A Simple Parallel Projection Optimization Algorithm Estimating a Large-size Input- Output Table for Environmental Impact Assessment Ting Yu, Julien Ugon, Manfred Lenzen Integrated Sustainability Analysis, University of Sydney, Australia School of Information Technology & Mathematical Sciences, University of Ballarat, Australia

What I will talk? Environment Impact Assessment: Economic Input-Output Life Cycle Assessment (EIO-LCA) A parallel optimization algorithm estimating a large-size input-output table

Environment Impact Assessment Definition: –An assessment of the possible impact (positive or negative) that a proposed project may have on the environment (consisting of the natural, social and economic aspects).

Purpose of EIA EIA becomes a part of standard corporate reports, the same as traditional accounting reports Encourage business and public to consider the environmental impact of their actions Government is able to implement its regulation Investors are able to assess the impact of their investment on the environment (consisting of the natural, social and economic aspects).

World Business Council for Sustainable Development (2002) “Corporate sustainability reports and sustainability ratings are increasingly used as key information for investment and lending decisions.” “There is a growing awareness that shareholders’ value is enhanced by increased corporate social and environmental responsibility.”

Dollar as intermediary Tone for CO2, Litre for water usage, Square metre for land usage, number of people for unemployment Universal and single measurement for all kinds of impacts Monetary measure for corporate reporting

Case 1: Investors & insurers need to see hidden risks, eg. GHG emissions Construction Pty C On-site emissions Embodied emissions from materials Water supplier Pty D On-site emissions Lower embodied emissions from materials

Real-world complexities (1) Trucost & Defra (May 2006)

Real-world complexities (2)

The problem of quantification  “… there is still a lack of quantification in most reporting. … the majority of reports lack depth, rigour or quantification.”  “Most business will have supply chain impacts that they should understand and consider reporting. There is no single, quantifiable measure that companies can use as a Key Performance Indicator for the effect of their upstream supply chain on the environment.” Trucost & Defra (May 2006)

Economic Input-Output Life Cycle Assessment (EIO-LCA) The EIA enables decision makers to evaluate a project by data and analysis rather than a feeling that the natural product is better A life cycle assessment (LCA) is the investigation and valuation of the environmental impacts of a given product or service caused or necessitated by its existence, and an evaluation of the environmental impacts of a product or process over its entire life cycle. –often thought of as "cradle to grave" and therefore as the most complete accounting of the environmental costs and benefits of a product or service Economic Input-Output Life Cycle Assessment (EIO-LCA) method uses information about industry transactions - purchases of materials by one industry from other industries, and the information about direct environmental emissions of industries, to estimate the total emissions throughout the supply chain (Hendrickson, Lave, & Matthews, 2006 )

Industrial interdependence in a modern economy: a “tree” of upstream production layers Lenzen & Murray, 2003

Production layers and structural paths: Example: Australian aluminium Lenzen & Murray, 2003 FRGESFRGESFRGESFRGESFRGES FRGESFRGESFRGESFRGESFRGES FRGESFRGESFRGESFRGESFRGES FRGESFRGESFRGESFRGESFRGES FRGESFRGESFRGESFRGESFRGES 4 3 FRGESFRGESFRGESFRGESFRGES 2 Aluminium for use FoodResourcesEnergyGoodsServices 0 1 Shipping to smelter Manufacture of ship Iron ore for steel Energy for iron ore mining Steel for ship

10 top upstream paths: energy use Electricity> Al> exports PJ (46.29%) Alumina> Al> exports PJ (14.39%) Al> exports 8.24 PJ (8.19%) Electricity> Alumina> Al> exports 1.40 PJ (1.39%) Electricity> Al> stocks 0.78 PJ (0.78%) Petroleum and coal products> Al> exports 0.40 PJ (0.40%) Electricity> Bauxite> Alumina> Al> exports 0.34 PJ (0.34%) Bauxite> Alumina> Al> exports 0.29 PJ (0.29%) Iron and steel> Al> exports 0.26 PJ (0.26%) Alumina> Al> stocks 0.24 PJ (0.24%)

Banking

Electricity Supply

Why we need input-output table? Input-output table The structure of the economy e.g. total emissions (direct plus indirect) e.g. direct (on-site) emissions e.g. purchases of a company

Integration National Input- Output Tables Physical & social data

Input-output Table

Agricult ure MiningManufac turing UtilitiesServices Agricultur e Mining Manufact uring Utilities Services Input to mining Input to services Output from mining Output from Services

Input Coefficients To Ag,For&FishMiningManufacturing Utilities,Trade,T ransport&Com municationServices Ag,For&Fish 10.9 ¢/$0.0 ¢/$4.5 ¢/$0.4 ¢/$0.2 ¢/$ Mining 0.1 ¢/$8.3 ¢/$4.5 ¢/$1.2 ¢/$0.1 ¢/$ Manufacturing 16.5 ¢/$10.6 ¢/$23.8 ¢/$15.2 ¢/$6.1 ¢/$ Utilities,Trade,Tra nsport&Communi cation 13.5 ¢/$12.8 ¢/$9.8 ¢/$17.1 ¢/$9.8 ¢/$ Services 5.7 ¢/$6.2 ¢/$5.2 ¢/$14.8 ¢/$20.3 ¢/$ 4.5c of agriculture is needed for every dollar’s worth of manufacturing

How much ghg does it take to provide $1000 worth of services (from this one supply chain) 0.4kgx0.128$utx0.45$mix0.238$manx0.061$manx$1000s $util$mining$manuf $services =0.033kg $1000 was the driver for this whole chain of reactions and its environmental consequences

For services For manufa -cturing For agricutl ure For utilities $1000 For mining ghg from utilities You spend $1000 on a weekend away. You have muffins for breakfast. They are manufactured. The manufacturer needs blueberries. They are farmed. The farm needs electricity. The power plant needs coal. The coal mine needs gas. The gas provider emits ghg.

A Simple Example of a Matrix Used in Economic Study 2008 China (1) Shoe (1)Retail (2) Australi a (1) NSW (1)Sheep (1) Oil (2) VIC (2)Sheep (1) Oil (2) 2009 China (2) Shoe (1)Retail (2) Australi a (1) NSW (1)Sheep (1) Oil (2) VIC (2)Sheep (1) Oil (2)

Where to get the input- output table? Google it? Or Estimate it?

Answers Survey, published by Australian Bureau of Statistics every 4 years Or estimate the Input-output table - Purpose: populate the matrix by using available information, (matrix completion? With full rank?) -Significance: matrices are widely used in economic study and transportation planning to represent the commodity or traffic flows between origin and destination. -Difficulties: available information often is not completed, with a large amount of noise

Available Data Data From Australian Bureau of Statistics: –Australian National Accounts: State Accounts –Environment and Energy –Economy, Industry, Value of Agricultural Commodities Produced Data from Australian business register Data from Reserve Bank of Australia Data from Sydney Water, and other private companies From State accounts Expenditure Components of GSP June 2005($m) Note: GSE components= GSP Expenditure components +M-ENSWVICQLDWASATASNTACT GSE1 HFC intra-state (aggregated into groups containing commodities i') Food Alcoholic beverages and tobacco Clothing and footwear Rent and other dwelling services Electricity, gas and other fuel Furnishings and other household equipment Health Transport Communications Recreation and culture Education services Hotels, cafes and restaurants Miscellaneous goods and services

Temporal-Spatial Estimation with Conflicting Information (1) Time series of Input-output tables Spatial information from national or regional government, private cooperate, and research institutes, for example: –Total commodity trade of given industries between regions –Total green house gas emission of the given industry of a region within the current year Conflicting information: –Caused by the data noise: error from the process of data collection –Change of underlying structure: non-stationary –Without considering the confliction, the problem becomes unsolvable.

Temporal-Spatial Estimation with Conflicting Information (2) IO table is estimated as a vector X Main algorithm: subject to where X is the target vector to be estimated, X0 is the vector of the previous year which is known, E is a vector of the error components (uncertainty) dis is a distance metric which quantifies the difference between two vectors. G is the coefficient matrix for the local constraints C is the right-hand side value for the local constraints.

Temporal-Spatial Estimation with Conflicting Information (3) The reason why the vector E is introduced is to solve the conflicting information. –the vector E is introduced to balance the influence between the conflicting information, and reaches a tradeoff between the conflicting information. Assumption: –the temporal stability, which assumes the industry structure of a certain region keeps constant or has very few changes within the given time period. This assumption is often required to be verified for long time period. Within the short time periods, dramatic change of the industry structure is relatively rare. The datasets often contain the temporal patterns between years, such as the trend of the total output of certain industry sections, and also much spatial information regarding the total emission within a certain region such as national total emission and state total emission. On the other hand, it is very common that either of datasets is not comprehensive and imperfect and even the conflicts between the datasets exist. Thereby, the estimation algorithm is required to consolidate the conflicted datasets to uncover underlying models.

Parallel Projection Method (1) Why parallel computing is needed? –A large amount of variables are estimated: a 2000-by-2000 matrix has 4,000,000 variables to be estimated –A large amount of available information is available to be utilized and need to be processed efficiently. Available supercomputing facility

Supercomputer at NCI

Parallel Projection Method (2) Original formula has to be rewritten: subject to: where Linear constraints and quadratic objective function => Convex function Partition the formula into many sub-problems:

Parallel Projection Method (3) Iterative process and convergence: where L is the relaxation parameter, and projection Covex combination, where is the solution of i-th subproblem

Test of Convergence The constraints converges to zero. the objective function converge to a constant level after the same number of iterations as the constraints are satisfied.

Performance A medium size optimization problem consists of 25,070 variables, 219 constraints. The optimization runs 5,000 iterations over 16 CPUs (or nodes). The whole process takes 01:15 minutes and uses 918MB memory totally. A large size optimization problem consists of 3,340,800 variables, over 3,100 constraints. The optimization runs over 2,000 iterations over 16 CPUs (or nodes). The whole process takes 37:29 minutes and uses 2,280MB memory totally. Available memory is update to 3GB*8*64 = 1,536 GB at the supercomputing facility.

Experiments (1) Direct evaluation of a large-size matrix is a rather difficult task. –A thousand-by-thousand matrix contains up to ten million numbers. Simple measurements such as the sum do not make too much sense, as the important deviation is submerged by the total deviation which normally is far larger than the individual ones. Indirect evaluation: –Estimate the impact of the change of matrix elements on the final output in the whole economic system –It is more suitable when researchers are more interested to find out how sensitive the system is regarding the error of the estimation.

Direct evaluation

Experiments (2) Indirect evaluation: sensitivity analysis by calculating the multipliers How to calculate the multipliers: where M is the multiplier, I is the identity matrix, D is the change in the final output, and A is the technique coefficients matrix, each entry of which is the ratio: X is a value from the matrix estimated by the previous mining algorithm

Change of Underlying Structure Basically two series basically follow the same pattern. The estimated multipliers are more volatile than the true underlying multipliers. This phenomenon indicates the estimated multipliers amplify the errors.

Conclusion Running over a supercomputing facility and reducing the computational time to 1.5 hours for estimating a 3000-by Input-output table. More importantly, the size of input- output table can be increased to 15,000-by-15,000, which is enough for the table representing global economic structure (150 countries). A large-size Input-output table enables to analysis the environmental impact from a global perspective. The ISA will publish the first version of global Input-output table very soon. Future development: –Speed up the algorithm –Vertically split the estimation algorithm

Sustainable Development is not a cover up!

European Union Emissions Trading System & Second phase % cut in 2005 levels polluters still avoid cuts by investing in CDMs free permits mean huge windfall profits. Third phase 2013 to 2020 permits to emit decided on EU-wide basis, rather than through national allocations Power producers to buy permits at auction

What ML and DM can do?

The University of Sydney