Understanding output variables

Steffi LaZerte

2024-10-02

Functions in LITAP output a lot of variables, many of which are based on the original LandMapR^* program, but including new ones as well. This resource is meant to explain what the various parameters mean, which files they can be found in, and whether they were included in the original LandMapR program (and under what name).

^* Interpretations of LandMapR variables are derived from the LandMapR C++ User Manual, October 2003. If you want a better understanding of these variables and their calculations it is highly recommended that you explore the manual and the references therein.

Generic variables

These variables are common to many files in LITAP and so for the sake of brevity, will be defined here.

Generic DEM file variables

These variables correspond to dem files, meaning there is a value for each cell in the dem file.

LITAP Parameters	LandMapR Name	Description
seqno	SeqNo	Cell number identifying a particular cell in the DEM
x	--	The horizontal (longitudinal) measure of position in the units of the original dem (or metres, if not supplied)
y	--	The vertical (latitudinal) measure of position in the units of the original dem (or metres, if not supplied)
row	Row	Row number
col	Col	Column number
elev	Elev	Elevation in metres
ddir	Ddir	Direction of water flow (1 = SW, 2 = S, 3 = SE, 4 = W, 5 = No flow, 6 = E, 7 = NW, 8 = N, 9 = NE)
drec	Drec	The cell number (seqno) of the cell this focal cell flows into
upslope	UpSlope	The number of cells which flow into and/or through the focal cell
upslope_m	--	The total area of cells which flow into and/or through the focal cell in metres
uced	--	Upslope cumulative elevation drop (UCED)
edge_map	--	Whether or not the focal cell is on the edge of the map
ridge	--	Whether or not the focal cell touches the cell belonging to a different local watershed

flow_mapper() variables

The following describes variables output by flow_mapper() to various files in the flow folder, e.g., dem_fill.csv or dem_inverted.rds depending on the file format chosen.

flow/dem_fill

Variables in flow/dem_fill (corresponds to FlowMapR’s XXXdem.dbf).

This list only includes variables not already described above in the Generic DEMs.

LITAP Parameters	LandMapR Name	Description
vol2fl	Vol2Fl	Volume (m³) to first flood. How much water would be present in the depression at the point when the focal cell would be first inundated.
mm2fl	Mm2Fl	mm to first flood. The amount of rainfall (in mm) required to fall and contribute to flow in order to reach the volume vol2fl
parea	PArea	The surface area (in cell units) of the pond at the point at which the focal cell is first inundated.
initial_shed	–	The watershed number identifying intial watersheds defined prior to omitting small or shallow depressions.
local_shed	ShedNo (`XXXdem.dbf`)	The watershed number identifying local watersheds after small or shallow depressions have been removed. Represents a local, closed depression
pond_shed	–	The watershed number identifying pond watersheds for sequential pit filling and the calculation of pond statistics. (Same cells as fill_shed but numbers may be different, reflecting a different order of filling)
fill_shed	ShedNow (`XXXdem.dbf`)	The watershed number identifying fill watersheds which are global catchments including surface flow to the edge of the DEM. Used in calculating of fill statistics (Same cells as pond_shed but numbers may be different, reflecting a different order of filling)
sgre	–	Slope gradient of rows in a easterly direction (+ = downslope towards east; - = upslope towards west
sgr	–	Overall slope gradient of rows (absolute sgre)
sgcn	–	Slope gradient of columns in a northerly direction (+ = downslope towards north; - = upslope towards south
sgc	–	Overall slope gradient of columns (absolute sgcn)
scr	–	Row slope curvature
scc	–	Column slope curvature
hill_r_dir	–	Direction the row slope is facing (2 = east facing, 4 = west facing
hill_c_dir	–	Direction the col slope is facing (1 = north facing, 3 = south facing
hill_r_n	–	Number of hillslopes in the focal row. Hillslope number increments when the slope changes from down to up and vice versa.
hill_r_cell	–	Order number of a cell within a row hillslope.
hill_c_n	–	Number of hillslopes in the focal column. Hillslope number increments when the slope changes from down to up and vice versa.
hill_c_cell	–	Order number of a cell within a column hillslope.

flow/dem_inverted

Variables in flow/dem_inverted (corresponds to FlowMapR’s XXXidem.dbf)

This list only includes variables not already described above in the Generic DEMs.

Note: We don’t calculate Vol2Fl, MM2Fl or PArea because in the original LandMapR they weren’t calculated specifically for the inverted DEM, but were identical to those in the non-inverted DEM.

LITAP Parameters	LandMapR Name	Description
inv_initial_shed	ShedNo	The watershed number identifying intial watersheds defined prior to omitting small or shallow depressions, calculated after inverting the DEM
inv_local_shed	Shednow	The inverted watershed number identifying local watersheds calculated after inverting the DEM.

flow/stats_XXX

These variables correspond to flow/stats files, which are non-dem summary files for flow_mapper().

Stats files

LITAP Parameters	LandMapR Name	Description
stats_pit	XXXpit	Information on final pits
stats_pond	XXXpond	Information on pond pits, including all ways in which local pits can over-spill and connect.
stats_fill	XXXfill	Information on fill pits, including mostly likely sequence in which local pits would connect. This has similar information to stats_pond but the order is different (and important)
stats_inverted	XXXipit	Same as stats_pit except that it is calculated for the inverted dem, so these represent peaks, rather than pits.

Stats variables

These files have all the same variables but differ in their order (e.g., pond vs. fill) and their values depending on whether the shed was inverted or not.

This list only includes variables not already described above in the Generic DEMs.

LITAP Parameters	LandMapR Name	Description
shedno	ShedNo	The watershed number identifying pond watersheds for sequential pit filling.
edge_pit	Edge	Whether or not the focal watershed touched the edge of the DEM
final	Final	Whether or not this pit is a ‘final’ pit which spills over beyond the edge of the dem
end_pit	EndPit	The final pit this watershed will eventually contribute to
shed_area	ShedArea	Total number of cells in the focal watershed cachment
pit_row	PitRow	Row number of the pit centre
pit_col	PitCol	Column number of the pit centre
pit_seqno	PitRec	Cell number of the pit centre
pit_elev	PitElev	Cell elevation of the pit centre
pour_elev	PourElev	Elevation of the pour point (lowest cell that can overspill into an adjacent watersched/cachment). Elevation recorded is the higher of the cell in the current watershed (in_elev) and the adjacent cell in a neighbouring watershed (out_elev)
pre_vol	PreVol	Total volume (in m * cells²; you can multiply by grid*2 to get m³) of the pit pouring into this one (always zero for local pits)
pit_vol	PitVol	Total volume (in cm * cells²; you can multiply by grid*2 to get m³) of the pit including all pits combined into this one
varatio	Varitio	Proxy for the amount of rainfall in mm required to fill a pit completely; Calculated as a volume to area ratio
pit_area	PitArea	Number of cells in a pit (you can multiply by grid*2 to get area in m²)
drains_to	DrainsTo	Adjacent watershed that this one is most likely to overspill into
next_pit	NextPit	Alternative adjacent watershed that this one would drain to if drains_to is already full
becomes	Becomes	New watershed number when this watershed is combined with another
in_row	InRow	Row number of the cell in the current watershed at the pour point
in_col	InCol	Column number of the cell in the current watershed at the pour point
in_seqno	InRec	Cell number of the cell in the current watershed at the pour point
in_elev	InElev	Elevation of the cell in the current watershed at the pour point
out_row	OutRow	Row number of the cell in the adjacent watershed at the pour point
out_col	OutCol	Column number of the cell in the adjacent watershed at the pour point
out_seqno	OutRec	Cell number of the cell in the adjacent watershed at the pour point
out_elev	OutElev	Elevation of the cell in the adjacent watershed at the pour point

form_mapper() variables

The following describes variables output by form_mapper() to various files in the form folder, e.g., dem_form.csv or dem_length.rds depending on the file format chosen.

form/dem_form

Variables in form/dem_form (corresponds to FlowMapR’s XXXform.dbf).

This list only includes variables not already described above in the Generic DEMs.

LITAP Parameters	LandMapR Name	Description
slope_pct	Slope	Slope gradient (%)*
slope_deg	–	Slope gradient (°)*
aspect	Aspect	Aspect*
new_asp	New_asp (FormMapR option ‘b’ or ‘c’)	New Aspect: Aspect rotated 45° counter-clockwise. Results in true NE having an aspect of 90° as opposed to 45°.*
prof	Prof	Profile*
plan	Plan	Plan curvature*
qarea1	Qarea (FormMapR option ‘a’)	Diffuse upslope area (units = cells)†
qarea2	Qarea (FormMapR option ‘b’ or ‘c’)	Diffuse upslope area (units = m²)†
qweti1	Qweti (FormMapR option ‘a’)	Wetness Index (derived from qarea measured in cells)†
qweti2	Qweti (FormMapR option ‘b’ or ‘c’)	Wetness Index (derived from qarea measured in m²)†
lnqarea1	–	Natural log of diffuse upslope area (derived from qarea measured in cells)
lnqarea2	Lnqarea (FormMapR option ‘b’ or ‘c’)	Natural log of diffuse upslope area (derived from qarea measured in m²)
* Calculated using equations by Eyton (1991)
† Calculated using the multiple descent flow accumulation algorithm by Quinn et al. (1991)

form/dem_length

Variables in form/dem_length (corresponds to a combination of FlowMapR’s XXXlen.dbf and XXXrelz.dbf files).

This list only includes variables not already described above in the Generic DEMs.

These variables reflect information on the relative position of the focal cell (seqno) and the first of each feature type the focal cell’s flow path would cross.

The features explored are streams/channels (st), crests/divides (cr), pits (pit) and peaks (peak).

Note: Variables prefaced by st, n2, cr, pit, and peak were only calculated in the original FormMapR when option c (compute full set of all possible derivatives) was selected.

LITAP Parameters	LandMapR Name	Description
st_row	St_row*	Row of the first connected stream/channel
st_col	St_col*	Column of the first connected stream/channel
st_elev	St_elev*	Elevation of the first connected stream/channel
z2st	Z2st†	Vertical elevation difference from stream/channel
n2st	N2st*	Number of flow cells to stream/channel
cr_row	Cr_row*	Row of the first connected crest/divide
cr_col	Cr_col*	Column of the first connected crest/divide
cr_elev	Cr_elev*	Elevation of the first connected crest/divide
z2cr	Z2cr†	Vertical elevation difference from crest/divide
n2cr	N2cr*	Number of flow cells to crest/divide
pit_row	Pit_row*	Row of the first connected pit
pit_col	Pit_col*	Column of the first connected pit
pit_elev	Pit_elev*	Elevation of the first connected pit
z2pit	Z2pit†	Vertical elevation difference from pit
n2pit	–	Number of flow cells to pit
peak_row	Pk_row*	Row of the first connected peak
peak_col	Pk_col*	Column of the first connected peak
peak_elev	Pk_elev*	Elevation of the first connected peak
z2peak	Z2peak†	Vertical elevation difference from peak
n2peak	N2peak*	Number of flow cells to peak
z2top	Z2top†	Vertical elevation difference from highest cell in watershed
zpit2peak	Zpit2peak†	Total elevation change from pit to peak for this flow path
zcr2st	Zcr2st†	Total elevation change from crest/divide to channel/stream for this flow path
zcr2pit	Zcr2pit*	Total elevation change from crest/divide to pit for this flow path
ztop2pit	Ztop2pit†	Total elevation change between the highest cell and the pit cell in the watershed
ncr2st	Ncr2st*	Number of flow cells between crest/divide and channel/stream for this flow path
pmin2max	Pmin2max†	Estimated % vertical distance above the lowest cell in the DEM relative to total elevation difference between the lowest and highest cells in the entire DEM.
pctz2st	Pctz2st†	Estimated % vertical distance above stream/channel relative to total elevation difference between crest/divide and stream/channel (zcr2st) for this flow path.
pctz2pit	Pctz2pit†	Estimated % vertical distance above pit relative to total elevation difference between pit and peak (zpit2peak) for this flow path.
pctz2top	Pctz2top†	Estimated % vertical distance above lowest cell in the watershed relative to total elevation difference between lowest and highest cells in the watershed.
pctn2st	Pctn2st*	% flow cells above stream/channel relative to total number of flow cells between crest/divide and stream/channel for this flow path
l2pit	L2pit‡	Horizontal, straight-line distance to pit (m)
l2peak	L2peak‡	Horizontal, straight-line distance to peak (m)
lpit2peak	Lpit2peak‡	Horizontal, straight-line distance from pit to peak (m)
ppit2peakl	Ppit2peakl‡	Relative slope position (%) as distance to pit (l2pit) by total distance between pit and peak (lpit2peak).
l2str	L2str‡	Horizontal, straight-line distance to stream/channel (m)
l2div	L2div‡	Horizontal, straight-line distance to crest/divide (m)
lstr2div	Lstr2div‡	Horizontal, straight-line distance from stream/channel to crest/divide (m)
pstr2divl	Pstr2divl‡	Relative slope position (%) as distance to stream/channel (l2str) by total distance between stream/channel and crest/divide (lstr2div)
* From XXXrelz.dbf when selecting option c (compute all possible terrain derivatives)
† From XXXrelz.dbf
‡ From XXXlen.dbf, created when selecting option c (compute all possible terrain derivatives)

facet_mapper() variables

The following describes variables output by facet_mapper() to various files in the facet folder, e.g., dem_fuza.csv or dem_fuzc.rds depending on the file format chosen.

facet/dem_fuza

Variables in facet/dem_fuza (corresponds to FlowMapR’s XXXfuza.dbf).

This list only includes variables not already described above in the Generic DEMs.

Note: Only fuzzy landform attributes values defined in the ARULE file will be in the dem_fuza file. Here we show the general attributes which have been calculated as the probability/likelihood of relatively having that particular attribute. For example, convex_d is the probability of being relatively convex in the down slope direction.

LITAP Parameters	LandMapR Name	Description
zone	ZONE	EXPERIMENTAL: Different zones may have different classifications in the original BC-PEM DSS proceedure.
convex_d	CONVEX_D	Convex in down slope direction
concave_d	CONCAVE_D	Concave in down slope direction
planar_d	PLANAR_D	Planar in down slope direction
convex_a	CONVEX_A	Convex across the slope
concave_a	CONCAVE_A	Concave across the slope
planar_a	PLANAR_A	Planar across the slope
high_wi	HIGH_WI	High wetness index
low_wi	LOW_WI	Low wetness index
near_level	NEAR_LEVEL	Near level slope gradient
rel_steep	REL_STEEP	Relatively steep slope gradient
near_div	NEAR_DIV	Near a local divide
near_half	NEAR_HALF	Near mid-point between divide and channel
near_chan	NEAR_CHAN	Near a local channel
near_peak	NEAR_PEAK	Near a local peak
near_mid	NEAR_MID	Near mid-point between peak and pit
near_pit	NEAR_PIT	Near a local pit
hi_above	HI_ABOVE	Relatively high above pit cell
planar_2x	PLANAR_2X	Planar in profile and plan (Average of planar_d and planar_a)
As in MacMillian et al. (2000)

facet/dem_fuzc

Variables in form/dem_fuzc (corresponds to FlowMapR’s XXXfuzc.dbf).

This list only includes variables not already described above in the Generic DEMs.

Note: Only landform element (facet) values defined in the CRULE file will be in the dem_fuzc file. Here we show some common elements included in the CRULE files included in the original LandMapR and LITAP. Be aware, however, that these can be custom created and could therefore represent something else entirely. These values represent the probability/likelihood of the cell being that particular landform element. For example, lcr is the probability of being a “Level crest”.

LITAP Parameters	LandMapR Name	Description
lcr	LCR	Level crest*
dsh	DSH	Divergent shoulder*
ude	UDE	Upper depression*
bsl	BSL	Back slope*
dbs	DBS	Divergent back slope*
cbs	CBS	Convergent back slope*
ter	TER	Terrace*
sad	SAD	Saddle*
mde	MDE	Mid-slope depression*
fsl	FSL	Foot slope*
tsl	TSL	Toe slope*
fan	FAN	Fan*
lsm	LSM	Lower-slope mound*
lls	LLS	Level lower slope*
dep	DEP	Lower depression*
cst	--	Crest†
ups	--	Upper slope†
mid	--	Mid slope†
low	--	Lower slope†
dep	--	Depression†
max_facet	max_facet	Number identifying the landform element/facet which has the max value for this cell (most likely facet to occur)
max_value	--	The highest computed likelihood value of the maximum facet
max_2nd_facet	next_facet	Number identifying the landformelement/facet which has the second highest likelihood value for this cell (second most likely facet to occur)
max_2nd_value	--	The value of the second highest facet
max_facet_name	--	3-letter code of the facet with the highest likelihood
max_2nd_facet_name	--	3-letter code of the facet with the second highest likelihood
* As described in MacMillian et al. (2000) and MacMillian (2003)
† As described in Sheng et al. (2011)

wepp_mapper() variables

The following describes variables output by wepp_mapper() to various files in the wepp folder, e.g., dem_wepp.csv or dem_wepp.rds depending on the file format chosen.

wepp/dem_wepp

Variables in wepp/dem_wepp (corresponds to FlowMapR’s XXXwepp.dbf).

This list only includes variables not already described above in the Generic DEMs.

Note: that the use of “top”, “left”, and “right” isn’t quite consistent. “Top” refers to coming in from the top to the cell (direction of flow is downwards). Whereas “right” and “left” refer to the direction of flow (towards the right, coming in to the cell from the left and vice versa). We leave this as is to be consistent with FlowMapR but may change this in future.

LITAP Parameters	LandMapR Name	Description
seedtype	SEEDTYPE	1 - Channel start (where the upslope value is greater than the upslope_threshold argument 2 - Channel junction (where two channels meet) 3 - Cell upslope of a junction which is not the main branch (end point of a segment) 4 - Split cell (where a channel is split to the maximum chan_length value; end point of a segment) 5 - Pit cell (end point of a segment) 6 - Channel end (end point of a segment) 7 - Cell upslope of a junction identifying the main branch (has the largest upslope area; endpoint of a segment) 8 - Cell immediate down stream from either a depression (pit) or a split-type seed cell [start of new channel segment]
shed_no	SHED_NO	The ID of the channel segment which a cell eventually flows into
shed_side	SHED_SIDE	The side from which this cell eventually flows into the channel. channel cell from the top (1) of the channel (downwards), from the left (towards the right; 2), or from the right (towards the left; 3) of the channel.
hill_no	HILL_HO	The ID of a hillside based on where the cells flow into a channel
chan_no	CHAN_NO	The ID of a channel
chan_side	CHAN_SIDE	A non-channel cell which drains into a channel cell from the top (1) of the channel (downwards), from the left (towards the right; 2), or from the right (towards the left; 3) of the channel.
segment_no	SEGMENT_NO	ID of an individual channel segment
l2st	L2ST	Line-of-sight distance from a cell to the cell where it flows into the channel

wepp/struct

Variables in wepp/struct (corresponds to FlowMapR’s XXXstruc.dbf).

This list only includes variables not already described above in the Generic DEMs.

Note: that the use of “top”, “left”, and “right” isn’t quite consistent. “Top” refers to coming in from the top to the cell (direction of flow is downwards). Whereas “right” and “left” refer to the direction of flow (towards the right, coming in to the cell from the left and vice versa). We leave this as is to be consistent with FlowMapR but may change this in future.

LITAP Parameters	LandMapR Name	Description
element_no	Element_no	ID of the channel or impoundment element
ele_type	Ele_type	Channel type (2) or impoundment type (3)
left_hill	Left_hill	The ID of hill slope which drains in
right_hill	Right_hill	The ID of hill slope which drains in
top_hill	Top_hill	The ID of hill slope which drains in
left_chan	Left_chan	The ID of the channel segment which drains in
right_chan	Right_chan	The ID of the channel segment which drains in
top_chan	Top_chan	The ID of the channel segment which drains in
left_imp	Left_imp	The ID of the impoundment which drains in
right_imp	Right_imp	The ID of the impoundment which drains in
top_imp	Top_imp	The ID of the impoundment which drains in
comments	Comment	Description of the element

wepp/segs

Variables in wepp/segs (corresponds to FlowMapR’s XXXsegs.dbf).

This list only includes variables not already described above in the Generic DEMs.

Note: that the use of “top”, “left”, and “right” isn’t quite consistent. “Top” refers to coming in from the top to the cell (direction of flow is downwards). Whereas “right” and “left” refer to the direction of flow (towards the right, coming in to the cell from the left and vice versa). We leave this as is to be consistent with FlowMapR but may change this in future.

LITAP Parameters	LandMapR Name	Description
initial_id	Initial_id	Original ID for a segment before sorting
down_seg	Down_seg	Downslope channel segment ID this segment drains into
sort_order	Sort_order	Topological order of sorting channel segments
final_id	Final_id	Final ID of a segment
drain_seqno	Drain_seqno	The number of the first cell where this segment drains
start_seqno	Start_seqno	Number of the first cell in this segment
start_row	Start_row	Row of the first cell in this segment
start_col	Start_col	Column of the first cell in this segment
start_type	Start_type	Seed type of this start of the segment (see seedtype above under wepp/dem_wepp)
start_elev	Start_elev	Elevation of the first cell in this segment
start_ddir	Start_ddir	Direction of water flow of the first cell in this segment
end_seqno	End_seqno	Number of the last cell in this segment
end_row	End_row	Row of the last cell in this segment
end_col	End_col	Column of the last cell in this segment
end_type	End_type	Seed type of this end of the segment (see seedtype above under wepp/dem_wepp)
end_elev	End_elev	Elevation of the last cell in this segment
impound	Impound	Whether this segment is an impoundment
center_seg	Center_seg	ID of the segment drainign in from the top
center_seqno	Center_seqno	Cell of the segment draining in from the top
right_seg	Right_seg	ID of the segment drainign in right
right_seqno	Right_seqno	Cell of the segment draining in right
left_seg	Left_seg	ID of the segment drainign in left
left_seqno	Left_seqno	Cell of the segment draining in left
len_cells	Len_cells	Length of the segment in cells
len_meters	Len_meters	Length of the segment in meters
flow2crow	Flow2crow	Empy
chan_shape	Chan_shape	Empy
width_m	Width_m	Empy

wepp/prof

Variables in wepp/prof (corresponds to FlowMapR’s XXXprof.dbf).

This list only includes variables not already described above in the Generic DEMs.

This is an intermediate file and isn’t documented by LandMapR.

wepp/hill

Variables in wepp/hill (corresponds to FlowMapR’s XXXhill.dbf).

This list only includes variables not already described above in the Generic DEMs.

Note: that the use of “top”, “left”, and “right” isn’t quite consistent. “Top” refers to coming in from the top to the cell (direction of flow is downwards). Whereas “right” and “left” refer to the direction of flow (towards the right, coming in to the cell from the left and vice versa). We leave this as is to be consistent with FlowMapR but may change this in future.

LITAP Parameters	LandMapR Name	Description
hill_width	Hill_width	Length of the WEPP channel that this hillslope drains to for left and rigth hill slopes
hill_area	Hill_area	The area of the hill slope
max_len	Max_len	Maximum distance to the channel
wepp_len	Wepp_len	hill_area / hill_width
num_points	Num_points	Number of points along the profile at which slope and aspect were calculated
profile	Profile	Profile: Sample of mean values for slope gradient and aspect at different relative distances along the feature

wepp/chan

Variables in wepp/chan (corresponds to FlowMapR’s XXXchan.dbf).

This list only includes variables not already described above in the Generic DEMs.

This is similar to the wepp/hill but with the channels, rather than hillslopes.

LITAP Parameters	LandMapR Name	Description
chan_len	Chan_len	The area of the channel (length * cell width)
mean_slope_pct	Mean_slope	The mean of the slope gradient across all cells in the channel
gen_slope_pct	Gen_slope	The general mean of the slope, as the absolute vertical drop divided by the length (area) of the channel.

Extra Data files (all_XXX, etc.)

There are several extra data files created at the end of facet_mapper() which are not part of the original FlowMapR runs, but are adapted from an Access workflow developed by Li, Sheng.

Variables in all_XXX.xlsx correspond to Li, Sheng’s XXX_AllData.txt and are collected from variables in the other LITAP outputs.

Note: We don’t calculate the lk_XXX variables in the original XXX_ALLData.txt files because they correspond to columns already included in the data. For example lk_st_row corresponse to st_row, etc. For variables like lk_st_x which were not originally included, they are now represented by st_x.

References

Eyton, J. R. 1991. Rate-of-change maps. Cartography and Geographic Information Systems. 18: 87-103

Macmillan, R.A. (2003). LandMapR Software Toolkit- C++ Version (2003): User’s Manual. Available: https://www.researchgate.net/publication/301726747_LandMapR_Software_Toolkit-_C_Version_2003_User's_Manual/

MacMillan, R.A., Pettapiece, W.W., Nolan, S.C., & Goddard, T.W. 2000. A generic procedure for automatically segmenting landforms into landform elements using DEMs, heuristic rules and fuzzy logic– Fuzzy sets and Systems 113: 81–109.

Quinn, P., K. Beven, P. Chevallier and O. Planchon. 1991. The prediction of hillslope flow paths for distributed hydrological modelling using digital terrain models. Hydrological Processes. 5: 59-79

Sheng Li, David A. Lobb, Brian G. McConkey, R. A. MacMillan, Alan Moulin, and Walter R. Fraser. 2011. Extracting topographic characteristics of landforms typical of Canadian agricultural landscapes for agri-environmental modeling. I. Methodology. Canadian Journal of Soil Science 91(2), 251-266. https://doi.org/10.4141/CJSS10080.