COCAP: A carbon dioxide analyser for small unmanned aircraft systems

Abstract

Unmanned aircraft systems (UASs) could provide a cost-effective way to close
gaps in the observation of the carbon cycle, provided that small yet accurate
analysers are available. We have developed a COmpact Carbon dioxide analyser
for Airborne Platforms (COCAP). The accuracy of COCAP's carbon dioxide
(CO2) measurements is ensured by calibration in an environmental
chamber, regular calibration in the field and by chemical drying of sampled
air. In addition, the package contains a lightweight thermal stabilisation
system that reduces the influence of ambient temperature changes on the
CO2 sensor by 2 orders of magnitude. During validation of COCAP's
CO2 measurements in simulated and real flights we found a measurement
error of 1.2 µmol mol−1 or better with
no indication of bias. COCAP is a self-contained package that has proven well
suited for the operation on board small UASs. Besides carbon dioxide dry air
mole fraction it also measures air temperature, humidity and pressure. We
describe the measurement system and our calibration strategy in detail to
support others in tapping the potential of UASs for atmospheric trace gas
measurements.

Full text

Atmos. Meas. Tech., 11, 1833–1849, 2018
https://doi.org/10.5194/amt-11-1833-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
COCAP: a carbon dioxide analyser for small unmanned
aircraft systems
Martin Kunz1, Jost V. Lavric1, Christoph Gerbig1, Pieter Tans2, Don Neff2, Christine Hummelgård3, Hans Martin3,
Henrik Rödjegård3, Burkhard Wrenger4, and Martin Heimann1,5
1Max Planck Institute for Biogeochemistry, Jena, Germany
2NOAA Earth System Research Laboratory, Global Monitoring Division, Boulder, Colorado, USA
3SenseAir AB, Delsbo, Sweden
4Ostwestfalen-Lippe University of Applied Sciences, Höxter, Germany
5Division of Atmospheric Sciences, Department of Physics, University of Helsinki, Helsinki, Finland
Correspondence: Martin Kunz (mkunz@bgc-jena.mpg.de)
Received: 21 June 2017 – Discussion started: 7 November 2017
Revised: 30 January 2018 – Accepted: 22 February 2018 – Published: 29 March 2018
Abstract. Unmanned aircraft systems (UASs) could provide
a cost-effective way to close gaps in the observation of the
carbon cycle, provided that small yet accurate analysers are
available. We have developed a COmpact Carbon dioxide
analyser for Airborne Platforms (COCAP). The accuracy of
COCAP’s carbon dioxide (CO2) measurements is ensured
by calibration in an environmental chamber, regular calibra-
tion in the field and by chemical drying of sampled air. In
addition, the package contains a lightweight thermal stabil-
isation system that reduces the influence of ambient tem-
perature changes on the CO2sensor by 2 orders of magni-
tude. During validation of COCAP’s CO2measurements in
simulated and real flights we found a measurement error of
1.2 µmol mol−1or better with no indication of bias. COCAP
is a self-contained package that has proven well suited for the
operation on board small UASs. Besides carbon dioxide dry
air mole fraction it also measures air temperature, humidity
and pressure. We describe the measurement system and our
calibration strategy in detail to support others in tapping the
potential of UASs for atmospheric trace gas measurements.
1 Introduction
Atmospheric measurements of carbon dioxide (CO2) are es-
sential for our understanding of the carbon cycle and how
it changes in a warming climate. Such measurements are
made on a regular basis by global networks of surface sta-
tions, by specially instrumented aircraft and by research
ships (Masarie and Tans, 1995). When local influences are
filtered out, the data from these measurements allow the iden-
tification of global trends and the characterisation of major
greenhouse gas sources and sinks, generally on the scale of
continents (Fan et al., 1998; Ciais et al., 2010). This top-
down approach to the quantification of the carbon cycle is
well established.
In contrast, for observations on smaller scales conven-
tional strategies often suffer from severe limitations. Specifi-
cally, the transition region between micro- and mesoscale in
the sense of Orlanski (1975) poses a challenge. It comprises
horizontal extents of 200 m to 20 km and periods from min-
utes to hours. Manned research aircraft do not fully cover
this region due to minimum flight altitude requirements and
their in most cases high airspeed. Missed approaches allow
the collection of air samples close to the ground, but this
manoeuvre may only be performed at sites where the air-
craft could actually land. Furthermore, because the operation
of manned aircraft is costly, they are typically deployed for
short periods of time only. On the other hand, stationary ob-
servations on instrumented masts or towers can deliver con-
tinuous data streams for long periods of time. However, they
are fixed to a single location and take measurements from
few vertical levels up to a maximum altitude limited by the
height of the structure.
Unmanned aircraft systems (UASs), also called remotely
piloted aircraft systems (RPASs), unmanned aerial vehi-
Published by Copernicus Publications on behalf of the European Geosciences Union.

1834 M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems
cles (UAVs) or “drones”, have the potential to fill this obser-
vational gap. Their use for research purposes has increased
substantially over the past years. UASs that are capable of
fully autonomous flight are now available for a few thou-
sand euros, which has become possible by the development
of small and cheap electronics for satellite navigation and in-
ertial measurements as well as a growing consumer market.
Especially smaller UASs with a mass of few kilograms are
becoming more and more attractive for research. They have
low system costs and can be operated by one or two persons.
Obtaining operating permission is easier for lightweight plat-
forms, and custom modifications do not require certification.
A fundamental limitation of small UASs is their pay-
load capacity, both in space and mass. One reason why
small UASs have been used in the field of meteorology for
many years (e.g. Egger et al., 2002; Spiess et al., 2007;
Reuder et al., 2008) is the availability of compact and
lightweight instrumentation for the measurement of air tem-
perature, humidity and pressure. Airborne studies of the car-
bon cycle, however, require accurate gas sensors, which are
hard to miniaturise. Atmospheric signals on the micro- and
mesoscale in CO2for example are typically in the range
1–100 µmol mol−1, while the background CO2dry air mole
fraction1xCO2is about 400 µmol mol−1. If the sensitivity of
a CO2sensor drifts by only 1 % during flight, e.g. due to
the changes in ambient temperature, the resulting change by
4 µmol mol−1will obscure small signals.
Solutions for the measurement of greenhouse gases on
board unmanned platforms have been found, but are not yet
widely used, likely for practical or financial reasons. Berman
et al. (2012) deployed a custom-built laser-based water
vapour, carbon dioxide and methane analyser on the NASA
SIERRA UAS, but the dimensions of 30cm ×30 cm ×28 cm
and the mass of 20 kg prevent the use of this analyser on
smaller systems. Khan et al. (2012) developed a smaller
laser-based analysers for carbon dioxide or methane dry
air mole fraction with a mass of 2 kg and a size of
20 cm ×5 cm ×5 cm. The estimated drift in xCO2during 5–
10 min flights with a small helicopter was 1 %, which limits
the system’s suitability for environmental studies. Watai et al.
(2006) deployed a 3.5 kg measurement package containing a
nondispersive infrared CO2sensor on a UAS. They reported
a comparably low bias of 0.21 µmol mol−1during tests with
temperature changes similar to the conditions during flight.
However, their setup requires 1 min of in-flight calibrations
every 6min and comprises two gas cylinders, a pump and a
drying cartridge in addition to a 20 cm ×14 cm ×8 cm main
module.
Recently, attempts have been made to equip UASs with
commercial, off-the-shelf CO2sensors designed for indoor
air quality measurements. Their advantages are low cost,
compact size and small mass of the measurement system.
1Throughout this paper, xCO2denotes the CO2dry air mole frac-
tion at a point, i.e. the result of an in situ measurement.
Brady et al. (2016) flew a 500 g payload containing such a
CO2sensor on a small multicopter, but due to its high un-
certainty (30 ppm plus 3% of reading according to manufac-
turer’s specifications) the resulting data are hard to interpret.
Numerous other groups have improved the accuracy of com-
pact sensors by custom calibrations (e.g. Yasuda et al., 2012;
Piedrahita et al., 2014; Shusterman et al., 2016; Martin et al.,
2017). In some of these studies, measurement uncertainties
below 5 µmol mol−1have been achieved (Shusterman et al.,
2016; Martin et al., 2017). However, none of these efforts
aimed at the deployment of the sensors on UASs, which re-
quires immunity to rapid changes in pressure and tempera-
ture as well as a high time resolution.
Aiming for a measurement package that is compact and
accurate, we have developed COCAP, the COmpact Carbon
dioxide analyser for Airborne Platforms. In Sect. 2 we pro-
vide a detailed description of our measurement system, con-
sisting of (1) COCAP, (2) a device that enables calibrations
in the field and (3) an unmanned aircraft that carries COCAP.
Section 3 focuses on our strategy to ensure accurate measure-
ments through calibration of COCAP’s sensors. In Sect. 4 we
present the results from different tests that we carried out to
assess COCAP’s performance.
2 The measurement system
2.1 COCAP
COCAP measures CO2dry air mole fraction, temperature,
relative humidity and pressure of ambient air. Furthermore,
flow rate, pressure and temperature at different locations in-
side the analyser are recorded. We designed COCAP as an
independent package containing not only sensors but also
control and data logging capabilities as well as a GPS re-
ceiver that provides position data and acts as a time source.
The mass of COCAP is 1 kg, excluding battery.
A schematic view of COCAP is provided in Fig. 1. The
different components are described in the following subsec-
tions.
2.1.1 Carbon dioxide sensor
COCAP measures carbon dioxide using a sensor from
SenseAir AB based on their HPP (High Performance Plat-
form) family of gas sensors (Hummelgård et al., 2015). It
is a nondispersive infrared sensor operating at a wavelength
of 4.26 µm. The optical path has a length of 128 cm, which
is obtained by 16 passes in an 8 cm long White cell (White,
1942). The total internal volume of the cell is 48 cm3. The
mirrors are fabricated using plastic moulding which lowers
the production cost. Heating elements and temperature sen-
sors that enable temperature stabilisation of the optics are
moulded into the mirrors. The sensor’s mass is 80g, includ-
ing electronics.
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M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems 1835
Figure 1. Flow of air, electrical power and data inside COCAP. FC – mass flow controller; TT – temperature transmitter (sensor); PT –
pressure transmitter; FT – mass flow transmitter. The NDIR (nondispersive infrared) CO2sensor contains additional temperature sensors
which are not included in this schematic view.
2.1.2 Other components in the gas sampling line
Air that is drawn into COCAP’s sample line is chemically
dried as a first step. We use magnesium perchlorate (105873,
Merck KGaA, Germany) in cartridges built in-house from
aluminium (Fig. S4 in the Supplement). For improved dry-
ing performance we sieve the magnesium perchlorate and use
only particles smaller than 2 mm. A single drying cartridge
holds 1.5 g of magnesium perchlorate, which is sufficient to
dry nearly saturated air at a temperature of 24 ◦C and a flow
rate of 300 mL min−1to a water mole fraction of less than
200 µmol mol−1for 1 h.
Downstream of the drying cartridge a 0.2 µm filter (CM-
0118, CO2Meter.com, USA) protects the pump, flow regu-
lator and CO2sensor from particles. The air flow through
the gas line is driven by a diaphragm pump (NMS 020 B,
KNF Neuberger GmbH, Germany) and throttled to a flow
rate of 300 mL min−1by the mechanical flow controller
(PCFCDH-1N1-V, Beswick Engineering Inc., USA). At this
flow rate the pump reaches a differential pressure of 350hPa,
whereas the flow controller is preset at the factory to a higher
pressure difference of 700 hPa. We lowered the setting of the
flow controller, but tests indicate that in the current configu-
ration the flow rate is directly proportional to ambient pres-
sure, i.e. the flow controller behaves like a needle valve. In
future designs we recommend to better tune the flow con-
troller for performance at low pressure differences or to re-
duce mass by replacing it with a needle valve.
The temperature of sample air is measured inside the in-
let and the outlet of the CO2sensor with miniature ther-
mistors (NCP15XH103F03RC, Murata Ltd., Japan) that are
suspended from 0.2 mm diameter wire (Figs. S2 and S3
in the Supplement). Pressure is measured with a compact
piezoresistive pressure sensor (LPS331AP, STMicroelec-
tronics, Switzerland). This model was chosen for its small
physical size, high resolution and digital interface. As it lacks
a connection port, we glued a 3-D-printed cap with a turned
stainless steel port connector to the PCB so that it forms an
airtight enclosure around the pressure sensor (Fig. S5 in the
Supplement). The sample pressure is measured downstream
of the CO2sensor close to its outlet. As the flow between the
measurement cell and this point is virtually unrestricted, we
assume equal pressure; i.e. we treat the reading of the pres-
sure sensor as the pressure of the air inside the CO2sensor’s
measurement cell.
Finally, the mass flow rate of the sample air is measured
with an analogue sensor (AWM3300V, Honeywell, USA).
Downstream of the mass flow sensor the sample air is re-
leased from the gas line into COCAP’s housing.
2.1.3 Ambient sensors
The measurement of features in temperature and humidity on
the scale of tens of metres with UASs that can move several
metres per second requires fast measurements with time con-
stants on the order of 1 s. This calls for unrestricted or even
forced ventilation of the sensing elements. To this end we de-
signed a small (60 mm×35mm) printed circuit board (PCB)
that can be mounted in the most suitable location for any
UAS (Fig. S6 in the Supplement). Temperature is measured
with a platinum resistance thermometer (Platinum 600 ◦C
MiniSens Pt1000, IST AG, Switzerland), humidity is mea-
sured with a capacitive humidity sensor (P14 rapid in wired
configuration, IST AG, Switzerland). Both sensors protrude
over the edge of the PCB, which minimises thermal mass
and improves ventilation. They are protected from mechani-
cal damage and contamination by an aluminium tube (length
30 mm, inner diameter 12 mm). The tube is polished on the
outside to prevent heating by the sun and anodised matte
black on the inside which avoids reflection and focussing of
sunlight onto the sensors. On fixed-wing UASs we mount the
PCB facing forward, while on rotary-wing UASs we mount
it facing upward in the downwash of the rotors.
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1836 M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems
2.1.4 Data logger
The data from all sensors are recorded to a memory card by
a data logger. For this purpose we modified an electronics
board designed for the operation with SenseAir’s HPP gas
sensors (Hök Instruments AB, Sweden) by adding connec-
tors that provide an interface for the GPS receiver and differ-
ent digital sensors. The board runs firmware written for CO-
CAP at the MPI for Biogeochemistry (Jeschag, 2014). Sen-
sor data are recorded at 1 Hz. If a sensor samples at a higher
rate, the measurements are averaged over 1s. Data are con-
tinuously output via a serial interface and can be transmitted
to a computer by means of an adaptor cable or a pair of radio
modules (XBee 868, Digi International Inc., USA), allowing
for real-time data visualisation and analysis. In addition, the
data logger controls the built-in heaters of the CO2sensor to
a user-adjustable temperature.
2.1.5 Temperature stabilisation
The temperature inside and outside COCAP influences the
measurement of carbon dioxide in different ways. First, the
density of the sample air and therefore the number of ab-
sorbing molecules in the measurement cell is inversely pro-
portional to absolute temperature (ideal gas law; Clapey-
ron, 1834). Secondly, electronic components and the optical
bandpass filter in the CO2sensor exhibit drift with temper-
ature (Wilson, 2011; SCHOTT, 2015). Thirdly, the intensity
of the absorption lines of any gas depends on temperature,
which makes the optical depth of the sample air temperature
dependent (McClatchey et al., 1973). Fourthly, changes in
temperature influence the emission strength of the IR source.
Fifthly, thermal expansion may cause mechanical deforma-
tions of the optical assembly. We correct the xCO2readings
for drift with temperature (see Sect. 3.1), but experience with
earlier setups shows that for best possible precision an active
stabilisation of temperature is needed.
The HPP CO2sensor has built-in heaters and temperature
sensors that are thermally coupled to the optical surfaces, the
IR source and the optical detector. In an earlier version of
COCAP we covered the CO2sensor with isolating material
and preheated the air stream with a heated tube that was con-
nected to the sensor inlet. In this setup, the temperature at
three points could be precisely controlled to 50 ◦C, but the
distribution of temperature was inhomogeneous and varying
with ambient conditions. Although a total of nine tempera-
ture sensors were present at different locations in COCAP,
the uneven temperature distribution made it impossible to
fully determine the system’s thermal state and a satisfactory
temperature correction could not be established.
Consequently, we redesigned the stabilisation system to
minimise temperature differences around the CO2sensor.
This goal requires a setup where the heat exchange between
different parts of the sensor happens much faster than dissi-
pation of heat from the sensor to the changing environment.
Figure 2. Fan and heating element used to stabilise temperature in-
side COCAP. The heating element is made of surface-mount tech-
nology resistors soldered to two concentric rings of wire. It is lo-
cated just above the air inlet of the radial fan.
In many instruments this is achieved by means of massive
bodies of copper or aluminium, which are characterised by
high thermal diffusivity. However, as the mass of large metal
parts is unacceptable for our application, we use air to trans-
port heat inside COCAP. The lower thermal diffusivity of air
is compensated for by forced convection driven by a fan. A
heater, a temperature sensor and a custom PCB are connected
and programmed as a control loop that stabilises the air tem-
perature at 50 ◦C. The warm air stream circulates throughout
COCAP’s housing (Fig. S1 in the Supplement) so that the
CO2sensor is not only decoupled from changes in ambient
temperature but all electronics boards benefit from the stabil-
isation as well.
While being flown on a UAS the temperature around CO-
CAP can change by several degrees within seconds. Com-
pensation for these changes requires a fast control loop,
which calls for a heating element and a temperature sensor
with low thermal mass. We built the heating element (Fig. 2)
from 38 surface-mount technology resistors (nominal resis-
tance 360 , length ×width 2 mm ×1.25 mm, rated power
0.5 W) which are connected in parallel and provide a maxi-
mum heating power of 15 W at 12 V.
We installed the heating element just above the air inlet
of the fan (RLF 35-8/12 N, ebm-papst Mulfingen GmbH &
Co. KG, Germany). Placing the heating element at the outlet
of the fan would reduce the response time, but would likely
result in a less homogeneous temperature distribution across
the air stream.
The temperature sensor (“air stream sensor”, Fig. 3) in the
control loop is a miniature thermistor (NCP15XH103F03RC,
Murata Ltd., Japan). It is placed close to the detector of the
CO2sensor and oriented perpendicular to the flow of circu-
lating air to minimise flow resistance.
Fan, heating element and air stream sensor are con-
nected to an in-house-built control board (Figs. S7 and
S8 in the Supplement) that runs a PID (proportional–
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M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems 1837
Figure 3. Sensor used for the measurement of the temperature of
the air circulating inside COCAP. The sensing element (located in
the centre of the blue 3-D-printed frame) is a miniature thermis-
tor (1 mm ×0.5 mm ×0.5mm). Two 23 mm long pieces of 0.5mm
wire are soldered to both sides of the thermistor. They conduct
heat, facilitating the measurement of a temperature that is averaged
across the air stream.
integral–derivative) controller implemented in software. The
temperature-dependent resistance of the air stream sensor is
measured in a Wheatstone bridge configuration with a reso-
lution of 1 mK at 50◦C. A trimmer potentiometer allows cal-
ibration of the temperature measurement. The control board
detects whether the thermistor is shorted or disconnected and
disables heating in such cases.
The power dissipation of the heating element is controlled
by pulse-width modulation with 16 bit resolution. The con-
trol board monitors the current drawn by the fan and powers
the heating element only if the fan is operating normally. This
protection prevents damage to the heating element, which
would overheat if the fan is disconnected or broken.
The performance of the temperature stabilisation under
flight conditions is discussed in Sects. 4.1.2 and 4.2.2.
2.1.6 Battery
COCAP requires a source of electrical power with a volt-
age in the range 10.2–14.0 V. We use a single lithium poly-
mer battery with a nominal voltage of 11.1 V. The battery life
time depends on the ambient temperature, but generally we
can operate COCAP for more than 1 h from a 2200mAh bat-
tery weighing 200 g. By choosing a different battery size the
package can be optimised for lower mass or longer run time.
2.2 Field calibration device
In order to make the handling of gas standards in the field
easier and safer we developed a field calibration device
(Fig. S9 in the Supplement). It consists of a gas cylin-
der dolly, accommodating two 10 L aluminium cylinders,
and a valve box. The cylinders are securely tied to the
dolly so that they can stay in place at all times, which
simplifies transportation. Inside the valve box a three way
valve allows switching between the two gas standards or
shutting off the gas stream. The flow rate is controlled to
400 mL min−1with a mechanical flow controller (PCFCDH-
1N1-V, Beswick Engineering Inc., USA). The connection to
COCAP has an open-split configuration so that there is al-
ways an 100 mL min−1overflow and the gas standard is de-
livered at ambient pressure. At a field site three steps are nec-
essary to make the system ready for use: (1) removing the
protective caps from the cylinders, (2) mounting (including
leak checking and flushing) of the pressure regulators (model
14, Air Liquide USA LLC) and (3) connecting them to the
valve box. For details of the field calibration sequence and
gas standards see Sect. 3.3
2.3 Unmanned aircraft system
COCAP has no dependence on any external system and can
therefore be deployed on a variety of UASs. The only re-
quirements are a payload capacity of typically 1.2 kg (de-
pending on the choice of battery; see Sect. 2.1.6) and space
for the 14 cm ×14 cm ×42 cm package, either inside the
fuselage or attached to the outside of the vehicle. Sufficient
ventilation must be ensured to prevent overheating. In Ger-
many, UASs can be operated without a permit at low heights
up to 100 m above ground level if their take-off mass is lower
than 5 kg. COCAP’s size and mass generally allow for this
limit to be met. We have operated COCAP on multicopters
and carried out successful tests on a fixed-wing aircraft.
2.3.1 Multicopters
Multicopters are rotorcraft with more than two rotors. They
are generally easier to handle than fixed-wing aircraft due
to their hovering ability and their built-in electronic con-
trol systems. Multicopters feature vertical take-off and land-
ing as well as arbitrarily low vertical and horizontal flight
speed. However, for aerodynamic reasons they typically have
a lower endurance than fixed-wing aircraft of similar mass.
Moreover, the strong mixing around and below the rotors
gives rise to an uncertainty of the origin of a measured air
sample. We alleviate this problem by sampling air through a
carbon fibre tube with the inlet placed sideways or above the
rotors.
So far we have flown COCAP on two different mul-
ticopters. One is an octocopter (S1000, DJI Ltd., China)
with a total take-off mass of 9.2kg. The other one is a
quadcopter (custom-built, Sensomotion UG, Germany, and
Ostwestfalen-Lippe University of Applied Sciences, Ger-
many, Fig. S10 in the Supplement) weighing 4.8 kg with CO-
CAP mounted. Both multicopters are electrically powered
and provide at least 10 min of flight time.
2.3.2 Fixed-wing aircraft
Fixed-wing aircraft require a minimum air speed to fly and
generally depend on an airstrip or additional equipment like
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1838 M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems
bungees and nets for take-off and landing. However, they
tend to have higher endurance and longer reach than multi-
copters. We carried out successful flight tests with an elec-
trically powered fixed-wing aircraft (X8, Skywalker Tech-
nology Ltd., China) using a dummy that has the same mass
and size as COCAP. The complete system weighed approxi-
mately 3.6 kg.
2.4 Cost estimation
The cost estimate provided here includes materials and com-
ponents in the state in which we procured them but excludes
any labour associated with their modification and assembly.
We estimate the material costs for COCAP at EUR 4500 and
for the field calibration device (including two cylinders, but
not the gas standards inside) at EUR 3300. The recurring
costs for gas standards and drying agent are a few euros per
flight and thus negligible.
Commercial off-the-shelf multicopters with a payload ca-
pacity of at least 1.2 kg are available for EUR 3000, including
essential equipment such as battery, charger and remote con-
trol.
3 Calibration
3.1 Calibration curve of the CO2sensor
A nondispersive infrared gas sensor measures the fraction
of one component in a mixture of gases utilising the char-
acteristic absorption bands that many substances exhibit in
the infrared. The HPP sensor inside COCAP outputs a signal
that is approximately proportional to the intensity of infrared
radiation that has passed through the gas mixture. Absorp-
tion by one constituent of the gas reduces the intensity, but
the relation between the mole fraction of this component and
the intensity is non-linear and depends on temperature and
pressure of the gas. Furthermore, sensor elements like the
infrared source and detector can have a temperature depen-
dence that influences the measurement. Generally, the carbon
dioxide mole fraction xCO2of the gas mixture can be calcu-
lated as
xCO2=f (s, TG,pG,. . .), (1)
where sis the infrared signal, TGand pGare temperature
and pressure of the gas mixture, respectively, and the ellipsis
indicates that other quantities may be included in the calcu-
lation. The function fwill henceforth be called the “calibra-
tion curve” of the carbon dioxide sensor.
Although an ab initio calculation of the calibration curve
is in principle possible, we did not follow this approach due
to lack of information (e.g. the precise transmission charac-
teristics of the optical bandpass filter). Instead, we made a
series of measurements with known CO2dry air mole frac-
tion under changing ambient conditions and used regression
Figure 4. Conditions during one of the experiments carried out to
define a calibration curve for the CO2sensor: (a) CO2dry air mole
fraction xCO2measured with a reference analyser, (b) ambient tem-
perature T, and (c) ambient pressure p.(d) Normalised infrared
signal sfrom the optical detector of COCAP’s CO2sensor. The
variations in pressure influence the observed signal more strongly
than the changes in xCO2by 200 µmol mol−1, which illustrates the
need for a precise pressure correction.
analysis to approximate the calibration curve. To this end we
placed COCAP in an environmental chamber where ambi-
ent temperature and pressure could be varied over the range
expected in field deployments (Fig. 4b, c).
Temperature was changed in a step pattern from 28 to 0 ◦C
while pressure was smoothly adjusted from 1100 to 700 hPa
and back during each temperature step. These disparate pat-
terns were chosen to ease the attribution of sensitivities to
one of the independent variables. Sample air with gradually
changing CO2dry air mole fraction was provided to COCAP
from a spherical, stainless steel, 8 L buffer volume that was
continuously flushed with air from one of two gas cylinders
(Fig. 5).
One cylinder contained a lower-than-ambient CO2dry air
mole fraction (349.9 µmol mol−1), while the other one was
enriched with CO2(648.6 µmol mol−1). At a flow rate of
400 mL min−1the buffer volume acted as a low-pass fil-
ter with a time constant of 20 min (Fig. 4a). Air leaving
COCAP was directed to a Picarro G2401 cavity ring-down
spectroscopy (CRDS) analyser (O’Keefe and Deacon, 1988)
that had been calibrated to the WMO CO2X2007 scale and
served as a reference. Open splits upstream and downstream
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M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems 1839
Figure 5. Setup used to determine a calibration curve for the CO2
sensor. FC is a mass flow controller. The 8 L buffer volume was
flushed with either of two gas standards differing in CO2content,
providing a slowly changing CO2dry air mole fraction. The second
three-way valve is used to deliver nitrogen with zero CO2at the
beginning and the end of each experiment.
of COCAP ensured that sample air was delivered to both
analysers at chamber pressure despite different flow rates
(COCAP 300 mL min−1, Picarro G2401 200mL min−1).
The dominant features in the infrared signal (Fig. 4d)
are the step changes in xCO2and the influence of pressure
changes. Note that in a nondispersive infrared sensor the sig-
nal is inversely related to the amount of absorbing molecules
in the measurement cell. Hence, both low xCO2and low pres-
sure lead to a high signal. The gradual changes in xCO2by
200 µmol mol−1between 00:40 and 06:30 h have a smaller
influence on the infrared signal than the changes in pressure
do. This shows the importance of a precise correction for am-
bient influences.
In total we carried out three experiments similar to the one
depicted in Fig. 4 on consecutive days. The variation in tem-
perature and pressure were the same for all experiments, but
the initial CO2dry air mole fraction in the buffer volume
differed and the switching between low-CO2and high-CO2
cylinders took place at different times.
Regression analysis of the experimental data was car-
ried out in GNU Octave using the leasqr function from the
optim package. It is an implementation of the Levenberg–
Marquardt algorithm for non-linear least-squares regression
that allows the variation of some parameters of a model while
others are fixed. This capability enabled a stepwise approach
in which we fitted one part of a model at a time until finally
all parameters could be set free In contrast, straightforward
fitting of a complete model at once did not converge. We at-
tribute this to the high number of parameters (10 or more)
and to the lack of initial values sufficiently close to the opti-
mum.
The models that we fitted to the experimental data are of
the form
xCO2=f (s , T , p, . . .), (2)
=g1(TInlet, TOutlet)
g2(p) ·g3(g4(s, . ..)) +c. (3)
The function g1represents the inlet temperature and g2the
pressure inside the measurement cell of the CO2sensor. The
fraction g1/g2originates from the ideal gas law, but in many
of our models it has a more general form, including constant
and quadratic terms to account for other effects like temper-
ature or pressure broadening of absorption lines. The func-
tion g3is a polynomial of second or third order that approx-
imates the non-linear relation between amount of absorbing
molecules in the measurement cell and light intensity at the
detector. Finally, the purpose of g4is to correct the detector
signal for disturbances, e.g. gain drift with temperature.
In our regression analysis we repeatedly performed three
steps: (1) formulation of a model, (2) fitting of the model
to the experimental data by minimising the sum of squared
residuals and (3) evaluation of the model performance. Given
the large number of parameters in the models, the second
step was susceptible to “overfitting”, i.e. fitting to a point
at which the model represents not only an underlying pro-
cess but also random variations in the experimental data. We
countered overfitting in two ways. On the one hand, we re-
jected models in which an additional parameter reduced the
sum of squared residuals only insignificantly. On the other
hand, we validated the fitted models against independent data
measured on a different day, which allowed us to assess the
stability of the parameters over time. Based on these consid-
erations we chose the following calibration curve:
xCO2=a1TOutlet +a2
p+a3(a4g3
4+a5g2
4+g4+a6)+a7,(4)
g4(s, p) =s+a8
a9p+a10 .(5)
a1through a10 are the parameters fitted in the regression. The
capability of this calibration curve to compensate for ambient
influences is illustrated in Fig. 6.
3.2 Calibration of ambient sensors
We calibrated COCAP’s temperature, humidity and pressure
sensors prior to measurements in the field. The general cal-
ibration approach was the same for all three sensor types:
As a first step, we placed them together with a reference in-
strument in an environmental chamber, varied the relevant
ambient conditions and recorded the indications of both the
sensor under test and the reference. As a second step, we fit-
ted a model that relates the indications of the sensor under
test to the reference measurements. This model can later be
used to correct sensor indications during field measurements.
Calibration of the temperature and humidity sensors was
carried out in a PSL-2KPH chamber (ESPEC Corp., Japan).
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1840 M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems
Table 1. Summary of the calibration of COCAP’s ambient sensors: conditions during calibration, correction model and root mean square
error (RMSE) of the corrected indications with respect to the reference. T,Uand pare uncorrected temperature, relative humidity and
pressure, respectively. TCis the corrected air temperature. n/a – not applicable.
Sensor Temperature Relative humidity Pressure Model RMSE
in ◦C in % in hPa
Temperature 5–40 50 1000 a1T2+a2T+a30.04 ◦C
Humidity 10–30 15–100 1000 a1U2+a2U+a3+a4U·TC+a5TC1.4 %
Pressure 0–40 n/a 400–1000 a1p2+a2p+a31.1 hPa
Figure 6. (a) Normalised infrared signal of COCAP’s CO2sen-
sor under changing ambient conditions. This is a subset of the data
shown in Fig. 4d. (b) xCO2calculated using the calibration curve
(Eqs. 4 and 5) compared to the measurements of a reference anal-
yser (Picarro G2401). The xCO2signal is recovered despite strong
influences from changing pressure.
A chilled-mirror dew point hygrometer (Michell Dewmet
TDH) with a measurement uncertainty of 0.1 ◦C for temper-
ature and 0.2 ◦C for dew point served as the reference. The
reference and the sensor under test were placed close to each
other and actively ventilated during the measurements.
The pressure sensors were calibrated in a CH3030 cham-
ber (SIEMENS AG, Germany). The reference instrument
(Druck DPI 740, General Electric Company, USA) has a
measurement uncertainty of 0.26 hPa.
Details of the calibrations are listed in Table 1. The correc-
tion model for the humidity sensor depends not only on the
raw humidity signal but also on air temperature. It therefore
relies on the corrected indication of the temperature sensor.
A potential source of error in the humidity calibrations are
the different response times of the chilled-mirror dew point
hygrometer and the slower reacting capacitive humidity sen-
sor. We avoid the introduction of a bias by calibrating with
slowly varying symmetric humidity patterns, i.e. by using the
same rate of change during humidity increase and decrease.
3.3 Field calibration
The CO2dry air mole fraction reported by COCAP drifts
over time (see Sect. 4.1.1), necessitating periodic calibration.
We decided against in-flight calibrations to reduce the sys-
tem mass, to save space and to have the full flight time avail-
able for the measurement of ambient air. Instead we sample
two gas standards before and after each flight using the field
calibration device described in Sect. 2.2. One of the stan-
dards has a CO2dry air mole fraction close to clean ambient
air (397.57 µmol mol−1); the other one is enriched with CO2
(447.44 µmol mol−1). Both standards consist of natural air
collected at the Max Planck Institute for Biogeochemistry in
Jena, Germany; i.e. the standards are similar in isotopic com-
position to the air that we typically measure in the field. This
way we avoid isotope-related errors that can occur with syn-
thetic air standards (Tohjima et al., 2009). The standards are
sampled for 5 min each. We discard the first 3min to ensure
that the measurement system is well flushed, leaving 2 min
for averaging. This time span is a compromise between noise
reduction (the minimum standard error of the mean would be
achieved by averaging over 4 min; see Sect. 4.1.1) on the one
hand and consumption of gas standards and time spent for
the field calibration (and lost for ambient measurements) on
the other.
During data analysis, the calibration curve (see Sect. 3.1)
is applied to all measurements of COCAP, resulting in a time
series of CO2dry air mole fraction. Averaging is carried out
for each gas standard and each sampling period by calculat-
ing the arithmetic mean of the CO2dry air mole fraction.
Next, “virtual” standard measurements are created by inter-
polating between the calculated averages linearly in time. Us-
ing these virtual standard measurements two correction pa-
rameters a(t ) (slope) and b(t) (offset) are calculated for each
point in time between the first and last standard measure-
ment such that the difference between corrected measure-
ment and assigned value vanishes. The corrected CO2dry
air mole fraction is thus calculated as
xCO2=a(t ) ·f (s, T , p, . . .) +b(t). (6)
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M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems 1841
Figure 7. Allan deviation of unfiltered CO2dry air mole fraction
σxCO2versus averaging period τ. Air from a cylinder was mea-
sured under laboratory conditions and during the simulated flights
described in Sect 4.1.2. The latter is depicted until τ=1000 s, i.e.
one-sixth of the length of the time series. The characteristic −1/2
slope of white noise is indicated by the black line.
4 Performance tests
4.1 In the lab
4.1.1 Allan deviation of CO2dry air mole fraction
The influence of white noise on a measurement can be re-
duced by averaging over several samples. However, the pre-
cision achievable by averaging is limited by drift of the in-
strument over time; i.e. over long averaging periods the im-
precision caused by drift becomes larger than the impreci-
sion caused by noise. Allan or two-sample variance σ2
y(τ ) is
a measure commonly used to analyse these two sources of
error. It is defined as (Allan, 1987)
σ2
y(τ ) =1
2D(1y)2E,(7)
where 1y is the difference between two consecutive averages
over a period of τand the angle brackets denote the expected
value. The square root of the Allan variance is called Allan
deviation σy.
To characterise noise and drift of COCAP we connected
the analyser in an open-split configuration to a cylinder
containing natural air with a CO2dry air mole fraction of
384.3 µmol mol−1. This air sample was measured in a lab
environment over a period of 24h. The Allan deviation of
this dataset (Fig. 7) reaches a minimum of approximately
0.2 µmol mol−1at an averaging period of 230s.
For averaging periods shorter than 100s the curve has
a slope of −1
2in the log–log plot, which is characteris-
tic of white noise. At τC=1800 s, the typical time be-
tween field calibrations, the Allan deviation is approxi-
mately 0.7 µmol mol−1and dominated by drift. Our correc-
tion scheme (see Sect. 3.3) removes offset and gain errors
Figure 8. Stability test in an environmental chamber. The variations
in ambient pressure pand temperature Tapproximately represent
three flights between 0 and 1000 m above sea level in the Interna-
tional Standard Atmosphere. Air with constant dry air mole fraction
of CO2was supplied to COCAP from a cylinder. Calibrations were
carried out before and after the flights (not shown) using two gas
standards (397.5 and 447.4 µmol mol−1). The dry air mole fraction
xCO2measured with COCAP has been smoothed by convolution
with a Gauss window of 200 s full width at half maximum in order
to reduce the high-frequency noise. The sharp features in pressure
were caused by turning the environmental chamber’s pressure reg-
ulation off after and back on before each flight.
at the point in time when the field calibrations were car-
ried out and uses linear interpolation between the calibra-
tions. Therefore, the largest uncorrected drift is expected to
be lower than 0.4 µmol mol−1, the Allan deviation for 1
2τC=
900 s. Figure 7 also shows the Allan deviation of COCAP’s
xCO2measurements during the simulated flights described in
Sect. 4.1.2. Forced ventilation and substantial changes in am-
bient pressure and temperature during the simulated flights
lead to an increased Allan deviation compared to the mea-
surements in a lab environment. Estimation of the expected
drift for 1
2τC=900 s is not feasible due to artefacts that be-
come visible at averaging periods beyond 400s.
4.1.2 Simulated flights
An instrument that is flown on a small UAS can be exposed
to rapid changes in temperature and pressure, especially if
the flight pattern covers a large range in altitude. To assess
the measurement error caused by such changes, we simu-
lated three consecutive flights between 0 and 1000m above
sea level (Fig. 8a, b) in an environmental chamber (CH3030,
SIEMENS AG, Germany).
Temperature and pressures were controlled to approxi-
mately resemble the International Civil Aviation Organiza-
tion Standard Atmosphere (ICAO, 1993). Each simulated
flight had a duration of 20 min with 5 min ascent and 15 min
descent. After a 20 min break without changes in temper-
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1842 M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems
Table 2. Mean T, standard deviation σand range Tmax −Tmin of
temperatures under simulated flight conditions.
Tin ◦Cσin mK Tmax −Tmin
in mK
Ambient 12.83 2366 8786
Air stream 50.00 4 79
Inlet 50.25 10 50
Outlet 50.12 32 110
Detector 54.86 10 50
ature and pressure this pattern was repeated. Only dry air
samples from cylinders were supplied to COCAP; hence no
drying cartridge was necessary. Otherwise, the analyser was
operated in standard configuration, including pump and flow
control. An open split with overflow upstream of the anal-
yser’s inlet ensured that air was sampled at the pressure of the
environmental chamber at all times. First we measured two
gas standards with CO2dry air mole fractions of 397.5 and
447.4 µmol mol−1for 5 min each at 15 ◦C and 100 kPa. Af-
terwards, air with 418.6 µmol mol−1CO2was supplied over
a period of 2 h while the environmental chamber was simu-
lating three flights as detailed above. Finally, we sampled the
two gas standards again for 5 min each at 15 ◦C and 100 kPa.
The xCO2measurement by COCAP is affected by different
sources of error: random noise, drift over time, calibration er-
rors and drift with temperature and pressure. We reduced the
noise by convoluting the time series with a Gauss window
of 200 s full width at half maximum (Fig. 8c). A two-point
calibration was derived from the standard measurements at
the beginning and end of the test and applied to the full time
series using linear interpolation in time. This cancelled out
linear drift over time, but due to the influence of noise on the
measurement of the gas standards and non-linearity in the
instrument response, a calibration error remains. Drift with
temperature and pressure is corrected for with the calibration
curve described in Sect. 3.1, but this correction does not com-
pletely eliminate the effect of these parameters on the mea-
surement result. The xCO2time series in Fig. 8c exhibits a
local minimum whenever pressure and temperature are min-
imal, with a maximum deviation from the assigned value
of the cylinder (418.6 µmol mol−1) of −1.2 µmol mol−1at
02:10 h. The bias of the mean over the whole test, represent-
ing the combined effect of the calibration error and drift with
temperature and pressure, was −0.03 µmol mol−1. The stan-
dard deviation of the 1 Hz time series before convolution with
a Gauss window was 2.7µmol mol−1; the standard deviation
after convolution was 0.41µmolmol−1.
Figure 9 shows time series of temperatures measured at
different points inside COCAP during the simulated flights.
Statistics of these time series are given in Table 2.
The differences in the observed patterns result from the air
circulation inside COCAP’s housing: first, heated air from
Figure 9. Temperatures inside and outside COCAP under simulated
flight conditions (depicted in Fig. 8a and b). The temperature sen-
sors in the detector, inlet and outlet of the CO2sensor are uncal-
ibrated; hence they have an unknown offset of up to 1.1 ◦C. The
detector is about 5 K warmer than the other parts (note the broken
temperature axis) due to heat transfer from the component block
which is heated to 55 ◦C. Ambient temperature is plotted at a dif-
ferent scale as it varies 2 orders of magnitude more than the sta-
bilised internal temperatures. The spikes in air stream temperature
are related to fast pressure changes in the environmental chamber
(see Fig. 8a).
the fan streams along the inlet tube of the CO2sensor. Next,
it passes the air stream sensor (see Sect 2.1.5). Finally, it
reaches the outlet tube and the detector of the CO2sensor.
The air stream sensor is part of the control loop and there-
fore its temperature stays close to the set point of 50 ◦C. The
inlet and outlet temperature sensors measure the temperature
of the sample gas, which indirectly reflects the temperature
of the air circulation because heat is exchanged through the
walls of the inlet and outlet tubes. The temperatures of the
outlet exhibit minima whenever the ambient temperature is
reduced. This is caused by increased heat transfer from the
circulating air to outside COCAP’s housing. The inlet shows
the inverse behaviour, i.e. increasing temperature under re-
duced ambient temperature, because it is located between fan
and air stream sensor. In a colder environment the air has to
be heated more to keep the temperature at the air stream sen-
sor constant, so the temperature at the inlet rises.
The temperature of the detector varied qualitatively simi-
larly to that of the outlet because detector and outlet are lo-
cated close to each other. However, the temperature of the de-
tector is approximately 5 K higher and the amplitude of the
temperature variations is roughly 3 times lower than at the
outlet. This is due to the detector’s thermal coupling to the
component block, which is temperature-controlled to 55 ◦C.
Overall, the temperature stabilisation reduces the variability
in the internal temperatures by 2 orders of magnitude com-
pared to the changes in ambient temperature (see Table 2).
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M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems 1843
4.2 Field deployment
4.2.1 Measurements with an instrumented van
Testing COCAP under realistic conditions requires the mea-
surement of xCO2in ambient air with varying composi-
tion. Specifically, changes in humidity are desirable to re-
veal potential problems with the drying of the sample gas
and changes in CO2content allow validation of COCAP’s
calibration curve. To this end, a reference instrument must
simultaneously sample the same air as COCAP. Laser-based
instruments are widely used for high-accuracy measurements
of greenhouse gases (e.g. Laurent, 2016) and therefore suit-
able to be used as a reference, but at a mass of more than
10 kg they are too large to fly on any UAS available for this
work. As an intermediate step between stationary indoor test-
ing and UAS flights we integrated COCAP into the “Mo-
bile Lab” (Pétron et al., 2012), an instrumented van equipped
with a CRDS analyser for carbon dioxide, carbon monoxide,
methane and water (G2401-m, Picarro Inc., USA). Air was
sampled at 3.5 m above street level. Field calibrations (see
Sect. 3.3) were carried out by injecting air from cylinders
with slightly higher-than-ambient pressure into the sampling
line at regular intervals.
As COCAP and the CRDS analyser were connected to
the same sampling line, delay and mixing caused by tubing
and inlet filter affected them equally. However, the flushing
time for the analyser’s measurement cells is different, which
makes direct comparison of their readings inappropriate. In
the following we explain how we handled this issue mathe-
matically.
The flushing process can be described as a convolution of
the CO2dry air mole fraction at the inlet of the sampling line,
xInlet(t ), with an analyser-specific instrument function f (t):
x(t ) =(xInlet∗f )(t), (8)
=
∞
Z
−∞
xInlet(t −t0)·f (t 0)dt0.(9)
The response x(t ) of the analyser is the reported CO2dry air
mole fraction. Due to causality, x(t) cannot depend on future
CO2dry air mole fractions at the inlet. Hence, the lower limit
of the integration can be set to zero:
x(t ) =
∞
Z
0
xInlet(t −t0)·f (t 0)dt0.(10)
The instrument function f (t) is not known a priori, but it can
be estimated from the response to a step change in xInlet(t ).
Such step changes occurred at the end of calibration mea-
surements when the supply of gas standard into the sampling
line was shut off. From the data we found that for both anal-
ysers the response xSC(t ) to a step change can be modelled
by an exponential decay of the form
xSC(t ) =(x0−x∞)·e−t/τ +x∞,(11)
where x0and x∞are the CO2dry air mole fractions before
and after the step change, respectively, and τis the charac-
teristic time constant of the flushing process. We determined
time constants of 13 s for COCAP and 25 s for the CRDS
analyser. To find the function f (t ) we differentiate Eq. 10:
d
dtx(t ) =d
dt
∞
Z
0
xInlet(t −t0)·f (t 0)dt0,(12)
=
∞
Z
0
f (t0)·d
dtxInlet(t −t0)dt0(13)
In the case of a step change at the inlet, the differentiation
yields the Dirac delta function δ, scaled by the height of the
step (x∞−x0):
d
dtxSC(t ) =
∞
Z
0
f (t0)·(x∞−x0)·δ(t −t0)dt0,(14)
=(x∞−x0)·f (t). (15)
Rearranging and applying Eq. 11,
f (t) =
d
dtxSC(t )
x∞−x0,(16)
=(x∞−x0)·e−t/τ
(x∞−x0)·τ,(17)
=e−t/τ
τ.(18)
This means that the instrument function of either analyser
can be described with an exponential decay which has the
same time constant as the analyser’s step response. For prac-
tical reasons, we treat f (t) as equal to zero outside 0 ≤t≤
5τ. Because no carbon dioxide is created or removed inside
the analysers, the time integral over f (t) must be equal to
one, necessitating normalisation of the truncated response
function:
f0(t) =




0 if t < 0
f (t)
1−e−5if 0 ≤t≤5τ
0 if t > 5τ .
(19)
Through the measurement process both analysers effectively
convolute the xCO2signal present at the inlet of the sampling
line with their respective instrument function. To make the
results comparable, we convolute the measurements of each
analyser with the instrument function of the other analyser.
If both measurements were perfect, this would yield identical
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1844 M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems
Figure 10. (a) CO2dry air mole fraction xCO2of ambient air mea-
sured by COCAP and a CRDS analyser during a car drive. The
three step-like patterns originate from the field calibration during
which two gas standards are sampled. The peak at 09:16 occurred
while waiting at a traffic light on a busy street. (b) Difference and
smoothed difference of xCO2measured by COCAP minus xCO2
measured by the CRDS analyser. The smoothing is implemented by
convolution with a Gauss window of 200 s full width at half maxi-
mum. The measurements of both analysers have been corrected us-
ing the field calibrations and the flushing times have been equalised
as explained in the text.
results because convolution is commutative:
xCOCAP ·fCRDS =(xInlet ·fCOCAP)·fCRDS,(20)
=(xInlet ·fCRDS)·fCOCAP,(21)
=xCRDS ·fCOCAP.(22)
Here xCOCAP and xCRDS are the CO2dry air mole fractions
measured by COCAP and the CRDS analysers, respectively.
Convoluting each analyser’s measurement with the instru-
ment function of the other analyser can therefore be viewed
as an equalisation of the flushing times of both analysers.
We carried out the experiment with the Mobile Lab in
Boulder, Colorado, USA, on 15 October 2015. We drove
up and down a road that covers 700m in elevation (1650–
2360 m above sea level), exposing COCAP to the same pres-
sure changes that would occur during a flight at these alti-
tudes. The temperature inside the van increased from 14 ◦C
to 20 ◦C during the drive. Despite the substantial changes in
ambient conditions, the measurements from both analysers
agree to within 2 µmol mol−1during most of the experiments
(Fig. 10).
Differences are mainly caused by limitations of the sim-
ple model for the instrument functions, which become ap-
parent during fast changes in xCO2, and by sensor noise.
They are reduced to less than 1 µmol mol−1when high-
frequency variations are filtered out. The negative bias
of about −0.8 µmol mol−1observed between 09:55 and
10:15 LT might be the effect of sunlight exposure. At the time
of the experiment, the temperature stabilisation described in
Figure 11. Stability of COCAP’s internal temperatures during a
flight to a maximum height of h=430 m above ground level. p
is ambient pressure, Tis temperature. Note the broken temperature
axis and the different scaling used for ambient, outlet and detector
temperature.
Sect. 2.1.5 had not yet been implemented, which is why CO-
CAP was sensitive to changes in ambient conditions.
4.2.2 Lannemezan flights
The so far highest flight of COCAP on a UAS was car-
ried out in Lannemezan, France, on 20 May 2016 at
15:30 UTC (17:30 local time). COCAP was mounted under
a custom-built multicopter (Sensomotion UG, Germany, and
Ostwestfalen-Lippe University of Applied Sciences, Ger-
many, Fig. S10 in the Supplement). Starting from an eleva-
tion of 600 m above sea level a maximum height of 430m
above ground level was reached. The flight took place under
clear sky in a light breeze (2 m s−1wind speed). It served
as a real-world test of COCAP’s temperature stabilisation
(Fig. 11).
While ambient pressure pchanged by 5 kPa and ambient
temperature TAmbient by 4.5 ◦C during the flight, the tempera-
ture of the air stream at the CO2sensor’s outlet TOutlet varied
by only 0.13 ◦C and the temperature of the optical detector
TDetector by only 0.02 ◦C.
4.2.3 Comparison to the atmospheric observatory
Lindenberg
In order to verify COCAP’s in-flight measurements of am-
bient CO2dry air mole fraction, we made a comparison
to the atmospheric observatory Lindenberg. The Lindenberg
observatory is part of the Integrated Carbon Observation
System (ICOS, http://www.icos-ri.eu) and meets the World
Meteorological Organization (WMO) Global Atmosphere
Watch (GAW) recommendations for high-accuracy atmo-
spheric trace gas measurements (WMO, 2016). The Linden-
berg observatory (ICOS short name: LIN) is located in the
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M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems 1845
eastern part of Germany (52◦100N, 14◦070E) in a flat, rural
area. At LIN a 99 m mast is equipped with inlets at 2.5, 10,
40 and 98 m above ground level. Air is drawn from all in-
lets continuously, but only one sampling line is analysed at
a time. The gas analyser is switched to a different sampling
line every 5min (“quasi-continuous sampling”). It measures
carbon dioxide and methane dry air mole fraction.
We mounted COCAP on the same multicopter that was
used in Lannemezan (see Sect. 4.2.2) and carried out a to-
tal of 21 flights close to the mast (distance less than 150 m)
on 18 and 27 October 2016, using the same setup on both
days. During each flight, the multicopter ascended vertically
to 100 m above ground level at a climb rate of 0.5ms−1, fol-
lowed by a descent at a rate of 2 m s−1. The same pattern
was then repeated at approximately 70 m distance from the
first ascent. Each flight lasted 9 min and the two ascents were
separated in time by 4 min. The only exception was flight 7,
which we had to abort after the first ascent due to a technical
problem with the multicopter.
In flight, the multicopter mixes the air around it. To avoid
artefacts in our measurements caused by this mixing, we
sampled air from 70 cm above the rotors. Furthermore, for
the analysis detailed below we used only the data collected
during the ascents, i.e. when the UAS was flying into and
sampling undisturbed air. In each flight, we carried out the
second ascent upwind of the first ascent, which ensured that
the mixing caused by the first ascent did not degrade the mea-
surements during the second ascent.
On the evening of 18 October, the sky was cloudy with
occasional drizzle, the wind speed was low (1.5m s−1), and
the lowest 100 m of the atmosphere was weakly stable. On
the early evening of 27 October, conditions were similar, but
without precipitation. After 21:00 LT on 27 October, the sky
cleared up, followed by the formation of radiation fog.
At the mast’s 2.5 and 10m inlets, the variability of the CO2
dry air mole fraction was larger than above due to respira-
tion fluxes from soil and vegetation that were intermittently
mixed upwards by turbulence. This high variability makes
these levels less suitable for comparison to COCAP, as our
flights were not synchronised with the sampling at the mast.
We were not allowed to fly higher than 100 m; hence the 98m
inlet was not well covered by the flight pattern. We therefore
focus our comparison on the 40 m inlet of the mast.
After applying the calibration curve to the measurements
of COCAP’s CO2sensor, we corrected for its temporal re-
sponse by deconvolution. For each ascent, we then calcu-
lated the arithmetic mean of the measurements taken between
a height of 30 and 50 m. Figure 12 shows these means to-
gether with the LIN measurements at 40 m plotted against
time. Overall, there is good agreement between COCAP and
LIN. The variability in COCAP’s data is higher, likely caused
by a low-pass effect of the mast’s sampling system. Further
differences are due to the measurements being taken 100–
150 m apart and at different times. Finally, instrument noise
leads to discrepancies. All these factors should have a zero
Figure 12. Large dots represent calibrated measurements taken by
COCAP during the ascents at a height of (40 ±10)m above ground,
small dots are measurements from the LIN mast’s 40m inlet. Times
are in local time (UTC+2). The sun set at 18:02 LT on 18 October
and at 17:43 LT on 27 October. The gaps in the station data are due
to the measurement of other inlets and working tanks at those times.
Figure 13. (a) Data from COCAP are same as in Fig 12. Measure-
ments from the mast’s 40m inlet have been averaged over a period
that starts 20 min before and ends 20 min after the respective flight.
No measurements from the mast are available for flight 10 because
calibration cylinders have been measured at this time. (b) xCO2
measured by COCAP minus xCO2measured by LIN. Error bars
indicate the noise level of COCAP’s CO2sensor after deconvolu-
tion (see text). Flights 1 through 9 were carried out on 18 October,
flights 10 through 21 on 27 October (indicated by dashed vertical
line).
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1846 M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems
Table 3. Mean of the difference between COCAP’s CO2dry air
mole fraction measurements xCOCAP and the corresponding mea-
surements by LIN xLIN (±1 standard error). Subsets of COCAP’s
measurements are also analysed.
COCAP measurements xCOCAP −xLIN
in µmol mol−1
All 0.23 ±0.45
18 October 0.16 ±0.85
27 October 0.28 ±0.49
All first ascents 0.39 ±0.66
All second ascents 0.06 ±0.52
mean effect, whereas a consistent bias between COCAP and
the Lindenberg observatory would indicate a problem with
the calibration. A change in bias over time would suggest
instrument drift.
To better assess the presence of bias, we averaged the mea-
surements from the mast’s 40m inlet over a period starting
20 min before and ending 20 min after the respective flight
(Fig. 13a).
We then calculated the difference between the measure-
ments by COCAP and LIN (Fig. 13b). Additionally, we es-
timated the noise level of COCAP’s CO2sensor. The cor-
rection for COCAP’s finite time response by deconvolution
has the side effect of amplifying high-frequency electronic
noise. Therefore, we did not use the Allan deviation of the
data described in Sect 4.1.1 but calculated the Allan devia-
tion of the deconvoluted time series. During each ascent, the
multicopter climbed from 30 to 50 m height in approximately
40 s. In analysing a period during which a standard gas was
measured, we found an Allan deviation of 1 µmol mol−1for
τ=40 s. This number is represented as error bars in Fig. 13b.
Table 3 contains the mean difference between the mea-
surements by COCAP and LIN. A bias of zero lies within 1
standard error of the mean difference. This is also true for
both nights considered individually and for both ascents of
all flights considered individually. Table 4 lists the results
of statistical tests of three hypotheses: (1) no bias between
COCAP and LIN, (2) no change in the mean difference be-
tween COCAP and LIN from 18 October to 27 October and
(3) no change in the mean difference between COCAP and
LIN from the first to the second ascends. None of the hy-
potheses was rejected (p > 0.7 in all cases).
The physical connection between COCAP and the mul-
ticopter did not include a dedicated shock absorber (see
Fig. S10 in the Supplement). Although COCAP’s plastic
foam housing and the flexibility of the mounting straps pro-
vided limited mechanical isolation, sudden movements and
vibrations of the multicopter due to turbulence, rotor unbal-
ance and flight manoeuvres have been partially transmitted to
the measurement system. In theory, these mechanical distur-
bances could deteriorate the accuracy of the xCO2measure-
Table 4. Statistical tests for bias. Here xdenotes measurements by
COCAP and the index defines a subset: “A” for all measurements,
“18” and “27” for 18 and 27 October, respectively, and “A1” and
“A2” for first and second ascent, respectively. D(x) represents the
difference between xand the corresponding measurements by LIN.
An overline denotes the arithmetic mean.
Null hypothesis Statistical test Test result p
D(xC)=0 Welch’s ttest 0.75
D(x18)=D(x27)Welch’s ttest 0.72
D(xA1)=D(xA2)Student’s ttest 0.75
ments, e.g. by causing misalignment of the optical bench of
the CO2sensor. The data collected during the flights at LIN,
however, do not exhibit increased noise levels or instrument
drift compared to data collected on the ground, suggesting
that the movements and vibrations did not degrade COCAP’s
performance.
We conclude that the measurements gave no indication of
(1) calibration problems, (2) uncorrected drift of COCAP be-
tween 18 and 27 October, (3) drift of COCAP during flight or
(4) degradation of COCAP’s accuracy due to vibrations and
sudden movements of the multicopter.
5 Summary and conclusions
With COCAP we have designed and built a self-contained
analyser for the measurement of CO2dry air mole fraction,
temperature, humidity and pressure of ambient air on board
UASs. COCAP is typically operated under ambient condi-
tions that change quickly and over wide ranges. These chal-
lenging conditions can compromise the accuracy of CO2sen-
sors. We ensure COCAP’s accuracy by (1) temperature sta-
bilisation, (2) drying of sample air, (3) a calibration curve
that includes correction terms for temperature and pressure
and (4) regular field calibrations. When high-frequency noise
is filtered out, COCAP’s measurements of CO2dry air mole
fraction were found to deviate from a reference by not more
than 1.2 µmol mol−1during simulated flights and by not
more than 1 µmol mol−1during deployment in an instru-
mented van. In a comparison to the ICOS observatory Lin-
denberg no indication of bias or uncorrected drift was ob-
served.
Since the design of COCAP, newer versions of SenseAir’s
HPP sensor family have become available. They exhibit
lower drift and lower noise at a slightly smaller form factor
(Arzoumanian et al., 2016). The integration of the newer sen-
sors into COCAP would be straightforward and is expected
to further improve the accuracy of the xCO2measurements.
With a volume of 14cm×14 cm ×42cm and a mass of
1 kg COCAP fits onto small UASs with a take-off mass be-
low 5 kg. It is therefore a cost-effective tool to study carbon
dioxide in the lowest 100–1000 m of Earth’s atmosphere. On
Atmos. Meas. Tech., 11, 1833–1849, 2018 www.atmos-meas-tech.net/11/1833/2018/

M. Kunz et al.: COCAP: a carbon dioxide analyser for small unmanned aircraft systems 1847
a multicopter or fixed-wing aircraft, COCAP enables mea-
surements at a finer scale than manned aircraft and without
restrictions of minimum flight altitude. On a tethered bal-
loon, COCAP can take measurements for longer time spans
without being bound to fixed altitudes like an instrumented
mast or tower.
The techniques presented in this article are applicable to
other measurement systems as well. Many sensors benefit
from a stable temperature, and we have shown how an ef-
fective temperature stabilisation can be achieved within the
mass, size and power restrictions of a small UAS. Likewise,
the presented method for obtaining a calibration curve can be
applied to other gas sensors. Regular calibrations are impor-
tant to ensure the accuracy of trace gas measurements and we
have given an example how to implement them in a practica-
ble way.
Flying a CO2analyser on small UASs opens up new possi-
bilities in studying the carbon cycle. As a first application we
have constrained nocturnal carbon dioxide fluxes of vegeta-
tion using series of xCO2profiles in a budget method (Kunz et
al., 2018). A similar approach could be used to estimate CO2
emissions of cities, ideally by simultaneously deploying sev-
eral UASs at different downwind locations. Furthermore, the
strength of point sources like power plants or factories could
be estimated by applying a mass balance technique as is com-
monly used in aircraft-based studies (Conley et al., 2017 and
references therein). The main advantages of small UASs over
manned aircraft in these applications is their full vertical cov-
erage from the ground to several hundred metres height and
their much lower acquisition and operating cost. As small
unmanned aircraft are typically limited to a range between 1
and 50 km in a single flight, they are best suited for studying
smaller areas. Their low air speed and high manoeuvrability
enables them to sample the atmosphere with high spatial res-
olution. Equipped with an analyser for carbon dioxide, UASs
could also become a powerful validation tool for efforts to
model dispersion of tracers on fine scales, e.g. inside street
canyons.
Due to their unique capabilities and low cost, we foresee
that the use of unmanned aircraft in the Earth sciences will
significantly increase in the near future. We have shown how
accurate measurements of the CO2dry air mole fraction can
be taken on board small UASs and we anticipate these plat-
forms to play an important role in closing gaps in the obser-
vation of the carbon cycle.
Data availability. The analyses presented here are based on many
different experiments and use a combination of two or three differ-
ent data sources in most cases. Compiling the data into a uniform,
self-describing collection suitable for upload to a repository would
be a great effort. Given the fact that our experiments were aimed
at characterising COCAP, reuse of the data by other groups seems
unlikely. Hence, we did not upload our measurement data to a repos-
itory. However, data from individual experiments are available from
the corresponding author upon request.
Data from the ICOS station Lindenberg can be requested
from ICOS-D (http://www.icos-infrastruktur.de/en/mitarbeiter/
atmosphaerenprogramm/).
The Supplement related to this article is available online
at https://doi.org/10.5194/amt-11-1833-2018-supplement.
Competing interests. Christine Hummelgård, Hans Martin and
Henrik Rödjegård work for SenseAir AB, the manufacturer of the
HPP sensor family. The other authors declare that they have no con-
flict of interest.
Acknowledgements. We thank Maksym Bryzgalov (SenseAir AB,
Sweden) for helping with the configuration and integration of
the CO2sensor. Hök Instruments AB (Sweden) kindly provided
software for COCAP’s data logger. We thank Wieland Jeschag
and Till Fastnacht for adapting this software to our needs. We
acknowledge Jürgen Kaulfuß, who designed and built the field
calibration device. Calibration standards were prepared by the
gas lab of the MPI for Biogeochemistry Jena and we are grateful
for their support. We thank Frank Beyrich, Matthias Lindauer,
Udo Rummel and Marcus Schumacher (Deutscher Wetterdienst,
Germany) for access to the Lindenberg station, technical support
and data sharing. We gratefully acknowledge the authors of various
open-source software packages that were used in the project and
for the preparation of the manuscript, in particular GNU Octave
(including the optim package), KiCad, gnuplot, GIMP, Inkscape,
LyX and LaTeX. We thank the Max Planck Society for generous fi-
nancial support. Martin Kunz thanks COST (European Cooperation
in Science and Technology) and the German Academic Exchange
Service (DAAD) for funding.
The article processing charges for this open-access
publication were covered by the Max Planck Society.
Edited by: Russell Dickerson
Reviewed by: two anonymous referees
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