8.8 KiB
2.7.1. Canopy Water¶
Liquid precipitation is either intercepted by the canopy, falls directly to the snow/soil surface (throughfall), or drips off the vegetation (canopy drip). Solid precipitation is treated similarly, with the addition of unloading of previously intercepted snow. Interception by vegetation is divided between liquid and solid phases \(q_{intr,\,liq}\) and \(q_{intr,\,ice}\) (kg m-2 s-1)
(2.7.2)¶\[q_{intr,\,liq} = f_{pi,\,liq} \ q_{rain}\]
(2.7.3)¶\[q_{intr,\,ice} = f_{pi,\,ice} \ q_{sno}\]
where \(f_{pi,\,liq}\) and \(f_{pi,\,ice}\) are the fractions of intercepted precipitation of rain and snow, respectively
(2.7.4)¶\[f_{pi,\,liq} = \alpha_{liq} \ tanh \left(L+S\right)\]
(2.7.5)¶\[f_{pi,\,ice} =\alpha_{sno} \ \left\{1-\exp \left[-0.5\left(L+S\right)\right]\right\} \ ,\]
and \(L\) and \(S\) are the exposed leaf and stem area index, respectively (section 2.2.1.4), and the \(\alpha\)'s scale the fractional area of a leaf that collects water (Lawrence et al. 2007). Default values of \(\alpha_{liq}\) and \(\alpha_{sno}\) are set to 1. Throughfall (kg m-2 s-1) is also divided into liquid and solid phases, reaching the ground (soil or snow surface) as
(2.7.6)¶\[q_{thru,\, liq} = q_{rain} \left(1 - f_{pi,\,liq}\right)\]
(2.7.7)¶\[q_{thru,\, ice} = q_{sno} \left(1 - f_{pi,\,ice}\right)\]
Similarly, the liquid and solid canopy drip fluxes are
(2.7.8)¶\[q_{drip,\, liq} =\frac{W_{can,\,liq}^{intr} -W_{can,\,liq}^{max } }{\Delta t} \ge 0\]
(2.7.9)¶\[q_{drip,\, ice} =\frac{W_{can,\,sno}^{intr} -W_{can,\,sno}^{max } }{\Delta t} \ge 0\]
where
(2.7.10)¶\[W_{can,liq}^{intr} =W_{can,liq}^{n} +q_{intr,\, liq} \Delta t\ge 0\]
and
(2.7.11)¶\[W_{can,sno}^{intr} =W_{can,sno}^{n} +q_{intr,\, ice} \Delta t\ge 0\]
are the the canopy liquid water and snow water equivalent after accounting for interception, \(W_{can,\,liq}^{n}\) and \(W_{can,\,sno}^{n}\) are the canopy liquid and snow water from the previous time step, and \(W_{can,\,liq}^{max }\) and \(W_{can,\,snow}^{max }\) (kg m-2 or mm of H2O) are the maximum amounts of liquid water and snow the canopy can hold. They are defined by
(2.7.12)¶\[W_{can,\,liq}^{max } =p_{liq}\left(L+S\right)\]
(2.7.13)¶\[W_{can,\,sno}^{max } =p_{sno}\left(L+S\right).\]
The maximum storage of liquid water is \(p_{liq}=0.1\) kg m-2 (Dickinson et al. 1993), and that of snow is \(p_{sno}=6\) kg m-2, consistent with reported field measurements (Pomeroy et al. 1998).
Canopy snow unloading from wind speed \(u\) and above-freezing temperatures are modeled from linear fluxes and e-folding times similar to Roesch et al. (2001)
(2.7.14)¶\[q_{unl,\, wind} =\frac{u W_{can,sno}}{1.56\times 10^5 \text{ m}}\]
(2.7.15)¶\[q_{unl,\, temp} =\frac{W_{can,sno}(T-270 \textrm{ K})}{1.87\times 10^5 \text{ K s}} > 0\]
(2.7.16)¶\[q_{unl,\, tot} =\min \left( q_{unl,\, wind} +q_{unl,\, temp} ,W_{can,\, sno} \right)\]
The canopy liquid water and snow water equivalent are updated as
(2.7.17)¶\[ W_{can,\, liq}^{n+1} =W_{can,liq}^{n} + q_{intr,\, liq} - q_{drip,\, liq} \Delta t - E_{v}^{liq} \Delta t \ge 0\]
and
(2.7.18)¶\[W_{can,\, sno}^{n+1} =W_{can,sno}^{n} + q_{intr,\, ice} - \left(q_{drip,\, ice}+q_{unl,\, tot} \right)\Delta t - E_{v}^{ice} \Delta t \ge 0\]
where \(E_{v}^{liq}\) and \(E_{v}^{ice}\) are partitioned from the stem and leaf surface evaporation \(E_{v}^{w}\) (Chapter 2.5) based on the vegetation temperature \(T_{v}\) (K) (Chapter 2.5) and its relation to the freezing temperature of water \(T_{f}\) (K) (Table 2.2.7)
(2.7.19)¶\[\begin{split}E_{v}^{liq} = \left\{\begin{array}{lr} E_{v}^{w} & T_v > T_{f} \\ 0 & T_v \le T_f \end{array}\right\}\end{split}\]
(2.7.20)¶\[\begin{split}E_{v}^{ice} = \left\{\begin{array}{lr} 0 & T_v > T_f \\ E_{v}^{w} & T_v \le T_f \end{array}\right\}.\end{split}\]
The total rate of liquid and solid precipitation reaching the ground is then
(2.7.21)¶\[q_{grnd,liq} =q_{thru,\, liq} +q_{drip,\, liq}\]
(2.7.22)¶\[q_{grnd,ice} =q_{thru,\, ice} +q_{drip,\, ice} +q_{unl,\, tot} .\]
Solid precipitation reaching the soil or snow surface, \(q_{grnd,\, ice} \Delta t\), is added immediately to the snow pack (Chapter 2.8). The liquid part, \(q_{grnd,\, liq} \Delta t\) is added after surface fluxes (Chapter 2.5) and snow/soil temperatures (Chapter 2.6) have been determined.
The wetted fraction of the canopy (stems plus leaves), which is required for surface flux (Chapter 2.5) calculations, is (Dickinson et al.1993)
(2.7.23)¶\[\begin{split}f_{wet} = \left\{\begin{array}{lr} \left[\frac{W_{can} }{p_{liq}\left(L+S\right)} \right]^{{2\mathord{\left/ {\vphantom {2 3}} \right.} 3} } \le 1 & \qquad L+S > 0 \\ 0 &\qquad L+S = 0 \end{array}\right\}\end{split}\]
while the fraction of the canopy that is dry and transpiring is
(2.7.24)¶\[\begin{split}f_{dry} = \left\{\begin{array}{lr} \frac{\left(1-f_{wet} \right)L}{L+S} & \qquad L+S > 0 \\ 0 &\qquad L+S = 0 \end{array}\right\}.\end{split}\]
Similarly, the snow-covered fraction of the canopy is used for surface alebdo when intercepted snow is present (Chapter 2.3)
(2.7.25)¶\[\begin{split}f_{can,\, sno} = \left\{\begin{array}{lr} \left[\frac{W_{can,\, sno} }{p_{sno}\left(L+S\right)} \right]^{{3\mathord{\left/ {\vphantom {3 20}} \right.} 20} } \le 1 & \qquad L+S > 0 \\ 0 &\qquad L+S = 0 \end{array}\right\}.\end{split}\]