, Ben Bond-Lamberty
[ctb] | Title: | Calculate Gross Biogeochemical Flux Rates from Isotope Pool Dilution Data |
|---|---|
| Description: | Pool dilution is a isotope tracer technique wherein a biogeochemical pool is artifically enriched with its heavy isotopologue and the gross productive and consumptive fluxes of that pool are quantified by the change in pool size and isotopic composition over time. This package calculates gross production and consumption rates from closed-system isotopic pool dilution time series data. Pool size concentrations and heavy isotope (e.g., 15N) content are measured over time and the model optimizes production rate (P) and the first order rate constant (k) by minimizing error in the model-predicted total pool size, as well as the isotopic signature. The model optimizes rates by weighting information against the signal:noise ratio of concentration and heavy- isotope signatures using measurement precision as well as the magnitude of change over time. The calculations used here are based on von Fischer and Hedin (2002) <doi:10.1029/2001GB001448> with some modifications. |
| Authors: | Kendalynn A. Morris [cre, aut]
, Ben Bond-Lamberty
[ctb] |
| Maintainer: | Kendalynn A. Morris <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 1.0.0 |
| Built: | 2024-12-17 06:51:15 UTC |
| Source: | CRAN |
Retrieve default k fractionation value for a pool
frac_k_default(pool)frac_k_default(pool)
pool |
Name of pool, character |
The default entry for pool listed
in pdr_fractionation.
frac_k_default("CH4")frac_k_default("CH4")
Retrieve default P fractionation value for a pool
frac_P_default(pool)frac_P_default(pool)
pool |
Name of pool, character |
The default entry for pool listed
in pdr_fractionation.
frac_P_default("CH4")frac_P_default("CH4")
Sequential measurements of methane concentration and isotopic signature were taken using a Picarro G2920 with a Small Sample Introduction module. This instrument provides gas concentrations in ppm and signatures in delta-13C, here we provide those data converted into volume of methane and atom percent.
Morris2023Morris2023
Sample ID, a factor
time in days between measurements, starting at 0
ml of 12C-CH4 at each timestep
ml of 13C-CH4 at each timestep
atom percent 13C-CH4 at each timestep
Cost function between observed and predicted pools
pdr_cost( params, time, m, n, m_prec, ap_prec, P, k, pool = "CH4", frac_P = frac_P_default(pool), frac_k = frac_k_default(pool), log_progress = NULL )pdr_cost( params, time, m, n, m_prec, ap_prec, P, k, pool = "CH4", frac_P = frac_P_default(pool), frac_k = frac_k_default(pool), log_progress = NULL )
params |
Named list holding optimizer-assigned values for parameters |
time |
Vector of numeric time values; first should be zero |
m |
Observed total pool size, same length as time |
n |
Observed pool size of heavy isotope, same length as time |
m_prec |
Instrument precision for pool size, expressed as a standard deviation |
ap_prec |
Instrument precision for atom percent, expressed as a standard deviation |
P |
production rate, unit pool size/unit time |
k |
first-order rate constant for consumption, 1/unit time |
pool |
Name of pool; see |
frac_P |
Fractionation value for production; see |
frac_k |
Fractionation value for consumption; see |
log_progress |
An optional logging function |
Returns a cost metric summarizing the difference between the
predicted and observed m (total pool size) and AP (atom percent).
This implements Equations 12-14 from von Fischer and Hedin (2002).
K.A. Morris & B. Bond-Lamberty
m <- c(10, 8, 6, 5, 4, 3) n <- c(1, 0.7, 0.6, 0.4, 0.3, 0.2) pdr_cost(params = list(P = 0.5, k = 0.3), time = 0:5, m, n, m_prec = 0.001, ap_prec = 0.01)m <- c(10, 8, 6, 5, 4, 3) n <- c(1, 0.7, 0.6, 0.4, 0.3, 0.2) pdr_cost(params = list(P = 0.5, k = 0.3), time = 0:5, m, n, m_prec = 0.001, ap_prec = 0.01)
Estimate initial k from heavy isotope concentration data
pdr_estimate_k0(time, n, frac_k, quiet = FALSE)pdr_estimate_k0(time, n, frac_k, quiet = FALSE)
time |
Vector of numeric time values (e.g. days); first should be zero |
n |
Observed heavy isotope (as a volume), same length as time |
frac_k |
Fractionation: 13C consumption as a fraction of 12C consumption |
quiet |
Suppress output message, logical |
Initial estimate of k0 (consumption rate constant)
pdr_estimate_k0(1:5, c(1, 0.9, 0.7, 0.65, 0.4), frac_k = 0.98)pdr_estimate_k0(1:5, c(1, 0.9, 0.7, 0.65, 0.4), frac_k = 0.98)
A compendium of possible production (P) and consumption (k) fractionation values, by pool.
pdr_fractionationpdr_fractionation
Name of pool (gas or solid)
Fractionation value of production (P)
Fractionation value of consumption (k)
Default for this pool? Logical
Source paper or URL
Currently there is only one set of fractionation values available, from von Fischer and Hedin (2002, 10.1029/2001GB001448).
Optimize production and consumption parameters for pool dilution data
pdr_optimize( time, m, n, m_prec, ap_prec, P, k, params_to_optimize = c("P", "k"), pool = "CH4", frac_P = NULL, frac_k = NULL, other_params = list(), cost_fn = pdr_cost, prediction_fn = pdr_predict, include_progress = FALSE, quiet = FALSE )pdr_optimize( time, m, n, m_prec, ap_prec, P, k, params_to_optimize = c("P", "k"), pool = "CH4", frac_P = NULL, frac_k = NULL, other_params = list(), cost_fn = pdr_cost, prediction_fn = pdr_predict, include_progress = FALSE, quiet = FALSE )
time |
Vector of numeric time values (e.g. days); first should be zero |
m |
Observed total pool size (as a volume), same length as time |
n |
Observed heavy isotope (as a volume), same length as time |
m_prec |
Instrument precision for pool size, expressed as a standard deviation |
ap_prec |
Instrument precision for atom percent, expressed as a standard deviation |
P |
production rate, unit gas/unit time |
k |
first-order rate constant for consumption, 1/unit time |
params_to_optimize |
Named vector of parameters ("P", "k", "frac_P", and/or "frac_k") to optimize against observations |
pool |
Name of pool to use when looking up fractionation values if they
are not supplied; see |
frac_P |
Fractionation value for production; see |
frac_k |
Fractionation value for consumption; see |
other_params |
Other parameters pass on to |
cost_fn |
Cost function to use; the default is |
prediction_fn |
Prediction function that the cost function will use;
the default is |
include_progress |
Include detailed optimizer progress data in output? |
quiet |
Suppress output messages, logical |
The output of optim.
Currently there is only one set of fractionation values available in
pdr_fractionation, from von Fischer and Hedin
(2002, 10.1029/2001GB001448).
tm <- 0:5 m <- c(10, 8, 6, 5, 4, 3) n <- c(1, 0.7, 0.6, 0.4, 0.3, 0.2) m_prec <- 0.001 ap_prec <- 0.01 # Optimize values for P (production) and k (consumption), provide starting values for P and k pdr_optimize(time = tm, m, n, m_prec, ap_prec, P = 0.5, k = 0.3) # If we don't provide a value for k, it can be estimated from the data pdr_optimize(tm, m, n, m_prec, ap_prec, P = 0.5) # Hold k and frac_k constant (ie., k = estimated k0, frac_k = default value), optimize P and frac_P pdr_optimize(tm, m, n, m_prec, ap_prec, P = 0.5, params_to_optimize = c("P", "frac_P")) # Optimize only k (provide P and exclude from params_to_optimize) pdr_optimize(tm, m, n, m_prec, ap_prec, P = 0.5, params_to_optimize = "k") # Optimize only k, bounding its possible values op <- list(lower = c("k" = 0.2), upper = c("k" = 0.3)) pdr_optimize(tm, m, n, m_prec, ap_prec, 0.5, 0.27, params_to_optimize = "k", other_params = op)tm <- 0:5 m <- c(10, 8, 6, 5, 4, 3) n <- c(1, 0.7, 0.6, 0.4, 0.3, 0.2) m_prec <- 0.001 ap_prec <- 0.01 # Optimize values for P (production) and k (consumption), provide starting values for P and k pdr_optimize(time = tm, m, n, m_prec, ap_prec, P = 0.5, k = 0.3) # If we don't provide a value for k, it can be estimated from the data pdr_optimize(tm, m, n, m_prec, ap_prec, P = 0.5) # Hold k and frac_k constant (ie., k = estimated k0, frac_k = default value), optimize P and frac_P pdr_optimize(tm, m, n, m_prec, ap_prec, P = 0.5, params_to_optimize = c("P", "frac_P")) # Optimize only k (provide P and exclude from params_to_optimize) pdr_optimize(tm, m, n, m_prec, ap_prec, P = 0.5, params_to_optimize = "k") # Optimize only k, bounding its possible values op <- list(lower = c("k" = 0.2), upper = c("k" = 0.3)) pdr_optimize(tm, m, n, m_prec, ap_prec, 0.5, 0.27, params_to_optimize = "k", other_params = op)
Optimize production and consumption parameters for pool dilution data
pdr_optimize_df(...)pdr_optimize_df(...)
... |
Parameters to be passed on to |
The output of pdr_optimize summarized in a data frame,
with one line per parameter estimates (P, k,
frac_P, and/or frac_k).
tm <- 0:5 m <- c(10, 8, 6, 5, 4, 3) n <- c(1, 0.7, 0.6, 0.4, 0.3, 0.2) m_prec <- 0.001 ap_prec <- 0.01 # Optimize values for P (production) and k (consumption) pdr_optimize_df(time = tm, m, n, m_prec, ap_prec, P = 0.5, k = 0.3)tm <- 0:5 m <- c(10, 8, 6, 5, 4, 3) n <- c(1, 0.7, 0.6, 0.4, 0.3, 0.2) m_prec <- 0.001 ap_prec <- 0.01 # Optimize values for P (production) and k (consumption) pdr_optimize_df(time = tm, m, n, m_prec, ap_prec, P = 0.5, k = 0.3)
Predict total pool, heavy isotope pool, and atom percent
pdr_predict( time, m0, n0, P, k, pool = "CH4", frac_P = frac_P_default(pool), frac_k = frac_k_default(pool) )pdr_predict( time, m0, n0, P, k, pool = "CH4", frac_P = frac_P_default(pool), frac_k = frac_k_default(pool) )
time |
Vector of numeric time values (e.g. days); first should be zero |
m0 |
total pool size at time zero, as a volume |
n0 |
pool size of heavy isotope at time zero, as a volume |
P |
production rate, unit gas/unit time |
k |
first-order rate constant for consumption, 1/unit time |
pool |
Name of pool; see |
frac_P |
Fractionation value for production; see |
frac_k |
Fractionation value for consumption; see |
Returns a data frame with mt, nt, and AP_pred (atom percent) for each time step
This is Eq. 11 from von Fischer and Hedin 2002 with a few modifications.
K.A. Morris & B. Bond-Lamberty
pdr_predict(time = 0:5, m0 = 10, n0 = 1, P = 0.5, k = 0.3)pdr_predict(time = 0:5, m0 = 10, n0 = 1, P = 0.5, k = 0.3)