## 2 Spectral Analysis of HY-2B Empirical Accelerations
### POD Processing and Models  
The reduced dynamic POD method makes use of GPS observations and well-established models for computing the acceleration acting on satellites. An overview of the supporting models and data processing strategies is presented in Table 1. The undifferenced processing was adopted, and dual-frequency ionosphere-free combinations of the GPS data were used as the basic observations for the HY-2B POD. The precise GNSS orbits, clock, and wide-lane bias products provided by the CNES/CLS were used to implement a single-receiver IAR for the HY-2B satellite. In order to be consistent with the standard IGS clock product, GPS observations with a measurement interval of 30 seconds were used. For processing GPS data with a sampling interval of below 30 seconds, the high-rate GRG clock offsets based on the CODE clock product is available for single-receiver IAR. Details of this concept and its implementation are described [20]. The GPS transmitter antenna phase center offsets (PCO) and PCV of the IGS model [32; 33] were taken into account. The GPS antenna offset calibration of the HY-2B and the empirical PCV corrections were considered in POD.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Description** \\ \hline
**Observation model** & \\ \hline Observation & Undifferenced ionosphere-free code and carrier phase combinations \\ Interval and arc length & 30 s and 30 h \\ GPS orbit and clocks & CNES-CLS ‘GRG’ products; 30 s sampling \\ GPS satellite biases & CNES-CLS wide-lane satellite biases \\ GPS satellite PCO and PCV & IGS ATX models [33] \\ HY-2B attitude & Nominal \\ HY-2B PCO and PCV & Corrected using calibrated values \\ \hline
**Dynamic model** & \\ \hline Earth gravity & EIGEN6C (120 \(\times\) 120) [34] \\ Solid Earth and pole tides & IERS 2010 conventions [35] \\ Ocean tides & FES 2004 (30 \(\times\) 30) [36] \\ N-body disturbance & JPL DE405 [37] \\ Relativity & IERS 2003 [38] \\ Solar radiation & 13-plate macro-model, radiation pressure coefficients (VIS and IR) [39] \\ Atmospheric drag & 13-plate macro-model, atmospheric density model \\ Empirical acceleration & adopting DTM-2013 [40] \\ \hline
**Estimated parameters** & \\ \hline Initial state & Position and velocity at the initial epoch \\ Receiver clock offset & Each epoch as white noise \\ Phase ambiguities & Each continuous tracking arc as a float \\ Solar radiation coefficients & One per 30 h arc \\ Drag coefficients & One per 180 min \\ Empirical coefficients & One per 180 min, amplitudes of periodic accelerations \\  & acting on the along- and cross-track directions \\ \hline \hline \end{tabular}
\end{table}
Table 1: Force models and datasets for HY-2B precise orbit determination and SLR validation.  
The flat-plate macro-model is widely adopted for the LEO mission and provides a proper tool to describe the non-gravitational force on the surfaces of a satellite [5; 23; 43]. The 13-plate macro-model obtained from [1] was used for HY-2B POD. The scale factors were taken into account for solar radiation pressure (SRP) and atmospheric drag force. The extended analytical SRP model developed by [39] was used, and photons in the visual (VIS) and infrared (IR) were considered in SRP. We assumed that 50% of the total solar radiation pressure is caused by shortwave and longwave radiations, and indicated this contribution as 1/2. The temporal variation in the solar radiation pressure can be ignored as it causes a very small effect [44]. The density values and composition data of the Earth's thermosphere obtained from DTM-2013 [40] were employed for a precise modeling of atmospheric forces. Moreover, empirical accelerations were introduced in POD solution to compensate for deficiencies of the modeled forces.