[R] Finding center of mass in a hydrologic time series

[Morway, Eric]

Eric B's response provided just the kind of quick & simple solution I was
hoping for (appears as the function com below).  However, I once again
failed to take advantage of the power of R and have reverted back to using
a for loop for the next step of the processing.  The example below (which
requires the library EGRET for pulling an example dataset) works, but
probably can be replaced with some version of the apply functionality?  So
far, I've been unable to figure out how to enter the arguments to the apply
function.  The idea is this: for each unique water year (variable 'wyrs' in
example below) in a 27 year continuous time series of daily values, find
the date of the 'center of mass', and build a vector of those dates.
Thanks, -Eric M

library(EGRET)

StartDate <- "1990-10-01"
EndDate <- "2017-09-30"
siteNumber <- "10310000"
QParameterCd <- "00060"

Daily <- readNWISDaily(siteNumber, QParameterCd, StartDate, EndDate)

# Define 'center of mass' function
com <- function(x) {
    match(TRUE, cumsum(x/sum(x)) > 0.5) - 1
}


wyrs <- unique(Daily$waterYear)
for(i in (1:length(wyrs))){
    OneYr <- Daily[Daily$waterYear==wyrs[i], ]
    mid <- com(OneYr$Q)
    if(i==1){
        midPts <- as.Date(OneYr$Date[mid])
    } else {
        midPts <- c(midPts, as.Date(OneYr$Date[mid]))
    }
}



Eric Morway
Research Hydrologist
Nevada Water Science Center
U.S. Geological Survey
2730 N. Deer Run Rd.
Carson City, NV 89701
(775) 887-7668
*orcid*:  0000-0002-8553-6140 <http://orcid.org/0000-0002-8553-6140>



On Sat, Dec 16, 2017 at 5:32 AM, Eric Berger <ericjberger at gmail.com> wrote:

> Hi Eric,
> How about
>
> match( TRUE, cumsum(hyd/sum(hyd)) > .5 ) - 1
>
> HTH,
> Eric
>
>
> On Sat, Dec 16, 2017 at 3:18 PM, Morway, Eric <emorway at usgs.gov> wrote:
>
>> The small bit of script below is an example of what I'm attempting to do -
>> find the day on which the 'center of mass' occurs.  In case that is the
>> wrong term, I'd like to know the day that essentially cuts the area under
>> the curve in to two equal parts:
>>
>> set.seed(4004)
>> Date <- seq(as.Date('2000-09-01'), as.Date('2000-09-30'), by='day')
>> hyd <- ((100*(sin(seq(0.5,4.5,length.out=30))+10) +
>> seq(45,1,length.out=30)) + rnorm(30)*8) - 800
>>
>> # View the example curve
>> plot(Date, hyd, las=1)
>>
>> # By trial-and-error, the day on which the center of mass occurs is the
>> 11th day:
>> # Add up the area under the curve for the first 11 days and compare
>> # with the last 19 days:
>>
>> sum(hyd[1:11])
>> # 3546.364
>> sum(hyd[12:30])
>> # 3947.553
>>
>> # Add up the area under the curve for the first 12 days and compare
>> # with the last 18 days:
>>
>> sum(hyd[1:12])
>> # 3875.753
>> sum(hyd[13:30])
>> # 3618.164
>>
>> By day 12, the halfway point has already been passed, so the answer that
>> would be returned would be:
>>
>> Date[11]
>> # "2000-09-11"
>>
>> For the larger problem, it'd be handy if the proposed function could
>> process a multi-year time series (a runoff hydrograph) and return the day
>> of the center of mass for each year in the time series.
>>
>> I appreciate any pointers...Eric
>>
>>         [[alternative HTML version deleted]]
>>
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>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>

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