Wolfram Data Repository

Immediate Computable Access to Curated Contributed Data

Mississippi River Flood Heights

Source Notebook

Maximum annual Mississippi River flood at Vicksburg, MS from 1922 to 2014

Details

This dataset contains the observed annual maximum flood heights (in feet) of the Mississippi River for the years 1922–2014. Each value represents a block maximum derived from daily measurements within a given year.
The data were recorded at a flood gauge located 1.6 miles downstream from the mouth of the Yazoo Diversion Canal, near river mile 435.4. The gauge is positioned at longitude 90.902332° W and latitude 32.311832° N. The designated flood stage at this location is 43 feet, while the highest recorded stage is 57.1 feet, measured on May 19, 2011.

(2 columns, 101 rows)

Examples

Basic Examples

In[1]:=
ResourceData[\!\(\* TagBox["\"\<Mississippi River Flood Heights\>\"", #& , BoxID -> "ResourceTag-Mississippi River Flood Heights-Input", AutoDelete->True]\)]
Out[1]=

Visualizations (1) 

Plot the maximum river flood height by year:

In[2]:=
dataset = ResourceData[\!\(\* TagBox["\"\<Mississippi River Flood Heights\>\"", #& , BoxID -> "ResourceTag-Mississippi River Flood Heights-Input", AutoDelete->True]\)]; ListPlot[dataset, Axes -> False, Frame -> True, PlotRange -> {20, 60}, FrameLabel -> {"year", "max flood (ft)"}]
Out[3]=

Analysis (4) 

The river flood data are of the form annual block maxima and can be modeled by the MaxStableDistribution. Goodness of fit can be assessed by comparing the observed and theoretical cumulative distribution functions. By convention the observed cumulative probability density at year i is defined to be CDF(i)=(m+1)-1i where m=101 is the number of years that data were recorded. Plot the measured and theoretical values, respectively shown as points and a solid line:

In[4]:=
dataset = ResourceData[\!\(\* TagBox["\"\<Mississippi River Flood Heights\>\"", #& , BoxID -> "ResourceTag-Mississippi River Flood Heights-Input", AutoDelete->True]\)]; year = Table[dataset[[i]][[1]], {i, 101}]; flood = Table[dataset[[i]][[2]], {i, 101}]; z = Sort[flood]; m = Length[flood]; edist1 = EstimatedDistribution[z, MaxStableDistribution[\[Mu], \[Sigma], k]]; {\[Mu]est, \[Sigma]est, kest} = {edist1[[1]], edist1[[2]], edist1[[3]]}; (*Ref: Coles(2004) chapter2, p. 36. *) CDFMeasured = N[1/(m + 1) Table[i, {i, 1, m}]]; CDFModeled = Table[CDF[edist1, z[[i]]], {i, 1, m}]; ListPlot[{Transpose[{z, CDFMeasured}], Transpose[{z, CDFModeled}]}, Joined -> {False, True}, PlotStyle -> {{PointSize[0.01], Black}, Blue}, Axes -> False, Frame -> True, FrameLabel -> {"return period (years)", "cumulative probability density"}]
Out[5]=

Create a Histogram of the observed maximum annual river heights compared to the theoretical probability density function for the MaxStableDistribution fit:

In[6]:=
g1 = Histogram[z, {20, 70, 3}, "PDF", Axes -> False, Frame -> True, FrameLabel -> {"maxannual river height (ft)", "probability density"}]; g2 = Plot[PDF[edist1, h], {h, 20, 70}, Axes -> False, Frame -> True, FrameLabel -> {"max annual river height (ft)", "probability density"}]; Show[g1, g2]
Out[8]=

The return period (in years) to obtain a flood of height z is (1-CDF(z))-1. Compare the observed return periods to the theoretical return period values predicted by the MaxStableDistribution:

In[9]:=
Tobs = 1/(1 - CDFMeasured); Tmod = 1/(1 - CDFModeled); returnobs = Transpose[{Tobs, z}]; returnmod = Transpose[{Tmod, z}]; ListLogLinearPlot[{returnobs, returnmod}, PlotRange -> {{0.9, 101}, {20, 60}}, Joined -> {False, True}, PlotStyle -> {{PointSize[0.01], Black}, Blue}, AspectRatio -> 1, Axes -> False, Frame -> True, FrameLabel -> {"return period (years)", "return height of annual max flood(ft)"}]
Out[11]=

In order to further analyze the difference between observed and theoretical return periods, 95% error bars are placed on the theoretical curves. These error bars are computed using method of error calculation. In this technique the method of least squares refinement is used to place error bounds on the three fit parameters in the MaxStableDistribution. The upper and lower bounds on these three parameters are used in turn to compute an upper and lower range on the return period-return height curve. The resulting error bars are shown in red:

In[12]:=
n\[Sigma] = 1.96; del = CDFMeasured - CDFModeled; SSD = del . del; \[Sigma]calc = (SSD/(m - 3))^(1/2); Clear[\[Mu], \[Sigma], k]; Arow = {D[E^-(1 + (k (x - \[Mu]))/\[Sigma])^(-1/k), \[Mu]], D[E^-(1 + (k (x - \[Mu]))/\[Sigma])^(-1/k), \[Sigma]], D[E^-(1 + (k (x - \[Mu]))/\[Sigma])^(-1/k), k]}; A = Table[ Arow /. {x -> z[[i]], \[Mu] -> edist1[[1]], \[Sigma] -> edist1[[2]], k -> edist1[[3]]}, {i, 1, m}]; P = Inverse[ Transpose[A] . A]; COV = \[Sigma]calc^2 P; {\[Sigma]\[Mu], \[Sigma]\[Sigma], \[Sigma]k} = Sqrt@Diagonal[COV]; returnmin = {}; returnmax = {}; Do[cdfmin = CDF[MaxStableDistribution[\[Mu]est - n\[Sigma]*\[Sigma]\[Mu], \[Sigma]est - n\[Sigma]*\[Sigma]\[Sigma], kest - n\[Sigma]*\[Sigma]k], z[[j]]]; cdfmax = CDF[MaxStableDistribution[\[Mu]est + n\[Sigma]*\[Sigma]\[Mu], \[Sigma]est + n\[Sigma]*\[Sigma]\[Sigma], kest + n\[Sigma]*\[Sigma]k], z[[j]]]; If[cdfmin < 1, returnmin = Join[returnmin, {{1/(1 - cdfmin), z[[j]]}}]]; If[cdfmax < 1, returnmax = Join[returnmax, {{1/(1 - cdfmax), z[[j]]}}]]; , {j, 1, Length[z]}]; ListLogLinearPlot[{returnobs, returnmod, returnmin, returnmax}, PlotRange -> {{0.9, 101}, {20, 60}}, Joined -> {False, True, True, True}, PlotStyle -> {{PointSize[0.01], Black}, Blue, Red, Red}, AspectRatio -> 1, Axes -> False, Frame -> True, FrameLabel -> {"return period (years)", "return height of annual max flood(ft)"}]
Out[20]=

Marshall Bradley, "Mississippi River Flood Heights" from the Wolfram Data Repository (2026)  

Data Resource History

  • Date Created:

Source Metadata

  • Citation: Source, reference or citation information

Publisher Information

  • Prepared for the Wolfram Data Repository By: Marshall Bradley
  • Publisher of Record: Marshall Bradley