earthkit.hydro.downstream.array

Module contents

earthkit.hydro.downstream.array.max(river_network, field, node_weights=None, edge_weights=None, return_type=None)

Computes the weighted maximum of a field over all downstream nodes.

For each node in the river network, this function identifies all downstream nodes in the river network and accumulates their contributions upstream, weighted by both node and edge weights.

The weighted maximum is defined as:

\begin{align*} x'_i &= w'_i \cdot x_i \\ m_j &= \mathrm{max} (x'_j,~\mathrm{max}_{i \in \mathrm{Down}(j)} w_{ij} \cdot m_i) \end{align*}

where:

• \(x_i\) is the input value at node \(i\) (e.g., rainfall),

• \(w'_i\) is the node weight (e.g., pixel area),

• \(w_{ij}\) is the edge weight from node \(i\) to node \(j\) (e.g. discharge partitioning ratio),

• \(\mathrm{Down}(j)\) is the set of downstream nodes flowing out of node \(j\),

• \(m_j\) is the weighted maximum at node \(j\).

Accumulation proceeds in inverse topological order from the sinks to the sources.

Parameters:

• river_network (RiverNetwork) – A river network object.

• field (array-like) – An array containing field values defined on river network nodes or gridcells.

• node_weights (array-like, optional) – Array of weights for each river network node or gridcell. Default is None (unweighted).

• edge_weights (array-like, optional) – Array of weights for each edge. Default is None (unweighted).

• return_type (str, optional) – Either “masked”, “gridded” or None. If None (default), uses river_network.return_type.

Returns:

Array of maximum values for every river network node or gridcell, depending on return_type.

Return type:

array-like

earthkit.hydro.downstream.array.mean(river_network, field, node_weights=None, edge_weights=None, return_type=None)

Computes the weighted mean of a field over all downstream nodes.

For each node in the river network, this function identifies all downstream nodes in the river network and accumulates their contributions upstream, weighted by both node and edge weights.

The weighted mean is defined as:

\begin{align*} x'_i &= w'_i \cdot x_i \\ n_j &= x'_j + \sum_{i \in \mathrm{Down}(j)} w_{ij} \cdot n_i \\ d_j &= w'_j + \sum_{i \in \mathrm{Down}(j)} w_{ij} \cdot d_i \\ \bar{x}_j &= \frac{n_j}{d_j} \end{align*}

where:

• \(x_i\) is the input value at node \(i\) (e.g., rainfall),

• \(w'_i\) is the node weight (e.g., pixel area),

• \(w_{ij}\) is the edge weight from node \(i\) to node \(j\) (e.g. discharge partitioning ratio),

• \(\mathrm{Down}(j)\) is the set of downstream nodes flowing out of node \(j\),

• \(n_j\) is the accumulated weighted value,

• \(d_j\) is the accumulated weight (denominator),

• \(\bar{x}_j\) is the weighted mean at node \(j\).

Accumulation proceeds in inverse topological order from the sinks to the sources.

Parameters:

• river_network (RiverNetwork) – A river network object.

• field (array-like) – An array containing field values defined on river network nodes or gridcells.

• node_weights (array-like, optional) – Array of weights for each river network node or gridcell. Default is None (unweighted).

• edge_weights (array-like, optional) – Array of weights for each edge. Default is None (unweighted).

• return_type (str, optional) – Either “masked”, “gridded” or None. If None (default), uses river_network.return_type.

Returns:

Array of mean values for every river network node or gridcell, depending on return_type.

Return type:

array-like

earthkit.hydro.downstream.array.min(river_network, field, node_weights=None, edge_weights=None, return_type=None)

Computes the weighted minimum of a field over all downstream nodes.

For each node in the river network, this function identifies all downstream nodes in the river network and accumulates their contributions upstream, weighted by both node and edge weights.

The weighted minimum is defined as:

\begin{align*} x'_i &= w'_i \cdot x_i \\ m_j &= \mathrm{min}(x'_j,~\mathrm{min}_{i \in \mathrm{Down}(j)} w_{ij} \cdot m_i) \end{align*}

where:

• \(x_i\) is the input value at node \(i\) (e.g., rainfall),

• \(w'_i\) is the node weight (e.g., pixel area),

• \(w_{ij}\) is the edge weight from node \(i\) to node \(j\) (e.g. discharge partitioning ratio),

• \(\mathrm{Down}(j)\) is the set of downstream nodes flowing out of node \(j\),

• \(m_j\) is the weighted minimum at node \(j\).

Accumulation proceeds in inverse topological order from the sinks to the sources.

Parameters:

• river_network (RiverNetwork) – A river network object.

• field (array-like) – An array containing field values defined on river network nodes or gridcells.

• node_weights (array-like, optional) – Array of weights for each river network node or gridcell. Default is None (unweighted).

• edge_weights (array-like, optional) – Array of weights for each edge. Default is None (unweighted).

• return_type (str, optional) – Either “masked”, “gridded” or None. If None (default), uses river_network.return_type.

Returns:

Array of minimum values for every river network node or gridcell, depending on return_type.

Return type:

array-like

earthkit.hydro.downstream.array.mode(river_network, field, node_weights=None, edge_weights=None, return_type=None)

Computes the mode (most frequent value) of a categorical field over all downstream nodes.

For each node in the river network, this function identifies all downstream nodes and determines the most frequently occurring category value.

For categorical data (e.g., land cover classes, soil types), the mode represents the dominant downstream category. Ties are broken by selecting the smallest category value.

Accumulation proceeds in inverse topological order from the sinks to the sources.

Parameters:

• river_network (RiverNetwork) – A river network object.

• field (array-like) – An array of categorical (integer) values defined on river network nodes or gridcells.

• node_weights (array-like, optional) – Not supported for mode calculation. Must be None.

• edge_weights (array-like, optional) – Not supported for mode calculation. Must be None.

• return_type (str, optional) – Either “masked”, “gridded” or None. If None (default), uses river_network.return_type.

Returns:

Array of mode (most frequent category) values for every river network node or gridcell, depending on return_type.

Return type:

array-like

Notes

• Mode calculation does not support node or edge weights.

• Input field must contain integer categorical values.

• Currently only supported for numpy backend.

Examples

Computing dominant downstream land cover class:

>>> land_cover = np.array([1, 2, 2, 3, 2])  # Land cover categories
>>> result = mode(river_network, land_cover)

earthkit.hydro.downstream.array.percentile(river_network, field, p, node_weights=None, edge_weights=None, return_type=None)

Computes the weighted percentile of a field over all downstream nodes.

For each node in the river network, this function identifies all downstream nodes (the draining area) and computes the requested percentile from the field values, optionally weighted by node weights.

The weighted percentile is defined as:

\begin{align*} \mathcal{D}(j) &= \{j\} \cup \bigcup_{i \in \mathrm{Down}(j)} \mathcal{D}(i) \\ P_p(x)_j &= \mathrm{percentile}_p \bigl(\{ w'_i \cdot x_i : i \in \mathcal{D}(j) \}\bigr) \end{align*}

where:

• \(x_i\) is the input value at node \(i\) (e.g., rainfall),

• \(w'_i\) is the node weight (e.g., pixel area),

• \(\mathrm{Down}(j)\) is the set of immediate downstream nodes flowing out of node \(j\),

• \(\mathcal{D}(j)\) is the full draining area of node \(j\) (all downstream nodes including \(j\) itself),

• \(P_p(x)_j\) is the \(p\)-th percentile at node \(j\).

Accumulation proceeds in inverse topological order from the sinks to the sources.

Parameters:

• river_network (RiverNetwork) – A river network object.

• field (array-like) – An array containing field values defined on river network nodes or gridcells.

• p (float) – Requested percentile expressed as a fraction between 0 and 1 inclusive (e.g. 0.5 for median, 0.95 for the 95th percentile).

• node_weights (array-like, optional) – Array of weights for each river network node or gridcell. Default is None (unweighted).

• edge_weights (array-like, optional) – Array of weights for each edge. Default is None (unweighted). Currently unsupported.

• return_type (str, optional) – Either “masked”, “gridded” or None. If None (default), uses river_network.return_type.

Returns:

Array of percentile values for every river network node or gridcell, depending on return_type.

Return type:

array-like

earthkit.hydro.downstream.array.std(river_network, field, node_weights=None, edge_weights=None, return_type=None)

Computes the weighted standard deviation of a field over all downstream nodes.

For each node in the river network, this function identifies all downstream nodes in the river network and accumulates their contributions upstream, weighted by both node and edge weights.

The weighted standard deviation is defined as:

\begin{align*} x'_i &= w'_i \cdot x_i \\ q'_i &= w'_i \cdot x_i^2 \\ n_j &= x'_j + \sum_{i \in \mathrm{Down}(j)} w_{ij} \cdot n_i \\ q_j &= q'_j + \sum_{i \in \mathrm{Down}(j)} w_{ij} \cdot q_i \\ d_j &= w'_j + \sum_{i \in \mathrm{Down}(j)} w_{ij} \cdot d_i \\ \bar{x}_j &= \frac{n_j}{d_j} \\ \mathrm{Var}(x)_j &= \frac{q_j}{d_j} - \bar{x}_j^2 \\ \mathrm{Std}(x)_j &= \sqrt{\mathrm{Var}(x)_j} \end{align*}

where:

• \(x_i\) is the input value at node \(i\) (e.g., rainfall),

• \(w'_i\) is the node weight (e.g., pixel area),

• \(w_{ij}\) is the edge weight from node \(i\) to node \(j\) (e.g., discharge partitioning ratio),

• \(\mathrm{Down}(j)\) is the set of downstream nodes flowing out of node \(j\),

• \(n_j\) is the accumulated weighted value,

• \(q_j\) is the accumulated weighted squared value,

• \(d_j\) is the accumulated weight (denominator),

• \(\bar{x}_j\) is the weighted average at node \(j\),

• \(\mathrm{Var}(x)_j\) is the weighted variance at node \(j\).

• \(\mathrm{Std}(x)_j\) is the weighted standard deviation at node \(j\).

Accumulation proceeds in inverse topological order from the sinks to the sources. This formulation computes the population standard deviation.

Parameters:

• river_network (RiverNetwork) – A river network object.

• field (array-like) – An array containing field values defined on river network nodes or gridcells.

• node_weights (array-like, optional) – Array of weights for each river network node or gridcell. Default is None (unweighted).

• edge_weights (array-like, optional) – Array of weights for each edge. Default is None (unweighted).

• return_type (str, optional) – Either “masked”, “gridded” or None. If None (default), uses river_network.return_type.

Returns:

Array of standard deviation values for every river network node or gridcell, depending on return_type.

Return type:

array-like

earthkit.hydro.downstream.array.sum(river_network, field, node_weights=None, edge_weights=None, return_type=None)

Computes the weighted sum of a field over all downstream nodes.

For each node in the river network, this function identifies all downstream nodes in the river network and accumulates their contributions upstream, weighted by both node and edge weights.

The weighted sum is defined as:

\begin{align*} x'_i &= w'_i \cdot x_i \\ n_j &= x'_j + \sum_{i \in \mathrm{Down}(j)} w_{ij} \cdot n_i \end{align*}

where:

• \(x_i\) is the input value at node \(i\) (e.g., rainfall),

• \(w'_i\) is the node weight (e.g., pixel area),

• \(w_{ij}\) is the edge weight from node \(i\) to node \(j\) (e.g. discharge partitioning ratio),

• \(\mathrm{Down}(j)\) is the set of downstream nodes flowing out of node \(j\),

• \(n_j\) is the weighted sum at node \(j\).

Accumulation proceeds in inverse topological order from the sinks to the sources.

Parameters:

• river_network (RiverNetwork) – A river network object.

• field (array-like) – An array containing field values defined on river network nodes or gridcells.

• node_weights (array-like, optional) – Array of weights for each river network node or gridcell. Default is None (unweighted).

• edge_weights (array-like, optional) – Array of weights for each edge. Default is None (unweighted).

• return_type (str, optional) – Either “masked”, “gridded” or None. If None (default), uses river_network.return_type.

Returns:

Array of sum values for every river network node or gridcell, depending on return_type.

Return type:

array-like

earthkit.hydro.downstream.array.var(river_network, field, node_weights=None, edge_weights=None, return_type=None)

Computes the weighted variance of a field over all downstream nodes.

For each node in the river network, this function identifies all downstream nodes in the river network and accumulates their contributions upstream, weighted by both node and edge weights.

The weighted variance is defined as:

\begin{align*} x'_i &= w'_i \cdot x_i \\ q'_i &= w'_i \cdot x_i^2 \\ n_j &= x'_j + \sum_{i \in \mathrm{Down}(j)} w_{ij} \cdot n_i \\ q_j &= q'_j + \sum_{i \in \mathrm{Down}(j)} w_{ij} \cdot q_i \\ d_j &= w'_j + \sum_{i \in \mathrm{Down}(j)} w_{ij} \cdot d_i \\ \bar{x}_j &= \frac{n_j}{d_j} \\ \mathrm{Var}(x)_j &= \frac{q_j}{d_j} - \bar{x}_j^2 \end{align*}

where:

• \(x_i\) is the input value at node \(i\) (e.g., rainfall),

• \(w'_i\) is the node weight (e.g., pixel area),

• \(w_{ij}\) is the edge weight from node \(i\) to node \(j\) (e.g., discharge partitioning ratio),

• \(\mathrm{Down}(j)\) is the set of downstream nodes flowing out of node \(j\),

• \(n_j\) is the accumulated weighted value,

• \(q_j\) is the accumulated weighted squared value,

• \(d_j\) is the accumulated weight (denominator),

• \(\bar{x}_j\) is the weighted average at node \(j\),

• \(\mathrm{Var}(x)_j\) is the weighted variance at node \(j\).

Accumulation proceeds in inverse topological order from the sinks to the sources. This formulation computes the population variance.

Parameters:

• river_network (RiverNetwork) – A river network object.

• field (array-like) – An array containing field values defined on river network nodes or gridcells.

• node_weights (array-like, optional) – Array of weights for each river network node or gridcell. Default is None (unweighted).

• edge_weights (array-like, optional) – Array of weights for each edge. Default is None (unweighted).

• return_type (str, optional) – Either “masked”, “gridded” or None. If None (default), uses river_network.return_type.

Returns:

Array of variance values for every river network node or gridcell, depending on return_type.

Return type:

array-like