Merge pull request ESCOMP#4048 from cenlinhe/review_SnowHydro

review Snow Hydrology Sect 2.8 in Technote

Author: slevis-lmwg

doc/source/tech_note/Snow_Hydrology/CLM50_Tech_Note_Snow_Hydrology.rst

@@ -3,7 +3,7 @@
 Snow Hydrology
 ===============
 
-The parameterizations for snow are based primarily on :ref:`Anderson (1976) <Anderson1976>`, :ref:`Jordan (1991) <Jordan1991>`, and :ref:`Dai and Zeng (1997) <DaiZeng1997>`. The snowpack can have up to twelve layers. These layers are indexed in the Fortran code as :math:`i=-11,-10,...,-1,0` where layer :math:`i=0` is the snow layer next to the top soil layer and layer :math:`i=-11` is the top layer of a twelve-layer snow pack. Since the number of snow layers varies according to the snow depth, we use the notation :math:`snl+1` to describe the top layer of snow for the variable layer snow pack, where :math:`snl` is the negative of the number of snow layers. Refer to :numref:`Figure three layer snow pack` for an example of the snow layer structure for a three layer snow pack.
+The parameterizations for snow are based primarily on :ref:`Anderson (1976) <Anderson1976>`, :ref:`Jordan (1991) <Jordan1991>`, and :ref:`Dai and Zeng (1997) <DaiZeng1997>`. The snowpack can have up to twelve layers. These layers are indexed in the Fortran code as :math:`i=-11,-10,...,-1,0` where layer :math:`i=0` is the snow layer next to the top soil layer and layer :math:`i=-11` is the top layer of a twelve-layer snowpack. Since the number of snow layers varies according to the snow depth, we use the notation :math:`snl+1` to describe the top layer of snow for the variable layer snowpack, where :math:`snl` is the negative of the number of snow layers. Refer to :numref:`Figure three layer snow pack` for an example of the snow layer structure for a three layer snowpack.
 
 .. _Figure three layer snow pack:
 
@@ -30,7 +30,7 @@ The state variables for snow are the mass of water :math:`w_{liq,i}` (kg m\ :sup
 
       \text{Water equivalent} = \text{Ice equivalent} \times \frac{\rho_\text{ice}}{\rho_\text{liq}}
 
-Section :numref:`Snow Covered Area Fraction` describes the calculation of fractional snow covered area, which is used in the surface albedo calculation (Chapter :numref:`rst_Surface Albedos`) and the surface flux calculations (Chapter :numref:`rst_Momentum, Sensible Heat, and Latent Heat Fluxes`). The following two sections (:numref:`Ice Content` and :numref:`Water Content`) describe the ice and water content of the snow pack assuming that at least one snow layer exists. Section :numref:`Black and organic carbon and mineral dust within snow` describes how black and organic carbon and mineral dust particles are represented within snow, including meltwater flushing. See Section :numref:`Initialization of snow layer` for a description of how a snow layer is initialized.
+Section :numref:`Snow Covered Area Fraction` describes the calculation of fractional snow covered area, which is used in the surface albedo calculation (Chapter :numref:`rst_Surface Albedos`) and the surface flux calculations (Chapter :numref:`rst_Momentum, Sensible Heat, and Latent Heat Fluxes`). Sections (:numref:`Ice Content` and :numref:`Water Content`) describe the ice and water content of the snowpack assuming that at least one snow layer exists. Section :numref:`Black and organic carbon and mineral dust within snow` describes how black and organic carbon and mineral dust particles are represented within snow, including meltwater scavenging. See Section :numref:`Initialization of snow layer` for a description of how a snow layer is initialized.
 
 .. _Snow Covered Area Fraction:
 
@@ -113,8 +113,8 @@ The temperature dependent term is given by (:ref:`van Kampenhout et al. (2017) <
 
    \rho_{T} =
    \left\{\begin{array}{lr}
-   50 + 1.7 \left(17\right)^{1.5} & \qquad T_{atm} >T_{f} +2 \ \\
-   50+1.7 \left(T_{atm} -T_{f} + 15\right)^{1.5} & \qquad T_{f} - 15 < T_{atm} \le T_{f} + 2 \ \\
+   50 + 1.7 \ \left(17\right)^{1.5} & \qquad T_{atm} >T_{f} +2 \ \\
+   50+1.7 \ \left(T_{atm} -T_{f} + 15\right)^{1.5} & \qquad T_{f} - 15 < T_{atm} \le T_{f} + 2 \ \\
    -3.833 \ \left( T_{atm} -T_{f} \right) - 0.0333 \ \left( T_{atm} -T_{f} \right)^{2}
    &\qquad T_{atm} \le T_{f} - 15
    \end{array}\right\}
@@ -167,7 +167,7 @@ The snow water equivalent :math:`W_{sno}` is capped to not exceed 10,000 kg m\ :
 Water Content
 ^^^^^^^^^^^^^^^^^^^
 
-The conservation equation for mass of water in snow layers is
+The conservation equation for mass of liquid water in snow layers is
 
 .. math::
    :label: 8.26
@@ -228,7 +228,7 @@ Equations :eq:`8.29` - :eq:`8.33` are solved sequentially from top (:math:`i=snl
 Black and organic carbon and mineral dust within snow
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-Particles within snow originate from atmospheric aerosol deposition (:math:`D_{sp}` in Table 2.3 (kg m\ :sup:`-2` s\ :sup:`-1`) and influence snow radiative transfer (sections :numref:`Snow Albedo`, :numref:`Snowpack Optical Properties`, and :numref:`Snow Aging`). Particle masses and mixing ratios are represented with a simple mass-conserving scheme. The model maintains masses of the following eight particle species within each snow layer: hydrophilic black carbon, hydrophobic black carbon, hydrophilic organic carbon, hydrophobic organic carbon, and four species of mineral dust with the following particle sizes: 0.1-1.0, 1.0-2.5, 2.5-5.0, and 5.0-10.0 :math:`\mu m`. Each of these species has unique optical properties (:numref:`Table Single-scatter albedo values used for snowpack impurities and ice`) and meltwater removal efficiencies (:numref:`Table Meltwater scavenging`).
+Particles within snowpack originate from atmospheric aerosol deposition (:math:`D_{sp}` in Table 2.3, kg m\ :sup:`-2` s\ :sup:`-1`) and influence snowpack radiative transfer (sections :numref:`Snow Albedo`, :numref:`Snowpack Optical Properties`, and :numref:`Snow Aging`). Particle masses and mixing ratios are represented with a simple mass-conserving scheme. The model maintains masses of the following eight particle species within each snow layer: hydrophilic black carbon, hydrophobic black carbon, hydrophilic organic carbon, hydrophobic organic carbon, and four species of mineral dust with the following particle sizes: 0.1-1.0, 1.0-2.5, 2.5-5.0, and 5.0-10.0 :math:`\mu m`. Each of these species has unique optical properties (:numref:`Table Single-scatter albedo values used for snowpack impurities and ice`) and meltwater removal efficiencies (:numref:`Table Meltwater scavenging`).
 
 The black carbon and organic carbon deposition rates described in Table 2.3 are combined into four categories as follows
 
@@ -252,7 +252,7 @@ The black carbon and organic carbon deposition rates described in Table 2.3 are
 
    D_{oc,\, hphob} =D_{oc,\, dryhphob}
 
-Deposited particles are assumed to be instantly mixed (homogeneously) within the surface snow layer and are added after the inter-layer water fluxes are computed (section :numref:`Water Content`) so that some aerosol is in the top layer after deposition and is not immediately washed out before radiative calculations are done. Particle masses are then redistributed each time step based on meltwater drainage through the snow column (section :numref:`Water Content`) and snow layer combination and subdivision (section :numref:`Snow Layer Combination and Subdivision`). The change in mass of each of the particle species :math:`\Delta m_{sp,\, i}` (kg m\ :sup:`-2`) is
+Deposited particles are assumed to be instantly mixed within the surface snow layer (black carbon and dust can be either internally or externally mixed with snow grains; section :numref:`Snow Albedo`) and are added after the inter-layer water fluxes are computed (section :numref:`Water Content`) so that some aerosol is in the top layer after deposition and is not immediately washed out before radiative calculations are done. Particle masses are then redistributed each time step based on meltwater drainage through the snow column (section :numref:`Water Content`) and snow layer combination and subdivision (section :numref:`Snow Layer Combination and Subdivision`). The change in mass of each of the particle species :math:`\Delta m_{sp,\, i}` (kg m\ :sup:`-2`) is
 
 .. math::
    :label: 8.38
@@ -469,7 +469,7 @@ The latter equation (for the mobility index :math:`M_\mathrm{O}`) is a simplific
 Snow Layer Combination and Subdivision
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-After the determination of snow temperature including phase change(Chapter :numref:`rst_Soil and Snow Temperatures`), snow hydrology (Chapter :numref:`rst_Snow Hydrology`), and the compaction calculations (section :numref:`Snow Compaction`), the number of snow layers is adjusted by either combining or subdividing layers. The combination and subdivision of snow layers is based on :ref:`Jordan (1991) <Jordan1991>`.
+After the determination of snow temperature including phase change (Chapter :numref:`rst_Soil and Snow Temperatures`), snow hydrology (Chapter :numref:`rst_Snow Hydrology`), and the compaction calculations (section :numref:`Snow Compaction`), the number of snow layers is adjusted by either combining or subdividing layers. The combination and subdivision of snow layers is based on :ref:`Jordan (1991) <Jordan1991>`.
 
 .. _Combination:
 
@@ -617,5 +617,5 @@ then adjusted as,
    T_{2}^{n+1} = T_{2}^{n} +\left(\frac{T_{1}^{n} -T_{2}^{n} }{{\left(\Delta z_{1} +\Delta z_{2}^{n} \right)\mathord{\left/ {\vphantom {\left(\Delta z_{1} +\Delta z_{2}^{n} \right) 2}} \right.} 2} } \right)\left(\frac{\Delta z_{2}^{n+1} }{2} \right) & \qquad T'_{3} <T_{f}
    \end{array}
 
-where here the subscripts 1, 2, and 3 denote three layers numbered from top to bottom. After layer subdivision, the node depths and layer interfaces are recalculated from equations :eq:`8.60` and :eq:`8.61`.
+where the subscripts 1, 2, and 3 denote three layers numbered from top to bottom. After layer subdivision, the node depths and layer interfaces are recalculated from equations :eq:`8.60` and :eq:`8.61`.