Example of a wind retrieval in a tornado over Sydney#
This shows an example of how to retrieve winds from 4 radars over Sydney.
We use smoothing to decrease the magnitude of the updraft in the region of the mesocyclone. The reduction of noise also helps the solution converge much faster since the cost function is smoother and therefore less susecptible to find a local minimum that is in noise.
The observational constraint is reduced to 0.01 from the usual 1 because we are factoring in many more data points as we are using 4 radars instead of the two in the Darwin example.
This example uses pooch to download the data files.
import pydda
import matplotlib.pyplot as plt
import numpy as np
grid1_path = pydda.tests.get_sample_file("grid1_sydney.nc")
grid2_path = pydda.tests.get_sample_file("grid2_sydney.nc")
grid3_path = pydda.tests.get_sample_file("grid3_sydney.nc")
grid4_path = pydda.tests.get_sample_file("grid4_sydney.nc")
grid1 = pydda.io.read_grid(grid1_path)
grid2 = pydda.io.read_grid(grid2_path)
grid3 = pydda.io.read_grid(grid3_path)
grid4 = pydda.io.read_grid(grid4_path)
# Set initialization and do retrieval
grid1 = pydda.initialization.make_constant_wind_field(grid1, vel_field="VRADH_corr")
new_grids, _ = pydda.retrieval.get_dd_wind_field(
[grid1, grid2, grid3, grid4],
Co=1e-2,
Cm=256.0,
Cx=10,
Cy=10,
Cz=10,
vel_name="VRADH_corr",
refl_field="DBZH",
mask_outside_opt=True,
wind_tol=0.5,
max_iterations=200,
engine="scipy",
)
# Make a neat plot
fig = plt.figure(figsize=(10, 7))
ax = pydda.vis.plot_horiz_xsection_quiver_map(
new_grids,
background_field="DBZH",
level=3,
show_lobes=False,
bg_grid_no=3,
vmin=0,
vmax=60,
quiverkey_len=20.0,
w_vel_contours=[1.0, 3.0, 5.0, 10.0, 20.0],
quiver_spacing_x_km=2.0,
quiver_spacing_y_km=2.0,
quiverkey_loc="top",
colorbar_contour_flag=True,
cmap="ChaseSpectral",
)
ax.set_xticks(np.arange(150.5, 153, 0.1))
ax.set_yticks(np.arange(-36, -32.0, 0.1))
ax.set_xlim([151.0, 151.35])
ax.set_ylim([-34.15, -33.9])
plt.show()
## You are using the Python ARM Radar Toolkit (Py-ART), an open source
## library for working with weather radar data. Py-ART is partly supported
## by the U.S. Department of Energy Office of Science as part of
## the Atmospheric Radiation Measurement (ARM) User Facility.
##
## If you use this software to prepare a publication, please cite:
##
## JJ Helmus and SM Collis, JORS 2016, doi: 10.5334/jors.119
Welcome to PyDDA 2.4.1
If you are using PyDDA in your publications, please cite:
Jackson et al. (2020) Journal of Open Research Science
Detecting Jax...
Jax/JaxOpt are not installed on your system, unable to use Jax engine.
Detecting TensorFlow...
Unable to load both TensorFlow and tensorflow-probability. TensorFlow engine disabled.
No module named 'tensorflow'
False
Calculating weights for radars 0 and 1
Calculating weights for radars 0 and 2
Calculating weights for radars 0 and 3
Calculating weights for radars 1 and 0
Calculating weights for radars 1 and 2
Calculating weights for radars 1 and 3
Calculating weights for radars 2 and 0
Calculating weights for radars 2 and 1
Calculating weights for radars 2 and 3
Calculating weights for radars 3 and 0
Calculating weights for radars 3 and 1
Calculating weights for radars 3 and 2
Calculating weights for models...
Starting solver
rmsVR = 7.359750110231316
Total points: 399749
The max of w_init is 0.0
Total number of model points: 0
Nfeval | Jvel | Jmass | Jsmooth | Jbg | Jvort | Jmodel | Jpoint | Max w
0|4080.4252| 0.0000| 0.0000| 0.0000| 0.0000| 0.0000| 0.0000| 0.0000
The gradient of the cost functions is 0.1119091690376132
Nfeval | Jvel | Jmass | Jsmooth | Jbg | Jvort | Jmodel | Jpoint | Max w
10| 92.4335| 17.0200| 0.0001| 0.0000| 0.0000| 0.0000| 0.0000| 48.1870
Max change in w: nan
---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Cell In[1], line 17
13 grid4 = pydda.io.read_grid(grid4_path)
14
15 # Set initialization and do retrieval
16 grid1 = pydda.initialization.make_constant_wind_field(grid1, vel_field="VRADH_corr")
---> 17 new_grids, _ = pydda.retrieval.get_dd_wind_field(
18 [grid1, grid2, grid3, grid4],
19 Co=1e-2,
20 Cm=256.0,
File ~/work/PyDDA/PyDDA/pydda/retrieval/wind_retrieve.py:1502, in get_dd_wind_field(Grids, u_init, v_init, w_init, engine, **kwargs)
1495 w_init = new_grids[0]["w"].values.squeeze()
1497 if (
1498 engine.lower() == "scipy"
1499 or engine.lower() == "jax"
1500 or engine.lower() == "auglag"
1501 ):
-> 1502 return _get_dd_wind_field_scipy(
1503 new_grids, u_init, v_init, w_init, engine, **kwargs
1504 )
1505 elif engine.lower() == "tensorflow":
1506 return _get_dd_wind_field_tensorflow(
1507 new_grids, u_init, v_init, w_init, **kwargs
1508 )
File ~/work/PyDDA/PyDDA/pydda/retrieval/wind_retrieve.py:614, in _get_dd_wind_field_scipy(Grids, u_init, v_init, w_init, engine, points, vel_name, refl_field, u_back, v_back, z_back, frz, Co, Cm, Cx, Cy, Cz, Cb, Cv, Cmod, Cpoint, cvtol, gtol, Jveltol, Ut, Vt, low_pass_filter, mask_outside_opt, weights_obs, weights_model, weights_bg, max_iterations, mask_w_outside_opt, filter_window, filter_order, min_bca, max_bca, upper_bc, model_fields, output_cost_functions, roi, wind_tol, tolerance, const_boundary_cond, max_wind_mag, parallel)
612 parameters.print_out = False
613 if engine.lower() == "scipy":
--> 614 winds = fmin_l_bfgs_b(
615 J_function,
616 winds,
617 args=(parameters,),
618 maxiter=max_iterations,
619 pgtol=tolerance,
620 bounds=bounds,
621 fprime=grad_J,
622 callback=_vert_velocity_callback,
623 )
624 else:
626 def loss_and_gradient(x):
File /usr/share/miniconda/envs/pydda-docs/lib/python3.14/site-packages/scipy/optimize/_lbfgsb_py.py:259, in fmin_l_bfgs_b(func, x0, fprime, args, approx_grad, bounds, m, factr, pgtol, epsilon, maxfun, maxiter, callback, maxls)
249 callback = _wrap_callback(callback)
250 opts = {'maxcor': m,
251 'ftol': factr * np.finfo(float).eps,
252 'gtol': pgtol,
(...) 256 'callback': callback,
257 'maxls': maxls}
--> 259 res = _minimize_lbfgsb(fun, x0, args=args, jac=jac, bounds=bounds,
260 **opts)
261 d = {'grad': res['jac'],
262 'task': res['message'],
263 'funcalls': res['nfev'],
264 'nit': res['nit'],
265 'warnflag': res['status']}
266 f = res['fun']
File /usr/share/miniconda/envs/pydda-docs/lib/python3.14/site-packages/scipy/optimize/_lbfgsb_py.py:420, in _minimize_lbfgsb(fun, x0, args, jac, bounds, maxcor, ftol, gtol, eps, maxfun, maxiter, callback, maxls, finite_diff_rel_step, workers, **unknown_options)
412 _lbfgsb.setulb(m, x, low_bnd, upper_bnd, nbd, f, g, factr, pgtol, wa,
413 iwa, task, lsave, isave, dsave, maxls, ln_task)
415 if task[0] == 3:
416 # The minimization routine wants f and g at the current x.
417 # Note that interruptions due to maxfun are postponed
418 # until the completion of the current minimization iteration.
419 # Overwrite f and g:
--> 420 f, g = func_and_grad(x)
421 elif task[0] == 1:
422 # new iteration
423 n_iterations += 1
File /usr/share/miniconda/envs/pydda-docs/lib/python3.14/site-packages/scipy/optimize/_differentiable_functions.py:412, in ScalarFunction.fun_and_grad(self, x)
410 if not np.array_equal(x, self.x):
411 self._update_x(x)
--> 412 self._update_fun()
413 self._update_grad()
414 return self.f, self.g
File /usr/share/miniconda/envs/pydda-docs/lib/python3.14/site-packages/scipy/optimize/_differentiable_functions.py:362, in ScalarFunction._update_fun(self)
360 def _update_fun(self):
361 if not self.f_updated:
--> 362 fx = self._wrapped_fun(self.x)
363 self._nfev += 1
364 if fx < self._lowest_f:
File /usr/share/miniconda/envs/pydda-docs/lib/python3.14/site-packages/scipy/_lib/_util.py:545, in _ScalarFunctionWrapper.__call__(self, x)
542 def __call__(self, x):
543 # Send a copy because the user may overwrite it.
544 # The user of this class might want `x` to remain unchanged.
--> 545 fx = self.f(np.copy(x), *self.args)
546 self.nfev += 1
548 # Make sure the function returns a true scalar
File ~/work/PyDDA/PyDDA/pydda/cost_functions/cost_functions.py:176, in J_function(winds, parameters)
166 winds = np.reshape(
167 winds,
168 (
(...) 173 ),
174 )
175 # Had to change to float because Jax returns device array (use np.float_())
--> 176 Jvel = _cost_functions_numpy.calculate_radial_vel_cost_function(
177 parameters.vrs,
178 parameters.azs,
179 parameters.els,
180 winds[0],
181 winds[1],
182 winds[2],
183 parameters.wts,
184 rmsVr=parameters.rmsVr,
185 weights=parameters.weights,
186 coeff=parameters.Co,
187 parallel=parameters.parallel,
188 )
189 # print("apples Jvel", Jvel)
191 if parameters.Cm > 0:
192 # Had to change to float because Jax returns device array (use np.float_())
File ~/work/PyDDA/PyDDA/pydda/cost_functions/_cost_functions_numpy.py:65, in calculate_radial_vel_cost_function(vrs, azs, els, u, v, w, wts, rmsVr, weights, coeff, parallel)
61 azs_arr = np.stack(azs)
62 wts_arr = np.stack(wts)
63 v_ar = (
64 np.cos(els_arr) * np.sin(azs_arr) * u[np.newaxis]
---> 65 + np.cos(els_arr) * np.cos(azs_arr) * v[np.newaxis]
66 + np.sin(els_arr) * (w[np.newaxis] - np.abs(wts_arr))
67 )
68 return lambda_o * np.sum(np.square(vrs_arr - v_ar) * weights)
70 J_o = 0
KeyboardInterrupt: