Modeling of Mineral Dust Emissions with a Weibull Wind Speed Distribution Including Subgrid-Scale Orography Variance
1. Introduction
For many geophysical studies, the wind speed close to the surface is a key parameter. This includes the analysis and modeling of mineral dust emissions. Primarily, the understanding of these emissions was performed using in situ or wind tunnel experiments (Gillette and Passi 1988; Shao et al. 1993). This means that the deduced parameterizations were first mainly representative of a local spatial area. Using these experimental studies, dust production models (DPM) were designed and later implemented in regional and global transport models. The transition between the local-scale and large-scale modeled fluxes is ensured by using tuning parameters. For example, Tegen and Fung (1994) uses a simple relationship for the vertical flux estimation, including a scaling factor; Marticorena et al. (1997) linked the horizontal (saltation) flux Fh to the vertical (sandblasting) flux Fυ using constant α factors, 
To fill the gap between locally estimated emissions and a regional scale model, recent studies explored the way to describe the DPM’s input parameters with distributions in place of single mean values (Grini and Zender 2004; Pryor et al. 2005; Menut 2008). This corresponds to the way to represent variables also with their subgrid-scale variability. This variability may be taken into account for many parameters in the DPM: recently, Menut et al. (2013b) use spatially high-resolution databases of roughness lengths, soil, and surface parameters to represent the existing variability in a model grid cell representing several tens of squared kilometers.
This is also essential for the wind speed used in the emissions calculation. The mean wind speed used in a model often represents averaged values both in the temporal and spatial dimensions. But, as the mineral dust emissions is a threshold problem, the use of a single mean value may induce large modeling errors. For example, for particular soil conditions, emissions of dust may appear only up to 8.5 m s−1: if the “real” mean wind speed is 8 m s−1, then there is no emission at all. But if the “modeled” wind speed is 9 m s−1, then emissions are calculated. This model error is possible, since the wind speed model uncertainty is 
In this study the main goal is to improve the subgrid-scale variability of the mean wind speed by adding additional information in the k parameter estimation. This additional information is the orography variance of a model grid cell. The choice to add this specific variability was done because this information is available but not used in the model and because it seems logical that the surface wind speed is not spatially constant over surfaces of tens of squared kilometers. Then, in a model, when using a “mean” wind speed, it is clear that this value does not reflect completely all possible values observed in a grid cell, where the orography may vary.
By adding a relationship between k and the orography, we add realism to the simulation and we also expect to reduce the uncertainty linked to the model resolution (the more realistic subgrid-scale variability is taken into account, the less the results depend on the horizontal resolution). Using the WRF and CHIMERE models, simulations are done with and without the modification of k. Using comparisons to measurements, we quantify whether the modeled results are improved.
First, the data and tools used in this study are presented with the observations in section 2 and the models in section 3. The Weibull distribution is presented in section 4, and the proposed modified formulation of the shape parameter k is presented in section 5. Results with an academic test case are presented in section 6. Then, in section 7, the impact of this additional term is evaluated on a realistic test case representing the simulation of the period January–April 2012 over a large domain encompassing the northern Africa (including Sahara and Sahel) and the Mediterranean regions. Conclusions are presented in section 8.
2. The observations
In this study an academic and a real test case are presented. For the real test case, several observations are used: (i) the surface concentrations of particulate matter (PM10) as measured by the Sahelian Dust Transect (SDT); and (ii) the AERONET photometers’ measurements for the AOD, the angstrom exponent (Ae), and the aerosol size distribution (ASD). Finally, the statistical scores used to quantify the results are presented in this section.
a. Surface concentrations of PM10
For the surface concentrations of PM10 we use the SDT measurements. These measurements are performed in Banizoumbou (Niger), Cinzana (Mali), and M’Bour and Bambey (Senegal) as described in Marticorena et al. (2010). The concentrations are measured using a tapered element oscillating microbalance with a PM10 inlet. These microbalances are at the same place as the photometers of the AERONET.
b. Aerosol optical depth
The stations are selected to be representative of different locations and different proximities to mineral dust sources. Banizoumbou and Cinzana are located in the center of western Africa and also correspond to stations of the SDT. They are considered as locations close to the sources. Dakar, Senegal, is located close to the coast on the western side of West Africa and Izana (Tenerife Island) is located on the Canary Islands. Dakar and Izana are more representative of stations “under mineral dust plumes” after long-range transport.
The aerosol optical properties are compared between observations and model using the AERONET measurements (Holben et al. 2001). First, the comparison is done using the AOD and a wavelength of λ = 550 nm. Second, the comparison is performed using the ASD estimated after inversion of the photometers’ data as described in Dubovik and King (2000). The level 2 data are used. For each AERONET station used in this study and listed in Table 1, the inversion algorithm provides a volume particle size distribution for 15 bins, logarithmically distributed for a radius between 0.05 and 15 µm.
Names and locations of the AERONET stations used for model comparisons to AOD and ASD data. The stations are ordered from south to north. The altitude MSL is not presented, the measurements being representative of the vertically integrated atmospheric column above ground level (AGL).
c. Statistical scores
3. The models
For the results calculations, several models are used. First, we describe the dust production model. Second, and for the real test case, we describe the Weather Research and Forecasting (WRF) Model, which calculates the meteorological fields; and the CHIMERE chemistry-transport model, which calculates the concentrations of mineral dust in the troposphere.
a. The dust production model
The surface and soil databases are described in Menut et al. (2013b). The soil characteristics are from the State Soil Geographic database of the FAO (STATSGO-FAO; Nachtergaele et al. 2009), a global dataset with a native resolution of 30′ × 30′. For the surface characteristics, the NCAR USGS database is used, with the same resolution as the soil database (Loveland et al. 2000). For each model grid cell, we thus have the relative percentage of all soil and surface characteristics. For each of these percentages, a sandblasting flux is calculated and then cumulated to have the total sandblasting flux in each model grid cell.
Complementary to the soil and surface characteristics, an erobility factor is also necessary to estimate the relative part of the grid cell that could emit mineral dust. A global database was derived using MODIS satellite data to estimate this factor, as described in Beegum et al. (2016). A map of erodibility is presented in Fig. 1.
The domain defined for the real test case. (top) Map of the erodibility (0:1). (bottom) Map of the orography variance (m2).
Citation: Journal of Atmospheric and Oceanic Technology 35, 6; 10.1175/JTECH-D-17-0173.1
This figure also shows the orography variance (m2) provided by the WRF Model database. This variance varies between 0 and 15 000 m2 on the domain. The most important variability is observed over mountainous areas, when the resolved topography corresponds to an average of very different altitudes above sea level.
b. The WRF and CHIMERE models
The WRF and CHIMERE models are used to calculate the concentration of aerosols in the troposphere. The system is an “offline” coupling model, meaning that the meteorological fields are first calculated with WRF and then these meteorological fields are used by CHIMERE for the transport.
WRF, version 3.6.1, is used (Skamarock et al. 2007). This regional modeling uses NCEP global meteorological fields using a spectral nudging to ensure that the large-scale circulation is well taken into account. The complete setup for this model is presented in Menut et al. (2016).
CHIMERE is used in its version described in Menut et al. (2013a) and includes the last updates presented in Mailler et al. (2017). For this study the gaseous and aerosol chemistry is not used. The only aerosol taken into account is mineral dust: emissions, transport, mixing, and wet and dry deposition. For all other parameters, we also used exactly the same configuration as in Menut et al. (2016). The modeled AOD is calculated by FastJX for several wavelengths (Wild et al. 2000). The boundary conditions for mineral dust are those of the climatology provided by GOCART (Ginoux et al. 2001) and described in Menut et al. (2013a).
To quantify the impact of our changes during a long period, the simulations range from 1 January to 1 May 2012. These four months correspond to the dry period in western Africa, when major mineral dust events occur. The modeled domain has a horizontal resolution of 60 km × 60 km, and represents a large domain encompassing the northern part of Africa and the Mediterranean Sea, as presented in Fig. 1. This domain is strictly the same for the WRF and CHIMERE models. The horizontal resolution was selected for different reasons: (i) this study is about subgrid-scale variability: with this resolution of tens of squared kilometers, the variability is nonnegligible; and (ii) for mineral dust studies, it is important to have a large modeled domain, encompassing all possible sources and long-range transport. With these simulations ranging over 4 months and a large domain, this resolution makes the computational cost manageable. Note that this resolution was used in previous studies, such as Menut et al. (2016), Briant et al. (2017), and Menut et al. (2017), and shows satisfactorily results compared to observations.
The main goal of this study is to change the wind speed. This wind speed is calculated by WRF and is then used by CHIMERE for several processes: the transport, the calculation of the friction velocity (for the dry deposition), and the mineral dust emissions. The use of the Weibull distribution is made only in CHIMERE and only for the mineral dust emissions. For all other processes, the mean wind speed remains unchanged and as it is provided by WRF.
4. The Weibull distribution
This section presents the main concept of the Weibull distribution, the parameters to define, and the way to estimate them.
a. The Weibull distribution formulation
b. Current estimate of k
The sensitivity to k is a well-known problem. Numerous studies were dedicated to its study and we present here only a few examples. Using measurements made at one site, Babiker et al. (1987) made a sensitivity study to quantify the impact of the mineral dust emissions fluxes to several k values ranging from 1 to 3. Also using measurements (30 years and 1432 different measurements sites in the United States), Gillette and Passi (1988) estimated k values between 0.5 and 3.86. Christofferson and Gillette (1987) proposed a methodology to estimate the k value from numerous wind speed observations. Pérez et al. (2007) used sodar data to retrieve wind speed values close to the surface: in this case, several k values are tested and compared to the observations, in a range from 1 to 4. Kelly et al. (2014) studied the potential variability of k and presented results with values ranging between 1.5 and 3. Gryning et al. (2016) presented a similar technique, but used mast and lidar measurements and concluded that k varies between 1.8 and 3.1 (depending on the altitude and the sites’ localization). He et al. (2010) used wind data from 720 stations (from 1979 to 1999) and showed that the k parameter could depend on the atmospheric stability: the Weibull distribution is narrower during the night, because of intermittent turbulence. Statistically, they showed that the k value could depend on the wind speed value with a larger distribution for weak winds (high wind variability) and narrower for strong winds (well-established wind speed regimes). The first studies showed that a constant value of k is not realistic and that this parameter has to be variable in space and time.
More specifically for the mineral dust emissions problem, some other studies were already dedicated to the best possible estimate of k. Menut (2008) used a constant value of k, limiting the variability. It was done to ensure a certain stability of the calculation in case of operational forecast calculations (i.e., no day-to-day tuning of the model). This approach has to be replaced in models in order to be more realistic. Ridley et al. (2013) made two simulations for the same domain and the same period: the first one, with a high resolution to explicitly calculate the wind speed variability; and the second one, with a coarse resolution, to test the deduced k parameters used with a Weibull distribution. The approach is realistic but valid mainly for one studied case. A change in the period of the domain requires replaying the two simulations, fine and coarse.
This expression does not take into account subgrid-scale variability, such as the orography. It considers that the Weibull shape mainly depends on the wind speed magnitude. This latter relation is used in many studies, such as Su and Toon (2009) with CAM3.0 applied over China; Zhang et al. (2016) with CAM5.0 and at the global scale (2° resolution); and Tegen et al. (2006) for the comparison to observed wind values in Bodele, north central Africa Note that in these studies, they are using a dust production model for which the size distribution is not dependent on the wind speed (unlike the model used in this study).
An example of wind speed distribution using k constant values (k = 3 and 4) and the expression of J78 is presented in Fig. 2. The distributions are calculated for 
For
For
Example of Weibull wind speed distribution for a mean value of 
Citation: Journal of Atmospheric and Oceanic Technology 35, 6; 10.1175/JTECH-D-17-0173.1
Having a k value evolving with the mean wind speed value, it is interesting to notice that for 
5. Adding the orography variability in k
The 
First, we have to ensure that k will evolve around its mean value and within an acceptable range. We thus define two constants,
We consider that over flat terrain, the wind speed module would have a lower variability that over complex terrain with a changing orography. The value of
The change is designed to act only over erodible surfaces, since this is applied only for mineral dust emissions. It is thus necessary to find the maximum of orography variance until the mineral dust emissions occur. The orography variance may be very large over mountainous areas, but these areas are nonerodible (being mainly constituted of rocks) and are thus not taken into account.
We also want to have a nonlinear dependency between k and the orography variance in order to have a smooth change between the minimum and maximum orography variance values.
The 
Citation: Journal of Atmospheric and Oceanic Technology 35, 6; 10.1175/JTECH-D-17-0173.1
6. Academic test case modeling
To understand the variability of k as a function of the mean wind speed and various values of orography variances, a simple academic test case is performed. For this test case the DPM of Alfaro and Gomes (2001) is used alone, in a 0D context (meaning that there is no time or space, only a calculation using a varying academic wind speed value). To quantify the maximum of the impact of the 
(top) Values of the k parameter values for the J78 parameterization and include the orographic weight factor proposed in this study. The two curves represent the extrema of the change, with 
Citation: Journal of Atmospheric and Oceanic Technology 35, 6; 10.1175/JTECH-D-17-0173.1
Results are first presented in Fig. 4 (top) for the evolution of k depending on 
For the same three expressions of k, the results are presented as a Weibull distribution in Fig. 4 (middle). The distribution with the J78 scheme without any change is in between the two other distribution when 
Finally, the impact on emissions fluxes are presented in Fig. 4 (bottom). The aerosol size distribution of the emissions flux is presented for 
Value of the vertical mineral dust flux calculated with the Alfaro and Gomes (2001) scheme and for 
Emissions are diagnosed for three main modes as defined previously. Here, they are expressed in radii, to be later compared with AERONET measurements. The highest impact on the fluxes appear for the fine mode of the distribution, rp = 0.75 µm. This mode corresponds to the optically efficient part of the size distribution. The change in k has thus an impact on the vertical flux but also on the deduced AOD. As presented in Table 2, with no variability, AOD = 0.92. If the orography variability is taken into account, then AOD = 0.54 and 1.10 for an orography variance of 1% and 100%, respectively. This huge impact, both on emissions fluxes and on AOD, shows the high sensitivity of the determination of the k parameter for mineral dust model studies.
7. Real test case
The two simulations, without and with the orography impact on the k parameter value, are called “J78” and “J78 + Var_oro,” respectively. The simulations contain only mineral dust as aerosol, and the results are compared to measurements performed in locations where mineral dust dominates the aerosol composition: the AERONET stations located in western Africa and the surface PM10 measurements of the Sahelian Transect.
a. Determination of the k parameter over the domain
The first step for the real test case is to calculate the parameters involved in Eq. (14). Among all parameters it is necessary to select a correct value for 
Distribution (%) of the orography variance, SSO variance (m2), over the whole modeled domain and for the erodible cells only.
Citation: Journal of Atmospheric and Oceanic Technology 35, 6; 10.1175/JTECH-D-17-0173.1
The results of the k parameter calculation using these criteria is presented in Fig. 6. Values are estimated for cells with an erodibility of 10% at least. For the other cells, the k parameter is defined in the model as described by J78, but it is not used for mineral dust calculation, because the cells are being considered as nonerodible. For a wind speed of 10 m s−1, the J78 scheme gives as result k = 2.97 (as presented in Table 2). Using the orography variance, the k values vary between 2.2 and 3.8. The lowest values are obtained where the orography is high: for example, to the north of the Bodele region and in the Hoggar. The highest values are defined where the orography is low, and these areas represents the majority of the erodible cells for the studied domain.
The k parameter values using the orographic weight factor proposed in this study, and for 
Citation: Journal of Atmospheric and Oceanic Technology 35, 6; 10.1175/JTECH-D-17-0173.1
Globally, we probably will have mineral dust emissions, which is less important than using only the J78 parameterization. But, we expect to have a different spatial variability of the emissions, since the change in the k parameter depends on varying orography over the whole domain.
b. Results for surface concentrations of PM10
The PM10 surface concentrations are compared between the model and the observations and with an hourly time step. The results are first presented as time series in Fig. 7 and for the sites of Banizoumbou, Cinzana, and Dakar. The observations, represented as symbols, show a large time variability and the values range from 0 to 2000 µg m−3.
Hourly PM10 surface concentrations time series from 1 Jan to 30 Apr 2012, for the model (with the two simulations without and with the orography variance) and the SDT sites Banizoumbou, Cinzana, and Dakar.
Citation: Journal of Atmospheric and Oceanic Technology 35, 6; 10.1175/JTECH-D-17-0173.1
The results mainly show the high temporal variability of the measurements and the fact that the model is able to reproduce this variability. The J78 + Var_oro configuration provides a PM10 lower than the J78 configuration. This means that over the erodible regions leading to mineral dust measured at these sites, we have an orography variance less important than the mean average value and thus an increased k parameter, leading to a broader Weibull distribution and thus less mineral dust emissions.
The results are quantified as statistical scores in Table 3. The first part of this table corresponds to the model results for J78 and the second part to J78 + Var_oro. For the correlation and the RMSE, the best statistical scores are bolded. For the correlation and the RMSE, the results are better for J78 + Var_oro than for J78 (except for the correlation in Banizoumbou, but the difference is low and only 0.01). The most important benefit with the J78 + Var_oro configuration is for the RMSE. This is mainly because k is increased, leading to a sharper Weibull distribution and thus less variability in the mineral dust emissions. The model error is reduced by at least 
Scores for the comparisons between observations (Sahelian Transect) and model (CHIMERE) for the surface concentrations of PM10. Results are presented with N (%) as the hourly mean available measurements for the period 1 Jan–1 May 2012, the mean values over the period [observations (Obs) and modeled (Mod) values], Rt, and the bias (model minus observations). Stations are sorted in increasing latitude, from south to north. Values are bolded for the simulation having the highest correlation or the lowest RMSE.
c. Aerosol optical depth time series
Results for the AOD comparisons with the AERONET data and the CHIMERE model outputs are displayed in Fig. 8 as time series, from 1 January to 30 April 2012.
AOD (λ = 675 nm) time series from 1 Jan to 30 Apr 2012, for the model and the AERONET sites. Observations are represented by symbols, and the two plain curves represent the model simulation without and with orographic variability of the k parameter.
Citation: Journal of Atmospheric and Oceanic Technology 35, 6; 10.1175/JTECH-D-17-0173.1
The time series show that several high peaks of mineral dust occurred during the four studied months. For all these peaks, the model is able to retrieve correctly their timing (the correct day and the duration) and their magnitude. A few peaks are missing (as in January in Banizoumbou or mid-April in Izana), but they are very peaked and probably correspond to local events, which is difficult to catch with the used model resolution, such as convective cold pools or sporadic wind speed extremes. In general, the model is able to estimate the background values and the major dust events. As for the PM10 time series, the J78 + Var_oro configuration simulates less AOD than the J78 configuration.
To quantify these results of AOD, statistical values are presented in Table 4. The simulation with the orography variance improves the model results compared to the observations—the RMSE is better for all stations—showing that the model error is globally reduced. For the correlation, the differences between the two simulations are less important, even if the best results are also mainly for the J78 + Var_oro version. The bias decreases with J78 + Var_oro, highlighting the results showed with the time series: for these stations, the AOD is generally lower than for the J78 version.
Scores for the comparisons between observations (AERONET) and model (CHIMERE) for the AOD. Results are presented with N (%) as the hourly mean available measurements for the period 1 Jan–1 May 2012, the mean values over the period [observations (Obs) and modeled (Mod) values], Rt, RMSE, and the bias (model minus observations). Values are bolded for the simulation having the highest correlation or the lowest RMSE.
d. Aerosol optical depth maps
As a complement to the time series and the statistical scores, maps of AOD values are presented in Fig. 9. The modeled period lasted 4 months and the maps represent 4 days during the period: 1200 UTC 15 January, 1200 UTC 15 February, 1200 UTC 15 March, and 1200 UTC 15 April 2012. Note that other maps were analyzed, and the discussion and conclusions are similar. The left column represents the AOD absolute values calculated with the J78 + Var_oro simulation and the right column corresponds to the difference of AOD calculated with AOD(J78 + Var_oro) − AOD(J78). The AOD highest values are located in different places according to the day. But for the 4 days, J78 + Var_oro corresponds always to a decrease in AOD, with the largest differences being collocated with the highest AOD values. It shows that the use of the orography variance leads to an increase in k and thus a decrease of emissions, thus AOD. It means that the change is mainly applied over erodible areas where the orography variance is low.
AOD (λ = 600 nm) maps for 1200 UTC on 15 Jan, 15 Feb, 15 Mar, and 15 Apr 2012. (left) Absolute values of AOD for the J78 + Var_oro simulation and (right) AOD differences for J78 + Var_oro − J78.
Citation: Journal of Atmospheric and Oceanic Technology 35, 6; 10.1175/JTECH-D-17-0173.1
For example, for 15 April 2012, two main plumes are visible: the first one in the center of Africa (over Niger and Chad), and the second one in Guinea and Senegal and transported toward the Atlantic sea. In these plumes the AOD values reach 2 at the maximum when the “background values” over Africa are between 0 and 1. For the AOD background values, the differences reach 0.2. In the plumes, where the AOD are maximum, the differences reach 0.8, corresponding to an important change in the AOD estimation.
e. Aerosol size distribution
As presented in Fig. 4, a change in the k parameter acts on the mineral dust emissions flux magnitude but also on its size distribution. To quantify the impact of the k changes on the size distribution, we compare here the model results to the AERONET inversion. In the AERONET database, note that all AOD measurements are not inverted and we had to find available data. Two comparisons are presented but many other size distributions were analyzed and the conclusions are similar. The results presented correspond to available data close to the results showed in Fig. 9, and correspond to 15 March and 15 April 2012. Comparisons are presented in Fig. 10. Note that, here, the distributions are expressed in radii (to be consistent with the raw data provided by AERONET).
ASD compared between the AERONET inversions and the CHIMERE modeled concentrations.
Citation: Journal of Atmospheric and Oceanic Technology 35, 6; 10.1175/JTECH-D-17-0173.1
For the 4 days and the four sites, the most important mode corresponds to the “coarse” mode with rp 
8. Conclusions
This study examined the impact of the wind speed Weibull distribution on the calculation of mineral dust emissions. This distribution depends mainly on one parameter, k, parameterized as a function of the mean wind speed. In this study we consider that for regional models, having a grid cell of tens of kilometers, the subgrid-scale orography may also be an important parameter to take into account in the estimation of k, since the orography has a direct impact on the value of the mean wind speed close to the surface.
Using the information of subgrid orography variance, we proposed an adjustment of the estimation of the k parameter. We first test this change with academic cases in order to estimate realistic boundaries to the potential evolution of the k value. Second, we applied this change in the framework of a realistic modeling: 4 months—from 1 January to 1 May 2012—and over a large domain, encompassing western Africa and Europe. The modeled results were compared to surface PM10 concentrations and AERONET aerosol optical depth and aerosol size distribution. Correlation, root-mean-square error, and bias were also calculated. We showed that for a large part of the comparisons between observation and model results, the correlation is slightly improved (
Even if the RMSE is better, the correlation is not really improved. It showed that the subgrid-scale variability of orography is not the main driver for the mineral dust emissions. This is surprising because a significant impact was expected: the DPM schemes are very sensitive to the mean wind speed and the mean wind speed is sensitive to the orography close to the surface. The fact to have quantified this impact remains useful even if the impact intensity is lower than expected. For processes such as mineral dust emissions, the subgrid-scale variability remains a way to link a local phenomenon and an averaged model grid cell. It is a better approach than the model tuning, sometimes efficient, but not able to explain the physics and often limited to a specific model, with its own parameterizations and resolution. The model tuning is also systematic where the change proposed in this study varies in each model grid cell, adding realism to the system. A potential future direction could be the convective cold pools, which are known to increase mineral dust emissions very locally and are certainly missing in many regional models.
Acknowledgments
For the Sahelian Dust Transect data, we thank Bernadette Chatenet, the technical PI of the Sahelian stations from 2006 to 2012; Béatrice Marticorena and Jean-Louis Rajot, the scientific co-PIs; and the African technicians who manage the stations. We thank the principal investigators and their staff for establishing and maintaining the AERONET sites used in this study.
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