Influence of Radiation on the Temperature Sensor Mounted on the ...

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JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY

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Influence of Radiation on the Temperature Sensor Mounted on the Swiss Radiosonde DOMINIQUE RUFFIEUX Aerological Station, MeteoSwiss, Payerne, Switzerland

JUERG JOSS Observatory of Locarno-Monti, MeteoSwiss, Locarno-Monti, Switzerland (Manuscript received 10 June 2002, in final form 20 March 2003) ABSTRACT The Swiss radiosonde (SRS400) measures the air temperature with a very thin copper–constantan thermocouple. The influence of the visible and infrared radiation, as well as the dependency of the air pressure on the measured temperature, is analyzed. After a brief review of the heat transfer by convection, diffusion, and radiation, two independent ways of estimating the difference of temperature between the sensor of the sonde and its environment are presented: 1) laboratory experiments followed by 2) a statistical analysis of aerological soundings. Good agreement between theory, laboratory experiments, and statistical analyses (based on day–night differences) was found. The overall influence of radiation amounts to about 0.8 K at 100 hPa (1.8 K at 10 hPa). At high altitude (low pressure), the heat transfer by diffusion equals the one by convection. Therefore, the diffusion term should not be neglected, as it is often reasonable for the larger sensors or at atmospheric pressure close to ground. As a result of applying the experiments in the laboratory to Eq. (1), the influence of longwave radiation is negligible compared to other influences. Based on the results herein, a second-degree polynomial fit was calculated for correcting the bias caused by radiation on the measured temperatures. This correction is operationally applied with success to the daytime soundings performed with the SRS400.

1. Introduction Since 1991, the Swiss radiosonde (SRS400) has been used in the operational service at the Aerological Station of Payerne (Switzerland). Its main characteristics can be found in Ruppert (1999). It uses temperature and pressure sensors directly based on physical laws. The temperature is measured with a thermocouple (Hoegger et al. 1999), the pressure with a hypsometer (measuring the boiling temperature of water; Richner et al. 1996), and the humidity with a carbon hygristor. The thermocouple of the SRS400 sonde is made of a 0.05-mm-diameter constantan wire soldered with a 0.063-mm-diameter copper wire (Fig. 1). Its small size has the advantage—compared with larger, bimetal thermometers (Luers 1990; Luers and Eskridge 1995)—of reducing the error caused by radiation and improving the time response (Hoegger et al. 1999). Nevertheless, the radiation still has a measurable effect on the temperature sensor. Various intercomparison campaigns showed significant deviations between the SRS400 and

Corresponding author address: Dr. Dominique Ruffieux, Aerological Station, MeteoSwiss, Case postale 316, Payerne CH-1530, Switzerland. E-mail: [email protected]

q 2003 American Meteorological Society

other systems that correct for the radiation influence, the Swiss sonde measuring higher mean stratospheric temperatures than the others. For example, Schmidlin et al. (1995) report a daytime temperature difference of 2 K at 10 hPa, between the SRS400 and a three-thermistor reference sensor (versus 1 K between the Vaisala RS-80 sensor and the same reference). Moreover, a systematic bias between the SRS400 and the European Centre for Medium-Range Weather Forecasts (ECMWF) model output was observed by Haimberger (2003). By comparing SRS400 soundings with numerical reanalyses using an objective interpolation method, he was able to show a systematic monthly mean bias of 0.5–1 K at 50 hPa. This analysis was performed using a dataset of 3.5 yr (1991–94). Because of the impossibility of comparing the measured temperature profiles with an absolute reference, two indirect ways of estimating the effect of radiation have been chosen. First, various laboratory experiments gave indications on how the SRS400 temperature sensor reacts, at various pressure levels, to radiation—visible (shortwave) and infrared (longwave)—versus orientation, sensor coating, and sensor size. These laboratory experiments were associated with dedicated aerological soundings. Then, a statistical approach based on the stratospheric difference of temperature between day and

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FIG. 1. SRS400 temperature sensor. (left) The two components of the thermocouple and (right) a general view of the SRS400 sonde with the temperature sensor positioned at a 458 angle on the upper-left side of the sonde.

night is discussed (i.e., with and without shortwave solar radiation on the sensor). Before describing and commenting on these two approaches, some theoretical aspects of the heat transfer between the temperature sensor and its environment are presented in the following section.

From Eq. (1), the deviation in temperature DT 5 (T x 2 T) can be expressed as DT ù

5

6

2A[ps«(T ) 4 1 p/2«R 1 gS(p/2 3 Alb 1 1)] . h (2) 21

The value of the heat transfer coefficient h (W K ) in Eq. (2) following McMillin et al. (1992) was modified to include the heat lost by diffusion through the air:

2. The heat transfer relationship, including diffusion Computation of radiation effect is based on the heat transfer equation (see, e.g., Schmidlin et al. 1986), modified for a long cylindrical wire: 2h(Tx 2 T ) 2 A[ps«(T ) 4 1 p/2«(Tc ) 4 1 gS(p/2 3 Alb 1 1)] 5 0,

(1)

where h 5 h c 1 h d 5 heat transfer by convection h c and diffusion h d (W K 21 ); T 5 true air temperature (K); T x 5 air temperature measured by the sensor (K); A 5 area of sensor exposed to the sun (m 2 ) calculated with d 3 l, diameter and length of sensor (m); T c 5 equivalent temperature to calculate the infrared radiation (W m 22 ) from the earth and atmosphere to the sensor; « 5 0.4, the sensor’s coefficient of emissivity for infrared radiation, estimated experimentally; g 5 0.73, the coefficient of absorption for solar radiation estimated experimentally; S 5 incident global irradiance (W m 22 ) from the sun at the sensor; s 5 Stefan–Boltzman constant (J K 21 ); and Alb 5 Albedo of clouds and earth [average, estimated by Ohmura and Gilgen (1993) to be around 30%]. TABLE 1. Reynolds numbers (Re) for various sondes (with sensor diameter) vs pressure level and temperature for an ascent speed V a 5 5 m s21 . Pressure (hPa) Temperature (8C)

950 20

100 270

10 260

6 260

SRS400 (0.063 mm) VIZ (1.27 mm) RS80 (1.6 mm)

19.31 389.32 490.49

3.93 79.30 99.90

0.36 7.27 9.16

0.22 4.36 5.50

h 5 h c 1 h d 5 kl(a 1 b Re m ),

(3)

where k 5 thermal conductivity of air (W m 21 K 21 ), as expressed following Mason (1971). Note that k is independent of the pressure, which is true as long as the free path of the molecules is shorter than the dimensions of the sensor:

1

k 5 0.024

2

T 273.16

0.913

.

(3a)

The coefficients a and b are determined by the geometry of the sensor. For the SRS400 they have been determined in the vacuum chamber (section 3 and Table 3). The Reynolds number Re is calculated as Re 5

rVa d . m

(3b)

The diameter d of the SRS400 temperature sensor is extremely small, compared to other types of sensors. It influences the surface A [Eq. (2)] and the Reynolds number in Eq. (3b). The low Reynolds numbers in Table 1 reflect the importance of the viscous flow and, with it, the heat transfer by diffusion. In Eq. (3b), V a 5 ascent rate of sonde (in m s 21 ); r 5 density of the air (in kg m 23 ):

1

r 5 1.28

211013.252 ;

273.16 T

P

(3c)

P 5 pressure (in hPa); and m 5 viscosity of the air (in J s m 23 ):

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TABLE 2. Dependence of air pressure of the temperature of the clouds and of the SRS400 together with resulting temperature deviation DT for summer and winter. The last column gives the DTyear calculated with Eq. (4) and used to operationally correct the mean influence of the daytime radiation. Pressure (hPa) 950 500 200 100 50 20 10

Tcloud, summer (8C) 10 25 230 230 230 230 225

m 5 1.717 3 1025

DT, summer (8C)

Tsonde, summer (8C) 20 210 253 255 251 245 234

1

0.23 0.37 0.64 0.86 1.10 1.45 1.68

2

T 273.16

0.8

.

(3d)

In Eq. (3) m is the exponent characterizing the dependence of the heat transfer from the Reynolds number Re. By measuring the local heat transfer from the front hemisphere of a smooth hailstone model, Aufdermaur and Joss (1967) found an excellent agreement between theory and experiment with m 5 0.5. This was verified for 4000 . Re . 66 000. This detailed analysis gives insight into the phenomena. On the rear side of the hailstone at Re . 16 000 or when turbulence becomes important, the exponent m increases, because of the different type of transfer. For a brief discussion of when turbulence and roughness become important, the reader is referred to Joss and Aufdermaur (1970).

Tcloud, winter (8C)

Tsonde, winter (8C)

DT, winter (8C)

DTyear, Eq. (4) (8C)

210 215 230 230 230 230 230

0 224 253 255 256 256 253

0.28 0.41 0.64 0.86 1.12 1.53 1.85

0.24 0.39 0.65 0.87 1.11 1.47 1.77

By analogy, a value of m 5 0.5 is a good estimate for the convective part of the heat transfer from the tiny thermocouple to its environment with small Re and turbulence (on the scale of the temperature sensor). This result was verified in the laboratory experiments described in section 3. However, the overall exponent m in Eq. (3) is significantly smaller than 0.5 because of the diffusion contribution (independent from the wind speed) becoming significant at low Reynolds numbers. Using the equations above, the difference DT between the measured air temperature and the true air temperature was calculated for two typical midlatitude profiles (Table 2). The temperature profiles as well as the corresponding DT are shown in Fig. 2. A surprisingly small difference in DT between summer and winter was found. The dominant influence on the heat transfer is caused by the change of air pressure versus height. The tem-

FIG. 2. Standard midlatitude summer (solid lines) and winter (dashed lines) (left) temperature profiles and (right) corresponding theoretical DT, calculated using Eq. (2).

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TABLE 3. Parameters and range of variation inside the vacuum chamber. The pressure was controlled using a vacuum pump, the wind speed in the vacuum chamber with an electric ventilator in a closed loop wind tunnel, and the radiation intensities with an artificial source of light from the outside through a window (transparent to the shortwave radiation). The position of the sensor in the chamber was chosen according to the desired angles. Parameters

Unit

Interval of variation

Pressure Wind speed Radiation angle of incidence Radiation intensities Angle between airflow and sensor

hPa m s21 Degrees W m22

9.35–984 0.25–6.5 08–908 1300–1500

Degrees

08, 458, and 908

perature of the clouds as well as of the sonde have relatively little influence on DT. 3. Laboratory experiments The coefficients a and b in Eq. (3), depending on the geometry of the sensor, were estimated in the vacuum chamber using an artificial source of light for simulating the shortwave solar radiation (Table 3). The diameter of the wire, the wind speed, and the pressure have been varied. For cylindrical wires that were long compared to their diameter, values of a 5 1.21 and b 5 1.92 were found by regression. Knowing the heat transfer from the thermocouple to the ambient air, the vacuum chamber was used with an artificial source of light (Table 3), as well as with the sun on a clear day, to determine the absorption of the shortwave radiation (g 5 0.73). The infrared radiation effect on the sensor was estimated from tests using an electrical heater providing around 3 kW m 22 of infrared radiation. The emissivity in the infrared («) was found to be between 0.2 and 0.6. This large experimental uncertainty does not have a significant impact on the measured temperature. Even at an air pressure of 10 hPa and cloud temperatures between 2608 and 08C, a small infrared influence of less than 0.1 K was found. The infrared radiation influence is reduced, because the radiation loss of a thermocouple at 2608C into the full space approximately compensates the radiation gain from the half-space filled by clouds of about 2308C along with downwelling radiation from space (equivalent blackbody temperature of less than 21008C). The results of these laboratory experiments were combined with those from aerological soundings performed with special sondes (equipped with multiple temperature sensors of various sizes and in suitable places on and around the sonde). The main uncertainties as well as their relative importance can be summarized as follows. • The type of surface immediately around the thermocouple. Insulation, tin-plated or silver-plated with residues of paint left on a 5-mm-long section of both wires, increased the solar radiation effect by a factor

•

•

• •

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of ;1.3 (5 mm is the order of magnitude of the influence region of the wires). The angle of incidence of the sun on the sensor. The effect is the largest at a perpendicular incidence of the solar radiation onto the sensor, a factor of ;1.3 relative to its average position. The quality of the soldering between the two wires. A poor, dirty, large solder-point increases the effect of the radiation by a factor of ;1.2, compared to a clean, shiny and small solder point. The diameter of the copper wire. Using a 0.063 mm copper wire instead of 0.050 mm increases the radiation effect by a factor of ;1.2. The thermocouple shape. For the shape of a ‘‘cross,’’ a radiation influence that is 1.05 times larger than with a ‘‘linear’’ shape was found; see also Daniels (1968).

By cumulating all these deviations and by adding the additional effects of the earth–cloud albedo and of contaminations like the balloon and the Styrofoam box, a factor of about 3 is found for the maximum value of the quotient DTmax /DTmin . This lets us expect, for individual single estimates of a sounding, a standard deviation of around a factor of 2. On average, if controllable parameters are not changed, the reproducibility as well as the absolute error are significantly smaller. Using the lessons learned in the laboratory, together with the theory, and using our knowledge from dedicated soundings (e.g., with compensated thermocouples), as well as the results of temperature differences between day and night (see section 4), a mean DTyear profile represented by a second-degree polynomial fit was calculated: DTyear 5 2.927 2 1.293 log(P) 1 0.131 log(P) 2 . (4) As already mentioned in section 2, only a minor improvement could be gained by including temperature in Eq. (4). This conclusion can be explained by the small size of the sensor and by two other facts: 1) close to ground, at high atmospheric pressure, the approximation is good, because the convection around the tiny sensor is efficient in dissipating the energy received by radiation; and 2) at high altitude, relatively little variation of temperature and of solar radiation are observed. The last column of Table 2 indicates the values of DTyear calculated with Eq. (4). It is simple, robust, and used for correcting the averaged influence of the daytime radiation in the Swiss operational soundings. For single estimates of temperature, the largest source of variation around these values, is caused by variations of the exposure of the sensor toward the sun. This fluctuation is not quantifiable nor known to us. Its influence is reduced by averaging many temperature estimates sampled every 3 s, while the sonde is turning around its vertical axis. The mean bias is corrected using Eq. (4). Because of the small size of the temperature sensor, errors are intrinsically small; therefore, the variation of the cloud cover and the precise shape and purity of the surface

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TABLE 4. Maximum diurnal and semidiurnal, tidal effect on temperatures and for various altitudes, 458N latitude (Lindzen 1968). The 50-km level corresponds to the maximal theoretical tidal effect.

FIG. 3. Calculated influence of radiation in mW cm 21 on the SRS400 temperature sensor: (left) the absolute influence of infrared radiation to space (open circles), infrared from clouds (solid circles), visible from clouds (open triangles), and visible from sun (solid triangles); (right) the estimated relative contribution of convection (solid line) and diffusion (dashed line).

around the thermocouple are less important than they have been for the former larger sensors. For a detailed analysis of the effect of the thermocouples shape, the reader is referred to Daniels (1968), who experimentally investigated the influence of radiation at ambient pressure. He gives instructions on how to build complex and multiple thermocouples, which compensate for the radiation effect. For our operational application, a better cost/benefit ratio was found when reducing the size of the wires, rather than trying to compensate for radiation effects using a fairly complicated sensor. A further reduction of the radiation could be achieved by reducing the absorption coefficient of the temperature sensor in the visible. First experiments in this direction have already been successful. At lower air pressure, the contribution to the heat transfer by diffusion from the sensor to the surrounding air must be considered. To estimate the relative contribution of variables to the heat transfer, several assumptions had to be made, such as the clouds’ temperature estimated from climatological profiles above Payerne and a mean cloud albedo of 30% taken from Ohmura and Gilgen (1991). The heat transfer between the environment and the thermocouple was estimated for various pressure levels using the temperatures given in Table 2. For the SRS400, the impact of the radiation components in Eq. (1) as well as of the cloud albedo and the relative contribution by convection and by diffusion are shown in Fig. 3. Note that, for this type of sensor, the transfer by diffusion around 10 hPa is of similar magnitude as by convection. Application of Eq. (4) is valid for statistically cor-

Altitude (km)

Maximal diurnal tide (K)

Maximal semidiurnal tide (K)

10 20 30 50

0.06 0.14 0.87 1.83

0.01 0.02 0.13 0.28

recting the mean bias. Under operational conditions, we would gain little with a more detailed correction, because too little is known about the instantaneous exposition of the sonde toward the sun, about the details of the thermocouple (solder point), about the temperature distribution on the box of the sonde, and about the instantaneous influence of the balloon. Studies are currently under way in Switzerland to design a thermocouple with even less sensitivity to radiation. As this reduction tackles the source of the problem, it will reduce not only the mean bias, but also single estimates errors. 4. Statistical approach The results showed that theory is well verified by laboratory experiments. Nevertheless, an mentioned before, there are uncertainties caused by the difficulties to reproduce or simulate high-altitude conditions affecting the temperature measurement. The various types of clouds, the appearance of the underlying terrain, and the radiosonde package itself are indeed variables that are difficult to grasp. In order to have another way of comparison, a statistical approach, completely independent of the previous one, was performed. A commonly used method for determining the effect of radiation on a temperature sensor is to compare soundings recorded in the night (without any shortwave radiation effect, the sonde being in the dark) with those performed during the daytime (see, e.g., Teweless and Finger 1960; Zhai and Eskridge 1996). With this method, mean temperature differences between day and night are assumed to be caused by (and to be representative for) the radiation error over the year. However, temperature differences between day and night are also modulated by the diurnal and semidiurnal thermal tides affecting the stratosphere and upper troposphere. Lindzen (1968, 1990) performed theoretical analyses in order to obtain the amplitudes of thermal tides while Nash and Forrester (1986) used satellite data in an attempt to quantify them. For midlatitudes, the maximum diurnal and semidiurnal amplitudes are shown in Table 4, following Lindzen (1968). The times when the maxima occur are correlated with the altitude and the latitude and are shifted, for midlatitudes, from noon and midnight by approximately 4 h. Finally, the presence of a topographic barrier like the Alps may slightly affect the phase and amplitude of the thermal tides over Switzerland.

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able number of samples varied as the pressure diminished, especially in altitudes corresponding to a pressure lower than 10 hPa (Fig. 4, middle panel). 5. Discussion

FIG. 4. Comparison between the statistical approach using the temperature DND of the operational soundings and the experimental approach: (left) the median DND calculated from the 1996–98 soundings (solid line with corresponding 61 std dev), and the fit calculated from the experimental approach (dashed line); (center) the number of samples used to calculate the median DND; (right) the difference between the experimental fit and the DND approach.

The median day–night difference (DND) was calculated by subtracting the temperature of each 1200 UTC sounding from an average of previous and next 0000 UTC soundings from 3 yr (1996–98) of data. With this method, more than 1000 days were analyzed. The avail-

In the left part of Fig. 4, the median DND method is compared with its laboratory estimate [Eq. (4)]. The two lines fit well together. The slight overestimate of the experimental fit compared to the DND below the tropopause (right panel) can be explained by the choice of a fixed cloud albedo in the laboratory approach. The overestimate of the DND above the tropopause may be caused by the tidal effect globally included in the statistical method and corresponding to the few tenths of a degree found in the literature (Lindzen 1968). For the midday (1200 UTC) sounding the variation of the solar angle is small and therefore neglected. In order to compensate for the reduced radiation at sunrise and sunset, an empirical correction is applied to all daytime soundings when the sun is close to the horizon. This is done at sun angles lower than 108 above horizon: there, the correction is varied proportional to the angle of the sun between 0% at (or below) the horizon and 100% at 108 (or more) over the horizon. 6. Verification of the correction in operational use Since 1 January 1999, all midday temperature soundings are operationally corrected using Eq. (4). These corrected

FIG. 5. Median temperature DND for the year 2001: (left) the median DND (solid line with corresponding 61 std dev) and the same DND uncorrected for radiation effects (dashed line); (center) the number of samples used to calculate the median DND; (right) the mean bias difference calculated between the 1200 and 0000 UTC ECMWF analyses and corresponding soundings for the year 2001.

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profiles are then sent to the dedicated data centers for various utilizations like for assimilation within global- and regional-scale numerical weather prediction models. The median DND for one year (2001) is shown in Fig. 5 (left panels). The correction reduces the raw DND differences (dashed line) to a small fraction of the initial difference (solid line). The influence of the diurnal and semidiurnal tides may cause the small differences between day and night, the upper part of the atmosphere being slightly warmed up during daytime (0.2–0.3 K at 7 hPa). The ECMWF calculates monthly biases the model analyses and the soundings performed at the European meteorological stations (at 1200 and 0000 UTC). The mean differences between the 1200 and the 0000 UTC biases, for the same year 2001, are shown in Fig. 5 (right panel). Note the good correspondence between the DND measured in situ and the DND calculated using the model ECMWF analyses. The analysis of three years of 1200 UTC and 0000 UTC soundings was performed to estimate the monthly variations of the DND, following McInturf (1979). Results show no significant seasonal differences except for a distinct increase of variability during winter, probably caused by more complex weather including cloud types occurring in central Europe during the cold season, as well as variation of soil covers. 7. Summary A small temperature sensor was chosen for the Swiss radiosonde SRS400 to reduce the influence of the radiation on the measured temperature. The contribution of the heat transfer by convection (produced by the rising speed of the sonde) decreases with altitude (at lower pressure), while the contribution of diffusion remains constant. The heat transfer by diffusion of the tiny Swiss thermocouple equals the one by convection at around 10 hPa. Both experimental and statistical analyses give similar results. The effect of incident longwave radiation (from the earth, clouds, and the housing of the sonde itself ) roughly counterbalances the radiation lost by the sensor to space. The total influence of the infrared radiation on the estimated temperature is negligible (below 0.1 K). The solar shortwave radiation causes, during daytime, a warming of the sensor of about 0.8 K at 100 hPa and 1.8 K at 10 hPa. As a result of these analyses, a second-degree polynomial fit was calculated and is currently applied operationally to all daytime soundings performed with the SRS400 radiosonde at Payerne. Verification using a 1yr dataset shows slight differences between day and night profiles of a few tenths of a degree. Above the tropopause, this difference could be caused by diurnal and semidiurnal tidal effects not included into the correction algorithm. Acknowledgments. The authors thank E. Tognini for his help in performing the laboratory experiments. We

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also recognize H. Richner, P. Jeannet, P. Ruppert, and P. Viatte for their useful advice in analyzing the data and preparing the paper. Last but not least, we would like to thank the three reviewers for their helpful comments. REFERENCES Aufdermaur, A., and J. Joss, 1967: A wind tunnel investigation on the local heat transfer from a sphere, including the influence of turbulence and roughness. J. Appl. Math. Phys., 18, 852–866. Daniels, G. E., 1968: Measurement of gas temperature and the radiation compensating thermocouple. J. Appl. Meteor., 7, 1026– 1035. Haimberger, L., 2003: Fit of ERA-40 analyses to observations. Proc. ECMWF Workshop on Re-analysis, Reading, United Kingdom, ECMWF, 177–192. Hoegger, B., G. Levrat, P. Viatte, and P. Ruppert, 1999: Advantages and disadvantages of thermocouple temperature sensors and full range hypsometer in the new Swiss radiosonde SRS400. Vero¨ffentlichungen der SMA-MeteoSchweiz Series No. 61, H. Richner, Ed., 133–140. Joss, J., and A. Aufdermaur, 1970: On the local heat transfer from rough spherical particles. Int. J. Heat Mass Transfer, 13, 213– 215. Lindzen, R. S., 1968: The application of classical atmospheric tidal theory. Proc. Roy. Meteor. Soc., A303, 200–316. ——, 1990: Dynamics in Atmospheric Physics. Cambridge University Press, 310 pp. Luers, J. K., 1990: Estimating the temperature error of the radiosonde rod thermistor under different environments. J. Atmos. Oceanic Technol., 7, 882–895. ——, and R. E. Eskridge, 1995: Temperature corrections for the VIZ and Vaisala radiosondes. J. Appl. Meteor., 34, 1241–1253. Mason, B. J., 1971: The Physics of Clouds. Clarendon Press Oxford, 614 pp. McInturff, R. M., F. G. Finger, K. W. Johnson, and J. D. Laver, 1979: Day–night differences in radiosonde observations of the stratosphere and troposphere. NOAA Tech. Memo. NWS NMC 63, 49 pp. McMillin, L., M. Uddstrom, and A. Coletti, 1992: A procedure for correcting radiosonde reports for radiation errors. J. Atmos. Oceanic Technol., 9, 801–811. Nash, J., and G. F. Forrester, 1986: Long-term monitoring of stratospheric temperature trends using radiance measurements obtained by the TIROS-N of NOAA spacecraft. Adv. Space Res., 6, 37–44. Ohmura, A., and H. Gilgen, 1993: Re-evaluation of the global energy balance. Interactions between Global Climate Subsystems, The Legacy of Hann, Geophys. Monogr., No. 75, IUGG Vol. 15, Amer. Geophys. Union, 93–110. Richner, H., J. Joss, and P. Ruppert, 1996: A water hypsometer utilizing high-precision thermocouples. J. Atmos. Oceanic Technol., 13, 175–182. Ruppert, P., 1999: Sensorik, telemetrie und aufbau der SRS400. Vero¨ffentlichungen der SMA-MeteoSchweiz Series No. 61, H. Richner, Ed., 55–67. Schmidlin, F., J. K. Luers, and P. D. Huffman, 1986: Preliminary estimates of radiosonde thermistor errors. NASA Tech. Paper 2637, 15 pp. ——, H. Sang Lee, and B. Ranganayakamma, 1995: Deriving the accuracy of different radiosonde types using the three-thermistor radiosonde technique. Preprints, Ninth Symp. on Meteorological Observation and Instrumentation, Charlotte, NC, Amer. Meteor. Soc., 27–31. Teweles, S., and F. G. Finger, 1960: Reduction of diurnal variation in the reported temperatures and heights of stratospheric constant-pressure surfaces. J. Meteor., 17, 177–193. Zhai, P., and R. E. Eskridge, 1996: Analyses of inhomogeneities in radiosonde temperature and humidity time series. J. Climate, 9, 884–895.