1. Introduction

A primary goal of air temperature measurement with weather station networks is to provide temperature data of high quality and fidelity that can be widely used for atmospheric and related sciences. Air temperature measurement is a process in which an air temperature sensor measures an equilibrium temperature of the sensor's physical body, which is optimally achieved through complete coupling between the atmosphere and air temperature sensor. The process accomplished in the air temperature radiation shield is somewhat dynamic, mainly due to the heat convection and heat conduction of a small sensor mass. Many studies have demonstrated that to reach a higher measurement accuracy both good radiation shielding and ventilation are necessary for air temperature measurements (Fuchs and Tanner 1965; Tanner 1990; Quayle et al. 1991; Guttman and Baker 1996; Lin et al. 2001a,b; Hubbard et al. 2001; Hubbard and Lin 2002). Most of these studies are strongly associated with the study of air temperature bias or errors caused by microclimate effects (e.g., airflow speed inside the radiation shields radiative properties of sensor surface and radiation shields, and effectiveness of the radiation shields). Essentially, these studies have assumed the equation governing the air temperature to be absolutely accurate, and the investigations have focused on the measurement accuracy and its dependence on how well the sensor is brought into equilibrium with the atmospheric temperature. Such findings are indeed very important for understanding air temperature measurement errors in climate monitoring, but it is well known that all microclimate-induced biases or errors also include the electronic biases or errors embedded in their temperature sensors and their corresponding data acquisition system components.

Three temperature sensors are commonly used in the weather station networks: A thermistor in the Cooperative Observing Program (COOP) that was formally recognized as a nationwide federally supported system in 1980; a platinum resistance thermometer (PRT) in the Automated Surface Observing System (ASOS), a network that focuses on aviation needs; and a thermistor in the Automated Weather Station (AWS) networks operated by states for monitoring evaporation and surface climate data. Each of these sensors has been used to observe climate data over at least a ten year period in the U.S. climate monitoring networks. The U.S. Climate Reference Network (USCRN) was established in 2001 and gradually and nationally deployed for monitoring long-term and high quality surface climate data. In the USCRN system, a PRT sensor was selected for the air temperature measurements. All sensing elements in these four climate monitoring networks are temperature-sensitive resistors, and the temperature sensors are referred to as the maximum–minimum temperature system (MMTS), sensor: HMP35C, HO-1088, and USCRN PRT sensors, respectively, in the COOP, AWS, ASOS, and USCRN networks (see Table 1). The basic specifications of each sensor system including operating temperature range, static accuracy, and display/output resolution can be found in operation manuals. However, these specifications do not allow a detailed evaluation, and some users even doubt the stated specifications and make their own calibrations before deploying sensors in the network. In fact, during the operation of either the MMTS sensor in the COOP or HO-1088 hygrothermometer in the ASOS, both field and laboratory calibrations were made by a simple comparison using one or two fixed precision resistors (National Weather Service 1983; ASOS Program Office 1992). This type of calibration is only effective under the assumption of temporal nonvariant sensors with a pure linear relation of resistance versus temperature. For the HMP35C, some AWS networks may regularly calibrate the sensors in the laboratory, but these calibrations are static (e.g., calibration at room temperature for the data acquisition system). It is not generally possible to detect and remove temperature-dependent bias and sensor nonlinearity with static calibration. In the USCRN, the PRT sensor was strictly calibrated from −50° to +50°C each year in the laboratory. However, this calibration does not include its corresponding datalogger.

To accurately trace air temperature trends over the past decades or in the future in the COOP, AWS, ASOS, and USCRN and to reduce the influence of time-variant biases in air temperature data, a better understanding of electronic bias in air temperature measurements is necessary. The objective of this paper is to carefully analyze the sensor and electronic biases/errors induced by the temperature sensing element, signal conditioning circuitry, and data acquisition system.

2. Sensor and its circuitry

a. Determining air temperature from resistance

The sensing elements in the MMTS and HMP35C sensors are thermistors that have a negative temperature coefficient; that is, their resistance decreases with the increase of sensing temperature. Experimental evidence shows that an individual thermistor curve can be very closely approximated through use of the Steinhart–Hart equation (Steinhart and Hart 1968):

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where the unit of temperature T is in kelvins and the resistance of the thermistor R_T is in ohms; A, B, and C are curve-fitting constants. This equation is able to fit within ±0.02°C of the calibration points for individual thermistors in the MMTS and HMP35C sensors.

The PRT in the ASOS and USCRN is a resistance temperature detector (RTD) constructed using platinum. It has a positive temperature coefficient. Typically, the resistance of a PRT changes by 0.392% °C⁻¹. The Callendar–Van Dusen equation describes the temperature curve within ±0.045°C as follows (Nachtigal 1990):

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where R₀ is the resistance at T = 0°C. It should be noted that the T is in degrees Celsius in Eq. (2). The coefficients α, β, and δ are constants determined by testing the PRT at four temperatures and solving the resulting equations. For the HO-1088 sensor, the designer utilized an approximate linear relation for the ASOS HO-1088 hygrothermometer. The resistance sensitivity of the HO-1088 and USCRN PRT is smaller than that of the thermistors in the MMTS and HMP35C sensors (Table 1).

In this study, Eqs. (1) and (2) are applied to the MMTS, HMP35C, HO-1088, and USCRN PRT sensors in the following error analysis.

b. Schematics of sensor signal conditioning

Measurements of resistance are usually taken with a full-bridge or half-bridge circuitry (voltage divider) with either a precision reference current or voltage to excite the resistance network. Figure 1 illustrates the main circuitry for the MMTS sensor's signal conditioning for the A1140 thermistor. It is a simple half-bridge measurement (R19 and A1140 thermistor) that is excited by a reference voltage output from ICL7109's pin 29. The reference voltage applied here is nominally 2.8 V below the voltage V₊(pin 40, nominally 5 V generated from an LM2930-5 regulator). The analog-to-digital convertor (ADC) ICL7109 is a 12-bit high-performance integrating device with polarity and over-range outputs. The half-bridge measurement is fed into the analog input (V_IN pins 34 and 35) of the ICL7109. The analog input (V_IN) required to generate a full-scale output of 4096 counts is V_IN = 2 V_REF, where the V_REF is the reference voltage that is a voltage across pins 36 and 39 (Fig. 1). Therefore, the V_REF here is 0.5(V₊ − 2.8) V according to the voltage divider constructed by R2, R3, and the reference output (V₊ − 2.8) of the ICL7109. The display count of the ICL7109 is designed as

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The resistance measurements in the HMP35C are configured by using a datalogger; for example, a CR10X datalogger (Campbell Scientific, Inc., Logan, Utah) is commonly selected in an AWS network. The UUT51J1 thermistor in the HMP35C is shown in Fig. 2. Its output signal is measured by a 2-V AC excitation (V_REF) provided by the CR10X datalogger. The analog signal output ranges from 0.46 to 7.05 mV with corresponding temperature from −40° to + 50°C. Therefore, the temperature signal (V_S) related to resistance is

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Due to the PRT's low sensitivity, the HO-1088 sensor signal conditioning circuitry contains two main components: one is a constant dc current generator (U8A, OP200AZ operational amplifier); the second is an inverting amplifier with zero and span adjustment (U8B) (Fig. 3). It should be noted that both air temperature and dewpoint temperature measurement in the HO-1088 sensor use exactly the same analog signal conditioning circuitry as in Fig. 3, and in both cases the same type of PRT device. A 5-mA constant dc current is generated from a 6.2-V reference voltage source through a precision 1240-ohm resistor (R13), and a feedback current of opposite polarity is equal to the U8A output voltage through the PRT of HO-1088. This configuration provides an output voltage approximately equal to −0.5 V at 0°C, −0.4 V at −50°C, and −0.6 V at +50°C. These values could be used directly for measurements and display purposes; however, they are amplified, inverted, and offset by U8B to a more convenient and linear scale approximately equal to −2 V at −50°C and 2 V at +50°C. The gain of U8B is set to 20 and the input offset value (−0.5 V at 0°C) is cancelled out by the signal through the R14, R35, and the 6.2-V reference voltage. Note that the 6.2-V reference voltage is provided by a temperature compensated zener reference diode (IN825, not shown in Fig. 3). Both amplifier gain and offset are slightly adjustable by varying the setting of two potentiometers, R34 and R35. These adjustments are used for the onboard calibration during the operation of the HO-1088. The analog temperature and dewpoint temperature signals are transmitted into the same ADC (ICL7109) as used in the MMTS through an analog multiplexor. The relationship between the analog temperature signals and the PRT resistance is

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where the R13, R14, R15, and R16 are fixed resistors with 0.1% tolerance, and R34 and R35 are two potentiometers (Fig. 3). Submitting nominal resistor values, determined by the gain and offset cancellation, Eq. (5a) can be simplified for the output count of the ADC ICL7109 as

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The USCRN PRT sensor is measured by a CR23X datalogger at the USCRN site. The measurement is taken through two voltage measurements on two adjacent single-ended channels with a 1.5-V excitation (V_REF) to determine the ratio of sensor resistance to a fixed resistance (1000 ohms) (Fig. 4). This three-wire half-bridge configuration of USCRN PRT resistance measurement compensates for the lead wire resistance. The ratiometric measurement of resistance conducted in Fig. 4 by the CR23X eliminates the reference voltage errors. In addition, the excitation polarity is reversed by the CR23X datalogger to eliminate the effects of external and internal offset voltage errors. Therefore, without considering the lead wire effects and reference voltage errors, the voltage outputs range from approximately 668 to 816 mV for two outputs (“High” and “Low” outputs in Fig. 4), corresponding to −50° to +50°C, respectively. In this treatment we follow the sensitivity of output voltage to other factors by taking the following derivation from Ohm's law:

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3. Error analysis and results

Air temperature errors originating with the sensing element, analog signal conditioning, and data acquisition system include the sensor interchangeability error, polynomial and linearization errors, self-heating error, voltage or current reference (excitation) error, total offset and drift in the amplifiers and ADC (associated with stability), and lead wire error. A root-sum-of-squares (RSS) of each error component was conducted for the total error of temperature measurement in the MMTS, HMP35C, and USCRN PRT sensors and these are in addition to any errors caused by ambient microclimate factors (radiation and insufficient convection effects). The sensor interchangeability errors were obtained from the sensor manufacturers. The polynomial error refers to the error caused by a polynomial computation for temperature measurement in the HMP35C with CR10X datalogger. The linerization error represents the error due to a linearized process conducted in the HO-1088 sensor. Any fixed resistors in the signal conditioning circuitry can produce the error of temperature measurement due to their tolerances and temperature coefficients (tempco). For the analog signal conditioning circuitry, we only presented significant errors that are caused by the fixed resistor's tolerance or tempco. The resistance measurement taken in the CR10X dataloggers is specified to have ±0.02% of full-scale range (FSR) of the input voltage on which the measurement is made in the range −25° to 50°C of the datalogger's operating temperature. For the CR23X datalogger, there are two specifications: accuracy ±0.015% of FSR for 0° to 40°C and accuracy ±0.02% of FSR elsewhere but still within −25° to +50°C. There is no specification when the datalogger's operating temperature is below −25°C. Note that the datalogger error for the HMP35C and USCRN PRT sensors was estimated by using a specification's value at −25°C. Therefore, the datalogger error might be underestimated when the operating temperature of the datalogger is below −25°C.

Because resistance measurement in the MMTS is a complete ratiometric approach (Fig. 1), the effect of stability or drift with temperatures of voltage reference (V_REF) can be negligible even though the voltage source comes from a simple LM2903-5 regulator. This point can also be found from Eq. (3); that is, the ADC output (count) depends on the R_T. Furthermore, the maximum self-heating power over the MMTS measurement range is about 0.05 mW, and its effect can be ignored. The least significant bit (LSB) error in the ADC of the MMTS is a reasonable estimate (ICL7109 Data Sheet from Harris Semiconductor, Melbourne, Florida) that brings about the temperature errors shown in Fig. 5. The lower circuitry sensitivity in the lower temperature ranges of the MMTS makes the MMTS resolution in the lower temperature around 0.25°C (0.27°C at temperature −50°C). This implies that the MMTS temperature observations are unable to discriminate ± 0.25°C changes in the lower temperature ranges (Fig. 5 and Table 2). The interchangeability of the MMTS thermistors is from ±0.2°C from temperature −40° to +40°C and ±0.45°C elsewhere (Fig. 4). Two fixed resistors (R2 and R3) with a 0.02% tolerance produced larger temperature errors of measurement in low temperatures, but the error caused by the fixed resistor R19 in Fig. 1 can be ignored. Therefore, the RSS errors in the MMTS are from 0.31° to 0.62°C from temperature −40° to −50°C (Fig. 5).

For the HMP35C sensor, Fig. 6 shows the sensor interchangeability, polynomial error, fixed resistor error, and CR10X datalogger error. The polynomial error rapidly increases when temperature is below −30°C. Two fixed resistors (1000 and 249 000 ohms with 0.1% tolerance) resulted in larger errors in higher temperatures. The CR10X datalogger error for the HMP35C was within 0.1°C. From the RSS error, the total temperature errors are quite large over 0.3°C when temperatures are beyond ±30°C (Fig. 6). Furthermore, the RSS error from −30° to −40°C is dramatically increased from 0.35° to 1.07°C. In the HMP35C sensor, the self-heating error is very small and can be ignored (Table 2).

Like the MMTS sensor, the HO-1088 hygrothermometer is not affected by voltage reference (V_REF = 6.2 V). Two stage amplifiers (OP200AZ) have very low input bias current (I_B + I_OS = 0.24 nA is typical value for temperatures from −55° to +125°C) and input offset voltage (V_OS = 45 μV, typical over the same temperature range) (data sheet of OP200AZ, Analog Devices, Norwood, Massachusetts); thus, transferring these values according to the schematics in Fig. 3, air temperature errors are less than 0.01°C. The major errors in the HO-1088 are interchangeability, linearization error, fixed resistor error, and self-heating error (Table 2 and Fig. 7). The linearization error in the HO-1088 is relatively serious because the analog signal (Fig. 3) is simply linearized from −50° to 50°C versus −2 to 2 V. The maximum magnitude of linerization error reached over 1°C (Fig. 7). There are four fixed precision resistors: R13, R14, R15, and R16 with a 0.1% tolerance. However, the error of temperature measurement caused by the R14, R15, and R16 can be eliminated by the adjustment of amplifier gain and offsets during onboard calibration operations in the HO-1088. The error caused by the input fixed resistor R13 is illustrated in Fig. 7. Since this error was constantly varied from −0.2° to −0.3°C, it can be cancelled during the onboard calibration. It is obvious that a 5-mA current flowing through the PRT in the HO-1088 is not appropriate, especially because it has a small sensing element (20 mm in length and 2 mm in diameter). The self-heating factor for the PRT in the HO-1088 is 0.25°C mW⁻¹ at 1 m s⁻¹ airflow (Omega Engineering 1995), corresponding to the self-heating errors 0.5°C when the self-heating power is 2 mW (Table 2 and Fig. 7). Compared to the linearization error and self-heating error, the interchangeability and LSB error in the HO-1088 sensor are relative small, ±0.1° and ±0.01°C, respectively (Table 2).

The RSS errors associated with using the CR23X datalogger and the USCRN PRT sensor were from 0.2° to 0.34°C (Fig. 8). Results in Fig. 8 indicate that the error from the CR23X datalogger was a major source of error for the USCRN PRT sensor. It should be noted that this result does not really imply the performance of CR23X, but it reveals that the USCRN PRT sensor is not suitable for the CR23X datalogger if a higher accuracy is required in the USCRN network. This is because the half-bridge circuitry in the USCRN PRT only utilizes a very small portion (668–816 mV) of the full-scale input range (±1000 mV) (Table 2). The analog output signals only use 7.4% of the full-scale input range in the USCRN PRT measurements. This suggests that to obtain a higher accuracy from the CR23X the USCRN PRT should be improved for its signal sensitivity. In addition, the self-heating power dissipated in the USCRN PRT sensor is relatively large for a standard PRT (1000 ohms) sensor (Table 2). Although the current through the USCRN PRT sensor is smaller than the 5-mA current in the HO-1088 sensor it is still not appropriate for the USCRN PRT sensor. The error by the fixed resistor's tolerance (1000 ohms, 0.01% tolerance, and 10 ppm °C⁻¹ in Fig. 4) increased from room temperature (25°C) to −50°C. The tempco error of the fixed resistor was less than 0.025°C.

4. Conclusions and discussion

This study provides a better understanding of temperature measurement errors caused by the sensor, analog signal conditioning, and data acquisition system.

The MMTS sensor and the HO-1088 sensor use the ratiometric method to eliminate voltage reference errors. However, the RSS errors in the MMTS sensor can reach 0.3–0.6 under temperatures beyond −40° to +40°C. Only under yearly replacement of the MMTS thermistor with the calibrated MMTS readout can errors be constrained within ±0.2°C under the temperature range from −40° to +40°C. Because the MMTS is a calibration-free device (National Weather Service 1983), testing of one or a few fixed resistors for the MMTS is unable to guarantee the nonlinear temperature relations of the MMTS thermistor. For the HO-1088 sensor, the self-heating error is quite serious and can make temperature 0.5°C higher under 1 m s⁻¹ airflow, which is slightly less than the actual normal ventilation rate in the ASOS shield (Lin et al. 2001a). The simple linear method for the PRT of the HO-1088 causes unacceptable errors that are more serious in the low temperature range. These findings are helpful for explaining the ASOS warm biases found by Kessler et al. (1993) in their climate data and Gall et al. (1992) in the climate data archives. For the dewpoint temperature measurements in the ASOS, such self-heating effects might be cancelled out by the chill mirror mechanism: heating or cooling the chill mirror body (conductively contains the dewpoint PRT inside) to reach an equilibrium thin dew layer–dewpoint temperature. Thus, in this case, the self-heating error for dewpoint temperature measurements might not be as large as the air temperature after correct calibration adjustment. Likewise, the relative humidity data from the ASOS network, derived from air temperature and dewpoint temperature, is likely be contaminated by the biased air temperature.

Both resistance measurements in the HMP35C and USCRN PRT sensors are interrogated by the dataloggers. The HMP35C is delivered from Campbell Scientific, Inc., with recommended measurement methods. Even so, the HMP35C sensor in the AWS network can experience more than 0.2°C errors in temperatures from −30° to +30°C. Beyond this range, the RSS error increases from 0.4° to 1.0°C due to thermistor interchangeability, polynomial error, and CR10X datalogger inaccuracy. For the USCRN PRT sensor in the USCRN network, the RSS errors can reach 0.2°–0.34°C due to the inaccuracy of CR23X datalogger, which suggests that the configuration of USCRN PRT and measurement taken in the CR23X could be improved if higher accuracy is needed. Since the USCRN network is a new setup, the current configuration of the USCRN PRT temperature sensor could be reconstructed for better measurements. This reconstruction should focus on the increase of signal sensitivity, the selection of fixed resistor(s) with smaller temperature coefficient of resistance, and the decrease of the self-heating power, so that it could be more compatible with the CR23X for long-term climate monitoring. These findings are applicable to the future of temperature data generated from the USCRN network and possible modification of the PRT sensor for higher quality measurements in the reference climate network.