population. To determine how ozone exposure has changed from 1990-
311 2017, we examine the percent of the global population exposed to intervals of OSDMA8 (Figure
312 5). Global ozone exposure increases over this period, with an increase in the global population
313 exposed to highest concentrations (>55 ppb). In 2017, 21.3% of the global population was
314 exposed to OSDMA8 higher than 65 ppb, more than double the percentage in any previous year.
315 Note that the OSDMA8 metric is not compared easily with national standards or WHO
316 guidelines, which are typically based on the daily 8-hr maximum. For perspective, the risk of all-
317 cause, circulatory, and respiratory mortality reportedly increases by 2%, 3%, and 12% per 10 ppb
318 increase in long-term OSDMA8, respectively, with some evidence that ozone influences
319 mortality at concentrations above about 35 ppb.²

320 We analyze the population-weighted trends from 1990–2017 for each world region
321 (Figure 5) and the most populous countries (Figure S32). Globally, there is a positive trend in
322 population weighted ozone for 1990–2017, driven in large part by positive trends in highly
323 populated and polluted regions of South-Central Asia, East Asia, and Africa. Low population-
324 weighted ozone occurs in South America and Oceania. Negative trends occur in North America
325 and Russia; Europe has a weak negative trend, with the European Union showing no change.
326 We caution that these trends are most uncertain before 2000 and in regions with few
327 observations; under these conditions our estimated trends mainly reflect models and a small
328 number of observations. Year-to-year changes in ozone in regions with few observations may
329 also result from using different model weights in individual years. These trends are supported by
330 a previous analysis of TOAR data for 2000–2014 summertime ozone, which found a positive
331 trend in East Asia and negative trends in North America and Europe.⁵⁷ Similarly, a study of
332 CNEMC observations showed increases in China for 2013–2017.31 One study suggests that the
333 2013-2017 increase over China was influenced most by the decrease of PM2.5, which increased
334 HOx radicals58; therefore, a PM2.5 increase might explain our estimated 2007-2013 ozone
335 decrease. Increasing trends in other regions with few observations, including Africa and South
336 Central Asia are supported by long-term aircraft59 and satellite column observations.47
<figure><img src="image_7.png" /><figcaption>**Figure 5.** (a) Percent of the global population exposed to 10 ppb intervals of OSDMA8 from 1990-2017. (b) Ozone trend regionally (regions defined in Figure S1) over 1990–2017 for the metric of population weighted OSDMA8. All trends have p-values less than 0.05, except for Europe and South America (Table S3). Uncertainty intervals are included in Figures S33-46.</figcaption></figure>
342 DISCUSSION

343 We create fine resolution yearly ozone distributions for 1990–2017 that incorporate

344 surface observations and output from nine atmospheric chemistry models, using a novel

345 combination of the M³Fusion method for creating a multi-model composite, which dominates the

346 large-scale ozone estimates, and BME data fusion which influences ozone estimates near

347 observation locations, smoothly integrating observations in space and time. Our analysis finds

348 that methods incorporating observations outperform ozone estimated from models only.

349 Additionally, the influence of an observation across multiple years in BME further improves our

350 ozone estimate. Our method’s major strengths include the incorporation of multiple data types,

351 the smooth weighting of observational influence across space and time, the ability to output a

352 variance at every estimation point, and the estimation of global ozone with fine spatial structure.

353 The improvement in model performance from using our combination of M³Fusion and BME

354 provides a caution against using simple spatial interpolations of observations or output of a

355 model without bias correction, to represent ozone. Although we improve upon the previous

356 GBD ozone estimate, some limitations remain. The lack of monitoring stations in large populous

357 regions limits our abilities to understand ozone exposure in these areas, where these uncertainties

358 affect both the multi-model composite and BME data fusion. Our method is limited in years with

359 fewer observations and models available; additionally, the fine resolution model output that

360 informs the fine spatial pattern of our output is only available for a single year. Future work may

361 apply a nonlinear bias correction, or use machine learning to correct bias,⁶⁰ to the multi-model

362 composite to improve the global offset, and thus the overall estimation. Our work also shows the

363 value of using multiple models in creating a multi-model composite, as output from each model

364 was selected (weight>0) in at least some regions and years.
Our method can be applied to future years as more observations and model output become available. Additionally, our method can be used to estimate ozone metrics other than OSDMA8, including for studies of vegetation and crop impacts.⁶¹ While model output and geostatistical techniques like BME can estimate global ozone, estimates suffer from the lack of observations in some world regions. Additional observations, especially in unmonitored regions with large populations including megacities in low- and middle-income nations, are essential to improve understanding of ozone exposure and health burden.

Ozone exposure is increasing globally, with global population-weighted ozone showing a positive trend from 1990-2017, driven by strong positive trends in highly populated and polluted regions of Asia and Africa. The increasing global exposure to ozone indicates that current ozone management policies are failing to reduce ozone exposure in many regions of the world. Our results can be used by policy makers to identify regions where ozone pollution could be mitigated through reductions of ozone precursor emissions, mainly from fossil-fuel combustion, on local, national and continental scales, or through international agreements to reduce emissions, including methane, that affect global background ozone.⁶²,⁶³

## 380 ASSOCIATED CONTENT

**Supporting Information.** The supporting information includes multi-model composite model weights, covariance parameters, fine resolution addition example, yearly maps for all relevant scenarios, cross validation statistics, and national ozone trends with uncertainty intervals.

## 384 AUTHOR INFORMATION

Corresponding Author: J. Jason West, jasonwest@unc.edu, 919-843-3928.

## 386 ACKNOWLEDGEMENTS
387 We acknowledge support from the NASA Health and Air Quality Applied Sciences Team
388 (#NNX16AQ30G) and the National Institute for Occupational Safety and Health (T42-
389 OH008673). Makoto Deushi was supported by the Japan Society for the Promotion of Science
390 (JP20K04070).

391

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