Niamtougou Rainfall Models

Cleaning Up Our Data and Adding Months

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333`,21.2`,29.7`,383.1`},{2010.791667`,21.6`,30.5`,288.5`},{2010.875`,19.9`,33.96666667`,9.5`},{2010.958333`,18.2`,34.7`,0},{2011.041667`,19.23333333`,33.6`,0},{2011.125`,22.23333333`,35.06666667`,10},{2011.208333`,23.73333333`,35.73333333`,48.9`},{2011.291667`,23.43333333`,35.26666667`,60.9`},{2011.375`,23.16666667`,32.66666667`,102.9`},{2011.458333`,22.56666667`,30.46666667`,161.2`},{2011.541667`,22.03333333`,29.7`,154.3`},{2011.625`,21.46666667`,28.66666667`,197.2`},{2011.708333`,20.53333333`,29.66666667`,265.7`},{2011.791667`,19.66666667`,31.93333333`,112.8`},{2011.875`,17.31333333`,34.45666667`,0},{2011.958333`,17.36666667`,33.1`,0},{2012.041667`,17.3`,33.46666667`,0},{2012.125`,19.92333333`,34.69333333`,40.2`},{2012.208333`,21.87`,35.98`,0},{2012.291667`,21.91666667`,33.88`,88.4`},{2012.375`,20.57`,31.66666667`,278.1`},{2012.458333`,20.23333333`,29.83333333`,222.1`},{2012.541667`,20.17`,28.33`,230.2`},{2012.625`,20.49666667`,28.79666667`,170},{2012.708333`,20.04666667`,29.48666667`,190.8`},{2012.791667`,20.18333333`,31.74`,352.6`},{2012.875`,19.25333333`,33.58666667`,69},{2012.958333`,18.58666667`,34.94666667`,0},{2013.041667`,18.72666667`,34.34666667`,0},{2013.125`,20.78666667`,36.02666667`,3},{2013.208333`,23.07`,35.52666667`,50.7`},{2013.291667`,22.47666667`,34.07`,100.6`},{2013.375`,21.47`,32.16`,162.5`},{2013.458333`,20.88333333`,30.17666667`,124.6`},{2013.541667`,20.50333333`,29.14666667`,149},{2013.625`,20.28333333`,27.73`,134.1`},{2013.708333`,20.12333333`,29.48`,239.3`},{2013.791667`,20.21`,31.8`,178.7`},{2013.875`,19.25333333`,34.14`,33.7`},{2013.958333`,17.47333333`,33.62333333`,0},{2014.041667`,18.9`,34.21`,0.9`},{2014.125`,21.20666667`,35.67666667`,0},{2014.208333`,22.63333333`,36.04333333`,34.6`},{2014.291667`,22.35333333`,33.83`,98.7`},{2014.375`,22.01333333`,32.87`,121.6`},{2014.458333`,20.85666667`,31.35`,127.3`},{2014.541667`,21.00333333`,29.13`,130.7`},{2014.625`,20.08333333`,27.90666667`,170},{2014.708333`,19.96`,29.81333333`,345.6`},{2014.791667`,20.67666667`,31.76333333`,195},{2014.875`,19.76`,33.11666667`,41.1`},{2014.958333`,18.22666667`,34.73666667`,0},{2015.041667`,17.72`,33.18`,0},{2015.125`,20.8`,35.69666667`,18.2`},{2015.208333`,22.53333333`,35.34`,19.3`},{2015.291667`,23.25`,36.49`,6.9`},{2015.375`,22.54`,34.19`,94.1`},{2015.458333`,22.00666667`,32.41333333`,88.5`},{2015.541667`,21.13666667`,29.8`,262.5`},{2015.625`,21.09333333`,28.83`,218.8`},{2015.708333`,20.97`,30.13333333`,293.9`},{2015.791667`,21.44666667`,32.56`,193.7`},{2015.875`,18.62`,34.25`,0},{2015.958333`,17.68`,31.95666667`,0}};
monthNumber=Round[FractionalPart[Part[Transpose[originalData],1]]*12+.5];
data=Transpose[Append[Transpose[originalData],monthNumber]];

Rainfall Vs. Minimum Temperature

Scatter Plot

rainfallVsMinTemp=Transpose[{Part[Transpose[data],2],Part[Transpose[data],4]}];
rainfallVsMinTempScatterPlot=Show[ListPlot[rainfallVsMinTemp],AxesLabel->{HoldForm[Minimum Temperature °C],HoldForm[Rainfall mm]},PlotLabel->HoldForm[Rainfall Vs.Minimum Temperature],LabelStyle->{GrayLevel[0]},ImageSize->Large]

Linear Model

Graph

rainfallVsMinTempLinearModel=LinearModelFit[rainfallVsMinTemp,t, t]
Show[rainfallVsMinTempScatterPlot,Plot[rainfallVsMinTempLinearModel[t],{t,12,26},PlotStyle->Red]]

Parameter Table

rainfallVsMinTempLinearModel["ParameterTable"]

Residual Plot

Show[ListPlot[rainfallVsMinTempLinearModel["FitResiduals"],Filling->Axis,PlotLabel->HoldForm[Rainfall Vs. Minmimum Temperature Linear Model Residuals]],ImageSize->Large]

R-Squared

rainfallVsMinTempLinearModel["RSquared"]

Quadratic Model

Graph

rainfallVsMinTempQuadraticModel=LinearModelFit[rainfallVsMinTemp,{t,(t^2)}, t]
Show[rainfallVsMinTempScatterPlot,Plot[rainfallVsMinTempQuadraticModel[t],{t,12,26},PlotStyle->Red]]

Parameter Table

rainfallVsMinTempQuadraticModel["ParameterTable"]

Residual Plot

Show[ListPlot[rainfallVsMinTempQuadraticModel["FitResiduals"],Filling->Axis,PlotLabel->HoldForm[Rainfall Vs. Minmimum Temperature Residuals]],ImageSize->Large]

R-Squared

rainfallVsMinTempQuadraticModel["RSquared"]

Logarithmic Model

Graph

rainfallVsMinTempLogarithmicModel=LinearModelFit[rainfallVsMinTemp,{t,(t^2),Log[t]}, t]
Show[rainfallVsMinTempScatterPlot,Plot[rainfallVsMinTempLogarithmicModel[x],{x,12,26},PlotStyle->Red]]

Parameter Table

rainfallVsMinTempLogarithmicModel["ParameterTable"]

Residual Plot

Show[ListPlot[rainfallVsMinTempLogarithmicModel["FitResiduals"],Filling->Axis,PlotLabel->HoldForm[Rainfall Vs. Minmimum Temperature Residuals]],ImageSize->Large]

R-Squared

rainfallVsMinTempLogarithmicModel["RSquared"]

Rainfall Vs. Maximum Temperature

Scatter Plot

rainfallVsMaxTemp=Transpose[{Part[Transpose[data],3],Part[Transpose[data],4]}];
rainfallVsMaxTempScatterPlot=Show[ListPlot[rainfallVsMaxTemp],AxesLabel->{HoldForm[Maximum Temperature °C],HoldForm[Rainfall mm]},PlotLabel->HoldForm[Rainfall Vs.Maximum Temperature],LabelStyle->{GrayLevel[0]},ImageSize->Large]

Linear Model

rainfallVsMaxTempLinearModel=LinearModelFit[rainfallVsMaxTemp,t,t]
Show[rainfallVsMaxTempScatterPlot,Plot[rainfallVsMaxTempLinearModel[t],{t,26,40},PlotStyle->Red]]

Parameter Table

rainfallVsMaxTempLinearModel["ParameterTable"]

Residual Plot

Show[ListPlot[rainfallVsMaxTempLinearModel["FitResiduals"],Filling->Axis,PlotLabel->HoldForm[Rainfall Vs. Maximum Temperature Linear Model Residuals]],ImageSize->Large]

R-Squared

rainfallVsMaxTempLinearModel["RSquared"]

Quadratic Model

rainfallVsMaxTempQuadraticModel=LinearModelFit[rainfallVsMaxTemp,{t,(t^2)}, t]
Show[rainfallVsMaxTempScatterPlot,Plot[rainfallVsMaxTempQuadraticModel[t],{t,26,40},PlotStyle->Red]]

Parameter Table

rainfallVsMaxTempQuadraticModel["ParameterTable"]

Residual Plot

Show[ListPlot[rainfallVsMaxTempQuadraticModel["FitResiduals"],Filling->Axis,PlotLabel->HoldForm[Rainfall Vs. Maximum Temperature Quadratic Model Residuals]],ImageSize->Large]

R-Squared

rainfallVsMaxTempQuadraticModel["RSquared"]

Rainfall Vs. Time

Scatter Plot

rainfallVsTime=Transpose[{Part[Transpose[data],1],Part[Transpose[data],4]}];
rainfallVsTimeScatterPlot=Show[ListPlot[rainfallVsTime],AxesLabel->{HoldForm[Year],HoldForm[Rainfall mm]},PlotLabel->HoldForm[Rainfall Vs.Time],LabelStyle->{GrayLevel[0]},ImageSize->Large]

Oscillating Model

Graph

rainfallVsTimeOscillatingModel=LinearModelFit[rainfallVsTime,{Sin[2Pi*t],Cos[2Pi*t]},t]
Show[rainfallVsTimeScatterPlot,Plot[rainfallVsTimeOscillatingModel[t],{t,1961,2015},PlotStyle->Red]]

Parameter Table

rainfallVsTimeOscillatingModel["ParameterTable"]

Residual Plot

Show[ListPlot[rainfallVsTimeOscillatingModel["FitResiduals"],Filling->Axis,PlotLabel->HoldForm[Rainfall Vs. Time Oscillating Residuals]],ImageSize->Large]

R-Squared

rainfallVsTimeOscillatingModel["RSquared"]

Linear Oscillating Model

Graph

rainfallVsTimeLinearOscillatingModel=LinearModelFit[rainfallVsTime,{Sin[2Pi*t],Cos[2Pi*t],t},t]

Show[rainfallVsTimeScatterPlot,Plot[rainfallVsTimeLinearOscillatingModel[x],{x,1961,2015},PlotStyle->Red]]

Parameter Table

rainfallVsTimeLinearOscillatingModel["ParameterTable"]

Residual Plot

Show[ListPlot[rainfallVsTimeLinearOscillatingModel["FitResiduals"],Filling->Axis,PlotLabel->HoldForm[Rainfall Vs. Time Linear Oscillating Residuals]],ImageSize->Large]

R-Squared

rainfallVsTimeLinearOscillatingModel["RSquared"]

Monthly Averages

Average Minimum Temperatures

minimumTemperatureMonthlyAverages=Table[Mean[Part[Transpose[Select[data,Part[#,5]==n&]],2]],{n,1,12}];

Show[ListPlot[minimumTemperatureMonthlyAverages,Joined->True,Mesh->Full],AxesLabel->{HoldForm[Month],HoldForm[Temperature °C]},PlotLabel->HoldForm[Average Minimum Temperature by Month],LabelStyle->{GrayLevel[0]},ImageSize->Large]

Average Maximum Temperatures

maximumTemperatureMonthlyAverages=Table[Mean[Part[Transpose[Select[data,Part[#,5]==n&]],3]],{n,1,12}];

Show[ListPlot[maximumTemperatureMonthlyAverages,Joined->True,Mesh->Full],AxesLabel->{HoldForm[Month],HoldForm[Temperature °C]},PlotLabel->HoldForm[Average Maximum Temperature by Month],LabelStyle->{GrayLevel[0]},ImageSize->Large]

Rainfall

rainfallMonthlyAverages=Table[Mean[Part[Transpose[Select[data,Part[#,5]==n&]],4]],{n,1,12}];

Show[ListPlot[rainfallMonthlyAverages,Joined->True,Mesh->Full],AxesLabel->{HoldForm[Month],HoldForm[Rainfall (mm)]},PlotLabel->HoldForm[Average Rainfall by Month],LabelStyle->{GrayLevel[0]},ImageSize->Large]

Contour & 3D Plots

𝒟=SmoothKernelDistribution[Transpose[{Part[Transpose[data],2],Part[Transpose[data],3]}]];
contour=Show[ContourPlot[PDF[𝒟,{x,y}]//Evaluate,{x,Min[Part[Transpose[data],2]],Max[Part[Transpose[data],2]]},{y,Min[Part[Transpose[data],3]],Max[Part[Transpose[data],3]]},PlotRange->All,AxesLabel->{"Min","Max"},PlotPoints->50,Contours->15,ColorFunction->"TemperatureMap"],AxesLabel->{None,None},FrameLabel->{{HoldForm[Maximum Temperature °C],None},{HoldForm[Minimum Temperature °C],None}},PlotLabel->None,LabelStyle->{GrayLevel[0]},ImageSize->Large]

dens=Show[Plot3D[PDF[𝒟,{x,y}]//Evaluate,{x,Min[Part[Transpose[data],2]],Max[Part[Transpose[data],2]]},{y,Min[Part[Transpose[data],3]],Max[Part[Transpose[data],3]]},PlotRange->All,PlotPoints->50,ColorFunction->"TemperatureMap",AxesLabel->{"Min","Max","PDF"}],ImageSize->Large]
Show[ListPointPlot3D[Transpose[{mintemp,maxtemp,rain}],PlotRange->All,ColorFunction->"TemperatureMap",AxesLabel->{"Min","Max","Rainfall"}],ImageSize->Large]

Show[ListPointPlot3D[Transpose[{Floor[Part[Transpose[data],1]],Part[Transpose[data],5],Part[Transpose[data],4]}],PlotRange->All,ColorFunction->"TemperatureMap",AxesLabel->{"Year","Month of the Year","Rainfall"}],ImageSize->Large]

Models for Minimum and Maximum Temperature Over Time

minTempModel=LinearModelFit[Transpose[{Part[Transpose[data],1],Part[Transpose[data],2]}],{t,Sin[2Pi*t],Cos[2Pi*t],Sin[4Pi*t],Cos[4Pi*t]},t]

minTempModel["ParameterTable"]

maxTempModel=LinearModelFit[Transpose[{Part[Transpose[data],1],Part[Transpose[data],3]}],{t,Sin[2Pi*t],Cos[2Pi*t],Sin[4Pi*t],Cos[4Pi*t]},t]

maxTempModel["ParameterTable"]

scaleRain=Part[Transpose[data],4]*.03/Max[Part[Transpose[data],4]];
Manipulate[
p1=ListPlot[{{Part[Transpose[data],2][[t]],Part[Transpose[data],3][[t]]}},PlotRange->All,PlotStyle->{Black,PointSize[0.02+scaleRain[[t]]]}];
p2=ListPlot[{{minTempModel[Part[Transpose[data],1][[t]]],maxTempModel[Part[Transpose[data],1][[t]]]}},PlotRange->All,PlotStyle->{Blue,PointSize[0.02+Max[{0,rainfallVsTimeOscillatingModel[Part[Transpose[data],1][[t]]]}]*.03/Max[Part[Transpose[data],4]]]}];
Show[contour,p1,p2],
{{t,1},1,Length[Part[Transpose[data],4]],1}
]