Reply to: "Comment on root orientation can affect detection accuracy of ground-penetrating radar"

We showed that root orientation affected a parameter of ground penetrating radar (GPR), amplitude area (A) (Tanikawa et al. Plant Soil 373:317-327, 2013). The aims of this reply to Wu et al. (2014) are (i) to correct the two inaccuracies in Tanikawa et al. (2013) and (ii) to improve our method of estimating A(90A degrees) using A(x) of root angle x. Measured A values of Tanikawa et al. (2013) were analyzed with the modified equations. The first inaccuracy was the use of incorrect units for the coefficient b (the phase shift) in the sinusoidal waveform of A(x). The units should have been radians instead of degrees. The second inaccuracy was the mis-derivation of A(x) into A(x + 90A degrees). In the modified method, A(90A degrees) was estimated by A(x) from two orthogonally intersecting transect lines and a transect line at a diagonal to them. The two inaccuracies did not affect the previous main conclusions that the parameter T was suitable for estimating root diameter and that grid transects are likely to identify clear hyperbolas reflecting roots in radar profiles (Tanikawa et al. 2013). By the improved method, we could accurately estimate root diameter by scanning using three transect lines intersecting at angles of x, x + 45A degrees, and x + 90A degrees.