def forecast(
R,
V,
timesteps,
n_cascade_levels=6,
R_thr=None,
extrap_method="semilagrangian",
decomp_method="fft",
bandpass_filter_method="gaussian",
ar_order=2,
conditional=False,
probmatching_method="cdf",
num_workers=1,
fft_method="numpy",
domain="spatial",
extrap_kwargs=None,
filter_kwargs=None,
measure_time=False,
):
"""Generate a nowcast by using the Spectral Prognosis (S-PROG) method.
Parameters
----------
R: array-like
Array of shape (ar_order+1,m,n) containing the input precipitation fields
ordered by timestamp from oldest to newest. The time steps between
the inputs are assumed to be regular.
V: array-like
Array of shape (2,m,n) containing the x- and y-components of the
advection field.
The velocities are assumed to represent one time step between the
inputs. All values are required to be finite.
timesteps: int or list of floats
Number of time steps to forecast or a list of time steps for which the
forecasts are computed (relative to the input time step). The elements of
the list are required to be in ascending order.
n_cascade_levels: int, optional
The number of cascade levels to use.
R_thr: float
The threshold value for minimum observable precipitation intensity.
extrap_method: str, optional
Name of the extrapolation method to use. See the documentation of
pysteps.extrapolation.interface.
decomp_method: {'fft'}, optional
Name of the cascade decomposition method to use. See the documentation
of pysteps.cascade.interface.
bandpass_filter_method: {'gaussian', 'uniform'}, optional
Name of the bandpass filter method to use with the cascade decomposition.
See the documentation of pysteps.cascade.interface.
ar_order: int, optional
The order of the autoregressive model to use. Must be >= 1.
conditional: bool, optional
If set to True, compute the statistics of the precipitation field
conditionally by excluding pixels where the values are
below the threshold R_thr.
probmatching_method: {'cdf','mean',None}, optional
Method for matching the conditional statistics of the forecast field
(areas with precipitation intensity above the threshold R_thr) with those
of the most recently observed one. 'cdf'=map the forecast CDF to the
observed one, 'mean'=adjust only the mean value,
None=no matching applied.
num_workers: int, optional
The number of workers to use for parallel computation. Applicable if dask
is enabled or pyFFTW is used for computing the FFT.
When num_workers>1, it is advisable to disable OpenMP by setting
the environment variable OMP_NUM_THREADS to 1.
This avoids slowdown caused by too many simultaneous threads.
fft_method: str, optional
A string defining the FFT method to use (see utils.fft.get_method).
Defaults to 'numpy' for compatibility reasons. If pyFFTW is installed,
the recommended method is 'pyfftw'.
domain: {"spatial", "spectral"}
If "spatial", all computations are done in the spatial domain (the
classical S-PROG model). If "spectral", the AR(2) models are applied
directly in the spectral domain to reduce memory footprint and improve
performance :cite:`PCH2019a`.
extrap_kwargs: dict, optional
Optional dictionary containing keyword arguments for the extrapolation
method. See the documentation of pysteps.extrapolation.
filter_kwargs: dict, optional
Optional dictionary containing keyword arguments for the filter method.
See the documentation of pysteps.cascade.bandpass_filters.py.
measure_time: bool
If set to True, measure, print and return the computation time.
Returns
-------
out: ndarray
A three-dimensional array of shape (num_timesteps,m,n) containing a time
series of forecast precipitation fields. The time series starts from
t0+timestep, where timestep is taken from the input precipitation fields
R. If measure_time is True, the return value is a three-element tuple
containing the nowcast array, the initialization time of the nowcast
generator and the time used in the main loop (seconds).
See also
--------
pysteps.extrapolation.interface, pysteps.cascade.interface
References
----------
:cite:`Seed2003`, :cite:`PCH2019a`
"""
_check_inputs(R, V, timesteps, ar_order)
if extrap_kwargs is None:
extrap_kwargs = dict()
if filter_kwargs is None:
filter_kwargs = dict()
if np.any(~np.isfinite(V)):
raise ValueError("V contains non-finite values")
print("Computing S-PROG nowcast:")
print("-------------------------")
print("")
print("Inputs:")
print("-------")
print("input dimensions: %dx%d" % (R.shape[1], R.shape[2]))
print("")
print("Methods:")
print("--------")
print("extrapolation: %s" % extrap_method)
print("bandpass filter: %s" % bandpass_filter_method)
print("decomposition: %s" % decomp_method)
print("conditional statistics: %s" % ("yes" if conditional else "no"))
print("probability matching: %s" % probmatching_method)
print("FFT method: %s" % fft_method)
print("domain: %s" % domain)
print("")
print("Parameters:")
print("-----------")
if isinstance(timesteps, int):
print("number of time steps: %d" % timesteps)
else:
print("time steps: %s" % timesteps)
print("parallel threads: %d" % num_workers)
print("number of cascade levels: %d" % n_cascade_levels)
print("order of the AR(p) model: %d" % ar_order)
print("precip. intensity threshold: %g" % R_thr)
if measure_time:
starttime_init = time.time()
fft = utils.get_method(fft_method, shape=R.shape[1:], n_threads=num_workers)
M, N = R.shape[1:]
# initialize the band-pass filter
filter_method = cascade.get_method(bandpass_filter_method)
filter = filter_method((M, N), n_cascade_levels, **filter_kwargs)
decomp_method, recomp_method = cascade.get_method(decomp_method)
extrapolator_method = extrapolation.get_method(extrap_method)
R = R[-(ar_order + 1) :, :, :].copy()
R_min = np.nanmin(R)
# determine the domain mask from non-finite values
domain_mask = np.logical_or.reduce(
[~np.isfinite(R[i, :]) for i in range(R.shape[0])]
)
# determine the precipitation threshold mask
if conditional:
MASK_thr = np.logical_and.reduce(
[R[i, :, :] >= R_thr for i in range(R.shape[0])]
)
else:
MASK_thr = None
# initialize the extrapolator
x_values, y_values = np.meshgrid(np.arange(R.shape[2]), np.arange(R.shape[1]))
xy_coords = np.stack([x_values, y_values])
extrap_kwargs = extrap_kwargs.copy()
extrap_kwargs["xy_coords"] = xy_coords
extrap_kwargs["allow_nonfinite_values"] = True
# advect the previous precipitation fields to the same position with the
# most recent one (i.e. transform them into the Lagrangian coordinates)
res = list()
def f(R, i):
return extrapolator_method(R[i, :], V, ar_order - i, "min", **extrap_kwargs)[-1]
for i in range(ar_order):
if not DASK_IMPORTED:
R[i, :, :] = f(R, i)
else:
res.append(dask.delayed(f)(R, i))
if DASK_IMPORTED:
num_workers_ = len(res) if num_workers > len(res) else num_workers
R = np.stack(list(dask.compute(*res, num_workers=num_workers_)) + [R[-1, :, :]])
# replace non-finite values with the minimum value
R = R.copy()
for i in range(R.shape[0]):
R[i, ~np.isfinite(R[i, :])] = np.nanmin(R[i, :])
# compute the cascade decompositions of the input precipitation fields
R_d = []
for i in range(ar_order + 1):
R_ = decomp_method(
R[i, :, :],
filter,
mask=MASK_thr,
fft_method=fft,
output_domain=domain,
normalize=True,
compute_stats=True,
compact_output=True,
)
R_d.append(R_)
# rearrange the cascade levels into a four-dimensional array of shape
# (n_cascade_levels,ar_order+1,m,n) for the autoregressive model
R_c = nowcast_utils.stack_cascades(
R_d, n_cascade_levels, convert_to_full_arrays=True
)
# compute lag-l temporal autocorrelation coefficients for each cascade level
GAMMA = np.empty((n_cascade_levels, ar_order))
for i in range(n_cascade_levels):
if domain == "spatial":
GAMMA[i, :] = correlation.temporal_autocorrelation(R_c[i], mask=MASK_thr)
else:
GAMMA[i, :] = correlation.temporal_autocorrelation(
R_c[i], domain="spectral", x_shape=R.shape[1:]
)
R_c = nowcast_utils.stack_cascades(
R_d, n_cascade_levels, convert_to_full_arrays=False
)
R_d = R_d[-1]
nowcast_utils.print_corrcoefs(GAMMA)
if ar_order == 2:
# adjust the lag-2 correlation coefficient to ensure that the AR(p)
# process is stationary
for i in range(n_cascade_levels):
GAMMA[i, 1] = autoregression.adjust_lag2_corrcoef2(GAMMA[i, 0], GAMMA[i, 1])
# estimate the parameters of the AR(p) model from the autocorrelation
# coefficients
PHI = np.empty((n_cascade_levels, ar_order + 1))
for i in range(n_cascade_levels):
PHI[i, :] = autoregression.estimate_ar_params_yw(GAMMA[i, :])
nowcast_utils.print_ar_params(PHI)
# discard all except the p-1 last cascades because they are not needed for
# the AR(p) model
R_c = [R_c[i][-ar_order:] for i in range(n_cascade_levels)]
if probmatching_method == "mean":
mu_0 = np.mean(R[-1, :, :][R[-1, :, :] >= R_thr])
# compute precipitation mask and wet area ratio
MASK_p = R[-1, :, :] >= R_thr
war = 1.0 * np.sum(MASK_p) / (R.shape[1] * R.shape[2])
if measure_time:
init_time = time.time() - starttime_init
R = R[-1, :, :]
print("Starting nowcast computation.")
if measure_time:
starttime_mainloop = time.time()
R_f = []
if isinstance(timesteps, int):
timesteps = range(timesteps + 1)
timestep_type = "int"
else:
original_timesteps = [0] + list(timesteps)
timesteps = nowcast_utils.binned_timesteps(original_timesteps)
timestep_type = "list"
R_f_prev = R
extrap_kwargs["return_displacement"] = True
D = None
t_prev = 0.0
# iterate each time step
for t, subtimestep_idx in enumerate(timesteps):
if timestep_type == "list":
subtimesteps = [original_timesteps[t_] for t_ in subtimestep_idx]
else:
subtimesteps = [t]
if (timestep_type == "list" and subtimesteps) or (
timestep_type == "int" and t > 0
):
is_nowcast_time_step = True
else:
is_nowcast_time_step = False
if is_nowcast_time_step:
print(
"Computing nowcast for time step %d... " % t,
end="",
flush=True,
)
if measure_time:
starttime = time.time()
for i in range(n_cascade_levels):
R_c[i] = autoregression.iterate_ar_model(R_c[i], PHI[i, :])
R_d["cascade_levels"] = [R_c[i][-1, :] for i in range(n_cascade_levels)]
if domain == "spatial":
R_d["cascade_levels"] = np.stack(R_d["cascade_levels"])
R_f_new = recomp_method(R_d)
if domain == "spectral":
R_f_new = fft.irfft2(R_f_new)
MASK = _compute_sprog_mask(R_f_new, war)
R_f_new[~MASK] = R_min
if probmatching_method == "cdf":
# adjust the CDF of the forecast to match the most recently
# observed precipitation field
R_f_new = probmatching.nonparam_match_empirical_cdf(R_f_new, R)
elif probmatching_method == "mean":
mu_fct = np.mean(R_f_new[MASK])
R_f_new[MASK] = R_f_new[MASK] - mu_fct + mu_0
R_f_new[domain_mask] = np.nan
# advect the recomposed precipitation field to obtain the forecast for
# the current time step (or subtimesteps if non-integer time steps are
# given)
for t_sub in subtimesteps:
if t_sub > 0:
t_diff_prev_int = t_sub - int(t_sub)
if t_diff_prev_int > 0.0:
R_f_ip = (
1.0 - t_diff_prev_int
) * R_f_prev + t_diff_prev_int * R_f_new
else:
R_f_ip = R_f_prev
t_diff_prev = t_sub - t_prev
extrap_kwargs["displacement_prev"] = D
R_f_ep, D = extrapolator_method(
R_f_ip,
V,
[t_diff_prev],
**extrap_kwargs,
)
R_f.append(R_f_ep[0])
t_prev = t_sub
# advect the forecast field by one time step if no subtimesteps in the
# current interval were found
if not subtimesteps:
t_diff_prev = t + 1 - t_prev
extrap_kwargs["displacement_prev"] = D
_, D = extrapolator_method(
None,
V,
[t_diff_prev],
**extrap_kwargs,
)
t_prev = t + 1
R_f_prev = R_f_new
if is_nowcast_time_step:
if measure_time:
print("%.2f seconds." % (time.time() - starttime))
else:
print("done.")
if measure_time:
mainloop_time = time.time() - starttime_mainloop
R_f = np.stack(R_f)
if measure_time:
return R_f, init_time, mainloop_time
else:
return R_f
def forecast(
R,
V,
timesteps,
n_ens_members=24,
n_cascade_levels=6,
R_thr=None,
kmperpixel=None,
timestep=None,
extrap_method="semilagrangian",
decomp_method="fft",
bandpass_filter_method="gaussian",
noise_method="nonparametric",
noise_stddev_adj=None,
ar_order=2,
vel_pert_method="bps",
conditional=False,
probmatching_method="cdf",
mask_method="incremental",
callback=None,
return_output=True,
seed=None,
num_workers=1,
fft_method="numpy",
domain="spatial",
extrap_kwargs=None,
filter_kwargs=None,
noise_kwargs=None,
vel_pert_kwargs=None,
mask_kwargs=None,
measure_time=False,
):
"""Generate a nowcast ensemble by using the Short-Term Ensemble Prediction
System (STEPS) method.
Parameters
----------
R: array-like
Array of shape (ar_order+1,m,n) containing the input precipitation fields
ordered by timestamp from oldest to newest. The time steps between the
inputs are assumed to be regular.
V: array-like
Array of shape (2,m,n) containing the x- and y-components of the advection
field. The velocities are assumed to represent one time step between the
inputs. All values are required to be finite.
timesteps: int or list of floats
Number of time steps to forecast or a list of time steps for which the
forecasts are computed (relative to the input time step). The elements of
the list are required to be in ascending order.
n_ens_members: int, optional
The number of ensemble members to generate.
n_cascade_levels: int, optional
The number of cascade levels to use.
R_thr: float, optional
Specifies the threshold value for minimum observable precipitation
intensity. Required if mask_method is not None or conditional is True.
kmperpixel: float, optional
Spatial resolution of the input data (kilometers/pixel). Required if
vel_pert_method is not None or mask_method is 'incremental'.
timestep: float, optional
Time step of the motion vectors (minutes). Required if vel_pert_method is
not None or mask_method is 'incremental'.
extrap_method: str, optional
Name of the extrapolation method to use. See the documentation of
pysteps.extrapolation.interface.
decomp_method: {'fft'}, optional
Name of the cascade decomposition method to use. See the documentation
of pysteps.cascade.interface.
bandpass_filter_method: {'gaussian', 'uniform'}, optional
Name of the bandpass filter method to use with the cascade decomposition.
See the documentation of pysteps.cascade.interface.
noise_method: {'parametric','nonparametric','ssft','nested',None}, optional
Name of the noise generator to use for perturbating the precipitation
field. See the documentation of pysteps.noise.interface. If set to None,
no noise is generated.
noise_stddev_adj: {'auto','fixed',None}, optional
Optional adjustment for the standard deviations of the noise fields added
to each cascade level. This is done to compensate incorrect std. dev.
estimates of casace levels due to presence of no-rain areas. 'auto'=use
the method implemented in pysteps.noise.utils.compute_noise_stddev_adjs.
'fixed'= use the formula given in :cite:`BPS2006` (eq. 6), None=disable
noise std. dev adjustment.
ar_order: int, optional
The order of the autoregressive model to use. Must be >= 1.
vel_pert_method: {'bps',None}, optional
Name of the noise generator to use for perturbing the advection field. See
the documentation of pysteps.noise.interface. If set to None, the advection
field is not perturbed.
conditional: bool, optional
If set to True, compute the statistics of the precipitation field
conditionally by excluding pixels where the values are below the threshold
R_thr.
mask_method: {'obs','sprog','incremental',None}, optional
The method to use for masking no precipitation areas in the forecast field.
The masked pixels are set to the minimum value of the observations.
'obs' = apply R_thr to the most recently observed precipitation intensity
field, 'sprog' = use the smoothed forecast field from S-PROG, where the
AR(p) model has been applied, 'incremental' = iteratively buffer the mask
with a certain rate (currently it is 1 km/min), None=no masking.
probmatching_method: {'cdf','mean',None}, optional
Method for matching the statistics of the forecast field with those of
the most recently observed one. 'cdf'=map the forecast CDF to the observed
one, 'mean'=adjust only the conditional mean value of the forecast field
in precipitation areas, None=no matching applied. Using 'mean' requires
that mask_method is not None.
callback: function, optional
Optional function that is called after computation of each time step of
the nowcast. The function takes one argument: a three-dimensional array
of shape (n_ens_members,h,w), where h and w are the height and width
of the input field R, respectively. This can be used, for instance,
writing the outputs into files.
return_output: bool, optional
Set to False to disable returning the outputs as numpy arrays. This can
save memory if the intermediate results are written to output files using
the callback function.
seed: int, optional
Optional seed number for the random generators.
num_workers: int, optional
The number of workers to use for parallel computation. Applicable if dask
is enabled or pyFFTW is used for computing the FFT. When num_workers>1, it
is advisable to disable OpenMP by setting the environment variable
OMP_NUM_THREADS to 1. This avoids slowdown caused by too many simultaneous
threads.
fft_method: str, optional
A string defining the FFT method to use (see utils.fft.get_method).
Defaults to 'numpy' for compatibility reasons. If pyFFTW is installed,
the recommended method is 'pyfftw'.
domain: {"spatial", "spectral"}
If "spatial", all computations are done in the spatial domain (the
classical STEPS model). If "spectral", the AR(2) models and stochastic
perturbations are applied directly in the spectral domain to reduce
memory footprint and improve performance :cite:`PCH2019b`.
extrap_kwargs: dict, optional
Optional dictionary containing keyword arguments for the extrapolation
method. See the documentation of pysteps.extrapolation.
filter_kwargs: dict, optional
Optional dictionary containing keyword arguments for the filter method.
See the documentation of pysteps.cascade.bandpass_filters.py.
noise_kwargs: dict, optional
Optional dictionary containing keyword arguments for the initializer of
the noise generator. See the documentation of pysteps.noise.fftgenerators.
vel_pert_kwargs: dict, optional
Optional dictionary containing keyword arguments 'p_par' and 'p_perp' for
the initializer of the velocity perturbator. The choice of the optimal
parameters depends on the domain and the used optical flow method.
Default parameters from :cite:`BPS2006`:
p_par = [10.88, 0.23, -7.68]
p_perp = [5.76, 0.31, -2.72]
Parameters fitted to the data (optical flow/domain):
darts/fmi:
p_par = [13.71259667, 0.15658963, -16.24368207]
p_perp = [8.26550355, 0.17820458, -9.54107834]
darts/mch:
p_par = [24.27562298, 0.11297186, -27.30087471]
p_perp = [-7.80797846e+01, -3.38641048e-02, 7.56715304e+01]
darts/fmi+mch:
p_par = [16.55447057, 0.14160448, -19.24613059]
p_perp = [14.75343395, 0.11785398, -16.26151612]
lucaskanade/fmi:
p_par = [2.20837526, 0.33887032, -2.48995355]
p_perp = [2.21722634, 0.32359621, -2.57402761]
lucaskanade/mch:
p_par = [2.56338484, 0.3330941, -2.99714349]
p_perp = [1.31204508, 0.3578426, -1.02499891]
lucaskanade/fmi+mch:
p_par = [2.31970635, 0.33734287, -2.64972861]
p_perp = [1.90769947, 0.33446594, -2.06603662]
vet/fmi:
p_par = [0.25337388, 0.67542291, 11.04895538]
p_perp = [0.02432118, 0.99613295, 7.40146505]
vet/mch:
p_par = [0.5075159, 0.53895212, 7.90331791]
p_perp = [0.68025501, 0.41761289, 4.73793581]
vet/fmi+mch:
p_par = [0.29495222, 0.62429207, 8.6804131 ]
p_perp = [0.23127377, 0.59010281, 5.98180004]
fmi=Finland, mch=Switzerland, fmi+mch=both pooled into the same data set
The above parameters have been fitten by using run_vel_pert_analysis.py
and fit_vel_pert_params.py located in the scripts directory.
See pysteps.noise.motion for additional documentation.
mask_kwargs: dict
Optional dictionary containing mask keyword arguments 'mask_f' and
'mask_rim', the factor defining the the mask increment and the rim size,
respectively.
The mask increment is defined as mask_f*timestep/kmperpixel.
measure_time: bool
If set to True, measure, print and return the computation time.
Returns
-------
out: ndarray
If return_output is True, a four-dimensional array of shape
(n_ens_members,num_timesteps,m,n) containing a time series of forecast
precipitation fields for each ensemble member. Otherwise, a None value
is returned. The time series starts from t0+timestep, where timestep is
taken from the input precipitation fields R. If measure_time is True, the
return value is a three-element tuple containing the nowcast array, the
initialization time of the nowcast generator and the time used in the
main loop (seconds).
See also
--------
pysteps.extrapolation.interface, pysteps.cascade.interface,
pysteps.noise.interface, pysteps.noise.utils.compute_noise_stddev_adjs
References
----------
:cite:`Seed2003`, :cite:`BPS2006`, :cite:`SPN2013`, :cite:`PCH2019b`
"""
_check_inputs(R, V, timesteps, ar_order)
if extrap_kwargs is None:
extrap_kwargs = dict()
if filter_kwargs is None:
filter_kwargs = dict()
if noise_kwargs is None:
noise_kwargs = dict()
if vel_pert_kwargs is None:
vel_pert_kwargs = dict()
if mask_kwargs is None:
mask_kwargs = dict()
if np.any(~np.isfinite(V)):
raise ValueError("V contains non-finite values")
if mask_method not in ["obs", "sprog", "incremental", None]:
raise ValueError(
"unknown mask method %s: must be 'obs', 'sprog' or 'incremental' or None"
% mask_method
)
if conditional and R_thr is None:
raise ValueError("conditional=True but R_thr is not set")
if mask_method is not None and R_thr is None:
raise ValueError("mask_method!=None but R_thr=None")
if noise_stddev_adj not in ["auto", "fixed", None]:
raise ValueError(
"unknown noise_std_dev_adj method %s: must be 'auto', 'fixed', or None"
% noise_stddev_adj
)
if kmperpixel is None:
if vel_pert_method is not None:
raise ValueError("vel_pert_method is set but kmperpixel=None")
if mask_method == "incremental":
raise ValueError("mask_method='incremental' but kmperpixel=None")
if timestep is None:
if vel_pert_method is not None:
raise ValueError("vel_pert_method is set but timestep=None")
if mask_method == "incremental":
raise ValueError("mask_method='incremental' but timestep=None")
print("Computing STEPS nowcast:")
print("------------------------")
print("")
print("Inputs:")
print("-------")
print("input dimensions: %dx%d" % (R.shape[1], R.shape[2]))
if kmperpixel is not None:
print("km/pixel: %g" % kmperpixel)
if timestep is not None:
print("time step: %d minutes" % timestep)
print("")
print("Methods:")
print("--------")
print("extrapolation: %s" % extrap_method)
print("bandpass filter: %s" % bandpass_filter_method)
print("decomposition: %s" % decomp_method)
print("noise generator: %s" % noise_method)
print("noise adjustment: %s" % ("yes" if noise_stddev_adj else "no"))
print("velocity perturbator: %s" % vel_pert_method)
print("conditional statistics: %s" % ("yes" if conditional else "no"))
print("precip. mask method: %s" % mask_method)
print("probability matching: %s" % probmatching_method)
print("FFT method: %s" % fft_method)
print("domain: %s" % domain)
print("")
print("Parameters:")
print("-----------")
if isinstance(timesteps, int):
print("number of time steps: %d" % timesteps)
else:
print("time steps: %s" % timesteps)
print("ensemble size: %d" % n_ens_members)
print("parallel threads: %d" % num_workers)
print("number of cascade levels: %d" % n_cascade_levels)
print("order of the AR(p) model: %d" % ar_order)
if vel_pert_method == "bps":
vp_par = vel_pert_kwargs.get("p_par", noise.motion.get_default_params_bps_par())
vp_perp = vel_pert_kwargs.get(
"p_perp", noise.motion.get_default_params_bps_perp()
)
print(
"velocity perturbations, parallel: %g,%g,%g"
% (vp_par[0], vp_par[1], vp_par[2])
)
print(
"velocity perturbations, perpendicular: %g,%g,%g"
% (vp_perp[0], vp_perp[1], vp_perp[2])
)
if conditional or mask_method is not None:
print("precip. intensity threshold: %g" % R_thr)
num_ensemble_workers = n_ens_members if num_workers > n_ens_members else num_workers
if measure_time:
starttime_init = time.time()
fft = utils.get_method(fft_method, shape=R.shape[1:], n_threads=num_workers)
M, N = R.shape[1:]
# initialize the band-pass filter
filter_method = cascade.get_method(bandpass_filter_method)
filter = filter_method((M, N), n_cascade_levels, **filter_kwargs)
decomp_method, recomp_method = cascade.get_method(decomp_method)
extrapolator_method = extrapolation.get_method(extrap_method)
x_values, y_values = np.meshgrid(np.arange(R.shape[2]), np.arange(R.shape[1]))
xy_coords = np.stack([x_values, y_values])
R = R[-(ar_order + 1) :, :, :].copy()
# determine the domain mask from non-finite values
domain_mask = np.logical_or.reduce(
[~np.isfinite(R[i, :]) for i in range(R.shape[0])]
)
# determine the precipitation threshold mask
if conditional:
MASK_thr = np.logical_and.reduce(
[R[i, :, :] >= R_thr for i in range(R.shape[0])]
)
else:
MASK_thr = None
# advect the previous precipitation fields to the same position with the
# most recent one (i.e. transform them into the Lagrangian coordinates)
extrap_kwargs = extrap_kwargs.copy()
extrap_kwargs["xy_coords"] = xy_coords
extrap_kwargs["allow_nonfinite_values"] = True
res = list()
def f(R, i):
return extrapolator_method(R[i, :, :], V, ar_order - i, "min", **extrap_kwargs)[
-1
]
for i in range(ar_order):
if not DASK_IMPORTED:
R[i, :, :] = f(R, i)
else:
res.append(dask.delayed(f)(R, i))
if DASK_IMPORTED:
num_workers_ = len(res) if num_workers > len(res) else num_workers
R = np.stack(list(dask.compute(*res, num_workers=num_workers_)) + [R[-1, :, :]])
# replace non-finite values with the minimum value
R = R.copy()
for i in range(R.shape[0]):
R[i, ~np.isfinite(R[i, :])] = np.nanmin(R[i, :])
if noise_method is not None:
# get methods for perturbations
init_noise, generate_noise = noise.get_method(noise_method)
# initialize the perturbation generator for the precipitation field
pp = init_noise(R, fft_method=fft, **noise_kwargs)
if noise_stddev_adj == "auto":
print("Computing noise adjustment coefficients... ", end="", flush=True)
if measure_time:
starttime = time.time()
R_min = np.min(R)
noise_std_coeffs = noise.utils.compute_noise_stddev_adjs(
R[-1, :, :],
R_thr,
R_min,
filter,
decomp_method,
pp,
generate_noise,
20,
conditional=True,
num_workers=num_workers,
)
if measure_time:
print("%.2f seconds." % (time.time() - starttime))
else:
print("done.")
elif noise_stddev_adj == "fixed":
f = lambda k: 1.0 / (0.75 + 0.09 * k)
noise_std_coeffs = [f(k) for k in range(1, n_cascade_levels + 1)]
else:
noise_std_coeffs = np.ones(n_cascade_levels)
if noise_stddev_adj is not None:
print("noise std. dev. coeffs: %s" % str(noise_std_coeffs))
# compute the cascade decompositions of the input precipitation fields
R_d = []
for i in range(ar_order + 1):
R_ = decomp_method(
R[i, :, :],
filter,
mask=MASK_thr,
fft_method=fft,
output_domain=domain,
normalize=True,
compute_stats=True,
compact_output=True,
)
R_d.append(R_)
# normalize the cascades and rearrange them into a four-dimensional array
# of shape (n_cascade_levels,ar_order+1,m,n) for the autoregressive model
R_c = nowcast_utils.stack_cascades(R_d, n_cascade_levels)
R_d = R_d[-1]
R_d = [R_d.copy() for j in range(n_ens_members)]
# compute lag-l temporal autocorrelation coefficients for each cascade level
GAMMA = np.empty((n_cascade_levels, ar_order))
for i in range(n_cascade_levels):
GAMMA[i, :] = correlation.temporal_autocorrelation(R_c[i], mask=MASK_thr)
nowcast_utils.print_corrcoefs(GAMMA)
if ar_order == 2:
# adjust the lag-2 correlation coefficient to ensure that the AR(p)
# process is stationary
for i in range(n_cascade_levels):
GAMMA[i, 1] = autoregression.adjust_lag2_corrcoef2(GAMMA[i, 0], GAMMA[i, 1])
# estimate the parameters of the AR(p) model from the autocorrelation
# coefficients
PHI = np.empty((n_cascade_levels, ar_order + 1))
for i in range(n_cascade_levels):
PHI[i, :] = autoregression.estimate_ar_params_yw(GAMMA[i, :])
nowcast_utils.print_ar_params(PHI)
# discard all except the p-1 last cascades because they are not needed for
# the AR(p) model
R_c = [R_c[i][-ar_order:] for i in range(n_cascade_levels)]
# stack the cascades into a list containing all ensemble members
R_c = [
[R_c[j].copy() for j in range(n_cascade_levels)] for i in range(n_ens_members)
]
# initialize the random generators
if noise_method is not None:
randgen_prec = []
randgen_motion = []
np.random.seed(seed)
for j in range(n_ens_members):
rs = np.random.RandomState(seed)
randgen_prec.append(rs)
seed = rs.randint(0, high=1e9)
rs = np.random.RandomState(seed)
randgen_motion.append(rs)
seed = rs.randint(0, high=1e9)
if vel_pert_method is not None:
init_vel_noise, generate_vel_noise = noise.get_method(vel_pert_method)
# initialize the perturbation generators for the motion field
vps = []
for j in range(n_ens_members):
kwargs = {
"randstate": randgen_motion[j],
"p_par": vp_par,
"p_perp": vp_perp,
}
vp_ = init_vel_noise(V, 1.0 / kmperpixel, timestep, **kwargs)
vps.append(vp_)
D = [None for j in range(n_ens_members)]
R_f = [[] for j in range(n_ens_members)]
if probmatching_method == "mean":
mu_0 = np.mean(R[-1, :, :][R[-1, :, :] >= R_thr])
R_m = None
if mask_method is not None:
MASK_prec = R[-1, :, :] >= R_thr
if mask_method == "obs":
pass
elif mask_method == "sprog":
# compute the wet area ratio and the precipitation mask
war = 1.0 * np.sum(MASK_prec) / (R.shape[1] * R.shape[2])
R_m = [R_c[0][i].copy() for i in range(n_cascade_levels)]
R_m_d = R_d[0].copy()
elif mask_method == "incremental":
# get mask parameters
mask_rim = mask_kwargs.get("mask_rim", 10)
mask_f = mask_kwargs.get("mask_f", 1.0)
# initialize the structuring element
struct = scipy.ndimage.generate_binary_structure(2, 1)
# iterate it to expand it nxn
n = mask_f * timestep / kmperpixel
struct = scipy.ndimage.iterate_structure(struct, int((n - 1) / 2.0))
# initialize precip mask for each member
MASK_prec = _compute_incremental_mask(MASK_prec, struct, mask_rim)
MASK_prec = [MASK_prec.copy() for j in range(n_ens_members)]
if noise_method is None and R_m is None:
R_m = [R_c[0][i].copy() for i in range(n_cascade_levels)]
fft_objs = []
for i in range(n_ens_members):
fft_objs.append(utils.get_method(fft_method, shape=R.shape[1:]))
if measure_time:
init_time = time.time() - starttime_init
R = R[-1, :, :]
print("Starting nowcast computation.")
if measure_time:
starttime_mainloop = time.time()
if isinstance(timesteps, int):
timesteps = range(timesteps + 1)
timestep_type = "int"
else:
original_timesteps = [0] + list(timesteps)
timesteps = nowcast_utils.binned_timesteps(original_timesteps)
timestep_type = "list"
extrap_kwargs["return_displacement"] = True
R_f_prev = [R for i in range(n_ens_members)]
t_prev = [0.0 for j in range(n_ens_members)]
t_total = [0.0 for j in range(n_ens_members)]
# iterate each time step
for t, subtimestep_idx in enumerate(timesteps):
if timestep_type == "list":
subtimesteps = [original_timesteps[t_] for t_ in subtimestep_idx]
else:
subtimesteps = [t]
if (timestep_type == "list" and subtimesteps) or (
timestep_type == "int" and t > 0
):
is_nowcast_time_step = True
else:
is_nowcast_time_step = False
if is_nowcast_time_step:
print(
"Computing nowcast for time step %d... " % t,
end="",
flush=True,
)
if measure_time:
starttime = time.time()
if noise_method is None or mask_method == "sprog":
for i in range(n_cascade_levels):
# use a separate AR(p) model for the non-perturbed forecast,
# from which the mask is obtained
R_m[i] = autoregression.iterate_ar_model(R_m[i], PHI[i, :])
R_m_d["cascade_levels"] = [R_m[i][-1] for i in range(n_cascade_levels)]
if domain == "spatial":
R_m_d["cascade_levels"] = np.stack(R_m_d["cascade_levels"])
R_m_ = recomp_method(R_m_d)
if domain == "spectral":
R_m_ = fft.irfft2(R_m_)
if mask_method == "sprog":
MASK_prec = _compute_sprog_mask(R_m_, war)
# the nowcast iteration for each ensemble member
def worker(j):
if noise_method is not None:
# generate noise field
EPS = generate_noise(
pp, randstate=randgen_prec[j], fft_method=fft_objs[j], domain=domain
)
# decompose the noise field into a cascade
EPS = decomp_method(
EPS,
filter,
fft_method=fft_objs[j],
input_domain=domain,
output_domain=domain,
compute_stats=True,
normalize=True,
compact_output=True,
)
else:
EPS = None
# iterate the AR(p) model for each cascade level
for i in range(n_cascade_levels):
# normalize the noise cascade
if EPS is not None:
EPS_ = EPS["cascade_levels"][i]
EPS_ *= noise_std_coeffs[i]
else:
EPS_ = None
# apply AR(p) process to cascade level
if EPS is not None or vel_pert_method is not None:
R_c[j][i] = autoregression.iterate_ar_model(
R_c[j][i], PHI[i, :], eps=EPS_
)
else:
# use the deterministic AR(p) model computed above if
# perturbations are disabled
R_c[j][i] = R_m[i]
EPS = None
EPS_ = None
# compute the recomposed precipitation field(s) from the cascades
# obtained from the AR(p) model(s)
R_d[j]["cascade_levels"] = [
R_c[j][i][-1, :] for i in range(n_cascade_levels)
]
if domain == "spatial":
R_d[j]["cascade_levels"] = np.stack(R_d[j]["cascade_levels"])
R_f_new = recomp_method(R_d[j])
if domain == "spectral":
R_f_new = fft_objs[j].irfft2(R_f_new)
if mask_method is not None:
# apply the precipitation mask to prevent generation of new
# precipitation into areas where it was not originally
# observed
R_cmin = R_f_new.min()
if mask_method == "incremental":
R_f_new = R_cmin + (R_f_new - R_cmin) * MASK_prec[j]
MASK_prec_ = R_f_new > R_cmin
else:
MASK_prec_ = MASK_prec
# Set to min value outside of mask
R_f_new[~MASK_prec_] = R_cmin
if probmatching_method == "cdf":
# adjust the CDF of the forecast to match the most recently
# observed precipitation field
R_f_new = probmatching.nonparam_match_empirical_cdf(R_f_new, R)
elif probmatching_method == "mean":
MASK = R_f_new >= R_thr
mu_fct = np.mean(R_f_new[MASK])
R_f_new[MASK] = R_f_new[MASK] - mu_fct + mu_0
if mask_method == "incremental":
MASK_prec[j] = _compute_incremental_mask(
R_f_new >= R_thr, struct, mask_rim
)
R_f_new[domain_mask] = np.nan
R_f_out = []
extrap_kwargs_ = extrap_kwargs.copy()
V_pert = V
# advect the recomposed precipitation field to obtain the forecast for
# the current time step (or subtimesteps if non-integer time steps are
# given)
for t_sub in subtimesteps:
if t_sub > 0:
t_diff_prev_int = t_sub - int(t_sub)
if t_diff_prev_int > 0.0:
R_f_ip = (1.0 - t_diff_prev_int) * R_f_prev[
j
] + t_diff_prev_int * R_f_new
else:
R_f_ip = R_f_prev[j]
t_diff_prev = t_sub - t_prev[j]
t_total[j] += t_diff_prev
# compute the perturbed motion field
if vel_pert_method is not None:
V_pert = V + generate_vel_noise(vps[j], t_total[j] * timestep)
extrap_kwargs_["displacement_prev"] = D[j]
R_f_ep, D[j] = extrapolator_method(
R_f_ip,
V_pert,
[t_diff_prev],
**extrap_kwargs_,
)
R_f_out.append(R_f_ep[0])
t_prev[j] = t_sub
# advect the forecast field by one time step if no subtimesteps in the
# current interval were found
if not subtimesteps:
t_diff_prev = t + 1 - t_prev[j]
t_total[j] += t_diff_prev
# compute the perturbed motion field
if vel_pert_method is not None:
V_pert = V + generate_vel_noise(vps[j], t_total[j] * timestep)
extrap_kwargs_["displacement_prev"] = D[j]
_, D[j] = extrapolator_method(
None,
V_pert,
[t_diff_prev],
**extrap_kwargs_,
)
t_prev[j] = t + 1
R_f_prev[j] = R_f_new
return R_f_out
res = []
for j in range(n_ens_members):
if not DASK_IMPORTED or n_ens_members == 1:
res.append(worker(j))
else:
res.append(dask.delayed(worker)(j))
R_f_ = (
dask.compute(*res, num_workers=num_ensemble_workers)
if DASK_IMPORTED and n_ens_members > 1
else res
)
res = None
if is_nowcast_time_step:
if measure_time:
print("%.2f seconds." % (time.time() - starttime))
else:
print("done.")
if callback is not None:
R_f_stacked = np.stack(R_f_)
if R_f_stacked.shape[1] > 0:
callback(R_f_stacked.squeeze())
if return_output:
for j in range(n_ens_members):
R_f[j].extend(R_f_[j])
R_f_ = None
if measure_time:
mainloop_time = time.time() - starttime_mainloop
if return_output:
outarr = np.stack([np.stack(R_f[j]) for j in range(n_ens_members)])
if measure_time:
return outarr, init_time, mainloop_time
else:
return outarr
else:
return None
def forecast(
vil,
velocity,
timesteps,
rainrate=None,
n_cascade_levels=8,
extrap_method="semilagrangian",
ar_order=2,
ar_window_radius=50,
r_vil_window_radius=3,
fft_method="numpy",
apply_rainrate_mask=True,
num_workers=1,
extrap_kwargs=None,
filter_kwargs=None,
measure_time=False,
):
"""
Generate a nowcast by using the autoregressive nowcasting using VIL
(ANVIL) method. ANVIL is built on top of an extrapolation-based nowcast.
The key features are:
1) Growth and decay: implemented by using a cascade decomposition and
a multiscale autoregressive integrated ARI(p,1) model. Instead of the
original time series, the ARI model is applied to the differenced one
corresponding to time derivatives.
2) Originally designed for using integrated liquid (VIL) as the input data.
In this case, the rain rate (R) is obtained from VIL via an empirical
relation. This implementation is more general so that the input can be
any two-dimensional precipitation field.
3) The parameters of the ARI model and the R(VIL) relation are allowed to
be spatially variable. The estimation is done using a moving window.
Parameters
----------
vil: array_like
Array of shape (ar_order+2,m,n) containing the input fields ordered by
timestamp from oldest to newest. The inputs are expected to contain VIL
or rain rate. The time steps between the inputs are assumed to be regular.
velocity: array_like
Array of shape (2,m,n) containing the x- and y-components of the
advection field. The velocities are assumed to represent one time step
between the inputs. All values are required to be finite.
timesteps: int or list of floats
Number of time steps to forecast or a list of time steps for which the
forecasts are computed (relative to the input time step). The elements
of the list are required to be in ascending order.
rainrate: array_like
Array of shape (m,n) containing the most recently observed rain rate
field. If set to None, no R(VIL) conversion is done and the outputs
are in the same units as the inputs.
n_cascade_levels: int, optional
The number of cascade levels to use.
extrap_method: str, optional
Name of the extrapolation method to use. See the documentation of
pysteps.extrapolation.interface.
ar_order: int, optional
The order of the autoregressive model to use. The recommended values
are 1 or 2. Using a higher-order model is strongly discouraged because
the stationarity of the AR process cannot be guaranteed.
ar_window_radius: int, optional
The radius of the window to use for determining the parameters of the
autoregressive model. Set to None to disable localization.
r_vil_window_radius: int, optional
The radius of the window to use for determining the R(VIL) relation.
Applicable if rainrate is not None.
fft_method: str, optional
A string defining the FFT method to use (see utils.fft.get_method).
Defaults to 'numpy' for compatibility reasons. If pyFFTW is installed,
the recommended method is 'pyfftw'.
apply_rainrate_mask: bool
Apply mask to prevent producing precipitation to areas where it was not
originally observed. Defaults to True. Disabling this may improve some
verification metrics but increases the number of false alarms. Applicable
if rainrate is None.
num_workers: int, optional
The number of workers to use for parallel computation. Applicable if
dask is installed or pyFFTW is used for computing the FFT.
When num_workers>1, it is advisable to disable OpenMP by setting
the environment variable OMP_NUM_THREADS to 1.
This avoids slowdown caused by too many simultaneous threads.
extrap_kwargs: dict, optional
Optional dictionary containing keyword arguments for the extrapolation
method. See the documentation of pysteps.extrapolation.
filter_kwargs: dict, optional
Optional dictionary containing keyword arguments for the filter method.
See the documentation of pysteps.cascade.bandpass_filters.py.
measure_time: bool, optional
If True, measure, print and return the computation time.
Returns
-------
out: ndarray
A three-dimensional array of shape (num_timesteps,m,n) containing a time
series of forecast precipitation fields. The time series starts from
t0+timestep, where timestep is taken from the input VIL/rain rate
fields. If measure_time is True, the return value is a three-element
tuple containing the nowcast array, the initialization time of the
nowcast generator and the time used in the main loop (seconds).
References
----------
:cite:`PCLH2020`
"""
_check_inputs(vil, rainrate, velocity, timesteps, ar_order)
if extrap_kwargs is None:
extrap_kwargs = dict()
else:
extrap_kwargs = extrap_kwargs.copy()
if filter_kwargs is None:
filter_kwargs = dict()
print("Computing ANVIL nowcast:")
print("------------------------")
print("")
print("Inputs:")
print("-------")
print("input dimensions: %dx%d" % (vil.shape[1], vil.shape[2]))
print("")
print("Methods:")
print("--------")
print("extrapolation: %s" % extrap_method)
print("FFT: %s" % fft_method)
print("")
print("Parameters:")
print("-----------")
if isinstance(timesteps, int):
print("number of time steps: %d" % timesteps)
else:
print("time steps: %s" % timesteps)
print("parallel threads: %d" % num_workers)
print("number of cascade levels: %d" % n_cascade_levels)
print("order of the ARI(p,1) model: %d" % ar_order)
if type(ar_window_radius) == int:
print("ARI(p,1) window radius: %d" % ar_window_radius)
else:
print("ARI(p,1) window radius: none")
print("R(VIL) window radius: %d" % r_vil_window_radius)
if measure_time:
starttime_init = time.time()
m, n = vil.shape[1:]
vil = vil.copy()
if rainrate is None and apply_rainrate_mask:
rainrate_mask = vil[-1, :] < 0.1
if rainrate is not None:
# determine the coefficients fields of the relation R=a*VIL+b by
# localized linear regression
r_vil_a, r_vil_b = _r_vil_regression(vil[-1, :], rainrate, r_vil_window_radius)
# transform the input fields to Lagrangian coordinates by extrapolation
extrapolator = extrapolation.get_method(extrap_method)
res = list()
def worker(vil, i):
return (
i,
extrapolator(
vil[i, :],
velocity,
vil.shape[0] - 1 - i,
allow_nonfinite_values=True,
**extrap_kwargs,
)[-1],
)
for i in range(vil.shape[0] - 1):
if not DASK_IMPORTED or num_workers == 1:
vil[i, :, :] = worker(vil, i)[1]
else:
res.append(dask.delayed(worker)(vil, i))
if DASK_IMPORTED and num_workers > 1:
num_workers_ = len(res) if num_workers > len(res) else num_workers
vil_e = dask.compute(*res, num_workers=num_workers_)
for i in range(len(vil_e)):
vil[vil_e[i][0], :] = vil_e[i][1]
# compute the final mask as the intersection of the masks of the advected
# fields
mask = np.isfinite(vil[0, :])
for i in range(1, vil.shape[0]):
mask = np.logical_and(mask, np.isfinite(vil[i, :]))
if rainrate is None and apply_rainrate_mask:
rainrate_mask = np.logical_and(rainrate_mask, mask)
# apply cascade decomposition to the advected input fields
bp_filter_method = cascade.get_method("gaussian")
bp_filter = bp_filter_method((m, n), n_cascade_levels, **filter_kwargs)
fft = utils.get_method(fft_method, shape=vil.shape[1:], n_threads=num_workers)
decomp_method, recomp_method = cascade.get_method("fft")
vil_dec = np.empty((n_cascade_levels, vil.shape[0], m, n))
for i in range(vil.shape[0]):
vil_ = vil[i, :].copy()
vil_[~np.isfinite(vil_)] = 0.0
vil_dec_i = decomp_method(vil_, bp_filter, fft_method=fft)
for j in range(n_cascade_levels):
vil_dec[j, i, :] = vil_dec_i["cascade_levels"][j, :]
# compute time-lagged correlation coefficients for the cascade levels of
# the advected and differenced input fields
gamma = np.empty((n_cascade_levels, ar_order, m, n))
for i in range(n_cascade_levels):
vil_diff = np.diff(vil_dec[i, :], axis=0)
vil_diff[~np.isfinite(vil_diff)] = 0.0
for j in range(ar_order):
gamma[i, j, :] = _moving_window_corrcoef(
vil_diff[-1, :], vil_diff[-(j + 2), :], ar_window_radius
)
if ar_order == 2:
# if the order of the ARI model is 2, adjust the correlation coefficients
# so that the resulting process is stationary
for i in range(n_cascade_levels):
gamma[i, 1, :] = autoregression.adjust_lag2_corrcoef2(
gamma[i, 0, :], gamma[i, 1, :]
)
# estimate the parameters of the ARI models
phi = []
for i in range(n_cascade_levels):
if ar_order > 2:
phi_ = autoregression.estimate_ar_params_yw_localized(gamma[i, :], d=1)
elif ar_order == 2:
phi_ = _estimate_ar2_params(gamma[i, :])
else:
phi_ = _estimate_ar1_params(gamma[i, :])
phi.append(phi_)
vil_dec = vil_dec[:, -(ar_order + 1) :, :]
if measure_time:
init_time = time.time() - starttime_init
print("Starting nowcast computation.")
if measure_time:
starttime_mainloop = time.time()
r_f = []
if isinstance(timesteps, int):
timesteps = range(timesteps + 1)
timestep_type = "int"
else:
original_timesteps = [0] + list(timesteps)
timesteps = nowcast_utils.binned_timesteps(original_timesteps)
timestep_type = "list"
if rainrate is not None:
r_f_prev = r_vil_a * vil[-1, :] + r_vil_b
else:
r_f_prev = vil[-1, :]
extrap_kwargs["return_displacement"] = True
dp = None
t_prev = 0.0
for t, subtimestep_idx in enumerate(timesteps):
if timestep_type == "list":
subtimesteps = [original_timesteps[t_] for t_ in subtimestep_idx]
else:
subtimesteps = [t]
if (timestep_type == "list" and subtimesteps) or (
timestep_type == "int" and t > 0
):
is_nowcast_time_step = True
else:
is_nowcast_time_step = False
if is_nowcast_time_step:
print(
"Computing nowcast for time step %d... " % t,
end="",
flush=True,
)
if measure_time:
starttime = time.time()
# iterate the ARI models for each cascade level
for i in range(n_cascade_levels):
vil_dec[i, :] = autoregression.iterate_ar_model(vil_dec[i, :], phi[i])
# recompose the cascade to obtain the forecast field
vil_dec_dict = {}
vil_dec_dict["cascade_levels"] = vil_dec[:, -1, :]
vil_dec_dict["domain"] = "spatial"
vil_dec_dict["normalized"] = False
vil_f = recomp_method(vil_dec_dict)
vil_f[~mask] = np.nan
if rainrate is not None:
# convert VIL to rain rate
r_f_new = r_vil_a * vil_f + r_vil_b
else:
r_f_new = vil_f
if apply_rainrate_mask:
r_f_new[rainrate_mask] = 0.0
r_f_new[r_f_new < 0.0] = 0.0
# advect the recomposed field to obtain the forecast for the current
# time step (or subtimesteps if non-integer time steps are given)
for t_sub in subtimesteps:
if t_sub > 0:
t_diff_prev_int = t_sub - int(t_sub)
if t_diff_prev_int > 0.0:
r_f_ip = (
1.0 - t_diff_prev_int
) * r_f_prev + t_diff_prev_int * r_f_new
else:
r_f_ip = r_f_prev
t_diff_prev = t_sub - t_prev
extrap_kwargs["displacement_prev"] = dp
r_f_ep, dp = extrapolator(
r_f_ip,
velocity,
[t_diff_prev],
allow_nonfinite_values=True,
**extrap_kwargs,
)
r_f.append(r_f_ep[0])
t_prev = t_sub
# advect the forecast field by one time step if no subtimesteps in the
# current interval were found
if not subtimesteps:
t_diff_prev = t + 1 - t_prev
extrap_kwargs["displacement_prev"] = dp
_, dp = extrapolator(
None,
velocity,
[t_diff_prev],
allow_nonfinite_values=True,
**extrap_kwargs,
)
t_prev = t + 1
r_f_prev = r_f_new
if is_nowcast_time_step:
if measure_time:
print("%.2f seconds." % (time.time() - starttime))
else:
print("done.")
if measure_time:
mainloop_time = time.time() - starttime_mainloop
if measure_time:
return np.stack(r_f), init_time, mainloop_time
else:
return np.stack(r_f)