| Title: | Lake Physics Tools |
|---|---|
| Description: | Standardized methods for calculating common important derived physical features of lakes including water density based based on temperature, thermal layers, thermocline depth, lake number, Wedderburn number, Schmidt stability and others. |
| Authors: | Luke Winslow, Jordan Read, Richard Woolway, Jennifer Brentrup, Taylor Leach, Jake Zwart, Sam Albers, Doug Collinge |
| Maintainer: | Luke Winslow <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.12.0 |
| Built: | 2024-11-10 05:15:12 UTC |
| Source: | https://github.com/gleon/rlakeanalyzer |
Estimates a depth-area curve for a lake using lake surface area, maximum depth and mean depth. Two methods for estimating the curve are available; 'cone' assumes the lake is shaped as a cone and requires only surface area and maximum depth; "voldev" uses the volume development (Vd) parameter from Hakanson (1981) and Johansson et al. (2007). Vd is a dimensionless parameter that describes lake basin shape in relation to the volume of cone whose base area and height equal the surface area and maximum lake depth, it is estimated as Vd = Zmean/Zmax (Hakanson et al. 2000). Method "voldev' requires lake surface area, mean and maximum depth. Depths at which the area is estimated can be set by as a numeric vector or as a regularly spaced sequence.
approx.bathy(Zmax, lkeArea, Zmean = NULL, method = "cone", zinterval = 1, depths = seq(0, Zmax, by = zinterval))approx.bathy(Zmax, lkeArea, Zmean = NULL, method = "cone", zinterval = 1, depths = seq(0, Zmax, by = zinterval))
Zmax |
a single value of the maxiumum depth of the lake (in m) |
lkeArea |
a sinlge value of the surface area of the lake (in m^2) |
Zmean |
a single value of the mean depth of the lake (in m) |
method |
specifies the method used to estimate depth-area relationship, can be "cone"(default) or "voldev". Method "voldev" requires Zmean. See notes for details. |
zinterval |
a sinlge value defining the depth interval at which volumes should be calculated, default is 1 m. |
depths |
a numeric vector of depths (in m) at which areas are estimated. If not specified depths is regularly spaced sequence of values with the interval set by zinterval. |
a dataframe which defines the lake area for each depth. Columns are depths (m) and Area.at.z (m^2). Area at 0 m should equal the user entered lkeArea.
Hakanson, L. (1981). On lake bottom dynamics - the energy- topography factor. Canadian Journal of Earth Sciences, 18, 899-909. Johansson, H., A. A. Brolin, and L. Hakanson. 2007. New approaches to the modelling of lake basin morphometry. Environ. Model. Assess. 12: 213-228.
Voldev.ex = approx.bathy(Zmax = 25, Zmean = 12, lkeArea = 39400000, method = "voldev") Voldevshallow.ex = approx.bathy(Zmax = 25, Zmean = 6, lkeArea = 39400000, method = "voldev") Cone.ex = approx.bathy(Zmax = 25, lkeArea = 39400000, method = "cone") # plot depth-area curves plot(Cone.ex$depths ~ Cone.ex$Area.at.z, xlab = "Area (m^3)", ylab = "Depth (m)", ylim = rev(range(Cone.ex$depths))) points(Voldev.ex$depths ~ Voldev.ex$Area.at.z, col = "red", ylim = rev(range(Voldev.ex$depths))) points(Voldevshallow.ex$depths ~ Voldevshallow.ex$Area.at.z, col = "blue", ylim = rev(range(Voldevshallow.ex$depths)))Voldev.ex = approx.bathy(Zmax = 25, Zmean = 12, lkeArea = 39400000, method = "voldev") Voldevshallow.ex = approx.bathy(Zmax = 25, Zmean = 6, lkeArea = 39400000, method = "voldev") Cone.ex = approx.bathy(Zmax = 25, lkeArea = 39400000, method = "cone") # plot depth-area curves plot(Cone.ex$depths ~ Cone.ex$Area.at.z, xlab = "Area (m^3)", ylab = "Depth (m)", ylim = rev(range(Cone.ex$depths))) points(Voldev.ex$depths ~ Voldev.ex$Area.at.z, col = "red", ylim = rev(range(Voldev.ex$depths))) points(Voldevshallow.ex$depths ~ Voldevshallow.ex$Area.at.z, col = "blue", ylim = rev(range(Voldevshallow.ex$depths)))
Calculate the buoyancy frequency (Brunt-Vaisala frequency) for a temperature profile.
buoyancy.freq(wtr, depths)buoyancy.freq(wtr, depths)
wtr |
a numeric vector of water temperature in degrees C |
depths |
a numeric vector corresponding to the depths (in m) of the wtr measurements |
Returns a vector of buoyancy frequency in units sec^-2.
Return value has attribute "depths" which define buoyancy frequency depths
(which differ from supplied depths).
thermo.depth, ts.buoyancy.freq
# A vector of water temperatures wtr = c(22.51, 22.42, 22.4, 22.4, 22.4, 22.36, 22.3, 22.21, 22.11, 21.23, 16.42, 15.15, 14.24, 13.35, 10.94, 10.43, 10.36, 9.94, 9.45, 9.1, 8.91, 8.58, 8.43) #A vector defining the depths depths = c(0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) b.f = buoyancy.freq(wtr, depths) plot(b.f, attr(b.f, 'depths'), type='b', ylab='Depth', xlab='Buoyancy Frequency', ylim=c(max(depths), min(depths)))# A vector of water temperatures wtr = c(22.51, 22.42, 22.4, 22.4, 22.4, 22.36, 22.3, 22.21, 22.11, 21.23, 16.42, 15.15, 14.24, 13.35, 10.94, 10.43, 10.36, 9.94, 9.45, 9.1, 8.91, 8.58, 8.43) #A vector defining the depths depths = c(0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) b.f = buoyancy.freq(wtr, depths) plot(b.f, attr(b.f, 'depths'), type='b', ylab='Depth', xlab='Buoyancy Frequency', ylim=c(max(depths), min(depths)))
Calculate the center of buoyancy using buoyancy frequency with a center of mass analysis. Brunt-Vaisala frequency is used for a temperature profile. Negative values for N2 are set to 0 (as they represent transient instabilities or sensor calibration issues) for this calculation.
center.buoyancy(wtr, depths)center.buoyancy(wtr, depths)
wtr |
a numeric vector of water temperature in degrees C |
depths |
a numeric vector corresponding to the depths (in m) of the wtr measurements |
Returns a value for the center of buoyancy.
buoyancy.freq, ts.buoyancy.freq,
center.buoyancy
# A vector of water temperatures wtr = c(22.51, 22.42, 22.4, 22.4, 22.4, 22.36, 22.3, 22.21, 22.11, 21.23, 16.42, 15.15, 14.24, 13.35, 10.94, 10.43, 10.36, 9.94, 9.45, 9.1, 8.91, 8.58, 8.43) #A vector defining the depths depths = c(0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) c.b = center.buoyancy(wtr, depths)# A vector of water temperatures wtr = c(22.51, 22.42, 22.4, 22.4, 22.4, 22.36, 22.3, 22.21, 22.11, 21.23, 16.42, 15.15, 14.24, 13.35, 10.94, 10.43, 10.36, 9.94, 9.45, 9.1, 8.91, 8.58, 8.43) #A vector defining the depths depths = c(0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) c.b = center.buoyancy(wtr, depths)
Soak period: water profiling instruments typically require a soak period where you let the instrument rest submerged at the surface. While it is "soaking" it is collecting data. We don't want that data
Upcast versus downcast: typically instruments are turned on before you put them in the water and turn them off once you pull them out. The data consequence of that is that you collect both the "downcast" and the "upcast". In some case the upcast is of interest but usually it isn't. And because we would prefer increasing depth data it is better to remove an upcast if it is present.
Heave: when lowering the instrument in rough weather a boat will heave side to side. Sometimes it will heave enough that you get small data groupings where the decreases a little while the boat heaves then go down. The overall trend is still down but those slight upticks in depth cause problems for our algorithm.
depth.filter(z0, run_length = 20, index = FALSE)depth.filter(z0, run_length = 20, index = FALSE)
z0 |
depth vector |
run_length |
Length of run upon which to start the soak removal |
index |
Logical: Should the function return an index value or actual value? |
index values of z0 of filtered data. Will return a warning if the function removed more than 10
Liberally looks for a datetime column and drops it, returning a data.frame with only water temperature. Errors if datetime column is ambiguous. Warns if there is no match.
drop.datetime(data, error = FALSE)drop.datetime(data, error = FALSE)
data |
data arg |
error |
defaults to FALSE |
A data.frame with only the data, after datetime has been dropped
Calculates volumetrically weighted average epilimnetic temperature using the supplied water temperature timeseries. If the lake is not stratified, the bottom of the epilimnion is calculated as the full depth of the lake.
epi.temperature(wtr, depths, bthA, bthD)epi.temperature(wtr, depths, bthA, bthD)
wtr |
a numeric vector of water temperature in degrees C. |
depths |
a numeric vector corresponding to the depths (in m) of the wtr measurements |
bthA |
a numeric vector of cross sectional areas (m^2) corresponding to bthD depths |
bthD |
a numeric vector of depths (m) which correspond to areal measures in bthA |
hypo.temperature whole.lake.temperature
Warns if unavailable then returns NULL.
get.datetime(data, error = FALSE)get.datetime(data, error = FALSE)
data |
data arg |
error |
defaults to FALSE |
Extracts the depth information from a data frame containing multi-depth observation data. Relies on the format of the header to get information and may fail if your file format is incorrect. Please follow 'VAR_##.#' format, where ##.# is the depth of data for that column. VAR is typically 'wtr' to indicate water temperature.
get.offsets(data)get.offsets(data)
data |
Data frame returned from |
A numeric vector of depth values. Should be the ncol(data) -
1 in length as the first column contains date/time data.
#Get the path for the package example file included exampleFilePath <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") #Load sparkling.temp = load.ts(exampleFilePath) #get the lake depths associated with each column depths = get.offsets(sparkling.temp) print(depths)#Get the path for the package example file included exampleFilePath <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") #Load sparkling.temp = load.ts(exampleFilePath) #get the lake depths associated with each column depths = get.offsets(sparkling.temp) print(depths)
Calculates volumetrically weighted average hypolimnetic temperature using the supplied water temperature timeseries. If the lake is not stratified, an NA value is returned.
hypo.temperature(wtr, depths, bthA, bthD)hypo.temperature(wtr, depths, bthA, bthD)
wtr |
a numeric vector of water temperature in degrees C. |
depths |
a numeric vector corresponding to the depths (in m) of the wtr measurements |
bthA |
a numeric vector of cross sectional areas (m^2) corresponding to bthD depths |
bthD |
a numeric vector of depths (m) which correspond to areal measures in bthA |
epi.temperature, whole.lake.temperature
Calculates the internal energy of the water column with temperature and hypsography
Internal energy is the thermal energy in the water column, which is calculated by multiplying the specific heat of water (J kg-1 K-1) by the temperature and mass of the water in the lake.
internal.energy(wtr, depths, bthA, bthD)internal.energy(wtr, depths, bthA, bthD)
wtr |
a numeric vector of water temperature in degrees C |
depths |
a numeric vector corresponding to the depths (in m) of the wtr measurements |
bthA |
a numeric vector of cross sectional areas (m^2) corresponding to bthD depths |
bthD |
a numeric vector of depths (m) which correspond to areal measures in bthA |
internal energy in Joules m-2. (Currently not vectorized..)
bthA <- c(1000,900,864,820,200,10) bthD <- c(0,2.3,2.5,4.2,5.8,7) wtr <- c(28,27,26.4,26,25.4,24,23.3) depths <- c(0,1,2,3,4,5,6) cat('Internal Energy for input is: ') cat(internal.energy(wtr, depths, bthA, bthD))bthA <- c(1000,900,864,820,200,10) bthD <- c(0,2.3,2.5,4.2,5.8,7) wtr <- c(28,27,26.4,26,25.4,24,23.3) depths <- c(0,1,2,3,4,5,6) cat('Internal Energy for input is: ') cat(internal.energy(wtr, depths, bthA, bthD))
The Lake Number, defined by Imberger and Patterson (1990), has been used to describe processes relevant to the internal mixing of lakes induced by wind forcings. Lower values of Lake Number represent a higher potential for increased diapycnal mixing, which increases the vertical flux of mass and energy across the metalimnion through the action of non-linear internal waves. Lake Number is a dimensionless index.
Lake Number has been used, for example, to estimate the flux of oxygen across the thermocline in a small lake (Robertson and Imberger, 1994), and to explain the magnitude of the vertical flux of ammonium in a lake (Romero et al., 1998). In Imberger and Patterson (1990), Lake Number was defined as Ln = (g * St * (zm - zT)) / (rho_0 * u*^2 * A0^3/2 * (zm - zg)) with all values referenced from the lake bottom, e.g., zm being the height of the water level, zT the height of metalimnion and zg the height of center volume. Our calculations assume that the reference is at the lake surface, therefore: height of metalimnion becomes metalimnion depth (average of meta top and bot): (zm - zT) –> (metaT + metaB)/2 height of center of volume depth becomes center of volume depth Zcv: (zm - zg) –> Zcv Further, we note that in that original work St was defined as St = int (z - zg) A(z) rho(z) dz and rLakeAnalyzer defines St as St = g/A0 int (z - zg) rho(z) dz Therefore, we calculate St_uC = St * Ao / g
lake.number(bthA, bthD, uStar, St, metaT, metaB, averageHypoDense)lake.number(bthA, bthD, uStar, St, metaT, metaB, averageHypoDense)
bthA |
a numeric vector of cross sectional areas (m2) corresponding to bthD depths, hypsographic areas |
bthD |
a numeric vector of depths (m) which correspond to areal measures in bthA, hypsographic depths |
uStar |
a numeric array of u* (m/s), water friction velocity due to wind stress |
St |
a numeric array of Schmidt stability (J/m2), as defined by Idso 1973 |
metaT |
a numeric array of the top of the metalimnion depth (m from the surface) |
metaB |
a numeric array of the bottom of the metalimnion depth (m from the surface) |
averageHypoDense |
a numeric array of the average density of the hypolimnion (kg/m3) |
A numeric vector of Lake Number [dimensionless]
Imberger, J., Patterson, J.C., 1990. Physical limnology. Advances in Applied Mechanics 27, 303-475.
Idso, S.B., 1973. On the concept of lake stability. Limnology and Oceanography 18, 681-683.
ts.lake.number wedderburn.number
bthA <- c(1000,900,864,820,200,10) bthD <- c(0,2.3,2.5,4.2,5.8,7) uStar <- c(0.0032,0.0024) St <- c(140,153) metaT <- c(1.34,1.54) metaB <- c(4.32,4.33) averageHypoDense <- c(999.3,999.32) cat('Lake Number for input vector is: ') cat(lake.number( bthA, bthD, uStar, St, metaT, metaB, averageHypoDense) )bthA <- c(1000,900,864,820,200,10) bthD <- c(0,2.3,2.5,4.2,5.8,7) uStar <- c(0.0032,0.0024) St <- c(140,153) metaT <- c(1.34,1.54) metaB <- c(4.32,4.33) averageHypoDense <- c(999.3,999.32) cat('Lake Number for input vector is: ') cat(lake.number( bthA, bthD, uStar, St, metaT, metaB, averageHypoDense) )
Generates a time series plot of Lake Number for appropriately formatted
data. See lake.number for more details on Lake Number and
reference.
lake.number.plot(wtr, wnd, wh, bth)lake.number.plot(wtr, wnd, wh, bth)
wtr |
Data frame of water temperature loaded with |
wnd |
A data frame containing hypsometric data. Loaded using
|
wh |
A value indicating the height of the anemometer above lake surface in meters. This value must be specified, there is no default. |
bth |
A data frame containing hypsometric data. Loaded using
|
#Get system data file paths wtr.path <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") bth.path <- system.file('extdata', 'Sparkling.bth', package="rLakeAnalyzer") wnd.path <- system.file('extdata', 'Sparkling.wnd', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. wtr = load.ts(wtr.path) wnd = load.ts(wnd.path) bth = load.bathy(bth.path) wh = 1 # user specified, here as 1 m. ## Not run: #generate default plot lake.number.plot(wtr,wnd,wh,bth) ## End(Not run)#Get system data file paths wtr.path <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") bth.path <- system.file('extdata', 'Sparkling.bth', package="rLakeAnalyzer") wnd.path <- system.file('extdata', 'Sparkling.wnd', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. wtr = load.ts(wtr.path) wnd = load.ts(wnd.path) bth = load.bathy(bth.path) wh = 1 # user specified, here as 1 m. ## Not run: #generate default plot lake.number.plot(wtr,wnd,wh,bth) ## End(Not run)
Late summer water profile taken from Quesnel Lake, British Columbia, Canada. Profile taken with Sea-Bird SBE19plus.
Depth, m
Temperature, degC
Salinity, PSU
Oxygen, ml/l
Oxygen saturation, percent saturation
Density, kg/m^3
...
latesummerlatesummer
An object of class data.frame with 881 rows and 6 columns.
This function calculates the average density of a layer of water between two depths.
layer.density(top, bottom, wtr, depths, bthA, bthD, sal = wtr * 0)layer.density(top, bottom, wtr, depths, bthA, bthD, sal = wtr * 0)
top |
Numeric value of the depth (m) of the top of the layer from the water surface |
bottom |
Numeric value of the depth (m) of the bottom of the layer from the water surface |
wtr |
Numeric vector of water temperature in degrees C |
depths |
Numeric vector of depths (m) corresponding to water temperature vector |
bthA |
Numeric vector of water body cross sectional area (m2) corresponding to bthD depths |
bthD |
Numeric vector of water body bathymetric depths (m) corresponding to areal bthA values |
sal |
Optional numeric vector of salinity in Practical Salinity Units corresponding to water temperature vector. If left blank, salinity is set to be zero |
Numeric value of average water density for bounded layer in kg/m^3
water.density
top <- 2 bottom <- 6 wtr <- c(25.2,25.1,24.1,22.0,19.8,15.3,12.0,11.1) depths <- c(0,1,2,3,4,5,6,7) bthA <- c(10000,8900,5000,3500,2000,1000,300,10) bthD <- c(0,1,2,3,4,5,6,7) layer.density(top,bottom,wtr,depths,bthA,bthD)top <- 2 bottom <- 6 wtr <- c(25.2,25.1,24.1,22.0,19.8,15.3,12.0,11.1) depths <- c(0,1,2,3,4,5,6,7) bthA <- c(10000,8900,5000,3500,2000,1000,300,10) bthD <- c(0,1,2,3,4,5,6,7) layer.density(top,bottom,wtr,depths,bthA,bthD)
This function calculates the average temperature of a layer of water between two depths.
layer.temperature(top, bottom, wtr, depths, bthA, bthD)layer.temperature(top, bottom, wtr, depths, bthA, bthD)
top |
Numeric value of the depth (m) of the top of the layer from the water surface |
bottom |
Numeric value of the depth (m) of the bottom of the layer from the water surface |
wtr |
Numeric vector of water temperature in degrees C |
depths |
Numeric vector of depths (m) corresponding to water temperature vector |
bthA |
Numeric vector of water body cross sectional area (m2) corresponding to bthD depths |
bthD |
Numeric vector of water body bathymetric depths (m) corresponding to areal bthA values |
Numeric value of average water temperature
layer.density
# Supply input data top <- 2 bottom <- 6 wtr <- c(25.2,25.1,24.1,22.0,19.8,15.3,12.0,11.1) depths <- c(0,1,2,3,4,5,6,7) bthA <- c(10000,8900,5000,3500,2000,1000,300,10) bthD <- c(0,1,2,3,4,5,6,7) #Return the average temperature of the water column between 2 and 6 meters. layer.temperature(top,bottom,wtr,depths,bthA,bthD)# Supply input data top <- 2 bottom <- 6 wtr <- c(25.2,25.1,24.1,22.0,19.8,15.3,12.0,11.1) depths <- c(0,1,2,3,4,5,6,7) bthA <- c(10000,8900,5000,3500,2000,1000,300,10) bthD <- c(0,1,2,3,4,5,6,7) #Return the average temperature of the water column between 2 and 6 meters. layer.temperature(top,bottom,wtr,depths,bthA,bthD)
Imports lake bathymetry data. Bathymetric data file must be a 2 column array where depth (in meters) and area (in meters^2) information are provided in columns with headers containing the words "depths" and "areas" respectively.
load.bathy(fPath)load.bathy(fPath)
fPath |
File path to the bathymetry file. |
data.frame of depth and area for given lake.
#Get the path for the package example file included exampleFilePath <- system.file('extdata', 'Sparkling.bth', package="rLakeAnalyzer") #Load and plot the hypsometric curve sparkling.bathy = load.bathy(exampleFilePath) #If successful, there will be two colums. "depths", and "areas". plot(sparkling.bathy$areas, sparkling.bathy$depths, type='l', ylim=c(20,0), ylab='Depths (m)', xlab='Areas (m^2)')#Get the path for the package example file included exampleFilePath <- system.file('extdata', 'Sparkling.bth', package="rLakeAnalyzer") #Load and plot the hypsometric curve sparkling.bathy = load.bathy(exampleFilePath) #If successful, there will be two colums. "depths", and "areas". plot(sparkling.bathy$areas, sparkling.bathy$depths, type='l', ylim=c(20,0), ylab='Depths (m)', xlab='Areas (m^2)')
A convenience function to load timeseries data into R based on the standardized format used by Lake Analyzer.
Timeseries files must follow a common format. The first column must have the label 'datetime' and be of the format yyyy-mm-dd HH:MM:SS (ISO 8601 without the "T" delimiter). The second can be skipped if not using sub-minute data.
load.ts(fPath, tz = "GMT")load.ts(fPath, tz = "GMT")
fPath |
The file path as a string. |
tz |
Timezone string to be supplied to |
A data frame in the required format for use with other rLakeAnalyzer timeseries functions.
For dataloading ts.meta.depths,
For analyzing
timeseries data, see ts.meta.depths,
ts.thermo.depth, ts.schmidt.stability,
ts.lake.number.
#Get the path for the package example file included exampleFilePath <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") #Load sparkling.temp = load.ts(exampleFilePath) #calculate and plot the thermocline depth t.d = ts.thermo.depth(sparkling.temp) plot(t.d$datetime, t.d$thermo.depth, type='l', ylab='Thermocline Depth (m)', xlab='Date')#Get the path for the package example file included exampleFilePath <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") #Load sparkling.temp = load.ts(exampleFilePath) #calculate and plot the thermocline depth t.d = ts.thermo.depth(sparkling.temp) plot(t.d$datetime, t.d$thermo.depth, type='l', ylab='Thermocline Depth (m)', xlab='Date')
Calculates the top and bottom depths of the metalimnion in a stratified lake. The metalimnion is defined as the water stratum in a stratified lake with the steepest thermal gradient and is demarcated by the bottom of the epilimnion and top of the hypolimnion.
meta.depths(wtr, depths, slope = 0.1, seasonal = TRUE, mixed.cutoff = 1)meta.depths(wtr, depths, slope = 0.1, seasonal = TRUE, mixed.cutoff = 1)
wtr |
a numeric vector of water temperature in degrees C |
depths |
a numeric vector corresponding to the depths (in m) of the wtr measurements |
slope |
a numeric vector corresponding to the minimum slope |
seasonal |
a logical value indicating whether the seasonal thermocline
should be returned. This is fed to thermo.depth, which is used as the
starting point. The seasonal thermocline is defined as the deepest density
gradient found in the profile. If |
mixed.cutoff |
A cutoff (deg C) where below this threshold, thermo.depth and meta.depths are not calculated (NaN is returned). Defaults to 1 deg C. |
A numeric vector of the top and bottom metalimnion depths in meters. Returns the bottom depth if no distinct metalimion top and bottom found.
Wetzel, R. G. 2001. Limnology: Lake and River Ecosystems, 3rd ed. Academic Press.
wtr = c(22.51, 22.42, 22.4, 22.4, 22.4, 22.36, 22.3, 22.21, 22.11, 21.23, 16.42, 15.15, 14.24, 13.35, 10.94, 10.43, 10.36, 9.94, 9.45, 9.1, 8.91, 8.58, 8.43) depths = c(0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) m.d = meta.depths(wtr, depths, slope=0.1, seasonal=FALSE) cat('The top depth of the metalimnion is:', m.d[1]) cat('The bottom depth of the metalimnion is:', m.d[2])wtr = c(22.51, 22.42, 22.4, 22.4, 22.4, 22.36, 22.3, 22.21, 22.11, 21.23, 16.42, 15.15, 14.24, 13.35, 10.94, 10.43, 10.36, 9.94, 9.45, 9.1, 8.91, 8.58, 8.43) depths = c(0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) m.d = meta.depths(wtr, depths, slope=0.1, seasonal=FALSE) cat('The top depth of the metalimnion is:', m.d[1]) cat('The bottom depth of the metalimnion is:', m.d[2])
Standardized methods for calculating common important derived physical features of lakes including water density based based on temperature, thermal layers, thermocline depth, lake number, Wedderburn number, Schmidt stability and others.
Generates a time series of Schmidt's stability where each value represents
water column stability for each time step of data. See
schmidt.stability for more details and reference.
schmidt.plot(wtr, bth)schmidt.plot(wtr, bth)
wtr |
Data frame of water temperature loaded with |
bth |
A data frame containing hypsometric data. Loaded using
|
# Get system data file paths wtr.path <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") bth.path <- system.file('extdata', 'Sparkling.bth', package="rLakeAnalyzer") # Load data for example lake, Sparkilng Lake, Wisconsin. wtr = load.ts(wtr.path) bth = load.bathy(bth.path) ## Not run: # Generate default plot schmidt.plot(wtr,bth) ## End(Not run)# Get system data file paths wtr.path <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") bth.path <- system.file('extdata', 'Sparkling.bth', package="rLakeAnalyzer") # Load data for example lake, Sparkilng Lake, Wisconsin. wtr = load.ts(wtr.path) bth = load.bathy(bth.path) ## Not run: # Generate default plot schmidt.plot(wtr,bth) ## End(Not run)
Schmidt stability, or the resistance to mechanical mixing due to the potential energy inherent in the stratification of the water column.
Schmidt stability was first defined by Schmidt (1928) and later modified by Hutchinson (1957). This stability index was formalized by Idso (1973) to reduce the effects of lake volume on the calculation (resulting in a mixing energy requirement per unit area).
schmidt.stability(wtr, depths, bthA, bthD, sal = 0)schmidt.stability(wtr, depths, bthA, bthD, sal = 0)
wtr |
a numeric vector of water temperature in degrees C |
depths |
a numeric vector corresponding to the depths (in m) of the wtr measurements |
bthA |
a numeric vector of cross sectional areas (m^2) corresponding to bthD depths |
bthD |
a numeric vector of depths (m) which correspond to areal measures in bthA |
sal |
a numeric vector of salinity in Practical Salinity Scale units |
a numeric vector of Schmidt stability (J/m^2)
Schmidt, W., 1928. Ueber Temperatur and Stabilitaetsverhaltnisse von Seen. Geo- graphiska Annaler 10, 145-177.
Hutchinson, G.E., 1957. A Treatise on Limnology, vol. 1. John Wiley & Sons, Inc., New York.
Idso, S.B., 1973. On the concept of lake stability. Limnology and Oceanography 18, 681-683.
ts.schmidt.stability lake.number
wedderburn.number
bthA <- c(1000,900,864,820,200,10) bthD <- c(0,2.3,2.5,4.2,5.8,7) wtr <- c(28,27,26.4,26,25.4,24,23.3) depths <- c(0,1,2,3,4,5,6) cat('Schmidt stability for input is: ') cat(schmidt.stability(wtr, depths, bthA, bthD))bthA <- c(1000,900,864,820,200,10) bthD <- c(0,2.3,2.5,4.2,5.8,7) wtr <- c(28,27,26.4,26,25.4,24,23.3) depths <- c(0,1,2,3,4,5,6) cat('Schmidt stability for input is: ') cat(schmidt.stability(wtr, depths, bthA, bthD))
This function calculates the location of the thermocline from a temperature profile. It uses a special technique to estimate where the thermocline lies even between two temperature measurement depths, giving a potentially finer-scale estimate than usual techniques.
thermo.depth(wtr, depths, Smin = 0.1, seasonal = TRUE, index = FALSE, mixed.cutoff = 1)thermo.depth(wtr, depths, Smin = 0.1, seasonal = TRUE, index = FALSE, mixed.cutoff = 1)
wtr |
a numeric vector of water temperature in degrees C |
depths |
a numeric vector corresponding to the depths (in m) of the wtr measurements |
Smin |
Optional paramter defining minimum density gradient for thermocline |
seasonal |
a logical value indicating whether the seasonal thermocline
should be returned. This is fed to thermo.depth, which is used as the
starting point. The seasonal thermocline is defined as the deepest density
gradient found in the profile. If |
index |
Boolean value indicated if index of the thermocline depth, instead of the depth value, should be returned. |
mixed.cutoff |
A cutoff (deg C) where below this threshold, thermo.depth and meta.depths are not calculated (NaN is returned). Defaults to 1 deg C. |
Depth of thermocline. If no thermocline found, value is NaN.
ts.thermo.depth, water.density
# A vector of water temperatures wtr = c(22.51, 22.42, 22.4, 22.4, 22.4, 22.36, 22.3, 22.21, 22.11, 21.23, 16.42, 15.15, 14.24, 13.35, 10.94, 10.43, 10.36, 9.94, 9.45, 9.1, 8.91, 8.58, 8.43) #A vector defining the depths depths = c(0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) t.d = thermo.depth(wtr, depths, seasonal=FALSE) cat('The thermocline depth is:', t.d)# A vector of water temperatures wtr = c(22.51, 22.42, 22.4, 22.4, 22.4, 22.36, 22.3, 22.21, 22.11, 21.23, 16.42, 15.15, 14.24, 13.35, 10.94, 10.43, 10.36, 9.94, 9.45, 9.1, 8.91, 8.58, 8.43) #A vector defining the depths depths = c(0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) t.d = thermo.depth(wtr, depths, seasonal=FALSE) cat('The thermocline depth is:', t.d)
Function for simplifying the calculation of buoyancy frequency. Can usually
be called directly on data loaded directly using load.ts and
load.bathy.
ts.buoyancy.freq(wtr, at.thermo = TRUE, na.rm = FALSE, ...)ts.buoyancy.freq(wtr, at.thermo = TRUE, na.rm = FALSE, ...)
wtr |
A data frame of water temperatures (in Celsius). Loaded using
|
at.thermo |
Boolean indicating if only buoyancy frequency at the thermocline should be returned. If false, full profile is returned. |
na.rm |
Boolean indicated if step-by-step removal of NA's should be tried. If false, a timestep with any NA values will likely return an NA value. If true, best effort will be made to calculate indices despite NA values. |
... |
Additional parameters will be passed on to |
Returns a data frame with the timeseries of buoyancy frequency in
units sec^-2. Includes a ‘datetime’ column.
Imberger, J., Patterson, J.C., 1990. Physical limnology. Advances in Applied Mechanics 27, 353-370.
buoyancy.freq
#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. sp.wtr = load.ts(wtr.path) N2 = ts.buoyancy.freq(sp.wtr, seasonal=FALSE) SN2 = ts.buoyancy.freq(sp.wtr, seasonal=TRUE) plot(N2, type='l', ylab='Buoyancy Frequency', xlab='Date') lines(SN2, col='red')#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. sp.wtr = load.ts(wtr.path) N2 = ts.buoyancy.freq(sp.wtr, seasonal=FALSE) SN2 = ts.buoyancy.freq(sp.wtr, seasonal=TRUE) plot(N2, type='l', ylab='Buoyancy Frequency', xlab='Date') lines(SN2, col='red')
Function for simplifying the calculation of the center of buoyancy. Can
usually be called directly on data loaded directly using
load.ts and load.bathy.
ts.center.buoyancy(wtr, na.rm = FALSE)ts.center.buoyancy(wtr, na.rm = FALSE)
wtr |
A data frame of water temperatures (in Celsius). Loaded using
|
na.rm |
Boolean indicated if step-by-step removal of NA's should be tried. If false, a timestep with any NA values will return an NA value. If true, best effort will be made to calculate indices despite NA values. |
Returns a data frame with the timeseries of the center of buoyancy frequency. Includes a ‘datetime’ column.
Imberger, J., Patterson, J.C., 1990. Physical limnology. Advances in Applied Mechanics 27, 353-370.
center.buoyancy, load.bathy, load.ts
#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. sp.wtr = load.ts(wtr.path) #calculate and plot the thermocline depth t.d = ts.thermo.depth(sp.wtr) center.N2 = ts.center.buoyancy(sp.wtr) plot(center.N2, type='l', ylab='Depth (m)', xlab='Date', ylim=c(19,0), lwd = 1.5) lines(t.d, type='l', col='red', lwd = 1.5) legend(x = t.d[3,1], y = .25, c('center of buoyancy','thermocline depth'), lty=c(1,1), lwd=c(1.5,1.5),col=c("black","red"), bty = "n")#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. sp.wtr = load.ts(wtr.path) #calculate and plot the thermocline depth t.d = ts.thermo.depth(sp.wtr) center.N2 = ts.center.buoyancy(sp.wtr) plot(center.N2, type='l', ylab='Depth (m)', xlab='Date', ylim=c(19,0), lwd = 1.5) lines(t.d, type='l', col='red', lwd = 1.5) legend(x = t.d[3,1], y = .25, c('center of buoyancy','thermocline depth'), lty=c(1,1), lwd=c(1.5,1.5),col=c("black","red"), bty = "n")
Functions for simplifying the calculation of physical indices for a
timeseries of observation data. Can usually be called directly on data
loaded directly using load.ts and load.bathy.
These are wrapper functions that accept a timeseries of data and call the
core physical metric functions (like schmidt.stability) on
each timestep.
ts.internal.energy(wtr, bathy, na.rm = FALSE)ts.internal.energy(wtr, bathy, na.rm = FALSE)
wtr |
A data frame of water temperatures (in Celsius). Loaded using
|
bathy |
A data frame containing hypsometric data. Loaded using
|
na.rm |
Boolean indicated if step-by-step removal of NA's should be tried. If false, a timestep with any NA values will return an NA value. If true, best effort will be made to calculate indices despite NA values. |
Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.
For loading input data load.ts,
load.bathy.
For the underlying functions operating at each timestep
meta.depths, thermo.depth,
schmidt.stability, lake.number,
internal.energy.
Other Timeseries functions for r Lake Analyzer: ts.lake.number,
ts.meta.depths,
ts.schmidt.stability,
ts.thermo.depth, ts.uStar
Functions for simplifying the calculation of physical indices for a
timeseries of observation data. Can usually be called directly on data
loaded directly using load.ts and load.bathy.
These are wrapper functions that accept a timeseries of data and call the
core physical metric functions (like schmidt.stability) on
each timestep.
ts.lake.number(wtr, wnd, wnd.height, bathy, seasonal = TRUE)ts.lake.number(wtr, wnd, wnd.height, bathy, seasonal = TRUE)
wtr |
A data frame of water temperatures (in Celsius). Loaded using
|
wnd |
A data frame of wind speeds (in m/s). Loaded using
|
wnd.height |
Height of the anemometer above the lake surface in meters |
bathy |
A data frame containing hypsometric data. Loaded using
|
seasonal |
Boolean indicating if seasonal thermocline should be used in calculation. |
Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.
For loading input data load.ts,
load.bathy.
For the underlying functions operating at each timestep
meta.depths, thermo.depth,
schmidt.stability, lake.number,
internal.energy.
Other Timeseries functions for r Lake Analyzer: ts.internal.energy,
ts.meta.depths,
ts.schmidt.stability,
ts.thermo.depth, ts.uStar
Function for simplifying the calculation of Wedderburn Number. Can usually
be called directly on data loaded directly using load.ts and
load.bathy.
ts.layer.temperature(wtr, top, bottom, bathy, na.rm = FALSE)ts.layer.temperature(wtr, top, bottom, bathy, na.rm = FALSE)
wtr |
A data frame of water temperatures (in Celsius). Loaded using
|
top |
Either a single numeric depth value to be used across the entire
timeseries, or a vector of same length as the timeseries (e.g.,
|
bottom |
Either a single numeric depth value to be used across the
entire timeseries, or a vector of same length as the timeseries (e.g.,
|
bathy |
A data frame containing hypsometric data. Loaded using
|
na.rm |
Boolean indicated if step-by-step removal of NA's should be tried. If false, a timestep with any NA values will return an NA value. If true, best effort will be made to calculate indices despite NA values. |
Returns a data frame with the timeseries of the average layer temperature. Includes ‘datetime’ and ‘layer.temp’ columns.
layer.temperature
#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") bathy.path <- system.file('extdata', 'Sparkling.bth', package="rLakeAnalyzer") #Load data for example lake, Sparkilng lake, in Wisconsin. sp.wtr = load.ts(wtr.path) sp.bathy = load.bathy(bathy.path) l.t = ts.layer.temperature(sp.wtr, 0, 18, sp.bathy) plot(l.t$datetime, l.t$layer.temp, type='l', ylab='Volumetrically averaged lake temperature', xlab='Date')#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") bathy.path <- system.file('extdata', 'Sparkling.bth', package="rLakeAnalyzer") #Load data for example lake, Sparkilng lake, in Wisconsin. sp.wtr = load.ts(wtr.path) sp.bathy = load.bathy(bathy.path) l.t = ts.layer.temperature(sp.wtr, 0, 18, sp.bathy) plot(l.t$datetime, l.t$layer.temp, type='l', ylab='Volumetrically averaged lake temperature', xlab='Date')
Functions for simplifying the calculation of physical indices for a
timeseries of observation data. Can usually be called directly on data
loaded directly using load.ts and load.bathy.
These are wrapper functions that accept a timeseries of data and call the
core physical metric functions (like schmidt.stability) on
each timestep.
ts.meta.depths(wtr, slope = 0.1, na.rm = FALSE, ...)ts.meta.depths(wtr, slope = 0.1, na.rm = FALSE, ...)
wtr |
A data frame of water temperatures (in Celsius). Loaded using
|
slope |
The minimum density gradient (kg/m^3/m) that can be called the thermocline |
na.rm |
Boolean indicated if step-by-step removal of NA's should be tried. If false, a timestep with any NA values will return an NA value. If true, best effort will be made to calculate indices despite NA values. |
... |
Additional parameters passed to underlying base function (e.g., index=TRUE for thermo.depth) |
Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.
For loading input data load.ts,
load.bathy.
For the underlying functions operating at each timestep
meta.depths, thermo.depth,
schmidt.stability, lake.number,
internal.energy.
Other Timeseries functions for r Lake Analyzer: ts.internal.energy,
ts.lake.number,
ts.schmidt.stability,
ts.thermo.depth, ts.uStar
#Get the path for the package example file included exampleFilePath <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") #Load sparkling.temp = load.ts(exampleFilePath) #calculate and plot the metalimnion depths m.d = ts.meta.depths(sparkling.temp) plot(m.d$datetime, m.d$top, type='l', ylab='Meta Depths (m)', xlab='Date', col='blue') lines(m.d$datetime, m.d$bottom, col='red')#Get the path for the package example file included exampleFilePath <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") #Load sparkling.temp = load.ts(exampleFilePath) #calculate and plot the metalimnion depths m.d = ts.meta.depths(sparkling.temp) plot(m.d$datetime, m.d$top, type='l', ylab='Meta Depths (m)', xlab='Date', col='blue') lines(m.d$datetime, m.d$bottom, col='red')
Functions for simplifying the calculation of physical indices for a
timeseries of observation data. Can usually be called directly on data
loaded directly using load.ts and load.bathy.
These are wrapper functions that accept a timeseries of data and call the
core physical metric functions (like schmidt.stability) on
each timestep.
ts.schmidt.stability(wtr, bathy, na.rm = FALSE)ts.schmidt.stability(wtr, bathy, na.rm = FALSE)
wtr |
A data frame of water temperatures (in Celsius). Loaded using
|
bathy |
A data frame containing hypsometric data. Loaded using
|
na.rm |
Boolean indicated if step-by-step removal of NA's should be tried. If false, a timestep with any NA values will return an NA value. If true, best effort will be made to calculate indices despite NA values. |
Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.
For loading input data load.ts,
load.bathy.
For the underlying functions operating at each timestep
meta.depths, thermo.depth,
schmidt.stability, lake.number,
internal.energy.
Other Timeseries functions for r Lake Analyzer: ts.internal.energy,
ts.lake.number,
ts.meta.depths,
ts.thermo.depth, ts.uStar
Functions for simplifying the calculation of physical indices for a
timeseries of observation data. Can usually be called directly on data
loaded directly using load.ts and load.bathy.
These are wrapper functions that accept a timeseries of data and call the
core physical metric functions (like schmidt.stability) on
each timestep.
ts.thermo.depth(wtr, Smin = 0.1, na.rm = FALSE, ...)ts.thermo.depth(wtr, Smin = 0.1, na.rm = FALSE, ...)
wtr |
A data frame of water temperatures (in Celsius). Loaded using
|
Smin |
The minimum density gradient cutoff (kg/m^3/m) defining the metalimion |
na.rm |
Boolean indicated if step-by-step removal of NA's should be tried. If false, a timestep with any NA values will return an NA value. If true, best effort will be made to calculate indices despite NA values. |
... |
Additional parameters passed to underlying base function (e.g., index=TRUE for thermo.depth) |
Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.
For loading input data load.ts,
load.bathy.
For the underlying functions operating at each timestep
meta.depths, thermo.depth,
schmidt.stability, lake.number,
internal.energy.
Other Timeseries functions for r Lake Analyzer: ts.internal.energy,
ts.lake.number,
ts.meta.depths,
ts.schmidt.stability,
ts.uStar
#Get the path for the package example file included exampleFilePath <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") #Load sparkling.temp = load.ts(exampleFilePath) #calculate and plot the thermocline depth t.d = ts.thermo.depth(sparkling.temp) plot(t.d$datetime, t.d$thermo.depth, type='l', ylab='Thermocline Depth (m)', xlab='Date')#Get the path for the package example file included exampleFilePath <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") #Load sparkling.temp = load.ts(exampleFilePath) #calculate and plot the thermocline depth t.d = ts.thermo.depth(sparkling.temp) plot(t.d$datetime, t.d$thermo.depth, type='l', ylab='Thermocline Depth (m)', xlab='Date')
Functions for simplifying the calculation of physical indices for a
timeseries of observation data. Can usually be called directly on data
loaded directly using load.ts and load.bathy.
These are wrapper functions that accept a timeseries of data and call the
core physical metric functions (like schmidt.stability) on
each timestep.
ts.uStar(wtr, wnd, wnd.height, bathy, seasonal = TRUE)ts.uStar(wtr, wnd, wnd.height, bathy, seasonal = TRUE)
wtr |
A data frame of water temperatures (in Celsius). Loaded using
|
wnd |
A data frame of wind speeds (in m/s). Loaded using
|
wnd.height |
Height of the anemometer above the lake surface in meters |
bathy |
A data frame containing hypsometric data. Loaded using
|
seasonal |
Boolean indicating if seasonal thermocline should be used in calculation. |
Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.
For loading input data load.ts,
load.bathy.
For the underlying functions operating at each timestep
meta.depths, thermo.depth,
schmidt.stability, lake.number,
internal.energy.
Other Timeseries functions for r Lake Analyzer: ts.internal.energy,
ts.lake.number,
ts.meta.depths,
ts.schmidt.stability,
ts.thermo.depth
Function for simplifying the calculation of Wedderburn Number. Can usually
be called directly on data loaded directly using load.ts and
load.bathy.
ts.wedderburn.number(wtr, wnd, wnd.height, bathy, Ao, seasonal = TRUE)ts.wedderburn.number(wtr, wnd, wnd.height, bathy, Ao, seasonal = TRUE)
wtr |
A data frame of water temperatures (in Celsius). Loaded using
|
wnd |
A data frame of wind speeds (in m/s). Loaded using
|
wnd.height |
Height of the anemometer above the lake surface in meters |
bathy |
A data frame containing hypsometric data. Loaded using
|
Ao |
Numeric value for the water body surface area (m^2) at zero meters depth |
seasonal |
Boolean indicating if seasonal thermocline should be used in calculation. |
Returns a data frame with the timeseries of Wedderburn number. Includes a ‘datetime’ column.
Imberger, J., Patterson, J.C., 1990. Physical limnology. Advances in Applied Mechanics 27, 353-370.
wedderburn.number,ts.lake.number
#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") wnd.path <- system.file('extdata', 'Sparkling.daily.wnd', package="rLakeAnalyzer") bathy.path <- system.file('extdata', 'Sparkling.bth', package="rLakeAnalyzer") #Load data for example lake, Sparkilng lake, in Wisconsin. sp.wtr = load.ts(wtr.path) sp.wnd = load.ts(wnd.path) sp.bathy = load.bathy(bathy.path) sp.area = 64e4 #Area of Sparkling lake in m^2 wnd.height = 2 #Height of Sparkling lake anemometer w.n = ts.wedderburn.number(sp.wtr, sp.wnd, wnd.height, sp.bathy, sp.area) plot(w.n$datetime, w.n$wedderburn.number, type='l', ylab='Wedderburn Number', xlab='Date')#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") wnd.path <- system.file('extdata', 'Sparkling.daily.wnd', package="rLakeAnalyzer") bathy.path <- system.file('extdata', 'Sparkling.bth', package="rLakeAnalyzer") #Load data for example lake, Sparkilng lake, in Wisconsin. sp.wtr = load.ts(wtr.path) sp.wnd = load.ts(wnd.path) sp.bathy = load.bathy(bathy.path) sp.area = 64e4 #Area of Sparkling lake in m^2 wnd.height = 2 #Height of Sparkling lake anemometer w.n = ts.wedderburn.number(sp.wtr, sp.wnd, wnd.height, sp.bathy, sp.area) plot(w.n$datetime, w.n$wedderburn.number, type='l', ylab='Wedderburn Number', xlab='Date')
uStar is the water friction velocity due to wind stress at the lake surface, it is calculated following the methods of Imberger (1985) as a function of the shear stress of air (Fischer et al., 1979), drag coefficient for momentum (Hicks, 1972), and a dimensionless constant (von Karman constant) that decribes the logarithmic velocity profile at the air-water interface
uStar(wndSpeed, wndHeight, averageEpiDense)uStar(wndSpeed, wndHeight, averageEpiDense)
wndSpeed |
a numeric vector of wind speed in m s-1 |
wndHeight |
a numeric vector of wind measurement height in m |
averageEpiDense |
a numeric vector of epilimnion density in kg m-3 |
a numeric vector of uStar
Hicks, B.B., 1972. A procedure for the formulation of bulk transfer coefficients over water bodies of different sizes. Boundary-Layer Meterology 3: 201-213.
Amorocho, J., DeVries, J.J., 1980. A new evaluation of the wind stress coefficient over water surfaces. Journal of Geophysical Research 85: 433-442.
Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, J., Brooks, N.H., 1979. Mixing in inland and coastal waters. Academic Press.
Imberger, J., 1985. The diurnal mixed layer. Limnology and Oceanography 30: 737-770.
wndSpeed <- c(5.1,6.3,6.3,5.2,7,7.2) wndHeight <- 2 averageEpiDense <- c(14,15,14.2,13,12,12) cat('uStar for input vector is: ') cat(uStar(wndSpeed,wndHeight,averageEpiDense))wndSpeed <- c(5.1,6.3,6.3,5.2,7,7.2) wndHeight <- 2 averageEpiDense <- c(14,15,14.2,13,12,12) cat('uStar for input vector is: ') cat(uStar(wndSpeed,wndHeight,averageEpiDense))
Density of water from temperature and salinity
water.density(wtr, sal = wtr * 0)water.density(wtr, sal = wtr * 0)
wtr |
a numeric vector of water temperature in degrees Celsius |
sal |
a numeric vector of salinity in Practical Salinity Scale units |
A numeric vector of water densities in kg/m^3.
Martin, J.L., McCutcheon, S.C., 1999. Hydrodynamics and Transport for Water Quality Modeling. Lewis Publications, Boca Raton, FL, 794pp.
Millero, F.J., Poisson, A., 1981. International one-atmosphere equation of state of seawater. UNESCO Technical Papers in Marine Science. No. 36.
#Plot water density for water between 1 and 30 deg C dens = water.density(1:30) plot(1:30, dens, xlab="Temp(deg C)", ylab="Density(kg/m^3)")#Plot water density for water between 1 and 30 deg C dens = water.density(1:30) plot(1:30, dens, xlab="Temp(deg C)", ylab="Density(kg/m^3)")
Wedderburn Number (Wn) is a dimensionless parameter measuring the balance between wind stress and bouyancy force and is used to estimate the amount of upwelling occuring in a lake. When Wn is much greater than 1, the bouyancy force is much greater than the wind stress and therefore there is a strong vertical stratification with little horizontal variation in the stratification. When Wn is much less than 1, the wind stress is much greater than the bouyancy force and upwelling is likely occuring at the upwind end of the lake. When Wn is near 1, the bouyance force and wind stress are nearly equal and horizontal mixing is considered important
wedderburn.number(delta_rho, metaT, uSt, Ao, AvHyp_rho)wedderburn.number(delta_rho, metaT, uSt, Ao, AvHyp_rho)
delta_rho |
Numeric value for the water density difference between the epilimnion and hypolimnion (kg/m^3) |
metaT |
Numeric value for the thickness of the water body's surface layer (m) |
uSt |
Numeric value for the water friction velocity due to wind stress (m/s) |
Ao |
Numeric value for the water body surface area (m^2) at zero meters depth |
AvHyp_rho |
Numeric value for the average water density of the hypolimnion layer (kg/m^3) |
The dimensionless numeric value of Wedderburn Number
Imberger, J., Patterson, J.C., 1990. Physical limnology. Advances in Applied Mechanics 27, 353-370.
ts.wedderburn.number lake.number
delta_rho <- c(3.1,1.5) metaT <- c(5.5,2.4) uSt <- c(0.0028,0.0032) Ao <- c(80300,120000) AvHyp_rho <- c(999.31,999.1) wedderburn.number(delta_rho, metaT, uSt, Ao, AvHyp_rho)delta_rho <- c(3.1,1.5) metaT <- c(5.5,2.4) uSt <- c(0.0028,0.0032) Ao <- c(80300,120000) AvHyp_rho <- c(999.31,999.1) wedderburn.number(delta_rho, metaT, uSt, Ao, AvHyp_rho)
Calculates volumetrically weighted average whole lake temperature using the supplied water temperature timeseries.
whole.lake.temperature(wtr, depths, bthA, bthD)whole.lake.temperature(wtr, depths, bthA, bthD)
wtr |
a numeric vector of water temperature in degrees C. |
depths |
a numeric vector corresponding to the depths (in m) of the wtr measurements |
bthA |
a numeric vector of cross sectional areas (m^2) corresponding to bthD depths |
bthD |
a numeric vector of depths (m) which correspond to areal measures in bthA |
hypo.temperature, epi.temperature
This creates a simple, default heatmap of water temperature.
wtr.heat.map(wtr, ...)wtr.heat.map(wtr, ...)
wtr |
Data frame of water temperature loaded with
|
... |
Additional parameters supplied to |
#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. sp.wtr = load.ts(wtr.path) #Plot default figure wtr.heat.map(sp.wtr) #Change defaults supplied to filled.contour wtr.heat.map(sp.wtr, zlim=c(0,15), plot.title="Sparkling Water Temp (C)")#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.daily.wtr', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. sp.wtr = load.ts(wtr.path) #Plot default figure wtr.heat.map(sp.wtr) #Change defaults supplied to filled.contour wtr.heat.map(sp.wtr, zlim=c(0,15), plot.title="Sparkling Water Temp (C)")
This creates a heat map of water temperature similar to
wtr.heat.map with additional lines drawn to denote the
thermocline, and the top and bottom of the metalimnion as calculated using
ts.meta.depths and thermo.depth.
wtr.heatmap.layers(wtr, ...)wtr.heatmap.layers(wtr, ...)
wtr |
Data frame of water temperature loaded with
|
... |
Additional parameters supplied to |
This plot cannot be used in customized multi-panel figures
usinglayout as layout is already used in the filled.contour
plotting function.
wtr.heat.map load.ts
ts.meta.depths ts.thermo.depth
#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. wtr = load.ts(wtr.path) # generate default plot ## Not run: wtr.heatmap.layers(wtr) ## End(Not run)#Get the path for the package example file included wtr.path <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. wtr = load.ts(wtr.path) # generate default plot ## Not run: wtr.heatmap.layers(wtr) ## End(Not run)
Extract water column parameters of a given parameter from a profile using the split-and-merge algorithm. The cline is defined as the midpoint of the layer of water where the physical property change in the greatest over a small difference. The exact cline depends on the specification of measure. For example if temperature is specified, then we can expect cline to output the thermocline.
wtr.layer(data, depth, measure, thres = 0.1, z0 = 2.5, zmax = 150, nseg = "unconstrained")wtr.layer(data, depth, measure, thres = 0.1, z0 = 2.5, zmax = 150, nseg = "unconstrained")
data |
data supplied as a bare (unquoted) value |
depth |
depth in metres; should be an increasing vector; supplied as a bare (unquoted) value |
measure |
parameter measured in the water column profile; supplied as a bare (unquoted) value |
thres |
error norm; defaults to 0.1 |
z0 |
initial depth in metres. Defaults to 2.5m |
zmax |
maximum depth in metres: defaults to 150m |
nseg |
optional parameter to define the number of segments a priori; defaults to an unconstrained approach whereby the algorithm determines segmentations by minimzing the error norm over each segment |
a dataframes with a list column. This includes: nseg (number of segments), mld (mix layer depth), cline (the midpoint of the segment connecting inflection points that has the maximum slope; thermocline for temperature measures) and segments calculated by the sm algorithm.
Thomson, R. and I. Fine. 2003. Estimating Mixed Layer Depth from Oceanic Profile Data. Journal of Atmospheric and Oceanic Technology. 20(2), 319-329.
data("latesummer") df1 <- wtr.layer(depth=latesummer$depth, measure = latesummer$temper) df1$mld df1$segments wtr.layer(data = latesummer, depth=depth, measure = temper, nseg=4)data("latesummer") df1 <- wtr.layer(depth=latesummer$depth, measure = latesummer$temper) df1$mld df1$segments wtr.layer(data = latesummer, depth=depth, measure = temper, nseg=4)
A non-heat map approach to visualizing a water temperature profile useful for identify temperature trends over time at discrete depths and diagnosing issues with data.
wtr.lineseries(wtr, ylab = "Temperature C", ...)wtr.lineseries(wtr, ylab = "Temperature C", ...)
wtr |
Data frame of water temperature loaded with
|
ylab |
y axis title |
... |
Additional parameters supplied to the plot function |
See load.ts and wtr.heat.map
exampleFilePath <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") wtr= load.ts(exampleFilePath) ## Not run: wtr.lineseries(wtr, ylab = "Temperature C") ## End(Not run)exampleFilePath <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") wtr= load.ts(exampleFilePath) ## Not run: wtr.lineseries(wtr, ylab = "Temperature C") ## End(Not run)
A line based plot of calculated depths of the thermocline, and top and bottom of the metalimnion from a temperature profile time series.
wtr.plot.temp(wtr, ...)wtr.plot.temp(wtr, ...)
wtr |
Data frame of water temperature loaded with
|
... |
Additional paramters supplied to |
wtr.path <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. wtr = load.ts(wtr.path) ## Not run: wtr.plot.temp(wtr) ## End(Not run)wtr.path <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer") #Load data for example lake, Sparkilng Lake, Wisconsin. wtr = load.ts(wtr.path) ## Not run: wtr.plot.temp(wtr) ## End(Not run)