Sensit Company
RR
Instrument
Calibration Constants (Lab & Field)
Simplified
field data processing
Processing Sensit Field Data
Introduction
The basic field saltation data site is comprised of a meteorological instrument tower, anemometers, sand catcher (figures 1,2), and the Sensit wind eroding mass flux sensor. This paper is intended to provide a brief background and suggested methods of processing Sensit field data.
Erosion monitoring sand catchers should be checked daily, samples collected, weighted and collection time recorded. This data is necessary as a total mass reference for processing Sensit data collected for an erosion event. Accurate catcher collection mass, data and time are very important values.
Sand Catchers
The BSNE catcher
(figure 1) is designed and produced by Dr. W. Fryrear of
The Cox Sand Catcher
(figure 2) is designed and produced by Bill Cox of Bishop,
Figure 1a - USDA (BSNE) Sand Catcher
Figure 1b - USDA Sand Catcher Model BSNE
Figure 2a - Cox Sand Catcher (CSC)
Figure 2b - Cox Sand Catcher (CSC)
Response
Threshold velocity is an influential term in most wind erosion equations and currently can only be directly determined by the Sensit eroding mass flux sensor.
Prior to the advent of the Sensit, threshold velocity was
difficult to determine. Threshold
changes dramatically with changing soil conditions. Changing crust conditions effect threshold
velocity and may be determined with Sensit™ data. Figure 3 displays the
high-resolution Sensit data taken at
Figure
3 - Response (Sensit-5cm-20cm-50cm)
Figure 4 - Response (Sensit, U*)
Threshold velocity can be determined when the shear stress[1] of the wind (U*) is compared to the Sensit' response data as shown in figure 4. The upper trace is U*, the lower is the Sensit response. The importance of the threshold velocity is the starting point or baseline of wind erosion. Observing the data of Figure 4, a horizontal line may be drawn on the U* trace above which Sensit response occurs. This identifies U*. A comparison between Sensit data and simple raw wind speed will not provide a consistent level where movement occurs.
The Sensit does not respond to suspended fine dust[2]. It responds to larger saltating[3] particles. It is important to note that fine dust[4] adhere to large particles vary tightly through valence bonding of water molecules. Kinetic energy of saltating particles is required to literally knock dust free. Therefore, by measuring saltation, we can assume dust is being produced. Because of this adhesion, dust particles do not begin movement at low friction velocities until the kinetic energy of saltating particles releases them.
Background
The Sensit wind eroding mass sensor is the successor of
early instrument designs for wind tunnel basic research studies at the NOAA[5]
laboratory located at
The first wind tunnel instrument was a vertically oriented array of ten flat rectangular piezoelectric sensors and was used for the investigation of horizontal momentum flux [Gillette and Stockton, 1986]. These were the first exploratory data.
After the prototype wind tunnel sensors were constructed, test results were encouraging. The USDA funded SBIR Phase I and Phase II awards making it possible to construct a laboratory drop tube test apparatus and perform several field tests. The drop tube provided control of the particle size, speed and rate. Results clearly showed excellent linearity to kinetic energy.
Drop Tube Test Results
Laboratory data were collected using a calibration apparatus referred to as the "drop tube" to determine the sensors response and limitations. The drop tube apparatus provides a uniform source of particle impacts without aerodynamic complications found within wind tunnel profiles. It also permits confidence of known size, shape, density and uniform particle velocity.
Field data recorded from actual erosion events was obtained by adding the Sensit instrument to operating field meteorological sites. Specially constructed multi-level kinetic energy sensors were produced to provide vertical profile information. Five sensors placed at heights of 2, 5, 10, 20 and 50cm were placed on a single one-inch diameter stainless steel mounting post.
The dynamic range of the electronics determines maximum data parameters. This is because the minimum measurement capability is determined by the ability of the particle to impact the sensor surface by overcoming its coefficient of drag. In the case of the drop tube tests, these electronic maximums were set low to obtain the highest possible data resolution for the very short sampling times of one second used in the tests.
Figure 5 - Drop Tube Apparatus
Sensor – Theory of operation
The charge portion of the energy within the crystal can be roughly expressed as:
Q = C * V
where
Q charge in coulombs.
C capacitance in farads.
V the voltage developed across the crystal.
conversely
Q = I * t
where
I current developed over time (t)
therefore
The charge developed is a representative portion of the energy instantaneously imparted to the crystal by the impacting particle.
The crystal is a damped harmonic oscillator, which has this basic equation of
motion:
X(t) = e-(fr)t A cos(fd t - θ)
where
X(t) displacement.
d damping resonance of crystal.
θ phase angle.
A constant of integration.
fr natural resonant frequency.
fd damped resonant frequency
The circuit used to measure this charge integrates the area of both alternations of the complex damped waveform from every impact. When the output of the integrator reaches a predetermined voltage, the integrator is reset. This reset is stretched to become the output pulse or data produced by the instrument.
Each output pulse of the instrument represents:
⌠t
KE = │ 1/2
m Vp2 dt
⌡
where
KE One kinetic energy instrument data unit.
Vp Particle velocity.
m Mass of each particle.
t Time to accumulate one data unit.
Instrument Calibration Constants (Lab & Field)
Two calibration constants common to the sensor can be considered. One produced by the laboratory drop tube and the other derived from field data can be called the field calibration constant. Although the filed calibration constant is only valid for the data set used to derive the value. Both are used to convert the kinetic energy response to kinetic energy.
The field calibration constant changes with unpredictable natural variables. It also has the capability of allowing the derivation of a particle velocity estimation for every data point. This is a complicated data processing task.
The lab cal (drop tube) involves known measurements of mass, velocity and kinetic energy and does not relate well to field data. It is only useful as a repeatable reference for comparing relative sensitivity during production. After many years of production, this comparison is no longer performed.
Laboratory Drop Tube Cal
The laboratory cal (KL) is accomplished using the laboratory drop tube apparatus. This lab cal (Kl) converts the sensor response (KE) and particle velocity (Vp) to units of kinetic energy using a known mass (m).
KL = m / 2 ∑ [ KE / Vp2 ]
where
m catcher mass
KE Sensit raw response per sampling period
Vp particle velocity
Field Cal
The simplified field cal (KF) relates the total sensor response to total mass allowing the Sensit to provide a representation of estimated mass flux. Most Sensit users prefer this simple relationship because empirical tests conducted by the United States Department of Agriculture (figure 9a), Great Basin Air Pollution Control District (figure 9b) and others consistently demonstrate a linear relationship between Sensit response to catcher mass. The mechanism responsible for this correlation is not known. The field cal (Kr) assumes the Sensit response is proportional to saltating mass flux for specific active area and height of the sensor.
Figure 9a – Sensit vs. Weighing Catcher Mass
Figure 9b displays the linear relationship of several Sensit responses vs. the mass caught by the Cox Sand Catcher (CSC, figure 9b). Figure 9c displays good correlation between the BSNE and Cox Sand Catchers.
Figure 9b – Sensit Response vs Cox Sand Catcher[6]
Figure 9c – Cox Sand Catcher vs BSNE
Simplified field data processing
KF = m / ∑[KE]
where:
m Catcher mass
KE Sensit raw response per sampling period
Process Sensit data to estimate mass flux per data point as
m’ = KF KE (per data point)
Figure 10 depicts a linear relationship between calculated mass and U*. This data is from a field of fairly uniform and narrow size distribution. It is also possible to use this graphical form of data to estimate threshold.
Particle Velocity
After determining the field cal incorporating U* as a term proportional to velocity, we can now estimate the velocity of the saltating particles (Vp).
____________________
Vp = √ (KF m’ / 2 KE)
Figure 11 – Particle Velocity (Brooking, 1983)
Figure 11 is the combined data of Sensit calculated particle
velocity and wind tunnel velocity data (Brookfield, Guelph, Canada, 1983). The
Figure 12 – Sensit Particle Velocity Data
Figure 12 shows indicates the relationship between U* and Sensit calculated particle velocity for the data set above.
Data Processing
For each data point, U* is calculated as:
U2 – U1
U* = k _________________
ln( Z2 / Z1 )
where
U1, U2 wind speed at heights Z1, Z2.
K von Karman constant = 0.4
Z1, Z2 anemometer heights
alternately
U 1 ┌ z ┐
___ = ____ ln │ ______ │
U* k └ Z0 ┘
where
U wind speed at heights Z
Z0 aerodynamic roughness height
