Source code for sup3r.models.surface

"""Special models for surface meteorological data."""

import logging
from fnmatch import fnmatch
from warnings import warn

import numpy as np
from PIL import Image
from sklearn import linear_model

from sup3r.utilities.utilities import RANDOM_GENERATOR, spatial_coarsening

from .linear import LinearInterp

logger = logging.getLogger(__name__)


[docs] class SurfaceSpatialMetModel(LinearInterp): """Model to spatially downscale daily-average near-surface temperature, relative humidity, and pressure Note that this model can also operate on temperature_*m, relativehumidity_*m, and pressure_*m datasets that are not strictly at the surface but could be near hub height. """ TEMP_LAPSE = 6.5 / 1000 """Temperature lapse rate: change in degrees C/K per meter""" PRES_DIV = 44307.69231 """Air pressure scaling equation divisor variable: 101325 * (1 - (1 - topo / PRES_DIV)**PRES_EXP)""" PRES_EXP = 5.25328 """Air pressure scaling equation exponent variable: 101325 * (1 - (1 - topo / PRES_DIV)**PRES_EXP)""" W_DELTA_TEMP = -3.99242830 """Weight for the delta-temperature feature for the relative humidity linear regression model.""" W_DELTA_TOPO = -0.01736911 """Weight for the delta-topography feature for the relative humidity linear regression model.""" def __init__( self, lr_features, s_enhance, noise_adders=None, temp_lapse=None, w_delta_temp=None, w_delta_topo=None, pres_div=None, pres_exp=None, interp_method='LANCZOS', input_resolution=None, fix_bias=True, ): """ Parameters ---------- lr_features : list List of feature names that this model will operate on for both input and output. This must match the feature axis ordering in the array input to generate(). Typically this is a list containing: temperature_*m, relativehumidity_*m, and pressure_*m. The list can contain multiple instances of each variable at different heights. relativehumidity_*m entries must have corresponding temperature_*m entires at the same hub height. s_enhance : int Integer factor by which the spatial axes are to be enhanced. noise_adders : float | list | None Option to add gaussian noise to spatial model output. Noise will be normally distributed with mean of 0 and standard deviation = noise_adders. noise_adders can be a single value or a list corresponding to the lr_features list. None is no noise. The addition of noise has been shown to help downstream temporal-only models produce diurnal cycles in regions where there is minimal change in topography. A noise_adders around 0.07C (temperature) and 0.1% (relative humidity) have been shown to be effective. This is unnecessary if daily min/max temperatures are provided as low res training features. temp_lapse : None | float Temperature lapse rate: change in degrees C/K per meter. Defaults to the cls.TEMP_LAPSE attribute. w_delta_temp : None | float Weight for the delta-temperature feature for the relative humidity linear regression model. Defaults to the cls.W_DELTA_TEMP attribute. w_delta_topo : None | float Weight for the delta-topography feature for the relative humidity linear regression model. Defaults to the cls.W_DELTA_TOPO attribute. pres_div : None | float Divisor factor in the pressure scale height equation. Defaults to the cls.PRES_DIV attribute. pres_exp : None | float Exponential factor in the pressure scale height equation. Defaults to the cls.PRES_EXP attribute. interp_method : str Name of the interpolation method to use from PIL.Image.Resampling (NEAREST, BILINEAR, BICUBIC, LANCZOS) LANCZOS is default and has been tested to work best for SurfaceSpatialMetModel. fix_bias : bool Some local bias can be introduced by the bilinear interp + lapse rate, this flag will attempt to correct that bias by using the low-resolution deviation from the input data input_resolution : dict | None Resolution of the input data. e.g. {'spatial': '30km', 'temporal': '60min'}. This is used to determine how to aggregate high-resolution topography data. """ self._lr_features = lr_features self._s_enhance = s_enhance self._noise_adders = noise_adders self._temp_lapse = temp_lapse or self.TEMP_LAPSE self._w_delta_temp = w_delta_temp or self.W_DELTA_TEMP self._w_delta_topo = w_delta_topo or self.W_DELTA_TOPO self._pres_div = pres_div or self.PRES_DIV self._pres_exp = pres_exp or self.PRES_EXP self._fix_bias = fix_bias self._input_resolution = input_resolution self._interp_name = interp_method self._interp_method = getattr(Image.Resampling, interp_method) if isinstance(self._noise_adders, (int, float)): self._noise_adders = [self._noise_adders] * len(self._lr_features) def __len__(self): """Get number of model steps (match interface of MultiStepGan)""" return 1 @staticmethod def _get_s_enhance(topo_lr, topo_hr): """Get the spatial enhancement factor given low-res and high-res spatial rasters. Parameters ---------- topo_lr : np.ndarray low-resolution surface elevation data in meters with shape (lat, lon) topo_hr : np.ndarray High-resolution surface elevation data in meters with shape (lat, lon) Returns ------- s_enhance : int Integer factor by which the spatial axes are to be enhanced. """ assert len(topo_lr.shape) == 2, 'topo_lr must be 2D' assert len(topo_hr.shape) == 2, 'topo_hr must be 2D' se0 = topo_hr.shape[0] / topo_lr.shape[0] se1 = topo_hr.shape[1] / topo_lr.shape[1] assert se0 % 1 == 0, f'Bad calculated s_enhance on axis 0: {se0}' assert se1 % 1 == 0, f'Bad calculated s_enhance on axis 1: {se1}' assert se0 == se1, 'Calculated s_enhance does not match along axis' return int(se0) @property def feature_inds_temp(self): """Get the feature index values for the temperature features.""" inds = [ i for i, name in enumerate(self._lr_features) if fnmatch(name, 'temperature_*') ] return inds @property def feature_inds_pres(self): """Get the feature index values for the pressure features.""" inds = [ i for i, name in enumerate(self._lr_features) if fnmatch(name, 'pressure_*') ] return inds @property def feature_inds_rh(self): """Get the feature index values for the relative humidity features.""" inds = [ i for i, name in enumerate(self._lr_features) if fnmatch(name, 'relativehumidity_*') ] return inds @property def feature_inds_other(self): """Get the feature index values for the features that are not temperature, pressure, or relativehumidity.""" finds_tprh = ( self.feature_inds_temp + self.feature_inds_pres + self.feature_inds_rh ) inds = [ i for i, name in enumerate(self._lr_features) if i not in finds_tprh ] return inds def _get_temp_rh_ind(self, idf_rh): """Get the feature index value for the temperature feature corresponding to a relative humidity feature at the same hub height. Parameters ---------- idf_rh : int Index in the feature list for a relativehumidity_*m feature Returns ------- idf_temp : int Index in the feature list for a temperature_*m feature with the same hub height as the idf_rh input. """ name_rh = self._lr_features[idf_rh] hh_suffix = name_rh.split('_')[-1] idf_temp = None for i in self.feature_inds_temp: same_hh = self._lr_features[i].endswith(hh_suffix) not_minmax = not any(mm in name_rh for mm in ('_min_', '_max_')) both_mins = '_min_' in name_rh and '_min_' in self._lr_features[i] both_maxs = '_max_' in name_rh and '_max_' in self._lr_features[i] if same_hh and (not_minmax or both_mins or both_maxs): idf_temp = i break if idf_temp is None: msg = ( 'Could not find temperature feature corresponding to ' '"{}" in feature list: {}'.format(name_rh, self._lr_features) ) logger.error(msg) raise KeyError(msg) return idf_temp
[docs] @classmethod def fix_downscaled_bias( cls, single_lr, single_hr, method=Image.Resampling.LANCZOS ): """Fix any bias introduced by the spatial downscaling with lapse rate. Parameters ---------- single_lr : np.ndarray Single timestep raster data with shape (lat, lon) matching the low-resolution input data. single_hr : np.ndarray Single timestep downscaled raster data with shape (lat, lon) matching the high-resolution input data. method : Image.Resampling.LANCZOS An Image.Resampling method (NEAREST, BILINEAR, BICUBIC, LANCZOS). NEAREST enforces zero bias but makes slightly more spatial seams. Returns ------- single_hr : np.ndarray Single timestep downscaled raster data with shape (lat, lon) matching the high-resolution input data. """ s_enhance = len(single_hr) // len(single_lr) re_coarse = spatial_coarsening( np.expand_dims(single_hr, axis=-1), s_enhance=s_enhance, obs_axis=False, )[..., 0] bias = re_coarse - single_lr bc = cls.downscale_arr(bias, s_enhance=s_enhance, method=method) single_hr -= bc return single_hr
[docs] @classmethod def downscale_arr( cls, arr, s_enhance, method=Image.Resampling.LANCZOS, fix_bias=False ): """Downscale a 2D array of data Image.resize() method Parameters ---------- arr : np.ndarray 2D raster data, typically spatial daily average data with shape (lat, lon) s_enhance : int Integer factor by which the spatial axes are to be enhanced. method : Image.Resampling.LANCZOS An Image.Resampling method (NEAREST, BILINEAR, BICUBIC, LANCZOS). LANCZOS is default and has been tested to work best for SurfaceSpatialMetModel. fix_bias : bool Some local bias can be introduced by the bilinear interp + lapse rate, this flag will attempt to correct that bias by using the low-resolution deviation from the input data """ im = Image.fromarray(arr) im = im.resize( (arr.shape[1] * s_enhance, arr.shape[0] * s_enhance), resample=method, ) out = np.array(im) if fix_bias: out = cls.fix_downscaled_bias(arr, out, method=method) return out
[docs] def downscale_temp(self, single_lr_temp, topo_lr, topo_hr): """Downscale temperature raster data at a single observation. This model uses a simple lapse rate that adjusts temperature as a function of elevation. The process is as follows: - add a scale factor to the low-res temperature field: topo_lr * TEMP_LAPSE - perform bilinear interpolation of the scaled temperature field. - subtract the scale factor from the high-res temperature field: topo_hr * TEMP_LAPSE Parameters ---------- single_lr_temp : np.ndarray Single timestep temperature (deg C) raster data with shape (lat, lon) matching the low-resolution input data. topo_lr : np.ndarray low-resolution surface elevation data in meters with shape (lat, lon) topo_hr : np.ndarray High-resolution surface elevation data in meters with shape (lat, lon) Returns ------- hi_res_temp : np.ndarray Single timestep temperature (deg C) raster data with shape (lat, lon) matching the high-resolution output data. """ assert len(single_lr_temp.shape) == 2, 'Bad shape for single_lr_temp' assert len(topo_lr.shape) == 2, 'Bad shape for topo_lr' assert len(topo_hr.shape) == 2, 'Bad shape for topo_hr' lower_data = single_lr_temp.copy() + topo_lr * self._temp_lapse hi_res_temp = self.downscale_arr( lower_data, self._s_enhance, method=self._interp_method ) hi_res_temp -= topo_hr * self._temp_lapse if self._fix_bias: hi_res_temp = self.fix_downscaled_bias( single_lr_temp, hi_res_temp, method=self._interp_method ) return hi_res_temp
[docs] def downscale_rh( self, single_lr_rh, single_lr_temp, single_hr_temp, topo_lr, topo_hr ): """Downscale relative humidity raster data at a single observation. Here's a description of the humidity scaling model: - Take low-resolution and high-resolution daily average temperature, relative humidity, and topography data. - Downscale all low-resolution variables using a bilinear image enhancement - The target model output is the difference between the interpolated low-res relative humidity and the true high-res relative humidity. Calculate this difference as a linear function of the same difference in the temperature and topography fields. - Use this linear regression model to calculate high-res relative humidity fields when provided low-res input of relative humidity along with low-res/high-res pairs of temperature and topography. Parameters ---------- single_lr_rh : np.ndarray Single timestep relative humidity (%) raster data with shape (lat, lon) matching the low-resolution input data. single_lr_temp : np.ndarray Single timestep temperature (deg C) raster data with shape (lat, lon) matching the low-resolution input data. single_hr_temp : np.ndarray Single timestep temperature (deg C) raster data with shape (lat, lon) matching the high-resolution output data. topo_lr : np.ndarray low-resolution surface elevation data in meters with shape (lat, lon) topo_hr : np.ndarray High-resolution surface elevation data in meters with shape (lat, lon) Returns ------- hi_res_rh : np.ndarray Single timestep relative humidity (%) raster data with shape (lat, lon) matching the high-resolution output data. """ assert len(single_lr_rh.shape) == 2, 'Bad shape for single_lr_rh' assert len(single_hr_temp.shape) == 2, 'Bad shape for single_hr_temp' assert len(topo_lr.shape) == 2, 'Bad shape for topo_lr' assert len(topo_hr.shape) == 2, 'Bad shape for topo_hr' interp_rh = self.downscale_arr( single_lr_rh, self._s_enhance, method=self._interp_method ) interp_temp = self.downscale_arr( single_lr_temp, self._s_enhance, method=self._interp_method ) interp_topo = self.downscale_arr( topo_lr, self._s_enhance, method=self._interp_method ) delta_temp = single_hr_temp - interp_temp delta_topo = topo_hr - interp_topo hi_res_rh = ( interp_rh + self._w_delta_temp * delta_temp + self._w_delta_topo * delta_topo ) if self._fix_bias: hi_res_rh = self.fix_downscaled_bias( single_lr_rh, hi_res_rh, method=self._interp_method ) return hi_res_rh
[docs] def downscale_pres(self, single_lr_pres, topo_lr, topo_hr): """Downscale pressure raster data at a single observation. This model uses a simple exponential scale height that adjusts temperature as a function of elevation. The process is as follows: - add a scale factor to the low-res pressure field: 101325 * (1 - (1 - topo_lr / PRES_DIV)**PRES_EXP) - perform bilinear interpolation of the scaled pressure field. - subtract the scale factor from the high-res pressure field: 101325 * (1 - (1 - topo_hr / PRES_DIV)**PRES_EXP) Parameters ---------- single_lr_pres : np.ndarray Single timestep pressure (Pa) raster data with shape (lat, lon) matching the low-resolution input data. topo_lr : np.ndarray low-resolution surface elevation data in meters with shape (lat, lon) topo_hr : np.ndarray High-resolution surface elevation data in meters with shape (lat, lon) Returns ------- hi_res_pres : np.ndarray Single timestep pressure (Pa) raster data with shape (lat, lon) matching the high-resolution output data. """ if np.max(single_lr_pres) < 10000: msg = ( 'Pressure data appears to not be in Pa with min/mean/max: ' '{:.1f}/{:.1f}/{:.1f}'.format( single_lr_pres.min(), single_lr_pres.mean(), single_lr_pres.max(), ) ) logger.warning(msg) warn(msg) const = 101325 * (1 - (1 - topo_lr / self._pres_div) ** self._pres_exp) lr_pres_adj = single_lr_pres.copy() + const if np.min(lr_pres_adj) < 0.0: msg = ( 'Spatial interpolation of surface pressure ' 'resulted in negative values. Incorrectly ' 'scaled/unscaled values or incorrect units are ' 'the most likely causes. All pressure data should be ' 'in Pascals.' ) logger.error(msg) raise ValueError(msg) hi_res_pres = self.downscale_arr( lr_pres_adj, self._s_enhance, method=self._interp_method ) const = 101325 * (1 - (1 - topo_hr / self._pres_div) ** self._pres_exp) hi_res_pres -= const if self._fix_bias: hi_res_pres = self.fix_downscaled_bias( single_lr_pres, hi_res_pres, method=self._interp_method ) if np.min(hi_res_pres) < 0.0: msg = ( 'Spatial interpolation of surface pressure ' 'resulted in negative values. Incorrectly ' 'scaled/unscaled values or incorrect units are ' 'the most likely causes.' ) logger.error(msg) raise ValueError(msg) return hi_res_pres
@property def input_dims(self): """Get dimension of model input. This is 4 for linear and surface models (n_obs, spatial_1, spatial_2, temporal) Returns ------- int """ return 4 def _get_topo_from_exo(self, exogenous_data): """Get lr_topo and hr_topo from exo_data dictionary. Parameters ---------- exogenous_data : dict For the SurfaceSpatialMetModel, this must be a nested dictionary with a main 'topography' key and two entries for exogenous_data['topography']['steps']. The first entry includes a 2D (lat, lon) or 4D (n_obs, lat, lon, temporal) array of low-resolution surface elevation data in meters (lat, lon must match spatial_1, spatial_2 from low_res), and the second entry includes a 2D (lat, lon) or 4D (n_obs, lat, lon, temporal) array of high-resolution surface elevation data in meters. e.g. .. code-block:: JSON {'topography': { 'steps': [{'data': lr_topo}, {'data': hr_topo'}] } } Returns ------- lr_topo : ndarray (lat, lon) hr_topo : ndarray (lat, lon) """ exo_data = [ step['data'] for step in exogenous_data['topography']['steps'] ] msg = 'exogenous_data is of a bad type {}!'.format(type(exo_data)) assert isinstance(exo_data, (list, tuple)), msg msg = 'exogenous_data is of a bad length {}!'.format(len(exo_data)) assert len(exo_data) == 2, msg lr_topo = exo_data[0] hr_topo = exo_data[1] if len(lr_topo.shape) == 4: lr_topo = lr_topo[0, :, :, 0] if len(hr_topo.shape) == 4: hr_topo = hr_topo[0, :, :, 0] return lr_topo, hr_topo # pylint: disable=unused-argument
[docs] def generate( self, low_res, norm_in=False, un_norm_out=False, exogenous_data=None ): """Use the generator model to generate high res data from low res input. This is the public generate function. Parameters ---------- low_res : np.ndarray Low-resolution spatial input data, a 4D array of shape: (n_obs, spatial_1, spatial_2, n_features), Where the feature channel can include temperature_*m, relativehumidity_*m, and/or pressure_*m norm_in : bool This doesnt do anything for this SurfaceSpatialMetModel, but is kept to keep the same interface as Sup3rGan un_norm_out : bool This doesnt do anything for this SurfaceSpatialMetModel, but is kept to keep the same interface as Sup3rGan exogenous_data : dict For the SurfaceSpatialMetModel, this must be a nested dictionary with a main 'topography' key and two entries for exogenous_data['topography']['steps']. The first entry includes a 2D (lat, lon) array of low-resolution surface elevation data in meters (must match spatial_1, spatial_2 from low_res), and the second entry includes a 2D (lat, lon) array of high-resolution surface elevation data in meters. e.g. .. code-block:: JSON {'topography': { 'steps': [{'data': lr_topo}, {'data': hr_topo'}] } } Returns ------- hi_res : ndarray high-resolution spatial output data, a 4D array of shape: (n_obs, spatial_1, spatial_2, n_features), Where the feature channel can include temperature_*m, relativehumidity_*m, and/or pressure_*m """ low_res = np.asarray(low_res) lr_topo, hr_topo = self._get_topo_from_exo(exogenous_data) lr_topo = np.asarray(lr_topo) hr_topo = np.asarray(hr_topo) logger.debug( 'SurfaceSpatialMetModel received low/high res topo ' 'shapes of {} and {}'.format(lr_topo.shape, hr_topo.shape) ) msg = f'topo_lr needs to be 2d but has shape {lr_topo.shape}' assert len(lr_topo.shape) == 2, msg msg = f'topo_hr needs to be 2d but has shape {hr_topo.shape}' assert len(hr_topo.shape) == 2, msg msg = ( 'lr_topo.shape needs to match lr_res.shape[:2] but received ' f'{lr_topo.shape} and {low_res.shape}' ) assert lr_topo.shape[0] == low_res.shape[1], msg assert lr_topo.shape[1] == low_res.shape[2], msg s_enhance = self._get_s_enhance(lr_topo, hr_topo) msg = ( 'Topo shapes of {} and {} did not match desired spatial ' 'enhancement of {}'.format( lr_topo.shape, hr_topo.shape, self._s_enhance ) ) assert self._s_enhance == s_enhance, msg hr_shape = ( len(low_res), int(low_res.shape[1] * self._s_enhance), int(low_res.shape[2] * self._s_enhance), len(self.hr_out_features), ) logger.debug( 'SurfaceSpatialMetModel with s_enhance of {} ' 'downscaling low-res shape {} to high-res shape {}'.format( self._s_enhance, low_res.shape, hr_shape ) ) hi_res = np.zeros(hr_shape, dtype=np.float32) for iobs in range(len(low_res)): for idf_temp in self.feature_inds_temp: _tmp = self.downscale_temp( low_res[iobs, :, :, idf_temp], lr_topo, hr_topo ) hi_res[iobs, :, :, idf_temp] = _tmp for idf_pres in self.feature_inds_pres: _tmp = self.downscale_pres( low_res[iobs, :, :, idf_pres], lr_topo, hr_topo ) hi_res[iobs, :, :, idf_pres] = _tmp for idf_rh in self.feature_inds_rh: idf_temp = self._get_temp_rh_ind(idf_rh) _tmp = self.downscale_rh( low_res[iobs, :, :, idf_rh], low_res[iobs, :, :, idf_temp], hi_res[iobs, :, :, idf_temp], lr_topo, hr_topo, ) hi_res[iobs, :, :, idf_rh] = _tmp for idf_rh in self.feature_inds_rh: idf_temp = self._get_temp_rh_ind(idf_rh) _tmp = self.downscale_rh( low_res[iobs, :, :, idf_rh], low_res[iobs, :, :, idf_temp], hi_res[iobs, :, :, idf_temp], lr_topo, hr_topo, ) hi_res[iobs, :, :, idf_rh] = _tmp for idf_other in self.feature_inds_other: _arr = self.downscale_arr( low_res[iobs, :, :, idf_other], self._s_enhance, method=self._interp_method, fix_bias=self._fix_bias, ) hi_res[iobs, :, :, idf_other] = _arr if self._noise_adders is not None: for idf, stdev in enumerate(self._noise_adders): if stdev is not None: noise = RANDOM_GENERATOR.uniform( 0, stdev, hi_res.shape[:-1] ) hi_res[..., idf] += noise return hi_res
@property def meta(self): """Get meta data dictionary that defines the model params""" return { 'temp_lapse_rate': self._temp_lapse, 's_enhance': self._s_enhance, 't_enhance': 1, 'noise_adders': self._noise_adders, 'input_resolution': self._input_resolution, 'weight_for_delta_temp': self._w_delta_temp, 'weight_for_delta_topo': self._w_delta_topo, 'pressure_divisor': self._pres_div, 'pressure_exponent': self._pres_exp, 'lr_features': self.lr_features, 'hr_out_features': self.hr_out_features, 'interp_method': self._interp_name, 'fix_bias': self._fix_bias, 'class': self.__class__.__name__, }
[docs] def train(self, true_hr_temp, true_hr_rh, true_hr_topo, input_resolution): """Trains the relative humidity linear model. The temperature and surface lapse rate models are parameterizations taken from the NSRDB and are not trained. Parameters ---------- true_hr_temp : np.ndarray True high-resolution daily average temperature data in a 3D array of shape (lat, lon, n_days) true_hr_rh : np.ndarray True high-resolution daily average relative humidity data in a 3D array of shape (lat, lon, n_days) true_hr_topo : np.ndarray High-resolution surface elevation data in meters with shape (lat, lon) input_resolution : dict Dictionary of spatial and temporal input resolution. e.g. {'spatial': '20km': 'temporal': '60min'} Returns ------- w_delta_temp : float Weight for the delta-temperature feature for the relative humidity linear regression model. w_delta_topo : float Weight for the delta-topography feature for the relative humidity linear regression model. """ self._input_resolution = input_resolution assert len(true_hr_temp.shape) == 3, 'Bad true_hr_temp shape' assert len(true_hr_rh.shape) == 3, 'Bad true_hr_rh shape' assert len(true_hr_topo.shape) == 2, 'Bad true_hr_topo shape' true_hr_topo = np.expand_dims(true_hr_topo, axis=-1) true_hr_topo = np.repeat(true_hr_topo, true_hr_temp.shape[-1], axis=-1) true_lr_temp = spatial_coarsening( true_hr_temp, s_enhance=self._s_enhance, obs_axis=False ) true_lr_rh = spatial_coarsening( true_hr_rh, s_enhance=self._s_enhance, obs_axis=False ) true_lr_topo = spatial_coarsening( true_hr_topo, s_enhance=self._s_enhance, obs_axis=False ) interp_hr_temp = np.full(true_hr_temp.shape, np.nan, dtype=np.float32) interp_hr_rh = np.full(true_hr_rh.shape, np.nan, dtype=np.float32) interp_hr_topo = np.full(true_hr_topo.shape, np.nan, dtype=np.float32) for i in range(interp_hr_temp.shape[-1]): interp_hr_temp[..., i] = self.downscale_arr( true_lr_temp[..., i], self._s_enhance ) interp_hr_rh[..., i] = self.downscale_arr( true_lr_rh[..., i], self._s_enhance ) interp_hr_topo[..., i] = self.downscale_arr( true_lr_topo[..., i], self._s_enhance ) x1 = true_hr_temp - interp_hr_temp x2 = true_hr_topo - interp_hr_topo x = np.vstack((x1.flatten(), x2.flatten())).T y = (true_hr_rh - interp_hr_rh).flatten() regr = linear_model.LinearRegression() regr.fit(x, y) if np.abs(regr.intercept_) > 1e-6: msg = ( 'Relative humidity linear model should have an intercept ' 'of zero but the model fit an intercept of {}'.format( regr.intercept_ ) ) logger.warning(msg) warn(msg) w_delta_temp, w_delta_topo = regr.coef_[0], regr.coef_[1] return w_delta_temp, w_delta_topo