Storm advection nowcasting
View Patent ↗Embodiments of the invention can predict the ground location and intensity of storm cells for a future time using radar reflectivity data. In some embodiments, a Sinc approximation of the general flow equation can be solved to predict the ground location and intensity of a storm cell. In some embodiments, to solve the Sinc approximation the velocity of a storm cell can be estimated using various techniques including solving the flow equation in the frequency domain. The results can provide efficient prediction of storm cell position in nowcasting applications.
1. A radar system for nowcasting weather patterns within a region of interest, the system comprising:
a radar source configured to propagate a radar signal;
a radar detector configured to collect radar data; and
a computational system in communication with the radar source and with the radar detector, the computational system comprising a processor and a memory coupled with the processor, the memory comprising a computer-readable medium having a computer-readable program embodied therein for direction operation of the radar system to investigate the region of interest, the computer-readable program including:
instructions for propagating the radar signal into the region of interest with the radar source;
instructions for collecting sampled radar reflectivity data from within the region of interest with the radar detector, wherein the sampled radar reflectivity data represents a reflectivity of the radar signal at points within the region of interest;
instructions for selecting a horizontal two-dimensional data set from the sampled radar reflectivity data;
instructions for determining a velocity for data points within the horizontal two-dimensional data set;
instructions for predicting a horizontal location of data points within the horizontal data set at a future time using a Sinc approximation of the general flow equation and the velocity for data points within the horizontal two-dimensional data set; and
instructions for returning the predicted horizontal location of the data points at the future time.
2. The radar system according to claim 1 wherein the computer-readable program further includes instructions for predicting the intensity of data points within the horizontal data set at a future time using a Sinc approximation of the general flow equation and the velocity for data points within the horizontal two-dimensional data set.
3. The radar system according to claim 1 wherein the computer-readable program further includes instructions for predicting the reflectivity of data points within the horizontal data set at the future time.
4. The radar system according to claim 1 wherein the Sinc approximation of the general flow equation comprises:
F
kl
(
t
+
δ
t
)
=
F
kl
(
t
)
-
δ
t
{
U
kl
Δ
x
[
AF
(
t
)
]
kl
+
V
kl
Δ
y
[
F
(
t
)
Z
]
kl
}
where U.sub.kl is the x-axis velocity at data point k-l, and V.sub.kl is the y-axis velocity at data point k-l.
5. The radar system according to claim 1 wherein the instructions for determining a velocity comprises instructions for determining an x-axis velocity and a y-axis velocity by solving a flow equation in the frequency domain for the horizontal two-dimensional data set.
6. The radar system according to claim 5 wherein the flow equation in the frequency domain comprises
k
t
F
DFT
(
k
x
,
k
y
,
k
t
)
=
-
[
1
N
x
N
y
]
∑
k
x
=
N
x
-
N
x
+
∑
k
y
=
N
y
-
N
y
+
[
U
DFT
(
k
x
′
,
k
y
′
)
T
x
/
T
t
]
(
k
x
-
k
x
′
)
DFT
(
k
x
-
k
x
′
,
k
y
-
k
y
′
,
k
t
)
-
[
1
N
x
N
y
]
∑
k
x
=
N
x
-
N
x
+
∑
k
y
=
N
y
-
N
y
+
[
V
DFT
(
k
x
′
,
k
y
′
)
T
y
/
T
t
]
(
k
y
-
k
y
′
)
DFT
(
k
x
-
k
x
′
,
k
y
-
k
y
′
,
k
t
)
-
(
i
2
π
)
[
T
t
·
S
DFT
(
k
x
,
k
y
,
k
t
)
]
.
7. A method for predicting the position of a storm field, the method comprising:
propagating a radar signal in to the region of interest;
collecting sampled time domain radar data scattered from within the region of interest, wherein the sampled time domain radar data represents a reflectivity of the radar signal at points within the region of interest;
determining an x-axis velocity and a y-axis velocity for data points within the sampled time domain radar data; and
predicting the future position of data points within the storm field by solving a flow equation using the velocity for data points within the horizontal two-dimensional data set and a Sinc kernel expansion.
8. The method according to claim 7 further comprising predicting the intensity of data points within the storm field by solving a flow equation using the velocity for data points within the horizontal two-dimensional data set and a Sinc kernel expansion.
9. The method according to claim 7 wherein a solution to the general flow equation using a Sinc kernel expansion comprises
F
kl
(
t
+
δ
t
)
=
F
kl
(
t
)
-
δ
t
{
U
kl
Δ
x
[
AF
(
t
)
]
kl
+
V
kl
Δ
y
[
F
(
t
)
Z
]
kl
}
.
10. The method according to claim 7 wherein the x-axis velocity and the y-axis velocity are determined by solving the flow equation in the frequency domain.
11. The method according to claim 7 the flow equation in the frequency domain includes:
k
t
F
DFT
(
k
x
,
k
y
,
k
t
)
=
-
[
1
N
x
N
y
]
∑
k
x
=
N
x
-
N
x
+
∑
k
y
=
N
y
-
N
y
+
[
U
DFT
(
k
x
′
,
k
y
′
)
T
x
/
T
t
]
(
k
x
-
k
x
′
)
DFT
(
k
x
-
k
x
′
,
k
y
-
k
y
′
,
k
t
)
-
[
1
N
x
N
y
]
∑
k
x
=
N
x
-
N
x
+
∑
k
y
=
N
y
-
N
y
+
[
V
DFT
(
k
x
′
,
k
y
′
)
T
y
/
T
t
]
(
k
y
-
k
y
′
)
DFT
(
k
x
-
k
x
′
,
k
y
-
k
y
′
,
k
t
)
-
(
i
2
π
)
[
T
t
·
S
DFT
(
k
x
,
k
y
,
k
t
)
]
.
12. A method comprising:
propagating a radar signal in to the region of interest;
collecting reflectivity radar data scattered from within the region of interest, wherein the reflectivity radar data represents reflectivity of the radar signal as a function of position within the region of interest;
determining a velocity at points within the region of interest; and
predicting the future location of points within the region of interest using a Sinc approximation of a flow equation and the velocity for data points within the horizontal two-dimensional data set.
13. The method according to claim 12 further comprising predicting the future intensity of points within the region of interest using a Sinc approximation of a flow equation and the velocity for data points within the horizontal two-dimensional data set.
14. The method according to claim 12 wherein the velocity includes orthogonal velocities estimated from the flow equation.
15. The method according to claim 12 wherein a solution to the Sinc approximation of the flow equation at future time comprises
F
kl
(
t
+
δ
t
)
=
F
kl
(
t
)
-
δ
t
{
U
kl
Δ
x
[
AF
(
t
)
]
kl
+
V
kl
Δ
y
[
F
(
t
)
Z
]
kl
}
.