# Error Correction of Water Vapor Radiometers for VLBI Observations in Deep-Space Networks
###### Abstract  
In this paper, we present the design and implementation tests of a water vapor radiometer (WVR) suitable for very long baseline interferometry (VLBI) observation. We describe the calibration method with an analysis of the sources of measurement errors. The experimental results show that the long-term measurement accuracy of the brightness temperature of the water vapor radiometer can reach 0.2 K under arbitrary ambient conditions by absolute calibration, receiver gain error calibration, and antenna feeder system temperature noise error calibration. Furthermore, we present a method for measurements of the calibration error of the oblique path measurement. This results in an oblique path wet delay measurement accuracy of the water vapor radiometer reaching 20 mm (within one month).  
water vapor radiometer; error correction; VLBI; receiver gain error; temperature noise error; absolute calibration; oblique path calibration; brightness temperature  
Received: 2 November 2021  
Accepted: 28 November 2021  
SubSubject: 30 November 2021  
WVR to analyze atmospheric tropospheric delays throughout 1994 [3]. In mid-1990, JPL developed the advanced water vapor radiometer (AWVR) with a stable narrow beam gain that can accurately estimate the propagation delay of water vapor in a semi-dry atmosphere with an accuracy of 1 mm [1]. [PERSON] et al. performed a water-vapor-radiometer-based tropospheric calibration experiment using VLBI observations over a 21 km baseline. They discussed sources of error, such as gain error, pointing error, and absorption model error, in wet path delay measurements of the AWVR [2]. [PERSON] et al. investigated the dual water vapor radiometer (DWVR) deployed at the Venus Goldstone site in 2008. The data processing method is given and the effect of error sources, such as injected liquid water, has been studied [4]. The team at Chinese Academy of Sciences (CAS) built the VLBI network, which is mainly used for astronomy. By combining the CAS VLBI network with the TT&C network, the orbit determination missions of Chang'e 1 to 4 were successfully accomplished. Since Chang'e-3, the water vapor radiometer has been added to improve the accuracy of the VLBI measurement delay. Figure 1 shows three water vapor radiometers equipped with the Shanghai Tianma telescope. The QFW-6000 series and HZD-X series microwave radiometers used for meteorological observation and deep-space VLBI observation were developed by China Research Institute of Radiowave Propagation (CRIRP). The HZD-X water vapor radiometer introduced in this paper is a prototype water vapor radiometer developed specifically for the deep-space VLBI observation network in China. It can correct the wet delay in the zenith direction to less than 15 mm and the dry region can be reduced to less than 10 mm. In Section 2, the basic principle and design scheme of the water vapor radiometer are presented. In Section 3, the analyses of the sources of measurement errors are described and the correction methods for the errors are given. These analyses are based on experimental results and can be effectively applied to engineering, instead of simply discussing error sources that cannot be applied in practice.