*3.1. Performance Evaluation of DDM Observables*

In this work, we assume that coherent and incoherent scattering simultaneously occurs on the land surface in the CYGNSS land observations, and only two scattering cases appear: coherent reflection mainly contributed to DDM or incoherent scattering mainly contributed to DDM. We classify the two cases based on the statistical characteristics of the predefined estimators. Since we have known that ocean surface observation belongs to the latter, the characteristic information of incoherent DDM can be obtained. To evaluate the performance of different classification estimators defined in Section 2.2, the CYGNSS collected land and ocean DDMs in January 2018 are used to calculate the PDF and accumulation distribution function (CDF) of each DDM observable separately. Figure 4 gives the PDF and CDF of TES, TEV, TEV\_POW calculated from CDW (top row), IDW (middle row), and DDW (bottom row). It can be found that the performance of the three types of DW-derived classification estimators is different. The PDF of TES between land and ocean observations is separated more and sharper, which means that the classification results of TES are generally better than the other two. TES values from ocean surface scattered signals are generally larger than land observation; its PDF appears on the right side of the figure. The reason is the L-band GNSS signals impinge on the ocean surface always occurring diffuse scattering, the time-delay, and Doppler-spreading cause DW to appear a significant "smearing" feature; in other words, the scattered power of the trailing edge will slowly decrease. In addition, the PDF of land reflected DDM-derived TES is more dispersed than ocean observations. In the first column of Figure 4, the closer TES to the left side of the x-axis, the greater the contribution of the coherent component to the DDM since the DW is much closer to the WAF correlation function. As the roughness of the land surface increases, the contribution of the incoherent component rapidly increases and begins to impact the scattering power of the DW trailing edge, so the TES value gradually approaches the ocean observations, two PDFs finally intersect. The performance of TEV\_POW is the worst; the distribution of PDF from the land and ocean observations is overlapped. It can be explained by the fact that the peak value of coherent DM is larger than incoherent DM, while the scattering power of incoherent DW declines slowly after the peak value, the final result is the average of

absolute scattering power within 5 time-delay bins between land and ocean DDM derived TEV\_POW are close. The performance of TEV is in the middle.

**Figure 4.** Statistic performance of trailing edge slope (TES), the average volume of the normalized time-delay waveform (DW) trailing edge (TEV), average absolute scattering power of the DW trailing edge (TEV\_POW) derived from central Doppler time-delay waveform (CDW; **a**–**c**), integrated timedelay waveform (IDW; **d**–**f**), and deviation of time-delay waveform (DDW, **g**–**i**) over land and ocean surface, dataset collected from the cyclone global navigation satellite system (CYGNSS) level-1B in January 2018.

Figure 5 shows the PDF of estimator DDMA, DDMA\_POW, and MF derived from the ocean and land DDMs. The performance of DDMA\_POW is very close to TEV\_POW; the distribution of two PDF almost overlaps, which can be explained by the same reason as TEV\_POW. Therefore, we can conclude that it is difficult to determine the coherence of the DDM based on the feature of its absolute power in the given window. In the rest of the paper, we will exclude the absolute power estimators. Here, MF shows the best performance; DDM from land generally has a higher correlation with the WAF in comparison with the ocean, which is in line with the previous assumption.

**Figure 5.** Average of the normalized scattering power DDM near its peak (DDMA) (**a**), an average of the absolute scattering power DDM near the peak (DDMA\_POW) (**b**), and WAF-matched filter (MF) (**c**) statistic performance over land and ocean area, dataset collected from the CYGNSS level-1B in January 2018.

The performance of different estimators is variant depending on the land surface scattering mechanisms; the classification threshold is determined by the intersection of two PDFs, which is represented by the magenta dotted line in the vertical direction in Figures 4 and 5. The horizontal magenta dotted lines indicate the accumulative probability density of the corresponding estimator computed from the CYGNSS land and ocean surface data, which not only presents the probability of detection (PD) of coherent DDM but also indicates the proportion of the coherent and incoherent data. Table 1 summarizes the classification threshold, PD, the probability of false alarm (PFA), and the probability of error (PE) of each estimator. It can be found that the PD between different observables is small except DDW-derived TEV, and the average PD of all estimators is 89.6%. Among eight estimators, the PD of TES calculated from normalized IDW (NIDW) is the largest, and the PE is the smallest. Comparing all the subgraphs in Figure 4, it can also be found that the PDF of NIDW-derived TES is more separated between land and ocean data. Moreover, it is more concentrated and sharper than normalized CDW, and normalized DDW derived TES. Hence, it is considered the best estimator to detect the coherent and incoherent DDM collected over the land surface in this study. In the rest of the paper, we just use NIDWderived TES as the classification estimator to recognize the high confidence coherent DDM in the CYGNSS land data for SM retrieval.


**Table 1.** The classification threshold and the probability of different DDM observables.
