Required Data Frames

The following table provides definitions of the four data frames that constitute the named list eBoot

There is also a data frame called caseSetUp (created with the trendSetUp function), which contains a number of important parameters that define the way that the test was implemented. They are presented here.

Histograms

The function plotHistogramTrend plots a histogram of all of the trend magnitudes (expressed in percentage change over the selected period) from the full set of replicates created by wBT. These magnitudes are stored in the eBoot list. These histograms serve the purpose of providing a graphical impression of the central tendency and the uncertainty about the size of a trend. They can be used to help answer questions like: “How sure are we that the trend is positive?” or “How sure are we that the decrease is at least a 20% decrease over the period of interest?” The plotHistogramTrend function can produce histograms either for Flow Normalized Concentration or for Flow Normalized Flux.

When creating a histogram it is important to carefully determine what “bins” to use. In this plot it is a good idea to make sure that the plot covers a range of both negative and positive values even though it might be the case that the entire range of the trend magnitudes is positive (or negative). The function is set up so that it defaults to setting up 10 bins and the bins are set to cover the full range of the magnitudes and at least cover magnitudes as low as -10% and as high as +10%. The bins are set up based on a minimum value (xMin), a maximum value (xMax), and a step size (xStep). The defaults used in an initial run can simply leave out these three arguments and will produce a plot. This first plot would not be suitable for publication or display, but is intended to guide the analyst to set these three arguments to produce a suitable plot.

Ulimately we want a plot with these characteristics: The value of xStep should be an integer such as 5, 10, or 20 so the width of the bins is 5%, 10% or 20%. xStep should be small enough so that the histogram looks relatively smooth. If it is too small the histogram bars will tend to be irregular. xStep should not be so large that there is poor resolution of the shape of the distribution. If a very smooth histogram is desired then the analyst needs to have run the wBT function with a high number of replicates (say nBoot = 200). The value of xStep should be less than the minimum value observed in the set of bootstrap replicates. xMin should be some negative integer multiple of step size. If no values were negative, then setting it at -1 times xStep would be a good choice. xMax should be larger than the maximum value in the set of bootstrap replicates and should be some positive integer multiple of xStep. If there are no positive values then 1 times xStep would be a good choice.

Note that the plots always show a vertical solid line at 0% trend, simply as a point of reference for the “no trend” result. They also show a dashed vertical line at the value of the ordinary WRTDS estimate of the trend magnitude in percent. This vertical line fall near the median value for all the bootstrap replicates.

This initial run will give the analyst the basic information needed to set up a good set of values for xMin, xMax and xStep.

library(EGRET)
library(EGRETci)

# Example data included in package:
eList <- Choptank_eList # Example data from EGRET package
eBoot <- Choptank_eBoot
caseSetUp <- Choptank_caseSetUp

#Concentration an initial run:
plotHistogramTrend(eList, eBoot, caseSetUp,  
                   flux=FALSE)

#Flux an initial run:
plotHistogramTrend(eList, eBoot, caseSetUp,
                   flux=TRUE)

Having seen these initial versions of the plot one can run the functions again with a set of arguments that will produce a plot that is suitable for presentation or publication.

Alternatively, the two plots can be shown side-by-side using a workflow. Use the par function to set up both functions to plot side-by-side:

par(mfrow=c(1,2))
#Concentration, presentation version:
plotHistogramTrend(eList, eBoot, caseSetUp,  
                   flux=FALSE, xMin = -5, xMax = 65, xStep = 5)

#Flux, presentation version:
plotHistogramTrend(eList, eBoot, caseSetUp,
                   flux=TRUE, xMin = -5, xMax = 55, xStep = 5)

# To return to figures printing in 1 row, 1 columns:
par(mfrow=c(1,1))                   

Or:

par(mfrow=c(2,1))
#Concentration, presentation version:
plotHistogramTrend(eList, eBoot, caseSetUp,  
                   flux=FALSE, xMin = -5, xMax = 65, xStep = 5)

#Flux, presentation version:
plotHistogramTrend(eList, eBoot, caseSetUp,
                  flux=TRUE, xMin = -5, xMax = 65, xStep = 5,
                  printTitle = FALSE)

# To return to figures printing in 1 row, 1 columns:
par(mfrow=c(1,1))                   

Introduction

The purpose here is to produce a graphic that looks just like those produced by plotConcHist or plotFluxHist but with the addition of confidence bands around the flow-normalized histories. There are two versions of the workflow for confidence bands, the first just uses a single computer core which means it takes a long time to run (jobs can take an hour or more), but it is simple to run. It uses the function ciCalculations and can be run interactively or in batch. Two scripts for that are provided below. It is best done in the Terminal or some other window, rather than in the console. If run in the console it will make it impossible for other work in R to take place while the job is running. The second way it can be done is using parallel computing in R. A script for that purpose is provided. It does require three extra packages be installed (foreach, doParallel, and iterators). It is also best to run this in the Terminal, because if it is run in the console, no other R work can be done while it is running.

Preliminary Steps

Regardless of the approach (single core or parallel) being taken to the computations, the user needs to set up any non-default values of the parameters for model estimation and period of analysis. For example:

If the period of analysis is to be anything other than a Water Year (paStart=10, paLong=12), the user must use the setPA function. For example if we want to do the analysis for the three months starting with April, the command would be eList <- setPA(eList, paStart = 4, paLong = 3).

If the desired value of windowY was 10 rather than the default value of 7, then the command needed would be eList$INFO$windowY <- 10, similar commands can be used for windowQ, windowS, minNumObs, minNumUncen and EdgeAdjust (see help page for modelEstimation).

It is imperative that the standard WRTDS trend analysis be run prior to running the code for the confidence bands. If the user has made changes in smoothing parameters or modified the data in any way since the last time modelEstimation was run, the standard running of modelEstimation must be done and the output saved as eList. The commands would be:

eList <- modelEstimation(eList)

Simple Workflow

This example workflow assumes that we use the default values for all of the model parameters and PA and uses the example eList provided in the package. Remember, this is a very long-running process:

library(EGRET)
library(EGRETci)

eList <- Choptank_eList

CIAnnualResults <- ciCalculations(eList)

save(eList,CIAnnualResults, file="CIAnnualResults.RData")

To run the ciCalculations function in batch mode, the only difference is that additional arguments are specified in the call to the function. For example the call to ciCalculations might read as follows:

CIAnnualResults <- ciCalculations(eList, nBoot = 100, blockLength = 200, widthCI = 90)

As long as all required arguments (nBoot, blockLength, and widthCI) are specified there will be no interaction needed.

Parallel Computing

Taking advantage of the foreach package to do parallel computing:

library(foreach)
library(doParallel)
library(iterators)
library(EGRET)
library(EGRETci)

eList <- Choptank_eList
eList <- modelEstimation(eList) 

nBoot <- 100
blockLength <- 200
coreOut <- 1 #Number of cores to leave out of processing tasks

widthCI <- 90
ciLower <- (50-(widthCI/2))/100
ciUpper <- (50+(widthCI/2))/100
probs <- c(ciLower,ciUpper)

nCores <- detectCores() - coreOut
cl <- makeCluster(nCores)
registerDoParallel(cl)
repAnnual <- foreach(n = 1:nBoot,.packages=c('EGRETci')) %dopar% {
   annualResults <- bootAnnual(eList, 
                               blockLength,
                               startSeed = n)  
}
stopCluster(cl)               

# save(repAnnual, file="repAnnual.RData")

CIAnnualResults <- ciBands(eList, repAnnual, probs)
save(eList,CIAnnualResults, file="CIAnnualResults.RData")

CI Result Plots

Regardless of the way that the computations are done the outputs that are needed for the graphics are contained in eList and CIAnnualResults (which in either script will end up in a file called CIAnnualResults.RData). Once that file is loaded the graphics can be produced using the functions plotConcHistBoot and plotFluxHistBoot. Each of these functions only require two arguments (eList and CIAnnualResults). However, the user can specify a number of other arguments. These other arguments are the same ones used in the plotConcHist and plotFluxHist functions in the base EGRET package.

The user can also view a table of the confidence interval values shown in these graphics simply by using the command CIAnnualResults (fluxes will be in units if kg/day).

Here is a script for producing these graphics, using the example eList and CIAnnualResults data frames included in the package.

eList <- Choptank_eList

CIAnnualResults <- Choptank_CIAnnualResults

plotConcHistBoot(eList, CIAnnualResults)

plotFluxHistBoot(eList, CIAnnualResults)