Methods and Systems for Optical Flow Modeling Applications for Wind and Solar Irradiance Forecasting
A method of forecasting cloud motion: gathering a time-series of satellite imagery; transforming the time-series of satellite imagery into a cloudiness index image by establishing an upper and lower limit of visible pixel values for time t; calculating the cloudiness index at each pixel location for time t to provide a cloudiness index image; applying optical flow modeling to the cloudiness index image by assuming pixel value constancy across time; assuming motion to be small and approximating the motion with a Taylor series; assuming vector field is smooth locally; selecting all pixels within d distance of location n with the same prior vector field (m*m pixels); solving system of m*m equations in the least square sense; repeat at multiple resolutions; and calculating cloud motion vectors from multiple resolution vector fields; applying the cloud motion vectors to the cloudiness index image to predict future cloud position and intensity.
1 . A computer implemented method of forecasting cloud motion, said method comprising the steps of:
gathering a time-series of satellite imagery including at least one of a time-series of visible satellite imagery and a time-series of infrared satellite imagery;
transforming the time-series of satellite imagery, by a computing device, including at least one of a time-series of visible satellite imagery and a time-series of infrared satellite imagery into a cloudiness index image by establishing a lower limit of visible pixel values for time t; establishing an upper limit of visible pixel values for time t; and calculating the cloudiness index at each pixel location for time t to provide a cloudiness index image;
applying optical flow modeling, by a computing device, to the cloudiness index image by assuming pixel value constancy across time; assuming motion to be small and approximating the motion with a Taylor series; assuming vector field is smooth locally; selecting all pixels within d distance of location n with the same prior vector field (m*m pixels); solving system of m*m equations in the least square sense; repeat at multiple resolutions the step of solving system of m*m equations in least square sense; and calculating cloud motion vectors from multiple resolution vector fields;
applying the cloud motion vectors, by a computing device, to the cloudiness index image to predict future cloud position and intensity.
2 . A method as in claim 1 , wherein the step of calculating the cloudiness index at each pixel location for time t to provide a cloudiness index image is determined by a computing device using only the time-series of visible satellite imagery and is according to the formula:
Cloudiness
Index
n
t
=
Visible
Pixel
n
t
-
Visible
Pixel
Lower
Limit
n
t
Visible
Pixel
Upper
Limit
n
t
-
Visible
Pixel
Lower
Limit
n
t
3 . A method as in claim 1 , wherein the step of calculating the cloudiness index at each pixel location for time t to provide a cloudiness index image is determined by a computing device using the time-series of visible satellite imagery and the time-series of infrared satellite imagery and is according to the formula:
Cloudiness
Index
n
t
=
C
1
Pixel
Value
n
t
-
Pixe
Value
Lower
Limit
n
t
Pixel
Value
Upper
Limit
n
t
-
Pixel
Value
Lower
Limit
n
t
+
∑
i
=
2
j
C
i
Infrared
Pixel
int
where Cx is a fitted coefficient corresponding to each variable.
4 . A method as in claim 1 , wherein the step of assuming pixel value constancy across time is performed by a computing device according to the formula:
I ( x,y,t )= I ( x+∂x,y+∂y,t+∂t )
5 . A method as in claim 1 , wherein the step of approximating the motion with a Taylor series is according to at least one of the following Taylor series:
a
.
I
(
x
+
∂
x
,
y
+
∂
y
,
t
+
∂
t
)
=
I
(
x
,
y
,
t
)
b
.
I
(
x
+
∂
x
,
y
+
∂
y
,
t
+
∂
t
)
=
I
(
x
,
y
,
t
)
+
∂
I
∂
x
∂
x
+
∂
I
∂
y
∂
y
+
∂
I
∂
t
∂
t
+
Higher
Order
Terms
c
.
∂
I
∂
x
∂
x
+
∂
I
∂
y
∂
y
+
∂
I
∂
t
∂
t
=
0
d
.
∂
I
∂
x
∂
x
∂
t
+
∂
I
∂
y
∂
y
∂
t
=
-
∂
I
∂
t
e
.
∇
I
T
·
V
⇀
=
-
I
t
6 . A method as in claim 1 , wherein the step of solving system of m*m equations in the least square sense is according to at least one of the following:
∇ I T ·{right arrow over (V)}=−I t a.
minΣ x εΩ W 2 ( {right arrow over (x)} )[∇ I T ( {right arrow over (x)},t )· {right arrow over (V)}+I t ( {right arrow over (x)},t )] 2 b.
A T W 2 A{right arrow over (V)}=A T W 2 b c.
A=[I ( x 1 ), . . . , I ( x n•n )] T i.
W =diag( W ( x 1 ), . . . , W ( x n•n )) ii.
b=[I t ( x 1 ), . . . , I t ( x n•n )] T iii.
7 . A method as in claim 1 , wherein the step of calculating cloud motion vectors from multiple resolution vector fields is according to:
V 4 =V 4 ′+((( V 3 ′) interpolated +V 2 ′) interpolated +V 1 ) interpolated
8 . A method of forecasting cloud motion, said method comprising the steps of:
gathering a time-series of sky imagery including at least one of a time-series of visible sky imagery and a time-series of infrared sky imagery;
transforming the time-series of sky imagery, by a computing device, including at least one of a time-series of visible sky imagery and a time-series of infrared sky imagery into a cloudiness index image by establishing a lower limit of visible pixel values for time t; establishing an upper limit of visible pixel values for time t; and calculating the cloudiness index at each pixel location for time t to provide a cloudiness index image;
applying optical flow modeling to the cloudiness index image, by a computing device, by assuming pixel value constancy across time; assuming motion to be small and approximating the motion with a Taylor series; assuming vector field is smooth locally; selecting all pixels within d distance of location n with the same prior vector field (m*m pixels); solving system of m*m equations in the least square sense; repeat at multiple resolutions the step of solving system of m*m equations in least square sense; and calculating cloud motion vectors from multiple resolution vector fields;
applying the cloud motion vectors, by a computing device, to the cloudiness index image to predict future cloud position and intensity.
9 . A method as in claim 8 , wherein the step of calculating the cloudiness index at each pixel location for time t to provide a cloudiness index image is determined by a computing device using the time-series of visible satellite imagery and the time-series of infrared satellite imagery and is according to the formula:
Cloudiness
Index
n
t
=
C
1
Pixel
Value
n
t
-
Pixe
Value
Lower
Limit
n
t
Pixel
Value
Upper
Limit
n
t
-
Pixel
Value
Lower
Limit
n
t
+
∑
i
=
2
j
C
i
Infrared
Pixel
int
where Cx is a fitted coefficient corresponding to each variable.
10 . A method as in claim 8 , wherein the step of assuming pixel value constancy across time is performed by a computing device according to the formula:
I ( x,y,t )= I ( x+∂x,y+∂y,t+∂t )
11 . A method as in claim 8 , wherein the step of approximating the motion with a Taylor series is according to at least one of the following Taylor series:
a
.
I
(
x
+
∂
x
,
y
+
∂
y
,
t
+
∂
t
)
=
I
(
x
,
y
,
t
)
b
.
I
(
x
+
∂
x
,
y
+
∂
y
,
t
+
∂
t
)
=
I
(
x
,
y
,
t
)
+
∂
I
∂
x
∂
x
+
∂
I
∂
y
∂
y
+
∂
I
∂
t
∂
t
+
Higher
Order
Terms
c
.
∂
I
∂
x
∂
x
+
∂
I
∂
y
∂
y
+
∂
I
∂
t
∂
t
-
0
d
.
∂
I
∂
x
∂
x
∂
t
+
∂
I
∂
y
∂
y
∂
t
=
-
∂
I
∂
t
e
.
∇
I
T
·
V
⇀
=
-
I
t
12 . A method as in claim 8 , wherein the step of solving system of m*m equations in the least square sense is according to at least one of the following:
∇ I T ·{right arrow over (V)}=−I t a.
minΣ x εΩ W 2 ( {right arrow over (x)} )[∇ I T ( {right arrow over (x)},t )· {right arrow over (V)}+I t ( {right arrow over (x)},t )] 2 b.
A T W 2 A{right arrow over (V)}=A T W 2 b c.
A=[I ( x 1 ), . . . , I ( x n•n )] T i.
W =diag( W ( x 1 ), . . . , W ( x n•n )) ii.
b=[I t ( x 1 ), . . . , I t ( x n•n )] T iii.
13 . A method as in claim 8 , wherein the step of calculating cloud motion vectors from multiple resolution vector fields is according to:
V 4 =V 4 ′+((( V 3 ′) interpolated +V 2 ′) interpolated +V 1 ) interpolated
14 . A computer implemented method of forecasting solar irradiance using optical flow based cloud motion forecasts, said method comprising the steps of:
determining a cloudiness index value transformed from at least one of satellite imagery and sky imagery and generated by a cloud forecasting model at location n at time t;
Applying, by a computing device, a motion vector of a pixel obtained from the cloud forecasting model for a time period length i at location n at time t and at respective locations to the cloudiness index value to forecast each cloudiness index at a forecasted location of pixel and a time of forecast to provide a forecasted cloudiness index;
Inputting, in a computing device, the forecasted cloudiness index as input to a solar irradiance model to estimate solar irradiance at location o at time u.
15 . A method as in claim 1 , wherein the step of calculating the cloudiness index at each pixel location for time t to provide a cloudiness index image is determined by a computing device using only the time-series of visible satellite imagery and is according to the formula:
Cloudiness
Index
n
t
=
Visible
Pixel
n
t
-
Visible
Pixel
Lower
Limit
n
t
Visible
Pixel
Upper
Limit
n
t
-
Visible
Pixel
Lower
Limit
n
t