net.finmath.climate.models.dice.submodels.EvolutionOfCarbonConcentration Maven / Gradle / Ivy

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finmath lib is a Mathematical Finance Library in Java. It provides algorithms and methodologies related to mathematical finance.

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package net.finmath.climate.models.dice.submodels;

import java.util.function.BiFunction;
import java.util.stream.IntStream;

import net.finmath.functions.LinearAlgebra;

/**
 * The evolution of the carbon concentration M with a given emission E.
 * \(
 * 	M(t_{i+1}) = \Phi M(t_{i}) + unitConversion * E(t_{i}) \Delta t_{i}
 * \)
 *
 * Note: the emission are in GtCO2/year while the carbon concentration is in GtC.
 *
 * Unit conversions
 * 
 * 	1 t Carbon = 3.666 t CO2
 * 
 *
 * Note: The function depends on the time step size.
 * TODO Fix time stepping
 *
 * @author Christian Fries
 */
public class EvolutionOfCarbonConcentration implements BiFunction {

	private static double conversionGtCarbonperGtCO2 = 3.0/11.0;

	private static double[][] transitionMatrixDefault;
	// Original transition matrix is a 5Y transition matrix
	static {
		final double b12 = 0.12;		// scale
		final double b23 = 0.007;		// scale
		final double mateq = 588;
		final double mueq = 360;
		final double mleq = 1720;

		final double zeta11 = 1 - b12;  //b11
		final double zeta21 = b12;
		final double zeta12 = (mateq/mueq)*zeta21;
		final double zeta22 = 1 - zeta12 - b23;
		final double zeta32 = b23;
		final double zeta23 = zeta32*(mueq/mleq);
		final double zeta33 = 1 - zeta23;

		transitionMatrixDefault = new double[][] { new double[] { zeta11, zeta12, 0.0 }, new double[] { zeta21, zeta22, zeta23 }, new double[] { 0.0, zeta32, zeta33 } };
	}

	private final double timeStep;
	private final double[][] transitionMatrix;		// phi in [i][j] (i = row, j = column)

	public EvolutionOfCarbonConcentration(double timeStep, double[][] transitionMatrix) {
		super();
		this.timeStep = timeStep;
		this.transitionMatrix = transitionMatrix;
	}

	public EvolutionOfCarbonConcentration(double timeStep) {
		// Parameters from original model
		this(timeStep, transitionMatrixDefault);
	}

	@Override
	/**
	 * Update CarbonConcentration over one time step with a given emission.
	 *
	 * @param carbonConcentration The CarbonConcentration in time \( t_{i} \)
	 * @param emissions The emissions in GtCO2 / year.
	 */
	public CarbonConcentration3DScalar apply(CarbonConcentration3DScalar carbonConcentration, Double emissions) {
		// TODO The parameters are calibrated to a 5 year time step. Should be a proper root here
		final double[] carbonConcentrationNext = LinearAlgebra.multMatrixVector(transitionMatrix, carbonConcentration.getAsDoubleArray());

		// TODO - matrix need rescaled from 5Y to 1Y
		final double[] carbonConcentrationNextScaled = IntStream.range(0, carbonConcentrationNext.length).mapToDouble(i -> carbonConcentration.getAsDoubleArray()[i] + timeStep/5.0 * (carbonConcentrationNext[i]-carbonConcentration.getAsDoubleArray()[i])).toArray();

		// Add emissions
		carbonConcentrationNextScaled[0] += emissions * timeStep * conversionGtCarbonperGtCO2;

		return new CarbonConcentration3DScalar(carbonConcentrationNextScaled);
	}
}