Author: dblodgett@usgs.gov

# Non-dendritic networks

#### dblodgett@usgs.gov

# 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.

1. A feature at the top of a diversion will have `divergence` set to 1.
2. All features that are part of a diversion that has not yet recombined with a main path, will have `stream calculator` set to 0.
3. 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.