The influence of photochemistry on outdoor to indoor NO2 in some European museums.

This paper reports 1 year of monthly average NO2 indoor to outdoor (I/O) concentrations measured in 10 European museums, and a simple steady-state box model that explains the annual variation. The measurements were performed in the EU FP5 project Master (EVK-CT-2002-00093). The work provides extensive documentation of the annual variation of NO2 I/O concentration ratios, with ratios above unity in the summer, in situations with no indoor emissions of NO2 . The modelling included the most relevant production and removal processes of NO2 and showed that the outdoor photolysis was the probable main explanation of the annual trends in the NO2 I/O concentration ratios.

Outdoor photolysis of NO2 and indoor back‐reaction of NO with O3 can contribute to higher indoor than outdoor exposures to NO2 in the summer. This is a health concern, and an objects conservation concern in museums. As indoor NO2 concentrations are seldom measured, but values for outdoor concentrations are often available from regulatory measurement stations, it is of interest to approximate the expected indoor integrated exposures from the outdoor values, with a relatively simple method that shows reasonable fit to measurements. A model expression for the NO2 indoor to outdoor ratio including the photolysis effect and meeting these criteria was presented.

INTRODUCTION

Nitrogen dioxide (NO2) can harm people's health and cultural heritage materials by its oxidizing and/or acidic effects. People spend much of their time indoors. The sometimes higher indoor as compared to outdoor exposure to NO2 adds to the total person, and object, exposure. A major motivation for understanding the outdoor to indoor NO2 concentrations in museums is the degradation due to the atmospheric exposure that has been reported of sensitive art materials. This work provides results from annual monthly measurements of NO2 I/O ratios in 10 European museums. Then, tentatively, a simple model that can approximate the indoor to outdoor (I/O) ratios of NO2, and higher than unity ratios that are often observed in the summer, from the outdoor NOx and O3 values that are more often available from regulatory measurement stations than indoor measured values. A recent paper reviewed the status of knowledge of indoor NO and NO2 concentrations and chemistry, among other acids and bases that influence indoor air quality. They stated that “in the absence of indoor sources, I/O concentration ratios of nitrogen monoxide (NO) tend to be close to unity, while those for NO2 tend to be in the range of 0.7 to 0.9 depending on the air exchange rate and relative humidity.” The source of the indoor NO2 is when excluding indoor emissions that are uncommon in museums, the outdoor NOx (NO + NO2) emissions and ventilation to the indoors, and the indoor reaction of NO with O3 to NO2. Annual NO2 I/O ratios of unity have been measured in for example the Victoria and Albert Museum in London. Higher indoor than outdoor concentrations of NO2 have, despite the indoor deposition, been measured in museums in the summer. This was explained by splitting of NO2 outdoors by ultraviolet (UV) light, to NO and O3, and reaction back to NO2 in the relative indoor darkness.

Weschler et al. showed that, in the absence of photolysis, due to the rapid reaction of NO with O3, only the surplus gas of the two will be present at any one time. The dynamic NOx‐O3 chemistry happens at similar rates as the typical exchanges of indoor air (~1 h−1), which is a reason why it affects the indoor air quality. With a surplus of O3 indoors most of the incoming NO will react to NO2. , , , Indoor NO2 is a source of nitric (HONO) and nitrous acid (HNO3) through heterogeneous and homogeneous reactions. The homogeneous reactions can involve ozone (O3) and volatile organic compounds. The HONO is mainly released back to the air after formation with water on the surfaces. The HNO3 can be formed together with HONO on the surfaces or deposit and react on the surfaces after oxidation of NO2 by O3 in air. , , , , , , Whereas exposure to peak concentrations can be the most damaging to health, it is the long duration accumulated exposure that is usually considered to damage sensitive heritage materials. Outdoor values of NO2 are more commonly available than values from indoor measurements. Museums can thus benefit from a simple model to estimate long duration indoor exposure doses from the outdoor concentration values. IAQ (Indoor Air Quality) models that calculate I/O gas concentration ratios, including O3 and NO2, have been proposed and tested in many studies. Dynamic models (e.g., , , ) some including advanced chemistry schemes, , , , , and steady‐state models (e.g., , , ) have been used. Wang provided a literature review of indoor air modelling involving photolysis. Weschler et al. described and explained the dynamic trends of, the O3, NO, and NO2 * (NOx minus NO) species. Drakou et al. observed higher than unity I/O NO2* (NO2 + HONO + HNO3 + PAN (peroxyacetyl nitrate) = NOx minus NO) ratios in a building in Thessaloniki, Greece. They found that this could not fully be explained by the reaction of NO with O3, but that in “the particular building, which was like a smog chamber, it seemed as if NO was transformed to NO2 mainly by heterogeneous processes and less through the reaction of O3 with NO.” They hypothesized that NO might be oxidized to NO2 through heterogeneous reactions involving the formation of HONO, and subsequently homogeneous reactions with OH radicals and VOCs that would “alter all the indoor gas‐phase chemistry.” They concluded that in this building “there seemed to be at times a contribution to indoor NO2 from HNO2 and at times from HNO3 and PAN, and that the homogeneous chemistry and the heterogeneous removal of air pollutants in the applied model (from Nazaroff and Cass ) could not fully explain the interplay among O3, NO, and NO2 in the building.” Zhou et al. reported concentrations of HONO that were on the level of NO2 in indoor air. As HONO is expected to have been reported with the NO2 from the passive sampling performed in this work, , the here reported “NO2” should, probably, be interpreted as NO2 + HONO (it is still described in the following simply as NO2—as reported from the analysis). The HONO would be a product of the indoor NO2 which was partly formed by reaction of NO with O3 (Equation (1) below). The inclusion of HONO with the NO2 seems thus not to disqualify the performed modelling approximation of the monthly averaged indoor NO2 (interpreted as NO2 + HONO). It seems, however, that it may have led to some underestimation of the deposition of the NO2 (exclusive of the HONO, which would be a product from this additional deposition). The above references testify to the complexity of the indoor NOx heterogeneous and homogeneous chemistry, which this work did, however, not try to simulate in detail.

The aim of this work was to add comparative annual monthly site data to the evidence of increased, and often higher than unity, summer NO2 I/O ratios. Then, to investigate if a simplified steady‐state NO2 I/O model, adding the effect of outdoor NO2 photolysis to the heterogeneous indoor removal, could reasonably explain the monthly averaged NO2 I/O ratios. The reported NO2 and O3 measurements were performed in 10 European museums some years ago, from 2004 to 2005, in the EU Master project. Although NO2 concentrations have since then decreased somewhat in Europe, the presence of nitrogen oxides (NOx) is still a major worldwide and European air quality challenge. , , , Few data on the annual variation and higher average NO2 indoor than outdoor concentrations in the summer seems to have been reported. It therefore seemed appropriate to report these results that documents many such cases. The presented steady‐state box model simplify the dynamic complexity of the homogeneous NOx‐O3 chemistry with the purpose of approximating the measured time‐integrated gas concentrations, and doses, in a single room.

Degradation due to the atmospheric exposure to NO2 and/or O3 has been reported of sensitive art materials such as pigments, dyes, and inks, , , , , , , , ) textiles (Whitmore and Cass, 1989, paper, , , varnish, and metals , , ). The damage might be due to both oxidation by the nitrate radical (NO3⋅) and acidic effects of nitric acid (HNO3). The NO3 radical will react with both saturated and unsaturated organic compounds and form gaseous and surface adsorbed/dissolved HNO3. The high water solubility and acidity of HNO3 means that its potential for reducing the surface pH is high, even at its common low indoor concentrations below one ppb. However, as the O3 + NO reaction decreases O3 concentrations as much as it increases the NO2 concentrations, it seems that the effect of this reaction depends on the relative sensitivity of materials to O3 versus NO2 and its reaction products. It has been recommended that the concentrations of the pollution gases in museums should be below measurable levels (1 µg m−3 ~ 0.5 ppb), based on the precautionary thinking that there is no lower threshold of their effects and that a “no observed adverse effect level” (NOAEL) has not generally been observed. Different materials are, however, clearly at different risk from exposure to the gases. , , To perform realistic evaluations of the damage risk of materials or objects more specific information is needed about the oxidizing and acidic reactions of the deposited gases. As an example, the longer duration degradation of oil paintings, happens by similar mechanisms as those involved in the initial curing. The oil‐containing paint film changes both by oxidation of unsaturated bonds and by hydrolysis of ester bonds in the oils, with both mechanisms leading to the formation of carboxylic groups and the possibility for subsequent metal complexation and substitution with fatty acids to create the often‐whitish disfiguring crystallizations of metal soaps. The oxidation of double bonds can be induced by UV irradiation, and/or, probably, by reaction with oxygen radicals and is accelerated by air pollutants such as NO2 and SO2, , and probably also by O3 and other oxidants, and progress by autoxidation. The hydrolysis reaction is RH‐dependent (Modugno et al., 2019). The influence of the deposition of oxidizing and acidic air pollutants on the detailed mechanisms and practical rates of such reactions in the objects at risk seems, however, in most cases not well known.

EXPERIMENTAL AND SITES

In the EU Master project an extensive field test was carried out to measure, and evaluate, the effect of the air environment and particularly of contaminant gases present indoors, on vulnerable art objects in museums. The measurements were performed indoors and just outdoors of galleries over one year with monthly changing of duplicate passive badge samplers of NO2 and O3 of the IVL type (Ferm and Bloom, 2010) in one urban and one rurally located museum in five different European regions represented by six different countries, 10 museums in all (Table 1). The supporting Table S1 provides the museums' materials and site description. In the following, the museums will, for simplicity and as the geographical location is of importance for the NO + O3 reaction, often be described by their geographical location, given in Table 1, rather than by the full museum name.

TABLE 1

Museums and site descriptions

Name of museum/historic building, (U) = Urban. (R) = rural	Location, Country
1. The Museum of Decorative Arts & Design (U)	Oslo, Norway
2. Trøndelag Folk Museum (U/R)	Trondheim, Norway
3. Tower of London, Bloody Tower (U)	London, UK
4. Blickling Hall (R)	Norfolk, UK
5. Haus der Geschichte Baden‐Württemberg (U)	Stuttgart, Germany
6. Schwarzwälder Trachtenmuseum (R)	Haslach, Germany
7. The Jan Matejko House (U)	Krakow, Poland
8. The Karol Szymanowski Museum “Atma” (R)	Zakopane, Poland
9. The Historical Museum of Crete (U)	Heraklion, Greece
10. Wignacourt Collegiate Museum (U/R)	Rabat, Malta

The monthly pollution gas uptake was found to be well within the chemical absorption capacity of the passive samplers. Røyset found that the NILU (Norwegian Institute for Air Research) produced passive NO2 samplers that were used in this work, were within 10%–20% of results from NO/NOx monitors calibrated against standards, that the detection limit was one µg m−3 (0.5 ppb) NO2 (7 days), that the precision was 5% and the accuracy 20%. No indoor NO2 sources were reported in the museums or observed on inspection. The visible (lux) and UV (W m−2) light levels were measured with light meters continuously (lux) in some sites, or with spot measurements mid‐day (12 a.m.) each month when the sum of the (possible) natural + artificial light intensity was at its maximum and was reported as mid‐day annual averages. The UV wavelength band of the individual light meters could unfortunately not be verified. Light meters used in museums typically measure the UV wavelength band 300–400 nm. The temperature and relative humidity (RH) were measured with the continuous loggers of the different types in regular use by the museums and reported as monthly averages. The area to volume ratios of the measurement rooms and description of ventilation from the museums are given in Table 3 of the modelling results, for easier comparison with those results. The values of the light measurements are, for simplicity, given in the same Table 3.

It is important to note that the conditions in Trondheim (no. 2), Zakopane (no. 8), and partly the Malta (no. 10) museum were found to be deviating in some respects. In the Trondheim site, a chimney was observed to emit smoke from the burning of fuel oil very close to the air intake of the ventilation system on the roof. Zakopane is a much‐frequented winter sports location at an elevation of ~850 m in the Tatra Mountains. In Wignacourt, the (natural) ventilation was much higher in the hot summer months, due to more opening of doors and windows, as is often the case in Malta (Cassar, J., 2005, personal communication).

RESULTS

Figure 1 shows the outdoor and indoor mean monthly concentrations of NO2 and O3 measured in the 10 museums.

FIGURE 1

Mean monthly outdoor and indoor NO2 and O3 concentrations measured from March 2004 to March 2005 in 10 European museums. The error bars represent the standard deviation of duplicate measurements

The outdoor O3 measurement in no. 4, Blicking Hall in September (9) failed. The NO2 outdoor concentration reported from the measurement in no. 6, Haslach in September (9) (0.6 ppb) was about one magnitude lower than in August and October. This out‐layer was considered highly dubious, and without it being possible to locate the reason for the deviance, the value was removed. The NO2 values in no. 7. The Jan Matejko House in October (8) were found to be suspicious but are reported. Figure 2 shows the NO2 I/O ratios measured in the 10 museums. The figure also shows the result from the model fitting (See Section 4).

FIGURE 2

Measured and modelled monthly indoor to outdoor NO2 I/O ratios from March 2004 to March 2005 in 10 European museums

The figure clearly shows the higher indoor summer than winter concentrations of NO2 measured in nine of the 10 museums and the higher than unity NO2 I/O ratios measured in the summer in some of them. The highest summer indoor NO2 concentrations and NO2 I/O ratios among the 10 museums were observed in Stuttgart, excepting the special case of Trondheim (see Experimental). The indoor concentrations of NO2 were measured to be higher than outdoors in Stuttgart from April to August. In the rural comparison, case in the same region (Germany), Haslach, near equal indoor and outdoor concentrations of NO2 were observed during the summer. The observations in these two museums (nos. 5 and 6) will be discussed in some more detail together with the other sites to understand the modelling parameter fit and in the final Discussion. The annual monthly average O3 indoor and outdoor measured values are given in Table 2. The average annual O3 I/O ratio over all the sites was found to be 0.16 (from Table 2).

TABLE 2

Annual average monthly O concentrations (ppb)

Site no:	1	2	3	4	5	6	7	8	9	10
O3(i)	18.1	25.6	13.4	22.0	15.8	17.4	14.3	18.6	31.1	31.2
O3(o)	1.0	5.7	3.6	1.0	2.5	4.5	0.6	2.2	9.5	3.2
O3 I/O	0.05	0.22	0.27	0.05	0.16	0.26	0.04	0.12	0.31	0.10

A weak positive single parameter correlation (ax + b, R 2) was observed over all the sites and months for the outdoor (a = 5, R 2 = 0.07) and for the indoor (a = 2, R 2 = 0.03) monthly temperatures, and the NO2 I/O ratio, which could be expected from the dependence of the annual variation in the NO2 I/O ratios on the season seen in Figure 2. No significant single parameter correlations were, however, observed between the monthly outdoor or indoor temperatures or RHs and the NO2 I/O ratios. Thus, the temperature and humidity variations seemed not to be major factors in explaining the annual variations in the NO2 I/O ratios.

MODELLING

Model derivation and model fitting

A steady‐state NO2 I/O model that included the effect of outdoor photolysis was developed and simplified to be applied with the available mean monthly experimental measurement values. By describing (consecutive) steady states such a model will not replicate the dynamic reactivity that will be important for the concentration changes and values on short‐time scales (hours). It will typically not well replicate concentration peaks or accumulated changes in long duration monotonous trends. The main influences on the NO2 I/O ratios in a situation without indoor NO emissions can be described as follows: The higher the NO2 ventilation from the outdoor is, and the (possible) indoor NO2 emissions are, the higher NO2 I/O ratios will be. The higher the deposition velocity of NO2 to indoor surfaces (e.g. , , , ), and the room surface area to volume (A/V) ratios, are, the lower NO2 I/O ratios will be. In addition, one needs to consider the effects of homogeneous reactions. The reversible reaction involving photolysis of NO2, to NO and O3 is that which mainly influences indoor NO2 concentrations : where h is Planck's constant, and υ is the frequency of light at wavelengths from 202 to 422 nm. This reaction moves toward the right outdoors, where NO2 is split to NO and O3 by sunlight, and to the left indoors, where there is much less light. , ,

Ozone can also react with NO2 to generate the nitrate radical (NO3⋅) which can react further to nitric acid. The second order rate constant of this reaction is, however, much slower than that of the reaction of O3 with NO (0.0028 ppb−1 h−1 as compared to 1.6 ppb−1 h−1 at 25°C) and it is “not expected to greatly influence the indoor concentrations of either NO2 or O3.” Nazaroff and Weschler further reported that due to the high rate of formation of NO2 by reaction (1), NO and O3 will usually not only be simultaneously present indoors at levels above 5 ppb, but also that the I/O ratios of NO tend to be close to unity. This is likely to be the case if near all the outdoor NO or O3 is consumed in their rapid reaction before ventilation to the indoors. As can be the case centrally in cities with the near‐total consumption of O3 by surplus NO from traffic emissions or oppositely the near‐total consumption of the remaining NO by surplus O3 some distance away from the traffic emissions. In such situations, a typical “urban tropospheric ozone hole” is formed in the center of cities, such as for example in London. The ventilation to the indoors of either O3 or NO will then be low, and the Equation (1) equilibrium will have little influence on the indoor concentrations.

The indoor reaction of O3 with NO is usually faster than other removal processes and thus has the potential to affect indoor concentrations, as is shown by the following examples: If an NO concentration of 5 ppb is ventilated to the indoors in the presence of O3, the indoor removal rate of O3 will be 7.9 h−1. This is near a magnitude higher than a typical natural ventilation rate of ~1 h−1 and higher than that expected of the deposition of O3 to the surfaces in a medium size room. For a typical deposition velocity of O3 of 1.8 m h−1 (5 x 10−4 m s−1) , , , and room surface area to volume (A/V) of unity (for example a room of dimensions ≈ 10*10*3.5 m) the deposition rate would be 1.8 h−1.

The reaction between NO and O3 will, because of its high rate, typically take place in a smaller volume than the whole room and at higher concentrations of the gases than the average (measured) room concentrations (see also Section 4.3). This “problem” was avoided by deriving a model with only the outdoor concentrations as input. If mainly O3 and NO2 is ventilated to the indoors, then, obviously, the situation would be different with expected smaller gradients.

The model expressions for the NO2 I/O ratio were derived based on the fundamental Equation (1), then with input from the below Equations (2), (4) and (6) that describe the rate of formation of indoor NO2, NO, and O3, and Equation (5) that describe the rate of formation of outdoor NO. From Equation (1) and the indoor air exchange rate with the outdoors, the change in the indoor concentration of NO2 is given by: where NO2(i), NO(i), and O3(i) are the indoor concentrations of NO2, NO, and O3 (ppb), NO2(o) is the outdoor concentration of NO2 (ppb), υd,NO2 is the indoor mean deposition velocity of NO2 (m s−1), k is the rate constant for the reaction of O3 with NO (=4.43*10−4 ppb−1 s−1 at 25°C), λ is the air exchange rate (s−1), A is the room surface area (m2), and V is the room volume (m3). Equation (2) assumes that there is no indoor photolysis of NO2 to NO. Nearly all the NO2 photolysis happens due to UV radiation (over 90% by radiation between 300 and 370 nm and not by radiation over 420 nm ). In line with Fiadzomor and based on previous studies, Carslaw reports that the attenuation of UV light from outdoor to indoor is typically about 0.03. She further refers to the modelling work of Nazaroff and Cass that showed an increase in indoor from outdoor NO2 (of 3%) when the indoor visible and UV light fluxes were 0.7% and 0.15% of outdoors. It is a general aim of museums to keep low light and especially UV levels to prevent damage to objects. The day maximum annual average visible, and UV light intensities measured in the museums of 200 lux in Blickling Hall and 15 mW m−2 in the Tower of London (Table 3) were about 0.3% in the winter to 1% in the summer (visible light), and 0.015% (UV light) of the outdoor radiation (of ~17 000 lux in the winter to 67 500 lux in the summer, and 100 W m−2 ). This shows a similar outdoor to indoor visible light attenuation (or alternatively outdoor natural to indoor artificial light intensity) as in the modelling example from Nazaroff and Cass and considerably higher outdoor to indoor UV attenuation in the museums than in that example and reported as typical in the general indoors by Carslaw. At the low UV levels in the museums, there should be little indoor NO2 photolysis, and as in the example of Nazaroff and Cass an increase in the indoor to outdoor NO2 concentration could be expected in the summer.

TABLE 3

The model, Equation (14) best fitting parameter values in the 10 European museums

Site no.	Measurements			Parameter boundaries					Combined evaluation parameter
				Min = 0.1, max = 10		Min = 0, max= 0.01	Min = 0, max = 0.25	Min = 0, max = 1
				Model parameters
	Visible light (Lux)	UV (W m−2)	Room A/V (m−1)	λ (h−1), modelled ventilation	λ (h−1), description from museums	vdNO2 (m s−1)	e (ppb s−1)	x	(e x x2)/(A/V x vdNO2)
1	2.0	0	1.0	1.5	Natural	0.0011	0.25	0.18	7.4
2	0.4	0	0.5	10	~4 h−1 during opening hours	0.00036	0.25	0.15	31
3	120	15	0.6	2.2	Natural, very considerable	0.0016	0.040	0.45	3.9
4	200	5	0.8	0.28	Natural, barely noticeable to noticeable	0.0092	0.0053	0.96	0.67
5	21	0	0.5	0.10	Barely noticeable	0.010	0.25	0.58	17
6	6.5	0	3.6	0.82	Barely to easily noticeable	0.00023	0.010	0.42	2.1
7	16	0.1	1.1	6.8	Natural	0.0032	0.0026	0.61	0.27
8	12	0	1.5	6.8	Natural	0.0028	0.25	0.13	1.0
9	140	0.7	1.3	9.4	Mechanical	0.0021	0.25	0.25	5.7
10	23	3	1.1	0.12	Natural, very still air	0.000091	0	0.16	0

The hatched horizontal lines distinguish between the two museums in each of the five European regions. The bold figures represent the highest combined evaluation parameter value of the two museums in each region. A ranking seemed not meaningful between Krakow (no. 7) and Zakopane (no. 8) due to the low R 2 in Zakopane (Figure 2).

The following derivation assumes that there were no indoor emissions in the museums, of NO or NO2 (that can happen from for example gas‐fired stoves for heating and cooking, cellulose nitrate films or wool textiles), of O3 (from for example photocopiers) or of terpenes or other VOC (volatile organic compounds, from for example plants, or chemical solvents) that react with O3 at a high rate. If needed a term for indoor emissions or homogeneous production of NO2 by another route than Equation (1) could be added to the right side of Equation (2). An expression for the NO2 I/O ratio in the steady state was derived from Equation (2) to give:

The interest was now to obtain an expression for the NO2 I/O ratio with the outdoor pollution (the outdoor concentrations of NO2 and O3, and the outdoor emission rate of NO) and indoor building parameters (the room volume and surface area, and the deposition velocities of NO2 and O3 to the room surfaces) as input. This was achieved by the following derivation of expressions for O3(i) and NO(i) from these parameters, to be input in Equation (3).

The change in the concentration of NO in the indoor air was calculated as: where NO(o) is the outdoor concentration of NO (ppb). The indoor deposition velocity of NO was set to 0. , In the absence of NO data, as input for NO(o) in the steady‐state solution of Equation (4) (see Equation (7) below), the change in the concentration of NO in outdoor air was calculated as: where O3(o) is the outdoor concentration of O3 (ppb), j is the photolysis rate constant for NO2 (s−1), and e is the outdoor emission rate of NO (ppb s−1). Finally, the change in the concentration of O3 in indoor air was calculated as: where υ (O3) is the indoor mean deposition velocity of O3 (m s−1). For a steady‐state situation, NO(i), NO(o), and O3(i) were then calculated from Equations (4), (5), and (6) to give, respectively, Equations (7), (8), and (9):

A new expression for NO(i) was then obtained by substituting NO(o) and O3(i) in Equation (7) with the expressions for these parameters given by Equations (8) and (9), and then solve as a second order polynomial to obtain: with

The expression for O3(i) given by Equation (9) and that for NO(i) given by Equations (10) to (13), were then inserted for these parameters in Equation (3) to obtain the needed expression for the NO2 I/O ratio. The outdoor emission rate of NO, e, given as concentration per time unit, was interpreted here as the contribution of outdoor emissions of NO to the concentration of NO at the air intake to the building. In the modelling, the NO emission rate was set to be constant through the year and contribute to the varying outdoor NO concentrations by Equation (8). It was beyond this work to collect traffic counts representative for the emissions at the study sites. However, some reports show little monthly variations in Europe. Statistical evaluations from Poland showed that month of the year was of little importance in explaining seasonal road traffic variations. Measurements of real‐time traffic flows in Athens, Greece from 1997 to 1999 showed no monthly variation in 10 months, but somewhat lower counts in July and August (see also Discussion). In other modelling cases, it may be more practical to use NO concentrations, from for example measurements, as input directly, and thus simply substitute Equation (8) and the similar last terms in Equation (12) and (13) with “NO(o).”

A model simplification was then derived to be used with the available monthly mean values for the outdoor concentrations of NO2. Instead of the, supposedly more physically correct, derivation of NO(i) and O3(i) described above as input in Equation (3), the I/O concentrations of NO and O3 (NO(i)/NO(o) and O3(i)/O3(o)) were in the simplification assumed to be a fraction, x, being present in a steady state through the year. The value of this fraction should be interpreted as the root product (x x x 0.5 of the average annual I/O ratio x of O3 and x of NO. From the literature, it seems that the I/O ratio of O3 is commonly about 0.5 and of NO closer to 1, which would give a single parameter value of x = 0.7. The overall annual average O3 I/O ratio measured at the sites in this work was 0.16 (Table 2), which would with an NO I/O ratio of 1 give a value of x = 0.4. With reaction of NO indoors to an NO I/O ratio < 1, x would be lower. By multiplying Equation (8) with k x O3(o) and then dividing the numerator and denominator of the fraction in the numerator of Equation (3) ([kO3(i) x NO(i)]/NO2(o)), with respectively, the left and right side of this developed Equation (8), and then substituting for the NO I/O‐ and O3 I/O‐concentration fractions their assumed equal ratios, x, the model simplification was obtained as:

The temperature‐dependent NO + O3 rate constant, k (Equation (2)), does not appear in Equation (14). The temperature dependence of the NO2 photolysis rate is slight in the ambient temperature ranges of the 10 museums. If the emission rate, e, in the Equation (14) is expressed by calculation from Equation (8), then Equation (14) is equal to Equation (3), only with xO3(o) and xNO(o) substituted for O3(i) and NO(i) in Equation (3). This simple formula, Equation (14), had the advantage that there was no need for measured values for, or complicated modelling of, the indoor concentrations of O3. The procedure for the calculation of the photolysis rate, j, of NO2, was adopted from the EMEP Unified model , :(22). The calculation was made from the general expressions, and coefficients for the NO2 photolysis, in :(22) for every day and hour of the year for each 10th degree of latitude from the Equator (0°) to the North Pole (90°). A cloud cover of 50% through the year was used for all the sites except Malta and Crete where a cloud cover of 30% was used, based on rough annual averages , , . Figure 3 shows the latitude‐dependent mean monthly averaged values for the photolysis rate constant for the O3 + NO reaction, with 50% cloud cover, that can be used as input in Equations (14), and (15), to avoid lengthy calculations of this.

FIGURE 3

Mean monthly photolysis rate constant for the outdoors splitting of the NO2 molecule dependent on month and latitude, at 50% cloud cover

From Equation (14), it can be observed that for a case when the outdoor photolysis of NO2 is the only source of indoor NO, and there is thus no ventilation from outdoor of directly emitted NO (e = 0), or indoor direct emissions of NO, then the concentration of NO2 indoors can still be larger than outdoors. This will be the case when the indoor formation rate of NO2 from NO and O3 (by Equation (1) and given in Equation (14) as the multiple of the indoor to outdoor fractions of NO and O3 and the photolysis rate, x), is larger than its deposition rate to the indoor surfaces (A/V x v d,NO2). Thus, the chance for an NO2 I/O ratio > 1 increases in the summer, except close to the equator, and more so at higher latitudes (Figure 3).

The model fitting to the annual NO2 I/O values at the 10 museums was performed with Equation (14) and was shown in Figure 2 with the experimental measurements. Mean monthly outdoor NO2 concentrations and the calculated mean monthly photolysis rates in a situation with 50% cloud cover (from Figure 3), or 30% cloud cover for the sites in Crete (No. 9) and Malta (No. 10), were used. The other parameters in Equation (14) were assumed constant throughout the year and their values found from the modelling. Maximum and minimum allowed model parameter boundary values (Table 3) were set to avoid modelling to unreasonable continuously increasing values with infinitesimal improvement in the fitting. The low boundary was set to zero, or to a “low” value where this was needed to obtain a result from Equation 14 (of the ventilation rate, Table 3). The high boundary was set to a value in the high range of what was thought realistic for any site, compared to reported values. Thus, it was assumed that a ventilation rate above 10 h−1 , a deposition velocity of NO2 above 0.01 m s−1, and an NO emission rate (e) over 0.25 to be unrealistic (Table 3). e = 0.25 represents a mean monthly NO concentration of 34 ppb by Equation (8) when assuming a photolysis rate of 0.0026 (Figure 4), or of 47 ppb mid‐summer (July 1st) in Madrid, Spain (see below), and equal NO2 and O3 concentrations of 20 ppb. The model fitting was performed with a least‐squares multiple parameter nonlinear regression method in SPSS . The parameter values were from the start of the manual modelling procedure set to the mid‐point within their boundary ranges (see Table 3). The parameter values were then changed, consecutively between the parameters, and iteratively one small step at a time, until the apparent best possible fit and R 2 was achieved. The procedure was repeated several times with some changing of the start values and orders of change in values of the parameters, to be confident about the solutions. In practice, the optimal (largest possible) R 2 was typically obtained by doing a few (3–4) initial rounds of iterations with initial larger changes in the parameter values to investigate the sensitivity, then with fine tuning with minor changes to obtain the maximum R 2. Figure 2 shows that Equation (14) could reasonably simulate the annual variation in the NO2 I/O ratio, except in Zakopane where the R 2 was low. The model fit was quite close for Blickling Hall in Norfolk, UK (no. 4) and the two German museums in Stuttgart and Haslach (nos. 5 and 6). Table 3 gives the parameter values from the modelling.

FIGURE 4

Room size, given by the room surface area to volume (A/V) where an NO2 I/O ratio = 1 is expected, without (e = 0, as a reference at latitude 40°N) and with (e = 0.03 ppb s−1) close to the building outdoor NO emissions, depending on month of the year and latitude. (NO2(o) = 20 ppb, v d,NO2 = 5 x 10−4 m s−1, x = 0.5). The room A/V ratios in some of the museums are given

Although the results from the manual iterations seemed convincing in finding the best possible fits, it was realized that this method might not guarantee the testing of all possible parameter value combinations and full randomization of the input. With the four independent variables (λ, v dNO2, e, and x) combined in Equation (14) and, additionally the ill‐defined A/V ratios it was suspected that the modelling might not result in parameter values that could be simply explained by the observed site characteristics (Table S1 and Table 3). It was expected that interpretation by the combined equation parameters: x x e, describing the contribution of the outdoor emission of NO and the I/O ratios of NO and O3 to the indoor NO2, and A/V x v dNO2 describing the heterogeneous indoor removal of NO2, might be more realistic, although it would give less specific information. This is not so surprising as the (non‐measured) individual independent parameters are in direct combination in Equation (14), and thus not clearly distinguishable in the modelling, and also, as this combined parameter start to resemble the full model expression in Equation (14). It can be observed in Table 3 that the combined parameter distinguishes roughly between the urban and more polluted sites, and rural and less polluted sites.

Model evaluation and sensitivity

The expression for the A/V ratio giving an NO2 I/O ratio equal to 1 can be derived from Equation (14) to be:

Figure 4 shows the room sizes, given by the room surface area to volume (A/V) from Equation (15), where an NO2 I/O ratio of unity is expected, depending on the month of the year and latitude, as given by the mean monthly photolysis rates of NO2, j, with a 50% cloud cover from Figure 3 and with outdoor NO emissions, e, of 0.03 ppb s−1 close to the building air intake. With an NO emission rate of 0.03 ppb s−1 the outdoor mean monthly NO concentration would, by Equation (8) and assuming equal NO2 and O3 concentrations of 20 ppb, be about 10 ppb in the summer, but varying with the photolysis rate through the year and depending on latitude, from 3.4 to 11 ppb. A mean annual average NO2 of 20 ppb was measured at the 10 museums. O3 concentrations can typically be below 20 ppb in city centers and above 20 ppb away from traffic emissions ( ). NO concentrations from 3.4 to 11 ppb represent typical annual measurements at stations in Europe. The NO2 deposition velocity to the indoor surfaces was set to 5 x 10−4 m s−1, and the multiple of the I/O ratios of NO and O3 (x) to 0.25 (x = 0.5) like the mean of the modelling results in Table 3 when excluding the deviating sites, no 2, 8, and 10 (see Experimental and sites), which is in the range of reported values and complemented with the O3 measurements in this work (see Modelling).

Rooms positioned under the curves in Figure 4, that is, with a smaller A/V ratio and thus being larger, are expected to have NO2 I/O ratios larger than unity. As A/V ratios are usually, due to the roughness of room surfaces, furniture, installations, and other features, larger than those calculated from the nominal room dimensions, rooms usually need to be larger than indicated by the nominal A/V ratios for NO2 I/O ratios above unity to be observed. Indoor deposition velocities are expected to vary more than one magnitude depending on the surface material, humidity, and temperature. An NO2 deposition velocity of 5 x 10−4 m s−1 is in the upper range of values measured for common room surface materials in the laboratory, and could include some measure of the effect of the typical more complex room features. As a an example, for a case as described by Figure 4 at 40°N (that could be in Madrid, Spain), and with an outdoor NO emission of 0.03 ppb s−1, it could be expected that mid‐summer, as an average for June and July, then for rooms with A/V ratios less than ~2 m−1 (i.e., of, unfurnished, dimensions larger than about 4 x 4 x 2 m) the indoor concentration of NO2 will be larger than the outdoor concentration. Around July 1st the photolysis rate would be at its largest in Madrid: j = 8.14*10−3 s−1. A larger indoor than outdoor concentration is then expected in volumes larger than 1.2 m3, and thus in practice nearly always. In other seasons the rooms would need to be larger for the NO2 I/O ratio to be above unity at the elsewise same conditions. With a higher photolysis rate than in Madrid, which could be expected further north in the summer or further south in the other seasons, and elsewise similar conditions as laid out above, higher NO2 I/O ratios could be expected in smaller rooms than in the Madrid example. With increasing infiltration of NO and O3 (to x > 0.5) the sizes of rooms where an NO2 I/O ratio above unity is expected is decreasing even more quickly, to an extent that the infiltration becomes relatively more important for the NO2 I/O ratio than the latitude or time of year (see Figure S1).

From the room A/V ratios (Figure 4) a much larger difference in the NO2 I/O ratios between the Stuttgart and Haslach sites than observed in Figure 2 might be expected, with ratios always above unity in Stuttgart and never above unity in Haslach. In comparison for three of the locations with an A/V ratio of between 1 and 1.5 (no. 3, Tower of London in Figure 4, and nos. 1 and 9 (Table 3), the prediction from Equation (14) of NO2 I/O ratios above unity in the summer (Figure 2) seems reasonably correct. Possible reasons for the smaller measured than modelled difference in the NO2 I/O ratio between the Stuttgart and Haslach sites can be evaluated through the model (Equation (14)) sensitivity to the input parameters. Figure 5 shows the change in the NO2 I/O ratios at the three sites (Stuttgart, Tower of London, and Haslach) estimated to happen by changing the value of each model parameter (Equation (14)) from those measured in June 2004 (the crossing points of each parameter curve with the horizontal line for the NO2 I/O ratios).

FIGURE 5

Sensitivity of the modelled June 2004 NO2 I/O ratios (by Equation (14)) to the input parameters in (A) Haslach, (B) Tower of London, and (C) Stuttgart. The three values in the brackets are the minimum (0%), the measured values at the sites that were kept constant when varying the other parameters, and maximum values (100%) in the modelling ranges over all the sites (nos. 1 to 10, Table 3), but in the monthly mean variation of j at the latitude (50° north) of the three sites, and in the NO2(o) concentration measured over the three sites (Figure 1). The arrows indicate the measured or likely direction of changes in the given parameter values and resulting NO2 I/O ratios from the average model values used in the calculations of the curves in Figure 4, for the Stuttgart and Haslach museums (according to Figure 1, NO2(o), and Table 3, A/V and vdNO2)

Figure 5 shows the negative influence on the NO2 I/O ratio of the indoor deposition velocity υd(NO2), of smaller rooms (higher A/V) and of the outdoor NO2 concentration, and a positive influence of the other parameters. The NO2 I/O ratio is at all the three sites most sensitive to changes in the indoor deposition velocity with a somewhat different ranking of the sensitivities to the parameters between the sites. The figure shows that the measured or most likely separate site deviances from the average modelling conditions, used in Figure 4, would reduce the difference in the I/O ratio between the sites observed in that figure: It may be that the deposition of NO2 in the mechanical ventilation system and through the modern building shell in Stuttgart was higher than the average value used in the modelling, which was also indicated by the high modelling results of the deposition velocity in Stuttgart (Table 3); the outdoor NO2 concentrations in Haslach were considerably lower (~5 ppb, Figure 1) than the used museums average of 20 ppb; and the larger complex of interconnected rooms in the Haslach museum may have had a lower effective A/V ratio then 3.6. A change in these directions along the parameter curves in Figure 5 (as visualized with the arrows) would reduce the NO2 I/O ratio in Stuttgart and increase it in Haslach, and thus work in the direction of the measurements (as compared to the modelling in Figure 4).

Limitation of the model and available data

It should be stressed that the steady‐state model presented in this paper does not include homogeneous reactions of NOx with other species (than O3), that were not measured but may have been present and had an influence on the NOx values. The reported monthly averaged data do not describe variations in the indoor concentrations of NOx and O3 due to the dynamic reaction between them. For that purpose, time‐dependent analytical solutions or, more reasonably, numerical modelling to much more time resolved concentration data (

There is, typically, large fluctuations in the diurnal concentrations of NOx and ground level O3, especially due to traffic emission cycles. The variations in the outdoor concentrations and rapid reaction between NO and O3 implies that homogeneous mixing of O3 and NO will seldom happen in rooms after ventilation to the indoors. Gradients in the indoor concentrations of the gases are expected from inlets to outlets and depending on the air flows and mixing situations. In low ventilation situations, the reaction of O3 with NO could go to completion close to the inflow of air into a room but depending on the UV light presence and NO2 photolysis. The reaction may thus happen in smaller volumes, than the total rooms, and at higher than measured mean indoor room concentrations. This might affect reaction rates and the NO2 I/O ratios in ways that were not captured by the performed modelling.

Four independent model parameters were not measured and are interdependent (more or less) in the model expression. This situation was expected to result in considerable uncertainty, and there may have been a risk for “overfitting” and obtaining too high explanatory power (R 2). Parameter value boundaries were set in the modelling to avoid this. The main reason for the model fit (R 2) to the annual trends in Figure 2, seemed to be the similar shape through the year of the curve of the NO2 photolysis rate as the NO2 I/O ratios. Fitting to the variations over the year (from the smooth change in the annual trend of the photolysis rate) was then obtained, to a larger or lesser degree, by varying the other model parameters. Resulting in clearly differing model fit between the museums. Without measured values for these properties in the museums (Table 3) that could be used as input and/or verification, caution was needed in the interpretation of their model values. Much of the experimental variation that could not be explained by the modelling (excluding effects of experimental uncertainty) might be explained by variations through the year in the assumed constant model parameters. Despite such imprecisions, the results seem to substantiate the, often, dominating effect of the outdoor NO2 photolysis in giving systematic annual variations in the NO2 I/O ratios with higher values in the summer. This seemed to be the case in nine of the 10 investigated museums.

DISCUSSION

In all the museums except in Zakopane, higher NO2 I/O ratios were measured in the summer than winter, corresponding with the higher outdoor photolysis rates in the summer and thus supporting the hypothesis that the difference in the outdoor to indoor photolysis rate of NO2 was a main reason for the observed monthly variations in the I/O NO2 ratios over the year. The lower than unity NO2 I/O ratios measured through the year in four of the 10 locations (nos. 4, 7, 8, and 10) indicate relatively larger indoor NO2 sinks and/or lower ventilation to the indoors of NO2, by the precursors NO and O3 in these than the other locations. In Trondheim (no. 2), it seemed that more NO2 from the close to the air intake chimney emissions were measured indoors than at the outdoors location, which was positioned at some distance from the chimney and lower down on a wall, and that this could explain the high NO2 I/O ratios > 1 in the winter. The comparison of the indoor and outdoor NO2 and O3 concentrations measured in Stuttgart (no. 5) and Haslach (no. 6; Figures 1 and 2) illustrate differences between a modern museum centrally located in a city, close to roads with expected significant NO traffic emissions, and a more traditional building in a rural location. A reason for the lower indoor O3 and higher NO2 I/O values in Stuttgart than Haslach in the summer seemed to be the higher NO outdoor emissions in Stuttgart and homogeneous NOx‐O3 chemistry. The NO2 concentrations were measured to be considerably higher in Stuttgart than Haslach, and the modelling results (Table 3) supported the expectation of higher outdoor NO emissions in Stuttgart. In the winter, the NO2 concentration was considerably higher outdoors than indoors at both sites. In the summer, the opposite situation, with considerably higher indoor than outdoor concentrations, was measured in Stuttgart whereas in Haslach the outdoor and indoor NO2 concentrations were found to be near similar. In Stuttgart more than Haslach, and especially in the summer, the indoor NO2 concentration followed the (pattern of the) variation in the outdoor O3 rather than outdoor NO2 concentrations, which indicates formation of NO2 indoor from O3 and NO by Equation (1). In Haslach the indoor NO2 followed the values and variations of the outdoor NO2, but with lower indoor than outdoor values in the winter months with expected less ventilation. In Stuttgart the indoor NO2 did not follow the values and variations of the outdoor NO2. This is clearly seen in the correlation diagrams for all the months of the year in Figure 6.

FIGURE 6

Correlation coefficient (C) and linear trend explanatory power (R 2) of the monthly averages of NO2 measured indoors (i) with those of NO2 and O3 measured outdoors (o) through the year in Stuttgart and Haslach

The higher outdoor and, more so, indoor O3 concentration in Haslach than Stuttgart from February to September support the hypothesis of more indoor O3 loss in Stuttgart than Haslach due to reaction with NO. It was speculated that some infiltration through a near window, which the museum however informed was always kept closed, might have contributed to the relatively higher O3 indoor values in Haslach.

The emission rates of NO were found in the modelling (Table 3) to be larger in three of the five regional urban than more rural sites. The two exceptions being the urban sites of Oslo (no. 1) and Krakow (no. 7), as compared to the smaller towns of Trondheim (no. 2) and Zakopane (no. 8; Table 3) both with, seemingly, special emission conditions, as was explained above. The literature indicated that road traffic counts, and then probably NO emissions, might in some cases be lower in the summer vacation months (July and August) than other months of the year. If this was the case at the museum sites it would imply less outdoor (Equation (5)) and then indoor (Equation (4)) NO, a lower NO2 I/O ratio (Equation (14) and Figure 6) in the summer, and an expected worse model fit. At the winter sports location of Zakopane, especially, it could be hypothesized that this was a factor. Lower NO2 I/O values were observed in Zakopane from July to November, contrary to the model expectations, giving the worst model fit among the museums. A meaningful comparison of the modelling results for the two Polish sites was thus difficult. One could speculate that during the colder winter than in Krakow, and with the winter sports activities in Zakopane, there was also relatively more NO emissions from solid fuel burning, of coal and wood, and/or from traffic emissions in the winter than summer in Zakopane than Krakow, that reacted indoors with O3 to NO2.

Unfortunately, measurements of the building and/or room ventilation rates were not generally available from the sites. The qualitative descriptions of the ventilation, and in one case (Trondheim) a quantification (Table 3), seemed to be in rough accordance with the values obtained from the modelling. A much higher natural ventilation in the Wignacourt Collegiate Museum in Malta in the summer than winter (see Experimental) probably explained the high values of the NO2 I/O ratio in July and August that the model could not be fit very well. The modelling gave a similar spread in the deposition velocity of NO between the museums, as has been measured in the laboratory (~two orders of magnitude), but with an average value about six times higher, 0.003 m s−1 as compared to 5 x 10−4 m s−1. The measurement data were not sufficient to explain the high values and differences between museums. They might be due to the modelling to a situation with the nominal (smaller than real) room areas, and possibly due to additional deposition happening along the infiltration path of the inflowing air in the museums, through the building shell and in ducts, and in adjoining rooms. It could be suggested that the low deposition velocity in the Wignacourt Collegiate Museum in Malta (no. 10) was related to low ventilation and air flows at that site. The model values of the NO and O3 I/O ratios, “x” in Equation (14), showed a wide variation between 0 and 1 (Table 3). The mean of x = 0.5 (when excluding the deviating sites, no 2, 8, and 10, see above) seems reasonable, but the data seemed insufficient to explain the variation between the sites.

CONCLUSION

The photolysis of NO2 outdoors and back‐reaction of NO and O3 to NO2 indoors can result in higher than unity NO2 I/O ratios in rooms that are sufficiently large for this production to by higher than the heterogeneous loss by surface deposition. This can happen especially on sunny summer days, in urban areas with high NO emissions. The measurements in 10 European museums clearly showed higher NO2 I/O ratios in the summer than winter and in the urban than more rural sites. A steady‐state model of the NO2 I/O ratio, including the photolysis effect and main indoor sources and sinks of NO2 were derived. With a fractional (x) reduction in O3 and NO from the outdoors to the indoors, a reasonable fit to the yearly trend of monthly mean NO2 I/O ratios was obtained in nine of the 10 museums. The model can be used to approximate (with considerable uncertainty) indoor from outdoor NO2 mean monthly concentrations and exposure doses that could be compared with recommended levels in museums. It is suggested that the model (Equation (14)) could, generally when other specific information is not available, be used with the average values of x = 0.5, υd(NO2) ≈ 0.003 m s−1 found from the modelling of the sites in this work and with nominal room surface areas. The location‐dependent mean monthly photolysis rate, j, at 50% cloud cover could be read from Figure 3. The emission rate of NO which is needed for the estimation can be found from the close to the building outdoor concentrations of NO2, O3, and NO (by Equation (8)). For outdoor concentrations of NO2 and O3 of 20 ppb, and a summer value of NO in Europe of about10 ppb, a value of the emission of NO of 0.03 ppb s−1 can be used. The model could in practice provide sufficiently good indications of high indoors, and in the summer sometimes higher than outdoors, NO2 values that would be a preventive conservation concern. The model and its sensitivity analysis might be equally useful as a tutorial. Measurements are still recommended to obtain certain site values. The photolysis part of the modelling could possibly be added to available I/O gaseous pollution estimation tools for cultural heritage, such as IMPACT. , Such integration may be needed for the model to be practically applicable in most situations.

CONFLICT OF INTEREST

No conflict of interest was declared.

Figure S1

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Table S1

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