Non-dendritic networks

Introduction

vignette("hydroloom") and vignette("advanced_network") cover the basics of network topology representation and the attributes that build on a strictly dendritic network. This vignette extends those topics to the hydroloom functionality that supports non-dendritic networks.

The term “non-dendritic” refers to any network that does not follow a dendritic flow pattern. Typically that means one or more flowlines diverting from a primary flow path. Non-dendritic can also refer to endorheic basins nested within an otherwise dendritic basin — but this article addresses the diverted-flowline case.

The terms “diversion” and “divergence” are used in similar contexts but carry distinct meanings. A diversion is a diverted flowline (waterbody), whereas a divergence is where the network diverges. “Diversion” is often associated with anthropogenic features, but a diversion can also be a naturally occurring diverted flow.

Non-dendritic topology attributes

In a non-dendritic network, one downstream path at each divergence is treated as primary and the others as secondary. hydroloom supports several attributes for tracking that primary/secondary categorization.

fromnode and tonode

fromnode and tonode store a flow network as an edge-node topology where every feature has exactly one upstream node and exactly one downstream node. Nodes give every confluence and divergence a single identifier, which makes converting a flow network to a graph and many downstream analyses cleaner.

divergence

The divergence attribute indicates if a downstream connection is primary (1) or secondary (2). If 0, a connection is not downstream of a divergence. This attribute is useful as it facilitates following a flow network in the “downstream mainstem” direction at every divergence.

return divergence

The return divergence attribute indicates that one or more of the features upstream of a given feature originates from a divergence. If 0, the upstream features are not part of a diversion. If 1, one or more of the upstream features is part of a diversion.

stream calculator

The stream calculator attribute is part of the modified Strahler stream order as implemented in the NHDPlus data model. It indicates if a given feature is part of the downstream mainstem dendritic network or is part of a diverted path. If 0, the path is part of a diversion. Otherwise stream calculator will be equal to stream order. When generating Strahler stream order, if stream calculator is 0 for a given feature, that feature is not considered for incrementing downstream stream order.

summary

As a system, stream calculator, divergence and return divergence support network navigation and processing in the context of diverted paths.

A feature at the top of a diversion will have divergence set to 1.
All features that are part of a diversion that has not yet recombined with a main path, will have stream calculator set to 0.
A feature that is just downstream of where a diversion recombines with a main path will have return divergence set to 1.

Divergence case study: dropped vs preserved secondary paths

Before applying the full pipeline to real data, look at what happens to a divergence when a non-dendritic network is forced into the dendritic hy_topo form. The five-edge example from vignette("hydroloom") has one divergence at feature 1 and one confluence at feature 5.

We start in hy_node form with fromnode/tonode and a divergence column marking the secondary path. The network looks like this, with feature 1 flowing into node N2, where it splits into feature 2 (main path) and feature 4 (diverted secondary path), both of which rejoin at node N4 and flow out through feature 5:

       N1
        |
        1
        | 
        v
       N2
      /  \
     2    4
    /      \ (4 is diverted)
   v        v
   N3       |
    \       |
     3      | 
      \    /
       v  v
        N4
         |
         5
         |
         v
         N5

library(hydroloom)

node_df <- data.frame(
  id         = c(1, 2, 3, 4, 5),
  fromnode   = c("N1", "N2", "N3", "N2", "N4"),
  tonode     = c("N2", "N3", "N4", "N4", "N5"),
  divergence = c(0,  2,  0,  1,  0)
)

x_node <- hy(node_df)
class(x_node)
#> [1] "hy_node"    "hy"         "tbl_df"     "tbl"        "data.frame"
nrow(x_node)
#> [1] 5

Converting to a dendritic edge list with add_toids(return_dendritic = TRUE) keeps one row per feature and drops the secondary downstream connection from feature 1:

x_topo <- add_toids(x_node, return_dendritic = TRUE)
class(x_topo)
#> [1] "hy_topo"    "hy"         "tbl_df"     "tbl"        "data.frame"
nrow(x_topo)
#> [1] 5
x_topo[, c("id", "toid")]
#> # hydroloom dendritic edge list (self-referencing): 5 features
#> # A tibble: 5 × 2
#>      id  toid
#>   <dbl> <dbl>
#> 1     1     4
#> 2     2     3
#> 3     3     5
#> 4     4     5
#> 5     5     0

Setting return_dendritic = FALSE preserves both downstream connections by repeating id == 1. The result is no longer dendritic, so hy() classifies it as hy_flownetwork:

x_fn <- add_toids(x_node, return_dendritic = FALSE)
class(x_fn)
#> [1] "hy_flownetwork" "tbl_df"         "tbl"            "data.frame"
nrow(x_fn)
#> [1] 6
x_fn[, c("id", "toid")]
#> # hydroloom flow network: 6 connections, 1 non-dendritic edges
#> # A tibble: 6 × 2
#>      id  toid
#>   <dbl> <dbl>
#> 1     1     2
#> 2     1     4
#> 3     2     3
#> 4     3     5
#> 5     4     5
#> 6     5     0

Both downstream paths from feature 1 are preserved. hy_capabilities() shows which functions are callable at each stage; that workflow is demonstrated end to end in vignette("network_navigation").

Bringing it all together

The example below shows how we can recreate the non-dendritic attributes and use them in practice.

We’ll start with the small sample watershed that’s included in hydroloom and select only the attributes required to recreate the non-dendritic network.

x <- sf::read_sf(system.file("extdata/new_hope.gpkg",
  package = "hydroloom"))

# First we select only an id, a name, and a feature type.
flow_net <- x |>
  select(COMID, GNIS_ID, FTYPE) |>
  sf::st_transform(5070)

# Now we convert the geometric network to an attribute topology
# and convert that to a node topology and join our attributes back
flow_net <- flow_net |>
  make_attribute_topology(min_distance = 5) |>
  hydroloom::make_node_topology(add_div = TRUE) |>
  left_join(sf::st_drop_geometry(flow_net), by = "COMID")

# We only have one outlet so it doesn't matter if it is coastal
# or inland but we have to provide it.
outlets <- filter(flow_net, !tonode %in% fromnode)

# We have these feature types. A larger dataset might include
# things like canals which would not be considered  "major"
unique(flow_net$FTYPE)
#> [1] "StreamRiver"    "Connector"      "ArtificialPath"

# compare dendritic vs non-dendritic toid row counts to see how many
# secondary paths exist in the data
flow_net_with_div <- add_divergence(flow_net,
  coastal_outlet_ids = c(),
  inland_outlet_ids = outlets$COMID,
  name_attr = "GNIS_ID",
  type_attr = "FTYPE",
  major_types = unique(flow_net$FTYPE))

dend <- add_toids(flow_net_with_div, return_dendritic = TRUE)
nondend <- add_toids(flow_net_with_div, return_dendritic = FALSE)

nrow(dend)
#> [1] 746
nrow(nondend)
#> [1] 832
nrow(nondend) - nrow(dend)
#> [1] 86

# now we run the add_divergence, add_toids, and add_streamorder
flow_net <- add_divergence(flow_net,
  coastal_outlet_ids = c(),
  inland_outlet_ids = outlets$COMID,
  name_attr = "GNIS_ID",
  type_attr = "FTYPE",
  major_types = unique(flow_net$FTYPE)) |>
  add_toids() |>
  add_streamorder() |>
  add_return_divergence()

# Make sure we reproduce what came from our source NHDPlus data.
sum(flow_net$divergence == 2)
#> [1] 84
sum(x$Divergence == 2)
#> [1] 84
all(flow_net$divergence == x$Divergence)
#> [1] TRUE
sum(flow_net$return_divergence == x$RtnDiv)
#> [1] 745

names(flow_net)
#>  [1] "COMID"             "toid"              "tonode"           
#>  [4] "GNIS_ID"           "FTYPE"             "divergence"       
#>  [7] "fromnode"          "stream_order"      "stream_calculator"
#> [10] "return_divergence"

With the above code, we removed all attributes other than an ID, a name and a feature type and recreated both a dendritic (toid) and non-dendritic (fromnode tonode) topology. We added divergence attribute, stream_order, stream_calculator, and return_divergence attributes.

dblodgett@usgs.gov