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.

Observational data

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.

Target parameters for calibration

The model parameters for which we desired good estimates are:

  1. Sapwood daily respiration rate (RERsapwood) - Used to modulate maintenance respiration demands of living sapwood tissues (parenchyma, cambium, phloem, etc.), which in large trees may also represent a large fraction of maintenance respiration.
  2. Sapwood maximum growth rate (RGRcambiummax) - Used to modulate tree maximum daily sapwood growth rates (relative to current cambium perimeter). Actual relative growth rates include temperature and sink limitations to growth.
  3. Sapwood daily senescence rate (SRsapwood) - Used to determine the daily proportion of sapwood that becomes heartwood. It regulates the area of functional sapwood, together with the sapwood maximum growth rate.

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.

Calibration procedure

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.

The following table shows the range of values explored for each parameter to be calibrated:
Minimum Maximum
RERsapwood 1.0e-06 1.0e-04
RGRcambiummax 1.0e-04 2.0e-02
SRsapwood 1.0e-05 2.5e-04
2.5e+01 9.5e+01

Calibration results

Error function

The following panel shows the distribution of the final (optimum) values of the error function (average relative MAE) by dominant species:

Parameter distribution and covariance

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:

Comparison of the basic and advanced sub-models

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.


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