From 9b23c4399119f0e06acd09977b1314f1c75212c8 Mon Sep 17 00:00:00 2001 From: richardarsenault Date: Sun, 28 Dec 2025 14:48:34 -0500 Subject: [PATCH 1/5] precipitation assimilation first pass --- .../oi_cross_validation.py | 196 +++ .../optimal_interpolation_precip.py | 1249 +++++++++++++++++ tests/ERA5_land_3_variables_raw_subset.nc | Bin 0 -> 3958512 bytes tests/stations_precip_DQAQ_ECCC_US_subset.nc | Bin 0 -> 71663 bytes tests/test_precip_oi.py | 34 + 5 files changed, 1479 insertions(+) create mode 100644 src/xhydro/optimal_interpolation/oi_cross_validation.py create mode 100644 src/xhydro/optimal_interpolation/optimal_interpolation_precip.py create mode 100644 tests/ERA5_land_3_variables_raw_subset.nc create mode 100644 tests/stations_precip_DQAQ_ECCC_US_subset.nc create mode 100644 tests/test_precip_oi.py diff --git a/src/xhydro/optimal_interpolation/oi_cross_validation.py b/src/xhydro/optimal_interpolation/oi_cross_validation.py new file mode 100644 index 00000000..199a43db --- /dev/null +++ b/src/xhydro/optimal_interpolation/oi_cross_validation.py @@ -0,0 +1,196 @@ +"""Evaluate cross-validation of optimal interpolation results.""" + +import cartopy +import cartopy.crs as ccrs +import numpy as np +import xarray as xr +from matplotlib import pyplot as plt +from matplotlib.colors import TwoSlopeNorm + + +def plot_cross_validation_rmse_results(filename_stations): + """ + Generate a plot of the RMSE improvements by performing the optimal interpolation. + + Parameters + ---------- + filename_stations : str + The path and name of the file that contains the stations (observations) data. Must be a netcdf file. + """ + # Get the list of validation stations from the run we just did. + validation_stations_precip = np.loadtxt("./validation_stations.txt").astype(np.int32) + all_stations = xr.open_dataset(filename_stations) + + # Get the latitude and longitude of all possible stations + all_latitudes = all_stations.latitude.values + all_longitudes = all_stations.longitude.values + + # Get the latitude and longitude of the stations used in validation + latitudes = all_latitudes[validation_stations_precip] + longitudes = all_longitudes[validation_stations_precip] + + # Load the RMSE errors calculated for the raw ERA5Land and the OI processed at the validation station locations. + validation_rmse_values_era5 = np.loadtxt("./Test_validation_rmse_values_ERA5.txt") + validation_rmse_values_oi = np.loadtxt("./Test_validation_rmse_values_OI.txt") + + # Make the figure showing the changes in RMSE + fig, (ax1, ax2, ax3) = plt.subplots(3, 1, subplot_kw={"projection": ccrs.PlateCarree()}) + + # Plot the raw results + plt.subplot(311) + sc1 = plt.scatter(x=longitudes, y=latitudes, c=validation_rmse_values_era5, s=5) + plt.title("Original") + plt.colorbar(sc1) + sc1.set_cmap("plasma") + ax1.set_aspect("equal", adjustable=None) + ax1.add_feature(cartopy.feature.BORDERS, linestyle="-", alpha=1) + ax1.add_feature(cartopy.feature.OCEAN, zorder=100, edgecolor="k") + ax1.coastlines() + ax1.gridlines(draw_labels=True) + + # Plot the OI results + plt.subplot(312) + sc2 = plt.scatter(x=longitudes, y=latitudes, c=validation_rmse_values_era5, s=3) + plt.title("Corrected") + plt.colorbar(sc2) + sc2.set_cmap("plasma") + ax2.set_aspect("equal", adjustable=None) + ax2.add_feature(cartopy.feature.BORDERS, linestyle="-", alpha=1) + ax2.add_feature(cartopy.feature.OCEAN, zorder=100, edgecolor="k") + ax2.coastlines() + ax2.gridlines(draw_labels=True) + + # Calculate and plot the differences between both (delta RMSE). + diffs = validation_rmse_values_era5 - validation_rmse_values_oi + col_norm = TwoSlopeNorm(vmin=np.nanmin(diffs), vcenter=0, vmax=np.nanmax(diffs)) + plt.subplot(313) + sc3 = plt.scatter(x=longitudes, y=latitudes, c=diffs, s=12, norm=col_norm, cmap="RdBu_r", edgecolors="k", linewidths=0.5) + plt.title("Difference (Original RMSE - OI RMSE): Higher is better ") + plt.colorbar(sc3) + ax3.set_aspect("equal", adjustable=None) + ax3.add_feature(cartopy.feature.BORDERS, linestyle="-", alpha=1) + ax3.add_feature(cartopy.feature.OCEAN, zorder=100, edgecolor="k") + ax3.coastlines() + ax3.gridlines(draw_labels=True) + + # Show the figure + plt.show() + + +def rmse_ignore_nan(y_true, y_pred): + """ + Compute the Root Mean Squared Error (RMSE) between two arrays while ignoring any positions containing NaN values. + + Parameters + ---------- + y_true : array_like + Ground truth (correct) target values. + y_pred : array_like + Estimated target values. + + Returns + ------- + float + The RMSE calculated only over positions where both y_true and y_pred are finite (non-NaN). + """ + # Ensure inputs are numpy arrays + y_true = np.asarray(y_true) + y_pred = np.asarray(y_pred) + + # Create a mask of valid (non-NaN) indices + mask = ~np.isnan(y_true) & ~np.isnan(y_pred) + + # Filter out NaN values from both arrays + y_true_valid = y_true[mask] + y_pred_valid = y_pred[mask] + + # If no valid values remain, return NaN + if y_true_valid.size == 0: + return np.nan + + # Compute Mean Squared Error on valid values + mse = np.mean((y_true_valid - y_pred_valid) ** 2) + + # Return the square root of MSE (RMSE) + return np.sqrt(mse) + + +def evaluate_cross_validation( + observed_precip_valid: np.array, + estimated_precip_reshaped: np.array, + precip_medians: np.array, + lat_obs_valid: list[float], + lon_obs_valid: list[float], + lat_est: list[float], + lon_est: list[float], +): + """ + Calculate and plot the evaluation of gains in performance using optimal interpolation compared to the raw data. + + Parameters + ---------- + observed_precip_valid : np.array + Observed precipitation for the validation set, used to compute evaluation metrics for cross-validation. + estimated_precip_reshaped : np.array + Estimated precipitation in a reshaped matrix such that it is compatible with the interpolator requirements. + precip_medians : np.array + Estimated precipitation at all locations of the background field. + lat_obs_valid : array-like + Latitude of the observation stations for the validation dataset. + lon_obs_valid : array-like + Longitude of the observation stations for the validation dataset. + lat_est : array-like + Latitude of the estimated gridpoints (complete grid). + lon_est : array-like + Longitude of the estimated gridpoints (complete grid). + """ + # Prepare the variables to store the precipitation and RMSE values and fill with NaN. + precip_table_stations = np.empty((observed_precip_valid.shape[1], observed_precip_valid.shape[0])) + precip_table_era5 = np.empty((observed_precip_valid.shape[1], observed_precip_valid.shape[0])) + precip_table_oi = np.empty((observed_precip_valid.shape[1], observed_precip_valid.shape[0])) + precip_table_stations[:] = np.nan + precip_table_era5[:] = np.nan + precip_table_oi[:] = np.nan + + # Preallocate the RMSE tables + rmse_values_era5 = np.empty(len(lon_obs_valid)) + rmse_values_oi = np.empty(len(lon_obs_valid)) + + # For each station, extract the nearest ERA5Land station, which should overlap exactly if data lat/lon are rounded. + # Get the precipitation values + for station in range(0, len(lon_obs_valid)): + pos = np.argwhere((lon_est == lon_obs_valid[station]) & (lat_est == lat_obs_valid[station])) + pos = pos[0][0] + precip_table_era5[:, station] = estimated_precip_reshaped[pos, :] + precip_table_stations[:, station] = observed_precip_valid[station, :] + precip_table_oi[:, station] = precip_medians[pos, :] + + # Again, for each station, now compute the RMSE values for the raw ERA5Land set and then the OI set. + for station in range(0, len(lon_obs_valid)): + rmse_values_era5[station] = rmse_ignore_nan(precip_table_stations[:, station], precip_table_era5[:, station]) + rmse_values_oi[station] = rmse_ignore_nan(precip_table_stations[:, station], precip_table_oi[:, station]) + + # Prepare plots + plt.plot(rmse_values_era5, "g") + plt.plot(rmse_values_oi, "r") + plt.plot(rmse_values_era5 - rmse_values_oi, "b") + plt.axhline(y=0.0, color="k", linestyle="-") + plt.legend(("Without OI", "With OI", "Difference (higher means OI is better)")) + plt.title("Precipitation OI results in validation") + plt.ylabel("RMSE [mm]") + plt.show() + + # Compute means of RMSE values + rmse_original = np.nanmean(rmse_values_era5) + rmse_oi = np.nanmean(rmse_values_oi) + + # Save variables to textfiles for future needs or inspection. + np.savetxt("Test_validation_stations_precip.txt", precip_table_stations) + np.savetxt("Test_validation_ERA5_precip.txt", precip_table_era5) + np.savetxt("Test_validation_OI_precip.txt", precip_table_oi) + np.savetxt("Test_validation_rmse_values_ERA5.txt", rmse_values_era5) + np.savetxt("Test_validation_rmse_values_OI.txt", rmse_values_oi) + np.savetxt("Test_validation_rmse_difference_OI_ERA5.txt", rmse_values_oi - rmse_values_era5) + np.savetxt("Test_validation_rmse_mean_values_Original_vs_OI.txt", np.array((rmse_original, rmse_oi))) + + print("Original RMSE is " + str(rmse_original) + " and the OI RMSE is " + str(rmse_oi) + ".") diff --git a/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py b/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py new file mode 100644 index 00000000..19b59ccc --- /dev/null +++ b/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py @@ -0,0 +1,1249 @@ +"""Apply optimal interpolation of precipitation data over a background field.""" + +import datetime as dt +from functools import partial +from pathlib import Path + +import haversine +import numpy as np +import pandas as pd +import xarray as xr +from numpy import ndarray +from scipy.optimize import minimize +from scipy.stats import norm +from xarray import Dataset + +import xhydro.optimal_interpolation.oi_cross_validation as cv + + +def check_netcdf_layout_gridded( + nc_path: str | Path, + var_name: str = "tp", + required_dims: tuple[str, str, str] = ("longitude", "latitude", "time"), + required_coords: tuple[str, str, str] = ("time", "latitude", "longitude"), +): + """ + Validate that a gridded NetCDF file contains coordinates, dimensions and variables required for the process. + + Parameters + ---------- + nc_path : Union[str, Path] + The path and name of the file that contains the stations (observations) data. Must be a netcdf file. + var_name : str + The name of the variable to be used for interpolation. + required_dims : Tuple[str, str, str] + The names of the longitude, latitude and time variables in the Dataset. + required_coords : Tuple[str, str, str] + The names of the coordinates in the dataset, corresponding to the longitude, latitude and time dimensions. + + Returns + ------- + bool : + True if valid, otherwise raises ValueError with a readable message. + """ + nc_path = Path(nc_path) + if not nc_path.exists(): + raise ValueError(f"File not found: {nc_path}") + + with xr.open_dataset(nc_path) as ds: + errors: list[str] = [] + + # --- Required dimensions exist --- + errors.extend(f"Missing dimension: {d!r}" for d in required_dims if d not in ds.dims) + + # --- Required coordinates exist and are 1D on their own dim --- + errors.extend( + [f"Missing coordinate: {c!r}" for c in required_coords if c not in ds.coords] + + [ + f"Coordinate {c!r} must be 1D with dims ({c!r},), got {tuple(ds[c].dims)}" + for c in required_coords + if c in ds.coords and tuple(ds[c].dims) != (c,) + ] + ) + + # --- Required variable exists and has the right dims (any order) --- + if var_name not in ds.data_vars: + errors.append(f"Missing data variable: {var_name!r}") + else: + v_dims = tuple(ds[var_name].dims) + required = set(required_dims) + got = set(v_dims) + + if required != got: + errors.append(f"Variable {var_name!r} must use exactly dims {required_dims} (any order), got {v_dims}") + + if errors: + raise ValueError("NetCDF layout check failed:\n- " + "\n- ".join(errors)) + + return True + + +def check_netcdf_layout_stations( + nc_path: str | Path, + time_dim: str = "time", + required_station_dim: str = "watershed", + required_precip_var: str = "precip", + required_station_vars: tuple[str, ...] = ("latitude", "longitude", "altitude"), +) -> bool: + """ + Validate that a NetCDF file for the stations data contains required information. + + Dimensions: + - time + - station ID + + Coordinates: + - time (time) [must exist as a coordinate, 1D along 'time'] + + Data variables: + - precip with dims being a permutation of (station, time) (order can differ) + - latitude (station) + - longitude (station) + - altitude (station) + - StationID_SEQ (station) + + Parameters + ---------- + nc_path : str | Path + Path to the the netcdf file containing the dataset to explore. + time_dim : str + Name of the time dimension in the Dataset. Most likely "time". + required_station_dim : str + Name of the station dimension. + required_precip_var : str + Name of the variable containing the precipitation values. + required_station_vars : Tuple[str, str, str] + A tuple containing the names of the variables describing information about + stations. + + Returns + ------- + bool + True if valid, otherwise raises ValueError with a readable message. + """ + nc_path = Path(nc_path) + if not nc_path.exists(): + raise ValueError(f"File not found: {nc_path}") + + with xr.open_dataset(nc_path) as ds: + errors: list[str] = [] + + # --- Required dimensions --- + errors.extend([f"Missing dimension: {d!r}" for d in (time_dim, required_station_dim) if d not in ds.dims]) + + # --- Required coordinate 'time' --- + errors.extend( + [f"Missing coordinate: {time_dim!r}"] + if time_dim not in ds.coords + else [] + + ( + [f"Coordinate {time_dim!r} must be 1D with dims ({time_dim!r},), got {tuple(ds[time_dim].dims)}"] + if tuple(ds[time_dim].dims) != (time_dim,) + else [] + ) + ) + + # --- precip variable dims: any order of (watershed, time) --- + if required_precip_var not in ds.data_vars: + errors.append(f"Missing data variable: {required_precip_var!r}") + else: + v_dims = tuple(ds[required_precip_var].dims) + required = {required_station_dim, time_dim} + got = set(v_dims) + if required != got: + errors.append( + f"Variable {required_precip_var!r} must use exactly dims ({required_station_dim!r}, {time_dim!r}) (any order), got {v_dims}" + ) + + # --- watershed-metadata variables: must be 1D on watershed --- + for v in required_station_vars: + if v not in ds.data_vars: + errors.append(f"Missing data variable: {v!r}") + else: + vdims = tuple(ds[v].dims) + if vdims != (required_station_dim,): + errors.append(f"Variable {v!r} must be 1D with dims ({required_station_dim!r},), got {vdims}") + + if errors: + raise ValueError("NetCDF layout check failed:\n- " + "\n- ".join(errors)) + + return True + + +def general_ecf(h: np.ndarray, par: list | np.ndarray, form: int): + """ + Define the form of the Error Covariance Function (ECF) equations. + + Parameters + ---------- + h : float or array + The distance or distances at which to evaluate the ECF. + par : list or array-like + Parameters for the ECF equation. + form : int + The form of the ECF equation to use (1, 2, 3 or 4). See :py:func:`correction` for details. + + Returns + ------- + float or array : + The calculated ECF values based on the specified form. + """ + if form == 1: # From Lachance-Cloutier et al. 2017. + return par[0] * (1 + h / par[1]) * np.exp(-h / par[1]) + elif form == 2: + return par[0] * np.exp(-0.5 * np.power(h / par[1], 2)) + elif form == 3: + return par[0] * np.exp(-h / par[1]) + elif form == 4: + return par[0] * np.exp(-(h ** par[1]) / par[0]) + else: + raise (Exception("Unknown form of the Error Covariance Function (ECF). Please use values from 1 to 4.")) + + +def find_position_of_observation_in_vectorized_grid(obslat: float, obslon: float, gridlat: list[float], gridlon: list[float]) -> int: + """ + Find the gridpoint in a 2D grid that corresponds to a unique observation station location. + + Parameters + ---------- + obslat : float + Latitude of the observation station that needs to be found in the gridded product. + obslon : float + Longitude of the observation station that needs to be found in the gridded product. + gridlat : array-like + Latitude of all the gridpoints we need to search. + gridlon : array-like + Longitude of all the gridpoints we need to search. + + Returns + ------- + np.array + The position of the gridpoint that corresponds to the observation station location. + """ + pos = np.argwhere((gridlon == obslon) & (gridlat == obslat)) + return pos[0][0] + + +def optimal_interpolation( + lat_obs: np.ndarray, + lon_obs: np.ndarray, + lat_est: np.ndarray, + lon_est: np.ndarray, + ecf: partial, + bg_var_obs: np.ndarray, + bg_var_est: np.ndarray, + var_obs: np.ndarray, + bg_departures: xr.DataArray, + bg_est: np.ndarray, + precalcs: dict, +) -> tuple[np.ndarray, np.ndarray, dict]: + """ + Perform optimal interpolation to estimate values at specified locations of a background field. + + Parameters + ---------- + lat_obs : np.ndarray + Vector of latitudes of the observation stations. + lon_obs : np.ndarray + Vector of longitudes of the observation stations. + lat_est : np.ndarray + Vector of latitudes of the estimation/simulation stations to be estimated in the background field. + lon_est : np.ndarray + Vector of longitudes of the estimation/simulation stations to be estimated in the background field. + ecf : partial + The function to use for the empirical distribution correction. It is a partial function from functools. + The error covariance is a function of distance h, and this partial function represents this relationship. + bg_var_obs : np.ndarray + Background field variance at the observation stations (vector of size "observation stations"). + bg_var_est : np.ndarray + Background field variance at estimation sites (vector of size "estimation stations"). + var_obs : np.ndarray + Observation variance at observation sites (vector of size "observation stations"). + bg_departures : DataArray + Difference between observation and background field at observation sites (vector of size "observation stations"). + bg_est : np.ndarray + Background field values at estimation sites (vector of size "estimation stations"). + precalcs : dict + Additional arguments and state information for the interpolation process, to accelerate calculations between timesteps. + + Returns + ------- + v_est : np.ndarray + Estimated values at the estimation sites (vector of size "estimation stations"). + var_est : np.ndarray + Estimated variance at the estimation sites (vector of size "estimation stations"). + precalcs : dict + Additional arguments and state information for the interpolation process, to accelerate calculations between timesteps. + This variable returns the pre-calculated distance matrices. + """ + # Number of simulation stations + estimated_count = len(bg_est) + + # Number of observed stations + observed_count = len(bg_var_obs) + + # This block's entire purpose is to skip calculating distances when not necessary. If the input points and the + # simulation points are the same as the previous time step (same NaN positions, so same stations contributing), then + # simply load the distance matrix that was computed at the previous timestep. If it did change, we need to + # recompute, and save it for the next iteration. + cond = False + if isinstance(precalcs, dict): + if "lat_obs" in precalcs: + cond = ( + np.array_equal(precalcs["lat_obs"], lat_obs) + and np.array_equal(precalcs["lon_obs"], lon_obs) + and np.array_equal(precalcs["lat_est"], lat_est) + and np.array_equal(precalcs["lon_est"], lon_est) + ) + + # Depending on the status of the "cond" flag, either use the precalculated values or recalculate them. + if cond: + distance_obs_vs_obs = precalcs["distance_obs_obs"] + distance_obs_vs_est = precalcs["distance_obs_vs_est"] + else: + # Not computed, so calculate and update the precalcs dict for later usage. + observation_latlong = list(zip(lat_obs, lon_obs, strict=True)) + distance_obs_vs_obs = haversine.haversine_vector(observation_latlong, observation_latlong, comb=True) + + # Also recompute the distance matrix between observation and estimation sites. + simulation_latlong = list(zip(lat_est, lon_est, strict=True)) + distance_obs_vs_est = haversine.haversine_vector(observation_latlong, simulation_latlong, comb=True) + + # And store for later + precalcs["distance_obs_obs"] = distance_obs_vs_obs + precalcs["lat_obs"] = lat_obs + precalcs["lon_obs"] = lon_obs + precalcs["distance_obs_vs_est"] = distance_obs_vs_est + precalcs["lat_est"] = lat_est + precalcs["lon_est"] = lon_est + + # Start doing the actual optimal interpolation math. "b" = background field variables; "o" = observations. + covariance_obs_vs_obs = ecf(distance_obs_vs_obs) / ecf(0) + + # Background error at observation site + beo_j = np.tile(bg_var_obs, (observed_count, 1)) + beo_i = beo_j.T + + # Background error covariance matrix at observation site + b_ij = covariance_obs_vs_obs * np.sqrt(beo_j) / np.sqrt(beo_i) + + # Observation error at observation site + o_eo_j = np.tile(var_obs, (observed_count, 1)) + o_eo_i = o_eo_j.T + + # Observation error covariance matrix + o_ij = (np.sqrt(o_eo_j) * np.sqrt(o_eo_i)) * np.eye(len(o_eo_j)) / beo_i + + # Background error at estimation site + b_e_e = np.tile(np.resize(bg_var_est, (1, observed_count)), (estimated_count, 1)) + b_e_o = np.tile(bg_var_obs, (estimated_count, 1)) + + # Data to estimation site covariance + c_oe = ecf(distance_obs_vs_est) / ecf(0) + + # Background error covariance matrix at estimation site + b_ei = c_oe * (np.sqrt(b_e_e) / np.sqrt(b_e_o)) + + # Matrix "I" for departures. + departures = np.tile(bg_departures[:, np.newaxis], (1, estimated_count)) + + # Get weights for each contributing station according to their covariance. + weights = np.linalg.solve(b_ij + o_ij, b_ei.T) + + # Get value estimation by adding the background estimation and adding the weighted average of expected departures. + v_est = bg_est + np.sum(weights * departures, axis=0) + + # Variance analysis for each estimated station based on weighted covariance. + weighted_b_ei = np.diagonal(np.matmul(b_ei, weights)) + var_est = bg_var_est * (1 - weighted_b_ei) + + return v_est, var_est, precalcs + + +def optimal_interpolation_operational_control( + estimated_precip_reshaped, + difference, + lat_obs, + lon_obs, + lat_est, + lon_est, + percentiles: list[float] | None, + ratio_var_bg: float, + ecf_fun: partial, + par_opt: list, +): + """ + Apply optimal interpolation to the entire domain for the selected time range. + + Parameters + ---------- + estimated_precip_reshaped : xr.Dataset + The dataset containing observed and simulated precipitation along with locations. Used + to calculate deviations between observation stations and the simulated (background field) values at those + locations. + difference : xr.Dataset + The dataset containing the simulated stations where we want to apply the optimal interpolation results. This is + the full background field, and is usually the complete simulated precipitation domain. + lat_obs : np.ndarray + Vector of latitudes of the observation stations. + lon_obs : np.ndarray + Vector of longitudes of the observation stations. + lat_est : np.ndarray + Vector of latitudes of the estimation/simulation stations to be estimated in the background field. + lon_est : np.ndarray + Vector of longitudes of the estimation/simulation stations to be estimated in the background field. + percentiles : array-like + The percentiles that we want to extract from the optimal interpolation at each station and timestep. + ratio_var_bg : float + The ratio of the observation variance to that of the background field (estimated). + ecf_fun : partial + The partial function related to the Error Covariance Function model that estimates error covariance as a + function of distance. + par_opt : array-like + The optimized parameters for the ecf_fun partial function. + + Returns + ------- + ndarray + An array containing the quantiles of the precipitation values for each percentile over the specified time range. + """ + # Set a default flow percentile to evaluate if none are provided. Median is used as the most likely to be useful. + if percentiles is None: + percentiles = [50.0] + + # Process data from the observations/simulations corresponding dataset + time_range = difference.shape[0] + + # Process data from the background simulation field (complete background field) + station_count = len(lat_est) + + # Get the simulated values at the estimated points, which also includes the observation locations. + vsim_at_est = estimated_precip_reshaped + + # Define the vector of precipitation quantiles. We compute one value per time step and per percentile as requested + # by user. + precipitation_quantiles = np.array([np.empty((time_range, station_count)) * np.nan] * len(percentiles)) + + # Object with the arguments to the OI that is passed along at each time step for calculations from previous steps + # and updated to save computation time. Starts empty but will be updated for each time range later. + precalcs = {} + + # For each timestep, build the interpolator and apply to the estimated locations (i.e. all background field points). + for j in range(time_range): + print("Interpolating for timestep: " + str(j)) + + # Get the values for the current day and identify which are not NaN. + val = difference[j, :] + idx = ~np.isnan(val) + + # Apply the interpolator and get outputs + v_est, var_est, precalcs = optimal_interpolation( + lat_obs=lat_obs[idx], + lon_obs=lon_obs[idx], + lat_est=lat_est, + lon_est=lon_est, + ecf=partial(ecf_fun, par=par_opt), + bg_var_obs=np.ones(idx.sum()), + bg_var_est=np.ones(len(lon_est)), + var_obs=np.ones(idx.sum()) * ratio_var_bg, + bg_departures=difference[j, idx], + bg_est=vsim_at_est[j, :], + precalcs=precalcs, + ) + + # Get variance properties + var_bg = np.var(difference[j, idx]) + var_est = var_est * var_bg + + # Correct values below zero + v_est[v_est < 0] = 0 + + # For all stations, we need to compute the percentiles and un-log-transform the log transformation of + # precipitation. + for stat in range(0, len(v_est)): + # Get the percentile values for each desired percentile. + vals = norm.ppf( + np.array(percentiles) / 100.0, + loc=v_est[stat], + scale=np.sqrt(var_est[stat]), + ) + + for k in range(0, len(percentiles)): + precipitation_quantiles[:, j, stat] = vals[k] + + # return the precipitation quantiles as desired. + return precipitation_quantiles + + +def prepare_initial_data( + filename_stations: str, + filename_gridded: str, + start_time: dt.datetime, + end_time: dt.datetime, + frac_validation: float, + do_cross_validation: bool, + grid_resolution: float, + var_name_gridded: str, + var_name_stations: str, + dims_gridded: tuple[str, str, str], + dims_stations: str, + coords_gridded: tuple[str, str, str], + station_req_vars: tuple[str, str, str], +) -> tuple[ndarray, ndarray, list[float], list[float], list[float], list[float], list[float], list[float], ndarray, list[int], ndarray, Dataset]: + """ + Perform the initial data processing steps to get data ready for the rest of the process according to user needs. + + Parameters + ---------- + filename_stations : str + The path and name of the file that contains the stations (observations) data. Must be a netcdf file. + filename_gridded : str + The path and name of the file that contains the estimated (background) data. Must be a netcdf file. + start_time : dt.datetime + The start date of the optimal interpolation period. + end_time : dt.datetime + The end date of the optimal interpolation period. + frac_validation : float | None + The fraction of stations to use for cross-validation, independent of the training data. Between 0 and 1. + do_cross_validation : bool + A flag to indicate that the user wants to perform a cross-validation step to assess the method's performance. + grid_resolution : float + Resolution of the gridded product, for rounding purposes. + var_name_gridded : str + Name of the meteo variable (i.e. precipitation) in the gridded dataset. + var_name_stations : str + Name of the meteo variable (i.e. precipitation) in the stations dataset. + dims_gridded : Tuple[str, str, str] + The three variable names that should be in the dataset, corresponding to latitude, longitude and time. For this + package we are expecting "latitude", "longitude", and "time". + dims_stations : str + The name of the dimensions for the station data file. Should be "station" or "number" or some other integer- + based ID. + coords_gridded : Tuple[str, str, str] + The coordinates of the gridded xr.Dataset that must be present, corresponding to latitude, longitude and time. + For this package we are expecting "latitude", "longitude", and "time". + station_req_vars : Tuple[str, str, str] + The required variables in the station Dataset along with the precipitation values. These correspond to the + latitude, longitude and altitude of stations. + + Returns + ------- + departures_train: np.array + Differences between observation stations and simulations at the observation station locations, for training + stations. + departures_valid: np.array + Differences between observation stations and simulations at the observation station locations, for validation + stations. + lat_obs_train: array-like + Latitude of the observation stations for the training dataset. + lon_obs_train: array-like + Longitude of the observation stations for the training dataset. + lat_obs_valid: array-like + Latitude of the observation stations for the validation dataset. + lon_obs_valid: array-like + Longitude of the observation stations for the validation dataset. + lat_est: array-like + Latitude of the estimated gridpoints (complete grid). + lon_est: array-like + Longitude of the estimated gridpoints (complete grid). + estimated_precip_reshaped: np.array + Estimated precipitation in a reshaped matrix such that it is compatible with the interpolator requirements. + original_shape: list[int] + Original shape of the estimated precipitation grid, to be able to plot it as a grid later. + observed_precip_valid: np.array + Observed precipitation for the validation set, used to compute evaluation metrics for cross-validation. + ds_gridded: Dataset + The original gridded dataset, loaded and subset for the correct time. Also used later for plotting in + cross-validation. + """ + # This first section processes the observation stations + # Read the station data. + check_netcdf_layout_stations( + nc_path=filename_stations, + time_dim="time", + required_station_dim=dims_stations, + required_precip_var=var_name_stations, + required_station_vars=station_req_vars, + ) + ds_stations_full = xr.open_dataset(filename_stations) + ds_stations_full = ds_stations_full.sel(time=slice(start_time, end_time)) + + # For cross validation, select a fraction of weather stations that we will keep for later. + number_stations = ds_stations_full.latitude.shape[0] + list_stations = np.arange(0, number_stations) + + # If we want to do cross-validation to evaluate the OI performance, we need to split into a training and a + # validation set. + # Shuffle the indices of the stations to select the training and validation stations at random + np.random.shuffle(list_stations) + valid_idx = list_stations[0 : round(number_stations * frac_validation)] + + # Make sure the user selected consistent options. We do not default to one or the other. The options must not + # conflict. + if (len(valid_idx) == 0) and do_cross_validation: + raise ( + Exception( + "Fraction of cross-validation stations is too low, no stations would be selected. Please " + "increase the cross-validation fraction or set cross-validation to False." + ) + ) + if (len(valid_idx) > 0) and not do_cross_validation: + raise ( + Exception( + "The fraction of cross-validation stations to use is not 0, but the user selected not to do " + "cross-validation. Please set do_cross_validation to True or set fraction of cross validation " + "stations to 0." + ) + ) + + # At this point, either we have: + # a. Empty valid_idx and do_cross_validation = False + # b. Some stations in valid_idx and do_cross_validation = True. + # Therefore, validation variables will be empty if there is no cross-validation but the code will still run without + # error. + + # Continue the process. Extract the training station indices. + train_idx = list_stations[round(number_stations * frac_validation) :] + + # Save the IDs of the validation and training stations for future reference + np.savetxt("./validation_stations.txt", valid_idx) + np.savetxt("./training_stations.txt", train_idx) + + # Extract the training stations and valid stations in the 2 different datasets + ds_stations_train = ds_stations_full.isel(watershed=train_idx) + ds_stations_valid = ds_stations_full.isel(watershed=valid_idx) + + # prepare lat and long values for observations + lat_obs_train = ds_stations_train.latitude.values + lon_obs_train = ds_stations_train.longitude.values + lat_obs_valid = ds_stations_valid.latitude.values + lon_obs_valid = ds_stations_valid.longitude.values + + # Get the precipitation values from the station data + observed_precip_train = ds_stations_train.precip.values + observed_precip_valid = ds_stations_valid.precip.values + + # Process the gridded data in this section. + # Read the background field data and ensure the format is correct and contains the desired variables. + check_netcdf_layout_gridded( + nc_path=filename_gridded, + var_name=var_name_gridded, + required_dims=dims_gridded, + required_coords=coords_gridded, + ) + + ds_gridded = xr.open_dataset(filename_gridded) + ds_gridded = ds_gridded.transpose("time", "longitude", "latitude") + ds_gridded = ds_gridded.sel(time=slice(start_time, end_time)) + + # Prepare lat and long values for background field/estimator + lat_est = ds_gridded.latitude.values + lon_est = ds_gridded.longitude.values + + # Prepare the latitudes and longitudes rounded to the nearest resolution unit to + # eliminate any machine-precision errors. Will depend on the product! + if grid_resolution == 0.1: + lat_est = np.round(lat_est, 1) + lon_est = np.round(lon_est, 1) + elif grid_resolution == 0.25: + lat_est = np.round(np.round(lat_est * 4, 0) / 4, 2) + lon_est = np.round(np.round(lon_est * 4, 0) / 4, 2) + else: + ValueError("Grid resolutions are currently restricted to 0.1° or 0.25°.") + + # Make grid from latlong vectors + lon_est, lat_est = np.meshgrid(lon_est, lat_est) + + # Transpose and extract data + estimated_precip = ds_gridded.tp.transpose("latitude", "longitude", "time").values + + # Flatten the dataset to vector form + original_shape = lat_est.shape + lat_est = lat_est.flatten("C") + lon_est = lon_est.flatten("C") + + # Still has 2D: all points in a line, all timesteps in columns. + estimated_precip_reshaped = estimated_precip.reshape(original_shape[0] * original_shape[1], -1) + + # Now calculate departures (error) between the stations and the background field for each day and station. + # Preallocate the departures vector, for corresponding observations and grid points + departures_train = np.empty((len(lat_obs_train), observed_precip_train.shape[1])) + departures_valid = np.empty((len(lat_obs_valid), observed_precip_valid.shape[1])) + + # Calculate departures for the training set + for station in range(0, len(lat_obs_train)): + pos = find_position_of_observation_in_vectorized_grid(lat_obs_train[station], lon_obs_train[station], lat_est, lon_est) + departures_train[station, :] = observed_precip_train[station, :] - estimated_precip_reshaped[pos, :] + + # Calculate departures for the validation set + for station in range(0, len(lat_obs_valid)): + pos = find_position_of_observation_in_vectorized_grid(lat_obs_valid[station], lon_obs_valid[station], lat_est, lon_est) + departures_valid[station, :] = observed_precip_valid[station, :] - estimated_precip_reshaped[pos, :] + + return ( + departures_train, + departures_valid, + lat_obs_train, + lon_obs_train, + lat_obs_valid, + lon_obs_valid, + lat_est, + lon_est, + estimated_precip_reshaped, + original_shape, + observed_precip_valid, + ds_gridded, + ) + + +def correction( + difference: np.ndarray, + centroid_lon_obs: np.ndarray, + centroid_lat_obs: np.ndarray, + variogram_bins: int = 10, + form: int = 1, + hmax_divider: float = 2.0, + p1_bnds: list | None = None, + hmax_mult_range_bnds: list | None = None, +) -> tuple: + """ + Perform correction on flow observations using optimal interpolation. + + Parameters + ---------- + difference : np.ndarray + A 2D array of differences for all stations over all time periods [nstat x time]. + centroid_lon_obs : np.ndarray + Longitude vector of the catchment centroids for the observed stations. + centroid_lat_obs : np.ndarray + Latitude vector of the catchment centroids for the observed stations. + variogram_bins : int, optional + Number of bins to split the data to fit the semi-variogram for the ECF. Defaults to 10. + form : int + The form of the ECF equation to use (1, 2, 3 or 4. See Notes below). + hmax_divider : float + Maximum distance for binning is set as hmax_divider times the maximum distance in the input data. Defaults to 2. + p1_bnds : list, optional + The lower and upper bounds of the parameters for the first parameter of the ECF equation for variogram fitting. + Defaults to [0.95, 1.0]. + hmax_mult_range_bnds : list, optional + The lower and upper bounds of the parameters for the second parameter of the ECF equation for variogram fitting. + It is multiplied by "hmax", which is calculated to be the threshold limit for the variogram sill. + Defaults to [0.05, 3.0]. + + Returns + ------- + tuple + A tuple containing the following: + - ecf_fun: Partial function for the error covariance function. + - par_opt: Optimized parameters for the interpolation. + + Notes + ----- + The possible forms for the ecf function fitting are as follows: + Form 1 (From Lachance-Cloutier et al. 2017; and Garand & Grassotti 1995) : + ecf_fun = par[0] * (1 + h / par[1]) * np.exp(-h / par[1]) + Form 2 (Gaussian form) : + ecf_fun = par[0] * np.exp(-0.5 * np.power(h / par[1], 2)) + Form 3 : + ecf_fun = par[0] * np.exp(-h / par[1]) + Form 4 : + ecf_fun = par[0] * np.exp(-(h ** par[1]) / par[0]) + """ + # Number of timesteps. If we have more than 1 timestep, we can use the mean climatological variogram later. + difference = difference.T + time_range = difference.shape[0] + + # Preallocate matrices for all timesteps for the heights of the histograms, the covariances and standard deviations + # of the values within each bin of the histogram. + heights = np.empty((time_range, variogram_bins)) * np.nan + covariances = np.empty((time_range, variogram_bins)) * np.nan + standard_deviations = np.empty((time_range, variogram_bins)) * np.nan + + # Ensure we have some bounds by default in case it is missed. + if p1_bnds is None: + p1_bnds = [0.95, 1] + if hmax_mult_range_bnds is None: + hmax_mult_range_bnds = [0.05, 3] + + # Pairwise distance between all observation stations. + observation_latlong = list(zip(centroid_lat_obs, centroid_lon_obs, strict=True)) + distance = haversine.haversine_vector(observation_latlong, observation_latlong, comb=True) + + # If there is more than 1 time step, we need to do a climatological mean ECF. + if time_range > 1: + # For each timestep, we will compute the histogram bins and other data required to provide the data for the ECF + # function optimizer. + for i in range(time_range): + # Check for NaN observed streamflow data points (if difference is NaN, necessarily obs is NaN. But in case a + # sim also provides a NaN, then take the difference instead). + is_nan = np.isnan(difference[i, :]) + + # Calculate the error for this particular day and remove NaN days. + day_diff = difference[i, ~is_nan] + day_diff = day_diff + np.random.rand(day_diff.shape[0]) / np.power(10, 5) + + # If there are at least as many stations worth of data as there are required bins, we can compute the + # histogram. + if len(day_diff) >= variogram_bins: + # Get the stations that did not have NaN observations. Since the matrix is 2D due to pairwise distances, + # need to remove rows and columns of NaN-stations from the distance matrix distance_pc. + distance_pc = np.delete(distance, is_nan, axis=0) + distance_pc = np.delete(distance_pc, is_nan, axis=1) + + # Sanity check: length of distance_pc should be equal to day_diff. + if len(day_diff) != distance_pc.shape[0]: + raise AssertionError("day_diff not equal to the size of distance_pc in histogram bin definition.") + + # Sort the data into bins and get their stats. + h_b, cov_b, std_b, num_p = eval_covariance_bin( + distances=distance_pc, + values=day_diff, + hmax_divider=hmax_divider, + variogram_bins=variogram_bins, + ) + + # If there are at least "variogram_bins" number of bins, then add it to the results matrix + if len(num_p[0]) >= variogram_bins: + heights[i, :] = h_b[0, 0 : variogram_bins + 1] + covariances[i, :] = cov_b[0, 0 : variogram_bins + 1] + standard_deviations[i, :] = std_b[0, 0 : variogram_bins + 1] + + # The histogram bins for each day have been calculated. Now is time to prepare the statistics overall for the + # ECF function fitting for the semi-variogram for the number of days (i.e. weighted average of climatology). + # This first function reformats the data according to the timestep and computes the weighted average histograms. + distance, covariance, covariance_weights, valid_heights = initialize_stats_variables( + heights, covariances, standard_deviations, variogram_bins + ) + + # And this second part does the binning of the histogram as was done before for all days. + h_b, cov_b, std_b = calculate_ecf_stats(distance, covariance, covariance_weights, valid_heights) + + else: + # Just compute the covariance bin as a one-shot deal + h_b, cov_b, std_b, num_p = eval_covariance_bin( + distances=distance, + values=np.squeeze(difference), + hmax_divider=hmax_divider, + variogram_bins=variogram_bins, + ) + + # Calculate the real maximum distance for the covariance estimation. + hmax = max(np.reshape(distance, (-1, 1))) / hmax_divider + + # This determines the shape of the fit that we want the optimizer to fit to the correlation variogram. + ecf_fun = partial(general_ecf, form=form) + + # Weight according to the inverse of the variance of each bin and then normalize them + weights = 1 / np.power(std_b, 2) + weights = weights / np.sum(weights) + + # Define the objective function used for the ECF function training. + def _rmse_func(par): + # Compute the RMSE of the fit between the observations and variogram fit according to the ecf_fun chosen. + return np.sqrt(np.mean(weights * np.power(ecf_fun(h=h_b, par=par) - cov_b, 2))) + + # Perform the training using the bounds for the parameters as passed by the users before. + par_opt = minimize( + _rmse_func, + x0=[np.mean(cov_b), np.mean(h_b) / 3], + bounds=( + [p1_bnds[0], p1_bnds[1]], + [hmax_mult_range_bnds[0] * hmax, hmax_mult_range_bnds[1] * hmax], + ), + )["x"] + + # Return the fitting function as determined by the user and the optimal calibrated parameter set. + return ecf_fun, par_opt + + +def calculate_ecf_stats( # noqa: N802 + distance: np.ndarray, + covariance: np.ndarray, + covariance_weights: np.ndarray, + valid_heights: np.ndarray, +) -> tuple[np.ndarray, np.ndarray, np.ndarray]: + """ + Calculate statistics for Empirical Covariance Function (ECF), climatological version. + + Uses the histogram data from all previous days and reapplies the same steps, but inputs are of size (timesteps x + variogram_bins). So if we use many days to compute the histogram bins, we get a histogram per day. This function + generates a single output from a new histogram. + + Parameters + ---------- + distance : np.ndarray + Array of distances. + covariance : np.ndarray + Array of covariances. + covariance_weights : np.ndarray + Array of weights for covariances. + valid_heights : np.ndarray + Array of valid heights. + + Returns + ------- + tuple[np.ndarray, np.ndarray, np.ndarray] + A tuple containing the following: + - h_b: Array of mean distances for each height bin. + - cov_b: Array of weighted average covariances for each height bin. + - std_b: Array of standard deviations for each height bin. + """ + valid_heights_count = len(valid_heights) + + # Create the empty arrays for the covariance, height and standard_deviation matrices for the correct number of bins + # (This is valid_heights_count -1) + cov_b = np.zeros(valid_heights_count - 1) + h_b = np.zeros(valid_heights_count - 1) + std_b = np.zeros(valid_heights_count - 1) + + # For each bin, get and aggregate the data that fits into that bin. + for i in range(valid_heights_count - 1): + # Find the indices of the data that need to go into that bin + ind = np.where((distance >= valid_heights[i]) & (distance < valid_heights[i + 1])) + + # Compute the mean distance of points in that bin + h_b[i] = np.mean(distance[ind]) + + # Get the weights for that bin + weight = covariance_weights[ind] / np.sum(covariance_weights[ind]) + + # Get the covariance, weighted average of the covariance + cov_b[i] = np.sum(weight * covariance[ind]) + average = np.average(covariance[ind], weights=weight) + + # Get the weighted average of the covariance error field + variance = np.average((covariance[ind] - average) ** 2, weights=weight) + + # Get the standard deviation of the error field + std_b[i] = np.sqrt(variance) + + return h_b, cov_b, std_b + + +def eval_covariance_bin( + distances: np.ndarray, + values: np.ndarray, + hmax_divider: float = 2.0, + variogram_bins: int = 10, +) -> tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]: + """ + Evaluate the covariance of a binomial distribution. + + Parameters + ---------- + distances : np.ndarray + Array of distances for each data point. + values : np.ndarray + Array of values corresponding to each data point. + hmax_divider : float + Maximum distance for binning is set as hmax_divider times the maximum distance in the input data. Defaults to 2. + variogram_bins : int, optional + Number of bins to split the data to fit the semi-variogram for the ECF. Defaults to 10. + + Returns + ------- + tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray] + Arrays for heights, covariance, standard deviation, row length. + """ + # Step 1: Calculate weights based on errors + weights = np.power(1 / np.ones(len(values)), 2) + weights = weights / np.sum(weights) + + # Step 2: Calculate weighted average and variances + weighted_average = np.sum(values * weights) / np.sum(weights) + variances = np.var(values, ddof=1) + + # Step 3: Calculate covariance matrix + weighted_values = values - weighted_average + covariance = weighted_values * weighted_values[:, np.newaxis] + covariance_weight = weights * weights[:, np.newaxis] + + # Flatten matrices for further processing and binning + covariance = covariance.reshape(len(values) * len(values)) + covariance_weight = covariance_weight.reshape(len(values) * len(values)) + distances = distances.reshape(len(distances) * len(distances)) + + # Step 4: Apply distance threshold (hmax) for binning. Keep only those catchments that are less than + # hmax/hmax_divider. + hmax = max(distances) / hmax_divider + covariance = covariance[distances < hmax] + distances = distances[distances < hmax] + + # Step 5: Define quantiles for binning + quantiles = np.linspace(0.0, 1.0, num=variogram_bins + 1) + + # Step 6: Get the edge values of each bin / class, based on the unraveled distance vector (timesteps x stations) + cl = np.unique(np.quantile(distances, quantiles)) + + # Initialize arrays for results, for all data that will go into each bin. Using the final bins after the unique + # function in case of many values in the same bin (ex. zeros), so len(cl)-1 = number of actual bins (because + # cl are edges). + returned_covariance = np.empty((1, len(cl) - 1)) * np.nan + returned_heights = np.empty((1, len(cl) - 1)) * np.nan + returned_standard = np.empty((1, len(cl) - 1)) * np.nan + returned_row_length = np.empty((1, len(cl) - 1)) * np.nan + + # Step 6: Iterate over distance bins. + for i in range(0, len(cl) - 1): + # For each bin (between edges), find all distance values falling in this bin. + ind = np.where((distances >= cl[i]) & (distances < cl[i + 1]))[0] + + # Take the mean value of all distances values within the bin. + returned_heights[:, i] = np.mean(distances[ind]) + # Take the covariance weights and covariance values of stations in the bin + selected_covariance_weight = covariance_weight[ind] + selected_covariance = covariance[ind] + + # Step 7: Calculate covariance, standard deviation, and row length + weight = selected_covariance_weight / np.sum(selected_covariance_weight) + + # Compute the weighted covariance within the bin + returned_covariance[:, i] = ( + np.sum(weight) / (np.power(np.sum(weight), 2) - np.sum(np.power(weight, 2))) * np.sum(weight * selected_covariance) + ) / variances + + # Get the standard variation of the covariances of stations in the bin + returned_standard[:, i] = np.sqrt(np.var(selected_covariance)) + + # Also get the number of stations within that bin. + returned_row_length[:, i] = len(ind) + + # Step 8: Return the final results as a tuple + return returned_heights, returned_covariance, returned_standard, returned_row_length + + +def initialize_stats_variables( + heights: np.ndarray, + covariances: np.ndarray, + standard_deviations: np.ndarray, + variogram_bins: int = 10, +) -> tuple: + """ + Initialize variables for statistical calculations in an Empirical Covariance Function (ECF). + + Parameters + ---------- + heights : np.ndarray + Array of heights. + covariances : np.ndarray + Array of covariances. + standard_deviations : np.ndarray + Array of standard deviations. + variogram_bins : int + Number of bins to split the data to fit the semi-variogram for the ECF. Defaults to 10. + + Returns + ------- + tuple + A tuple containing the following: + - distance: Array of distances. + - covariance: Array of covariances. + - covariance_weights: Array of weights for covariances. + - valid_heights: Array of valid heights. + """ + quantiles = np.linspace(0.0, 1.0, variogram_bins + 1) + valid_heights = np.unique(np.quantile(heights[~np.isnan(heights)], quantiles)) + + distance = heights.T.reshape(len(heights) * len(heights[0])) + covariance = covariances.T.reshape(len(covariances) * len(covariances[0])) + covariance_weights = 1 / np.power( + standard_deviations.T.reshape(len(standard_deviations) * len(standard_deviations[0])), + 2, + ) + + return distance, covariance, covariance_weights, valid_heights + + +def main( + start_time: dt.datetime, + end_time: dt.datetime, + filename_stations: str, + filename_gridded: str, + filename_output: str, + grid_resolution: float, + var_name_gridded: str, + var_name_stations: str, + dims_gridded: tuple[str, str, str], + dims_stations: str, + coords_gridded: tuple[str, str, str], + station_req_vars: tuple[str, str, str], + percentiles: list[float] | None, + p1_bnds: list[float] | None, + hmax_mult_range_bnds: list[float] | None, + var_bg_ratio: float | None = 0.15, + variogram_bins: int | None = 10, + hmax_divider: float | None = 2.0, + ecf_form: int = 1, + do_cross_validation: bool = True, + frac_validation: float | None = 0.20, +): + """ + Main optimal interpolation access point and controller. + + Parameters + ---------- + start_time : dt.datetime + The start date of the optimal interpolation period. + end_time : dt.datetime + The end date of the optimal interpolation period. + filename_stations : str + The path and name of the file that contains the stations (observations) data. Must be a netcdf file. + filename_gridded : str + The path and name of the file that contains the estimated (background) data. Must be a netcdf file. + filename_output : str + The path and name of the file that will be output, containing the processed optimal interpolation. Must be a + netcdf file. + grid_resolution : float + Resolution of the gridded product, for rounding purposes. + var_name_gridded : str + Name of the meteo variable (i.e. precipitation) in the gridded dataset. + var_name_stations : str + Name of the meteo variable (i.e. precipitation) in the stations dataset. + dims_gridded : Tuple[str, str, str] + The three variable names that should be in the dataset, corresponding to latitude, longitude and time. For this + package we are expecting "latitude", "longitude", and "time". + dims_stations : str + The name of the dimensions for the station data file. Should be "station" or "number" or some other integer- + based ID. + coords_gridded : Tuple[str, str, str] + The coordinates of the gridded xr.Dataset that must be present, corresponding to latitude, longitude and time. + For this package we are expecting "latitude", "longitude", and "time". + station_req_vars : Tuple[str, str, str] + The required variables in the station Dataset along with the precipitation values. These correspond to the + latitude, longitude and altitude of stations. + percentiles : list[float] | None + The percentiles of the distribution to sample after generating the optimal interpolation. + p1_bnds : list[float] | None + Bounds of the parameter p1 in the ECF function. + hmax_mult_range_bnds : list[float] | None + Bounds of the hmax parameter in the ECF function. + var_bg_ratio : float | None + Variance ratio of the background field (estimated gridpoints). + variogram_bins : int | None + Number of bins to categorize data to build the ECF. Needs to be scaled such that each bin has a sufficient number + of data points. + hmax_divider : float | None + Parameter that divides the hmax distance to know how far to look for station covariance. Higher means a smaller + range. + ecf_form : int + Form of the ECF fitting equation. Can be between 1 and 4. Use trial and error to determine the best empirical + fit. See notes below for more details. + do_cross_validation : bool + A flag to indicate that the user wants to perform a cross-validation step to assess the method's performance. + frac_validation : float | None + The fraction of stations to use for cross-validation, independent of the training data. Between 0 and 1. + + Notes + ----- + The possible forms for the ecf function fitting are as follows: + Form 1 (From Lachance-Cloutier et al. 2017; and Garand & Grassotti 1995) : + ecf_fun = par[0] * (1 + h / par[1]) * np.exp(-h / par[1]) + Form 2 (Gaussian form) : + ecf_fun = par[0] * np.exp(-0.5 * np.power(h / par[1], 2)) + Form 3 : + ecf_fun = par[0] * np.exp(-h / par[1]) + Form 4 : + ecf_fun = par[0] * np.exp(-(h ** par[1]) / par[0]) + """ + # Initialize variables if not provided + if percentiles is None: + percentiles = [50] + + if p1_bnds is None: + p1_bnds = [0.95, 1.0] + + if hmax_mult_range_bnds is None: + hmax_mult_range_bnds = [0.05, 3] + + # Prepare all the initial data for cross-validation + ( + departures_train, + departures_valid, + lat_obs_train, + lon_obs_train, + lat_obs_valid, + lon_obs_valid, + lat_est, + lon_est, + estimated_precip_reshaped, + original_shape, + observed_precip_valid, + ds_gridded, + ) = prepare_initial_data( + filename_stations, + filename_gridded, + start_time, + end_time, + frac_validation, + do_cross_validation, + grid_resolution, + var_name_gridded, + var_name_stations, + dims_gridded, + dims_stations, + coords_gridded, + station_req_vars, + ) + + # create the weighting function parameters using climatological errors (i.e. over many timesteps) + ecf_fun, par_opt = correction( + difference=departures_train, + centroid_lon_obs=lon_obs_train, + centroid_lat_obs=lat_obs_train, + variogram_bins=variogram_bins, + form=ecf_form, + hmax_divider=hmax_divider, + p1_bnds=p1_bnds, + hmax_mult_range_bnds=hmax_mult_range_bnds, + ) + + # Do the actual implementation of optimal interpolation and return the estimated precipitation percentiles at all + # grid cells of the background field. + precip_percentiles = optimal_interpolation_operational_control( + estimated_precip_reshaped.T, + difference=departures_train.T, + lat_obs=lat_obs_train, + lon_obs=lon_obs_train, + lat_est=lat_est, + lon_est=lon_est, + percentiles=percentiles, + ratio_var_bg=var_bg_ratio, + ecf_fun=ecf_fun, + par_opt=par_opt, + ) + + # Save results before going any further. This is an intensive computation so saving results before processing is + # recommended. + # Generate time vector from start and end dates. + time_list = pd.date_range(start_time, end_time) + + # Create the final dataset that cab be used in other processes at a later time. + ds_final = xr.Dataset( + { + "tp": ( + ("percentile", "time", "latitude", "longitude"), + precip_percentiles.reshape(len(percentiles), len(time_list), original_shape[0], original_shape[1]), + ) + }, + coords={ + "percentile": percentiles, + "time": pd.date_range(start_time, end_time), + "latitude": ds_gridded.latitude, + "longitude": ds_gridded.longitude, + }, + ) + ds_final.to_netcdf(filename_output) + + # Now let's evaluate how good the optimal-interpolation gridded product is on the validation set. + if do_cross_validation: + # For testing purposes, select a percentile value. We only have 1 here (50th) and + # it occupies the 1st (and only) element in the 1st dimension. Extract all values + # for this percentile. + precip_medians = precip_percentiles[0, :, :].T + + # Calculate some indices and RMSE values + cv.evaluate_cross_validation(observed_precip_valid, estimated_precip_reshaped, precip_medians, lat_obs_valid, lon_obs_valid, lat_est, lon_est) + + # Plot them for quick analysis + cv.plot_cross_validation_rmse_results(filename_stations) diff --git a/tests/ERA5_land_3_variables_raw_subset.nc b/tests/ERA5_land_3_variables_raw_subset.nc new file mode 100644 index 0000000000000000000000000000000000000000..261935acae6917e8d39afe598757688254a138be GIT binary patch literal 3958512 zcmeFacT^P1+o;=sAR;Ir5)6m}3PwOwnCY(fEkp!FM1mMlK{249sDPMVfLTCM zF@uU?WK0+^V9tmU#e^9X+?l3ef7|{2zIDz$>)!Lv?zNqVs_Lq)sj7auy1HlWWLIYw z9jz8xs+yWy-B!c4%CWo{Wy2B-`gLABz}4AXReQf`J26hJE>m5WKdGh4sVMi<)m46; 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zDh>Qh8sKvC*^9p1{Ox62YrLM9o41^Gxw%aAjg{6;SyytsdGlG;n?{XQD5)>%f^&%o z^3=h<-g?#r=M%C+2us|HwcwO3M+k=JT5vwJqPPJ4tC5#_Xn_Cwq8s2JFK=&vJ+Gtv z&UG}v9&TU`jg3rBgv|?D2GiS*EgH5s9d<-DrMq`{aI7{lDO;TbW3}PY;YWBiGFIC^ zJUM)D0y`yae$Kj68XVPal^8C~=wj@YdPKyR{_N|g&uX||bgt*38t!7L6~XXA4foU) zMMHjn_sTEOkcTh2A-{Y{dqeJi9T~Ei3^wi;XLJ1q>A3N4ta$mXCi7M2-f&S(1|Al{ T@b7CfU%jemLK`3Xt5^Rolq{vr literal 0 HcmV?d00001 diff --git a/tests/test_precip_oi.py b/tests/test_precip_oi.py new file mode 100644 index 00000000..ac4b7afe --- /dev/null +++ b/tests/test_precip_oi.py @@ -0,0 +1,34 @@ +import datetime as dt + +import xhydro.optimal_interpolation.optimal_interpolation_precip as oi + + +start_time = dt.datetime(1970, 1, 1) +end_time = dt.datetime(1970, 12, 31) +filename_stations = "./stations_precip_DQAQ_ECCC_US_subset.nc" +filename_gridded = "./ERA5_land_3_variables_raw_subset.nc" +filename_output = "./ERA5Land_with_OI_flags_validation_subset.nc" + +oi.main( + start_time=start_time, + end_time=end_time, + filename_stations=filename_stations, + filename_gridded=filename_gridded, + filename_output=filename_output, + grid_resolution=0.1, + var_name_gridded="tp", + var_name_stations="precip", + dims_gridded=("longitude", "latitude", "time"), + dims_stations="watershed", + coords_gridded=("time", "latitude", "longitude"), + station_req_vars=("latitude", "longitude", "altitude"), + percentiles=[50], + p1_bnds=[0.95, 1.0], + hmax_mult_range_bnds=[0.05, 3], + var_bg_ratio=0.15, + variogram_bins=10, + hmax_divider=2.0, + ecf_form=1, + do_cross_validation=False, + frac_validation=0.0, +) From 9503b333305662fef5f878303fa9d5a836df96b1 Mon Sep 17 00:00:00 2001 From: richardarsenault Date: Mon, 29 Dec 2025 09:05:08 -0500 Subject: [PATCH 2/5] Cleaned some input files and fixed a bug caused by dynamic variable name --- .../optimal_interpolation_precip.py | 8 ++++---- ...RA5Land_with_OI_flags_validation_subset.nc | Bin 0 -> 2640879 bytes ...bset.nc => stations_flags_clean_subset.nc} | Bin 71663 -> 71663 bytes tests/test_precip_oi.py | 4 ++-- 4 files changed, 6 insertions(+), 6 deletions(-) create mode 100644 tests/ERA5Land_with_OI_flags_validation_subset.nc rename tests/{stations_precip_DQAQ_ECCC_US_subset.nc => stations_flags_clean_subset.nc} (99%) diff --git a/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py b/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py index 19b59ccc..30b27063 100644 --- a/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py +++ b/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py @@ -610,8 +610,8 @@ def prepare_initial_data( np.savetxt("./training_stations.txt", train_idx) # Extract the training stations and valid stations in the 2 different datasets - ds_stations_train = ds_stations_full.isel(watershed=train_idx) - ds_stations_valid = ds_stations_full.isel(watershed=valid_idx) + ds_stations_train = ds_stations_full.isel(indexers={dims_stations: train_idx}) + ds_stations_valid = ds_stations_full.isel(indexers={dims_stations: valid_idx}) # prepare lat and long values for observations lat_obs_train = ds_stations_train.latitude.values @@ -620,8 +620,8 @@ def prepare_initial_data( lon_obs_valid = ds_stations_valid.longitude.values # Get the precipitation values from the station data - observed_precip_train = ds_stations_train.precip.values - observed_precip_valid = ds_stations_valid.precip.values + observed_precip_train = ds_stations_train[var_name_stations].values + observed_precip_valid = ds_stations_valid[var_name_stations].values # Process the gridded data in this section. # Read the background field data and ensure the format is correct and contains the desired variables. diff --git a/tests/ERA5Land_with_OI_flags_validation_subset.nc b/tests/ERA5Land_with_OI_flags_validation_subset.nc new file mode 100644 index 0000000000000000000000000000000000000000..ca54694a068e3ad368b459458b10147b9f52629b GIT binary patch literal 2640879 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60 zcmaFAp5^^|mI delta 60 zcmaFAp5^^|mI;v7c-c8DODEPLvCwekJZ_l)8I D!ZZ(m diff --git a/tests/test_precip_oi.py b/tests/test_precip_oi.py index ac4b7afe..8e3cac75 100644 --- a/tests/test_precip_oi.py +++ b/tests/test_precip_oi.py @@ -5,7 +5,7 @@ start_time = dt.datetime(1970, 1, 1) end_time = dt.datetime(1970, 12, 31) -filename_stations = "./stations_precip_DQAQ_ECCC_US_subset.nc" +filename_stations = "./stations_flags_clean_subset.nc" filename_gridded = "./ERA5_land_3_variables_raw_subset.nc" filename_output = "./ERA5Land_with_OI_flags_validation_subset.nc" @@ -19,7 +19,7 @@ var_name_gridded="tp", var_name_stations="precip", dims_gridded=("longitude", "latitude", "time"), - dims_stations="watershed", + dims_stations="station", coords_gridded=("time", "latitude", "longitude"), station_req_vars=("latitude", "longitude", "altitude"), percentiles=[50], From cf529beb4a9870717bcbbad43c9dbddceb80346a Mon Sep 17 00:00:00 2001 From: richardarsenault Date: Mon, 2 Feb 2026 20:22:42 -0500 Subject: [PATCH 3/5] updated precip_oi tests with xhydro-testdata data --- ...RA5Land_with_OI_flags_validation_subset.nc | Bin 2640879 -> 0 bytes tests/ERA5_land_3_variables_raw_subset.nc | Bin 3958512 -> 0 bytes tests/stations_flags_clean_subset.nc | Bin 71663 -> 0 bytes tests/test_precip_oi.py | 8 +++++--- 4 files changed, 5 insertions(+), 3 deletions(-) delete mode 100644 tests/ERA5Land_with_OI_flags_validation_subset.nc delete mode 100644 tests/ERA5_land_3_variables_raw_subset.nc delete mode 100644 tests/stations_flags_clean_subset.nc diff --git a/tests/ERA5Land_with_OI_flags_validation_subset.nc b/tests/ERA5Land_with_OI_flags_validation_subset.nc deleted file mode 100644 index ca54694a068e3ad368b459458b10147b9f52629b..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 2640879 zcmeFZc|4X|+cz#GDoRRs{xip8LM{?|$C*cfX&{^ZvE3y|=I9Tq1JRM_n#Kg4b_fw`> zQ@{LaoaxIQIy*ysPNr$o=2L~t)5zy{^*_imo6>kLvBs1^RG6l7QBPPzDVceycJ!1Y 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-0500 Subject: [PATCH 4/5] Changed testdata path to merged xhydro-testdata path --- src/xhydro/testing/helpers.py | 2 +- src/xhydro/testing/registry.txt | 5 +++++ tests/test_precip_oi.py | 6 +++--- 3 files changed, 9 insertions(+), 4 deletions(-) diff --git a/src/xhydro/testing/helpers.py b/src/xhydro/testing/helpers.py index ebd31e25..8244bd30 100644 --- a/src/xhydro/testing/helpers.py +++ b/src/xhydro/testing/helpers.py @@ -29,7 +29,7 @@ "populate_testing_data", ] -default_testdata_version = "v2025.8.14" +default_testdata_version = "v2026.02.04" """Default version of the testing data to use when fetching datasets.""" default_testdata_repo_url = "https://raw.githubusercontent.com/hydrologie/xhydro-testdata/" diff --git a/src/xhydro/testing/registry.txt b/src/xhydro/testing/registry.txt index 4152058c..2f69afb6 100644 --- a/src/xhydro/testing/registry.txt +++ b/src/xhydro/testing/registry.txt @@ -15,6 +15,11 @@ optimal_interpolation/OI_data.zip sha256:9cd881a19fc82bda560e636d3f6a2c40718b82f optimal_interpolation/OI_data_corrected.zip sha256:48ee08325bd35c6bce5c0e52e3ee25df27c830720929060f607fb0417c476941 pmp/CMIP.CCCma.CanESM5.historical.r1i1p1f1.day.gn.zarr.zip sha256:d5775b2f09381f2f3a7cc06af76f62fb216b60252aab3a602280a513554d59ad pmp/CMIP.CCCma.CanESM5.historical.r1i1p1f1.fx.gn.zarr.zip sha256:dc7c92fc098ca5adf43e76b25e3f79b70815ed961e945952983bb68b3c380cf1 +precip_oi/ERA5Land_with_OI_flags_validation_subset.nc sha256:50fc8d562443efe82998735c50268019532493bc02b47e4a47f6672708c87b5f +precip_oi/ERA5_land_3_variables_raw_subset.nc sha256:09ee75f73bb4e88bddb6c9184245766ebe8cc6b13b58ef58a4754e523138ff1f +precip_oi/stations_flags_clean_subset.nc sha256:03513b859e6c99ab02728f49b0e3e7382375e7311c68e33c8d59d6f734eb08d1 +pygmet/subset_grid_temperature.nc sha256:66a3086d9aaacbedac6633050380b9b7685407c952a3f8629a16caea4d1ef8db +pygmet/subset_oi_tp.nc sha256:1cddcb439168891e4ad025c7708c6d0ce1017bbb013ac2fe46589dc3fb5953da ravenpy/Debit_Riviere_Rouge.nc sha256:d0a27de5eb3cb466e60669d894296bcbc4e9f590edc1ae2490685babd10b2d22 ravenpy/ERA5_Riviere_Rouge_global.nc sha256:341ac746130a0d3e3189d3a41dc8528d6bd22869a519b68e134959407ad200a3 ravenpy/hru_subset.zip sha256:969b4a0d0c1f0c24dbb5baca98676f2573178cd58ef4162aa6b9fce51ceecf06 diff --git a/tests/test_precip_oi.py b/tests/test_precip_oi.py index cd862fec..09b39ffd 100644 --- a/tests/test_precip_oi.py +++ b/tests/test_precip_oi.py @@ -7,9 +7,9 @@ start_time = dt.datetime(1970, 1, 1) end_time = dt.datetime(1970, 12, 31) -filename_stations = deveraux(branch="pygmet").fetch("precip_oi/stations_flags_clean_subset.nc") -filename_gridded = deveraux(branch="pygmet").fetch("precip_oi/ERA5_land_3_variables_raw_subset.nc") -filename_output = deveraux(branch="pygmet").fetch("precip_oi/ERA5Land_with_OI_flags_validation_subset.nc") +filename_stations = deveraux().fetch("precip_oi/stations_flags_clean_subset.nc") +filename_gridded = deveraux().fetch("precip_oi/ERA5_land_3_variables_raw_subset.nc") +filename_output = deveraux().fetch("precip_oi/ERA5Land_with_OI_flags_validation_subset.nc") oi.main( start_time=start_time, From 560b898382f9d7636e6960cb3639008bb7aae3e4 Mon Sep 17 00:00:00 2001 From: richardarsenault Date: Sun, 15 Feb 2026 22:09:17 -0500 Subject: [PATCH 5/5] simplified tests data and added assertions --- .../optimal_interpolation_precip.py | 23 +++++-- tests/test_precip_oi.py | 62 ++++++++++--------- 2 files changed, 53 insertions(+), 32 deletions(-) diff --git a/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py b/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py index 30b27063..c6a3aa1d 100644 --- a/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py +++ b/src/xhydro/optimal_interpolation/optimal_interpolation_precip.py @@ -555,6 +555,10 @@ def prepare_initial_data( ds_gridded: Dataset The original gridded dataset, loaded and subset for the correct time. Also used later for plotting in cross-validation. + train_idx: ndarray + Indices of the training stations for calibrating OI. + valid_idx: ndarray + Indices of the validation stations. """ # This first section processes the observation stations # Read the station data. @@ -605,10 +609,6 @@ def prepare_initial_data( # Continue the process. Extract the training station indices. train_idx = list_stations[round(number_stations * frac_validation) :] - # Save the IDs of the validation and training stations for future reference - np.savetxt("./validation_stations.txt", valid_idx) - np.savetxt("./training_stations.txt", train_idx) - # Extract the training stations and valid stations in the 2 different datasets ds_stations_train = ds_stations_full.isel(indexers={dims_stations: train_idx}) ds_stations_valid = ds_stations_full.isel(indexers={dims_stations: valid_idx}) @@ -693,6 +693,8 @@ def prepare_initial_data( original_shape, observed_precip_valid, ds_gridded, + train_idx, + valid_idx, ) @@ -1134,6 +1136,15 @@ def main( frac_validation : float | None The fraction of stations to use for cross-validation, independent of the training data. Between 0 and 1. + Returns + ------- + ds_final: xr.Dataset + The dataset after optimal interpolation. + train_idx: ndarray + Indices of the training stations for calibrating OI. + valid_idx: ndarray + Indices of the validation stations. + Notes ----- The possible forms for the ecf function fitting are as follows: @@ -1170,6 +1181,8 @@ def main( original_shape, observed_precip_valid, ds_gridded, + train_idx, + valid_idx, ) = prepare_initial_data( filename_stations, filename_gridded, @@ -1247,3 +1260,5 @@ def main( # Plot them for quick analysis cv.plot_cross_validation_rmse_results(filename_stations) + + return ds_final, train_idx, valid_idx diff --git a/tests/test_precip_oi.py b/tests/test_precip_oi.py index 09b39ffd..31532799 100644 --- a/tests/test_precip_oi.py +++ b/tests/test_precip_oi.py @@ -1,36 +1,42 @@ import datetime as dt +import tempfile import xhydro.optimal_interpolation.optimal_interpolation_precip as oi from xhydro.testing.helpers import deveraux -start_time = dt.datetime(1970, 1, 1) -end_time = dt.datetime(1970, 12, 31) +def test_precip_oi(): + start_time = dt.datetime(1970, 1, 1) + end_time = dt.datetime(1970, 12, 31) -filename_stations = deveraux().fetch("precip_oi/stations_flags_clean_subset.nc") -filename_gridded = deveraux().fetch("precip_oi/ERA5_land_3_variables_raw_subset.nc") -filename_output = deveraux().fetch("precip_oi/ERA5Land_with_OI_flags_validation_subset.nc") + filename_stations = deveraux().fetch("precip_oi/stations_flags_clean_subset.nc") + filename_gridded = deveraux().fetch("precip_oi/ERA5_land_3_variables_raw_subset.nc") -oi.main( - start_time=start_time, - end_time=end_time, - filename_stations=filename_stations, - filename_gridded=filename_gridded, - filename_output=filename_output, - grid_resolution=0.1, - var_name_gridded="tp", - var_name_stations="precip", - dims_gridded=("longitude", "latitude", "time"), - dims_stations="station", - coords_gridded=("time", "latitude", "longitude"), - station_req_vars=("latitude", "longitude", "altitude"), - percentiles=[50], - p1_bnds=[0.95, 1.0], - hmax_mult_range_bnds=[0.05, 3], - var_bg_ratio=0.15, - variogram_bins=10, - hmax_divider=2.0, - ecf_form=1, - do_cross_validation=False, - frac_validation=0.0, -) + filename_output = tempfile.mkdtemp() + "/ERA5Land_with_OI_flags_validation_subset.nc" + + ds_final, train_idx, valid_idx = oi.main( + start_time=start_time, + end_time=end_time, + filename_stations=filename_stations, + filename_gridded=filename_gridded, + filename_output=filename_output, + grid_resolution=0.1, + var_name_gridded="tp", + var_name_stations="precip", + dims_gridded=("longitude", "latitude", "time"), + dims_stations="station", + coords_gridded=("time", "latitude", "longitude"), + station_req_vars=("latitude", "longitude", "altitude"), + percentiles=[50], + p1_bnds=[0.95, 1.0], + hmax_mult_range_bnds=[0.05, 3], + var_bg_ratio=0.15, + variogram_bins=10, + hmax_divider=2.0, + ecf_form=1, + do_cross_validation=False, + frac_validation=0.0, + ) + + assert ds_final["percentile"] == 50 + assert valid_idx.shape[0] == 0

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