# Sea Ice Detection Based on Differential Delay-Doppler Maps from UK TechDemoSat-1
## 2 Theory and Method
### Proposed Identification Approach
#### 2.4.2 Deriving Thresholds  
As discussed above, the scenarios can be divided into different-surface (i.e., ice-water and water-ice transition) and same-surface (i.e., ice-ice and water-water transition). For PS-D based method, if the maximum absolute power summation value of same-surface (\(|PS|_{\text{max}}^{s}\)) is always smaller than the minimum absolute value of different-surface (\(|PS|_{\text{min}}^{d}\)), it will be error free to distinguish between different-surface and same-surface. Similarly, if the maximum absolute pixel number value of same-surface (\(|PN|_{\text{max}}^{s}\)) is smaller than the minimum absolute value of different-surface (\(|PN|_{\text{min}}^{d}\)), different-surface and same-surface can be correctly distinguished from each other.  
After determining the thresholds for identifying ice-water and water-ice transition, datasets only collected over only ice or water are used to derive the thresholds for distinguishing between ice-ice and water-water transition. Theoretically, if the maximum absolute \(PS\) and \(PN\) values of ice-ice transition are always smaller than the minimum absolute values of water-water transition, it will be error free to distinguish ice-ice transition from water-water transition. While the difference between ice-ice transition and water-water transition is much smaller than that between different-surface and same-surface. Therefore, it may be difficult to obtain such error free thresholds. Actually, if more than eighty percent of dDDMs of one dataset collected over only one type of observing surfaces are determined as ice-ice transition, the type of surface of this dataset can be determined as ice.  
In order to apply this sea ice detection scheme, six sets of DDM data [46] were used as training data to derive these thresholds so that they may be used as a guideline in the algorithm development.  
Sea ice edge maps [47] with a resolution of 10 km \(\times\) 10 km provided by OSI SAF are used as reference data for deriving thresholds. The power value threshold (\(DDM_{T}\)) for identifying ice-water and water-ice transition is set as 0.2 firstly and increased with a step size of 0.01. Then, different _PS_ and _PN_ results for each \(DDM_{T}\) can be obtained according to PS-D and PN-D respectively. After deriving thresholds for identifying ice-water and water-ice transition, datasets only collected over ice or water field can be identified. Then, the power value threshold (\(DDM_{T}^{\prime}\)) for distinguishing between ice-ice and water-water transition is set as \(DDM_{T}\) (\(DDM_{T}=0.2\)) firstly and decreased with a step size of 0.01. Then, different _PS_' and _PN_' results for each \(DDM_{T}\) can be obtained according to PS-D and PN-D respectively. For PS-D based method, if the maximum absolute _PS_ value of more than 85% of ice-ice transition dDDMs (\(|PS\prime|_{\text{max}}^{ice}\)) is smaller than the minimum absolute value of water-water transition (\(|PS\prime|_{\text{min}}^{water}\)), it will provide the basis for distinguishing ice-ice transition from water-water transition. Similarly, if the maximum absolute _PN_ value of more than 85% of ice-ice transition dDDMs (\(|PN\prime|_{\text{max}}^{ice}\)) is smaller than the minimum absolute value of water-water transition (\(|PN\prime|_{\text{min}}^{water}\)), ice-ice transition and water-water transition can be correctly distinguished from each other. It was found that \(DDM_{T}\) ranging from 0.22 to 0.53 and \(DDM_{T}^{\prime}\) ranging from 0.12 to 0.26 can obtain the best detection results. The process of obtaining thresholds is illustrated in Figure 6.  
Figure 6: Flowchart of threshold determination for sea ice detection scheme. Six datasets over the Arctic region from TDS-1 are used as training data and sea ice edge data from OSI SAF is used as ground-truth data for determining thresholds.