Author: dblodgett@usgs.gov

# Hydroloom Overview

#### dblodgett@usgs.gov

# hydroloom

Hydroloom is designed to provide general hydrologic network functionality for any hydrographic or hydrologic data. This is accomplished with 1) the `hy` S3 class, 2) a collection of utility functions, 3) functions to work with a hydrologic network topology as a graph, 4) functions to create and add useful network attributes, 5) and functions to index data to a network of flow network lines and waterbody polygons.

This introduction covers the `hy` S3 class and the core flow network topology concepts necessary to use hydroloom effectively.

For the latest development and to open issues, please visit the package github repository.

# `hy` S3 class

Hydroloom implements an `hy` S3 class designed to simplify integration of `hydroloom` with existing data and workflows. `hy()` converts a data.frame to an `hy` `data.frame` with attributes compatible with `hydroloom` functions. `hy_reverse()` converts a `hy` `data.frame` back to its original attribute names. You can teach `hydroloom` how to map your attributes to `hydroloom_name_definitions()` with the `hydroloom_names()` function.

Most `hydroloom` functions will work with either a `hy` object or a `data.frame` containing names registered with `hydroloom_names()`. Any attributes added to the `data.frame` will contain names from `hydroloom` and must be renamed in the calling environment.

Internally, the `hy` S3 class has an attribute `orig_names` as shown below. The `orig_names` attribute is used to convert original attribute names back to their original values. Using the `hydroloom` names and the `hy` S3 object are not required but adopting `hydroloom_names_definitions()` may be helpful for people aiming for consistent, simple, and accurate attribute names.

    library(hydroloom)

    hy_net <- sf::read_sf(system.file("extdata/new_hope.gpkg", package = "hydroloom")) |>
      dplyr::select(COMID, REACHCODE, FromNode, ToNode, Hydroseq, TerminalFl, Divergence)

    hy(hy_net[1:3, ])
    #> Simple feature collection with 3 features and 7 fields
    #> Geometry type: MULTILINESTRING
    #> Dimension:     XY
    #> Bounding box:  xmin: 1517192 ymin: 1555954 xmax: 1518702 ymax: 1557298
    #> Projected CRS: +proj=aea +lat_0=23 +lon_0=-96 +lat_1=29.5 +lat_2=45.5 +x_0=0 +y_0=0 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
    #> # A tibble: 3 × 8
    #>        id aggregate_id    fromnode    tonode topo_sort terminal_flag divergence
    #>     <int> <chr>              <dbl>     <dbl>     <dbl>         <int>      <int>
    #> 1 8893864 03030002000018 250031721 250031853 250016373             0          0
    #> 2 8894490 03030002000018 250031895 250031854 250015665             0          0
    #> 3 8894494 03030002000018 250031897 250031895 250015826             0          0
    #> # ℹ 1 more variable: geom <MULTILINESTRING [m]>

    attr(hy(hy_net), "orig_names")
    #>           COMID       REACHCODE        FromNode          ToNode        Hydroseq
    #>            "id"  "aggregate_id"      "fromnode"        "tonode"     "topo_sort"
    #>      TerminalFl      Divergence            geom
    #> "terminal_flag"    "divergence"          "geom"

# Network Representation

## Representing Dendritic Network Topology

A network of flowlines can be represented as an edge-to-edge (e.g. edge list) or edge-node topology. An edge list only expresses the connectivity between edges (flowlines in the context of rivers), requiring nodes (confluences in the context of rivers) to be inferred.

    #>  id toid fromnode tonode
    #>   1    3       N1     N3
    #>   2    3       N2     N3
    #>   3   NA       N3     N4

In an edge-node topology, edges are directed to nodes which are then directed to other edges. An edge-to-edge toplogy does not include intervening nodes.

The “toid” of a terminal flowline can be either NA or, by convention, 0 or ““. Using 0 or an empty string is preferred within `hydroloom` but both are handled in most cases. Further, as long as 0 is not in the set of IDs, there is little practical difference.

In `hydroloom`, edge-to-edge topology is referred to with “id and toid” attributes.

## Representing Non-Dendritic Network Topology

As discussed in the `vignette("non-dendritic")` vignette, a hydrologic flow network can be represented as an edge to edge (e.g. edge list) topology or an edge-node topology. In the case of dendritic networks, an edge list can be stored as a single “toid” attribute on each feature and nodes are redundant as there would be one and only one node for each feature. In non-dendritic networks, an edge list can include multiple “toid” attributes for each feature, necessitating a one to many relationship that can be difficult to interpret. Nevertheless, the U.S. National Hydrography Dataset uses an edge-list format in its “flow table” and the format is capable of storing non-dendritic feature topology.

Using a node topology to store a flow network, each feature flows from one and only one node and flows to one and only one node. This one to one relationship between features and their from and to nodes means that the topology fits in a table with one row per feature as is common practice in spatial feature data.

For this reason, the NHDPlus data model converts the NHD “flow table” into node topology in its representation of non dendritic topology. The downside of this approach is that it requires creation of a node identifier. These node identifiers are a table deduplication device that enables a one to many relationship (the flow table) to be represented as two one to one relationships. Given this, in hydrologic flow networks, node identifiers can be created based on an edge list and discarded when no longer needed.

In this example of an edge list topology and a node topology for the same system, feature ‘1’ flows to two edges but only one node. We can represent this in tabular form with a duplicated row for the divergence downstream of ‘1’ or with the addition of node identifiers as shown in the following tables.

id | fromnode | tonode
--- | --- | ---
1 | N1 | N2
2 | N2 | N3
3 | N3 | N4
4 | N2 | N4
5 | N4 | N5

id | toid
--- | ---
1 | 2
1 | 4
2 | 3
3 | 5
4 | 5
5 | 0

## Network Graph Representation

The `make_index_ids()` `hydroloom` function creates an adjacency matrix representation of a flow network as well as some convenient content that is useful when traversing the graph. This adjacency matrix is used heavily in `hydroloom` functions and may be useful to people who want to write their own graph traversal algorithms.

In the example below we’ll add a dendritic toid and explore the `make_index_ids()` output.

    y <- add_toids(hy_net, return_dendritic = TRUE)

    ind_id <- make_index_ids(y)

    names(ind_id)
    #> [1] "to"      "lengths" "to_list"

    dim(ind_id$to)
    #> [1]   1 746

    max(lengths(ind_id$lengths))
    #> [1] 1

    names(ind_id$to_list)
    #> [1] "id"      "indid"   "toindid"

    sapply(ind_id, class)
    #> $to
    #> [1] "matrix" "array"
    #>
    #> $lengths
    #> [1] "numeric"
    #>
    #> $to_list
    #> [1] "data.frame"

Now we’ll look at the same thing but for a non dendritic set of toids. Notice that the `to` element of `ind_id` now has three rows. This indicates that one or more of the connections in the matrix has three downstream neighbors. The `lengths` element indicates how many non `NA` values are in each column of the matrix in the `to` element.

    y <- add_toids(st_drop_geometry(hy_net), return_dendritic = FALSE)

    ind_id <- make_index_ids(y)

    names(ind_id)
    #> [1] "to"      "lengths" "to_list"
    dim(ind_id$to)
    #> [1]   3 746

    max(ind_id$lengths)
    #> [1] 3

    sum(ind_id$lengths == 2)
    #> [1] 84
    sum(ind_id$lengths == 3)
    #> [1] 1

    names(ind_id$to_list)
    #> [1] "id"      "indid"   "toindid"

    sapply(ind_id, class)
    #> $to
    #> [1] "matrix" "array"
    #>
    #> $lengths
    #> [1] "numeric"
    #>
    #> $to_list
    #> [1] "data.frame"

The default `mode = "to"` produces a downstream-directed graph. Setting `mode = "from"` inverts the direction so that each column’s entries point to upstream neighbors instead. The output uses `froms` and `froms_list` naming to distinguish from the downstream version.

    from_id <- make_index_ids(y, mode = "from")

    names(from_id)
    #> [1] "froms"      "lengths"    "froms_list"

    dim(from_id$froms)
    #> [1]   3 746

    # a confluence: two upstream connections
    max(from_id$lengths)
    #> [1] 3

    sum(from_id$lengths == 2)
    #> [1] 227

Setting `mode = "both"` returns a list containing both the `to` and `from` graphs, which is useful when an algorithm needs to traverse the network in both directions without creating the graph twice.

    both_id <- make_index_ids(y, mode = "both")

    names(both_id)
    #> [1] "to"   "from"

    # each direction covers the same set of features
    ncol(both_id$to$to) == ncol(both_id$from$froms)
    #> [1] TRUE

## Using the Graph Representation

Most `hydroloom` functions that need a graph create it internally from `id` and `toid` attributes. Functions like `sort_network()`, `accumulate_downstream()`, `add_levelpaths()`, `add_streamorder()`, and `subset_network()` all call `make_index_ids()` behind the scenes so users do not need to construct the graph themselves.

The exception is `navigate_network_dfs()`, which accepts either a data.frame or a pre-built index_ids list. When calling `navigate_network_dfs()` many times (e.g., starting from every feature in a network), passing a pre-built graph avoids reconstructing it on each call.

    # navigate_network_dfs creates the graph internally from a data.frame
    navigate_network_dfs(y, starts = y$id[1], direction = "down")
    #> list()

    # or accept pre-built index ids -- use "to" for downstream, "from" for upstream
    to_index <- make_index_ids(y, mode = "to")
    navigate_network_dfs(to_index, starts = y$id[1], direction = "down")
    #> list()

    from_index <- make_index_ids(y, mode = "from")
    navigate_network_dfs(from_index, starts = y$id[1], direction = "up")
    #> list()