Table 1. Variables for the models, their symbols, and units.
Variable Symbol Unit
Plot size Plotsize m2
Cumulative annual daily mean temperatures above +5 °C DDY degree days (d.d.)
Height above sea level Altitude m
Slope Slope %
Latitude Latitude min
Mean total age of stand Age years
Number of stems N N ha–1
Basal area BA m2 ha–1
Mean diameter, basal area weighted DG cm
Basal area of pine trees BApine m2 ha–1
Basal area of spruce trees BAspruce m2 ha–1
Basal area of broadleaved trees BAbrd m2 ha–1
Proportion of pine basal area of total basal area BApineRel
Proportion of broadleaved basal area of total basal area BAbrdRel
Number of dead tree stems N_dead N ha–1
Basal area of dead trees BA_dead m2 ha–1
Mean diameter of dead trees, basal area weighted DG_dead cm
Occurence of mortality mortality {0, 1}
Soil type peatland PEAT {0, 1}
Aspect between 225 and 315 degrees, when max was 360 WEST {0, 1}
Growth period between measurements Period years
Thinning within 5 years of the studied period TH5 {0, 1}
Quadratic mean diameter, √(BA/qN) DQ cm
Occurrence of mortality: 0 = mortality occur; 1 = no mortality occur; Peatland: 0 = no peatland, 1 = peatland; Western aspect: 0 = no western aspect, 1 = western aspect; Thinning within 5 yrs: 0 = not thinned, 1 = thinned
Table 2. Description of combined Swedish and Norwegian NFI data for modelling the occurrence of no mortality.
Data set SWEDEN (n = 16 459 ) NORWAY (n = 11 767)
Variable mean min max mean min max
Plotsize, m2 314.2 314.2 314.2 250.0 250.0 250.0
DDY, d.d. 1133.6 426.8 1760.4 881.1 303.5 2049.3
Altitude, m 228.7 0.0 787.0 379.4 0.0 1080.0
Slope, % 4.8 0.0 41.5 25.0 0.0 150.0
Latitude, min 6104.0 5540.0 6830.0 6156.8 5800.5 7001.4
Age, yr 80.6 11.0 325.0 102.6 19.0 374.0
N, ha–1 685.8 95.5 2387.3 579.1 120.0 2560.0
BA, m2 ha–1 21.7 1.4 73.0 17.5 1.8 113.2
DG, cm 23.6 15.0 93.7 23.3 15.0 71.2
BApine, m2 ha–1 9.2 0.0 60.1 6.3 0.0 57.2
BAspruce, m2 ha–1 9.1 0.0 73.0 7.4 0.0 113.2
BAbrd, m2 ha–1 3.4 0.0 60.6 3.8 0.0 53.4
BApineRel 0.5 0.0 1.0 0.4 0.0 1.0
BAbrdRel 0.2 0.0 1.0 0.3 0.0 1.0
N_dead, ha–1 13.5 0.0 954.9 17.2 0.0 680.0
BA_dead, m2 ha–1 0.376 0.0 44.3 0.391 0.0 25.8
DG_dead, cm 17.8 10.0 75.8 16.4 10.0 58.9
mortality, {0, 1} 0.3 0.0 1.0 0.3 0.0 1.0
Table 3. Description of sub data, which contained mortality at the following period, for modelling the amount of mortality.
Data set SWEDEN (n = 4218) NORWAY (n = 3107)
Variable mean min max mean min max
DDY, d.d. 1141.2 426.8 1732.9 890.4 303.5 1873.1
Altitude, m 226.8 0.0 761.0 354.1 2.0 1015.0
Slope, % 5.0 0.0 33.1 28.8 0.0 130.0
Latitude, min 6096.2 5540.0 6800.0 6172.1 5800.5 7001.4
Age, yr 84.1 11.0 325.0 100.5 19.0 318.0
N, ha–1 826.4 95.5 2387.3 748.9 120.0 2560.0
BA, m2 ha–1 25.2 2.1 61.9 22.2 1.8 113.2
DG, cm 23.3 15.0 71.0 23.1 15.0 56.6
BApine, m2 ha–1 9.1 0.0 51.1 5.0 0.0 54.6
BAspruce, m2 ha–1 11.4 0.0 58.6 10.8 0.0 113.2
BAbrd, m2 ha–1 4.7 0.0 54.9 6.3 0.0 53.4
BApineRel 0.38 0.00 1.00 0.24 0.00 1.00
BAbrdRel 0.20 0.00 1.00 0.36 0.00 1.00
N_dead, ha–1 52.7 31.8 954.9 65.1 40.0 680.0
BA_dead, m2 ha–1 1.5 0.3 44.3 1.5 0.3 25.8
DG_dead, cm 17.8 10.0 75.8 16.4 10.0 58.9
BArelMort 0.062 0.050 0.986 0.083 0.050 0.970
Table 4. Description of the model application data, which contained 57 unmanaged spruce-dominated plots in Finland (see Peltoniemi and Mäkipää 2011).
Plot size
m2 		Period
yrs 		DDY
d.d. 		Age
yrs 		BA
m2 ha–1 		N
ha–1 		DQ
cm 		DG
cm 		N_dead
ha–1 		BA_dead
m2 ha–1
mean 1585.5 10.9 1147.8 152.1 38.9 1020.9 22.8 29.8 131.8 3.7
stdev 587.9 2.1 86.2 37.6 8.9 375.9 3.5 4.6 71.6 2.2
min 750.0 7.0 928.0 80.0 18.3 340.0 14.6 20.1 8.0 0.1
max 3150.0 15.0 1411.0 290.0 65.0 1700.0 29.7 39.9 344.4 10.4
Table 5. Estimated parameters for the linear part (X'b) for the probability of no mortality occurrence (Model 1).
Variable Estimate Std Error t Value Pr > |t|
Intercept 3.1751 0.07359 43.15 <0.0001
Age –0.00417 0.000416 –10.01 <0.0001
DQ1.5 0.01382 0.000556 24.86 <0.0001
√BA –0.6693 0.01557 –42.99 <0.0001
BApineRel × Age 0.004356 0.000423 10.31 <0.0001
BAbrdRel × Age –0.01112 0.000622 –17.88 <0.0001
Slope/100 –1.0542 0.09451 –11.15 <0.0001
WEST 0.1354 0.03443 3.93 <0.0001
TH5 × BA 0.005803 0.001818 3.19 0.0014
PEAT –0.2201 0.05102 –4.31 <0.0001
1

Fig. 1. The predicted probability of mortality during next 5-year period with respect to stand age for stands having different species composition (pure vs 50% mixture). The stand basal area of 23 m2 ha–1, stem number of 970 ha–1 for younger stands and 700 ha–1 for older stands, DQ of 17.4 cm and 20.4 cm, respectively, are reflecting means for the Swedish modelling data group into stands below or above 100 year of stand age.

2

Fig. 2. Observed vs predicted 5-yr probability of mortality (with 95% confidence limits) by classes of A) stand age, B) quadratic mean dbh, DQ and C) basal area weighted mean dbh, DG. The line depicts the number of observations in each class. View larger in new window/tab.

3

Fig. 3. Observed vs predicted 5-yr probability of mortality (with 95% confidence limits) by classes of A) stem number and B) basal area. The line depicts the number of observations in each class. View larger in new window/tab.

Fig. 4. Observed vs predicted 5-yr probability of mortality (with 95% confidence limits) by classes of A) proportion of spruce, B) proportion of pine and C) proportion of broadleaved species of basal area. The line depicts the number of observations in each class. View larger in new window/tab.

Table 6. Estimated parameters for the linear part (X'b) for the proportion of basal area in surviving trees (Model 2).
Variable Estimate Approx Approximate 95% Confidence
Std Error Limits
Intercept –7.3745 0.7404 –8.8259 –5.9230
ln(N) 1.4010 0.1356 1.1351 1.6668
√N –0.0296 0.0131 –0.0554 –0.0039
BA –0.0117 0.0037 –0.0190 –0.0044
ln(DQ) 0.5633 0.1569 0.2556 0.8709
BApineRel × ln(Age) 0.0790 0.0100 0.0595 0.0986
BAbrdRel × ln(Age) –0.0500 0.0105 –0.0706 –0.0293
Slope/100 × West 0.2438 0.1212 0.0062 0.4814
NORWAY 0.1657 0.0304 0.1060 0.2254
NORWAY: dummy variable for Norwegian NFI data.
5

Fig. 5. Mean observed vs mean predicted 5-yr amount of mortality in m2 ha–1 (with 95% confidence limits) by classes of A) age, B) DQ, and C) DG. The line depicts the number of observations in each class. View larger in new window/tab.

6

Fig. 6. Mean observed vs mean predicted 5-yr amount of mortality (with 95% confidence limits) as proportion of basal area (Figs. A, C) and absolute basal area of dead trees (Figs. B, D) by classes of stand basal area (Figs. A, B) and stem number (Figs. C, D). The line depicts the number of observations in each class. View larger in new window/tab.

7

Fig. 7. Mean observed vs mean predicted 5-yr amount of mortality (with 95% confidence limits) as proportion of basal area (A, C) and absolute basal area (B, D) by the proportion of broadleaves (A, B) and proportion of Scots pine (C, D) of stand basal area. The line depicts the number of observations in each class. View larger in new window/tab.

Table 7. The observed and predicted basal area (BA) of dead trees in the Finnish natural spruce-dominated stands within the observed period length (7–15 yrs) simulated in 5-year steps and the remaining shorter step (e.g. 2-year step when period length was 7 yrs) in Motti.
Mean St. deviation Minimum Maximum
Observed BA of dead trees, m2 ha–1 3.68 2.23 0.05 10.39
Predicted BA of dead trees, m2 ha–1 3.73 1.74 0.94 8.57
Prediction error in the BA of dead trees, m2 ha–1 –0.051 2.48 –5.25 5.68
8

Fig. 8. Prediction errors (× = observed – predicted) in amount of mortality by classes of predicted basal area of dead trees (A) and by classes of stand age (B) in unmanaged spruce dominated stands in Finland. Filled circles showed the average bias within 1-m2 ha–1 basal area and 20-year age classes and thick line showed the ± standard deviation of the prediction error. View larger in new window/tab.