❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛s ❆t♠♦s❢ér✐❝❛s ❡ ❈❧✐♠át✐❝❛s Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛s ❈❧✐♠át✐❝❛s
❉♦✉t♦r❛❞♦ ❡♠ ❈✐ê♥❝✐❛s ❈❧✐♠át✐❝❛s
❊♥❡r❣✐❛ ❡ó❧✐❝❛ ❡♠ ❛❧t♦ ♠❛r✿ ❞✐str✐❜✉✐çã♦ ❞♦s
r❡❝✉rs♦s ❡ ❝♦♠♣❧❡♠❡♥t❛r✐❞❛❞❡ ❤í❞r✐❝❛
❆❧❧❛♥ ❘♦❞r✐❣✉❡s ❙✐❧✈❛
❆❧❧❛♥ ❘♦❞r✐❣✉❡s ❙✐❧✈❛
❊♥❡r❣✐❛ ❡ó❧✐❝❛ ❡♠ ❛❧t♦ ♠❛r✿ ❞✐str✐❜✉✐çã♦ ❞♦s r❡❝✉rs♦s ❡
❝♦♠♣❧❡♠❡♥t❛r✐❞❛❞❡ ❤í❞r✐❝❛
❚❡s❡ ❞❡ ❉♦✉t♦r❛❞♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛s ❈❧✐♠át✐❝❛s ❞♦ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❉♦✉t♦r ❡♠ ❈✐ê♥❝✐❛s ❈❧✐♠át✐❝❛s✳
❖r✐❡♥t❛❞♦r
Pr♦❢✳ ❉r✳ ❋❡❧✐♣❡ ▼❡♥❞♦♥ç❛ P✐♠❡♥t❛
❯❋❘◆ ✕ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ❈❈❊❚ ✕ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❛ ❚❡rr❛
❉❈❆❈ ✕ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❈✐ê♥❝✐❛s ❆t♠♦s❢ér✐❝❛s ❡ ❈❧✐♠át✐❝❛s PP●❈❈ ✕ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛s ❈❧✐♠át✐❝❛s
UFRN / Biblioteca Central Zila Mamede Catalogação da Publicação na Fonte
Silva, Allan Rodrigues.
Energia eólica em alto mar: distribuição dos recursos e complementaridade hídrica / Allan Rodrigues Silva. - Natal, RN, 2015.
139 f. : il.
Orientador: Prof. Dr. Felipe Mendonça Pimenta.
Tese (Doutorado) - Universidade Federal do Rio Grande do Norte. Ciências Exatas e da Terra. Pós-Graduação em Ciências Climáticas.
1. Energias renováveis - Tese. 2. Energia eólica offshore - Tese. 3. Energia hidroelétrica - Tese. 4. Regime hidrológico - Tese. 5. Teoria de Monin-Obukhov - Tese. 6. Camada limite atmosférica - Tese. I. Pimenta, Felipe Mendonça. II. Título.
❆❣r❛❞❡❝✐♠❡♥t♦s
❊♠ ♣r✐♠❡✐r♦ ❧✉❣❛r ❛ ❉❡✉s✱ ♣❡❧❛ ❜ê♥çã♦ ❞❛ s❛ú❞❡✱ s❛❜❡❞♦r✐❛ ❡ ❞❛ ❢♦rç❛ q✉❡ s❡♠♣r❡ ♠❡ ❞❡✉✳ P❡❧❛s ♦♣♦rt✉♥✐❞❛❞❡s q✉❡ ♠❡ ❢♦r❛♠ ❞❛❞❛s ♥❛ ✈✐❞❛✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛s ♣❡ss♦❛s q✉❡ ❝♦♥❤❡❝✐✱ ♣♦r t❡r ✈✐✈✐❞♦ ❢❛s❡s ❞✐❢í❝❡✐s✱ q✉❡ ❢♦r❛♠ ♠❛tér✐❛ ♣r✐♠❛ ❞❡ ❛♣r❡♥❞✐③❛❞♦ ❤♦❥❡ ❡ s❡♠♣r❡✳
❆♦s ♠❡✉s ♣❛✐s✱ ●❛s♣❛r ❙✐❧✈❛ ❡ ▼❛r✐❛ ❞♦ ❈❛r♠♦ ❘♦❞r✐❣✉❡s ❙✐❧✈❛✱ ♠✐♥❤❛s ✐r♠ãs ❙❤❡②❧❧❛ ❘♦❞r✐❣✉❡s ❡ ❆❧❞❛ ❘❡❣✐♥❛✱ ❛♦ ♠❡✉ ✐r♠ã♦ ●❛❜r✐❡❧ ❈♦rr❡✐❛ ❘♦❞r✐❣✉❡s q✉❡ s❡♠♣r❡ sã♦ ♦ ♣✐❧❛r ♣r✐♥❝✐♣❛❧ ❞❡ s✉st❡♥t❛çã♦ ❞❛ ♠✐♥❤❛ ✈✐❞❛✳ ❖❜r✐❣❛❞♦ ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s ❡ ♣♦r s❡♠♣r❡ ❡st❛r❡♠ ❞♦ ♠❡✉ ❧❛❞♦✱ ❛♣♦✐❛♥❞♦ ❡ ❛❝r❡❞✐t❛♥❞♦ ♥♦s ♠❡✉s s♦♥❤♦s✳
❆❣r❛❞❡ç♦ ❛♦ ❛♣♦✐♦ ❞❛ ❉♦♥❛ ❚â♥✐❛ ❡ ❙r✳ ❩♦r✐❧❞♦ ✭♠✐♥❤❛ s❡❣✉♥❞❛ ❢❛♠í❧✐❛✮ q✉❡ s❡♠♣r❡ ❝♦♥✜❛r❛♠ ❡♠ ♠✐♠✳ ❆❣r❛❞❡ç♦ ♣❡❧♦ ♠♦♠❡♥t♦s ❥✉♥t♦s ❡ ♣♦r ❝♦❧♦❝❛r ♥❡ss❡ ♠✉♥❞ã♦ ❛ ♠✐♥❤❛ ❝♦♠♣❛♥❤❡✐r❛ ❚❤❛❧②t❛ ❙✳ ❙✳ ❙✐❧✈❛✳
❚❤❛❧②t❛ ♠❛✐s ✉♠❛ ✈❡③ ❛❣r❛❞❡ç♦ ♣♦r ❡st❛r ❛♦ ♠❡✉ ❧❛❞♦✱ ♣❛ss❛♥❞♦ ♣♦r t♦❞❛s ❛s ❞✐✜❝✉❧✲ ❞❛❞❡s ❡ t♦❞❛s ❛s ❛❧❡❣r✐❛s ❥✉♥t♦s✳ ◆♦ss❛ ✉♥✐ã♦ ❝♦♠♣❧❡t♦✉ ❤♦❥❡ ✸✽✼✽ ❞✐❛s ✭✶✵✳✻ ❛♥♦s✮ ❡ ❞❡s❞❡ q✉❡ t❡ ❝♦♥❤❡❝✐ ✈❡♥❤♦ ❛♣r❡❝✐❛♥❞♦ s❡✉ ❥❡✐t♦ ❡ ❝♦♠♣♦rt❛♠❡♥t♦✳ ◗✉❡ ❉❡✉s ♥♦s ❞ê s❛❜❡❞♦r✐❛ ♣❛r❛ ✈✐✈❡r ❝❛❞❛ ❞✐❛ ❝♦♠♦ s❡ ❢♦ss❡ ♦ ú❧t✐♠♦✱ ♣♦rq✉❡ ❛ss✐♠ ♥ã♦ ♥♦s ♣r❡♥❞❡♠♦s ❛ ❞❡t❛❧❤❡s ♣❡q✉❡♥♦s q✉❡ ❛tr❛♣❛❧❤❛♠ ♥♦ss❛ ✉♥✐ã♦✳ ❘❡♣✐t♦ ❛q✉✐ ♦ q✉❡ ✈♦❝ê ♠❡ ❞✐ss❡✱ ❖❜r✐❣❛❞♦ ♣♦r ♠❡ ❢❛③❡r s❡♥t✐r tã♦ ❛♠❛❞♦✱ ♠❡s♠♦ ♥♦s ♠♦♠❡♥t♦s ♠❛✐s ❞✐❢í❝❡✐s ❞❛ ♥♦ss❛ ✈✐❞❛✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ ❋❡❧✐♣❡ ▼❡♥❞♦♥ç❛ P✐♠❡♥t❛✱ ♣❡❧❛ ❞❡❞✐❝❛çã♦✱ ♣❛❝✐ê♥❝✐❛ ❡ ❡♥s✐♥❛♠❡♥✲ t♦s✳ P♦r t❡r ♠♦str❛❞♦ ❝♦♠♦ s❡r ✉♠ ♣❡sq✉✐s❛❞♦r✱ ❛❣✐♥❞♦ ❝♦♠ ❞❡❞✐❝❛çã♦✱ ♣❛❝✐ê♥❝✐❛ ❡ ❛♠♦r ♣❡❧❛ ❝✐ê♥❝✐❛✳
➚ P❛trí❝✐❛ ❊✐❝❤❧❡r✱ às ♣❡q✉❡♥❛s ●❛❜✐ ❡ ❏ú❧✐❛✱ ❧✐♥❞❛s✱ ❝❛r✐♥❤♦s❛s ❡ r❡❝❡♣t✐✈❛s✳ ❆♦ ❙r✳ ❖tt♦ ❍❡❧❜❡rt ❡ ❙r❛✳ ❇❡❛tr✐③ ❊✐❝❤❧❡r ♣❡❧♦ ❝❛r✐♥❤♦✱ ♠❡ ❢❛③❡♥❞♦ s❡♥t✐r ♣❛rt❡ ❞❛ ❢❛♠í❧✐❛✳
❆♦s ♠❡✉s ❛♠✐❣♦s ❞❡ ❧♦♥❣❛ ❞❛t❛ q✉❡ ✜③❡r❛♠ ♣❛rt❡ ❞❡st❛ ❥♦r♥❛❞❛✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ❆❧✐♥❡ ❈❛str♦✱ ❇r✉♥❛ ❙✐❧✈❡✐r❛✱ ❈r✐st✐♥❛ ❙❝❤✉❧t③✱ ❘✐t❛ ❘✐❝❛rt❡✱ s❡♠♣r❡ ❞✐s♣♦♥í✈❡✐s ❛ ♠❡ ❛❥✉❞❛r✳
❡ ♦ ❝♦❧❡❣❛ ❯❧②✮✱ ◆❛t❤❛❧✐❛ ❉✉❛rt❡ ❡ ❙♦♥❛❧❧② ❙✐q✉❡✐r❛ ✭▼❡✉ ♣♦rt♦ s❡❣✉r♦✮✱ q✉❡ t❛♥t♦ ♠❡ ✐♥❝❡♥t✐✈❛r❛♠ ❡ t♦r❝❡r❛♠ ♣♦r ♠✐♠✳ ❈r✐❛♠♦s ✉♠❛ ❣r❛♥❞❡ ❢❛♠í❧✐❛ P♦t✐❣✉❛r✳
❆♦s ❛♠✐❣♦s ❞❡ ❞♦✉t♦r❛❞♦ ❉❛r❧❛♥ ❙❝❤♠✐❞t✱ ▼❛r❝♦s ❆✉r❡❧✐♦✱ ❘❡❜❡♥ ●♦♠❡s✱ ❈❛r❧♦s ▼❛❣♥♦✱ ●❡♦r❣❡ P❡❞r❛✱ ❏♦sé ❯❡❧✐t♦♥✱ ❊❞♠✐r ❏❡s✉s✱ ◆❡t❡ ❇❛rr❡t♦✱ Pr✐s❝✐❧❧❛ ❚❡❧❡s✱ ❆♥❛ ❈❛r❧❛✱ ▼✐❝❡❥❛♥❡ ❈♦st❛✱ ❊❧✐❛♥❡ ❙❛♥t♦s✱ ▼❛②tê ❉✉❛rt❡✱ ❡ t♦❞♦s ❛q✉✐ ♥ã♦ ❝✐t❛❞♦s✱ ♣❡❧♦ ❛♣♦✐♦ s❡♠♣r❡ q✉❡ ♣r❡❝✐s❡✐✳
❉❡ ♠❛♥❡✐r❛ ✐♥❝♦♠✉♠ ❣♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r ❛ ❞♦✐s s❡r❡s q✉❡ ❡♥t❡♥❞❡♠ ❝❛❞❛ s❡♥t✐✲ ♠❡♥t♦ ♠❡✉✱ P✐♥❣♦ ❡ ●✉♥❣❛ ✭♠❡✉s ❝❛❝❤♦rr✐♥❤♦s ❞❡ ❡st✐♠❛çã♦✮✳ ◗✉❡r♦ ❞❡✐①❛r r❡❣✐str❛❞❛ ❛ ✐♠♣♦rtâ♥❝✐❛ q✉❡ ✈♦❝ês t❡♠ ♣❛r❛ ♠✐♠✱ ✈♦❝ês ❛❧❡❣r❛♠ ♦s ♠❡✉s ❞✐❛s✳
➚ ❯❋❘◆ ❡ ❛♦ ♣r♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛s ❈❧✐♠át✐❝❛s✱ ♣❡❧❛ ♦♣♦rt✉♥✐❞❛❞❡✳ ➚ ❈❆P❊❙ ♣❡❧♦ ❛♣♦✐♦ r❡❝❡❜✐❞♦ ❛tr❛✈és ❞❡ ❜♦❧s❛ ❞❡ ❡st✉❞♦✳ ❆ ❋❆P❊❘◆ ♣❡❧♦ ❛♣♦✐♦ ❛♦ ♣r♦❥❡t♦ ❆❘❊❊❙❆❚ ✭PPP ✵✺✮ ❡ ❛♦ ❈◆P◗ ✭✹✵✻✽✵✶ ✲✷✵✶✸✴✵✹✮✳
➚ t♦❞♦s ♦s ♣r♦❢❡ss♦r❡s q✉❡ ❢❛③❡♠ ♣❛rt❡ ❞❛ PP●❈❈✱ ♣❡❧♦ ❛♣r❡♥❞✐③❛❞♦✳
❆♦s ♣r♦❢❡ss♦r❡s ❞❛ ❜❛♥❝❛ ❡①❛♠✐♥❛❞♦r❛ Pr♦❢❛ ❉r❛ ▼❛r✐❛ ❍❡❧❡♥❛✱ Pr♦❢♦ ❉r ❆r❝✐❧❛♥
❚r❡✈❡♥③♦❧✐✱ Pr♦❢♦ ❉r ❘♦s✐❜❡rt♦ ❙❛❧✉st✐❛♥♦ ❡ Pr♦❢♦ ❉r ❱✐♥✐❝✐♦ ❞❡ ❙♦✉③❛✱ ♣❡❧❛ ♣❛rt✐❝✐♣❛çã♦
❡ ❝♦❧❛❜♦r❛çã♦✳
❊♥❡r❣✐❛ ❡ó❧✐❝❛ ❡♠ ❛❧t♦ ♠❛r✿ ❞✐str✐❜✉✐çã♦ ❞♦s r❡❝✉rs♦s ❡
❝♦♠♣❧❡♠❡♥t❛r✐❞❛❞❡ ❤í❞r✐❝❛
❆✉t♦r✿ ❆❧❧❛♥ ❘♦❞r✐❣✉❡s ❙✐❧✈❛ ❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❋❡❧✐♣❡ ▼✳ P✐♠❡♥t❛
❘❡s✉♠♦
❆ ❡st❛❜✐❧✐③❛çã♦ ❞❛ ♦❢❡rt❛ ❞❡ ❡♥❡r❣✐❛ ♥♦ ❇r❛s✐❧ t❡♠ s✐❞♦ ✉♠ ❞❡s❛✜♦ ♣❛r❛ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞♦ ❙✐st❡♠❛ ■♥t❡r❧✐❣❛❞♦ ◆❛❝✐♦♥❛❧ ❞✐❛♥t❡ ❞❛s ✈❛r✐❛çõ❡s ❤✐❞r♦❧ó❣✐❝❛s ❡ ❝❧✐♠át✐❝❛s✳ ❚❡r♠♦✲ ❡❧étr✐❝❛s sã♦ ✉t✐❧✐③❛❞❛s ❝♦♠♦ ❢♦♥t❡ ❡♠❡r❣❡♥❝✐❛❧ ♥♦ ♣❡rí♦❞♦ ❞❡ ❡s❝❛ss❡③ ❤í❞r✐❝❛ ❡❧❡✈❛♥❞♦ ♦ ❝✉st♦ ❞❡ ♣r♦❞✉çã♦ ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛ ❡♥❡r❣✐❛ ❡ó❧✐❝❛ ❡♠ ❛❧t♦ ♠❛r ✭♦✛s❤♦r❡✮ ✈❡♠ ❣❛♥❤❛♥❞♦ ✐♠♣♦rtâ♥❝✐❛ ♥♦ ❝❡♥ár✐♦ ✐♥t❡r♥❛❝✐♦♥❛❧✱ ❛ ♣♦♥t♦ ❞❡ t♦r♥❛r✲s❡ ✉♠❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❢✉t✉r❛ ❞❡ ❣❡r❛çã♦ ♥♦ ❇r❛s✐❧✳ ◆❡ss❡ s❡♥t✐❞♦✱ ♦ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ❞❡st❛ t❡s❡ ❢♦✐ ✐♥✈❡st✐❣❛r ❛ ♠❛❣♥✐t✉❞❡ ❡ ❞✐str✐❜✉✐çã♦ ❞♦s r❡❝✉rs♦s ❡ó❧✐❝♦s ♦✛s❤♦r❡✱ ✈❡r✐✜❝❛♥❞♦ t❛♠❜é♠ ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ ❝♦♠♣❧❡♠❡♥t❛r✐❞❛❞❡ ❝♦♠ ❛ ❢♦♥t❡ ❤í❞r✐❝❛✳ P❛r❛ t❛♥t♦✱ ❢♦✐ ✉t✐❧✐③❛❞♦ ✉♠❛ sér✐❡ ❞❡ ❞❛❞♦s ❞❡ ♣r❡❝✐♣✐t❛çã♦ ❞♦ ❈❧✐♠❛t✐❝ ❘❡s❡❛r❝❤ ❯♥✐t ✭❈❘❯✮ ❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s s❛t❡❧✐tár✐♦s ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ❞♦ ♣r♦❥❡t♦ ❇❧❡♥❞❡❞ ❙❡❛ ❲✐♥❞s ❞❛ ◆❛t✐♦♥❛❧ ❈❧✐♠❛t✐❝ ❉❛t❛ ❈❡♥t❡r ✭◆❈❉❈✴◆❖❆❆✮✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❝r✐tér✐♦s ❡st❛tíst✐❝♦s ❡♥❝♦♥tr❛r❛♠✲s❡ três t✐♣♦s ❞❡ ❝♦♠♣❧❡♠❡♥t❛r✐❞❛❞❡ ♥♦ t❡rr✐tór✐♦ ❜r❛s✐❧❡✐r♦✿ ❤í❞r✐❝❛ × ❤í❞r✐❝❛✱ ❡ó❧✐❝❛ × ❡ó❧✐❝❛ ❡
❤í❞r✐❝❛×❡ó❧✐❝❛✳ ◆♦t♦✉✲s❡ ✉♠ ❝♦♠♣❧❡♠❡♥t♦ ❜❛st❛♥t❡ s✐❣♥✐✜❝❛t✐✈♦ ✭r❂✲✵✱✻✺✮ ❡♥tr❡ ❛s ❢♦♥✲
t❡s ❤í❞r✐❝❛ ❡ ❡ó❧✐❝❛✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❛s ❜❛❝✐❛s ❤✐❞r♦❣rá✜❝❛s ❞♦ ❙✉❞❡st❡ ❡ ❈❡♥tr♦✕❖❡st❡ ❝♦♠ ♦s ✈❡♥t♦s ❞♦ ◆♦r❞❡st❡✳ ❈♦♠ ✐♥t✉✐t♦ ❞❡ r❡✜♥❛r ❛ ❡①tr❛♣♦❧❛çã♦ ❞♦s ✈❡♥t♦s s♦❜r❡ ♦ ♦❝❡❛♥♦✱ ❛♣❧✐❝♦✉✲s❡ ♠ét♦❞♦ ❜❛s❡❛❞♦ ♥❛ t❡♦r✐❛ ❞❡ ▼♦♥✐♥✲❖❜✉❦❤♦✈ ♣❛r❛ ♠♦❞❡❧❛r ❛ ❡st❛❜✐✲ ❧✐❞❛❞❡ ❞❛ ❝❛♠❛❞❛ ❧✐♠✐t❡ ❛t♠♦s❢ér✐❝❛✳ ❯t✐❧✐③♦✉✲s❡ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❞❡ ✢✉①♦s ❞❡ ❝❛❧♦r✱ t❡♠♣❡r❛t✉r❛ ❡ ✉♠✐❞❛❞❡ ❞♦ Pr♦❥❡t♦ ❖❜❥❡❝t✐✈❡❧② ❆♥❛❧✐③❡❞ ❆✐r✲❙❡❛ ❋❧✉① ✭❖❆❋❧✉①✮✱ ❛❧é♠ ❞❡ ❞❛❞♦s ❞❡ ♣r❡ssã♦ ❛♦ ♥í✈❡❧ ❞♦ ♠❛r ❞♦ ♣r♦❥❡t♦ ◆❈❊P✴◆❈❆❘ ❡ ♦ ♠♦❞❡❧♦ ❞❡ r❡❧❡✈♦ ❊❚❖P❖✶ ❞❛ ◆❛t✐♦♥❛❧ ●❡♦♣❤②s✐❝❛❧ ❉❛t❛ ❈❡♥t❡r ✭◆●❉❈✴◆❖❆❆✮✳ ❱❡r✐✜❝♦✉✲s❡ ✉♠ ❜♦♠ r❡❝✉rs♦ ❡♠ á❣✉❛s r❛s❛s✱ ❡♥tr❡ ✵✲✷✵ ♠❡tr♦s✱ ❡st✐♠❛❞♦s ❡♠ ✺✺✾ ●❲✳ ❆ ❝♦♥tr✐❜✉✐çã♦ ❞♦ r❡❝✉rs♦ ❡ó❧✐❝♦ ❡♠ ✉♠ r❡s❡r✈❛tór✐♦ ❢♦✐ ✐♥✈❡st✐❣❛❞❛ ❝♦♠ ✉♠ ♠♦❞❡❧♦ ❤í❜r✐❞♦ ❡ó❧✐❝♦✲❤✐❞rá✉❧✐❝♦ s✐♠♣❧✐✜❝❛❞♦ q✉❡ ♣❡r♠✐t✐✉ ♦ ❝á❧❝✉❧♦ ❞♦ ♥í✈❡❧ ❞♦s r❡s❡r✈❛tór✐♦s ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s ❞❡ ✈❛③ã♦ ❛✢✉❡♥t❡✱ ❞❡✢✉❡♥t❡ ❡ ♣r♦❞✉çã♦ ❞❡ t✉r❜✐♥❛✳ ◆♦t♦✉✲s❡ q✉❡ ♦ s✐st❡♠❛ ❤í❜r✐❞♦ ❡✈✐t❛ ♦s ♣❡rí♦❞♦s ❞❡ ❡st✐✲ ❛❣❡♠✱ ♣♦✉♣❛♥❞♦ ❝♦♥t✐♥✉❛♠❡♥t❡ á❣✉❛ ❞♦s r❡s❡r✈❛tór✐♦s ❛tr❛✈és ❞❛ ♣r♦❞✉çã♦ ❡ó❧✐❝❛✳ ❆ss✐♠✱ ❛ ♣❛rt✐r ❞♦s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s✱ é ♣♦ssí✈❡❧ ❛✜r♠❛r q✉❡ ♦s ❜♦♥s ✈❡♥t♦s ❞❛ ❝♦st❛ ❜r❛s✐❧❡✐r❛ ♣♦❞❡♠✱ ❛❧é♠ ❞❡ ❞✐✈❡rs✐✜❝❛r ❛ ♠❛tr✐③ ❡❧étr✐❝❛✱ ❡st❛❜✐❧✐③❛r ❛s ✢✉t✉❛çõ❡s ❤í❞r✐❝❛s ❡✈✐t❛♥❞♦ r❛❝✐♦♥❛♠❡♥t♦s ❡ ❛♣❛❣õ❡s✱ r❡❞✉③✐♥❞♦ ♦ ✉s♦ ❞❛s tér♠✐❝❛s q✉❡ ❡❧❡✈❛ ♦ ❝✉st♦ ❞❡ ♣r♦❞✉çã♦ ❡ ❛ ❡♠✐ssã♦ ❞❡ ❣❛s❡s ♣♦❧✉❡♥t❡s✳ P♦❧ít✐❝❛s ♣ú❜❧✐❝❛s ✈♦❧t❛❞❛s ❛♦ ✐♥❝❡♥t✐✈♦ ❞❛ ❡♥❡r❣✐❛ ❡ó❧✐❝❛ ♦✛s❤♦r❡ s❡rã♦ ♥❡❝❡ssár✐❛s ♣❛r❛ s❡✉ ♣❧❡♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦✳
❖✛s❤♦r❡ ✇✐♥❞ ❡♥❡r❣②✿ r❡s♦✉r❝❡ ❞✐str✐❜✉t✐♦♥ ❛♥❞
❝♦♠♣❧❡♠❡♥t❛r✐t② t♦ ❤②❞r♦❧♦❣✐❝❛❧ r❡s♦✉r❝❡s
❆✉t❤♦r✿ ❆❧❧❛♥ ❘♦❞r✐❣✉❡s ❙✐❧✈❛ ❆❞✈✐s♦r✿ Pr♦❢✳ ❉r✳ ❋❡❧✐♣❡ ▼✳ P✐♠❡♥t❛
❆❜str❛❝t
❚❤❡ st❛❜✐❧✐③❛t✐♦♥ ♦❢ ❡♥❡r❣② s✉♣♣❧② ✐♥ ❇r❛③✐❧ ❤❛s ❜❡❡♥ ❛ ❝❤❛❧❧❡♥❣❡ ❢♦r t❤❡ ♦♣❡r❛t✐♦♥ ♦❢ t❤❡ ◆❛t✐♦♥❛❧ ■♥t❡r❝♦♥♥❡❝t❡❞ ❙②st❡♠ ✐♥ ❢❛❝❡ ♦❢ ❤②❞r♦❧♦❣✐❝❛❧ ❛♥❞ ❝❧✐♠❛t✐❝ ✈❛r✐❛t✐♦♥s✳ ❚❤❡r✲ ♠♦❡❧❡❝tr✐❝ ♣❧❛♥ts ❤❛✈❡ ❜❡❡♥ ✉s❡❞ ❛s ❛♥ ❡♠❡r❣❡♥❝② s♦✉r❝❡ ❢♦r ♣❡r✐♦❞s ♦❢ ✇❛t❡r s❝❛r❝✐t②✳ ❚❤❡ ✉t✐❧✐③❛t✐♦♥ ♦❢ ❢♦ss✐❧ ❢✉❡❧s✱ ❤♦✇❡✈❡r✱ ❤❛s ❡❧❡✈❛t❡❞ t❤❡ ❝♦st ♦❢ ❡❧❡❝tr✐❝✐t②✳ ❖♥ t❤❡ ♦t❤❡r ❤❛♥❞✱ ♦✛s❤♦r❡ ✇✐♥❞ ❡♥❡r❣② ❤❛s ❣❛✐♥❡❞ ✐♠♣♦rt❛♥❝❡ ✐♥ t❤❡ ✐♥t❡r♥❛t✐♦♥❛❧ ❝♦♥t❡①t ❛♥❞ ✐s ❝♦♠♣❡t✐t✐✈❡ ❡♥♦✉❣❤ t♦ ❜❡❝♦♠❡ ❛ ♣♦ss✐❜✐❧✐t② ❢♦r ❢✉t✉r❡ ❣❡♥❡r❛t✐♦♥ ✐♥ ❇r❛③✐❧✳ ■♥ t❤✐s s❝❡✲ ♥❛r✐♦✱ t❤❡ ♠❛✐♥ ❣♦❛❧ ♦❢ t❤✐s t❤❡s✐s ✇❛s t♦ ✐♥✈❡st✐❣❛t❡ t❤❡ ♠❛❣♥✐t✉❞❡ ❛♥❞ ❞✐str✐❜✉t✐♦♥ ♦❢ ♦✛s❤♦r❡ ✇✐♥❞ r❡s♦✉r❝❡s✱ ❛♥❞ ❛❧s♦ ✈❡r✐❢② t❤❡ ♣♦ss✐❜✐❧✐t✐❡s ♦❢ ❝♦♠♣❧❡♠❡♥t✐♥❣ ❤②❞r♦♣♦✇❡r✳ ❆ ❞❛t❛ s❡r✐❡s ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ❢r♦♠ t❤❡ ❈❧✐♠❛t✐❝ ❘❡s❡❛r❝❤ ❯♥✐t ✭❈❘❯✮ ❇❧❡♥❞❡❞ ❙❡❛ ❲✐♥❞s ❢r♦♠ t❤❡ ◆❛t✐♦♥❛❧ ❈❧✐♠❛t✐❝ ❉❛t❛ ❈❡♥t❡r ✭◆❈❉❈✴◆❖❆❆✮ ✇❡r❡ ✉s❡❞✳ ❆❝❝♦r❞✐♥❣ t♦ st❛t✐s✲ t✐❝❛❧ ❝r✐t❡r✐❛✱ t❤r❡❡ t②♣❡s ♦❢ ❝♦♠♣❧❡♠❡♥t❛r✐t② ✇❡r❡ ❢♦✉♥❞ ✐♥ t❤❡ ❇r❛③✐❧✐❛♥ t❡rr✐t♦r②✿ ❤②❞r♦
× ❤②❞r♦✱ ✇✐♥❞ × ✇✐♥❞ ❛♥❞ ❤②❞r♦ × ✇✐♥❞✳ ■t ✇❛s ♥♦t❡❞ ❛ s✐❣♥✐✜❝❛♥t ❝♦♠♣❧❡♠❡♥t❛r✐t②
❜❡t✇❡❡♥ ✇✐♥❞ ❛♥❞ ❤②❞r♦ r❡s♦✉r❝❡s ✭r ❂ ✲✵✳✻✺✮✱ ♠❛✐♥❧② ❢♦r t❤❡ ❤②❞r♦❣r❛♣❤✐❝❛❧ ❜❛s✐♥s ♦❢ t❤❡ s♦✉t❤❡❛st ❛♥❞ ❝❡♥tr❛❧ r❡❣✐♦♥s ✇✐t❤ ◆♦rt❤❡❛st❡r♥ ❇r❛③✐❧ ✇✐♥❞s✳ ❚♦ r❡✜♥❡ t❤❡ ❡①tr❛♣♦❧❛✲ t✐♦♥ ♦❢ ✇✐♥❞s ♦✈❡r t❤❡ ♦❝❡❛♥✱ ❛ ♠❡t❤♦❞ ❜❛s❡❞ ♦♥ t❤❡ ▼♦♥✐♥✲❖❜✉❦❤♦✈ t❤❡♦r② ✇❛s ✉s❡❞ t♦ ♠♦❞❡❧ t❤❡ st❛❜✐❧✐t② ♦❢ t❤❡ ❛t♠♦s♣❤❡r✐❝ ❜♦✉♥❞❛r② ❧❛②❡r✳ ❖❜❥❡❝t✐✈❡❧② ❆♥❛❧②③❡❞ ❆✐r✲❙❡❛ ❋❧✉① ✭❖❆❋▲❯❳✮ ❞❛t❛s❡ts ❢♦r ❤❡❛t ✢✉①✱ t❡♠♣❡r❛t✉r❡ ❛♥❞ ❤✉♠✐❞✐t②✱ ❛♥❞ ❛❧s♦ s❡❛ ❧❡✈❡❧ ♣r❡ss✉r❡ ❞❛t❛ ❢r♦♠ ◆❈❊P✴◆❈❆❘ ✇❡r❡ ✉s❡❞✳ ❚❤❡ ❊❚❖P❖✶ ❢r♦♠ t❤❡ ◆❛t✐♦♥❛❧ ●❡♦♣❤②s✐❝❛❧ ❉❛t❛ ❈❡♥t❡r ✭◆●❉❈✴◆❖❆❆✮ ♣r♦✈✐❞❡❞ ❜❛t❤②♠❡tr✐❝ ❞❛t❛✳ ■t ✇❛s ❢♦✉♥❞ t❤❛t s❤❛❧❧♦✇ ✇❛t❡rs✱ ❜❡t✇❡❡♥ ✵✲✷✵ ♠❡t❡rs✱ ❤❛✈❡ ❛ r❡s♦✉r❝❡ ❡st✐♠❛t❡❞ ❛t ✺✺✾ ●❲✳ ❚❤❡ ❝♦♥tr✐❜✉t✐♦♥ ♦❢ ✇✐♥❞ r❡s♦✉r❝❡s t♦ ❤②❞r♦❡❧❡❝tr✐❝ r❡s❡r✈♦✐r ♦♣❡r❛t✐♦♥ ✇❛s ✐♥✈❡st✐❣❛t❡❞ ✇✐t❤ ❛ s✐♠♣❧✐✜❡❞ ❤②❜r✐❞ ✇✐♥❞✲❤②❞r❛✉❧✐❝ ♠♦❞❡❧✱ ❛♥❞ r❡s❡r✈♦✐r ❧❡✈❡❧✱ ✐♥✢♦✇✱ ♦✉t✢♦✇ ❛♥❞ t✉r❜✐♥❡ ♣r♦❞✉❝t✐♦♥ ❞❛t❛✳ ■t ✇❛s ❢♦✉♥❞ t❤❛t t❤❡ ❤②❜r✐❞ s②st❡♠ ❛✈♦✐❞s ❞r♦✉❣❤t ♣❡r✐♦❞s✱ ❝♦♥t✐♥✉♦✉s❧② s❛✈✐♥❣ ✇❛t❡r ❢r♦♠ r❡s❡r✈♦✐rs t❤r♦✉❣❤ ✇✐♥❞ ♣r♦❞✉❝t✐♦♥✳ ❚❤❡r❡❢♦r❡✱ ❢r♦♠ t❤❡ r❡s✉❧ts ♦❜t❛✐♥❡❞✱ ✐t ✐s ♣♦s✲ s✐❜❧❡ t♦ st❛t❡ t❤❛t t❤❡ ❣♦♦❞ ✇✐♥❞s ❢r♦♠ t❤❡ ❇r❛③✐❧✐❛♥ ❝♦❛st ❝❛♥✱ ❜❡s✐❞❡s ❞✐✈❡rs✐❢②✐♥❣ t❤❡ ❡❧❡❝tr✐❝ ♠❛tr✐①✱ st❛❜✐❧✐③❡ t❤❡ ❤②❞r♦❧♦❣✐❝❛❧ ✢✉❝t✉❛t✐♦♥s ❛✈♦✐❞✐♥❣ r❛t✐♦♥✐♥❣ ❛♥❞ ❜❧❛❝❦♦✉ts✱ r❡❞✉❝✐♥❣ t❤❡ ✉s❡ ♦❢ t❤❡r♠❛❧ ♣♦✇❡r ♣❧❛♥ts✱ ✐♥❝r❡❛s✐♥❣ t❤❡ ♣r♦❞✉❝t✐♦♥ ❝♦st ❛♥❞ ❡♠✐ss✐♦♥ ♦❢ ❣r❡❡♥❤♦✉s❡ ❣❛s❡s✳ P✉❜❧✐❝ ♣♦❧✐❝✐❡s t❛r❣❡t❡❞ t♦ ♦✛s❤♦r❡ ✇✐♥❞ ❡♥❡r❣② ✇✐❧❧ ❜❡ ♥❡❝❡ss❛r② ❢♦r ✐ts ❢✉❧❧ ❞❡✈❡❧♦♣♠❡♥t✳
▲✐st❛ ❞❡ ✜❣✉r❛s
✶ P❛rq✉❡ ❡ó❧✐❝♦ ❞♦ ❘❡✐♥♦ ❯♥✐❞♦ ✭Pr♦❥❡t♦ ▲♦♥❞♦♥ ❆rr❛②✮✳ ❈ré❞✐t♦ ■♠❛❣❡♠✿
▲♦♥❞♦♥ ❆rr❛② ❈♦♥s♦rt✐✉♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✼ ✷ ■t❛✐♣✉ ❇✐♥❛❝✐♦♥❛❧✱ s❡❣✉♥❞❛ ♠❛✐♦r ✉s✐♥❛ ❞♦ ♠✉♥❞♦✱ ❝♦♠ ❝❛♣❛❝✐❞❛❞❡ ❞❡
❣❡r❛çã♦ ❞❡ ✶✹✳✵✵✵ ▼❲✳ ❈ré❞✐t♦ ■♠❛❣❡♠✿ ✭❯◆❊❙❈❖✱ ✷✵✶✷✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✼ ✸ ❘❡s❡r✈❛tór✐♦ ❞❡ ■t✉♠❜✐❛r❛ ❧♦❝❛❧✐③❛❞♦ ❡♥tr❡ ▼✐♥❛s ●❡r❛✐s ❡ ●♦✐ás✱ ❡♠
♥♦✈❡♠❜r♦ ❞❡ ✷✵✶✷✱ ❝♦♠ ❛♣❡♥❛s ✶✸✳✹✻✪ ❞❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❛r♠❛③❡♥❛♠❡♥t♦
✭❋♦t♦❣r❛✜❛ ❣❡♥t✐❧♠❡♥t❡ ❝❡❞✐❞❛ ♣♦r ❲❡✐♠❡r ❈❛r✈❛❧❤♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✽ ✹ ❈♦♥t✐♥❡♥t❛❧ t♦♣♦❣r❛♣❤② ❛♥❞ ♦❝❡❛♥ ❜❛t❤②♠❡tr② ❜❛s❡❞ ♦♥ t❤❡ ❞✐❣✐t❛❧ ♠♦✲
❞❡❧ ❊t♦♣♦✺ ✭❊❉❲❆❘❉❙✱ ✶✾✽✾✮✳ ❆r❡❛ ♦❢ st✉❞②✱ ✇✐t❤ t❤❡ r❡s♣❡❝t✐✈❡ ♣♦✐♥ts
❢♦r ❛♥❛❧②s✐s ✭❲✶ t♦ ❲✶✷✮ ❛♥❞ t❤❡ ❞r❛✐♥❛❣❡ ❜❛s✐♥s ✭❍✶ t♦ ❍✶✷✮✳ ❚❤❡ ❝♦♥✲ t✐♥✉♦✉s ❧✐♥❡ r❡♣r❡s❡♥ts t❤❡ ✺✵ ♠ ✐s♦❜❛t❤✳ ❚❤❡ ❞❛s❤❡❞ ❧✐♥❡ ✐♥❞✐❝❛t❡s t❤❡
❊①❝❧✉s✐✈❡ ❊❝♦♥♦♠✐❝ ❩♦♥❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✸ ✺ ✭❛✮ P♦✇❡r ❝✉r✈❡ ❢♦r t❤❡ ❘❊♣♦✇❡r ✻▼❲ ✇✐♥❞ t✉r❜✐♥❡✳ ✭❜✮ ❚✉r❜✐♥❡ ✐♥st❛❧✲
❧❡❞ ♦♥ ❛ ❥❛❝❦❡t ❢♦✉♥❞❛t✐♦♥ ✐♥ t❤❡ ❚❤♦r♥t♦♥ ❇❛♥❦ ■■ ✇✐♥❞ ❢❛r♠ ✭❈♦✉rt❡s②
♦❢ ❘❊♣♦✇❡r✱ ♥♦✇ ❙❡♥✈✐♦♥✳ P❤♦t♦❣r❛♣❤❡r ❚♦♠ ❉✬❍❛❡♥❡♥s✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✹ ✻ P♦✇❡r ❞❡♥s✐t② ✭P d✮ ❬❲ ♠−2❪ ✭❜❧❛❝❦ ❝♦♥t♦✉r ❧✐♥❡s✮ ❛♥❞ t✉r❜✐♥❡ ♣♦✇❡r
✭P t✮ ❬▼❲❪ ✭❛r❡❛ ✐♥ ❝♦❧♦r✮ ♠❛♣s ❢♦r t❤❡ ♣❡r✐♦❞ ♦❢ ✶✾✽✾ t♦ ✷✵✵✾✳ ❈♦❛st❛❧
st❛t❡s ❛r❡ ✐♥❞✐❝❛t❡❞ ❜② ❧❛❜❡❧s ✐♥ t❤❡ ✜rst ♣❛♥❡❧✿ ❆♠❛♣á ✭❆P✮✱ ▼❛r❛♥❤ã♦ ✭▼❆✮✱ P✐❛✉í ✭P■✮✱ ❈❡❛rá ✭❈❊✮✱ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ✭❘◆✮✱ P❛r❛í❜❛ ✭P❇✮✱ P❡r♥❛♠❜✉❝♦ ✭P❊✮✱ ❆❧❛❣♦❛s ✭❆▲✮✱ ❙❡r❣✐♣❡ ✭❙❊✮✱ ❇❛❤✐❛ ✭❇❆✮✱ ❊s♣✐r✐t♦ ❙❛♥t♦ ✭❊❙✮✱ ❘✐♦ ❞❡ ❏❛♥❡✐r♦ ✭❘❏✮✱ ❙ã♦ P❛✉❧♦ ✭❙P✮✱ P❛r❛♥á ✭P❘✮✱ ❙❛♥t❛
❈❛t❛r✐♥❛ ✭❙❈✮ ❛♥❞ ❘✐♦ ●r❛♥❞❡ ❞♦ ❙✉❧ ✭❘❙✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✺ ✼ ▼❡❛♥ s✉r❢❛❝❡ r✉♥♦✛ ∆f ❬♠♠ ♠♦♥t❤s−1❪✭❛r❡❛ ✐♥ ❝♦❧♦r✮ ❛♥❞ ❛✈❡r❛❣❡ r❛✐♥✲
❢❛❧❧ P ❬♠♠ ♠♦♥t❤−1❪ ✭❝♦♥t♦✉rs✮ ❢♦r t❤❡ ♣❡r✐♦❞ ♦❢ ✶✾✽✾ t♦ ✷✵✵✾✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✻
✽ ▼♦♥t❤❧② ❛✈❡r❛❣❡s ❢♦r ✇✐♥❞ ♣♦✇❡r ❞❡♥s✐t② ✭❜❧❛❝❦ ❧✐♥❡✮✱ ❝❧✐♠❛t♦❧♦❣✐❝❛❧ ♠❡❛♥ ✇✐t❤ ±1σ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ✭❣r❛② s❤❛❞✐♥❣✮✱ tr❡♥❞ ❧✐♥❡ ✭r❡❞ ❧✐♥❡✮
❛♥❞ ♦✈❡r❛❧❧ ♠❡❛♥ ✭❞♦tt❡❞ ❣r❛②✮ ❢♦r t❤❡ ♣❡r✐♦❞ ♦❢ ✶✾✽✾ t♦ ✷✵✵✾✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✼ ✾ ▼♦♥t❤❧② ❛✈❡r❛❣❡s ❢♦r ♣r❡❝✐♣✐t❛t✐♦♥ ✭❜❧❛❝❦ ❧✐♥❡✮✱ ❝❧✐♠❛t♦❧♦❣✐❝❛❧ ♠❡❛♥ ✇✐t❤
±1σ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ✭❣r❛② s❤❛❞✐♥❣✮✱ tr❡♥❞ ❧✐♥❡ ✭r❡❞ ❧✐♥❡✮ ❛♥❞ ♦✈❡r❛❧❧
♠❡❛♥ ✭❣r❛② ❞♦tt❡❞✮ ❢♦r t❤❡ ♣❡r✐♦❞ ♦❢ ✶✾✽✾ t♦ ✷✵✵✾✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✽ ✶✵ ❙❡❛s♦♥❛❧ ✇✐♥❞ s♣❡❡❞ ❛♥❞ ♣r❡❝✐♣✐t❛t✐♦♥ ❢♦r t❤❡ ♣❡r✐♦❞ ♦❢ ✶✾✽✾ t♦ ✷✵✵✾✳ ✳ ♣✳ ✺✾ ✶✶ ❈♦❤❡r❡♥❝❡ ❜❡t✇❡❡♥ t❤❡ s❡r✐❡s ❤②❞r♦ × ✇✐♥❞ ✭❧❡❢t ♣❛♥❡❧✮✱ ✇✐♥❞ × ✇✐♥❞
✶✷ ❉❡♥❞r♦❣r❛♠ r❡s✉❧t✐♥❣ ❢r♦♠ t❤❡ ❝❧✉st❡r ❛♥❛❧②s✐s ♦❢ t❤❡ ✶✷ ❞r❛✐♥❛❣❡ ❜❛s✐♥s ✉s✐♥❣ ❲❛r❞✬s ❛❣❣❧♦♠❡r❛t✐✈❡ ❤✐❡r❛r❝❤✐❝❛❧ ♠❡t❤♦❞ ✇✐t❤ st❛♥❞❛r❞✐③❡❞ ❞❛t❛ ❢♦r ♠❡❛♥ ♠♦♥t❤❧② r✉♥♦✛✳ ❋✐✈❡ ❤♦♠♦❣❡♥❡♦✉s ❣r♦✉♣s ✭❍❙✱ ❍▼❲✱ ❍❊❆✱ ❍◆❊ ❛♥❞ ❍◆✮ ❛r❡ ❢♦r♠❡❞✱ ✇❤✐❝❤ ♠❛❦❡ ✉♣ t❤❡ r❡❣✐♦♥s ❙♦✉t❤✱ ▼✐❞✇❡st✱
❆t❧❛♥t✐❝ ❊❛st✱ ◆♦rt❤❡❛st ❛♥❞ ◆♦rt❤✱ r❡s♣❡❝t✐✈❡❧②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✶ ✶✸ ❉❡♥❞r♦❣r❛♠ r❡s✉❧t✐♥❣ ❢r♦♠ t❤❡ ❝❧✉st❡r ❛♥❛❧②s✐s ♦❢ t❤❡ ✶✷ ♦✛s❤♦r❡ ✇✐♥❞
s♣❡❡❞ ♣♦✐♥ts ✉s✐♥❣ ❲❛r❞✬s ❛❣❣❧♦♠❡r❛t✐✈❡ ❤✐❡r❛r❝❤✐❝❛❧ ♠❡t❤♦❞ ✇✐t❤ st❛♥✲ ❞❛r❞✐③❡❞ ♠♦♥t❤❧② ❞❛t❛✳ ❚❤❡ ✜✈❡ ❤♦♠♦❣❡♥❡♦✉s ❣r♦✉♣s ✭❲◆❊✱ ❲❊❆✱ ❲❙✱ ❲◆1 ❛♥❞ ❲◆2✮ ♠❛❦❡ ✉♣ t❤❡ r❡❣✐♦♥s ◆♦rt❤❡❛st✱ ❊❛st✱ ❙♦✉t❤ ❛♥❞ ◆♦rt❤
✶ ❛♥❞ ◆♦rt❤ ✷✱ r❡s♣❡❝t✐✈❡❧②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✷ ✶✹ ▼♦♥t❤❧② ✈❛r✐❛❜✐❧✐t② ♦❢ t❤❡ ❣r♦✉♣s ♦❜t❛✐♥❡❞ ❜② ❝❧✉st❡r ❛♥❛❧②s✐s✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✸ ✶✺ ❙✉♠♠❛r② ♦❢ t❤❡ ♠❛✐♥ r❡s✉❧ts✳ P❛♥❡❧s ✐❧❧✉str❛t❡ t❤❡ ❝♦♠♣❧❡♠❡♥t❛r✐t② ♦❢
r❡s♦✉r❝❡s ✭❆✮ ❤②❞r♦ × ❤②❞r♦✱ ✭❇✮ ✇✐♥❞ × ❤②❞r♦ ❛♥❞ ✭❈✮ ✇✐♥❞ × ✇✐♥❞✳
❈♦❧♦rs ♦♥ t❤❡ ♠❛♣ ❛♥❞ ❜❛♥❞s ❛❧♦♥❣ t❤❡ ❝♦❛st ✐♥❞✐❝❛t❡ r❡❣✐♦♥s ✇✐t❤ s✐♠✐❧❛r ❞r❛✐♥❛❣❡ ❜❛s✐♥s ❛♥❞ ✇✐♥❞ r❡❣✐♠❡s✱ ❛s r❡✈❡❛❧❡❞ ❜② t❤❡ ❝❧✉st❡r ❛♥❛❧②s✐s✳ ❆rr♦✇s ✐♥❞✐❝❛t❡ s✐❣♥✐✜❝❛♥t st❛t✐st✐❝❛❧ ❝♦rr❡❧❛t✐♦♥s t❤❛t ❛r❡ ❝❧♦s❡ t♦ ③❡r♦
♦r ♥❡❣❛t✐✈❡ ✭r≤0✮ ✭s❡❡ ❚❛❜❧❡ ✸✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✹
✶✻ ■♥❢♦r♠❛çõ❡s ❡st❛tíst✐❝❛s s♦❜r❡ ❡♥❡r❣✐❛ ♦✛s❤♦r❡ ♥❛ ❊✉r♦♣❛ ❡♠ ✷✵✶✹✳ ❋♦♥t❡✿
❤tt♣✿✴✴✇✇✇✳❡✇❡❛✳♦r❣✳ ❆❝❡ss❛❞♦ ❡♠✿ ✵✷✴✵✸✴✷✵✶✺✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✸ ✶✼ ❱❛r✐❛çã♦ tí♣✐❝❛ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ❝♦♠ ❛❧t✉r❛ ♥❛ ❝❛♠❛❞❛ ❧✐♠✐t❡ ♣❛r❛
❞✐❢❡r❡♥t❡s ❝♦♥❞✐çõ❡s ❛t♠♦s❢ér✐❝❛✳ ❆ ❧✐♥❤❛ ♠❛❣❡♥t❛ ✐♥❞✐❝❛ ❛t♠♦s❢❡r❛ ✐♥s✲ tá✈❡❧✱ ❛ ❧✐♥❤❛ ✈❡r❞❡✱ ♥❡✉tr❛✱ ❡ ❛ ❧✐♥❤❛ ❛③✉❧ ❛t♠♦s❢❡r❛ ❡stá✈❡❧✳ ✭❲❆▲▲❆❈❊❀
❍❖❇❇❙✱ ✷✵✵✻❜✱ ♣✳ ✸✾✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✹
✶✽ ➪r❡❛ ❞❡ ❡st✉❞♦✱ ❝♦♥t❡♠♣❧❛ ❛ ❝♦st❛ ❜r❛s✐❧❡✐r❛ ❝♦♠ ❛s ❞✐✈✐sõ❡s ❡st❛❞✉❛✐s✳ ❇❛t✐♠❡tr✐❛ ❞♦ ♦❝❡❛♥♦ ✭❡♠ ❝♦r❡s✮ ❡ ❩❊❊ ✭❡♠ ❝♦♥t♦r♥♦✮✳ P♦❧í❣♦♥♦s ✭r❡✲ t❛♥❣✉❧❛r❡s✮ r❡❢❡r❡♠✲s❡ ❛s ár❡❛s ❜❛t✐♠étr✐❝❛s ✉t✐❧✐③❛❞❛s ♣❛r❛ ❡st✐♠❛t✐✈❛s ❞♦s r❡❝✉rs♦s ❛♦ ❧♦♥❣♦ ❞❛ ❝♦st❛✳ ❊ss❡s r❡tâ♥❣✉❧♦s ✭♣♦❧í❣♦♥♦s✮ ❧✐♠✐t❛♠✲s❡ ❛ ❩❊❊✱ ✐♥✐❝✐❛♥❞♦ ❞❡ ♥♦rt❡ ❛ s✉❧✱ ♣❛r❛ ❝❛❧❝✉❧❛r ❛ ❞✐stâ♥❝✐❛ ❛♦ ❧♦♥❣♦ ❞❛
♣❧❛t❛❢♦r♠❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✺ ✶✾ ✭❛✮ ❈✉r✈❛ ❞❡ ♣♦t❡♥❝✐❛ ❞❛s t✉r❜✐♥❛s ❡ó❧✐❝❛s ♦✛s❤♦r❡✳ ✭❜✮ ❊str✉t✉r❛s ❞❡
❛♣♦✐♦ ♣❛r❛ t♦rr❡s ❡ó❧✐❝❛s ♦✛s❤♦r❡ ❡ s✉❛ ❛♣❧✐❝❛çã♦ ❡♠ ❢✉♥çã♦ ❞❛ ♣r♦✲ ❢✉♥❞✐❞❛❞❡ ❞♦ ♠❛r✳ ❋♦♥t❡✿ ✭❛✮ ❊❧❛❜♦r❛❞♦ ♣❡❧♦ ❛✉t♦r✳ ✭❜✮ ❆❞❛♣t❛❞♦ ❞❡
✭❆❘❆P❖●■❆◆◆■❀ ●❊◆❆❈❍❚❊✱ ✷✵✶✸✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✻
✷✵ ❈❧✐♠❛t♦❧♦❣✐❛ ♠❡♥s❛❧ ❞♦ ✢✉①♦ ❞❡ ❝❛❧♦r ❧❛t❡♥t❡ ❬W m−2❪✱ ❝❛❧❝✉❧❛❞♦s s♦❜r❡
♦ ♣❡rí♦❞♦ ❞❡ ✶✾✽✽✲✷✵✶✸✳ ✭◗✉❛❞r♦ ❡sq✉❡r❞♦✮ r❡♣r❡s❡♥t❛ ♠é❞✐❛ ♠❡♥s❛❧ ❡♠
❥❛♥❡✐r♦❀ ✭◗✉❛❞r♦ ❞✐r❡✐t♦✮ r❡♣r❡s❡♥t❛ ♠é❞✐❛ ♠❡♥s❛❧ ❡♠ ❥✉❧❤♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✼ ✷✶ ❈❧✐♠❛t♦❧♦❣✐❛ ♠❡♥s❛❧ ❞♦ ✢✉①♦ ❞❡ ❝❛❧♦r s❡♥sí✈❡❧ ❬W m−2❪✱ ❝❛❧❝✉❧❛❞♦s s♦❜r❡
♦ ♣❡rí♦❞♦ ❞❡ ✶✾✽✽✲✷✵✶✸✳ ✭P❛✐♥❡❧ ❡sq✉❡r❞♦✮ r❡♣r❡s❡♥t❛ ♠é❞✐❛ ♠❡♥s❛❧ ❡♠
❥❛♥❡✐r♦❀ ✭P❛✐♥❡❧ ❞✐r❡✐t♦✮ s✐❣♥✐✜❝❛ ♠é❞✐❛ ♠❡♥s❛❧ ❡♠ ❥✉❧❤♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✽ ✷✷ P❛râ♠❡tr♦ ❞❡ ❡st❛❜✐❧✐❞❛❞❡ ❛t♠♦s❢ér✐❝❛ ❛❞✐♠❡♥s✐♦♥❛❧ ✭ψ✮ ❞❡ ✶✾✽✽✲✷✵✶✸✳
✭P❛✐♥❡❧ ❡sq✉❡r❞♦✮ r❡♣r❡s❡♥t❛ ♠é❞✐❛ ♠❡♥s❛❧ ❡♠ ❥❛♥❡✐r♦❀ ✭P❛✐♥❡❧ ❞✐r❡✐t♦✮
✷✸ ❉✐❢❡r❡♥ç❛ ❡♥tr❡ ♦s ❝❛♠♣♦s ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❛ ✾✺ ♠❡tr♦s✱ ✉s❛♥❞♦ ❛ ❡①tr❛✲ ♣♦❧❛çã♦ ❝♦♠ ❢❛t♦r ❝♦rr❡çã♦ ▼♦♥✐♥✕❖❜✉❦❤♦✈ ✭Um✮ ❡ ❝❧áss✐❝❛ ❧♦❣❛rít♠✐❝❛
✭Ul✮✱ ♣❛r❛ ♦s ♣❡rí♦❞♦s ❞❡ ❥❛♥❡✐r♦ ❡ ❥✉❧❤♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✵
✷✹ ▼❛♣❛s ❞❡ ♣r♦❞✉çã♦ ❞❡ t✉r❜✐♥❛ ♣❛r❛ ❝✐♥❝♦ ❞✐❢❡r❡♥t❡s t✉r❜✐♥❛s✳ ❆ ❜❛rr❛ ❞❡ ❝♦r ❧✐♠✐t❛✲s❡ ❛ ♣♦tê♥❝✐❛ ♥♦♠✐♥❛❧ ❞❛ r❡s♣❡❝t✐✈❛ t✉r❜✐♥❛✳ ❖s P❛✐♥é✐s s✉♣❡r✐✲ ♦r❡s ❝♦rr❡s♣♦♥❞❡ ❛♦ ♣❡rí♦❞♦ ❞❡ ❥❛♥❡✐r♦ ✭✈❡rã♦✮✱ ❡♥t❛♥t♦ q✉❡ ♦s ✐♥❢❡r✐♦r❡s
❛ ❥✉❧❤♦ ✭✐♥✈❡r♥♦✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✶ ✷✺ P❛✐♥é✐s ✐❧✉str❛t✐✈♦s q✉❡ ❡①✐❜❡♠ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦s r❡❝✉rs♦s ❞✐s✲
♣♦♥í✈❡✐s ❛♦ ❧♦♥❣♦ ❞❛ ❝♦st❛ ❜r❛s✐❧❡✐r❛✳ ❖ ❡✐①♦ ✈❡rt✐❝❛❧ ❡①✐❜❡ ❛ ❡①t❡♥sã♦ ❞❡ ♥♦rt❡ ❛ s✉❧ ♥❛ ❝♦st❛ ❜r❛s✐❧❡✐r❛ ✼✳✵✵✵ ❦♠✱ ❛♣r♦①✐♠❛❞❛♠❡♥t❡✳ ❆s ár❡❛s ❡ ❛s ❧✐♥❤❛s ❡♠ ❝♦r❡s r❡♣r❡s❡♥t❛♠ ♦s ♥í✈❡✐s ❜❛t✐♠étr✐❝♦s ❞❡♥tr♦ ❞❛ ❩❊❊✳ ❖ ♣❛✐♥❡❧ à ❡sq✉❡r❞❛ ❡①✐❜❡ ❛ ár❡❛✱ ❡♠ ❦♠2
✱ ❛ s❡r ❡①♣❧♦r❛❞❛ ♥❛ ♣❧❛t❛❢♦r♠❛ ♦❝❡â♥✐❝❛✱ ❞✐✈✐❞✐❞❛ ♣♦r ♥í✈❡✐s ❞❡ ♣r♦❢✉♥❞✐❞❛❞❡✱ q✉❡ ✈ã♦ ❞❡ ✵ ❛ ✶✳✵✵✵ ♠✳ ❖ ♣❛✐♥❡❧ ❝❡♥tr❛❧ ❡①✐❜❡ ♦s r❡❝✉rs♦s ❞✐s♣♦♥í✈❡✐s ❛❝✉♠✉❧❛❞♦s✱ ❡♠ ●❲✱ ♣♦r ♣r♦❢✉♥❞✐❞❛❞❡✳ ❊ ♦ ♣❛✐♥❡❧ ❞✐r❡✐t♦ ✐❧✉str❛ ❛ ♣♦tê♥❝✐❛ ❞❛ t✉r❜✐♥❛ r❡❢❡r❡♥t❡ ❛ ❝❛❞❛ ✐♥t❡r✈❛❧♦ ❜❛t✐♠étr✐❝♦✱ ❡♠ ▼❲✳ ❚♦❞❛s ❡ss❛s ❝❛r❛❝t❡ríst✐❝❛s sã♦ ❞❡❧✐♠✐t❛❞❛s ♣♦r ❧✐♥❤❛s tr❛❝❡❥❛❞❛s q✉❡ ✐♥❞✐❝❛♠ ♦s ❧✐♠✐t❡s ❞♦s ❡st❛❞♦s ❜r❛✲
s✐❧❡✐r♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✷ ✷✻ ❈❛♣❛❝✐❞❛❞❡ ✐♥st❛❧❛❞❛ ❡ ❡♠ ❝♦♥str✉çã♦ ♥♦ ❇r❛s✐❧ ♣❛r❛ ❛♥♦ ❞❡ ✷✵✶✸ ✭♠♦❞✐✲
✜❝❛❞♦ ❞❡ ●❲❊❈ ✭✷✵✶✹✮✮✳ ❖ ♠❛♣❛ ❡ ❛ ❡s❝❛❧❛ ❡♠ ❝♦r❡s ✐❧✉str❛♠ ❛ ♣♦tê♥❝✐❛ ♠é❞✐❛ ❣❡r❛❞❛ ♣♦r ✉♠❛ t✉r❜✐♥❛ ❞❡ ✻✳✶✺ ▼❲ ❡ ❝❛❧❝✉❧❛❞❛ ❛ ♣❛rt✐r ❞❡ ❞❛❞♦s
s❛t❡❧✐tár✐♦s ♣❛r❛ ♦ ♣❡rí♦❞♦ ❡♥tr❡ ✶✾✽✽ ❡ ✷✵✶✹✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✾ ✷✼ ❈♦♠♣♦s✐çã♦ ❞❛ ▼❛tr✐③ ❊❧étr✐❝❛ ◆❛❝✐♦♥❛❧✳ ❋♦♥t❡✿ ❊P❊✱ ✷✵✶✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✾ ✷✽ ✭❛✮ ❘❡❣✐ã♦ ❤✐❞r♦❣rá✜❝❛ ❞♦ ❙ã♦ ❋r❛♥❝✐s❝♦ ❡ s❡❧❡çã♦ ❞❛s ❡st❛çõ❡s ❞❡ ✈❡♥t♦✳
✭❜✮ ❉✐❛❣r❛♠❛ ❡sq✉❡♠át✐❝♦ ❞❛s ✉s✐♥❛s ❝♦♠♣♦♥❡♥t❡s ❞♦ ❈♦♠♣❧❡①♦ P❛✉❧♦
❆❢♦♥s♦ ✭❖◆❙✱ ✷✵✶✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✵
✷✾ ❛✮ ❈✉r✈❛ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ♣♦tê♥❝✐❛ ♣❛r❛ t✉r❜✐♥❛ ❘❊♣♦✇❡r ✻▼✳ ✭❜✮ ❚✉r✲ ❜✐♥❛ ✐♥st❛❧❛❞❛ s♦❜r❡ ❡str✉t✉r❛ ❡♠ ❥❛q✉❡t❛ ♥♦ ♣❛rq✉❡ ❡ó❧✐❝♦ ❞❡ ❚❤♦r♥t♦♥ ❇❛♥❦ ■■ ✭❈♦rt❡s✐❛ ❘❊♣♦✇❡r✱ ❛❣♦r❛ ❙❡♥✈✐♦♥✳ ❈♦♣②r✐❣❤t✿ ❈✲P♦✇❡r ◆✳❱✳✱
♣❤♦t♦❣r❛♣❤❡r ❚♦♠ ❉❍❛❡♥❡♥s✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✵ ✸✵ ❱❛③ã♦ ♠é❞✐❛ ♠❡♥s❛❧ ❛✢✉❡♥t❡ ♥♦s r❡s❡r✈❛tór✐♦s✳ ❛✮ ▼♦①♦tó✱ ❜✮ P❛✉❧♦
❆❢♦♥s♦ ✹✱ ❝✮ P❛✉❧♦ ❆❢♦♥s♦ ✶✱✷✱✸ ❡ ❞✮ ❈♦♠♣❧❡①♦ P❛✉❧♦ ❆❢♦♥s♦ ✲ ▼♦①♦tó✳ ♣✳ ✶✶✶ ✸✶ ▼é❞✐❛ ♠❡♥s❛❧ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ❛ ✶✵✵ ♠❡tr♦s✱ ♥♦ ♣❡rí♦❞♦ ❡♥tr❡
✶✾✽✽ ❡ ✷✵✶✹✱ ❡♠ três ♣♦♥t♦s ♦✛s❤♦r❡ ♥♦ ♥♦r❞❡st❡ ❜r❛s✐❧❡✐r♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✶ ✸✷ ❈♦♠♣❛r❛çã♦ ❞❛s ✈❛③õ❡s ❛✢✉❡♥t❡s ❞♦ ❈♦♠♣❧❡①♦ P❛✉❧♦ ❆❢♦♥s♦ ✲ ▼♦①♦tó
✸✸ ❛✮ ❙ér✐❡ ♠❡♥s❛❧ ❜r✉t❛ ❞❛ ✈❛③ã♦ ❞♦ ❘✐♦ ❙ã♦ ❋r❛♥❝✐s❝♦ ✭❧✐♥❤❛ ❛③✉❧ ❝❧❛r♦✮ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♠é❞✐❛ ❝❧✐♠❛t♦❧ó❣✐❝❛ ♠❡♥s❛❧ ✭❧✐♥❤❛ ♣r❡t❛✮✳ ❜✮ ❙ér✐❡ ♠❡♥✲ s❛❧ ❜r✉t❛ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ♦✛s❤♦r❡ ❞♦ P✷ ✭❧✐♥❤❛ ✈❡r❞❡ ❝❧❛r❛✮ ❡ sér✐❡ ❝❧✐♠❛t♦❧ó❣✐❝❛ ♠❡♥s❛❧ ✭❧✐♥❤❛ ♣r❡t❛✮✳ ❝✮ ❆♥♦♠❛❧✐❛s ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ❡♠ P✷ ✭✈❡r❞❡✮ ❡ ✈❛③ã♦ ❛✢✉❡♥t❡ ❞♦ ❘✐♦ ❙ã♦ ❋r❛♥❝✐s❝♦ ✭❛③✉❧ ❝❧❛r♦✮✱ ♣❛r❛ ♣❡rí♦❞♦ ❡♥tr❡ ✶✾✽✽ ❡ ✷✵✶✸✳ ❆q✉✐ ❛ ❛♥♦♠❛❧✐❛ é ❝❛❧❝✉❧❛❞❛ ❛ ♣❛rt✐r ❞♦ s✐♥❛❧ ❜r✉t♦✱ s✉❜tr❛✐♥❞♦ ♦ s✐♥❛❧ ❝❧✐♠❛t♦❧ó❣✐❝♦ ❡ ♥♦r♠❛❧✐③❛♥❞♦ ♣❡❧❛ ❛♠♣❧✐t✉❞❡ ❞♦ s✐♥❛❧ ❝❧✐♠❛t♦❧ó❣✐❝♦✳ ❆ ♦❝♦rrê♥❝✐❛ ❞♦ ❢❡♥ô♠❡♥♦ ❣❧♦❜❛❧ ❡st❛ ✐♥❞✐❝❛❞♦ ♣♦r ❝♦r❡s ♥♦ ❡✐①♦✱ s❡♥❞♦ ❊❧✲◆✐ñ♦ ✭✈❡r♠❡❧❤♦✮ ❡ ▲❛✲◆✐ñ❛ ✭❛③✉❧✮ ✭❍❯❆◆● ❡t
❛❧✳✱ ✷✵✶✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✸
✸✹ ▼♦❞❡❧♦ ❝♦♥❝❡✐t✉❛❧ ❞♦ s✐st❡♠❛ ❤í❜r✐❞♦ ❡ó❧✐❝♦✲❤✐❞rá✉❧✐❝♦ ✭P✐♠❡♥t❛ ❡ ❆ss✐✲ r❡✉✱ ✷✵✶✹✮✳ ❖s sí♠❜♦❧♦s r❡❢❡r❡♠✲s❡ ❛♦ ♥í✈❡❧ ❞❛ á❣✉❛ h✱ ❝♦♥tr✐❜✉✐çõ❡s ❞❛
❞❡s❝❛r❣❛ ❞♦ r✐♦Qriver✱ ♣r❡❝✐♣✐t❛çã♦Qprec✱ ❡ ♣❡r❞❛s ❛tr❛✈és ❞❛ ❡✈❛♣♦r❛çã♦ Qevap ❡ ❞❛ ✈❛③ã♦ ❞❡✢✉❡♥t❡ Qhydro✳Phydro r❡❢❡r❡✲s❡ à ❣❡r❛çã♦ ❤✐❞r❡❧étr✐❝❛✳ Pwind r❡❢❡r❡✲s❡ à ♣♦tê♥❝✐❛ ❣❡r❛❞❛ ♣♦r ❢❛③❡♥❞❛s ❡ó❧✐❝❛s ❧♦❝❛✐s ♦✉ r❡♠♦t❛s✳ Pgrid r❡❢❡r❡✲s❡ à ❡♥❡r❣✐❛ ❞❡s♣❛❝❤❛❞❛ à r❡❞❡✳ Ar é ár❡❛ ❞❡ s✉♣❡r❢í❝✐❡ ❡ V ♦
✈♦❧✉♠❡ ❞♦ r❡s❡r✈❛tór✐♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✷✸ ✸✺ ❱❡♥t♦s ✉t✐❧✐③❛❞♦s ♥❛ s✐♠✉❧❛çã♦ ❞♦ s✐st❡♠❛ ❤í❜r✐❞♦ ❡ó❧✐❝♦✲❤✐❞rá✉❧✐❝♦✳ ◆♦
t♦♣♦ ♦❜s❡r✈❛♠♦s ❛ sér✐❡ ❞❡ ❞❛❞♦s ♦✛s❤♦r❡ ♦❜s❡r✈❛❞♦s ♣❛r❛ ❛ ❝♦st❛ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡✳ ❆ ❧✐♥❤❛ ❝✐♥③❛ r❡♣r❡s❡♥t❛ ♠é❞✐❛s ❞✐ár✐❛s✱ ❡♥q✉❛♥t♦ ❛ ❧✐♥❤❛ ♣r❡t❛ ♠é❞✐❛s ♠❡♥s❛✐s✳ ❖s ❣rá✜❝♦s ✐♥t❡r♠❡❞✐ár✐♦s r❡♣r❡s❡♥t❛♠ ✈❡♥t♦s t❡ór✐❝♦s ❚✶ ❡ ❚✷✳ ❆ sér✐❡ ❚✶ ❡♥❝♦♥tr❛✲s❡ ❡♠ ❢❛s❡ ❝♦♠ ❛ ❡st❛çã♦ ❘◆✱ ❡♥q✉❛♥❞♦ ❚✷ ❡stá ❞❡❢❛s❛❞♦ ❡♠ ✻ ♠❡s❡s✳ ❖ ♣❛✐♥❡❧ ✐♥❢❡r✐♦r✱ ✐❧✉str❛ ❛ s✐♠✉❧❛çã♦ ❞❛s ♣r♦❞✉çõ❡s ♠❡♥s❛✐s ❞❛s ❡st❛çõ❡s ❚✶ ❡ ❚✷✱ ❝♦♥s✐❞❡r❛♥❞♦
✉♠❛ t✉r❜✐♥❛ ❞❡ ♣♦tê♥❝✐❛ ♥♦♠✐♥❛❧ ❞❡ ✻✱✶✺ ▼❲✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✷✹ ✸✻ ❱❛r✐❛❜✐❧✐❞❛❞❡ ❛♥✉❛❧ ❞♦ r❡❣✐♠❡ ❤í❞r✐❝♦ ❡ ❡ó❧✐❝♦✳ ❆ ✈❛r✐❛çã♦ ❤í❞r✐❝❛ ❡stá
✐❧✉str❛❞❛ ♣❡❧❛ ✈❛③ã♦ ❛✢✉❡♥t❡ ✭qr✐✈❡r✱ ♠♠ ❞✐❛−1✮✳ ❖ r❡❣✐♠❡ ❡ó❧✐❝♦ ❡stá
r❡♣r❡s❡♥t❛❞♦ ♣❡❧❛ ♣r♦❞✉çã♦ ❞❡ ❡♥❡r❣✐❛✱ ❝♦♥s✐❞❡r❛♥❞♦ ✉♠❛ t✉r❜✐♥❛ ❡ó❧✐❝❛ ❞❡ ♣♦tê♥❝✐❛ ♥♦♠✐♥❛❧ ❞❡ ✻✱✶✺ ▼❲✳ ❆s sér✐❡s ❞❡ ✈❡♥t♦ t❡ór✐❝❛s ✭❚✶ ❡ ❚✷✮ ❡ ♦❜s❡r✈❛❞❛s ✭❘◆✮ ❡stã♦ ✐♥❞✐❝❛❞❛s✳ ▲✐♥❤❛s ❣r♦ss❛s r❡♣r❡s❡♥t❛♠ ❛s ♠é❞✐❛s ✭✶✾✾✹✲✷✵✶✷✮✳ P❛r❛ qriver ❛ ár❡❛ ❛③✉❧ r❡♣r❡s❡♥t❛ ❛ ✈❛r✐❛çã♦ ❞❡ ± ✉♠
❞❡s✈✐♦ ♣❛❞rã♦✳ ❆ ❝♦rr❡❧❛çã♦ P❡❛rs♦♥ ✭❘✮ ❞♦s r❡❣✐♠❡s ❡ó❧✐❝♦s ❝♦♠ ♦ r❡❣✐♠❡ ❤í❞r✐❝♦ ❡stá ✐♥❞✐❝❛❞❛✳ ◆♦t❡ q✉❡ ❛ ❝♦rr❡❧❛çã♦ ❡♥tr❡ ✈❛③ã♦ ✭qr✐✈❡r✮ ❡ ♦s ♣♦♥t♦s ❡♠ ❘◆ ❡ ❚✶ t❡♥❞❡♠ ♣❛r❛ ❘ → −1✳ ❊♥q✉❛♥t♦ q✉❡ ♦ ♣♦♥t♦ ❚✷
t❡♥❞❡ ♣❛r❛ ❘ →1✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✷✺
✸✼ ❘❡s✉❧t❛❞♦s ❞❛ s✐♠✉❧❛çã♦ ❞♦ s✐st❡♠❛ ❤í❜r✐❞♦ ❡ó❧✐❝♦✲❤✐❞rá✉❧✐❝♦✳ ❛✮ ✈❛③õ❡s ❛✢✉❡♥t❡s ✭qriver✮ ❡ ❞❡✢✉❡♥t❡s ❤✐stór✐❝❛s ❞♦ s✐st❡♠❛ ✭qhydro✮✳ ❖s ♣❛✐♥é✐s
❜✱ ❝ ❡ ❞ ✐❧✉str❛♠ r❡s♣❡❝t✐✈❛♠❡♥t❡ ❛s ❝♦♥tr✐❜✉✐çõ❡s ❞❡ á❣✉❛ ♣♦✉♣❛❞❛ ✭qwind✮ ♣❛r❛ ✈❡♥t♦s t❡ór✐❝♦s ❚✶✱ ❚✷ ❡ ✈❡♥t♦s ♦❜s❡r✈❛❞♦s ❞❛ ❝♦st❛ ❞♦
❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ✭❘◆✮✳ ❡✮ ◆í✈❡❧ ❞♦ r❡s❡r✈❛tór✐♦ ❞❡ ■t✉♠❜✐❛r❛ ♣❛r❛ ♦ ♣❡rí♦❞♦ ❞❡ ✶✾✾✹ ❛ ✷✵✶✶✳ ❖ ♥í✈❡❧ ❤✐stór✐❝♦ ❡♥❝♦♥tr❛✲s❡ ✐♥❞✐❝❛❞♦ ♣❡❧❛ ❧✐♥❤❛ ❝✐♥③❛✱ ♦s ♥í✈❡✐s s✐♠✉❧❛❞♦s ♣❛r❛ ❚✶✱ ❚✷ ❡ ❘◆ ♣♦r ❧✐♥❤❛s ❧❛r❛♥❥❛✱ ✈❡r❞❡ ❡ ♣r❡t❛ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ◆♦t❡ q✉❡ ♦ s✐st❡♠❛ ❤í❜r✐❞♦ ❡✈✐t❛ ♦s ♣❡rí♦❞♦s ❞❡ ❡st✐❛❣❡♠ ❡ ❞❡♠♦♥str❛ ♠❡❧❤♦r ❞❡s❡♠♣❡♥❤♦ ♣❛r❛ ❛q✉❡❧❡s ✈❡♥t♦s ✭❚✶ ❡ ❘◆✮ q✉❡ sã♦ ✐♥✈❡rs❛♠❡♥t❡ ❝♦rr❡❧❛❝✐♦♥❛❞♦s ✭❝♦♠♣❧❡♠❡♥t❛r❡s✮ ❝♦♠ ♦
▲✐st❛ ❞❡ t❛❜❡❧❛s
✶ ❈❤❛r❛❝t❡r✐st✐❝s ♦❢ t❤❡ s❛t❡❧❧✐t❡✲❜❛s❡❞ ♦✛s❤♦r❡ ✇✐♥❞ st❛t✐♦♥s✳ ❍❡r❡ Uref
r❡❢❡rs t♦ t❤❡ ✇✐♥❞ s♣❡❡❞ ✭♠ s−1✮ ❛t r❡❢❡r❡♥❝❡ ❤❡✐❣❤t ✭✶✵ ♠✮ ❛♥❞ U r❡❢❡rs
t♦ ♠❡❛♥ ✇✐♥❞ s♣❡❡❞ ✭♠ s−1✮ ❛t r♦t♦r ❤❡✐❣❤t ✭✶✵✵ ♠❡t❡rs✮✳
Pd r❡❢❡rs t♦
✇✐♥❞ ♣♦✇❡r ❞❡♥s✐t② ✭❲ ♠−2✮✱ Pt t♦ t❤❡ t✉r❜✐♥❡ ♣♦✇❡r ✭❦❲✮✱ Ap t♦ t❤❡
❛r❡❛ ♦❢ t❤❡ ❝♦♥t✐♥❡♥t❛❧ s❤❡❧❢ ❜❡t✇❡❡♥ ✵ ❛♥❞ ✺✵ ♠ ❛♥❞ Pr t♦ t❤❡ r❡s♦✉r❝❡
♣♦t❡♥t✐❛❧ ✭●❲✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✺ ✷ ❈❤❛r❛❝t❡r✐st✐❝s ♦❢ t❤❡ ❇r❛③✐❧✐❛♥ ❞r❛✐♥❛❣❡ ❜❛s✐♥s✳ ❍❡r❡Qf ✭♠3
s−1✮ r❡❢❡rs
t♦ t❤❡ ♠❡❛♥ ✐♥t❡❣r❛t❡❞ r✉♥♦✛ ✭❊q✳ ✷✳✽✮ ♦❢ t❤❡ ❞r❛✐♥❛❣❡ ❜❛s✐♥✱ P r❡❢❡rs
t♦ ♠❡❛♥ ♣r❡❝✐♣✐t❛t✐♦♥ ✭♠♠ ♠♦♥t❤ −1✮✱ Ep r❡❢❡rs t♦ ♠❡❛♥ t❤❡♦r❡t✐❝❛❧
❡♥❡r❣② ♣♦t❡♥t✐❛❧ ✭❊q✳ ✷✳✾✮✱ Qp r❡❢❡rs t♦ ♠❡❛♥ Qp =P
αPiAi ❛♥❞ r❡♣r❡✲
s❡♥ts t❤❡ ♠❡❛♥ ✐♥t❡❣r❛t❡❞ ♣r❡❝✐♣✐t❛t✐♦♥ ❢♦r ❡❛❝❤ ❞r❛✐♥❛❣❡ ❜❛s✐♥ ✭✇✐t❤♦✉t ❡✈❛♣♦r❛t✐♦♥✮✳ Ph r❡❢❡rs t♦ t❤❡ ♠❛①✐♠✉♠ t❤❡♦r❡t✐❝❛❧ ♣♦✇❡r✱ Pa
tec r❡❢❡rs
t♦ t❡❝❤♥✐❝❛❧ ❤②❞r♦ ♣♦t❡♥t✐❛❧ ♣❡r ❊P❊ ✭▼▼❊✱ ✷✵✵✼✮ ❛♥❞ Pb
tec ♣❡r ❙■P❖❚
✭❊▲❊❚❘❖❇❘➪❙✱ ✷✵✶✹❜✮ ✭❊▲❊❚❘❖❇❘➪❙✱ ✷✵✶✹❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✻
✸ ❈r♦ss✲❝♦rr❡❧❛t✐♦♥ ❝♦❡✣❝✐❡♥t ❜❡t✇❡❡♥ ❞✐✛❡r❡♥t st❛t✐♦♥s✿ ❤②❞r♦ × ❤②❞r♦
✭◗✉❛❞r❛♥t ❆✮✱ ✇✐♥❞ ×❤②❞r♦ ✭◗✉❛❞r❛♥t ❇✮ ❛♥❞ ✇✐♥❞×✇✐♥❞ ✭◗✉❛❞r❛♥t
❈✮✳ ❚❤❡ ❣r❛② ❝♦❧♦rs r❡♣r❡s❡♥t ❝♦rr❡❧❛t✐♦♥s t❤❛t ❛r❡ ♥♦t st❛t✐st✐❝❛❧❧② s✐❣♥✐✲ ✜❝❛♥t ✭p >0.05✮✳ ▼♦♥t❤❧② t✐♠❡s s❡r✐❡s ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ❛♥❞ ✇✐♥❞ s♣❡❡❞s
✇❡r❡ ✉s❡❞ t♦ ❝♦♠♣✉t❡ t❤❡ ❝♦rr❡❧❛t✐♦♥s s❤♦✇♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✼ ✹ ❊st✉❞♦s ♦✛s❤♦r❡ ♥♦ ❇r❛s✐❧ ✕ ❞❛❞♦s ❝♦♠♣❛r❛t✐✈♦s ❡ r❡❝✉rs♦s ❡♥❡r❣ét✐❝♦s✳ ♣✳ ✾✸ ✺ ❈❛r❛❝t❡ríst✐❝❛s ❡ ❡s♣❡❝✐✜❝❛çõ❡s té❝♥✐❝❛s ❞♦s ❛❡r♦❣❡r❛❞♦r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✹ ✻ P♦t❡♥❝✐❛❧ ❞♦s r❡❝✉rs♦s ❡ó❧✐❝♦s ♦✛s❤♦r❡ ❡♠ ❢✉♥çã♦ ❞♦ ✐♥t❡r✈❛❧♦ ❜❛t✐♠étr✐❝♦
❡ ❞♦ t✐♣♦ ❞❡ t✉r❜✐♥❛✳ ❖s ♥ú♠❡r♦s r❡❢❡r❡♠✲s❡ ❛ ♣♦tê♥❝✐❛ ♠é❞✐❛ ✭●❲✮ ❡st✐♠❛❞♦ ❛ ♣❛rt✐r ❞♦s ♠ét♦❞♦s ❞❡ ❡①tr❛♣♦❧❛çã♦ ❞❡ ▼♦♥✐♥✕❖❜✉❦❤♦✈ ❡
▲♦❣❛rít♠✐❝❛ ✭❡♥tr❡ ♣❛rê♥t❡s❡s✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✺ ✼ ❈❛r❛❝t❡ríst✐❝❛s té❝♥✐❝❛s ✲ ❘❊♣♦✇❡r ✻▼✱ ❛❣♦r❛ ❙❡♥✈✐♦♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✷ ✽ ❉❡♥s✐❞❛❞❡ ❞❡ ♣♦tê♥❝✐❛ ✭❲ ♠−2✮ ❡ ♣♦tê♥❝✐❛ ❞❛ t✉r❜✐♥❛ ✭❲✮✱ ❡st✐♠❛t✐✈❛
♠❡♥s❛❧ ❞❡ ❡♥❡r❣✐❛ ❛ ♣❛rt✐r ❞❡ ✉♠❛ t✉r❜✐♥❛ ❤✐♣♦tét✐❝❛ ❞❡ ✻✱✶✺ ▼❲ ❞❡ ♣♦tê♥❝✐❛ ♥♦♠✐♥❛❧ ❡ ✾✵ ♠❡tr♦s ❞❡ ❛❧t✉r❛✳X r❡❢❡r❡✲s❡ ❛ ♠é❞✐❛ ❡σ ♦ ❞❡s✈✐♦
♣❛❞rã♦✳ ▼é❞✐❛s ❝❧✐♠❛t♦❧ó❣✐❝❛s ❡♥tr❡ ✶✾✽✽ ❡ ✷✵✶✸✱ ♣❛r❛ ♦s ♣♦♥t♦s ❧♦❝❛❧✐✲
③❛❞♦s ♥♦ ♥♦r❞❡st❡ ❞♦ ♣❛ís✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶✸ ✾ ▼❛tr✐③ ❞❡ ❝♦rr❡❧❛çã♦ r ❞❛s sér✐❡s ❤✐stór✐❝❛ ♠❡♥s❛❧ ❤í❞r✐❝❛ ① ❡ó❧✐❝❛✳ ✳ ✳ ✳ ♣✳ ✶✶✹
✶✵ ❈♦rr❡❧❛çã♦ r ❡♥tr❡ ❊◆❖❙✱ ✈❛r✐á✈❡✐s ❤í❞r✐❝❛ ❡ ❡ó❧✐❝❛✳ ❖s ✈❛❧♦r❡s ❝♦♠ ❛s✲
✶✶ ❛✮ ❝♦rr❡❧❛çã♦ ❞❛ sér✐❡s ❜r✉t❛ ❞❡ ✈❛③ã♦ ❡ ✈❡❧♦❝✐❞❛❞❡✱ ❜✮ ❝♦rr❡❧❛çã♦ ❡♥tr❡ ❝❧✐♠❛t♦❧♦❣✐❛ ♠❡♥s❛❧ ❞❛ ✈❛③ã♦ ❡ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ❡ ❝✮ ❝♦rr❡❧❛çã♦ ❡♥tr❡ ❛♥♦♠❛❧✐❛s ♥♦r♠❛❧✐③❛❞❛s ✭♣❡❧❛ ❛♠♣❧✐t✉❞❡ s❛③♦♥❛❧✮ ❞❛ ✈❛③ã♦ ❡ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦✳ ❆ ❝♦r ❝✐♥③❛ r❡♣r❡s❡♥t❛ ❝♦rr❡❧❛çã♦ q✉❡ ♥ã♦ sã♦ ❡st❛t✐st✐❝❛♠❡♥t❡
▲✐st❛ ❞❡ ❛❜r❡✈✐❛t✉r❛s ❡ sí♠❜♦❧♦s
∆f ❡s❝♦❛♠❡♥t♦ s✉♣❡r✜❝✐❛❧ ✭♠♠ ♠ês−1✮
wθV0 ✢✉①♦ ♠é❞✐♦ t✉r❜✉❧❡♥t♦ ✭❲ ♠
−2✮
∆t ♥ú♠❡r♦s ❞❡ s❡❣✉♥❞♦s ❡♠ ✉♠ ♠ês
κ ❝♦♥st❛♥t❡ ❞❡ ❱♦♥✲❑❛r♠❛♥ ✭❛❞✐♠❡♥s✐♦♥❛❧✮
θV t❡♠♣❡r❛t✉r❛ ♣♦t❡♥❝✐❛❧ ✈✐rt✉❛❧ ✭❑✮
ψ ♣❛râ♠❡tr♦ ❞❡ ❡st❛❜✐❧✐❞❛❞❡ ❛t♠♦s❢ér✐❝❛
ψm ❢✉♥çã♦ ❞❡ ❡st❛❜✐❧✐❞❛❞❡ ❛t♠♦s❢ér✐❝❛
ρ ❞❡♥s✐❞❛❞❡ ❞♦ ❛r ✭❦❣ ♠−3✮
A ár❡❛ ✈❛rr✐❞❛ ♣❡❧♦ r♦t♦r ❞❛ t✉r❜✐♥❛ ❡ó❧✐❝❛ ✭♠2
✮
Ai ár❡❛ ❞❛ ❝é❧✉❧❛ ♥❛ ❣r❛❞❡ ✭♠
2
✮
Ap ár❡❛ ♣❛r❛ ❝❛❞❛ ♣♦♥t♦ ❞❛ ❣r❛❞❡ ✭❦♠2
✮
Ar ár❡❛ ❞♦ r♦t♦r ✭♠2✮
Cp ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝♦♥✈❡rsã♦ ♠❡❝â♥✐❝❛ ❡ ❡❧étr✐❝❛ ✭❛❞✐♠❡♥s✐♦♥❛❧✮
cp ❝❛❧♦r ❡s♣❡❝í✜❝♦ ❛ ♣r❡ssã♦ ❝♦♥st❛♥t❡ ✭❏ ❦❣−1 ❑−1✮
d ❞✐â♠❡tr♦ ❞♦ r♦t♦r ✭♠✮
Dt ♥ú♠❡r♦ ❞❡ t✉r❜✐♥❛s ♣♦r ❦♠2
Ep ❡♥❡r❣✐❛ ♣♦t❡♥❝✐❛❧ ✭❏♦✉❧❡s✮
Ev ❡✈❛♣♦r❛çã♦ ✭♠♠ ♠ês−1✮
g ❛❝❡❧❡r❛çã♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ✭♠ s−2✮
h ❛❧t✉r❛ ❡①tr❛♣♦❧❛❞❛ ♣❛r❛ ❡✐①♦ ❞♦ r♦t♦r ✭♠✮
H0 ✢✉①♦ ❞❡ ❝❛❧♦r s❡♥sí✈❡❧ ✭❲ ♠− 2
✮
hi ❛❧t✉r❛ ❞❛ ❝é❧✉❧❛ ❡♠ r❡❧❛çã♦ ❛♦ ♥í✈❡❧ ♠é❞✐♦ ❞♦ ♠❛r ✭♠✮
href ❛❧t✉r❛ ❞❡ r❡❢❡rê♥❝✐❛ ✭♠✮
L ❝♦♠♣r✐♠❡♥t♦ ❞❡ ▼♦♥✐♥✕❖❜✉❦❤♦✈ ✭♠✮
L0 ✢✉①♦ ❞❡ ❝❛❧♦r ❧❛t❡♥t❡ ✭❲ ♠− 2
lV ❝❛❧♦r ❧❛t❡♥t❡ ❞❡ ❡✈❛♣♦r❛çã♦ ❞❛ á❣✉❛ ✭❏ ❦❣−1✮
n ♥ú♠❡r♦ ❞❡ ♣♦♥t♦s ❞❛ ❣r❛❞❡
P ♣r❡❝✐♣✐t❛çã♦ ✭♠♠ ♠ês−1✮
Pc
grid ❣❡r❛çã♦ ❤✐❞r❡❧étr✐❝❛ ❝❧áss✐❝❛ ✭❲❛tts✮
Pd ❞❡♥s✐❞❛❞❡ ❞❡ ♣♦tê♥❝✐❛ ✭❲ ♠−2✮
Ph ♣♦t❡♥❝✐❛❧ ❤✐❞rá✉❧✐❝♦ t❡ór✐❝♦ ✭●❲✮
Pr ♣♦t❡♥❝✐❛❧ ❞♦s r❡❝✉rs♦s ❡ó❧✐❝♦s ♦✛s❤♦r❡ ✭●❲✮
Pt ♣♦tê♥❝✐❛ ❞❛ t✉r❜✐♥❛ ✭❲❛tts✮
Ptec ♣♦t❡♥❝✐❛❧ té❝♥✐❝♦ ❤✐❞rá✉❧✐❝♦ ✭●❲✮
Pwind ❣❡r❛çã♦ ❡ó❧✐❝❛ ✭❲❛tts✮
Q ✈❛③ã♦ ❞❡✢✉❡♥t❡ ♠é❞✐❛ ✭♠3
s−1✮
qa ✉♠✐❞❛❞❡ ❡s♣❡❝í✜❝❛ ✭❣ ❦❣−1✮
Qf ✈❛③ã♦ ✐♥t❡❣r❛❞❛ ✭♠3
s−1✮
Qi ✈❛③ã♦ ♣♦r ❝é❧✉❧❛ ♥❛ ❣r❛❞❡ ✭♠3 s−1✮
Qeco ✈❛③ã♦ ❡❝♦❧ó❣✐❝❛ ✭♠
3
s−1✮
Qevap ❡✈❛♣♦r❛çã♦ ✭♠3 s−1✮
Qhydro ✈❛③ã♦ ❤✐❞r❡❧étr✐❝❛ ✭♠3
s−1✮
Qprec ♣r❡❝✐♣✐t❛çã♦ ✭♠3
s−1✮
Qriver ❞❡s❝❛r❣❛ ✢✉✈✐❛❧ ✭♠3 s−1✮
Qspill ✈❛③ã♦ ✈❡rt❡❞♦✉r♦ ✭♠3
s−1✮
Qturb ✈❛③ã♦ t✉r❜✐♥❛❞❛ ✭♠3 s−1✮
Qh
turb ✈❛③ã♦ ❞♦ s✐st❡♠❛ ❤í❜r✐❞♦ ✭♠
3
s−1✮
r ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝♦rr❡❧❛çã♦ ❞❡ P❡❛rs♦♥
T t❡♠♣❡r❛t✉r❛ ❞♦ ❛r ✭K✮
Ta t❡♠♣❡r❛t✉r❛ ❞♦ ❛r ✭◦C✮
Ts t❡♠♣❡r❛t✉r❛ ❞❛ s✉♣❡r❢í❝✐❡ ❞♦ ♠❛r ✭◦C✮
U ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ✐♥❝✐❞❡♥t❡ ♥❛ ❛❧t✉r❛ ❞❛ t✉r❜✐♥❛ ❡ó❧✐❝❛ ✭♠ s−1✮
u ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ♥❛ ❛❧t✉r❛ ❡①tr❛♣♦❧❛❞❛ ✭♠ s−1✮
Ul ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ✉t✐❧✐③❛♥❞♦ ❛ ❡①tr❛♣♦❧❛çã♦ ❧♦❣❛rít♠✐❝❛ ✭♠ s−1✮
Um ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ✉t✐❧✐③❛♥❞♦ ❛ ❡①tr❛♣♦❧❛çã♦ ▼♦♥✐♥✕❖❜✉❦❤♦✈ ✭♠ s−1
✮
uref ✈❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ♥❛ ❛❧t✉r❛ ❞❡ r❡❢❡rê♥❝✐❛ ✭♠ s−1✮
V ✈♦❧✉♠❡ út✐❧ ✭♠3
z ❛❧t✉r❛ ♠é❞✐❛ ❞♦s ❛❡r♦❣❡r❛❞♦r❡s ✭♠✮
z0 ❝♦♠♣r✐♠❡♥t♦ ❞❡ r✉❣♦s✐❞❛❞❡ ✭♠✮
❈✉t✲✐♥ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ♣❛rt✐❞❛
❈✉t✲♦✉t ✈❡❧♦❝✐❞❛❞❡ ❞❡ ❝♦rt❡ ✭s❡❣✉r❛♥ç❛✮ ❘❛t❡❞ P♦✇❡r ♣♦tê♥❝✐❛ ♥♦♠✐♥❛❧
❆▲ ❊st❛❞♦ ❞❡ ❆❧❛❣♦❛s
❆▼❙❘✲❊ ❆❞✈❛♥❝❡❞ ▼✐❝r♦✇❛✈❡ ❙❝❛♥♥✐♥❣ ❘❛❞✐♦♠❡t❡r ❆◆❆ ❆❣ê♥❝✐❛ ◆❛❝✐♦♥❛❧ ❞❡ ➪❣✉❛s
❆◆❊❊▲ ❆❣ê♥❝✐❛ ◆❛❝✐♦♥❛❧ ❞❡ ❊♥❡r❣✐❛ ❊❧étr✐❝❛ ❆P ❊st❛❞♦ ❞♦ ❆♠❛♣á
❆❙❆❙ ❆♥t✐❝✐❝❧♦♥❡ ❙✉❜tr♦♣✐❝❛❧ ❞♦ ❆t❧â♥t✐❝♦ ❙✉❧ ❇❆ ❊st❛❞♦ ❞❛ ❇❛❤✐❛
❇❙❲ ❇❧❡♥❞❡❞ ❙❡❛ ❲✐♥❞s ❈❇ ❈♦rr❡♥t❡ ❞♦ ❇r❛s✐❧ ❈❊ ❊st❛❞♦ ❞♦ ❈❡❛rá
❈❊❇❉❙ ❈♦♥s❡❧❤♦ ❊♠♣r❡s❛r✐❛❧ ❇r❛s✐❧❡✐r♦ ♣❛r❛ ♦ ❉❡s❡♥✈♦❧✈✐♠❡♥t♦ ❙✉st❡♥tá✈❡❧ ❈❍P❆▼ ❈♦♠♣❧❡①♦ ❍✐❞r♦❡❧étr✐❝♦ ❞❡ P❛✉❧♦ ❆❢♦♥s♦✲▼♦①♦tó
❈◆❘❍ ❈♦♥s❡❧❤♦ ◆❛❝✐♦♥❛❧ ❞❡ ❘❡❝✉rs♦s ❍í❞r✐❝♦s ❈❘❯ ❈❧✐♠❛t❡ ❘❡s❡❛r❝❤ ❯♥✐t
❉❚▼ ▼♦❞❡❧♦ ❉✐❣✐t❛❧ ❞❡ ❚❡rr❡♥♦
❊❈▼❲❋ ❊✉r♦♣❡❛♥ ❈❡♥tr❡ ❢♦r ▼❡❞✐✉♠✲❘❛♥❣❡ ❲❡❛t❤❡r ❋♦r❡❝❛sts ❊◆❖❙ ❊❧✲◆✐ñ♦ ❖s❝✐❧❛çã♦ ❙✉❧
❊P❊ ❊♠♣r❡s❛ ❞❡ P❡sq✉✐s❛ ❊♥❡r❣ét✐❝❛ ❊❙ ❊st❛❞♦ ❞♦ ❊s♣ír✐t♦ ❙❛♥t♦
●❲❊❈ ❈♦♥s❡❧❤♦ ●❧♦❜❛❧ ❞❡ ❊♥❡r❣✐❛ ❊ó❧✐❝❛ ●❲❊❈ ●❧♦❜❛❧ ❲✐♥❞ ❊♥❡r❣② ❈♦✉♥❝✐❧ ❍✶✲❍✶✷ ❇❛❝✐❛s ❤✐❞r♦❣rá✜❝❛s ❞♦ ❇r❛s✐❧
❍❊❆ ●r✉♣♦s ❢♦r♠❛❞♦s ♣❡❧❛s ❜❛❝✐❛s ❍✼✱ ❍✻ ❡ ❍✽ ❍▼❲ ●r✉♣♦s ❢♦r♠❛❞♦s ♣❡❧❛s ❜❛❝✐❛s ❍✾ ❡ ❍✶✵ ❍◆ ●r✉♣♦s ❢♦r♠❛❞♦s ♣❡❧❛s ❜❛❝✐❛s ❍✶✱ ❍✷ ❡ ❍✹ ❍◆❊ ●r✉♣♦s ❢♦r♠❛❞♦s ♣❡❧❛s ❜❛❝✐❛s ❍✸ ❡ ❍✺ ❍❙ ●r✉♣♦s ❢♦r♠❛❞♦s ♣❡❧❛s ❜❛❝✐❛s ❍✶✶ ❡ ❍✶✷ ▼❆ ❊st❛❞♦ ❞♦ ▼❛r❛♥❤ã♦
▼▼❊ ▼✐♥✐stér✐♦ ❞❡ ▼✐♥❛s ❡ ❊♥❡r❣✐❛ ◆❈❉❈ ◆❛t✐♦♥❛❧ ❈❧✐♠❛t✐❝ ❉❛t❛ ❈❡♥t❡r
◆❈❊P ◆❛t✐♦♥❛❧ ❈❡♥t❡rs ❢♦r ❊♥✈✐r♦♥♠❡♥t❛❧ Pr❡❞✐❝t✐♦♥ ◆❊❇ ◆♦r❞❡st❡ ❞♦ ❇r❛s✐❧
◆●❉❈ ◆❛t✐♦♥❛❧ ●❡♦♣❤②s✐❝❛❧ ❉❛t❛ ❈❡♥t❡r
◆❖❆❆ ◆❛t✐♦♥❛❧ ❖❝❡❛♥✐❝ ❛♥❞ ❆t♠♦s♣❤❡r✐❝ ❆❞♠✐♥✐str❛t✐♦♥ ❖❆❋❧✉① ❖❜❥❡❝t✐✈❡❧② ❆♥❛❧②③❡❞ ❛✐r✲s❡❛ ❍❡❛t ❋❧✉①❡s
❖◆❙ ❖♣❡r❛❞♦r ◆❛❝✐♦♥❛❧ ❞♦ ❙✐st❡♠❛ P❆ ❊st❛❞♦ ❞♦ P❛rá
P❇ ❊st❛❞♦ ❞❛ P❛r❛í❜❛ P❊ ❊st❛❞♦ ❞❡ P❡r♥❛♠❜✉❝♦ P■ ❊st❛❞♦ ❞♦ P✐❛✉í
P■❘❆❚❆ P✐❧♦t ❘❡s❡❛r❝❤ ▼♦♦r❡❞ ❆rr❛② ✐♥ t❤❡ ❚r♦♣✐❝❛❧ P❘ ❊st❛❞♦ ❞♦ P❛r❛♥á
P❙❉ P❤②s✐❝❛❧ ❙❝✐❡♥❝❡s ❉✐✈✐s✐♦♥ ❘❏ ❊st❛❞♦ ❞♦ ❘✐♦ ❞❡ ❏❛♥❡✐r♦
❘◆ ❊st❛❞♦ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ◆♦rt❡ ❘❙ ❊st❛❞♦ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ❙✉❧ ❙❆ ❆♠ér✐❝❛ ❙✉❧
❙❈ ❊st❛❞♦ ❞❡ ❙❛♥t❛ ❈❛t❛r✐♥❛ ❙❊ ❊st❛❞♦ ❞❡ ❙❡r❣✐♣❡
❙■◆ ❙✐st❡♠❛ ■♥t❡r❧✐❣❛❞♦ ◆❛❝✐♦♥❛❧ ❙P ❊st❛❞♦ ❞❡ ❙ã♦ P❛✉❧♦
❙❙▼■ ❙♣❡❝✐❛❧ ❙❡♥s♦r ▼✐❝r♦✇❛✈❡ ■♠❛❣❡r
❚❆❖ ❚r♦♣✐❝❛❧ ❆t♠♦s♣❤❡r❡ ❖❝❡❛♥ Pr♦❥❡❝t ❆t❧❛♥t✐❝ ❚❊P ❚♦♥❡❧❛❞❛ ❡q✉✐✈❛❧❡♥t❡ ❞❡ ♣❡tró❧❡♦
❚▼■ ▼✐❝r♦✇❛✈❡ ■♠❛❣❡r
❚❘▼▼ ❚r♦♣✐❝❛❧ ❘❛✐♥❢❛❧❧ ▼❡❛s✉r✐♥❣ ▼✐ss✐♦♥
❯◆❊❙❈❖ ❖r❣❛♥✐③❛çã♦ ❞❛s ♥❛çõ❡s ✉♥✐❞❛s ♣❛r❛ ❛ ❡❞✉❝❛çã♦✱ ❛ ❝✐ê♥❝✐❛ ❡ ❛ ❝✉❧t✉r❛ ❯❚❈ ❚❡♠♣♦ ❯♥✐✈❡rs❛❧ ❈♦♦r❞❡♥❛❞♦
❲✶✲❲✶✷ ❊st❛çõ❡s ❡ó❧✐❝❛s s♦❜r❡ ♦ ♦❝❡❛♥♦✱ ✈✐❞❡ ❋✐❣✉r❛ ✶ ❡ ❚❛❜❡❧❛ ✶ ❲❊❆ ●r✉♣♦ ❢♦r♠❛❞♦ ♣❡❧❛s ❡st❛çõ❡s ❲✻✱ ❲✼✱ ❲✽ ❡ ❲✾
❲❍❖■ ❲♦♦❞s ❍♦❧❡ ❖❝❡❛♥♦❣r❛♣❤✐❝ ■♥st✐t✉t✐♦♥ ❲◆1 ❘❡❢❡r❡♥t❡ ❛ ❡st❛çã♦ ❲✶
❲◆2 ❘❡❢❡r❡♥t❡ ❛ ❡st❛çã♦ ❲✷
❲◆❊ ●r✉♣♦ ❢♦r♠❛❞♦ ♣❡❧❛s ❡st❛çõ❡s ❲✸✱ ❲✹ ❡ ❲✺ ❲❙ ●r✉♣♦ ❢♦r♠❛❞♦ ♣❡❧❛s ❡st❛çõ❡s ❲✶✵✱ ❲✶✶ ❡ ❲✶✷ ❲❲❊❆ ❆ss♦❝✐❛çã♦ ▼✉♥❞✐❛❧ ❞❡ ❊♥❡r❣✐❛ ❊ó❧✐❝❛
❙✉♠ár✐♦
✶ ■♥tr♦❞✉çã♦ ❣❡r❛❧ ♣✳ ✷✸
✶✳✶ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✾ ✶✳✷ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✾ ✶✳✷✳✶ ❖❜❥❡t✐✈♦ ❣❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✾ ✶✳✷✳✷ ❖❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✵ ✶✳✸ ❊str✉t✉r❛ ❞❛ t❡s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✵
✷✳✹✳✹ ❚✐♠❡ s❡r✐❡s ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✺ ✷✳✹✳✺ ❙❡❛s♦♥❛❧ ❛♥❛❧②s✐s ♦❢ ✇✐♥❞s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻ ✷✳✹✳✻ ❙❡❛s♦♥❛❧ ❛♥❛❧②s✐s ♦❢ ♣r❡❝✐♣✐t❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻ ✷✳✹✳✼ ❈♦rr❡❧❛t✐♦♥ ❛♥❞ ❝♦❤❡r❡♥❝❡ ❛♥❛❧②s✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻ ✷✳✹✳✽ ❈❧✉st❡r ❛♥❛❧②s✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✽ ✷✳✺ ❈♦♥❝❧✉s✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✾ ✷✳✻ ❆❝❦♥♦✇❧❡❞❣♠❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✷
✸ ❆✈❛❧✐❛çã♦ ❞♦ ♣♦t❡♥❝✐❛❧ ❡ó❧✐❝♦ ♦✛s❤♦r❡ ❜r❛s✐❧❡✐r♦ ♣✳ ✻✽ ❘❡s✉♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✾ ✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✵ ✸✳✶✳✶ ❘❡tr♦s♣❡❝t✐✈❛ ❞❛ ❡♥❡r❣✐❛ ❡ó❧✐❝❛ ♦✛s❤♦r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✵ ✸✳✷ ▼❡t♦❞♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✷ ✸✳✷✳✶ ➪r❡❛ ❞❡ ❡st✉❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✷ ✸✳✷✳✷ ❉❛❞♦s ❞❡ ✈❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✷ ✸✳✷✳✸ ❋❧✉①♦s ❞❡ ❝❛❧♦r✱ ❝❛♠♣♦s ❞❡ t❡♠♣❡r❛t✉r❛ ❡ ✉♠✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✸ ✸✳✷✳✹ Pr❡ssã♦ ❛♦ ♥í✈❡❧ ❞♦ ♠❛r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✸ ✸✳✷✳✺ ❇❛t✐♠❡tr✐❛ ❡ ❢✉♥❞❛çã♦ ❞❛s t✉r❜✐♥❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✸ ✸✳✷✳✻ ❊①tr❛♣♦❧❛çã♦ ✈❡rt✐❝❛❧ ❞♦s ✈❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✹ ✸✳✷✳✼ Pr♦❞✉çã♦ ❞❡ t✉r❜✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✺ ✸✳✷✳✽ P♦t❡♥❝✐❛❧ té❝♥✐❝♦ ❡ó❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✻ ✸✳✸ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✻ ✸✳✸✳✶ ❚❡♠♣❡r❛t✉r❛ ❡ ✢✉①♦s ❞❡ ❝❛❧♦r ♥❛ ✐♥t❡r❢❛❝❡ ♦❝❡❛♥♦✕❛t♠♦s❢❡r❛ ✳ ✳ ♣✳ ✼✻ ✸✳✸✳✷ ❊st❛❜✐❧✐❞❛❞❡ ❛t♠♦s❢ér✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✼ ✸✳✸✳✸ P♦t❡♥❝✐❛❧ ❡ó❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✽ ✸✳✸✳✸✳✶ ❱❡❧♦❝✐❞❛❞❡ ❞♦ ✈❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✽ ✸✳✸✳✸✳✷ P♦tê♥❝✐❛ ❞❛ t✉r❜✐♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✾ ✸✳✸✳✸✳✸ ❊st✐♠❛t✐✈❛ ❞♦ ♣♦t❡♥❝✐❛❧ ❡ó❧✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✵ ✸✳✸✳✸✳✹ ❱❛r✐❛çã♦ ❞♦s r❡❝✉rs♦s ❛♦ ❧♦♥❣♦ ❞❛ ❝♦st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✶ ✸✳✹ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✷ ✸✳✺ ❋✐❣✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✸
♣❧❡①♦ ❍✐❞r❡❧étr✐❝♦ ❞❡ P❛✉❧♦ ❆❢♦♥s♦✲▼♦①♦tó ♣✳ ✾✻ ❘❡s✉♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✼ ✹✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾✽ ✹✳✷ ▼❛t❡r✐❛❧ ❡ ♠ét♦❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✵ ✹✳✷✳✶ ❉❛❞♦s ❤✐❞r♦❧ó❣✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✵ ✹✳✷✳✷ ❉❛❞♦s ❞❡ ✈❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✵ ✹✳✷✳✸ ❊①tr❛♣♦❧❛çã♦ ✈❡rt✐❝❛❧ ❞♦s ✈❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✵ ✹✳✷✳✹ ❉❡♥s✐❞❛❞❡ ❞❡ ♣♦tê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✶ ✹✳✷✳✺ ❈✉r✈❛ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ♣♦tê♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✶ ✹✳✷✳✻ ❈♦❡✜❝✐❡♥t❡ ❞❡ ❝♦rr❡❧❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✷ ✹✳✸ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✸ ✹✳✸✳✶ ❘❡❣✐♠❡ ❤✐❞r♦❧ó❣✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✸ ✹✳✸✳✷ ❘❡❣✐♠❡ ❞♦s ✈❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✸ ✹✳✸✳✸ Pr♦❞✉çã♦ ❞❡ ❡♥❡r❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✹ ✹✳✸✳✹ ❈♦♠♣❧❡♠❡♥t❛r✐❞❛❞❡ ❤í❞r✐❝❛ ① ❡ó❧✐❝❛ ♦✛s❤♦r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✹ ✹✳✸✳✺ ❱❛r✐❛çõ❡s ✐♥t❡r❛♥✉❛✐s ❤✐❞r♦❧ó❣✐❝❛s ❡ ❡ó❧✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✺ ✹✳✹ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✻ ✹✳✺ ❆❣r❛❞❡❝✐♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵✽
✺ ❊❢❡✐t♦ ❞❛ ❞❡❢❛s❛❣❡♠ t❡♠♣♦r❛❧ ❞♦s ✈❡♥t♦s ♥❛ s✐♠✉❧❛çã♦ ❞❡ ✉♠ s✐st❡♠❛
❤í❜r✐❞♦ ❡ó❧✐❝♦✲❤✐❞rá✉❧✐❝♦ ♣✳ ✶✶✺
