Fitting Wave Height Data to a Probability Distribution - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Applications and Example Worksheets : Science and Engineering : applications/WaveHeight

Fitting Wave Height Data to a Probability Distribution

Introduction

The University of Maine records real-time accelerometer data from buoys deployed in the Gulf of Maine and the Caribbean (http://gyre.umeoce.maine.edu/buoyhome.php). The data can be downloaded from their website, and includes the significant wave height recorded at regular intervals for the last few months.

 

This application does the following:

 

• 

Downloads accelerometer data for Buoy PR206 (located just off the coast of Puerto Rico at a latitude of 18° 28.46' N and a longitude of 66° 5.94' W)

• 

Fits the significant wave height to a Weibull distribution by using two methods: maximum likelihood estimation and moment matching

• 

Plots the fitted distributions on top of a histogram of the experimental data

 

The Google Maps component below gives the location of buoy PR206.

 

Latitude

Longitude

Zoom Level

Map Type

 

 

 

 

 

 

 

 

 

 

Download and Plot Significant Wave Height Data in a Histogram

restart:

withplots:withStatistics:withOptimization:

urlhttp://gyre.umeoce.maine.edu/data/gomoos/buoy/php/view_csv_file.php?ncfile=/data/gomoos/buoy/archive/PR206/realtime/PR206.waves.triaxys.realtime.nc:

dataImportMatrixurl

data 8274 x 6 MatrixData Type: anythingStorage: rectangularOrder: Fortran_order

(2.1)

sigWaveHeightRemoveNonNumericdata..,2:

nnumelemssigWaveHeight

n8273

(2.2)

numBins40:

p1HistogramsigWaveHeight,bincount=numBins,color=COLORRGB,150255,40255,27255,thickness=0,style=patchnogrid,transparency=0.5,background=ColorTools:-ColorRGB,236255,240255,241255,axis=gridlines=10,color=RGB1,1,1,axesfont=Arial,labels=Significant Wave Height (m),Distribution,labeldirections=horizontal,vertical,labelfont=Arial,size=800,500:

displayp1

Maximum Likelihood Estimation

PunapplyProbabilityDensityFunctionWeibullalpha,beta,t,t,alpha,beta

Pt&comma;α&comma;β0t<0βt1+β&ExponentialE;tαβαβotherwise

(3.1)

maxLike:=α&comma;βaddlnPsigWaveHeighti&comma;α&comma;β&comma;i&equals;1..n&colon;

resultsMLEMaximizemaxLikeα&comma;β&comma;&alpha;&equals;0.01..5&comma;&beta;&equals;0.01..5

resultsMLE−4839.27465547207703&comma;α=1.34452570778020&comma;β=2.83250005643047

(3.2)

p2plotevalPt&comma;alpha&comma;beta&comma;resultsMLE2 &comma;t&equals;minsigWaveHeight..maxsigWaveHeight&comma;color&equals;black&comma;legend&equals;Maximum Likelihood Estimation&comma;thickness&equals;3&comma;legendstyle&equals;font&equals;Arial&colon;

Moment Matching

resultsMM:=fsolveMomentsigWaveHeight&comma;1&equals;MomentWeibull&alpha;&comma;&beta;&comma;1&comma;MomentsigWaveHeight&comma;2&equals;MomentWeibull&alpha;&comma;&beta;&comma;2&comma;&alpha;&equals;1&comma;&beta;&equals;1

resultsMMα=1.342796022&comma;β=2.958762705

(4.1)

p3plotevalPt&comma;alpha&comma;beta&comma;resultsMM &comma;t&equals;minsigWaveHeight..maxsigWaveHeight&comma;color&equals;RGB150255&comma;40255&comma;27255&comma;thickness&equals;3&comma;legend&equals;Moment Matching&comma;legendstyle&equals;font&equals;Arial&colon;

Results

displayp1&comma;p2&comma;p3&comma;size&equals;800&comma;500