Robust rescaling methods for integrated water, food, energy security management under uncertainty

Robust Rescaling Methods for Integrated

Water, Food,

Energy Security Management under

Uncertainty:

downscaling from GLOBIOM model

_{Tatiana Ermolieva}

Yuri Ermoliev, Petr Havlik, Aline Mosnier, Michael Obersteiner

Motivations for developing

downscaling of land use and

land-cover changes

2

Global models (multiregional) cannot produce results at fine resolutions

Local models oversee global drivers and tendencies. Conversely, aggregate global models miss local implications, drivers, processes, uncertainties

New estimation problem; fine resolution information/data recovery from aggregate scales using all available information

Although GIS provides detailed geographical information, the social, economic,

environmental data and drivers ussually exist on aggregate level, e.g., national, regional

Local – global interdependencies

Approach: fussion (integration) of Global Biosphere Management (GLOBIOM)

partial equilibrium land use planning model and probabilistic (in general, non-Bayesian) downscaling to “project” GLOBIOM results to finer resolutions

At IIASA – assessment and downscaling of GLOBIOM SSP

Natural Forests

Managed

Forests

Forest

Cropland

Pastures

Other

natural land

GLOBIOM is a land use planning model

producing projections of land use and l.c.

changes:

Recursive dynamics:

land use change

transmitted from one

period to another

GLOBIOM is a multi-sectoral model

4 Crops for Food Sawn wood Pulp Fuel wood Sugarcane Corn Cassava Soybeans Wheat etc…

LAND USE PRIMARY

PRODUCTS PROCESS FINAL PRODUCTS

Wood

Refineries

Biofuel Biogas

Heat Saw and Pulp

mills Cattle Sheep and Goats Pigs Poultry Slaughterhouse Lamb Beef Pork Chicken Eggs

Deterministic optimization problem: to achieve

the highest consumption level at the lowest cost

under constraints on land availability,

environmental pollution, etc.

Stochastic optimization problem - yields/weather,

supply, prod. costs, demand elasticities are in

general stochastic;

to achieve highest consumption at lowest cost

under food security constraints (represented by

Combination of biophysical and

economic models

Quantity Price Supply Demand Equilibrium

Land productivity depends on

geography (climate, soil,

The economic model:

Main model outputs



_{Land use change}



_Production



Consumption



Prices



_{Trade flows}



_{Water use}



_{GHG emissions}

Main exogenous drivers



_{Population growth}



_{GDP growth}



Technological change



Bio-energy demand (POLES

team)



_{Diet patterns (FAO, 2006)}

6

 Recursive dynamic: solution computed every 10-year period and

transmitted to the next period

30 regions

A global model with the possibility to

zoom into one region and …

30 Regions are

interconnected

through international

8

Land uses and land use

changes

allowed in GLOBIOM

Crop land to Planted forest Natural forest to Crop land

Natural forest to Grass land Grass land to Crop land

Grass land to Planted forest Natural land to Crop land

Natural land to Planted forest Natural land to Grass land

Crop land to Natural land Planted forest to Natural land

Grass land to Natural land

Land use

transformations

Land

uses

Crop land

Natural forest

Grass land Planted forest

Natural land

i

Land use type

Region

r

t

Time

t ir

A

Land in land use

t ijr

A



Land converted from i to j in region r and time t















 j t jir j t ijr t ir t ir

A

A

A

A

1

At regional level





Land use change

downscaling:

GLOBIOM model

t ijlr

z

Find shares of aggregate area change transformed from i to j in l that

t ilr l t jir t jilr l t ijr t ijlr t ilr

z

A

z

A

A

A

1















l r m i t ilr

L

A

=

1











   n j m i l t ijlr t ijlr t ijlr

z

q

z

1 1 1

)

/

ln(





1

l t ijlr

q

Downscaling problem

t ijr j t ijr t ijlr

A

A

z













1

l t ijlr

z

i.e.

Cross-entropy: Maximize Kulback-Leibler information distance

Maximum Entropy and Minimax

Likelihood

Maximal Likelihood: let random value has N independent observations:



)

1

(



, …, . The problem is to estimate the



(N

)

true probability distribution:



j



pj ob  

Pr _{by maximizing the probability of observing the sample:}



  r j j p 1 1 subject to , ,

p

_j



0

N N j j 



1  or maximizing . solution is .

The log-likelihood function is the sample mean approximation of the

In downscaling, information is given not by observations but by various

constraints connecting the distribution with characteristics of observ. variables

Let P be a set of all possible distributions satisfying constraints:

Proposition: If , then .

x



(

x

₁

,...,

x

_r

)









   r j j r j j p x ln p x ln x max







(

x

₁

,...,

x

_r

)

x



  r j j j p p Ep 1 * ln 





_



    r j j N k j p k ob 1 1 ) ( Pr    N pN_j 



_j /





   r j j j r j i p p i 1 1 ln ln  

Examples of priors

Priors for downscaling aggregate land use changes are estimated

based on comparative profitability of land use activities

Crop land to Planted

forest

1  t Pltlr t Pltlr

A

y







 s t slr t slr t jr t lr

P

y

A

1 t r t r t r t lr t lr T T T T min max min     t lr

T

Yield of planted forest

Crop land production value

Normalized transportation time

Average time to closest market

 

 







_{ }    







l t lr t r l Plt t r l Plt t lr t lr t r l Plt t r l Plt t lr t Plt CropL r l

A

y

A

y

q

1 1 , , , , 1 1 1 , , , , 1 _ , ,

)

(

)

(





Grass land to Planted

forest















_{  }     



l t r l Grass t r l Grass t Pltlr t Pltlr t lr t r l Grass t r l Grass t Pltlr t Pltlr t lr t Plt GrassL r l

A

y

A

y

A

y

A

y

q

1 1 , , , , 1 1 1 1 , , , , 1 1 _ , ,

)

(

)

(





1  t Pltlr t Pltlr

A

y

Yield of planted forest

1  t Pltlr t Pltlr

A

y







 s t slr t slr t jr t lr

P

y

A

1 t r t r t r t lr t lr T T T T min max min     t lr

T

Yield of planted forest

Crop land production value

Normalized transportation time

Forest land to Crop

land

    s t slr t slr t jr t lr P y A 1

Crop land production value

1 , , , ,  t Forest r l t Forest r l

A

y

Forest yield

Timber price





















    l t r l t Forest r l t Forest r l t Forest r l t r l t Forest r l t Forest r l t Forest r l t CropL ForestL r l

P

A

y

P

A

y

q

, 1 , , 1 , , , , , 1 , , 1 , , , , _ , , t Forest r l

P

_{, ,}

Dynamics of forest and planted forest land, 2010 – 2100, in 1000 ha

20 Optimal land use transition

shares: “Crop to grass” and “crop to other natural land”, 2010–2100

Robust downscaling









j i s ij ij ij s ij ij ij s

z

z

q

z

z

q

z

z

F

,

ln(

/

)

ln(

/

(

))

max

)

(

 



s i j s ij ij ij s

z

z

q

z

F

,

ln(

/

)

max

)

(











S s 1



s

1

 H















1

/

2

A set of priors defines alternative feasible distributions Q 



qs,s 1: S



22













_      ij s ij ij S s s H ij ij ij S s i j s ij ij ij s H q z z z q z z z F( ) max ln( / ) ln min ( ln ) 1 1 , _   ) ln ( min 1 s ij S s s ij ij H







z q 



 ks



k



 ij s ij ij s z q c : ln



_  S s s s H c 1 min   K k 1,



K_ k k k u u 1 max 



  K k 1



ksuk cs u  (u1,....,uk)

Minimize F(z) with respect to z. F(z) is non-convex in : (z,



)



  S s 1



ks



s



k



  S s 1



ks



s



k Denote Dual problem





 ij s ij ij kksuk z lnq s 1:S zZ













_      ij s ij ij S s s H ij ij ij S s i j s ij ij ij s H q z z z q z z z F( ) max ln( / ) ln min ( ln ) 1 1 , _   Minimization of F(z) (z,



)





 k k k ij zij lnzij



u

is equivalent to minimization w.r.t. (z,u) of

s.t.

24

Robust

_Alternativ

Robust

_Alternativ

e

26

Robust

_Alternativ

Robust

_Alternativ

e

28

30