def test_cannon(self, cannon_2015_rvs):
ref, hist, sim = cannon_2015_rvs(15000)
DQM = DetrendedQuantileMapping(kind="*", group="time")
DQM.train(ref, hist)
p = DQM.adjust(sim)
np.testing.assert_almost_equal(p.mean(), 41.6, 0)
np.testing.assert_almost_equal(p.std(), 15.0, 0)
def test_mon_U(self, mon_series, series, mon_triangular, kind, name,
spatial_dims):
"""
Train on
hist: U
ref: U + monthly cycle
Predict on hist to get ref
"""
n = 10000
u = np.random.rand(n)
# Define distributions
xd = uniform(loc=2, scale=0.1)
yd = uniform(loc=4, scale=0.1)
noise = uniform(loc=0, scale=1e-7)
# Generate random numbers
x = xd.ppf(u)
y = yd.ppf(u) + noise.ppf(u)
# Test train
hist, ref = series(x, name), mon_series(y, name)
trend = np.linspace(-0.2, 0.2, n) + int(kind == MULTIPLICATIVE)
ref_t = mon_series(apply_correction(y, trend, kind), name)
sim = series(apply_correction(x, trend, kind), name)
if spatial_dims:
hist = hist.expand_dims(**spatial_dims)
ref = ref.expand_dims(**spatial_dims)
sim = sim.expand_dims(**spatial_dims)
ref_t = ref_t.expand_dims(**spatial_dims)
DQM = DetrendedQuantileMapping(kind=kind,
group="time.month",
nquantiles=5)
DQM.train(ref, hist)
mqm = DQM.ds.af.mean(dim="quantiles")
p = DQM.adjust(sim)
if spatial_dims:
mqm = mqm.isel({crd: 0 for crd in spatial_dims.keys()})
np.testing.assert_array_almost_equal(mqm, int(kind == MULTIPLICATIVE),
1)
np.testing.assert_array_almost_equal(p, ref_t, 1)
def test_quantiles(self, series, kind, name):
"""Train on
hist: U
ref: Normal
Predict on hist to get ref
"""
ns = 10000
u = np.random.rand(ns)
# Define distributions
xd = uniform(loc=10, scale=1)
yd = norm(loc=12, scale=1)
# Generate random numbers with u so we get exact results for comparison
x = xd.ppf(u)
y = yd.ppf(u)
# Test train
hist = sim = series(x, name)
ref = series(y, name)
DQM = DetrendedQuantileMapping(kind=kind,
group="time",
nquantiles=50,
interp="linear")
DQM.train(ref, hist)
p = DQM.adjust(sim)
q = DQM.ds.quantiles
ex = apply_correction(xd.ppf(q), invert(xd.mean(), kind), kind)
ey = apply_correction(yd.ppf(q), invert(yd.mean(), kind), kind)
expected = get_correction(ex, ey, kind)
# Results are not so good at the endpoints
np.testing.assert_array_almost_equal(DQM.ds.af[2:-2], expected[2:-2],
1)
# Test predict
# Accept discrepancies near extremes
middle = (x > 1e-2) * (x < 0.99)
np.testing.assert_array_almost_equal(p[middle], ref[middle], 1)
# Test with simure not equal to hist
ff = series(np.ones(ns) * 1.1, name)
sim2 = apply_correction(sim, ff, kind)
ref2 = apply_correction(ref, ff, kind)
p2 = DQM.adjust(sim2)
np.testing.assert_array_almost_equal(p2[middle], ref2[middle], 1)
# Test with actual trend in sim
trend = series(
np.linspace(-0.2, 0.2, ns) + (1 if kind == MULTIPLICATIVE else 0),
name)
sim3 = apply_correction(sim, trend, kind)
ref3 = apply_correction(ref, trend, kind)
p3 = DQM.adjust(sim3)
np.testing.assert_array_almost_equal(p3[middle], ref3[middle], 1)
def test_cannon_and_from_ds(self, cannon_2015_rvs, tmp_path):
ref, hist, sim = cannon_2015_rvs(15000)
DQM = DetrendedQuantileMapping.train(ref, hist, kind="*", group="time")
p = DQM.adjust(sim)
np.testing.assert_almost_equal(p.mean(), 41.6, 0)
np.testing.assert_almost_equal(p.std(), 15.0, 0)
file = tmp_path / "test_dqm.nc"
DQM.ds.to_netcdf(file)
ds = xr.open_dataset(file)
DQM2 = DetrendedQuantileMapping.from_dataset(ds)
xr.testing.assert_equal(DQM.ds, DQM2.ds)
p2 = DQM2.adjust(sim)
np.testing.assert_array_equal(p, p2)
def test_mon_U(self, mon_series, series, kind, name, add_dims):
"""
Train on
hist: U
ref: U + monthly cycle
Predict on hist to get ref
"""
n = 5000
u = np.random.rand(n)
# Define distributions
xd = uniform(loc=2, scale=0.1)
yd = uniform(loc=4, scale=0.1)
noise = uniform(loc=0, scale=1e-7)
# Generate random numbers
x = xd.ppf(u)
y = yd.ppf(u) + noise.ppf(u)
# Test train
hist, ref = series(x, name), mon_series(y, name)
trend = np.linspace(-0.2, 0.2, n) + int(kind == MULTIPLICATIVE)
ref_t = mon_series(apply_correction(y, trend, kind), name)
sim = series(apply_correction(x, trend, kind), name)
if add_dims:
ref = ref.expand_dims(lat=[0, 1, 2]).chunk({"lat": 1})
hist = hist.expand_dims(lat=[0, 1, 2]).chunk({"lat": 1})
sim = sim.expand_dims(lat=[0, 1, 2]).chunk({"lat": 1})
ref_t = ref_t.expand_dims(lat=[0, 1, 2])
DQM = DetrendedQuantileMapping.train(ref,
hist,
kind=kind,
group="time.month",
nquantiles=5)
mqm = DQM.ds.af.mean(dim="quantiles")
p = DQM.adjust(sim)
if add_dims:
mqm = mqm.isel(lat=0)
np.testing.assert_array_almost_equal(mqm, int(kind == MULTIPLICATIVE),
1)
np.testing.assert_allclose(p.transpose(..., "time"),
ref_t,
rtol=0.1,
atol=0.5)
def cannon_2015_figure_2():
n = 10000
ref, hist, sim = tu.cannon_2015_rvs(n, random=False)
QM = EmpiricalQuantileMapping(kind="*", group="time", interp="linear")
QM.train(ref, hist)
sim_eqm = QM.predict(sim)
DQM = DetrendedQuantileMapping(kind="*", group="time", interp="linear")
DQM.train(ref, hist)
sim_dqm = DQM.predict(sim, degree=0)
QDM = QuantileDeltaMapping(kind="*", group="time", interp="linear")
QDM.train(ref, hist)
sim_qdm = QDM.predict(sim)
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(11, 4))
x = np.linspace(0, 105, 50)
ax1.plot(x, gaussian_kde(ref)(x), color="r", label="Obs hist")
ax1.plot(x, gaussian_kde(hist)(x), color="k", label="GCM hist")
ax1.plot(x, gaussian_kde(sim)(x), color="blue", label="GCM simure")
ax1.plot(x, gaussian_kde(sim_qdm)(x), color="lime", label="QDM future")
ax1.plot(x,
gaussian_kde(sim_eqm)(x),
color="darkgreen",
ls="--",
label="QM future")
ax1.plot(x,
gaussian_kde(sim_dqm)(x),
color="lime",
ls=":",
label="DQM future")
ax1.legend(frameon=False)
ax1.set_xlabel("Value")
ax1.set_ylabel("Density")
tau = np.array([0.25, 0.5, 0.75, 0.95, 0.99]) * 100
bc_gcm = (scoreatpercentile(sim, tau) -
scoreatpercentile(hist, tau)) / scoreatpercentile(hist, tau)
bc_qdm = (scoreatpercentile(sim_qdm, tau) -
scoreatpercentile(ref, tau)) / scoreatpercentile(ref, tau)
bc_eqm = (scoreatpercentile(sim_eqm, tau) -
scoreatpercentile(ref, tau)) / scoreatpercentile(ref, tau)
bc_dqm = (scoreatpercentile(sim_dqm, tau) -
scoreatpercentile(ref, tau)) / scoreatpercentile(ref, tau)
ax2.plot([0, 1], [0, 1], ls=":", color="blue")
ax2.plot(bc_gcm, bc_gcm, "-", color="blue", label="GCM")
ax2.plot(bc_gcm, bc_qdm, marker="o", mfc="lime", label="QDM")
ax2.plot(
bc_gcm,
bc_eqm,
marker="o",
mfc="darkgreen",
ls=":",
color="darkgreen",
label="QM",
)
ax2.plot(
bc_gcm,
bc_dqm,
marker="s",
mec="lime",
mfc="w",
ls="--",
color="lime",
label="DQM",
)
for i, s in enumerate(tau / 100):
ax2.text(bc_gcm[i],
bc_eqm[i],
f"{s} ",
ha="right",
va="center",
fontsize=9)
ax2.set_xlabel("GCM relative change")
ax2.set_ylabel("Bias adjusted relative change")
ax2.legend(loc="upper left", frameon=False)
ax2.set_aspect("equal")
plt.tight_layout()
return fig