def _adjust(
self,
sim: xr.DataArray,
scen: xr.DataArray,
*,
frac: float = 0.25,
power: float = 1.0,
interp: str = "linear",
extrapolation: str = "constant",
):
# Quantiles coord : cheat and assign 0 - 1 so we can use `extrapolate_qm`.
ds = self.ds.assign(
quantiles=(np.arange(self.ds.quantiles.size) + 1)
/ (self.ds.quantiles.size + 1)
)
scen = extremes_adjust(
ds.assign(sim=sim, scen=scen),
cluster_thresh=self.cluster_thresh,
dist=stats.get_dist("genpareto"),
frac=frac,
power=power,
interp=interp,
extrapolation=extrapolation,
group="time",
)
return scen
def ts_fit_graph(ts, params):
"""Create graphic showing an histogram of the data and the distribution fitted to it.
Parameters
----------
ts : str
Path to netCDF file storing the time series.
params : str
Path to netCDF file storing the distribution parameters.
Returns
-------
fig
"""
from xclim.indices.stats import get_dist
n = ts.nbasins.size
dist = params.attrs["scipy_dist"]
fig, axes = plt.subplots(n, figsize=(10, 6), squeeze=False)
for i in range(n):
ax = axes.flat[i]
ax2 = plt.twinx(ax)
p = params.isel(nbasins=i)
# Plot histogram of time series as density then as a normal count.
density, bins, patches = ax.hist(
ts.isel(nbasins=i).dropna(dim="time"),
alpha=0.5,
density=True,
bins="auto",
label="__nolabel__",
)
ax2.hist(
ts.isel(nbasins=i).dropna(dim="time"),
bins=bins,
facecolor=(1, 1, 1, 0.01),
edgecolor="gray",
linewidth=1,
)
# Plot pdf of distribution
dc = get_dist(dist)(*params.isel(nbasins=i))
mn = dc.ppf(0.01)
mx = dc.ppf(0.99)
q = np.linspace(mn, mx, 200)
pdf = dc.pdf(q)
ps = ", ".join(["{:.1f}".format(x) for x in p.values])
ax.plot(q, pdf, "-", label="{}({})".format(params.attrs["scipy_dist"], ps))
# Labels
ax.set_xlabel("{} (${:~P}$)".format(ts.long_name, units2pint(ts.units)))
ax.set_ylabel("Probability density")
ax2.set_ylabel("Histogram count")
ax.legend(frameon=False)
plt.tight_layout()
return fig
def test_get_lm3_dist(self, dist):
"""Check that parameterization for lmoments3 and scipy is identical."""
pytest.importorskip("lmoments3")
dc = stats.get_dist(dist)
lm3dc = stats.get_lm3_dist(dist)
par = self.params[dist]
expected = dc(**par).pdf(self.inputs_pdf)
values = lm3dc(**par).pdf(self.inputs_pdf)
np.testing.assert_array_almost_equal(values, expected)
def robust_data(request):
norm = get_dist("norm")
ref = np.tile(
np.array([
norm.rvs(loc=274, scale=0.8, size=(40, ), random_state=r)
for r in [101083, 19377, 473820, 483625]
]),
(4, 1, 1),
)
fut = np.array([
[
norm.rvs(loc=loc, scale=sc, size=(40, ), random_state=r)
for loc, sc, r in shps
] for shps in (
[
(274.0, 0.7, 176378),
(274.0, 0.6, 839789),
(274.0, 0.7, 393239),
(275.6, 1.1, 747390),
], # 3 no change, 1 positive change
[
(272.5, 1.2, 743920),
(272.4, 0.8, 138489),
(275.5, 0.8, 673683),
(275.6, 1.1, 969383),
], # 2 neg change
[
(275.6, 0.8, 696857),
(275.8, 1.2, 379949),
(276.5, 0.8, 268395),
(277.6, 1.1, 456544),
], # All pos change
[
(np.nan, 0.3, 746323),
(np.nan, 1.2, 5643723),
(275.5, 0.8, 118294),
(275.6, 1.1, 574732),
], # Some NaN
)
])
ref = xr.DataArray(ref, dims=("lon", "realization", "time"), name="tas")
ref["time"] = xr.cftime_range("2000-01-01", periods=40, freq="YS")
fut = xr.DataArray(fut, dims=("lon", "realization", "time"), name="tas")
fut["time"] = xr.cftime_range("2040-01-01", periods=40, freq="YS")
if request.param:
ref = ref.chunk({"lon": 1}).to_dataset()
fut = fut.chunk({"lon": 1}).to_dataset()
return ref, fut
def _train(
cls,
ref: xr.DataArray,
hist: xr.DataArray,
*,
cluster_thresh: str,
ref_params: xr.Dataset = None,
q_thresh: float = 0.95,
):
cluster_thresh = convert_units_to(cluster_thresh, ref)
# Approximation of how many "quantiles" values we will get:
N = (1 - q_thresh) * ref.time.size
# ref_params: cast nan to f32 not to interfere with map_blocks dtype parsing
# ref and hist are f32, we want to have f32 in the output.
ds = extremes_train(
xr.Dataset(
{
"ref": ref,
"hist": hist,
"ref_params": ref_params or np.float32(np.NaN),
}
),
q_thresh=q_thresh,
cluster_thresh=cluster_thresh,
dist=stats.get_dist("genpareto"),
quantiles=np.arange(int(N)),
group="time",
)
ds.px_hist.attrs.update(
long_name="Probability of extremes in hist",
description="Parametric probabilities of extremes in the common domain of hist and ref.",
)
ds.af.attrs.update(
long_name="Extremes adjustment factor",
description="Multiplicative adjustment factor of extremes from hist to ref.",
)
ds.thresh.attrs.update(
long_name=f"{q_thresh * 100}th percentile extreme value threshold",
description=f"Mean of the {q_thresh * 100}th percentile of large values (x > {cluster_thresh}) of ref and hist.",
)
return ds.drop_vars(["quantiles"]), {"cluster_thresh": cluster_thresh}
def test_pwm_fit(self, dist):
"""Test that the fitted parameters match parameters used to generate a random sample."""
pytest.importorskip("lmoments3")
n = 500
dc = stats.get_dist(dist)
par = self.params[dist]
da = xr.DataArray(
dc(**par).rvs(size=n),
dims=("time", ),
coords={"time": xr.cftime_range("1980-01-01", periods=n)},
)
out = stats.fit(da, dist=dist, method="PWM").compute()
# Check that values are identical to lmoments3's output dict
l3dc = stats.get_lm3_dist(dist)
expected = l3dc.lmom_fit(da.values)
for key, val in expected.items():
np.testing.assert_array_equal(out.sel(dparams=key), val, 1)
def adjust(
self,
scen: xr.DataArray,
sim: xr.DataArray,
frac: float = 0.25,
power: float = 1.0,
):
"""Return second order bias-adjusted data. Refer to the class documentation for the algorithm details.
Parameters
----------
scen: DataArray
Bias-adjusted time series.
sim : DataArray
Time series to be bias-adjusted, source of scen.
kwargs :
Algorithm-specific keyword arguments, see class doc.
"""
if not self._trained:
raise ValueError("train() must be called before adjusting.")
def _adjust_extremes_1d(scen, sim, ref_params, thresh, *, dist,
cluster_thresh):
# Clusters of large values of sim
_, _, sim_posmax, sim_maxs = get_clusters_1d(
sim, thresh, cluster_thresh)
new_scen = scen.copy()
if sim_posmax.size == 0:
# Happens if everything is under `cluster_thresh`
return new_scen
# Fit the dist, force location at thresh
sim_fit = stats._fitfunc_1d(sim_maxs,
dist=dist,
nparams=len(ref_params),
method="ML",
floc=thresh)
# Cumulative density function for extreme values in sim's distribution
sim_cdf = dist.cdf(sim_maxs, *sim_fit)
# Equivalent value of sim's CDF's but in ref's distribution.
new_sim = dist.ppf(sim_cdf, *ref_params) + thresh
# Get the transition weights based on frac and power values
transition = (((sim_maxs - sim_maxs.min()) /
((sim_maxs.max()) - sim_maxs.min())) / frac)**power
np.clip(transition, None, 1, out=transition)
# Apply smooth linear transition between scen and corrected scen
new_scen_trans = (new_sim * transition) + (scen[sim_posmax] *
(1.0 - transition))
# We change new_scen to the new data
new_scen[sim_posmax] = new_scen_trans
return new_scen
new_scen = xr.apply_ufunc(
_adjust_extremes_1d,
scen,
sim,
self.ds.fit_params,
self.ds.thresh,
input_core_dims=[["time"], ["time"], ["dparams"], []],
output_core_dims=[["time"]],
vectorize=True,
kwargs={
"dist": stats.get_dist("genpareto"),
"cluster_thresh": convert_units_to(self.cluster_thresh, sim),
},
dask="parallelized",
output_dtypes=[scen.dtype],
)
params = f"frac={frac}, power={power}"
new_scen.attrs["xclim_history"] = update_history(
f"Second order bias-adjustment with {str(self)}.adjust(sim, {params})",
sim)
return new_scen
def ts_fit_graph(ts, params):
"""Create graphic showing an histogram of the data and the distribution fitted to it.
The graphic contains one panel per watershed.
Parameters
----------
ts : xr.DataArray
Stream flow time series with dimensions (time, nbasins).
params : xr.DataArray
Fitted distribution parameters returned by `xclim.land.fit` indicator.
Returns
-------
fig
Figure showing a histogram and the parameterized pdf.
"""
# Note: The hover tool could be customized to show the histogram count in addition to the frequency.
from xclim.indices.stats import get_dist
n = ts.nbasins.size
if n > 1:
raise NotImplementedError
ts = ts.isel(nbasins=0)
params = params.isel(nbasins=0)
# Using matplotlib's default binning strategy
hist, bins, mh = plt.hist(ts, bins="auto", density=True)
# Histogram graphic object
h = hv.Histogram((hist, bins), kdims=ts.name, label="Histogram")
# PDF domain
mn = np.min(bins)
mx = np.max(bins)
q = np.linspace(mn, mx, 200)
# Compute PDF
dist = params.attrs["scipy_dist"]
dc = get_dist(dist)(*params) # Works because dparams is the first dimension.
pdf = xr.DataArray(
data=dc.pdf(q),
dims=(ts.name,) + params.dims[1:],
coords={ts.name: q},
name="pdf",
)
# PDF line label
ps = ", ".join(
[
f"{key}={x:.1f}".format(x)
for (key, x) in zip(params.dparams.data, params.values)
]
)
label = f"{dist}({ps})"
# PDF graphic object
p = pdf.hvplot.line(label=label, xlabel=ts.attrs["long_name"], color="orange")
# Layout
return (h * p).opts(hv.opts.Histogram(tools=["hover"]))
def ts_fit_graph(ts, params):
"""Create graphic showing an histogram of the data and the distribution fitted to it.
The graphic contains one panel per watershed.
Parameters
----------
ts : xr.DataArray
Stream flow time series with dimensions (time, nbasins).
params : xr.DataArray
Fitted distribution parameters returned by `xclim.land.fit` indicator.
Returns
-------
fig
Figure showing a histogram and the parameterized pdf.
"""
from xclim.indices.stats import get_dist
n = ts.nbasins.size
dist = params.attrs["scipy_dist"]
fig, axes = plt.subplots(n, figsize=(10, 6), squeeze=False)
for i in range(n):
ax = axes.flat[i]
ax2 = plt.twinx(ax)
p = params.isel(nbasins=i)
t = ts.isel(nbasins=i).dropna(dim="time")
# Plot histogram of time series as density then as a normal count.
density, bins, patches = ax.hist(
t,
alpha=0.5,
density=True,
bins="auto",
label="__nolabel__",
)
ax2.hist(
t,
bins=bins,
facecolor=(1, 1, 1, 0.01),
edgecolor="gray",
linewidth=1,
)
# Plot pdf of distribution
dc = get_dist(dist)(*params.isel(nbasins=i))
mn = dc.ppf(0.01)
mx = dc.ppf(0.99)
q = np.linspace(mn, mx, 200)
pdf = dc.pdf(q)
ps = ", ".join([f"{x:.1f}" for x in p.values])
ax.plot(q,
pdf,
"-",
label="{}({})".format(params.attrs["scipy_dist"], ps))
# Labels
ax.set_xlabel(f"{ts.long_name} (${units2pint(ts.units):~P}$)")
ax.set_ylabel("Probability density")
ax2.set_ylabel("Histogram count")
ax.legend(frameon=False)
plt.tight_layout()
return fig
