Reality → model → math. form.

t A 1 = x A 1 v A t A 2 = x A 2 v A t B = x B v B t A 2 ⩽t B ⩽t A 1 ⇒ crash
Models can be "wrong" in both the translation of elements that matter in the modelling idea (assumptions) or in their formalisations (e.g.

Spatial representation

Decoupling the spatial scale of the market module (country and regional) from those of the resource and management modules (pixel level)

• regional scale reasonably adequate for the market module

Forest resources -types

Primary forest A primary forest is a forest that has never been logged and has developed following natural disturbances and under natural processes, regardless of its age.

Secondary forest

A secondary forest is a forest that has been logged and has recovered naturally or artificially. Not all secondary forests provide the same value to sustaining biological diversity, or goods and services, as did primary forest in the same location.

Plantation forest

A plantation forest may be afforested land or a secondary forest established by planting or direct seeding.A gradient exists among plantation forests from even-aged, single species monocultures of exotic species with a fibre production objective to mixed species, native to the site with both fibre and biodiversity objectives. Using multipliers sc,px,ft,t key input biological variables can change from the regional average along the spatial and temporal dimensions according to the CC scenario under study:

P.S.: Classification may vary

-2.3 0.1 -3.4 -5.0 -2.3 -2.5 -2.2 -4.6 -2.3 4.6 -5.4 -east & south -5.1 -2.4 -2.8 -3.3 -6.1 -2.9 -3.2 -2.7 -3.5 -1.7 -2.2 -4.4 -north -3.1 -1.0 -1.2 -1.7 -4.3 -1.2 -0.4 -2.3 -2.4 -0.9 -1.7 -1.4 -west & central -5.0 -2.5 3.3 -3.9 -4.1 -2.0 -2.2 -1.8 -7.2 -3.9 17.5 -8.3 Asia -0.2 2.6 1.2 0.0 -0.4 2.
• time of passage:

HWP markets

Supply

It depends from own price and availability of the resource:

Demand

It depends uniquely from the own price (recently a cross-price elasticity has been added):

International trade

While products in different regions are assumed perfectly homogeneous (and hence regional price depends diverge only by transport costs), national vs international products are assumed partially heterogeneous. A parameter (the Armington elasticity) defines how local prices are more or less dependant by local market condition vs external international prices:

Net Present Value

The Net Present Value (NPV) is the sum of all the benefits and costs involved during the investment, each discounted at the indicated interest rate from the planned time to the starting time of the investment.

It is therefore computed as:

where T is the total length of the forest investment (its rotation period), B t are the total benefits coming from the activities planned at time t in current prices, and C t are the total costs arising from such activities and i is the interest rate.

A NPV value greater than zero means that the investment is profitably at the given interest rate. However it is not directly comparable between investment of different length. Where NPV it the Net Present Value of a single rotation (the production cycle), T is the rotation length (typically the number of years) and i is the market interest rate.

NPV = ∑ t=0 T ( B t
Differently from the NPV, it allows to compare forest investments of different duration. Forest investment decisions -CBA analysis to retrieve NPV, SEV and IRR

The computation of the NPV or SEV (and the closely related Internal Rate of Return -IRR, that is the value of interest rate that lead the NPV to zero) is often done numerically and in discrete form: following "guidelines" for the specific forest investment, each year are reported the expected operations that will generate revenues or costs and then the NPV is the actualised present value of both of them. This easily allows to include in the analysis also externalities and compute a separate profitability for the forest owner ("Financial Analysis") or for the society as a whole ("Economic Analysis") and to include risk analysis. -As (a) forest investments involve a certain risk, (b) this risk is different for the different investments, and (c) the aversion for the risk is different for the various managers, the comparison is carried on over a certain equivalent SEV of the investment, computed as:

where CESEV i,j is the certain equivalent SEV of forest investment i for the forest manager j, SEV i is the original SEV, ra j is the risk aversion coefficient for forest manager j and cumMort i is the average cumulative mortality expected for forest investment i before maturation.

-Future mortality and growth rates needed to compute the SEV can be those forecasted by the specific scenario or those prevailing at time to make the investment, depending from forest manager expectations Climate change -introduction

CESEV i , j =SEV i * (1-ra j * cumMort i )
1 7 5 1 1 7 5 9 1 7 6 7 1 7 7 5 1 7 8 3 1 7 9 1 1 7 9 9 1 8 0 7 1 8 1 5 1 8 2 3 1 8 3 1 1 8 3 9 1 8 4 7 1 8 5 5 1 8 6 3 1 8 7 1 1 8 7 9 1 8 8 7 1 8 9 5 1 9 0 3 1 9 1 1 1 9 1 9 1 9 2 7 1 9 3 5 1 9 4 3 1 9 5 1 1 9 5 9 1 9 6 7 1 9 7 5 1 9 8 3 1 9 9 1 1 9 9 9 2 0 0 7

Simulation of carbon stocks in the French forests

There is large scientific evidence that the pool is becoming saturated -hence it will be less able in the future to absorb additional CO2 from the atmosphere

Filière

Filière

  effect on forest resources CC effects on the forest dynamics are exogenous to FFSM. Conversely, consequences on the management of the forest are explicitly accounted for.

Filière•

  Area allocation module: agent based micro-economic model; area allocation endogenised; regeneration = f (π(prices, growth, mortality )); forest managers heterogeneous for (a) managed forest resources, (b) degree of risk-aversion (prices and growth vs. mortality), (c) level of expectations (observed vs. future prices, growth, mortality); • Forest investments are chosen based (comparing) on the SEV. • Two corrections are made before the comparison: -Transaction costs are subtracted from the SEV. These transaction costs are defined for each couple of current forest type, compared forest type.

FilièreFilière

  (area allocation module) Heterogeneous expectations are important as.. we don't all have the same opinion about climate change !

FilièreFilière

  Storing carbon in the terrestrial biosphere, within the fast domain sinks is a bit like sweeping the dirt under the carpet

Filière•

  Carbon module: "registers and accounts" forest and forest sector carbon emitted/sequestrered/substituted; Squares: carbon pools; ellipses: processes. The clock icon denotes multi-period flows. Elements accounted for in the module are drawn using wider contours.

  photosynthesis (primary growth)for. operations emissions

, Bois et Commercialisation (Ing2A-SCD1) A.A. 2016/2017

  Ok, we developed a model.. but what is a model ??Modellisation of the French forest SectorRecursive bio-economic model with coupled biological forest growth model and partial equilibrium market of forest products.

	int main (){ float xa1, xa2, yb, va; float vb, ta1, ta2, tb; cin >> xa1; cin >> xa2; cin >> yb; cin >> va; cin >> vb; ta1 = xa1/va; ta2 = xa2/va; tb = yb/vb; if (tb >= ta2 && tb <= ta1){ cout << "Crash..." << endl; } else { cout << "No crash.." << endl; } } Antonello Lobianco 2 -available volumes 4 -harvesting volumes 5 -local prices Forest Forest Dynamics 6 -harvested area A modular approach 1 -growth, mortality (share 2) 9 -regeneration area Dynamics Module Module Forest resource s Area Area Allocation Allocation Module Module Forest manager s Marke Marke t t Modul Modul e e Wood product s market s Climate scenari o 3 -international prices 7 -future growth and mortality expectations Carbon Carbon module module Carbon emission s Carbo n stock s volumes, death biomass harvesting, transportation, wood products supply 8 -harvested area (share 1) Four interconnected modules: Forest dynamics module: model forest resources Market module: HWP markets (supply, demand, trade..) Area allocation module: forest investment choises Carbon module: mitigation potentials of the forest sector Filièrediapo 10 sur 33 Pathogen module: simulation of a spatially explicit pathogen

Mariner 1, 1962

satellite, Mars Climate Orbiter 1998) A.A. 2016/2017 Modellisation of the French forest Sector diapo 11 sur 33 Antonello Lobianco

Filière, Bois et Commercialisation (Ing2A-SCD1) A.A. 2016/2017 Modellisation of the French forest Sector

	Forest resources -how, which and where
	Africa Africa	Forest 1000ha 2000 624,103 Wooded land Primary 2005 2010 Type % Nat. reg. Plantation 2015 2000 21.6 71.5 2.6 -4.9	Oth. wooded land Forest 1000ha 2005 2010 367,041 2015 % land area Other wooded land Wooded land 2000 2005 2010 ha cap. % world 33.2 0.86	2015 19.0
	-east & south	274,886	2.1	96.3	1.7	171,344	44.6	1.04	8.6
	-north	36,217	3.7	53.3	23.3	60,091	10.1	0.40	1.9
	-west & central	313,000	40.9	51.9	1.0	135,606	43.4	0.92	8.6
	Asia	593,362	19.8	58.1	21.7	234,729	26.6	0.19	15.9
	-east	257,047	12.9	51.3	35.7	108,762	31.6	0.23	7.0
	-south & south-easth	292,804	27.6	62.1	10.2	60,673	42.2	0.15	6.8
	-west & central	43,511	7.1	70.5	15.6	65,294	9.7	0.25	2.1
	Europe	1,015,482	27.3	64.0	8.1	100,014	50.4	1.51	21.4
	-Italy	9,297	1.0	92.1	6.9	1,813	37.8	0.18	0.2
	-France	16,989	0.0	88.4	11.6	590	32.1	0.27	0.3
	-Germany	11,419	0.0	53.6	46.4	0	32.8	0.14	0.2
	-Sweden	28,073	8.6	42.5	48.9	2,432	74.3	3.17	0.6
	North and central Am.	750,653	42.6	51.6	5.8	89,049	39.3	1.48	16.1
	-central	20,250	26.9	71.4	1.7	6,116	51.9	0.57	0.5
	-caribbeans	7,195	3.2	85.4	10.2	1,066	36.7	0.19	0.2
	-north	723,207	43.5	50.7	5.8	81,868	39.1	1.68	15.5
	Oceania	173,524	15.5	81.7	2.5	257,208	50.7	10.96	8.3
	South America	842,011	47.6	43.7	1.8	156,429	57.2	2.42	19.2
	World	3,999,134	31.9	58.5	7.2	1,204,471	39.9	0.72	100.0
				Source: FAO FRA 2015
					diapo 14 sur 33			Antonello Lobianco

Filière, Bois et Commercialisation (Ing2A-SCD1) A.A. 2016/2017 Modellisation of the French forest Sector diapo 15 sur 33 Antonello Lobianco

Forest resources -trends (1)

Filière, Bois et Commercialisation (Ing2A-SCD1)

		Exports		Imports
		Supply	Transformation	Demand
		(harvesting)
				Hardwood Sawnwood
	Socioeconomic development Broadleaved dc15, dc25, dc35.... Coniferous dc15, dc25, dc35....	CC models Hardwood model scenarios.. Vegetational Roundwood Softwood Roundwood Industrial Paper wood Pannels Plywoods Softwood Sawnwood Forest managers adaptations Pulp	National consumers
	Forest resources	Uncertainty Primary products	?? Transformed products

• mortality rate:

An exogenous parameter allows the model to consider (again, exogenously) land use changes with reference to the forest (forestChangeAreaIncrementsRel sc,r,t or forestChangeAreaIncrementsHa sc,r,t ) Scenario based analysis:

tP sc , px , ft ,dc ,t = tP r ,

ft , dc , t =0 * tpMultiplier sc , px , ft , t mort sc , px , ft , dc , t = mort r , ft ,dc ,t =0 * mort sc , px , ft ,t Filière, Bois et Commercialisation (Ing2A-SCD1) A.A. 2016/2017 Modellisation of the French forest Sector diapo 19 sur 33 Antonello Lobianco

HWP markets

• Market module: 3 primary products and 6 transformed products (Leontief transformation), imperfect substitutability national vs international products, regional trade A.A. 2016/2017 Modellisation of the French forest Sector diapo 21 sur 33 Antonello Lobianco

  The Soil Expectation Value (SEV) is the maximum amount that you would pay for the bare land holding the forest, given the expected flow of incomes and costs of the project under analysis. It is effectively the Net Present Value of an infinite series of identical forest rotation for the project under analysis It is computed as:

	Forest investment decisions
	-Soil Expected Value
	Soil Expected Value
	diapo 23 sur 33	Antonello Lobianco

-C t 1+i ) t Filière, Bois et Commercialisation (Ing2A-SCD1) A.A. 2016/2017 Modellisation of the French forest Sector

Bois et Commercialisation (Ing2A-SCD1) A.A. 2016/2017

  Modellisation of the French forest Sector

	Climate change -forest mitigation potential
	12 1751 -2012 global fossil fuels and cement production CO 2 emissions ATMOSPHERE 829 PgC TERRESTRIAL BIOSPHERE 123.3
		10		119.7 + 1.1	4,200 PgC
		8	78.4	0.1 + 7.8
	PgCy-1	6	80		0.2
		4		0.9
		2 OCEANS	0.2	LITOSPHERE
		38,703 PgC		(fossil fuels)
		0			1,471 (~6,000) PgC
		Source: Carbon Dioxide Information Analysis Center (CDIAC) fast domain (few years to millenia)	slow domain ( > 10,000 years)
				diapo 30 sur 33	Antonello Lobianco

Filière, Bois et Commercialisation (Ing2A-SCD1) A.A. 2016/2017 Modellisation of the French forest Sector diapo 29 sur 33 Antonello Lobianco Climate change -introduction Filière, Source: Lobianco et al. (2016), adapted from Ciais and Sabine (2013)


T Mannel

P Boakes

How MIDAS improved our understanding of micrometresized cometary dust

The MIDAS atomic force microscope on the Rosetta orbiter was an instrument developed to investigate, for the first time, the morphology of nearly unaltered cometary dust. It acquired the 3D topography of about 1 -50 µm sized dust particles with resolutions down to a few nanometres. These images showed the agglomerate character of the dust and confirmed that the smallest subunit sizes were less than 100 nm. MIDAS acquired the first direct proof of a fractal dust particle, opening a new approach to investigate the history of our early Solar System and of comets.

Introduction

As comets are considered the least altered bodies in our Solar System, the properties of their building blocks are key parameters in understanding our early Solar System and its evolution. Remote observations, fly-by missions and sample return have provided a foundation for our knowledge about cometary dust particles, which has been tested and greatly extended by the dust instruments onboard Rosetta, namely COSIMA, GIADA and MIDAS. The latter was a novel instrument selected to investigate the morphology of micro-to nanometer sized particles collected around the comet. Being able to collect the least altered cometary dust particles from a known body, MIDAS gave a first view of the morphology at the smallest scales. This paper summarises advances in the understanding of the smallest cometary dust with focus on the findings of MIDAS and suggests possible directions for future research.

The MIDAS atomic force microscope

MIDAS was designed to make the first in situ atomic force microscope (AFM) measurements of cometary dust to address key questions about the size, shape, texture and morphology of the smallest particles [START_REF] Riedler | MIDAS The Micro-Imaging Dust Analysis System for the Rosetta Mission[END_REF]. It collected dust by exposing specially coated silicon targets to the dust flux coming from comet 67P/Churyumov-Gerasimenko and imaged the particles with an AFM [START_REF] Riedler | MIDAS The Micro-Imaging Dust Analysis System for the Rosetta Mission[END_REF][START_REF] Bentley | Aggregate dust particles at comet 67P/Chruyumov-Gerasimenko[END_REF]. The key data were 3D topographic images with nano-to micrometre resolution which gave the first view on the smallest, nearly pristine, cometary particles.

Post-Rosetta knowledge

Pre-Rosetta models of cometary dust predicted that cometary dust at the (sub-)micrometre scale would fall in two groups: compact particles and porous agglomerates [START_REF] Levasseur-Regourd | Physical properties of cometary and interplanetary dust[END_REF][START_REF] Kearsley | Dust from comet Wild 2: Interpreting particle size, shape, structure, and composition from impact features on the Stardust aluminum foils[END_REF]. Contrary to these expectations MIDAS only found an agglomerate character at all size scales and for all collection periods. The particle surfaces show clusters of small, bulbous subunits. These characteristic features can also be found for the order of magnitude larger dust particles collected with the COSIMA instrument at comet 67P [START_REF] Langevin | Typology of dust particles collected by the COSIMA mass spectrometer in the inner coma of 67P/Churyumov Gerasimenko[END_REF] and for the most primitive interplanetary dust particles (IDPs) collected in Earth's atmosphere [START_REF] Bentley | Aggregate dust particles at comet 67P/Chruyumov-Gerasimenko[END_REF]. However, in contrast to IDPs, MIDAS observed no evidence of euhedral crystalline structures. The larger dust particles show an extreme fragility, which often leads to fragmentation during AFM scans. None of the particles broken apart in this way showed an interior structure different from that observed on the surface, suggesting that most of the tens of micron-sized cometary particles are indeed agglomerates throughout. Despite this commonality, dust at 67P falls in two groups. The majority shows an arrangement of the subunits with a medium packing density. However, due to the gentle dust collection at Rosetta, one extremely porous particle was detected. Its structure was found to be fractal with a dimension of 1.7 ± 0.1 [START_REF] Mannel | Fractal cometary dusta window into the early Solar system[END_REF]. As the existence of a majority of denser dust particles and a minority of fractal dust was confirmed by the GIADA instrument [START_REF] Fulle | Comet 67P/Churyumov-Gerasimenko preserved the pebbles that formed planetesimals[END_REF], comet 67P is suggested to consist mainly of the denser dust particles, where the voids between them can be filled by fractals [START_REF] Blum | Evidence for the formation of comet 67P/Churyumov-Gerasimenko through gravitational instability of a pebble cloud[END_REF]. The latter structure is characteristic of early dust agglomeration in the protoplanetary disc but is thought to be compacted to denser, non-fractal dust before inclusion in comets. The existence of fractals nevertheless strongly constrains the dust environment in the early Solar System and the evolution of the comet [START_REF] Fulle | Fractal dust constrains the collisional history of comets[END_REF]. This theory is supported by the surprisingly similar subunit sizes of the fractal and more compact particles. The smallest subunits comprising the agglomerates are less than 100 nm in size [START_REF] Bentley | On the building blocks of cometary dust[END_REF]. However, these measurements appear to be still limited by instrument resolution and the presence of smaller dust grains cannot be excluded.

A further surprise was the size of the collected dust. The number of collected particles was estimated by optical observations and data from the Halley fly-by, which had large uncertainties for the flux of the small, micro-to nanometre sized particles [START_REF] Riedler | MIDAS The Micro-Imaging Dust Analysis System for the Rosetta Mission[END_REF]. However, it was always expected that in a given period more small than large dust particles would be collected. Surprisingly, this was not the case; MIDAS detected several particles larger than about tens of micrometres, but only few with micrometre size and none at smaller sizes [START_REF] Bentley | Aggregate dust particles at comet 67P/Chruyumov-Gerasimenko[END_REF]. To date it is not clear if the dust size distribution of comet 67P is depleted in particles smaller than some micrometres, or if there was a bias preventing their detection (e.g. spacecraft charging).

Conclusions and possible directions for future research

MIDAS acquired a unique dataset revealing the morphology of dust particles with sizes between about 1 and 50 µm at resolutions of 8 to 1500 nm per pixel. The expectation of porous agglomerate dust particles with subunits having sizes down to less than 100 nm was confirmed. A new approach to decipher the processes in our early Solar System and its evolution might be found in the shape of the fractal dust population. The lack of individual compact particles, the absence of clear euhedral structures, and the low flux of particles smaller than a few micrometres were surprising and are not yet fully understood. As MIDAS data has not yet been exhaustively analysed, it still holds the potential to reveal a wealth of cometary dust properties as, e.g., its material strength or the detection of magnetic inclusions. Further open questions concern the true end of the smallest subunit sizes, and the internal structure of the particles. Answering these would further define processes in the early Solar System, and help to understand cometary physics like, e.g., the comet's internal structure, heat transport, and the to date unclear mechanism leading to dust ejection.

Acknowledgements

We thank ESA, NASA and all funding agencies for MIDAS for their support. A.C.L.-R acknowledges support from the French Space Agency, CNES. M.S.B. and T.M. acknowledge funding from the Austrian Science Fund (FWF): P 28100-N36. R.S. thanks the Austrian Research Promotion Agency (FFG) for financial support.