vignettes/parametrization/GrowthCalibration.Rmd
GrowthCalibration.Rmd
The growth model included in medfate implements processes regulating plant carbon balance and growth. Species-level parameter values for these processes are obtained from: (a) global functional trait databases; (b) meta-modelling exercises; (c) model calibration exercises. The main goal of the current exercise is to obtain suitable values (via model calibration) for parameters related with the maintenance respiration costs, formation rates and senescence rates of sapwood, because these are difficult to obtain using other means. At the same time, the exercise provides information on the performance of the model to predict secondary growth at the tree and stand levels.
The calibration data set corresponds to 75 permanent forest plots of the Spanish National Forest Inventory located in Catalonia. Forest plots correspond to pure stands whose dominant species are Fagus sylvatica, Pinus halepensis, Pinus nigra, Pinus sylvestris or Quercus pubescens. There are 15 plots per each dominant species and each set of 15 plots encompass a range of climatic aridity. Plot characteristics are described in Rosas et al. (2019). Dendrochronological series are available for up to 6 trees per plot and were sampled in December 2015. Note that a sixth species (Quercus ilex) was included in Rosas et al (2019), but dendrochronological dating is not available.
The model parameters for which we desired good estimates are:
In addition, soil stoniness in the target plots had been estimated
from surface stoniness classes. Since soil rock fragment content
(rfc
) has a strong influence on soil water capacity, we
decided to include the proportion of rocks in the second soil layer
(between 30 and 100 cm) as a parameter to be calibrated.
For each forest plot in the first data set, we matched each available dendrochronological series with a forest inventory tree cohort by finding which tree (in the IFN3 sampling) had the DBH most similar to that estimated from the dendrochronology at year 2000. Then, we took the series of annual basal area increments (BAI) as the observations to be matched by model secondary growth predictions for the matched tree cohort. For each forest plot of the second data set, we took all available dendrochronological series between 1990 and 2004. Available diameter increments (DI) were used to infer DBH at year 1990 and we transformed DI into annual BAI.
Simulations were performed using daily weather data for each target
plot, obtained via interpolation using package
meteoland (2001 - 2015 period or 1990-2004 period,
depending on the data set), and soil physical characteristics where
drawn from SoilGrids data base. Transpiration and photosynthesis
parameters were given values resulting from the meta-modelling
exercise, whereas other parameters of the sensitivity analysis were
left to the species-level defaults of SpParamsMED
. We
calibrated the four target parameters for the target dominant species of
the target plot using a genetic algorithm (function ga
from
package GA). Model parameter values were assumed to be
the same for all cohorts of the target species, while the remaining
species in the plot were given default constant parameter values. The
objective function for the genetic algorithm was the average, across
cohorts with observed dendrochronology series, of the mean absolute
error (MAE) resulting from comparing observed and predicted annual BAI
series. Population size for the genetic algorithm was set to 40
individuals. A maximum of 25 iterations of the genetic algorithm were
allowed, and the calibration procedure stopped if the best parameter
combination did not change during 5 consecutive iterations.
Minimum | Maximum | |
---|---|---|
RERsapwood | 1.0e-06 | 1.0e-04 |
RGRcambiummax | 1.0e-04 | 2.0e-02 |
SRsapwood | 1.0e-05 | 2.5e-04 |
rfc@2 | 2.5e+01 | 9.5e+01 |
The following panel shows the distribution of the final (optimum) values of the error function (average relative MAE) by dominant species:
The following panels show the distribution of calibrated parameter values by species (gray dashed lines indicate the parameter value limits used in the calibration procedure):
The following table shows mean error and parameter values by species and overall means:
value_cal | RERsapwood_cal | RGRcambiummax_cal | SRsapwood_cal | rfc_cal | |
---|---|---|---|---|---|
Fagus sylvatica | 43.95563 | 5.11e-05 | 0.0028215 | 0.0001262 | 47.72419 |
Pinus halepensis | 46.25125 | 5.51e-05 | 0.0022197 | 0.0001026 | 56.32354 |
Pinus nigra | 41.97312 | 4.18e-05 | 0.0017254 | 0.0001391 | 72.48055 |
Pinus sylvestris | 40.50649 | 6.05e-05 | 0.0023457 | 0.0001416 | 72.13271 |
Quercus pubescens | 39.70155 | 4.88e-05 | 0.0015056 | 0.0001644 | 54.51127 |
All | 42.47761 | 5.15e-05 | 0.0021236 | 0.0001348 | 60.63445 |
Statistically significant differences can be observed between species
for RERsapwood
and RGRcambiummax
, as shown in
the following ANOVA tables:
## Analysis of Variance Table
##
## Response: RERsapwood_cal
## Df Sum Sq Mean Sq F value Pr(>F)
## Species 4 2.9480e-09 7.3699e-10 1.3127 0.2738
## Residuals 70 3.9301e-08 5.6144e-10
## Analysis of Variance Table
##
## Response: RGRcambiummax_cal
## Df Sum Sq Mean Sq F value Pr(>F)
## Species 4 1.6290e-05 4.0726e-06 3.1039 0.02068 *
## Residuals 70 9.1846e-05 1.3121e-06
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Variance Table
##
## Response: SRsapwood_cal
## Df Sum Sq Mean Sq F value Pr(>F)
## Species 4 3.0774e-08 7.6935e-09 2.3528 0.06226 .
## Residuals 70 2.2890e-07 3.2700e-09
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Variance Table
##
## Response: rfc_cal
## Df Sum Sq Mean Sq F value Pr(>F)
## Species 4 7429.4 1857.34 5.6629 0.0005235 ***
## Residuals 70 22959.0 327.99
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Finally, the following panels illustrate the overall lack of covariance between calibrated parameter values:
Since the calibration exercise had been conducted using the basic sub-model, it is expected that growth simulations with the advanced sub-model have larger error rates and, potentially, larger bias. To check this, we repeated growth simulations using the calibrated parameters for each plot and the advanced sub-model.
The following figures show the bias and mean absolute error of annual basal area increments obtained in simulations using the basic and advanced sub-models, in both cases using the calibrated parameters.