Generate 3D landscape from an Optimal Channel Network

Function that calculates the elevation field generated by the OCN and the partition of the domain into different catchments.

Usage

landscape_OCN(OCN, slope0 = 1, zMin = 0, optimizeDZ = FALSE,
  optimMethod = "BFGS", optimControl = list(maxit = 100 *
  length(OCN$FD$outlet), trace = 1), displayUpdates = 0)

Arguments

OCN

A river object as produced by create_OCN.

slope0

slope of the outlet pixel (in elevation units/planar units).

zMin

Elevation of the lowest pixel (in elevation units).

optimizeDZ

If TRUE, when there are multiple catchments, minimize differences in elevation at the catchment borders by lifting catchments, while respecting zMin. If FALSE, all outlet pixels have elevation equal to zMin. This option is not effective for OCNs generated via create_general_contour_OCN.

optimMethod

Optimization method used by function optim (only used if optimizeDZ = TRUE).

optimControl

List of control parameters used by function optim (only used if optimizeDZ = TRUE).

displayUpdates

State if updates are printed on the console while landscape_OCN runs.

0: No update is given.
1: Concise updates are given.
2: More extensive updates are given (this might slow down the total function runtime).

Note that the display of updates during optimization of elevations (when optimizeDZ = TRUE) is controlled by parameter optimControl$trace.

Value

A river object that contains all objects contained in OCN, in addition to the objects listed below. A new sublist CM, containing variables at the catchment aggregation levels, is created.

FD$slope: Vector (of length OCN$FD$nNodes) of slope values (in elevation units/planar units) for each FD pixel, as derived by the slope/area relationship.
FD$leng: Vector (of length OCN$FD$nNodes) of pixel lengths. OCN$FD$leng[i] = OCN$FD$cellsize if flow direction in i is horizontal or vertical; OCN$FD$leng[i] = OCN$FD$cellsize*sqrt(2) if flow direction in i is diagonal.
FD$toCM: Vector (of length OCN$FD$nNodes) with catchment index values for each FD pixel. Example: OCN$FD$toCM[i] = j if pixel i drains into the outlet whose location is defined by outletSide[j], outletPos[j].
FD$XDraw: When periodicBoundaries = TRUE, it is a vector (of length OCN$FD$nNodes) with real X coordinate of FD pixels. If periodicBoundaries = FALSE, it is equal to OCN$FD$X.
FD$YDraw: When periodicBoundaries = TRUE, it is a vector (of length OCN$FD$nNodes) with real Y coordinate of FD pixels. If periodicBoundaries = FALSE, it is equal to OCN$FD$Y.
FD$Z: Vector (of length OCN$FD$nNodes) of elevation values for each FD pixel. Values are calculated by consecutive implementation of the slope/area relationship along upstream paths.
CM$A: Vector (of length OCN$nOutlet) with values of drainage area (in square planar units) for each of the catchments identified by the corresponding OCN$FD$outlet.
CM$W: Adjacency matrix (OCN$nOutlet by OCN$nOutlet) at the catchment level. Two catchments are connected if they share a border. Note that this is not a flow connection. Unlike the adjacency matrices at levels FD, RN, AG, this matrix is symmetric. It is a spam object.
CM$XContour (CM$Y_contour): List with number of objects equal to OCN$FD$nOutlet. Each object i is a list with X (Y) coordinates of the contour of catchment i for use in plots with exactDraw = FALSE (see functions draw_contour_OCN, draw_thematic_OCN). If catchment i is constituted by regions that are only connected through a diagonal flow direction, CM$XContour[[i]] (CM$Y_contour[[i]]) contains as many objects as the number of regions into which catchment i is split.
CM$XContourDraw (CM$YContourDraw): List with number of objects equal to OCN$FD$nOutlet. Each object i is a list with X (Y) coordinates of the contour of catchment i for use in plots with exactDraw = TRUE (see functions draw_contour_OCN, draw_thematic_OCN). If catchment i is constituted by regions that are only connected through a diagonal flow direction, CM$XContourDraw[[i]] (CM$YContourDraw[[i]]) contains as many objects as the number of regions into which catchment i is split.
OptList: List of output parameters produced by the optimization function optim (only present if optimizeDZ = TRUE).

Finally, slope0 and zMin are passed to the river as they were included in the input.

Details

The function features an algorithm (which can be activated via the optional input optimizeDZ) that, given the network configuration and a slope0 value, finds the elevation of OCN$nOutlet - 1 outlets relative to the elevation of the first outlet in vectors outletSide, outletPos such that the sum of the absolute differences elevation of neighboring pixels belonging to different catchments is minimized. Such objective function is minimized by means of function optim. The absolute elevation of the outlet pixels (and, consequently, of the whole lattice) is finally attributed by imposing OCN$FD$Z >= zMin. Note that, due to the high dimensionality of the problem, convergence of the optimization algorithm is not guaranteed for large OCN$nOutlet (say, OCN$nOutlet > 10).

Examples

# 1) draw 2D elevation map of a 20x20 OCN with default options
OCN2 <- landscape_OCN(OCN_20)

if (FALSE) { # \dontrun{
# 2) generate a 100x50 OCN; assume that the pixel resolution is 200 m
# (the total catchment area is 20 km2)
set.seed(1)
OCN <- create_OCN(100, 50, cellsize = 200, 
    displayUpdates = 0) # this takes about 40 s
# use landscape_OCN to derive the 3D landscape subsumed by the OCN
# by assuming that the elevation and slope at the outlet are 200 m 
# and 0.0075, respectively
OCN <- landscape_OCN(OCN, zMin = 200, slope0 = 0.0075)
# draw 2D and 3D representations of the landscape
draw_elev2D_OCN(OCN)
draw_elev3D_OCN(OCN)
draw_elev3Drgl_OCN(OCN)
} # }

if (FALSE) { # \dontrun{
# 3) generate a 100x50 OCN with 4 outlets
set.seed(1)
OCN <- create_OCN(100, 50, cellsize = 200, 
    nOutlet = 4, displayUpdates = 0) # this takes about 40 s
# use landscape_OCN and optimize elevation of outlets  
OCN <- landscape_OCN(OCN, slope0 = 0.0075, 
    optimizeDZ = TRUE)
# display elevation of outlets and 2D elevation map
OCN$FD$Z[OCN$FD$outlet]  
draw_elev2D_OCN(OCN)  
} # }