quadrature_error {neonSoilFlux}

Helper function to quickly compute the quadrature error

Description

Assume a derived quantity y is a function of inputs x_i: y = f(x_1,x_2,x_3, ...)

Given uncertainties (x_err) for each x_i, then this function will compute the corresponding y_err via quadrature. Inputs are the vector of partial derivaties df/dx_i, evaluated at (x_1,x_2,x_3,...).

Resulting y_err is the square root of the sum of (df/dx_1)^2 * (x_err)^2 + (df/dx_2)^2 * (x_err)^2 + (df/dx_3)^2 * (x_err)^2 ...

Usage

quadrature_error(x_pd, x_err)

Arguments

x_pd

Required. Input vector of partial derivatives for y = f(x), evaluated at x_i

x_err

Required. Error vector of measurements

Value

A value of quadrature error

Author(s)

John Zobitz [e-mail]

Examples

# Let's say we have 5 temperature measurements w/ error::
temperature <- c(31.108, 30.689, 30.463, 30.381, 30.250)
temperature_error <- c(0.1508,0.1507,0.1497,0.1496,0.1497)

# The sample mean is the sum of all measurements divided by the average:
sum(temperature)/5  # (Can also be computed with mean(temperature))

# The vector of partial derivatives is just 1/n for each measurement:
temperature_pd <- c(1/5,1/5,1/5,1/5,1/5)
quadrature_error(temperature_pd,temperature_error)
# Note: quadrature_error(1/5,temperature_error) is also allowed.