reconstruction of chlorophyll concentration pro le in o ... filereconstruction of chlorophyll...
Post on 21-Oct-2019
2 Views
Preview:
TRANSCRIPT
Reconstruction of ChlorophyllConcentration Pro�le
in O�shore Ocean Water
Roberto Pinto Souto - LNCCrpsouto@lncc.br
3rd Workshop on Modeling andSensing Environmental Systems (MoSES-III)
MoSES-III - Petrópolis - August 8th, 2011LNCC () MoSES-III August 8th, 2011 1 / 79
Motivation
Outline
1 Motivation
2 Hydrologic OpticsRadiative Transfer Equation - RTEInverse Problem - IPIP: radiances in di�erent depthsIP: multispectral radiances only in surface
3 Applying Data Assimilation
4 Final Remarks
LNCC () MoSES-III August 8th, 2011 2 / 79
Motivation
Phytoplankton
Oceanic micro-organisms with chlorophyll-a pigments(Chl-a);
They are the base of the ocean's life;
About half of the earth oxygen comes fromphotosynthesis made by phytoplankton;
They are responsible by nearly 40% of the carbonsequestration.
LNCC () MoSES-III August 8th, 2011 3 / 79
Motivation
Chlorophyll Concentration
LNCC () MoSES-III August 8th, 2011 4 / 79
Motivation
Satellite Ocean Color
LNCC () MoSES-III August 8th, 2011 5 / 79
Motivation
Climate Changes Impact
LNCC () MoSES-III August 8th, 2011 6 / 79
Hydrologic Optics
Outline
1 Motivation
2 Hydrologic OpticsRadiative Transfer Equation - RTEInverse Problem - IPIP: radiances in di�erent depthsIP: multispectral radiances only in surface
3 Applying Data Assimilation
4 Final Remarks
LNCC () MoSES-III August 8th, 2011 7 / 79
Hydrologic Optics Radiative Transfer Equation - RTE
Outline
1 Motivation
2 Hydrologic OpticsRadiative Transfer Equation - RTEInverse Problem - IPIP: radiances in di�erent depthsIP: multispectral radiances only in surface
3 Applying Data Assimilation
4 Final Remarks
LNCC () MoSES-III August 8th, 2011 8 / 79
Hydrologic Optics Radiative Transfer Equation - RTE
(ζ,µ,ϕ)
(0,−µ,ϕ)(0,µ,ϕ)
(ζ,−µ,ϕ)
b
p( )
a
Θ
LL
θ
0
internalsources
air
Sun
ζ
LL
ϕ
water
Θ
radiance: L
τ=
=τ
bottom
LNCC () MoSES-III August 8th, 2011 9 / 79
Hydrologic Optics Radiative Transfer Equation - RTE
Inherent Optical Properties - IOPs
optical depth: τ = ζ
τ is the optical variable:dτ = c(z)dzτ =
∫z
0c(z ′)dz ′
z =∫
τ
0
1
c(τ ′)dτ ′
scattering coe�cient: b(τ,λ )
absorption coe�cient: a(τ,λ )
attenuation coe�cient: c(τ,λ ) = a(τ,λ )+b(τ,λ )
LNCC () MoSES-III August 8th, 2011 10 / 79
Hydrologic Optics Radiative Transfer Equation - RTE
Inherent Optical Properties - IOPs
single scattering albedo : ϖ0(τ,λ ) = b(τ,λ )/c(τ,λ )
scattering phase function : p(Θ) = p(µ,ϕ ;µ ′,ϕ ′)
*µ = cosθ and ϕ are polar and azimuthal directions
LNCC () MoSES-III August 8th, 2011 11 / 79
Hydrologic Optics Radiative Transfer Equation - RTE
Radiative Transfer Equation (RTE)
µ∂
∂τLλ (τ,µ,ϕ) =−Lλ (τ,µ,ϕ)
ϖ0(τ,λ )
4π
∫1
−1
∫2π
0
p(µ,ϕ ;µ ′,ϕ ′)Lλ (τ,µ′,ϕ ′)dϕ
′dµ′
+Sλ (τ,µ,ϕ)
subjects to
Lλ (0,µ,ϕ) = Fδ (µ−µ0)δ (ϕ−ϕ0)
Lλ (ζ ,−µ,ϕ) = 0,
for µ ∈ (0,1] e ϕ ∈ [0,2π].
LNCC () MoSES-III August 8th, 2011 12 / 79
Hydrologic Optics Inverse Problem - IP
Outline
1 Motivation
2 Hydrologic OpticsRadiative Transfer Equation - RTEInverse Problem - IPIP: radiances in di�erent depthsIP: multispectral radiances only in surface
3 Applying Data Assimilation
4 Final Remarks
LNCC () MoSES-III August 8th, 2011 13 / 79
Hydrologic Optics Inverse Problem - IP
Inverse Problems
BOUNDARY
PARAMETERS
CONDITIONS
+
DATA
OBSERVED
DIRECT MODEL
INVERSE MODEL
Causes Effects
LNCC () MoSES-III August 8th, 2011 14 / 79
Hydrologic Optics Inverse Problem - IP
E�ect:Radiance
Causes:Boundary ConditionsScattering phase functionAbsorption coe�cientScattering coe�cientInternal source
LNCC () MoSES-III August 8th, 2011 15 / 79
Hydrologic Optics Inverse Problem - IP
Plane-parallel geometry
0
τ1
τ
τr
τ
τR−1
R
τ = 0
τ = ζ
R−2
τ2
r−1
τ
. . . .
. . . .
region 2
region 1
region r
Superface
region R−1
region R
LNCC () MoSES-III August 8th, 2011 16 / 79
Hydrologic Optics Inverse Problem - IP
Bio-optical models
ϖr ,λ =br ,λ
ar ,λ +br ,λ
ar ,λ =[aw
λ+0.06 ac
λC 0.65r
]×[1+0.2 e−0.014(λ−440)
]
br ,λ =
(550
λ
)0.30 C 0.62
r
*Typically, in o�shore oceanic waters, most of attenuationis due to chlorophyll pigments found in phytoplankton, asis required for the above bio-optical models.
LNCC () MoSES-III August 8th, 2011 17 / 79
Hydrologic Optics Inverse Problem - IP
The original inverse problem of absorption and scatteringcoe�cients estimation yields to recovering chlorophyllvertical pro�le, discretized in R+1 depths:
C = [ C (τ0) C (τ1) C (τ2) · · · C (τR) ]= [ C1 C2 C3 · · · CR+1 ]
LNCC () MoSES-III August 8th, 2011 18 / 79
Hydrologic Optics Inverse Problem - IP
Real chlorophyll pro�le
0 0.2 0.4 0.6 0.8 1 1.2 1.4−80
−70
−60
−50
−40
−30
−20
−10
0
Clorofila mg/m3
Pro
fund
idad
e [m
etro
s]
LNCC () MoSES-III August 8th, 2011 19 / 79
Hydrologic Optics Inverse Problem - IP
The real pro�le can be modeled with a Gaussian model:
C (z) = C0+h
s√2 π
e−1
2( z−zmax
s)2
where z is the geometric depth given in meters.
LNCC () MoSES-III August 8th, 2011 20 / 79
Hydrologic Optics Inverse Problem - IP
C0 h s zmax0.2 144 9 17
0 1 2 3 4 5 6 7 8−40
−35
−30
−25
−20
−15
−10
−5
0
C (mg/m3)
geo
met
ric
dep
th z
(m
)
LNCC () MoSES-III August 8th, 2011 21 / 79
Hydrologic Optics IP: radiances in di�erent depths
Outline
1 Motivation
2 Hydrologic OpticsRadiative Transfer Equation - RTEInverse Problem - IPIP: radiances in di�erent depthsIP: multispectral radiances only in surface
3 Applying Data Assimilation
4 Final Remarks
LNCC () MoSES-III August 8th, 2011 22 / 79
Hydrologic Optics IP: radiances in di�erent depths
Objective Function
Radiances observed in each depth
J(C ) =Nµ
∑i=1
R
∑r=0
[Lobs(τr ,µi)−L
C(τr ,µi)]2
+ γ Γ(C )
Regularization Term:
γ Γ(C ) = γ
R
∑r=2
(Cr−1−2Cr +Cr+1)2
LNCC () MoSES-III August 8th, 2011 23 / 79
Hydrologic Optics IP: radiances in di�erent depths
Ant Colony Optimization (ACO)
It is a metaheuristic based on collective behavior of ants,searching the smallest path between the ant colony andthe source of food [Dorigo et al., 1996].
LNCC () MoSES-III August 8th, 2011 24 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO parameters
ns: number of parameter (assigned to points in agraph) to �nd.
np: number of paths between two parameters (twopoints).
na: number of ants
Tij = To : initial amount of pheromone in all pathsi = 1, . . . ,ns e j = 1, . . . ,np
ρ : pheromone evaporation rate Tij = (1−ρ)Tij
mit : maximum number of iterations
qo : decision threshold
LNCC () MoSES-III August 8th, 2011 25 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO scheme
At each iteration the smallest objective function costsolution {ijmin} is chosen.The path traveled by the ant is assigned as thesmallest cost solution, and it is marked withpheromone:
Tijmin= (1−ρ)Tijmin
+To
LNCC () MoSES-III August 8th, 2011 26 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO - 90 ants
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
De
pth
z (
m)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 27 / 79
Hydrologic Optics IP: radiances in di�erent depths
Original upward radiances
−40
−30
−20
−10
0
−1
−0.8
−0.6
−0.4
−0.2
00
0.05
0.1
0.15
0.2
noiselessLNCC () MoSES-III August 8th, 2011 28 / 79
Hydrologic Optics IP: radiances in di�erent depths
Upward radiances with depth correction
−40
−30
−20
−10
0
−1
−0.8
−0.6
−0.4
−0.2
00
0.05
0.1
0.15
0.2
noiselessLNCC () MoSES-III August 8th, 2011 29 / 79
Hydrologic Optics IP: radiances in di�erent depths
Original downward radiances
−40
−30
−20
−10
0
0
0.2
0.4
0.6
0.8
10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
noiselessLNCC () MoSES-III August 8th, 2011 30 / 79
Hydrologic Optics IP: radiances in di�erent depths
Downward radiances with depth correction
−40
−30
−20
−10
0
0
0.2
0.4
0.6
0.8
10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
noiselessLNCC () MoSES-III August 8th, 2011 31 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO - 90 ants
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
De
pth
z (
m)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 32 / 79
Hydrologic Optics IP: radiances in di�erent depths
Original upward radiances
−40
−30
−20
−10
0
−1
−0.8
−0.6
−0.4
−0.2
00
0.05
0.1
0.15
0.2
noise 5%LNCC () MoSES-III August 8th, 2011 33 / 79
Hydrologic Optics IP: radiances in di�erent depths
Upward radiances with depth correction
−40
−30
−20
−10
0
−1
−0.8
−0.6
−0.4
−0.2
00
0.05
0.1
0.15
0.2
noise 5%LNCC () MoSES-III August 8th, 2011 34 / 79
Hydrologic Optics IP: radiances in di�erent depths
Original downward radiances
−40
−30
−20
−10
0
0
0.2
0.4
0.6
0.8
10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
noise 5%LNCC () MoSES-III August 8th, 2011 35 / 79
Hydrologic Optics IP: radiances in di�erent depths
Downward radiances with depth correction
−40
−30
−20
−10
0
0
0.2
0.4
0.6
0.8
10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
noise 5%LNCC () MoSES-III August 8th, 2011 36 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO (5% noisy data) - 90 ants
0 1 2 3 4 5 6 7 8−40
−35
−30
−25
−20
−15
−10
−5
0Identificacao do perfil de concentracao de clorofila
C (mg/m3)
prof
undi
dade
geo
met
rica
z (m
)realestimado
LNCC () MoSES-III August 8th, 2011 37 / 79
Hydrologic Optics IP: radiances in di�erent depths
Original upward radiances
−40
−30
−20
−10
0
−1
−0.8
−0.6
−0.4
−0.2
00
0.05
0.1
0.15
0.2
noise 10%LNCC () MoSES-III August 8th, 2011 38 / 79
Hydrologic Optics IP: radiances in di�erent depths
Upward radiances with depth correction
−40
−30
−20
−10
0
−1
−0.8
−0.6
−0.4
−0.2
00
0.05
0.1
0.15
0.2
noise 10%LNCC () MoSES-III August 8th, 2011 39 / 79
Hydrologic Optics IP: radiances in di�erent depths
Original downward radiances
−40
−30
−20
−10
0
0
0.2
0.4
0.6
0.8
10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
noise 10%LNCC () MoSES-III August 8th, 2011 40 / 79
Hydrologic Optics IP: radiances in di�erent depths
Downward radiances with depth correction
−40
−30
−20
−10
0
0
0.2
0.4
0.6
0.8
10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
noise 10%LNCC () MoSES-III August 8th, 2011 41 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO (10% noisy data) - 90 ants
0 1 2 3 4 5 6 7 8−40
−35
−30
−25
−20
−15
−10
−5
0Identificacao do perfil de concentracao de clorofila
C (mg/m3)
prof
undi
dade
geo
met
rica
z (m
)realestimado
LNCC () MoSES-III August 8th, 2011 42 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO with Intrinsic Regularization -ACOwIR
It uses a pre-selection of candidate solutions in eachACO iteration [Preto et al., 2004][Souto et al., 2006],according 2nd -order Tikhonov criterion.
For instance, 15 of 90 ants (solutions) are chosenaccording their smoothness.
It is reached a gain of performance.
LNCC () MoSES-III August 8th, 2011 43 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO - 90 ants
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
De
pth
z (
m)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 44 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO - 15 ants
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
De
pth
z (
m)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 45 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACOwIR - 15 of 90 ants
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
De
pth
z (
m)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 46 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO Fuzzy
An amount of pheromone is also deposited in theneighbor paths, with weigths w1 and w2.
Tijmin−2 = (1−ρ)Tijmin−2+w2To
Tijmin−1 = (1−ρ)Tijmin−1+w1To
Tijmin= (1−ρ)Tijmin
+To
Tijmin+1= (1−ρ)Tijmin+1
+w1To
Tijmin+2= (1−ρ)Tijmin+2
+w2To
where w2 < w1 < 1.0
LNCC () MoSES-III August 8th, 2011 47 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO Fuzzy: Example
w = [w1 w2]T = [0.4 0.1]T
Tijmin−2 = (1−ρ)Tijmin−2+0.1To
Tijmin−1 = (1−ρ)Tijmin−1+0.4To
Tijmin= (1−ρ)Tijmin
+To
Tijmin+1= (1−ρ)Tijmin+1
+0.4To
Tijmin+2= (1−ρ)Tijmin+2
+0.1To
LNCC () MoSES-III August 8th, 2011 48 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACOwIR - 15 of 90 ants
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
De
pth
z (
m)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 49 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACOwIR Fuzzy - 15 of 90 ants
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
De
pth
z (
m)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 50 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO - 15 ants
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
De
pth
z (
m)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 51 / 79
Hydrologic Optics IP: radiances in di�erent depths
ACO Fuzzy - 15 ants
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
De
pth
z (
m)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 52 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Outline
1 Motivation
2 Hydrologic OpticsRadiative Transfer Equation - RTEInverse Problem - IPIP: radiances in di�erent depthsIP: multispectral radiances only in surface
3 Applying Data Assimilation
4 Final Remarks
LNCC () MoSES-III August 8th, 2011 53 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Objective Function
Multispectral radiances observed in water surface (z=0)
J(C ) =Nλ
∑j=1
Nµ/2
∑i=1
[Lobs(0,−µi)−L
C
λj(0,−µi)
]2+ γ Γ(C ).
LNCC () MoSES-III August 8th, 2011 54 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Noiseless multispectral radiancesementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 360 12 500 0.03 0.0{63,77,81,95,99}
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 55 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Negative Concavity: step-1sementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 360 12 500 0.03 0.0{63,77,81,95,99}
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 56 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Negative Concavity: step-2sementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 360 12 500 0.03 0.0{63,77,81,95,99}
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 57 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Negative Concavity: step-1, noise 1%sementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 360 12 500 0.03 0.0{63,77,81,95,99}
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 58 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Negative Concavity: step-2 noise 1%sementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 360 12 500 0.03 0.0{63,77,81,95,99}
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 59 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Negative Concavity: step-1sementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 360 12 500 0.03 0.0{63,77,81,95,99}
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 60 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Negative Concavity: step-2sementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 360 12 500 0.03 0.0{63,77,81,95,99}
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 61 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Negative Concavity: step-1, noise 1%sementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 360 12 500 0.03 0.0{63,77,81,95,99}
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 62 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Negative Concavity: step-2, noise 1%sementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 360 12 500 0.03 0.0{63,77,81,95,99}
-40
-35
-30
-25
-20
-15
-10
-5
0
0 2 4 6 8 10
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 63 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Negative Concavity, noiselesssementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 300 12 500 0.03 0.0{63,77,81,95,99}
-80
-70
-60
-50
-40
-30
-20
-10
0
0 0.1 0.2 0.3 0.4 0.5
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 64 / 79
Hydrologic Optics IP: multispectral radiances only in surface
Negative Concavity, noise 1%sementes ns np na nap mit ρ q0
{03,15,21,31,45} 10 3000 300 12 500 0.03 0.0{63,77,81,95,99}
-80
-70
-60
-50
-40
-30
-20
-10
0
0 0.1 0.2 0.3 0.4 0.5
Dep
th z
(m
)
C (mg/m3)
EXACTAVG. SOL.
SEED SOL.
LNCC () MoSES-III August 8th, 2011 65 / 79
Applying Data Assimilation
Outline
1 Motivation
2 Hydrologic OpticsRadiative Transfer Equation - RTEInverse Problem - IPIP: radiances in di�erent depthsIP: multispectral radiances only in surface
3 Applying Data Assimilation
4 Final Remarks
LNCC () MoSES-III August 8th, 2011 66 / 79
Applying Data Assimilation
Data Assimilation
Elements description
Ce Exact Chl-a pro�leCb Recovered Chl-a pro�le (background)N Number of recovered Chl-a pro�les
(number of observations/measurements/samples)Nb Number of components of Chl-a pro�leεb absolute error between Cb e Ce
Pb Covariance error matrix (Nb×Nb) of background
LNCC () MoSES-III August 8th, 2011 67 / 79
Applying Data Assimilation
Data Assimilation
Elements description
Le Exact radiance values due to Ce
Lo Observed radiance dataNo Number of observed radiance dataεo error between Lo e LePo Covariance error matrix (No×No) of observationsH non-linear RTE modelH Jacobian matrix (No×Nb) of model H
due to small variations of Cb
W gain matrix (Nb×No)Ca Chl-a pro�le analysis (result of assimilation)
LNCC () MoSES-III August 8th, 2011 68 / 79
Applying Data Assimilation
Data Assimilation
Formulation
Ca = Cb +W [Lo−H (Cb)]
W = PbHT (HPbH
T +Po)−1
Pb = E{εbεTb }
Po = E{εoεTo }
LNCC () MoSES-III August 8th, 2011 69 / 79
Applying Data Assimilation
Data Assimilation
Case Study
Radiances in each depthNb 10 depthsNo 100 (10 polar directions × 10 depths)N 200 samples
LNCC () MoSES-III August 8th, 2011 70 / 79
Applying Data Assimilation
Best (but not typical) result of 200 samples
-80
-70
-60
-50
-40
-30
-20
-10
0
0 0.1 0.2 0.3 0.4 0.5
Dep
th z
(m
)
C (mg/m3)
SIZE:200 SAMPLE #033 SQUARE ERROR: BKGD=0.047239 ANLS=0.0090695EXACT
BKGD.
ANLR.
LNCC () MoSES-III August 8th, 2011 71 / 79
Applying Data Assimilation
Worst result of 200 samples
-80
-70
-60
-50
-40
-30
-20
-10
0
0 0.1 0.2 0.3 0.4 0.5
Dep
th z
(m
)
C (mg/m3)
SIZE:200 SAMPLE #128 SQUARE ERROR: BKGD=0.043895 ANLS=0.056691EXACT
BKGD.
ANLR.
LNCC () MoSES-III August 8th, 2011 72 / 79
Applying Data Assimilation
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8 1
BKGD/ANLS SQUARE ERROR RATIO20 OF SAMPLE SIZE 20
20 OF SAMPLE SIZE 200200 OF SAMPLE SIZE 200
BKGD SQR ERROR = ANLS SQR ERROR
LNCC () MoSES-III August 8th, 2011 73 / 79
Final Remarks
Outline
1 Motivation
2 Hydrologic OpticsRadiative Transfer Equation - RTEInverse Problem - IPIP: radiances in di�erent depthsIP: multispectral radiances only in surface
3 Applying Data Assimilation
4 Final Remarks
LNCC () MoSES-III August 8th, 2011 74 / 79
Final Remarks
Data Assimilation
It is still necessary further studies about the use of dataassimilation:
How to best estimate covariance error matrices?
How many samples is need to reach a better analysis?
Apply it to surface multispectral radiances.
LNCC () MoSES-III August 8th, 2011 75 / 79
Final Remarks
Computational Performance
Another important issue is computational performance:
Case study was shown for radiances with azimuthalsymmetry (isotropic medium);
In anisotropic medium the computational cost ismuch higher;
Strategies of parallelism with MPI: ACO hasindependent ants, and RTE solver performsindependent azimuthal modes;
Strategies of parallelism with OpenMP and CUDA:exploring multi and manycore architectures to solvelinear systems and eigenvalues routines.
LNCC () MoSES-III August 8th, 2011 76 / 79
Final Remarks
Further Case Studies
Besides to employ an anisotropic medium, it is possible:
Increase the level of discretization of Chl-a. At leastone value of chlorophyll pro�le in each meter of deph.
Use of real, not synthetic, remote sensing data, fromocean optics spectrometers and satellites.
LNCC () MoSES-III August 8th, 2011 77 / 79
Final Remarks
Acknownledgements
PCI/CNPq/LNCC - processes number 381243/2010-9 and 300338/2011-2
LNCC () MoSES-III August 8th, 2011 78 / 79
Final Remarks
Thank you
LNCC () MoSES-III August 8th, 2011 79 / 79
Final Remarks
Carvalho, A., de Campos Velho, H., adn R.P. Souto,S. S., Becceneri, J., and Sandri, S. (2008).Fuzzy ant colony optimization for estimatingchorophyll concentration pro�le in o�shore sea water.Inverse Problems in Science and Engineering,16(6):705�715.
Dorigo, M., Maniezzo, V., and Colorni, A. (1996).The ant system: optimization by a colony ofcooperating agents.IEEE Transactions on Systems, Man, andCybernetics�Part B, 26(2):29�41.
Preto, A. J., CamposVelho, H. F., Becceneri, J. C.,Arai, N. N., Souto, R. P., and Stephany, S. (2004).
LNCC () MoSES-III August 8th, 2011 79 / 79
Final Remarks
A new regularization technique for an ant-colony basedinverse solver applied to a crystal growth problem.In Anais..., pages 147�153, Cincinnati. Inverse Problemin Engineering Seminar.
Souto, R. P., CamposVelho, H. F., Stephany, S., andSandri, S. (2006).Estimating vertical chlorophyll concentration ino�shore ocean water using a modi�ed ant colonysystem.Journal of Mathematical Modelling and Algorithms(JMMA).
LNCC () MoSES-III August 8th, 2011 79 / 79
top related