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Conversion of uncertainty information

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msrocka edited this page Apr 17, 2014 · 5 revisions

This page describes the conversion of uncertainty information between openLCA and other LCA data formats.

openLCA

In openLCA we store uncertainty information for exchanges, LCIA factors, parameters, etc. in instances of the class org.openlca.core.model.Uncertainty. This class contains three fields for storing distribution parameters. Depending on the uncertainty type, these fields have the following values:

Parameter 1

  • Normal distribution: arithmetic mean value (mean)
  • Lognormal distribution: geometric mean value (gmean)
  • Triangle distribution: min value (min)
  • Uniform distribution: min value (min)
  • None: mean / resulting amount (mean)

Parameter 2

  • Normal distribution: arithmetic standard deviation (sd)
  • Lognormal distribution: geometric standard deviation (gsd)
  • Triangle distribution: most likely value (mode)
  • Uniform distribution: max value (max)

Parameter 3

  • Triangle distribution: max value (max)

EcoSpold 1

In EcoSpold 1 uncertainty information can be stored in exchange elements (which are also used as LCIA factors in LCIA method data sets). The attribute uncertaintyType indicates the uncertainty distribution type with the following values:

  • 0=undefined,
  • 1=lognormal (default),
  • 2=normal,
  • 3=triangular,
  • 4=uniform

The following exchange attributes are used to store the distribution parameters [1]:

meanValue

  • Undefined: arithmetic mean (mean)
  • Lognormal: geometric mean (gmean)
  • Normal: arithmetic mean (mean)
  • Triangular: arithmetic mean (mean)
  • Uniform: arithmetic mean (mean)

standardDeviation95

  • Lognormal: square of the geometric standard deviation (gsd^2)
  • Normal: two times standard deviation (sd*2)

minValue

  • Triangular: min value (min)
  • Uniform: min value (min)

maxValue

  • Triangular: max value (max)
  • Uniform: max value (max)

mostLikelyValue

  • Triangular: most likely value (mode)

ILCD

In the ILCD format an enumeration for the uncertainty distribution types that can be used in exchanges, LCIA factors, and parameters is defined with the following values [2]:

  • undefined
  • log-normal
  • normal
  • triangular
  • uniform

The following distribution parameters are defined:

meanValue

It is not clearly stated in the format documentation but from the documentation of the field relativeStandardDeviation95In (see below) it can be assumed that for the log-normal distribution the geometric mean should be entered and the arithmetic mean for the other distribution types as in the EcoSpold 1 data format (see above):

  • Undefined: arithmetic mean (mean)
  • Lognormal: geometric mean (gmean)
  • Normal: arithmetic mean (mean)
  • Triangular: arithmetic mean (mean)
  • Uniform: arithmetic mean (mean)

relativeStandardDeviation95In

This field has the following definition in the format SDK [2]:

The resulting overall uncertainty of the calculated variable value considering uncertainty of measurements, modelling, appropriateness etc. [Notes: For log-normal distribution the square of the geometric standard deviation (SDg^2) is stated. Mean value times SDg^2 equals the 97.5% value (= Maximum value), Mean value divided by SDg^2 equals the 2.5% value (= Minimum value). For normal distribution the doubled standard deviation value (2SD) is entered. Mean value plus 2SD equals 97.5% value (= Maximum value), Mean value minus 2*SD equals 2.5% value (= Minimum value). This data field remains empty when uniform or triangular uncertainty distribution is applied.]

Thus, the meaning is the same as for the EcoSpold 1 standardDeviation95 field:

  • Lognormal: square of the geometric standard deviation (gsd^2)
  • Normal: two times standard deviation (sd*2)

minimumAmount

  • Triangular: min value (min)
  • Uniform: min value (min)

maximumAmount

  • Triangular: max value (max)
  • Uniform: max value (max)

SimaPro CSV

As the EcoSpold 1 and ILCD format, the SimaPro CSV format supports the following uncertainty distribution types:

  • Lognormal
  • Normal
  • Triangle
  • Uniform
  • Undefined

The arithmetic mean or the geometric mean in case of a log-normal distribution are stored the amount field. Other distribution parameters are stored in three possible parameter fields:

Parameter 1

  • Normal: doubled standard deviation (sd*2)
  • Lognormal: squared geometric standard deviation (gsd^2)
  • Triangle: empty
  • Uniform: empty

Parameter 2

  • Normal: empty
  • Lognormal: empty
  • Triangle: minimum (min)
  • Uniform: minimum (min)

Parameter 3

  • Normal: empty
  • Lognormal: empty
  • Triangle: maximum (max)
  • Uniform: maximum (max)

EcoSpold 2

In the EcoSpold 2 format the following uncertainty distribution types are defined [3]:

  • lognormal
  • normal
  • triangular
  • uniform
  • beta
  • gamma
  • binomial
  • undefined

Each distribution type is defined as an XML element type with distribution specific parameters (in the following only the parameters of the distributions also available in the other formats are listed):

Lognormal

  • @meanValue: Geometric mean
  • @mu: Arithmetic mean of the underlying normal distribution
  • @variance: Unbiased variance of the underlying normal distribution
  • @varianceWithPedigreeUncertainty: Unbiased variance of the underlying normal distribution, basic uncertainty with pedigree uncertainty

Normal

  • @meanValue: Arithemtic mean
  • @variance: Unbiased variance
  • @varianceWithPedigreeUncertainty: Unbiased variance, basic uncertainty with pedigree uncertainty

Triangular

  • @minValue: Minimum value
  • @mostLikelyValue: Mode
  • @maxValue: Maximum value

Uniform

  • @minValue: Minimum value
  • @maxValue: Maximum value

Conversion

Scaling

The openLCA class org.openlca.core.model.Uncertainty provides a method for scaling the distribution parameters by a given factor. This multiplies the distribution parameters with the given factor except for the geometric standard deviation in the log-normal distribution as this parameter is scale-independent.

The scheme for the application of a conversion factor f in the import is:

  1. map the parameters of the exchange format to an openLCA uncertainty instance u
  2. scale u by f

and for the export:

  1. scale u by f
  2. map the parameters of u to the parameters of the exchange format.

EcoSpold 2 - Lognormal

The attribute @meanValue is directly mapped to the openLCA parameter for the geometric mean (gmean). The attribute @mu is the arithmetic mean of the underlying normal distribution µ [4]:

gmean = exp(µ)    <=>     µ = ln(gmean)

The attribute @variance contains unbiased variance of the underlying normal distribution (var). As for the geometric mean there is the following relation between the geometric standard deviation gsd and the standard deviation sigmaof the underlying normal distribution:

gsd = exp(sigma)    <=>     sigma = ln(gsd)

where

sigma = sqrt(var)   <=>     var = sigma^2

Thus, we have the following conversions for the import:

gmean = @meanValue
gsd = exp(sqrt(var))

And for the export:

@meanValue = gmean
@mu = ln(gmean)
@variance = ln(gsd)^2
@varianceWithPedigreeUncertainty = ln(gsd)^2

[1] Rolf Frischknecht, Niels Jungbluth: Overview and Methodology, ecoinvent report No. 1, Dübendorf, December 2007 (http://www.ecoinvent.org/fileadmin/documents/en/01_OverviewAndMethodology.pdf)

[2] ILCD Format SDK

[3] EcoSpold 2 Format SDK

[4] http://en.wikipedia.org/wiki/Log-normal_distribution, geometric moments; http://www.alceon.com/ln%26lnpp.pdf

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