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In[]:=
data=Transpose[{year,month,rain}];
In[]:=
ListDensityPlot[data,ImageSize700,ColorFunction"Rainbow",AspectRatio1/3,GridLinesAutomatic,FrameLabel{Style["Year from 1986 ",16,Black],Style["Month of the year",16,Black]},FrameTicksStyleDirective[Black,14],PlotRangePaddingNone,ScalingFunctions{None,"Reverse"},PlotLegendsPlaced[Automatic,Right],LabelStyle{FontSize14}]
Out[]=