\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{pgfplots}
\usepgfplotslibrary{patchplots}

\begin{document}
\begin{preview}
\pgfplotsset{
    colormap={whitered}{
        color(0cm)=(white);
        color(1cm)=(orange!75!red)
    }
}
\begin{tikzpicture}
    \begin{axis}[
    colormap name=whitered,
    width=15cm,
    view={45}{45},
    enlargelimits=false,
    grid=major,
    domain=-90:90,
    y domain=-90:90,
    % ymode=log,
    samples=46, %57 : TeX capacity exceeded, sorry [main memory size=3000000].
                % see also http://tex.stackexchange.com/a/7954/5645
    % zlabel=f,
    %colorbar,
    %colorbar style={
    %    at={(-0.1,0)},
    %    anchor=south west,
    %    height=0.25*\pgfkeysvalueof{/pgfplots/parent axis height},
    %    title={$f(x,y)$}
    %}
    ]
      %\addplot3[patch,patch type=bilinear,mesh,black] {0};
      \addplot3[blue,/pgfplots/quiver,
        quiver/u=4 * sin(x) * cos(x) * (cos(x)^2 + cos(y)^2),
        quiver/v=4 * sin(y) * cos(y) * (cos(x)^2 + cos(y)^2),
        quiver/w=0,
        quiver/scale arrows=4,
        -stealth,samples=15] {-4};
      \addplot3[surf,opacity=0.9] {-(cos(x)^2 + cos(y)^2)^2};
    \end{axis}
\end{tikzpicture}
\end{preview}
\end{document}