Table 1. The number of observations by pulpwood assortments in the green density prediction study material. | ||||||||

Pulpwood assortment | Total | Year | ||||||

2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | ||

Pine ^{1)} | 20 299 | 3421 | 2488 | 4677 | 3699 | 2456 | 1867 | 1691 |

Spruce ^{2)} | 10 769 | 1120 | 1072 | 1344 | 1706 | 2015 | 1955 | 1557 |

Spruce, decayed ^{3)} | 2991 | 221 | 238 | 304 | 447 | 789 | 538 | 454 |

Birch ^{4)} | 17 423 | 2854 | 2455 | 3111 | 3027 | 2446 | 1852 | 1678 |

Aspen ^{5)} | 2293 | 281 | 222 | 215 | 365 | 522 | 385 | 303 |

^{1) }Contain mainly Scots Pine (Pinus sylvestris); ^{2), 3)} mainly Norway spruce (Picea abies); ^{4)} mainly downy birch (Betula pubescens) or/and silver birch (Betula pendula); ^{5)} mainly aspen (Populus tremula). |

Table 2. Green density (kg m^{–3}) values and storage time of green density prediction study material by pulpwood assortments. | |||||||

Pulpwood assortment | Number of observations | Green density, kg m^{–3} | Storage time, days | ||||

Mean | Std | Median | Mean | Std | Median | ||

Pine | 20 299 | 878.9 | 71.0 | 892 | 70 | 83 | 40 |

Spruce | 10 769 | 845.7 | 64.3 | 854 | 38 | 48 | 21 |

Spruce, decayed | 2991 | 731.6 | 56.4 | 732 | 43 | 56 | 26 |

Birch | 17 423 | 868.3 | 65.9 | 881 | 70 | 79 | 40 |

Aspen | 2293 | 804.4 | 60.2 | 809 | 50 | 57 | 29 |

Table 3. Parameter estimates of models for green density (kg m^{–3}) of the pulpwood assortments (MODELS 1). The standard error of the estimates is presented in parenthesis. | |||||

Pine | Spruce | Spruce, decayed | Birch | Aspen | |

Variable | Estimate | Estimate | Estimate | Estimate | Estimate |

Intercept | 908.07 (3.753) | 865.05 (3.431) | 749.79 (6.566) | 931.56 (6.644) | 362.91 (113.98) |

WEEK | –1.224 (0.466) | –4.078 (1.048) | |||

WEEK_{>22} | 5.431 (1.176) | 2.085 (0.672) | |||

WEEK^{2} | –0.061 (0.014) | 0.339 (0.068) | |||

WEEK^{2}_{>15} | 0.535 (0.098) | ||||

WEEK^{2}_{>20} | 0.194 (0.083) | ||||

WEEK^{2}_{>22} | 1.015 (0.172) | ||||

WEEK^{3} | –0.0052 (0.001) | –0.01165 (0.002) | –0.0014 (0.0006) | ||

STORAGE | –0.219 (0.043) | –0.307 (0.068) | –1.033 (0.080) | –0.733 (0.038) | –0.496 (0.092) |

STORAGE_{>300 days} | 0.284 (0.020) | 0.259 (0.107) | 0.245 (0.053) | 0.295 (0.021) | |

STORAGE_{Nov-March} | 0.264 (0.047) | 0.204 (0.075) | 0.686 (0.042) | ||

STORAGE_{Oct}_{-Apr} | 1.125 (0.073) | ||||

STORAGE_{Dec}_{-March} | 0.345 (0.104) | ||||

STORAGE_{May} | –0.333 (0.087) | 0.445 (0.084) | |||

STORAGE_{June} | –0.716 (0.094) | –1.268 (0.144) | 0.395 (0.104) | ||

STORAGE_{July} | –0.539 (0.109) | ||||

TS | –0.157 (0.008) | –0.162 (0.015) | –0.034 (0.007) | –0.067 (0.010) | |

TEMP | –0.532 (0.166) | –6.439 (1.189) | |||

ln(TEMP+30) | 138.19 (33.746) | ||||

TEMP_{3month} | –0.791 (0.126) | –0.767 (0.290) | –0.765 (0.121) | ||

TEMP_{max20} | 0.550 (0.102) | 0.821 (0.201) | 0.433 (0.083) | ||

ln(TEMP_{max20 }+1) | –4.081 (0.902) | ||||

RAINFALL | 0.304 (0.022) | 0.126 (0.031) | 0.146 (0.011) | 0.258 (0.036) | |

RAINFALL_{3month} | –0.080 (0.010) | ||||

RAINFALL_{water} | 0.247 (0.012) | ||||

AREA_{E}×MONTH_{Feb-May} | 13.652 (1.838) | ||||

AREA_{B}×TS | 0.020 (0.002) | ||||

AREA_{C}×TS | 0.038 (0.007) | ||||

AREA_{E}×TS | –0.018 (0.004) | ||||

var(w_{ij}) | 147.34 | 149.06 | 131.51 | 177.03 | 148.98 |

corr(w_{ij}) | 0.843 | 0.785 | 0.915 | 0.882 | 0.793 |

var(e_{ijk}) | |||||

MONTH_{Jan-May }× STORAGE_{<1month} | 1802.89 | 1725.79 | 2098.89 | 1118.45 | 1784.02 |

MONTH_{Jan-May }× STORAGE_{>1month} | 2512.92 | 2545.36 | 2067.21 | 1594.11 | 1895.57 |

MONTH_{June-Dec }× STORAGE_{<1month} | 2175.07 | 2318.61 | 2144.50 | 1574.23 | 1875.02 |

MONTH_{June-Dec }× STORAGE_{>1month} | 3357.90 | 3240.48 | 2671.54 | 1929.57 | 1980.89 |

WEEK, delivery date of pulpwood at the mill expressed as week number (1–52); WEEK_{>15}, dummy variable for wood delivered after week number 15 expressed as WEEK-15 (week); WEEK_{>20}, dummy variable for wood delivered after week number 20 expressed as WEEK-20 (week); WEEK_{>22}, dummy variable for wood delivered after week number 22 expressed as WEEK-22 (week); STORAGE, storage time of pulpwood (day); STORAGE_{>300}, dummy variable for storage time of pulpwood exceeded >300 days (day); STORAGE_{Nov-March}, dummy variable for storage time of pulpwood between November and March (day); STORAGE_{Oct-Apr}, dummy variable for storage time of pulpwood between October and April (day); STORAGE_{Dec-March}, dummy variable for storage time of pulpwood between December and March (day); STORAGE_{May}, dummy variable for storage time of pulpwood in May (day); STORAGE_{June}, dummy variable for storage time of pulpwood in June (day); STORAGE_{July}, dummy variable for storage time of pulpwood in July (day); TS, temperature sum with a +5 °C threshold (dd); TEMP, average temperature of the storage time (°C); TEMP_{3month}, average temperature of the last three months or whole storage time when storage time <3 months (°C); TEMP_{max20}, the number of storage days when maximum temperature of the day is >20 °C; RAINFALL, precipitation during the storage time (mm); RAINFALL_{3month}, precipitation of the last three months or whole storage time when storage time <3 months (mm); RAINFALL_{water}, precipitation during the storage time when average temperature of the days is >0 °C (mm); MONTH_{Feb-May}, dummy variable for delivery time between February and May (0.1); AREA_{B}, dummy variable for sub-area B; AREA_{C}, dummy variable for sub-area C; AREA_{E}, dummy variable for sub-area E; var(w_{ij}), variance of random week effect; corr(w_{ij}), autocorrelation of the successive weeks, var(e_{ijk}) error variance of pulpwood group k; MONTH_{Jan-May}, MONTH_{June-Dec}, error variance of group k when delivery date is January–May or June–December, STORAGE_{<}_{1month} and STORAGE_{>1month}, error variance of group k when storage time is less than or more than 1 month. |

Table 4. Relative root mean squared prediction errors (%) of green density calculated from the single parcels for four prediction methods: using the fixed part of the new models only (Fixed), correcting Fixed by the predicted week effect (Calibrated), using mill-specific trimmed moving averages of the last seven sample measurements (MOVING AVG), and using fixed green density factors (FGDF). | ||||

Pulpwood assortment | rRMSE, % | |||

Fixed | Calibrated | MOVING AVG | FGDF | |

Pine | 6.70 | 6.30 | 7.91 | 8.89 |

Spruce | 6.63 | 6.63 | 7.61 | 7.12 |

Spruce, decayed | 6.06 | 5.98 | 7.25 | 6.86 |

Birch | 5.23 | 4.79 | 6.45 | 6.63 |

Aspen | 6.11 | 5.74 | 7.06 | 7.98 |

Table 5. Relative root mean squared prediction errors (%) of green density calculated from weekly averages; using the fixed part of the new models only (Fixed), correcting Fixed by the predicted week effect (Calibrated), using mill-specific trimmed moving averages of the last seven sample measurements (MOVING AVG), and using fixed green density factors (FGDF). | ||||

Pulpwood assortment | rRMSE, % | |||

Tree species | Fixed | Calibrated | MOVING AVG | FGDF |

Pine | 2.20 | 1.34 | 1.39 | 4.54 |

Spruce | 1.40 | 1.22 | 1.51 | 2.64 |

Spruce, decayed | 2.96 | 2.62 | 3.38 | 3.24 |

Birch | 2.09 | 0.90 | 1.33 | 2.82 |

Aspen | 4.05 | 3.40 | 4.99 | 5.48 |

Table 6. Differences in the annual averages over the whole test data (year 2019) between the predicted and measured green densities (kg m^{–3}) by pulpwood assortments; predictions both with fixed part of the model and after calibration, using the predicted week effects. | |||

Pulpwood assortment | N | Prediction error Mean | |

Fixed | Nationwide calibration | ||

Pine | 1691 | –14.6 | –2.7 |

Spruce | 1557 | –4.2 | –1.8 |

Spruce, decayed | 454 | –3.6 | –1.1 |

Birch | 1678 | –13.6 | –0.8 |

Aspen | 303 | –15.7 | –7.4 |

N, number of observations in test data (2019); Fixed, fixed predictions of the developed models; Nationwide calibration, predictions calibrated at national level. |

Table 7. Differences in the annual sub-area level averages over the whole test data (year 2019) between the predicted and measured green densities (kg m^{–3}) by pulpwood assortments; predictions both with fixed part of the model and after calibration, using the predicted week effects. | ||||

Sub-area | N | Prediction error Mean | ||

Fixed | Nationwide calibration | Regional calibration | ||

A | 193 | –17.3 | –7.0 | –8.4 |

B | 826 | –18.3 | –5.7 | –4.1 |

C | 38 | –16.0 | –3.8 | NA* |

D | 506 | –16.3 | –4.5 | –6.2 |

E | 128 | 19.8 | 31.3 | 8.3 |

N, number of observations in test data (2019); Fixed, fixed predictions of the developed models; Nationwide calibration, predictions calibrated at national level; Regional calibration, predictions calibrated at reginal level. *Could not be estimated due to low number of observations. |