Error Analysis
The purpose of this document is to explain the calculation of error and error bars
for orientation and bed thickness measurements presented in the manuscript.
Error of 
Error was calculated for each  according to the following equation, using the error
of strike measurements (listed in ts01):
  1/n 
n
 strike
2
i
(A1)
i1
Error of 
Error was calculated for the average dip measurements according to the following
 the error of individual dip measurements (listed in ts01):
equation, using
  1/n 
n
 
2
i
(A2)
i1
Error of bed thickness, t, measurements
To calculate error bars for each bed thickness measurement, we propagate the

errors of orientation
measurements (, ) as well as the errors in the DTM (DTM
resolution and vertical precision), according to the mathematical operations in the
Eqs. 5 and 6 presented in the main text.
Bed thickness is calculated according to the following equations:
t  h cos  sin   v cos
(5)
t  hcos sin   vcos
(6)
 whether the dip of the beds is in the same or opposite direction as the
Depending on
topographic slope. Thickness error is:

t  (h cos  sin  ) 2  (v cos ) 2
(A3)
The horizontal distance, h, along the measured section line between the upper and
lower bed boundaries is calculated using (x, y) coordinates extracted from the DTM

and the distance formula.
h  (x2  x1)2  (y2  y1)2
The absolute error of h is therefore:

(A4)
h  1/2  h  {[(x 2  x1 ) 2  (y 2  y1 ) 2 ]/[( x 2  x1 ) 2  (y 2  y1 ) 2 ]}
(A5)
Where:


[(x2  x1)2  (y2  y1)2 ]  [(x 2  x1)]2 [(y2  y1)]2
(A6)
[(x 2  x1) 2 ]  2  (x 2  x1)2  (x 2  x1) /(x 2  x1)
(A7)
[(y 2  y1) 2 ]  2  (y 2  y1)2  (y 2  y1) /(y 2  y1)
(A8)

Since DEM horizontal resolution is 1 m:


(x 2  x1)  (DEM) 2  (DEM) 2  12 12  2
(A9)
(y 2  y1)  (DEM) 2  (DEM) 2  12 12  2
(A10)
The elevation difference between the upper and lower boundaries for each bed is
calculated according to the formula:

v  z2  z1
(A11)
The absolute error of v is calculated by propagating the error of the two elevation
values, assumed here to be the expected vertical precision of the DEM, EP:

v  (EP) 2  (EP) 2
(A12)
(v cos )  v cos  (v /v) 2  ((cos  ) /cos  ) 2
(A13)

Where error is approximated in trigonometric functions by the following equations:


(cos  )  cos   cos(   )
(A14)
(sin  )  sin   sin(    )
(A15)
(cos  )  cos  cos(   )
(A16)

By substituting Eqs. A1, A2, and A4-A16 into Eq. A3, the following equation is
derived for the propagated absolute error of each thickness measurement:

t  (h cos sin (1/ 2 

(2 2 (x2  x 1 )) 2  (2 2 (y 2  y 1 )) 2
(x 2  x 1 ) 2  (y 2  y 1 ) 2
)2  (
cos  cos(   )
cos
)2  (
sin  sin(   )
sin
) 2 ) 2  (v cos (
(EP) 2  (EP) 2
v
)2  (
cos  cos(   )
cos
)2 )2
(A17)
For sections where no correction is made for the dip of the beds, bed thickness error is:
t  v  (EP)2  (EP)2
(A18)
where EP is the DTM expected precision.

Error of Total Section Thickness
Since the total section thickness (Table 3) was calculated by adding all individual
bed thickness measurements for a section, the error of total section thickness was
calculated by the formula:
TotalThickness 
n
 t
i 1
(A19)
2
i
Error of Mean Bed Thickness
Mean bed thickness for each section was calculated by adding all individual bed
thickness measurements for a section, then dividing by the number of beds. Error of

mean bed thickness is calculated by the formula:
MeanThickness  1/ n 
n
 t
i 1

i
2
(A20)