VADYtele

Benjamin Lang
Institut für Geographie, Universität Augsburg

Version from June 22, 2015


benjamin.lang@geo.uni-augsburg.de

1 Introduction

Teleconnections like the North Atlantic Oscillation (NAO) denote recurring and persistent, large-scale patterns of pressure and circulation anomalies that spans vast geographical areas. Since they have a strong influence on the weather activity of affected regions, their predictability on inter-annual to decadal time scales is of great interest. The VADYtele plug-in evaluates the predictability of indices of well-known teleconnections, like the North Atlantic Oscillation (NAO), the Pacific North American Pattern (PNA) or the Southern Oscillation Index (SOI).

In section 2, the methods concerning the calculation of the teleconnection indices and the applied skill scores are described. Sections 3 and 4 explain the input and the output, respectively, of the VADYtele plug-in.

2 Methods

2.1 Teleconnections

Several teleconnection indices from both the Northern Hemisphere (e. g. NAO, PNA) and the Southern Hemisphere (e. g. SOI, SAM) can be analysed concerning their predictability on inter-annual to decadal time scales (cf. Table 1). They include different calculation methods – zonal means, grid point values or (Rotated) Principal Component Analysis ((R)PCA) – but all of them are based on monthly / seasonally aggregated anomaly fields of sea level pressure (psl) or geopotential heights (zg).

Please note the indicated references for detailed information about the calculation methods of the particular indices.


Index (abbr.) Index Calculation Reference
EA East Atlantic Pattern (after CPC) RPCA Barnston and Livezey [1987]
EAWR East Atlantic / Western Russia Pattern (after CPC) RPCA Barnston and Livezey [1987]
EPNP East Pacific / North Pacific Pattern (after CPC) RPCA Barnston and Livezey [1987]
NAO-CPC North Atlantic Oscillation (after CPC) RPCA Barnston and Livezey [1987]
NAO-HUR North Atlantic Oscillation (after Hurrell) PCA Hurrell [1995]
PNA Pacific / North American Pattern (after CPC) RPCA Barnston and Livezey [1987]
POL Polar / Eurasia Pattern (after CPC) RPCA Barnston and Livezey [1987]
SAM Southern Annular Mode Zonal means Nan and Li [2003]
SCAND Scandinavia Pattern (after CPC) RPCA Barnston and Livezey [1987]
SOI Southern Oscillation Index Grid point values Trenberth [1984]
TNH Tropical / Northern Hemisphere Pattern (after CPC) RPCA Barnston and Livezey [1987]
WP West Pacific Pattern (after CPC) RPCA Barnston and Livezey [1987]
Table 1: Overview of the available teleconnection indices.

2.2 Skill scores

2.2.1 Correlation (CORR)

The Pearson product-moment correlation coefficient is calculated between the observation and the forecast (CORRfc,τ) or the reference (CORRref,τ) for a specific lead time τ.

Figure 1 shows selected results for CORR.


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Figure 1: Example of CORR between observed and forecast SOI (prototype of MPI-ESM-LR with with 15 ensemble members) and between observed SOI and the reference (historical runs of MPI-ESM-MR with 3 ensemble members) with dots indicating results for the single ensemble members and the solid line for the ensemble mean.


2.2.2 Mean Squared Error Skill Score (MSESS)

The Mean Squared Error Skill Score (MSESS) is based on the Mean Squared Error (MSE), which is calculated for the different lead years τ of the forecast (MSEfc,τ ; shown in (1)) and the reference (MSEref,τ):

MSEfc,τ = 1 I i=1I(F τ,i Ot(τ,i))2 (1)

Fτ,i is the mean forecast derived from the ensemble for initialisation i for a specific forecast lead time τ and Ot(τ,i) the observation for time t(τ,i), corresponding to the time of initialisation i and forecast lead time τ.

Finally, MSESS is calculated [Goddard et al.2013] by relating forecast to reference:

MSESSτ = 1 MSEfc,τ MSEref,τ (2)

Figure 2 shows selected results for MSESS.


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Figure 2: Example of MSESS for SOI (forecast: prototype of MPI-ESM-LR with 15 ensemble members; reference: historical runs of MPI-ESM-MR with 3 ensemble members; observation: ERA-Interim) with dots indicating results for all possible combinations (between forecast and reference) of the single ensemble members and the solid line indicating results for the ensemble mean.


2.2.3 Ranked Probability Skill Score (RPSS)

The Ranked Probability Skill Score (RPSS) is based on the Ranked Probability Score (RPS), which is calculated for the different lead years τ of the forecast (RPSfc,τ ; shown in 3) and the reference (RPSref,τ):

RPSfc,τ = 1 I i=1I k=1K(F τ,i,k Ot(τ,i),k)2 (3)

Fτ,i,k is the cumulative probability derived from the ensemble for initialisation i within class k (with three equiprobable classes (below normal, normal, above normal), i.e. K = 3) for a specific forecast lead time τ, that is the fraction of ensemble members forecasting the occurrence of class k or lower. Ot(τ,i),k is the cumulative probability of class k from observations for the time t(τ,i), corresponding to the time of initialisation i and forecast lead time τ and effectively the Heaviside step function with Ot(τ,i),k = 0 if a value within a class higher than k is observed or else Ot(τ,i),k = 1 [Kruschke et al.2014].

Since it is biased for finite ensemble size m, the VADYtele plug-in calculates the RPS with hypothetical ensemble size M as estimation of RPSfc,τ,m [Ferro et al.2008]:

RPSfc,τ,M = RPSfc,τ,m M mi M(mi 1)I i=1I k=1KF τ,i,k(1 Fτ,i,k) (4)

Therefore, the comparison of forecasts and references with different ensemble sizes is possible and RPSS can be calculated as:

RPSSτ = 1 RPSfc,τ RPSref,τ (5)

Figure 3 shows selected results for RPSS.


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Figure 3: Example of RPSS for SOI (forecast: prototype of MPI-ESM-LR with 15 ensemble members; reference: historical runs of MPI-ESM-MR with 3 ensemble members; observation: ERA-Interim).


3 Input

This sections describes the various options for the plug-in. For this purpose, table 2 lists and explains all possible options. You have to choose i.a. the FORECAST (“1”), REFERENCE (“2”) and OBSERVATION of your choice (Please note: REFERENCE and OBSERVATION are remapped to the resolution of the FORECAST).


Output

Output directory

mandatory

default: /scratch/$user/evaluation_system/output/vadytele/

Index

Teleconnection index for evaluation

mandatory

Project1

FORECAST project, e.g. ”baseline0”, ”baseline1”, ”prototype”.

mandatory

Product1

FORECAST product, e.g. ”output2”, ”output1”.

mandatory

Institute1

FORECAST institute of experiment, e.g. ”mpi-m”.

mandatory

Model1

FORECAST model of experiment, e.g. ”mpi-esm-lr”.

mandatory

Experiment1

Prefix for FORECAST experiment, e.g. ”decs4e” or ”decadal”.

mandatory

Ensemblemembers1

FORECAST ensemble members as list, e.g. ”r1i1p1,r2i1p1,r3i1p1”

mandatory

Project2

REFERENCE project, e.g. ”baseline0”, ”baseline1”, ”prototype”

mandatory

Product2

REFERENCE product, e.g. ”output2”, ”output1”.

mandatory

Institute2

REFERENCE institute of experiment, e.g. ”mpi-m”.

mandatory

Model2

REFERENCE model of experiment, e.g. ”mpi-esm-lr”.

mandatory

Experiment2

Prefix for REFERENCE experiment, e.g. ”decs4e” or ”decadal”.

mandatory

Ensemblemembers2

REFERENCE ensemble members as list, e.g. ”r1i1p1,r2i1p1,r3i1p1”

mandatory

Season

Season, e.g. ”MAM”, ”JJA”, or a comma separated list with the month(s) of interest, i.e. ”2,4,6,7”

mandatory

Observation

Observation, e.g. ”eraint” or ”merra”

mandatory

Aggregation

Level of aggregation: ”monthly” or ”seasonal”

mandatory

Integrative

Set TRUE for integrative calculation (with all lead years) of the selected index (default=False, i.e. index is calculated separately for all lead years.

mandatory

Table 2: Options for VADYtele.

4 Output

The processed files can be found in the selected Output folder for every lead year τ. It contains i. a. plots of the teleconnections patterns (figure 4), the teleconnection index (figure 5) and the rank histogram (figure 6).


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Figure 4: Example of SOI patterns for the ensemble mean (left, here: prototype of MPI-ESM-LR with 15 ensemble members) and the observation (right, here: ERA-Interim) for lead year 1.



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Figure 5: Example of the SOI index for the forecast (red, here: prototype of MPI-ESM-LR with 15 ensemble members with solid line indicating ensemble mean and shaded area indicating ensemble spread) and the observation (black, here: ERA-Interim) for lead year 1.



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Figure 6: Example of the rank histogram for the forecast (here: prototype of MPI-ESM-LR with 15 ensemble members) for lead year 1.


The output also encompasses raw data files of the teleconnection index and the skill scores (CORR, MSESS, RPSS; given as netCDF and ASCII files, respectively), which can be used for further analysis (cf. figure 7).


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Figure 7: Overview of RPSS for different lead years and seasons. Selected results are shown for baseline1 of MPI-ESM-LR with 15 ensemble members (b1) minus baseline0 of MPI-ESM-LR with 3 ensemble members (b0).


References

   A.G. Barnston and R.E. Livezey. Classification, Seasonality and Persistence of Low-Frequency Atmospheric Circulation Patterns. Mon. Weather Rev., 115: 1083–1126, 1987. doi: 10.1175/1520-0493(1987)115.

   C.A.T. Ferro, D.S. Richardson, and A.P. Weigel. On the effect of ensemble size on the discrete and continuous ranked probability scores. Meteorol. Appl., 15:19–24, 2008. doi: 10.1002/met.45.

   L. Goddard, A. Kumar, A. Solomon, D. Smith, G. Boer, P. Gonzalez, V. Kharin, W. Merryfield, C. Deser, S. J. Mason, B. P. Kirtman, R. Msadek, R. Sutton, E. Hawkins, T. Fricker, G. Hegerl, C. A. T. Ferro, D. B. Stephenson, G. A. Meehl, T. Stockdale, R. Burgman, A. M. Greene, Y. Kushnir, M. Newman, J. Carton, I. Fukumori, and T. Delworth. A verification framework for interannual-to-decadal predictions experiments. Clim. Dyn., 40:245–272, 2013. doi: 10.1007/s00382-012-1481-2.

   J.W. Hurrell. Decadal Trends in the North Atlantic Oscillation: Regional Temperatures and Precipitation. Science, 269:676–679, 1995. doi: 10.1126/science.269.5224.676.

   T. Kruschke, H.W. Rust, C. Kadow, G.C. Leckebusch, and U. Ulbrich. Evaluating decadal predictions of northern hemispheric cyclone frequencies. Tellus A, 66, 22830, 2014. doi: 10.3402/tellusa.v66.22830.

   S. Nan and J. Li. The relationship between the summer precipitation in the Yangtze River valley and the boreal spring Southern Hemisphere annular mode. Geophys. Res. Lett., 30:2266–2269, 2003. doi: 10.1029/2003GL018381.

   K.E. Trenberth. Signal Versus Noise in the Southern Oscillation. Mon. Weather Rev., 112:326–332, 1984. doi: 10.1175/1520-0493(1984)112.