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Table 1. The gross vehicle weights, number of axles, and truck and trailer models of the combination vehicles in the study.
Truck Gross vehicle weight (t) Axles
(truck + trailer) 		Brand and model, truck Brand and model, trailer
68_1 68 3 + 5 Scania R 650 Feber Intercars 42P0D6
68_2 68 3 + 5 Scania R 560 Feber Intercars 42P0D6
76_1 76 4 + 5 Scania R 580 Närko D4HS11T11
76_2 76 4 + 5 Scania R 580 Närko D4HS11T11
76_3 76 4 + 5 Scania R 580 Närko D4HS11T11
76_4 76 4 + 5 Scania R 580 Närko D4HS11T11
76_5 76 4 + 5 Scania R 730 Jyki V52-t0
76_6 76 4 + 5 Scania R 730 Weckman
1

Fig. 1. Tare weight measurements of eight timber trucks over a year. The horizontal lines represent the tare weights in the national transport register (excluding the weight of a loader and other accessories). View larger in new window/tab.

2

Fig. 2. Filtered tare weights of eight timber trucks over a year. The red lines indicate the normal tare, i.e., the 95th percentile of the tare measurements in summertime. View larger in new window/tab.

3

Fig. 3. Monthly median loss of payload of eight timber trucks over a year. The error bars indicate the 10th and 90th percentiles. View larger in new window/tab.

Table 2. Equivalent annual loss of transport payload due to increased winter tare weight.
Truck id Gross vehicle weight (kg) Normal tare
(kg) 		Maximum
payload (kg) 		Annual loss
of payload (kg) 		Annual loss
in payloads 		Total loads per
year in the study
68_1 68 000 25 359 42 641 209 740 4.9 338
68_2 68 000 24 459 43 541 90 000 2.1 188
76_1 76 000 26 305 49 695 84 718 1.7 163
76_2 76 000 26 314 49 686 101 100 2.0 217
76_3 76 000 26 422 49 578 54 260 1.1 225
76_4 76 000 26 321 49 679 60 960 1.2 207
76_5 76 000 23 940 52 060 168 300 3.2 588
76_6 76 000 25 722 50 278 140 580 2.8 324
4

Fig. 4. Spearman correlation factors between payload loss and the weather variables in the training data. The variables (unit in parentheses): temp = momentary temperature (°C), wind_speed = momentary wind speed (m s–1), rel_humid = momentary humidity (%), prec = 3h rainfall (mm), pot_evap = 3h potential evaporation (mm), payload_loss_p95 = potential loss of payload (kg). Significance levels: *** = 0.001, ** = 0.01. View larger in new window/tab.

Table 3. Model coefficients for logistic regression of probability of no payload loss.
Term Estimate Standard error z-score p-value
Intercept –2.29 0.125 –18.3 <0.001
Temperature 0.245 0.0153 16.1 <0.001
Table 4. Confusion matrices for the prediction of zero / non-zero payload loss in the training and test data sets.
Training data Test data
Predicted non-zero
payload loss 		Predicted zero
payload loss 		Predicted non-zero
payload loss 		Predicted zero
payload loss
True non-zero payload loss 949 48 231 16
True zero payload loss 121 178 23 42
5

Fig. 5. Probability of zero payload loss as a function of temperature.

Table 5. Model coefficients of the gamma regression of positive payload loss. Notation a:b means an interaction term between variables a and b.
Term Estimate Standard error z-score p-value
Intercept 4.952 0.171 28.897 <0.001
Temperature 0.033 0.020 1.635 0.102
Relative humidity 0.014 0.002 7.357 <0.001
Precipitation 0.193 0.040 4.855 <0.001
Temperature: Relative humidity –0.001 0.0002 –5.513 <0.001
Temperature: Precipitation –0.026 0.006 –4.476 <0.001
6

Fig. 6. The model for payload loss as a function of temperature, humidity and rainfall. View larger in new window/tab.