Guide and example on how to use nested grids with DataTrees#
This is an example on how to use PyDDA’s ability to handle nested grids using xarray DataTrees. In this example, we load radars with two pre-generated Cf/Radial grid. The fine grids are higher resolution grids that are contained within the coarser grid.
The DataTree structure that PyDDA follows is:
::
root
|---nest_0/radar_1
|---nest_0/radar_2
|---nest_0/radar_n
|---nest_1/radar_1
|---nest_1/radar_2
|---nest_1/radar_m
Each member of this tree is a DataTree itself. PyDDA will know if the
DataTree contains data from a radar when the name of the node begins
with radar_. The root node of each grid level, in this example,
root and inner_nest will contain the keyword arguments that are
inputs to :code:pydda.retrieval.get_dd_wind_field as attributes for the
tree. PyDDA will use the attributes at each level as the arguments for the
retrieval, allowing the user to vary the coefficients by grid level.
Using :code:pydda.retrieval.get_dd_wind_field_nested will allow PyDDA
to perform the retrieval on the 0th grid first. It will then
perform on the subsequent grid levels, using the previous nest as both the
horizontal boundary conditions and initialization for the retrieval in the next
nest. Finally, PyDDA will update the winds in the first grid by nearest-
neighbor interpolation of the latter grid into the overlapping portion between
the inner and outer grid level.
PyDDA will then return the retrieved wind fields as the “u”, “v”, and “w” DataArrays inside each of the root nodes for each level, in this case root and inner_nest.
## Do imports
import pydda
import matplotlib.pyplot as plt
import warnings
from xarray import DataTree
warnings.filterwarnings("ignore")
"""
We will load pregenerated grids for this case.
"""
test_coarse0 = pydda.io.read_grid(pydda.tests.get_sample_file("test_coarse0.nc"))
test_coarse1 = pydda.io.read_grid(pydda.tests.get_sample_file("test_coarse1.nc"))
test_fine0 = pydda.io.read_grid(pydda.tests.get_sample_file("test_fine0.nc"))
test_fine1 = pydda.io.read_grid(pydda.tests.get_sample_file("test_fine1.nc"))
"""
Initalize with a zero wind field. We have HRRR data already generated for this case inside
the example data files to provide a model constraint.
"""
test_coarse0 = pydda.initialization.make_constant_wind_field(
test_coarse0, (0.0, 0.0, 0.0)
)
"""
Specify the retrieval parameters at each level
"""
kwargs_dict = dict(
Cm=256.0,
Co=1e-2,
Cx=50.0,
Cy=50.0,
Cz=50.0,
Cmod=1e-5,
model_fields=["hrrr"],
refl_field="DBZ",
wind_tol=0.5,
max_iterations=150,
engine="scipy",
)
"""
Enforce equal times for each grid. This is required for the DataTree structure since time is an
inherited dimension.
"""
test_coarse1["time"] = test_coarse0["time"]
test_fine0["time"] = test_coarse0["time"]
test_fine1["time"] = test_coarse1["time"]
"""
Provide the overlying grid structure as specified above.
"""
tree_dict = {
"/nest_0/radar_ktlx": test_coarse0,
"/nest_0/radar_kict": test_coarse1,
"/nest_1/radar_ktlx": test_fine0,
"/nest_1/radar_kict": test_fine1,
}
tree = DataTree.from_dict(tree_dict)
tree["/nest_0/"].attrs = kwargs_dict
tree["/nest_1/"].attrs = kwargs_dict
"""
Perform the retrieval
"""
grid_tree = pydda.retrieval.get_dd_wind_field_nested(tree)
"""
Plot the coarse grid output and finer grid output
"""
fig, ax = plt.subplots(1, 2, figsize=(10, 5))
pydda.vis.plot_horiz_xsection_quiver(
grid_tree["nest_0"],
ax=ax[0],
level=5,
cmap="ChaseSpectral",
vmin=-10,
vmax=80,
quiverkey_len=10.0,
background_field="DBZ",
bg_grid_no=1,
w_vel_contours=[1, 2, 5, 10],
quiver_spacing_x_km=50.0,
quiver_spacing_y_km=50.0,
quiverkey_loc="bottom_right",
)
pydda.vis.plot_horiz_xsection_quiver(
grid_tree["nest_1"],
ax=ax[1],
level=5,
cmap="ChaseSpectral",
vmin=-10,
vmax=80,
quiverkey_len=10.0,
background_field="DBZ",
bg_grid_no=1,
w_vel_contours=[1, 2, 5, 10],
quiver_spacing_x_km=50.0,
quiver_spacing_y_km=50.0,
quiverkey_loc="bottom_right",
)
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 as part of the Atmospheric
## Radiation Measurement (ARM) Climate Research Facility, an Office of
## Science 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 1 and 0
Calculating weights for models...
Starting solver
rmsVR = 16.213679825765688
Total points: 412470
The max of w_init is 0.0
Total number of model points: 2342081
Nfeval | Jvel | Jmass | Jsmooth | Jbg | Jvort | Jmodel | Jpoint | Max w
0|4115.2916| 0.0000| 0.0000| 0.0000| 0.0000|11243.5276| 0.0000| 0.0000
---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
Cell In[1], line 68
64 """
65 Perform the retrieval
66 """
67
---> 68 grid_tree = pydda.retrieval.get_dd_wind_field_nested(tree)
69
70 """
71 Plot the coarse grid output and finer grid output
File ~/work/PyDDA/PyDDA/pydda/retrieval/nesting.py:56, in get_dd_wind_field_nested(grid_tree, **kwargs)
54 elif len(grid_list) > 0:
55 my_kwargs = tree_attrs
---> 56 output_grids, output_parameters = get_dd_wind_field(grid_list, **my_kwargs)
57 output_parameters = output_parameters.__dict__
58 if in_parent is True:
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:281, in fmin_l_bfgs_b(func, x0, fprime, args, approx_grad, bounds, m, factr, pgtol, epsilon, iprint, maxfun, maxiter, disp, callback, maxls)
269 callback = _wrap_callback(callback)
270 opts = {'disp': disp,
271 'iprint': iprint,
272 'maxcor': m,
(...) 278 'callback': callback,
279 'maxls': maxls}
--> 281 res = _minimize_lbfgsb(fun, x0, args=args, jac=jac, bounds=bounds,
282 **opts)
283 d = {'grad': res['jac'],
284 'task': res['message'],
285 'funcalls': res['nfev'],
286 'nit': res['nit'],
287 'warnflag': res['status']}
288 f = res['fun']
File /usr/share/miniconda/envs/pydda-docs/lib/python3.14/site-packages/scipy/optimize/_lbfgsb_py.py:469, in _minimize_lbfgsb(fun, x0, args, jac, bounds, disp, maxcor, ftol, gtol, eps, maxfun, maxiter, iprint, callback, maxls, finite_diff_rel_step, workers, **unknown_options)
461 _lbfgsb.setulb(m, x, low_bnd, upper_bnd, nbd, f, g, factr, pgtol, wa,
462 iwa, task, lsave, isave, dsave, maxls, ln_task)
464 if task[0] == 3:
465 # The minimization routine wants f and g at the current x.
466 # Note that interruptions due to maxfun are postponed
467 # until the completion of the current minimization iteration.
468 # Overwrite f and g:
--> 469 f, g = func_and_grad(x)
470 elif task[0] == 1:
471 # new iteration
472 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:603, in _ScalarFunctionWrapper.__call__(self, x)
600 def __call__(self, x):
601 # Send a copy because the user may overwrite it.
602 # The user of this class might want `x` to remain unchanged.
--> 603 fx = self.f(np.copy(x), *self.args)
604 self.nfev += 1
606 # Make sure the function returns a true scalar
File ~/work/PyDDA/PyDDA/pydda/cost_functions/cost_functions.py:207, in J_function(winds, parameters)
204 Jmass = 0
206 if parameters.Cx > 0 or parameters.Cy > 0 or parameters.Cz > 0:
--> 207 Jsmooth = _cost_functions_numpy.calculate_smoothness_cost(
208 winds[0],
209 winds[1],
210 winds[2],
211 parameters.dx,
212 parameters.dy,
213 parameters.dz,
214 Cx=parameters.Cx,
215 Cy=parameters.Cy,
216 Cz=parameters.Cz,
217 )
218 else:
219 Jsmooth = 0
File ~/work/PyDDA/PyDDA/pydda/cost_functions/_cost_functions_numpy.py:216, in calculate_smoothness_cost(u, v, w, dx, dy, dz, Cx, Cy, Cz)
214 dvdy = np.gradient(v, dy, axis=1)
215 dvdz = np.gradient(v, dz, axis=0)
--> 216 dwdx = np.gradient(w, dx, axis=2)
217 dwdy = np.gradient(w, dy, axis=1)
218 dwdz = np.gradient(w, dz, axis=0)
File /usr/share/miniconda/envs/pydda-docs/lib/python3.14/site-packages/numpy/lib/_function_base_impl.py:1338, in gradient(f, axis, edge_order, *varargs)
1336 dx_0 = ax_dx if uniform_spacing else ax_dx[0]
1337 # 1D equivalent -- out[0] = (f[1] - f[0]) / (x[1] - x[0])
-> 1338 out[tuple(slice1)] = (f[tuple(slice2)] - f[tuple(slice3)]) / dx_0
1340 slice1[axis] = -1
1341 slice2[axis] = -1
KeyboardInterrupt: