More Related Content Similar to AtmosphericTurbulence Similar to AtmosphericTurbulence (20) 2.
Abstract
Two Campbell Scientific sonic anemometerthermometers (CSATs) and an NRLITE net
radiometer were used to measure wind speeds in the x, y, and z directions (U, V, and W) and net
radiation from the earth and sun. During the first week of the experiment, installation and data
logging of the atmospheric sensors were done while covering the radiometer on each side and
fanning the CSATs in different directions to ensure proper operation. On the second week, data
was collected for 20 minutes and plotted against time. The average velocities in the x, y, and z
direction were then respectively found to be , , and for.05 .18− 0 ± 0 s
m
.14 .170 ± 0 s
m
.03 .090 ± 0 s
m
sensor 1, and , , and for sensor 2. The average net.1 .2− 0 ± 0 s
m
.14 .190 ± 0 s
m
.03 .110 ± 0 s
m
radiation was found to be , which was used to estimate Earth’s radiation of99.8 .3 W/m1 ± 0 2
. The mean temperature was found to be ºC for sensor 1 and ºC98 1− 3 ± 1 W
m2 4.8 .52 ± 0 4.7 .52 ± 0
for sensor 2. The covariance and correlation coefficient of the Sensible Heat Flux were
calculated to be 0.008 and respectively for Sensor 1, showing a positive correlation. For.0519 0
Sensor 2, it was found to be 0.0016 and 0.0674. The Latent Heat Flux covariance and correlation
coefficients were also respectively calculated to be 0.0029 and 0.0627 for Sensor 1, showing a
positive correlation. For Sensor 2, it was found to be 0.0021 and 0.0423. The wind velocity was
modeled with a log law profile and used to calculate the average velocity of .2647m/s0
compared to the actual value of , indicating a error. The CSATs and net.1449m/s0 2.68%8
radiometer made it possible to model the relationships between wind velocities and air
temperature with momentum and heat fluxes, which lead to a better understanding about the
effects of turbulence on atmospheric transport and surface energy balance.
1
4.
List of Tables
Table Description Page
A Mean Velocity and Temperature of Sensor 1 & 2 10
B Covariance and Correlation Coefficient of Sensible Heat Flux 15
C Covariance and Correlation Coefficient of Latent Flux 15
D Wiring Instructions for CSAT 25
E Wiring Instructions for Net Radiometer 25
F Solar Irradiation at 10AM 26
G Matlab Code 26
3
5.
List of Figures
Figure Description Page
1 Wind Speed in X, Y, Z Direction, Temperature, and Net Radiation 11
2.0 Mean Velocity/Fluctuation in XYZ Direction and Mean
Temperature/Fluctuation Plot
12
2.1 Mean Velocity and Fluctuation in X Direction Plot 12
2.2 Mean Velocity and Fluctuation in Y Direction Plot 13
2.3 Mean Velocity and Fluctuation in Z Direction Plot 13
2.4 Mean Temperature and Fluctuation Plot 14
3 Covariance of UW and WT Plot 15
4
6.
Introduction
Atmospheric turbulence is a process that mixes and churns the atmosphere and distributes
different gases and energy. When solar radiation heats the surface, the air also heats up and the
cooler air above it descends, causing even more mixing and turbulence (“atmospheric
turbulence”). This experiment was conducted to analyze the effects of turbulence on atmospheric
transport and the surface energy balance. The purpose and main objectives of this experiment is
to master installation and data logging of atmospheric sensors, data analysis with MATLAB, and
atmospheric turbulence overall. Mastering these elements is important for a deeper
understanding how radiation, convection, heat flux, and wind velocity are related and how they
affect atmospheric turbulence. This knowledge of turbulence and how gases like emissions are
dispersed and mixed into the atmosphere can help environmental engineers figure out ways to
mitigate human impact on the environment.
The experimental approach was to use two Campbell Scientific sonic
anemometerthermometers (CSATs) to measure wind speed and temperature at two different
heights using the doppler effect. An NRLITE net radiometer was also used to measure net
radiation by performing an algebraic sum of upwelling and downwelling shortwave and
longwave radiation from the earth and sun. The equipment was set up in a sunny, undisturbed
area, and the data collected was analyzed to determine the convective heat flux. Relating wind
speeds with height resulted in a heat transfer profile, which helped determine the distribution of
radiative solar energy.
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7.
Theory
Both solar energy and gravitational energy are the fundamental sources of energy for the
Earth’s climate system. The energy that drives the climate system comes from the Sun. When the
Sun’s energy reaches the Earth, it is partially absorbed in different parts of the climate system.
The Earth’s net radiation is the balance between the incoming and outgoing energy at the Earth’s
surface and atmosphere. Since the Earth’s surface is not a perfect black body surface, it will
inevitably result in the Earth reflecting the radiation back. The net radiation, , can also beRnet
determined using a net radiometer, which performs an algebraic sum of the upwelling and
downwelling short and longwave radiation. The energy balance can be described in the following
form:
Rnet = Rsolar + REarth (1)
The Earth’s energy balance can also be written as the sum of three energy sink components:
conduction heat flux to the ground (G), latent heat flux (LH), and sensible heat flux (SH):
H HRnet = G + L + S (2)
When speaking of energy in the atmosphere, there are two types of heat, latent and
sensible heat. Sensible heat is the energy required to change the temperature of a substance with
no phase change. The sensible heat flux can be found from:
H c W TS = ρa p ′ ′ (3)
where is the density of air, is the specific heat of air, is the temperature fluctuation, andρa cp T′
is the wind speed fluctuation. The latent heat can be found using:W′
HL = U W′ ′ (4)
The temperature and wind speed fluctuation can be calculated using these equations:
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8.
W = W + W′ (5)
T = T + T′ (6)
where and are the average of W and T respectively over the time period. In addition to theW T
fluctuations, the covariance is also calculated, which measures how two random variables change
together. If the greater value of one variable mainly correspond with the greater values of the
other variable, and the same holds for the smaller values, the covariance is positive, and vice
versa for when covariance is negative.
Turbulent flow create eddies that carry heat, momentum, and other forms of energies. All
atmospheric entities display short term fluctuations about a mean value, which can be separated
using the Reynolds Decomposition:
S = S + S′ (7)
Understanding atmospheric turbulence is important to know how the atmosphere is
affected by wind and temperature. Turbulence in the atmosphere mixes and churns the
atmosphere and causes water vapour, smoke, and other substance such as energy, to become
distributed both vertically and horizontally. Solar radiation also plays a role as it heat the surface,
and the air above it becomes warmer and more buoyant, and cooler, denser air descends to
displace it. At night time, this changes as the surface cools rapidly resulting in the wind speed
and gustiness to both decrease sharply. In analyzing atmospheric turbulence, velocity profiles are
calculated to visualize the wind speed using the following equation:
ln( )U
U* = 1
K
z
z0
+ ϕ (8)
where U is the average horizontal velocity, , is the friction velocity, k is taken to equal 0.4U*
and is known as the von Karman constraint, z is the height above the surface, and is thez0
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9.
roughness length, and is the correlation factor for nonneutral conditions. can be foundϕ U*
using the equation:
(uw) vw) ]u* = [ ′ ′
2
+ ( ′ ′
2 1/4
(9)
where U’ and V’ are the turbulent fluctuations of the horizontal velocities in the x and y
directions, respectively. As the turbulent fluctuations increase, the friction velocity will also
increase, ultimately resulting in the increase of atmospheric turbulence and eddies.
Experimental Procedure
Week 1 Procedure
In order to take the measurements of the wind speed and temperature, two CSAT are used
at two different heights. First by locating the respective CSAT anemometer head with the CSAT
electronic box, the entire equipment was moved into a sunny area in the EBU II quad where the
two CSATs were mounted as level to the ground as possible using the bubble level indicator.
The anemometers were both pointed towards the West direction of campus. The CSAT with the
SDM address 3 was mounted in the lower position, 1 meter above the ground, while the CSAT
with the SDM address 4 was mounted in the upper position. The wire from the anemometer head
to the “Transducer head” port of the electronic box was connected, then the SDM and power
wires to the +12V SDM port was connected.
After the CSAT and electronic box were properly arranged and connected, the SDM and
power wires were connected to the SDM ports following the wiring instructions in Table (3).
Then the wires from the net radiometer was connected to the differential ports following the
wiring instructions on Table (4). After the datalogger was connected with the battery. Then in
order to begin data collection, the datalogger was connected to a laptop using the RS232 and
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10.
USB connection wire. Logging into the Loggernet program, under Main, the Connect was
pressed; then CR1000_mae126a was highlighted in the Stations Menu and then connect was
pressed again. After successful connection the clock on the datalogger was set, then the Send
button was pressed to begin the data collecting. The data was checked by selecting ‘Table 1’ in
the table monitor passive monitoring block. The datalogger sampled at a frequency of 10Hz,
which then the data could be visualized by clicking on graph 1, graph 2, and graph 3.
In order to check if the instruments were working properly, air was blown into the
CSATs to see whether the graphs on the computer changed. In order to check if the net
radiometer was working, the upper side of the radiometer was covered using our hand and then
the lower side of the radiometer was then covered using our hand again and noted how the
readings were changing. Lastly, in order to download the data, the collect now button was
pressed where the data was downloaded and transferred onto the computer.
Week 2 Procedure
For week 2, the same procedures as in Week 1 was used in setting up the instruments. For
Week 2, however, the measurements were taken not in the EBU quad, but in an open area in
Warren Court where a good amount of sunlight was shining. In order to ensure accurate data to
be measured, the instruments was placed in a region undisturbed by traffic with the lab
teammates preventing anyone from getting near the instruments.
In collecting the data, the same procedures were used as from Week 1, with the only
difference being that the data was collected for 20 minutes at 10 Hz frequency, which resulted in
about 12,000 samples. In downloading the data, the same procedures were used as in Week 1.
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11.
After obtaining the data, MATLAB scripts were written to create plots of different
comparisons and trends. MATLAB analysis was done by writing a MATLAB code to plot the
entire time series of U, V , W , T , compute mean Rnet, U, V , W , plot the fluctuations U ’, V ’,
W ’, T ’, and plot the time series of U ′ W ′ and W ′ T ′.
Week 3 Procedure
In the last week of lab, the group came in to get the MATLAB scripts and analysis
checked by the TA.
Data and Results
For the first week of the experiment, the sensors are setup to test out the functionality and
the significance of the measurement. To test the change of wind speed in different directions, we
blow on CSATs and observe significant changes on the graph generated by computer. This
strategy is used to calibrate the functionality and coordinations of CSATs. To test if the net
radiometer works, we covered the top part of the net radiometer and then the bottom part. The
value of the net radiometer drops when being covered on the top because less radiation is
received on the top part, and net radiation value raises when being covered on the bottom
because less radiation is received on the bottom part.
The original data collected on week 2 (February 10, 2016) consists a total of 12346 sets
of data between 10:10AM and 10:30AM. Using Matlab, the following values with their standard
deviations are computed and plotted against one another (See Table F in Appendix for Code)
Mean Velocity in
xdirection (m/s)
Mean Velocity in
ydirection (m/s)
Mean Velocity in
zdirection (m/s)
Mean Temperature
(Degree C)
Sensor 1 0.0465 .1838± 0 0.1372 .1740± 0 0.0292 .0855± 0 24.8418 .5398± 0
Sensor 2 0.0946 .2166± 0 0.1387 .1893± 0 0.0257 .1078± 0 24.6902 .4533± 0
10
12.
Table A. Mean Velocity and Temperature of Sensor 1 & 2
Figure 1. Wind Speed in X, Y, Z Direction, Temperature, and Net Radiation
The data from two sensors are relatively close to each other, where U, V, W represents
wind speed in X, Y, Z directions. On the day of the experiment, the wind was very still on the
field, resulting in very little data oscillations in all directions (between 1 m/s and 1 m/s). The
temperature measurement of the was around 25°C with less than 2° oscillation range, this was
due to the convection of wind on the sensor. The mean net radiation was 99.82021 1.09581 ± 3
.W/m2
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16.
Sensor Covariance Correlation Coefficient
1 0.008 0.0519
2 0.0016 0.0674
Table B. Covariance and Correlation Coefficient of Sensible Heat Flux, W T′ ′
Sensor Covariance Correlation Coefficient
1 0.0029 0.0627
2 0.0021 0.0423
Table C. Covariance and Correlation Coefficient of Latent Flux, uw′ ′
The values of the covariance and correlation were all relatively small. Sensor 2 displayed
a negative value for the covariance of as well as the correlation coefficient of . Auw′ ′ uw′ ′
negative correlation value shows that as U velocity increases, the W velocity component
decreases. While positive correlations show that the particular parameter increases with the
other. For example, since the correlation for sensible heat flux was positive, as temperature
increases, so does the Wdirection velocity.
In finding the velocity profile in the log layer, Equation (8) is utilized. First, is foundU
by taking the square root of the sum of the squares of U and V for each sensor; the value of isU1
0.1449 m/s and is 0.1679 m/s. Using a k value of 0.4 and a value of 10 in Equation (9),U2 /zz 0
U1* is found to be 0.0460 m/s and U2* is found to be 0.0706 m/s. Now using Equation (8), the
estimated value of is 0.2647 m/s and estimated value of is 0.4065 m/s. The averageU1:est U2:est
velocity of the first sensor has an error of 82.68% and the second sensor has an error of 142.11%.
We believe this error comes from the fact that the velocity of the wind in the zdirection was not
15
17.
significantly smaller than the velocity in the xdirection, so it affected the estimated value much
more than desired. At higher horizontal velocities in the x and ydirection, the velocity in the
zdirection would not have affected the result as much, but since the wind was very still during
the day of our experiment, the estimation was greatly skewed.
Discussion and Error Analysis
The experient looked at the atmospheric turbulence in the boundary layer over the Earth’s
surface. The air motion in the boundary layer is usually in a state of turbulent motion, which can
be described as smallscale, irregular air motions characterized by winds that vary in speed and
direction. Due to these constant turbulent motions, air is almost always never still. Air is always
moving and varying in speed with people walking, temperature gradient, pressure gradient, and
even people breathing can cause the air to move, within a lab for example. As for the air outside
the lab in an open area, air can be turbulent for different reasons. The first possibility is
convection. Since the Earth’s atmosphere may have different temperature gradient, if the lower
part of an atmosphere heats up for example, the atmosphere can become convectively unstable
ultimately pushing the warmer region upward, causing wind to occur. Wind can also move in
directions where there is a pressure drop.
In measuring the different velocities and temperature of the wind, the CSATs were
utilized. To check if the CSATs were functioning properly, air was blown into the CSATs to see
how the readings changed. First the anemometer was seen to be constantly fluctuating and
nonzero which indicated constant moving air, even inside the lab as mentioned earlier. When air
was blown into the sensors, the readings showed spikes in wind speed as well as slight increase
in temperature, as expected. Since the blowing of wind from the mouth resulted in a velocity
16
18.
higher than that of the ambient air, since there was not much wind at the time, a peak in velocity
was expected. Slight increase in temperature is also expected since the air blown from a person
can be warmer than the temperature of ambient air. Next, the top and bottom of the radiometer
was covered to see how the readings changed. By covering the top of the radiometer, the
irradiation readings dropped dramatically, indicating that the majority of radiation that the sensor
was reading came from above, or from direct contact with the Sun. Since covering the
radiometer decreases the amount of radiation directly hitting the sensor, seeing a decrease in
irradiation was expected. When the bottom of the radiometer was covered, the readings also
showed a decrease in irradiation, but not as significant as covering the top. This indicated that the
bottom of the sensor was not receiving as much radiation from the Sun. While the majority of the
radiation hitting the top of the sensor may have come directly from the Sun, the radiation hitting
the bottom side of the sensor came from the radiation bouncing off the ground, which explains
why the bottom of the sensor received less radiation. Performing these simple tasks helped to
understand how sensitive the sensors were and also to understand the physical meanings of the
data.
In Week 2 of the experiment, the equipment was taken in a more open area out in Warren
Court where there was plenty of direct sunlight, but at the same time more people walking by as
well. The sensors were faced towards the West side of campus, in the likely direction of the
wind. This is to setup the coordinate of the mean wind because we want the majority of the wind
velocity in x direction. This would results in significant difference between the x and y direction
data, which helps to distinguish changes in the wind speed during the data collection process.
The sensors were able to measure in all three coordinates, x, y, and z direction, as seen in Table
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19.
(1). By plotting the data obtained from week 2, it can be noted that the wind velocity in the
ydirection had the largest mean velocity of 0.1372m/s & 0.1387m/s for Sensor 1 & 2
respectively, while the zdirection had the smallest mean velocity of 0.0292m/s & 0.0257m/s for
sensor 1 & 2 respectively. This was unexpected since the ydirection of the sensors were facing
North to South and we expected most of the wind to blow West to East (from the coast inland).
However, the zdirection was measuring wind speed that was going up and down, which did not
have as big of a change in wind velocity, since wind does not blow very much vertically. If mean
velocity in the zdirection is not zero, that means zdirection wind velocity will be part of the
calculation for mean wind speed, which increases the magnitude of the estimated mean wind
speed value. As for the wind temperature, there was very minimal change in temperature
throughout time for the two sensors, with mean values of 24.8418°C and 24.6902°C for Sensor 1
and 2 respectively, which were very close to one another. The irradiance, however, displayed a
varying fluctuation throughout the duration of the experiment as seen in Figure (1). The varying
readings of irradiance probably occurred due to several reasons. One possibility could have been
due to the movement of the clouds in the sky, which would cover the Sunlight more and less
throughout the experiment. The clouds covering the Sunlight would exhibit similar readings as
with covering the radiometer with paper as in Week 1. Another possibility could have been from
the varying wind speed as well as the temperature of the wind, which plays a role in the amount
of radiation the sensor reads. This correlation with temperature, wind speed, and irradiation will
be covered further on this report. As seen in Figure 1, U, V, W, and T have minute oscillations
with an occasional spike over the 20 minute interval, resulting in a relatively constant trend for
wind speeds in each direction. Because the velocity components were not constant in magnitude
18
21.
very sunny and hot day. To estimate, we took the irradiation at 10AM of the most recent seven
days, according to the website, and averaged the sunny days. Out of the seven days, February 18
had a significantly lower solar irradiation. It was rainy overnight and in the morning so it is safe
to assume that it was a cloudy around 10AM; therefore, we can take this day’s value out when
calculating the estimated solar irradiation (see Table F in the appendix). The mean and standard
deviation gives the average solar radiation at 10AM by EBUII.
98 1Rsolar = 5 ± 1 W
m2
98 1Rearth = Rnet − Rsolar = − 3 ± 1 W
m2
Using Equations (3) and (4), the fluctuations of u’, v’, w’, and T’ were plotted against
time in Figure (2.0)(2.4) and analyzed. As seen in the Figures, the mean velocity in the
ydirection has the biggest fluctuations while the fluctuations in the zdirection was the least. The
spikes for all three differed at times, but some of larger spikes were at the same time. These
larger spikes were most likely due to people walking by at the time, or some of the bigger ones
were from people on bikes or skateboards. This is expected since these riders carry with them
high tailwind velocity, which are larger than people who may be just walking. The mean
temperature had very small fluctuation, which is also expected since the data was obtained
within a 20 minute time period and at a time of the day when the temperature was not drastically
increasing or decreasing.
Next using the data and calculations found, the covariance and correlation of the different
parameters were calculated and measured. Plots were created with u’ against w’ as well as w’
against T’, which gives insight on the relationship each had against another see Figure (3). The
small correlation coefficient values of W and T (0.0627 for Sensor 1 and 0.0423 for Sensor 2)
20
23.
Conclusion
The CSATs at two different heights and radiometer were used to obtain mean x, y, and z
velocities (U, V, and W), mean temperature, and mean irradiation. This data was used to
calculate the average net radiation as . From this value, the estimate of the net99.8 .3 W/m1 ± 0 2
radiation on Earth was calculated to be .98 1− 3 ± 1 W
m2
From mean velocity and temperature data plots, a different relationship between
temperature and velocity in the z direction(w) was observed in each sensor. The velocity and
temperature fluctuations were used to calculate a covariance of 0.0029 and 0.0021 for sensor 1
and 2 respectively and correlation coefficients of 0.0627 and 0.0423, which implies a positive
relationship in the top sensor and negative correlation on the bottom. The mean velocity plots
also showed a positive correlation between velocities in the x and z direction (U and W), which
was proved with positive covariance values of 0.008 and 0.0016 and positive correlation
coefficients of 0.0519 and 0.0674 for sensors 1 and 2 respectively.
Using measurements from the CSATs, the average velocity of Sensor 1 was calculated to
be 0.2647 m/s compared to the actual wind speed of 0.1449 m/s with a 82.68% discrepancy,
while the average velocity of Sensor 2 was calculated to be 0.4065 m/s with the actual wind
speed 0.1679 m/s.
22
26.
W2s=std(W2);
T1s=std(T1);
T2s=std(T2);
Rs=std(Rnet);
%%Part1
figure(1)
subplot(5,1,1)
hold on
plot(Time,Sonic1(:,1),'r') % u [ms1]
plot(Time,Sonic2(:,1),'b') % u [ms1]
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
title('Wind Speed in X Direction')
legend('Sensor 1', 'Sensor 2')
xlabel('Time')
ylabel('Velocity (m/s)')
subplot(5,1,2)
hold on
plot(Time,Sonic1(:,2),'r') % v [ms1]
plot(Time,Sonic2(:,2),'b') % v [ms1]
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
title('Wind Speed in Y Direction')
legend('Sensor 1', 'Sensor 2')
xlabel('Time')
ylabel('Velocity (m/s)')
subplot(5,1,3)
hold on
plot(Time,Sonic1(:,3),'r') % w [ms1]
plot(Time,Sonic2(:,3),'b') % w [ms1]
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
title('Wind Speed in Z Direction')
legend('Sensor 1', 'Sensor 2')
xlabel('Time')
ylabel('Velocity (m/s)')
subplot(5,1,4)
hold on
plot(Time,Sonic1(:,4),'r') % T [C]
plot(Time,Sonic2(:,4),'b') % T [C]
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
title('Temperature Measurement')
legend('Sensor 1', 'Sensor 2')
xlabel('Time')
25
27.
ylabel('Temperature (Degree C)')
subplot(5,1,5)
plot(Time,Rnet) % [Wm2]
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
title('Net Radiation')
xlabel('Time')
ylabel('Radiation (W/m^2)')
%%Part2
U1m=mean(Sonic1(:,1));
V1m=mean(Sonic1(:,2));
W1m=mean(Sonic1(:,3));
T1m=mean(Sonic1(:,4));
U2m=mean(Sonic2(:,1));
V2m=mean(Sonic2(:,2));
W2m=mean(Sonic2(:,3));
T2m=mean(Sonic2(:,4));
u1=Sonic1(:,1)U1m;
v1=Sonic1(:,2)V1m;
w1=Sonic1(:,3)W1m;
t1=Sonic1(:,4)T1m;
u2=Sonic2(:,1)U2m;
v2=Sonic2(:,2)V2m;
w2=Sonic2(:,3)W2m;
t2=Sonic2(:,4)T2m;
figure(2)
subplot(4,1,1)
hold on
plot(Time, u1,'k')
plot(Time, U1m*ones(size(Time)),'k')
plot(Time, u2,'r')
plot(Time, U2m*ones(size(Time)),'r')
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
title('Mean Velocity and Fluctuation in X Direction')
legend('Sensor 1 Fluctuation', 'Sensor 1 Mean', 'Sensor 2 Fluctuation', 'Sensor 2 Mean')
xlabel('Time')
ylabel('Fluctuation (m/s)')
subplot(4,1,2)
hold on
plot(Time, v1,'k')
plot(Time, V1m*ones(size(Time)),'k')
plot(Time, v2,'r')
plot(Time, V2m*ones(size(Time)),'r')
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
title('Mean Velocity and Fluctuation in Y Direction')
legend('Sensor 1 Fluctuation', 'Sensor 1 Mean', 'Sensor 2 Fluctuation', 'Sensor 2 Mean')
xlabel('Time')
ylabel('Fluctuation (m/s)')
26
28.
subplot(4,1,3)
hold on
plot(Time, w1,'k')
plot(Time, W1m*ones(size(Time)),'k')
plot(Time, w2,'r')
plot(Time, W2m*ones(size(Time)),'r')
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
title('Mean Velocity and Fluctuation in Z Direction')
legend('Sensor 1 Fluctuation', 'Sensor 1 Mean', 'Sensor 2 Fluctuation', 'Sensor 2 Mean')
xlabel('Time')
ylabel('Fluctuation (m/s)')
subplot(4,1,4)
hold on
plot(Time, t1,'k')
plot(Time, T1m*ones(size(Time)),'k')
plot(Time, t2,'r')
plot(Time, T2m*ones(size(Time)),'r')
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
title('Mean Temperature and Fluctuation')
legend('Sensor 1 Fluctuation', 'Sensor 1 Mean', 'Sensor 2 Fluctuation', 'Sensor 2 Mean')
xlabel('Time')
ylabel('Fluctuation (Degree C)')
%%Part3
uw1=u1.*w1;
uw2=u2.*w2;
wt1=w1.*t1;
wt2=w2.*t2;
a=cov(U1,W1);
b=cov(U2,W2);
c=cov(W1,T1);
d=cov(W2,T2);
e=corrcoef(U1,W1);
f=corrcoef(U2,W2);
g=corrcoef(W1,T1);
h=corrcoef(W2,T2);
UWc1=a(1,2);
UWc2=b(1,2);
WTc1=c(1,2);
WTc2=d(1,2);
UWcc1=e(1,2);
UWcc2=f(1,2);
WTcc1=g(1,2);
WTcc2=h(1,2);
figure(3)
subplot(2,1,1)
hold on
plot(Time,uw1,'r') % u [ms1]
plot(Time,uw2,'b') % u [ms1]
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
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29.
title('Fluctuation of U and W')
legend('Sensor 1', 'Sensor 2')
xlabel('Time')
ylabel('U Fluctuation * W Fluctuation')
subplot(2,1,2)
hold on
plot(Time,wt1,'r') % u [ms1]
plot(Time,wt2,'b') % u [ms1]
set(gca, 'XTick', Time(1:3000:end))
set(gca, 'XTickLabel', datestr(Time(1:3000:end)))
title('Fluctuation of W and T')
legend('Sensor 1', 'Sensor 2')
xlabel('Time')
ylabel('W Fluctuation * T Fluctuation')
%%Part5
U1bar=sqrt(U1m^2+V1m^2);
U1star=((mean(u1.*w1))^2+(mean(v1.*w1))^2)^(1/4);
U1est=log(10)*U1star/0.4;
U2bar=sqrt(U2m^2+V2m^2);
U2star=((mean(u2.*w2))^2+(mean(v2.*w2))^2)^(1/4);
U2est=log(10)*U2star/0.4;
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