commit affe8cd69f6dc009583f900ec275434592df045a
parent 1970eaca93044bbfffdf3863435d73cf74f9bfc2
Author: Ivan Gankevich <i.gankevich@spbu.ru>
Date: Mon, 29 Mar 2021 10:47:16 +0300
Velocity verification.
Diffstat:
| main.tex | | | 37 | ++++++++++++++++++++++++++++++++++++- |
1 file changed, 36 insertions(+), 1 deletion(-)
diff --git a/main.tex b/main.tex
@@ -153,7 +153,7 @@ Then the final formula for both sides is written as
b_2 c_2 \exp\left(-\left|b_2\upsilon_x'-g\left(c_2\right)\right|^{c_2}\right)
\qquad \text{if } \upsilon_x \geq \Mode\upsilon_x \\
- \end{cases}.
+ \end{cases}\label{eq-velocity-distribution}.
\end{equation}
Here \(b_{1,2}>0\) and \(c_{1,2}>0\) are parameters of the distribution
that control the scale and the shape.
@@ -245,6 +245,41 @@ distributions close to unimodal, so we could easily fit them into the model.
\subsection{Verification of wind velocity distribution}
+The data collected with three-axis anemometer showed that for each two-hour
+interval the shape of the wind velocity distribution for each axis can be
+approximated by~\eqref{eq-velocity-distribution}. If the wind blows in positive
+\(x\) direction, then the right part of the distribution is steep and if the
+wind blows in negative \(x\) direction, then the left part of the distribution
+is steep.
+
+We failed to gather the data where the distribution is unimodal: in most
+intervals the distribution is bimodal. However, the second peak is often small
+enough to have small effect on least-squares fitting. Distributions for each
+axis are presented in figure~\ref{fig-velocity-distributions} and their
+parameters in table~\ref{tab-velocity-distributions}.
+
+\begin{figure}
+ \centering
+ TODO
+ \caption{Per-axis wind velocity distributions fitted into the model
+ described by~\eqref{eq-velocity-distribution}.
+ Data intervals with the smallest error (the first row),
+ data intervals with the largest error (the second row).
+ \label{fig-velocity-distributions}}
+\end{figure}
+
+\begin{table}
+ \centering
+ \begin{tabular}{ll}
+ \toprule
+ TODO \\
+ \bottomrule
+ \end{tabular}
+ \caption{Model fitting errors for each graph in
+ figure~\ref{fig-velocity-distributions}.\label{tab-velocity-distributions}}
+\end{table}
+
+
\subsection{Verification of wind direction distribution}
\cite{carta2008}
