# iccsa-21-wind

git clone https://git.igankevich.com/iccsa-21-wind.git
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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}.

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}