[R] Question regarding reservoir volume and water level

Mon Apr 8 05:55:59 CEST 2024

Dear all;
Many thanks for your replies. This was not homework. I apologize.
Let me explain more.
There is a dam constructed in a valley with the highest elevation of 1255
m. The area of its reservoir can be calculated by drawing a polygon around
the water and it is known.
I have the Digital Elevation Model (DEM) of the region (reservoir and its
surrounding area). I have calculated the volume of the current reservoir
(7e6 m3) using the following codes.
library(raster)
library(terra)
library(exactextractr)
library(dplyr)
library(sf)
# Calculate volume for polygon
# Read the DEM raster file
r <- rast("E:/...DEM.tif")
# Read the polygon shapefile
p <- st_read("E:/...Dam.shp")

r <- crop(r, extent(p))
r <- mask(r, p)

# Extract the cells in each polygon and calculate the area of each cell
x <- exact_extract(r, p, coverage_area = TRUE)
# Extract polygon values as a dataframe
x1 = as.data.frame(x[1])
head(x1)
x1 = na.omit(x1)
# Calculate the height above the minimum elevation in the polygon
x1$Height = max(x1[,1]) - x1[,1]
# Calculate the volume of each cell
x1$Vol = x1[,2] * x1[,3]
sum(x1$Vol)
x2 = x1[,c(1,2,4)]
x2 = sort(x2,'value')
head(x2)
x3 <- aggregate(Vol ~ value, data = x2, FUN = sum)
x4 <- aggregate(coverage_area ~ value, data = x2, FUN = sum)
x5 = cbind(x3, Area = x4[,2])
library(dplyr)
x6 <- x5 %>%
  mutate(V_sum = cumsum(Vol)) %>%
  mutate(A_sum = cumsum(Area))
plot(x6$value~x6$V_sum)

And I thought that it is possible to get the elevation for a specific
volume by linear model between elevation and volume, as follow:

# Get a linear model between elevation and the volume
lm1 <- lm(value ~ V_sum, data = x6)
d <- data.frame(V_sum = 14e6)  #
predict(lm1, newdata = d)

But it is not possible through the LM.
Now I want to know what would be the water level in the reservoir if the
reservoir volume doubled or we adding a known volume to it?
Also what would be the volume if the water level increases to 1250 m?

I would be more than happy if you help me to do this.
Sincerely

On Mon, Apr 8, 2024 at 12:23 AM <avi.e.gross using gmail.com> wrote:

> John,
>
> Your reaction was what my original reaction was until I realized I had to
> find out what a DEM file was and that contains enough of the kind of
> depth-dimension data you describe albeit what may be a very irregular cross
> section to calculate for areas and thence volumes.
>
> If I read it correctly, this can be a very real-world problem worthy of a
> solution, such as in places like California where they had a tad more rain
> than usual and some reservoirs may overflow. Someone else provided what
> sounds like a mathematical algorithm but my guess is what is needed here is
> perhaps less analytic since there may be no trivial way to create formulas
> and take integrals and so on, but simply an approximate way to calculate
> incremental volumes for each horizontal "slice" and keep adding or
> subtracting them till you reach a target and then read off another variable
> at that point such as depth.
>
> Some care must be taken as water level has to be relative to something and
> many natural reservoirs have no unique bottom level. Some water may also be
> stored underground and to the side and pour in if the level lowers or can
> be
> used to escape if the level rises.
>
>
> -----Original Message-----
> From: R-help <r-help-bounces using r-project.org> On Behalf Of Sorkin, John
> Sent: Sunday, April 7, 2024 3:08 PM
> To: Rui Barradas <ruipbarradas using sapo.pt>; javad bayat <j.bayat194 using gmail.com
> >;
> R-help <R-help using r-project.org>
> Subject: Re: [R] Question regarding reservoir volume and water level
>
> Aside from the fact that the original question might well be a class
> exercise (or homework), the question is unanswerable given the data given
> by
> the original poster. One needs to know the dimensions of the reservoir,
> above and below the current waterline. Are the sides, above and below the
> waterline smooth? Is the region currently above the waterline that can
> store
> water a mirror image of the region below the waterline? Is the region above
> the reservoir include a flood plane? Will the additional water go into the
> flood plane?
>
> The lack of required detail in the question posed by the original poster
> suggests that there are strong assumptions, assumptions that typically
> would
> be made in a class-room example or exercise.
>
> John
>
> John David Sorkin M.D., Ph.D.
> Professor of Medicine, University of Maryland School of Medicine;
> Associate Director for Biostatistics and Informatics, Baltimore VA Medical
> Center Geriatrics Research, Education, and Clinical Center;
> PI Biostatistics and Informatics Core, University of Maryland School of
> Medicine Claude D. Pepper Older Americans Independence Center;
> Senior Statistician University of Maryland Center for Vascular Research;
>
> Division of Gerontology and Paliative Care,
> 10 North Greene Street
> GRECC (BT/18/GR)
> Baltimore, MD 21201-1524
> Cell phone 443-418-5382
>
>
>
>
> ________________________________________
> From: R-help <r-help-bounces using r-project.org> on behalf of Rui Barradas
> <ruipbarradas using sapo.pt>
> Sent: Sunday, April 7, 2024 10:53 AM
> To: javad bayat; R-help
> Subject: Re: [R] Question regarding reservoir volume and water level
>
> Às 13:27 de 07/04/2024, javad bayat escreveu:
> > Dear all;
> > I have a question about the water level of a reservoir, when the volume
> > changed or doubled.
> > There is a DEM file with the highest elevation 1267 m. The lowest
> elevation
> > is 1230 m. The current volume of the reservoir is 7,000,000 m3 at 1240 m.
> > Now I want to know what would be the water level if the volume rises to
> > 1250 m? or what would be the water level if the volume doubled
> (14,000,000
> > m3)?
> >
> > Is there any way to write codes to do this in R?
> > I would be more than happy if anyone could help me.
> > Sincerely
> >
> >
> >
> >
> >
> >
> >
> >
> Hello,
>
> This is a simple rule of three.
> If you know the level l the argument doesn't need to be named but if you
> know the volume v then it must be named.
>
>
> water_level <- function(l, v, level = 1240, volume = 7e6) {
>    if(missing(v)) {
>      volume * l / level
>    } else level * v / volume
> }
>
> lev <- 1250
> vol <- 14e6
>
> water_level(l = lev)
> #> [1] 7056452
> water_level(v = vol)
> #> [1] 2480
>
>
> Hope this helps,
>
> Rui Barradas
>
>
> --
> Este e-mail foi analisado pelo software antivírus AVG para verificar a
> presença de vírus.
> http://www.avg.com/
>
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.r-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>

-- 
Best Regards
Javad Bayat
M.Sc. Environment Engineering
Alternative Mail: bayat194 using yahoo.com

	[[alternative HTML version deleted]]