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[1] The tipping curve calibration method has been an important calibration technique for ground-based microwave radiometers that measure atmospheric water vapor and cloud liquid water. The method calibrates a radiometer system using the brightness temperatures at various viewing angles in the atmosphere. In this paper, the tipping calibration was carried out by digital gain compensative microwave radiometer (DGCMR) in Inner Mongolia, China, in August 2006. The frequencies of the radiometers are 23.8 and 31.65 GHz with rectangle horn and paraboloid antenna. Using the relationship between correction value and scanning angle, the brightness temperature of the antenna sidelobe contribution is corrected. The comparison of the correction results for the two antenna types shows that the antenna sidelobe error for the rectangular horn antenna can be corrected more effectively.

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[2] Ground-based microwave radiometers have been widely used to measure atmospheric water vapor and cloud liquid water [Liljegren, 1994]. In recent years, the deeper investigation of precipitable water vapor (PWV) has motivated a closer look at the accuracy of radiometer calibration. The frequencies on 22.235 GHz and 31.65 GHz are in the water vapor absorption band and absorption window region respectively. These frequency channels differ in their response to water vapor and cloud liquid water.

[3] There are mainly two radiometric calibration techniques for the passive microwave radiometer: the liquid nitrogen LN2-cooled blackbody target method and tipping calibration method. The LN2 method is not applicable for long-term and automatic measurement, and it does not include the antenna sidelobe effect. In this, it is very different from the tipping curve technique. The tipping calibration method couples a radiometer equation and atmospheric radiative transfer theory and gets the calibration equation by measuring the atmosphere at two or more observation angles [Hogg et al., 1983; Han et al., 1994]. Han and Westwater [2000] analyzed tipping calibration uncertainties because of gain variations of the radiometer or by violation of the assumptions in the theory for ground-based microwave radiometers and provided the method to reduce them.

[4] In this paper, the calibrated system is dual-channel digital gain compensative microwave radiometer (DGCMR) operated at 23.8 GHz and 31.65 GHz [Zhang and Zhao, 1996]. There are radiometers which are multiple channels such as those of Ware et al. [2003], Rose et al. [2005], Iturbide-Sanchez et al. [2007], and Cimini et al. [2003]. Researchers in our laboratory carried out the ground-based atmosphere measurement using the dual-channel and dual-antenna system composed of DGCMR and two types of antennas (rectangular horn and paraboloid) in the artificial rainfall base of Inner Mongolia during 16 to 28 August 2006. The tipping calibration and correction of antenna sidelobe contribution were performed during the experiment. The calibration result can be compensated by the regression relationship between the correction value including antenna sidelobe contribution and the scanning angle in correction procedure.

2. Tipping Calibration and Correction Method

2.1. Tipping Calibration Method

[5] It is assumed that between the radiometer output voltage V and the sky brightness temperature T_{B} there is a linear relationship, which is given as:

[6] Where a and b are the calibration coefficients. θ is the zenith angle of observation.

[7] At each frequency the sky brightness temperature T_{B} measured by a microwave radiometer can be expressed in terms of extraterrestrial and atmospheric contributions [Westwater, 1978]:

[8] Where T_{C} is the cosmic background temperature (T_{C} = 2.75 K); τ is the atmospheric opacity; T_{mr} is the mean radiating temperature of the atmosphere (in Kelvin) estimated from surface temperature and relative humidity measurements and fitted by linear regression to the estimator [Liljegren et al., 2001]:

[9] The research reported by Liljegren et al. showed the regression parameters d, e, f derived using all clear and cloudy profiles, T_{mr} at 23.8 GHz and 31.65 GHz can be expressed as:

[10] Where T_{sfc} is surface air temperature (in Kelvin); RH is the fractional relative humidity. All these parameters can be acquired by weather station. T_{b} is the amount of radiation emitted by blackbody, which is equal to T_{sfc}. Also, V_{b} is the output voltage at T_{b}.

[12] The opacity at the direction θ is defined as the ratio of the opacity at zenith (θ = 90°) to sin(θ_{i}) at this angle under the clear air:

[13] T_{B}(90°) can be calculated by radiometer equation and atmospheric radiative transfer theory. The sky brightness temperature T_{B}(θ_{i}) is obtained from equations (2) to (7) at various scanning angles.

[14] Firstly the calibration is carried out without considering the effect of antenna sidelobe contribution, the input-output expression as (1).

2.2. Correction Method to Reduce the Effect of Antenna Sidelobe Contribution

[15] Following Ulaby et al. [1981], the antenna radiometric temperature T_{A} is

[16] Where η_{m} is the antenna main-beam efficiency; T_{SL} is sidelobe contribution antenna effective apparent temperature.

[17] The observation objects are different from antenna main-lobe and sidelobe in ground-based microwave remote sensing measurement. Black body calibration is carried out before tipping measurement. It includes the entire antenna beams, the sidelobe contribution cannot be confirmed. In ground-based measurement, the main problem is the antenna sidelobe contribution. Sidelobe contribution is related to the physical temperature of land around, small change can be ignored using the antenna with high main-lobe efficiency in small change of air temperature. It has a scale factor between physical temperature of land around and air temperature. The effect can be estimated by air temperature.

[18] Substituting (1) into (8), we can obtain the following relationship, which includes the receiving brightness temperature by sidelobe antenna. Where a, b are independent from the observation angle.

[19] Where a′ = aη_{m} + (1 − η_{m}) T_{SL}, b′ = η_{m}b, equation (9) assumes that the main-lobe antenna contribution gives the measure of the brightness temperature T_{B}, (9) is transformed to (10)

[20] The calibration error may stem from the antenna sidelobe contribution. To correct a calibration, we firstly need to define the calibration error ΔT(θ_{i}). To reveal the angular dependence of the calibration correction, we perform corrections using the relationship between ΔT(θ_{i}) and θ_{i}. The corrected atmospheric radiation brightness temperature T′_{B} is equal to T_{A}(θ_{i}) − ΔT(θ_{i}), in other words, T′_{B}(θ_{i}) = T_{A}(θ_{i}) − ΔT(θ_{i}). With the corrections, the calibration equation can provide the relationship between sky brightness temperature and radiometer output voltage at different viewing angles, so as to determine the atmospheric parameters.

3. Calibration Experiment

[21] From 16 to 28 August 2006, clear-sky atmosphere observation experiment was conducted at the artificial rainfall base in Hohhot, Inner Mongolia (East longtitude 111°7′, North latitude 40°8′). During the experiment, the tipping calibration and antenna sidelobe correction were operated according to the radiative transfer model and meteorological data. The instruments are the dual-channel DGCMR operated at 23.8 GHz and 31.65 GHz designed by Northeast Institute of Geography and Agricultural Ecology, CAS, and the antenna types are rectangular horn and paraboloid. For simplicity, we use type A to express the rectangular horn antenna and type B to express the paraboloid antenna. Tables 1 and 2 list the parameters of antenna and radiometer. The photos of DGCMR with paraboloid antenna and rectangular horn antenna are shown in Figures 1 and 2.

[22] The radiometer performed automatic scanning at 19:00 on 21 August and 07:00 on 22 August respectively. The scanning period of every angle is more than 30 seconds. We obtained the average output voltages at every angle after acquiring the data set. Black body calibration was finished in a small microwave darkroom. It was an external calibration and the entire antenna beams were covered by main-lobe and sidelobe. The blackbody output voltages is expressed as V_{b}. During the same time, the collected meteorological parameters contain surface air temperature T_{sfc}, surface barometric pressure P_{sfc}, surface partial pressure due to water vapor e_{sfc}, fractional relative humidity RH and temperature T. These meteorological parameters provided by weather station are listed in Table 3.

Table 3. Meteorological Parameters on 21 and 22 August

Date

T_{sfc}, K

RH

e_{sfc}, hPa

P_{sfc}, hPa

T, K

21 August 19:00

300.96

0.33

123

890.0

300.86

22 August 07:00

292.36

0.58

128

892.5

292.26

[23] For convenience, the sign K1 expresses the channel of 23.8 GHz with type A antenna, Ka1 expresses the 31.65 GHz radiometer with type A antenna, K2 expresses the 23.8 GHz radiometer with type B antenna and Ka2 expresses the 31.65 GHz radiometer with type B antenna in this paper.

[24] The blackbody brightness temperature T_{b} and output voltage V_{b} are listed in Table 4.

Table 4. Blackbody Brightness Temperature and Output Voltage

K1

K2

Ka1

Ka2

V_{b} (code)

2879.4

2940.5

3408

3439

T_{b}, K

297.1

296.6

297.2

296.9

4. Calibration and Correction Results

4.1. Results of K1

[25] According to the meteorological data collected by weather station, the mean radiating temperatures T_{mr} are 278.04 K and 271.25 K at these two experiments respectively. The uncorrected calibration equation is

[26] The correction curves with a polynomial fit relationship ΔT(θ_{i}) ∼ θ_{i} are shown in Figures 3a and 3b.

[27] The 2nd-order polynomial fit function is

[28] The corrected calibration equation is

4.2. Results of Ka1

[29] According to the meteorological data collected by weather station, the mean radiating temperatures T_{mr} are 272.5 K and 265.83 K at these two experiments respectively. The uncorrected calibration equation is

[30] The correction curves with a relationship ΔT(θ_{i}) ∼ θ_{i} are shown in Figures 4a and 4b.

[31] The correction function is

[32] The corrected calibration equation is

[33] From Figures 3 and 4, we can note that there is a good polynomial fit relationship between correction values and scanning angles in these two channels. The results show that the brightness temperature of antenna sidelobe contribution may be corrected with this method. Thus the corrected calibration curves can denote well the relationship between sky brightness temperature and radiometer output voltage at different viewing angles.

4.3. Results of K2 and Ka2

[34] The correction curves of K2 are shown in Figures 5a and 5b.

[35] The correction relationship can be written as linear fit function:

[36] For Ka2, the relationship between scanning angle and correction value are shown in Figures 6a and 6b.

[37] From Figures 6a and 6b, it is difficult to express the correction relationship between the correction values and scanning angles using any polynomial fit.

5. Conclusion and Discussion

[38] This paper provides the method of tipping calibration and correction by the ground-based dual-channel DGCMR operated at 23.8 GHz and 31.65 GHz. The correction relationship can be established by the regression expression of ΔT(θ_{i}) ∼ θ_{i}, which reflects the antenna sidelobe contribution.

[39] From 16 to 28 August 2006, we carried out the clear-sky atmosphere observation experiment at the artificial rainfall base in Hohhot, Inner Mongolia. The calibration equation and correction results are obtained at the radiometer channels of 23.8 GHz and 31.65 GHz installed with two types of antennas which are rectangle horn and paraboloid. The results show that with the rectangular horn antenna, there is a good correction relationship between correction value and viewing angle. However, for the paraboloid antenna, the relationship between ΔT(θ_{i}) and θ_{i} cannot been well expressed by a correction function. Thus this correction method is more effective to the radiometer with rectangle horn antenna (the beam width is 4.2°and 5.2°) than paraboloid antenna.