The working hypothesis for this study was that the vertical flux of PM10 (Fa), measured in g m−2 s−1, is proportional to the total horizontal flux of sand-sized particles (q); that is,
where K is a dimensional constant having units of m−1 and q (g m−1 s−1) is the horizontal flux of sand-sized particles in a 1-m-thick layer above the ground, as defined in equation (2):
Here, C(z) is the concentration of sand-sized grains at height z, and VH is the horizontal velocity of the sand grains. Experimental evidence for a relationship between Fa and q is discussed in section 2.1.
 As shown conceptually in Figure 1, wind erosion involves particles that creep along the ground and sand-sized particles or agglomerates that bounce or saltate across the surface. These creeping and saltating particles loosen other particles and sandblast the surface, causing finer particles, including PM10, to be ejected and to mix vertically in the turbulent air stream. The amount of PM10 emitted is generally proportional to the horizontal saltation flux. Using this working hypothesis, Fa could be estimated from sand flux measurements taken with instruments placed in the saltation zone. This zone typically ranges from the ground to about 1 m above the surface. As discussed in section 3, the ratio Fa/q can be inferred by comparing monitored PM10 concentrations with the predicted concentrations from an air quality model. It was assumed that the relationship between Fa and q would remain fairly stable in all but a few exceptional circumstances that may be unique to Owens Lake and that these exceptional circumstances would not account for more than a small fraction of the total PM10. The hypothesis that Fa could be estimated from q made possible a program of efficient sampling based on sand flux measurements that could reveal the location of sources of PM10 and also characterize their dust production rates and the time and duration of their activity.
 Sand flux is often modeled instead of measured. For example, Gillette et al.  and Owen  showed that sand flux is generally proportional to u* (u*2 − u*t2), where u*t is the minimum aerodynamic threshold friction velocity. Previous measurements at Owens Lake showed that despite the uniform appearance of the lake bed, u*t was highly variable in time and space and would have to be closely monitored if it was used to model q. Because of this variability, we opted not to model q but rather to use a more direct measurement approach. For about the same effort to monitor u*t we surmised that one could directly measure q (or a surrogate in this case) and obtain a more accurate sand flux rate.
 Although much of the lake bed produces dust, some areas of the 285 km2 lake bed are consistently covered by a durable crust or are wet and are normally nonemissive. The potentially emissive areas for this study cover about 135 km2. Figure 2 shows a map of the study area. The portion of the lake bed not covered by the sampling grid generally indicates areas that are normally nonemissive areas. Some source areas inside the grid have been observed to be active all year and may be highly emissive, while others were seasonal and sometimes sporadic. The focus of this study was to better characterize the time, place, and strength of erosion activity for areas within the sampling grid. This information would be used with the Calpuff model [Scire et al., 2000a] to determine in which areas dust controls should be placed. As shown in Figure 2, 135 sand flux sites, spaced 1 km apart, were installed to monitor hourly sand flux rates within the potential erosion area.
 The sampling grid was separated into four source areas, as shown in Figure 2, for the purpose of determining large-scale ratios for Fa/q for each area. These areas were selected because of differing geomorphology or source activity that seemed to be somewhat independent of each other. The Keeler Dunes, for example, are sand dunes that differ in geomorphology from the surrounding area and were a frequent source of dust. The “north area” and the “south area” were seen to be strong source areas that often started at different times during dust storm days. Activity in the “central area” was more sporadic than in the other three areas.
2.1. Experimental Evidence for a Relationship Between Fa and q
 Bagnold  and Iversen et al.  showed that there is a minimum aerodynamic threshold friction velocity (u*t) for individual particles to be entrained into the air stream by aerodynamic forces from a smooth surface. This u*t varies with particle size, roughness of the surface, crusting of the soil surface, soil texture, soil moisture, and salt content [Gillette et al., 1980; Gillette et al., 1982; Gillette, 1988; Breuninger et al., 1989]. However, for observations of natural wind erosion for a range of friction velocities smaller than u*t, one can find emissions of 10 μm particles [Cahill et al., 1996; Gillette, 1977]. Because aerodynamic forces cannot have been responsible for them and because sandblasting of the soil was observed at the time of their emissions, it is highly probable that sandblasting was the dominant mechanism for their input.
 The chemical composition of PM10 is the same as aggregated coatings of PM10-sized particles on sand-sized particles [Gillette and Walker, 1977]. Evidence showed that some individual PM10 particles are similar to clay platelets that adhere to the surfaces of larger quartz particles. As the clay particles were not found to exist in the parent soil except as coatings on quartz particles, the airborne particles of the fine mode were almost certainly removed from quartz grains by collisions with the larger particles. The collisions (sandblasting) acted to release portions of aggregated particles and may also have broken the crystalline structure of mineral particles.
 Experiments by Shao et al.  and Houser and Nickling  showed that particle-particle interaction (sandblasting) on an erodible surface is an important and probably dominant mechanism that produces suspended particle flux. Both experiments used wind tunnels, the floors of which contained clay-rich material. Experiments by Shao et al.  used finely divided clay, while Houser and Nickling's  experiment used crusted clay material. In both experiments, high winds first yielded exceedingly small amounts of fine material, then large amounts of PM10 when sand-sized grains were fed into the stream. Aerodynamic forces alone were able to entrain only small amounts of PM10. At the same wind speeds, however, sandblasting caused steady entrainment of PM10.
 Gillette's  work, which simultaneously measured horizontal fluxes of sand-sized particles (q) and vertical PM10 fluxes (Fa) on agricultural soils in Texas, formed a body of experimental work with which to compare results at Owens Lake. Gillette's results showed that the ratio Fa/q is consistent when grouped by soil-surface-texture type. Testing the largest group of observations for a single texture type (fine sand) of Gillette's data further led us to accept the null hypothesis that there is no correlation between Fa/q and u* or between Fa/q and q at the 5% level of significance, even though the data showed that q is a strong function of u*, in agreement with the theory of Owen . Results by Nickling and Gillies  and by Alfaro and Gomes  show that Fa/q is largely independent of friction velocity (and also q) for friction velocities well above the threshold friction velocity. However, for friction velocities closer to the threshold friction velocity, Fa/q seems to increase with friction velocity. Since dust emissions close to the threshold friction velocity are much smaller than for those well above, the overall behavior is dominated by Fa/q being largely independent of friction velocity.
2.2. Theoretical Justification for a Relationship Between Fa and q
 The sandblasting abrasion rate is proportional to the kinetic energy flux from the sand-sized particles, which is proportional to u*3. Greeley and Iversen  summarized a body of research directed toward the aeolian abrasion of rocks and minerals and concluded that the mass of rock or mineral abraded per impact of sand-sized particles is directly proportional to the kinetic energy of the impacting particle. From dimensional analysis, Gillette and Stockton  showed that the kinetic energy flux of the wind is proportional to the cube of the friction velocity. Since we can assume that the kinetic energy of the wind is absorbed and carried to the surface by saltating particles at the surface, it follows that the vertical kinetic energy flux carried by saltating particles is proportional to u*3.
 According to the classical formulations of Bagnold  and Owen  as well as to many formulae listed by Greeley and Iversen , the horizontal mass flux of saltating sand-sized particles (q) is roughly proportional to u*3 for u* well above threshold. Since both abrasion and the horizontal mass flux of saltating sand-sized particles are roughly proportional to the same variable, they are therefore roughly proportional to each other. Physically, sand-sized particles localize kinetic energy onto small target areas, while the energy from fluid transfer is spread out over a much larger area.
 The Shao et al.  expression for the particle flux of suspended particles produced by the impact of saltating particles is
where Ψ is binding energy, γ is a constant, md is mass per particle, g is acceleration of gravity, VH is the horizontal velocity of the saltating particle, and u* is friction velocity. Both γ and g are constants, and the function f (VH/u*) has been shown by Owen  to be almost constant. Therefore the ratio Fa/q may be expressed as
where Γ = γgf(VH/u*). Using equation (4) to evaluate Fa/q requires evaluation of the binding energies of suspension-sized particles to the soil and the sizes of typical saltation particles. Such evaluation, however, is a difficult task.
 Subtleties within the size distribution of PM10 are caused by sandblasting. Alfaro et al.  proposed a theory following along the lines of the Shao et al.  theory: that the size distributions of the saltating particles are vitally important because the kinetic energy of individual saltating grains, along with the kinetic energy required to release suspendible particles, determines the quantity and size distribution of the suspended aerosol produced by sandblasting. Details of the size distribution of particles smaller than 10 μm are explained in Alfaro et al.'s  theory by the sandblasting mechanism.
 The theory of Lu and Shao  expresses Fa as proportional to either q or to qu*. The case in which Fa is proportional to qu* assumes a lifting mechanism other than sandblasting. Such a mechanism should be detectable for Owens Lake by plotting Fa/q versus q, friction velocity, or wind speed. If Fa/q is constant with wind speed, the Owens Lake data will be supportive of a sandblasting mechanism for dust emission. If Fa/q increases roughly proportional to wind speed, the Owens Lake data will be supportive of Lu and Shao's  alternative theory for dust emission.
2.3. Possibility of Non-Saltation-Driven PM10 Emissions
 Direct suspension of particles may occur when wind speeds are high enough or when sand-sized and larger particles are not the dominant loose particles on a surface. The emission of PM10 by the erosion of salt “fluff” has been observed at Owens Lake for brief periods following efflorescence of salt. It is possible that during these brief periods, PM10 may be emitted by direct suspension. When only fine-grain sediments are available as loose particles on the surface, direct entrainment can occur without the necessity of sandblasting. Ablation of this fluff does not seem to be correlated with significant sand-sized particle movement at the beginning of dust storms [Saint-Amand et al., 1986]. During the emission of fluff the weak structure of this material may well be crushed by a short initial surge of wind, after which direct aerodynamic entrainment can take place. Also, since the salt fluff is limited in supply, its PM10 flux is limited both in total mass and in time. From observations over a period of years we estimate that the contribution of total PM10 flux by direct aerodynamic entrainment is small. For example, one of the authors observed dust storms at Owens Lake commencing on 11 March 1993 and ending with rainfall on 25 March 1993. White salt-rich aerosol from fluff was produced for only a half hour to an hour, whereas the total time of wind erosion accompanied by vigorous sand-sized particle movement was about 35 hours.
 Finally, the term “sand-sized particles” is used rather than sand in this study because several areas of Owens Lake have little sand but nonetheless have an abundance of sand-sized particles. An example of such an area is the clay rich area to the northeast of Dirty Socks. Here, clay-rich sediments can aggregate and crack into sand-sized aggregates. These sand-sized aggregates act very similarly to sand particles composed entirely of a solid piece of only one mineral.
2.4. K Factor Approach and Variability of the Vertical Flux of PM10 Dust
 K is defined as the ratio of Fa to q:
For a specific time, K and q are variable quantities for a given location that may be expressed as overall means for the lake bed plus fluctuations for given positions:
Both sums of all q′ and all k′ are zero. For a single storm the vertical flux of PM10 dust at a particular square kilometer may be expressed as
Analysis of Gillette's  data showed that q and K are not correlated; that is,
The middle term on the right-hand side of equation (8) (k′) has a mean of zero since the mean of k′ is zero. Values of q typically range from zero in some subareas to 1 g cm−1 s−1 for high wind speeds in a given area of the lake (several km2 in area); K values typically range two or more orders of magnitude [Gillette et al., 1997a]. Consequently, q has a larger range of variability than K. Our results show that average K factors may change by one order of magnitude and that q may change by three orders of magnitude (excluding q = 0).
 One can grid the lake surface such that individual horizontal positions west-east and south-north may be labeled “i” and “j,” respectively. For successive grid (i and j) positions separated by 1 km an individual measurement of q or Fa at position i, j may be made. Individual measurements of qij were used to represent q for a square kilometer at position i, j. Then, the rate of total mass of dust produced in a given storm is weighted by the area of each measurement (1 km2):
 Mtot is estimated by measurements of PM10 concentrations at the shoreline of the lake bed and modeling of the dust transport from the lake bed. Details of the modeling are available in section 3.6.
 The “K factor” method of estimating the vertical flux approximates the vertical mass flux of PM10 at each i, j position by using the mean value of K for the area being considered times the individual qij value at each position for the estimate of Faij. Thus for each position, equation (8) is rewritten as
where εij is the difference between the true vertical flux of dust at position i, j and qij (alternatively, the sum of the last two terms of the right-hand side of equation (8)). The mean of εij for the entire area is zero. The mean vertical PM10 mass flux for the area of the lake considered is
We did not evaluate εij of equation (11) since there was no data on k′. This K factor method neglects the error term εij to give an approximate value for the individual Faij,
so that each individual Faij has an error εij. Although individual fluxes at specific locations have associated error with the K factor method, the total flux for the lake is well estimated. The mean K (K factor) is expressed (from equation (10)) as
The mean K is often dominated by strong source subregions of the lake that have large sand flux qs. Therefore the mean K (K factor) may not be a good estimator of individual Ks for weak source areas (small qs) if these Ks are significantly different. Consequently, the estimation of K might be representative of primarily the strong source areas of the lake. For example, if the strong sources were eliminated, this method would more accurately represent the weaker source areas. During small emission episodes, K factor measurements are expected to have more variability. This variability may be real, or it may be caused by increased error in the measurement of q since only parts of the square kilometer cells may have active erosion during small events.
 Gillette et al.'s [1997a] alternative method of measuring vertical PM10 fluxes at Owens Lake might improve estimation of Fa at individual points. However, this method would require at least 10 particle concentration measurements for each of our 135 measuring locations on the lake and an accuracy of measurement that may not be technically achievable at this time. We opted to use the K factor method based on the above analysis since it adequately estimated Fa for strong source subareas on the lake surface for the large and highly variable (in time) surface area with which we were concerned.