from earthkit.hydro.upstream.array import _operations
[docs]
def percentile(
river_network, field, p, node_weights=None, edge_weights=None, return_type=None
):
r"""
Computes the weighted percentile of a field over all upstream nodes.
For each node in the river network, this function identifies all upstream nodes
(the contributing area) and computes the requested percentile from the field values,
optionally weighted by node weights.
The weighted percentile is defined as:
.. math::
:nowrap:
\begin{align*}
\mathcal{A}(j) &= \{j\} \cup \bigcup_{i \in \mathrm{Up}(j)} \mathcal{A}(i) \\
P_p(x)_j &= \mathrm{percentile}_p \bigl(\{ w'_i \cdot x_i : i \in \mathcal{A}(j) \}\bigr)
\end{align*}
where:
- :math:`x_i` is the input value at node :math:`i` (e.g., rainfall),
- :math:`w'_i` is the node weight (e.g., pixel area),
- :math:`\mathrm{Up}(j)` is the set of immediate upstream nodes flowing into node :math:`j`,
- :math:`\mathcal{A}(j)` is the full contributing area of node :math:`j` (all upstream nodes including :math:`j` itself),
- :math:`P_p(x)_j` is the :math:`p`-th percentile at node :math:`j`.
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-like
Array of percentile values for every river network node or gridcell, depending on `return_type`.
"""
if edge_weights is not None:
raise NotImplementedError("edge_weights are currently unsupported.")
if river_network.array_backend != "numpy":
raise NotImplementedError(
"Only numpy backend is currently supported for percentiles."
)
if p < 0 or p > 1:
raise ValueError(
"The requested percentile `p` must be between 0 and 1 inclusive."
)
return _operations.percentile(
river_network=river_network,
field=field.astype("float64"),
weights=node_weights,
p=p,
return_type=return_type,
)
[docs]
def var(river_network, field, node_weights=None, edge_weights=None, return_type=None):
r"""
Computes the weighted variance of a field over all upstream nodes.
For each node in the river network, this function identifies all upstream nodes in the river network
and accumulates their contributions downstream, weighted by both node and edge weights.
The weighted variance is defined as:
.. math::
:nowrap:
\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{Up}(j)} w_{ij} \cdot n_i \\
q_j &= q'_j + \sum_{i \in \mathrm{Up}(j)} w_{ij} \cdot q_i \\
d_j &= w'_j + \sum_{i \in \mathrm{Up}(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:
- :math:`x_i` is the input value at node :math:`i` (e.g., rainfall),
- :math:`w'_i` is the node weight (e.g., pixel area),
- :math:`w_{ij}` is the edge weight from node :math:`i` to node :math:`j` (e.g., discharge partitioning ratio),
- :math:`\mathrm{Up}(j)` is the set of upstream nodes flowing into node :math:`j`,
- :math:`n_j` is the accumulated weighted value,
- :math:`q_j` is the accumulated weighted squared value,
- :math:`d_j` is the accumulated weight (denominator),
- :math:`\bar{x}_j` is the weighted average at node :math:`j`,
- :math:`\mathrm{Var}(x)_j` is the weighted variance at node :math:`j`.
Accumulation proceeds in topological order from the sources to the sinks. 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-like
Array of variance values for every river network node or gridcell, depending on `return_type`.
"""
return _operations.var(
river_network=river_network,
field=field,
node_weights=node_weights,
edge_weights=edge_weights,
return_type=return_type,
)
[docs]
def std(river_network, field, node_weights=None, edge_weights=None, return_type=None):
r"""
Computes the weighted standard deviation of a field over all
upstream nodes.
For each node in the river network, this function identifies all upstream nodes in the river network
and accumulates their contributions downstream, weighted by both node and edge weights.
The weighted standard deviation is defined as:
.. math::
:nowrap:
\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{Up}(j)} w_{ij} \cdot n_i \\
q_j &= q'_j + \sum_{i \in \mathrm{Up}(j)} w_{ij} \cdot q_i \\
d_j &= w'_j + \sum_{i \in \mathrm{Up}(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:
- :math:`x_i` is the input value at node :math:`i` (e.g., rainfall),
- :math:`w'_i` is the node weight (e.g., pixel area),
- :math:`w_{ij}` is the edge weight from node :math:`i` to node :math:`j` (e.g., discharge partitioning ratio),
- :math:`\mathrm{Up}(j)` is the set of upstream nodes flowing into node :math:`j`,
- :math:`n_j` is the accumulated weighted value,
- :math:`q_j` is the accumulated weighted squared value,
- :math:`d_j` is the accumulated weight (denominator),
- :math:`\bar{x}_j` is the weighted average at node :math:`j`,
- :math:`\mathrm{Var}(x)_j` is the weighted variance at node :math:`j`.
- :math:`\mathrm{Std}(x)_j` is the weighted standard deviation at node :math:`j`.
Accumulation proceeds in topological order from the sources to the sinks. 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-like
Array of standard deviation values for every river network node or gridcell, depending on `return_type`.
"""
return _operations.std(
river_network=river_network,
field=field,
node_weights=node_weights,
edge_weights=edge_weights,
return_type=return_type,
)
[docs]
def mean(river_network, field, node_weights=None, edge_weights=None, return_type=None):
r"""
Computes the weighted mean of a field over all upstream nodes.
For each node in the river network, this function identifies all upstream nodes in the river network
and accumulates their contributions downstream, weighted by both node and edge weights.
The weighted mean is defined as:
.. math::
:nowrap:
\begin{align*}
x'_i &= w'_i \cdot x_i \\
n_j &= x'_j + \sum_{i \in \mathrm{Up}(j)} w_{ij} \cdot n_i \\
d_j &= w'_j + \sum_{i \in \mathrm{Up}(j)} w_{ij} \cdot d_i \\
\bar{x}_j &= \frac{n_j}{d_j}
\end{align*}
where:
- :math:`x_i` is the input value at node :math:`i` (e.g., rainfall),
- :math:`w'_i` is the node weight (e.g., pixel area),
- :math:`w_{ij}` is the edge weight from node :math:`i` to node :math:`j` (e.g. discharge partitioning ratio),
- :math:`\mathrm{Up}(j)` is the set of upstream nodes flowing into node :math:`j`,
- :math:`n_j` is the accumulated weighted value,
- :math:`d_j` is the accumulated weight (denominator),
- :math:`\bar{x}_j` is the weighted mean at node :math:`j`.
Accumulation proceeds in topological order from the sources to the sinks.
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-like
Array of mean values for every river network node or gridcell, depending on `return_type`.
"""
return _operations.mean(
river_network=river_network,
field=field,
node_weights=node_weights,
edge_weights=edge_weights,
return_type=return_type,
)
[docs]
def sum(river_network, field, node_weights=None, edge_weights=None, return_type=None):
r"""
Computes the weighted sum of a field over all upstream nodes.
For each node in the river network, this function identifies all upstream nodes in the river network
and accumulates their contributions downstream, weighted by both node and edge weights.
The weighted sum is defined as:
.. math::
:nowrap:
\begin{align*}
x'_i &= w'_i \cdot x_i \\
n_j &= x'_j + \sum_{i \in \mathrm{Up}(j)} w_{ij} \cdot n_i
\end{align*}
where:
- :math:`x_i` is the input value at node :math:`i` (e.g., rainfall),
- :math:`w'_i` is the node weight (e.g., pixel area),
- :math:`w_{ij}` is the edge weight from node :math:`i` to node :math:`j` (e.g. discharge partitioning ratio),
- :math:`\mathrm{Up}(j)` is the set of upstream nodes flowing into node :math:`j`,
- :math:`n_j` is the weighted sum at node :math:`j`.
Accumulation proceeds in topological order from the sources to the sinks.
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-like
Array of sum values for every river network node or gridcell, depending on `return_type`.
"""
return _operations.sum(
river_network=river_network,
field=field,
node_weights=node_weights,
edge_weights=edge_weights,
return_type=return_type,
)
[docs]
def min(river_network, field, node_weights=None, edge_weights=None, return_type=None):
r"""
Computes the weighted minimum of a field over all upstream nodes.
For each node in the river network, this function identifies all upstream nodes in the river network
and accumulates their contributions downstream, weighted by both node and edge weights.
The weighted minimum is defined as:
.. math::
:nowrap:
\begin{align*}
x'_i &= w'_i \cdot x_i \\
m_j &= \mathrm{min}(x'_j,~\mathrm{min}_{i \in \mathrm{Up}(j)} w_{ij} \cdot m_i)
\end{align*}
where:
- :math:`x_i` is the input value at node :math:`i` (e.g., rainfall),
- :math:`w'_i` is the node weight (e.g., pixel area),
- :math:`w_{ij}` is the edge weight from node :math:`i` to node :math:`j` (e.g. discharge partitioning ratio),
- :math:`\mathrm{Up}(j)` is the set of upstream nodes flowing into node :math:`j`,
- :math:`m_j` is the weighted minimum at node :math:`j`.
Accumulation proceeds in topological order from the sources to the sinks.
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-like
Array of minimum values for every river network node or gridcell, depending on `return_type`.
"""
return _operations.min(
river_network=river_network,
field=field,
node_weights=node_weights,
edge_weights=edge_weights,
return_type=return_type,
)
[docs]
def max(river_network, field, node_weights=None, edge_weights=None, return_type=None):
r"""
Computes the weighted maximum of a field over all upstream nodes.
For each node in the river network, this function identifies all upstream nodes in the river network
and accumulates their contributions downstream, weighted by both node and edge weights.
The weighted maximum is defined as:
.. math::
:nowrap:
\begin{align*}
x'_i &= w'_i \cdot x_i \\
m_j &= \mathrm{max} (x'_j,~\mathrm{max}_{i \in \mathrm{Up}(j)} w_{ij} \cdot m_i)
\end{align*}
where:
- :math:`x_i` is the input value at node :math:`i` (e.g., rainfall),
- :math:`w'_i` is the node weight (e.g., pixel area),
- :math:`w_{ij}` is the edge weight from node :math:`i` to node :math:`j` (e.g. discharge partitioning ratio),
- :math:`\mathrm{Up}(j)` is the set of upstream nodes flowing into node :math:`j`,
- :math:`m_j` is the weighted maximum at node :math:`j`.
Accumulation proceeds in topological order from the sources to the sinks.
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-like
Array of maximum values for every river network node or gridcell, depending on `return_type`.
"""
return _operations.max(
river_network=river_network,
field=field,
node_weights=node_weights,
edge_weights=edge_weights,
return_type=return_type,
)
[docs]
def mode(river_network, field, node_weights=None, edge_weights=None, return_type=None):
r"""
Computes the mode (most common value) of categorical data over all upstream nodes.
For each node in the river network, this function identifies all upstream nodes
and finds the most frequent categorical value (spatial majority) among them.
This is designed for categorical/integer data such as land cover classifications.
The mode is computed as:
.. math::
:nowrap:
\begin{align*}
c_j^{(k)} &= \mathrm{count}(x_i = k,~i \in \{\mathrm{Up}(j) \cup \{j\}\}) \\
\mathrm{Mode}(x)_j &= \arg\max_{k} c_j^{(k)}
\end{align*}
where:
- :math:`x_i` is the categorical value at node :math:`i` (e.g., land cover class),
- :math:`\mathrm{Up}(j)` is the set of upstream nodes flowing into node :math:`j`,
- :math:`c_j^{(k)}` is the count of category :math:`k` at node :math:`j`,
- :math:`\mathrm{Mode}(x)_j` is the most common category at node :math:`j`.
In case of ties, the smallest category value is returned. The computation is performed
using a performant Rust implementation with parallel processing.
Parameters
----------
river_network : RiverNetwork
A river network object.
field : array-like
An array containing integer categorical values defined on river network nodes or gridcells.
Values should be integers representing categories (e.g., 1=forest, 2=grassland, 3=urban).
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-like
Array of mode (most common category) values for every river network node or gridcell,
depending on `return_type`.
Notes
-----
- Mode calculation currently only supports the numpy backend.
- The Rust extension must be available for this function to work.
- Node weights and edge weights are not supported for mode calculation.
- Field values are converted to int64 internally.
Examples
--------
>>> import earthkit.hydro as ekh
>>> # Compute mode of land cover categories
>>> mode_landcover = ekh.upstream.array.mode(river_network, landcover_field)
"""
return _operations.mode(
river_network=river_network,
field=field,
node_weights=node_weights,
edge_weights=edge_weights,
return_type=return_type,
)