Dr. Timo Pukkala

Metsätalouden suunnittelun professori

Luonnontieteiden ja metsätieteiden tiedekunta
Itä-Suomen yliopisto, Joensuu kampus
PL 111 (Yliopistokatu 7), 80101 Joensuu
p. 050 4423 372, sähköposti: etunimi.sukunimi@uef.fi
Työhuone: Borealis 374, www.uef.fi/fi/metsa/timo-pukkala

Recent articles in peer-reviewed journals

209  Pukkala, T. 2015. Plenterwald, Dauerwald, or clearcut? Forest Policy and Economics.

208  Hernández-Rodríguez, M., de-Miguel, S., Pukkala, T, Oria-de-Rueda, JA. 2015. Climate-sensitive models for mushroom yields in Cistus ladanifer scrublands. Agricultural and Forest Meteorology 213: 173-182.

207  Zubizarreta-Gerendiain, A., Pukkala, T. & Peltola, H. 2015. Effects of wood harvesting and utilization policies on the carbon balance of forestry under changing climate: a Finnish case study. Forest Policy and Economics.

206  Arias-Rodil, M., Pukkala, T., Gonzalez-Gonzalez, J.R., Barrio-Anta, M. & Dieguez-Aranda, U. 2015.  Use of depth-first search and direct search methods to optimize even-aged stand management: a case study involving maritime pine in Asturias (northwest Spain). Canadian Journal of Forest Research 45: 1269-1279.

205  Wang, L., W., Gunulf, A., Pukkala, T. & Ronnberg,J. 2015. Simulated Heterobasidion disease development in Picea abies stands following precommercial thinning and the economic justification for control measures. Scandinavian Journal of Forest Research 30(2): 174-185.

204  Pukkala, T. 2015. Optimizing continuous cover management of boreal forest when timber prices and tree growth are stochastic. Forest Ecosystems 2(6): 1-13.

203  Delgado-Matas, C., Mola-Yudego, B., Gritten, D., Kiala-Kalusinga, D. & Pukkala, T. 2015. Land use evolution and management under recurrent conflict conditions: Umbundu agroforestry system in the Angolan Highlands. Land Use Policy 42(2015): 460-470.

202  Zubizarreta-Gerendiain, A., Pukkala, T., Kellomäki, S., Garcia-Gonzalo, J., Ikonen, V.-P. & Peltola, H. 2015. Effects of climate change on optimized stand management in the boreal forests of central Finland. European Journal of Forest Research 134(2): 273-280.

201  Delgado-Matas, C. & Pukkala, T. 2014. Growth models for six Eucalyptus species in Angola. Southern Forests 2014: 1-12.

200  Juma, R., Pukkala, T. & de-Miguel, S. 2014. Evaluation of different approaches to individual tree growth and survival modelling usig data collected at irregular intervals – a case for Pinus patula in Kenya. Forest Ecosystems 1:14 (13 p)

199  Möykkynen, T. & Pukkala, T. 2014. Modelling the spread of a potential invasive pest, the Siberian moth (Dendrolimus sibiricus) in Europe. Forest Ecosystems 1:10 (12 p).

198  de-Miguel, S., Bonet, JA, Pukkala, T. & Martinez de Aragon, J. 2014. Impact of management intensity on landscape-level mushroom productivity: A regional model-based scenario analysis. Forest Ecology and Management 330: 218-227.

197  Möykkynen, T., Capretti, P, Pukkala, T. 2014. Modelling the potential spread of Fusarium circinatum, the causal agen of pitch canker in Europe. Annals of Forest Science 71(1): 101-112.

196  Pukkala, T., Lähde, E. & Laiho, O. 2014. Optimizing any-aged management of mixed boreal under residual basal area constraints. Journal of Forestry Research 25(3): 627-636.

195  de-Miguel, S., Pukkala, T. & Yesil, A. 2014. Integrating pine honeydew honey into forest management optimization. European Journal of Forest Research 133(3): 423:432.

194  de-Miguel, S., Pukkala, T. & Morales, M. 2014. Using optimization to solve tree misidentification and uneven measurement interval problems in individual-tree modeling of Balsa stand dynamics. Ecological Engineering 69: 232-236.

193  Pukkala, T. 2014. Does biofuel harvesting and continuous cover management increase carbon sequestration? Forest Policy and Economics 43: 41-50.

192  Pukkala, T., Möykkynen, T. & Robinet, C. 2014. Comparison of the potential spread of pinewood nematode (Bursaphelencus xylophilus) in Finland and Iberia simulated with a cellular automaton model. Forest Pathology 44(5): 341-352.

191  Laiho, O., Pukkala, T. & Lähde, E. 2014. Height increment of understorey Norway spruces under different tree canopies. Forest Ecosystems 1:4 (8 p).

190  Pukkala, T., Lähde, E. & Laiho, O. 2014. Stand management optimization – the role of simplifications. Forest Ecosystems 1:3 (11 p).

189  de-Miguel, Pukkala, T., Nabil, A. & Shater, Z. 2014. Intra-specific differences in allometric equations for aboveground biomass of eastern Mediterranean Pinus brutia. Annals of Forest Science 71: 101-112.

188  Delgado-Matas, C. & Pukkala, T. 2014. Optimization of the traditional land-use system in the Angolan highlands. International Journal of Sustainable Development & World Ecology 21(2): 138-148.

187  Bayat, M., Pukkala, T., Namiranian, M & Zobeiri, M. 2013 Productivity and optimal management of the uneven-aged hardwood forests of Hyrcania. European Journal of Forest Research 132(5): 851-864.

186  Manso, R., Pukkala, T., Pardos, M., Miina, J. & Calama, R. 2013. Modelling Pinus pinea forest management to attain natural regeneration under present and future climatic scenarios. Canadian Journal of Forest Research. Doi. 10.1139/cjfr-2013-0179

185  Pukkala, T., Lähde, E. & Laiho, O. 2013. Species interactions in the dynamics of even- and uneven-aged boreal forests. Journal of Sustainable Forestry 32: 1-33

184  Delgado-Matas, C. & Pukkala, T. 2013. Growth models based on radial increment observations for eight pine species in Angola. Southern Forests 75(1) xxx-xxx.

183  de-Miguel, S., Guzmán, G. & Pukkala, T. 2013. A comparison of fixed- and mixed-effects modeling in tree growth and yield prediction of an indigenous neotropical species (Centrolobium tomentosum) in a plantation system. Forest Ecology and Management 291: 249-258.

182  Heiðarsson, L. & Pukkala, T. 2012. Models for simulating the development of Siberian larch (Larix sibirica Ledeb.) plantations in Hallormsstaður Iceland. Icelandic Agricultural Sciences 25: 13-23.

181  Islam, N., Pukkala, T., Kurttila, M., Mehtätalo, L. & Heinonen, T. 2012. Effects of forest inventory errors on the area and spatial layout of harvest blocks. European Journal of Forest Research 131: 1943-1955.

180  Peña, F, de-Miguel, S., Pukkala, T. Bonet, J.A., Ortega-Martínez, P., Aldea, J. & Martínez de Aragón, J. 2012. Yield models for ectomycorrhizal mushrooms in Pinus sylvestris forests with special focus on Boletus edulis and Lactarius group deliciosus. Forest Ecology and Management 282: 63-69.

179  de Miguel, S., Mehtätalo, L., Shater, Z., Kraid, B. & Pukkala, T. 2012. Evaluating marginal and conditional predictions of taper models in the absence of calibration data? Canadian Journal of Forest Research 42: 1383-1394.

178  de Miguel, S., Pukkala, T., Assaf, N. & Bonet, J.-A. 2012. Even-aged or uneven-aged modeling approach? A case for Pinus brutia. Annals of Forest Science 69: 455-465. DOI 10.1007/s13595-011-0171-2.

177  Pukkala, T. & Kellomäki, S. 2012. Anticipatory vs. adaptive optimization of stand management when tree growth and timber prices are stochastic. Forestry 85(4): 463-472.

176  Guzmán, G., Morales, M., Pukkala, T., de-Miguel, S. 2012. A model for predicting the growth of Eucalyptus globulus seedling stands in Bolivia. Forest Systems 21(2): 202-209.

175  Pukkala, T., Sulkava, R., Lähde, E. & Jaakkola, L. 2012. Relationships between economic profitability and habitat quality of Siberian jay in uneven-aged Norway spruce forest. Forest Ecology and Management 276: 224-230.

174  Bonet, J.A., de Miquel, S., Martínez de Aragón, J., Pukkala, T. & Palahí, M. 2012. Immediate effect of thinning on the yield of Lactarius group deliciosus in Pinus pinaster forests in Norteastern Spain. Forest Ecology and Management. 265: 211-217.

173  Delgado-Matas, C. & Pukkala, T. 2012. Growth and yield of nine pine species in Angola. Journal of Forestry Research 23(2): 197-204. Doi: 10.1155/2011/980259.

172  Selkimäki, M., Gonzaléz-Olabarria, J.R. & Pukkala, T. 2012. Site and stand characteristics related to surface erosion occurrence in forests of Catalonia (Spain). European Journal of Forest Research131:727-738

171  Guzmán, G., Pukkala, T., Palahí, M. & de-Miquel, S. 2012. Predicting the growth and yield of Pinus radiata in Bolivia. Annals of Forest Science 69: 335-343

170  Delgado-Matas, C. & Pukkala, T. 2011. Comparison of the growth of six Eucalyptus species in Angola. International Journal of Forestry Research. Doi: 10.1155/2011/980259.

169  Heiðarsson, L. & Pukkala, T. 2011. Taper functions for lodgepole pine (Pinus contorta) and Siberian larch (Larix sibirica) in Iceland. Icelandic Agricultural Sciences 24: 3-11.

168  Packalén, P., Heinonen, T., Pukkala, T., Vauhkonen, J. and Maltamo, M. 2011. Dynamic treatment units in Eucalyptus plantations. Forest Science 57(5): 416-426.

167  Laiho, O., Lähde, E. and Pukkala, T. 2011. Uneven- vs. even-aged management in Finnish boreal forests. Forestry 84(5): 547-556.

166  Pukkala, T., Lähde, E. and Laiho, O. 2011. Variable-density thinning in uneven-aged forest management – a case for Norway spruce in Finland. Forestry 84(5): 557-565.

165  Gonzaléz-Olabarria, J.R., Mola-Yudego, B., Pukkala, T. and Palahí, M. 2011. Using multiscale spatial analysis to assess fire ignition density in Catalonia, Spain. Annals of Forest Science. 68: 861-871.

164  Garcia-Gonzalo, J., Pukkala, T. and Borges, J.G. 2011. Integrating fire risk in stand management scheduling. An application to Maritime pine stands in Portugal. Annals of Operations Research. DOI: 10.1007/s10479-011-0908-1

163  Mehtätalo, L., Comas, C., Pukkala, T. and Palahí, M. 2011. Combining a predicted diameter distribution with an estimate based on a small sample of diameters. Can. J. For. Res. 41: 750–762.

162  Shater, Z., de-Miguel, S., Kraid, B, Pukkala, T. & Palahí, M. 2011. A growth and yield model for even-aged Pinus brutia Ten. stands in Syria. Annals of Forest Science 68: 149-157.

161  Pukkala, T. 2011. Optimizing forest management in Finland with carbon subsidies and taxes. Forest Policy and Economics 13: 425-434.

160  Pukkala, T., Lähde, E., Laiho, O. Salo, K. & Hotanen, J.-P. 2011. A multifunctional comparison of even-aged and uneven-aged forest management in a boreal region. Canadian Journal of Forest Research 41: 851-862.

159  Pukkala, T., Lähde, E. & Laiho, O. 2011. Using optimization for fitting individual-tree growth models for uneven-aged stands. European Journal of Forest Research 130(5): 829-839.

158  Coll, L., González-Olabarria, J.R., Mola-Yudego, B. Pukkala, T. & Messier, C. 2011. Predicting understory maximum shrubs cover using altitude and overstory basal area in different Mediterranean forests. European Journal of Forest Research 130: 55-65.

157  Möykkynen, T. & Pukkala, T. 2011. Effect of planting Scots pine around Norway spruce stumps on the spread of Heterobasidion coll. Forest Pathology 41: 212-220.

156  Heinonen, T., Pukkala, T., Ikonen, V.-P., Peltola, H., Gregow, H. & Venäläinen, A. 2011. Consideration of strong winds, their directional distribution and snow loading in wind risk assessment related to landscape level forest planning. Forest Ecology and Management 261: 710-719.

155  González-Olabarria, J.-R. & Pukkala, T. 2011 Integrating risk considerations in landscape-level forest planning. Forest Ecology and Management 261: 278-287.

154  de Miguel, S., Pukkala, T., Shater, Z., Assaf, N., Kraid, B. & Palahí, M. 2010. Models for simulating the development of even-aged Pinus brutia stands in Middle East. Forest Systems 19(3), 449-457.

153  Delgado-Matas, C. & Pukkala, T. 2010. Growth models for Pinus patula in Angola. Southern Forests 2010, 72(3/4): 153-161.

152  Islam, N. Md., Kurttila, M. Mehtätalo, L. & Pukkala, T.2010.  Inoptimality losses in forest management decisions caused by errors in an inventory based on airborne laser scanning and aerial photographs. Canadian Journal of Forest Research 40: 2427-2438.

151  Zeng, H., Pukkala, T., Peltola, H. & Kellomäki, S. 2010. Optimization of irregular-grid cellular automata and application in risk management of wind damage in forest planning. Canadian Journal of Forest Research 40: 1064-1075.

150  Tahvonen, O., Pukkala, T., Laiho, O., Lähde, E. & Niinimäki, S. 2010. Optimal management of uneven-aged Norway spruce stands.  Forest Ecology and Management 260: 106-115.

149  Pukkala, T., Hokkanen, T. & Nikkanen, T. 2010. Prediction models for the annual seed crop of Picea abies (L.) Karst. (Norway spruce) and Pinus sylvestris L. (Scots pine) in Finland. Silva Fennica 44(4): 629-642.

148  Pasalodos-Tato, M., Pukkala, T. & Rojo Alboreca, A.2010. Optimal management of Pinus pinaster in Galicia (north-western Spain) under endogenous risk of fire. International Journal of Wildland Fire 19: 937-948.

147  Miina, J., Pukkala, T., Hotanen, J.-P. & Salo, K. 2010. Optimizing the joint production of timber and bilberries. Forest Ecology and Management 259: 2065-2071.

146  Möykkynen, T. & Pukkala, T. 2010. Optimizing the management of Norway spruce and Scots pine mixtures on a site infected by Heterobasidion coll. Scandinavian Journal of Forest Research 40: 347-356.

145  Bonet, J.A., Palahí, M., Colinas, C., Pukkala, T., Fischer, C., Miina, J. & Martinez de Aragon, J. 2010. Modelling the production of wild mushrooms in pine forests in the Central Pyrenees in northeastern Spain. Canadian Journal of Forest Research 40: 347-356.

144  Pukkala, T., Lähde, E. & Laiho, O. 2010. Optimizing the structure and management of uneven-sized stands in Finland. Forestry 83(2): 129-142.

Books

11  Lähde, E. & Pukkala, T. (toim.). 2013. Alikasvoksesta ylispuuksi. Joen Forest Program Consulting. 141 p.

10  Pukkala, T. & von Gadow, K. (eds.). 2012. Continuous Cover Forestry. Second Edition. Managing Forest Ecosystems 23. Springer Science+Business Media B.V.296 p.

9  Pukkala, T., Lähde, E. & Laiho, O. 2011. Metsän jatkuva kasvatus. Joen Forest Program Consulting, Joensuu. 228 p.

8  von Gadow, K. & Pukkala, T. (eds.). 2008. Designing green landscapes. Managing Forest Ecosystems 15. Springer Science+Business Media B.V.286 p.

7  Pukkala, T. 2007. Metsäsuunnittelun menetelmät. Joen Forest Program Consulting, Joensuu. 208 p.

6  Pukkala, T. (ed.). 2002. Multi-objective forest planning. Managing Forest Ecosystems 6. Kluwer Academic Publishers, Dorhrecht, The Netherlands. 207 p.

5  von Gadow, K., Pukkala, T. & Tome, M.(eds.). 2000. Sustainable forest management. Managing Forest Ecosystems 1. Kluwer Academic Publishers, Dorhrecht, The Netherlands. 356 p.

4  Auvinen, P., Pukkala, T. & Vesa, L. 1997. Metsän kartoitus. Opetushallitus. 153 p.

3  Pukkala, T. 1994. Metsäsuunnittelun perusteet. Joen Forest Program Consulting, Joensuu. 242 p.

2  Pukkala, T. & Pohjonen, V. 1989. Forest inventory and management planning in the fuelwood plantations of Ethiopia. Silva Carelica 13. 110 p. + App.

1  Pukkala, T. 1985. Metsän kaukokartoituksen perus­teet (4. painos 1988). Silva Carelica 4. 166 p.

  1. Plenterwald, Dauerwald, or clearcut?
  2. Effects of wood harvesting and utilization policies on the carbon balance of forestry
  3. Optimizing continuous cover management of boreal forest when timber prices and tree growth are stochastic
  4. Evaluation of different approaches to individual tree growth modelling – a case for Pinus patula in Kenya
  5. Modelling the spread of Siberian moth in Europe

1. Plenterwald, Dauerwald, or clearcut?

Timo Pukkala

Forest Policy and Economics xxx(x): xxx-xxx (2015)

Forest landowners are interested in management alternatives, which do not involve clearfelling and planting. Also many citizens that do not own forest are against clear-felling do to its harmful effects on amenity values and ecosystem services. Most studies on continuous cover forest management (CCF) deal with regular, steady state uneven-aged forests (Plenterwald), or with the conversion of stands into steady-state structure. However, people who want CCF management seldom want Plenterwald in particular; continuous tree cover would in most cases be sufficient and regular stand structure or regular cuttings are less important. This type of management corresponds to the German Dauerwald concept. This study compared the profitability of Plenterwald, Dauerwald and clear-cutting schedules in Finnish spruce forests. As expected, Dauerwald was more profitable than cutting schedules that converted the stand into a steady-state Plenterwald structure. The difference in net present value decreased with increasing number of conversion cuttings. Clear-cutting and planting was more profitable than optimal CCF only in a mature initial stand when the planted spruces were assumed to grow 20% faster in dbh and height, compared to naturally regenerated spruces. In young, medium-aged and uneven-aged initial stands, CCF was more profitable even when a 20-% tree breeding benefit was assumed in the plantation that was established in the clear-felling site.

NPV of optimal CCF and clearfelling (CC) schedules for four initial stands when the growth prediction of the plantation forest (seedlings planted after clear felling) is multiplied by 1 or 1.2.

NPV of optimal CCF and clearfelling (CC) schedules for four initial stands when the growth prediction of the plantation forest (seedlings planted after clear felling) is multiplied by 1 or 1.2.

2. Effects of wood harvesting and utilisation policies on the carbon balance of forestry: a case for Finnish boreal forest

Ane Zubizarreta-Gerendiain, Timo Pukkala & Heli Peltola               

Forest Policy and Economics xxx(x): xxx-xxx (2015)

The aim of this study was to quantify the effects of different wood harvesting and utilisation policies on the carbon balance and economic profitability of forestry. Carbon balance included changes in the carbon pools of living forest biomass (living above- and below-ground forest biomass), dead organic matter and wood products, as well as carbon releases from harvesting, transporting and manufacturing. Reduced carbon emissions due to the use of construction wood instead of fossil-intensive materials and forest biomass-based fuels instead of fossil fuels were also taken into account. Sixty-year carbon balance was calculated for two Finnish boreal case study areas under the current and gradually changing climate (A1B climate scenario). One case study area was dominated by Scots pine and broadleaf species and the other was dominated by Norway spruce. In addition to the business-as-usual (baseline) management scenario (even-aged forestry: thinning from below, harvesting only timber for wood-based products from thinning and final felling), five other scenarios were applied by changing the timing and type of thinning and the utilisation of harvested trees. Net present value (NPV, calculated with 2% discount rate) and carbon balance of forestry were maximised in each management scenario with even-flow net income constraint. In both case study areas, postponing the thinning of young stands compared to the current recommendations (baseline management) and using thinning from above instead of thinning from below improved both carbon balance and NPV. The use of pulpwood, logging residues and stumps as biofuel also increased carbon balance. Climate warming increased carbon balance and NPV when harvests were not increased from those under the current climate.

60-year carbon balance  for six wood harvesting and utilization scenarios. Changes to the "Low thinning as recommended" scenario were done one at a time. The scenario "Clear-felling residues used as energy" includes also all previous  changes.

3. Optimizing continuous cover management of boreal forest when timber prices and tree growth are stochastic

Timo Pukkala

Forest Ecosystems 2(6): 1-13 (2015)

Decisions on forest management are made under risk and uncertainty because the stand development cannot be predicted exactly and future timber prices are unknown. Deterministic calculations may lead to biased advice on optimal forest management. The study optimized continuous cover management of boreal forest in a situation where tree growth, regeneration, and timber prices include uncertainty. Both anticipatory and adaptive optimization approaches were used. The future prices of different timber assortments were described by cross-correlated auto-regressive models. The high variation around ingrowth model was simulated using a model that describes the cross- and autocorrelations of the regeneration results of different species and years.  Tree growth was predicted with individual tree models, the predictions of which were adjusted on the basis of a climate-induced growth trend, which was stochastic. Residuals of diameter growth (deviations from deterministic model prediction) were also simulated, and they consisted of random tree factors and cross- and autocorrelated temporal terms. Of the analyzed factors, timber price caused most uncertainty in the calculation of the net present value of a certain management schedule. Ingrowth and climate trend were less significant sources of risk and uncertainty than tree growth. Stochastic anticipatory optimization led to more diverse post-cutting stand structures than obtained in deterministic optimization. Cutting interval was shorter when risk and uncertainty was included in the analyses. In the adaptive approach, reservation price function was optimized instead of cutting years. Adaptive optimization and management led to 6–14% higher net present values than obtained in management that was based on anticipatory optimization.

Average net present value of 1000 stochastic simulations with the optimal values of decision variables obtained in different problem formulations. "Adaptive a1 = 1" is a simulation in which the optimized value of parameter a1 of the tinning intensity curve was replaced by a constant value (a1=1). 

4. Evaluation of different approaches to individual tree growth and survival modelling using data collected at irregular intervals – a case study for Pinus patula in Kenya

Rita Juma, Timo Pukkala, Sergio de-Miguel & Mbae Muchiri

Forest Ecosystems 1(14): 1-13 (2014)

The minimum set of sub-models for simulating stand dynamics on an individual-tree basis consists of tree-level models for diameter increment and survival. Ingrowth model is a necessary third component in uneven-aged management. The development of this type of model set needs data from permanent plots, in which all trees have been numbered and measured at regular intervals for diameter and survival. New trees passing the ingrowth limit should also be numbered and measured. Unfortunately, few datasets meet all these requirements. The trees may not have numbers or the length of the measurement interval varies. Ingrowth trees may not have been measured, or the number tags may have disappeared causing errors in tree identification. This article discussed and demonstrated the use of an optimization-based approach to individual-tree growth modelling, which makes it possible to utilize data sets having one or several of the above deficiencies. The idea is to estimate all parameters of the sub-models of a growth simulator simultaneously in such a way that, when simulation begins from the diameter distribution at the first measurement occasion, it yields a similar ending diameter distribution as measured in the second measurement occasion. The method was applied to Pinus patula permanent sample plot data from Kenya. In this dataset, measurement interval varied from 1 to 13 years. Two simple regression approaches were used and compared to the optimization-based model recovery approach. The optimization-based approach resulted by far more accurate simulations of stand basal area and number of surviving trees than the equations fitted through regression analysis.

Predicted one-year diameter increment and one-year survival rate according to the fixed-effects models developed by three different modelling approaches.

5. Modelling of the spread of a potential invasive pest, the Siberian moth (Dendrolimus sibiricus) in Europe

Timo Möykkynen & Timo Pukkala

Forest Ecosystems 1(10): 1-12 (2014)

The Siberian moth (Dendrolimus sibiricus) (SM) defoliates several tree species from the genera Larix, Picea and Abies in northern Asia, east of the Urals. The SM is a potential invasive forest pest in Europe because Europe has several suitable host species and climatic conditions of central and northern Europe are favourable for the SM. This study developed a grid-based spatio-temporal model for simulating the spread of the SM in case it enters Europe from Russia via border stations. The spread rate was modeled as a function of the spatial distribution of host species, climatic suitability of different locations for the SM, human population density, transportation of moth-carrying material, and flying of moths from tree to tree. The simulations showed that the SM is most likely to spread in the forests of northeast Belarus, the Baltic countries, and southern and central Finland. Climatic conditions affected the occurrence of the SM more than human population density and the coverage of suitable host species.

Infection probability map of the Siberian moth. Probability that the Siberian moth spreads to different locations from border stations between Russia and non-Russian European countries when there are 5 arrivals per year from each station and the arrivals last for 3 years. Blue = high probability (70–90%), turquoise 50–60%, yellow = (30–40%), red = low probability (<10%).