Reinforcement learning -based forest management simultaneously addressing timber production and carbon sink enhancement

Abstract

Devices, methods and computer programs for reinforcement learning -based forest management simultaneously addressing timber production and carbon sink enhancement are disclosed.

Description

[0001]REINFORCEMENT LEARNING -BASED FOREST MANAGEMENT SIMULTANEOUSLY ADDRESSING TIMBER PRODUCTION AND CARBON SINK ENHANCEMENT TECHNICAL FIELD The present disclosure relates to the field of machine learning, and, more particularly, to reinforce- ment learning -based forest management simultaneously addressing timber production and carbon sink enhancement. BACKGROUND Forest management is a branch of forestry. The basic unit in forest management is a forest stand, a uniform forest compartment that is usually around one hectare in size. Forests are a valuable multifunctional re- source that provide a wide range of ecosystem services beyond timber production. Aims to limit global warming and mitigate climate change have highlighted the role of forests as carbon (C) sinks. Estimates suggest that forests, including soils, hold approximately three times more C than the atmosphere, and boreal forests alone store one-third of all terrestrial C. In addition to various ecological and environmental factors, the ca- pacity of forests to sequester C is influenced espe- cially by forest management practices. Accordingly, at least in some situations, there may be a need for forest management tools that simultaneously address both timber production and carbon sink enhancement. SUMMARY The scope of protection sought for various ex- ample embodiments of the invention is set out by the independent claims. The example embodiments and fea- tures, if any, described in this specification that do not fall under the scope of the independent claims are to be interpreted as examples useful for understanding various example embodiments of the invention. An example embodiment of an apparatus is configured to access input data related to a forest stand. The apparatus is further configured to determine one or more forest management execution parameters for simultaneously addressing timber production and carbon sink enhancement of the forest stand, by applying a reinforcement learning, RL, process to the accessed input data. The RL process utilizes a forest development simulation model for the forest stand. The apparatus is further configured to provide the determined one or more forest management execution parameters for execution. The forest development simulation model comprises at least a carbon model for the forest stand. An example embodiment of a method comprises accessing, by an apparatus, input data related to a forest stand. The method further comprises determining, by the apparatus, one or more forest management execu- tion parameters for simultaneously addressing timber production and carbon sink enhancement of the forest stand, by applying a reinforcement learning, RL, process to the accessed input data. The RL process utilizes a forest development simulation model for the forest stand. The method further comprises providing, by the apparatus, the determined one or more forest management execution parameters for execution. The forest develop- ment simulation model comprises at least a carbon model for the forest stand. An example embodiment of an apparatus comprises means for carrying out the method according to the above example embodiment. An example embodiment of a computer program comprises instructions for causing an apparatus to per- form at least the following: accessing input data to a forest stand; determining one or more forest management execution parameters for simultaneously addressing timber production and carbon sink enhancement of the forest stand, by applying a reinforcement learning, RL, process to the accessed input data, the RL process uti- lizing a forest development simulation model for the forest stand; and providing the determined one or more forest management execution parameters for execution. The forest development simulation model comprises at least a carbon model for the forest stand. An example embodiment of an apparatus comprises at least one processor, and at least one memory storing instructions that, when executed by the at least one processor, cause the apparatus at least to access input data related to a forest stand. The instructions, when executed by the at least one processor, further cause the apparatus at least to determine one or more forest management execution parameters for simultaneously addressing timber production and carbon sink enhancement of the forest stand, by applying a reinforcement learn- ing, RL, process to the accessed input data. The RL process utilizes a forest development simulation model for the forest stand. The instructions, when executed by the at least one processor, further cause the appa- ratus at least to provide the determined one or more forest management execution parameters for execution. The forest development simulation model comprises at least a carbon model for the forest stand. In an example embodiment, alternatively or in addition to the above-described example embodiments, the carbon model comprises at least one of a soil carbon model, a living tree carbon model, or a wood product carbon model. In an example embodiment, alternatively or in addition to the above-described example embodiments, the input data comprises at least one of size data, species data, quantity data, or age data of trees in the forest stand. In an example embodiment, alternatively or in addition to the above-described example embodiments, the input data further comprises at least one of data on physical sizes of litter in soil of the forest stand, or data on chemical compounds in the soil of the forest stand. In an example embodiment, alternatively or in addition to the above-described example embodiments, the input data further comprises data on carbon content in wood products from harvested timber in the forest stand. In an example embodiment, alternatively or in addition to the above-described example embodiments, the determined one or more forest management execution pa- rameters comprise at least one of a rotation length, a thinning timing, or a thinning intensity for the forest stand. In an example embodiment, alternatively or in addition to the above-described example embodiments, the soil carbon model for the forest stand comprises at least one of a continuous time model or a discrete time model for at least one of a carbon sink or a carbon source. In an example embodiment, alternatively or in addition to the above-described example embodiments, the carbon sinks comprise first carbon sinks resulting from tree growth in the forest stand and second carbon sinks resulting from litter production in the forest stand, and the carbon sources comprise first carbon sources resulting from soil of the forest stand and second car- bon sources resulting from wood products from harvested timber in the forest stand. In an example embodiment, alternatively or in addition to the above-described example embodiments, the soil carbon model for the forest stand is configured to model carbon decay development over time in soil of the forest stand. In an example embodiment, alternatively or in addition to the above-described example embodiments, the soil carbon model for the forest stand is configured to model carbon decay development over time in wood prod- ucts from harvested timber in the forest stand. In an example embodiment, alternatively or in addition to the above-described example embodiments, the determination of the one or more forest management ex- ecution parameters for the simultaneous addressing of the timber production and the carbon sink enhancement of the forest stand comprises determining one or more forest management execution parameters that maximize simultaneous timber production and carbon sinks over time. DESCRIPTION OF THE DRAWINGS The accompanying drawings, which are included to provide a further understanding of the embodiments and constitute a part of this specification, illustrate embodiments and together with the description help to explain the principles of the embodiments. In the draw- ings: FIG. 1 illustrates forest development under rotation forestry and continuous cover forestry; FIG. 2 shows an example embodiment of the sub- ject matter described herein illustrating an apparatus; and FIG. 3 shows an example embodiment of the sub- ject matter described herein illustrating a method for the apparatus of Fig. 2. Like reference numerals are used to designate like parts in the accompanying drawings. DETAILED DESCRIPTION Reference will now be made in detail to embod- iments, examples of which are illustrated in the accom- panying drawings. The detailed description provided be- low in connection with the appended drawings is intended as a description of the present examples and is not intended to represent the only forms in which the pre- sent example may be constructed or utilized. The de- scription sets forth the functions of the example and the sequence of steps for constructing and operating the example. However, the same or equivalent functions and sequences may be accomplished by different examples. An element of forest management is harvesting, i.e., the felling of trees. E.g., in boreal and temper- ate forests of Europe and North America, forest manage- ment regimes may be divided into rotation forestry (RF) with clearcuts and continuous cover forestry (CCF). Fig. 1 illustrates forest development under rotation forestry 110 and continuous cover forestry 120. In rotation for- estry 110, a forest stand may be thinned (only a part of the trees is harvested) but is eventually clearcut (all trees are harvested) at the end of a rotation (the time between two clearcuts) which is followed by arti- ficial regeneration of the stand. In contrast, in con- tinuous cover forestry 120, a stand is never clearcut and forestry relies on natural regeneration of trees and revenues from thinnings. In the following, various concepts and terms that may be relevant to at least some example embodi- ments will be discussed. At least some embodiments may utilize an eco- nomic–ecological optimization model that may, e.g., com- bine individual-tree models for forest growth, with a comprehensive model for soil carbon and product carbon. At least in some situations, unlike existing rotation forestry (RF) models, the disclosed model may be solved without restrictions on rotation period length or thin- nings. This may result in a new level of detail along with offering novel insights that may aid integrating forests into climate policies. Next, an example of forest dynamics in the dis- closed economic–ecological optimization model is de- scribed. Per hectare number of trees in size class q ∈ {1, 2,…m} in the beginning of period t ∈ {0, 1, 2,…} may be denoted by xt,q, where the total number of size classes is m. The diameter at breast height for each size class is denoted by dt,q. Stand state at the begin- ning of a period t may be denoted, e.g., by vectors: of each period, a harvesting decision may be made and the number of trees after the (possible) harvest may be given as: is the numbers of harvested trees from each size class. Stand growth may be described, e.g., using em- pirically estimated Scots pine diameter increment and survival functions, such as those described in Pukkala et al. (2021). Diameter increment I(x)q of size class q for stand state (x, d) during a five-year period t may where: is the temperature sum set to 1100 degree-days, area (m2ha−1) of the stand, is the basal area of trees larger than in size class q, and δ0,…,δ6 are regression coefficients. The fraction of survived trees in size class q after a 5-year period t may be given, e.g., by equation: where δ7,…,δ10 are regression coefficients. The initial state at t = 0 may correspond to bare land, i.e., there are no trees in the stand. After the artificial regeneration, at period t0, the stand may be brought, e.g., to a state with 2200 trees divided evenly between 50 size classes q with diameters at equi- distant intervals between 5 cm and 10 cm. The periods to reach t0 may depend on site fertility and may be set, e.g., to five (five-year) periods (25 years) in average productivity sub-xeric stands, four periods in high productivity mesic stands and six periods in low produc- tivity xeric stands. During the first t0 periods after the start of artificial regeneration, it may be assumed that the stand volume grows linearly. Clearcut may reset stand state to bare land state, followed by a new rota- tion period initiated by artificial regeneration. The stand development between t0 periods after a bare land and clear-cut may be characterized, e.g., by the following difference equations: for all q=1,…,m and for all t excluding the first t0 periods after bare land. Next, an example of value of timber production in the disclosed economic–ecological optimization model is described. The gross revenues from timber production at period t may be calculated, e.g., as: where p1=€69.69 m3, p2=€38.55 m3may represent example roadside pulp and sawlog prices, and functions ν1(dt,q), ν2(dt,q) may give example pulp and sawlog volume yields for a dt,qsize tree. The harvesting cost may comprise, e.g., fixed costs and / or variable costs. The fixed cost may com- prise, e.g., planning, and equipment transportation may be, e.g., Cf=€500ha−1. The variable costs may be defined for thinning and clearcut, e.g., as: where j ∈ {th, cl} denotes thinning or clear- cut, and νq = ν1(dt,q) + ν2(dt,q) is the commercial stem volume of tree in class q. In the case of a clear-cut, there may also be the artificial regeneration cost Cr, which is the net present value of the artificial regen- eration operations. The total harvest cost may thus be, e.g.,: The net revenues from harvesting at period t may be, In the following, various example embodiments will be discussed. At least some of these example em- bodiments may allow reinforcement learning -based forest management simultaneously addressing timber production and carbon sink enhancement. Fig. 2 is a block diagram of apparatus 200, in accordance with an example embodiment. Apparatus 200 may comprise one or more proces- sors 202 and one or more memories 204 that may comprise computer program code. Apparatus 200 may also include other elements not shown in Fig. 2. Although apparatus 200 is depicted to include only one processor 202, apparatus 200 may include more processors. In an embodiment, memory 204 is capable of storing instructions, such as an operating system and / or various applications. Furthermore, memory 204 may in- clude a storage that may be used to store, e.g., at least some of the information and data used in the disclosed embodiments, such as forest development sim- ulation model 251 described in more detail below. Furthermore, processor 202 is capable of exe- cuting the stored instructions. In an embodiment, pro- cessor 202 may be embodied as a multi-core processor, a single core processor, or a combination of one or more multi-core processors and one or more single core pro- cessors. For example, processor 202 may be embodied as one or more of various processing devices, such as a coprocessor, a microprocessor, a controller, a digital signal processor (DSP), a processing circuitry with or without an accompanying DSP, or various other processing devices including integrated circuits such as, for ex- ample, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a mi- crocontroller unit (MCU), a hardware accelerator, a spe- cial-purpose computer chip, a neural network (NN) chip, an artificial intelligence (AI) accelerator, a tensor processing unit (TPU), a neural processing unit (NPU), or the like. In an embodiment, processor 202 may be configured to execute hard-coded functionality. In an embodiment, processor 202 is embodied as an executor of software instructions, wherein the instructions may spe- cifically configure processor 202 to perform the algo- rithms and / or operations described herein when the in- structions are executed. Memory 204 may be embodied as one or more vol- atile memory devices, one or more non-volatile memory devices, and / or a combination of one or more volatile memory devices and non-volatile memory devices. For ex- ample, memory 204 may be embodied as semiconductor mem- ories (such as mask ROM, PROM (programmable ROM), EPROM (erasable PROM), flash ROM, RAM (random access memory), etc.). Apparatus 200 may comprise a computing device, a server device, a cloud computing device, or the like. Apparatus 200 is configured to access input data related to a forest stand. For example, in at least some embodiments, the instructions, when executed by at least one processor 202, may cause apparatus 200 to perform the accessing of the input data related to the forest stand. As used herein, the term “forest stand” refers to a uniform forest compartment or a basic unit in forest management. For example, the forest stand may comprise a single-species forest stand or a multiple-species for- est stand. At least in some embodiments, the forest stand may comprise an even-aged forest stand (all the trees are roughly the same age) or an uneven-aged forest stand (trees of different ages). For example, the input data may comprise size data, species data, quantity data, and / or age data of trees in the forest stand. At least in some embodiments, the input data may further comprise data on physical sizes of litter in soil of the forest stand, and / or data on chemical compounds in the soil of the forest stand. At least in some embodiments, the input data may further comprise data on carbon content in wood products from harvested timber in the forest stand. Apparatus 200 is further configured to deter- mine one or more forest management execution parameters for simultaneously addressing timber production and carbon sink enhancement of the forest stand, by applying a reinforcement learning (RL) process to the accessed input data. The RL process utilizes forest development simulation model 251 (i.e., a machine learning (ML) model) for the forest stand. Forest development simula- tion model 251 comprises at least a carbon model for the forest stand. For example, the carbon model may comprise a soil carbon model, a living tree carbon model, and / or a wood product carbon model. At least in some embodi- ments, the forest development simulation model 251 may further comprise the above-described economic–ecologi- cal optimization model. For example, in at least some embodiments, the instructions, when executed by at least one processor 202, may cause apparatus 200 to perform the determina- tion of the one or more forest management execution parameters. For example, the determined one or more forest management execution parameters may comprise a rotation length, a thinning timing, and / or a thinning intensity for the forest stand. At least in some embodiments, the soil carbon model for the forest stand may comprise a continuous time model and / or a discrete time model for a carbon sink and / or a carbon source. For example, the carbon sinks may comprise first carbon sinks resulting from tree growth in the forest stand and second carbon sinks resulting from litter production in the forest stand, and the carbon sources may comprise first carbon sources resulting from soil of the forest stand and second car- bon sources resulting from wood products from harvested timber in the forest stand. As an example, coupling of continuous time mod- els for C sinks and sources with a five-year-period discrete-time forest growth model may include at least some of the following. Sinks may be divided as either resulting from tree growth or from litter production, while sources may be categorized as resulting from ei- ther soil or products. C captured from the atmosphere via trees may be considered a sink at the time of cap- ture, and C released to the atmosphere via soil or prod- ucts may be considered an emission at the time of re- lease. For a stand state denoted by vectors xt, dt, a total commercial volume may be calculated, e.g., as: , where x and d are the tree count and diameter vectors, respectively. The mass of C stored in the trees may be, e.g., ρϕω(xt,dt), where ρ = 0.3774 is a density factor that converts the commercial stem volume (in- cluding bark) into dry mass, η =1.99146 is an expansion factor that converts the stem dry mass into whole-tree dry mass, and ϕ = 0.5 is a coefficient that converts the whole-tree dry mass into C mass. θ = 44 / 12 may denote a factor that converts C mass into CO2. Thus, the value of the living trees CO2sink during a 5-year growth period may be calculated, e.g., as: denotes the stand state before the possible harvest, and α spreads the sinks evenly within the five- year period. This sink may obtain either positive or negative values. During the five-year periods, trees may die from natural mortality and a continuous process re- generates dead branches, roots, etc., implying a C lit- ter flow to forest soil and the value of this sink may be, e.g.,: where btkis the annual soil C input for litter size class k. The value of this sink may always be positive. In addition to continuous C flow from living trees into the soil, point inputs may occur at the times of harvests in the form of harvest residues (foliage, branches, stump, roots, and fine roots of harvested trees). Both of these inputs may turn to emissions after a delay that may be determined, e.g., by a Yasso C model (Tuomi et al. 2009, Tuomi et al. 2011b,a). The Yasso model, as a system of 15 linear differential equations, implies that the CO2source effect of each C input may be computed separately. This may allow specifying the values of the CO2sources as their present values at the moment when the input occurs. The present value of these soil emissions may be denoted, e.g., as: w T where the row vector transforms the litter vector input and the harvest residue C vector input bˆt to their present values over an infinite horizon. The CO2source from a utilized biomass or prod- ucts may occur partly during the manufacturing process and partly after a delay from the decaying wood products and from using biomass in energy production. The C decay in the product categories may be modelled using a system of linear differential equations. Let: denote the mass of the C content of timber and vector ^ the proportion of manufacturing (forest bio- mass) C source in each product class. The present value of wood product C release may then be, e.g.,: transforms the wood products C into discounted values of CO2source over an infinite time horizon. At least in some embodiments, the determination of the one or more forest management execution parame- ters for the simultaneous addressing of the timber production and the carbon sink enhancement of the forest stand may comprise determining one or more forest management execution parameters that maximize simulta- neous timber production and carbon sinks over time. For example, an example objective function and optimization methods for determining the net present value of CO2sinks and timber production may include at least some of the following. Let: be the sum of net revenues from timber produc- tion and net CO2sinks at time: Let Δ denote the (five-year) period length, r the annual discount rate, and γ the discount factor 1 / (1+r). The objective is to maximize simultaneous tim- ber production and CO2sinks over an infinitely long time horizon, e.g., as follows: subject to equations (3)–(5), and 0 ≤ ht≤ xt. As an outcome of the deterministic model formulation, optimal solutions may comprise, e.g., an infinite series of identical rotations even while equation (8) does not explicitly force this. Harvesting decisions may be made at each period, but because the system may return to the same state at each clearcut, the same harvest decisions may be made at each rotation period. Thus, the number of decision variables may be finite. This form of an optimization problem may be equivalent to a Markov De- cision Process, and may be solved efficiently using, e.g., reinforcement learning. At least in some embodiments, the soil carbon model for the forest stand may be configured to model carbon decay development over time in soil of the forest stand. At least in some embodiments, the soil carbon model for the forest stand may be configured to model carbon decay development over time in wood products from harvested timber in the forest stand. For example, at least in some embodiments, an example soil carbon decay may be determined, e.g., as follows. To specify soil C decay, e.g., a Yasso07 model (Liski et al. 2005, Tuomi et al. 2009, 2011a,b), i.e., a climate-dependent linear system that accounts the physical size of litter input and chemical compounds, may be used. Parameter values, e.g., from Tuomi et al. (2011b), may be applied using, e.g., a 3.3◦C mean annual temperature and 0.65 m annual precipitation. The litter may be divided, e.g., into size classes 0–2 cm, 2–10 cm and >10 cm (Tuomi et al. 2011a). The C within each size class may be divided, e.g., into five chemical pools: acid-hydrolyzable compounds, water-soluble compounds, ethanol-soluble compounds, non-soluble compounds, wa- ter-soluble compounds, ethanol-soluble compounds, non- soluble compounds, and slowly decaying humus. Let: denote the mass of C stored in the five com- pound groups in size class i=1,2,3 at moment τ. Vector: may then represent all soil C divided in size and chemical classes. Litter inputs are denoted by cor- responding vector b(τ). Let Aibe a matrix with decay rates between compound groups within size class i. The development of soil C over time without litter feeds may then be defined, e.g., by: where g0is the initial state of soil C, and: is a diagonal block matrix. The solution of (D.1) may be, e.g.,: where etAis the matrix exponential of tA. With- out litter feeds, all soil C may eventually return to the atmosphere, so the real-parts of the eigenvalues of A may be negative, which may guarantee the existence of the inverse matrix A−1. Inclusion of litter inputs b(τ) may yield a non-homogenous system, e.g.,: The litter feeds may include continuous and / or point feeds. The applied stand growth model (Pukkala et al. 2021) may be defined, e.g., for discrete time steps of 5 years but Yasso07 has continuous time. It is assumed that continuous feeds are constant during individual periods. Thus, b(τ) is piecewise constant, with point masses that may be represented by Dirac deltas at har- vest times. This assumption allows to discretize the process described by (D.3). If τ is the time since the beginning of a pe- riod, and b(τ) = b, the soil C development during the period may be solved from (D.3), e.g., as: A discretized version of the C decay may be defined by sampling the continuous process (D.3), e.g., at 5-year intervals before possible harvests by setting: The rate of continuous litter feed at time step t is bt, and the harvesting-related instantaneous C in- put is: Then, may be set, and τ =Δ in (D.4), which yields a discretized soil C process as, e.g.,: The total mass of soil C may change, e.g., at rate: The net present value from CO2released during period t discounted to the beginning of the period may be, e.g.,: where γ is the annual discount factor, pcis the social price of CO2in € per tCO2, and θ = 44 / 12 is a factor that converts C mass into CO2. The net present value of the net CO2flow to and from soil may then be, e.g.,: This formulation may be used for computing the CO2development over time, but using ctas part of the reward signal in reinforcement learning setting may be non-ideal at least in some situations for two reasons. First, it may lead to delayed rewards because the CO2releases to the atmosphere gradually over long time pe- riods after entering the soil. Second, computing ctfor each period may require keeping track of the vector gtfor every step leading to state space with unnecessarily high dimensions. Linearity of (D.3) may guarantee that C enter- ing the soil at time τ will be released according to a schedule determined by (D.1) regardless of CO2flows before or after τ. Thus, the value of CO2emissions caused by a point feed may be given in closed form discounted to the moment when the point feed occurs. The net present value of a point feed: at time τ =0 may be obtained, e.g., as: and assuming no further litter input. The decay follows (D.1). Let: be the interest rate that satisfies: The integral in the above expression is a La- place transform of function: and has a value: for interest rates: higher than the largest real part of the eigenvalues of A. The real parts of the eigenvalues of A may be negative so the expression may be defined at least for all: Thus, the following may be obtained, e.g.,: By defining a vector w such that for each com- this may be written, e.g., as: For a constant continuous feed with rate b, the net present value may be calculated, e.g., by using the formula for the NPV of point feed and integrating over the duration of a time step, e.g., as follows: may also be useful later on when computing net present values for continuous flows that are constant during a period of duration Δ. The CO2release shown in (6) may be obtained, e.g., by combining (D.8) and (D.9). For example, at least in some embodiments, an example product carbon decay may be determined, e.g., as follows. The C in wood products may be divided, e.g., into three categories: 1: sawn wood and plywood, 2: chemical pulp and paper, and 3: biofuel. When harvested timber is assigned to these categories, a proportion of the C content of the merchantable stem volume may be released in manufacturing. The remaining C, represented by vector: may be released according to a linear system: where τ denotes time since the harvest, and the elements Apare the rates of decay between product cat- egories, including the reuse of other products as bio- be, e.g.: The decay of C products may have a similar functional form to the soil C decay, so at least some of the same steps may be followed to determine the net present value of product CO2release vp(z), e.g., as: where w′ is a vector of column sums of the matrix: equation (7). Apparatus 200 is further configured to provide the determined one or more forest management execution parameters for execution. For example, in at least some embodiments, the instructions, when executed by at least one processor 202, may cause apparatus 200 to perform the providing of the determined one or more forest management execution parameters for the execution. Fig. 3 illustrates an example flow chart of method 300 for apparatus 200, in accordance with an example embodiment. At operation 301, apparatus 200 accesses the input data related to the forest stand. At operation 302, apparatus 200 determines the one or more forest management execution parameters for simultaneously addressing the timber production and the carbon sink enhancement of the forest stand, by applying the RL process to the accessed input data. The RL process utilizes forest development simulation model 251 for the forest stand. As detailed above, forest development sim- ulation model 251 comprises at least the carbon model (such as a soil carbon model, a living tree carbon model, and / or a wood product carbon model, as discussed in more detail above) for the forest stand. At operation 303, apparatus 200 provides the determined one or more forest management execution pa- rameters for execution. Embodiments and examples with regard to Fig. 3 may be carried out by apparatus 200 of Fig. 2. Operations 301-303 may, for example, be carried out by at least one processor 202 and at least one memory 204. Further fea- tures of method 300 directly resulting from the func- tionalities and parameters of apparatus 200 are not re- peated here. Method 300 can be carried out by computer programs or portions thereof. Another example of an apparatus suitable for carrying out the embodiments and examples with regard to Fig. 3 comprises means for: accessing, at operation 301, the input data related to the forest stand; determining, at operation 302, the one or more forest management execution parameters for simultaneously addressing the timber production and the carbon sink enhancement of the forest stand, by applying the RL process to the accessed input data, the RL process utilizing forest development simulation model 251 for the forest stand; and providing, at operation 303, the determined one or more forest management execution parameters for ex- ecution, wherein forest development simulation model 251 comprises the at least a carbon model for the forest stand. The functionality described herein can be per- formed, at least in part, by one or more computer program product components such as software components. Accord- ing to an embodiment, apparatus 200 may comprise a pro- cessor or processor circuitry, such as for example a microcontroller, configured by the program code when executed to execute the embodiments of the operations and functionality described. Alternatively, or in addi- tion, the functionality described herein can be per- formed, at least in part, by one or more hardware logic components. For example, and without limitation, illus- trative types of hardware logic components that can be used include Field-programmable Gate Arrays (FPGAs), Application-specific Integrated Circuits (ASICs), Ap- plication-specific Standard Products (ASSPs), System- on-a-chip systems (SOCs), Complex Programmable Logic Devices (CPLDs), Tensor Processing Units (TPUs), and Graphics Processing Units (GPUs). In the disclosed example embodiments, it may be possible to train one machine learning (ML) model / neural network (NN) with a specific architecture, then derive another ML model / NN from that using processes such as compilation, pruning, quantization or distilla- tion. The ML model / NN may be executed using any suit- able apparatus, for example a CPU, GPU, ASIC, FPGA, compute-in-memory, analog, or digital, or optical appa- ratus. It is also possible to execute the ML model / NN in an apparatus that combines features from any number of these, for instance digital-optical or analog-digital hybrids. In some examples, weights and required compu- tations in these systems may be programmed to correspond to the ML model / NN. In some examples, the apparatus may be designed and manufactured so as to perform the task defined by the ML model / NN so that the apparatus is configured to perform the task when it is manufac- tured without the apparatus being programmable as such. Any range or device value given herein may be extended or altered without losing the effect sought. Also, any embodiment may be combined with another em- bodiment unless explicitly disallowed. Although the subject matter has been described in language specific to structural features and / or acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as examples of implementing the claims and other equiv- alent features and acts are intended to be within the scope of the claims. It will be understood that the benefits and advantages described above may relate to one embodiment or may relate to several embodiments. The embodiments are not limited to those that solve any or all of the stated problems or those that have any or all of the stated benefits and advantages. It will further be un- derstood that reference to 'an' item may refer to one or more of those items. The steps of the methods described herein may be carried out in any suitable order, or simultaneously where appropriate. Additionally, individual blocks may be deleted from any of the methods without departing from the spirit and scope of the subject matter de- scribed herein. Aspects of any of the embodiments de- scribed above may be combined with aspects of any of the other embodiments described to form further embodiments without losing the effect sought. The term 'comprising' is used herein to mean including the method, blocks or elements identified, but that such blocks or elements do not comprise an exclu- sive list and a method or apparatus may contain addi- tional blocks or elements. List of References: Liski et al. 2005: Liski J, Palosuo T, Pel- toniemi M, Sievänen R (2005) Carbon and decomposition model yasso for forest soils. Ecological modelling 189(1-2): pages 168–182. Pukkala et al. (2021): Pukkala T, Vauhkonen J, Korhonen KT, Packalen T (2021) Self-learning growth sim- ulator for modelling forest stand dynamics in changing conditions. Forestry: An International Journal of Forest Research 94(3): pages 333–346. Tuomi et al. 2009: Tuomi M, Thum T, Järvinen H, Fronzek S, Berg B, Harmon M, Trofymow J, Sevanto S, Liski J (2009) Leaf litter decomposition—estimates of global variability based on yasso07 model. Ecological Modelling 220(23): pages 3362–3371. Tuomi et al. 2011a: Tuomi M, Laiho R, Repo A, Liski J (2011a) Wood decomposition model for boreal for- ests. Ecological Modelling 222(3): pages 709–718. Tuomi et al. 2011b: Tuomi M, Rasinmäki J, Repo A, Vanhala P, Liski J (2011b) Soil carbon model yasso07 graphical user interface. Environmental Modelling & Software 26(11): pages 1358–1362. It will be understood that the above descrip- tion is given by way of example only and that various modifications may be made by those skilled in the art. The above specification, examples and data provide a complete description of the structure and use of exem- plary embodiments. Although various embodiments have been described above with a certain degree of particu- larity, or with reference to one or more individual embodiments, those skilled in the art could make numer- ous alterations to the disclosed embodiments without departing from the spirit or scope of this specifica- tion.

Claims

CLAIMS:

1. An apparatus (200), configured to: access input data related to a forest stand; determine one or more forest management execu- tion parameters for simultaneously addressing timber production and carbon sink enhancement of the forest stand, by applying a reinforcement learning, RL, process to the accessed input data, the RL process utilizing a forest development simulation model (251) for the forest stand; and provide the determined one or more forest management execution parameters for execution, wherein the forest development simulation model (251) comprises at least a carbon model for the forest stand.

2. The apparatus (200) according to claim 1, wherein the carbon model comprises at least one of a soil carbon model, a living tree carbon model, or a wood product carbon model.

3. The apparatus (200) according to claim 1 or 2, wherein the input data comprises at least one of size data, species data, quantity data, or age data of trees in the forest stand.

4. The apparatus (200) according to any of claims 1 to 3, wherein the input data further comprises at least one of data on physical sizes of litter in soil of the forest stand, or data on chemical compounds in the soil of the forest stand.

5. The apparatus (200) according to any of claims 1 to 4, wherein the input data further comprises data on carbon content in wood products from harvested timber in the forest stand.

6. The apparatus (200) according to any of claims 1 to 5, wherein the determined one or more forest management execution parameters comprise at least one of a rotation length, a thinning timing, or a thinning intensity for the forest stand.

7. The apparatus (200) according to any of claims 2 to 6, wherein the soil carbon model for the forest stand comprises at least one of a continuous time model or a discrete time model for at least one of a carbon sink or a carbon source.

8. The apparatus (200) according to claim 7, wherein the carbon sinks comprise first carbon sinks resulting from tree growth in the forest stand and sec- ond carbon sinks resulting from litter production in the forest stand, and the carbon sources comprise first car- bon sources resulting from soil of the forest stand and second carbon sources resulting from wood products from harvested timber in the forest stand.

9. The apparatus (200) according to any of claims 2 to 8, wherein the soil carbon model for the forest stand is configured to model carbon decay development over time in soil of the forest stand.

10. The apparatus (200) according to any of claims 2 to 9, wherein the soil carbon model for the forest stand is configured to model carbon decay development over time in wood products from harvested timber in the forest stand.

11. The apparatus (200) according to any of claims 1 to 10, wherein the determination of the one or more forest management execution parameters for the simultaneous addressing of the timber production and the carbon sink enhancement of the forest stand comprisesdetermining one or more forest management execution pa- rameters that maximize simultaneous timber production and carbon sinks over time.

12. A method (300), comprising: accessing (301), by an apparatus (200), input data related to a forest stand; determining (302), by the apparatus (200), one or more forest management execution parameters for simultaneously addressing timber production and carbon sink enhancement of the forest stand, by applying a reinforcement learning, RL, process to the accessed input data, the RL process utilizing a forest develop- ment simulation model (251) for the forest stand; and providing (303), by the apparatus (200), the determined one or more forest management execution pa- rameters for execution, wherein the forest development simulation model (251) comprises at least a carbon model for the forest stand.

13. An apparatus, comprising means for carry- ing out the method (300) according to claim 12.

14. A computer program comprising instructions for causing an apparatus to perform at least the fol- lowing: accessing input data to a forest stand; determining one or more forest management ex- ecution parameters for simultaneously addressing timber production and carbon sink enhancement of the forest stand, by applying a reinforcement learning, RL, process to the accessed input data, the RL process utilizing a forest development simulation model for the forest stand; and providing the determined one or more forest management execution parameters for execution,wherein the forest development simulation model comprises at least a carbon model for the forest stand.

15. An apparatus (200), comprising: at least one processor (201); and at least one memory (202) storing instructions that, when executed by the at least one processor (202), cause the apparatus (200) at least to: access input data related to a forest stand; determine one or more forest management execu- tion parameters for simultaneously addressing timber production and carbon sink enhancement of the forest stand, by applying a reinforcement learning, RL, process to the accessed input data, the RL process utilizing a forest development simulation model (251) for the forest stand; and provide the determined one or more forest management execution parameters for execution, wherein the forest development simulation model (251) comprises at least a carbon model for the forest stand.

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