Correlation of Environmental Data and Growth

Before describing the fitted models for the single tree based growth simulator, a short description of the correlation of environmental variables with growth param-eters can be helpful. In the following section the correlation that is being referred to stands for the Spearman correlation coefficient. The latter was chosen here because the relationship could not always be assumed as linear. The responses were chosen here corresponding to the modeling procedure laid out in Section 2.1.5. For survival models the survival percentage was arcsine square root trans-formed (see Thomas, 2006) for simplicity. Figure 2.4 contains a display of all Spearman correlations between the responses of the growth models and selected soil parameters. Only indicators of general soil quality like the German agricul-tural soil quality rating (Bodenzahl: BZ) and soil water storage indicators in form of the available water capacity, calculated according to different methodologies, are presented here. Regarding the latter, the KA5 standard (Ad-Hoc-Arbeitsgruppe Boden der Staatlichen Geologischen Dienste und der Bundesanstalt für Geowis-senschaften und Rohstoffe and Sponagel, 2005) relating to the soil depth 0 to 60 cm and the changes suggested by Renger et al. (2009) relating to the same depth and additionally relating to the effective rooting depth were used.

The overall impression is that the correlation coefficients are not too high here.

The highest values were reached for available water capacity and mean stand height after the first year lM eanY1 with 0.54. It should be minded though that the other responses incorporate a higher number of causes for variance because the single tree level is considered here. Considering this framework, the soil quality ratingBZ shows comparably high correlation with most responses except survival after resproutsurvY4. The available water capacity variables all show a higher correlation in the first rotation for estimating the mean stand height after the first rotation. The available water capacity calculated according to Renger et al.

(2009) and relating to the soil depth of 0 to 60 cm has the highest correlation with growth responses in the first rotation. All 3 available water capacity variables

0.29 0.4 0.3 0.25

0.21 0.07 0.08 0.1

0.4 0.54 0.5 0.44

0.32 0.21 0.21 0.11

0.14 0 0 0

0 0.33 0.24 0.25

incrHR2 incrHY4 survY4 incrHR1 lMeanY1 survY1

BZ

awc_KA5_00to60 awc_WR_00to60 awc_WR_effRD

Soil variable

Response variable

−1.0

−0.5 0.0 0.5 1.0

Spearman correlation

Figure 2.4: Spearman correlation between the responses of all 6 growth models and 4 soil variables. The magnitude of the correlation is indicated by a color gradient. If thep-value of the correlation test indicated that the correlation coef-ficient did not significantly differ from 0, the value was set to 0 for the graph. The responses are survival at the end of the first year after planting (survY1), mean stand height at the end of the first year after planting (lM eanY1), height incre-ment within year 2 and 3 during the first rotation (incrHR1), survival after cop-picing at the end of the fourth year (survY4), the height growth after coppicing at the end of the fourth year (incrHY4) and height increment within year 5 and 6 during the second rotation (incrHR2). The soil variables are the Bodenzahl (BZ), the available water capacity in soil depth 0 to 60 cm (awc_KA5_00to60) calculated according to Ad-Hoc-Arbeitsgruppe Boden der Staatlichen Geolo-gischen Dienste und der Bundesanstalt für Geowissenschaften und Rohstoffe and Sponagel (2005), the available water capacity in soil depth 0 to 60 cm (awc_W R_00to60) calculated according to Renger et al. (2009) and the avail-able water capacity in the effective rooting depth (awc_W R_ef f RD) calculated according to Renger et al. (2009).

In Figure 2.5 the focus is shifted from soil to climate by displaying the Spear-man correlation between the responses of the same growth and survival models and climate variables aggregated by different time spans. The monthly aggrega-tions that are used here were gathered from publicaaggrega-tions that established their influence on growth. While different aggregations were chosen for temperature and precipitation by Amthauer Gallardo (2014) and Ali (2009), here all aggrega-tions were tested for both precipitation and temperature. The former in the form of mean annual sum of precipitation and the latter as mean of the annual mean temperature in the respective period.

Overall, the correlation coefficients values are on a comparable level as it was the case for the soil variables. The highest values were reached for mean stand height after the first year lM eanY1 and mean sum of precipitation from April to July and May to June. The correlations between growth responses and precipita-tion are mainly positive and for temperature mainly negative which is expectable.

Focusing on precipitation, the survival models survY1 and survY4 seem to be less closely correlated with the precipitation variables tested here. This is also the case for growth within the second rotation incrHR2. Comparing the differ-ent monthly aggregations, the time period May to June which was taken from Ali (2009) performs best. Within the temperature facet in Figure 2.5 it is of interest that some of the aggregations focusing on time spans early in the vegetation pe-riod have a positive correlation with mean stand height and height increment in the first rotation. The latter is less distinctive and might originate from the corre-lation of lM eanY1 and incrHR1to some degree. The temperature in the same period has nevertheless an adversary effect on the survival. This was not further investigated as the full model parameterization and variable selection pointed to-wards the temperature in June and July as suited best for prediction.

Generally, it should be minded here that the description in this Section only gives a first impression on how single variables are correlated with each other while for the final growth models multiple covariates and their interaction were tested for their influence on the response which can produce differing results.

These are described in the next Section.

0.4 0.39 0.37 0.2 0.03 0.09 0.28

0.03 0.1 0 −0.06 −0.11 0 0.13

0.44 0.44 0.37 0.3 0 0.13 0.36

0.29 0.34 0.29 0.12 0.05 0.12 0.3

0 0.19 0 0 0 0 0.13

0 0 0 0 0.17 0 0

0.05 0.06 0.04 −0.03 −0.04 −0.04 −0.02

−0.3 −0.29 −0.29 −0.33 −0.28 −0.27 −0.3

0.12 0.15 0.12 0 0 0 0

−0.08 −0.08 −0.08 −0.2 −0.13 −0.14 −0.13

−0.31 −0.31 −0.26 −0.25 −0.18 −0.16 −0.21

−0.26 −0.26 −0.25 −0.25 −0.25 −0.25 −0.25

PrecipitationTemperature

4 to 7 5 to 6 5 to 7 6 to 7 7 to 8 7 to 9 5 to 9 incrHR2

incrHY4 survY4 incrHR1 lMeanY1 survY1

incrHR2 incrHY4 survY4 incrHR1 lMeanY1 survY1

Month aggregation

Response variable

−1.0

−0.5 0.0 0.5 1.0

Spearman correlation

Figure 2.5: Spearman correlation between the responses of all 6 growth models and 7 different temporal aggregations for climate variables. The magnitude of the correlation is indicated by a color gradient. If the p-value of the correlation test indicated that the correlation coefficient did not significantly differ from 0, the value was set to 0 for the graph. The responses are survival at the end of the first year after planting (survY1), mean stand height at the end of the first year after planting (lMeanY1), height increment within year 2 and 3 dur-ing the first rotation (incrHR1), survival after coppicdur-ing at the end of the fourth year (survY4), the height growth after coppicing at the end of the fourth year (incrHY4) and height increment within year 5 and 6 during the second rota-tion (incrHR2). The climate variables are aggregated for different months and time spans according to Amthauer Gallardo (2014), Ali (2009) and Hammes (1983). Additionally the time span of the forestry vegetation period from May to September according to Arbeitskreis Standortskartierung in der Arbeitsge-meinschaft Forsteinrichtung (2016) is given. Temperatures are given as mean values over the trial period, precipitation is given as the mean sum of precipita-tion, also over the trial period.