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--- scenario_simulation [2023/09/08 11:46] – [Behavioural equations for supply, feed demand and land markets] massfeller
+++ scenario_simulation [2023/09/08 12:07] (current) – [Land use, land use change and forestry (LULUCF)] massfeller
@@ Line 1278: / Line 1278: @@
 The disadvantage of the behavioural functions above is the fact that they might generate non-positive values. That situation might be interpreted as a combination of prices where the marginal costs exceed marginal revenues. Accordingly, a fudging function is applied for supply, feed and (see below) processing demand which ensures strictly positive quantities. That fudging function is highly non-linear, and therefore only switched on on demand.
-====Land use, land use change and forestry (LULUCF) in the basic model====
+====Land use, land use change and forestry (LULUCF) ====
+===LULUCF in the basic model ===
+Before SUPREMA LULUCF and area-based carbon accounting were not depicted in the global market model. Land demand was conceptually derived from maximising farmers profit. Land supply was represented with a function that links supply to agricultural land rents with an elasticity. Non-agricultural land use that complements farm land to give the total region area was disaggregated into forestry, built up areas (urban or “artificial” land) and a remaining “other land” category. There was neither a mapping of land use categories in the market model to the UNFCCC categories, nor a modelling of the transition matrix accompanied by a very limited product-based carbon accounting which was not in line with IPCC.
+The pre-SUPREMA specification may be described as follows.
+Agricultural outputs i (barley, wheat, beef ...) have land requirements LV<sub>i</sub> derived from production of these outputs (via yields that respond to prices according to yield elasticities). Adding up all land requirements gives total agricultural land (LT<sub>ag</sub>).
+$${LT}_{ag} = \sum_{i}^{}{{LV}_{i}(\mathbf{P},R_{ag})}$$
+Land demand depends on a vector of prices and the agricultural and rent R<sub>ag</sub> (treated separately). Total agricultural land is just one of several land types (l) that play a role:
+l = {ag, tc, pc, fd, no, fr, ur, ot, iw}, where
+ag = total agricultural land
+tc = temporary (non-fodder) crops
+pc = permanent crops
+fd = temporary fodder, permanent grassland and fallow land
+no = non-agricultural land
+fr = forest land
+ur = settlements, industrial, built up md any other artificial areas
+ot = other land
+iw = inland waters (exogenous)
+Matching with land demand there is a land supply function for total agricultural land
+$${LT}_{ag} = \alpha{R_{ag}}^{\beta}$$
+Given agricultural land and an exogenous region area as well as exogenous inland waters permits to compute total non-agricultural land residually:
+$${LT}_{no} = T - {LT}_{ag} - {LT}_{iw}$$
+This total non-agricultural land (beyond inland waters) is currently allocated to non-agricultural land types n = { fr, ur, ot} according to the shares of “intermediate” areas for non-agricultural land types:
+$${LT}_{n} = {LT}_{no}*{\widehat{LT}}_{n}/\sum_{n}^{}{\widehat{LT}}_{n}$$
+The “intermediate” areas in turn result from the change in the non-agricultural area against the baseline, considering elasticities that reflect the responsiveness of land types to imbalances:
+$${{\widehat{LT}}_{n} = LT}_{n}^{0}*\left( \frac{{LT}_{no}^{}}{{LT}_{no}^{0}} \right)^{\gamma_{n}}$$
+The concept of elasticities of land types to imbalances expresses the expectation that any disequilibrium in the land balance is very unlikely to be removed by changes in settlement area, and probably only to a small extent by changes in forest land and therefore most of all by changes in other land category.
+In spite of full consistency, we have changed this specification under SUPREMA, as 1) it is difficult to reconcile with welfare accounting, 2) it turned out that the scaling mechanism may dominate the planned responsiveness of land types, 3) the asymmetric specifications for supply of agricultural and non-agricultural land is ad-hoc and intransparent and 4) it does not link to standard empirical parameter estimation.
+== Land transitions via Gamma density and Marcov chain  ==
+The area-based carbon modelling and accounting requires the land transition matrix describing how an initial allocation of land uses (either from the base year or from an intermediate simulation year) is transformed into the currently simulated one. The transition matrix may be expressed in terms of absolute areas L<sub>jk</sub> changing from land use LU<sub>j</sub> in the initial year s into another land use LU<sub>k</sub> in the final year t or in terms of a transition matrix sh<sub>jk</sub> giving the share (probability in a Markov chain) of initial land use LU<sub>j</sub> converted into the final LU<sub>k</sub> over the whole horizon of (t-s):
+$${LU}_{k,t} = \sum_{j}^{}{{sh}_{jk}{LU}_{j,s} = \sum_{j}^{}L_{jk}}$$
+Where the shares (probabilities) have to add up to one:
+$$1 = \sum_{k}^{}{{sh}_{jk},\ \forall j}$$
+The total areas converted from initial land use j into final land use k over the horizon (t-s) are denoted L<sub>jk</sub> above. For those land transitions we would expect that the pattern of changes resembles that observed in the past, at least if total land uses LU<sub>j</sub> change similarly as in the past. This expectation corresponds to the most likely land transitions maximising a Gamma density, giving for each transition a corresponding FOC:
+$$\ \left( \lambda_{jk} - 1 \right)L_{jk}^{- 1} - \mu_{jk} + \tau_{k}^{} + \tau_{j}^{initial} = 0$$
+Where λ<sub>jk</sub> and μ<sub>jk</sub> are parameters related to the mode (determined from the database or baseline projection) and standard deviation (assumed = 1) of the Gamma density. The variables τ<sub>k</sub> and τ<sub>j</sub> are shadow values paired with the final year land use accounting from transition probabilities and the adding up condition for probabilities.
+The original specification for land transitions as used in the CAPRI supply models involve 6x(t-s) = 120 equations for a 20 years time horizon to represent a Markov chain of annual land transitions for each region. The advantage of this specification was that annual transitions were explicit model variables that could be used to compute annual carbon effects. These were hence comparable to annual non-CO2 effects related to agricultural production and could be added therefore to obtain total GHG effects from the LULUCF sector and non-CO2 GHGs. Having annual land transitions in each regional was also acceptable from a computational viewpoint for the relatively small regional supply models of CAPRI (about 1500 equations).
+However, in the global market model all regions (about 80 with agents like farmers, consumers or landowners) have to be solved simultaneously such that the additional equations and variables for the extended land use modelling and carbon accounting (addressed in the following section) could increase solution time beyond critical limits. Given that the standard market model already includes about 80000 equations the above framework was adjusted to give the land transitions in //one// step for the change from the initial years to the final year t, while still considering that we need annual carbon effects for comparability with the annual non-CO2 emissions. This has been achieved
+  * by re-specifying the total land transitions as average transitions per year times the projection horizon and
+  * by considering for the remaining class without land use change (on the diagonal of the land transition matrix) only the annual carbon effects per ha, relevant for the case of gains via forest management.
+=== LULUCF and carbon accounting if SUPREMA is active ===
+Within the SUPREMA project two major changes were made:
+First, integration across spatial scales was improved: a) the land activity and LULUCF representation was extended to non-European countries and b) the product-based carbon accounting was replaced by an area-based carbon accounting.
+Second, the methodological approach was changed including a) statistical estimation of land use changes assuming a gamma density as in the supply model, b) re-specification of the total land transitions as average transitions per year times the projection horizon as in the supply model (replacement of the Markov chain approach) and c) representation of the disaggregated land supply in the market model through multinomial logit form to. These changes in the SUPREMA project allow for a more symmetric land use representation and carbon accounting between the supply models for European NUTS2 regions and in the global market model of CAPRI.
+== Multinomial logit function ==
+Under SUPREMA we have introduced a multinomial logit form for land supply of all major endogenous land types f = g = h = m = {ag, fr, ur, ot}. This approach is conceptually fully in line with land supply in the regional supply models. In this way we have integrated and replaced the above separate treatment of land supply for agricultural and non-agricultural land:
+$${LT}_{m} = {SH}_{m}*T$$
+where the area share of land type m is
+$${SH}_{g} = \frac{\exp\left( \delta_{g0} + \sum_{f}^{}{\delta_{gf}R_{f}} \right)}{\sum_{m}^{}{\exp\left( \delta_{m0} + \sum_{f}^{}{\delta_{mf}R_{f}} \right)}}$$
+and the elasticity of share g (and due to constant region area also land type LT<sub>g</sub>) with respect to rent R<sub>h</sub> may be derived as
+$$\varepsilon_{gh} = \frac{\partial{SH}_{g}}{\partial R_{h}}\frac{R_{h}}{{SH}_{g}} = R_{h}\left( \delta_{gh} - \sum_{m}^{}{\delta_{mh}{SH}_{m}} \right)$$
+which permits to make use of the same empirical information (on elasticities of agricultural land supply) and assumptions (on the ranking of responsiveness of non-agricultural areas) that have been used so far in the pre-SUPREMA version. For this purpose, a calibration problem has been set up that minimises weighted squared differences to the starting values by modifying parameters δ<sub>mh</sub>. Due to its symmetric treatment of all major land uses the system also includes supply elasticities for non-agricultural areas. In “standard” scenarios these are unlikely to play a relevant role. The key parameters are the “cross-rent” elasticities of non-agricultural areas with respect to agricultural rents as these are steering now which non-agricultural areas are increasing if agricultural area declines and vice versa. However, in the context of global carbon price scenarios also the supply elasticities of non-agricultural areas play an important role even though we do not introduce assumptions on changing prices of urban land, forest land or other land. This is because a global carbon price creates an endogenous mark-up for land rental prices of non-agricultural areas that reflect the value of the carbon effects from changing land use. In particular the rental price of forest land R<sub>fr</sub> is strongly reduced and might become negative in scenarios with high carbon prices.
+== Spatial extension ==
+Under SUPREMA the land use categories of the market model are mapped to the UNFCCC categories. The mapping of market model land types LT<sub>l</sub> to UNFCCC land use LU<sub>k</sub> will rely on the most recent historical shares ϕ<sub>kl</sub> of UNFCCC land use k in CAPRI land type l:
+$${LU}_{k} = \sum_{l}^{}{\varphi_{kl}{LT}_{l}}$$
+These shares are trivially zero or one in case that certain land types like “temporary non-fodder crops” (tc) and permanent crops (pc) are exclusively mapped to one UNFCCC category (cropland). The remainder to total cropland derives from temporary fodder and fallow land which is a fraction of total fodder area with the remainder being (productive) permanent grassland. The allocation of “other land” (ot) to grassland (ϕ<sub>glot</sub>), wetland (ϕ<sub>wlot</sub>) and residual land (ϕ<sub>rlot</sub>) may occur as in the European database but required that some CAPRI code in use for the supply models was transferred into the context of the extended global market model.
+== Land transitions as average transitions per year times the projection horizon  ==
+The new accounting in the CAPRI global market model may be explained as follows, starting from a calculation of the total GHG effects G over horizon h = t-s from total land transitions L<sub>jk</sub> and carbon effects per ha for the whole period e<sub>jk</sub>:
+$$G = \Gamma \bullet h = \sum_{i,j}^{}{e_{ij}L_{ij}}$$
+Where Γ collects the annual GHG effects that correspond to the total GHG effects divided by the time horizon G / h. These annual effects may be calculated as based on average annual transitions and annual effects for the remaining class as follows:
+$
+$$$\Gamma = \sum_{i,j}^{}{e_{ij}L_{ij}/h} = \sum_{i \neq j}^{}{e_{ij}\Lambda_{ij}} + \sum_{i}^{}{\varepsilon_{ii}L_{ii}}$$
+Where Λ<sub>ij</sub> = L<sub>ij</sub> / h is the average land use change per year and ε<sub>ii</sub> is the annual carbon effect on a remaining class (relevant might be an annual increase due to growing forests while this will be zero for most effects based on IPCC default assumptions).
+Using these average annual transitions for true (off-diagonal) LUC we may compute the final classes as follows:
+$${LU}_{k,t} = \sum_{j}^{}L_{jk} = \sum_{j \neq k}^{}\Lambda_{jk} \bullet h + L_{kk}$$
+While adding up of shares (or probabilities) of LUC from class I to k over all receiving classes k continues to hold as stated above. It should be highlighted that the land use accounting implemented under SUPREMA avoids the need to explicitly trace the annual transitions in the form of a Markov chain and thereby economised on equations and variables. In this form LUC by CAPRI region and the associated accounting of carbon effects turned out computationally feasible even though the number of equations in the global market model increased from about 78000 to about 83000. Apart from feasibility the format above also permitted to retain the typical CAPRI accounting identity that some total “quantity” (“GROF”) should be computable as the effects “per activity” times activity levels. It was therefore also adopted in the CAPRI supply models.
+=== Technical aspects ===
+Concerning the improvements made under SUPREMA from a technical perspective, the changes are merged to the trunk. The approach is controlled by globals in capmod\set_global_variables.gms. If the global variable %supremaMrk% == on, the yearly transition rate p_lucAnnualFac_sup is calculated, land activity is expaned to non-european countries and the multinomial logit form approach is used to model land supply responsiveness. If it is %supremaMrk% == off, the old approach using the Marcov chain is used with the respective variable v_luYearly (for details on Marcov chain approach see [[module_for_agricultural_supply_at_regional_level|supply model description]]). The FOC-approach to calculate LUC as described above is standard and independent from if the global variable supremaMrk is on or off.
+=== Carbon accounting ===
+A last recent change concerns the transfer of the existing carbon accounting equations from the supply model to the global market model. These equations run if the global variable %supremaMrk% == on. More information on the equations can be found in the [[module_for_agricultural_supply_at_regional_level|description of the supply model]]. The equations concerned are, indicated with their present “CAPRI names” in the supply models and plus “Mrk” in the market model:
+Table 3. Equations concerning mitigation modelling in CAPRI
+^__Supply model__^__Market model__  ^
+|GWPCO2BIO_      |GWPCO2BIOMrk_(RMS)|
+|GWPCO2SOI_      |GWPCO2SOIMrk_(RMS)|
+|GWPN2OSOI_      |GWPN2OSOIMrk_(RMS)|
+|GWPCO2BUR_      |GWPCO2BURMrk_(RMS)|
+|GWPCH4BUR_      |GWPCH4BURMrk_(RMS)|
+|GWPN2OBUR_      |GWPN2OBURMrk_(RMS)|
+|GWPCO2HIS_      |GWPCO2HISMrk_(RMS)|
+|GWPCH42HIS_     |GWPCH4HISMrk_(RMS)|
+As most CAPRI regions combine only a small number of climate zones and we may assume for an illustrative calculation three (out of 9). In this case we would have 22 additional equations for carbon accounting per region and 1738 equations in total (on top of those for land use modelling mentioned above), confirming the order of magnitude for the additional equations that was mentioned above.
+For the technical coefficients we could rely on the FAO data compiled for the implementation of LULUCF accounting in the supply models. Here they served often only a fall-back solution in case that some European dataset was missing, but for the global market model the FAO data are often the only source of data readily available.
+There is one new element required for the planned implementation of a carbon tax deriving from land use and land use changes: In the supply models the tax is simply added as a cost element in the existing income accounting for the regional farms to make it effective. In the global market model there is no explicit income accounting. The carbon tax levied so far on non-CO2 emissions has been translated therefore into a tax on outputs, depending on the product based non-CO2 emission factors of outputs that may be changed implicitly. For LULUCF an explicit tax on land use has been introduced. This required to treat land demand and land supply for temporary and permanent crops and fodder as separate qualities with distinct rental prices for market clearing.
 ====Behavioural equations for final demand====