# Evaluation of Forward Models for GNSS Radio Occultation Data Processing and Assimilation
## 2 Experiments
### Experiment 1: Algorithm Comparison  
Experiment 1 aims to determine the most accurate FM by comparing FM algorithms that considered interpolation methods.  
There are three types of bias in RO data processing: observation errors, ionospheric errors, and errors incurred within the data processing. We focused on the third error in experiment 1, mainly the bias from the Abel numerical integral and interpolation methods. The Abel integral methods considered in this experiment were the direct, exp, and exp_T algorithms. The interpolation methods were log-cubic and log-linear, indicated in the subsequent figures by no label and \"lin\", respectively. The log-cubic maps refractivity into the log space and then interpolates it by the cubic spline method; the log-linear also projects refractivity into the log space, but interpolates it in a linear fashion.  
In this experiment, 368 FY3D BA profiles in September 2019 were regarded as the true value (T). The collocated refractivity profiles of EC4 Dvar were the experimental value (E), which were calculated via Equation (1) on the data's inherent 137 levels. The temporal and spatial collocation of both sets of data is described in Section 2.1, as well as the further 4 QCs for collocation. From the statistical perspective, we used the mean to analyze the results, which would not be affected by outliers s. Two statistics were selected for the analysis: the difference of the BA, i.e., \((\mathrm{E}-\mathrm{T})\); and the relative difference (RD) of the BA, i.e., \((\mathrm{(E}-\mathrm{T})/\mathrm{T}\times 100\%)\). Based on these statistics, we determine how close an FM's result is to the true value; Another form of RD, which is the difference between two experimental values, i.e., \((\mathrm{(E_{1}-E_{2})/E_{2}\times 100\%)}\), can avoid introducing the bias of true value and provide the difference between the two experimental values. Subsequently, the relatively better FM can be obtained.  
Figure 1 shows the process of experiment 1. (1) FY3D profiles collocated with the EC4 Dvar atmospheric profiles with respect to time, longitude, and latitude. Subsequently, the EC4 Dvar profiles of atmospheric parameters were transformed to refractivity profiles. Then, the 4 QC was performed for FY3D and EC4 Dvar. We regarded the 4 QC-passed FY3D BA as the true value (T). (2) The EC4 Dvar refractivity profiles on 137 levels were interpolated into a resolution of 100 m by the log-cubic space and log-linear methods. (3) The interpo  
lated refractivity was then transformed into the BA by three different integral methods. (4) The forward-modeled EC4 Dvar BA was regarded as the experimental value (E) and was compared with the FY3D BA in terms of the difference (E \(-\) T) and RD (E \(-\) T)/T \(\times\) 100%. Note that the log-cubic interpolation was applied to the impact parameter instead of the mean sea level (MSL) height, since impact parameter \(x\) equals refractivity(\(n\)) multiple position vector (\(r\)). Because dn/dr is extremely large near a high-water-vapor region, which cannot satisfy the condition of applying cubic spline interpolation: the value to be interpolated should be continuously incremented.  
It is noteworthy that the true value and experimental value are only an estimated value to their actual values. Therefore, the difference between any FM and FY3D, (E\({}_{\text{FMX}}-\) T), is just an estimate showing which algorithm is closer to the truth. By contrast, the difference between any two FMs (E\({}_{\text{FM1}}-\) E\({}_{\text{FM2}}\)) is the absolute difference value. Experiment one shows which FM is better, instead of expressing how much error is incurred from the FM. Through experiment 1, although we can determine which FM is better, how much error exactly is incurred from the FM cannot be expressed. Such a question can refer to experiment 2.