From Uncertain Depositions to Uncertain Critical Load

Exceedances

Maximilian Posch

RIVM

Coordination Center for Effects (CCE/TF M&M)

Balancing Critical Loads Data Aggregation and Uncertainties

From critical load function to protection/exceedance isolines:

•Every ecosystem characterized by an acidity critical load (CL) function•There are many CL-functions in a grid square•From these protection/exceedance isolines can be calculated (=3-D CDF)•These are used in the IAMs•Details see CCE Status Reports 97/99

0 500 1000 1500Ndep

0

500

1000

1500

Sdep

0

0.25

0.5

0.75

1

P

Expected Isoline

Probability of protection along the ray

0 500 1000 1500Ndep

0 500 1000 1500Ndep

0

50010001500

Sdep

00.0010.002

0.0030.004

P

Expected Isoline

Protection probability density of the isoline along the ray

0 500 1000 1500Ndep

5001000

1500Ndep

500 1000 1500Sdep

0210-6410-6610-6

P

5001000

1500Ndep

500 1000 1500Sdep

0 200 400 600 800 1000 1200 1400

0

200

400

600

800

1000

1200

1400

Uncertainty in CL parameters results in uncertainty band around every isoline:

Integration yields uncertain protection percentages:

S and N deposition are also uncertain and correlated in every grid square:

Overlaying (=integration) yields probabilities to protect a certain percentage of ecosystems

Ecosystem protection percentages for a selected confidence level:

For a given deposition (e.g. 1990) for every grid cell the protection percentage (e.g. 50%) for any given confidence level can be computed and mapped

Uncertainty range: 5%-95%Ecosystem protection percentage for 50% (deterministic,left) and 95% (“on safe side”) confidence level

From uncertain CLs to uncertain protection% (1-D):

Assuming independent uncertainties of CLs within a grid cell leads to cancellation of uncertainties (and loss of spatial information) but widening of range in protection CDF.Cancellations (narrowing of uncertainty band) depend the degree of overlap of CLs.

Examples:

Realistic example:

NSNSDNSnDn DDDDfDDPfP dd ),( ),(0 0

meanDmeanC

sigD

Uncertainty in computation of exceedances (protection %):Uncertainty depends of difference in means as well as (ratio of) variances

The larger the difference in the meansthe larger can be the uncertainty.

Protection probability for given deposition:

Dependence of uncertainty on grid size:Case 1:

Subdivision of grid does not reduce CL variability(var-left = var-right=var-tot; “self-similar”)If also deposition is the same, no reduction in uncertainty.

Case 2:

Subdivision of grid reduces CL variabilityPossible reductions of uncertainties depends onhow deposition changes!

Needed: Screening and classification of grids where improvements can be achievedby reducing grid size. (related: optimal number of data points in grid)

Summary and Recommendations:

• Tool available to do uncertainty analyses for LRTAP IA (though technical improvements desirable)• Including uncertainties requires additional choices to be made by decision makers (confidence levels, etc.) •Efforts have to be made to present results in comprehensible formats• Focus on areas (grid cells) where deposition are (will be) similar to CLs• Investigate grid size - (CL) variability - data requirement issues • Parties have to provide good uncertainty estimates of input data -- as well as resources -- to allow meaningful uncertainty analyses. Not only (co-)variances, but especially possible biases.