def detrend(data):
"""
detrend(data)
Function for removing a linear trend from a 1 dimensional data series, but retains the mean.
Parameters
----------
data : signal you wish to detrend
Returns
-------
data_detrend : detrended signal
Libraries necessary to run function
-----------------------------------
import numpy as np
from unweighted_least_square_fit import least_square_fit
"""
# import libraries
import numpy as np
from lsf import least_square_fit
# Check if data is a 1 dimensional array
assert data.ndim == 1, "Data is not a one dimensional array"
# fit a linear trend at grid point:
data_trend, x_trend = least_square_fit(data,
trend="linear",
parameters=2,
period=12)
# initialize time vector and linear trend:
time = np.arange(1, len(data) + 1, 1)
linear_trend = x_trend[0] + x_trend[1] * time
# remove linear trend:
data_detrend = data - linear_trend + np.mean(linear_trend)
return data_detrend
# Call data for each grid point:
ts_grid = ts_month[:, ilat, ilon]
# Do not preform decorrelation analysis if time series has any masked values.
if ts_grid.mask.all() == False:
# Count the number of data point in the time series
ndata = np.count_nonzero(~np.ma.getmask(ts_grid))
# Proceed with decorrelation time scale calculation if time series has more than one data point.
if ndata > 1:
# Preform any necessary detrending:
# detrend grid point:
ts_trend, x_trend = least_square_fit(data=ts_grid,
trend="linear",
parameters=2,
period=12)
# remove linear trend:
ts_detrend = ts_grid - ts_trend
# Compute decorrelation time scale:
(
ds,
ds_N,
coef_pos,
coef_neg,
upper_95_CI,
lower_95_CI,
) = decor_scale(
data=ts_detrend,
def regional_clima(
data_mean,
data_var,
data_n,
lon,
lat,
lon_grid,
lat_grid,
ngrid,
dcor,
loc,
lsf,
parameters,
):
"""
regional_clima(data_mean, data_var, data_n, lon, lat, lon_grid, lat_grid, ngrid, dcor, loc, lsf, parameters)
Function to compute the regional climatology from monthly climatological data with specified grid and location
in the ocean.
Parameters
----------
data_mean : Monthly Climatology data with the following dimensions in 2D masked geospatial arrays:
(ntime, nlat, nlon) = (12, 133, 360)
date_var : Monthly Climatology data's variance with the following dimensions in 2D masked
geospatial arrays: (ntime, nlat, nlon) = (12, 133, 360)
data_n : Number of observations used in computing Monthly Climatology mean and variance with the
following dimensions: (ntime, nlat, nlon) = (12, 133, 360). Used to compute the standard
error of the mean for error bars.
lon : Longitude vector
ex: lon = np.arange(0, 360, 1)
lat : Latitude vector
ex: lon = np.arange(-66, 66, 1)
lon_grid : Initial longitude grid point to compute the regional climatology
ex: lon_grid = 230
lat_grid : Initial latitude grid point to compute the regional climatology
ex: lon_grid = 230
ngrid : Specifies the size of the n by n grid box that the regional climatology will computed in.
ex: n_grid = 2
dcor : Decorrelation scale (climatological resolution) used for computing degrees of freedom or dof
(used to compute standard error of the mean) where dof is defined as:
dof = n_eff = nobs/dcor where nobs = number of observations in time series. dcor must be an array.
loc : Specifies if the regional climatology is in the northern or southern hemisphere or if it is east or
west of the prime meridian.
ex: loc = [loc_lat, loc_lon] loc[0] = 'NH' or loc[0] = 'SH' and loc[1] = 'west' or loc[1] = 'east'
lsf : Specifies whether the least squares fit model is weighted or unweighted. Options
include: lsf = 'weighted' or 'unweighted'
parameters : Specifies the amount of paramaters for the model. Look at weighted_least_squares_fit.py
documentation for details.
Returns
-------
data_reg_mean : Regional climatology mean
ex: data_reg_mean.shape = (1,12)
data_reg_stdm : Regional climatology standard error of the mean
ex: data_reg_stdm.shape = (1,12)
hfit : Least square fit model.
x_data : Least squares fit model coefficients.
residual : Difference between the model and data.
grid_coordinates : Indices from longitude and latitude which the climatology is computed for.
Libraries necessary to run function
-----------------------------------
import numpy as np
from unweighted_least_square_fit import least_square_fit
from weighted_least_square_fit import weighted_least_square_fit
"""
# Set path to my functions:
import sys
sys.path.append("../tools/")
# import libraries
import numpy as np
# import my functions
from lsf import least_square_fit, weighted_least_square_fit
# case 1: west of prime meridian
if loc[1] == "west":
loc_lon = 360
# case 2: east of prime meridian
elif loc[1] == "east":
loc_lon = 0
# latitude and longitude grid points that will be averaged over:
lat_grid_i = lat[lat_grid]
lat_grid_f = lat[lat_grid + ngrid - 1]
lon_grid_i = lon[lon_grid] - loc_lon
lon_grid_f = lon[lon_grid + ngrid - 1] - loc_lon
grid_cor = [lat_grid_i, lat_grid_f, lon_grid_i, lon_grid_f]
# call mean, variance, number of observations, and decorrelation scale from grid box indices:
data_grid_mean = data_mean[:, lat_grid:(lat_grid + ngrid),
lon_grid:(lon_grid + ngrid)]
data_grid_var = data_var[:, lat_grid:(lat_grid + ngrid),
lon_grid:(lon_grid + ngrid)]
data_grid_n = data_n[:, lat_grid:(lat_grid + ngrid),
lon_grid:(lon_grid + ngrid)]
data_grid_dcor = dcor[:, lat_grid:(lat_grid + ngrid),
lon_grid:(lon_grid + ngrid)]
# Compute the mean and average variance, decorrelation scale number of observations for the region
data_reg_mean = np.ma.mean(np.ma.mean(data_grid_mean,
axis=1,
dtype=np.float64),
axis=1)
data_reg_var = np.ma.mean(np.ma.mean(data_grid_var,
axis=1,
dtype=np.float64),
axis=1)
dcor_reg = np.ma.mean(np.ma.mean(data_grid_dcor, axis=1, dtype=np.float64),
axis=1)
data_reg_n_mean = np.ma.mean(np.ma.mean(data_grid_n,
axis=1,
dtype=np.float64),
axis=1)
# Compute N_eff:
n_eff = data_grid_n / data_grid_dcor
# Compute the average number degrees of freedom (n_eff):
n_eff_mean = np.ma.mean(np.ma.mean(n_eff, axis=1, dtype=np.float64),
axis=1)
# compute the standard error of the mean
data_reg_stdm = np.sqrt(data_reg_var) / np.sqrt(n_eff_mean)
# compute the least square fit:
if lsf == "weighted":
hfit, x_data, x_data_sigma = weighted_least_square_fit(
data=np.ma.copy(data_reg_mean),
sigma=np.ma.copy(data_reg_stdm),
trend="sinusoidal",
parameters=parameters,
period=12,
)
elif lsf == "unweighted":
hfit, x_data = least_square_fit(
data=np.ma.copy(data_reg_mean),
trend="sinusoidal",
parameters=parameters,
period=12,
)
# compute the residue between the model and regional climatology:
residual = hfit - data_reg_mean
# For SH regional climatologies, shift the time series such that austral summer months are center in the figure
if loc[0] == "SH":
# Shift
data_reg_mean = np.reshape(
np.ma.array([data_reg_mean[6:13], data_reg_mean[0:6]]), (1, 12))[0]
data_reg_stdm = np.reshape(
np.ma.array([data_reg_stdm[6:13], data_reg_stdm[0:6]]), (1, 12))[0]
hfit = np.reshape(np.ma.array([hfit[6:13], hfit[0:6]]), (1, 12))[0]
residual = np.reshape(np.ma.array([residual[6:13], residual[0:6]]),
(1, 12))[0]
return data_reg_mean, data_reg_stdm, hfit, x_data, residual, grid_cor