From 6476f5f49b373cd4cf05f2e73389df83e437d597 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Thu, 13 Feb 2025 16:30:31 +0100 Subject: Axis legend formatting, update vignettes --- docs/articles/twa.html | 178 ++++++++++++++++++++++--------------------------- 1 file changed, 79 insertions(+), 99 deletions(-) (limited to 'docs/articles/twa.html') diff --git a/docs/articles/twa.html b/docs/articles/twa.html index 5452a5e5..19bc4761 100644 --- a/docs/articles/twa.html +++ b/docs/articles/twa.html @@ -5,86 +5,71 @@ - Calculation of time weighted average concentrations with mkin • mkin - - - - - - + + + + - -

- + +

@@ -93,12 +78,13 @@

Calculation of time weighted average concentrations with mkin

+ +

Calculation of time weighted average concentrations with mkin

Johannes Ranke

Last change 18 September 2019 -(rebuilt 2023-11-16)

+(rebuilt 2025-02-13) Source: vignettes/twa.rmd

twa.rmd

@@ -118,48 +104,44 @@ model are calculated using the formulas given in the FOCUS kinetics guidance (FOCUS Work Group on Degradation Kinetics 2014, 251):

SFO:

\[c_\textrm{twa} = c_0 \frac{\left( 1 - -e^{- k t} \right)}{ k t} \]

$c_\textrm{twa} = c_0 \frac{\left( 1 - e^{- k t} \right)}{ k t}$

FOMC:

\[c_\textrm{twa} = c_0 \frac{\beta}{t (1 - -\alpha)} - \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} -- 1 \right) \]

$c_\textrm{twa} = c_0 \frac{\beta}{t (1 - \alpha)} + \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right)$

DFOP:

\[c_\textrm{twa} = \frac{c_0}{t} \left( +

$c_\textrm{twa} = \frac{c_0}{t} \left( \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + - \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) \] -HS for$ $t > t_b$: -\[c_\textrm{twa} = \frac{c_0}{t} \left( + \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right)

HS for + $t > t_b$ :

$c_\textrm{twa} = \frac{c_0}{t} \left( \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + - \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} -\right) \right) \] + \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right) \right)$

Often, the ratio between the time weighted average concentration -$c_\textrm{twa}$ and the initial -concentration $c_0$

\[f_\textrm{twa} = -\frac{c_\textrm{twa}}{c_0}\]

c_\textrm{twa}

+and the initial concentration +

c_0

$f_\textrm{twa} = \frac{c_\textrm{twa}}{c_0}$

is needed. This can be calculated from the fitted initial -concentration $c_0$ and the time -weighted average concentration $c_\textrm{twa}$, or directly from the -model parameters using the following formulas:

+concentration +

c_0

+and the time weighted average concentration +

c_\textrm{twa}

, +or directly from the model parameters using the following formulas:

SFO:

\[f_\textrm{twa} = \frac{\left( 1 - e^{- k -t} \right)}{k t} \]

$f_\textrm{twa} = \frac{\left( 1 - e^{- k t} \right)}{k t}$

FOMC:

\[f_\textrm{twa} = \frac{\beta}{t (1 - -\alpha)} - \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} -- 1 \right) \]

$f_\textrm{twa} = \frac{\beta}{t (1 - \alpha)} + \left( \left(\frac{t}{\beta} + 1 \right)^{1 - \alpha} - 1 \right)$

DFOP:

\[f_\textrm{twa} = \frac{1}{t} \left( +

$f_\textrm{twa} = \frac{1}{t} \left( \frac{g}{k_1} \left( 1 - e^{- k_1 t} \right) + - \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right) \] -HS for$ $t > t_b$: -\[f_\textrm{twa} = \frac{1}{t} \left( + \frac{1-g}{k_2} \left( 1 - e^{- k_2 t} \right) \right)

HS for + $t > t_b$ :

$f_\textrm{twa} = \frac{1}{t} \left( \frac{1}{k_1} \left( 1 - e^{- k_1 t_b} \right) + - \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} -\right) \right) \] + \frac{e^{- k_1 t_b}}{k_2} \left( 1 - e^{- k_2 (t - t_b)} \right) \right)$

Note that a method for calculating maximum moving window time weighted average concentrations for a model fitted by ‘mkinfit’ or from parent decline model parameters is included in the @@ -173,28 +155,26 @@ Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in EU Registration. 1.1 ed. http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics.

- - + + -- cgit v1.2.1