Changes between Version 50 and Version 51 of doc/tec/bc

Timestamp:

Nov 19, 2018 11:23:05 AM (6 years ago)

Author:

suehring

Comment:

--

doc/tec/bc

@@ -313 +313 @@
 #!Latex
 \begin{equation*}
-R_{i,i} = u_{*} ( 0.35\,(-\frac{z_i}{\kappa\,L})^\frac{2}{3}) + (5 - 4\,\frac{z}{z_i}, \: (i \in (1,2) )\,,
+R_{i,i} = u_{*}^2\,( 0.35\,(-\frac{z_i}{\kappa\,L})^\frac{2}{3}) + (5 - 4\,\frac{z}{z_i}) )\,, \: (i \in (1,2)\,,
 \end{equation*}
 }}}
@@ -321 +321 @@
 ''L'' is computed from the area-averaged surface temperature, sensible heat flux profile and roughness length in the model domain. 
 ''z,,i,,'' is estimated from the bulk Richardson criterion, with ''z,,i,,'' being the height where the bulk Richardson first exceeds the critical Richardson number of 0.25, according to [=#heinze2017 Heinze et al. (2017)]. 
-In case of stable stratification (''L'' > 0) or neutral stratification (''L'' = 0), the first term is omitted for the computation of ''R,,ii,,''.  
-
+In case of stable stratification (''L'' > 0) or neutral stratification (''L'' = 0), the first term is omitted for the computation of ''R,,ii,,''.  \\
+Further, vertical velocity variances are parametrized as 
+{{{
+#!Latex
+\begin{equation*}
+R_{i,i} = w_{m}^2\,( 1.5\,(\frac{z}{z_i})^\frac{2}{3}\,\exp{-2\,\frac{z}{z_i}} + (1.7 - \frac{z}{z_i})\,(\frac{u_{*}}{w_m})^2)\,, \: (i \in (3)\,,
+\end{equation*}
+}}}
+with
+{{{
+#!Latex
+\begin{equation*}
+w_m = (u_{*}^{3} + 0.6\,w_{*}^{3})^\frac{1}{3}
+\end{equation*}
+}}}
+being the momentum velocity scale, with the convective velocity scale ''w,,*,,''. In case of stable or neutral stratification, ''w,,m,, = u,,*,,''.