A dual thermistor radiosonde (DTR) comprising two
(aluminium-coated and black) sensors with different emissivities was
developed to correct the effects of solar radiation on temperature probes
based on in situ radiation measurements. Herein, the DTR performance is
characterised in terms of the uncertainty via a series of ground-based
facilities and an intercomparison radiosounding test. The DTR
characterisation procedure using laboratory facilities is as follows:
individually calibrate the temperature of the thermistors in a climate
chamber from -70 to 30 ∘C to evaluate the uncertainty of raw
temperature measurement before radiation correction; test the effect of
temperature on the resistance reading using radiosonde boards in the climate
chamber from -70 to 20 ∘C to identify a potential source of errors
owing to the boards, especially at cold temperatures; individually perform
radiation tests on thermistors at room temperature to investigate the degree of heating of aluminium-coated and black sensors (the average ratio = 1 : 2.4) and use the result for obtaining unit-specific radiation correction
formulas; and perform parameterisation of the radiation measurement and
correction formulas with five representative pairs of sensors in terms of
temperature, pressure, ventilation speed, and irradiance using an upper air
simulator. These results are combined and applied to the DTR sounding test
conducted in July 2021. Thereafter, the effective irradiance is measured
using the temperature difference between the aluminium-coated and black
sensors of the DTR. The measured irradiance is then used for the radiation
correction of the DTR aluminium-coated sensor. The radiation-corrected
temperature of the DTR is mostly consistent with that of a commercial
radiosonde (Vaisala, RS41) within the expanded uncertainty
(∼ 0.35 ∘C) of the DTR at the coverage factor k= 2. Furthermore, the
components contributing to the uncertainty of the radiation measurement and
correction are analysed. The DTR methodology can improve the accuracy of
temperature measurement in the upper air within the framework of the
traceability to the International System of Units.
Introduction
Measurement of essential climate variables, such as temperature and water
vapour (i.e. humidity) is important as they are essential input data for
weather and climate prediction models (Bojinski et al., 2014). The
temperature and humidity in the upper air are frequently and widely measured
using radiosondes. A radiosonde is a telemetry device comprising various
sensors that measure meteorological parameters and transmit the collected
measurement data via radio frequency while being flown by a weather balloon
up to about 35 km in altitude. Radiosonde observations can be co-located
with global navigation satellite system radio occultation and these
measurements are compared with each other to enhance the applicability and
reliability of both techniques. The measurement accuracy of radiosondes
needs to be improved in terms of uncertainty within the framework of the
traceability to the International System of Units (SI).
Joint research programs between the metrology and the meteorology and
climate communities, such as the MeteoMet–Metrology for Meteorology
project, were initiated (Merlone et al., 2015, 2018) to
acquire high-quality observational data on meteorological variables. Reference
facilities have been developed through the project for calibrating the
meteorological observation instruments to be used in the meteorological
community. Additionally, low-temperature and low-pressure humidity chambers
have been developed for calibrating radiosonde humidity sensors in the
environments imitating the upper troposphere/lower stratosphere
(Sairanen et al., 2015; Cuccaro et al., 2018). To investigate the
climate change, a certain level of measurement uncertainty in radiosoundings
should be secured in a SI-traceable way. Hence, the Global Climate Observing
System (GCOS) Reference Upper Air Network (GRUAN) was founded to establish a
dataset of traceable measurements with quantified uncertainties
(GCOS, 2007). The required measurement accuracy of temperature
specified by GRUAN is 0.2 ∘C in the stratosphere (GCOS,
2007).
A difficulty in improving the measurement accuracy of radiosondes is the
correction of the solar radiation-induced heating of sensors during the
daytime. The radiative heating of sensors is also affected by environmental
conditions, such as temperature, air pressure and air ventilation, that are
involved in convective cooling (Lee et al., 2018b, 2020).
All these parameters should be considered together to precisely evaluate the
radiation correction of radiosonde temperature sensors. Although most
radiosonde manufacturers apply radiation corrections to their products
(Nash et al., 2011), they do not disclose the detailed
methodologies, including reference systems and correction algorithms. To
independently evaluate the radiosondes, GRUAN has built a ground-based
calibration facility and established a correction algorithm for the GRUAN
data processing (GDP) of the Vaisala RS92 radiosonde (Dirksen et al.,
2014). The uncertainty of the GDP of RS92 during daytime was gradually
increased from 0.2 ∘C at the surface to 0.6 ∘C at 30 km with the coverage factor k= 2 (Dirksen et al., 2014). Recently,
the same group built a new simulator to investigate the solar temperature
error of radiosondes (SISTER) and derived a new GDP algorithm for the
Vaisala RS41 radiosonde (von Rohden et al., 2022). The setup can
control the irradiance, air pressure, ventilation, sensor rotation and
tilting of the light incident angle. Using the setup, the uncertainty of the
GDP of RS41 is evaluated to be about 0.3 ∘C (k= 2) at 35 km. It is also found that the daytime GRUAN profile is 0.35 ∘C warmer
than the manufacturer's at 35 km (von Rohden et al., 2022); however, the surrounding temperature, which also affects the radiation
correction, cannot be changed. Furthermore, an upper-air simulator (UAS) was
developed by the Korea Research Institute of Standards and Science (KRISS)
to similarly evaluate radiosondes (Lee et al., 2020). The UAS at
KRISS can simultaneously control the temperature, pressure, ventilation and
irradiance, and the UAS was recently supplemented with sensor tilting and
rotation functions. Using this setup, a radiation correction formula of the
RS41 radiosonde is presented (Lee et al., 2022); however, the radiation correction processes by GRUAN and KRISS assume that
the solar irradiance is known. In fact, the solar irradiance is dependent on
various parameters, such as cloud conditions, solar elevation angle, season
and location. To date, the direct in situ measurements of solar irradiance are difficult without using additional pyranometers measuring on the same
payload of radiosondes (Philipona et al., 2013). An alternative
approach comprises the simulation of solar irradiance with appropriate cloud
scenarios, surface albedo and solar angle (Key and Schweiger, 1998).
From the perspective of the radiation correction uncertainty, the SI
traceability of the simulated irradiance is incomplete when the sky is clear
or cloudy because the simulated irradiance is constructed from the average
of clear and cloudy sky cases (von Rohden et al., 2022). This
results in the increase of the radiation correction uncertainty in the
troposphere.
To resolve this issue, the concept of a dual thermistor radiosonde (DTR)
comprising two temperature sensors with different emissivities was
introduced to measure the effective irradiance using the temperature
difference between them (Lee et al., 2018a, b). The DTR
operation principle was demonstrated by investigating the effects of air
ventilation as well as temperature and pressure using a wind tunnel and a climate
chamber system, respectively. The temperature difference between the dual
thermistors was shown to be linearly proportional to the effective irradiance,
and the radiation-induced heating of the sensors was corrected according to
the measured effective irradiance. Only the slope of the linear function of
the radiation measurements and correction formulas changed with the
environmental parameters, and the linearity itself was not altered; however,
these DTR formulas were obtained using two separate setups that cannot be
combined, and thus, the correction formula was incomplete in terms of the SI
traceability.
Herein, the combined effect of temperature, pressure, ventilation and
irradiance on DTR is investigated using the UAS at KRISS for the
parameterisation of the radiation measurement and correction. The obtained
formulas are used in an intercomparison sounding test performed in July
2021. Furthermore, a series of laboratory characterisations of DTR is
conducted, including individual calibration of thermistors, test of
temperature effect on resistance reading by radiosonde boards and individual
radiation test on thermistors. The uncertainties due to parameterisation of
the radiation correction formula using UAS and other characterisations are
also evaluated. Then, the uncertainty components and their combined budget
for the measured irradiance and corrected temperature in the sounding test
are presented. Finally, the corrected temperatures of the DTR and the RS41
from parallel soundings are compared and the difference between them is
discussed in terms of the uncertainty.
Introduction to DTRDual thermistors with different emissivity
Figure 1a shows a DTR comprising two temperature sensors that are
chip-in-glass type negative temperature coefficient (NTC) thermistors
(Shibaura electronics, Model: PB7-41E). The glass bead encapsulating the
sensing element is ellipsoidal in shape with 0.55 ± 0.1 mm diameter and
1.1 ± 0.3 mm length. The two thermistors are attached to the sensor
boom via soldering and followed by epoxy for electrical insulation. The
thermistors and sensor boom are coated with aluminium (Al) via thermal
evaporation. One sensor is additionally coated with a black epoxy (Loctite,
Model: STYCAST 2850 FT) to differentiate the emissivity (absorptivity)
between them (inset of Fig. 1a). For convenience, the sensor
coated with only Al is referred to as the white sensor, while the other
sensor is referred to as the black sensor.
(a) Dual thermistor radiosonde (DTR) with a white and black sensor and (b) operation principle of DTR for irradiance measurement and correction of radiation effect based on the measured irradiance. The temperature difference between the dual thermistors (TB_raw-TW_raw) is linearly proportional to the
irradiance, and the radiation-induced heating of the white sensor
(TW_raw-TW_cor) is corrected based
on the irradiance measured by (TB_raw-TW_raw).
DTR operation principle
Previously, a pioneer work using multiple thermistors with different
spectral responses (emissivity and absorptivity) was conducted for the
radiation correction. In the work, however, complete knowledge on material
properties of air and sensors and sensor geometry is required to solve
multiple heat balance equations (Schmidlin et al., 1986). DTR
utilises the purely experimental temperature difference between the white
and black sensors to measure the effective irradiance and correct its effect
on the white sensor (Fig. 1b). The temperature increase of each sensor due
to solar irradiation is linearly proportional to the effective irradiance,
as previously investigated by various theoretical and experimental studies
(Lee et al., 2018b, a; Luers, 1990; McMillin et al.,
1992). Additionally, the temperature of the black sensor
(TB_raw) is higher than that of the white sensor
(TW_raw) due to its high light absorptivity. Thus, the
temperature difference between them (TB_raw-TW_raw) is also linearly proportional to the effective
irradiance. Although other environmental parameters, e.g. air pressure and
ventilation, affect the degree of heating of sensors via convective cooling;
they only change the slope of the linear function and do not affect the
linearity itself. The effect of other environmental parameters on the
temperature difference and the temperature increase of the white sensor are
investigated using the UAS developed at KRISS (Lee
et al., 2022). Experimental results of the UAS are used to determine a
formula to measure the effective irradiance based on the temperature
difference between the two thermistors. Section 4 describes the procedure to
obtain these formulas for the measurement of irradiance and the correction
of the white sensor using the UAS in more detail.
DTR characterisationCharacterisation procedure
The DTR characterisation procedure is summarised in Fig. 2a–e. The
characterisation process is categorised into laboratory experiments and
sounding tests. First, the calibration of thermistors attached to the sensor
boom is conducted from -70 to 30 ∘C in a climate chamber (Fig. 2a) and the uncertainty of raw temperature measurement is evaluated. Then,
the temperature effect on the resistance reading by radiosonde boards is
tested in the climate chamber from -70 to 20 ∘C to identify a
potential source of errors owing to the boards, especially at cold
temperatures (Fig. 2b). The temperature increase of all thermistors due to
irradiation is individually recorded at room temperature (Fig. 2c) to
include the differences in the sensitivities of the individual thermistors
in the radiation correction. The radiation measurement and correction
formulas of DTR are obtained in terms of temperature, pressure, ventilation
speed and irradiance using the UAS (Fig. 2d). The laboratory experimental
results are combined and applied to the DTR sounding system. Then, the
sounding results of DTR are compared with those of a commercial radiosonde
through dual soundings (Fig. 2e). Each characterisation procedure is
discussed in detail in the following sections.
Characterisations of DTR. (a) Individual calibration of
thermistors in a climate chamber, (b) test of the effect of temperature on the resistance reading using the radiosonde boards in the climate chamber, (c) radiation test on individual thermistors, (d) parameterisation of radiation measurement and correction formulae using an upper air simulator and (e) sounding test by applying laboratory characterisation results.
Individual calibration of thermistors in a climate chamber
All thermistors are individually calibrated in a climate chamber (Kambic,
Model: KK-190 CHULT). Figure 3a displays the calibration setup showing the
sensors on the booms in the climate chamber, a digital multimeter (Keysight,
Model: 34980A) to record the sensor resistances and a data acquisition
computer. The setup can calibrate 35 pairs (7 × 5) of dual
thermistors that are located on the same rectangular plane (230 mm × 190 mm). Five platinum resistance thermometers (PRT) with a nominal resistance of 100 Ω (PT100) are used as reference
thermometers. They were calibrated at KRISS with an uncertainty of 0.05 ∘C at a coverage factor k= 2 and installed at the centre and four
corners in the same rectangular plane as the thermistors. The average of the
temperatures measured by the five reference PRTs (TRef_aver) is used as the reference temperature for calibration. Six
calibration points are selected from -70 to 30 ∘C (Fig. 3b), of
which the y-axis denotes the spatial temperature deviations
(TRef_devi) represented by the maximum deviation from
TRef_aver. Although the calibration range should be
extended to -90 ∘C to cover temperatures over tropical and polar
regions, it is not feasible using the climate chamber because the typical
lowest temperature limit is approximately -80 ∘C.
Calibration of individual thermistors in a climate chamber. (a) Calibration setup showing thermistors on booms (left), a digital multimeter to read the sensor resistance (top right) and a data acquisition computer (bottom right). (b) Maximum temperature deviations (TRef_devi) with respect to the average of five reference thermometers (TRef_aver) as a function of TRef_aver. Distribution of the residuals of the (c) white and (d) black sensors by individually applying the calibration curves. (e) The uncertainty budget on the radiosonde thermistor calibration, U(Ts_cal), with a coverage factor k= 2. Uncertainty factors including reference temperature deviations U(TRef_devi), stability U(TRef_stab) and calibration U(TRef_cal), radiosonde sensor
stability U(Ts_stab) and fitting residual
U(Ts_fit_resid) are considered for
U(Ts_cal).
Generally, the Steinhart-Hart equation is used for the calibration of NTC
thermistors (White, 2017); however, the application of a third-order
polynomial equation, i.e. the inclusion of a quadratic term, which is not
present in the Steinhart-Hart equation, yields smaller fitting residuals
than that of a second-order equation (Yang et al., 2021). In the work
of Yang et al. (2021), the maximum value of the residuals was 117 and 13 mK for the second-order polynomial and the third-order polynomial, respectively.
Therefore, the Steinhart-Hart equation is modified for the calibration as
follows:
1Ts=a0+a1lnRs+a2ln(Rs)2+a3ln(Rs)3,
where Ts is the sensor temperature obtained based on the sensor
resistance Rs and a0, a1, a2 and a3 are the fitting
coefficients. The distributions of the fitting residuals of the white and
black sensors are shown in Fig. 3c and d, respectively. In total, 696
data points are obtained, collected from 6 calibration points of 116
thermistors of the same colour. No essential difference is observed between
the white and black sensors in the distributions of the residuals, implying
that the emissivity difference plays a negligible role in the sensor
calibration process.
Furthermore, the uncertainty of radiosonde sensors (thermistors) due to
calibration U(Ts_cal) at k= 2 is calculated, as shown in
Fig. 3e. The contributing uncertainty factors are temperature deviations
U(TRef_devi), stability U(TRef_stab) and
calibration U(TRef_cal) of the reference PRTs and the
temperature stability U(Ts_stab) and fitting residuals
U(Ts_fit_resid) of the sensors
(thermistors). Consequently, the uncertainty of thermistors due to
calibration is about 0.1–0.3 ∘C (k= 2) between 30 and -70 ∘C. The uncertainty due to spatial temperature deviations
U(TRef_devi) in the chamber dominates the calibration
uncertainty. The deviations are due to the temperature difference between
the front door side and the rear fan side of the chamber. One of the
practical ways to improve the calibration uncertainty is to find a location
with reduced spatial temperature deviations in the climate chamber. More
recently, the deviations were reduced by about one quarter of Fig. 3b at
-70 ∘C by moving the thermistor set (35 pairs) lower than the rear
side fan to avoid the direct wind. The temperature deviations can be
affected by the thermal insulation of the door and the aisles for data
cables as well as the ventilation by the fan in the chamber.
Test of temperature effect on resistance reading by radiosonde boards
To properly measure the temperature using the thermistors via Eq. (1), the
effect of the temperature of the radiosonde electronics board on the
thermistor resistance measurement should be investigated in the same
temperature range of the thermistor calibration. Thus, 10 radiosonde
prototypes covered with expanded polystyrene foam are installed in the
climate chamber with varying temperatures. The radiosonde boards are wired
to external reference resistors (Cropico, Model: 008-B) instead of
thermistors, as shown in Fig. 4a. The resistance measured by radiosonde
boards is collected by a computer via wired communication.
Test of the temperature effect on resistance reading by radiosonde
boards. (a) Test setup showing the radiosonde boards in a climate chamber (left), reference resistors (top right) and a data acquisition computer (bottom right). (b) Difference between the reference resistance and radiosonde reading as a function of the reference resistance. (c) Residual after conversion of resistance to temperature as a function of temperature.
Figure 4b shows the difference between the reference resistance and
radiosonde reading as a function of the reference resistance. The reference
resistance is changed according to the environmental temperature of the
radiosonde boards, which is varied from -70 to 20 ∘C. For example,
a reference resistance of 700 kΩ is chosen to imitate the sensor
resistance of -70 ∘C when the temperature of the climate chamber
measured by reference PRTs (TRef_aver) is -70 ∘C. Thereafter, both the reference resistance and resistance reading
by radiosonde boards are converted into temperatures using a calibration
curve based on Eq. (1). The resultant temperature error by radiosonde boards
with varying temperature is shown in Fig. 4c. Assuming that the
probability distribution is a normal distribution function, the standard
deviation (SD) of all data points (0.04 ∘C) is used for standard
uncertainty due to the influence of the temperature of radiosonde
electronics boards on the resistance (or temperature) measurement.
Individual radiation test on radiosonde thermistors
The purpose of the calibration of thermistors and the investigation of the
temperature effect on radiosonde electronics boards is to assess the
accuracy (or uncertainty) of raw temperature measurement before radiation
correction. The following step is to investigate the sensitivity of
individual thermistors to irradiation because the amount of radiation
correction varies for individual radiosondes, presumably related to the
production process of the thermistors. This can be attributed to the
irregularity in the thermistor glass bead sizes, the black epoxy coating and
the sensor connection to the boom via soldering and epoxy. Effective
irradiance to thermistors and the cooling by convection can be changed based
on the glass bead sizes and the Al and black epoxy coatings. The connection
between the sensor leads and the boom may be irregular because the soldering
and the coating of epoxy resin were conducted manually. Radiative heating of
glass beads, leads, and connection parts between the sensor leads and the
boom should be affected by their size as previously reported (de
Podesta et al., 2018); however, obtaining radiation correction formulas of
radiosondes individually using UAS with varying temperature, pressure, air
ventilation speed and irradiance is time-consuming and economically
unfavourable. Therefore, a rotational radiation test (RRT) is performed on
all thermistors in a vacuum chamber at room temperature (∼ 25 ∘C), and the results are correlated to the UAS experiments to
acquire sensor-specific radiation correction formulas that reflect the unit
difference. The RRT irradiance at the sensor position is 800 W m-2 with 0.8 % standard deviation for each irradiation. The
ventilation and the pressure in the chamber are not measured. Since they
depend on the performance of the vacuum pump and the sealing of the chamber
lid using an O-ring, there can be slight variations in the ventilation and
the pressure.
Rotational radiation test (RRT) on radiosonde thermistors
individually. (a) RRT setup showing the radiosonde thermistors in a chamber, solar simulator, and vacuum pump (left), a digital multimeter (top right) and a data acquisition computer (bottom right). (b) Temperature measured by a white (TW) and black (TB) sensor with/without light irradiation by the solar simulator. (c) Distribution of the temperature difference between the paired white and black sensors. (d) Distribution of the temperature increase of white sensors by the irradiation. Five pairs of a white and black sensors were selected for radiation correction experiments using an upper air simulator (UAS), as indicated by black arrows in (c) and (d).
Figure 5a shows an individual radiation test setup comprising a solar
simulator, vacuum pump, vacuum chamber, digital multimeter and computer. A
pair of dual thermistors is illuminated through a window in the lid of the
vacuum chamber. The diameter (D) of the beam spot on the sensor is 45 mm and the distance between the sensor bead and the beam boundary is 25 mm. The
rotation of 12 pairs of sensors and the light irradiation of the solar
simulator are automatically controlled using a computer program. When a pair
of dual thermistors arrives and stops beneath the window during rotation,
the window is screened by a shutter to block the light irradiation. At this
time, the irradiance is measured using a calibrated pyranometer on the
shutter. Then, the shutter is opened and closed for 180 s each and this
process is repeated 3 times for the illumination on each pair of
thermistors. The temperatures of the white (TW) and black (TB) sensors are recorded (Fig. 5b), and 107 pairs of dual thermistors are
tested in total. The temperature rise by the irradiation is determined by
the difference of the average temperature for the last 30 s (30 data
points) before the shutter is opened and closed. The mean temperature rise
of the three repeated measurements is assigned as the RRT value for each
pair of thermistors. The average ratio of the radiative heating of
aluminium-coated and black sensors is 1 : 2.4 in the RRT experiment. Figure 5c and d show the temperature difference distributions between a pair of thermistors (TB_on-TW_on) and the
temperature increase of the white sensor (TW_on-TW_off), respectively. The subscripts on and off indicate
when the light irradiation is turned on and off, respectively. These values
are used as parameters for the sensor-specific radiation correction formulas
obtained by UAS experiments. Although the irradiance is constant for each
sensor, the cooling efficiency of the sensors may vary depending on the bead
size of thermistors, air flow, and the pressure. Five representative pairs
of thermistors are selected for the radiation correction experiments using
UAS, as indicated by black arrows in Fig. 5c and d.
Parameterisation for radiation measurement and correction by DTR using UASRadiation measurement by DTR
The DTR is installed upside down in the test chamber of the UAS with the
thermistors and the sensor boom in parallel with the air flow but
perpendicular to the irradiation. Figure 6a–e show the UAS
measurements for five representative temperature differences
(TB_on-TW_on) between a pair of
dual thermistors selected from the RRT in Fig. 5c. Previous studies
reported that UAS has the capability of simultaneously varying environmental
parameters for the radiation correction of commercial radiosondes (Lee et
al., 2020, 2022). In Fig. 6, air pressure (P) is varied from 5 to
500 hPa and temperature (TW_off) is varied from -68 to
20 ∘C with a fixed irradiance (S0= 960 W m-2)
and ventilation speed (v0= 5 m s-1). As expected, the
level of (TB_on-TW_on)RRT is
positively correlated with the degree of (TB_on-TW_on)UAS, exhibiting a gradual decrease of
(TB_on-TW_on)UAS with
decreasing (TB_on-TW_on)RRT
(Fig. 6a–e).
Temperature differences between paired white and black sensors
(TB_on-TW_on) investigated using UAS. (a–e) (TB_on-TW_on) of the five paired radiosonde thermistors as a function of air pressure with varying temperature. (f) Residual irradiance calculated on the basis of (TB_on-TW_on) obtained in UAS and the rotational radiation test.
To parameterise the radiation measurement formula, (TB_on-TW_on) of the UAS is fitted with empirical equations
as follows:
(TB_on-TW_on)UAS=T0(TW_on)+A0(TW_on)⋅exp-P⋅P0(TW_on)-1+A1(TW_on)⋅exp-P⋅P1(TW_on)-1,
where T0(TW_on), A0(TW_on),
P0(TW_on), A1(TW_on) and
P1(TW_on) are the fitting coefficients being
functions of TW_on and units of ∘C,
∘C, hPa, ∘C and hPa, respectively. The dashed lines in
Fig. 6a–e represent the fittings.
Interestingly, the level of (TB_on-TW_on) gradually increases as the temperature decreases
especially for low pressures. A similar phenomenon was previously observed
in a chamber with no apparent air ventilation (Lee et al., 2018a).
The observed effect of temperature on (TB_on-TW_on) is because the convective heat transfer between
the sensor and air is reduced at cold temperatures with positive
correlations between the thermal conductivity and the viscosity of air and
the air temperature (Lee et al., 2022). To
incorporate the effect of temperature (TW_on) in Eq. (2),
its coefficients of T0(TW_on), A0(TW_on), P0(TW_on), A1(TW_on)
and P1(TW_on) are fitted with linear functions of
TW_on as follows:
3T0(TW_on)=a0⋅TW_on+a1,4A0(TW_on)=b0⋅TW_on+b1,5P0(TW_on)=c0⋅TW_on+c1,6A1(TW_on)=d0⋅TW_on+d1,7P1(TW_on)=e0⋅TW_on+e1,
where a0, a1, b0, b1, c0, c1, d0, d1,
e0 and e1 are the fitting coefficients. These coefficients are
collected from five pairs of thermistors and each coefficient is again
functionalised with (TB_on-TW_on)RRT to incorporate the individuality of thermistors observed in
RRT into Eq. (2) as follows:
CoefficientRad_meas=SlopeRad_meas⋅(TB_on-TW_on)RRT+InterceptRad_meas,
where CoefficientRad_meas represents a0,
a1, b0, b1, c0, c1, d0, d1, e0 and e1 from the five pairs of dual thermistors, and SlopeRad_meas and InterceptRad_meas
are the corresponding fitting coefficients. Table 1 presents the
SlopeRad_meas and
InterceptRad_measvalues. The applied concept of
transferring the individual radiation sensitivities from the RRT based on
the five chosen units to Eq. (2) does not necessarily rely on “realistic”
irradiation and ventilation conditions in the RRT setup, but rather on the
consistence of the existing conditions in the RRT over the radiation tests
of all other sondes. The representativeness of the RRT results of the five
thermistor pairs as part of all thermistors is based on the proportionality
with the UAS results.
SlopeRad_meas and InterceptRad_meas of a0, a1, b0, b1, c0, c1, d0, d1, e0 and e1.
During soundings, the irradiance (S) is unknown but can be found using
(TB-TW) of DTR. Hence, Eq. (2) is employed to measure the in situ irradiance using (TB_raw-TW_raw), where TB_raw and TW_raw are raw
temperatures of the black and white sensors, respectively, based on the fact
that the temperature difference between two sensors is linearly proportional
to S (Lee et al., 2018a, b):
S=S0×(TB_raw-TW_raw)⋅(TB_on-TW_on)UAS-1,
where the result of the individual radiation test (TB_on-TW_on)RRT is incorporated using Eqs. (2)–(8).
Consequently, Fig. 6f shows the fitting residual. Although the temperature
difference of the five pairs of thermistors is different by nearly a factor
of 3, as shown in Fig. 6a–e, the residuals are within ±20 % due to the parameterisation of the RRT value into Eq. (9).
In Eq. (9), the air ventilation speed (v) imitating the ascent speed of
radiosondes is fixed at v0= 5 m s-1 and thus the
effect of air ventilation cannot be identified in Fig. 6f. As determined
by a separate pair of thermistors, (TB_on-TW_on)UAS decreases by 0.08 ∘C on average
when v increases by 1 m s-1 due to the convective cooling in
the range of v= 4–6.5 m s-1 and P= 7–100 hPa (data not shown). Thus, Eq. (9) can be revised to include the effect of air
ventilation speed as follows:
S=S0×(TB_raw-TW_raw)⋅(TB_on-TW_on)UAS-0.08⋅(v-v0)-1.
The standard deviation of the residual for a pair of thermistors is 4.1 %
with Eq. (9), while it is reduced to 3.4 % with Eq. (10) when the air
ventilation is actually changed (4–6.5 m s-1). The absolute
value of the sensitivity coefficient (-0.08 ∘C (m s-1)-1) against the ventilation speed will be significantly bigger when
v is lower than 4 m s-1 while it will be a bit smaller when
P is higher than 100 hPa. Note that Eq. (10) is used for the intercomparison sounding test, as described later.
Radiation correction by DTR
Figure 7a–e shows the (TW_on-TW_off) measured for obtaining the radiation correction
values of the white sensors selected from the RRT in Fig. 5d. The
experimental conditions of P, TW_off, S0 and v0
are identical to that of Fig. 6. Since the (TW_on-TW_off)RRT shows a positive correlation with the
(TW_on-TW_off)UAS, the
(TW_on-TW_off)RRT can be
parameterised into a radiation correction formula based on
(TW_on-TW_off)UAS to
neutralise the difference among units.
Radiation correction value of white sensors (TW_on-TW_off) investigated using UAS. (a–e) (TW_on-TW_off) of the five radiosonde white sensors as a function of air pressure with varying temperature. (f) Residual of correction value calculated on the basis of (TW_on-TW_off) in UAS and the rotational radiation test.
To obtain the radiation correction formula of the DTR white sensors, the
values of (TW_on-TW_off)UAS
are fitted with empirical functions (dashed lines in Fig. 7) as follows:
(TW_on-TW_off)UAS=T1(TW_on)+A2(TW_on)⋅exp-P⋅P2(TW_on)-1+A3(TW_on)⋅exp-P⋅P3(TW_on)-1,
where T1(TW_on), A2(TW_on),
P2(TW_on), A3(TW_on) and
P3(TW_on) are the fitting coefficients as a function
of TW_on having units of ∘C, ∘C,
hPa, ∘C and hPa, respectively.
The (TW_on-TW_off)UAS is
dependent on the temperature. The (TW_on-TW_off)UAS at -68 ∘C is 118.9 ± 3.5 % (mean ± SD of 5 units) of that at 20 ∘C, when P= 5 hPa. In the previous study, the ratio for RS41 investigated by the same manner was 119 % (Lee et al., 2022). The
thermal conductivity and the viscosity of air decrease as the air
temperature decreases while the density of air is inversely correlated with
the temperature. The net effect of these air properties is that the heat
transfer from the sensor to air is positively correlated with the air
temperature (Lee et al., 2022). The effect of
long-wave radiation from the sensor is minor compared with that of
convective heat transfer.
The effect of temperature (TW_on) in Eq. (11) is
incorporated into the coefficients of T1(TW_on), A2(TW_on), P2(TW_on), A3(TW_on) and P3(TW_on) by fitting them with empirical linear functions of TW_on as follows:
12T1(TW_on)=f0⋅TW_on+f1,13A2(TW_on)=g0⋅TW_on+g1,14P2(TW_on)=h0⋅TW_on+h1,15A3(TW_on)=i0⋅TW_on+i1,16P3(TW_on)=j0⋅TW_on+j1,
where f0, f1, g0, g1, h0, h1, i0, i1,
j0 and j1 are the fitting coefficients. These coefficients are
obtained from five pairs of thermistors selected from the RRT and then each
coefficient is changed into a function of (TW_on-TW_off)RRT to incorporate the RRT result into Eq. (11):
CoefficientRad_cor=SlopeRad_cor⋅(TW_on-TW_off)RRT+InterceptRad_cor,
where CoefficientRad_cor represents f0,
f1, g0, g1, h0, h1, i0, i1, j0 and j1, and SlopeRad_cor and
InterceptRad_cor represent the corresponding
fitting coefficients. The SlopeRad_cor and
the InterceptRad_corvalues are presented in
Table 2.
SlopeRad_cor and InterceptRad_cor of f0, f1, g0, g1, h0, h1, i0, i1, j0 and j1.
Although the irradiance (S0) is fixed as 960 W m-2
herein, (TW_on-TW_off)UAS is
linearly proportional to S, as experimentally and theoretically studied in
previous studies (McMillin et al., 1992; Lee et al., 2018b). To include
the irradiance (S) obtained using Eq. (10) into the radiation correction
formula, Eq. (11) is revised as follows:
(TW_raw-TW_cor)=S⋅S0-1×(TW_on-TW_off)UAS,
where TW_raw and TW_cor are the raw
temperature and radiation-corrected temperature of the white sensor, respectively. The
result of the individual radiation test (TW_on-TW_off)RRT is incorporated using Eqs. (11)–(17).
The fitting residual obtained using Eq. (18) is shown in Fig. 7f. Although
the radiation correction values of the 5 pairs of thermistors differ by
more than a factor of 2, as shown in Fig. 5a–e, the residuals are
within ±0.2 ∘C due to the RRT results considered for Eq. (18).
The effect of air ventilation speed is studied by a separate pair of
thermistors and consequently, the (TW_on-TW_off)UAS decreases by 0.1 ∘C on average
when v increases by 1 m s-1 in the range of v= 4–6.5 m s-1 and P= 7–100 hPa (data not shown). Thus, Eq. (18)
can be slightly modified to incorporate the effect of v as follows:
(TW_raw-TW_cor)=(S⋅S0-1)×(TW_on-TW_off)UAS-0.1⋅(v-v0).
If the air ventilation is actually changed (4–6.5 m s-1),
the standard deviation of the residual for a pair of thermistors is 0.10 ∘C by Eq. (18) while it reduces to 0.04 ∘C with Eq. (19).
The absolute value of the sensitivity coefficient (-0.1 ∘C (m s-1)-1) will significantly grow as v is lowered below 4 m s-1 whereas it will become smaller when P is higher than
100 hPa. It should be noted that Eq. (19) is applied to the DTR radiation
correction in the intercomparison sounding test.
Sounding test of DTR
The radiation measurement and correction formulas of the DTR obtained via
laboratory characterisations were applied to the sounding test performed
during July 2021 in Jeju Island, South Korea. One, two, or three DTRs were
tested in parallel with a RS41 in a single flight. The number of comparison
(N) was N= 12 at daytime from 7 soundings. The daytime sounding was
performed from 11:00 to 17:00 local time. The sky was normally cloudy.
Figure 8a shows an example of the temperature difference
(TB_raw-TW_raw) between the two
sensors during sounding in the daytime. Note that (TB_raw-TW_raw) in the sounding data corresponds to the
(TB_on-TW_on)UAS of the UAS
experiment. Figure 8b displays the irradiance measured by the DTR based on
the temperature difference between the dual thermistors and environmental
parameters, including TW_raw, P and v. The irradiance
measured by the DTR is the net effective irradiance to or from the thermistors
including the components of direct solar irradiation, its reflection and
scattering, the long-wave radiation from the earth, and the long-wave
radiation from the thermistors; however, these components cannot be
distinguished through DTR measurements. The radiation correction formula of
the DTR is obtained based on the portion of the long-wave and the short-wave
radiation from the solar simulator used as a radiation source in the UAS
experiments. The emissivity and absorptivity are dependent on the
wavelength. In this respect, the radiative heating of the DTR in soundings
can be affected by the actual ratio of the long-wave and the short-wave
radiation. For aluminium coating, the reflectance was 0.8–0.9 below 1000 nm and 0.9 above 1000 nm in wavelength. This means that the influence of the
ratio between the long-wave and short-wave radiation would be a few percent of
the radiative heating of the DTR even when the portion below 1000 nm is
drastically different between the laboratory experiments and soundings.
Then, using the effective irradiance (S), the radiation correction value
(TW_raw-TW_cor) of the white
sensor is obtained using Eq. (19), as shown in Fig. 8c. The correction
value of the white sensor tends to gradually increase from the ground to the
stratosphere with some fluctuations in the troposphere due to clouds.
Sounding test of dual thermistor radiosondes. (a) Raw temperature difference between the white and black sensors (TB_raw-TW_raw), (b) effective irradiance based on (TB_raw-TW_raw) calculated by Eq. (10) and (c) radiation correction value of the white sensor in the daytime
calculated by Eq. (19).
Uncertainty evaluation and intercomparisonUncertainty budget on radiation measurement by DTR
According to the radiation measurement formula by the DTR (Eq. 10), the
factors for the uncertainty of radiation measurement U(S) are
TW_on, P, v, S0 and fitting residuals in Fig. 6f.
These factors contribute to U(S) as follows:
20∂S∂TW_on⋅U(TW_on),21∂S∂P⋅U(P),22∂S∂v⋅U(v),23∂S∂S0⋅U(S0),24S100⋅U(Fitting).
Here, U(parameter) represents the expanded uncertainty of each
parameter at k= 2, and the partial differential terms represent the
sensitivity coefficients. The sensitivity coefficient of the uncertainty due
to the fitting error U(Fitting) is S/100 because it is provided
as a percentage in Fig. 6f. Then, U(S) is obtained by combining the
contributions from these factors based on the uncertainty propagation law:
U(S)=∂S∂TTW_on2⋅U(TW_on)2+∂S∂P2⋅U(P)2+∂S∂v2⋅U(v)2+∂S∂S02⋅U(S0)2+S1002⋅U(Fitting)2.
Figure 9a shows the average of the effective irradiance measured by DTR
with the expanded uncertainty (k= 2) calculated using Eq. (25) in daytime. Radiation measurements by DTR from N= 12 are averaged in daytime. Examples
of the uncertainty budget for the radiation measurement by the DTR at an
altitude of 30 km are summarised in Table 3.
Uncertainty analysis on the DTR and intercomparison with Vaisala
RS41. (a) Daytime effective irradiance measured by DTR with uncertainty (k= 2). (b) Uncertainty factors contributing to the uncertainty of the corrected temperature U(TW_cor) of DTR in daytime. (c) Temperature difference between DTR and RS41 with DTR uncertainty (k= 2) at daytime.
Daytime uncertainty budget on radiation measurement of S= 1141 W m-2 by DTR at an altitude of 30 km.
UncertaintyConditionUnitUncertaintyContribution to uncertainty offactorat 30 km(k= 2)radiation measurement (k= 2)TW_on-41.5∘C0.23106 W m-2P12.6hPa0.35 W m-2v6.1m s-10.125 W m-2S0960W m-26173 W m-2Fitting error–%23.4268 W m-2U(S), Expanded uncertainty for radiation 297 W m-2measurement of 1141 W m-2 (k= 2) Uncertainty of radiation correction by DTR
The radiation-corrected temperature (TW_cor) of DTR is
obtained by subtracting the radiation correction value calculated using Eq. (19) from the raw temperature (TW_raw) of the white
sensor:
TW_cor=TW_raw-S⋅S0-1⋅(TW_on-TW_off)UAS-0.1⋅(v-v0).
Then, the uncertainty of the corrected temperature
U(TW_cor) is calculated as follows:
U(TW_cor)2=U(TW_raw)2+US⋅S0-1⋅(TW_on-TW_off)UAS-0.1⋅(v-v0)2,
where U(parameter) is the expanded uncertainty (k= 2). U(TW_raw)2 is the uncertainty of the raw
temperature that is related to the uncertainty due to the calibration
U(TS_cal)2 of thermistors in
the climate chamber (Fig. 3) and the uncertainty due to the temperature
effect on the radiosonde board U(TBoard_temp)2 (Fig. 4). US⋅S0-1⋅(TW_on-TW_off)UAS-0.1⋅(v-v0)2 is the
uncertainty of the radiation correction value that is obtained using Eq. (19), comprising uncertainty factors TW_on, P, v and
S0 and fitting residuals. The fitting residuals include the uncertainty
due to RRT U(TRRT)2 (Fig. 7).
Consequently, the expanded uncertainty of the corrected temperature of the
DTR is as follows:
U(TW_cor)=∂TW_cor∂TW_on2⋅U(TW_on)2+∂TW_cor∂P2⋅U(P)2+∂TW_cor∂v2⋅U(v)2+∂TW_cor∂S02⋅U(S0)2+12⋅U(TRRT)2+12⋅U(TS_cal)2+12⋅U(TBoard_temp)2.
Figure 9b shows U(TW_cor) and
its uncertainty components in daytime. In daytime the DTR uncertainty
gradually increases up to about 0.35 ∘C at the tropopause and is
maintained in the stratosphere (0.33 ∘C at 30 km). An example of
the uncertainty budget on the radiation-corrected temperature of the DTR
(TW_cor) at an altitude of 30 km is summarised in
Table 4.
Uncertainty budget on radiation-corrected temperature by
DTR in daytime at an altitude of 30 km.
The altitude-dependent U(TW_cor) of DTR (k= 2) in daytime is
summarised in Table 5. The uncertainty at the tropopause
(∼ 15 km) is higher than other regions mainly because the
calibration uncertainty of the thermistors increases as the temperature is
lowered (Fig. 3e). This means that a reduction of the calibration
uncertainty of a massive amount of thermistors is needed to improve the
uncertainty of radiation-corrected temperature of the DTR.
The radiation-corrected temperature of DTR (TW_cor=TDTR) is compared to that of a commercial radiosonde (Vaisala, RS41) via
parallel sounding. Figure 9c displays the difference between the DTR and
RS41 temperatures (TDTR-TRS41) with the DTR uncertainty (k= 2)
as error bars during the daytime. Generally, the two temperatures are within
the DTR uncertainty during daytime. The manufacturer specifies that the
uncertainty of RS41 is 0.3 ∘C in altitudes of 0–16 km and 0.4 ∘C above 16 km (Vaisala, 2022). Then,
the combined uncertainty of the RS41 (0.4 ∘C) and the DTR
(0.33–0.35 ∘C) is 0.52–0.53 ∘C (k= 2) at 16 km and
higher. Thus, the observed differences between the RS41 and the DTR are
within their combined uncertainty in daytime. Nevertheless, the
radiation-corrected temperature of DTR is about 0.4 ∘C higher
than that of RS41 around 30 km in daytime. A similar trend is observed in
the radiation correction of the RS41 radiosonde by the GRUAN using the
SISTER setup (von Rohden et al., 2022). The radiation-corrected
temperature of the RS41 obtained by the GRUAN is 0.35 ∘C warmer
than that provided by Vaisala at 35 km although the difference in
temperature between the GRUAN and Vaisala is within their combined
uncertainty.
Recently, we have obtained a radiation correction formula of RS41 under a
well-defined irradiance in the UAS (Lee et al.,
2022); however, the correction formula cannot be applied to RS41 because the
irradiance and its uncertainty in soundings are unknown. In this respect, the
GRUAN uses a simulated irradiance calculated by the average of clear and
cloudy sky cases for the radiation correction of RS41 (von
Rohden et al., 2022). The maximum uncertainty of RS41 by the GRUAN is about
0.3 ∘C at k= 2, which is larger than our previous work on RS41
(0.17 ∘C at k= 2). This is because the irradiance in our work
is assumed to be 1360 W m-2 in the stratosphere with a small
uncertainty obtained by the laboratory experiments corresponding to the
irradiance. Therefore, one of the prerequisites for the uncertainty
evaluation on the radiation correction is to know the irradiance and its
uncertainty in soundings. This work may contribute to improving the
measurement of the irradiance and the estimation of its uncertainty using
dual thermistor radiosondes.
Conclusions
The performance and uncertainty of DTR were evaluated via a series of
laboratory setups and intercomparison sounding with a commercial radiosonde
(Vaisala, RS41). The DTR comprises two temperature sensors (white and black)
with different emissivities; their temperature difference can be used for
the in situ measurement of the effective irradiance and the correction of the
radiation-induced bias of the white sensor. The thermistors were
individually calibrated in the range of -70–30 ∘C in a climate
chamber, and the uncertainty due to the calibration was evaluated. Moreover,
the effect of temperature on resistance reading by radiosonde boards was
investigated from -70 to 20 ∘C in the climate chamber, and the
corresponding uncertainty was evaluated. The RRT was individually performed on
the thermistors to compensate for the unit difference. Parameterisation of
the radiation measurements and correction formulas of DTR was performed via
UAS experiments with varying temperature, pressure and ventilation speed.
The fitting residual of the five DTRs selected from RRT was within 0.2 ∘C. The radiation measurement and correction formulas obtained by UAS were applied to the sounding test of DTR conducted in July 2021. The
method of obtaining the radiation correction value of DTR using the
effective irradiance measured by the temperature difference between dual
sensors during sounding was discussed. Then, the contributing uncertainty
factors on the corrected temperature of DTR were summarised for daytime.
Generally, the uncertainty of the radiation-corrected temperature of DTR was
about 0.35 ∘C in daytime with the coverage factor k= 2. The
corrected temperature of the DTR was about 0.4 ∘C higher than
that of RS41 around 30 km in daytime although the difference is within the
combined uncertainty (∼ 0.5 ∘C at k= 2) of the
RS41 and the DTR. The DTR methodology aims at enhancing the accuracy of the
temperature measurement in the upper air based on in situ radiation measurements.
Future works include an optimisation of each process shown in this study,
such as the fabrication of the DTR and the evaluation using laboratory
setups to improve the uncertainties due to irregularities in the production
and testing of sensors. In addition, more parallel sounding tests in various
conditions including daytime and nighttime and/or cloudy and windy weather
will be conducted to better characterise the performance of the DTR.
The radiation correction of the DTR, in particular, is expected to be different
from others while and after passing through clouds because the DTR responds to
an in situ radiation flux. Moreover, an extension of the environmental ranges, such
as temperature and pressure, is desirable to cover the upper air
environments of global areas. Since the radiation correction formula
presented in this study is valid for the ventilation speed of 4–6.5 m s-1, the range should be widened to extend the
applicability of the DTR.
Code availability
The operation programme of the upper-air simulator based on LabVIEW software is available upon request.
Data availability
The laboratory experimental data and sounding data used for Figs. 1–9 are available upon request.
Author contributions
SWL analysed the experimental data and wrote the paper. SKi, YSL, JKY and JS conducted the experiments. BIC revised the experimental setup. SL and SKw developed the measurement software. YGK designed the experiments.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
The authors would like to thank Inseok Yang and Young Hee Lee for providing an analysis tool for thermistor calibration and calibrating the thermistors, respectively.
Financial support
This research has been supported by the Korea Research Institute of Standards and Science (grant no. GP2021-0005-02).
Review statement
This paper was edited by Roeland Van Malderen and reviewed by Christoph von Rohden and two anonymous referees.
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