Modeling Particulate Matter Concentrations in Makkah , Applying a Statistical Modeling Approach

Particulate matter originates from a variety of sources in Makkah, Saudi Arabia. Since Makkah is situated in an arid region and is a very busy city due to its religious importance in the Muslim world, PM10 concentrations here exceed the international and national air quality standards set for the protection of human health. The main aim of this paper is to model PM10 concentrations with the aid of meteorological variables (wind speed, wind direction, temperature, and relative humidity) and traffic related air pollutant concentrations (carbon monoxide (CO), nitric oxide (NO), nitrogen dioxide (NO2), sulphur dioxide (SO2) and lag_PM10 concentrations), which are measured at the same location near Al-Haram (the Holy Mosque) in Makkah. A Generalized Additive Model was developed for predicting hourly PM10 concentrations. Predicted and observed PM10 concentrations are compared, and several metrics, including the coefficients of determination (R = 0.52), Root Mean Square Error (RMSE = 84), Fractional Bias (FB = –0.22) and Factor of 2 (FAC2 = 0.88), are calculated to assess the performance of the model. The results of these, along with a graphical comparison of the predicted and observed concentrations, show that model is able to perform well. While effects of all the covariates were significant (p-value < 0.01), the meteorological variables, such as temperature and wind speed, seem to be the major controlling factors with regard to PM10 concentrations. Traffic related air pollutants showed a weak association with PM10 concentrations, suggesting road traffic is not the major source of these. No modeling study has been published with regards to air pollution in Makkah and thus this is the first work of this kind. Further work is required to characterize road traffic flow, speed and composition and quantify the contribution of each source, which is part of the ongoing project for managing the air quality in Makkah.


INTRODUCTION
Fine particles are considered to be responsible for respiratory health effects.There is a strong link between elevated particle concentration and increased mortality and morbidity (WHO, 2004).Exposure to particulate matter can aggravate chronic respiratory and cardiovascular diseases, alter host defenses, damage lung tissue, lead to premature death, and possibly contribute to cancer (WHO, 2004;Hassan, 2006).Particle shape and size are critical factors controlling the extent to which particles can penetrate into the respiratory tract, how and where particles are deposited, and at what rate particles are cleared from respiratory tract.Furthermore, smaller particles have a greater reactive surface area than an equivalent mass of larger particles and have a higher likelihood of reaching the deepest regions of the lungs.Ultrafine airborne particles, below 1 μm in diameter have been related to premature death, aggravated asthma, increased hospital admissions, and increased respiratory problems (Hassan, 2006).Particles also have a range of important nonbiological impacts including soiling of man-made materials and buildings, reducing visibility and affecting heterogeneous atmospheric chemistry.
High levels of PM 10 concentrations in Makkah, especially during the Hajj period when several million people visit the city to perform Hajj, have been reported by several authors (e.g., Al-Jeelani, 2009;Othman et al., 2010;Seroji, 2011;Habeebullah et al., 2012).A brief review of the studies conducted in Saudi Arabia is shown in Table 1.The reasons for the high particulate matter concentrations are most probably high volume of traffic, construction work, resuspension of particles, geographical conditions (Arid Regions) and the role of atmospheric conditions.Most of the area of Saudi Arabia is made of deserts, thus leading to  Sabbak, 1995 Jeddah, Saudi Arabia Iron (Fe), zinc (Zn), cobalt (Co), chromium (Cr), nickel (Ni), lead (Pb), manganese (Mn) and sodium (Na).Fe and Na were the major components of the air dust.Alharbi et al., 2012 Saudi Arabia Saudi Arabian dust storm event and its reasons.Large-scale atmospheric instability, high surface winds, and dry rich dust sources cause dust storms in Saudi Arabia.a high concentration of dust in the air as wind blows into inhabited areas from the neighbouring desert lands (PME, 2012).The concentration of PM 10 in the atmosphere is dependent on the number and strength of the sources (e.g., road traffic), meteorological variables (e.g., wind, relative humidity) and the concentrations of other air pollutants (e.g., SO 2 , NO x ).For effective management of PM 10 in Makkah, it is vital to quantify the contribution of each source and understand the role of meteorology and other air pollutants.
PM 10 concentrations have been monitored in Makkah for long time, however no published work on modeling of particulate matter was found.Therefore, this is the first effort to model PM 10 concentrations in Makkah, where no traffic characteristics and source apportionment data are available.In this study the association of PM 10 with meteorological variables and other traffic related air pollutants is described and a model is developed for predicting hourly PM 10 concentrations, using a Generalized Additive Model (GAM).GAM relaxes the assumption of normality and can handle the non-linearity in the association of dependent and independent variables (Wood, 2006).Davis and Speckman (1999), Aldrin and Haff (2005), Carslaw et al. (2007), and Westmoreland et al. (2007) used GAM for modeling the concentrations of various air pollutants in different countries of the World.
More recently, Paciorek et al. (2009) applied GAM for modeling the spatio-temporal variation of particulate matter in South Carolina.

Data Source
This research project was conducted at the Hajj Research Institute (HRI), Umm Al-Qura University in Makkah.The City of Makkah is at an elevation of 277 m above sea level, and approximately 80 km inland from the Red Sea.The city is surrounded by mountains, which define the contemporary expansion of the city with a population of 1,700,000, which gets doubled or even more during the season of Hajj and the month of Ramadhan.The city centers on the Masjid al-Haram area, which is the lowest and most crowded area in the city.The monitoring site used in this project (AQMS-112) is situated near the Holy Mosque (Al-Haram) as shown in Figs. 1 and 2. It is important to note that the AQMS-112 site is run by Presidency of Meteorology and Environment (PME) and shares data with HRI.Fig. 1 shows the monitoring network in Makkah run by HRI and Fig. 2 shows a detailed maps of the 39°49'44.44''E)site and potential sources of emissions in the surrounding area, which include a construction side, a busy road and bus stations (discussed later).
Hourly mean data of these parameters from November 2011 to July 2012 were obtained, which were further analyzed using the methodology described in below.A summary of these variables is given in Table 2. Road transport is considered as one of the major sources of traffic related air pollutants including PM 10 and therefore traffic flow and speed should have been included as explanatory variables in the model.However traffic data for the study area were not available and therefore trafficrelated air pollutants (e.g., CO and NO) were included in the model as surrogates for the traffic characteristics (Pont and Fontan, 2000) and as a source of secondary air pollutants (e.g.SO 2 and NO 2 leading to the formation of SO 4 2-and NO 3 -).

Measurement of PM 10
Several methods, such as the Tapered Element Oscillating Microbalance (TEOM) system, the Beta-Attenuation Monitor (BAM) and Partisol are used for measuring the concentration of PM 10 in the atmosphere.TEOM determines particulate concentration by continuously weighing particles deposited on a filter, whereas BAM consists of a paper band filter located between a source of beta rays and a radiation detector.A pump draws ambient air through the filter and the reduction in intensity of beta-radiation measured at the detector is proportional to the mass of particulate deposited on the filter.The Partisol is a gravimetric sampler that collects daily samples onto a filter for subsequent weighing to determine the PM 10 concentration.
The standard EU reference method for particulate measurement refers to three devices which might be used for measuring PM 10 concentrations: (a) Low Volume System: the LVS-PM 10 Sampler; (b) High Volume System: the HVS-PM 10 Sampler; and (c) Super-high Volume System: SHVS-PM 10 also known as Wide Range Aerosol Classifiersampler (WRAC-PM 10 ).At HRI two types of monitors are used for measuring the concentrations of PM 10 : BAM 1020 and HVS PM 10 samplers.Continuous monitoring of PM 10 is carried out using Dust Monitor (BAM 1020), which provides 30 minutes concentrations in the units of μg/m 3 .HVS PM 10 Samplers are used as a portable device for measuring PM 10 concentrations, providing 24 hr average concentrations.At HRI the later is generally used to monitor PM 10 concentrations for a short period of time, such as during Hajj and the Month of Ramadan.

Data Quality
A summary of PM 10 and independent variables is presented in Table 2, where most of the variables have over 95% data capture (%DC), except SO 2 (79%) and PM 10 (88%).EU standard for DC is 75%, suggesting any variable with less than 75% DC should be removed from the analysis.Data for PM 10 and covariates were obtained from the AQMS-112 monitoring site, near the Haram in Makkah from November 2011 to June 2012 for model training and for July 2012 for model testing.

General Statistics
Correlation analysis is applied to estimate the extent of relationship between PM 10 concentrations and other variables.Furthermore, graphical presentations (e.g., bivariate polar plots and scatter diagram) are used to present the outputs of the analysis.
Several metrics were calculated to assess the model performance.These metrics are: Root Mean Square Error (RMSE), Normalised Mean Gross Error (NMGE), Correlation coefficient (R), Normalised Mean Bias (NMB), Fractional Bias (FB) and Factor of 2 (FAC2).The RMSE is a commonly used metric that provides a good overall measure of how close modelled values are to predicted values.The Mean Bias (MB) is an indication of the mean over or under In the table SO 2 stands for sulphur dioxide(µg/m 3 ), CO for carbon monoxide(mg/m 3 ), NO for nitric oxide(µg/m 3 ), NO 2 for nitrogen dioxide(µg/m 3 ), O 3 for ozone(µg/m 3 ), PM 10 for particles having diameter less than 10 um(µg/m 3 ), WS for wind speed (m/s), WD for wind direction (degrees), T for temperature (°C), RH for relative humidity (%), RF for rainfall (mm), PR for atmospheric pressure (hPa), Min for minimum, Max for maximum, NA's for missing data (not available), and DC for data capture (valid data in percentage).estimate of prediction.To estimate NMB the value of MB is divided by the observed concentration.NMGE is the same as NMB, but it ignores whether a prediction is an over or under estimate (absolute value).The correlation coefficient is a measure of the strength of the linear relationship between two variables.Most often correlation coefficient is squared to calculate coefficient of determination (R 2 ).FB is used to identify if the model shows asystematic tendency to over or under prediction.FB value varies between +2 and -2 and has an ideal value of zero.Negative values suggest a model over-prediction and positive values suggest a model under-prediction.FAC2 is the fraction of modeled values within a factor of two of the observed values.In other words FAC2 is a count of the fraction of points within 0.5 and 2 times the observed values and satisfies that 0.5 ≤ Mi/Oi ≤ 2.0, where Mi and Oi stand for the modeled and observed values of PM 10 concentrations.For more details on these metrics and their mathematical formulae see Carslaw (2011) and Derwent et al. (2010).
Statistical Software R programming language (R Development Core Team, 2012), with package mgcv, version 1.7-12 (Wood, 2012) and openair version 2.13.2 (Carslaw and Ropkins, 2012) are used for running GAMs, other statistical tests and making graphs.

Generalized Additive Model (GAM)
GAMs are statistical models developed by Hastie and Tibshirani (1990) for blending properties of generalized linear models with additive models.GAMs assume that the mean of the dependent variable depends on additive predictors through a nonlinear link function.GAMs permit the response probability distribution to be any member of the exponential family (e.g., normal, exponential, gamma, Poisson and many other) (Wood, 2006).GAM uses smoothing components to establish the shape of relationship and these are determined by the data itself (i.e., the relationship is not forced to take a particular functional form, e.g., linear or exponential).The additive model in a general form can be described as below (Eq.( 1)).
where Y is the response variable and s is a smoothing term which corresponds to an associated explanatory variable (X).

Model Development
In this paper, the main aim is to find the combination of explanatory variables which can describe a high degree of the pollutant concentration variability (R 2 ) in Makkah.PM 10 was used as response variable and the concentrations of some traffic related air pollutants (Carbon Monoxides (CO mg/m 3 ), Nitric Oxide (NO μg/m 3 ), Nitrogen Dioxide (NO 2 μg/m 3 ), Sulphur Dioxide (SO 2 μg/m 3 ) and lag_PM 10 (concentration of PM 10 from the previous day)); and meteorological variables (Wind Speed (WS m/s), Wind Direction (WD degree from the north), temperature (T °C) and Relative Humidity (RH %) as independent (explanatory) variables.A summary of the parameters is given in Table 2. Traffic data were not available in the study areas, therefore the concentration of other air pollutants were used instead, which provide a surrogate to traffic flow (Pont and Fontan, 2000) and a source for secondary particles formation.Some authors (e.g., Carslaw et al., 2007;Westmoreland et al., 2007) have suggested that wind speed and wind direction should be included in the model as interactive term (u, v), where u is [wind speed] × sine (wind direction) and v is [wind speed] × cosine (wind direction), however this did not improve the model performance significantly and therefore the actual values of wind speed and wind directions, which are easier to follow were used in the model.Precipitation and cloud cover may help reduce PM 10 concentration by washing out effect and by affecting relative humidity and temperature of the atmosphere; however the values of rain fall and cloud cover were zero for the whole time period considered in this paper and therefore were removed from the model.The final GAM model for PM 10 is shown in Eq. ( 2).

RESULTS AND DISCUSSIONS
The outputs of the GAM model are depicted in Fig. 3.The p-values being less than 0.01 show highly significant effect of all independent variables included in the model.Coefficient of determination (R 2 -adjusted) was 0.50, deviance explained was 51%, and GCV score was 8658.Several other metrics were estimated to assess the performance of the model, as suggested by Carslaw (2011) and Derwent et al. (2010).
Fig. 3 shows the outputs of GAM model (given in Eq. ( 2)), where it is shown how the association of PM 10 concentrations changes with the levels of other variables, for example CO and NO both being primary traffic related pollutants show different effects on PM 10 concentrations.CO shows negative whereas NO shows positive effect on PM 10 concentrations and the strength of the effect increases with increasing CO and NO concentrations.This might indicate that a considerable proportion of PM 10 in Makkah has different sources of emission to these other air pollutants.For example, NO and CO are mainly emitted by road traffic in the surrounded area, whereas PM 10 , in addition to road traffic, is generated by other sources as well, such as construction work and resuspension of the dust particles.Simple correlation analysis showed a strong correlation between CO and NO (R = +0.62)and a weak correlation between PM 10 and NO (R = +0.02)and PM 10 and CO (R = -0.11).Correlation coefficients of PM 10 were -0.08 and -0.11 with NO 2 and SO 2 , respectively.It is well known that SO 2 and NO x are the two important sources of secondary particulate matter (e.g., NO 3 -and SO 4 2- ) and generally have positive contribution to PM 10 concentrations (e.g., Harrison,  2001b).Here the negative correlation of PM 10 with these air pollutants might indicate that PM 10 concentrations are predominantly controlled by construction work and resuspension of dust particles due the arid nature of the regions.Positive association between PM 10 and lag_PM 10 is expected and understandable, as fine and extra fine particles stay in the atmosphere for long time and contribute positively to the measured concentration hours or even days later (AQEG, 2005).In Makkah during Hajj season and the month of Ramadhan due to increase in transport and other activities (such as walking), the resuspension of sand and dust is enhanced, which further increases the concentrations of particulate matter in the atmosphere (Seroji, 2011).Modeling and source apportionment of these sources is a challenging task, which may add to uncertainties in the model outputs.
A decrease or increase in air pollution concentration is the result of an imbalance between air pollutants production rates (emission of primary pollutants from sources and formation of secondary pollutants in the atmosphere) and air pollutants removal rates (dilution and loss from the atmosphere) (Andersson et al., 2006).Meteorology plays a vital role in secondary particles formation and their removal from or dilution in the atmosphere.Meteorological factors such as temperature, solar radiations, relative humidity, and wind speed can influence the transport, dispersion and chemical reactions of air pollutants (Harrison, 2001b).Fig. 3 shows strong positive effect of wind speed and temperature on PM 10 concentrations.Wind speed plays a vital role in the dispersion of air pollutants and transportation of air pollutants from one place to another ranging from local to regional or global scale (Liu et al., 2011 and the references therein).High wind speed and high temperature both increase turbulence and resuspension of the dust particles (Kim et al., 2006).In an arid region like Saudi Arabia which mostly has no rain for months and where most of the area is made of sandy deserts, high wind speed lifting sand and dust particles leads to high concentrations of dust as wind blows into inhabited areas from the neighbouring desert lands (PME, 2012).Simple correlation analysis showed a strong correlation between PM 10 concentration and wind speed (R = +0.42)and temperature (R = +0.38).Sand and dust storms is a common phenomenon, during high wind speed in Saudi Arabia.High relative humidity increases chemical reactivity in the atmosphere; and is generally linked with night time hours when dust concentration is low and therefore shows negative correlation with PM 10 concentrations.Duenas et al. (2002) has reported that relative humidity plays an important role in air quality, as relative humidity may play a role in the overall reactivity of the atmospheric system, either by affecting chain termination reactions or in the production of wet aerosols, which in turn affect the flux of ultraviolet radiation.Furthermore, relative humidity is also considered to be a limiting factor in the disposition of NO 2 because high percentages of humidity favour the reaction of the NO 2 with salt particles, e.g., sodium chloride (NaCl).
The effect of wind speed and wind direction is further elaborated in Fig. 4 in the form of a bivariate polar plot.The plots are constructed by averaging pollutant concentration by wind speed categories (0-1 m/s, 1-2 m/s, etc.) as well as wind direction (0-10, 10-20, etc.).In polar plots (Fig. 4) the levels of different variables are shown as a continuous surface, which are calculated through using Generalized Additive Models smoothing techniques (Carslaw and Ropkins, 2012).It can be observed in Fig. 4 that high PM 10 concentration is related with high wind speed from the west direction (between 225 to 360°).Further investigation of the local area revealed that there was a large construction work going on near Al-Haram in southwest to northwest direction (Fig. 2).There are some barriers (e.g., a part of Al-Haram building) between the monitoring site and construction location, however when westerly wind is blowing at speed greater 2 m/s, the dusts manage to reach the Haram and results in high concentrations of PM 10 .On the eastern side, there is a busy road (Masjid Al-Haram Road) and a couple of bus stations (shown in Fig. 2), which probably contribute to the monitored concentration.However this contribution seems considerably lower than the western side contribution, as shown by the colour of the polar plot.Polar plots developed for NO, CO and SO 2 showed high concentrations on the eastern side (Habeebullah et al., 2012), indicating high contribution of road traffic.This probably indicates that most of the PM 10 concentrations come from other sources rather than road traffic, otherwise the pattern of PM 10 concentrations and other air pollutants would have been the same.

Assessment of the Model Performance
Various metrics (R 2 , RMSE, NMB, FB and FAC2) were calculated to assess the model performance.These metrics have been defined above and their values for the testing dataset (July, 2012) were 0.52, 84, 0.21, -0.22, and 0.88 for R 2 , RMSE, NMB, FB, and FAC2, respectively.FB (-0.22) shows a tendency towards slightly over predicting the PM 10 concentrations and therefore an adjustment factor might be required.When the adjustment factor (regression coefficient or slope of the line between observed and predicted PM 10 concentrations) of 0.75 was applied the FB value changed to 0.06.The values of other metrics improved as well.
Figs. 5 and 6 compare predicted (without any adjustment) and monitored PM 10 concentrations for the testing dataset (July, 2012).FAC2 value of 0.88 shows that 88% of datapoints lie between 0.5:1 and 2:1 lines.Observed and predicted PM 10 concentrations are also compared in Fig. 6 with the help of a time series plot and a bivariate polar plot, which show closer relationship between the two concentrations.It  should be noted that the right side polar plot, representing the predicted PM 10 concentrations (p) has considerably larger scale, which again confirms the over prediction of the model, as discussed above.These polar plots have the same characteristics as in Fig. 4 (developed for the training dataset), highlighting the sources towards the west and northwest.However, the model prediction seems slightly biased towards the north but still successfully correlate high prediction with high wind speed, as explained in above.This is the first effort to model PM 10 concentration in Makkah, where multiple sources including road traffic, resuspension and construction work contribute to the observed PM 10 concentrations.Further work is required to quantify the contribution of each source, particularly road traffic, being the main sources of several air pollutants in urban areas, which is part of the ongoing project for improving air quality in Makkah.

CONCLUSIONS
This study aims to model variations in PM 10 concentration with the help of meteorological variables and traffic related air pollutants (e.g., CO and NO x ).Traffic related air pollutants can provide a surrogate for traffic flow and are sources of secondary particles, such as SO 4 2-and NO 3 -.Meteorological variables play a vital role in particles dispersion, resuspension, and atmospheric reactivity.Using a GAM model, these covariates can explain a considerable amount of variations in PM 10 concentrations.Predicted and observed PM 10 concentrations are strongly correlated, with R 2 (0.52), RMSE (84), FB (-0.22) and FAC2 (0.88).The values of these metrics and graphical comparison (polar and scatter plots) put confidence in the model performance.The effects of all covariates were significant (p-value < 0.01), however meteorological variables, for instance temperature and wind speed due to their strong positive association seem to play dominant role in controlling PM 10 concentrations in Makkah.This may suggest that high PM 10 concentrations in Makkah are as a result of the arid nature of the region.Traffic related air pollutants showed weak association with PM 10 concentration, which suggests that road traffic is not the major emission source of PM 10 .Further work is required to quantify the contribution of each source of PM 10 in Makkah, which is part of the ongoing project for improving air quality in Makkah.

ACKNOWLEDGEMENT
This work, which is a part of the improving air quality project in Makkah and Madinah, is funded by HRI, Umm Al-Qura University.We greatly appreciate their support.Thanks are also extended to PME for providing us the data and to all staff of the HRI, particularly to the staff of the Department of Environment and Health Research for their support.
We are grateful to the anonymous reviewers for reviewing this paper and giving us suggestions, as a result of which the manuscript has considerably improved.

Fig. 1 .
Fig. 1.Map of the air quality and meteorological monitoring sites in Makkah, where AQMS-112 shows the site, where the data used in this paper was measured.

Fig. 2 .
Fig. 2. Map of the monitoring site (AQMS-112) showing various sources of emissions.Blue circle shows construction area and red circles show bus stands, along the Masjid Al-Haram Road.

Fig. 3 .
Fig. 3.The outputs of the model, where PM 10 was used as independent variable and concentrations of some other air pollutants, i.e., Carbon Monoxides (CO mg/m 3 ), Nitric Oxide (NO µg/m 3 ), Nitrogen Dioxide (NO 2 µg/m 3 ), Sulphur Dioxide (SO 2 µg/m 3 ) and lag_PM 10 (concentration of PM 10 from the previous day µg/m 3 ) and meteorological variables, i.e., Wind Speed (WS m/s), Wind Direction (WD degree from the north), temperature (T °C) and Relative Humidity (RH %) as independent variables.The data come from the air quality monitoring station near Al-Haram, Makkah Saudi Arabia, November 2011 to June 2012.The dashed lines are the estimated 95% confidence intervals.The vertical lines adjacent to the lower x-axis show the presence of data.

Fig. 5 .
Fig. 5. Scatter plot of observed and predicted PM 10 concentrations.The dashed lines show the within factor of two (FAC2) region.The middle line is 1:1, the above is 0.5:1 line and below is 2:1 line.

Fig. 6 .
Fig. 6.Comparison of observed and predicted PM 10 concentrations for the month of July 2012, in Makkah.(a) shows a time series comparison and (b) shows bivariate polar plot comparison, where PM 10 shows observed concentrations and p shows predicted concentration.

Table 1 .
A brief review of previous studies in Saudi Arabia.Name, year and location Main pollutants and results Nasrallah and Seroji, 2008 Makkah, Saudi Arabia TSP, PM 10 and PM 2.5 Daily PM 10 concentration ranged 191-262 µg/m 3 , TSP concentrations reached 665 µg/m 3 .Chemical analysis showed high levels of sulphate, ammonium, nitrate and chloride.Nasrallah and Seroji, 2007 Makkah, Saudi Arabia NO 2 , NO, NO x , non-methane hydrocarbon (NMHC) and ozone.Hourly mean NO x levels reached more than 800 µg/m 3 and ozone hourly level reached 160 µg/m 3 in Makkah.Highest level of ozone was recorded in May and lowest in February.Al-Jeelani, 2009a Makkah, Saudi Arabia NO 2 , SO 2 , CO, ozone, methane (CH 4 ) and total hydrocarbons (THC) as well as some meteorological parameters (temperature, wind speed and wind direction), November 2002 to October 2003 were measured and analyzed.Daily cycles of these pollutants were analyzed.Al-Jeelani, 2009b Makkah, Saudi Arabia NO 2 , SO 2 , CO, ozone, CH 4 and THC and WS, WD and temperature.CO, NO, NO 2 varied during the day, whereas SO 2 concentrations were relatively constant.Ozone concentration was associated with photochemical activities.Othman et al., 2010 Makkah, Saudi Arabia PM 10 PM 10 was high during Hajj season than other months Kutiel and Furman, 2003 Middles East Dust storms Middle East, Sudan, Iraq, Saudi Arabia and the Persian Gulf, are the regions that reported the greatest occurrence of dust storms.

Table 2 .
Presenting a summary of PM 10 concentrations and independent variables from November 2011 to June 2012 at AQMS-112 site in Makkah.