Continental-Scale Living Forest Biomass and Carbon Stock: A Robust Fuzzy Ensemble of IPCC Tier 1 Maps for Europe. de Rigo, D.; Barredo, J. I.; Busetto, L.; Caudullo, G.; and San-Miguel-Ayanz, J. 413:271–284.
Continental-Scale Living Forest Biomass and Carbon Stock: A Robust Fuzzy Ensemble of IPCC Tier 1 Maps for Europe [link]Paper  doi  abstract   bibtex   
Forest ecosystems play a key role in the global carbon cycle. Spatially explicit data and assessments of forest biomass and carbon are therefore crucial for designing and implementing effective sustainable forest management options and forest related policies. In this contribution, we present European-wide maps of forest biomass and carbon stock spatially disaggregated at 1km x 1km. The maps originated from a spatialisation improvement of the IPCC methodology for estimating the forest biomass at IPCC Tier 1 level (IPCC-T1). [\n] Using a categorical map of ecological zones within the mapping technique may originate boundary effects between the ecological zones. This may induce undue artifacts in the outcomes, as evident in previously published maps generated with the IPCC-T1 methodology. Here we present a novel method for IPCC-T1 biomass mapping which mitigates these artifacts. [\n] We propose the use of a fuzzy similarity map of the FAO ecological zones computed by estimating the relative distance similarity (RDS) of each grid-cell's climate and geography with respect to the FAO ecological zones. A robust ensemble approach was used to merge an array of simple models with spatially distributed fuzzy set-membership. This allowed the boundary artifacts to be reduced, while mitigating the impact of model semantic extrapolation. The chain of semantically enhanced data-transformations is described following the semantic array programming paradigm. [\n] Preliminary results obtained from the application of this novel approach are presented along with a discussion of its impact on the derived maps. [Excerpt: Introduction] Forest ecosystems play a key role in the global carbon cycle and are considered large and persistent carbon sinks [1]. Spatially explicit data and assessments of forest biomass and carbon are therefore of great importance for the design and implementation of effective sustainable forest management options and forest related policies. In complex, wide scale problems, the effectiveness of the science-policy interface might depend on the availability, understandability and multiplicity of estimations, even for correctly assessing the extent and sources of critical uncertainties [2-7]. In this context, European-wide maps of forest biomass and carbon stock spatially disaggregated at 1 km × 1 km (LAEA grid) were recently developed [8], exploiting the IPCC Tier 1 level methodology described in [9]. This is a cost-effective approach for biomass and carbon mapping over large geographical regions where gaps in accurate biomass information exist. [\n] According to this methodology [8], above ground living biomass B_c for a given cell c of a generic regular grid may be estimated by aggregating the biomass contributions by forest type {typ} [13] - coniferous (con) and broadleaved (bro) - and management type {man} - semi-natural forest (sn) and plantations (pl) [...] [\n] The contributions B_c{ag,man,typ} are determined on the basis of two factors. [::] First, the fraction fc_c{ag,man,typ} of the cell's area covered by each combination {man,typ}. [::] Second, the average above-ground biomass b_c{ag,man} associated to semi-natural forest and plantations in the ecological zone (e.g. boreal, temperate, subtropical; mountain vs. steppe etc.; from hereafter, EZ) to which c belongs [...] [\n] For their pan-European IPCC-T1 application, [8] used as inputs the CORINE land cover map of 2006 [14] to determine the fraction of surface occupied by coniferous and broadleaved forests within 1 km × 1 km cells of a pan-European grid. Each cell was associated with an EZ, following the map of Global Ecological Zones for the Global Forest Reporting [15,16]. Biomass and carbon stock for each cell were finally computed using eqs. 1-3. This method relies on the simplistic assumption that within a given EZ the coefficients of tab. 1 are constant. [...] [\n] The variability of the estimated quantities within each EZ is therefore only driven by the varying percentage of forest area within the cells, and evident artefacts in the output maps are present on the ecozones' boundaries (see also fig. 3). [\n] In order for these effects to be mitigated, we propose an innovative fuzzy similarity map of EZs as an alternative input dataset so as to associate the different areas of Europe with more consistent average biomass amounts and carbon fraction coefficients. This fuzzy set map was computed by estimating the relative distance similarity (RDS) [18] of each grid-cells climatic and geographic conditions from the distribution of values typically observed within the FAO EZs. An unsupervised robust ensemble approach was used to merge an array of simple models with spatially distributed fuzzy set-membership. This allowed the boundary artifacts to be reduced, while mitigating the impact of model semantic extrapolation. The chain of semantically enhanced data-transformation models (D-TM) is described following the semantic array programming paradigm [19,20]. [\n] The theoretical basis and the preliminary results obtained from the application of this novel approach are presented along with a discussion of its impact on the derived maps. [...] [Materials and Methods] [...] [::From Crisp Ecological Zones to a Fuzzy Similarity Map] FAO produced an expert-based EZ map considering not only bioclimatic variables, but also potential and national vegetation maps [16]. The FAO classification does not match exactly with the Holdridge one, based exclusively on bioclimatic data [25], and in general is not meant to be fully reproduced as a computational model. [\n] FAO EZs embed a broad semantic understanding of climatic specificities such as the mass elevation effect (MEE), for which altitude influences vegetation less ” on larger mountains than on smaller ones” [16]. Our method exploits the FAO crisp map as input for training a fuzzy EZ classification with a set of N C bioclimatic covariates (tab. 2). Besides temperature and precipitation derived factors, geographic ones are also used - elevation range and solar irradiation - so as to better discriminate e.g. polar, alpine and boreal EZs. Evapotranspiration is not used [30]. MEE is considered with neighbourhood analysis (spatial average moving windows) in two covariates. [...] [::Fuzzy Ecozones for Biomass and Carbon Stock Ensembles] The final D-TM of eq.4c ensures μez to show a series of desirable properties for unsupervised fuzzy ensemble applications. [::] First, the aforementioned semantic properties ez of η_c also hold for μ_c{ez}. [::] Second, a weighted median of quantities of choice (e.g. EZ biomasses or carbon stocks), done using as weights the fuzzy scores μ_c{ez}, would always select the quantity corresponding to the dominant EZ in c. This provides a very intuitive and coherent way for estimating defuzzified (crisp) ensembles: selecting a very robust ensemble operator such as the weighted median automatically implies a crisp ensemble. [\n] On the other hand, a weighted average would instead use all the above-median best fuzzy scores and would merge the corresponding associated quantities (but not the ones having worst scores, thus automatically behaving as a robust statistics). Classic intermediate robust statistics as the trimmed mean would show intermediate behaviour, as the intuition would expect. Furthermore, jack-knife resampling techniques might safely be applied by iteratively removing one fuzzy EZ per time. In the worst case, the removal would decrease the overall sum of remaining μ_c{ez} to not less than 50 %, thus ensuring a quite robust statistical resampling. [...] [Results and Discussion] [...] Although preliminary, these results suggest the proposed methodology for deriving fuzzy EZ maps to be beneficial in mitigating undue artifacts in IPCC-T1 large-scale biomass and carbon mapping. It must however be remembered that, although the quantities are disaggregated at 1 km × 1 km spatial resolution in the resulting maps, the intrinsic limitations of the IPCC-T1 methodology (i.e., the use of constant coefficients to describe the typical characteristics of forests over huge spatial extents) suggest that local patterns should be considered as merely indicative. [\n] Nevertheless, the method might prove helpful for interpolating spatial gaps in more detailed maps. The exemplified fuzzy ensemble modelling strategy - whose D-TM detailed computational description [32] is reproducible [33-35] and entirely based on free software [36] and data [37, 38] - lies within a family of semantically-enhanced ensemble techniques [39-42] which might also serve as reference for merging multiple partially independent estimations of biomass and carbon stock [43] and deriving new improved maps. [...] [Conclusions] A pan-European similarity analysis has been performed - at 1x1 km spatial grid resolution - by comparing each grid-cell climate and geography with respect to the FAO ecological zones. A rank-based mapping of the relative distance similarity (RDS) for each spatial cell c to the eco-zones EZ in the crisp classification system of FAO leaded to a robust fuzzy ecological classification. The resulting array of simple models offered a spatially distributed fuzzy set-membership of the ecological zones which extends the FAO system in the European continent by moving from crisp categorical classes to a semantic fuzzy composition of them. [\n] The use of the derived novel fuzzy EZ maps as an input dataset for the computation of pan-European forest biomass and carbon maps using the IPCC Tier 1 methodology highlighted their usefulness for modelling applications relying on EZ maps as categorical input datasets. A noticeable characteristic of the modelling approach for deriving the fuzzy EZ maps is also that it entirely relies on geographic and climate information routinely estimated by global and regional climate models. This makes the method also suitable for modelling applications in which the spatial shift of ecological zones and of eco-zone dependant quantities need to be assessed under climate change scenarios.
@article{derigoContinentalscaleLivingForest2013,
  title = {Continental-Scale Living Forest Biomass and Carbon Stock: A Robust Fuzzy Ensemble of {{IPCC Tier}} 1 Maps for {{Europe}}},
  author = {de Rigo, Daniele and Barredo, José I. and Busetto, Lorenzo and Caudullo, Giovanni and San-Miguel-Ayanz, Jesús},
  editor = {Hrebicek, J. and Schimak, G. and Rizzoli, A. E. and Kubasek, M.},
  date = {2013},
  journaltitle = {IFIP Advances in Information and Communication Technology},
  volume = {413},
  pages = {271--284},
  issn = {1868-4238},
  doi = {10.1007/978-3-642-41151-9_26},
  url = {https://doi.org/10.1007/978-3-642-41151-9_26},
  abstract = {Forest ecosystems play a key role in the global carbon cycle. Spatially explicit data and assessments of forest biomass and carbon are therefore crucial for designing and implementing effective sustainable forest management options and forest related policies. In this contribution, we present European-wide maps of forest biomass and carbon stock spatially disaggregated at 1km x 1km. The maps originated from a spatialisation improvement of the IPCC methodology for estimating the forest biomass at IPCC Tier 1 level (IPCC-T1). [\textbackslash n] Using a categorical map of ecological zones within the mapping technique may originate boundary effects between the ecological zones. This may induce undue artifacts in the outcomes, as evident in previously published maps generated with the IPCC-T1 methodology. Here we present a novel method for IPCC-T1 biomass mapping which mitigates these artifacts. [\textbackslash n] We propose the use of a fuzzy similarity map of the FAO ecological zones computed by estimating the relative distance similarity (RDS) of each grid-cell's climate and geography with respect to the FAO ecological zones. A robust ensemble approach was used to merge an array of simple models with spatially distributed fuzzy set-membership. This allowed the boundary artifacts to be reduced, while mitigating the impact of model semantic extrapolation. The chain of semantically enhanced data-transformations is described following the semantic array programming paradigm. [\textbackslash n] Preliminary results obtained from the application of this novel approach are presented along with a discussion of its impact on the derived maps.

[Excerpt: Introduction] Forest ecosystems play a key role in the global carbon cycle and are considered large and persistent carbon sinks [1]. Spatially explicit data and assessments of forest biomass and carbon are therefore of great importance for the design and implementation of effective sustainable forest management options and forest related policies. In complex, wide scale problems, the effectiveness of the science-policy interface might depend on the availability, understandability and multiplicity of estimations, even for correctly assessing the extent and sources of critical uncertainties [2-7]. In this context, European-wide maps of forest biomass and carbon stock spatially disaggregated at 1 km × 1 km (LAEA grid) were recently developed [8], exploiting the IPCC Tier 1 level methodology described in [9]. This is a cost-effective approach for biomass and carbon mapping over large geographical regions where gaps in accurate biomass information exist. 

[\textbackslash n] According to this methodology [8], above ground living biomass B\_c for a given cell c of a generic regular grid may be estimated by aggregating the biomass contributions by forest type {typ} [13] - coniferous (con) and broadleaved (bro) - and management type {man} - semi-natural forest (sn) and plantations (pl) [...]

[\textbackslash n] The contributions B\_c{ag,man,typ} are determined on the basis of two factors. [::] First, the fraction fc\_c{ag,man,typ} of the cell's area covered by each combination {man,typ}.

[::] Second, the average above-ground biomass b\_c{ag,man} associated to semi-natural forest and plantations in the ecological zone (e.g. boreal, temperate, subtropical; mountain vs. steppe etc.; from hereafter, EZ) to which c belongs [...]

[\textbackslash n] For their pan-European IPCC-T1 application, [8] used as inputs the CORINE land cover map of 2006 [14] to determine the fraction of surface occupied by coniferous and broadleaved forests within 1 km × 1 km cells of a pan-European grid. Each cell was associated with an EZ, following the map of Global Ecological Zones for the Global Forest Reporting [15,16]. Biomass and carbon stock for each cell were finally computed using eqs. 1-3. This method relies on the simplistic assumption that within a given EZ the coefficients of tab. 1 are constant. [...]

[\textbackslash n] The variability of the estimated quantities within each EZ is therefore only driven by the varying percentage of forest area within the cells, and evident artefacts in the output maps are present on the ecozones' boundaries (see also fig. 3). [\textbackslash n] In order for these effects to be mitigated, we propose an innovative fuzzy similarity map of EZs as an alternative input dataset so as to associate the different areas of Europe with more consistent average biomass amounts and carbon fraction coefficients. This fuzzy set map was computed by estimating the relative distance similarity (RDS) [18] of each grid-cells climatic and geographic conditions from the distribution of values typically observed within the FAO EZs. An unsupervised robust ensemble approach was used to merge an array of simple models with spatially distributed fuzzy set-membership. This allowed the boundary artifacts to be reduced, while mitigating the impact of model semantic extrapolation. The chain of semantically enhanced data-transformation models (D-TM) is described following the semantic array programming paradigm [19,20].

[\textbackslash n] The theoretical basis and the preliminary results obtained from the application of this novel approach are presented along with a discussion of its impact on the derived maps. [...]

[Materials and Methods] [...]

[::From Crisp Ecological Zones to a Fuzzy Similarity Map] FAO produced an expert-based EZ map considering not only bioclimatic variables, but also potential and national vegetation maps [16]. The FAO classification does not match exactly with the Holdridge one, based exclusively on bioclimatic data [25], and in general is not meant to be fully reproduced as a computational model.

[\textbackslash n] FAO EZs embed a broad semantic understanding of climatic specificities such as the mass elevation effect (MEE), for which altitude influences vegetation less ” on larger mountains than on smaller ones” [16]. Our method exploits the FAO crisp map as input for training a fuzzy EZ classification with a set of N C bioclimatic covariates (tab. 2). Besides temperature and precipitation derived factors, geographic ones are also used - elevation range and solar irradiation - so as to better discriminate e.g. polar, alpine and boreal EZs. Evapotranspiration is not used [30]. MEE is considered with neighbourhood analysis (spatial average moving windows) in two covariates. [...]

[::Fuzzy Ecozones for Biomass and Carbon Stock Ensembles] The final D-TM of eq.4c ensures μez to show a series of desirable properties for unsupervised fuzzy ensemble applications. 

[::] First, the aforementioned semantic properties ez of η\_c also hold for μ\_c{ez}. 

[::] Second, a weighted median of quantities of choice (e.g. EZ biomasses or carbon stocks), done using as weights the fuzzy scores μ\_c{ez}, would always select the quantity corresponding to the dominant EZ in c. This provides a very intuitive and coherent way for estimating defuzzified (crisp) ensembles: selecting a very robust ensemble operator such as the weighted median automatically implies a crisp ensemble.

[\textbackslash n] On the other hand, a weighted average would instead use all the above-median best fuzzy scores and would merge the corresponding associated quantities (but not the ones having worst scores, thus automatically behaving as a robust statistics). Classic intermediate robust statistics as the trimmed mean would show intermediate behaviour, as the intuition would expect. Furthermore, jack-knife resampling techniques might safely be applied by iteratively removing one fuzzy EZ per time. In the worst case, the removal would decrease the overall sum of remaining μ\_c{ez} to not less than 50 \%, thus ensuring a quite robust statistical resampling. [...]

[Results and Discussion] [...] Although preliminary, these results suggest the proposed methodology for deriving fuzzy EZ maps to be beneficial in mitigating undue artifacts in IPCC-T1 large-scale biomass and carbon mapping. It must however be remembered that, although the quantities are disaggregated at 1 km × 1 km spatial resolution in the resulting maps, the intrinsic limitations of the IPCC-T1 methodology (i.e., the use of constant coefficients to describe the typical characteristics of forests over huge spatial extents) suggest that local patterns should be considered as merely indicative.

[\textbackslash n] Nevertheless, the method might prove helpful for interpolating spatial gaps in more detailed maps. The exemplified fuzzy ensemble modelling strategy - whose D-TM detailed computational description [32] is reproducible [33-35] and entirely based on free software [36] and data [37, 38] - lies within a family of semantically-enhanced ensemble techniques [39-42] which might also serve as reference for merging multiple partially independent estimations of biomass and carbon stock [43] and deriving new improved maps. [...]

[Conclusions] A pan-European similarity analysis has been performed - at 1x1 km spatial grid resolution - by comparing each grid-cell climate and geography with respect to the FAO ecological zones. A rank-based mapping of the relative distance similarity (RDS) for each spatial cell c to the eco-zones EZ in the crisp classification system of FAO leaded to a robust fuzzy ecological classification. The resulting array of simple models offered a spatially distributed fuzzy set-membership of the ecological zones which extends the FAO system in the European continent by moving from crisp categorical classes to a semantic fuzzy composition of them.

[\textbackslash n] The use of the derived novel fuzzy EZ maps as an input dataset for the computation of pan-European forest biomass and carbon maps using the IPCC Tier 1 methodology highlighted their usefulness for modelling applications relying on EZ maps as categorical input datasets. A noticeable characteristic of the modelling approach for deriving the fuzzy EZ maps is also that it entirely relies on geographic and climate information routinely estimated by global and regional climate models. This makes the method also suitable for modelling applications in which the spatial shift of ecological zones and of eco-zone dependant quantities need to be assessed under climate change scenarios.},
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