Method and apparatus for measuring extinction using an unmanned aerial vehicle
A method and apparatus used to determine atmospheric extinction coefficients in conjunction with an unmanned aerial vehicle are provided. The unmanned aerial vehicle may include a central body, at least one motor operatively connected to the central body, a condensation particle detection payload, and a data acquisition board including memory operatively connected to the data acquisition board, and a processor configured to generate extinction information.
1 . An unmanned aerial vehicle comprising:
a) a central body comprising a first enclosure housing:
i. a flight controller configured to direct movement of the unmanned aerial vehicle;
ii. a navigation system configured to generate three-dimensional position information of the unmanned aerial vehicle in three-dimensional space; and
iii. a payload mounting interface;
b) at least one motor operatively connected to the central body with at least one respective propeller, wherein each motor is operatively connected to the flight controller;
c) a condensation particle detection payload mounted to the central body via the payload mounting interface, wherein the condensation particle detection payload is configured to generate first particle count information and first particle size information each including information regarding particles of sizes less than 10 microns; and
d) a data acquisition board operatively connected to the condensation particle detection payload configured to obtain the first particle count information and to determine first extinction information at one or more locations in three-dimensional space based on the first particle count information, by the steps of:
i. obtaining the first particle count information from the condensation particle detection payload; and
ii. determining first extinction information based on the first particle count information, wherein the first extinction information is determined by the formula:
β
e
,
s
,
a
(
λ
)
=
∫
r
1
r
2
Q
e
,
s
,
a
(
n
,
λ
,
r
)
π
r
2
d
N
(
r
)
r
ln
10
d
(
log
r
)
dt
≈
∑
i
=
r
min
r
max
Q
e
,
s
,
a
(
n
,
λ
,
r
i
)
π
r
i
2
d
N
i
r
i
ln
10
d
(
log
r
i
)
Δ
r
i
,
where β e,s,a (λ) are first wavelength-specific normalized extinction, scattering, and absorption coefficients, Q e,s,a (n, λ, r i ) are aerosol-constituent specific extinction, scattering, and absorption efficiency, and r is a modal radius associated with the first particle size information.
2 . The unmanned aerial vehicle of claim 1 , wherein the data acquisition board is further configured to determine first transmission information over a first distance based on the first extinction information.
3 . The unmanned aerial vehicle of claim 1 , wherein the data acquisition board is housed in the first enclosure.
4 . The unmanned aerial vehicle of claim 1 , wherein the data acquisition board is housed in a second enclosure mounted to the central body.
5 . The unmanned aerial vehicle of claim 1 , wherein the at least one motor comprises four motors, each of the four motors being operatively connected to the flight controller and having at least one respective propeller.
6 . The unmanned aerial vehicle of claim 1 , wherein the condensation particle detection payload is configured to generate the first particle count information by the steps of:
1. ingesting, by an inlet of the condensation particle detection payload, a first air sample at a first volumetric flow rate, wherein the first air sample comprises a plurality of atmospheric aerosol particles and a plurality of water vapor particles, and wherein the inlet is operatively connected to a wick of the condensation particle detection payload;
2. cooling, by a conditioner of the condensation particle detection payload enclosing the wick, the first air sample;
3. condensing, by the conditioner, the plurality of water vapor particles to form a plurality of liquid water particles;
4. heating, by an initiator of the condensation particle detection payload enclosing the wick, the first air sample and the plurality of liquid water particles to supersaturate the first air sample and heat the plurality of atmospheric aerosol particles;
5. enlarging, by a growth component of the condensation particle detection payload, the heated plurality of atmospheric aerosol particles;
6. recycling the plurality of liquid water particles to the wick; and
7. determining, by a detector of the condensation particle detection payload, the first particle count information associated with the first air sample based on the enlarged plurality of atmospheric aerosol particles.
7 . The unmanned aerial vehicle of claim 6 , wherein the first particle count information is measured between 5 nanometers and 2.5 microns.
8 . An unmanned aerial vehicle comprising:
a) a central body comprising a first enclosure housing:
i. a flight controller configured to direct movement of the unmanned aerial vehicle;
ii. a navigation system configured to generate three-dimensional position information of the unmanned aerial vehicle in three-dimensional space; and
iii. a payload mounting interface;
b) at least one motor operatively connected to the central body with at least one respective propeller, wherein each motor is operatively connected to the flight controller;
c) a condensation particle detection payload mounted to the central body via the payload mounting interface, wherein the condensation particle detection payload is configured to generate first particle count information and first particle size information each including information regarding particles of sizes less than 10 microns; and
d) a data acquisition board operatively connected to the condensation particle detection payload configured to obtain the first particle count information and to determine first extinction information at one or more locations in three-dimensional space based on the first particle count information, by the steps of:
i. obtaining the first particle count information from the condensation particle detection payload; and
ii. determining first extinction information based on the first particle count information, wherein the data acquisition board is further configured to determine first transmission information over a first distance based on the first extinction information,
wherein determining first transmission information comprises the steps of:
i. generating first optical depth information by the formula:
τ
(
z
1
,
z
2
)
=
∫
z
1
z
2
β
(
z
)
dz
.
where τ is first optical depth information, β(z) is a layer volume extinction coefficient, and z is a geometric height; and
ii. generating the first transmission information by the formula:
t
(
τ
)
=
e
-
τ
/
|
cos
θ
|
,
where t is the first transmission information, τ is the first optical depth information, and θ is a source angle of incidence upon a parallel plane.
9 . The unmanned aerial vehicle of claim 8 , wherein the first extinction information is determined based on the first particle count information and first particle size information.
10 . The unmanned aerial vehicle of claim 9 , wherein the first particle size information is generated by the steps of:
1. generating, by a first humidity sensor mounted on the unmanned aerial vehicle and operatively connected to the data acquisition board, first relative humidity information associated with a first relative humidity;
2. obtaining the first relative humidity information by the data acquisition board from the first humidity sensor; and
3. determining the first particle size information based on the first relative humidity information.
11 . The unmanned aerial vehicle of claim 10 , wherein the first particle size information is determined by the formula:
log
r
(
a
w
)
=
±
[
-
ln
(
N
D
2
π
log
σ
)
2
(
log
σ
)
2
]
1
/
2
+
log
r
M
,
where r(a w ) is a first humidity-altered radius value, ND is a normalized radius-specific particle number density per unit volume value, σ is a first standard deviation, and r M is a modal radius value for the first relative humidity information.
12 . A method for measuring extinction using an unmanned aerial vehicle comprising:
a. generating, by a condensation particle detection payload operatively connected to a data acquisition board, both of which are mounted on the unmanned aerial vehicle, first particle count information associated with a first volumetric particle density at the condensation particle detection payload;
b. generating, by a first humidity sensor mounted on the unmanned aerial vehicle and operatively connected to the data acquisition board, first relative humidity information associated with a first relative humidity;
c. transmitting, from the condensation particle detection payload to the data acquisition board, the first particle count information;
d. transmitting, from the first humidity sensor to the data acquisition board, the first relative humidity information;
e. storing, in memory operatively connected to the data acquisition board, the first particle count information and the first relative humidity information;
f. determining, by the data acquisition board, first particle size information based on the first relative humidity information, wherein the first particle size information is determined by the formula:
log
r
(
a
w
)
=
±
[
-
ln
(
N
D
2
π
log
σ
)
2
(
log
σ
)
2
]
1
/
2
+
log
r
M
,
where r(a w ) is a first humidity-altered radius value, ND is a normalized radius-specific particle number density per unit volume value, σ is a first standard deviation, and r M is a modal radius value for the first relative humidity information;
g. generating, by the data acquisition board, first extinction information based on the first particle count information and the first particle size information; and
h. transmitting, by the data acquisition board to an optical system, the first extinction information.
13 . The method of claim 12 , wherein the generating step a) further comprises:
i. ingesting, by an inlet of the condensation particle detection payload, a first air sample at a first volumetric flow rate, wherein the first air sample comprises a plurality of atmospheric aerosol particles and a plurality of water vapor particles, and wherein the inlet is operatively connected to a wick of the condensation particle detection payload;
ii. cooling, by a conditioner of the condensation particle detection payload enclosing the wick, the first air sample;
iii. condensing, by the conditioner, the plurality of water vapor particles to form a plurality of liquid water particles;
iv. heating, by an initiator of the condensation particle detection payload enclosing the wick, the first air sample and the plurality of liquid water particles to supersaturate the first air sample;
v. enlarging, by a growth component of the condensation particle detection payload, the heated plurality of atmospheric aerosol particles;
vi. recycling the plurality of liquid water particles to the wick; and
vii. determining, by a detector of the condensation particle detection payload, the first particle count information associated with the first air sample based on the enlarged plurality of atmospheric aerosol particles.
14 . The method of claim 13 , wherein the first particle count information is measured between 5 nanometers and 2.5 microns.
15 . The method of claim 12 , further comprising determining, by the optical system, first transmission information over a first distance based on the first extinction information, by the steps of:
i. generating first optical depth information based on the first extinction information by the formula:
τ
(
z
1
,
z
2
)
=
∫
z
1
z
2
β
(
z
)
dz
.
where τ is the first optical depth information, β(z) is a layer volume extinction coefficient, and z is a geometric height; and
ii. generating the first transmission information based on the first optical depth information by the formula:
t
(
τ
)
=
e
-
τ
/
|
cos
θ
|
,
where t is the first transmission information, τ is the first optical depth information, and θ is a first source angle of incidence upon a parallel plane.
16 . A method for measuring extinction using an unmanned aerial vehicle comprising:
a. generating, by a condensation particle detection payload operatively connected to a data acquisition board, both of which are mounted on the unmanned aerial vehicle, first particle count information associated with a first volumetric particle density at the condensation particle detection payload;
b. generating, by a first humidity sensor mounted on the unmanned aerial vehicle and operatively connected to the data acquisition board, first relative humidity information associated with a first relative humidity;
c. transmitting, from the condensation particle detection payload to the data acquisition board, the first particle count information;
d. transmitting, from the first humidity sensor to the data acquisition board, the first relative humidity information;
e. storing, in memory operatively connected to the data acquisition board, the first particle count information and the first relative humidity information;
f. determining, by the data acquisition board, first particle size information based on the first relative humidity information;
g. generating, by the data acquisition board, first extinction information based on the first particle count information and the first particle size information, wherein the first extinction information is determined by the formula:
β
e
,
s
,
a
(
λ
)
=
∫
r
1
r
2
Q
e
,
s
,
a
(
n
,
λ
,
r
)
π
r
2
d
N
(
r
)
r
ln
10
d
(
log
r
)
dt
≈
∑
i
=
r
min
r
max
Q
e
,
s
,
a
(
n
,
λ
,
r
i
)
π
r
i
2
d
N
i
r
i
ln
10
d
(
log
r
i
)
Δ
r
i
,
where β e,s,a (λ) are first wavelength-specific normalized extinction, scattering, and absorption coefficients, Q e,s,a (n, λ, r i ) are aerosol-constituent specific extinction, scattering, and absorption efficiency, and r is a modal radius associated with the first particle size information; and
h. transmitting, by the data acquisition board to an optical system, the first extinction information.
17 . The method of claim 16 , further comprising determining, by the optical system, first transmission information over a first distance based on the first extinction information, by the steps of:
a. generating first optical depth information based on the first extinction information by the formula:
τ
(
z
1
,
z
2
)
=
∫
z
1
z
2
β
(
z
)
dz
.
where τ is the first optical depth information, β(z) is a layer volume extinction coefficient, and z is a geometric height; and
ii. generating the first transmission information based on the first optical depth information by the formula:
t
(
τ
)
=
e
-
τ
/
|
cos
θ
|
,
where t is the first transmission information, τ is the first optical depth information, and θ is a first source angle of incidence upon a parallel plane.