# Sea Ice Detection Based on Differential Delay-Doppler Maps from UK TechDemoSat-1
## 2 Theory and Method
### Proposed Identification Approach
#### 2.4.1 Approach Description  
The power values of \(\text{DDM}_{D}(\tau,f)\) range from \(-1\) to \(1\), so a power value threshold (\(DDM_{T}\), which ranges from \(0\) to \(1\)) can be chosen to identify ice-water and water-ice transition. Another power value threshold \(DDM_{T}^{\prime}\) (\(DDM_{T}^{\prime}\leq DDM_{T}\)) is chosen to distinguish ice-ice transition from water-water transition. Two methods are proposed to identify the transition-case, which are presented as follows:  
1. Power Summation of dDDM (PS-D)  
The power summation (\(PS\)) of the grids with absolute values (\(|\overline{\text{DDM}_{D}}(\tau,f)|\)) greater than a preset threshold (\(DDM_{T}\)) can be obtained using Equation (5). Similarly, the power summation (\(PS\)') of the grids with absolute values (\(|\overline{\text{DDM}_{D}}(\tau,f)|\)) greater than a threshold (\(DDM_{T}^{\prime}\)) can also be obtained using Equation (5). If the power summation threshold for determining ice-water and water-ice  
Figure 5: Four scenarios for one dataset which includes: (**a**) DDMs only collected over sea ice field, (**b**) DDMs only collected over sea water field, (**c**,**d**) DDMs collected over both sea ice and water field.  
transition is defined as \(P_{T}\), the threshold for distinguishing ice-ice transition from water-water transition is defined as \(P_{T}^{\prime}\), the identification procedure is described as follows:  
* If \(PS>P_{T}\), two adjacent DDMs are determined as ice-water transition;
* If \(PS<-P_{T}\), two adjacent DDMs are determined as water-ice transition;
* If \(-P_{T}\leq PS\leq P_{T}\), two adjacent DDMs are determined as the same observing surface and further processing should be done to distinguish between ice-ice and water-water transition:
* If \(|PS^{\prime}|>P_{T}^{\prime}\), two adjacent DDMs are determined as water-water transition;
* If \(|PS^{\prime}|\leq P_{T}^{\prime}\), two adjacent DDMs are determined as ice-ice transition.
2. Pixel Number of dDDM (PN-D)  
Similar to PS-D, the abstract pixel number (\(PN\) and \(PN\)') of the grids with absolute values (\(|\overline{\text{DDM}}_{D}(\tau,f)|\)) greater than a preset threshold (\(DDM_{T}\) and \(DDM_{T}^{\prime}\)) of each normalized dDDM can be obtained using Equation (6). If the pixel number threshold for determining ice-water and water-ice transition is defined as \(N_{T}\), the threshold for distinguishing between ice-ice and water-water transition is defined as \(N_{T}^{\prime}\), the corresponding sea ice detection scheme can be presented as follows:  
* If \(PN>N_{T}\), two adjacent DDMs are determined as ice-water transition;
* If \(PN<-N_{T}\), two adjacent DDMs are determined as water-ice transition;
* If \(-N_{T}\leq PN\leq N_{T}\), two adjacent DDMs are determined as the same observing surface and further processing should be done to distinguish between ice-ice and water-water transition:
* If \(|PN^{\prime}|>N_{T}^{\prime}\), two adjacent DDMs are determined as water-water transition;
* If \(|PN^{\prime}|\leq N_{T}^{\prime}\), two adjacent DDMs are determined as ice-ice transition.  
As illustrated above, water-ice and ice-water transition can be figured out firstly using PS-D and PN-D while the discrimination between ice-ice and water-water transition need further processing. The observing surface types of DDMs from datasets collected over both ice and water field (Figure 5c) can be derived according to ice-water and water-ice transition. DDMs of datasets only collected over ice (Figure 5a) are distinguished from those of datasets only collected over water (Figure 5b) through using similar scheme for determining ice-water and water-ice transition.