Variable:Area types

2021-07-27T08:11:19Z

Peder:

<includeonly>
{{VariableCategory}}
</includeonly>

Variable:Area types

2021-07-27T08:06:56Z

Peder: Created page with "A"

[[Category:Variable|A]]

2021-07-26T15:53:08Z

Peder: /* Examples */

[[Category:Reference Manual]]
[[Category:User's Guides]]
[[Category:Result Variables]]
[[Category:Definitions]]

==About time periods, time points and treatment years==
Heureka is using a discrete time period model, typically using five-year time intervals. The term time period is somewhat misleading, because a "time period" may refer to a time point or a period, depending on context. For example, if you use StandWise to project the growth of a stand, the "time period" is actually better interpreted as a time index marking the beginning of a period. For a case with many stands in PlanWise or RegWise on the other hand, the time index marks the midpoint of a time period. The motivation for this is that although all stands scheduled for harvest in the first period have been assigned the same treatment year (year 2.5) in the model, they should harvested simultaneously, but the harvest activities would be spread out evenly over the five-year period.

[[File:Growth.png|450px]]

==Use period midpoints in PlanWise==
When running a TPG simulation in PlanWise, period midpoints are used as default. This means that the initial state is projected 2.5 years, before the actual harvest scheduling begins. After that, five-year intervals are used. The reason for using period midpoints, is that usually some of the stands scheduled for harvesting in a certain five-year period, will not be harvested in the beginning of the period. Instead, some will be harvested early in the period, and other later in the period. Therefore, if period midpoints were not used, the harvest volumes would be underestimated.

We have no definite answer on how few or how many stands there should be to use midpoints, but if you want the results to reflect that "some time during this period these stands should be harvested", then you should use period midpoints.

==Do not use period midpoints in StandWise==
In StandWise you can use period midpoints too, but it would probably make little sense expect if the purpose was to make some comparison or addition to a PlanWise simulation (for a certain stand).

==Period year and treatment year==
In Heureka, each period has an associated year (found in TreatmentData.Year), which refers no the number of years that has passed since the start.

Year 0: Now (start of the analysis) 
Year 5: Five year after the start = Beginning of the sixth year.

Note that when using period midpoints (default in PlanWise), the first period index (0) refers starting states for the analysis. In this case, the first actual planning period where optional treatments can be simulated is period 1. Period 1 has period year 2.5, i.e. the midpoint of the first five years, meaning that the period covers year 1 to 5. Period 2 covers years 6-10, and so on.

===Examples ===

[[File:Periods when NOT periodmidpoint.png|none|thumb|500px]]
Period meaning when period midpoints ARE NOT USED.
{| {{table}}
| align="left" style="background:#f0f0f0;"|'''Period index'''
| align="left" style="background:#f0f0f0;"|'''Description '''
| align="left" style="background:#f0f0f0;"|'''Value of period year '''
| align="left" style="background:#f0f0f0;"|'''Possible treatment years'''
| align="left" style="background:#f0f0f0;"|'''Date range'''
|-
| 0||Index för the first period ||0||0-4||2020-01-01 - 2024-12-31
|-
| 1||Index for the second period||5||5-9||2025-01-01 - 2029-12-31
|-
| 2||etc||10||10-14||2030-01-01 -- 2034-12-31
|-
|
|}

[[File:Periods when using periodmidpoint.png|none|thumb|500px]]
Period meaning when period midpoints are used.
{| {{table}}
| align="left" style="background:#f0f0f0;"|'''Period index'''
| align="left" style="background:#f0f0f0;"|'''Description '''
| align="left" style="background:#f0f0f0;"|'''Value of period year '''
| align="left" style="background:#f0f0f0;"|'''Possible treatment years'''
| align="left" style="background:#f0f0f0;"|'''Date range'''
|-
| 0||Start time index ||0||0||2020-01-01
|-
| 1||Index for the first harvest period||2.5||0-4-9||2020-01-01 - 2024-12-31
|-
| 2||etc||10||10-14||
|-
|
|}

Note that period 0 includes the same date interval when we do not apply period midpoints as period 1 does when we apply midpoints. However, the calculated values (volumes etc.) will differ. Assuming harvesting takes places in the beginnning of a period ignores that the trees have grown in average 2.5 years before the forst harvest is carried out.

==”Before” and “After” values==
In Heureka, most variables has a before and after-component, which refers to the state or value before treatment, and immediately after treatment, respectively. Only before-treatment values are saved in the result database (when you run PlanWise or RegWise or save a simulation in StandWise).

==State, yield and change variables==
====State variable====
A '''state''' variable refers to a description variable for a stand at a certain time, for example the mean age or the volume.
====Yield variable====
A '''yield''' variable refers to some output from an activity, such as the harvest volume.

====Change variable====
A third type of variable describes '''change''' of a stand, for example growth and mortality. Growth and mortality that are reported in a certain time period t, represents the growth and mortality that has occurred after harvesting in the previous period (t -1) to the current period year.

==Basic calculation steps==
As a Heureka user, it is important that you have a fundamental understanding of how a prognosis is done. The following principal steps are performed when making a prognosis from one time point (t) to another (t+1):

#Calculate state variables for the stand at time t from tree-level data, for example stand volume and mean diameter. This is the Before-value.
#Apply treatment, if a treatment should be applied, and update the After-value for the treatment unit. “After” is the state immediately after the treatment.
#Calculate diameter growth, height growth and mortality for each tree.
#Calculate ingrowth of new trees.
#Update attributes (such as volume, age, diameter, weight) for each tree. The weight is the number of stems that a tree object represents, and is reduced by the mortality rate and by harvesting (for example a thinning will reduce the weight for one or more tree objects).
#Let t = t + 1. Update the tree list for this period and repeat from step 1.

==Subtract half a period’s harvest volume to obtain standing stock if many stands==
If you want to create for example a graph of how the standing stock (the total volume) of a large forest holding develops over time according to a simulation in PlanWise, and you have used period midpoints (the default in a TPG-simulation), you should subtract half the period’s harvest volume from the Before-value. The reason is that the Before-value has been adjusted for a half a period’s growth and mortality, but not for half a periods harvesting. In reality, in a case with many stands, some of the stands will be harvested early in the period, other stands in the middle of the period, and other stand at the end of the period. But in the model, all harvesting takes place in the middle of the period. Extracting half a periods harvesting is a simple way to at least approximately adjust for this error.

==Understanding how growth is calculated==
Growth and mortality [[#change|change]] refers to how a forest stand is changing from one time point to the next. Growth is reported as gross growth and net growth. Gross growth includes mortality, net growth does not.

see [[Growth Results]]

File:Periods when using periodmidpoint.png

2021-07-26T15:39:29Z

Peder:

About time periods

2021-07-26T15:36:12Z

Peder: /* Examples */

[[Category:Reference Manual]]
[[Category:User's Guides]]
[[Category:Result Variables]]
[[Category:Definitions]]

==About time periods, time points and treatment years==
Heureka is using a discrete time period model, typically using five-year time intervals. The term time period is somewhat misleading, because a "time period" may refer to a time point or a period, depending on context. For example, if you use StandWise to project the growth of a stand, the "time period" is actually better interpreted as a time index marking the beginning of a period. For a case with many stands in PlanWise or RegWise on the other hand, the time index marks the midpoint of a time period. The motivation for this is that although all stands scheduled for harvest in the first period have been assigned the same treatment year (year 2.5) in the model, they should harvested simultaneously, but the harvest activities would be spread out evenly over the five-year period.

[[File:Growth.png|450px]]

==Use period midpoints in PlanWise==
When running a TPG simulation in PlanWise, period midpoints are used as default. This means that the initial state is projected 2.5 years, before the actual harvest scheduling begins. After that, five-year intervals are used. The reason for using period midpoints, is that usually some of the stands scheduled for harvesting in a certain five-year period, will not be harvested in the beginning of the period. Instead, some will be harvested early in the period, and other later in the period. Therefore, if period midpoints were not used, the harvest volumes would be underestimated.

We have no definite answer on how few or how many stands there should be to use midpoints, but if you want the results to reflect that "some time during this period these stands should be harvested", then you should use period midpoints.

==Do not use period midpoints in StandWise==
In StandWise you can use period midpoints too, but it would probably make little sense expect if the purpose was to make some comparison or addition to a PlanWise simulation (for a certain stand).

==Period year and treatment year==
In Heureka, each period has an associated year (found in TreatmentData.Year), which refers no the number of years that has passed since the start.

Year 0: Now (start of the analysis) 
Year 5: Five year after the start = Beginning of the sixth year.

Note that when using period midpoints (default in PlanWise), the first period index (0) refers starting states for the analysis. In this case, the first actual planning period where optional treatments can be simulated is period 1. Period 1 has period year 2.5, i.e. the midpoint of the first five years, meaning that the period covers year 1 to 5. Period 2 covers years 6-10, and so on.

===Examples ===
Period meaning when period midpoints ARE NOT USED.
{| {{table}}
| align="left" style="background:#f0f0f0;"|'''Period index'''
| align="left" style="background:#f0f0f0;"|'''Description '''
| align="left" style="background:#f0f0f0;"|'''Possible treatment years'''
| align="left" style="background:#f0f0f0;"|'''Date range
| 0||Index för the first period ||0-4||2020-01-01 - 2024-12-31
|-
| 1||Index for the second period||5-9||2025-01-01 - 2029-12-31
|-
| 2||etc||10-14||
|-
|
|}

[[File:Periods when NOT periodmidpoint.png|left|thumb|500px]]
 

==”Before” and “After” values==
In Heureka, most variables has a before and after-component, which refers to the state or value before treatment, and immediately after treatment, respectively. Only before-treatment values are saved in the result database (when you run PlanWise or RegWise or save a simulation in StandWise).

==State, yield and change variables==
====State variable====
A '''state''' variable refers to a description variable for a stand at a certain time, for example the mean age or the volume.
====Yield variable====
A '''yield''' variable refers to some output from an activity, such as the harvest volume.

====Change variable====
A third type of variable describes '''change''' of a stand, for example growth and mortality. Growth and mortality that are reported in a certain time period t, represents the growth and mortality that has occurred after harvesting in the previous period (t -1) to the current period year.

==Basic calculation steps==
As a Heureka user, it is important that you have a fundamental understanding of how a prognosis is done. The following principal steps are performed when making a prognosis from one time point (t) to another (t+1):

#Calculate state variables for the stand at time t from tree-level data, for example stand volume and mean diameter. This is the Before-value.
#Apply treatment, if a treatment should be applied, and update the After-value for the treatment unit. “After” is the state immediately after the treatment.
#Calculate diameter growth, height growth and mortality for each tree.
#Calculate ingrowth of new trees.
#Update attributes (such as volume, age, diameter, weight) for each tree. The weight is the number of stems that a tree object represents, and is reduced by the mortality rate and by harvesting (for example a thinning will reduce the weight for one or more tree objects).
#Let t = t + 1. Update the tree list for this period and repeat from step 1.

==Subtract half a period’s harvest volume to obtain standing stock if many stands==
If you want to create for example a graph of how the standing stock (the total volume) of a large forest holding develops over time according to a simulation in PlanWise, and you have used period midpoints (the default in a TPG-simulation), you should subtract half the period’s harvest volume from the Before-value. The reason is that the Before-value has been adjusted for a half a period’s growth and mortality, but not for half a periods harvesting. In reality, in a case with many stands, some of the stands will be harvested early in the period, other stands in the middle of the period, and other stand at the end of the period. But in the model, all harvesting takes place in the middle of the period. Extracting half a periods harvesting is a simple way to at least approximately adjust for this error.

==Understanding how growth is calculated==
Growth and mortality [[#change|change]] refers to how a forest stand is changing from one time point to the next. Growth is reported as gross growth and net growth. Gross growth includes mortality, net growth does not.

see [[Growth Results]]

About time periods

2021-07-26T15:34:00Z

Peder: /* Period year and treatment year */

[[Category:Reference Manual]]
[[Category:User's Guides]]
[[Category:Result Variables]]
[[Category:Definitions]]

==About time periods, time points and treatment years==
Heureka is using a discrete time period model, typically using five-year time intervals. The term time period is somewhat misleading, because a "time period" may refer to a time point or a period, depending on context. For example, if you use StandWise to project the growth of a stand, the "time period" is actually better interpreted as a time index marking the beginning of a period. For a case with many stands in PlanWise or RegWise on the other hand, the time index marks the midpoint of a time period. The motivation for this is that although all stands scheduled for harvest in the first period have been assigned the same treatment year (year 2.5) in the model, they should harvested simultaneously, but the harvest activities would be spread out evenly over the five-year period.

[[File:Growth.png|450px]]

==Use period midpoints in PlanWise==
When running a TPG simulation in PlanWise, period midpoints are used as default. This means that the initial state is projected 2.5 years, before the actual harvest scheduling begins. After that, five-year intervals are used. The reason for using period midpoints, is that usually some of the stands scheduled for harvesting in a certain five-year period, will not be harvested in the beginning of the period. Instead, some will be harvested early in the period, and other later in the period. Therefore, if period midpoints were not used, the harvest volumes would be underestimated.

We have no definite answer on how few or how many stands there should be to use midpoints, but if you want the results to reflect that "some time during this period these stands should be harvested", then you should use period midpoints.

==Do not use period midpoints in StandWise==
In StandWise you can use period midpoints too, but it would probably make little sense expect if the purpose was to make some comparison or addition to a PlanWise simulation (for a certain stand).

==Period year and treatment year==
In Heureka, each period has an associated year (found in TreatmentData.Year), which refers no the number of years that has passed since the start.

Year 0: Now (start of the analysis) 
Year 5: Five year after the start = Beginning of the sixth year.

Note that when using period midpoints (default in PlanWise), the first period index (0) refers starting states for the analysis. In this case, the first actual planning period where optional treatments can be simulated is period 1. Period 1 has period year 2.5, i.e. the midpoint of the first five years, meaning that the period covers year 1 to 5. Period 2 covers years 6-10, and so on.

===Examples ===
Period meaning when period midpoints ARE NOT USED.
{| {{table}}
| align="left" style="background:#f0f0f0;"|'''Period index'''
| align="left" style="background:#f0f0f0;"|'''Description '''
| align="left" style="background:#f0f0f0;"|'''Possible treatment years'''
| align="left" style="background:#f0f0f0;"|'''Date range
| 0||Index för the first period ||0-4||2020-01-01 - 2024-12-31
|-
| 1||Index for the second period||5-9||2025-01-01 - 2029-12-31
|-
| 2||etc||10-14||
|-
|
|}

[[File:Periods when NOT periodmidpoint.png|left|thumb|500px]]

==”Before” and “After” values==
In Heureka, most variables has a before and after-component, which refers to the state or value before treatment, and immediately after treatment, respectively. Only before-treatment values are saved in the result database (when you run PlanWise or RegWise or save a simulation in StandWise).

==State, yield and change variables==
====State variable====
A '''state''' variable refers to a description variable for a stand at a certain time, for example the mean age or the volume.
====Yield variable====
A '''yield''' variable refers to some output from an activity, such as the harvest volume.

====Change variable====
A third type of variable describes '''change''' of a stand, for example growth and mortality. Growth and mortality that are reported in a certain time period t, represents the growth and mortality that has occurred after harvesting in the previous period (t -1) to the current period year.

==Basic calculation steps==
As a Heureka user, it is important that you have a fundamental understanding of how a prognosis is done. The following principal steps are performed when making a prognosis from one time point (t) to another (t+1):

#Calculate state variables for the stand at time t from tree-level data, for example stand volume and mean diameter. This is the Before-value.
#Apply treatment, if a treatment should be applied, and update the After-value for the treatment unit. “After” is the state immediately after the treatment.
#Calculate diameter growth, height growth and mortality for each tree.
#Calculate ingrowth of new trees.
#Update attributes (such as volume, age, diameter, weight) for each tree. The weight is the number of stems that a tree object represents, and is reduced by the mortality rate and by harvesting (for example a thinning will reduce the weight for one or more tree objects).
#Let t = t + 1. Update the tree list for this period and repeat from step 1.

==Subtract half a period’s harvest volume to obtain standing stock if many stands==
If you want to create for example a graph of how the standing stock (the total volume) of a large forest holding develops over time according to a simulation in PlanWise, and you have used period midpoints (the default in a TPG-simulation), you should subtract half the period’s harvest volume from the Before-value. The reason is that the Before-value has been adjusted for a half a period’s growth and mortality, but not for half a periods harvesting. In reality, in a case with many stands, some of the stands will be harvested early in the period, other stands in the middle of the period, and other stand at the end of the period. But in the model, all harvesting takes place in the middle of the period. Extracting half a periods harvesting is a simple way to at least approximately adjust for this error.

==Understanding how growth is calculated==
Growth and mortality [[#change|change]] refers to how a forest stand is changing from one time point to the next. Growth is reported as gross growth and net growth. Gross growth includes mortality, net growth does not.

see [[Growth Results]]

2021-07-26T13:29:41Z

Peder: /* Net present value */

<noinclude>
{{Languages}}</noinclude>
===Net present value===
In PlanWise and StandWise, Heureka calcuated the net present value (npv) for each treatment unit and management schedule generated. It is the sum of discounted revenues minus costs, for an approximately infinite time horizon, and with the real discount rate set by the user. For even-aged management, Heureka approximates an infinite time horizon by assuming that the third forest rotation management regime will be repeated in perpetuity. For uneven-aged management, the last cutting is assumed to be repeated in perpetuity with a cutting time interval equal to the time elapsed between the last two cuttings projected.

For each alternative generated in even-aged management, Heureka generates up to three unique rotations. The reason for not just repeating the second management regime is to allow for the possible chang in growth conditions over time. The climate model, if activated in a simulation, affects site fertility so that a certain rotation will have a different growth potential than the previous one, and consequently the management regime should be adapted to that. The growth of plantations will also be affected by at which time planting is done, since breeding effects is assumed to increase over time. For example, trees planted in twenty years will give higher yields that trees planted today.

====Even-aged management====
The net present value for even-aged management is calculated as 

<math>NPV_{evenaged} = \displaystyle \sum_{t=0}^{S} \delta_t R_t + \delta_{S}\cdot SEV</math> 
where 
''S'' = Final felling year for the rotation preceeding the last rotation simulated, and 
<math>R_t = </math>Net revenue in year ''t'', with ''t'' = 0 marking year 0 of the planning horizon, and 
''r'' = Real discount rate, and 
<math>\delta_t = \displaystyle (1+r)^{-t}=</math>discount factor for year t, and 
''SEV'' = Soil expectation value as given below

====Soil expectation value====
The soil expectation value (SEV) is by definition the net present value for an infinite time horizon when starting from bare land. In Heureka, the soil expecation value refers to the net present value of the last rotation simulated (assumed repeated in perpetuity). If you want to calculate the SEV with Heureka starting from today (year 0), you should use bare land as initial state.

The SEV is calculated as: 

<math>SEV = \displaystyle \alpha_{SEV}\sum_{t=0}^{T} \delta_t R_t </math>
where 
where ''T'' = Rotation length for the last forest generation, 

''αSEV'' = "discount repeat factor" derived from a [https://en.wikipedia.org/wiki/Geometric_series geometric series]. A geometric series is the sum of an infinite number of terms that have a constant ratio (qSEV) between successive terms. If ||''qSEV''|| < 0, then

<math>\alpha_{SEV} = \displaystyle \frac{1}{1-q_{SEV}}</math>

where 
<math>q_{SEV} = \displaystyle {(1+r)}^{-T}</math> 
 Note that if the discount rate r is 0, then q_SEV will be 1 and the sum will be infinitely large.

====Uneven-aged management (CCF)====
When calculating the net present value for uneven-aged stand management program, some estimation of the terminal value at the end of the planning horizon must be included. One way is to assume that a steady state is reached at some point in the future. In analogy to even-aged management where a series of identical rotation regimes is assumed to be repeated in perpetuity, we can assume that a series of selection fellings is repeated with a certain cutting cycle after the end of the planning horizon. In the forest economic literature that address the stand-level optimization problem, one solution for this is called the equilibrium endpoint problem (Haight & Getz 1987, used by for example Wikström 2000, p. 454). A steady state here implies that the number of stems in each diameter class after harvest is the same in two subsequent periods, separated by a certain time interval. Another approach is to use a very long time horizon, such as 150 years, in which the discounted terminal value can be practically negligible of the discount rate is large enough. For example, with a 3 percent discount rate the discount factor for outcomes in 150 years is 1.1 percent. In Heureka a simplified approach is used combining the two approaches, with both a time horizon of at least 100 years (unless explicitly changed by the user), and assuming that the last harvest is repeated with a time interval equal to that passed between the last two harvests during the planning horizon. If there are less than two harvest periods during the planning horizon, Heureka searches up to 50 years beyond the last period. If there are still less than two harvest periods found, Heureka generates an unmanaged program instead. However, Heureka is not currently able to enforce any equilibrium constraints for the tree diameter distribution as described above. Instead, it is assumed that the minimum volume constraint (SVL10, “virkesförrådskurvan”) and the thinning algorithm, which has the same parameters in all periods, both should lead to a steady state after 100 years, at least from an economic perspective.

The net present value for uneven-aged management is calculated as follows. Note that the first summation is done up to the period
before the last cutting period T, since the revenue in period T is already included in the so called Managed Forest Value (MFV). MFV is mathematically analogues to SEV but the value refers to an establied steady state forest, instead of bare land 

<math>NPV_{CCF} = \displaystyle \sum_{t=0}^{T-1} \delta_t R_t + \delta_{T}\cdot MFV</math> 
with the same notations as above, and 
''T'' = Last cutting period 
''MFV'' = So called managed forest value, which is simply a [https://en.wikipedia.org/wiki/Geometric_series geometric series], with a constant yield every n_th year, where n is the (assumed) fixed cutting cycle.

The MFV is simply calculated as

====Terminal value====
Heurekas also calculates a result variable called Terminal Value, which has an associated Terminal Value Year. The Terminal Value Year is usually the same as the year after the last planning period. The terminal value represents the part of the net present value that remains after the last planning period. The terminal value is calculated by subtracting the sum of discounted net revenues (that occurs until the last planning period) from the net present value, and the prolonging that value to the last year.

For mer info on terminal value calculation, see [[Media:Berakning_terminala_varden.pdf | Berakning_terminala_varden.pdf]]

{{VariableCategory}}

Net present value

2021-07-26T13:19:05Z