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,

Horizon 2020 Societal challenge 5:

Climate action, environment, resource

efficiency and raw materials

BINGO

Bringing INnovation to onGOing water management –

a better future under climate change

Grant Agreement n° 641739, Research and Innovation Action

Deliverable number: D2.2

Deliverable name: Data downscaled to 12km/daily, Europe, for the period 2015-2024

WP / WP number: WP2: Climate predictions and downscaling to extreme weather

Delivery due date: Project month 12 (30/06/2016)

Actual date of submission: 30/06/2016

Dissemination level: Public

Lead beneficiary: FUB

Responsible scientist/administrator: Uwe Ulbrich, Henning Rust

Estimated effort (PM): 12PM

Contributor(s): Komlan A. Kpogo-Nuwoklo, Edmund Meredith, Henning Rust, Uwe Ulbrich

(all FUB)

Estimated effort contributor(s) (PM): 12PM

Internal reviewer: Paula Lorza, March Scheibel (both Wupperverband), George Zittis (CYI)

Ref. Ares(2016)3128411 - 30/06/2016

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Changes with respect to the DoW

With justification if applicable In the DoW, it was stated that the decadal climate

predictions (2015-2024) would be downscaled to 12km/1d over the entire EURO-

CORDEX region. In order to reduce computational cost, we have instead carried out

the downscaling over two European sub-regions (see Figure 1, page 7). These regions

cover Iberia and north-west Europe, encompassing all five research sites that the FUB

is responsible for providing data for. An additional benefit of this approach is that the

reduced computational expense allows us to downscale more realizations of the

decadal predictions than would be possible for the whole EURO-CORDEX domain.

Dissemination and uptake

These data can be used by all partners within the project, though cannot be publicly

disseminated without prior consent.

Short Summary of results

This deliverable describes the decadal predictions (2015-2024) produced by WP2, to be

subsequently used as input data for the hydrological models used in WP3. The data

have been dynamically downscaled to a horizontal resolution of 0.11° (12 km) and are

available at a daily frequency. As with all data produced in Work Package 2 (see, e.g.,

Deliverable 2.1), the data are available to all project partners via the online Freva

portal, where the data is converted to a format suitable for specific hydrological

models and the option of applying a bias correction to the data is also available.

Evidence of accomplishment

1. BINGO-DECO plug-in of the FreVa evaluation system https://freva.met.fu-

berlin.de/plugins/bingo_deco/detail/ (log-in required)

2. DECO Documentation: DECO – A plug-in for data extraction and conversion

developed within and for BINGO, H.W. Rust, A. Richling, E. Meredith, M. Fischer, C.

Vagenas, C. Kadow, and U. Ulbrich, 2016, Technical Report. Available online at

http://users.met.fu-berlin.de/~HenningRust/BINGO/DECO_docu.pdf (See also

Appendix 2)

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TABLE OF CONTENTS

1. Introduction ..................................................................................................................................... 4

2. Data downscaled to 12km/daily, Europe, for the period 2015-2024 ........................................... 5

2.1. MiKlip forced decadal predictions ................................................................................................. 5

2.2. Bias correction of decadal predictions .......................................................................................... 8

2.3. Data dissemination ....................................................................................................................... 8

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1. Introduction

Work Package 2 – Climate predictions and downscaling to extreme weather – of the

BINGO Project is tasked with producing high-resolution climate data, which will be

subsequently used as input data for the hydrological models being used in the other

work packages. Deliverable 2.2, the focus of this document, is specifically tasked with

providing these data for the period 2015-2024, based on decadal climate predictions of

the MiKlip decadal prediction system.

The work carried out for Deliverable 2.2 builds on what was previously implemented

for Deliverable 2.1. As such, the same approach to data processing, storage and

distribution is adopted, which can be read in detail in Deliverable 2.1.

This document describes the data produced for Deliverable 2.2, how it was produced,

and how it can be accessed by project partners.

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2. Data downscaled to 12km/daily, Europe, for the period

2015-2024

This chapter describes the regional climate simulations carried out for Deliverable 2.2,

the data produced for BINGO partners (including their bias correction), and how these

data can be accessed by project partners.

2.1. MiKlip forced decadal predictions

The relatively new field of decadal climate prediction, e.g. Smith et al. (2007), aims to

simulate both the climate response to future anthropogenic forcing and the future

evolution (from the present) of the climate due to internal climate variability

(Marotzke et al., 2016). This differs from the approach taken in climate projections,

e.g. the CMIP5 project (Taylor et al., 2012), where the focus is on the response of the

climate to anthropogenic forcing and the impacts of internal climate variability are

(supposed to be) nullified via multi-decadal climate model integrations. The earth

system models (ESMs) used in decadal prediction systems are initialized with an

observed state of the climate system, i.e. ocean, atmosphere, soil, ice, etc. Skill in

predicting internal climate variability on a decadal scale is derived from the long-term

memory (i.e. sensitivity to the initial state) of certain components of the climate

system, predominantly the ocean. As such, decadal predictions (unlike climate

projections) are reliant on a high-quality initialization of the ESM for those components

which exhibit long-term memory.

The MiKlip project (http://www.fona-miklip.de) is funded by the German Ministry for

Education and Research with the aim of developing a world-class decadal prediction

system. The MiKlip decadal prediction system is based on the Max Planck Institute's

earth system model, MPI-ESM (http://www.mpimet.mpg.de/en/science/models/mpi-

esm/), and has an atmospheric horizontal resolution of T63 (1.875°). The first phase of

the MiKlip project showed significant skill (e.g. Müller et al., (2012), Pohlmann et al.,

(2013)) in the MiKlip system, based on the evaluation of decadal hindcast simulations

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which were initialized yearly between 1960 and 2010. In addition to this, the MiKlip

system was also used for future decadal prediction running up to 2024, for 10

realizations and with an initialization in 2015. Module C of the first phase of the MiKlip

project was devoted to the regionalisation of the MiKlip global model output, via

dynamical downscaling. This was carried out over a European domain for the entire

MiKlip period (1960-2024) using the CCLM at 0.44° resolution.

For the BINGO project, the FUB have further dynamically downscaled the first four

realizations of the future decadal predictions (2015-2024) from 0.44° to 0.11° using the

CCLM (see the attached Technical Report (Rust et al.), Appendix 2, for a description of

the CCLM). To reduce computational expense, this has been carried out over two sub-

domains (Fig. 1):

(1) NW-EUR-11: which contains the research sites at Bergen, Veluwe and Wupper.

(2) IBERIA-11: which contains the research sites at Tagus and Badalona.

The 0.11° resolution matches that used in the downscaling carried out for D2.1,

creating a total set of simulations spanning 1979-2024, crucially all at the same spatial

resolution.

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Figure 1 | BINGO domains for MiKlip decadal predictions. The area covered by the MiKlip 0.44°

regionalisation is shown in colour, with red representing the 0.44° land mask and blue the sea. The

IBERIA-11 and NW-EUR-11 domains of the BINGO project are shown in green and cyan.

The variables, all of which can be bias corrected, produced for BINGO partners and

their temporal resolution also match those of D2.1. That is, D2.2 provides the following

variables at a daily frequency, as well as their daily min/max values:

Total Cloud Fraction

Near-Surface Relative Humidity

Near-Surface Specific Humidity

Precipitation

Surface Air Pressure

Sea Level Pressure

Surface Downwelling Longwave Radiation

Surface Downwelling Shortwave Radiation

Near-Surface Wind Speed

Near-Surface Air Temperature

Near-Surface Dew Point Temperature

Eastward Near-Surface Wind

Northward Near-Surface Wind

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2.2. Bias correction of decadal predictions

As discussed in detail in Deliverable 2.1, climate models often show systematic biases with

respect to observations in their representation of certain variables. As such, the later work

packages are best served by having the option to input bias corrected data to their

hydrological models.

Bias correction of the 0.11° decadal predictions is carried out using a method based on the

cumulative distribution functions of the model output and historical observations. Broadly

speaking, this involves estimating the bias of historical MiKlip data and bias correcting the

future MiKlip data based on this. This method also takes account of the fact that the

highest resolution historical data available from the MiKlip project is 0.44°, and that

having produced 0.11° data for the decadal future predictions, BINGO does not have the

computational resources to additionally produce 0.11° resolution data for the historical

period. The concept behind the method is described in detail in Appendix 1 and in section

3.3 of Appendix 2.

2.3. Data dissemination

The dissemination method for the data provided for D2.2 is via the Freva system, using

the DECO plugin. This is identical to the method adopted for D2.1; users simply need to

select the correct experi e t decadal-predictio s from the DECO menu. As such, the

method will not be described in detail again here. For a recap, the reader is referred to

either Appendix 2 or Deliverable 2.1.

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3. References

J Marotzke, WA Müller, FSE Vamborg, P Becker, U Cubasch, H Feldmann, F Kaspar, C

Kottmeier, C Marini, I Polkova. Miklip – a national research project on decadal climate

prediction. Bulletin of the American Meteorological Society, 2016.

WA Mueller, J Baehr, H Haak, JH Jungclaus, J Kröger, D Matei, H Pohlmann, JS Storch, and J

Marotzke. Forecast skill of multi-year seasonal means in the decadal prediction system of

the max planck institute for meteorology. Geophysical Research Letters, 39(22), 2012.

H. Pohlmann, W. A. Mueller, K. Kulkarni, M. Kameswarrao, D. Matei, FSE Vamborg, C.

Kadow, S. Illing, and J. Marotzke. Improved forecast skill in the tropics in the new miklip

decadal climate predictions. Geophysical Research Letters, 40(21):5798-5802, 2013.

D. M. Smith, S. Cusack, A. W. Colman, C. K. Follard, G. R. Harris, and J. M. Murphy.

Improved surface temperature prediction for the coming decade from a global climate

model. Science, 317(5839):796-799, 2007.

K. E. Taylor, R. J. Stouffer, and G. A. Mehl. An overview of CMIP5 and the experiment

design. Bull. Amer. Meteor. Soc., 94(4):485-498, 2012.

Appendix 1

Bias Correction of MiKlip Decadal Predictions

❆ ♣r♦♣♦s❡❞ s❝❤❡♠❡ ❢♦r ▼✐❑❧✐♣ ❢✉t✉r❡ s✐♠✉❧❛t✐♦♥s ❜✐❛s ❝♦rr❡❝t✐♦♥

❏✉♥❡ ✷✾✱ ✷✵✶✻

❖✉r ❣♦❛❧ ✐s t♦ ❜✐❛s ❝♦rr❡❝t t❤❡ ▼✐❦❧✐♣ ❢✉t✉r❡ s✐♠✉❧❛t✐♦♥s ❢♦r ❛ s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.11◦ ✉s✐♥❣ t❤❡❈❉❋✲❚r❛♥s❢♦r♠ ♠❡t❤♦❞✳ ❚❤✐s ❜✐❛s ❝♦rr❡❝t✐♦♥ ♠❡t❤♦❞ ❝❛♥ ❜❡ s❡❡♥ ❛s ❛♥ ❡①t❡♥s✐♦♥ ♦❢ t❤❡ ❝❧❛ss✐❝❛❧

q✉❛♥t✐❧❡ ♠❛♣♣✐♥❣ ✐♥ ✇❤✐❝❤ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s ❛r❡ ❝♦rr❡❝t❡❞ s♦ t❤❛t t❤❡✐r ❈✉♠✉❧❛t✐✈❡ ❉✐str✐❜✉t✐♦♥

❋✉♥❝t✐♦♥s ✭❈❉❋✮ ♠❛t❝❤ t❤❡ ♦♥❡s ♦❢ t❤❡ ♦❜s❡r✈❛t✐♦♥s✳ ❚❤❡ ❈❉❋✲❚r❛♥s❢♦r♠ ♠❡t❤♦❞✱ ✐♥ ❛❞❞✐t✐♦♥✱

❛✐♠s t♦ ♣r♦✈✐❞❡ ❛♣♣r♦①✐♠❛t✐✈❡ ❈❉❋ ♦❢ t❤❡ ♦❜s❡r✈❛t✐♦♥s ❢♦r t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞ ❜❛s❡❞ ♦♥ ✐♥❢♦r♠❛t✐♦♥

❧❡❛r♥❡❞ ❢r♦♠ t❤❡ ❤✐st♦r✐❝❛❧ ♣❡r✐♦❞ ✭s❡❡ ❆♣♣❡♥❞✐① ✷✱ s❡❝t✐♦♥ ✸✳✸✱ ❢♦r ♠♦r❡ ❞❡t❛✐❧s✮✳

■♥ t❤❡ ❚❛❜❧❡ ✶✱ t❤❡ ❛✈❛✐❧❛❜❧❡ ❞❛t❛ ❢♦r ❤✐st♦r✐❝❛❧ ❛♥❞ ❢✉t✉r❡ ♣❡r✐♦❞s ❛r❡ s✉♠♠❛r✐③❡❞✳ ❲❆❚❈❍

❞❛t❛ s❡r✈❡s ❤❡r❡ ❛s ♦❜s❡r✈❛t✐♦♥s✳

❘❡s♦❧✉t✐♦♥ 0.44◦ ❘❡s♦❧✉t✐♦♥ 0.11◦

❍✐st♦r✐❝❛❧ ❋✉t✉r❡ ❍✐st♦r✐❝❛❧ ❋✉t✉r❡

▼✐❑❧✐♣ F(M44)h

F(M44)f F

(M11)h

F(M11)f

❲❆❚❈❍ F(W44)h

F(W44)f F

(W11)h

F(W11)f

❚❛❜❧❡ ✶✿ ❚❛❜❧❡ s✉♠♠❛r✐③✐♥❣ t❤❡ ❞❛t❛✿ ❋ st❛♥❞s ❢♦r ❈❉❋s✳ ❈❉❋s t❤❛t ❝❛♥ ♥♦t ❜❡ ❝♦♠♣✉t❡❞ ❞✐r❡❝t❧②

❢r♦♠ t❤❡ ❛✈❛✐❧❛❜❧❡ ❞❛t❛ ❛r❡ ✐♥❞✐❝❛t❡❞ ✐♥ ❜❧✉❡✳

❚❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ♦❢ ▼✐❑❧✐♣ ❢✉t✉r❡ s✐♠✉❧❛t✐♦♥s ❢♦r s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.11◦ ✐s q✉✐t❡ ❝❤❛❧❧❡♥❣✐♥❣❜❡❝❛✉s❡ ❤✐st♦r✐❝❛❧ s✐♠✉❧❛t✐♦♥s ❢♦r t❤❡ s❛♠❡ r❡s♦❧✉t✐♦♥ ❛r❡ ♥♦t ❛✈❛✐❧❛❜❧❡✳ ❍♦✇❡✈❡r✱ ✇❡ ❤❛✈❡ ▼✐❦❧✐♣

s✐♠✉❧❛t✐♦♥s ❢♦r ❜♦t❤ ❤✐st♦r✐❝❛❧ ❛♥❞ ❢✉t✉r❡ ♣❡r✐♦❞s ❛t ❛ s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.44◦✳ ❚❤❛♥❦s t♦ t❤❡ ❈❉❋✲❚r❛♥s❢♦r♠✱ ✐t ✐s ♣♦ss✐❜❧❡ t♦ ❡st✐♠❛t❡ ❈❉❋s ♦❢ ▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ s✐♠✉❧❛t✐♦♥s ❢♦r s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢

0.11◦ ❜② ♠♦❞❡❧❧✐♥❣ t❤❡ ♠❛t❤❡♠❛t✐❝❛❧ ❧✐♥❦ ❜❡t✇❡❡♥ t❤❡s❡ t✇♦ r❡s♦❧✉t✐♦♥s✳ ❚❤✉s✱ t❤❡ ♣r♦♣♦s❡❞ ♠❡t❤♦❞

t♦ ❝♦rr❡❝t t❤❡ ▼✐❑❧✐♣ ❢✉t✉r❡ s✐♠✉❧❛t✐♦♥s ❢♦r s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.11◦✱ ✉s✐♥❣ ❈❉❋✲❚r❛♥s❢♦r♠ ❝❛♥

❜❡ ❧✐st❡❞ ❛s ❢♦❧❧♦✇❡❞ ✭s❡❡ ❋✐❣✉r❡ ✶ ❢♦r ❣r❛♣❤✐❝ ✐❧❧✉str❛t✐♦♥✮✿

✶✳ ❊st✐♠❛t❡ ❈❉❋s ♦❢ t❤❡ ▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ s✐♠✉❧❛t✐♦♥s ❢♦r ❛ s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.11◦ ✭F(M11)h (x)✮

✉s✐♥❣ ✐♥❢♦r♠❛t✐♦♥ ♣r♦✈✐❞❡❞ ❜② t❤❡ ❧❛r❣❡ s❝❛❧❡ ✭0.44◦✮ ▼✐❑❧✐♣ ❞❛t❛ ✭❙❡❝t✐♦♥ ✶✮✳

✷✳ ❊st✐♠❛t❡ ❈❉❋s ♦❢ t❤❡ ❲❆❚❈❍ ❞❛t❛ ✭0.11◦✮ ❢♦r t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞ ✭F(W11)f (x)✮ ✉s✐♥❣ t❤❡ ▼✐❑❧✐♣

❤✐st♦r✐❝❛❧ ❛♥❞ ❢✉t✉r❡ s✐♠✉❧❛t✐♦♥s ❛♥❞ ❲❆❚❈❍ ❤✐st♦r✐❝❛❧ ❞❛t❛ ❢♦r s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢ 0.11◦

✭❙❡❝t✐♦♥ ✷✮✳

✸✳ ❖♥❝❡ ❈❉❋s ♦❢ t❤❡ ❲❆❚❈❍ ❞❛t❛ ✭0.11◦✮ ❢♦r t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞ ❛r❡ ❡st✐♠❛t❡❞✱ ❛ q✉❛♥t✐❧❡ ♠❛♣♣✐♥❣

❝❛♥ ✜♥❛❧❧② ❜❡ ❛♣♣❧✐❡❞ ❜❡t✇❡❡♥ F(M11)f (x) ❛♥❞ F

(W11)f (x)✳ ❚❤❡ ❝♦rr❡❝t❡❞ ✈❛❧✉❡ xbc ✐s t❤❡♥

xbc = F(W11)

−1f

[

F(M11)f (x)

]

. ✭✶✮

✶

❋✐❣✉r❡ ✶✿ ■❧❧✉str❛t✐♦♥ ♦❢ tr❛♥s❢♦r♠❛t✐♦♥s ✐♥✈♦❧✈❡❞ ✐♥ t❤❡ ♣r♦♣♦s❡❞ ♠❡t❤♦❞

✷

✶ ❊st✐♠❛t✐♦♥ ♦❢ ▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ ❈❉❋ ✭F(M11)h (x)✮ ❢r♦♠ t❤❡ ▼✐❑❧✐♣

0.44◦ ❞❛t❛✿ ♣r♦❜❛❜✐❧✐st✐❝ ❞♦✇♥s❝❛❧✐♥❣

❲❡ ❛❧s♦ ♠❛❦❡ t❤❡ ❛ss✉♠♣t✐♦♥ t❤❛t t❤❡r❡ ✐s ❛ ♠❛t❤❡♠❛t✐❝❛❧ tr❛♥s❢♦r♠❛t✐♦♥ T (44−11) t❤❛t ❛❧❧♦✇s t♦

❣♦ ❢r♦♠ t❤❡ ❈❉❋ ♦❢ t❤❡ ❧❛r❣❡ s❝❛❧❡ ▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ ❞❛t❛ ✭F(M44)h (x)✮ t♦ t❤❡ ❈❉❋ ♦❢ t❤❡ s♠❛❧❧ s❝❛❧❡

▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ ❞❛t❛ ✭F(M11)h (x)✮ ✱

T (44−11)[

F(M44)h (x)

]

= F(M11)h (x). ✭✷✮

❯♥❞❡r ❛ss✉♠♣t✐♦♥ t❤❛t T (11−44) st✐❧❧ ✈❛❧✐❞ ❢♦r t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞✱

T (44−11)[

F(M44)f (x)

]

= F(M11)f (x), ✭✸✮

✐t ❝❛♥ ❜❡ ♠♦❞❡❧❧❡❞ ❜② r❡♣❧❛❝✐♥❣ x ❜② F(M44)

−1f (u) ✐♥ ✭✸✮✱ ✇❤❡r❡ u ✐s ❛♥② ♣r♦❜❛❜✐❧✐t② ✐♥ [0, 1]✱

T (44−11)(u) = F(M11)f

[

F(M44)

−1f (u)

]

. ✭✹✮

■♥s❡rt✐♥❣ ✭✹✮ ✐♥ ✭✷✮ ❧❡❛❞s t♦ ❛ ♠♦❞❡❧❧✐♥❣ ♦❢ F(M11)h (x)✱

F(M11)h (x) = F

(M11)f

{

F(M44)

−1f

[

F(M44)h (x)

]}

. ✭✺✮

✷ ❊st✐♠❛t✐♦♥ ♦❢ ❲❆❚❈❍ ❢✉t✉r❡ ❈❉❋ ✭F(W11)f (x)✮

❲❡ ♠❛❦❡ ❛ss✉♠♣t✐♦♥ t❤❛t t❤❡r❡ ✐s ❛ ♠❛t❤❡♠❛t✐❝❛❧ tr❛♥s❢♦r♠❛t✐♦♥ T (MW ) t❤❛t ❛❧❧♦✇s t♦ ❣♦ ❢r♦♠

t❤❡ ❈❉❋ ♦❢ t❤❡ ▼✐❑❧✐♣ ❤✐st♦r✐❝❛❧ ❞❛t❛ ✭F(M11)h (x)✮ t♦ t❤❡ ❈❉❋ ♦❢ t❤❡ ❲❆❚❈❍ ❤✐st♦r✐❝❛❧ ❞❛t❛

✭F(W11)h (x)✮✱

T (MW )[

F(M11)h (x)

]

= F(W11)h (x). ✭✻✮

❲❡ s✉♣♣♦s❡ t❤❛t t❤✐s tr❛♥s❢♦r♠❛t✐♦♥ ✐s st✐❧❧ ✈❛❧✐❞ ❢♦r t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞✱

T (MW )[

F(M11)f (x)

]

= F(W11)f (x). ✭✼✮

❇② ♠♦❞❡❧❧✐♥❣ T (MW )✱ ✐t ✐s t❤❡♥ ♣♦ss✐❜❧❡ t♦ ❛♣♣r♦①✐♠❛t❡ t❤❡ ❈❉❋ ♦❢ ❲❆❚❈❍ ❢✉t✉r❡ ❞❛t❛

✭F(W11)f (x)✮✳ ❚❤❡ s✐♠♣❧❡ ✇❛② t♦ ♠♦❞❡❧ T (MW ) ✐s t♦ r❡♣❧❛❝❡ x ❜② F

(M11)−1

h (u) ✐♥ ✭✻✮✱ ✇❤❡r❡ u ✐s

❛♥② ♣r♦❜❛❜✐❧✐t② ✐♥ [0, 1]✳ ❲❡ t❤❡♥ ♦❜t❛✐♥

T (MW )(u) = F(W11)h

[

F(M11)

−1h (u)

]

, ✭✽✮

❝♦rr❡s♣♦♥❞✐♥❣ t♦ t❤❡ s✐♠♣❧❡ ❞❡✜♥✐t✐♦♥ ♦❢ T (MW )✳ ■♥s❡rt✐♥❣ ✭✽✮ ✐♥ ✭✼✮ ❧❡❛❞s t♦ ❛ ♠♦❞❡❧❧✐♥❣ ♦❢

F(W11)f (x)✱

F(W11)f (x) = F

(W11)h

{

F(M11)

−1h

[

F(M11)f (x)

]}

. ✭✾✮

■♥ ❡q✉❛t✐♦♥ ✭✾✮ t❤❡ ✐♥✈❡rs❡ ❈❉❋ ♦❢ t❤❡ ❤✐st♦r✐❝❛❧ ▼✐❦❧✐♣ ❞❛t❛ F(M11)

−1h ✐s ✉♥❦♥♦✇♥ ❛♥❞ ♥❡❡❞s t♦

❜❡ ❡st✐♠❛t❡❞✳ ❖♥❡ ✇❛② t♦ ❞♦ s♦ ✐s t♦ ❛♣♣❧② t❤❡ ❈❉❋✲t ❛s ❛ ♣r♦❜❛❜✐❧✐st✐❝ ❞♦✇♥s❝❛❧✐♥❣ t♦ r❡❧❛t❡ ❈❉❋s

❢r♦♠ t❤❡ ❧❛r❣❡ s❝❛❧❡ ✭0.44◦✮ t♦ ❈❉❋s ❢r♦♠ t❤❡ s♠❛❧❧ s❝❛❧❡ ✭0.11◦✮✳

✸

Appendix 2

Technical Report: Available data and the Freva system/DECO

plugin through which it is distributed

❇■◆●❖ ❲♦r❦ ♣❛❝❦❛❣❡ ✷❈❧✐♠❛t❡ ♣r❡❞✐❝t✐♦♥s ❛♥❞ ❞♦✇♥s❝❛❧✐♥❣ t♦ ❡①tr❡♠❡ ✇❡❛t❤❡r

❉❊❈❖

✕❆ ♣❧✉❣✲✐♥ ❢♦r ❞❛t❛ ❡①tr❛❝t✐♦♥ ❛♥❞ ❝♦♥✈❡rs✐♦♥

❞❡✈❡❧♦♣❡❞ ✇✐t❤✐♥ ❛♥❞ ❢♦r

❇■◆●❖

❍❡♥♥✐♥❣ ❲✳ ❘✉st✱ ❆♥❞② ❘✐❝❤❧✐♥❣✱ ❊❞♠✉♥❞ ▼❡r❡❞✐t❤✱

▼❛❞❧❡♥ ❋✐s❝❤❡r✱ ❈❤r✐st♦s ❱❛❣❡♥❛s✱

❈❤r✐st♦♣❤❡r ❑❛❞♦✇ ❛♥❞ ❯✇❡ ❯❧❜r✐❝❤

❱❡rs✐♦♥ ❢r♦♠ ❏✉♥❡ ✷✽✱ ✷✵✶✻

❚❤❡ ❇■◆●❖ ♣r♦❥❡❝t ❤❛s r❡❝❡✐✈❡❞ ❢✉♥❞✐♥❣ ❢r♦♠ t❤❡ ❊✉r♦♣❡❛♥ ❯♥✐♦♥✬s❍♦r✐③♦♥ ✷✵✷✵ ❘❡s❡❛r❝❤ ❛♥❞ ■♥♥♦✈❛t✐♦♥ ♣r♦❣r❛♠♠❡✱ ✉♥❞❡r t❤❡ ●r❛♥t❆❣r❡❡♠❡♥t ♥✉♠❜❡r ✻✹✶✼✸✾✳

❆❜str❛❝t

❉❊❈❖ ✐s ❛ ♣❧✉❣✲✐♥ t♦ t❤❡ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥ ❊✈❛❧✉❛t✐♦♥ ❋r❛♠❡✇♦r❦ ❢♦r ❊❛rt❤ ❙②s✲

t❡♠ ❙❝✐❡♥❝❡ ✭❋r❡❱❛✮ ❛♥❞ ❛✐♠s ❛t ❡①tr❛❝t✐♥❣ ❛♥❞ ❝♦♥✈❡rt✐♥❣ ❈❖❙▼❖✲❈▲▼ r❡❣✐♦♥❛❧ ❝❧✐✲♠❛t❡ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s ❢r♦♠ ❛ ❝❡♥tr❛❧ ❞❛t❛ st♦r❛❣❡ ♦♥ ❞❡♠❛♥❞ ✈✐❛ ❛ ✇❡❜✲❜❛s❡❞ ♣❧❛t❢♦r♠✳❚❤❡ ❞❛t❛ ✐s t♦ ❜❡ ✉s❡❞ ❛s ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞r✐✈✐♥❣ ❞❛t❛ ❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s ❛t t❤❡ s✐①❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s ✭❇■◆●❖ ❞❡❧✐✈❡r❛❜❧❡ ❉✷✳✶✮✳ ❈✉rr❡♥t❧②✱ t❤❡ s♣❛t✐❛❧ r❡s♦❧✉t✐♦♥ ♦❢t❤❡ r❡❣✐♦♥❛❧ ♠♦❞❡❧ ✐s ✶✷❦♠ ❛♥❞ ❞❛t❛ ✇✐❧❧ ❜❡ ♠❛❞❡ ❛✈❛✐❧❛❜❧❡ ❛s ❞❛✐❧② ✈❛❧✉❡s✳ ❚❤❡ ❝❧✐♠❛✲t♦❧♦❣② ❢♦r t❤❡ s✐♠✉❧❛t❡❞ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ♣❛r❛♠❡t❡rs✱ ✐✳❡✳ t❤❡✐r s❡❛s♦♥❛❧❧② ✈❛r②✐♥❣ ♠❡❛♥✭❛♥❞ ❤✐❣❤❡r ♠♦♠❡♥ts✮ ❞✐✛❡r ❢r♦♠ t❤❡ ♦❜s❡r✈❡❞ ♦♥❡✱ ❛ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❝❛♥ ❜❡ ♦♣t✐♦♥❛❧❧②❛♣♣❧✐❡❞ ❜❡❢♦r❡ ❝♦♥✈❡rt✐♥❣ t❤❡ ❞❛t❛ ❛♥❞ ✜❧❡ ❢♦r♠❛t t♦ t❤❡ ♣❛rt✐❝✉❧❛r ♥❡❡❞s ♦❢ t❤❡ ✐♥❞✐✲✈✐❞✉❛❧ ♠♦❞❡❧✐♥❣ ❣r♦✉♣s ❛t t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡s✳ ❚❤❡ ❧❛tt❡r ✐♠♣❧✐❡s ❛ ❝♦♥✈❡rs✐♦♥ ❢r♦♠ t❤❡♥❛t✐✈❡ ❈❖❙▼❖✲❈▲▼ ❣r✐❞ t♦ st❛t✐♦♥ ❧♦❝❛t✐♦♥s ♦r t♦ ❛ ❞✐✛❡r❡♥t ❣r✐❞✱ ❛ ❝❤❛♥❣❡ ♦❢ ✉♥✐ts✱❛s ✇❡❧❧ ❛s ✇r✐t✐♥❣ t❤❡ ❞❛t❛ t♦ t❤❡ ❞❡s✐r❡❞ ✜❧❡ ❢♦r♠❛t✳ ❚❤✐s ♦♥✲❞❡♠❛♥❞ ♣♦st✲♣r♦❝❡ss✐♥❣❛♥❞ ❝♦♥✈❡rs✐♦♥ ❛♣♣r♦❛❝❤ ❛❧❧♦✇s ❢♦r ❛♥ ❡✣❝✐❡♥t ❞❛t❛ st♦r❛❣❡✱ ♠❛①✐♠❛❧ r❡♣r♦❞✉❝✐❜✐❧✐t②❛♥❞ tr❛♥s♣❛r❡♥❝②✱ ❛s ✇❡❧❧ ❛s tr❛♥s❢❡r❛❜✐❧✐t② t♦ ♥❡✇ ❞❛t❛ s❡ts✳ ❚❤❡ ❛♣♣❧✐❝❛t✐♦♥ ❞❡✈❡❧♦♣❡❞❤❡r❡ ❝❛♥ ❜❡ ❛❝❝❡ss❡❞ ✈✐❛ ❛ ✇❡❜✲♣❧❛t❢♦r♠ ♦r ❛ ❝♦♠♠❛♥❞ ❧✐♥❡ ✐♥t❡r❢❛❝❡✳ ❉❡✈❡❧♦♣♠❡♥t ✐ss✉❜❥❡❝t❡❞ t♦ ❛ str✐❝t ✈❡rs✐♦♥ ❝♦♥tr♦❧ t♦ ❡♥s✉r❡ r❡♣r♦❞✉❝✐❜✐❧✐t②✳

✸

❈♦♥t❡♥ts

✶ ❉❊❈❖ ✕ ❆✐♠s ❛♥❞ str❛t❡❣② ✻

✷ ❉❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥s ✽✷✳✶ ▼♦❞❡❧ ❉❡s❝r✐♣t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷✳✷ ❉❡s❝r✐♣t✐♦♥ ♦❢ ❙✐♠✉❧❛t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

✷✳✷✳✶ ❘❡❛♥❛❧②s✐s✲❢♦r❝❡❞ ❡✈❛❧✉❛t✐♦♥ r✉♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷✳✷✳✷ ❍✐❣❤✲r❡s♦❧✉t✐♦♥ ✭t❡st✮ s✐♠✉❧❛t✐♦♥s ♦❢ ❡①tr❡♠❛❧ ❡♣✐s♦❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷✳✷✳✸ ▼✐❑❧✐♣ ❢♦r❝❡❞ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷

✸ ❇✐❛s ❝♦rr❡❝t✐♦♥ ✶✹✸✳✶ ❘❡❢❡r❡♥❝❡ ❞❛t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✸✳✷ ❙❡❛s♦♥❛❧ ●❡♥❡r❛❧✐③❡❞ ▲✐♥❡❛r ▼♦❞❡❧ ♠❡t❤♦❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✸✳✷✳✶ ❯♥❞❡r❧②✐♥❣ ♣r✐♥❝✐♣❧❡ ❛♥❞ ♠♦❞❡❧✐♥❣ ❛♣♣r♦❛❝❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺✸✳✷✳✷ ❆t ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✸✳✸ ❈✉♠✉❧❛t✐✈❡ ❉✐str✐❜✉t✐♦♥ ❋✉♥❝t✐♦♥ ❚r❛♥s❢♦r♠ ♠❡t❤♦❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✸✳✸✳✶ ◗✉❛♥t✐❧❡✲▼❛♣♣✐♥❣ ▼❡t❤♦❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✸✳✸✳✷ ❈❉❋✲❚r❛♥s❢♦r♠ ▼❡t❤♦❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷✸✳✸✳✸ ❆♣♣❧✐❝❛t✐♦♥ ♦❢ ❈❉❋✲t ❛t ❇■◆●❖ r❡s❡❛r❝❤ s✐t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✹ ❉❊❈❖ ✕ ❆ ❇■◆●❖ ♣❧✉❣✲✐♥ ❢♦r ❋r❡❱❛ ✷✽✹✳✶ ❋r❡❱❛ ✕ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽✹✳✷ ❉♦❝✉♠❡♥t❛t✐♦♥ ♦❢ ❉❊❈❖ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾

✹✳✷✳✶ ■♥tr♦❞✉❝t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾✹✳✷✳✷ Pr❡♣r♦❝❡ss✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵✹✳✷✳✸ ■♥♣✉t ♣❛r❛♠❡t❡rs ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶✹✳✷✳✹ ❖✉t♣✉t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

✺ ❙✉♠♠❛r② ✸✼

❇✐❜❧✐♦❣r❛♣❤② ✸✽

✺

❈❤❛♣t❡r ✶

❉❊❈❖ ✕ ❆✐♠s ❛♥❞ str❛t❡❣②

❚❤❡ ❇■◆●❖❲♦r❦ P❛❝❦❛❣❡ ❲P✷ ❈❧✐♠❛t❡ ♣r❡❞✐❝t✐♦♥s ❛♥❞ ❞♦✇♥s❝❛❧✐♥❣ t♦ ❡①tr❡♠❡ ✇❡❛t❤❡r

❛✐♠s ❛t ♣r♦✈✐❞✐♥❣ ❤✐❣❤ r❡s♦❧✉t✐♦♥ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞r✐✈✐♥❣ ❞❛t❛ ❢♦r ✈❛r✐♦✉s ❤②❞r♦❧♦❣✐❝❛❧♠♦❞❡❧s✳ ❋♦r ♠♦st ♠♦❞❡❧s✱ t❤✐s ✐♥❝❧✉❞❡s ♣r❡❝✐♣✐t❛t✐♦♥✱ t❡♠♣❡r❛t✉r❡✱ ♣r❡ss✉r❡✱ ✇✐♥❞ s♣❡❡❞✱✐♥❝♦♠✐♥❣ s♦❧❛r r❛❞✐❛t✐♦♥ ❛♥❞ ♦t❤❡rs✳ ❚❤✐s ❞❛t❛ ✐s ❣❡♥❡r❛t❡❞ ♦♥ ❛ r❡❣✐♦♥❛❧ ❧❡✈❡❧ ✭❢♦r t❤✐s❞❡❧✐✈❡r❛❜❧❡ ❛t ❛ ❊✉r♦♣❡❛♥ ❧❡✈❡❧✮ ❜② ❞②♥❛♠✐❝❛❧❧② ❞♦✇♥s❝❛❧✐♥❣ ❝♦❛rs❡ r❡s♦❧✉t✐♦♥ ❣❧♦❜❛❧❞❛t❛✱ s❡❡ ❛❧s♦ t❤❡ r❡❞ ❜♦① ♦❢ ❋✐❣✳ ✶✳✶✳ ❚♦ ❜❡ ✉s❛❜❧❡ ❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✱ t❤✐s ❞❛t❛

❋✐❣✉r❡ ✶✳✶✿ ❙❦❡t❝❤ ♦❢ t❤❡ str❛t❡❣② ✐♥ ❲P✷✳

♥❡❡❞s t♦ ❜❡ ❛♣♣r♦♣r✐❛t❡❧② ♣♦st✲♣r♦❝❡ss❡❞ ❛♥❞ ❝♦♥✈❡rt❡❞ t♦ t❤❡ ♥❡❡❞s ♦❢ t❤❡ ✶✺ ❛♥❞ ♠♦r❡✐♥❞✐✈✐❞✉❛❧ ♠♦❞❡❧s ✉s❡❞ ❛t t❤❡ ✻ ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s✳

❋♦r tr❛♥s♣❛r❡♥❝② ❛♥❞ r❡♣r♦❞✉❝✐❜✐❧✐t② ✇✐t❤✐♥ ❇■◆●❖✱ ✇❡ ♠✉st ❡♥s✉r❡ t❤❛t t❤❡ ✈❡r②s❛♠❡ ❞r✐✈✐♥❣ ❞❛t❛ ✐s ❛✈❛✐❧❛❜❧❡ t❤r♦✉❣❤♦✉t t❤❡ ♣r♦❥❡❝t ❛♥❞ ❜❡②♦♥❞✳ ❚❤✉s✱ ✐t ♠✉st ❜❡ ❡✐t❤❡rst♦r❡❞ ✐♥ t❤❡ ✈❛r✐♦✉s ❞✐✛❡r❡♥t ✜❧❡ ❢♦r♠❛ts ♥❡❡❞❡❞ ❜② t❤❡ ✐♥❞✐✈✐❞✉❛❧ ♠♦❞❡❧s✱ ♦r ✕ t♦ ❜❡♠♦r❡ ❡✣❝✐❡♥t ♦♥ ♠❡♠♦r② ❝♦♥s✉♠♣t✐♦♥ ✕ ♦♥❡ ❞❛t❛ s❡t ✐s st♦r❡❞ ✐♥ ❛ ❝♦♠♠♦♥ st❛♥❞❛r❞✐③❡❞❢♦r♠❛t ❢♦r ❝❧✐♠❛t❡ ♠♦❞❡❧s ❛♥❞ ❛❞❞✐t✐♦♥❛❧❧② ❞❛t❛ ❝♦♥✈❡rs✐♦♥ ❛❧❣♦r✐t❤♠s ❛r❡ s♣❡❝✐✜❝❛❧❧②t❛✐❧♦r❡❞ ❢♦r ❛❧❧ t❤❡ ✐♥❞✐✈✐❞✉❛❧ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✳ ❇❡s✐❞❡s t❤❡ ❡✣❝✐❡♥t ✉s❡ ♦❢ ♠❡♠♦r②✱t❤❡r❡ ❛r❡ ♦t❤❡r ❛❞✈❛♥t❛❣❡s t♦ t❤❡ ❧❛tt❡r ♣r♦❝❡❞✉r❡✿ ■✮ t❤❡s❡ ❝♦♥✈❡rs✐♦♥ ❛❧❣♦r✐t❤♠s ❝❛♥

✻

❜❡ r❡✉s❡❞ ❢♦r ♠♦r❡ ❞❛t❛ t♦ ❝♦♠❡ ✇✐t❤ t❤❡ ❢♦❧❧♦✇✐♥❣ ❞❡❧✐✈❡r❛❜❧❡s ❛ss♦❝✐❛t❡❞ ✇✐t❤ ❲P✷✱■■✮ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❝❛♥ ❜❡ ❡①❝❤❛♥❣❡ ✇✐t❤ ❛ ♠♦r❡ s♦♣❤✐st✐❝❛t❡❞ ♦♥❡ ✐❢ ❛✈❛✐❧❛❜❧❡✱ ❛♥❞ ■■■✮♠❛♥② ♦t❤❡r ❛✈❛✐❧❛❜❧❡ ❞❛t❛ s❡ts ✐♥ t❤✐s st❛♥❞❛r❞✐③❡❞ ❢♦r♠❛t ❝❛♥ ❜❡ ✉s❡❞ ❛❞❞✐t✐♦♥❛❧❧② t♦t❤❡ ❞❛t❛ ♣r♦❞✉❝❡❞ ♣❛rt✐❝✉❧❛r❧② ❢♦r ❇■◆●❖✳

●✐✈❡♥ t❤❡s❡ ❛❞✈❛♥t❛❣❡s✱ ❲P✷ ❧❡❛❞❡rs ❞❡❝✐❞❡❞ t♦ ❞❡✈❡❧♦♣ ❛ ❤②❜r✐❞ ❛♣♣❧✐❝❛t✐♦♥ ✭❝♦♠♠❛♥❞✲❧✐♥❡✲✐♥t❡r❢❛❝❡ ❛♥❞ ✇❡❜✲❜❛s❡❞✮ t♦ ❡①tr❛❝t t❤❡ ❞❛t❛ ♥❡❡❞❡❞ ❢♦r t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡s✱ ♣♦st✲♣r♦❝❡ss ❛♥❞ ❝♦♥✈❡rt ✐t t♦ t❤❡ ♥❡❡❞s ♦❢ ❛❧❧ ✐♥❞✐✈✐❞✉❛❧ ♠♦❞❡❧✐♥❣ ❣r♦✉♣s✳ ❚❤❡s❡ ❝♦♥✈❡rs✐♦♥r♦✉t✐♥❡s ❝❛♥ ❛❧s♦ ❜❡ ❛❞❛♣t❡❞ t♦ ✐♥❝♦r♣♦r❛t❡ ♥❡✇ ♠♦❞❡❧s ♦r t♦ ❝❤❛♥❣✐♥❣ ♥❡❡❞s ♦❢ ❡①✐st✐♥❣♠♦❞❡❧s✳ ❋✉rt❤❡r♠♦r❡✱ ✉s❡rs ❝❛♥ ❛❧s♦ ❣❡t ❜❛❝❦ t♦ ❞❛t❛ ❣❡♥❡r❛t❡❞ ❡❛r❧✐❡r ❛♥❞ ❡①tr❛❝t t❤❡s❡✉s✐♥❣✱ ❡✳❣✳✱ ❛ ♥❡✇ ❜✐❛s ❝♦rr❡❝t✐♦♥ ♠❡t❤♦❞ ♦r ❛ s❧✐❣❤t❧② ❝❤❛♥❣❡❞ ❝♦♥✈❡rs✐♦♥ r♦✉t✐♥❡✳ ❆❞✲❞✐t✐♦♥❛❧❧② t♦ ❡✣❝✐❡♥t❧② ❛r❝❤✐✈✐♥❣ ❝❧✐♠❛t❡ ❞❛t❛ ✐♥ ❛ ❝❡♥tr❛❧ ♣❧❛❝❡✱ t❤❡ ♣❧✉❣✲✐♥ ❞❡✈❡❧♦♣❡rs✐♥ ❲P✷ ✉s❡ ❣✐t✶ t♦ ❡♥s✉r❡s ❛ ♣r♦♣❡r ✈❡rs✐♦♥✐♥❣ ♦❢ t❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❛♥❞ ❝♦♥✈❡rs✐♦♥❛❧❣♦r✐t❤♠s✳

❉✉r✐♥❣ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ ♣❧✉❣✲✐♥ ❝♦♠♠❡♥ts ✇❡r❡ r❡q✉❡st❡❞ ❞✐r❡❝t❧② ❢r♦♠ t❤❡♠♦❞❡❧✐♥❣ ❣r♦✉♣s ❛t t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡✳ ❍②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧❡rs ✇❡r❡ ❛❧s♦ ❛s❦❡❞ t♦ t❡st t❤❡♦✉t♣✉t ♦❢ t❤❡ ♣❧✉❣✲✐♥ ✇✐t❤ t❤❡✐r ♠♦❞❡❧s ❛♥❞ r❡✈✐❡✇ t❤❡ ♣❧✉❣✲✐♥ ❞✉r✐♥❣ ❞❡✈❡❧♦♣♠❡♥t✳ ❆s❢♦r ❛❧❧ ♣✐❡❝❡s ♦❢ s♦❢t✇❛r❡✱ ❛❧s♦ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❉❊❈❖ ✐s ♥♦t ✜♥✐s❤❡❞ ❜✉t ♦♣❡♥ t♦ ❜❡✐♥❣❝♦♥t✐♥✉❡❞✳ ❈♦♥✈❡rs✐♦♥ r♦✉t✐♥❡s ❢♦r ♦t❤❡r ♠♦❞❡❧s ❝♦✉❧❞ ❜❡ ✐♥t❡❣r❛t❡❞✱ ❛s ✇❡❧❧ ❛s ♥❡✇ ❜✐❛s❝♦rr❡❝t✐♦♥ s❝❤❡♠❡s✳

❚❤✐s ❞♦❝✉♠❡♥t ❞❡s❝r✐❜❡s t❤❡ ❞❛t❛ ❣❡♥❡r❛t❡❞ ✇✐t❤ t❤❡ ❈❖❙▼❖✲❈▲▼ ❞r✐✈❡♥ ❜② ❊❘❆✲■♥t❡r✐♠ ✭❙❡❝t✳ ✷✮✱ t❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ✉s❡❞ ✭❙❡❝t✳ ✸✮ ❛♥❞ t❤❡ ❡①tr❛❝t✐♦♥ ❛♥❞ ❝♦♥✈❡rs✐♦♥❛❧❣♦r✐t❤♠s ❢♦r t❤❡ ✐♥❞✐✈✐❞✉❛❧ ♠♦❞❡❧s ❛t t❤❡ r❡s❡❛r❝❤ ❙✐t❡s ✭❙❡❝t✳ ✹✮✳

✶❤tt♣s✿✴✴❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣✴✇✐❦✐✴●✐t❴✪✷✽s♦❢t✇❛r❡✪✷✾

✼

❈❤❛♣t❡r ✷

❉❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❝❧✐♠❛t❡

s✐♠✉❧❛t✐♦♥s

❆❧❧ s✐♠✉❧❛t✐♦♥s ❞❡s❝r✐❜❡❞ ✐♥ t❤✐s ❝❤❛♣t❡r ❤❛✈❡ ❜❡❡♥ ❝❛rr✐❡❞ ♦✉t ✉s✐♥❣ t❤❡ ❈❖❙▼❖✲❈▲▼r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧ ✭❘♦❝❦❡❧ ❡t ❛❧✳✱ ✷✵✵✽✮✱ ❢♦r ❛ ❞♦♠❛✐♥ ❝❡♥tr❡❞ ♦✈❡r ❊✉r♦♣❡✳ ■♥ t❤✐s❝❤❛♣t❡r✱ ❛ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❈❖❙▼❖✲❈▲▼ r❡❣✐♦♥❛❧ ♠♦❞❡❧ ✐s ♣r♦✈✐❞❡❞✱ ❢♦❧❧♦✇❡❞ ❜② ❞❡t❛✐❧s♦❢ t❤❡ s✐♠✉❧❛t✐♦♥s ♣❡r❢♦r♠❡❞✳

✷✳✶ ▼♦❞❡❧ ❉❡s❝r✐♣t✐♦♥

❚❤❡ ❈❖❙▼❖✲❈▲▼ ✭❈❈▲▼✮ ✐s ❛ st❛t❡✲♦❢✲t❤❡✲❛rt ♥♦♥❤②❞r♦st❛t✐❝ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✱t❤❛t ✐s t❤❡ ❝❧✐♠❛t❡ ✈❡rs✐♦♥ ♦❢ t❤❡ ❈❖❙▼❖ ♥✉♠❡r✐❝❛❧ ✇❡❛t❤❡r ♣r❡❞✐❝t✐♦♥ ♠♦❞❡❧ ✉s❡❞❜② t❤❡ ●❡r♠❛♥ ❲❡❛t❤❡r ❙❡r✈✐❝❡ ✭❉❲❉✮✳ ❈❈▲▼ ✐s ❞❡✈❡❧♦♣❡❞ ❢♦r ❝❧✐♠❛t❡ ♣✉r♣♦s❡s ❜②t❤❡ ❈▲▼✲❈♦♠♠✉♥✐t② ✭❤tt♣✿✴✴✇✇✇✳❝❧♠✲❝♦♠♠✉♥✐t②✳❡✉✴✮ ❛♥❞ ❢❡❛t✉r❡s ❛ s♦❢t✇❛r❡ ❛r❝❤✐✲t❡❝t✉r❡ ❛❧❧♦✇✐♥❣ ❢♦r ❝♦♠♣✉t❛t✐♦♥❛❧ ♣❛r❛❧❧❡❧✐s♠ ❛♥❞ s②st❡♠ ❡①t❡♥s✐❜✐❧✐t②✳ ■t ✐s s✉✐t❛❜❧❡❢♦r ❛ ❜r♦❛❞ s♣❡❝tr✉♠ ♦❢ ❛♣♣❧✐❝❛t✐♦♥s ❛❝r♦ss s❝❛❧❡s r❛♥❣✐♥❣ ❢r♦♠ ❤✉♥❞r❡❞s ♦❢ ♠❡tr❡s t♦t❤♦✉s❛♥❞s ♦❢ ❦✐❧♦♠❡tr❡s✳ ❚❤❡ ♠♦❞❡❧ ❝♦♠♣♦♥❡♥ts ✐♥❝❧✉❞❡ ❛♥ ❛t♠♦s♣❤❡r✐❝ ♠♦❞❡❧ ❞✐r❡❝t❧②❝♦✉♣❧❡❞ t♦ ❛ ❧❛♥❞✲s✉r❢❛❝❡✴s♦✐❧ ♠♦❞❡❧✱ ❛♥❞ ❛♥ ❛❡r♦s♦❧ ♠♦❞❡❧✳ ❙❡❛ s✉r❢❛❝❡ t❡♠♣❡r❛t✉r❡s♠✉st ❜❡ ♣r❡s❝r✐❜❡❞ ❛s ❛ ❜♦✉♥❞❛r② ❝♦♥❞✐t✐♦♥✳

✷✳✷ ❉❡s❝r✐♣t✐♦♥ ♦❢ ❙✐♠✉❧❛t✐♦♥s

✷✳✷✳✶ ❘❡❛♥❛❧②s✐s✲❢♦r❝❡❞ ❡✈❛❧✉❛t✐♦♥ r✉♥s

❚♦ ❝r❡❛t❡ ❛ ❝❧✐♠❛t♦❧♦❣② ❛♥❞ ❝♦♥t✐♥✉♦✉s t✐♠❡ s❡r✐❡s ♦❢ ❦❡② ❤②❞♦r♦❧♦❣✐❝❛❧ ✈❛r✐❛❜❧❡s✱ ❞♦✇♥✲s❝❛❧✐♥❣ s✐♠✉❧❛t✐♦♥s ❤❛✈❡ ❜❡❡♥ ❝❛rr✐❡❞ ♦✉t ✇✐t❤ t❤❡ ❈❈▲▼ ♦✈❡r t❤❡ ❊❯❘❖✲❈❖❘❉❊❳❞♦♠❛✐♥ ✭❋✐❣✳ ✷✳✶✮✱ ✇✐t❤ ❛ ❤♦r✐③♦♥t❛❧ r❡s♦❧✉t✐♦♥ ♦❢ ✵✳✶✶➦ ✭❛❜♦✉t ✶✷❦♠✮ ❛♥❞ s♣❛♥♥✐♥❣ t❤❡t✐♠❡ ♣❡r✐♦❞ ✶✾✼✾✲✷✵✶✺✳ ❆t t❤❡ ❞♦♠❛✐♥ ❧❛t❡r❛❧ ❜♦✉♥❞❛r✐❡s✱ t❤❡ ♠♦❞❡❧ ✐s ❝♦♥str❛✐♥❡❞ ❜②t❤❡ ❧❛t❡st ❣❡♥❡r❛t✐♦♥ ♦❢ r❡❛♥❛❧②s❡s ❢r♦♠ t❤❡ ❊✉r♦♣❡❛♥ ❈❡♥tr❡ ❢♦r ▼❡❞✐✉♠✲r❛♥❣❡ ❲❡❛t❤❡r❋♦r❡❝❛st✐♥❣✱ ❊❘❆✲■♥t❡r✐♠ ✭❉❡❡ ❡t ❛❧✳✱ ✷✵✶✶✮✱ ✇❤✐❝❤ ♣r♦✈✐❞❡ ✉♣❞❛t❡❞ ❧❛t❡r❛❧ ❜♦✉♥❞❛r②❝♦♥❞✐t✐♦♥s ❡✈❡r② ✻ ❤♦✉rs✳ ❚❤❡ ❡♥t✐r❡ ♣❡r✐♦❞ ❝♦✈❡r❡❞ ❜② t❤❡ ❊❘❆✲■♥t❡r✐♠ r❡❛♥❛❧②s✐s ❤❛s

✽

❜❡❡♥ ❞♦✇♥s❝❛❧❡❞ ✭✶✾✼✾✲✷✵✶✺✮✳ ■♥✐t✐❛❧ ❝♦♥❞✐t✐♦♥s✱ s❡❛ s✉r❢❛❝❡ t❡♠♣❡r❛t✉r❡✱ ❛♥❞ s❡❛✲✐❝❡❝♦✈❡r ❛❧s♦ ❝♦♠❡ ❢r♦♠ t❤❡ ❊❘❆✲■♥t❡r✐♠ r❡❛♥❛❧②s✐s✳

❋✐❣✉r❡ ✷✳✶✿ ❊❯❘❖✲❈❖❘❉❊❳ ❉♦♠❛✐♥✳ ❚❤❡ ❊❯❘❖✲❈❖❘❉❊❳ ❞♦♠❛✐♥ ✐s ❛ st❛♥❞❛r❞ r❡❢❡r❡♥❝❡❞♦♠❛✐♥ ❢♦r ❊✉r♦♣❡ ❞❡✜♥❡❞ ❛s ♣❛rt ♦❢ t❤❡ ❈❖❘❉❊❳ ❊①♣❡r✐♠❡♥t ✭❤tt♣✿✴✴✇✇✇✳❝♦r❞❡①✳♦r❣✴✮✳

❈♦♠♣✉t❛t✐♦♥❛❧ ❧✐♠✐t❛t✐♦♥s ♣r♦❤✐❜✐t s✐♠✉❧❛t✐♦♥ ❛t t❤❡ ❦✐❧♦♠❡tr❡✲s❝❛❧❡ ♦✈❡r s✉❝❤ ❛ ❧❛r❣❡❞♦♠❛✐♥ ❛♥❞ t✐♠❡ ♣❡r✐♦❞✳ ❆ ❤♦r✐③♦♥t❛❧ r❡s♦❧✉t✐♦♥ ♦❢ ✵✳✶✶➦ ❤❛s t❤✉s ❜❡❡♥ ❝❤♦s❡♥✱ ✇❤✐❝❤r❡♣r❡s❡♥ts s♦♠❡✇❤❛t ♦❢ ❛ ✏❜r❡❛❦t❤r♦✉❣❤✑ r❡s♦❧✉t✐♦♥ ❛♥❞ ❤❛s ❜❡❡♥ s❤♦✇♥ t♦ ❛❞❞ s✐❣♥✐✜❝❛♥t✈❛❧✉❡ t♦ ❝♦❛rs❡r ❣❧♦❜❛❧ ♠♦❞❡❧ ♦✉t♣✉t ❢♦r t❤❡ s✐♠✉❧❛t✐♦♥ ♦❢ ✭♥♦♥✲❝♦♥✈❡❝t✐✈❡✮ ♣r❡❝✐♣✐t❛t✐♦♥❡①tr❡♠❡s ✭❍❡✐❦❦✐❧ä✳ ❡t ❛❧✳✱ ✷✵✶✶✮✱ ♣❛rt✐❝✉❧❛r❧② ✐♥ ♠♦✉♥t❛✐♥♦✉s r❡❣✐♦♥s✱ ❛♥❞ ❝❛♥ ♠♦❞✉❧❛t❡t❤❡ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ s✐❣♥❛❧ ♦❢ ❝♦❛rs❡ r❡s♦❧✉t✐♦♥ ❣❧♦❜❛❧ ♠♦❞❡❧s ✭❚♦r♠❛ ❡t ❛❧✳✱ ✷✵✶✺✮✳

❚❤❡ s✐♠✉❧❛t✐♦♥s ❤❛✈❡ ❜❡❡♥ ❝❛rr✐❡❞ ♦✉t ✈✐❛ t❤r❡❡ s❡♣❛r❛t❡ ♠♦❞❡❧ r✉♥s✱ ❡❛❝❤ ♦❢ ✇❤✐❝❤ ✐s❝♦♥t✐♥✉♦✉s ❞✉r✐♥❣ t❤❡ t✐♠❡ ♣❡r✐♦❞ ✐♥❞✐❝❛t❡❞ ✐♥ ❚❛❜ ✷✳✶ ✭♠✐❞❞❧❡ ❝♦❧✉♠♥✮✳ ❘✉♥s ✶ ❛♥❞ ✸✇❡r❡ ❝❛rr✐❡❞ ♦✉t ❛t t❤❡ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥❀ r✉♥ ✷ ❤❛❞ ♣r❡✈✐♦✉s❧② ❜❡❡♥ ❝❛rr✐❡❞ ♦✉t ❜②t❤❡ ❈▲▼ ❝♦♠♠✉♥✐t②✱ ❛♥❞ ✇❡ ✉t✐❧✐s❡ t❤✐s t♦ ❦❡❡♣ ❝♦♠♣✉❛t✐♦♥❛❧ ❡①♣❡♥s❡ t♦ ❛ ♠✐♥✐♠✉♠✳❲✐t❤✐♥ ❡❛❝❤ ♠♦❞❡❧ r✉♥✱ ✐t ✐s ♥❡❝❡ss❛r② t♦ ❛❧❧♦✇ s✉✣❝✐❡♥t t✐♠❡ ❛❢t❡r ✐♥✐t✐❛❧✐s❛t✐♦♥ ❢♦r t❤❡s♣✐♥✲✉♣ ♦❢ s♦✐❧ ♠♦✐st✉r❡ ❛♥❞ s♦✐❧✲r❡❧❛t❡❞ ♣r♦❝❡ss❡s ✇✐t❤✐♥ t❤❡ ❤✐❣❤❡r r❡s♦❧✉t✐♦♥ ❈❈▲▼✳ ■♥❡❛❝❤ r✉♥✱ ❛ ♠✐♥✐♠✉♠ ♦❢ t✇♦ ♠♦♥t❤s ✐s ❛❧❧♦✇❡❞ ❢♦r s♣✐♥✲✉♣✳ ▼♦❞❡❧ ♦✉t♣✉t ❢r♦♠ t❤✐s ♣❡r✐♦❞✐s t❤✉s ♥♦t ✐♥❝❧✉❞❡❞ ✐♥ t❤❡ ✜♥❛❧ ❞❛t❛✱ ✐✳❡✳ t❤❡ ❞❛t❛ t♦ ❜❡ ✉s❡❞ ❢♦r r❡s❡❛r❝❤ ♣✉r♣♦s❡s✳ ❚❤❡✜♥❛❧ ❞❛t❛ t❤✉s ❝♦✈❡rs t❤❡ ♣❡r✐♦❞ ▼❛r❝❤ ✶✾✼✾ ✲ ❏✉❧② ✷✵✶✺✱ s✉♠♠❛r✐s❡❞ ✐♥ ❚❛❜ ✷✳✶ ✭r✐❣❤t❝♦❧✉♠♥✮✳ ❚❤❡ ♠♦❞❡❧ ♦✉t♣✉t ❝❛♥ ❜❡ ❡①t❡♥❞❡❞ ❜❡②♦♥❞ ❏✉❧② ✷✵✶✺ ✐❢ t❤❡r❡ ✐s ❛❣r❡❡♠❡♥t❛♠♦♥❣st ♣r♦❥❡❝t ♣❛rt♥❡rs ❛♥❞ ✐❢ r❡❛♥❛❧②s✐s ❞❛t❛ ❢♦r t❤❛t ♣❡r✐♦❞ ✐s ❛✈❛✐❧❛❜❧❡✳

❋♦r ♠♦st ❦❡② ❇■◆●❖ ✈❛r✐❛❜❧❡s✱ ✵✳✶✶➦ ❈❈▲▼ ♦✉t♣✉t ✐s ❛✈❛✐❧❛❜❧❡ ❛t ✸✲❤♦✉r❧② ❢r❡q✉❡♥❝②✳❚❤❡ ❡①❝❡♣t✐♦♥ t♦ t❤✐s ✐s ♣r❡❝✐♣✐t❛t✐♦♥✱ ✇❤✐❝❤ ✐s ❛✈❛✐❧❛❜❧❡ ❛t ❤♦✉r❧② ❢r❡q✉❡♥❝②✳ ❇■◆●❖✈❛r✐❛❜❧❡s ❛✈❛✐❧❛❜❧❡ ❛♥❞ t❤❡✐r t❡♠♣♦r❛❧ ❢r❡q✉❡♥❝✐❡s ❛r❡ s✉♠♠❛r✐s❡❞ ✐♥ ❚❛❜❧❡ ✷✳✷✳

✾

▼♦❞❡❧ ❘✉♥ P❡r✐♦❞ ♦❢ ❘✉♥ ❉❛t❛ ❆✈❛✐❧❛❜❧❡✶ ✵✶✳✵✶✳✶✾✼✾ ✲ ✵✶✳✵✹✳✶✾✽✾ ✵✶✳✵✸✳✶✾✼✾ ✲ ✵✶✳✵✸✳✶✾✽✾

✷ ✵✶✳✵✶✳✶✾✽✾ ✲ ✵✶✳✵✶✳✷✵✵✾ ✵✶✳✵✸✳✶✾✽✾ ✲ ✵✶✳✶✷✳✷✵✵✾

✸ ✵✶✳✵✾✳✷✵✵✽ ✲ ✵✶✳✵✽✳✷✵✶✺ ✵✶✳✶✷✳✷✵✵✾ ✲ ✵✶✳✵✽✳✷✵✶✺

❚❛❜❧❡ ✷✳✶✿ ▲✐st ♦❢ ♠♦❞❡❧ r✉♥s✳

✷✳✷✳✷ ❍✐❣❤✲r❡s♦❧✉t✐♦♥ ✭t❡st✮ s✐♠✉❧❛t✐♦♥s ♦❢ ❡①tr❡♠❛❧ ❡♣✐s♦❞❡s

❚❤❡♦r② ❛♥❞ ▼❡t❤♦❞s

❊①tr❡♠❛❧ ✇❡❛t❤❡r ♣❛tt❡r♥s ❛♥❞ ✐♥❞✐✈✐❞✉❛❧ ❡✈❡♥ts ♦❢ ❤②❞r♦❧♦❣✐❝❛❧ s✐❣♥✐✜❝❛♥❝❡ s❤❛❧❧ ❜❡✐❞❡♥t✐✜❡❞ ❢r♦♠ t❤❡ ✵✳✶✶➦ ❈❈▲▼ s✐♠✉❧❛t✐♦♥s✱ ❢♦r ❡❛❝❤ ♦❢ t❤❡ ✻ r❡s❡❛r❝❤ s✐t❡s✳ ❚❤❡s❡ s❤❛❧❧❜❡ s✉❜❥❡❝t❡❞ t♦ ♠♦r❡ ❞❡t❛✐❧❡❞ ❛♥❛❧②s✐s✳ ■♥ t❤❡ ❝❛s❡ ♦❢ ❡①tr❡♠❡ ♣r❡❝✐♣✐t❛t✐♦♥ ❡✈❡♥ts✱ ✇❤✐❝❤❛r❡ ❛ ♣❤❡♥♦♠❡♥♦♥ ✇✐t❤ ❤✐❣❤ s♣❛t✐❛❧ ✈❛r✐❛❜✐❧✐t②✱ t❤✐s ✐♥✈♦❧✈❡s ❢✉rt❤❡r ❞②♥❛♠✐❝ ❞♦✇♥s❝❛❧✐♥❣♦❢ t❤❡ ✐❞❡♥t✐✜❡❞ ❡✈❡♥ts ✉♣ t♦ ❛ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ r❡s♦❧✉t✐♦♥ ♦❢ ✵✳✵✷➦ ✭✷✳✷ ❦♠✮ t♦ ♣r♦✲✈✐❞❡ ❜❡tt❡r r❡♣r❡s❡♥t❛t✐♦♥ ♦❢ t❤❡ ❞②♥❛♠✐❝s ❞r✐✈✐♥❣ ❛♥② ❝❤❛♥❣❡s ✐♥ ❤②❞r♦❧♦❣✐❝❛❧ ❡①tr❡♠❡s❛♥❞ ❤❡♥❝❡ ❛ ♠♦r❡ ❞❡t❛✐❧❡❞ ✐♥♣✉t ❢♦r t❤❡ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✳ ■♥ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣s✐♠✉❧❛t✐♦♥s✱ ❞❡❡♣ ❝♦♥✈❡❝t✐✈❡ ♣r♦❝❡ss❡s ❝❛♥ ❜❡ ❡①♣❧✐❝✐t❧② s✐♠✉❧❛t❡❞ ❜② t❤❡ ♠♦❞❡❧✱ ✇❤❡r❡t❤❡② ❤❛✈❡ t♦ ❜❡ ♦t❤❡r✇✐s❡ ♣❛r❛♠❡tr✐③❡❞ ✐♥ ❧♦✇❡r✲r❡s♦❧✉t✐♦♥ s✐♠✉❧❛t✐♦♥s✱ ✐✳❡✳ ♦✉r ✵✳✶✶➦❈❈▲▼ ✐♥t❡❣r❛t✐♦♥✳ ❚❤❡ ❢✉rt❤❡r ❞♦✇♥s❝❛❧✐♥❣ t♦ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ r❡s♦❧✉t✐♦♥ ✐s ❛ ❦❡②st❡♣✱ ❛s r❡❝❡♥t st✉❞✐❡s ❤❛✈❡ s❤♦✇♥ t❤❛t ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ r❡s♦❧✉t✐♦♥ ✐s ❡ss❡♥t✐❛❧ t♦❛❝❝✉r❛t❡❧② ❝❛♣t✉r❡ t❤❡ r❡s♣♦♥s❡ ♦❢ ❝♦♥✈❡❝t✐✈❡ ♣r❡❝✐♣✐t❛t✐♦♥ ❡①tr❡♠❡s t♦ ❝❧✐♠❛t✐❝ ❝❤❛♥❣❡s✭❑❡♥❞♦♥ ❡t ❛❧✳✱ ✷✵✶✹❀ ❇❛♥ ❡t ❛❧✳✱ ✷✵✶✺✮✱ ✇❤✐❝❤ ❝❛♥ ❜❡ ❤✐❣❤❧② ♥♦♥❧✐♥❡❛r ✭▼❡r❡❞✐t❤ ❡t ❛❧✳✱✷✵✶✺✮✳

❚❤❡ ✐ss✉❡ ♦❢ s♣❛t✐❛❧ s♣✐♥✉♣ ✲ ♠❡❛♥✐♥❣ t❤❡ ❞✐st❛♥❝❡ ❢r♦♠ t❤❡ ❧❛t❡r❛❧ ❜♦✉♥❞❛r✐❡s ❛t ✇❤✐❝❤✜♥❡✲s❝❛❧❡ ❢❡❛t✉r❡s ❝❛♥ ❜❡ ❛❝❤✐❡✈❡❞ ✲ ✐s ❛♥ ✐♠♣♦rt❛♥t ❝♦♥s✐❞❡r❛t✐♦♥ ✇❤❡♥ ❞❡s✐❣♥✐♥❣ r❡✲❣✐♦♥❛❧ ❞♦✇♥s❝❛❧✐♥❣ ❡①♣❡r✐♠❡♥ts✳ ❋♦r ❝♦♥s✐st❡♥❝②✱ ✇❡ ✐♥t❡♥❞ t♦ ✉s❡ ❛ ❝♦♠♠♦♥ ❞♦♠❛✐♥ ❢♦r❛❧❧ ❤✐❣❤✲r❡s♦❧✉t✐♦♥ s✐♠✉❧❛t✐♦♥s ❛t ❡❛❝❤ r❡s❡❛r❝❤ s✐t❡✳ ❆s t❤❡ ❧❛r❣❡✲s❝❛❧❡ ❢♦r❝✐♥❣ ❜❡❤✐♥❞✐♥❞✐✈✐❞✉❛❧ ❡①tr❡♠❡s ❝❛♥ ❝♦♠❡ ❢r♦♠ ❛♥② s✐❞❡ ♦❢ t❤❡ ❞♦♠❛✐♥✱ ✇❡ ❝❡♥tr❡ ♦✉r ❤✐❣❤✲r❡s♦❧✉t✐♦♥❞♦♠❛✐♥s ♦✈❡r ❡❛❝❤ r❡s❡❛r❝❤ s✐t❡ ❛♥❞ ✉s❡ ❛ ✷✵✶ ① ✷✵✶ ❣r✐❞✱ ✇✐t❤ ✺✵ ✈❡rt✐❝❛❧ ❧❡✈❡❧s✳ ❚❤✐s❛❧❧♦✇s ❛t ❧❡❛st ✶✵✵ ❣r✐❞✲❧❡♥❣t❤s ❜❡t✇❡❡♥ t❤❡ ❧❛t❡r❛❧ ❜♦✉♥❞❛r✐❡s ❛♥❞ t❤❡ ❝❡♥tr❡ ♦❢ ❡❛❝❤r❡s❡❛r❝❤ s✐t❡✳ ❇r✐ss♦♥ ❡t ❛❧✳ ✭✷✵✶✺✮ ✐♥✈❡st✐❣❛t❡❞ t❤❡ ✐♠♣❛❝t ♦❢ ❞♦♠❛✐♥ s✐③❡ ♦♥ t❤❡ s✐♠✉❧❛✲t✐♦♥ ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ✐♥ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ ♠♦❞❡❧s✱ ✉s✐♥❣ ❛ ❤♦r✐③♦♥t❛❧ ❣r✐❞ s♣❛❝✐♥❣ ♦❢✸ ❦♠✳ ❚❤❡② ❝♦♥❝❧✉❞❡❞ t❤❛t ❛ s♣❛t✐❛❧ s♣✐♥✉♣ ♦❢ ❛t ❧❡❛st ✹✵ ❣r✐❞ ❝❡❧❧s ✐s ♥❡❝❡ss❛r② ❢♦r t❤❡r❡❛❧✐st✐❝ s✐♠✉❧❛t✐♦♥ ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ♣❛tt❡r♥s✳ ❋♦r ♠♦r❡ ❞❡t❛✐❧❡❞ ❞✐s❝✉ss✐♦♥ ♦❢ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ ♠♦❞❡❧❧✐♥❣ t❤❡ r❡❛❞❡r ✐s r❡❢❡rr❡❞ t♦ Pr❡✐♥ ❡t ❛❧✳ ✭✷✵✶✺✮✳

❚❤❡ ❙✐♠✉❧❛t✐♦♥s

❲✐t❤ t❤❡ ❛✐❞ ♦❢ t❤❡ q✉❡st✐♦♥♥❛✐r❡ r❡s♣♦♥s❡s ❢r♦♠ ❡❛❝❤ r❡s❡❛r❝❤ s✐t❡✱ ♦♥❡ ❡①tr❡♠❡ ♣r❡✲❝✐♣✐t❛t✐♦♥ ❡✈❡♥t ❤❛s ❜❡❡♥ ✐❞❡♥t✐✜❡❞ ❢r♦♠ t❤❡ ✵✳✶✶➦✲❈❈▲▼ s✐♠✉❧❛t✐♦♥s ❢♦r ❡❛❝❤ s✐t❡

✶✵

❱❛r✐❛❜❧❡❉❡s❝r✐♣t✐♦♥

❱❛r✐❛❜❧❡■❉

❋r❡q✉❡♥❝②

❚✐♠

❡▼❡t❤♦❞✯

▼✐♥✴▼❛①❸

❚♦t❛❧❈❧♦✉❞❋r❛❝t✐♦♥

❝❧t

✸✲❤r✱❞❛②

■♥st❛♥t❛♥❡♦✉s

❉❛✐❧②

◆❡❛r✲❙✉r❢❛❝❡❘❡❧❛t✐✈❡❍✉♠✐❞✐t②

❤✉rs

✸✲❤r✱❞❛②

■♥st❛♥t❛♥❡♦✉s

❉❛✐❧②

◆❡❛r✲❙✉r❢❛❝❡❙♣❡❝✐✜❝❍✉♠✐❞✐t②

❤✉ss

✸✲❤r✱❞❛②

■♥st❛♥t❛♥❡♦✉s

❉❛✐❧②

Pr❡❝✐♣✐t❛t✐♦♥

♣r

✶✲❤r✱✸✲❤r✱❞❛②

▼❡❛♥

❉❛✐❧②

❙✉r❢❛❝❡❆✐rPr❡ss✉r❡

♣s

✸✲❤r✱❞❛②

■♥st❛♥t❛♥❡♦✉s

❉❛✐❧②

❙❡❛

▲❡✈❡❧Pr❡ss✉r❡

♣s❧

✸✲❤r✱❞❛②

■♥st❛♥t❛♥❡♦✉s

❉❛✐❧②

❙✉r❢❛❝❡❉♦✇

♥✇❡❧❧✐♥❣▲♦♥❣✇

❛✈❡❘❛❞✐❛t✐♦♥

r❧❞s

✸✲❤r✱❞❛②

▼❡❛♥

❉❛✐❧②

❙✉r❢❛❝❡❉♦✇

♥✇❡❧❧✐♥❣❙❤♦rt✇❛✈❡❘❛❞✐❛t✐♦♥

rs❞s

✸✲❤r✱❞❛②

▼❡❛♥

❉❛✐❧②

◆❡❛r✲❙✉r❢❛❝❡❲✐♥❞❙♣❡❡❞

s❢❝❲

✐♥❞

✸✲❤r✱❞❛②

■♥st❛♥t❛♥❡♦✉s

❉❛✐❧②

◆❡❛r✲❙✉r❢❛❝❡❆✐r❚❡♠

♣❡r❛t✉r❡

t❛s

✸✲❤r✱❞❛②

■♥st❛♥t❛♥❡♦✉s

❉❛✐❧②

◆❡❛r✲❙✉r❢❛❝❡❉❡✇

P♦✐♥t❚❡♠

♣❡r❛t✉r❡

t❞♣s

✸✲❤r✱❞❛②

■♥st❛♥t❛♥❡♦✉s

❉❛✐❧②

❊❛st✇❛r❞◆❡❛r✲❙✉r❢❛❝❡❲✐♥❞

✉❛s

✸✲❤r✱❞❛②

■♥st❛♥t❛♥❡♦✉s

❉❛✐❧②

◆♦rt❤✇❛r❞◆❡❛r✲❙✉r❢❛❝❡❲✐♥❞

✈❛s

✸✲❤r✱❞❛②

■♥st❛♥t❛♥❡♦✉s

❉❛✐❧②

❚❛❜❧❡

✷✳✷✿❇■◆

●❖

❱❛r✐❛❜❧❡s✳

✯❚✐♠

❡♠❡t❤♦❞r❡❢❡rs

t♦t❤❡❤✐❣❤❡st❢r❡q✉❡♥

❝②❞❛t❛❀

❞❛✐❧②

♠❡❛♥s❛r❡❝❛❧❝✉❧❛t❡❞❜②❛✈❡r❛❣

✐♥❣t❤❡❤✐❣❤❡st

❢r❡q✉❡♥

❝②❞❛t❛✳

❸❱❛r✐❛❜❧❡

■❉s❢♦r❞❛✐❧②

♠✐♥✴♠

❛①❛r❡❢♦r♠

❡❞❜②❛♣

♣❡♥

❞✐♥❣❡✐t❤❡r

✬♠✐♥✬♦r

✬♠❛①

✬t♦

t❤❡✈❛r✐❛❜

❧❡■❉

✱❡✳❣✳

❝❧t❬♠✐♥⑤♠

❛①❪✳

❆✏❞❛②

✑✐s

❞❡✜

♥❡❞

❛s✷✹

✲❤♦✉

rs❢r♦♠

✵✵✿✵✵❯❚❈✳❆❧❧t✐♠❡✲st❛♠

♣s✐♥

t❤❡♦✉

t♣✉t❞❛t❛❛r❡✐♥

❯❚❈✳

✶✶

✭❡①❝❧✉❞✐♥❣ ❈②♣r✉s✮✱ ❛♥❞ ❤❛s ❜❡❡♥ ❢✉rt❤❡r ❞♦✇♥s❝❛❧❡❞ t♦ ✵✳✵✷➦ r❡s♦❧✉t✐♦♥ ✭✷✳✷ ❦♠✮ ✇✐t❤t❤❡ ❈❈▲▼✳ ❚❤❡ ❡✈❡♥ts ❢♦r t❤❡s❡ t❡st✲s✐♠✉❧❛t✐♦♥s ✇❡r❡ s✉❜❥❡❝t✐✈❡❧② ✐❞❡♥t✐✜❡❞ ❢r♦♠ t❤❡✵✳✶✶➦ ❞❡❣r❡❡ ♠♦❞❡❧ ♦✉t♣✉t✱ ❜❛s❡❞ ♦♥ t❤❡ q✉❡st✐♦♥♥❛✐r❡ ❞❡s❝r✐♣t✐♦♥s ♦❢ ♣❛st ❡①tr❡♠❡s ❛t❡❛❝❤ s✐t❡ ❛♥❞ t❤❡ ✵✳✶✶➦ ♠♦❞❡❧❧❡❞ ♣r❡❝✐♣✐t❛t✐♦♥✳

❚❤❡ ♦✉t♣✉t ✈❛r✐❛❜❧❡s ❛r❡ ❛t ❛♥ ❤♦✉r❧② ❢r❡q✉❡♥❝② ❛♥❞ ❤❛✈❡ ❜❡❡♥ ♠❛❞❡ ❛✈❛✐❧❛❜❧❡ ❢♦r t❤❡s❛♠❡ ♣❛r❛♠❡t❡rs ❛s s❤♦✇♥ ✐♥ ❚❛❜❧❡ ✷✳✷✱ t❤♦✉❣❤ t❤❡r❡ ❛r❡ ♦❜✈✐♦✉s❧② ♥♦ ❞❛✐❧② ♠✐♥✴♠❛①✬s♣r♦✈✐❞❡❞✳ ❆❧❧ ❞❛t❛ ❛r❡ ❛✈❛✐❧❛❜❧❡ t❤r♦✉❣❤ t❤❡ ❋r❡✈❛ ❉❊❈❖ ♣❧✉❣✐♥✱ ❛♥❞ ❛r❡ ❜❡st ❛❝❝❡ss❡❞❜② s❡❧❡❝t✐♥❣ ✏t❡st✲❡✈❡♥ts✑ ✐♥ t❤❡ ❡①♣❡r✐♠❡♥t ✜❡❧❞ ❛♥❞ t❤❡♥ t❤❡ ❛♣♣r♦♣r✐❛t❡ r❡s❡❛r❝❤ s✐t❡✭✐✳❡✳ ❇❛❞❛❧♦♥❛✱ ❇❡r❣❡♥✱ ❚❛❣✉s✱ ❱❡❧✉✇❡✱ ❲✉♣♣❡r✮ ✐♥ t❤❡ ♣r♦❞✉❝t ✜❡❧❞✳ ❆s ♦❢ ✶✵✲✵✻✲✷✵✶✻✱t❤❡ t❡st✲❡✈❡♥ts ❢♦r t❤❡ ❚❛❣✉s r❡s❡❛r❝❤ s✐t❡ ❛r❡ ♥♦t ②❡t ❛✈❛✐❧❛❜❧❡ t❤r♦✉❣❤ t❤❡ ❉❊❈❖ ♣❧✉❣✐♥✳❲❡ ❤♦♣❡ t♦ r❡♠❡❞② t❤✐s ❛s❛♣✱ ❛❢t❡r ❝❧❛r✐❢②✐♥❣ t❤❡ ✐♥♣✉t r❡q✉✐r❡♠❡♥ts ♦❢ t❤❡ ♣❛rt✐❝✉❧❛r❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧ ❜❡✐♥❣ ✉s❡❞ ❢♦r t❤❡ s✐t❡✳

Pr♦❥❡❝t ♣❛rt♥❡rs ❛r❡ ❛s❦❡❞ t♦ ❞♦✇♥❧♦❛❞ t❤❡ ❤✐❣❤✲r❡s♦❧✉t✐♦♥ t❡st✲s✐♠✉❧❛t✐♦♥s ❢♦r t❤❡✐r r❡✲s♣❡❝t✐✈❡ r❡s❡❛r❝❤ s✐t❡s ❛♥❞ t❡st t❤❡ ❞❛t❛ ♦♥ t❤❡✐r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✳ ❋❡❡❞❜❛❝❦ s❤♦✉❧❞t❤❡♥ ❜❡ ♣r♦✈✐❞❡❞ ❛s s♦♦♥ ❛s ♣♦ss✐❜❧❡✳ ❚❤❡ ❡❛r❧✐❡r ❢❡❡❞❛❝❦ ✐s r❡❝❡✐✈❡❞✱ t❤❡ ♠♦r❡ ❧✐❦❡❧② t❤❛t❛♥② ❝♦♥❝❡r♥s r❛✐s❡❞ ❝❛♥ ❜❡ s❛t✐s❢❛❝t♦r✐❧② ❛❞❞r❡ss❡❞✳ ❋❡❡❞❜❛❝❦ ♦♥ t❤❡ t❡st✲s✐♠✉❧❛t✐♦♥s ✐s❜❡st ♣r♦✈✐❞❡❞ t♦ ❊❞♠✉♥❞ ▼❡r❡❞✐t❤ ✭❡❞♠✉♥❞✳♠❡r❡❞✐t❤❅♠❡t✳❢✉✲❜❡r❧✐♥✳❞❡✮✳

✷✳✷✳✸ ▼✐❑❧✐♣ ❢♦r❝❡❞ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s

❚❤❡ r❡❧❛t✐✈❡❧② ♥❡✇ ✜❡❧❞ ♦❢ ❞❡❝❛❞❛❧ ❝❧✐♠❛t❡ ♣r❡❞✐❝t✐♦♥✱ ❡✳❣✳ ❙♠✐t❤ ❡t ❛❧✳ ✭✷✵✵✼✮✱ ❛✐♠st♦ s✐♠✉❧❛t❡ ❜♦t❤ t❤❡ ❝❧✐♠❛t❡ r❡s♣♦♥s❡ t♦ ❢✉t✉r❡ ❛♥t❤r♦♣♦❣❡♥✐❝ ❢♦r❝✐♥❣ ❛♥❞ t❤❡ ❢✉t✉r❡❡✈♦❧✉t✐♦♥ ✭❢r♦♠ t❤❡ ♣r❡s❡♥t✮ ♦❢ t❤❡ ❝❧✐♠❛t❡ ❞✉❡ t♦ ✐♥t❡r♥❛❧ ❝❧✐♠❛t❡ ✈❛r✐❛❜✐❧✐t② ✭▼❛r♦t③❦❡❡t ❛❧✳✱ ✷✵✶✻✮✳ ❚❤✐s ❞✐✛❡rs ❢r♦♠ t❤❡ ❛♣♣r♦❛❝❤ t❛❦❡♥ ✐♥ ❝❧✐♠❛t❡ ♣r♦❥❡❝t✐♦♥s✱ ❡✳❣✳ t❤❡ ❈▼■P✺♣r♦❥❡❝t ✭❚❛②❧♦r ❡t ❛❧✳✱ ✷✵✶✷✮✱ ✇❤❡r❡ t❤❡ ❢♦❝✉s ✐s ♦♥ t❤❡ r❡s♣♦♥s❡ ♦❢ t❤❡ ❝❧✐♠❛t❡ t♦ ❛♥✲t❤r♦♣♦❣❡♥✐❝ ❢♦r❝✐♥❣ ❛♥❞ t❤❡ ✐♠♣❛❝ts ♦❢ ✐♥t❡r♥❛❧ ❝❧✐♠❛t❡ ✈❛r✐❛❜✐❧✐t② ❛r❡ ✭s✉♣♣♦s❡❞ t♦ ❜❡✮♥✉❧❧✐✜❡❞ ✈✐❛ ♠✉❧t✐✲❞❡❝❛❞❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧ ✐♥t❡❣r❛t✐♦♥s✳ ❚❤❡ ❡❛rt❤ s②st❡♠ ♠♦❞❡❧s ✭❊❙▼s✮✉s❡❞ ✐♥ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥ s②st❡♠s ❛r❡ ✐♥✐t✐❛❧✐③❡❞ ✇✐t❤ ❛♥ ♦❜s❡r✈❡❞ st❛t❡ ♦❢ t❤❡ ❝❧✐♠❛t❡s②st❡♠✱ ✐✳❡✳ ♦❝❡❛♥✱ ❛t♠♦s♣❤❡r❡✱ s♦✐❧✱ ✐❝❡✱ ❡t❝✳ ❙❦✐❧❧ ✐♥ ♣r❡❞✐❝t✐♥❣ ✐♥t❡r♥❛❧ ❝❧✐♠❛t❡ ✈❛r✐❛❜✐❧✲✐t② ♦♥ ❛ ❞❡❝❛❞❛❧ s❝❛❧❡ ✐s ❞❡r✐✈❡❞ ❢r♦♠ t❤❡ ❧♦♥❣✲t❡r♠ ♠❡♠♦r② ✭✐✳❡✳ s❡♥s✐t✐✈✐t② t♦ t❤❡ ✐♥✐t✐❛❧st❛t❡✮ ♦❢ ❝❡rt❛✐♥ ❝♦♠♣♦♥❡♥ts ♦❢ t❤❡ ❝❧✐♠❛t❡ s②st❡♠✱ ♣r❡❞♦♠✐♥❛♥t❧② t❤❡ ♦❝❡❛♥✳ ❆s s✉❝❤✱❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s ✭✉♥❧✐❦❡ ❝❧✐♠❛t❡ ♣r♦❥❡❝t✐♦♥s✮ ❛r❡ r❡❧✐❛♥t ♦♥ ❛ ❤✐❣❤✲q✉❛❧✐t② ✐♥✐t✐❛❧✐③❛t✐♦♥♦❢ t❤❡ ❊❙▼ ❢♦r t❤♦s❡ ❝♦♠♣♦♥❡♥ts ✇❤✐❝❤ ❡①❤✐❜✐t ❧♦♥❣✲t❡r♠ ♠❡♠♦r②✳

❚❤❡ ▼✐❑❧✐♣ ♣r♦❥❡❝t ✭❤tt♣✿✴✴✇✇✇✳❢♦♥❛✲♠✐❦❧✐♣✳❞❡✮ ✐s ❢✉♥❞❡❞ ❜② t❤❡ ●❡r♠❛♥ ▼✐♥✐str②❢♦r ❊❞✉❝❛t✐♦♥ ❛♥❞ ❘❡s❡❛r❝❤ ✇✐t❤ t❤❡ ❛✐♠ ♦❢ ❞❡✈❡❧♦♣✐♥❣ ❛ ✇♦r❧❞✲❝❧❛ss ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s②st❡♠✳ ❚❤❡ ▼✐❑❧✐♣ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥ s②st❡♠ ✐s ❜❛s❡❞ ♦♥ t❤❡ ▼❛① P❧❛♥❝❦ ■♥st✐t✉t❡✬s❡❛rt❤ s②st❡♠ ♠♦❞❡❧✱ ▼P■✲❊❙▼✱ ❛♥❞ ❤❛s ❛♥ ❛t♠♦s♣❤❡r✐❝ ❤♦r✐③♦♥t❛❧ r❡s♦❧✉t✐♦♥ ♦❢ ❚✻✸✭✶✳✽✼✺➦✮✳ ❚❤❡ ✜rst ♣❤❛s❡ ♦❢ t❤❡ ▼✐❑❧✐♣ ♣r♦❥❡❝t s❤♦✇❡❞ s✐❣♥✐✜❝❛♥t s❦✐❧❧ ✭❡✳❣✳ ▼✉❡❧❧❡r❡t ❛❧✳ ✭✷✵✶✷✮✱ P♦❤❧♠❛♥♥ ❡t ❛❧✳ ✭✷✵✶✸✮✮ ✐♥ t❤❡ ▼✐❑❧✐♣ s②st❡♠ ❜❛s❡❞ ♦♥ t❤❡ ❡✈❛❧✉❛t✐♦♥♦❢ ❞❡❝❛❞❛❧ ❤✐♥❞❝❛st s✐♠✉❧❛t✐♦♥s ✐♥✐t✐❛❧✐③❡❞ ②❡❛r❧② ❢r♦♠ ✶✾✻✵✲✷✵✶✵✳ ■♥ ❛❞❞✐t✐♦♥ t♦ t❤✐s✱

✶✷

t❤❡ ▼✐❑❧✐♣ s②st❡♠ ✇❛s ❛❧s♦ ✉s❡❞ ❢♦r ❢✉t✉r❡ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥ r✉♥♥✐♥❣ ✉♣ t♦ ✷✵✷✹✱ ❢♦r✶✵ r❡❛❧✐③❛t✐♦♥s ❛♥❞ ✇✐t❤ ❛♥ ✐♥✐t✐❛❧✐③❛t✐♦♥ ✐♥ ✷✵✶✺✳ ▼♦❞✉❧❡ ❈ ♦❢ t❤❡ ✜rst ♣❤❛s❡ ♦❢ t❤❡▼✐❑❧✐♣ ♣r♦❥❡❝t ✇❛s ❞❡✈♦t❡❞ t♦ t❤❡ r❡❣✐♦♥❛❧✐s❛t✐♦♥ ♦❢ t❤❡ ▼✐❑❧✐♣ ❣❧♦❜❛❧ ♠♦❞❡❧ ♦✉t♣✉t✱✈✐❛ ❞②♥❛♠✐❝❛❧ ❞♦✇♥s❝❛❧✐♥❣✳ ❚❤✐s ✇❛s ❝❛rr✐❡❞ ♦✉t ♦✈❡r ❛ ❊✉r♦♣❡❛♥ ❞♦♠❛✐♥ ❢♦r t❤❡ ❡♥t✐r❡▼✐❑❧✐♣ ♣❡r✐♦❞ ✭✶✾✻✵✲✷✵✷✹✮ ✉s✐♥❣ t❤❡ ❈❈▲▼ ❛t ✵✳✹✹➦ r❡s♦❧✉t✐♦♥✳

❋♦r t❤❡ ❇■◆●❖ ♣r♦❥❡❝t✱ t❤❡ ❋❯❇ ❤❛✈❡ ❢✉rt❤❡r ❞②♥❛♠✐❝❛❧❧② ❞♦✇♥s❝❛❧❡❞ ❢♦✉r r❡❛❧✐③❛t✐♦♥s♦❢ t❤❡ ❢✉t✉r❡ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s ✭✷✵✶✺✲✷✵✷✹✮ ❢r♦♠ ✵✳✹✹➦ t♦ ✵✳✶✶➦ ✉s✐♥❣ t❤❡ ❈❈▲▼✳ ❚♦r❡❞✉❝❡ ❝♦♠♣✉t❛t✐♦♥❛❧ ❡①♣❡♥s❡✱ t❤✐s ❤❛s ❜❡❡♥ ❝❛rr✐❡❞ ♦✉t ♦✈❡r t✇♦ s✉❜✲❞♦♠❛✐♥s ✭❋✐❣✳ ✷✳✷✮✿

✭✶✮ ◆❲✲❊❯❘✲✶✶✿ ✇❤✐❝❤ ❝♦♥t❛✐♥s t❤❡ r❡s❡❛r❝❤ s✐t❡s ❛t ❇❡r❣❡♥✱ ❱❡❧✉✇❡ ❛♥❞❲✉♣♣❡r✳✭✷✮ ■❇❊❘■❆✲✶✶✿ ✇❤✐❝❤ ❝♦♥t❛✐♥s t❤❡ r❡s❡❛r❝❤ s✐t❡s ❛t ❚❛❣✉s ❛♥❞ ❇❛❞❛❧♦♥❛✳

❚❤❡ s❛♠❡ ✈❛r✐❛❜❧❡s ❛♥❞ ❢r❡q✉❡♥❝✐❡s ❛s ❧✐st❡❞ ✐♥ ❚❛❜❧❡ ✷✳✷ ❛r❡ ❛✈❛✐❧❛❜❧❡ ❛♥❞ ❛r❡ ❞♦✇♥❧♦❛❞✲❛❜❧❡ ✈✐❛ t❤❡ ♦♥❧✐♥❡ ❉❊❈❖ ♣❧✉❣✐♥✳

❋✐❣✉r❡ ✷✳✷✿ ❇■◆●❖ ❉♦♠❛✐♥s ❢♦r ▼✐❑❧✐♣ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥s ✭✷✵✶✺✲✷✵✷✹✮✳ ❚❤❡ ❛r❡❛❝♦✈❡r❡❞ ❜② t❤❡ ▼✐❑❧✐♣ ✵✳✹✹➦ r❡❣✐♦♥❛❧✐s❛t✐♦♥ ✐s s❤♦✇♥ ✐♥ ❝♦❧♦✉r✱ ✇✐t❤ r❡❞ r❡♣r❡s❡♥t✐♥❣ t❤❡ ✵✳✹✹➦❧❛♥❞ ♠❛s❦ ❛♥❞ ❜❧✉❡ t❤❡ s❡❛✳ ❚❤❡ ■❇❊❘■❆✲✶✶ ❛♥❞ ◆❲✲❊❯❘✲✶✶ ❞♦♠❛✐♥s ♦❢ t❤❡ ❇■◆●❖ ♣r♦❥❡❝t❛r❡ t❤❡♥ ♠❛r❦❡❞ ✐♥ ❣r❡❡♥ ❛♥❞ ❝②❛♥✳

✶✸

❈❤❛♣t❡r ✸

❇✐❛s ❝♦rr❡❝t✐♦♥

❚②♣✐❝❛❧❧②✱ s②st❡♠❛t✐❝ ❞✐✛❡r❡♥❝❡s ❜❡t✇❡❡♥ t❤❡ ❝❧✐♠❛t❡ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥ ❛♥❞ ♦❜s❡r✈❡❞❞❛t❛ ❡①✐st✳ ❚❤❡ ♠♦st ♣r♦♠✐♥❡♥t ❞✐✛❡r❡♥❝❡ ✐s ❛ s❤✐❢t ✐♥ t❤❡ ♠❡❛♥ ✈❛❧✉❡✳ ❈❧✐♠❛t❡ ♠♦❞❡❧s✐♠✉❧❛t✐♦♥s ❛r❡ t❤✉s t②♣✐❝❛❧❧② ♣♦st✲♣r♦❝❡ss❡❞ ✉s✐♥❣ ❛ ❜✐❛s ❝♦rr❡❝t✐♦♥✳ ❚❤✐s ❝❤❛♣t❡r ❛✐♠s❛t ♦✉t❧✐♥✐♥❣ t❤✐s ❦✐♥❞ ♦❢ ♣♦st✲♣r♦❝❡ss✐♥❣✳ ❚✇♦ ❞✐✛❡r❡♥t ❜✐❛s ❝♦rr❡❝t✐♦♥ ♠❡t❤♦❞s ❛r❡♣r❡s❡♥t❡❞ ✐♥ t❤✐s ❝❤❛♣t❡r✿ ❙❡❛s♦♥❛❧ ●❡♥❡r❛❧✐③❡❞ ▲✐♥❡❛r ▼♦❞❡❧ ♠❡t❤♦❞ ❛♥❞ ❈✉♠✉❧❛t✐✈❡❉✐str✐❜✉t✐♦♥ ❋✉♥❝t✐♦♥ ❚r❛♥s❢♦r♠ ♠❡t❤♦❞✳

❚❤❡ ✜rst ❙❡❝t✐♦♥ ✸✳✶ ❝♦✈❡rs t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛s❡ts ✉s❡❞✳ ❚❤❡ ❙❡❛s♦♥❛❧ ●❡♥❡r❛❧✐③❡❞▲✐♥❡❛r ▼♦❞❡❧ ♠❡t❤♦❞ ✐s ❞❡s❝r✐❜❡ ✐♥ ✸✳✷ ❢♦❧❧♦✇❡❞ ❜② ❛ ❞❡s❝r✐♣t✐♦♥ ♦❢ ❈✉♠✉❧❛t✐✈❡ ❉✐str✐✲❜✉t✐♦♥ ❋✉♥❝t✐♦♥ ❚r❛♥s❢♦r♠ ♠❡t❤♦❞ ✐♥ ❙❡❝t✐♦♥ ✸✳✸✳

✸✳✶ ❘❡❢❡r❡♥❝❡ ❞❛t❛

❉❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡s ❛♥❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✱ t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛ ❢♦r ❜✐❛s❝♦rr❡❝t✐♦♥ ✈❛r✐❡s✳ ■♥ ❝❛s❡ t❤❡ ❞r✐✈✐♥❣ ❞❛t❛ ✐s r❡q✉❡st❡❞ ❣❛✉❣❡ ❜❛s❡❞ ❛♥❞ ❣❛✉❣❡s ❜❛s❡❞r❡❢❡r❡♥❝❡ ❞❛t❛ ✐s ❛✈❛✐❧❛❜❧❡✱ ✇❡ ✉s❡ t❤✐s ❞❛t❛ ❢♦r ❜✐❛s ❝♦rr❡❝t✐♦♥✳ ❋♦r ❣r✐❞❞❡❞ ♣r♦❞✉❝ts✱ ✇❡✉s❡ t❤❡ ❲❆❚❈❍ ❢♦r❝✐♥❣ ❞❛t❛ ❊❘❆✲■♥t❡r✐♠ ✭❲❋❉❊■✱ ❲❡❡❞♦♥ ❡t ❛❧✳✱ ✷✵✶✹✮ ❛s ❛ r❡❢❡r❡♥❝❡✐♥ ❝❛s❡ ♥♦ ♦t❤❡r ❣r✐❞❞❡❞ r❡❢❡r❡♥❝❡ ♣r♦❞✉❝t ✇❛s ♣r♦✈✐❞❡❞✳ ❆s ❜✐❛s ❝♦rr❡❝t✐♦♥ ♦❢ ❣r✐❞❞❡❞♣r♦❞✉❝ts ❜❛s❡❞ ♦♥ ❣❛✉❣❡✲❜❛s❡❞ r❡❢❡r❡♥❝❡ ❞❛t❛ ✐s ❛ ❧♦t ❧❡ss str❛✐❣❤t❢♦r✇❛r❞✱ t❤✐s ✇✐❧❧ ♥♦t❜❡ ✐♥❝❧✉❞❡❞ ✐♥ t❤✐s ❞❡❧✐✈❡r❛❜❧❡✳ ❚❤❡ ❢♦❧❧♦✇✐♥❣ ❧✐st ❣✐✈❡s ❛♥ ♦✈❡r✈✐❡✇ ♦✈❡r t❤❡ r❡❢❡r❡♥❝❡❞❛t❛ ✉s❡❞ ❛t ❞✐✛❡r❡♥t ❘❡s❡❛r❝❤ ❙✐t❡s✳

❘❙✶ ❇❡r❣❡♥ ❛ ❣r✐❞❞❡❞ ❞❛t❛ ♣r♦❞✉❝t ✐s r❡q✉❡st❡❞ ❛♥❞ t❤✉s ❲❋❉❊■ ❞❛t❛s❡t ✐s ✉s❡❞ ❛sr❡❢❡r❡♥❝❡✳

❘❙✷ ❱❡❧✉✇❡ ❛ ❣r✐❞❞❡❞ ❞❛t❛ ♣r♦❞✉❝t ✐s r❡q✉❡st❡❞ ❛♥❞ t❤✉s ❲❋❉❊■ ❞❛t❛s❡t ✐s ✉s❡❞ ❛sr❡❢❡r❡♥❝❡✳

❘❙✸ ❲✉♣♣❡r ❛ ❣r✐❞❞❡❞ ❞❛t❛ ♣r♦❞✉❝t ✐s r❡q✉❡st❡❞ ❛♥❞ t❤✉s ❲❋❉❊■ ❞❛t❛s❡t ✐s ✉s❡❞ ❛sr❡❢❡r❡♥❝❡✳

❘❙✹ ❇❛❞❛❧♦♥❛ ❛ ❣r✐❞❞❡❞ ❞❛t❛ ♣r♦❞✉❝t ✐s r❡q✉❡st❡❞ ❛♥❞ t❤✉s ❲❋❉❊■ ❞❛t❛s❡t ✐s ✉s❡❞❛s r❡❢❡r❡♥❝❡✳

✶✹

❘❙✺ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮ ❛ ❣❛✉❣❡✲❜❛s❡❞ ❞❛t❛ ♣r♦❞✉❝t ❢♦r t❤❡ t❤❡ ✈❛r✐❛❜❧❡s ♣r❡✲❝✐♣✐t❛t✐♦♥ ✭♠♠✴❞❛②✮✱ ❞❛✐❧② ♠❛①✐♠✉♠ ❛♥❞ ♠✐♥✐♠✉♠ ♥❡❛r✲s✉r❢❛❝❡ ❛✐r t❡♠♣❡r❛t✉r❡✭◦❈✮✱ s✉r❢❛❝❡ ❞♦✇♥✇❡❧❧✐♥❣ s❤♦rt✇❛✈❡ ✢✉① ✐♥ ❛✐r ✭❲✴♠2✮✱ ✇✐♥❞ s♣❡❡❞ ✭♠✴s✮ ❛♥❞ s✉r✲❢❛❝❡ ❛✐r ♣r❡ss✉r❡ ✭❦P❛✮ ❛t ❞❛✐❧② r❡s♦❧✉t✐♦♥ ✐s t♦ ❜❡ ♣r♦✈✐❞❡❞✳ ●❛✉❣❡ ❧♦❝❛t✐♦♥s ❤❛✈❡❜❡❡♥ ♣r♦✈✐❞❡❞ ❜✉t ♥♦t ❛❧❧ ❣❛✉❣❡s r❡❝♦r❞ ❛❧❧ t❤❡ r❡q✉❡st❡❞ ✈❛r✐❛❜❧❡s✳ ❈♦♥s❡q✉❡♥t❧②✱❜✐❛s ❝♦rr❡❝t✐♦♥ ❝❛♥ ♦♥❧② ❜❡❡♥ ♠❛❞❡ ❢♦r t❤♦s❡ q✉❛♥t✐t✐❡s ✇❤❡r❡ r❡❢❡r❡♥❝❡ ❤❛s ❜❡❡♥♣r♦✈✐❞❡❞✳ ❚❤❛t ✐s

❼ ▼❛①✐♠✉♠ ❛♥❞ ♠✐♥✐♠✉♠ t❡♠♣❡r❛t✉r❡✱ ✇✐♥❞ s♣❡❡❞ ✭♠♦♥t❤❧②✮ ❢♦r ❚❛♣❛❞❛ ❞❛❆❥✉❞❛✱ ❙❛❧✈❛t❡rr❛ ❞❡ ▼❛❣♦s✱ ❉♦✐s P♦rt♦s✱ ❙❛♥t❛r❡♠✱ ❆❧✈❡❣❛✱ ❛♥❞

❼ Pr❡❝✐♣✐t❛t✐♦♥ ✭❞❛✐❧②✮ ❢♦r ❱✐❧❛ ◆♦❣✉❡✐r❛✱ ▼♦✐♥❤♦❧❛✱ ❈❛♥❤❛✱ ❇❛rr❛❣❡♠ ❞❡ ▼❛❣♦s✱❇❛rr❛❣❡♠ ❞❡ ▼♦♥t❛r❣✐❧✱ ❖t❛✱ ▼❛r✐❛♥♦s✱ ❙❛♥t❛r❡♠ ❊❙❆✱ ❚♦❥❡✐r❛s ❞❡ ❈✐♠❛✱❇❡♠♣♦st❛✱ ❛♥❞ P❡r♥❡s✳

❘❙✻ ❚r♦♦❞♦s✲▼♦✉♥t❛✐♥s ♥♦ ❞❛t❛ ♣r♦❞✉❝ts r❡q✉❡st❡❞✳

❋♦r ♠♦st ♦❢ t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡s ❛ s❡❛s♦♥❛❧❧② r❡s♦❧✈❡❞ ❝❧✐♠❛t♦❧♦❣② ❝♦♠♣✉t❡❞ ❢r♦♠❲❋❉❊■ ✐s t❤❡ r❡❢❡r❡♥❝❡ ❢♦r t❤❡ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥s✳ ❚❤✐s ❢♦r❝✐♥❣ ❞❛t❛ s❡t ✐s ❜❡❡♥ ❢r❡✲q✉❡♥t❧② ✉s❡❞ ✐♥ t❤❡ ❝♦♥t❡①t ♦❢ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧✐♥❣ ✭❡✳❣✳✱ ●✉❞♠✉♥❞ss♦♥ ❡t ❛❧✳✱ ✷✵✶✶❀❑♦❝❤ ❡t ❛❧✳✱ ✷✵✶✸❀ Pr✉❞❤♦♠♠❡ ❡t ❛❧✳✱ ✷✵✶✹✮✳ ❍♦✇❡✈❡r✱ ❢♦r t❤✐s ❞❛t❛ s❡t✱ ❘✉st ❡t ❛❧✳✭✷✵✶✺✮ ❢♦✉♥❞ t❤❛t ❞✉❡ t♦ t❤❡ ✇❛② ♦❢ ♠❡r❣✐♥❣ t❤❡ ❊❘❆✲■♥t❡r✐♠ r❡❛♥❛❧②s✐s ✇✐t❤ ❛ ❣r✐❞❞❡❞♦❜s❡r✈❛t✐♦♥✲❜❛s❡❞ ❞❛t❛ ♣r♦❞✉❝t ❢r♦♠ ❈❘❯ ✐♠♣❧❛✉s✐❜❧❡ ❞✐✛❡r❡♥❝❡s ✐♥ ❞❛✐❧② t❡♠♣❡r❛t✉r❡s❛❝r♦ss ❜♦✉♥❞❛r✐❡s ♦❢ ❝❛❧❡♥❞❡r ♠♦♥t❤ ♠✐❣❤t ❛r✐s❡ ❢♦r s♦♠❡ r❡❣✐♦♥s✳ ❋♦r ❊✉r♦♣❡✱ ❤♦✇❡✈❡r✱t❤❡s❡ ❞✐✛❡r❡♥❝❡s ❛r❡ ✐♥s✐❣♥✐✜❝❛♥t✳

❋♦r ❜✐❛s ❝♦rr❡❝t✐♦♥ t❤❡ ❢♦❧❧♦✇✐♥❣ ✈❛r✐❛❜❧❡s ♦❢ t❤❡❲❋❉❊■ ❛r❡ ❛✈❛✐❧❛❜❧❡✿ ♠❡❛♥✴♠✐♥✴♠❛①t❡♠♣❡r❛t✉r❡✱ t♦t❛❧ ♣r❡❝✐♣✐t❛t✐♦♥✱ s✉r❢❛❝❡ ❛✐r ♣r❡ss✉r❡✱ ♥❡❛r✲s✉r❢❛❝❡ ✇✐♥❞ s♣❡❡❞✱ ❧♦♥❣✲✴s❤♦rt✇❛✈❡ ✐♥❝✐❞❡♥t r❛❞✐❛t✐♦♥ ❛♥❞ ♥❡❛r✲s✉r❢❛❝❡ s♣❡❝✐✜❝ ❤✉♠✐❞✐t②✳ ❆ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❢♦r♠❡❛♥✴♠✐♥✴♠❛① r❡❧❛t✐✈❡ ❤✉♠✐❞✐t② ✇✐❧❧ ❜❡ ❞♦♥❡ ✐♥ ❧❛t❡r st❛❣❡s✳ ❲❋❉❊■ ❞♦❡s ♥♦t ♣r♦✈✐❞❡✈❡❝t♦r✐❛❧ ✐♥❢♦r♠❛t✐♦♥ ♦❢ t❤❡ ✇✐♥❞ ♥♦r ✐ts ❞✐r❡❝t✐♦♥s✱ t❤✉s ✇✐♥❞ ❞✐r❡❝t✐♦♥ ❝❛♥♥♦t ❜❡ ❝♦r✲r❡❝t❡❞✳ ❚❤✐s ✐s✱ ❤♦✇❡✈❡r✱ ♥♦t ❛ ♣r♦❜❧❡♠ ❢♦r ♠♦st ♦❢ t❤❡ ❝❛s❡s r❡❧❡✈❛♥t t♦ ❇■◆●❖✳ ❲❋❉❊■❝♦♠❡s ♦♥ ❛ ❝♦❛rs❡r r❡s♦❧✉t✐♦♥ t❤❛♥ t❤❡ ❈❖❙▼❖✲❈▲▼ s✐♠✉❧❛t✐♦♥ ✉s❡❞ ❢♦r ❉✷✳✶✳ ✐t ❤❛st❤✉s ❜❡❡♥ ✐♥t❡r♣♦❧❛t❡❞ t♦ t❤❡ ❣r✐❞ ♦❢ t❤❡ ❈❖❙▼❖✲❈▲▼✳

✸✳✷ ❙❡❛s♦♥❛❧ ●❡♥❡r❛❧✐③❡❞ ▲✐♥❡❛r ▼♦❞❡❧ ♠❡t❤♦❞

■♥ t❤✐s ❙❡❝t✐♦♥✱ t❤❡ ❙❡❛s♦♥❛❧ ●❡♥❡r❛❧✐③❡❞ ▲✐♥❡❛r ▼♦❞❡❧ ❜✐❛s ❝♦rr❡❝t✐♦♥ ♠❡t❤♦❞ ✐s ❞❡✲s❝r✐❜❡❞✳ ❚❤❡ ✉♥❞❡r❧②✐♥❣ ✐❞❡❛ ♦❢ t❤❡ ❛♣♣r♦❛❝❤ ✐s ✜rst ♣r❡s❡♥t❡❞ ✭❙❡❝t✳ ✸✳✷✮ ❢♦❧❧♦✇❡❞ ❜②t❤❡ ❝♦♥❝r❡t❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ t❤❡ ❛♣♣r♦❛❝❤ ❛t t❤❡ ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s ✐♥ ❙❡❝t✳ ✸✳✷✳✷✳

✸✳✷✳✶ ❯♥❞❡r❧②✐♥❣ ♣r✐♥❝✐♣❧❡ ❛♥❞ ♠♦❞❡❧✐♥❣ ❛♣♣r♦❛❝❤

❚❤❡ ✉♥❞❡r❧②✐♥❣ ✐❞❡❛ ♦❢ t❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❛♣♣❧✐❡❞ ❤❡r❡ ✐s t❤❡ ❛ss✉♠♣t✐♦♥ t❤❛t t❤❡ ❝❧✐✲♠❛t♦❧♦❣✐❝❛❧ s❡❛s♦♥❛❧ ❝②❝❧❡ ♦❢ ❜♦t❤✱ s✐♠✉❧❛t✐♦♥s ❛♥❞ ♦❜s❡r✈❛t✐♦♥s✱ ✐s ❛ s♠♦♦t❤ ❢✉♥❝t✐♦♥♦❢ t❤❡ ❞❛② ♦❢ t❤❡ ②❡❛r✳ ■❢ t❤❡ s✐♠✉❧❛t❡❞ s❡❛s♦♥❛❧ ❝②❝❧❡ ❞♦❡s ♥♦t ♠❛t❝❤ t❤❡ ♦❜s❡r✈❡❞ ♦♥❡✱

✶✺

✐t ♥❡❡❞s t♦ ❜❡ ❛❞❥✉st❡❞✳ ❚❤❡ s♠♦♦t❤ ❢✉♥❝t✐♦♥s ❛r❡ ♠♦❞❡❧❡❞ ✉s✐♥❣ ❛ ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r♠♦❞❡❧ ✭●▲▼✱ ▼❝❈✉❧❧❛❣❤ ❛♥❞ ◆❡❧❞❡r✱ ✶✾✽✾✮ ✇✐t❤ ❤❛r♠♦♥✐❝ ❢✉♥❝t✐♦♥ ✭s✐♥❡ ❛♥❞ ❝♦s✐♥❡✮♦❢ t❤❡ ❞❛② ♦❢ t❤❡ ②❡❛r ❛s ♣r❡❞✐❝t♦rs✳ P❡r✐♦❞✐❝ ❢✉♥❝t✐♦♥s✱ s✉❝❤ ❛s t❤❡ s❡❛s♦♥❛❧ ❝②❝❧❡✱ ❝❛♥❜❡ ❛❧✇❛②s ❞❡s❝r✐❜❡❞ ✇✐t❤ ❛ s❡r✐❡s ♦❢ ❤❛r♠♦♥✐❝ ❢✉♥❝t✐♦♥s✭❡✳❣✳✱ Pr✐❡st❧❡②✱ ✶✾✾✷✮❀ t❤❡ ♠♦r❡❢❡❛t✉r❡s t❤❡ ❝②❝❧❡ ❤❛s✱ t❤❡ ❤✐❣❤❡r t❤❡ ♦r❞❡r ♦❢ t❤❡ s❡r✐❡s ❡①♣❛♥s✐♦♥ ♠✉st ❜❡✳ ●❡♥❡r❛❧✐③❡❞❧✐♥❡❛r ♠♦❞❡❧s ❛r❡ ♥♦t r❡str✐❝t❡❞ t♦ ●❛✉ss✐❛♥ r❡s✐❞✉❛❧s ❛s t❤❡ st❛♥❞❛r❞ ❧✐♥❡❛r r❡❣r❡ss✐♦♥✐s✱ ❘❡s✐❞✉❛❧s ❝❛♥ ❜❡ ❢r♦♠ ❛♥② ❞✐str✐❜✉t✐♦♥ ✐♥ t❤❡ ❡①♣♦♥❡♥t✐❛❧ ❢❛♠✐❧② ♦❢ ♣r♦❜❛❜✐❧✐t② ❞✐s✲tr✐❜✉t✐♦♥s ✭▼❝❈✉❧❧❛❣❤ ❛♥❞ ◆❡❧❞❡r✱ ✶✾✽✾✮✱ ❡✳❣✳ ❊①♣♦♥❡♥t✐❛❧✱ ●❛♠♠❛✱ ❇✐♥♦♠✐❛❧✱ P♦✐ss♦♥✳❋♦r ♦✉r ❝❛s❡s ♣❛rt✐❝✉❧❛r❧② ✐♥t❡r❡st✐♥❣ ❞✐str✐❜✉t✐♦♥s ❛r❡ t❤♦s❡ ✇✐t❤ ♣♦s✐t✐✈❡ s✉♣♣♦rt ❢♦r♠♦❞❡❧✐♥❣ ♣r❡❝✐♣✐t❛t✐♦♥ ❛♥❞ ♦t❤❡r ♥♦♥✲♥❡❣❛t✐✈❡ q✉❛♥t✐t✐❡s✳

❖♥❝❡ t❤❡ t✇♦ s❡❛s♦♥❛❧ ❝②❝❧❡s ❤❛✈❡ ❜❡❡♥ ♦❜t❛✐♥❡❞ ✭♠♦❞❡❧✐♥❣ st❡♣✮✱ ❛ ❞✐✛❡r❡♥❝❡ ✭♦rr❛t✐♦ ✐♥ ❝❛s❡ ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥✮ ✐s ♦❜t❛✐♥❡❞ ❛♥❞ t❤✐s ✐s ✉s❡❞ ❢♦r ❛❞❥✉st✐♥❣ t❤❡ s✐♠✉❧❛t❡❞❞❛t❛ ✭❛❞❥✉st♠❡♥t st❡♣✮✳

❚❤❡ ♠♦❞❡❧

❆s ❛ s✐♠✉❧t❛♥❡♦✉s tr❡❛t♠❡♥t ♦❢ ❛❧❧ ❞❛t❛ ✐s ❛❞✈❛♥t❛❣❡♦✉s ♦✈❡r ❛ s❡♣❛r❛t❡ tr❡❛t♠❡♥t ♦❢❞❛t❛ ✐♥ ❞✐✛❡r❡♥t ♠♦♥t❤s✱ t❤❡ s❡❛s♦♥❛❧ ✈❛r✐❛t✐♦♥s ♦❢ t❤❡ ✈❛r✐❛❜❧❡s ❝❛♥ ❜❡ ❝❛♣t✉r❡❞ ❜②✉s✐♥❣ ❤❛r♠♦♥✐❝ ❢✉♥❝t✐♦♥s✱ ❛s ♠❡♥t✐♦♥❡❞ ❛❜♦✈❡✳ ❋♦r t❤❡ ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ♠♦❞❡❧✱ s✉❝❤ ❛❞❡s❝r✐♣t✐♦♥ ✐s ❣✐✈❡♥ ✐♥ ❊q✳ ✭✸✳✶✮ ❢♦r t❤❡ ❡①♣❡❝t❛t✐♦♥ ✈❛❧✉❡ µ(t)✳

µ(t) = µ0 +

N∑

n=1

µn1 sin(nω · t) +

N∑

n=1

µn2 cos(nω · t) ✭✸✳✶✮

✇✐t❤ ω = 2π365.25 ✱ t = 1, . . . , 366 ❜❡✐♥❣ t❤❡ t✐♠❡ ✈❛r✐❛❜❧❡ r✉♥♥✐♥❣ ♦✈❡r ❛❧❧ ♣♦ss✐❜❧❡ ❞❛②s

♦❢ t❤❡ ②❡❛r✳ ❋♦r ♣❛r❛♠❡t❡r ❡st✐♠❛t✐♦♥✱ t ✇✐❧❧ ❜❡ ❝❡♥t❡r❡❞ ❛t t❤❡ ♠♦♥t❤s ♦❢ t❤❡ ②❡❛r❀ ❛❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ s❡❛s♦♥❛❧ ❝②❝❧❡ ✐s✱ ❤♦✇❡✈❡r✱ ♣♦ss✐❜❧❡ ❛t ❛ ❞❛✐❧② t✐♠❡ r❡s♦❧✉t✐♦♥✱ t❤✉st = 1, . . . , 366✳ ❚❤❡ ❝❤♦✐❝❡ ♦❢ ❞✐str✐❜✉t✐♦♥ ❢♦r t❤❡ r❡s✐❞✉❛❧s ✭❛♥♦♠❛❧✐❡s✮ ❞♦❡s ✈❛r② ✇✐t❤t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ♣❛r❛♠❡t❡r ❝♦♥s✐❞❡r❡❞✱ t❤❡ ♠♦❞❡❧ ❢♦r t❤❡ ❡①♣❡❝t❛t✐♦♥ ❣✐✈❡♥ ✐♥ ❊q✳ ✭✸✳✶✮r❡♠❛✐♥s ❜❛s✐❝❛❧❧② t❤❡ s❛♠❡✳

❉✐str✐❜✉t✐♦♥❛❧ ❛ss✉♠♣t✐♦♥s

Pr❡❝✐♣✐t❛t✐♦♥ Pr❡❝✐♣✐t❛t✐♦♥ ✐s ❛ s♦♠❡✇❤❛t ♣❛rt✐❝✉❧❛r q✉❛♥t✐t②✳ ■t s❤♦✇s ❛ ❝♦♥t✐♥✉♦✉s♣r♦❜❛❜✐❧✐t② ❞✐str✐❜✉t✐♦♥ ❢♦r str✐❝t❧② ♣♦s✐t✐✈❡ ✈❛❧✉❡s ❜✉t ❤❛s ❛ ❞✐s❝♦♥t✐♥✉✐t② ❛t ③❡r♦✳ ❋♦r❛ st❛t✐st✐❝❛❧ ❞❡s❝r✐♣t✐♦♥✱ t❤✐s ✐s t②♣✐❝❛❧❧② ❝❛♣t✉r❡❞ ✇✐t❤ ❛ ❝♦♠♣♦✉♥❞ ♠♦❞❡❧ ❝♦♥s✐st✐♥❣♦❢ ❛ ❇✐♥♦♠✐❛❧ ✈❛r✐❛❜❧❡ ❢♦r ❞❡s❝r✐❜✐♥❣ ❞r② ❛♥❞ ✇❡t ❞❛②s ❛♥❞ ❛ str✐❝t❧② ♣♦s✐t✐✈❡ ✈❛r✐❛❜❧❡✭●❛♠♠❛ ♦r ❊①♣♦♥❡♥t✐❛❧✮ ❢♦r t❤❡ q✉❛♥t✐t② ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ♦♥ r❛✐♥② ❞❛②s✳ ❍❡r❡✱ ✇❡ ❛❞❥✉st♦♥❧② t❤❡ ❛♠♦✉♥t ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ♦♥ r❛✐♥② ❞❛②s ❛♥❞ ♥♦t t❤❡ ❞✐str✐❜✉t✐♦♥ ♦❢ ❞r② ❛♥❞ ✇❡t❞❛②s✳ ❚❤✐s ✐s t♦ ❛✈♦✐❞ ✐♥❝♦♥s✐st❡♥❝✐❡s ✐♥ t❤❡ ♣♦st✲♣r♦❝❡ss✐♥❣ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s✱ s✉❝❤ ❛s♣r❡❝✐♣✐t❛t✐♦♥ ♦♥ ❞❛②s ✇✐t❤ ♥♦ ❝❧♦✉❞s✳

❖t❤❡r ✈❛r✐❛❜❧❡s ❚❛❜❧❡ ✸✳✶ ❣✐✈❡s ❛♥ ♦✈❡r✈✐❡✇ ♦✈❡r ❛❧❧ ✈❛r✐❛❜❧❡s ❛♥❞ t❤❡ ❛ss♦❝✐❛t❡❞♠♦❞❡❧ ❞✐str✐❜✉t✐♦♥s✳ ❚❤❡ ♦r❞❡r ♦❢ t❤❡ ❤❛r♠♦♥✐❝ s❡r✐❡s ❡①♣❛♥s✐♦♥ ✭♠♦❞❡❧ s❡❧❡❝t✐♦♥✮ ❤❛s

✶✻

✈❛r✐❛❜❧❡ ❧♦♥❣ ♥❛♠❡ ❞✐str✐❜✉t✐♦♥

T1 ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ Tmax ❛♥❞ Tmin ❧♦❣✲●❛✉ss✐❛♥T2 s✉♠ ♦❢ Tmax ❛♥❞ Tmin ●❛✉ss✐❛♥

Tmean ♠❡❛♥ s✉r❢❛❝❡ t❡♠♣❡r❛t✉r❡ ●❛✉ss✐❛♥RR ♣r❡❝✐♣✐t❛t✐♦♥ ❣❛♠♠❛v ♥❡❛r✲s✉r❢❛❝❡ ✇✐♥❞ s♣❡❡❞ ❧♦❣✲●❛✉ss✐❛♥P s✉r❢❛❝❡ ❛✐r ♣r❡ss✉r❡ ●❛✉ss✐❛♥

LWdown ❧♦♥❣✇❛✈❡ ✐♥❝✐❞❡♥t r❛❞✐❛t✐♦♥ ❧♦❣✲●❛✉ss✐❛♥SWdown s❤♦rt✇❛✈❡ ✐♥❝✐❞❡♥t r❛❞✐❛t✐♦♥ ❧♦❣✲●❛✉ss✐❛♥Qair ♥❡❛r✲s✉r❢❛❝❡ s♣❡❝✐✜❝ ❤✉♠✐❞✐t② ❧♦❣✲●❛✉ss✐❛♥

❚❛❜❧❡ ✸✳✶✿ ❇✐❛s✲❝♦rr❡❝t❡❞ ✈❛r✐❛❜❧❡s ❛♥❞ ❛ss♦❝✐❛t❡❞ ♠♦❞❡❧ ❞✐str✐❜✉t✐♦♥s✳

❜❡❡♥ ❝❤♦s❡♥ ♦♥ t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛s❡ts✳ ❍❛r♠♦♥✐❝ s❡r✐❡s t♦ ✺t❤ ♦r❞❡r ❤❛✈❡ ❜❡❡♥ ❝♦♥s✐❞❡r❡❞❛♥❞ s❡❧❡❝t❡❞ ✇✐t❤ t❤❡ ❇❛②❡s✐❛♥ ■♥❢♦r♠❛t✐♦♥ ❈r✐t❡r✐♦♥ ✭❇■❈✮✳ ❚❤❡ ♠♦❞❡❧ t❤✉s ♦❜t❛✐♥❡❞❤❛s ❜❡❡♥ ✉s❡❞ t♦ ❞❡s❝r✐❜❡ t❤❡ ❝❧✐♠❛t❡ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s ❛♥❞ t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛✳

▼✐♥✐♠✉♠ ❛♥❞ ♠❛①✐♠✉♠ t❡♠♣❡r❛t✉r❡

P❛rt✐❝✉❧❛r ❝❛r❡ ♥❡❡❞s t♦ ❜❡ t❛❦❡♥ ✇❤❡♥ ❝♦rr❡❝t✐♦♥ ♠✐♥✐♠✉♠ ❛♥❞ ♠❛①✐♠✉♠ t❡♠♣❡r❛t✉r❡t♦ ❛✈♦✐❞ ✐♥❝♦♥s✐st❡♥❝✐❡s s✉❝❤ ❛s Tmax < Tmin✳ ❍❡r❡✱ ❛ ✈❛r✐❛❜❧❡ tr❛♥s❢♦r♠❛t✐♦♥ ❣✐✈❡♥ ✐♥❊q✳ ✭✸✳✷✮ ❡♥s✉r❡s ♣❤②s✐❝❛❧ ❝♦♥s✐st❡♥❝②✳

T1 = Tmax − Tmin ✭✸✳✷✮

T2 = Tmax + Tmin ✭✸✳✸✮

❆❢t❡r ❝♦rr❡❝t✐♥❣ T1 ❛♥❞ T2 ❜❛s❡❞ ♦♥ t❤❡ r❡❢❡r❡♥❝❡✱ t❤❡ ❝♦rr❡❝t❡❞ ✈❛❧✉❡s ❢♦r Tmax ❛♥❞ Tmin

❝❛♥ ❜❡ ❞❡r✐✈❡❞ ❜② ❜❛❝❦✲tr❛♥s❢♦r♠✐♥❣ t❤❡ ✈❛r✐❛❜❧❡s✳

✸✳✷✳✷ ❆t ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s

❋♦r r❡❛s♦♥s ♦❢ ❞❛t❛ ❛✈❛✐❧❛❜✐❧✐t② ❛♥❞ ❢♦r ❛ r♦❜✉st ✜t✱ ✇❡ ✉s❡ ♠♦♥t❤❧② ♠❡❛♥s t♦ ❡st✐♠❛t❡t❤❡ ♠♦❞❡❧ ♣❛r❛♠❡t❡rs ✭❝♦❡✣❝✐❡♥ts ♦❢ t❤❡ ❤❛r♠♦♥✐❝ ❢✉♥❝t✐♦♥s✮✳ ❋♦r s♦♠❡ ❝❛s❡s✱ ❛ ✈❡❝t♦r❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ♠♦❞❡❧ ✭❱●▲▼✱ ❨❡❡✱ ✷✵✶✺✮ ❤❛s ❜❡❡♥ ✉s❡❞✳ ❊①❡♠♣❧❛r✐❧②✱ ❋✐❣✳ ✸✳✶ s❤♦✇st❤❡ ♠♦♥t❤❧② ♠❡❛♥ ♣r❡❝✐♣✐t❛t✐♦♥ ❢♦r t❤❡ r❡❢❡r❡♥❝❡ st❛t✐♦♥s ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦✱❧♦❝❛t❡❞ ♦♥ t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮✳

■♥ t❤❡ ♠♦❞❡❧✐♥❣ st❡♣✱ t❤❡ s❡❛s♦♥❛❧✐t② ♦❢ t❤❡ ♠♦❞❡❧ ♦✉t♣✉t ❛♥❞ t❤❡ r❡s♣❡❝t✐✈❡ r❡❢❡r❡♥❝❡❞❛t❛ ❛r❡ ❞❡r✐✈❡❞ ✉s✐♥❣ t❤❡ ❛♣♣r♦❛❝❤ ❞❡s❝r✐❜❡❞ ❛❜♦✈❡✳ ❋✐❣✉r❡ ✸✳✷ s❤♦✇s ❛♥ ❡①❛♠♣❧❡ ♦❢t❤❡ t✇♦ s❡❛s♦♥❛❧ ❝②❝❧❡s ❢♦r ♣r❡❝✐♣✐t❛t✐♦♥ ❛t t❤❡ st❛t✐♦♥ ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦ ♦♥ t❤❡❘❡s❡❛r❝❤ ❙✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮✳

❚❤❡ ❛❞❥✉st♠❡♥t st❡♣ ❞❡♣❡♥❞s ♦♥ t❤❡ ✈❛r✐❛❜❧❡ ❝♦♥s✐❞❡r❡❞✿ ❋♦r ●❛✉ss✐❛♥ ❞✐str✐❜✉t✐♦♥st❤❡ ❞✐✛❡r❡♥❝❡ ✭❝❛s❡ ✶✮ ❛♥❞ ❢♦r ♣♦s✐t✐✈❡ ✈❛r✐❛❜❧❡s ✭❡✳❣✳ ●❛♠♠❛ ♦r ❧♦❣✲♥♦r♠❛❧✮ t❤❡ q✉♦t✐❡♥t✭❝❛s❡ ✷✮ ♦❢ t❤❡ ❡st✐♠❛t❡❞ s❡❛s♦♥❛❧ ❝②❝❧❡ ❢♦r t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛ s❡t r̄(t) ❛♥❞ t❤❡ s✐♠✉❧❛t❡❞

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❋✐❣✉r❡ ✸✳✷✿ ❙❡❛s♦♥❛❧✐t② ♦❢ t❤❡ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥ ♦✉t♣✉t ✭❜❧✉❡✮ ❛♥❞ t❤❡ r❡❢❡r❡♥❝❡ ♦❜s❡r✈❛t✐♦♥✭❜❧❛❝❦✮ ❢♦r ♣r❡❝✐♣✐t❛t✐♦♥ ❛t t❤❡ st❛t✐♦♥ ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦ ✐♥ t❤❡ r❡s❡❛r❝❤ s✐t❡ ❚❛❣✉s✲❘✐✈❡r✭P♦rt✉❣❛❧✮ ✐♥ ❛ ❞❛✐❧② r❡s♦❧✉t✐♦♥ ❞❡r✐✈❡❞ ❜② ❛ ❱●▲▼ tr❛✐♥❡❞ ✇✐t❤ ♠♦♥t❤❧② ♠❡❛♥ ✈❛❧✉❡s✳

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Jan Mär Mai Jul Sep Nov Jan

010

20

30

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month

pre

cip

itation [m

m/d

ay]

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bias−corrected data

raw data

❋✐❣✉r❡ ✸✳✸✿ Pr❡❝✐♣✐t❛t✐♦♥ ♦❢ t❤❡ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥ ❛t t❤❡ st❛t✐♦♥ ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦ ✐♥t❤❡ r❡s❡❛r❝❤ s✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮ ❢♦r t❤❡ ②❡❛r ✶✾✽✾ ❜❡❢♦r❡ t❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ✭❜❧❛❝❦✮ ❛♥❞❛❢t❡r ✭❜❧✉❡✮✳

❞❛t❛ s❡t x̄(t) ❛r❡ ♦❜t❛✐♥❡❞✱ s❡❡ ❊q✳ ✭✸✳✹✮✳

∆(t) =

{

r̄(t)− x̄(t) ●❛✉ss✐❛♥r̄(t)x̄(t) ♣♦s✐t✐✈❡

✭✸✳✹✮

❋✐♥❛❧❧②✱ t❤❡ ❛❞❥✉st❡❞ ✭❜✐❛s ❝♦rr❡❝t❡❞✮ ✈❛❧✉❡s ❛r❡ ❝❛❧❝✉❧❛t❡❞ ❜② ❡✐t❤❡r ❛❞❞✐♥❣ ✭❝❛s❡ ✶✮♦r ♠✉❧t✐♣❧②✐♥❣ ✭❝❛s❡ ✷✮ t❤❡ t❤✉s ♦❜t❛✐♥❡❞ ✈❛❧✉❡s t♦ t❤❡ ❝❧✐♠❛t❡ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s✱ s❡❡❊q✳ ✭✸✳✺✮✳

xcorrected(t) =

{

x(t) + ∆(t) ●❛✉ss✐❛♥

x(t) ·∆(t) ♣♦s✐t✐✈❡✭✸✳✺✮

❋✐❣✉r❡ ✸✳✸ ❛♥❞ ❋✐❣✉r❡ ✸✳✹ s✉❣❣❡st t❤❛t t❤❡ ♣r❡❝✐♣✐t❛t✐♦♥ ❞❛t❛s❡t ❛t t❤❡ st❛t✐♦♥ ❱✐❧❛◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦ ✐♥ t❤❡ r❡s❡❛r❝❤ s✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮ ✇❛s ❝♦rr❡❝t❡❞ ✐♥ ❣❡♥❡r❛❧t♦✇❛r❞s ❧♦✇❡r ✈❛❧✉❡s✳

✷✵

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❋✐❣✉r❡ ✸✳✹✿ Pr❡❝✐♣✐t❛t✐♦♥ ♦❢ t❤❡ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥ ❛t t❤❡ st❛t✐♦♥ ❱✐❧❛ ◆♦❣✉❡✐r❛ ❞❡ ❆③❡✐t❛♦ ✐♥t❤❡ r❡s❡❛r❝❤ s✐t❡ ❚❛❣✉s✲❘✐✈❡r ✭P♦rt✉❣❛❧✮ ❜❡❢♦r❡ t❤❡ ❜✐❛s ❝♦rr❡❝t✐♦♥ ✭①✲❛①✐s✮ ❛♥❞ ❛❢t❡r ✭②✲❛①✐s✮✳

✷✶

✸✳✸ ❈✉♠✉❧❛t✐✈❡ ❉✐str✐❜✉t✐♦♥ ❋✉♥❝t✐♦♥ ❚r❛♥s❢♦r♠ ♠❡t❤♦❞

❲❡ ♣r❡s❡♥t ❤❡r❡ ❛ ♠❡t❤♦❞✱ ♥❛♠❡❧② t❤❡ ❈❉❋✲❚r❛♥s❢♦r♠✱ ✇❤✐❝❤ ❝❛♥ ❜❡ ♣❡r❝❡✐✈❡❞ ❛s ❛♥❡①t❡♥s✐♦♥ ♦❢ t❤❡ ❝❧❛ss✐❝❛❧ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ❛♣♣r♦❛❝❤ ✭P❛♥♦❢s❦② ❛♥❞ ❇r✐❡r✱ ✶✾✻✽✮✳ ❚❤✐s♠❡t❤♦❞ ❤❛s ❜❡❡♥ ❞❡✈❡❧♦♣❡❞ ❜② ✭▼✐❝❤❡❧❛♥❣❡❧✐ ❡t ❛❧✳✱ ✷✵✵✾✮ ❛♥❞ ❛♣♣❧✐❡❞ ✐♥ ♠❛♥② ❝❧✐♠❛t❡✲r❡❧❛t❡❞ st✉❞✐❡s ✭❡✳❣✳ ✭❈♦❧❡tt❡ ❡t ❛❧✳✱ ✷✵✶✷✮✱ ✭❚✐ss❡✉✐❧ ❡t ❛❧✳✱ ✷✵✶✷✮✱ ✭❱✐❣❛✉❞ ❡t ❛❧✳✱ ✷✵✶✸✮✱✭❱r❛❝ ❛♥❞ ❋r✐❡❞❡r✐❝❤s✱ ✷✵✶✺✮✮✳ ■♥ t❤❡ ❢♦❧❧♦✇✐♥❣✱ ✇❡ ✜rst r❡❝❛♣ t❤❡ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣♠❡t❤♦❞ ✭❙❡❝t✳ ✸✳✸✳✶✮ ❢♦❧❧♦✇❡❞ ❜② ❛ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ ❈❉❋✲❚r❛♥s❢♦r♠ ♠❡t❤♦❞ ✭❙❡❝t✳✸✳✸✳✷✮ ❛♥❞ s♦♠❡ ❝♦♥❝r❡t❡ ❛♣♣❧✐❝❛t✐♦♥s ♦❢ t❤❡ ❛♣♣r♦❛❝❤ ❛t t❤❡ ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s✭❙❡❝t✳ ✸✳✸✳✸✮✳

✸✳✸✳✶ ◗✉❛♥t✐❧❡✲▼❛♣♣✐♥❣ ▼❡t❤♦❞

▲❡t Fo st❛♥❞ ❢♦r t❤❡ ❈❉❋ ✭❈✉♠✉❧❛t✐✈❡ ❉✐str✐❜✉t✐♦♥ ❋✉♥❝t✐♦♥✮ ♦❢ ❛ ❝❧✐♠❛t❡ r❛♥❞♦♠ ✈❛r✐✲❛❜❧❡ xo ✭t❡♠♣❡r❛t✉r❡✱ ♣r❡❝✐♣✐t❛t✐♦♥✱ ✇✐♥❞✱ ❡t❝✳✮ ♦❜s❡r✈❡❞ ❛t ❛ ❣✐✈❡♥ ✇❡❛t❤❡r st❛t✐♦♥❞✉r✐♥❣ t❤❡ ❤✐st♦r✐❝❛❧ t✐♠❡ ♣❡r✐♦❞✱ ❛♥❞ Fm ❢♦r t❤❡ ❈❉❋ ♦❢ t❤❡ s❛♠❡ ✈❛r✐❛❜❧❡ xm ❢r♦♠ t❤❡♠♦❞❡❧✱ ❢♦r t❤❡ s❛♠❡ t✐♠❡ ♣❡r✐♦❞✳ ❚❤❡ ✐❞❡❛ ♦❢ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ✐s t♦ ❝♦rr❡❝t t❤❡ ❞✐str✐✲❜✉t✐♦♥ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ♠♦❞❡❧❧❡❞ ❝❧✐♠❛t❡ ✈❛r✐❛❜❧❡ t♦ ❛❣r❡❡ ✇✐t❤ t❤❡ ♦❜s❡r✈❡❞ ❞✐str✐❜✉t✐♦♥❢✉♥❝t✐♦♥✿

Fo(xo) = Fm(xm). ✭✸✳✻✮

❚❤❡ ❝♦rr❡❝t❡❞ ✈❛❧✉❡ xbc ❝❛♥ ❜❡ ♦❜t❛✐♥❡❞ ❡♠♣✐r✐❝❛❧❧② ❢r♦♠ ✭s❡❡ ❋✐❣✉r❡ ✸✳✺✮✱

xbc = F−1o [Fm(xm)]. ✭✸✳✼✮

✇❤❡r❡ F−1o ✱ ❞❡✜♥❡❞ ❢r♦♠ ❬✵✱✶❪✱ ✐s t❤❡ ✐♥✈❡rs❡ ❢✉♥❝t✐♦♥ ♦❢ Fo✳

❚❤❡ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ♠❡t❤♦❞ ✐s ♦♥❧② s✉✐t❛❜❧❡ ✇❤❡♥ ♦❜s❡r✈❛t✐♦♥s ❛r❡ ❛✈❛✐❧❛❜❧❡ ❢♦r t❤❡s❛♠❡ t✐♠❡ ♣❡r✐♦❞ ❛s ❢♦r t❤❡ ♠♦❞❡❧ ♦✉t♣✉t ✭❱r❛❝ ❛♥❞ ❋r✐❡❞❡r✐❝❤s✱ ✷✵✶✺✮✳ ❍♦✇❡✈❡r✱ ✐t ♦❢t❡♥❤❛♣♣❡♥s t❤❛t ♦♥❡ ♥❡❡❞s t♦ ❝♦rr❡❝t ♠♦❞❡❧ ♦✉t♣✉t t❤❛t ❝♦✈❡rs ❛ t✐♠❡ ♣❡r✐♦❞ ❧♦♥❣❡r t❤❛♥t❤❛t ♦❢ t❤❡ ♦❜s❡r✈❛t✐♦♥s✳ ❆♥♦t❤❡r ❝❛s❡ ✇❤❡r❡ t❤❡ ❝❧❛ss✐❝❛❧ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ✐s ♥♦t s✉✐t❡❞t♦ ❜✐❛s ❝♦rr❡❝t✐♦♥ ✐s t❤❡ ❝♦rr❡❝t✐♦♥ ♦❢ ♠♦❞❡❧ ❢✉t✉r❡ ♣r❡❞✐❝t✐♦♥s ✭✇❤❡r❡ ♦❜s❡r✈❛t✐♦♥s ❛r❡♦❜✈✐♦✉s❧② ♥♦t ❛✈❛✐❧❛❜❧❡✮✳ ❚❤✐s ♠❡t❤♦❞ ❞♦❡s ♥♦t t❛❦❡ ✐♥t♦ ❛❝❝♦✉♥t t❤❡ ✐♥❢♦r♠❛t✐♦♥ ♦♥ t❤❡❞✐str✐❜✉t✐♦♥ ♦❢ t❤❡ ❢✉t✉r❡ ♠♦❞❡❧❧❡❞ ❞❛t❛s❡t✳ ❚❤❡ ❈❉❋✲❚r❛♥s❢♦r♠ ♠❡t❤♦❞ ✐s ♣r♦♣♦s❡❞ t♦♦✈❡r❝♦♠❡ t❤✐s ♣♦t❡♥t✐❛❧ ✐ss✉❡✳

✸✳✸✳✷ ❈❉❋✲❚r❛♥s❢♦r♠ ▼❡t❤♦❞

❚❤❡ ❈❉❋✲❚r❛♥s❢♦r♠ ❛♣♣r♦❛❝❤ ✭❤❡r❡❛❢t❡r ✧❈❉❋✲t✧✮ ❝❛♥ ❜❡ ♣❡r❝❡✐✈❡❞ ❛s ❛♥ ❡①t❡♥s✐♦♥ ♦❢q✉❛♥t✐❧❡s✲♠❛♣♣✐♥❣✱ ❞✐r❡❝t❧② ❞❡❛❧✐♥❣ ✇✐t❤ ❛♥❞ ♣r♦✈✐❞✐♥❣ ❈❉❋s ✭▼✐❝❤❡❧❛♥❣❡❧✐ ❡t ❛❧✳✱ ✷✵✵✾✮✳

▲❡t Fo,h st❛♥❞ ❢♦r t❤❡ ❈❉❋ ♦❢ ❛ ❝❧✐♠❛t❡ r❛♥❞♦♠ ✈❛r✐❛❜❧❡ ♦❜s❡r✈❡❞ ❛t ❛ ❣✐✈❡♥ ✇❡❛t❤❡rst❛t✐♦♥ ❞✉r✐♥❣ t❤❡ ❤✐st♦r✐❝❛❧ t✐♠❡ ♣❡r✐♦❞ ✭tr❛✐♥✐♥❣ ♣❡r✐♦❞✮ ❛♥❞ Fm,h ❢♦r t❤❡ ❈❉❋ ♦❢ t❤❡

✷✷

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x

CDF

Observation

Model

xbc

xm

❋✐❣✉r❡ ✸✳✺✿ ■❧❧✉str❛t✐♦♥ ♦❢ t❤❡ ◗✉❛♥t✐❧❡✲▼❛♣♣✐♥❣ ▼❡t❤♦❞

✷✸

s❛♠❡ ✈❛r✐❛❜❧❡ ❢r♦♠ t❤❡ ♠♦❞❡❧ ♦✉t♣✉t ❞✉r✐♥❣ t❤❡ s❛♠❡ ♣❡r✐♦❞✳ Fo,f ✭✉♥❦♥♦✇♥✮ ❛♥❞ Fm,f

❛r❡ t❤❡ ❈❉❋s ❡q✉✐✈❛❧❡♥t t♦ Fo,h ❛♥❞ Fm,h ❜✉t ❢♦r ❛ ❢✉t✉r❡ ✭♦r s✐♠♣❧② ❞✐✛❡r❡♥t✮ t✐♠❡♣❡r✐♦❞ ✭s❡❡ ❚❛❜❧❡ ✸✳✷✮✳ ❚❤❡ ♠❛✐♥ ❣♦❛❧ ♦❢ t❤❡ ❈❉❋✲t ✐s t♦ ❛♣♣r♦①✐♠❛t❡ t❤❡ ❈❉❋ ♦❢ t❤❡♦❜s❡r✈❛t✐♦♥s ✐♥ t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞ ✭Fo,f (x)✮ ❜❛s❡❞ ♦♥ ❤✐st♦r✐❝❛❧ ✐♥❢♦r♠❛t✐♦♥ ❛♥❞ t❤❡♥ t♦❛♣♣❧② q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ❜❡t✇❡❡♥ Fo,f (x) ❛♥❞ Fm,f (x)✳

❍✐st♦r✐❝❛❧ ♣❡r✐♦❞ ❋✉t✉r❡ ♣❡r✐♦❞

❖❜s❡r✈❛t✐♦♥ Fo,h(x) Fo,f (x) ✭✉♥❦♥♦✇♥✮▼♦❞❡❧ Fm,h(x) Fm,f (x)

❚❛❜❧❡ ✸✳✷✿ ❚❛❜❧❡ s✉♠♠❛r✐③✐♥❣ ❈❉❋ ♥♦t❛t✐♦♥s

❆ss✉♠✐♥❣ t❤❛t ✇❡ ❦♥♦✇ Fm,f ✭✇❤✐❝❤ ❝❛♥ ❜❡ ♠♦❞❡❧❧❡❞ ✈✐❛ ❢✉t✉r❡ ♠♦❞❡❧ ♦✉t♣✉t✮✱ ❛♥❞t❤❛t t❤❡r❡ ❡①✐sts ❛ tr❛♥s❢♦r♠❛t✐♦♥ ❚✿ [0, 1] → [0, 1] s✉❝❤ t❤❛t

T (Fm,h(x)) = Fo,h(x) ✭✸✳✽✮

❚❤❡ ❈❉❚✲t ♠❡t❤♦❞ ✐s ❜❛s❡❞ ♦♥ t❤❡ ❛ss✉♠♣t✐♦♥✱ ✇❤✐❝❤ ✐s ♠❛❞❡ ❜② ♠♦st st❛t✐st✐❝❛❧❜✐❛s ❝♦rr❡❝t✐♦♥ ❛♣♣r♦❛❝❤❡s✱ t❤❛t t❤❡ tr❛♥s❢♦r♠❛t✐♦♥ T ✐s st✐❧❧ ✈❛❧✐❞ ✐♥ t❤❡ ❢✉t✉r❡ ♣❡r✐♦❞

T (Fm,f (x)) = Fo,f (x). ✭✸✳✾✮

❯♥❞❡r t❤✐s ❛ss✉♠♣t✐♦♥✱ ✇❡ ❝❛♥ ❛♣♣r♦①✐♠❛t❡ Fo,f ❜② ❛♣♣❧②✐♥❣ T t♦ Fm,f ✳

❚❤❡ ✜rst st❡♣ ✐s t♦ ♠♦❞❡❧ T ❛♥❞ t❤❡ s✐♠♣❧❡ ✇❛② t♦ ❞♦ s♦ ✐s t♦ r❡♣❧❛❝❡ x ❜② F−1m,h(u)

✐♥ ✭✸✳✽✮✱ ✇❤❡r❡ u ✐s ❛♥② ♣r♦❜❛❜✐❧✐t② ✐♥ [0, 1]✳ ❲❡ t❤❡♥ ♦❜t❛✐♥

T (u) = Fo,h(F−1m,h(u)), ✭✸✳✶✵✮

❝♦rr❡s♣♦♥❞✐♥❣ t♦ t❤❡ s✐♠♣❧❡ ❞❡✜♥✐t✐♦♥ ♦❢ ❚✳ ■♥s❡rt✐♥❣ ✭✸✳✶✵✮ ✐♥ ✭✸✳✽✮ ❧❡❛❞s t♦ ❛ ♠♦❞❡❧❧✐♥❣♦❢ Fm,f ✱

Fo,f = Fo,h(F−1m,h(Fm,f (x))). ✭✸✳✶✶✮

❋r♦♠ ❛ t❡❝❤♥✐❝❛❧✴❛❧❣♦r✐t❤♠✐❝ ♣♦✐♥t ♦❢ ✈✐❡✇✱ t❤❡ ❈❉❋ tr❛♥s❢♦r♠ ❛♣♣r♦❛❝❤ ✐s ❞❡✜♥❡❞✐♥ t❤r❡❡ st❡♣s ❢♦❧❧♦✇✐♥❣ ✭▼✐❝❤❡❧❛♥❣❡❧✐ ❡t ❛❧✳✱ ✷✵✵✾✮ ✿

✶✳ ❚❤❡ ❡st✐♠❛t❡s ♦❢ Fo,h✱ F−1m,h ❛♥❞ Fm,f ✱ r❡s♣❡❝t✐✈❡❧② F̂o,h✱ F̂

−1m,h ❛♥❞ F̂m,f ✱ ❛r❡ ❡♠✲

♣✐r✐❝❛❧❧② ♠♦❞❡❧❧❡❞ r❡s♣❡❝t✐✈❡❧② ❢r♦♠ t❤❡ ❤✐st♦r✐❝❛❧ ♦❜s❡r✈❛t✐♦♥s ❛♥❞ t❤❡ ❤✐st♦r✐❝❛❧❛♥❞ ❢✉t✉r❡ ♠♦❞❡❧ ♦✉t♣✉t ❞❛t❛✳

✷✳ ❚❤❡♥✱ ❜② ❝♦♠❜✐♥✐♥❣ t❤❡♠ ❛❝❝♦r❞✐♥❣ t♦ ❡q✉❛t✐♦♥ ✭✸✳✶✶✮✱ ✇❡ ❞✐s♣♦s❡ ♦❢ F̂0,f ✱ ❛♥❡st✐♠❛t✐♦♥ ♦❢ F0,f ✳ ◆♦t❡ t❤❛t ✐t ✐s ❛❧s♦ ♣♦ss✐❜❧❡ t♦ ✉s❡ ♣❛r❛♠❡tr✐❝ ❈❉❋s✳

✸✳ ❖♥❝❡ F̂m,f ❛♥❞ F̂o,f ❛r❡ ❡st✐♠❛t❡❞✱ q✉❛♥t✐❧❡✲♠❛♣♣✐♥❣ ✐s ❛♣♣❧✐❡❞ ❛s ✐♥ ❙❡❝t✐♦♥ ✸✳✸✳✶

✷✹

❋✐❣✉r❡ ✸✳✻✿ ■❧❧✉str❛t✐♦♥ ♦❢ t❤❡ ❢✉t✉r❡ ♦❜s❡r✈❛t✐♦♥s ❈❉❋ ✭Fo,f ✮ ❡st✐♠❛t✐♦♥

◆♦t❡ t❤❛t✱ ✐♥ t❤❡ ❡q✉❛t✐♦♥ ✭ ✸✳✶✶✮✱ Fo,f ✐s ♦♥❧② ❞❡✜♥❡❞ ❢♦r x ∈ [mh,Mh]✱ ✇❤❡r❡ mh

❛♥❞ Mh ❛r❡ r❡s♣❡❝t✐✈❡❧② t❤❡ ♠✐♥✐♠✉♠ ❛♥❞ t❤❡ ♠❛①✐♠✉♠ ♦❢ t❤❡ ♠♦❞❡❧ ♦✉t♣✉ts ✐♥ t❤❡❤✐st♦r✐❝❛❧ ♣❡r✐♦❞✳ ❖✉ts✐❞❡ [mh,Mh]✱ Fo,f ❣✐✈❡s t❤❡ s❛♠❡ ❝♦♥st❛♥t ✈❛❧✉❡✳ ❆s ✐♥ ✭❉éq✉é✱✷✵✵✼✮ ♦r ✭▼✐❝❤❡❧❛♥❣❡❧✐ ❡t ❛❧✳✱ ✷✵✵✾✮ ❛ ✧❝♦♥st❛♥t ❝♦rr❡❝t✐♦♥✧ ♠❡t❤♦❞ ✐s ❛♣♣❧✐❡❞ ✇❤❡♥❡✈❡rx ✐s ♦✉ts✐❞❡ [mh;Mh] ❡✳❣✳ ✐❢ t❤❡ ♠❛①✐♠✉♠ ✈❛❧✉❡ ♦❢ x ✐♥ t❤❡ r❛♥❣❡ ♦❢ [mh;Mh] ✐s ❝♦rr❡❝t❡❞❜② x0✱ ❛❧❧ x s✉❝❤ ❛s x > Mf ✐s ❝♦rr❡❝t❡❞ ❜② x0✳ ■t ✐s ✐♠♣♦rt❛♥t t♦ ♠❡♥t✐♦♥❡❞ t❤❛t t❤❡♣♦rt✐♦♥ ♦❢ ❞❛t❛ ❢♦r ✇❤✐❝❤ t❤❡ ✧❝♦♥st❛♥t ❝♦rr❡❝t✐♦♥✧ ♠❡t❤♦❞ ✐s ❛♣♣❧✐❡❞ ✐s ✈❡r② s♠❛❧❧✳

✸✳✸✳✸ ❆♣♣❧✐❝❛t✐♦♥ ♦❢ ❈❉❋✲t ❛t ❇■◆●❖ r❡s❡❛r❝❤ s✐t❡s

❲❆❚❈❍ ❢♦r❝✐♥❣ ❞❛t❛ ❊❘❆✲■♥t❡r✐♠ ✭❲❋❉❊■✮ ❛r❡ ✉s❡❞ ❛s r❡❢❡r❡♥❝❡ ❞❛t❛ ❢♦r ❛❧❧ r❡s❡❛r❝❤s✐t❡s✳ ❚❤❡ ❛✈❛✐❧❛❜❧❡ ✈❛r✐❛❜❧❡s ✐♥ ❲❋❉❊■ ❢♦r ❜✐❛s ❝♦rr❡❝t✐♦♥ ❛r❡✿ t❡♠♣❡r❛t✉r❡✱ t♦t❛❧♣r❡❝✐♣✐t❛t✐♦♥✱ s✉r❢❛❝❡ ❛✐r ♣r❡ss✉r❡✱ ♥❡❛r✲s✉r❢❛❝❡ ✇✐♥❞ s♣❡❡❞✱ ❧♦♥❣✴s❤♦rt✇❛✈❡ ✐♥❝✐❞❡♥t r❛✲❞✐❛t✐♦♥ ❛♥❞ ♥❡❛r✲s✉r❢❛❝❡ s♣❡❝✐✜❝ ❤✉♠✐❞✐t②✳ ❚♦ t❛❦❡ ❝❛r❡ ♦❢ t❤❡ s❡❛s♦♥❛❧✐t②✱ t❤❡ ❈❉❋✲t ✐s❛♣♣❧✐❡❞ s❡♣❛r❛t❡❧② ❢♦r ❡❛❝❤ ❝❛❧❡♥❞❡r ♠♦♥t❤✳ ❚❤❡ ❝❛❧✐❜r❛t✐♦♥ ♣❡r✐♦❞ ✐s s❡t t♦ ✶✾✽✵✲✷✵✶✸✳

❙♣❡❝✐❛❧ ❛tt❡♥t✐♦♥ ✐s ❣✐✈❡♥ t♦ ♣r❡❝✐♣✐t❛t✐♦♥ s✐♥❝❡ ✐t s❤♦✇s ❛ ❝♦♥t✐♥✉♦✉s ♣r♦❜❛❜✐❧✐t② ❞✐s✲tr✐❜✉t✐♦♥ ❢♦r str✐❝t❧② ♣♦s✐t✐✈❡ ✈❛❧✉❡s ❜✉t ❤❛s ❛ ❞✐s❝♦♥t✐♥✉✐t② ❛t ③❡r♦✳ ❚❤❡ ❈❉❋✲t ✐s ❛♣♣❧✐❡❞❢♦r ❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥ ❛♠♦✉♥ts ❣r❡❛t❡r t❤❛♥ ❛ ✜①❡❞ t❤r❡s❤♦❧❞✳ ❚❤❡ ❝❤♦s❡♥ t❤r❡s❤♦❧❞ ✐s✵✳✶♠♠ ❢♦r ❲❋❉❊■ ❛♥❞ ❢♦r t❤❡ ♠♦❞❡❧✱ t❤❡ t❤r❡s❤♦❧❞ ✐s ❛❞❥✉st❡❞ s♦ t❤❛t t❤❡ ❢r❡q✉❡♥❝② ♦❢✇❡t ❞❛②s ✐s t❤❡ s❛♠❡ ❛s ✐♥ t❤❡ ❲❋❉❊■✳

✷✺

❋✐❣✉r❡s ✸✳✼ ❛♥❞ ✸✳✽ s❤♦✇ s♦♠❡ r❡s✉❧ts ♦❜t❛✐♥❡❞ ❢♦r ♣r❡❝✐♣✐t❛t✐♦♥ ❛t t❤❡ ❣r✐❞ ♣♦✐♥t♦❢ ❝♦♦r❞✐♥❛t❡s ✭❧♦♥❣✐t✉❞❡❂✼✳✹✻ ❛♥❞ ❧❛t✐t✉❞❡❂✺✶✳✶✶✮✳ ■♥ ✜❣✉r❡ ✸✳✼✱ ❛s ❡①♣❡❝t❡❞✱ ❛ ❣♦♦❞❛❣r❡❡♠❡♥t ❝❛♥ ❜❡ ♦❜s❡r✈❡❞ ❜❡t✇❡❡♥ t❤❡ r❡❢❡r❡♥❝❡ ❞❛t❛ q✉❛♥t✐❧❡s ❛♥❞ t❤❡ q✉❛♥t✐❧❡s ♦❢t❤❡ ♠♦❞❡❧ ❛❢t❡r ❜✐❛s ❝♦rr❡❝t✐♦♥✳ ❆❧t❤♦✉❣❤ ❈❉❋✲t ✐s ❜❛s❡❞ ♦♥ ❝✉♠✉❧❛t✐✈❡ ❞✐str✐❜✉t✐♦♥❢✉♥❝t✐♦♥✱ ✐t ✐s ❛❜❧❡ t♦ ❝♦rr❡❝t ❛❧s♦ t❤❡ ♠❡❛♥ ❛♥❞ t❤❡ ✈❛r✐❛♥❝❡✳ ■♥❞❡❡❞✱ ✐♥ ❋✐❣✉r❡ ✸✳✽ ✇❡❝♦♠♣❛r❡ t❤❡ ♠♦♥t❤❧② ♠❡❛♥ ✭❧❡❢t✮ ❛♥❞ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ✭r✐❣❤t✮ ♦❢ ❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥❛♥❞ t❤❡r❡ ✐s ❛ ❣♦♦❞ ❛❣r❡❡♠❡♥t ❜❡t✇❡❡♥ t❤❡ r❡❢❡r❡♥❝❡ ❛♥❞ t❤❡ ♠♦❞❡❧ ❛❢t❡r ❈❉❋✲t ❜✐❛s❝♦rr❡❝t✐♦♥✳

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●

●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●

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●●

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●●

● ●●

●

●

●

0 10 20 30 40 50

010

20

30

40

50

WFDEI

CO

SM

O−

CLM

lon= 7.46 lat= 51.11

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●

●●●●●●●●

●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●

●●●●●●●●●●●

●●

●●

●

●

●

●

●

●

●

●

●

0 10 20 30 40 50

010

20

30

40

50

WFDEI

CO

SM

O−

CLM

●

●

Model without correction

Model with CDFt correction

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●●●●●

●●●●●●●●●●●●●

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●

●● ●

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● ●

●

●●

●

0 10 20 30 40

010

20

30

40

WFDEI

CO

SM

O−

CLM

lon= 7.46 lat= 51.11

●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●

●●●●●●●●●

●●●●●●●

●●●●●●●●●

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●●●●●

●●

●

●

●

●

●

●

●

●

0 10 20 30 40

010

20

30

40

WFDEI

CO

SM

O−

CLM

●

●

Model without correction

Model with CDFt correction

❋✐❣✉r❡ ✸✳✼✿ ◗✉❛♥t✐❧❡✲q✉❛♥t✐❧❡ ♣❧♦t ♦❢ ❲❋❉❊■ ❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥ ✭♠♠✴❞❛②✮ ❛♥❞ ❈❖❙▼❖✲❈▲▼❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥ ✭♠♠✴❞❛②✮ ✇✐t❤♦✉t ❛♥❞ ✇✐t❤ ❈❉❋✲t ❜✐❛s ❝♦rr❡❝t✐♦♥ ❛t ❧♦❝❛t✐♦♥ ❞❡✜♥❡❞ ❜②❧♦♥❣✐t✉❞❡❂✼✳✹✻ ❛♥❞ ❧❛t✐t✉❞❡❂✺✶✳✶✶✳ ❚❤❡ ❧❡❢t ♣❧♦t ❝♦rr❡s♣♦♥❞s t♦ ❏❛♥✉❛r② ❛♥❞ t❤❡ r✐❣❤t ♣❧♦t t♦t❤❡ ❆✉❣✉st

✷✻

lon= 7.46 lat= 51.11

Mean o

f pre

cip

itation [m

m/d

ay]

23

45

67

8

●

●

●

●

●

●●

●

●

● ●

●

J F M A M J J A S O N D

●

●

●

●

●

● ●

●

●

●

●

●

●

●

●

●

●

●

● ●

●

●

●

●

●

●

●

WFDEI

COSMO−CLM without correction

COSMO−CLM with CDFt correction

lon= 7.46 lat= 51.11

Std

of pre

cip

itation [m

m/d

ay]

24

68

10

J F M A M J J A S O N D

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

● ●

●●

●

●

●

●

●

●

●

●

●

●●

●

●

●

●

●

●

WFDEI

COSMO−CLM without correction

COSMO−CLM with CDFt correction

❋✐❣✉r❡ ✸✳✽✿ ▼♦♥t❤❧② ♠❡❛♥ ✭❧❡❢t✮ ❛♥❞ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ✭r✐❣❤t✮ ♦❢ ❞❛✐❧② ♣r❡❝✐♣✐t❛t✐♦♥ ❛t ❧♦❝❛✲t✐♦♥ ❞❡✜♥❡❞ ❜② ❧♦♥❣✐t✉❞❡❂✼✳✹✻ ❛♥❞ ❧❛t✐t✉❞❡❂✺✶✳✶✶✳ ❚❤❡ ♠❡❛♥ ❛♥❞ t❤❡ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ❛r❡❝❛❧❝✉❧❛t❡❞ ♦♥❧② ❢♦r ✇❡t ❞❛②s

lon= 7.46 lat= 51.11

Mean o

f pre

cip

itation [m

m/h

]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

●

●

●

●

●

● ● ● ●●

●●

J F M A M J J A S O N D

●

● ●

●

●●

●

●

●

●

● ●

●

●

●

●

●

●

●●

●

●

●●

●

●

●

Observation

Model without correction

Model with CDFt correction

lon= 7.46 lat= 51.11

Std

of pre

cip

itation [m

m/h

]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

J F M A M J J A S O N D

●

●

●

●

●

●●

●

●

●

●

●

●

● ●

●

●

●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

Observation

Model without correction

Model with CDFt correction

❋✐❣✉r❡ ✸✳✾✿ ▼♦♥t❤❧② ♠❡❛♥ ✭❧❡❢t✮ ❛♥❞ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ✭r✐❣❤t✮ ♦❢ ✸ ❤♦✉r❧② ♣r❡❝✐♣✐t❛t✐♦♥ ❛t❧♦❝❛t✐♦♥ ❞❡✜♥❡❞ ❜② ❧♦♥❣✐t✉❞❡❂✼✳✹✻ ❛♥❞ ❧❛t✐t✉❞❡❂✺✶✳✶✶✳

✷✼

❈❤❛♣t❡r ✹

❉❊❈❖ ✕ ❆ ❇■◆●❖ ♣❧✉❣✲✐♥ ❢♦r ❋r❡❱❛

✹✳✶ ❋r❡❱❛ ✕ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥ ❡✈❛❧✉❛t✐♦♥ s②st❡♠

❋r❡✈❛ ✐s t❤❡ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥ ❊✈❛❧✉❛t✐♦♥ ❋r❛♠❡✇♦r❦ ❢♦r ❊❛rt❤ ❙②st❡♠ ❙❝✐❡♥❝❡✳❚❤❡ ❢✉❧❧② ♦♣❡r❛t✐♦♥❛❧ ❤②❜r✐❞ ❢❡❛t✉r❡s ❛ ❍P❈ s❤❡❧❧ ❛❝❝❡ss ❛♥❞ ❛♥ ✉s❡r ❢r✐❡♥❞❧② ✇❡❜✲✐♥t❡r❢❛❝❡✳ ■t ❡♠♣❧♦②s ♦♥❡ ❝♦♠♠♦♥ s②st❡♠ ✇✐t❤ ❛ ✈❛r✐❡t② ♦❢ ✈❡r✐✜❝❛t✐♦♥ t♦♦❧s ❛♥❞ ✈❛❧✐❞❛✲t✐♦♥ ❞❛t❛ ❢r♦♠ ❞✐✛❡r❡♥t ♣r♦❥❡❝ts ✐♥✲ ❛♥❞ ♦✉ts✐❞❡ ♦❢ t❤❡ ❋❯❇✳ ❚❤❡ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✐s❧♦❝❛t❡❞ ❛t t❤❡ ❋❯❇✱ t❤❡ ❉❲❉ ❛♥❞ ●❡r♠❛♥ ❈❧✐♠❛t❡ ❈♦♠♣✉t✐♥❣ ❈❡♥tr❡ ✭❉❑❘❩✮✱ ❡s♣❡✲❝✐❛❧❧② t❤✐s ❤❛s ❞✐r❡❝t ❛❝❝❡ss t♦ t❤❡ ❜✉❧❦ ♦❢ ✐ts ❊❙●❋ ♥♦❞❡ ✐♥❝❧✉❞✐♥❣ ♠✐❧❧✐♦♥s ♦❢ ❝❧✐♠❛t❡♠♦❞❡❧ ❞❛t❛ s❡ts✱ ❡✳❣✳ ❢r♦♠ ❈▼■P✺ ❛♥❞ ❈❖❘❉❊❳✳ ❚❤❡ ❞❛t❛❜❛s❡ ✐s ♦r❣❛♥✐③❡❞ ❜② t❤❡✐♥t❡r♥❛t✐♦♥❛❧ ❈▼❖❘ st❛♥❞❛r❞ ✉s✐♥❣ t❤❡ ♠❡t❛ ✐♥❢♦r♠❛t✐♦♥ ♦❢ t❤❡ s❡❧❢✲❞❡s❝r✐❜✐♥❣ ♠♦❞❡❧✱r❡❛♥❛❧②s✐s ❛♥❞ ♦❜s❡r✈❛t✐♦♥❛❧ ❞❛t❛ s❡ts✳ ❆♣❛❝❤❡ ❙♦❧r ✐s ✉s❡❞ ❢♦r ✐♥❞❡①✐♥❣ t❤❡ ❞✐✛❡r❡♥t ❞❛t❛♣r♦❥❡❝ts ✐♥t♦ ♦♥❡ ❝♦♠♠♦♥ s❡❛r❝❤ ❡♥✈✐r♦♥♠❡♥t✳ ❚❤✐s ✐♠♣❧❡♠❡♥t❡❞ ♠❡t❛ ❞❛t❛ s②st❡♠ ✇✐t❤✐ts ❛❞✈❛♥❝❡❞ ❜✉t ❡❛s② t♦ ❤❛♥❞❧❡ s❡❛r❝❤ t♦♦❧ s✉♣♣♦rts ✉s❡rs✱ ❞❡✈❡❧♦♣❡rs ❛♥❞ t❤❡✐r t♦♦❧st♦ r❡tr✐❡✈❡ t❤❡ r❡q✉✐r❡❞ ✐♥❢♦r♠❛t✐♦♥✳ ❆ ❣❡♥❡r✐❝ ❛♣♣❧✐❝❛t✐♦♥ ♣r♦❣r❛♠♠✐♥❣ ✐♥t❡r❢❛❝❡ ✭❆P■✮❛❧❧♦✇s s❝✐❡♥t✐✜❝ ❞❡✈❡❧♦♣❡rs t♦ ❝♦♥♥❡❝t t❤❡✐r ❛♥❛❧②s✐s t♦♦❧s ✇✐t❤ t❤❡ ❡✈❛❧✉❛t✐♦♥ s②st❡♠✐♥❞❡♣❡♥❞❡♥t❧② ♦❢ t❤❡ ♣r♦❣r❛♠♠✐♥❣ ❧❛♥❣✉❛❣❡ ✉s❡❞✳ ❯s❡rs ♦❢ t❤❡ ❡✈❛❧✉❛t✐♦♥ t❡❝❤♥✐q✉❡s❜❡♥❡✜t ❢r♦♠ t❤❡ ❝♦♠♠♦♥ ✐♥t❡r❢❛❝❡ ♦❢ t❤❡ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✇✐t❤♦✉t ❛♥② ♥❡❡❞ t♦ ✉♥❞❡r✲st❛♥❞ t❤❡ ❞✐✛❡r❡♥t s❝r✐♣t✐♥❣ ❧❛♥❣✉❛❣❡s✳ ❋❛❝✐❧✐t❛t✐♥❣ t❤❡ ♣r♦✈✐s✐♦♥ ❛♥❞ ✉s❛❣❡ ♦❢ t♦♦❧s ❛♥❞❝❧✐♠❛t❡ ❞❛t❛ ✐♥❝r❡❛s❡s ❛✉t♦♠❛t✐❝❛❧❧② t❤❡ ♥✉♠❜❡r ♦❢ s❝✐❡♥t✐sts ✇♦r❦✐♥❣ ✇✐t❤ t❤❡ ❞❛t❛ s❡ts❛♥❞ ✐❞❡♥t✐❢② ❞✐s❝r❡♣❛♥❝✐❡s✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ❤✐st♦r② ❛♥❞ ❝♦♥✜❣✉r❛t✐♦♥ s✉❜✲s②st❡♠ st♦r❡s❡✈❡r② ❛♥❛❧②s✐s ♣❡r❢♦r♠❡❞ ✇✐t❤ t❤❡ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✐♥ ❛ ▼②❙◗▲ ❞❛t❛❜❛s❡✳ ❈♦♥✜❣✉✲r❛t✐♦♥s ❛♥❞ r❡s✉❧ts ♦❢ t❤❡ t♦♦❧s ❝❛♥ ❜❡ s❤❛r❡❞ ❛♠♦♥❣ s❝✐❡♥t✐sts ✈✐❛ s❤❡❧❧ ♦r ✇❡❜✲s②st❡♠✳❚❤❡r❡❢♦r❡✱ ♣❧✉❣❣❡❞✲✐♥ t♦♦❧s ❣❛✐♥ ❛✉t♦♠❛t✐❝❛❧❧② ❢r♦♠ tr❛♥s♣❛r❡♥❝② ❛♥❞ r❡♣r♦❞✉❝✐❜✐❧✐t②✳❋✉rt❤❡r♠♦r❡✱ ✇❤❡♥ ❝♦♥✜❣✉r❛t✐♦♥s ♠❛t❝❤ ✇❤✐❧❡ st❛rt✐♥❣ ❛ ❡✈❛❧✉❛t✐♦♥ t♦♦❧✱ t❤❡ s②st❡♠s✉❣❣❡sts t♦ ✉s❡ r❡s✉❧ts ❛❧r❡❛❞② ♣r♦❞✉❝❡❞ ❜② ♦t❤❡r ✉s❡rs✕s❛✈✐♥❣ ❈P❯ t✐♠❡✱ ■✴❖ ❛♥❞ ❞✐s❦s♣❛❝❡✳ ✇❡❜s✐t❡✿ ❢r❡✈❛✳♠❡t✳❢✉✲❜❡r❧✐♥✳❞❡ ✈✐s✐t♦r✲❧♦❣✐♥✿ ❝❧✐❝❦ ♦♥ ✧●✉❡st✧✳ ❆ ❞❡t❛✐❧❧❡❞ ❞❡✲s❝r✐♣t✐♦♥ ✐s ❝✉rr❡♥t❧② ❜❡✐♥❣ ♣r❡♣❛r❡❞ ❢♦r ●❡♦s❝✐❡♥t✐✜❝ ▼♦❞❡❧ ❉❡✈❡❧♦♣♠❡♥t ✭❑❛❞♦✇ ❡t ❛❧✳✱✐♥ ♣r❡♣❛r❛t✐♦♥✮✳

✷✽

✹✳✷ ❉♦❝✉♠❡♥t❛t✐♦♥ ♦❢ ❉❊❈❖

✹✳✷✳✶ ■♥tr♦❞✉❝t✐♦♥

❚❤❡ ❇■◆●❖✲❉❊❈❖ ❋r❡❱❛ ♣❧✉❣✲✐♥ ♣r♦❞✉❝❡s ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❛♥❞ ❝❧✐♠❛t♦❧♦❣✐❝❛❧ ✐♥♣✉t ❞❛t❛❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s ✇✐t❤✐♥ t❤❡ ❇■◆●❖ ♣r♦❥❡❝t✳ ❋♦r ❛ ❧✐st ♦❢ ♠♦❞❡❧s s❡❡ ❚❛❜✳ ✹✳✶ ✐♥❙❡❝t✳ ✹✳✷✳✷✳ ❚❤❡ ♣❧✉❣✲✐♥ ✐s ♣❛rt ♦❢ ❛♥ ❣❡♥❡r❛❧ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✭❙❡❝t✳ ✹✳✶✮❀ ❛ s❦❡t❝❤ ♦❢t❤✐s s②st❡♠ ✇✐t❤ t❤❡ ❇■◆●❖✲❉❊❈❖ ♣❧✉❣✲✐♥ ❤✐❣❤❧✐❣❤t❡❞ ✐s ❣✐✈❡♥ ✐♥ ❋✐❣✳ ✹✳✶✳ ❋r❡❱❛ ✐s

❋✐❣✉r❡ ✹✳✶✿ ❙❦❡t❝❤ ♦❢ t❤❡ ❋r❡❱❛ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ✇✐t❤ t❤❡ ❇■◆●❖✲❉❊❈❖ ♣❧✉❣✐♥ ❤✐❣❤❧✐❣❤t❡❞✳

❛ ❢r❛♠❡✇♦r❦ ❤♦st✐♥❣ s❡✈❡r❛❧ ♣❧✉❣✲✐♥s ✭❛♣♣❧✐❝❛t✐♦♥s✮ ✇❤✐❝❤ ❤❛✈❡ ❛❧❧ ❛❝❝❡ss t♦ ❛ ❝♦♠♠♦♥❞❛t❛ ♣♦♦❧✳ ❉❛t❛ ✐♥ t❤✐s ♣♦♦❧ ✐s st❛♥❞❛r❞✐③❡❞ s✉❝❤ t❤❛t ♣❧✉❣✲✐♥s ❝❛♥ ✐♥st❛♥t❧② ❛❝❝❡ss♥❡✇ ❞❛t❛ ✇❤✐❝❤ ❝♦♠❡s ✐♥t♦ t❤✐s ♣♦♦❧✳ ❚❤❡ ❝❧✐♠❛t❡ ❞❛t❛ ♣r♦❞✉❝❡❞ ❢♦r ❇■◆●❖ ✇✐❧❧ ❜❡♣❛rt ♦❢ t❤✐s ♣♦♦❧✳ ❚♦ ✉s❡ t❤❡ ❢r❛♠❡✇♦r❦✱ ✉s❡rs ♠✉st r❡❣✐st❡r ✈✐❛ t❤❡ ❋r❡❱❛ ✇❡❜✲♣❛❣❡❤tt♣s✿✴✴❢r❡✈❛✳♠❡t✳❢✉✲❜❡r❧✐♥✳❞❡✴ ❛♥❞ ❛❝❝❡ss ✐s ❣r❛♥t❡❞ ❜② t❤❡ ❋r❡❱❛ t❡❛♠✳ ❚❤❡ t❡❛♠ ❤❛s❝✉rr❡♥t❧② ❛ ❧✐st ♦❢ ❇■◆●❖ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧❡rs ♣r♦✈✐❞❡❞ ❜② ❲P✸✳

❘❡❣❛r❞❧❡ss ♦❢ t❤❡ ❝❤♦s❡♥ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞❛t❛ s❡t t♦ ❜❡ ♣r♦❝❡ss❡❞✱ t❤❡ ♣❧✉❣✲✐♥ ♣r❡♣❛r❡s❛ s♣❡❝✐✜❝ ❞♦✇♥❧♦❛❞❛❜❧❡ st❛♥❞❛r❞ ♦✉t♣✉t ❛❝❝♦r❞✐♥❣ t♦ t❤❡ s❡❧❡❝t❡❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧ ❛♥❞❘❡s❡❛r❝❤ ❙✐t❡ r❡s♣❡❝t✐✈❡❧② ✭❚❛❜✳ ✹✳✸✮✳ ❇❡s✐❞❡s ♣r❡♣❛r✐♥❣ t❤❡ ♦r✐❣✐♥❛❧ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞❛t❛❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✱ t❤❡ ♣❧✉❣✲✐♥ ❤❛s ❛♥ ♦♣t✐♦♥ t♦ ❜✐❛s✲❝♦rr❡❝t t❤❡ ❞❛t❛ ❜❛s❡❞ ♦♥❞✐✛❡r❡♥t ♠❡t❤♦❞s ❜❡❢♦r❡❤❛♥❞✱ s❡❡ ❈❤❛♣✳ ✸ ✳

❚❤✐s s❡❝t✐♦♥ ✐s str✉❝t✉r❡❞ ❛s ❢♦❧❧♦✇s✿ ❙❡❝t✐♦♥ ✹✳✷✳✷ ❞❡s❝r✐❜❡s t❤❡ ♣r❡♣r♦❝❡ss✐♥❣✱ ❙❡❝✲t✐♦♥s ✹✳✷✳✸ ❛♥❞ ✹✳✷✳✹ ❣✐✈❡ ❛♥ ♦✈❡r✈✐❡✇ ♦✈❡r t❤❡ ✐♥♣✉t ❛♥❞ t❤❡ ♦✉t♣✉t ♦❢ t❤❡ ❇■◆●❖✲❉❊❈❖

✷✾

♣❧✉❣✲✐♥✱ r❡s♣❡❝t✐✈❡❧②✳

✹✳✷✳✷ Pr❡♣r♦❝❡ss✐♥❣

❚❤❡ ♣r❡♣r♦❝❡ss✐♥❣ ❝♦♥s✐sts ❜❛s✐❝❛❧❧② ♦❢ ❛ s♣❛t✐❛❧ s❡❧❡❝t✐♦♥ ♦❢ t❤❡ r❡❣✐♦♥✴st❛t✐♦♥s✱ ❛s ✇❡❧❧ ❛s❛ t❡♠♣♦r❛❧ s❡❧❡❝t✐♦♥ ♦❢ ❞❛t❡s ♣❧✉s ❛ ❝♦♥✈❡rs✐♦♥ ♦❢ ✈❛r✐❛❜❧❡s ❛♥❞ t❤❡✐r ❛ss♦❝✐❛t❡❞ ✉♥✐ts✳ ❚♦❛✈♦✐❞ ✉♥♥❡❝❡ss❛r② ❣r✐❞ r❡♠❛♣♣✐♥❣✱ ✐♥ t❤❡ ✜rst ✈❡rs✐♦♥ ♦❢ t❤❡ ♣❧✉❣✲✐♥ t❤❡ s♣❛t✐❛❧ s❡❧❡❝t✐♦♥✐s ❛♣♣❧✐❡❞ ♦♥ t❤❡ ♥❛t✐✈❡ ❣r✐❞ ♦❢ t❤❡ ❝❤♦s❡♥ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t ❞❛t❛✳ ❋♦r st❛t✐♦♥ ❞❛t❛✱ ❛♥❡❛r❡st ♥❡✐❣❤❜♦r r❡♠❛♣♣✐♥❣ ✭s❡❡ ❝❞♦ ✲r❡♠❛♣♥♥ ✐♥ t❤❡ ❈❉❖ ❯s❡r✬s ●✉✐❞❡ ✭❙❝❤✉❧③✇❡✐❞❛✱✷✵✶✺✮✮ ✐s ❛♣♣❧✐❡❞ t♦ ❣❡t t❤❡ ♥❡❛r❡st ❣r✐❞ ❝❡❧❧ ♦❢ ❛ ❣✐✈❡♥ ❧♦♥❣✐t✉❞❡✴❧❛t✐t✉❞❡ ❧♦❝❛t✐♦♥✳ ❋♦rt❤❡ r❡❣✐♦♥ s❡❧❡❝t✐♦♥✱ ❛ ❜♦① ✇✐❧❧ ❜❡ s❡❧❡❝t❡❞ ✭❝❞♦ ✲s❡❧❧♦♥❧❛t❜♦①✮ r❡❣❛r❞✐♥❣ t♦ ❛ ❞❡✜♥❡❞❧♦♥❣✐t✉❞❡✴❧❛t✐t✉❞❡ r❡❝t❛♥❣❧❡✳ ❚❤✐s ❞❡✜♥✐t✐♦♥ ♦❢ r❡❝t❛♥❣❧❡ ✐s ❜❛s❡❞ ♦♥ t❤❡ r❡♣❧✐❡s t♦ t❤❡❤②❞r♦❧♦❣✐❝❛❧✲♠♦❞❡❧✲❜❛s❡❞ q✉❡st✐♦♥♥❛✐r❡s✱ s❡♥t ❛r♦✉♥❞ ❜② ❇■◆●❖ ❲P✸✳ ❘❡s✉❧ts ♦❢ t❤❡s❡q✉❡st✐♦♥♥❛✐r❡s ❛r❡ ❣✐✈❡♥ ✐♥ ❚❛❜✳ ✹✳✶✳ ◆♦t❡✱ t❤❛t ❞✉❡ t♦ t❤❡ ✉s❡ ♦❢ ♥❛t✐✈❡ ❣r✐❞✱ t❤❡✜♥❛❧ s❡❧❡❝t❡❞ ❣r✐❞ ❜♦✉♥❞❛r② ✐s ❧❛r❣❡r ❛♥❞ ❞♦❡s ♥♦t ❡①❛❝t❧② ♠❛t❝❤ t❤❡ ❞❡✜♥❡❞ r❡❝t❛♥❣❧❡✳◆❡✈❡rt❤❡❧❡ss✱ ❛❧❧ ❣r✐❞ ❝❡❧❧ ❝❡♥t❡rs ♦❢ t❤❡ s❡❧❡❝t❡❞ ♥❛t✐✈❡ ❣r✐❞ ❛r❡ ❞❡✜♥✐t✐✈❡❧② ✐♥s✐❞❡ t❤❡❞❡✜♥❡❞ r❡❝t❛♥❣❧❡ r❛♥❣❡ ❜② ✉s❡rs✳ ❲✐t❤ ✜♥❡r ❣r✐❞s ✐♥ ❧❛t❡r ♣r♦❥❡❝t st❛❣❡s✱ t❤✐s ❡✛❡❝t❜❡❝♦♠❡s ♠♦r❡ ❛♥❞ ♠♦r❡ ♥❡❣❧✐❣✐❜❧❡✳

❚❛❜❧❡ ✹✳✶✿ ◆❛♠✐♥❣ ❝♦♥✈❡♥t✐♦♥ ♦❢ ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s ❛♥❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s ✇❤✐❝❤ ❛r❡✉s❡❞ ✐♥ t❤❡ ❇■◆●❖✲❉❊❈❖ ♣❧✉❣✲✐♥✳ ❆❞❞✐t✐♦♥❛❧❧②✱ t❤❡ ❞❡✜♥❡❞ ❧♦♥✴❧❛t r❡❝t❛♥❣❧❡ ❜❛s❡❞ ♦♥ t❤❡ ✉s❡r✲q✉❡st✐♦♥♥❛✐r❡ ✐s s❤♦✇♥✳ ◆♦t❡✱ ✐♥ ❝❛s❡ ✇❡ ❞✐❞ ♥♦t ❣❡t ❢❡❡❞❜❛❝❦ r❡❧❛t❡❞ t♦ t❤❡ r❡❣✐♦♥ ❜♦✉♥❞❛r✐❡s✱✇❡ ❞❡✜♥❡❞ ❛ r❡❝t❛♥❣❧❡ ♠❛t❝❤✐♥❣ t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡✳

★ ❈♦✉♥tr② ❘❡s❡❛r❝❤ ❙✐t❡ ❍②❞r♦❧✳ ▼♦❞❡❧ ❧♦♥✴❧❛t r❡❝t❛♥❣❧❡

✶ ◆❖❘ ❇❡r❣❡♥ ❊◆❑■ ✺✳✶✵◦❊ ✲ ✺✳✼✻◦❊

✻✵✳✶✸◦◆ ✲ ✻✵✳✻✹◦◆

✷ ◆❖❘ ❇❡r❣❡♥ ❍❇❱ ✺✳✶✵◦❊ ✲ ✺✳✼✻◦❊

✻✵✳✶✸◦◆ ✲ ✻✵✳✻✹◦◆

✸ ◆❊❉ ❱❡❧✉✇❡ ❆❩❯❘❊ ✸✳✵✸✾✻✶✺◦❊ ✲ ✼✳✺✻✾✶✾✾◦❊

✺✵✳✺✽✵✶✼✺◦◆ ✲ ✺✸✳✼✸✼✾✷✷◦◆

✹ ●❊❘ ❲✉♣♣❡r ◆❆❙■▼ ✻✳✾✶✹◦❊ ✲ ✼✳✻✷✵◦❊

✺✵✳✾✾✺◦◆ ✲ ✺✶✳✸✼✵◦◆

✺ ●❊❘ ❲✉♣♣❡r ❚❆▲❙■▼ ✻✳✾✶✹◦❊ ✲ ✼✳✻✷✵◦❊

✺✵✳✾✾✺◦◆ ✲ ✺✶✳✸✼✵◦◆

✻ ❊❙P ❇❛❞❛❧♦♥❛ ■♥❢♦✇♦r❦s✲■❈▼ ✶✳✾✸✺✵✵✵◦❊ ✲ ✷✳✹✵✶✽✼✺◦❊

✹✶✳✷✹✵✵◦◆ ✲ ✹✶✳✻✵✹✹✻◦◆

✼ ❊❙P ❇❛❞❛❧♦♥❛ ▼♦❤✐❞ ✵✳✵✻◦❊ ✲ ✸✳✻✵◦❊

✹✵✳✶◦◆ ✲ ✹✸✳✶◦◆

✸✵

❚❛❜❧❡ ✹✳✷ ❝♦♥t✐♥✉❡❞

✽ P❖❘ ❚❛❣✉s✲❘✐✈❡r ❈❊✲◗❯❆▲✲❲✷ ◆❆ ✭st❛t✐♦♥ ❞❛t❛✮

✾ P❖❘ ❚❛❣✉s✲❘✐✈❡r ❊❈❖✲❙❊▲❋❊ ✾✳✻◦❲ ✲ ✽✳✻◦❲

✸✽✳✹◦◆ ✲ ✸✾✳✸◦◆

✶✵ P❖❘ ❚❛❣✉s✲❘✐✈❡r ❋❡✢♦✇✲❇❆▲❙❊◗ ◆❆ ✭st❛t✐♦♥ ❞❛t❛✮

✶✶ P❖❘ ❚❛❣✉s✲❘✐✈❡r ❍❊❈❍▼❙ ✾✳✸✵◦❲ ✲ ✾✳✵✺◦❲

✸✽✳✼✺✵✵◦◆ ✲ ✸✽✳✾✽✸✸◦◆

✶✷ P❖❘ ❚❛❣✉s✲❘✐✈❡r ◗❯❆▲✲✷❑ ◆❆ ✭st❛t✐♦♥ ❞❛t❛✮

✶✸ P❖❘ ❚❛❣✉s✲❘✐✈❡r ❙❈❍■❙▼ ✾✳✻◦❲ ✲ ✽✳✻◦❲

✸✽✳✹◦◆ ✲ ✸✾✳✸◦◆

✶✹ ❈❨P ❚r♦♦❞♦s✲ ❲❘❋✲❍②❞r♦ ✸✷✳✵◦❲ ✲ ✸✺✳✵◦❲

▼♦✉♥t❛✐♥s ✸✹✳✵◦◆ ✲ ✸✻✳✵◦◆

✹✳✷✳✸ ■♥♣✉t ♣❛r❛♠❡t❡rs

❯s✐♥❣ t❤❡ ✜rst ♦♣t✐♦♥ ♦❢ t❤❡ ♣❧✉❣✲✐♥ ❧❡ts t❤❡ ✉s❡r ❝❤♦♦s❡ ❛♠♦♥❣ t❤❡ ❘❡s❡❛r❝❤ ❙✐t❡s ❛♥❞ t❤❡❛ss♦❝✐❛t❡❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s ❝♦♠❜✐♥❛t✐♦♥ ✭❘❡s❡❛r❝❤ s✐t❡ ❛♥❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧✮✳❚❤❡ ♦♣t✐♦♥ ❉❛t❡ r❛♥❣❡ s♣❡❝✐✜❡s t❤❡ t✐♠❡ ♣❡r✐♦❞ t♦ ❜❡ ♣r♦❝❡ss❡❞✳ ❚❤❡ ♣❛r❛♠❡t❡r ❇✐❛s❝♦rr❡❝t✐♦♥ ♦♣t✐♦♥❛❧❧② ❧❡❛❞s t♦ ❛ s✉❜s❡q✉❡♥t ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❛ ❜✐❛s ❝♦rr❡❝t✐♦♥ s❝❤❡♠❡✭❙❡❝t✳ ✸ t♦ t❤❡ s✐♠✉❧❛t❡❞ ❞❛t❛❀ ❝❤♦♦s❡ ◆♦♥❡ ❢♦r ♥♦ ❜✐❛s ❝♦rr❡❝t✐♦♥ ❛♥❞ ♦✉t♣✉t ♦❢ t❤❡♥❛t✐✈❡✱ ✉♥❝♦rr❡❝t❡❞ ❞❛t❛ ✐♥st❡❛❞✳ ❇✐❛s ❝♦rr❡❝t✐♦♥ ✐s ❛♣♣❧✐❡❞ ✇✐t❤ r❡❢❡r❡♥❝❡ t♦ st❛t✐♦♥❞❛t❛ ✐♥ ❝❛s❡ t❤❡s❡ ❞❛t❛ ✇❛s ♠❛❞❡ ❛❝❝❡ss✐❜❧❡ ❢♦r ✉s ❛♥❞ ✇✐t❤ r❡❢❡r❡♥❝❡ t♦ t❤❡ ❲❆❚❈❍❋♦r❝✐♥❣ ❉❛t❛ ❊❘❆✲■♥t❡r✐♠ ✭❲❋❉❊■✮✭❲❡❡❞♦♥ ❡t ❛❧✳✱ ✷✵✶✹✮ ♦t❤❡r✇✐s❡✳

❚❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t ❞❛t❛ t♦ ❜❡ ❝❤♦s❡♥ ❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧ ❝❛♥ ❜❡ ✉♥✐q✉❡❧②❛❞❞r❡ss❡❞ ❜② s♣❡❝✐❢②✐♥❣ s❡✈❡♥ ♣❛r❛♠❡t❡rs✳ ❚❤❡s❡ ♣❛r❛♠❡t❡rs r❡s✉❧t ❢r♦♠ t❤❡ st❛♥❞❛r❞✲✐③❡❞ st♦r❛❣❡ ♦❢ ❝❧✐♠❛t❡ ♠♦❞❡❧ ❞❛t❛ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ❈▼❖❘ ❝♦♥✈❡♥t✐♦♥ ❛❧s♦ ✉s❡❞ ✐♥ t❤❡❈♦✉♣❧❡❞ ▼♦❞❡❧ ■♥t❡r✲❝♦♠♣❛r✐s♦♥ Pr♦❥❡❝t ✺ ✭❈▼■P✺✱ ❚❛②❧♦r ❡t ❛❧✳✱ ✷✵✶✷✮✳ ❋♦r t❤❡ ❞❡❧✐✈✲❡r❛❜❧❡ ❉✷✳✶ t❤❡s❡ ❛r❡ s❡t ❜② ❞❡❢❛✉❧t✳ ❋♦r ❝♦♠♣❧❡t❡♥❡ss✱ t❤❡s❡ ♦♣t✐♦♥s ❛r❡ ❉❛t❛♣r♦❥❡❝t✱❉❛t❛♣r♦❞✉❝t✱ ■♥st✐t✉t❡ ❛♥❞ ▼♦❞❡❧ ♣r♦✈✐❞✐♥❣ ✐♥♣✉t ❞❛t❛✳ ❋✉rt❤❡r✱ t❤❡ ❊①♣❡r✐✲♠❡♥t✱ ❊♥s❡♠❜❧❡ ♠❡♠❜❡r ❛♥❞ ❚✐♠❡ ❢r❡q✉❡♥❝② ♦❢ ♣r♦✈✐❞❡❞ ✐♥♣✉t ❞❛t❛ ♠✉st ❜❡s♣❡❝✐✜❡❞✳ ▼❛♥② ♦❢ t❤❡s❡ ♣❛r❛♠❡t❡rs ✇✐❧❧ ♠❛❦❡ s❡♥s❡ ❛t ❛ ❧❛t❡r st❛❣❡ ♦❢ ❇■◆●❖✳

❲✐t❤ t❤❡ ❢♦❧❧♦✇✐♥❣ ♣❛r❛♠❡t❡rs ✈❛r✐♦✉s t❡❝❤♥✐❝❛❧ ♦♣t✐♦♥s ❝❛♥ ❜❡ s❡t✿ ❆ s♣❡❝✐✜❝ ♦✉t♣✉t✭❖✉t♣✉t❞✐r✮ ❛♥❞ ❝❛❝❤❡ ❞✐r❡❝t♦r② ✭❈❛❝❤❡❞✐r✮ ❝❛♥ ❜❡ ❞❡✜♥❡❞✱ ♣❧✉s t❤❡ ❖✉t♣✉t t②♣❡✳❇② s❡❧❡❝t✐♥❣ t❤❡ ♦♣t✐♦♥ ❇❛s✐❝ ♦♥❧② ♦♥❡ ❝♦♠♣r❡ss❡❞ ③✐♣✲✜❧❡ ❝♦♥t❛✐♥✐♥❣ t❤❡ ❤②❞r♦❧♦❣✐❝❛❧✲♠♦❞❡❧✲s♣❡❝✐✜❝✲❢♦r♠❛tt❡❞ ❞❛t❛ ✜❧❡s ✇✐❧❧ ❜❡ ♣r♦❞✉❝❡❞✱ ✇❤✐❧❡ ❆❞❞✐t✐♦♥❛❧ ✇✐❧❧ r❡s✉❧t ✐♥ ❛♥❛❞❞✐t✐♦♥❛❧ ◆❡t❈❉❋✲✜❧❡ ❝♦♥t❛✐♥✐♥❣ ❛❧❧ ✈❛r✐❛❜❧❡s✱ t✐♠❡ st❡♣s ❛♥❞ ❧♦❝❛t✐♦♥s✳ ❚❤❡ s✉❜s❡q✉❡♥t♦♣❡r❛t♦r ❈❛❝❤❡❝❧❡❛r ❛❧❧♦✇s t❤❡ ❝❛❝❤❡ ❞✐r❡❝t♦r② t♦ ❜❡ ❝❧❡❛r❡❞ ❛♥❞ t❤❡ ✐♥t❡r♠❡❞✐❛t❡ ❞❛t❛✉s❡❞ ❢♦r ♣r♦❝❡ss✐♥❣ t♦ ❜❡ ❞❡❧❡t❡❞ ♦r ♥♦t✱ ✐♥ ❝❛s❡ ♦♥❡ ✇❛♥ts t♦ ❣✉❛r❞ t❤❡s❡ ❞❛t❛✳ ■♥◆t❛s❦t❤❡ ♥✉♠❜❡r ♦❢ ♣❛r❛❧❧❡❧✲♣r♦❝❡ss✐♥❣ t❛s❦ ❝❛♥ ❜❡ s❡❧❡❝t❡❞✱ t♦ ♦♣t✐♠✐③❡ t❤❡ ✉s❛❣❡ ♦❢ ❝♦♠♣✉t❡r

✸✶

r❡s♦✉r❝❡s✳ ❙❡tt✐♥❣ t❤❡ ♦♣t✐♦♥ ❉r②r✉♥ t♦ ❚r✉❡ ❣✐✈❡s ♦♥❧② ❛ ❧✐st ♦❢ t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞❛t❛❝❤♦s❡♥✳ ❋✐♥❛❧❧②✱ ❛ ❝❛♣t✐♦♥ ❝❛♥ ❜❡ ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ r❡s✉❧ts ♣r♦❞✉❝❡❞ ❜② t❤✐s r✉♥✳ ❚❤❡❧❛st ♣❛r❛♠❡t❡r ♦♣t✐♦♥ ❯♥✐q✉❡ ♦✉t♣✉t ✐❞ ✇✐❧❧ ♣r❡✈❡♥t ②♦✉ ❢r♦♠ ♦✈❡r✇r✐t✐♥❣ ❛♥ ❡①✐st✐♥❣r❡s✉❧t✳ ❆ ❢✉❧❧ ❧✐st ♦❢ ❛❧❧ ❛✈❛✐❧❛❜❧❡ ♣❛r❛♠❡t❡rs ❛♥❞ t❤❡✐r ❞❡s❝r✐♣t✐♦♥s ❝❛♥ ❜❡ ❢♦✉♥❞ ✐♥❚❛❜✳ ✹✳✷

❚❛❜❧❡ ✹✳✷✿ ■♥♣✉t ♣❛r❛♠❡t❡rs ❢♦r t❤❡ ❇■◆●❖✲❉❊❈❖ ♣❧✉❣✲✐♥✳

❘❡s❡❛r❝❤ s✐t❡ ❛♥❞❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧

❈♦♠❜✐♥❛t✐♦♥ ♦❢ ❘❡s❡❛r❝❤ ❙✐t❡ ❛♥❞ ❍②❞r♦❧♦❣✐❝❛❧ ▼♦❞❡❧ ❢♦r✇❤✐❝❤ ②♦✉ ✇❛♥t t♦ ♣r♦❞✉❝❡ t❤❡ ✐♥♣✉t ❞❛t❛✳

♠❛♥❞❛t♦r②

❉❛t❡ r❛♥❣❡ ❚✐♠❡ ♣❡r✐♦❞ ❢♦r ✇❤✐❝❤ ②♦✉ ✇❛♥t t♦ ♣r♦❝❡ss t❤❡ ❞❛t❛✭❝♦♠♠❛✲s❡♣❛r❛t❡❞ ❢♦r♠❛t✿ ❨❨❨❨✲▼▼✲❉❉✱❨❨❨❨✲▼▼✲❉❉✮✳

♠❛♥❞❛t♦r②

❇✐❛s ❝♦rr❡❝t✐♦♥ ❇✐❛s✲❝♦rr❡❝t✐♦♥ ♠❡t❤♦❞✳

♠❛♥❞❛t♦r②

❉❛t❛♣r♦❥❡❝t ♣r♦✈✐❞✐♥❣✐♥♣✉t ❞❛t❛

❚❤❡ ❞❛t❛ ♣r♦❥❡❝t ♣r♦✈✐❞✐♥❣ t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞❛t❛✱ ❡✳❣✳❜✐♥❣♦✳

♠❛♥❞❛t♦r②

❉❛t❛♣r♦❞✉❝t ♣r♦✈✐❞✐♥❣✐♥♣✉t ❞❛t❛

❚❤❡ ❞❛t❛ ♣r♦❞✉❝t ♣r♦✈✐❞✐♥❣ t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t❞❛t❛✱ ❡✳❣✳ ❡✉r✲✶✶✳

♠❛♥❞❛t♦r②

■♥st✐t✉t❡ ♣r♦✈✐❞✐♥❣✐♥♣✉t ❞❛t❛

❚❤❡ ✐♥st✐t✉t❡ ♣r♦✈✐❞✐♥❣ t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t ❞❛t❛✱ ❡✳❣✳❝❧♠❝♦♠✳

♠❛♥❞❛t♦r②

▼♦❞❡❧ ♣r♦✈✐❞✐♥❣✐♥♣✉t ❞❛t❛

❚❤❡ ♠♦❞❡❧ ♣r♦✈✐❞✐♥❣ t❤❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t ❞❛t❛✱ ❡✳❣✳❡❝♠✇❢✲❡r❛✐♥t✲❝❧♠❝♦♠✲❝❝❧♠✹✲✽✲✶✼✲✈✶✳

♠❛♥❞❛t♦r②

❊①♣❡r✐♠❡♥t ♦❢♣r♦✈✐❞❡❞ ✐♥♣✉t ❞❛t❛

❚❤❡ ❡①♣❡r✐♠❡♥t ♥❛♠❡ ♦❢ t❤❡ ♣r♦✈✐❞❡❞ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥✲♣✉t ❞❛t❛✱ ❡✳❣✳ ❡✈❛❧✉❛t✐♦♥✳

♠❛♥❞❛t♦r②

❊♥s❡♠❜❧❡ ♠❡♠❜❡r ♦❢♣r♦✈✐❞❡❞ ✐♥♣✉t ❞❛t❛

❚❤❡ ❡♥s❡♠❜❧❡ ♠❡♠❜❡r ♦❢ t❤❡ ♣r♦✈✐❞❡❞ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥✲♣✉t ❞❛t❛✱ ❡✳❣✳ r✶✐✶♣✶✳

♠❛♥❞❛t♦r②

❚✐♠❡ ❢r❡q✉❡♥❝② ♦❢♣r♦✈✐❞❡❞ ✐♥♣✉t ❞❛t❛

❚❤❡ t✐♠❡ ❢r❡q✉❡♥❝② ♦❢ t❤❡ ♣r♦✈✐❞❡❞ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ✐♥♣✉t❞❛t❛✱ ❡✳❣✳ ❞❛②✳

♠❛♥❞❛t♦r②

❖✉t♣✉t❞✐r ❖✉t♣✉t ❞✐r❡❝t♦r②

✸✷

❚❛❜❧❡ ✹✳✷ ❝♦♥t✐♥✉❡❞

♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ✴♥❡t✴s❝r❛t❝❤✴✉s❡r✴❡✈❛❧✉❛t✐♦♥❴s②st❡♠✴♦✉t♣✉t✴❜✐♥❣♦❴❞❡❝♦✴t✐♠❡st❡♠♣

❈❛❝❤❡❞✐r ❈❛❝❤❡ ❞✐r❡❝t♦r②

♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ✴♥❡t✴s❝r❛t❝❤✴✉s❡r✴❡✈❛❧✉❛t✐♦♥❴s②st❡♠✴❝❛❝❤❡✴❜✐♥❣♦❴❞❡❝♦✴t✐♠❡st❡♠♣

❖✉t♣✉t t②♣❡ ❚②♣❡ ♦❢ ♦✉♣✉t✳ ❇❛s✐❝✿ ❖♥❡ ❝♦♠♣r❡ss❡❞ ③✐♣✲✜❧❡ ✭st♦r❡❞✐♥ ❖✉t♣✉t❞✐r✴❩■P✮ ❝♦♥t❛✐♥✐♥❣ t❤❡ ❤②❞r♦❧♦❣✐❝❛❧✲♠♦❞❡❧✲s♣❡❝✐✜❡❞✲❢♦r♠❛tt❡❞ ❞❛t❛ ✜❧❡s✳ ❆❞❞✐t✐♦♥❛❧✿ ❆❞❞✐t✐♦♥❛❧❧②✱♦♥❡ ◆❡t❈❉❋✲✜❧❡ ✭st♦r❡❞ ✐♥ ❖✉t♣✉t❞✐r✴◆❊❚❈❉❋✮ ❝♦♥✲t❛✐♥✐♥❣ ❛❧❧ ✈❛r✐❛❜❧❡s✱ t✐♠❡ st❡♣s ❛♥❞ ❧♦❝❛t✐♦♥s✳

♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ❇❛s✐❝

❈❛❝❤❡❝❧❡❛r ❖♣t✐♦♥ t♦ ❝❧❡❛r t❤❡ ❝❛❝❤❡ ❞✐r❡❝t♦r②✳

♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ❚r✉❡

◆t❛s❦ ◆✉♠❜❡r ♦❢ ♣❛r❛❧❧❡❧✲♣r♦❝❡ss✐♥❣ t❛s❦s✳

♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ✻

❉r②r✉♥ ❙❡t ✧❚r✉❡✧ ❢♦r ❥✉st s❤♦✇✐♥❣ t❤❡ ❧✐st ♦❢ ❢♦✉♥❞ ✜❧❡s ♦❢ ②♦✉r❝❤♦s❡♥ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞❛t❛✳ ❙❡t ✧❋❛❧s❡✧ t♦ ♣r♦❝❡ss ❞❛t❛✳

♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ❋❛❧s❡

❈❛♣t✐♦♥ ❆♥ ❛❞❞✐t✐♦♥❛❧ ❝❛♣t✐♦♥ t♦ ❜❡ ❞✐s♣❧❛②❡❞ ✇✐t❤ t❤❡ r❡s✉❧ts✳

♦♣t✐♦♥❛❧

❯♥✐q✉❡ ♦✉t♣✉t ✐❞ ■❢ tr✉❡ ❛♣♣❡♥❞ t❤❡ ❢r❡✈❛ r✉♥ ✐❞ t♦ ❡✈❡r② ♦✉t♣✉t ❢♦❧❞❡r✳

♠❛♥❞❛t♦r② ❞❡❢❛✉❧t ✿ ❚r✉❡

✹✳✷✳✹ ❖✉t♣✉t

❚❤❡ r❡s✉❧t✐♥❣ ❞❛t❛ ✜❧❡s ❛r❡ st♦r❡❞ ✐♥ t❤❡ ❝❤♦s❡♥ ❖✉t♣✉t❞✐r ❛♥❞ ❝❛♥ ❜❡ ❛❝❝❡ss❡❞ ❡✐t❤❡r❞✐r❡❝t❧② ✈✐❛ t❤❡ ✇❡❜ ❞♦✇♥❧♦❛❞ ❢r♦♠ t❤❡ ❋r❡❱❛ s②st❡♠ ♦r ❜② ✉s✐♥❣ s❡❝✉r❡ ❝♦♣② ✭s❝♣✮♦r s❡❝✉r❡ s❤❡❧❧ ✭ss❤✮✶✳ ❚❤❡ ❞♦✇♥❧♦❛❞❛❜❧❡ ❝♦♠♣r❡ss❡❞ ③✐♣✲✜❧❡ ✇❤✐❝❤ ❝♦♥t❛✐♥s t❤❡ ❞❛t❛✜❧❡s ❢♦r♠❛tt❡❞ ❛s s♣❡❝✐✜❡❞ ❢♦r t❤❡ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧ ✐s st♦r❡❞ ✐♥ t❤❡ ❖✉t♣✉t❞✐r✴❩■P❞✐r❡❝t♦r②✳ ❆♥ ❛❞❞✐t✐♦♥❛❧❧② ♣r♦❞✉❝❡❞ ◆❡t❈❉❋ ✜❧❡s ✭✐❢ ❖✉t♣✉t t②♣❡ ✐s s❡t ❆❞❞✐t✐♦♥❛❧✮❛r❡ ❧♦❝❛t❡❞ ✐♥ t❤❡ ❖✉t♣✉t❞✐r✴◆❊❚❈❉❋ ❞✐r❡❝t♦r②✳ ◆♦t❡ t❤❛t✱ ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡ ❝❤♦s❡♥r❡s❡❛r❝❤ s✐t❡ ❛♥❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧✱ t❤❡ ✜❧❡s ✐♥ t❤❡ t✇♦ ❞✐r❡❝t♦r✐❡s ❝♦✉❧❞ ❜❡ t❤❡ s❛♠❡✳❙♦♠❡ ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t t❤❡ ♦✉t♣✉t ❝❛♥ ❜❡ ❢♦✉♥❞ ✐♥ ❚❛❜✳ ✹✳✸✳ ❚❤❡ s♣❡❝✐✜❝ ♦✉t♣✉t ❝♦♥t❡♥t❛♥❞ ❢♦r♠❛t ✐s ❜❛s❡❞ ♦♥ t❤❡ q✉❡st✐♦♥♥❛✐r❡ s❡♥❞ ♦✉t ❜② ❲P✸✳ ■♥ ❝❛s❡ ✇❡ ❞✐❞ ♥♦t ❣❡t ❛♥②❢❡❡❞❜❛❝❦ ❛ st❛♥❞❛r❞ ♦✉t♣✉t ✭◆❡t❈❉❋ ✜❧❡✮ ✇✐❧❧ ❜❡ ♣r♦✈✐❞❡❞✳

✶P❧❡❛s❡ ❝♦♥t❛❝t t❤❡ ❞❡✈❡❧♦♣❡rs ✐❢ ②♦✉ ❧✐❦❡ t♦ ✉s❡ s❝♣ ❛♥❞ ss❤✳

✸✸

❚❛❜❧❡ ✹✳✸✿ ❋✐❧❡ ❢♦r♠❛ts✱ ✈❛r✐❛❜❧❡s ✇✐t❤ ✉♥✐ts ❛♥❞ t❤❡✐r ❞❡s❝r✐♣t✐♦♥ ❣✐✈❡♥ ❢♦r ❡❛❝❤ ❘❡s❡❛r❝❤ ❙✐t❡❛♥❞ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧ ❝♦♠❜✐♥❛t✐♦♥✳

★ ❚②♣❡ ❋♦r♠❛t ❱❛r✐❛❜❧❡ ❬✉♥✐t❪ ❱❛r✐❛❜❧❡ ❉❡s❝r✐♣t✐♦♥

✶ ❣r✐❞ ♥❝ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮

❝✉r✈✐❧✐♥❡❛r t❛s ❬◦❈❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

✉❛s ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

✈❛s ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥

❤✉ss ❬✶❪ ◆❡❛r✲❙✉r❢❛❝❡ ❙♣❡❝✐✜❝ ❍✉♠✐❞✐t②

✷ ❣r✐❞ ♥❝ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞✴❧✐q✉✐❞✮

❝✉r✈✐❧✐♥❡❛r t❛s♠✐♥ ❬◦❈❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

t❛s♠❛① ❬◦❈❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

✸ ❣r✐❞ ♥❝ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮

❝✉r✈✐❧✐♥❡❛r t❛s ❬◦❈❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

♣s ❬P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡

❤✉rs ❬✪❪ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②

s❢❝❲✐♥❞ ❬♠✴s❪ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞ ❙♣❡❡❞

rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥

✹ ❣r✐❞ ♥❝ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮

❝✉r✈✐❧✐♥❡❛r t❛s ❬❑❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

♣s ❬P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡

✉❛s ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

✈❛s ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥

❤✉ss ❬✶❪ ◆❡❛r✲❙✉r❢❛❝❡ ❙♣❡❝✐✜❝ ❍✉♠✐❞✐t②

✺ ❣r✐❞ ♥❝ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮

❝✉r✈✐❧✐♥❡❛r t❛s ❬◦❈❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

✉❛s ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

✈❛s ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

♣s ❬P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡

✸✹

❚❛❜❧❡ ✹✳✸ ❝♦♥t✐♥✉❡❞

rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥

❤✉ss ❬✶❪ ◆❡❛r✲❙✉r❢❛❝❡ ❙♣❡❝✐✜❝ ❍✉♠✐❞✐t②

✻ ❣r✐❞ ♥❝✹ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮

❝✉r✈✐❧✐♥❡❛r

✼ ❣r✐❞ ♥❝✹ ✉❛s ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

❝✉r✈✐❧✐♥❡❛r ✈❛s ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

t❛s ❬◦❈❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

❤✉rs ❬✪❪ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②

❝❧t ❬✪❪ ❚♦t❛❧ ❈❧♦✉❞ ❋r❛❝t✐♦♥

✽ st❛t✐♦♥ ❝s✈ Pr❡❝ ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮

❚♠✐♥ ❬◦❈❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

❚♠❛① ❬◦❈❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

❘❍♠✐♥ ❬✪❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②

❘❍♠❛① ❬✪❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②

✈✈ ❬♠✴s❪ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞ ❙♣❡❡❞

P ❬❦P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡

❘s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

✾ ❣r✐❞ ♥❝ st♠♣ ❬❑❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

❝✉r✈✐❧✐♥❡❛r ✉✇✐♥❞ ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

✈✇✐♥❞ ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

♣r♠s❧ ❬P❛❪ ❙❡❛ ▲❡✈❡❧ Pr❡ss✉r❡

❞s✇r❢ ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

❞❧✇r❢ ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥

s♣❢❤ ❬✶❪ ◆❡❛r✲❙✉r❢❛❝❡ ❙♣❡❝✐✜❝ ❍✉♠✐❞✐t②

✶✵ st❛t✐♦♥ ❝s✈ Pr❡❝ ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮

❚♠✐♥ ❬◦❈❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

❚♠❛① ❬◦❈❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

❘❍♠✐♥ ❬✪❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②

❘❍♠❛① ❬✪❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②

✈✈ ❬♠✴s❪ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞ ❙♣❡❡❞

✸✺

❚❛❜❧❡ ✹✳✸ ❝♦♥t✐♥✉❡❞

P ❬❦P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡

❘s ❬❦P❛❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

✶✶ ❣r✐❞ ❝s✈ ♣r ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮

❝✉r✈✐❧✐♥❡❛r t❛s ❬◦❈❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

♣s❧ ❬P❛❪ ❙❡❛ ▲❡✈❡❧ Pr❡ss✉r❡

❤✉rs ❬✪❪ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②

s❢❝❲✐♥❞ ❬❦♠✴❤❪ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞ ❙♣❡❡❞

rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥

✶✷ st❛t✐♦♥ ❝s✈ Pr❡❝ ❬♠♠✴❞❛②❪ Pr❡❝✐♣✐t❛t✐♦♥ ✭s♦❧✐❞ ✰ ❧✐q✉✐❞✮

❚♠✐♥ ❬◦❈❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

❚♠❛① ❬◦❈❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

❘❍♠✐♥ ❬✪❪ ▼✐♥✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②

❘❍♠❛① ❬✪❪ ▼❛①✳ ◆❡❛r ❙✉r❢❛❝❡ ❘❡❧❛t✐✈❡ ❍✉♠✐❞✐t②

✈✈ ❬♠✴s❪ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞ ❙♣❡❡❞

P ❬❦P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡

❘s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

✶✸ ❣r✐❞ ♥❝ ✉✇✐♥❞ ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

❝✉r✈✐❧✐♥❡❛r ✈✇✐♥❞ ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

♣r♠s❧ ❬P❛❪ ❙❡❛ ▲❡✈❡❧ Pr❡ss✉r❡

✶✹ ❣r✐❞ ♥❝ t❛s ❬❑❪ ◆❡❛r ❙✉r❢❛❝❡ ❆✐r ❚❡♠♣❡r❛t✉r❡

❝✉r✈✐❧✐♥❡❛r ✉❛s ❬♠✴s❪ ❊❛st✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

✈❛s ❬♠✴s❪ ◆♦rt❤✇❛r❞ ◆❡❛r✲❙✉r❢❛❝❡ ❲✐♥❞

♣s ❬P❛❪ ❙✉r❢❛❝❡ ❆✐r Pr❡ss✉r❡

rs❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ❙❲ ❘❛❞✐❛t✐♦♥

r❧❞s ❬❲✴♠2❪ ❙✉r❢❛❝❡ ❉♦✇♥✇❡❧❧✐♥❣ ▲❲ ❘❛❞✐❛t✐♦♥

❤✉ss ❬✶❪ ◆❡❛r✲❙✉r❢❛❝❡ ❙♣❡❝✐✜❝ ❍✉♠✐❞✐t②

✸✻

❈❤❛♣t❡r ✺

❙✉♠♠❛r②

❚❤✐s ❞♦❝✉♠❡♥t ❞❡s❝r✐❜❡s t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ✇❡❜ ❜❛s❡❞ ❛♣♣❧✐❝❛t✐♦♥ ❢♦r t❤❡ ❡①tr❛❝t✐♦♥❛♥❞ ❝♦♥✈❡rs✐♦♥ ♦❢ ❝❧✐♠❛t❡ ♠♦❞❡❧ s✐♠✉❧❛t✐♦♥s✳ ❈❧✐♠❛t❡ ♠♦❞❡❧ ❞❛t❛ ✐s ❡①tr❛❝t❡❞ ❢r♦♠ ❛❝❡♥tr❛❧ ❞❛t❛ ♣♦♦❧✱ ♣♦st✲♣r♦❝❡ss❡❞ ✭❜✐❛s✲❝♦rr❡❝t❡❞✱ r❡❣r✐❞❞❡❞✮ ❛♥❞ ❝♦♥✈❡rt❡❞ t♦ ❛ s❡t ♦❢♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞r✐✈✐♥❣ ❞❛t❛ ❞✐r❡❝t❧② ✉s❛❜❧❡ ❢♦r ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s✳ ❚❤✐s ❛♣♣❧✐❝❛t✐♦♥❤❛s ❜❡❡♥ r❡❛❧✐③❡❞ ❛s ❛ ♣❧✉❣✲✐♥ t♦ t❤❡ ❋r❡✐❡ ❯♥✐✈❡rs✐tät ❇❡r❧✐♥ ❊✈❛❧✉❛t✐♦♥ ❋r❛♠❡✇♦r❦

❢♦r ❊❛rt❤ ❙②st❡♠ ❙❝✐❡♥❝❡ ✭❋r❡❱❛✮ ✇❤✐❝❤ ❝❛♥ ❤♦❧❞ ✈❛r✐♦✉s t②♣❡s ♦❢ ❡✈❛❧✉❛t✐♦♥ ✇♦r❦✢♦✇s❤❛✈✐♥❣ ❛❝❝❡ss t♦ ❛♥ ✐♥❞❡①❡❞ ❞❛t❛ ♣♦♦❧✳ ❲♦r❦✢♦✇s ❝❛♥ ❜❡ ❛❝❝❡ss❡❞ ✈✐❛ ❛ ✇❡❜✲♣❧❛t❢♦r♠ ♦rt❤❡ ❝♦♠♠❛♥❞ ❧✐♥❡ ✐♥t❡r❢❛❝❡✳ ❚❤❡ ❇■◆●❖✲❉❊❈❖ ♣❧✉❣✲✐♥ ❤❛s ❜❡❡♥ s♣❡❝✐✜❝❛❧❧② ❞❡s✐❣♥❡❞❢♦r t❤❡ ❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧s ❛t t❤❡ s✐① ❇■◆●❖ ❘❡s❡❛r❝❤ ❙✐t❡s ❜✉t ❝❛♥ ✐♥ ♣r✐♥❝✐♣❧❡ ❜❡❡①t❡♥❞❡❞ t♦ ♦t❤❡r ♠♦❞❡❧s✳ ❆ ♠❛❥♦r ❛❞✈❛♥t❛❣❡ ✐s t❤❡ ♦♥✲❞❡♠❛♥❞ ♣♦st✲♣r♦❝❡ss✐♥❣ ❛♥❞❝♦♥✈❡rs✐♦♥ ♦❢ t❤❡ ❞r✐✈✐♥❣ ❞❛t❛ ❢r♦♠ ❛ st❛♥❞❛r❞✐③❡❞ ❝❧✐♠❛t❡ ♠♦❞❡❧ ❞❛t❛ s♦✉r❝❡✳ ■♥st❡❛❞♦❢ st♦r✐♥❣ ❛♥❞ ❦❡❡♣✐♥❣ t❤❡ ✈❡r② s❛♠❡ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❞r✐✈✐♥❣ ✐♥❢♦r♠❛t✐♦♥ ✐♥ ❞✐✛❡r❡♥t❢♦r♠❛ts✱ t❤❡ s②st❡♠ ❤♦❧❞s t❤❡ ❝♦♥✈❡rs✐♦♥ r♦✉t✐♥❡s ❛♥❞ ❣❡♥❡r❛t❡s t❤❡ ❞❛t❛ ♦♥ ❞❡♠❛♥❞✳❚❤✐s ✐s st♦r❛❣❡ ❡✣❝✐❡♥t ❛♥❞ ❡♥s✉r❡s r❡♣r♦❞✉❝✐❜❧❡ ❛♥❞ tr❛♥s♣❛r❡♥t r❡s✉❧ts✳

✸✼

❇✐❜❧✐♦❣r❛♣❤②

◆✐❦♦❧✐♥❛ ❇❛♥✱ ❏✉❡r❣ ❙❝❤♠✐❞❧✐✱ ❛♥❞ ❈❤r✐st♦♣❤ ❙❝❤är✳ ❍❡❛✈② ♣r❡❝✐♣✐t❛t✐♦♥ ✐♥ ❛ ❝❤❛♥❣✐♥❣❝❧✐♠❛t❡✿ ❉♦❡s s❤♦rt✲t❡r♠ s✉♠♠❡r ♣r❡❝✐♣✐t❛t✐♦♥ ✐♥❝r❡❛s❡ ❢❛st❡r❄ ●❡♦♣❤②s✐❝❛❧ ❘❡s❡❛r❝❤

▲❡tt❡rs✱ ✹✷✭✹✮✿✶✶✻✺✕✶✶✼✷✱ ✷✵✶✺✳

❊r✇❛♥ ❇r✐ss♦♥✱ ▼❛tt❤✐❛s ❉❡♠✉③❡r❡✱ ❛♥❞ ◆✐❝♦❧❡ P▼ ✈❛♥ ▲✐♣③✐❣✳ ▼♦❞❡❧❧✐♥❣ str❛t❡❣✐❡s❢♦r ♣❡r❢♦r♠✐♥❣ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ ❝❧✐♠❛t❡ s✐♠✉❧❛t✐♦♥s✳ ▼❡t❡♦r♦❧♦❣✐s❝❤❡ ❩❡✐ts❝❤r✐❢t✱✷✵✶✺✳

❆✉❣✉st✐♥ ❈♦❧❡tt❡✱ ❘♦❜❡rt ❱❛✉t❛r❞✱ ❛♥❞ ▼ ❱r❛❝✳ ❘❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ❞♦✇♥s❝❛❧✐♥❣ ✇✐t❤ ♣r✐♦rst❛t✐st✐❝❛❧ ❝♦rr❡❝t✐♦♥ ♦❢ t❤❡ ❣❧♦❜❛❧ ❝❧✐♠❛t❡ ❢♦r❝✐♥❣✳ ●❡♦♣❤②s✐❝❛❧ ❘❡s❡❛r❝❤ ▲❡tt❡rs✱ ✸✾✭✶✸✮✱ ✷✵✶✷✳

❉✳ P✳ ❉❡❡ ❡t ❛❧✳ ❚❤❡ ❊❘❆✲✐♥t❡r✐♠ r❡❛♥❛❧②s✐s✿ ❝♦♥✜❣✉r❛t✐♦♥ ❛♥❞ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡ ❞❛t❛❛ss✐♠✐❧❛t✐♦♥ s②st❡♠✳ ◗✳ ❏✳ ❘✳ ▼❡t❡♦r✳ ❙♦❝✳✱ ✶✸✼✭✻✺✻✮✿✺✺✸✕✺✾✼✱ ✷✵✶✶✳ ■❙❙◆ ✶✹✼✼✲✽✼✵❳✳❞♦✐✿ ✶✵✳✶✵✵✷✴q❥✳✽✷✽✳

▼✐❝❤❡❧ ❉éq✉é✳ ❋r❡q✉❡♥❝② ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ❛♥❞ t❡♠♣❡r❛t✉r❡ ❡①tr❡♠❡s ♦✈❡r ❢r❛♥❝❡ ✐♥ ❛♥❛♥t❤r♦♣♦❣❡♥✐❝ s❝❡♥❛r✐♦✿ ♠♦❞❡❧ r❡s✉❧ts ❛♥❞ st❛t✐st✐❝❛❧ ❝♦rr❡❝t✐♦♥ ❛❝❝♦r❞✐♥❣ t♦ ♦❜s❡r✈❡❞✈❛❧✉❡s✳ ●❧♦❜❛❧ ❛♥❞ P❧❛♥❡t❛r② ❈❤❛♥❣❡✱ ✺✼✭✶✮✿✶✻✕✷✻✱ ✷✵✵✼✳

▲✳ ●✉❞♠✉♥❞ss♦♥✱ ▲✳ ▼✳ ❚❛❧❧❛❦s❡♥✱ ❑✳ ❙t❛❤❧✱ ❛♥❞ ❆✳ ❑✳ ❋❧❡✐❣✳ ▲♦✇✲❢r❡q✉❡♥❝② ✈❛r✐❛❜✐❧✐t②♦❢ ❡✉r♦♣❡❛♥ r✉♥♦✛✳ ❍②❞r♦❧✳ ❊❛rt❤ ❙②st❡♠ ❙❝✐✳✱ ✶✺✭✾✮✿✷✽✺✸✕✷✽✻✾✱ ✷✵✶✶✳

❯✳ ❍❡✐❦❦✐❧ä✳✱ ❆✳ ❙❛♥❞✈✐❦✳✱ ❛♥❞ ❆✳ ❙♦rt❡❜❡r❣✳ ❉②♥❛♠✐❝❛❧ ❞♦✇♥s❝❛❧✐♥❣ ♦❢ ❊❘❆✲✹✵ ✐♥❝♦♠♣❧❡① t❡rr❛✐♥ ✉s✐♥❣ t❤❡ ✇r❢ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✳ ❈❧✐♠✳ ❉②♥✳✱ ✸✼✭✼✲✽✮✿✶✺✺✶✕✶✺✻✹✱✷✵✶✶✳

❈✳ ❑❛❞♦✇✱ ❙✳ ■❧❧✐♥❣✱ ❖✳ ❑✉♥st✱ ❚✳ ❙❝❤❛rt♥❡r✱ ■✳ ❑✐r❝❤♥❡r✱ ❍✳❲✳ ❘✉st✱ ❯✳ ❈✉❜❛s❝❤✱ ❛♥❞❯ ❯❧❜r✐❝❤✳ ❋r❡✈❛ ✲ ❢r❡✐❡ ✉♥✐✈ ❡✈❛❧✉❛t✐♦♥ ❢r❛♠❡✇♦r❦ ❢♦r s❝✐❡♥t✐✜❝ ✐♥❢r❛str✉❝t✉r❡s ✐♥ ❡❛rt❤s②st❡♠ ♠♦❞❡❧✐♥❣✳ ●❡♦s❝✐❡♥t✐❢✳ ▼♦❞❡❧ ❉❡✈❡❧♦♣✳✱ ✐♥ ♣r❡♣❛r❛t✐♦♥✳

❊❧✐③❛❜❡t❤ ❏ ❑❡♥❞♦♥✱ ◆✐❣❡❧ ▼ ❘♦❜❡rts✱ ❍❛②❧❡② ❏ ❋♦✇❧❡r✱ ▼❛❧❝♦❧♠ ❏ ❘♦❜❡rts✱ ❙t❡✈❡♥ ❈❈❤❛♥✱ ❛♥❞ ❈❛t❤❡r✐♥❡ ❆ ❙❡♥✐♦r✳ ❍❡❛✈✐❡r s✉♠♠❡r ❞♦✇♥♣♦✉rs ✇✐t❤ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ r❡✲✈❡❛❧❡❞ ❜② ✇❡❛t❤❡r ❢♦r❡❝❛st r❡s♦❧✉t✐♦♥ ♠♦❞❡❧✳ ◆❛t✉r❡ ❈❧✐♠❛t❡ ❈❤❛♥❣❡✱ ✹✭✼✮✿✺✼✵✕✺✼✻✱✷✵✶✹✳

✸✽

❍✳ ❑♦❝❤✱ ❙✳ ▲✐❡rs❝❤✱ ❛♥❞ ❋✳ ❍❛tt❡r♠❛♥♥✳ ■♥t❡❣r❛t✐♥❣ ✇❛t❡r r❡s♦✉r❝❡s ♠❛♥❛❣❡♠❡♥t ✐♥❡❝♦✲❤②❞r♦❧♦❣✐❝❛❧ ♠♦❞❡❧❧✐♥❣✳ ■♥t❡❣r❛t✐✈❡ ❲❛t❡r ❘❡s♦✉r❝❡ ▼❛♥❛❣❡♠❡♥t ✐♥ ❛ ❈❤❛♥❣✐♥❣

❲♦r❧❞✿ ▲❡ss♦♥s ▲❡❛r♥t ❛♥❞ ■♥♥♦✈❛t✐✈❡ P❡rs♣❡❝t✐✈❡s✱ ♣❛❣❡ ✶✸✱ ✷✵✶✸✳

❏♦❝❤❡♠ ▼❛r♦t③❦❡✱ ❲♦❧❢❣❛♥❣ ❆ ▼ü❧❧❡r✱ ❋r❡❥❛ ❙❊ ❱❛♠❜♦r❣✱ P❛✉❧ ❇❡❝❦❡r✱ ❯❧r✐❝❤ ❈✉❜❛s❝❤✱❍❡♥❞r✐❦ ❋❡❧❞♠❛♥♥✱ ❋r❛♥❦ ❑❛s♣❛r✱ ❈❤r✐st♦♣❤ ❑♦tt♠❡✐❡r✱ ❈❛♠✐❧❧❡ ▼❛r✐♥✐✱ ■✉❧✐✐❛P♦❧❦♦✈❛✱ ❡t ❛❧✳ ▼✐❦❧✐♣✲❛ ♥❛t✐♦♥❛❧ r❡s❡❛r❝❤ ♣r♦❥❡❝t ♦♥ ❞❡❝❛❞❛❧ ❝❧✐♠❛t❡ ♣r❡❞✐❝t✐♦♥✳ ❇✉❧✲❧❡t✐♥ ♦❢ t❤❡ ❆♠❡r✐❝❛♥ ▼❡t❡♦r♦❧♦❣✐❝❛❧ ❙♦❝✐❡t②✱ ✭✷✵✶✻✮✱ ✷✵✶✻✳

P✳ ▼❝❈✉❧❧❛❣❤ ❛♥❞ ❏✳ ◆❡❧❞❡r✳ ●❡♥❡r❛❧✐③❡❞ ▲✐♥❡❛r ▼♦❞❡❧s✳ ❈❘❈ Pr❡ss✱ ❇♦❝❛ ❘❛t♦♥✱ ❋❧❛✱✷ ❡❞✐t✐♦♥✱ ✶✾✽✾✳

❊❞♠✉♥❞ P ▼❡r❡❞✐t❤✱ ❱❧❛❞✐♠✐r ❆ ❙❡♠❡♥♦✈✱ ❉♦✉❣❧❛s ▼❛r❛✉♥✱ ❲♦♥s✉♥ P❛r❦✱ ❛♥❞ ❆❧❡①❛♥✲❞❡r ❱ ❈❤❡r♥♦❦✉❧s❦②✳ ❈r✉❝✐❛❧ r♦❧❡ ♦❢ ❜❧❛❝❦ s❡❛ ✇❛r♠✐♥❣ ✐♥ ❛♠♣❧✐❢②✐♥❣ t❤❡ ✷✵✶✷ ❦r②♠s❦♣r❡❝✐♣✐t❛t✐♦♥ ❡①tr❡♠❡✳ ◆❛t✉r❡ ●❡♦s❝✐❡♥❝❡✱ ✷✵✶✺✳

P✲❆ ▼✐❝❤❡❧❛♥❣❡❧✐✱ ▼❛tt❤✐❡✉ ❱r❛❝✱ ❛♥❞ ❍ ▲♦✉❦♦s✳ Pr♦❜❛❜✐❧✐st✐❝ ❞♦✇♥s❝❛❧✐♥❣ ❛♣♣r♦❛❝❤❡s✿❆♣♣❧✐❝❛t✐♦♥ t♦ ✇✐♥❞ ❝✉♠✉❧❛t✐✈❡ ❞✐str✐❜✉t✐♦♥ ❢✉♥❝t✐♦♥s✳ ●❡♦♣❤②s✐❝❛❧ ❘❡s❡❛r❝❤ ▲❡tt❡rs✱✸✻✭✶✶✮✱ ✷✵✵✾✳

❲♦❧❢❣❛♥❣ ❆ ▼✉❡❧❧❡r✱ ❏♦❤❛♥♥❛ ❇❛❡❤r✱ ❍❡❧♠✉t❤ ❍❛❛❦✱ ❏♦❤❛♥♥ ❍ ❏✉♥❣❝❧❛✉s✱ ❏ür❣❡♥❑rö❣❡r✱ ❉❛♥✐❡❧❛ ▼❛t❡✐✱ ❉✐r❦ ◆♦t③✱ ❍♦❧❣❡r P♦❤❧♠❛♥♥✱ ❏❙ ❙t♦r❝❤✱ ❛♥❞ ❏♦❝❤❡♠ ▼❛r♦t③❦❡✳❋♦r❡❝❛st s❦✐❧❧ ♦❢ ♠✉❧t✐✲②❡❛r s❡❛s♦♥❛❧ ♠❡❛♥s ✐♥ t❤❡ ❞❡❝❛❞❛❧ ♣r❡❞✐❝t✐♦♥ s②st❡♠ ♦❢ t❤❡ ♠❛①♣❧❛♥❝❦ ✐♥st✐t✉t❡ ❢♦r ♠❡t❡♦r♦❧♦❣②✳ ●❡♦♣❤②s✐❝❛❧ ❘❡s❡❛r❝❤ ▲❡tt❡rs✱ ✸✾✭✷✷✮✱ ✷✵✶✷✳

❍❛♥s ❆ P❛♥♦❢s❦② ❛♥❞ ●❧❡♥♥ ❲✐❧s♦♥ ❇r✐❡r✳ ❙♦♠❡ ❛♣♣❧✐❝❛t✐♦♥s ♦❢ st❛t✐st✐❝s t♦ ♠❡t❡♦r♦❧♦❣②✳❯♥✐✈❡rs✐t② P❛r❦ ✿ P❡♥♥✳ ❙t❛t❡ ❯♥✐✈❡rs✐t②✱ ❈♦❧❧❡❣❡ ♦❢ ❊❛rt❤ ❛♥❞ ▼✐♥❡r❛❧ ❙❝✐❡♥❝❡s✱ ✶✾✻✽✳

❍♦❧❣❡r P♦❤❧♠❛♥♥✱ ❲♦❧❢❣❛♥❣ ❆ ▼✉❡❧❧❡r✱ ❑ ❑✉❧❦❛r♥✐✱ ▼ ❑❛♠❡s✇❛rr❛♦✱ ❉❛♥✐❡❧❛ ▼❛t❡✐✱❋❙❊ ❱❛♠❜♦r❣✱ ❈ ❑❛❞♦✇✱ ❙ ■❧❧✐♥❣✱ ❛♥❞ ❏♦❝❤❡♠ ▼❛r♦t③❦❡✳ ■♠♣r♦✈❡❞ ❢♦r❡❝❛st s❦✐❧❧ ✐♥t❤❡ tr♦♣✐❝s ✐♥ t❤❡ ♥❡✇ ♠✐❦❧✐♣ ❞❡❝❛❞❛❧ ❝❧✐♠❛t❡ ♣r❡❞✐❝t✐♦♥s✳ ●❡♦♣❤②s✐❝❛❧ ❘❡s❡❛r❝❤ ▲❡tt❡rs✱✹✵✭✷✶✮✿✺✼✾✽✕✺✽✵✷✱ ✷✵✶✸✳

❆♥❞r❡❛s ❋ Pr❡✐♥✱ ❲♦❧❢❣❛♥❣ ▲❛♥❣❤❛♥s✱ ●✐♦r❣✐❛ ❋♦ss❡r✱ ❆♥❞r❡✇ ❋❡rr♦♥❡✱ ◆✐❦♦❧✐♥❛ ❇❛♥✱❑❧❛✉s ●♦❡r❣❡♥✱ ▼✐❝❤❛❡❧ ❑❡❧❧❡r✱ ▼❡r❥❛ ❚ö❧❧❡✱ ❖❧✐✈❡r ●✉t❥❛❤r✱ ❋r❛✉❦❡ ❋❡s❡r✱ ❡t ❛❧✳ ❆ r❡✲✈✐❡✇ ♦♥ r❡❣✐♦♥❛❧ ❝♦♥✈❡❝t✐♦♥✲♣❡r♠✐tt✐♥❣ ❝❧✐♠❛t❡ ♠♦❞❡❧✐♥❣✿ ❉❡♠♦♥str❛t✐♦♥s✱ ♣r♦s♣❡❝ts✱❛♥❞ ❝❤❛❧❧❡♥❣❡s✳ ❘❡✈✐❡✇s ♦❢ ❣❡♦♣❤②s✐❝s✱ ✺✸✭✷✮✿✸✷✸✕✸✻✶✱ ✷✵✶✺✳

▼✳ ❇✳ Pr✐❡st❧❡②✳ ❙♣❡❝tr❛❧ ❆♥❛❧②s✐s ❛♥❞ ❚✐♠❡ ❙❡r✐❡s✳ ❆❝❛❞❡♠✐❝ Pr❡ss✱ ▲♦♥❞♦♥✱ ✶✾✾✷✳

❈✳ Pr✉❞❤♦♠♠❡✱ ■✳ ●✐✉♥t♦❧✐✱ ❊✳ ▲✳ ❘♦❜✐♥s♦♥✱ ❉✳ ❈❧❛r❦ ❇✱ ◆✳ ❲✳ ❆r♥❡❧❧✱ ❘✳ ❉❛♥❦❡rs✱❇✳ ▼✳ ❋❡❦❡t❡✱ ❲✳ ❋r❛♥ss❡♥✱ ❉✳ ●❡rt❡♥✱ ❙✳ ◆✳ ●♦s❧✐♥❣✱ ❡t ❛❧✳ ❍②❞r♦❧♦❣✐❝❛❧ ❞r♦✉❣❤ts✐♥ t❤❡ ✷✶st ❝❡♥t✉r②✱ ❤♦ts♣♦ts ❛♥❞ ✉♥❝❡rt❛✐♥t✐❡s ❢r♦♠ ❛ ❣❧♦❜❛❧ ♠✉❧t✐♠♦❞❡❧ ❡♥s❡♠❜❧❡❡①♣❡r✐♠❡♥t✳ Pr♦❝✳ ◆❛t✳ ❆❝❛❞✳ ❙❝✐✳✱ ✶✶✶✭✾✮✿✸✷✻✷✕✸✷✻✼✱ ✷✵✶✹✳

❇✳ ❘♦❝❦❡❧✱ ❆✳ ❲✐❧❧✱ ❛♥❞ ❆✳ ❍❡♥s❡✳ ❚❤❡ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧ ❈❖❙▼❖✲❈▲▼ ✭❈❈▲▼✮✳▼❡t❡♦r♦❧✳ ❩✳✱ ✶✼✭✹✮✿✸✹✼✕✸✹✽✱ ✷✵✵✽✳

✸✾

❍✳ ❲✳ ❘✉st✱ ❚✳ ❑r✉s❝❤❦❡✱ ❆✳ ❉♦❜❧❡r✱ ▼✳ ❋✐s❝❤❡r✱ ❛♥❞ ❯✳ ❯❧❜r✐❝❤✳ ❉✐s❝♦♥t✐♥✉♦✉s ❞❛✐❧②t❡♠♣❡r❛t✉r❡s ✐♥ t❤❡ ✇❛t❝❤ ❢♦r❝✐♥❣ ❞❛t❛s❡ts✳ ❏✳ ❍②❞r♦♠❡t❡♦r✳✱ ✶✻✭✶✮✿✹✻✺✕✹✼✷✱ ✷✵✶✺✳

❯✳ ❙❝❤✉❧③✇❡✐❞❛✳ ❈❧✐♠❛t❡ ❉❛t❛ ❖♣❡r❛t♦rs✿ ❈❉❖ ❯s❡r✬s ●✉✐❞❡✳ ▼P■ ❢♦r ▼❡t❡♦r♦❧♦❣②✱ ❖❝✲t♦❜❡r ✷✵✶✺✳ ❯❘▲ ❤tt♣s✿✴✴❝♦❞❡✳③♠❛✇✳❞❡✴♣r♦❥❡❝ts✴❝❞♦✴❡♠❜❡❞❞❡❞✴❝❞♦✳♣❞❢✳ ❱❡rs✐♦♥✶✳✼✳✵✳

❉♦✉❣ ▼ ❙♠✐t❤✱ ❙t❡♣❤❡♥ ❈✉s❛❝❦✱ ❆♥❞r❡✇ ❲ ❈♦❧♠❛♥✱ ❈❤r✐s ❑ ❋♦❧❧❛♥❞✱ ●❧❡♥ ❘ ❍❛rr✐s✱❛♥❞ ❏❛♠❡s ▼ ▼✉r♣❤②✳ ■♠♣r♦✈❡❞ s✉r❢❛❝❡ t❡♠♣❡r❛t✉r❡ ♣r❡❞✐❝t✐♦♥ ❢♦r t❤❡ ❝♦♠✐♥❣ ❞❡❝❛❞❡❢r♦♠ ❛ ❣❧♦❜❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✳ s❝✐❡♥❝❡✱ ✸✶✼✭✺✽✸✾✮✿✼✾✻✕✼✾✾✱ ✷✵✵✼✳

❑✳ ❊✳ ❚❛②❧♦r✱ ❘✳ ❏✳ ❙t♦✉✛❡r✱ ❛♥❞ ●✳ ❆✳ ▼❡❡❤❧✳ ❆♥ ♦✈❡r✈✐❡✇ ♦❢ ❈▼■P✺ ❛♥❞ t❤❡ ❡①♣❡r✐♠❡♥t❞❡s✐❣♥✳ ❇✉❧❧✳ ❆♠❡r✳ ▼❡t❡♦r✳ ❙♦❝✳✱ ✾✸✭✹✮✿✹✽✺✕✹✾✽✱ ✷✵✶✷✳

❈❧é♠❡♥t ❚✐ss❡✉✐❧✱ ▼ ❱r❛❝✱ ● ●r❡♥♦✉✐❧❧❡t✱ ❆❏ ❲❛❞❡✱ ▼ ●❡✈r❡②✱ ❚❤✐❡rr② ❖❜❡r❞♦r✛✱ ❏✲❇ ●r♦❞✇♦❤❧✱ ❛♥❞ ❙ ▲❡❦✳ ❙tr❡♥❣t❤❡♥✐♥❣ t❤❡ ❧✐♥❦ ❜❡t✇❡❡♥ ❝❧✐♠❛t❡✱ ❤②❞r♦❧♦❣✐❝❛❧ ❛♥❞s♣❡❝✐❡s ❞✐str✐❜✉t✐♦♥ ♠♦❞❡❧✐♥❣ t♦ ❛ss❡ss t❤❡ ✐♠♣❛❝ts ♦❢ ❝❧✐♠❛t❡ ❝❤❛♥❣❡ ♦♥ ❢r❡s❤✇❛t❡r❜✐♦❞✐✈❡rs✐t②✳ ❙❝✐❡♥❝❡ ♦❢ t❤❡ t♦t❛❧ ❡♥✈✐r♦♥♠❡♥t✱ ✹✷✹✿✶✾✸✕✷✵✶✱ ✷✵✶✷✳

❈✳ ❚♦r♠❛✱ ❋✳ ●✐♦r❣✐✱ ❛♥❞ ❊✳ ❈♦♣♣♦❧❛✳ ❆❞❞❡❞ ✈❛❧✉❡ ♦❢ r❡❣✐♦♥❛❧ ❝❧✐♠❛t❡ ♠♦❞❡❧✐♥❣ ♦✈❡r❛r❡❛s ❝❤❛r❛❝t❡r✐③❡❞ ❜② ❝♦♠♣❧❡① t❡rr❛✐♥✖♣r❡❝✐♣✐t❛t✐♦♥ ♦✈❡r t❤❡ ❆❧♣s✳ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳✿❆t♠♦s♣❤❡r❡s✱ ✶✷✵✭✾✮✿✸✾✺✼✕✸✾✼✷✱ ✷✵✶✺✳ ✷✵✶✹❏❉✵✷✷✼✽✶✳

◆ ❱✐❣❛✉❞✱ ▼ ❱r❛❝✱ ❛♥❞ ❨ ❈❛❜❛❧❧❡r♦✳ Pr♦❜❛❜✐❧✐st✐❝ ❞♦✇♥s❝❛❧✐♥❣ ♦❢ ❣❝♠ s❝❡♥❛r✐♦s ♦✈❡rs♦✉t❤❡r♥ ✐♥❞✐❛✳ ■♥t❡r♥❛t✐♦♥❛❧ ❏♦✉r♥❛❧ ♦❢ ❈❧✐♠❛t♦❧♦❣②✱ ✸✸✭✺✮✿✶✷✹✽✕✶✷✻✸✱ ✷✵✶✸✳

▼❛t❤✐❡✉ ❱r❛❝ ❛♥❞ P❡tr❛ ❋r✐❡❞❡r✐❝❤s✳ ▼✉❧t✐✈❛r✐❛t❡✲✐♥t❡r✈❛r✐❛❜❧❡✱ s♣❛t✐❛❧✱ ❛♥❞ t❡♠♣♦r❛❧✲❜✐❛s ❝♦rr❡❝t✐♦♥✳ ❏♦✉r♥❛❧ ♦❢ ❈❧✐♠❛t❡✱ ✷✽✭✶✮✿✷✶✽✕✷✸✼✱ ✷✵✶✺✳

●✳ P✳ ❲❡❡❞♦♥✱ ●✳ ❇❛❧s❛♠♦✱ ◆✳ ❇❡❧❧♦✉✐♥✱ ❙✳ ●♦♠❡s✱ ▼✳ ❏✳ ❇❡st✱ ❛♥❞ P✳ ❱✐t❡r❜♦✳ ❚❤❡✇❢❞❡✐ ♠❡t❡♦r♦❧♦❣✐❝❛❧ ❢♦r❝✐♥❣ ❞❛t❛ s❡t✿ ❲❛t❝❤ ❢♦r❝✐♥❣ ❞❛t❛ ♠❡t❤♦❞♦❧♦❣② ❛♣♣❧✐❡❞ t♦❡r❛✲✐♥t❡r✐♠ r❡❛♥❛❧②s✐s ❞❛t❛✳ ❲❛t❡r ❘❡s♦✉r✳ ❘❡s✳✱ ✺✵✭✾✮✿✼✺✵✺✕✼✺✶✹✱ ✷✵✶✹✳

❚✳ ❲✳ ❨❡❡✳ ❱❡❝t♦r ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ❛♥❞ ❛❞❞✐t✐✈❡ ♠♦❞❡❧s✳ ❙♣r✐♥❣❡r✱ ✷✵✶✺✳

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