1. Introduction
In a thunderstorm, the melting, evaporation, and sublimation of hydrometeors generate downdrafts that form a spreading cold pool at low levels (Byers 1949). The cold pool is denser than its environment and therefore spreads as a density current (e.g., Simpson 1999). The cold pool plays a dual role in the life cycle of the thunderstorm: it increases the low-level atmospheric stability and locally inhibits convection but additionally lifts the surrounding, warmer air and triggers new convective cells (Byers 1949).
The cold pool outflow creates a front of wind gusts at its leading edge. Over arid ground, the wind gusts can be strong enough to lift mineral dust. This process was first documented in peer-reviewed literature for Karthoum and described as “haboob” (Sutton 1925). Since then, haboobs have been reported over all major sources of mineral dust worldwide [see Knippertz (2014), and references therein]. Dust uplift is found in cold pool outflows of different space and time scales: mesoscale convective systems (Houze 2004) can produce long-lived haboobs (Roberts and Knippertz 2014); small, strong downdrafts (microbursts; Fujita 1985) can produce short-lived haboobs (Miller et al. 2008); even small cold pools from precipitating congestus can produce dust uplift (Marsham et al. 2009). As all processes are related to convection, they are referred to as convective dust storms.
Convective dust storms of different origins have been observed over the Sahara during recent field campaigns: created by orographic convection over the northwestern Sahara [during the Saharan Mineral Dust Experiment (SAMUM; Knippertz et al. 2007)]; embedded within the monsoon flow over the southern Sahara [during the African Monsoon Multidisciplinary Analysis (AMMA; Flamant et al. 2007; Bou Karam et al. 2008)] and over the western Sahara [during the Geostationary Earth Radiation Budget Intercomparison of Longwave and Shortwave Radiation (GERBILS; Marsham et al. 2008b)]; and over the central Sahara, from locally generated moist convection, as well as mesoscale convective systems that propagate from the Sahel [from Fennec supersite observations (Marsham et al. 2013b; Allen et al. 2013)]. Observational (Marsham et al. 2008b, 2013b) and modeling studies (Heinold et al. 2013) suggest that convective dust storms contribute a large fraction of dust emission over the Sahara in summer. The Sahara is the main source of mineral dust worldwide, and convective dust storms may contribute to the local and remote impacts of Saharan dust on health, oceanic biochemistry, and atmospheric dynamics [see Knippertz and Todd (2012) for a review of mineral dust over the Sahara].
Investigating the systematic impact of convective dust storms is challenging: the ground observation network is sparse over the Sahara, and convective clouds often hide dust in satellite observations (Heinold et al. 2013; Kocha et al. 2013). Furthermore, most operational models lack convective dust storms (Marsham et al. 2011; Garcia-Carreras et al. 2013), since they do not explicitly resolve convection and rely on parameterization schemes. Parameterization schemes lack microbursts, because they do not account for subgrid-scale winds. Parameterization schemes also lack mesoscale convective systems, because they do not account for grid-scale organization of convection (e.g., Knippertz and Todd 2012). A parameterization of convective dust storms is needed to account for their contribution to dust uplift in large-scale models.
Several authors have parameterized wind gusts according to convective downdrafts: Nakamura et al. (1996) assumed conservation of horizontal momentum in downdrafts to compute peak wind gusts in numerical weather prediction models; Redelsperger et al. (2000) defined subgrid gustiness as a function of the downdraft mass flux to enhance surface fluxes in global circulation models; Cakmur et al. (2004) scaled a probability distribution of subgrid wind with the downdraft mass flux to compute dust uplift in global circulation models. Building on these previous studies, we suggest a parameterization of subgrid winds for dust uplift based on the downdraft mass flux of a convective parameterization scheme. Our parameterization aims at remaining simple in order to be applied online or offline to any model with a mass-flux convection scheme. It contrasts with the integrated approach of Hourdin et al. (2014), which improves the representation of wind and dust emissions in a global model—although it does not address the issue of convective dust storms—but requires a complete modification of subgrid parameterization schemes. Our parameterization also complements statistical downscaling methods, which improve dust emissions in global models but still lack the contribution from convective dust storms, such as the one by Ridley et al. (2013).
Section 2 describes the configuration of the model runs used to formulate the parameterization, compares their representation of cold pools and dust-generating winds, and details the reference used to calibrate the parameterization. Section 3 explains and illustrates the conceptual model of the parameterization and its tuning. Section 4 gives the results of the parameterization for both the geographical distribution and diurnal cycle. Finally, section 5 concludes the paper and discusses perspectives for future work.
2. Model runs
a. Configuration
The parameterization of convective dust storms is based on a set of model runs with the Met Office Unified Model. The Unified Model uses a seamless approach, from weather forecast to climate projection and from limited area to global domain (Walters et al. 2011). In the framework of the Cascade project, the model was run in a limited area configuration over West Africa at different spatial resolutions, with and without parameterizations of moist convection and for different time periods during the summer 2006. The Cascade project allowed an investigation of the representation of tropical convection (Pearson et al. 2010, 2014; Birch et al. 2014a), its impact on the monsoon (Marsham et al. 2013a; Birch et al. 2014b), and its impact on dust emission (Marsham et al. 2011; Heinold et al. 2013).
The present study is mainly based on two runs with 4- and 12-km grid spacings for the 60-day period from 1 June to 30 July 2006. Diagnostics for convective mass fluxes, which are essential for the formulation of the parameterization of convective dust storms, were saved during this time period only. Additional runs for the 10-day period from 25 July to 3 August 2006 are also discussed, because the model was run at higher resolution with 1.5-km grid spacing for this time period, in addition to the 4- and 12-km grid spacings. As convective mass fluxes were not saved for this 10-day period, the additional runs cannot be used for the parameterization of convective dust storms. The relevant characteristics of the different runs are summarized in Table 1.
Relevant characteristics of the model runs discussed in the text.
The model was run over limited area domains on a rotated cylindrical grid. Figure 1 illustrates the orography, soil fraction, and surface roughness over the 12-km domain. Figure 1a further displays the 4- and 1.5-km domains. Operational analyses from the European Centre for Medium-Range Weather Forecasts (ECMWF) provided the initial conditions and lateral boundaries for the 12-km runs (Table 1). The 12-km runs provided the lateral boundaries conditions for the nested 4-km runs. The 4-km run for the 10-day period, in turn, provided the lateral boundaries for the nested 1.5-km run. Terrain-following hybrid coordinates were used in the vertical, with 70 levels starting at 2.5 m in the 4- and 1.5-km runs and with 38 levels starting at 10 m in the 12-km run (Table 1). The model configuration is detailed in Pearson et al. (2010).
(a) Orography, (b) soil fraction, and (c) surface roughness in the 12-km run. The thick and thin boxes in (a) show the nested 4- and 1.5-km domains, respectively.
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
The 1.5- and 4-km runs fundamentally differ in their representation of convection, as compared to the 12-km run: the convection is permitted to develop explicitly with 1.5- and 4-km grid spacings, while it is parameterized with 12-km grid spacing (Table 1). In the Unified Model, the parameterization of moist convection is based on a convective available potential energy (CAPE) closure (Gregory and Rowntree 1990). Following a parcel theory modified by entrainment and detrainment, an ensemble of subgrid convective clouds is described by updraft and downdraft mass fluxes. Updrafts are initiated if a layer is positively buoyant; ascent occurs until the parcel becomes negatively buoyant. In turn, downdrafts are initiated as a fraction of updrafts if a layer is negatively buoyant; descent occurs until the parcel becomes positively buoyant or too close to the surface.
b. Representation of cold pools
Figure 2 compares the representation of cold pools in the 1.5-, 4-, and 12-km runs on 31 July 2006 (10-day period; Table 1). The respective peak of the diurnal cycle of precipitation is illustrated; it occurs at 1200 UTC in the 12-km run (Fig. 2g), instead of at 1700 UTC in the 1.5- and 4-km runs (Figs. 2a,d). The parameterization scheme triggers convection too early in the 12-km run (Marsham et al. 2013a; Birch et al. 2014b; Pearson et al. 2014), which is a common and well-documented issue in tropical regions (Yang and Slingo 2001; Dai 2006; Nikulin et al. 2012; Bechtold et al. 2014). Note that the three runs are not expected to look the same at any particular time because they are only constrained at the lateral boundaries. The panels in Fig. 2 are used for illustration purposes only.
Example of convection on 31 Jul 2006 in the (a)–(c) 1.5-, (d)–(f) 4-, and (g)–(i) 12-km runs: (a),(d),(g) instantaneous precipitation rate (mm h−1); (b),(e),(h) 950-hPa temperature (K); and (c),(f),(i) 10-m wind speed (m s−1).
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
In both the 1.5- and 4-km runs, convective cells produce strong precipitation above 10 mm h−1 (Figs. 2a,d). The evaporation, melting, and sublimation of hydrometeors create cold pools at low levels with temperature contrast above 5 K (Figs. 2b,e). The outflow of cold pools produces strong surface winds above 10 m s−1 (Figs. 2c,f). Convective cells produce small, circular cold pools, which grow and merge into larger, more complex structures. In contrast, the convection scheme produces weak precipitation below 10 mm h−1 in the 12-km run (Fig. 2g). The evaporation of precipitation is too weak and too widespread to produce distinct cold pools (Fig. 2h). The 12-km run therefore lacks high winds resulting from convective cold pool outflows (Fig. 2i).
This qualitative comparison suggests that the 4- and 1.5-km runs offer a similar representation of convection and strongly contrast with the 12-km run. Earlier studies showed that convection in the 1.5- and 4-km runs occurs with a good timing compared to satellite observations, while convection occurs too early in the 12-km run (Marsham et al. 2013a; Birch et al. 2014b; Pearson et al. 2014). Furthermore, the development and growth of convective organization is weakly sensitive to the resolution between the 1.5- and 4-km runs (Pearson et al. 2014). Weisman et al. (1997) also found that the structure and evolution of mesoscale convective systems varied little between runs with 4- and 1-km grid spacing, although convection was slightly delayed with the coarser grid spacing. In contrast with the 1.5- and 4-km runs, the 12-km run lacks organized convection (Birch et al. 2014a; Pearson et al. 2014) and cold pools (Marsham et al. 2011, 2013a; Heinold et al. 2013).
A quantitative comparison is given by the frequency of surface wind speed over the Sahara in the runs during the 10-day period (Fig. 3). While the 12-km-run distribution drops near 12 m s−1, the 4-km run matches the 1.5-km run and captures the tail of distribution up to 20 m s−1. Convective dust storms contribute most of the tail of distribution (not shown). This further supports that the representation of cold pool outflows is similar in the 4- and 1.5-km runs. Johnson et al. (2014) also show that the timing and structure of a convective outflow are successfully represented with a 4-km grid spacing. The 4-km run is then the only available run that explicitly represents convection and captures the cold pool outflows during the 60-day period, for which the convective mass-flux diagnostics were saved (Table 1). As observations are sparse over the Sahara, the 4-km run is used as a reference for the parameterization of convective dust storms. It provides robust statistics with a large number (many hundreds) of convective dust storms that develop during the 60-day period.
Probability density function of the 10-m wind speed in the 1.5- (black curve), 4- (blue curve), and 12-km runs (red curve). The wind speed is taken from 25 Jul to 3 Aug 2006 over the area indicated by the boxes in Fig. 4.
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
c. Dust uplift potential
The geographical distribution of DUP exhibits similar patterns in the 4- and 12-km runs (Fig. 4). Highest DUP is found over the Saharan heat-low region from eastern Mauritania to northern Mali (18°–22°N, 12°–2°W) and over the Bodélé Depression in northern Chad (16°–20°N, 15°–20°E). High DUP is found over southwestern Algeria (24°–27°N, 5°W–0°), where it is related to the flow around the Hoggar Mountains (Birch et al. 2012) and over northeastern Niger (20°–24°N, 10°–18°E). High DUP is also found along the coast of Mauritania and Western Sahara, where the Atlantic inflow produces strong winds during the afternoon and evening (Grams et al. 2010).
Dust uplift potential from the model wind (shading; m3 s−3) and 925-hPa geopotential height (contours below 790 m; interval of 5 gpm) averaged from 1 Jun to 30 Jul 2006 in the (a) 4- and (b) 12-km runs. The geopotential height is omitted where it lies below the model orography. The displayed area is the northern part of the 4-km domain (Fig. 1). The dust uplift potential is defined in section 2c. The boxes show the area used to compute the probability density function in Fig. 3 and the diurnal cycles in Figs. 5 and 6.
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
Apart from the Atlantic coast, the areas of high DUP coincide with the areas of highest fraction of bare soil (Fig. 1b). However, the pattern of bare soil does not directly impact the pattern of DUP: omitting ν in Eq. (1) produces a similar pattern of DUP (not shown). Instead, the low roughness length over bare soil (Fig. 1c) allows for strong winds that result in high DUP (Fig. 4). The sharp border in DUP along the Sahel (near 16°N in Fig. 4) matches the strong gradient in roughness length (Fig. 1c). The roughness length increases over mountain ranges, because it accounts for subgrid orography (Fig. 1a). High roughness length prevents strong winds and DUP over the Tibesti (19°–24°N, 16°–20°E) and Hoggar (22°–27°N, 3°–13°E) mountain ranges (Fig. 4).
Figure 5 displays the diurnal cycle of DUP over the Sahara. A strong peak occurs in the morning and is attributed to the breakdown of the nocturnal low-level jet (Knippertz 2008; Fiedler et al. 2013). The 12-km run underestimates the amplitude of the peak compared to the 4-km run (Fig. 5). In contrast, the 12-km run overestimated the amplitude of the peak during the 10-day period, because of a deeper Saharan heat low and, thus, a stronger pressure gradient compared to the 4-km run (Marsham et al. 2013a; Heinold et al. 2013). Here, the 12-km run exhibits a shallower Saharan heat low than the 4-km run (contours in Fig. 4). This demonstrates how sensitive the monsoon circulation is to the time period and representation of convection in a given model (Marsham et al. 2013a). The weaker pressure gradient in the 12-km run results in weaker nocturnal low-level jets and therefore weaker DUP in the morning compared to the 4-km run (Fig. 5). Heinold et al. (2013) showed that low-level jets can form in aged cold pools such that some of the differences between the two runs may indirectly be related to the lack of organized convection in the 12-km run.
Diurnal cycle of dust uplift potential from the model wind in the 4- (blue curve) and 12-km runs (red curve). The dust uplift potential is averaged from 1 Jun to 30 Jul 2006 over the area displayed in Fig. 4.
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
A second, weaker peak in DUP occurs in the afternoon, in both 4- and 12-km runs (Fig. 5). This peak is attributed to dry convection in the boundary layer, which reaches its peak in the afternoon and which was observed to enhance dust uplift (Chaboureau et al. 2007; Marsham et al. 2008a). DUP then remains high in the evening in the 4-km run, while it drops in the 12-km run. The weaker DUP in the 12-km run was attributed to the lack of convective dust storms in the evening during the 10-day period (Marsham et al. 2011; Heinold et al. 2013). The contribution of convective dust storms to DUP in the 4-km run is discussed below.
d. Identification of convective dust storms
Convective dust storms need to be identified in the 4-km run, which is used as a reference to calibrate the parameterization. Following Heinold et al. (2013), surface winds are attributed to convective dust storms if they occur within 40 km of a grid point of rapid cooling and strong vertical velocities. These conditions are met at the leading edge of cold pool outflows (see example of cold pool outflow in section 3a). Additional conditions in potential temperature and wind divergence suggested by Heinold et al. (2013) were found redundant here with the conditions in cooling and vertical velocity, respectively.
A visual inspection of several cold pool outflows in the 4-km run delivered thresholds 
The thresholds are close to those defined by Heinold et al. (2013). Figure 6 shows the diurnal cycle of identified convective dust storms using a range of 
Diurnal cycle of dust uplift potential attributed to convective dust storms in the 4-km run: sensitivity to thresholds in (a) 
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
Heinold et al. (2013) found low sensitivity to the exact thresholds used. Here, multiplying 
3. Conceptual model
To address the problem of lacking cold pool dust emission in models with parameterized convection, we now present the conceptual model on the basis of which our parameterization of convective dust storms is built. Section 3a presents the general formulation, while section 3b shows an illustrative example, which is used to tune the parameterization in section 3c.
a. Formulation
Schematic of the conceptual model, with 
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
Example of a cold pool outflow at 1500 UTC 1 Jul 2006 in the 4-km run: (a),(c) wind speed (shading; m s−1) and (b),(d) vertical velocity (shading; m s−1), in (a),(b) horizontal and (c),(d) vertical cross sections, showing the section-parallel wind (vectors above 3 m s−1 according to the scale) and potential temperature (contours every 1 K) in the cross sections. Horizontal scales are in kilometers, and vertical scales are in meters. The red lines in (a) and (b) show the trace of (c) and (d), respectively.
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
When a cold pool propagates as a density current, its radius increases and its propagation speed decreases.1 In contrast, convective parameterizations assume the quasi equilibrium of subgrid boundary layer processes (Bechtold et al. 2014). A parameterization of propagating subgrid cold pools therefore requires the complete coupling with the parameterization of subgrid convection (Grandpeix and Lafore 2010). Such a coupling is beyond the scope of our work. We rather base our parameterization on a single, static cold pool of representative size (with sensitivity to assumptions of size tested in section 3c). The conceptual model is therefore independent of the model time step if applied online or of the temporal sampling of model output if applied offline.
b. Illustration
Given the estimated parameters, the conceptual model yields 
Figure 9 illustrates the resulting wind field. The conceptual model captures the asymmetric structure of the cold pool outflow and its magnitude in the 4-km run (Figs. 8a,c). The exact intensity of surface winds can be obtained by tuning the parameters carefully. The strong wind speed along the downdraft at the center of the cold pool (Figs. 8c,d) is lacking in the conceptual model (Fig. 9b), but it does not affect the surface wind. New updrafts and downdrafts at the leading edge of the cold pool (Figs. 8b,d) are also lacking, as expected, in the conceptual model, but they play a minor role during the early development of the cold pool.
Parameterization applied to the example of Fig. 8: wind speed (shading; m s−1) and parallel wind (vectors above 3 m s−1 according to the scale) in (a) horizontal and (b) vertical cross sections. Horizontal scales are in kilometers, and the vertical scales are in meters. The red line in (a) shows the trace of (b).
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
The 4-km run exhibits variability in the structure of cold pool outflows (Fig. 2f). The conceptual model does not account for finescale processes that impact the development of cold pools [e.g., surface inhomogeneities; Lothon et al. (2011)]. However, the crescent shape of surface winds (Fig. 9) matches the typical structure of cold pool outflows in the 4-km run (Fig. 2f). This suggests that the simple assumptions of the conceptual model (Fig. 7) deliver a realistic, albeit idealized, representation of cold pool outflows.
c. Tuning
The downdraft mass flux computed from the vertical velocity of downdrafts [Eq. (11)] reaches 
Probability distribution functions of (a) 
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
Several parameters control the wind speed in the conceptual model: R [Eq. (2)], h [Eqs. (2) and (5)], zmax [Eqs. (3) and (5)], and 
The free parameter R is tuned for the average parameterized DUP to match the average reference DUP (the calibration area is discussed in section 4). The parameterized DUP is computed from the parameterized subgrid wind and averaged over the grid cells in the 12-km run, while the reference DUP is computed from the model wind attributed to convective dust storms in the 4-km run. Using a trial-and-error method, the best match of the parameterized DUP with the reference DUP is found for 
An additional, hidden parameter of the conceptual model is the height at which 
4. Space and time distribution of convective dust storms
DUP from convective dust storms is first discussed in the 4-km run. Identified convective dust storms produce DUP over the southern Sahara mainly (around 18°N, Fig. 11a), where the monsoon flow brings the necessary moisture to trigger convection. Highest DUP is found over the Saharan heat low from eastern Mauritania to northern Mali, as for the total DUP (Fig. 4a). In contrast, low DUP is found over the Bodélé Depression in northern Chad and over southwestern Algeria (Fig. 11a), consistent with known wind sources that are not related to cold pools in these regions (Washington and Todd 2005; Birch et al. 2012). Local concentrations of DUP are found over southern Algeria and northeastern Niger, in the vicinity of mountain ranges (Fig. 4a), consistent with orographic triggering of moist convection.
Dust uplift potential from convective dust storms (shading; m3 s−3) and precipitation (smoothed contour at 20 mm) averaged from 1 Jun to 30 Jul 2006 in the (a) 4- and (b) 12-km runs. Convective dust storms are (a) identified in the 4-km run and (b) parameterized in the 12-km run. The boxes show the area used to compute the diurnal cycle in Fig. 12.
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
The parameterization of convective dust storms in the 12-km run succeeds at producing high DUP over the southern Sahara (around 18°N, Fig. 11b). The parameterized DUP is shifted eastward compared to DUP from identified convective dust storms in the 4-km run (Fig. 11a). The eastward shift in the location of DUP is due to the eastward shift in the location of precipitation between the 12- and the 4-km runs (contours in Fig. 11). The location of precipitation is coupled with the pressure gradient of the Saharan heat low (contours in Fig. 4) through the dynamics of the monsoon (Marsham et al. 2013a; Birch et al. 2014b). The parameterized DUP further lacks local concentrations in the vicinity of mountain ranges compared to the 4-km run (Fig. 11) because of the relative lack of moist convection in the vicinity of mountain ranges in the 12-km run.
Although most DUP over the Sahel south of 16°N is attributed to convective dust storms in the 4-km run, it remains small compared to DUP over the Sahara (Figs. 4a and 11a). The parameterized DUP extends farther south across the Sahel (Fig. 11b). This appears more realistic than the sharp border in the 4-km run, as convective dust storms have been observed along a transect around 14°N at the beginning of the monsoon (Marticorena et al. 2010). The high roughness length over the Sahel (Fig. 1c) prevents strong winds in the model runs; it is possibly too high for the beginning of the monsoon, when the vegetation has not yet developed.
High DUP is also attributed to convective dust storms along the coast in the 4-km run (Fig. 11a). The Atlantic inflow is identified as a cold pool outflow, because its front propagates as a density current (Grams et al. 2010). However, the Atlantic inflow does not result from convection; it is therefore excluded from the calibration area (boxes in Fig. 11). The northern and eastern margins of the nested 4-km domain are also excluded from the calibration area to avoid contamination from the lateral boundaries. The calibration area also excludes the area south of 15°N, because the reference 4-km run may underestimate DUP over the Sahel.
As seen in Fig. 6, DUP from convective dust storms exhibits a strong diurnal cycle in the 4-km run (Fig. 12, blue curve). Convective dust storms contribute 27% of the total DUP from 1300 to 0600 UTC and 16% of the total daily DUP over the calibration area displayed in Fig. 11a. The parameterized DUP succeeds at exhibiting a strong diurnal cycle (Fig. 12, red curve). As expected, however, the peak of parameterized DUP occurs at 1200 UTC instead of 1800 UTC in the 4-km run because convection is triggered too early in the 12-km run (Marsham et al. 2013a; Birch et al. 2014b; Pearson et al. 2014). The parameterized DUP then decreases too quickly after the peak since the moist convection is too short lived in the 12-km run. As the parameterization is calibrated with the daily DUP, the amplitude of the peak is overestimated compared to the 4-km run (Fig. 12). Therefore, the main biases in timing and amplitude of DUP are due to biases in the convective parameterization scheme and not to the parameterization of convective dust storms.
Diurnal cycle of dust uplift potential from convective dust storms identified in the 4-km run (blue curve) and parameterized in the 12-km run (red curve). The dust uplift potential is averaged from 1 Jun to 30 Jul 2006 over the area indicated by the boxes in Fig. 11.
Citation: Journal of the Atmospheric Sciences 72, 6; 10.1175/JAS-D-14-0341.1
5. Conclusions
We suggest a parameterization of convective dust storms for models with mass-flux convection schemes. The parameterization is based on a set of Unified Model runs over West Africa for June and July 2006. It is applied to a convection-parameterized run with 12-km grid spacing, which lacks convective dust storms. A convection-permitting run with 4-km grid spacing captures the dynamics of convective dust storms and is used as a reference for validation and tuning.
Our conceptual model of convective dust storms follows simple assumptions (Fig. 7). The downdraft mass flux—a known value from the convective parameterization scheme—spreads out radially in a static, cylindrical cold pool. The resulting radial wind adds to the steering wind of the downdraft. Together, they follow a logarithmic profile below the “nose” of the cold pool and decrease linearly with height above. The conceptual model reproduces the structure and magnitude of wind speed for a developing cold pool in the reference run.
The parameterization produces a distribution of subgrid wind in each grid cell of the 12-km run. It is calibrated to match the integrated dust-generating winds [dust uplift potential (DUP)] from identified convective dust storms over the Sahara in the reference run. The geometry of the cold pools is constrained in the parameterization based on a developing cold pool in the reference run. The only free parameter is the radius of the cold pools, which is taken as constant for the whole domain and the whole period. The calibration delivers a radius of 2.0 km, consistent with the subgrid downdraft mass fluxes producing subgrid cold pools.
The parameterization of convective dust storms successfully produces high DUP over the southern Sahara. The parameterized DUP is more spread out than in the reference run: it lacks local concentrations over the central Sahara and extends farther east over the southern Sahara. Over the Sahel, the parameterized DUP extends farther south and appears more realistic than the reference run, which shows a sharp border at 16°N. The parameterization of convective dust storms also successfully produces a strong diurnal cycle of DUP. The parameterized DUP peaks 6 h earlier and reaches higher amplitude than in the reference run.
Compared to the reference run, differences in the geographical distribution of parameterized convective dust storms originate from differences in the monsoon flow between the model runs. Differences in the timing of convective dust storms also originate from differences in the timing of convection between the model runs. The dynamics of the West African monsoon (e.g., Marsham et al. 2013a) and the diurnal cycle of tropical convection (e.g., Bechtold et al. 2014) are known issues for modeling and are topics of active research. These issues are separate from the lack of convective dust storms addressed here, and solving them is beyond the scope of this paper.
The results suggest that the new parameterization allows a useful estimate of dust uplift due to convective dust storms. The distribution and timing of DUP are weakly sensitive to the parameters of the conceptual model if the radius of cold pools is carefully calibrated. The main uncertainty originates from the calibration, which is sensitive to the model resolution, the chosen domain and period, the identification of convective dust storms, and the estimate of dust uplift in the reference run. The uncertainty, however, remains small compared to large uncertainties in the estimation of dust uplift from models and observations (Huneeus et al. 2011).
As the parameterization produces a distribution of subgrid wind, it can be implemented in a full model for dust emission. If required, the parameterization can alternatively produce a distribution of subgrid friction velocity. A more accurate estimate of dust uplift can then be used instead of the simple DUP to tune the parameterization for the full model. The uplifted dust will then be transported beyond the grid cell, mixed, or deposited by the meteorology of the model. Through both wetting of the soil and scavenging, convective precipitation within a column may reduce the efficiency of convective dust storms in that column in a full dust model. To account for the spatial separation between the gust front and the precipitation in a realistic convective dust storm, the best approach may be to switch off the soil moisture effect and the scavenging during time steps when the parameterization is activated. A more detailed investigation of this effect is left for future applications in a fully online coupled system.
Further work is needed to test the sensitivity of the parameterization to different periods, grid spacings, and models. Current parameters of the conceptual model may vary: for example, the radius of cold pools, which is expected to increase with increasing grid spacing. Parameterized convective dust storms would have more realistic dimensions with grid spacings on the order of 100 km. Additional parameters may be included in the conceptual model: for example, the vertical wind shear, which is crucial for the organization of convection (Rotunno et al. 1988). If proven robust, the parameterization will substantially improve the representation of a key ingredient to dust emission and allow studies of the impact of convective dust storms in large-scale weather and climate models that use mass-flux convection schemes.
Acknowledgments
We thank Françoise Guichard and her colleagues at the CNRM in Toulouse for valuable discussions about the parameterization of convective dust storms and Adrian Lock at the Met Office in Exeter for helpful explanations about the boundary layer in the Unified Model. We also thank three anonymous reviewers for their useful comments on an earlier version of this manuscript. This work was funded by ERC Grant 257543 “Desert Storms.” The Cascade project was funded by NERC Grant NE/E003826.
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The theoretical propagation speed of a cold pool follows 
