The directions of maximum continuity in variogram map were examined again. We modified the directions for some grids according to the two criteria below,

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α ϒ black line: direction estimated from variogram maps red line: direction calculated from Qx/Qy at low flow green line: direction calculated from Qx/Qy at medium flow blue line: direction calculated from Qx/Qy at high flow α is the ABSOLUTE angle between black and red lines. β is the ABSOLUTE angle between black and green lines ϒ is the ABSOLUTE angle between black and blue lines. β

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The directions of maximum continuity in variogram map were examined again. We modified the directions for some grids according to the two criteria below, and it is used to the comparison for mid- and high- flow data. However, the comparison for low- and high- low data does not use the modified results in previous power point file. Thats why the results seems to be incorrect. (1) The fitting ellipse is nearly circular. The determination of direction of maximum continuity would be problematic. Therefore, we remove it. (2) The direction (magenta line) of maximum continuity in Fig. 2(a) is misjudged. We use the direction in Fig. 2(b). Fig. 1Fig. 2(a)Fig. 2(b) red: low-flow water green: mid-flow water blue: high-flow water black: variogram map ( 1 = 5, 2 = 35) In right figure, only low- and high- flow data are used. The red line will be chosen. In left figure, only mid- and high- flow data are used. Thus, the blue line will be chosen. black line: direction estimated from variogram maps red line: direction calculated from Qx/Qy at low flow green line: direction calculated from Qx/Qy at medium flow blue line: direction calculated from Qx/Qy at high flow is the ABSOLUTE angle between black and red lines. is the ABSOLUTE angle between black and green lines is the ABSOLUTE angle between black and blue lines. For each 6m x 6m cell with vgm result If < If | - | > 1 < 2 and < 2 Check the magnitude of and Check flow data availability Both low- and high-flow availableOnly high-flow available Draw (type I) High-flow as blue If < 2 Draw (type III) High-flow as blue Vgm as black > 2 and > 2 > 2 and < 2 2 Draw (type II) Low-flow as red Draw (type I) High-flow as blue Draw (type V) Low-flow as red High-flow as blue Vgm as black Draw (type IV) Low-flow as red High-flow as blue Draw (type II) Low-flow as red Draw (type I) High-flow as blue yes no yes no yes no Type I Type III Type II Type IV Type V Drawings: For each grid, the differences , and are evaluated. 1. The , and values need to be less than 2 to be valid. 2. and are considered the same if their difference is less than 1. and are considered the same if their difference is less than 1. and are considered the same if their difference is less than If 1 < , , < 2, the min(, , ) is chosen, and plotted on the map. 4. If , , > 2, all available data (vgm map data, low-, mid-, and high- flow data) are plotted on the map. After the above criteria were applied, we remove the grids which have vegetation presence. The extent of each grid are adjusted to 7m 7m. If the area of the vegetation in the grid exceeds 1 m 2, the grid is removed. Area A ( 1 = 5, 2 = 35) good matches for mid-flow data red: low-flow water green: mid-flow water blue: high-flow water black: variogram map perfect matches for low-, mid-, and high-flow data All the contours are 0.5 m interval. Area B ( 1 = 5, 2 = 35) good matches for mid-flow data red: low-flow water green: mid-flow water blue: high-flow water black: variogram map good matches for high-flow data good matches for low-flow data Area C ( 1 = 5, 2 = 35) red: low-flow water green: mid-flow water blue: high-flow water black: variogram map Area D ( 1 = 5, 2 = 35) red: low-flow water green: mid-flow water blue: high-flow water black: variogram map good matches for mid-flow data good matches for low-flow data good matches for high-flow data