Derivation of Geodesic Flow Fields and Spectrum in Digital Topographic Basins

Table 1

Details of synthetic and realistic digital topographies considered with their grey levels’ and corresponding elevation/or depth ranges, and entropy values estimated for each threshold elevation/depth decomposed set of each digital topographic basin.

Case	Type	Dyn range	No. dec	Grey value range	Elevation range (m)	Used SE	No. flow field	Entropy
Case 1	Synthetic	0-1	1	0-1	0-1	Rhombus	113	2.014109
Case 2	Synthetic	0–3	3	0-1	0-1	Rhombus	97	0.335195
				1-2	2		39	0.666177
				2-3	3		46	0.987891
Case 3	Synthetic	0–7	8	0-1	0-1	Rhombus	108	0.174197
				1-2	2		39	0.421361
				2-3	3		67	0.136298
				3-4	4		32	0.272975
				4-5	5		90	0.164091
				5-6	6		29	0.562372
				6-7	7		14	0.122462
				7-8	8		17	0.332124
SF-Bay	Bathymetry	0–255	7	0–33	−115 to −106	Octagon	34	0.048562
				34–59	−105 to −91		146	0.593921
				60–100	−90 to −68		57	0.365169
				101–150	−67 to −46		57	0.604285
				151–201	−45 to −27		23	0.304051
				202–233	−26 to −15		56	0.321996
				234–255	−14 to 0		22	0.120496
SC-Topo	Topography	0–255	14	0-1	0-1	Octagon	60	0.084891
				2–14	2–14		65	0.150806
				15–34	15–35		36	0.163969
				35–65	36–67		36	0.147204
				66–85	68–88		32	0.131617
				86–102	89–105		31	0.11603
				103–124	106–128		35	0.190187
				125–157	129–162		73	0.239391
				158–182	163–188		27	0.288595
				183–197	189–203		12	0.130263
				198–212	204–218		17	0.129661
				213–239	219–246		18	0.104142
				240–252	247–260		11	0.078623
				253–255	261–263		7	0.024073