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β b
α β
H
0
> 0
α β
α β
α β
E
t
P − Q
10
◦
25
◦
b
β b η
0
0; 0,25; 0,50; 0,75 0,90
β = 1,0 β = 1,5 β = 3,0
β = 1,0 β = 1,5 β = 3,0
E
ts
Q
∗
×
dQ
∗
dτ
η
0
0,25 0,50 0,75 0,90
Q
∗
×
dQ
∗
dτ
η
0
0 0,25
0,50 0,75 0,90
η
0
0,25 0,50 0,75 0,90
T
r
A
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
− Q
i
E
ti
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E − t
P − Q E
t
P −Q E
t
P −Q E
t
P − Q E
t
P Q
E
t
P Q
E
t
P Q
E
t
P Q
E
t
P Q
E
t
T
ar
h
r
q n v
R
li
LE
pi
LE
si
LE
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
P − Q E
t
α β
α β
E
t
a
a
j
j
0, 1, 2, ... ∞
a
p
a
th
a
tm
b
b
p
b
tm
c
0
c
1
c
2
c
3
e
∗
a
Pa
e
∗
s
Pa
e
a
Pa
e
ai
i Pa
e
∗
ai
i Pa
f
f(u) kg m
−2
s
−1
Pa
−1
f
1
f
1
f
s
cm
3
cm
−3
h
x t
h H H
0
0,3465H
1
m
h
0
(x)
x
m
h
α
rad
h
H
H
0
x t
m
h
n+1
i
m
h
n+1
i
m
h
r
%
i
j ∞
k mm dia
−1
m
m
c
E
ts
c
dia
m
d
E
ts
d
dia
m
e
E
ts
e
dia
n
h
n
c
i E
ts
c
dia
n
d
i E
ts
d
dia
n
e
i E
ts
e
dia
N
h
h
n
h
h
n
i
dia
n
br
ndm
i
dia
p
b
X
q g kg
−1
q
kg kg
−1
q
e
m s
−1
r
2
%
r
sol
s E
t
mm dia
−1
t
dia, m s, ano
t
r
T
a
u m s
−1
u
1
u
2
v m s
−1
v
b
w
m s
−1
w
q
w
q
m s
−1
kg kg
−1
w
b
x
y
y
b
A m
2
A
1
A
2
A
3
A
4
A
5
B
2,365219
C m
C
th
DAT E
ti
mm dia
−1
E
kg m
−2
s
−1
E
f
kg m
−2
s
−1
E
p
mm s
−1
E
s
mm s
−1
E
t
mm dia
−1
E
sup−i
i
mm dia
−1
E
sup
mm dia
−1
E
t
i
i mm dia
−1
E
th
cm m s
−1
E
ti
mm dia
−1
E
tp
mm
E
tr
mm
E
ts
mm dia
−1
E
ts
c
i
mm dia
−1
E
ts
d
i
mm dia
−1
E
ts
e
i
mm dia
−1
E
tw
mm
EMQ mm dia
−1
F
H
H
0
H
1
L J kg
−1
L
x
LE
pi
i W m
−2
LE
si
i
W m
−2
LE
ti
i W m
−2
P mm dia
−1
P
0
Pa
P
i
i mm dia
−1
P
s
mm dia
−1
Q mm dia
−1
Q
∗
Q
0
l s
−1
Q
f
mm dia
−1
Q
i
i mm dia
−1
Q
s
mm dia
−1
Q
t
mm dia
−1
Q
t−1
mm dia
−1
R
a
W m
−2
R
e
W m
−2
R
l
W m
−2
R
s
W m
−2
R
ac
W m
−2
R
li
i W m
−2
R
sea
W m
−2
R
so
W m
−2
S
mm
S
f
mm
S
i
mm
S
i
i mm
S
t
i mm
S
max
mm
S
t−ndm
i − ndm mm
T dia
T
a
K
T
r
dia
T
s
K
T
ar
◦
C
T
m
m
◦
C
T
s
K
W ξ τ
X m
X
y
Y
x t
α
Q × −
dQ
dt
α
∗
dQ
∗
dτ
× Q
∗
α
b
α
alb
α
2
br
m
2
dia
−1
α
pt
β
Q × −
dQ
dt
β
HEM
η
η
η
0
η
1
η
2
η
3
η
n+1
i
η
n+1
i
γ Pa K
−1
γ
b
γ
c
κ
Q(t) × Q(t + ∆t)
κ
a
λ
2
ρ kg m
−3
σ
W m
−2
K
−4
τ
θ
n
h
N
h
υ
ε
ε
ac
ξ
ξ
1
∆
x
T
x
Pa K
−1
∆t
dia
Γ
Υ
B
z
B
1380 × 10
15
m
3
423 × 10
12
m
3
ano
−1
mm ano
−1
Atmosfera 0,013 x 10 m
15 3
Oceanos
1.350 x 10 m
15 3
33,6 x 10 m
15 3
Evapotranspiraçao
Precipitaçao
Precipitaçao
Escoamento
12 3
361 x 10 m /ano
324 x 10 m /ano
12 3
62 x 10 m /ano
12 3
99 x 10 m /ano
12 3
37 x 10 m /ano
12 3
Biosfera
Rios e Lagos
Aguas Subterraneas
Geleiras
Continentes
~
Evaporaçao
~
~
~
´ ^
E = f(u)(e
∗
s
− e
a
),
E kg m
−2
s
−1
f(u)
kg m
−2
s
−1
Pa
−1
u m s
−1
e
∗
s
Pa e
a
Pa
E
f
E
f
= ρw
q
,
ρ kg m
−3
w
q
w
m s
−1
q
kg kg
−1
E
th
= C
th
T
a
th
m
,
E
th
T
m
m m = 1, 2, 3, ... C
th
a
th
E
p
E
p
=
1
L
∆
x
∆
x
+ γ
R
l
+
γ
∆
x
+ γ
f(u)(e
∗
a
− e
a
),
∆
x
=
e
∗
s
− e
∗
a
T
s
− T
a
≈
de
∗
dT
T
x
,
∆
x
Pa K
−1
T
x
T
x
= T
a
T
a
K
T
s
K e
∗
a
Pa R
l
W m
−2
γ 66,5 Pa K
−1
L
2,462 × 10
6
J kg
−1
16
◦
C
f(u) kg m
−2
s
−1
Pa
−1
f(u) = a
tm
+ b
tm
u,
a
tm
b
tm
3,01 × 10
−8
1,63 × 10
−8
u
m s
−1
u
E
s
=
α
pt
L
∆
x
∆
x
+ γ
R
l
,
E
s
α
pt
1,26 ∆
x
T
s
T
a
α
pt
1,26
25
◦
C
1,32 α
pt
1,02 1,32 1,01 1,20
1,00 1,06
E
tr
+ E
tp
= 2E
tw
,
E
tr
mm E
tp
mm E
tw
mm
dS
dt
= P − Q − E
t
,
S mm t
P mm dia
−1
Q
mm dia
−1
E
t
mm dia
−1
Q = Q
0
.κ
t
a
,
Q t l s
−1
Q
0
l s
−1
κ
a
t
Q×t
Q
S
Q = aS
b
,
a b
E
t
=
1
A
−
Q
1−b
b
a
1
b
b
dQ
dt
− Q
,
Q Q
t
Q
t−1
dQ
dt
=
Q
t
− Q
t−1
∆t
;
∆t A
Q
t
= Q
t+1
dQ
dt
a b
10.000 km
2
Superficie do solo
´
Zona saturada
´
~
e gravitacional)
´
Agua contida no solo
Franja capilar
´
¨
´
Zona nao saturada
ou zona aerada
´ ´Superficie do lençol d’agua
Aquifero
(Agua pelicular
Camada impermeavel
´
Zona intermediaria
P = 0
dS
dt
= −(Q + E
t
) ≤ −Q.
Q = f (S),
S = f
−1
(Q).
∆t
S
i
mm S
f
mm
i f ∆t
∆t
• ∆t < Q
f
Q
f
Q
f
• ∆t Q
f
≤ 1,0 mm dia
−1
• ∆t > Q
f
≤ 2,0 mm dia
−1
Q(mm.dia
−1
)
t(dias)
Hidrograma
S
i
= f
−1
(Q) S
f
= f
−1
(Q)
∆ t
Q = aS
b
b = 1,0
a b
S = (
1
a
Q)
1/b
−
dQ
dt
≥ a
1/b
bQ
2b−1
b
α = a
1/b
b β =
2b−1
b
−
dQ
dt
≥ αQ
β
.
α
β b = 1,0
α β
Q×−
dQ
dt
Q Q =
Q
t+1
+Q
t
2
dQ
dt
=
Q
t+1
−Q
t
∆t
∆t
β = 1,0 α = a
β = 1,0
a
T
r
dQ
dt
≤ −
1
T
r
Q,
∆t
Q(t + ∆t) ≤ Q(t)e
−
∆t
T
r
.
κ = e
−∆t/T
r
Q(t + ∆t) ≤ κQ(t).
κ Q(t) × Q(t +
∆t)
Q
t
= Q
t+1
κ = 0,945
0
5
10
15
20
25
0 5 10 15 20 25
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
a) Jangada
Envolt´oria superior
0
5
10
15
20
25
0 5 10 15 20 25
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
b) das Cinzas
Envolt´oria superior
κ = 0,965 ∆t = 1
Q
t
= Q
t+1
β
1,5 β
1,0 1,5
β
β
0.6
0.8
1
1.2
1.4
t+4t+3t+2t+1tt−1
Q(mm.dia
−1
)
t(dias)
medição
interpolação
β = 1,0
β = 3,0
β = 1,0 β = 1,5
β = 1,0 α
β α
T
r
β = 1,0
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100 1000
−dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
b) Jangada
β=1,0
β=1,5
β=3,0
1e-04
0.001
0.01
0.1
1
10
0.01 0.1 1 10 100 1000
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
b) das Cinzas
β = 1,5
β = 1,0
β = 3,0
α β
α β T
r
0,012
0,012
0,002
0,005
0,009
0,004
α
10
o
25
o
β
1,0 T
r
T
r
T
r
T
r
Q(t) ×Q(t + ∆t)
a = 1/T
r
b = 1
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100 1000
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
a) Jangada
α=0,05492; β=1,05
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100 1000
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
b) das Cinzas
α=0,02907; β=1,0
Envolt´oria inferior
10
◦
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100 1000
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
a) Jangada
α=0,04099; β=1,05
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100 1000
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
b) das Cinzas
α=0,01686; β=1,0
Envolt´oria inferior
25
◦
β b
a = [α(2 − β)]
1
2−β
b =
1
2−β
α β
α
β b
b β
β = 2 b +∞ −∞
β
β = 0 −
dQ
dt
= α β < 0 −
dQ
dt
Q =
aS
b
= −(αS)
−1
α S
-4
-2
0
2
4
0 1 2 3 4 5
b
β
b
β b
η
0
β b
β 1,36 1,64
β
b = 2,0
a b
1
1.1
1.2
1.3
1.4
1.5
0 0.2 0.4 0.6 0.8 1
β
η
0
a)
num´erico
ajuste
1
1.2
1.4
1.6
1.8
2
0 0.2 0.4 0.6 0.8 1
b
η
0
b)
num´erico
ajuste
β b η
0
0; 0,25; 0,50; 0,75 0,90
E
t
a b
Q
t+1
= Q
t
E
t
β = 1,0
1
10
100
1000
1946 1952 1958 1964 1970 1976 1982 1988
mmdia
−1
Ano
β = 1,0
mm dia
−1
a b
1
10
100
1000
04 05 06 07 08 09
mmdia
−1
Mˆes
a)
β = 1,0
1
10
100
1000
04 05 06 07 08 09
mmdia
−1
Mˆes
b)
β = 1,5
1
10
100
1000
04 05 06 07 08 09
mmdia
−1
Mˆes
c)
β = 3,0
β = 1,0 β = 1,5 β = 3,0
E
t
• β = 1,0 β = 1,5
1
10
100
06 07 08 09 10 11
mmdia
−1
Mˆes
a)
β = 1,0
1
10
100
06 07 08 09 10 11
mmdia
−1
Mˆes
b)
β = 1,5
10
100
1000
06 07 08 09 10 11
mmdia
−1
Mˆes
c)
β = 3,0
β = 1,0 β = 1,5 β = 3,0
• β = 3,0
•
• a b
•
0.1
1
10
100
04 05 06 07 08 09
mmdia
−1
Mˆes
a) Bacia do Rio Jangada (1946)
β = 1,0
0.1
1
10
100
06 07 08 09 10 11
mmdia
−1
Mˆes
b) Bacia do Rio das Cinzas (1950)
β = 1,0
α β
∆t
S
f
− S
i
∆t
=
P
s
− Q
s
− E
ts
,
P
s
Q
s
E
ts
mm dia
−1
E
ts
= P
s
− Q
s
−
S
f
− S
i
∆t
.
∆t
∆t
0
20
40
60
20
10
0
20
10
0
5
0
110907050301110907050301
E
ts
(mm.dia
−1
) S(mm) Q (mm.dia
−1
) P (mm.dia
−1
)
mˆes
E
ts
E
ts
∆t i
E
t
i
=
n
e
E
ts
e
+ n
c
E
ts
c
+ n
d
E
ts
d
n
e
+ n
c
+ n
d
,
E
t
i
i E
ts
e
E
ts
c
E
ts
d
e c d
i m
e
m
c
m
d
n
e
n
c
n
d
E
ts
e
E
ts
c
E
ts
d
E
t
i
n
i
=
m
e
n
e
+ m
c
n
c
+ m
d
n
d
n
e
+ n
c
+ n
d
.
n
i
E
t
i
i
E
t
i
i+2i+1ii−1
E
ts
(mm.dia
−1
)
mês
|
< < <> > >
< < <> > >
E
tse
E
tsc
E
tsd
m
e
m
c
m
d
n
e
n
c
n
d
S
f
S
i
S
f
n
i
α β
CHUVA
P
α =
e
a b
Q
s
s
Q
dos hidrogramas (∆ t) e
/ b( 2b − 1 )
/b1
β =
CHUVA média sazonal
pluviométricas e fluviométrica
CHUVA média
VAZÃO
VAZÃO média sazonal
BACIA HIDROGRÁFICA
diária diária
diária sobre a bacia
Cálculo da
Cálculo da
Determinação da
e determinação de
Determinação do armazenamento
Análise de recessão Determinação dos períodos
das vazões do último dia de
recessão da série
Escolha da
Levantamento das estações
do último dia de recessão
evapotranspiração média mensal
Cálculo da
ts
evapotranspiração média sazonal
Cálculo da
i , f
S = ( 1
f
/a Q )
1/b
f
E
ti
E
k f
s
k f
s
k
∂h
∂t
=
k
f
s
∂
∂x
h∂h
∂x
,
h t
x
H H
1
L
x
H
0
x
h
L
x
H
H
1
H
0
h(x, t)
1
L
x
H
1
h
h(x, t) = h
H
(x, t) + H
0
,
h
H
H
0
∂h
H
∂t
=
k
f
s
∂
∂x
(h
H
+ H
0
)∂h
H
∂x
=
k
f
s
∂
∂x
h
H
∂h
H
∂x
+
H
0
∂
2
h
H
∂x
2
.
H
0
h
H
H
0
h
H
H
0
h
H
h(x, 0) = h
0
(x), x > 0,
h
0
(x)
x m
h(0, t) = H
0
, t > 0,
∂h
∂x
x=L
x
= 0.
H
0
= 0
H
0
= 0
H
0
≥ 0
L
x
H
h(x, 0) = h
0
(x), x > 0,
h(0, t) = H
0
= 0, t > 0,
lim
x→∞
h(x, t) = H.
H
0
> 0
h(x, t)
•
h(x, t) = H
0
+ 4
H − H
0
π
∞
n
br
=1,3,5,...
1
n
br
πn
br
2L
x
x
e
−
π
2
n
2
br
4L
2
x
α
2
br
t
,
n
br
n
br
α
2
br
k
f
s
h h
H+H
0
2
p
br
H
1
p
br
= 0,3465
H
0
≈ H
•
h(x, t) =
h
0
(x)
(1 +
1,115Hkt
f
s
L
2
x
)
,
h
0
(x) HF (
x
L
)
F
•
h(x, t) = HB
Y − 2Y
4
+ 3Y
7
−
4
11
Y
10
+
705
154
Y
13
...
,
B
2,365219 Y 0,4873
x
2
f
s
kHt
H
0
h(x = L
x
, t) =
H
9
8
1 −
B
z
B
2
kHt
f
s
L
2
x
+ 1
,
B B
z
H
0
t → ∞ h → 0
x = 0 H
0
> 0
H
0
= 0 B
z
= 0
H
0
> 0
Q = Q(t) = 2Chq
e
,
C
m q
e
m s
−1
q
e
= k
dh
dx
.
α β
α β
•
Q = 8
C
2
k
h(H − H
0
)
A
e
−
π
2
4L
2
x
α
2
br
t
,
•
Q = 1,724
kCH
2
L
x
(1 + γ
b
t)
2
•
Q = 0,6642CH
3/2
kf
s
t
−1/2
.
L
x
L
x
=
A
2C
,
A
C
A
α β
dQ
dt
h
H+H
0
2
α C H k f
s
H
0
= 0
C
α β
α β
π
2
C
2
A
2
k
f
s
h
4,8308
k
1/2
C
f
s
A
3/2
1,1334
C
2
H
3
kf
s
k f
s
H
H
α
H
0
H
0
H
α β
∂η
∂τ
=
∂
∂ξ
η
∂η
∂ξ
,
ξ τ η
ξ =
x
L
x
,
τ =
ktH
f
s
L
2
x
η(ξ, τ) =
h
H
.
Q
∗
Q
∗
(τ) =
A
4C
2
H
2
k
Q.
η Q
∗
dQ
∗
dτ
•
η(ξ, 0) = 1,0.
η(0, τ ) =
H
0
H
= η
0
∂η
∂ξ
(1, τ) = 0,
η
0
η(ξ, τ) = η
0
+
4(1 − η
0
)
π
∞
n
br
=1,3,5,...
1
n
br
πn
br
2
ξ
e
−
π
2
n
2
br
4
ητ
,
η
1,0+η
0
2
Q
∗
= 2η(1 − η
0
)e
−
π
2
n
2
br
4
ητ
τ
−
dQ
∗
dτ
=
π
2
4
ηQ
∗
,
π
2
4
η α
∗
dQ
∗
dτ
× Q
∗
•
η(ξ, 0) = F (ξ).
η(0, τ ) = 0
∂η
∂ξ
(0, τ)
ξ=1
= 0.
η(ξ, τ) =
F (ξ)
1 + 1,115τ
,
F
Q
∗
=
α
b
(1,115τ + 1)
2
,
α
b
0,862
−
dQ
∗
dτ
= 2,4342Q
∗
1,5
,
α
∗
= 2,4342
•
η(ξ, 0) = 1.
η(0, τ ) = 0
lim
ξ→1
η(ξ, τ) = 1.
η(ξ, τ) = 2,365219(W − 2W
4
+ 3W
7
−
4
11
W
11
−
705
154
W
13
+ ...),
W 0,4873
ξ
2
√
τ
Q
∗
= 0,332105τ
−0,5
−
dQ
∗
dτ
= 4,53335Q
∗
3
,
α
∗
= 4,53335
h
∆x
h
h
h
n+1
i
h
n+1
i
h
n+1
i
= h
n
i
+
k∆t
f
s
∆x
2
(h
n
i+1
)
2
− 2(h
n
i
)
2
+ (h
n
i−1
)
2
h
n+1
i
= h
n
i
+
k∆t
2f
s
∆x
2
(
h
n+1
i+1
)
2
− 2(
h
n+1
i
)
2
+ (
h
n+1
i−1
)
2
+ (h
n
i+1
)
2
− 2(h
n
i
)
2
+ (h
n
i−1
)
2
.
η
n+1
i
= η
n
i
+
∆τ
∆ξ
2
(η
n
i+1
)
2
− 2(η
n
i
)
2
+ (η
n
i−1
)
2
η
n+1
i
= η
n
i
+
∆τ
2∆ξ
2
(
η
n+1
i+1
)
2
− 2(η
n+1
i
)
2
+ (η
n+1
i−1
)
2
+ (η
n
i+1
)
2
− 2(η
n
i
)
2
+ (η
n
i−1
)
2
,
η
n+1
i
η
n+1
i
α β
−dQ/dt
−dQ/dt
α β
0.1
1
10
100
0.1 1 10
−
dQ
∗
dτ
Q
∗
Q
∗
× −
dQ
∗
dτ
F
η(0, τ ) = 0
F
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
η(ξ,τ)
ξ
τ=0.10
τ=0.20
τ=0.40
τ=0.80
analítico
numérico
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
η(ξ,τ)
ξ
τ = 0.0
τ = 0.1
τ = 0.9
analítico
numérico
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
η(ξ,τ)
ξ
τ = 0.01
τ = 0.10
τ = 1.00
analítico
numérico
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
η(ξ,τ)
ξ
τ = 0.01
τ = 0.066
τ = 0.26
τ = 1.00
Polubarinova−Kochina
Boussinesq
numérico
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
η(ξ,τ)
ξ
τ = 0.00
τ = 0.05
τ = 0.20
τ = 0.90
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
η(ξ,τ)
ξ
τ = 0.00
τ = 0.05
τ = 0.20
τ = 0.90
η(ξ, 0) = ξ(2 − ξ) η(ξ, 0) = ξ
F η
0
= 0
τ η
0
= 0
τ = 2,3
Q
∗
×
dQ
∗
dt
β = 3,0
β 1,0 1,5
k f
s
H H
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6
Q
∗
τ
τ × Q
∗
Glover
Boussinesq
Polubarinova-Kochina
num´erica
0.1
1
10
100
0.1 1 10 100
−
dQ
∗
dτ
Q
∗
Q
∗
× −
dQ
∗
dτ
β = 1.0
β = 1.5
β = 3.0
num´erica
Q
∗
×
dQ
∗
dτ
H
0
> 0
H
0
> 0
H
0
> 0
η(0, τ ) = η
0
0,25 0,50 0,75 0,90
η(ξ, 0) = 1,0
• H
0
≈ H
• β = 3,0
• β = 3,0 α
∗
η
0
• β
η
0
Q ×−
dQ
dt
H H
0
η
0
H H
0
α H H
0
β = 1,0
β = 3,0
1,0 < β < 1,5
β 1,5 η
0
= 0 1,01 η
0
= 0,90
η
0
η = 1,0
1
0.8
0.6
0.4
0.2
0 0.2 0.4 0.6 0.8 1
η(ξ,τ)
ξ
a)
τ=0.10
τ=0.20
τ=0.40
τ=0.80
analítico
numérico
1
0.8
0.6
0.4
0 0.2 0.4 0.6 0.8 1
η(ξ,τ)
ξ
b)
τ=0.10
τ=0.20
τ=0.40
τ=0.80
analítico
numérico
1
0.9
0.8
0.7
0 0.2 0.4 0.6 0.8 1
η(ξ,τ)
ξ
c)
τ=0.10
τ=0.20
τ=0.40
τ=0.80
analítico
numérico
1
0.95
0.9
0.85
0 0.2 0.4 0.6 0.8 1
η(ξ,τ)
ξ
d)
τ=0.10 τ=0.20
τ=0.40
τ=0.80
analítico
numérico
η
0
0,25 0,50 0,75 0,90
0.01
0.1
1
10
100
0.01 0.1 1 10
−
dQ
∗
dτ
Q
∗
Simula¸c˜ao Num´erica
η
0
= 0,00
η
0
= 0,25
η
0
= 0,50
η
0
= 0,75
η
0
= 0,90
Q
∗
×
dQ
∗
dτ
η
0
0 0,25 0,50
0,75 0,90
0.01
0.1
1
10
100
0.01 0.1 1 10
−
dQ
∗
dτ
Q
∗
a) η
0
= 0,25
β = 1
num´erica
0.01
0.1
1
10
100
0.01 0.1 1 10
−
dQ
∗
dτ
Q
∗
b) η
0
= 0,50
β = 1
num´erica
0.01
0.1
1
10
100
0.01 0.1 1 10
−
dQ
∗
dτ
Q
∗
c) η
0
= 0,75
β = 1
num´erica
0.01
0.1
1
10
100
0.01 0.1 1 10
−
dQ
∗
dτ
Q
∗
d) η
0
= 0,90
β = 1
num´erica
η
0
0,25 0,50 0,75 0,90
26
◦
30
50
◦
20
23
◦
24
◦
30
50
◦
1.200 m
800 m 1.055 km
2
80 km
1.200 m 600 m
50 km 264 km
380 m
5.622 km
2
1.800 mm
1.350 mm
◦
C
◦
C
16
◦
C 24
◦
C
Araucaria angustifolia
P inus elliottii P inus taeda
P inus elliotti P inus taeda
2
20
◦
23
◦
43
◦
47
◦
2.500 m
670,20 m
127,00 m
m
1450 mm 1750 mm
◦
C
◦
C
◦
C
◦
C
m
23
◦
05
50
◦
17
24
◦
47
50
◦
00
23
◦
10
49
◦
58
24
◦
14
49
◦
42
23
◦
06
50
◦
27
24
◦
43
50
◦
08
23
◦
46
49
◦
57
26
◦
29
51
◦
25
26
◦
39
51
◦
20
26
◦
22
51
◦
15
26
◦
33
51
◦
19
26
◦
24
51
◦
24
26
◦
38
51
◦
28
A
2
26
◦
22
51
◦
15
23
◦
05
50
◦
17
200 m
m
20
◦
58
43
◦
48
20
◦
45
44
◦
43
20
◦
57
44
◦
55
20
◦
53
44
◦
30
20
◦
46
45
◦
16
20
◦
27
45
◦
25
20
◦
57
45
◦
50
21
◦
17
43
◦
49
21
◦
11
43
◦
58
21
◦
14
43
◦
44
21
◦
26
43
◦
58
21
◦
13
43
◦
45
21
◦
03
44
◦
45
21
◦
57
44
◦
12
21
◦
07
44
◦
15
21
◦
58
44
◦
56
21
◦
57
44
◦
53
21
◦
19
44
◦
52
21
◦
31
44
◦
55
21
◦
29
44
◦
20
21
◦
09
44
◦
09
21
◦
41
44
◦
26
21
◦
59
44
◦
02
21
◦
58
44
◦
35
21
◦
44
44
◦
18
21
◦
03
44
◦
12
21
◦
41
44
◦
21
21
◦
44
44
◦
21
21
◦
12
44
◦
20
21
◦
59
44
◦
27
21
◦
09
44
◦
55
21
◦
56
44
◦
50
21
◦
38
44
◦
39
21
◦
54
45
◦
05
21
◦
42
45
◦
14
21
◦
56
45
◦
16
21
◦
51
45
◦
25
21
◦
46
45
◦
32
21
◦
41
45
◦
14
21
◦
13
45
◦
48
21
◦
46
45
◦
25
21
◦
11
45
◦
27
21
◦
24
45
◦
45
21
◦
26
45
◦
58
21
◦
22
45
◦
31
21
◦
28
45
◦
14
21
◦
18
46
◦
42
21
◦
17
46
◦
22
21
◦
43
46
◦
27
21
◦
47
46
◦
07
21
◦
22
46
◦
31
21
◦
01
46
◦
31
21
◦
18
46
◦
48
22
◦
07
44
◦
52
22
◦
10
44
◦
25
22
◦
02
44
◦
09
22
◦
10
44
◦
38
22
◦
18
44
◦
56
22
◦
12
44
◦
59
22
◦
15
45
◦
43
22
◦
40
45
◦
28
22
◦
41
45
◦
44
22
◦
31
45
◦
17
22
◦
12
45
◦
17
22
◦
25
45
◦
47
22
◦
28
45
◦
38
22
◦
03
45
◦
41
22
◦
13
45
◦
56
22
◦
20
45
◦
06
22
◦
23
45
◦
27
22
◦
33
45
◦
53
22
◦
07
45
◦
59
22
◦
22
45
◦
53
22
◦
24
45
◦
10
22
◦
18
45
◦
22
22
◦
02
45
◦
50
22
◦
09
45
◦
31
22
◦
44
45
◦
44
A
2
21
◦
29
44
◦
20
22
◦
10
44
◦
38
21
◦
58
44
◦
35
21
◦
59
44
◦
27
21
◦
44
44
◦
21
21
◦
44
44
◦
18
21
◦
41
44
◦
21
21
◦
31
44
◦
57
21
◦
19
44
◦
52
21
◦
16
43
◦
49
21
◦
11
44
◦
01
21
◦
26
43
◦
58
21
◦
10
44
◦
10
21
◦
07
44
◦
17
21
◦
02
44
◦
12
21
◦
12
44
◦
22
21
◦
08
44
◦
46
21
◦
02
44
◦
49
21
◦
09
44
◦
56
21
◦
21
45
◦
11
21
◦
16
45
◦
12
20
◦
54
45
◦
10
22
◦
41
45
◦
29
22
◦
31
45
◦
17
22
◦
25
45
◦
27
22
◦
24
45
◦
10
22
◦
23
45
◦
27
22
◦
28
45
◦
38
22
◦
15
45
◦
43
22
◦
41
45
◦
44
22
◦
33
45
◦
52
22
◦
25
45
◦
47
22
◦
22
45
◦
53
22
◦
03
45
◦
42
21
◦
35
45
◦
39
22
◦
17
44
◦
59
21
◦
54
45
◦
05
21
◦
57
44
◦
53
21
◦
56
45
◦
16
21
◦
42
45
◦
16
21
◦
41
45
◦
14
21
◦
46
45
◦
25
21
◦
36
45
◦
30
21
◦
47
46
◦
07
21
◦
42
45
◦
54
21
◦
16
46
◦
21
P
i
Q
i
7
6
5
4
3
2
1
0
2
1
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
Q
i
(mm.dia
−1
) P
i
(mm.dia
−1
)
mˆes do ano
Climatologia mensal (1946-1990)
Jangada
Cinzas
1000 × 1000 m
2
21
◦
T
r
T
r
10
100
1000
10 100 1000 10000 100000
T
r
(dia)
A (km
2
)
r
2
= 0,4964
Jangada
Cinzas
Furnas
T
r
= 24,0258 A
0,229597
T
r
A
T
r
α β a b T
r
T
r
b = 1
α β a b T
r
• E
t
•
•
E
t
19,5
◦
•
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
19 − 61145000 − 1/1974−12/2001
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
23 − 61250000 − 1/1974−12/1994
P
i
Q
i
E
ti
P
i
Q
i
E
ti
E
ti
P
i
− Q
i
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
33 − 61370000 − 1/1974−12/1991
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
36 − 61429000 − 1/1974−12/2001
P
i
Q
i
E
ti
P
i
Q
i
E
ti
P − Q E
t
−4
−2
0
2
4
6
8
10
194819471946
mm.dia
−1
ano
a) Jangada (1946−1948)
P
i
−
Q
i
E
ti
−4
−2
0
2
4
6
8
10
194319421941
mm.dia
−1
ano
b) das Cinzas (1941−1943)
P
i
−
Q
i
E
ti
−4
−2
0
2
4
6
8
10
197619751974
mm.dia
−1
ano
c) Furnas (1 − 61012000 − 1974−1975)
P
i
−
Q
i
E
ti
P
i
−Q
i
E
ti
E
t
P −Q
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
194819471946
mm
ano
a) Jangada (1946−1948)
P − Q
E
t
0
500
1000
1500
2000
2500
3000
3500
194319421941
mm
ano
b) das Cinzas (1941−1943)
P − Q
E
t
0
200
400
600
800
1000
1200
1400
1600
1800
2000
197619751974
mm
ano
c) Furnas (1 − 61012000 − 1974−1975)
P − Q
E
t
P − Q E
t
0
1000
2000
3000
4000
5000
6000
1980197919781977197619751974
mm
ano
61012000
P − Q
E
t
P −Q
E
t
E
ti
P
i
−Q
i
mm dia
−1
mm dia
−1
P
i
− Q
i
E
ti
−2
0
2
4
6
8
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
a) Jangada − 1/1946−12/1990
E
ti
P
i
−
Q
i
−2
0
2
4
6
8
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
b) Cinzas − 1/1941−12/1991
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
1 − 61012000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
2 − 61014000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
3 − 61024000 − 1/1974−12/1997
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
4 − 61031000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
5 − 61045000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
6 − 61052000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
P − Q E
t
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
7 − 61060000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
8 − 61075000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
9 − 61078000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
10 − 61085000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
11 − 61090000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
12 − 61100000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
13 − 61105000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
14 − 61107000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
P − Q E − t
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
15 − 61115000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
16 − 61122000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
17 − 61135000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
18 − 61140000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
19 − 61145000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
20 − 61173000 − 1/1974−12/1999
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
21 − 61175000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
22 − 61202000 − 1/1974−12/2000
E
ti
P
i
−
Q
i
P − Q E
t
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
23 − 61250000 − 1/1974−12/1994
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
24 − 61267000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
25 − 61271000 − 1/1975−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
26 − 61280000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
27 − 61285000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
28 − 61295000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
29 − 61305000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
30 − 61320000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
P − Q E
t
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
31 − 61343000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
32 − 61350000 − 1/1974−12/1990
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
33 − 61370000 − 1/1974−12/1991
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
34 − 61410000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
35 − 61425000 − 1/1974−12/1993
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
36 − 61429000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
37 − 61460000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
38 − 61473000 − 1/1974−12/2001
E
ti
P
i
−
Q
i
P −Q E
t
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
39 − 61500000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
40 − 61510000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
41 − 61520000 − 1/1974−12/1995
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
42 − 61530000 − 1/1974−12/1993
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
43 − 61537000 − 1/1974−12/1999
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
44 − 61565000 − 1/1974−12/1998
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
45 − 61568000 − 1/1974−12/1991
E
ti
P
i
−
Q
i
−2
−1
0
1
2
3
4
5
6
7
DezNovOutSetAgoJulJunMaiAbrMarFevJan
mm.dia
−1
mês
46 − 61610000 − 1/1974−12/1997
E
ti
P
i
−
Q
i
P −Q E
t
•
◦
C
◦
C
•
•
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
a) Compara¸c˜ao entre bacias
Jangada
Cinzas
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
b) Compara¸c˜ao entre bacias
2-61014000
4-61031000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
c) Compara¸c˜ao entre bacias
1-61014000
7-61024000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
d) Compara¸c˜ao entre bacias
5-61045000
6-61052000
P Q
E
t
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
a) Compara¸c˜ao entre bacias
9-61078000
21-61175000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
b) Compara¸c˜ao entre bacias
10-61085000
11-61090000
13-61105000
14-61107000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
c) Compara¸c˜ao entre bacias
15-61115000
16-61122000
10-61085000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
d) Compara¸c˜ao entre bacias
17-61135000
18-61140000
22-61202000
P Q
E
t
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
a) Compara¸c˜ao entre bacias
21-61175000
41-61520000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
b) Compara¸c˜ao entre bacias
24-61267000
26-61280000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
c) Compara¸c˜ao entre bacias
25-61271000
27-61285000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
d) Compara¸c˜ao entre bacias
30-61320000
31-61343000
28-61295000
P Q
E
t
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
a) Compara¸c˜ao entre bacias
29-61305000
32-61350000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
b) Compara¸c˜ao entre bacias
34-61410000
40-61510000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
c) Compara¸c˜ao entre bacias
35-61425000
43-61537000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
d) Compara¸c˜ao entre bacias
37-61460000
38-61473000
39-61500000
P Q
E
t
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
a) Compara¸c˜ao entre bacias
41-61520000
42-61530000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
b) Compara¸c˜ao entre bacias
8-61075000
12-61100000
33-61370000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
c) Compara¸c˜ao entre bacias
23-61250000
36-61429000
44-61565000
10
7.5
5
2.5
0
5
2.5
0
5
2.5
0
DezNovOutSetAgoJulJunMaiAbrMarFevJan
E
t
(mm dia
−1
) Q(mm dia
−1
) P (mm dia
−1
)
mˆes
d) Compara¸c˜ao entre bacias
45-61568000
46-61610000
P Q
E
t
21
◦
38,5
45
◦
32,4
957 m
21
◦
54,5
45
◦
06,0
866 m
km
2
E
t
6
5
4
3
2
1
0
5
4
3
2
1
0
05 07 09 11 01 03 05 07 09 11 01 03
Santa Cruz × 40-61510000 Olho d’´agua × 43-61537000
mˆes
Medi¸c˜ao × BHS de E
t
(mm.dia
−1
)
medi¸c˜ao(2003-2005)
BHS
2 × desvio padr˜ao
n
i
E
ti
E
sup
E
ti
E
sup
= β
HEM
,
β
HEM
E
sup
β
HEM
β
HEM
β
HEM
P − Q
E
ti
E
sup−i
= c
0
+ c
1
P
i
−
Q
i
+ c
2
(
e
∗
ai
− e
ai
) + c
3
S
i
E
ti
E
sup−i
= c
0
+ c
1
1 −
Q
i
P
i
+ c
2
1 −
e
ai
e
∗
ai
+ c
3
1 −
S
i
S
max
,
E
sup−i
i mm dia
−1
e
∗
ai
i Pa e
ai
i Pa S
i
i mm S
max
mm c
0
c
1
c
2
c
3
S
i
=
S
t−ndm
+ S
t
2
,
S
t
i mm S
t−ndm
i −ndm mm t
S
t=0
= 0 ndm
i
t
S
t
− S
t−ndm
∆t
=
P
i
− Q
i
− E
ti
,
∆t i E
sup−i
E
sup
E
ti
E
ti
n
i
E
ti
E
ti
β
HEM
E
ti
n
i
≤ 45
E
ti
Levantamento das estaçõesAplicar o BHS e
− Penman;
Análise dos dados e cálculo
Definir as variáveis
β
E
− Radiação líquidar;
hidrometeorológica da região.estimar o
ti .
BACIA HIDROGRÁFICA.
Ajuste de equação
via regressão linear multivariada,
HEM
independentes do
− Priestley−Taylor.
Escolha de uma
das médias e de E
sup
1. CALIBRAÇÃO e
dividir a série em duas etapas:
usando E E
sup
e
ti
,
2. VALIDAÇÃO
1. CALIBRAÇÃO
Aplicar a equação ajustada na
calibração e fazer análises
estatísticas entre as estimativas
β
2. VALIDAÇÃO.
.
.
feitas pelo BHS e HEM.
Selecionar dados n
i
<
45 dias
HEM
HEM uso:
eliminar patamares;
estimar de outras regiões.E
t
26
◦
22
51
◦
06
26
◦
08
51
◦
65
23
◦
00
50
◦
02
26
◦
46
51
◦
67
T
ar
◦
C
h
r
q g kg
−1
n h v m s
−1
25
20
15
10
90
80
70
16
12
8
10
8
6
4
4
3
2
1
0
JanDezNovOutSetAgoJulJunMaiAbrMarFevJan
v (m.s
−1
) n (horas) q (g.kg
−1
) h
r
(%) T
ar
(
o
C)
mˆes
Climatologia das vari´aveis meteorol´ogicas
Jangada
Cinzas
T
ar
h
r
q n v
R
l
E
p
E
s
a
p
b
p
a
p
b
p
R
li
LE
pi
LE
si
LE
ti
W m
−2
0
50
100
150
200
DezNovOutSetAgoJulJunMaiAbrMarFevJan
W.m
−2
mˆes
a) Bacia Jangada (1975-1990)
R
li
LE
pi
LE
si
LE
ti
0
50
100
150
200
DezNovOutSetAgoJulJunMaiAbrMarFevJan
W.m
−2
mˆes
b) Bacia Cinzas (1961-1991)
R
li
LE
pi
LE
si
LE
ti
R
li
LE
pi
LE
si
LE
ti
R
li
LE
pi
LE
si
LE
ti
E
sup−i
R
li
E
pi
LE
si
× E
sup−i
×
r
2
s EMQ mm dia
−1
mm dia
−1
E
ti
mm dia
−1
DAT
P
i
− Q
i
e
∗
ai
− e
ai
E
sup−i
= LE
pi
E
sup−i
= R
li
E
sup−i
r
2
s EMQ DAT
mm dia
−1
mm dia
−1
mm dia
−1
mm dia
−1
R
li
e
∗
ai
− e
ai
−0,179 0,901 −0,089
P
i
− Q
i
e
∗
ai
− e
ai
−0,173 0,898 −0,081
LE
pi
e
∗
ai
− e
ai
−0,241 0,839 −0,184
P
i
− Q
i
e
∗
ai
− e
ai
−0,203 0,800 −0,124
LE
si
e
∗
ai
− e
ai
−0,163 1,002 −0,040
P
i
− Q
i
e
∗
ai
− e
ai
−0,174 1,005 −0,058
R
li
P
i
− Q
i
e
∗
ai
− e
ai
−0,204 0,613 −0,172
P
i
− Q
i
e
∗
ai
−
e
ai
S
i
−0,152 0,608 −0,229
LE
pi
P
i
− Q
i
e
∗
ai
− e
ai
−0,223 0,622 −0,195
P
i
− Q
i
e
∗
ai
− e
ai
S
i
−0,174 0,616 −0,252
LE
si
P
i
− Q
i
e
∗
ai
− e
ai
−0,216 0,609 −0,168
P
i
− Q
i
e
∗
ai
− e
ai
S
i
−0,193 0,605 −0,235
R
li
P
i
− Q
i
e
∗
ai
− e
ai
−0,231 0,891 −0,172
P
i
− Q
i
e
∗
ai
− e
ai
S
i
−0,497 1,010 −0,229
LE
pi
P
i
− Q
i
e
∗
ai
−
e
ai
−0,220 0,763 −0,195
P
i
− Q
i
e
∗
ai
− e
ai
S
i
−0,482 0,904 −0,252
LE
si
P
i
− Q
i
e
∗
ai
− e
ai
−0,234 0,642 −0,168
P
i
− Q
i
e
∗
ai
− e
ai
S
i
−0,296 1,043 −0,235
E
sup−i
r
2
s EMQ DAT
mm dia
−1
mm dia
−1
mm dia
−1
mm dia
−1
R
li
P
i
− Q
i
0,029 0,738 0,055
P
i
− Q
i
e
∗
ai
− e
ai
−0,114 0,698 −0,048
LE
pi
P
i
− Q
i
e
∗
ai
− e
ai
−0,034 0,755 0,008
P
i
− Q
i
e
∗
ai
− e
ai
S
i
−0,224 0,810 −0,137
LE
si
P
i
− Q
i
e
∗
ai
− e
ai
−0,082 0,717 −0,011
1 −
Q
i
P
i
1 −
e
ai
e
∗
ai
−0,044 0,705 −0,182
R
li
P
i
− Q
i
−0,092 0,766 0,003
P
i
− Q
i
e
∗
ai
− e
ai
−0,044 0,795 −0,015
LE
pi
P
i
− Q
i
e
∗
ai
−
e
ai
0,035 0,819 0,056
1 −
Q
i
P
i
1 −
e
ai
e
∗
ai
0,026 0,806 −0,012
LE
si
P
i
− Q
i
−0,032 0,780 0,060
P
i
− Q
i
e
∗
ai
−
e
ai
−0,001 0,802 0,026
R
li
P
i
− Q
i
0,111 0,715 0,003
P
i
− Q
i
e
∗
ai
− e
ai
0,055 0,659 −0,015
LE
pi
P
i
− Q
i
e
∗
ai
− e
ai
0,189 0,743 0,056
1 −
Q
i
P
i
1 −
e
ai
e
∗
ai
0,095 0,642 −0,012
LE
si
P
i
− Q
i
−0,196 0,787 0,060
P
i
− Q
i
e
∗
ai
− e
ai
0,122 0,702 0,026
LE
ti
= LE
pi
2,055 + 0,057(
P
i
− Q
i
) − 0,003(e
∗
ai
− e
ai
)
,
LE
ti
= R
li
0,489 + 0,122(P
i
− Q
i
) − 0.00029(e
∗
ai
− e
ai
)
.
0
1
2
3
4
5
6
7
1990198519801975
E
ti
(mm.dia
−1
)
Ano
a) Jangada
BHS
HEM
0
1
2
3
4
5
6
7
8
1990198519801975197019651961
E
ti
(mm.dia
−1
)
Ano
b) Cinzas
BHS
HEM
6
5
4
3
2
1
0
908988878685
P
E
t
(×1000 mm)
Ano
a) Bacia do Rio Jangada
HEM
BHS
12
11
10
9
8
7
6
5
4
3
2
1
0
9190898887868584838281
P
E
t
(×1000 mm)
Ano
b) Bacia do Rio das Cinzas
HEM
BHS
H
0
H
0
H
0
Q = aS
b
dQ/dt = αQ
β
•
H
0
= 0
• β 3,0
H H
0
α H H
0
• β 1,0 1,5 β = 1,0
• β = 1,5 H
0
= 0 α
H
•
•
H
0
H
0
H
β = 1,0
H
0
H
0
(t) H
0
(t)
Q = aS
b
α β
•
•
•
•
α
k f
s
k f
s
α
W m
−2
R
l
= R
s
(1 − α
alb
) − εR
a
− R
e
,
R
s
W m
−2
α
alb
ε
R
a
W m
−2
R
e
W m
−2
R
s
= R
sea
(a
p
+ b
p
n
h
N
h
),
N
h
=
24h
α
π
;
h
α
= arccos(−tan ϕ tan δ);
R
sea
W m
−2
n
h
N
h
N
h
ϕ
δ h a
p
b
p
h
α
R
sea
r
sol
R
sea
=
R
so
r
2
sol
π
h
α
ϕ δ + cos ϕ cos δ h
α
),
R
so
1395 W m
−2
r
sol
R
a
R
a
R
a
= θ
n
h
N
h
R
ac
,
θ
θ(
n
h
N
h
) = (1 + 0, 22(1 −
n
h
N
h
)
2
);
R
ac
R
ac
= ε
ac
σT
a
4
.
ε
ac
e
a
T
a
σ
5,6697.10
−8
W m
−2
K
−4
ε
ac
= 0.64(
e
a
T
a
)
1
7
,
e
a
e
a
= h
r
e
∗
a
;
h
r
e
∗
a
e
∗
a
= P
0
e
(13,3185t
r
−1,9760t
r
2
−0,6445t
r
3
−0,1299t
r
4
)
;
P
0
101.325 Pa t
r
t
r
= 1 −
375, 15
T
a
.
R
e
= εσT
s
4
,
T
s
q
e
= k
dh
dx
.
Q = 2Ckh
dh
dx
.
∂h
∂t
= α
br
2
∂
2
h
∂x
2
,
α
br
2
=
k
f
s
h h h
H+H
0
2
h(x, 0) h
0
(x)
h(0, t) = H
0
∂h
∂x
x=L
x
= 0
y= h − H
0
∂y
∂t
= α
br
2
∂
2
y
∂x
2
,
y(x, 0) = H − H
0
x > 0,
y(0, t) = H
0
− H
0
= 0 t > 0
dy
dx
x=L
x
= 0 t > 0.
y(x, t) = X T X(x)
m T (t)
XT
= α
br
2
X

T
T
α
2
br
T
=
X

X
= −λ
2
,
x t
λ
2
T
T
= −λ
2
α
2
br
X

+ λ
2
X = 0
y(x, t) = [A
1
cos(λx) + A
2
(λx)]e
−λ
2
α
2
br
t
,
A
1
A
2
y(0, t) = A
1
e
−λ
2
α
2
br
t
= 0
A
1
∂y
∂x
x=L
x
= 0
A
2
λ cos(λL
x
)e
−λ
2
α
2
br
t
= 0,
cos(λL
x
) λ
π.n
br
2L
x
n
br
n
br
=
y(x, 0) = y(x) = A
2
(λx) = H − H
0
A
2
=
1
L
x
L
x
−L
x
y(x)
(λx)dx
=
1
L
x
2L
x
0
y(x) (λx)dx
= 4
H − H
0
n
br
π
h(x, t) = H
0
+ 4
H − H
0
π
∞
n
br
=1,3,5,...
1
n
br
πn
br
2L
x
x
e
−
π
2
n
2
br
4L
2
x
α
2
br
t
.
H
0
= 0
h(x, t) = 4
H
π
∞
n
br
=1,3,5,...
1
n
br
π.n
br
2L
x
x
e
−
π
2
n
2
br
4L
2
x
α
2
br
t
.
x
H
0
= 0
h x t h
h(x, t) = X(x)T (t).
X(x) T (t) X(x)
x T(t) t
∂XT
∂t
=
k
f
s
∂
∂x
XT ∂XT
∂x
.
x
t x t
−λ
2
1
X
∂
2
X
2
∂x
2
=
2f
s
T
2
k
∂T
∂t
= −λ
2
.
∂
2
X
2
∂x
2
= −λ
2
X
∂T
∂t
=
−λ
2
k
2f
s
T
2
.
•
∂X
2
∂x
= p
b
p
b
X
∂
2
X
2
∂x
2
=
∂
∂X
2
∂X
2
∂x
∂X
2
∂x
.
p
b
∂
∂X
2
p
2
b
2
= −λ
2
X
p
b
=
−
4
3
λ
2
X
3
+ A
3
,
A
3
p
b
∂X
2
∂x
=
−
4
3
λ
2
X
3
+ A
3
.
x = L
x
∂X
∂x
= 0,
A
3
A
3
=
4
3
λ
2
X
3
L
x
,
X
L
x
X x = L
x
A
3
∂x =
2X
4
3
λ
2
(X
3
L
x
− X
3
)
∂X,
x = 0 x = L
x
L
x
0
∂x =
3
λ
2
X
L
x
0
X
X
3
L
x
− X
3
∂X,
X
L
x
0
X/X
L
x
1 − X
3
/X
3
L
x
∂X/X
L
x
=
L
2
x
λ
2
3X
L
x
.
X/X
L
x
= υ υ(X =
0) = 0 υ(X = X
L
x
) = 1
1
0
υ
√
1 − υ
3
∂υ =
L
2
x
λ
2
3X
L
x
.
B
B(v
b
, w
b
) =
1
0
y
v
b
−1
b
(1 − y
b
)
w
b
−1
dy
b
=
Γ(v
b
)Γ(w
b
)
Γ(v
b
+ y
b
)
,
v
b
> 0 w
b
> 0 y
b
Γ
Γ(γ
b
) =
1
0
e
−y
b
y
γ
b
−1
b
dy
b
,
γ
b
Γ(γ
b
− 1) = γ
b
Γ(γ
b
).
Γ(1/2) =
√
π
υ
3
= Υ
Υ
1
0
υ
√
1 − υ
3
∂υ =
1
0
1
3
Υ
−1/3
(1 − Υ)
−1/2
∂Υ.
v
b
w
b
1
3
B
2
3
,
1
2
=
√
πΓ(2/3)
3Γ(7/6)
≈ 0,862.
λ
2
λ
2
=
2,229X
L
x
L
2
x
.
λ
2
x
L
x
+ A
4
=
1
0,862
F
0
X/X
L
x
1 − (X/X
L
x
)
3
∂X/X
L
x
,
A
4
F
F
x
L
x
+ A
4
=
X
X
L
x
,
F
x = 0 x = L
x
x = L
x
A
4
X
X(x) = F
x
L
x
X
L
x
.
•
∂T
T
2
= −
kλ
2
2f
s
∂t,
T =
1
A
5
+ kλ
2
t/(2f
s
)
,
A
5
X(x)T (t)
h(x, t) =
X
L
x
A
5
F
x
L
x
1 +
2,229kX
L
x
t
2f
s
A
5
L
2
x
,
h(x, 0) = h
0
(x) h(0, t) =
∂h(x,t)
∂x
x=L
x
= 0
h(x, 0) =
X
L
x
A
5
F
x
L
x
= h
0
(x),
h x = L
x
h
0
(L
x
) = H =
X
L
x
A
5
,
A
5
=
X
L
x
H
A
5
h
0
(x) = HF (
x
L
x
).
A
5
h(x, t) =
h
0
(x)
(1 +
1,115Hkt
f
s
L
2
x
)
.
h = Hu
1
,
u
1
η
1
=
x
2
f
s
kHt
,
η
1
η
1
x t
∂η
1
∂x
=
1
2
f − s
kHt
∂η
1
∂t
= −
x
4
f
s
kHt
3
.
h = Hu
1
d
dη
1
u
1
du
1
dη
1
+ 2η
1
du
1
dη
1
= 0
du
1
u
1
du
1
+ 2η
1
= 0,
u
1
= u
1
(η
1
)
ξ
1
u
1
η
1
ξ
1
dη
1
dξ
1
= u
1
.
u
1
=
du
1
dη
1
=
1
u
1
du
1
dξ
1
=
1
u
1
d
2
η
1
dξ
2
1
,
u
1
u
1
=
d
2
η
1
dξ
2
1
.
d
d
2
η
1
dξ
2
1
du
1
+ 2η
1
= 0,
d
d
2
η
1
dξ
2
1
dξ
1
dξ
1
du
1
+ 2η
1
= 0
d
3
η
1
dξ
3
1
+ 2η
1
d
2
η
1
dξ
2
1
= 0.
η
1
η
2
2
= η
1
η
2
η
2
= 2η
1
= x
f
s
kHt
.
d
3
η
2
dξ
3
1
+ 2η
2
d
2
η
2
dξ
2
1
= 0.
η
2
=
∞
j=0
a
j
ξ
j
1
j!
,
a
j
j
• x = 0 t > 0
η
2
(x = 0, t) = η
2
(ξ
1
= 0) = 0
η
2
(0) =
dη
2
dξ
1
= u
1
(x = 0, t) =
h(x=0,t)
H
= u
1
(ξ
1
= 0) = 0
• x = ∞ t > 0
η
2
(∞) = u
1
(x = ∞, t) =
h(x=∞,t)
H
= u
1
(ξ
1
= ∞) = 1
a
0
= 0 a
1
= 0
a
3
+ a
4
ξ
1
+
a
2
2
4
ξ
2
1
+
a
5
2
ξ
2
1
+
a
2
a
3
3
ξ
3
1
+
a
6
6
ξ
3
1
+
a
2
3
12
ξ
4
1
+
7a
2
a
4
48
ξ
4
1
+
a
7
24
ξ
4
1
+
a
3
a
4
16
ξ
5
1
+
11a
2
a
5
240
ξ
5
1
+
a
8
120
ξ
5
1
+
a
2
4
96
ξ
6
1
+
13a
3
a
5
720
ξ
6
1
+
2a
2
a
6
90
ξ
6
1
+
a
9
720
ξ
6
1
+
a
10
5040
ξ
7
1
+
a
4
a
5
180
ξ
7
1
+
a
3
a
6
240
ξ
7
1
+
11a
2
a
7
50400
ξ
7
1
+
a
11
40320
ξ
8
1
+
a
2
5
1440
ξ
8
1
+
7a
4
a
6
5760
ξ
8
1
+
a
3
a
7
1260
ξ
8
1
+
29a
2
a
8
80640
ξ
8
1
+
a
12
362880
ξ
9
1
+
a
5
a
6
3456
ξ
9
1
+
a
4
a
7
4480
ξ
9
1
+
31a
3
a
8
241920
ξ
9
1
+
37a
2
a
9
725760
ξ
9
1
+... = 0.
a
3
= 0
a
4
= 0
a
2
2
4
+
a
5
2
= 0
a
2
a
3
3
+
a
6
6
= 0
a
2
3
12
+
7a
2
a
4
48
+
a
7
24
= 0
a
3
a
4
16
+
11a
2
a
5
240
+
a
8
120
= 0
a
2
4
96
+
13a
3
a
5
720
+
2a
2
a
6
90
+
a
9
720
= 0
a
10
5040
+
a
4
a
5
180
+
a
3
a
6
240
+
11a
2
a
7
50400
= 0
a
11
40320
+
a
2
5
1440
+
7a
4
a
6
5760
+
a
3
a
7
1260
+
29a
2
a
8
80640
= 0
a
12
362880
+
a
5
a
6
3456
+
a
4
a
7
4480
+
31a
3
a
8
241920
+
37a
2
a
9
725760
= 0
...... = 0
...... = 0.
a
3
= a
4
= a
6
= a
7
= a
9
= a
10
= a
12
= ... = 0; a
5
= −
a
2
2
2
; a
8
=
11a
3
2
2
2
; a
11
=
−
375a
4
2
2
3
; a
14
=
27897a
5
2
2
4
; a
17
= −
3817137a
6
2
2
5
; ...
α
1
= a
2
η
2
=
α
1
2
0
× 2!
ξ
2
1
−
α
2
1
2
1
× 5!
ξ
5
1
+
11α
3
1
2
2
× 8!
ξ
8
1
−
375α
4
1
2
3
× 11!
ξ
11
1
...
u
1
= η
2
= α
1
ξ
1
−
α
2
1
ξ
4
1
2 × 4!
+
11α
3
1
ξ
7
1
2
2
× 7!
−
375α
4
1
ξ
10
1
2
3
× 10!
....
α
1
0,33206
η
2
u
1
η
3
2
u
2
2
η
3
u
2
η
3
= α
1
ξ
2
1
−
α
1
ξ
5
1
2
0
× 5!
+
11α
2
1
ξ
8
1
2
1
× 8!
−
375α
3
1
ξ
11
1
2
2
× 11!
...
,
u
2
= η
3
= 2α
1
ξ
1
−
α
2
1
ξ
4
1
4!
+
11α
3
1
ξ
7
1
2 × 7!
−
375α
4
1
ξ
10
1
2
2
× 10!
....
η
3
ξ
1
Y =
η
3
α
−1/3
1
(5!)
−2/3
X
y
=
α
1/3
1
(5!)
−1/3
ξ
1
Y = X
p
(1 − X
3
p
+
55X
6
p
28
−
625X
9
p
154
+
232475X
12
p
28028
−
31809475X
15
p
1905904
+ ...)
1/2
= X
p
−
X
4
p
2
+
6X
7
p
7
−
493X
10
p
308
+
5965X
13
p
2002
−
20901051X
16
p
3811808
+ ....
X
p
= Y +
X
4
p
2
−
6X
7
p
7
+
493X
10
p
308
−
5965X
13
p
2002
+
20901051X
16
p
3811808
− ....
X
p
Y
X
p
= Y +
Y
4
2
+
Y
7
7
−
4Y
10
11
−
765Y
13
2002
+ ....,
ξ
1
X
p
u
2
= η
3
= α
2
3
1
(5!)
1
3
2X
p
− 5X
4
p
+
110
7
X
7
p
−
625
14
X
10
p
+
232475
2002
X
13
p
− ...
,
X
p
u
2
= η
3
= α
2
3
1
(5!)
1
3
2Y − 4Y
4
+ 6Y
7
−
8
11
Y
10
−
705
77
Y
13
...
.
u
1
H = h(x, t)
u
1
= η
2
= B
Y − 2Y
4
+ 3Y
7
−
4
11
Y
10
−
705
154
Y
13
...
,
B = α
2
3
1
(5!)
1
3
= 2,365219
Y =
2η
2
α
−1/3
1
(5!)
−2/3
= 0,4873
√
η
1
= 0,4873
x
2
f
s
kHt
h(0, t) = 0 t > 0
h(∞, t) = H t > 0,
h(x, 0) = H x > 0.
f
1
=
x
k/f
s
Ht
,
f
1
=
h
H
,
−f
1
∂f
1
∂f
1
= 2
∂
∂f
1
f
1
∂f
1
∂f
1
.
f
1
(0) = 0 f
1
(∞) = 1
• f
1
≤ 2,6
f
1
= 1,15249(f
1
/2)
1/2
−
4/15(f
1
/2)
2
1 + 0,17355(f
1
/2)
3/2
+ 0,02768(f
1
/2)
3
• f
1
> 2,6
f
1
= 1 − 0,41387erfc
f
1
/2
1 + (0,934/2f
3
1
)e
−(f
1
/2)
2
α β
Q = 2Ck
h
dh
dx
,
dh
dx
= 4
h
0
π
∞
n
br
=1,3,5,...
π
2L
x
cos
πn
br
2L
x
x
e
−
π
2
n
2
br
4L
2
x
α
2
br
t
,
Q = 4Ck
h
h
0
L
x
∞
n
br
=1,3,5,...
cos
πn
br
2L
x
x
e
−
π
2
n
2
br
4L
2
x
α
2
br
t
.
x = 0 L
x
=
A
2C
Q = 4Ckh
h
0
A
2C
∞
n
br
=1,3,5,...
e
−
π
2
n
2
br
4L
2
x
α
2
br
t
.
Q(n
br
= 1) Q(n
br
= 3) Q(n
br
= 5)...
Q = 8
C
2
k
hh
0
A
e
−
π
2
4L
2
x
α
2
br
t
dQ
dt
= −8
C
2
khh
0
A
π
2
C
2
A
2
α
2
br
e−
π
2
4L
2
x
α
2
br
t,
dQ
dt
= −
π
2
C
2
A
2
α
2
br
Q.
b = 1,0
α
2
br
=
k
f
s
h
dQ
dt
= −
π
2
C
2
A
2
k
f
s
hQ.
α =
π
2
C
2
A
2
k
f
s
h
α β
h(x, t) =
h
0
(x)
(1 + γ
c
t)
,
γ
c
1,115Hk
f
s
L
2
x
h
0
(x) = HF (
x
L
x
)
q
e
= k
H
(1 + γ
c
t)
dF (
x
L
x
)
dx
,
dF (
x
L
x
)
dx
=
dF (
x
L
x
)
d
x
L
x
d
x
L
x
dx
.
X/X
L
x
= s A
4
= 0 F
d
x
L
x
dF
=
1
0,862
d
dF
F
0
s
√
1 − s
3
ds
.
1
0,862
d
dF
F
0
s
√
1 − s
3
ds
=
1
0,862
F
0
d
dF
s
√
1 − s
3
ds
+
F
√
1 − F
3
dF
dF
−
0
√
1 − 0
3
d0
dF
=
1
0.862
F
√
1 − F
3
,
dF
d
x
L
x
=
0,862
√
1 − F
3
F
.
q = k
H
(1 + γ
c
t)
0,862
√
1 − F
3
F
1
L
x
,
Q = 2C
kH
L
x
(1 + γ
c
t)
2
0,862h
0
(x)
√
1 − F
3
F
,
F
h
0
= 0 x = 0
Q = 1,724
kCH
2
L
x
(1 + γ
c
t)
2
.
1,724
kCH
2
L
x
ζ
Q =
ζ
(1 + γ
c
t)
2
,
dQ
dt
= −2
ζγ
c
(1 + γ
c
t)
3
.
dQ
dt
= −2ζ
−1/2
γ
c
ζ
(1 + γ
c
t)
2
3/2
.
dQ
dt
dQ
dt
= −2ζ
−1/2
γ
c
Q
3/2
,
ζ γ
c
L
x
=
A
2C
dQ
dt
= −4,8308
k
1/2
C
f
s
A
3/2
Q
3/2
.
α β −4,8308
k
1/2
C
f
s
A
3/2
3/2
α β
q
e
= k
dh
dx
= k
dh
dY
dY
d
√
η
1
d
√
η
1
dx
= kBH(1 − 8Y
3
+ 21Y
6
−
40
11
Y
9
− 62, 01Y
12
+ ...)
0,4873
2
√
η
1
1
2
f
s
kHt
Q = 2Chq
= 2CBH
Y − 2Y
4
+ 3Y
7
−
4
11
Y
10
+
705
154
Y
13
...
= kBH(1 − 8Y
3
+ 21Y
6
−
40
11
Y
9
− 62,01Y
12
+ ...)
0,4873
2
√
η
1
1
2
f
kHt
,
Y = 0,4873
√
η
1
Q = 2CB
2
H
2
k
0,4873
2
2
− 0,4873
2
Y
3
+
3
2
0,4873
2
.Y
6
−
4
11
0,4873
2
Y
9
−
705
154
0,4873
2
Y
12
...
= (1 − 8Y
3
+ 21Y
6
−
40
11
Y
9
− 62,01Y
12
+ ...)
1
2
f
s
kHt
.
Q x = 0 Y = 0
Q = 2CB
2
H
2
k
0,4873
2
2
1
2
f
s
kHt
= 0,6642CH
3/2
kf
s
t
−1/2
,
dQ
dt
= −0,3321CH
3/2
kf
s
t
−3/2
.
−
dQ
dt
=
1,1334
C
2
H
3
kf
Q
3
.
α β
1,1334
C
2
H
3
kf
s
3
Q
t
×Q
t+1
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
1 − 61012000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
2 − 61014000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
3 − 61024000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
4 − 61031000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
5 − 61045000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
6 − 61052000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
7 − 61060000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
8 − 61075000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
9 − 61078000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
10 − 61085000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
11 − 61090000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
12 − 61100000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
13 − 61105000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
14 − 61107000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
15 − 61115000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
16 − 61122000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
17 − 61135000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
18 − 61140000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
19 − 61145000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
20 − 61173000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
21 − 61175000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
22 − 61202000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
23 − 61250000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
24 − 61267000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
25 − 61271000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
26 − 61280000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
27 − 61285000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
28 − 61295000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
29 − 61305000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
30 − 61320000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
31 − 61343000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
32 − 61350000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
33 − 61370000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
34 − 61410000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
35 − 61425000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
36 − 61429000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
37 − 61460000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
38 − 61473000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
39 − 61500000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
40 − 61510000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
41 − 61520000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
42 − 61530000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
43 − 61537000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
44 − 61565000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
45 − 61568000
Envoltória superior
0
2
4
6
8
10
0 2 4 6 8 10
Q
t+1
(mm.dia
−1
)
Q
t
(mm.dia
−1
)
46 − 61610000
Envoltória superior
Q
m
×
dQ
dt
α β
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
1 - 61012000
α=0,00732; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
2 - 61014000
α=0,00401; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
3 - 61024000
α=0,00532; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
4 - 61031000
α=0,00369; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
5 - 61045000
α=0,00867; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
6 - 610520000
α=0,00548; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
7 - 61060000
α=0,00775; β=1,15
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
8 - 61075000
α=0,00700; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
9 - 61078000
α=0,00695; β=1,00
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
10 - 61085000
α=0,00679; β=1,39
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
11 - 61090000
α=0,00781; β=1,15
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
12 - 61100000
α=0,00379; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
13 - 61105000
α=0,00597; β=1,30
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
14 - 61107000
α=0,00574; β=1,15
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
15 - 61115000
α=0,01058; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
16 - 61122000
α=0,00895; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
17 - 61135000
α=0,00712; β=1,07
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
18 - 61140000
α=0,01048; β=1,00
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
19 - 61145000
α=0,0045; β=1,00
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
20 - 61173000
α=0,00637; β=1,00
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
21 - 61175000
α=0,00658; β=1,00
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
22 - 61202000
α=0,00402 β=1,43
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
23 - 61250000
α=0,00533; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
24 - 61267000
α=0,00638; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
25 - 61271000
α=0,01097; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
26 - 61280000
α=0,00495; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
27 - 61285000
α=0,00993; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
28 - 61295000
α=0,01267; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
29 - 61305000
α=0,00880; β=1,15
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
30 - 61320000
α=0,01067; β=1,09
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
31 - 61343000
α=0,00830; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
32 - 61350000
α=0,01054; β=1,00
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
33 - 61370000
α=0,00989; β=1,38
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
34 - 61410000
α=0,01135; β=1,19
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
35 - 61425000
α=0,00899; β=1,00
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
36 - 61429000
α=0,00803; β=1,50
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
37 - 61460000
α=0,00709; β=1,25
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
38 - 61473000
α=0,00794; β=1,40
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
39 - 61500000
α=0,00752; β=1,35
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
40 - 61510000
α=0,00829; β=1,0
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
41 - 61520000
α=0,00593; β=1,12
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
42 - 61530000
α=0,00543; β=1,0
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
43 - 61537000
α=0,00710; β=1,00
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
44 - 61565000
α=0,01183; β=1,09
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
45 - 61568000
α=0,00885; β=1,00
Envolt´oria inferior
1e-04
0.001
0.01
0.1
1
10
100
0.01 0.1 1 10 100
dQ/dt (mm.dia
−2
)
Q (mm.dia
−1
)
46 - 61610000
α=0,00571; β=1,50
Envolt´oria inferior
∆t
0
5
10
15
20
199019801970196019501946
mm.dia
−1
ano
a) Jangada (1946−1990)
P
i
Q
i
E
ti
0
5
10
15
20
199019801970196019501941
mm.dia
−1
ano
b) das Cinzas (1941−1991)
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
1 − 61012000 − 1/1974−12/2001
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
2 − 61014000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
3 − 61024000 − 1/1974−12/1997
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
4 − 61031000 − 1/1974−12/2001
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
5 − 61045000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
6 − 61052000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
7 − 61060000 − 1/1974−12/2001
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
8 − 61075000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
9 − 61078000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
10 − 61085000 − 1/1974−12/2001
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
11 − 61090000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
12 − 61100000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
13 − 61105000 − 1/1974−12/2001
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
14 − 61107000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
15 − 61115000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
16 − 61122000 − 1/1974−12/2001
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
17 − 61135000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
18 − 61140000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
19 − 61145000 − 1/1974−12/2001
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
20 − 61173000 − 1/1974−12/1999
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
21 − 61175000 − 1/1974−12/1995
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
22 − 61202000 − 1/1974−12/2000
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
23 − 61250000 − 1/1974−12/1994
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
24 − 61267000 − 1/1974−12/1995
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
25 − 61271000 − 1/1975−12/1995
P
i
Q
i
E
ti
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
26 − 61280000 − 1/1974−12/2001
P
i
Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
27 − 61285000 − 1/1974−12/1995
P
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Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
28 − 61295000 − 1/1974−12/1995
P
i
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E
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P
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Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
29 − 61305000 − 1/1974−12/1995
P
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Q
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ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
30 − 61320000 − 1/1974−12/1995
P
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0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
31 − 61343000 − 1/1974−12/1995
P
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P
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Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
32 − 61350000 − 1/1974−12/1990
P
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Q
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E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
33 − 61370000 − 1/1974−12/1991
P
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0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
34 − 61410000 − 1/1974−12/2001
P
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P
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Q
i
E
ti
0
5
10
15
20
200019951990198519801975
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35 − 61425000 − 1/1974−12/1993
P
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Q
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0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
36 − 61429000 − 1/1974−12/2001
P
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0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
37 − 61460000 − 1/1974−12/1995
P
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P
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Q
i
E
ti
0
5
10
15
20
200019951990198519801975
mm.dia
−1
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38 − 61473000 − 1/1974−12/2001
P
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0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
39 − 61500000 − 1/1974−12/1995
P
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0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
40 − 61510000 − 1/1974−12/1995
P
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0
5
10
15
20
200019951990198519801975
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41 − 61520000 − 1/1974−12/1995
P
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0
5
10
15
20
200019951990198519801975
mm.dia
−1
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42 − 61530000 − 1/1974−12/1993
P
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0
5
10
15
20
200019951990198519801975
mm.dia
−1
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43 − 61537000 − 1/1974−12/1999
P
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Q
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0
5
10
15
20
200019951990198519801975
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44 − 61565000 − 1/1974−12/1998
P
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0
5
10
15
20
200019951990198519801975
mm.dia
−1
ano
45 − 61568000 − 1/1974−12/1991
P
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Q
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0
5
10
15
20
200019951990198519801975
mm.dia
−1
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46 − 61610000 − 1/1974−12/1997
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E
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P − Q
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Acumulada 1 - 61012000 - 1/1974-12/2001
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Acumulada 2 - 61014000 - 1/1974-12/2001
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Acumulada 3 - 61024000 - 1/1974-12/1997
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Ano
Acumulada 4 - 61031000 - 1/1974-12/2001
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Acumulada 5 - 61045000 - 1/1974-12/2001
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Acumulada 6 - 61052000 - 1/1974-12/2001
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Ano
Acumulada 7 - 61060000 - 1/1974-12/2001
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Ano
Acumulada 8 - 61075000 - 1/1974-12/2001
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Ano
Acumulada 9 - 61078000 - 1/1974-12/2001
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Acumulada 10 - 61085000 - 1/1974-12/2001
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Ano
Acumulada 11 - 61090000 - 1/1974-12/2001
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Ano
Acumulada 12 - 61100000 - 1/1974-12/2001
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Acumulada 14 - 61107000 - 1/1974-12/2001
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Acumulada 22 - 61202000 - 1/1974-12/2000
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Acumulada 23 - 61250000 - 1/1974-12/1994
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Acumulada 24 - 61267000 - 1/1974-12/1995
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Acumulada 30 - 61320000 - 1/1974-12/1995
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Acumulada 32 - 61350000 - 1/1974-12/1990
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Acumulada 44 - 61565000 - 1/1974-12/1998
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Acumulada 45 - 61568000 - 1/1974-12/1991
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