220 lines
11 KiB
ReStructuredText
220 lines
11 KiB
ReStructuredText
.. _rst_Dust Model:
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Dust Model
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==============
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Atmospheric dust is mobilized from the land by wind in the CLM. The most
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important factors determining soil erodibility and dust emission include
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the wind friction speed, the vegetation cover, and the soil moisture.
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The CLM dust mobilization scheme (:ref:`Mahowald et al. 2006<Mahowaldetal2006>`)
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accounts for these factors based on the DEAD (Dust Entrainment and Deposition)
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model of :ref:`Zender et al. (2003)<Zenderetal2003>`. Please refer to the
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:ref:`Zender et al. (2003)<Zenderetal2003>` article for additional
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information regarding the equations presented in this section.
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The total vertical mass flux of dust, :math:`F_{j}`
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(kg m\ :sup:`-2` s\ :sup:`-1`), from the ground into transport bin
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:math:`j` is given by
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.. math::
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:label: 29.1
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F_{j} =TSf_{m} \alpha Q_{s} \sum _{i=1}^{I}M_{i,j}
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where :math:`T` is a global factor that compensates for the DEAD model’s
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sensitivity to horizontal and temporal resolution and equals 5 x
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10\ :sup:`-4` in the CLM instead of 7 x 10\ :sup:`-4` in
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:ref:`Zender et al. (2003)<Zenderetal2003>`. :math:`S` is the source
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erodibility factor set to 1 in the CLM and serves as a place holder
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at this time.
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The grid cell fraction of exposed bare soil suitable for dust
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mobilization :math:`f_{m}` is given by
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.. math::
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:label: 29.2
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f_{m} =\left(1-f_{lake} \right)\left(1-f_{sno} \right)\left(1-f_{v} \right)\frac{w_{liq,1} }{w_{liq,1} +w_{ice,1} }
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where :math:`f_{lake}` and :math:`f_{sno}`
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are the CLM grid cell fractions of lake (section
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:numref:`Surface Data`) and snow cover (section
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:numref:`Snow Covered Area Fraction`), all ranging from zero to one. Not mentioned
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by :ref:`Zender et al. (2003)<Zenderetal2003>`, :math:`w_{liq,\, 1}` and
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:math:`{}_{w_{ice,\, 1} }` are the CLM top soil layer liquid water and
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ice contents (mm) entered as a ratio expressing the decreasing ability
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of dust to mobilize from increasingly frozen soil. The grid cell
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fraction of vegetation cover,\ :math:`{}_{f_{v} }`, is defined as
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.. math::
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:label: 29.3
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0\le f_{v} =\frac{L+S}{\left(L+S\right)_{t} } \le 1{\rm \; \; \; \; where\; }\left(L+S\right)_{t} =0.3{\rm \; m}^{2} {\rm m}^{-2}
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where equation applies only for dust mobilization and is not related to
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the plant functional type fractions prescribed from the CLM input data
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or simulated by the CLM dynamic vegetation model (Chapter 22). :math:`L`
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and :math:`S` are the CLM leaf and stem area index values
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(m :sup:`2` m\ :sup:`-2`) averaged at the land unit level so
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as to include all the pfts and the bare ground present in a vegetated
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land unit. :math:`L` and :math:`S` may be prescribed from the CLM
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input data (section :numref:`Phenology and vegetation burial by snow`)
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or simulated by the CLM biogeochemistry model (Chapter
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:numref:`rst_Vegetation Phenology and Turnover`).
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The sandblasting mass efficiency :math:`\alpha` (m :sup:`-1`) is
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calculated as
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.. math::
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:label: 29.4
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\alpha =100e^{\left(13.4M_{clay} -6.0\right)\ln 10} {\rm \; \; }\left\{\begin{array}{l} {M_{clay} =\% clay\times 0.01{\rm \; \; \; 0}\le \% clay\le 20} \\ {M_{clay} =20\times 0.01{\rm \; \; \; \; \; \; \; \; 20<\% }clay\le 100} \end{array}\right.
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where :math:`M_{clay}` is the mass fraction of clay
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particles in the soil and %clay is determined from the surface dataset
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(section :numref:`Surface Data`). :math:`M_{clay} =0` corresponds to sand and
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:math:`M_{clay} =0.2` to sandy loam.
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:math:`Q_{s}` is the total horizontally saltating mass flux (kg
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m\ :sup:`-1` s\ :sup:`-1`) of “large” particles (:numref:`Table Dust Mass fraction`),
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also referred to as the vertically integrated streamwise mass flux
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.. math::
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:label: 29.5
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Q_{s} = \left\{
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\begin{array}{lr}
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\frac{c_{s} \rho _{atm} u_{*s}^{3} }{g} \left(1-\frac{u_{*t} }{u_{*s} } \right)\left(1+\frac{u_{*t} }{u_{*s} } \right)^{2} {\rm \; } & \qquad {\rm for\; }u_{*t} <u_{*s} \\
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0{\rm \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; } & \qquad {\rm for\; }u_{*t} \ge u_{*s}
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\end{array}\right.
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where the saltation constant :math:`c_{s}` equals 2.61 and
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:math:`\rho _{atm}` is the atmospheric density (kg m\ :sup:`-3`)
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(:numref:`Table Atmospheric input to land model`), :math:`g` the acceleration of gravity (m
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s\ :sup:`-2`) (:numref:`Table Physical constants`). The threshold wind friction speed for saltation :math:`u_{*t}` (m s\ :sup:`-1`) is
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.. math::
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:label: 29.6
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u_{*t} =f_{z} \left[Re_{*t}^{f} \rho _{osp} gD_{osp} \left(1+\frac{6\times 10^{-7} }{\rho _{osp} gD_{osp}^{2.5} } \right)\right]^{\frac{1}{2} } \rho _{atm} ^{-\frac{1}{2} } f_{w}
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where :math:`f_{z}` is a factor dependent on surface roughness but set
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to 1 as a place holder for now, :math:`\rho _{osp}` and
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:math:`D_{osp}` are the density (2650 kg m\ :sup:`-3`) and
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diameter (75 x 10\ :math:`{}^{-6}` m) of optimal saltation particles,
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and :math:`f_{w}` is a factor dependent on soil moisture:
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.. math::
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:label: 29.7
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f_{w} =\left\{\begin{array}{l} {1{\rm \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; for\; }w\le w_{t} } \\ {\sqrt{1+1.21\left[100\left(w-w_{t} \right)\right]^{0.68} } {\rm \; \; for\; }w>w_{t} } \end{array}\right.
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where
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.. math::
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:label: 29.8
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w_{t} =a\left(0.17M_{clay} +0.14M_{clay}^{2} \right){\rm \; \; \; \; \; \; 0}\le M_{clay} =\% clay\times 0.01\le 1
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and
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.. math::
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:label: 29.9
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w=\frac{\theta _{1} \rho _{liq} }{\rho _{d,1} }
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where :math:`a=M_{clay}^{-1}` for tuning purposes,
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:math:`\theta _{1}` is the volumetric soil moisture in the top soil
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layer (m :math:`{}^{3 }`\ m\ :sup:`-3`) (section :numref:`Soil Water`),
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:math:`\rho _{liq}` is the density of liquid water (kg
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m\ :sup:`-3`) (:numref:`Table Physical constants`), and :math:`\rho _{d,\, 1}`
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is the bulk density of soil in the top soil layer (kg m\ :sup:`-3`)
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defined as in section :numref:`Soil and Snow Thermal Properties`
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rather than as in :ref:`Zender et al. (2003)<Zenderetal2003>`.
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:math:`Re_{*t}^{f}` from equation is the threshold friction Reynolds
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factor
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.. math::
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:label: 29.10
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Re_{*t}^{f} =\left\{\begin{array}{l} {\frac{0.1291^{2} }{-1+1.928Re_{*t} } {\rm \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; for\; 0.03}\le Re_{*t} \le 10} \\ {0.12^{2} \left(1-0.0858e^{-0.0617(Re_{*t} -10)} \right)^{2} {\rm \; for\; }Re_{*t} >10} \end{array}\right.
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and :math:`Re_{*t}` is the threshold friction Reynolds number
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approximation for optimally sized particles
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.. math::
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:label: 29.11
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Re_{*t} =0.38+1331\left(100D_{osp} \right)^{1.56}
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In :eq:`29.5` , :math:`u_{*s}` is defined as the wind friction speed
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(m s\ :sup:`-1`) accounting for the Owen effect (:ref:`Owen 1964<Owen1964>`)
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.. math::
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:label: 29.12
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u_{\*s} = \left\{
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\begin{array}{lr}
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u_{\*} & \quad {\rm \; for \;} U_{10} <U_{10,t} \\
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u_{*} +0.003\left(U_{10} -U_{10,t} \right)^{2} & \quad {\rm \; for\; }U_{10} \ge U_{10,t}
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\end{array}\right.
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where :math:`u_{*}` is the CLM wind friction speed (m s\ :sup:`-1`),
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also known as friction velocity (section :numref:`Monin-Obukhov Similarity Theory`),
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:math:`U_{10}` \ is the 10-m wind speed (m s\ :sup:`-1`)
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calculated as the wind speed at the top of the canopy in section 4.3 of
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:ref:`Bonan (1996)<Bonan1996>` but here for 10 m above the ground, and
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:math:`U_{10,\, t}` is the threshold wind speed at 10 m (m
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s\ :sup:`-1`)
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.. math::
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:label: 29.13
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U_{10,t} =u_{*t} \frac{U_{10} }{u_{*} }
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In equation we sum :math:`M_{i,\, j}` over :math:`I=3` source modes
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:math:`i` where :math:`M_{i,\, j}` is the mass fraction of each source
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mode :math:`i` carried in each of *:math:`J=4`* transport bins :math:`j`
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.. math::
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:label: 29.14
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M_{i,j} =\frac{m_{i} }{2} \left[{\rm erf}\left(\frac{\ln {\textstyle\frac{D_{j,\max } }{\tilde{D}_{v,i} }} }{\sqrt{2} \ln \sigma _{g,i} } \right)-{\rm erf}\left(\frac{\ln {\textstyle\frac{D_{j,\min } }{\tilde{D}_{v,i} }} }{\sqrt{2} \ln \sigma _{g,i} } \right)\right]
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where :math:`m_{i}` , :math:`\tilde{D}_{v,\, i}` , and
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:math:`\sigma _{g,\, i}` are the mass fraction, mass median diameter,
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and geometric standard deviation assigned to each particle source mode
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:math:`i` (:numref:`Table Dust Mass fraction`), while :math:`D_{j,\, \min }` and
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:math:`D_{j,\, \max }` are the minimum and maximum diameters (m) in
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each transport bin :math:`j` (:numref:`Table Dust Minimum and maximum particle diameters`).
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.. _Table Dust Mass fraction:
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.. table:: Mass fraction :math:`m_{i}` , mass median diameter :math:`\tilde{D}_{v,\, i}` , and geometric standard deviation :math:`\sigma _{g,\, i}` , per dust source mode :math:`i`
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+-------------+-----------------------------+-----------------------------------+-----------------------------+
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| :math:`i` | :math:`m_{i}` (fraction) | :math:`\tilde{D}_{v,\, i}` (m) | :math:`\sigma _{g,\, i}` |
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+=============+=============================+===================================+=============================+
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| 1 | 0.036 | 0.832 x 10\ :math:`{}^{-6}` | 2.1 |
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+-------------+-----------------------------+-----------------------------------+-----------------------------+
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| 2 | 0.957 | 4.820 x 10\ :math:`{}^{-6}` | 1.9 |
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+-------------+-----------------------------+-----------------------------------+-----------------------------+
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| 3 | 0.007 | 19.38 x 10\ :math:`{}^{-6}` | 1.6 |
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+-------------+-----------------------------+-----------------------------------+-----------------------------+
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.. _Table Dust Minimum and maximum particle diameters:
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.. table:: Minimum and maximum particle diameters in each dust transport bin :math:`j`
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+-------------+-------------------------------+-------------------------------+
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| :math:`j` | :math:`D_{j,\, \min }` (m) | :math:`D_{j,\, \max }` (m) |
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+=============+===============================+===============================+
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| 1 | 0.1 x 10\ :math:`{}^{-6}` | 1.0 x 10\ :math:`{}^{-6}` |
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+-------------+-------------------------------+-------------------------------+
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| 2 | 1.0 x 10\ :math:`{}^{-6}` | 2.5 x 10\ :math:`{}^{-6}` |
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+-------------+-------------------------------+-------------------------------+
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| 3 | 2.5 x 10\ :math:`{}^{-6}` | 5.0 x 10\ :math:`{}^{-6}` |
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+-------------+-------------------------------+-------------------------------+
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| 4 | 5.0 x 10\ :math:`{}^{-6}` | 10.0 x 10\ :math:`{}^{-6}` |
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+-------------+-------------------------------+-------------------------------+
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