Development of a parameterization scheme for calculating dry deposition velocity of fine , coarse and giant particles

Introduction Conclusions References


Introduction
The parameter known as dry deposition velocity (V d ) has been commonly used in chemical transport models as well as in monitoring networks to associate a chemical species' mass flux density to the surface with its ambient concentration, i.e., a species' flux is a product of its V d and its ambient concentration.Knowledge of V d for atmo-Introduction

Conclusions References
Tables Figures

Back Close
Full spheric particles can be found in previous review papers (Sehmel, 1980;Nicholson et al., 1988;Sievering, 1989;Ruijgrok et al., 1995;Gallagher et al., 1997;Zufall and Davidson, 1998;Zhang and Vet, 2006;Petroff et al., 2008;Pryor et al., 2008;Fowler et al., 2009;Nemitz, 2012).V d for atmospheric particles strongly depends on particle size, among other factors.In most air quality and climate studies where both particle number and mass concentrations need to be considered, a size-resolved particle dry deposition scheme (e.g., Sehmel and Hodgson, 1980;Giorgi, 1986;Zhang et al., 2001;Nho-Kim et al., 2004;Feng, 2008;Petroff and Zhang, 2010;Kouznetsov and Sofiev, 2012) is needed.However, in many environmental assessments the dry deposition rate of a pollutant or a group of pollutants of interest to various ecosystems is the only concern.In this case, a simple empirical formula of V d -or the so-called bulk V d parameterization scheme, combined with monitored air concentration is sufficient.Several size-resolved V d schemes are available in literature that can be applied to any particle species and over any different surfaces (Zhang and Vet, 2006).However, no "universal" V d scheme is available for bulk aerosol particles which are monitored in various atmospheric deposition networks.Wesely et al. (1985) derived an empirical bulk V d formula for sulfate particles using sulfate flux data over grassland and this formula was later widely applied to sulfate as well as to many other fine particle species over various surface types.Other empirical formulas were also developed at later times for various particle species and/or size ranges.For example, Ruijgrok et al. (1997) generated a bulk V d formula for water-soluble inorganic ions, which include species of both fine and coarse particles, using flux data over forest canopies, and Laumaud et al. (1994) and Gallagher et al. (2002) derived formulas for submicron particles.None of these bulk V d formulas can be considered as universally applicable, e.g. to any particle species or over any different surfaces.
The present study aims to fill this gap by developing a bulk V d scheme taking the sizeresolved V d scheme of Zhang et al. (2001) as the benchmark.The reasons for choosing the scheme of Zhang et al. (2001) as the benchmark are that (1) it is a widely used scheme in the community, (2) it can be applied to any surface types, and (3) it seems Introduction

Conclusions References
Tables Figures

Back Close
Full to predict reasonable V d for most particle size ranges and over most surface types.The scheme might overpredict V d of small particles (e.g., < 0.1 µm) over smooth surfaces (Petroff and Zhang, 2010).However, small particles have very low mass fractions and thus small contributions to the bulk V d .According to the findings of Zhang et al. (2012), the new scheme should be developed for calculating V d of PM 2.5 , PM 2.5-10 and PM 10+ , instead of for specific particle species, and be applicable to various natural surfaces.
The new scheme is expected to produce similar V d values to the original size-resolved scheme, but is much easier to implement at atmospheric deposition monitoring networks.

Methodology
Particle dry deposition velocity can be calculated according to (Slinn et al., 1982;Zhang et al., 2001;Gallagher et al., 2002): where V g is the gravitational settling velocity, R a is the aerodynamic resistance above the canopy, and R s is the surface resistance.Note that the inverse of R s is also referred to as surface deposition velocity (V ds ) (Gallagher et al., 2002;Petroff and Zhang, 2010).Equation (1) applies to both bulk and size-segregated V d .Theoretically, a bulk V d should be obtained by integrating size-segregated V d according to particle size distribution.Considering that R a does not change with particle size and simple analytical formulas are available in literature for calculating R a , an alternative approach would be to first obtain a bulk V ds and a bulk V g ; the bulk V d can then be obtained from using Eq.(1).Parameterizing a bulk V ds and a bulk V g would be much simpler than parameterizing a bulk V d due to the avoidance of R a (and thus the parameters characterizing the planetary boundary layer).Note that although V g depends strongly on particle size, Introduction

Conclusions References
Tables Figures

Back Close
Full it only changes slightly with particle density and ambient temperature; a constant value can thus be used for a fixed particle size or size distribution.The size-resolved particle dry deposition scheme of Zhang et al. (2001) was used to derive V ds values for any particle size.The size-segregated V ds was then integrated to obtain bulk V ds for PM 2.5 , PM 2.5-10 and PM 10+ assuming a lognormal size distribution for each of the three size ranges.The geometric mass median diameter and geometric standard deviation were chosen as 0.4 µm and 2.2, respectively, for PM 2.5 ; 4.5 µm and 1.6 for PM 2.5-10 ; and 20 µm and 1.6 for PM 10+ .Regression equations were then generated using the bulk V ds data.
The original version of Zhang et al. (2001) used 15 land use categories (LUCs) and was later extended to 26 LUCs, consistent with those used in Zhang et al. (2003) (also see Supplement of Zhang et al., 2012).The 26 LUCs was also used in the present study, although they were put into different groups (Sect.3.1) or categories (Sects.3.2 and 3.3) for easy presentation.According to Zhang et al. (2001), V ds was calculated as: Where ε 0 is an empirical constant (taken as 3.0), u * is friction velocity, E B , E IM , E IN are collection efficiency from Brownian diffusion, impaction and interception, respectively, and R 1 is the correction factor representing the fraction of particles that stick to the surface (taken as 1.0 in this study which means no particle rebound is considered).
V ds only depends on u * and LUC-specific parameters.Thus, the bulk V ds can be parameterized as a function of u * for each LUC with the possibility of including additional LUC-specific parameters (e.g., leaf area index -LAI that changes with time of the year for some LUCs).
V g depends strongly on particle size, only slightly on particle density and meteorological conditions, but not on LUC.Thus, a constant V g can be used for a fixed particle size distribution.V g was also calculated using the same lognormal size distributions tained for PM 2.5 , PM 2.5-10 and PM 10+ , respectively, when choosing a particle density of 2.0 g cm −3 and a temperature of 15 • C. V g could vary by 10-20 % if temperature increase or decrease by 20 • C. V g was not discussed in Sect. 3 below and only V ds was described.Note that a particle density of 2.0 g cm −3 was used throughout the study.
3 Development and validation of the parameterization scheme

PM 2.5
The bulk V ds for PM 2.5 as a function of u * was generated for all the 26 LUC (see Fig. S1 in Supplement).Based on the regression equation shown in Fig. S1, V ds (m s −1 ) for PM 2.5 can be parameterized as a simple linear function of u * (m s −1 ) over all the LUCs: Where a 1 is the LUC dependent empirical constant.If LUCs with similar a 1 values are grouped together, the original 26 LUCs can be regrouped into five groups (Fig. 1).a 1 ranged from 0.0034 to 0.0069 for the five groups.Note that in the figures V ds is in cm s −1 for easy plotting; a 1 values shown in the figures were divided by 100 when applying to Eq. ( 3).These values are similar to (although slightly larger than) those found in previous studies which focused on dry deposition of fine particles (see Table 1 of Gallagher et al., 2002 for a summary of earlier studies).
The bulk V d for PM 2.5 can then be calculated as: Note that V g (PM 2.5 ) is in the order of 10 −5 m s −1 (see above in Sect.2), much smaller than the second term (e.g., 10 −4 to 10 −3 m s −1 ) in Eq. ( 4) under typical u * values, and Introduction

Conclusions References
Tables Figures

Back Close
Full thus can be omitted for simplicity if preferred.Apparently, the main difference between the new (Eq.4) and the original scheme (Eq. 1) is the different averaging procedure of size-segregated deposition velocity (V ds vs. V d ).
A comparison of V d (PM 2.5 ) between the new (Eq.4) and the original scheme (Eq. 1) was performed using a 1 values generated from Fig. 1.In this comparison, V d (PM 2.5 ) from the original scheme was obtained from integrating the size-segregated V d (not V ds ) using the same lognormal size distribution mentioned above.R a and u * were the same in the two schemes and were generated by varying day of the year (for covering different LAI values), wind speed (2-12 m s −1 ), and temperature differences between the reference height and the surface (for covering stable, neutral and unstable turbulent conditions).As shown in Fig. 2, the two schemes basically produced the same results over all the rough surfaces.It is worth pointing out that R a is generally much smaller than surface resistance (the inverse of V ds ) over rough surface so the different averaging procedures from the above two schemes caused little differences in their final V d values.For smooth surfaces (LUCs 1, 2, 3, 22 and 24), V d (PM 2.5 ) produced from the new scheme was a few percent (6-8 %) smaller than that from the original scheme; but this was thought to be acceptable considering that the original scheme likely overpredicted V d for small particles over smooth surfaces (Petroff and Zhang, 2010).The slight differences in the results between the smoother and the rougher surfaces were caused by the different R a values over these surfaces because R a was much larger over smoother surfaces (due to smaller roughness lengths) under the same wind speed conditions.

PM 2.5-10
The bulk V ds for PM 2.5-10 as a function of u * was also generated for all the 26 LUCs (see Fig. S2 in the Supplement).It was found from Fig. S2 that for a fixed u * value, only one V ds value was generated for some LUCs but multiple values were obtained for the other LUCs.The former case was for LUCs with a constant LAI (including 0 value) (i.e., LUCs 1-5, 8-10, 12-13, 20, 23-24) or with an LAI varying in a narrow range (i.e., LUCs 21-22, 25-26) (referred to category 1 below) while the latter case was for 31295 Introduction

Conclusions References
Tables Figures
Regression analysis shows high coefficient of determination (with R 2 > 0.82) between V ds and u * if a polynomial function (power of 3) for all the LUCs is used (Fig. S2).
Based on regression equations shown in Figs.S2 and 3, V ds can be simply parameterized as a function of u * for category 1 LUCs: Where b 1 , b 2 and b 3 are the LUC dependent empirical constants and are listed in Table 2a.Note that in Figs.S2 and 3, V ds is in cm s −1 for easy plotting; b 1 , b 2 and b 3 values shown in the figures were divided by 100 when applying to Eq. ( 5).Equation ( 5) also fits well to category 2 LUCs if the LAI value does not change.Taking LUC 6 as an example (Fig. 3b), the top curve represents V ds under maximum LAI (LAI max ) condition and the bottom curve for minimum LAI condition.For a fixed u * , an exponential increase in V ds was found with increasing LAI (Fig. 4a).Thus, Eq. ( 5) was first used to parameterize V ds for maximum LAI for each category 2 LUC.An adjustment factor as an exponential function of LAI was then added to Eq. ( 5) for different LAI conditions.The new equation becomes: The parameter k in the above equation was found to change with u * .Thus, k values were generated as a function of u * using the data shown in Fig. S2.k values for LUC 6 were shown in Fig. 4b as an example.Coincidently k can also be fitted into a polynomial function of u * :

Conclusions References
Tables Figures

Back Close
Full  2b.The final equation for V ds becomes: The bulk V d for PM 2.5-10 can then be calculated as: A comparison of V ds (PM 2.5-10 ) from using Eqs.( 5) and ( 8) and from the original scheme is shown in Fig. S3 with assumed u * .V ds (PM 2.5-10 ) calculated using the newly developed equations agreed very well with the values calculated from the original scheme with differences of ∼ 10 % or less over all the LUCs.No systematic difference was identified if considering all the LUCs together.Note that V g (PM 2.5-10 ) was in a similar order of magnitude to V ds (PM 2.5-10 ) under low u * values but was much smaller than V ds (PM 2.5-10 ) under high u * values.
A comparison of V d (PM 2.5-10 ) between the new scheme (Eq.9) and the original scheme (Eq. 1) is shown in Fig. 5, using the same input parameters (day of the year, wind speed, and temperature) as was used for PM 2.5 .The differences in V d  between the new and the old scheme were within 10 % over all the LUCs except LUCs 2, 15, 22 and 24 for which the differences were up to 20 %.Considering the large uncertainties in any existing dry deposition schemes, the differences of 20 % or smaller was considered acceptable.Introduction

Conclusions References
Tables Figures

Back Close
Full

PM 10+
The procedure generating V ds parameterization for PM 10+ was similar to that of PM 2.5-10 .Here, only the final equations are given: Where d 1 , d 2 ,d 3 , f 1 , f 2 and f 3 are the LUC dependent empirical constants and are also shown in Table 2a and b.The bulk V d for PM 10+ can then be calculated as: Using the same approach as in Sect.3.2, a comparison of V ds (PM 10+ ) from using Eqs.( 10) and ( 11) and from the original scheme is shown in Fig. S4, and a comparison of V d (PM 10+ ) between the new (Eq.12) and the original scheme (Eq. 1) is shown in Fig. 6.Similar to what was found for PM 2.5-10 , V ds (PM 10+ ) calculated using the newly developed equations agrees within ∼ 10 % of the original scheme over most LUCs and within ∼ 20 % over a few LUCs (22,24).V d (PM 2.5-10 ) from the new scheme were also within 10-20 % difference over all the LUCs.Again, such small percentage differences were considered acceptable in practical applications.

Conclusions
Monitoring networks have been established around the world to quantify atmospheric deposition of criteria pollutants to various ecosystems where the dry deposition component is estimated as a product of monitored air concentration and calculated V d of pollutants of interest.For aerosol particles, several size-resolved V d schemes are available in literature that can be applied to any particle species and over any different Introduction

Conclusions References
Tables Figures

Back Close
Full surfaces, but this is not the case for bulk aerosol particles which are monitored in various networks.To fill this gap, a parameterization scheme is developed taking a widely used size-resolved V d scheme as the benchmark.The new scheme produces similar V d values to the original size-resolved scheme for fine, coarse and giant particles.The new scheme is easier to use than the original one at monitoring locations where air concentrations are monitored for quantifying atmospheric dry deposition.If the mass fractions in fine, coarse and giant particles are known or can be assumed for a particle species, its bulk V d can then be obtained by weighting V d (PM 2.5 ), V d (PM 2.5-10 ) and V d (PM 10+ ).The uncertainties in V d from the new scheme are similar to those from the more sophisticated size-resolved schemes.Introduction

Conclusions References
Tables Figures

Conclusions References
Tables Figures

Back Close
Full Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | mentioned above and values of 3.7 × 10 −5 , 1.8 × 10 −3 and 3.4 × 10 −2 m s −1 were ob-Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Where c 1 , c 2 and c 3 are the LUC dependent empirical constants.b 1 , b 2 ,b 3 , c 1 , c 2 and c 3 for Category 2 LUCs are shown in Table Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Table Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .
Fig. 1.Bulk V ds (PM 2.5 ) as a function of u * for five group LUCs.

Table 2b .
Empirical constants for use in Eqs. (