The Effects of Turbulence on Atmospheric Transport and Surface Energy Balance

Presented to the University of California, San Diego

Department of Mechanical and Aerospace Engineering MAE 126A

February 23, 2016

Prepared by

Justin Bosch Sik Cho Gene Lee

Robert Zhang

Group EE2 Wednesday AM

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 sm .14 .170 ± 0 s

m .03 .090 ± 0 sm

sensor 1, and , , and for sensor 2. The average net.1 .2− 0 ± 0 sm .14 .190 ± 0 s

m .03 .110 ± 0 sm

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 Wm2 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

Table of Contents

List of Tables……………………………………………………………………………………... 3

List of Figures……………………………………………………………………………………..4

Introduction………………………………………………………………………………………..5

Theory……………………………………………………………………………………………..6

Experimental Procedure………………………………………………………………………...... 8

Data and Results…………………………………………………………………………………10

Discussion and Error Analysis……………………………………………………………...........16

Conclusion……………………………………………………………………………………..... 22

References……………………………………………………………………………………......23

Appendices and Raw Data……………………………………………………………………….24

2

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

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

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.

5

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 = UW′ ′ (4)

The temperature and wind speed fluctuation can be calculated using these equations:

6

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( )UU* = 1

Kzz0+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

7

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

8

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.

9

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

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

11

Figure 2.0 Mean Velocity/Fluctuation in XYZ Direction and Mean Temperature/Fluctuation Plot

Figure 2.1 Mean Velocity and Fluctuation in X Direction Plot

The sensor was set­up facing the west, and the negative mean velocity indicates that the

overall x­directional wind between 10:10AM and 10:30AM was going to the west. The

fluctuation of the data shows that the wind velocity in the x­direction was constantly changing.

Figure 2.2 Mean Velocity and Fluctuation in Y Direction Plot

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The figure above shows the plot for mean velocity in the y­direction vs fluctuation. The

figure display some big peaks at certain times and is generally fluctuating throughout the whole

duration of the experiment.

Figure 2.3 Mean Velocity and Fluctuation in z Direction Plot

Z­direction is the vertical direction of the wind velocity measurement. Because wind

doesn’t normally blow in the vertical direction, z­direction mean velocity is the closest to zero

and with the least fluctuation, compared to the x and y direction fluctuations.

Figure 2.4 Mean Temperature and Fluctuation Plot

13

The temperature throughout the experiment was between 23 and 27°C with a mean value

a little less than 25°C. The measurement and the fluctuation of the measurement of both sensors

are relatively close to one another since temperature is relatively constant.

Figure 3. Covariance of UW and WT Plot

The figure above show that both sensor have similar correlation of fluctuations, this

might be because of the similarities of data reading from both sensors. The correlation of

fluctuations between U and W is how much x­direction wind and z­direction wind change

together. The plot spikes indicates that around 10:11AM and 10:24AM, there is a significant

positive correlation of wind fluctuations, and around 10:13AM, there is a significant negative

correlation. However, the majority of the data shows little correlation, and the range is only

between ­0.2 and 0.2. The correlation of fluctuations between z­direction and temperature is also

shown in the figure above. The most significant correlation is around 10:13AM where the

z­directional wind and temperature spike together. When wind velocity goes up, it can be

considered forced convection on the sensor; therefore, it has a positive correlation.

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Sensor Covariance Correlation Coefficient

1 0.008 0.0519

2 0.0016 0.0674 Table B. Covariance and Correlation Coefficient of Sensible Heat Flux, WT′ ′

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

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

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

17

(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

or direction and fluctuated between positive and negative values, it is implied that 3­dimensional

eddies and thus turbulent flow formed around the CSATs.

With the data, the mean values of the velocity, temperature, and radiation were

calculated. Errors of velocities come from the instrumental limitations of the CSAT (+/­ 0.08 m/s

in x and y direction & +/­ 0.04 m/s in z direction for each data point). The standard deviation

shows the fluctuation of all 12,346 data points over the duration of the data collection.

Instrumental limitations δlim = δ

√N

CSAT #1* (1.51% error).0465 .0007U lim = U ± 0.08

√12346 sm = − 0 ± 0 s

m (0.51% error).1372 .0007V lim = V ± 0.08

√12346 sm = 0 ± 0 s

m (1.37% error).0292 .0004W lim = W ± 0.04

√12346 sm = 0 ± 0 s

m

CSAT #2* (0.74% error).0946 .0007U lim = U ± 0.08

√12346 sm = − 0 ± 0 s

m (0.50% error).1387 .0007V lim = V ± 0.08

√12346 sm = 0 ± 0 s

m (1.56% error).0257 .0004W lim = W ± 0.04

√12346 sm = 0 ± 0 s

m *subscript “lim” means “instrumental limitation”*

4.8 .5ºC 4.7 .5ºCT 1 = 2 ± 0 | |T 2 = 2 ± 0

Errors of net radiation also comes from the instrumental limitations (+/­ 30 W/m2). The standard

deviation again shows the fluctuation of all the data points over the duration of the data

collecting.

.27 99.8 .3 (0.15% error)δlim = 30√12346

Wm2 = 0 W

m2 ⇒ Rnet:lim = 1 ± 0 Wm2

1.0958 00 0σ = 3 Wm2 ⇒ Rnet:sd = 2 ± 3 W

m2

Unfortunately, we did not record the solar irradiation at the exact time and day of the lab,

February 10, using the website provided in the lab1. We know the day we collected data was a

19

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 Wm2

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

show that the correlation between W and T is far from a linear relationship, especially since the

sign for each sensor is different and they were only 0.7 meters away from each other in the z

direction. The physical meaning of the small values of covariance between T and W, which were

0.0039 for sensor 1 and ­ 0.0021 for sensor 2, shows that changes in temperature is not closely

related to changes in z­direction wind speed. The covariance W and T is a measurement to show

how much the series plot of w’ and T’ change together. The correlation coefficient for U and W

was 0.0519 and 0.0674 for sensors 1 and 2 respectively, which both imply a very weak positive

relationship.

The resolution of the CSATs in the x and y direction of velocity is 0.0001 m/s; the

resolution in the z direction of velocity is 0.0005 m/s. The net radiometer resolution when

measuring radiation is 0.1 W/m2. Since the resolutions are significantly smaller than the actual

measurements of velocity and radiation, we can conclude that these instruments operate at high

precision. Also, since thousands of data points were taken, the effect of error would also be

decreased.

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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 Wm2

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

References

1. Lave, Matthew. UCSD DEMROES Weather Monitoring Stations. Solar Resource

Assessment. University of California, San Diego. http://solar.ucsd.edu/demroes/

2. "Atmospheric Turbulence". Encyclopædia Britannica. Encyclopædia Britannica Online.

Encyclopædia Britannica Inc., 2016. Web. 20 Feb. 2016

http://www.britannica.com/science/atmospheric­turbulence.

3. Kleissl, J., Garai, A. “Atmospheric Turbulence Measurement Laboratory Procedures,”

UCSD Department of Mechanical and Aerospace Engineering, Feb 2016.

4. Campbell Scientific Inc. NR­LITE Net Radiometer: Instruction Manual. Copyright

1998­2010.

5. Campbell Scientific Inc. CSAT3 Three Dimensional Anemometer: Instruction Manual.

Copyright 1998­2010.

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Appendices and Raw Data

Table D. Wiring Instructions for CSAT

Table E. Wiring Instructions for Net Radiometer

Table F. Solar Irradiation at 10AM (W/m2)

2/16/16 2/17/16 2/18/16 2/19/16 2/20/16 2/21/16 2/22/16

598.2 586.7 94 594.7 587.1 605.8 616.8

Table G. Matlab Code %%Part0 U1=Sonic1(:,1); U2=Sonic2(:,1); V1=Sonic1(:,2); V2=Sonic2(:,2); W1=Sonic1(:,3); W2=Sonic2(:,3); T1=Sonic1(:,4); T2=Sonic2(:,4); Rm=mean(Rnet); U1s=std(U1); U2s=std(U2); V1s=std(V1); V2s=std(V2); W1s=std(W1);

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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')

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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)')

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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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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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