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.

Estimate hypsography curve

Description

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.

Usage

approx.bathy(Zmax, lkeArea, Zmean = NULL, method = "cone", zinterval = 1,
  depths = seq(0, Zmax, by = zinterval))

Arguments

Value

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.

References

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.

Examples

 
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)")
  points(Voldev.ex$depths ~ Voldev.ex$Area.at.z, col = "red")
  points(Voldevshallow.ex$depths ~ Voldevshallow.ex$Area.at.z, col = "blue")
 

Calculates buoyancy frequency.

Description

Calculate the buoyancy frequency (Brunt-Vaisala frequency) for a temperature profile.

Usage

buoyancy.freq(wtr, depths)

Arguments

Value

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).

See Also

thermo.depth, ts.buoyancy.freq

Examples

	# 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)))

Calculates the center of buoyancy.

Description

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.

Usage

center.buoyancy(wtr, depths)

Arguments

Value

Returns a value for the center of buoyancy.

See Also

buoyancy.freq, ts.buoyancy.freq, center.buoyancy

Examples

	# 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)

Calculate cline of series of segments

Description

Cline depth is defined as the midpoint of the segment connecting inflection points that has the maximum slope. A cline cannot occur over a depth range of less than 1m and also cannot be the shallowest segment. Violating both conditions will thrown warnings though this function handles both differently. Used mostly with wtr_layer

Usage

cline_calc(z_seg = z_seg, sigma_seg = sigma_seg)

Arguments

Value

the depth of the cline

References

Fiedler, Paul C. Comparison of objective descriptions of the thermocline. Limnology and Oceanography: Methods 8.6 (2010): 313-325.

See Also

wtr_layer()

Data filter to remove soak, heave and upcast

Description

• 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.

Usage

depth.filter(z0, run_length = 20, index = FALSE)

Arguments

Value

index values of z0 of filtered data. Will return a warning if the function removed more than 10

Find and drop the datetime column from the datatable

Description

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.

Usage

drop.datetime(data, error = FALSE)

Arguments

Value

A data.frame with only the data, after datetime has been dropped

Get volumetrically averaged epilimnion temp

Description

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.

Usage

epi.temperature(wtr, depths, bthA, bthD)

Arguments

See Also

hypo.temperature whole.lake.temperature

Search for and return the datetime column from a ts data.frame

Description

Warns if unavailable then returns NULL.

Usage

get.datetime(data, error = FALSE)

Arguments

Gets depths from data frame containing profile info.

Description

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.

Usage

get.offsets(data)

Arguments

Value

A numeric vector of depth values. Should be the ncol(data) - 1 in length as the first column contains date/time data.

See Also

load.ts

Examples

#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 volumetrically averaged hypolimnion temp

Description

Calculates volumetrically weighted average hypolimnetic temperature using the supplied water temperature timeseries. If the lake is not stratified, an NA value is returned.

Usage

hypo.temperature(wtr, depths, bthA, bthD)

Arguments

See Also

epi.temperature, whole.lake.temperature

Internal energy function (Joules)

Description

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.

Usage

internal.energy(wtr, depths, bthA, bthD)

Arguments

Value

internal energy in Joules m-2. (Currently not vectorized..)

Examples

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))

Calculate Lake Number

Description

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).

Usage

lake.number(bthA, bthD, uStar, St, metaT, metaB, averageHypoDense)

Arguments

Value

A numeric vector of Lake Number [dimensionless]

References

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.

See Also

ts.lake.number wedderburn.number

Examples

	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) )

Plots time series of Lake Number

Description

Generates a time series plot of Lake Number for appropriately formatted data. See lake.number for more details on Lake Number and reference.

Usage

lake.number.plot(wtr, wnd, wh, bth)

Arguments

See Also

wtr.lineseries

Examples

	#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 Profile

Description

Late summer water profile taken from Quesnel Lake, British Columbia, Canada. Profile taken with Sea-Bird SBE19plus.

depth

Depth, m

temper

Temperature, degC

salinity

Salinity, PSU

oxygen

Oxygen, ml/l

oxygen.sat

Oxygen saturation, percent saturation

density

Density, kg/m^3

...

Usage

latesummer

Format

An object of class data.frame with 881 rows and 6 columns.

Returns the average density of a layer between two depths.

Description

This function calculates the average density of a layer of water between two depths.

Usage

layer.density(top, bottom, wtr, depths, bthA, bthD, sal = wtr * 0)

Arguments

Value

Numeric value of average water density for bounded layer in kg/m^3

See Also

water.density

Examples

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)

Returns the average temperature of a layer between two depths.

Description

This function calculates the average temperature of a layer of water between two depths.

Usage

layer.temperature(top, bottom, wtr, depths, bthA, bthD)

Arguments

Value

Numeric value of average water temperature

See Also

layer.density

Examples

	# 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)

Import lake bathymetry data.

Description

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.

Usage

load.bathy(fPath)

Arguments

Value

data.frame of depth and area for given lake.

See Also

load.ts

Examples

  #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)')
  

Load timeseries from properly formatted text file.

Description

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.

Usage

load.ts(fPath, tz = "GMT")

Arguments

Value

A data frame in the required format for use with other rLakeAnalyzer timeseries functions.

See Also

For dataloading ts.meta.depths,
For analyzing timeseries data, see ts.meta.depths, ts.thermo.depth, ts.schmidt.stability, ts.lake.number.

Examples

	#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')

Calculate the Top and Bottom Depths of the Metalimnion

Description

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.

Usage

meta.depths(wtr, depths, slope = 0.1, seasonal = TRUE, mixed.cutoff = 1)

Arguments

Value

A numeric vector of the top and bottom metalimnion depths in meters. Returns the bottom depth if no distinct metalimion top and bottom found.

References

Wetzel, R. G. 2001. Limnology: Lake and River Ecosystems, 3rd ed. Academic Press.

See Also

ts.meta.depths, thermo.depth

Examples

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])

Creates a time series plot of Schmidt's stability

Description

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.

Usage

schmidt.plot(wtr, bth)

Arguments

References

See schmidt.stability

See Also

schmidt.stability

Examples

	# 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)

Calculate the Schmidt stability

Description

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).

Usage

schmidt.stability(wtr, depths, bthA, bthD, sal = 0)

Arguments

Value

a numeric vector of Schmidt stability (J/m^2)

References

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.

See Also

ts.schmidt.stability lake.number wedderburn.number

Examples

	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))

Calculate depth of the thermocline from a temperature profile.

Description

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.

Usage

thermo.depth(wtr, depths, Smin = 0.1, seasonal = TRUE, index = FALSE,
  mixed.cutoff = 1)

Arguments

Value

Depth of thermocline. If no thermocline found, value is NaN.

See Also

ts.thermo.depth, water.density

Examples

# 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)

Calculate the buoyancy (Brunt-Vaisala) frequency for a temperature profile.

Description

Function for simplifying the calculation of buoyancy frequency. Can usually be called directly on data loaded directly using load.ts and load.bathy.

Usage

ts.buoyancy.freq(wtr, at.thermo = TRUE, na.rm = FALSE, ...)

Arguments

Value

Returns a data frame with the timeseries of buoyancy frequency in units sec^-2. Includes a ‘datetime’ column.

References

Imberger, J., Patterson, J.C., 1990. Physical limnology. Advances in Applied Mechanics 27, 353-370.

See Also

buoyancy.freq

Examples

	#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')
	

Calculates the center of buoyancy for multiple temperature profiles.

Description

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.

Usage

ts.center.buoyancy(wtr, na.rm = FALSE)

Arguments

Value

Returns a data frame with the timeseries of the center of buoyancy frequency. Includes a ‘datetime’ column.

References

Imberger, J., Patterson, J.C., 1990. Physical limnology. Advances in Applied Mechanics 27, 353-370.

See Also

center.buoyancy, load.bathy, load.ts

Examples

  #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")
	

Calculate physical indices for a timeseries.

Description

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.

Usage

ts.internal.energy(wtr, bathy, na.rm = FALSE)

Arguments

Value

Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.

See Also

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

Calculate physical indices for a timeseries.

Description

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.

Usage

ts.lake.number(wtr, wnd, wnd.height, bathy, seasonal = TRUE)

Arguments

Value

Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.

See Also

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

Calculate volume-weighted average water temperature across a range of depths for a timeseries.

Description

Function for simplifying the calculation of Wedderburn Number. Can usually be called directly on data loaded directly using load.ts and load.bathy.

Usage

ts.layer.temperature(wtr, top, bottom, bathy, na.rm = FALSE)

Arguments

Value

Returns a data frame with the timeseries of the average layer temperature. Includes ‘datetime’ and ‘layer.temp’ columns.

See Also

layer.temperature

Examples

	#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')
	

Calculate physical indices for a timeseries.

Description

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.

Usage

ts.meta.depths(wtr, slope = 0.1, na.rm = FALSE, ...)

Arguments

Value

Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.

See Also

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

Examples

	#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')
  
  

Calculate physical indices for a timeseries.

Description

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.

Usage

ts.schmidt.stability(wtr, bathy, na.rm = FALSE)

Arguments

Value

Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.

See Also

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

Calculate physical indices for a timeseries.

Description

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.

Usage

ts.thermo.depth(wtr, Smin = 0.1, na.rm = FALSE, ...)

Arguments

Value

Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.

See Also

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

Examples

	#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')
  

Calculate physical indices for a timeseries.

Description

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.

Usage

ts.uStar(wtr, wnd, wnd.height, bathy, seasonal = TRUE)

Arguments

Value

Returns a data frame with the timeseries of calculated derivatives. All include a ‘datetime’ column, but derivative columns differ between functions.

See Also

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

Calculate Wedderburn number for a timeseries.

Description

Function for simplifying the calculation of Wedderburn Number. Can usually be called directly on data loaded directly using load.ts and load.bathy.

Usage

ts.wedderburn.number(wtr, wnd, wnd.height, bathy, Ao, seasonal = TRUE)

Arguments

Value

Returns a data frame with the timeseries of Wedderburn number. Includes a ‘datetime’ column.

References

Imberger, J., Patterson, J.C., 1990. Physical limnology. Advances in Applied Mechanics 27, 353-370.

See Also

wedderburn.number,ts.lake.number

Examples

	#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')
	

Calculates the water friction velocity, uStar

Description

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

Usage

uStar(wndSpeed, wndHeight, averageEpiDense)

Arguments

Value

a numeric vector of uStar

References

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.

See Also

ts.uStar layer.density

Examples

  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))

Estimate Water Density

Description

Density of water from temperature and salinity

Usage

water.density(wtr, sal = wtr * 0)

Arguments

Value

A numeric vector of water densities in kg/m^3.

References

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.

Examples

#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)")

Calculates Wedderburn Number for a lake.

Description

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

Usage

wedderburn.number(delta_rho, metaT, uSt, Ao, AvHyp_rho)

Arguments

Value

The dimensionless numeric value of Wedderburn Number

References

Imberger, J., Patterson, J.C., 1990. Physical limnology. Advances in Applied Mechanics 27, 353-370.

See Also

ts.wedderburn.number lake.number

Examples

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)

Get volumetrically averaged whole lake temperature

Description

Calculates volumetrically weighted average whole lake temperature using the supplied water temperature timeseries.

Usage

whole.lake.temperature(wtr, depths, bthA, bthD)

Arguments

See Also

hypo.temperature, epi.temperature

Plots a heat-map of water temperature.

Description

This creates a simple, default heatmap of water temperature.

Usage

wtr.heat.map(wtr, ...)

Arguments

See Also

load.ts

Examples

	#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)")

Plots water temperature heatmap with major limnetic layers indicated

Description

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.

Usage

wtr.heatmap.layers(wtr, ...)

Arguments

Note

This plot cannot be used in customized multi-panel figures usinglayout as layout is already used in the filled.contour plotting function.

See Also

wtr.heat.map load.ts ts.meta.depths ts.thermo.depth

Examples

  #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)

Exploration of lake water column layers

Description

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.

Usage

wtr.layer(data, depth, measure, thres = 0.1, z0 = 2.5, zmax = 150,
  nseg = "unconstrained")

Arguments

Value

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.

References

Thomson, R. and I. Fine. 2003. Estimating Mixed Layer Depth from Oceanic Profile Data. Journal of Atmospheric and Oceanic Technology. 20(2), 319-329.

Examples

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)

Creates a line based plot of temperature profile time series

Description

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.

Usage

wtr.lineseries(wtr, ylab = "Temperature C", ...)

Arguments

See Also

See load.ts and wtr.heat.map

Examples

exampleFilePath <- system.file('extdata', 'Sparkling.wtr', package="rLakeAnalyzer")
wtr= load.ts(exampleFilePath)
## Not run: 
wtr.lineseries(wtr, ylab = "Temperature C")

## End(Not run)

Creates a time series plot of the thermocline and top and bottom of the metalimnion

Description

A line based plot of calculated depths of the thermocline, and top and bottom of the metalimnion from a temperature profile time series.

Usage

wtr.plot.temp(wtr, ...)

Arguments

See Also

load.ts and wtr.lineseries

Examples

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)