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"""
Functions for computing remote sensing band indices on Digital Earth Africa
data.
"""
# Import required packages
import warnings
import numpy as np
# Define custom functions
def calculate_indices(
ds,
index=None,
collection=None,
satellite_mission=None,
custom_varname=None,
normalise=True,
drop=False,
deep_copy=True,
):
"""
Takes an xarray dataset containing spectral bands, calculates one of
a set of remote sensing indices, and adds the resulting array as a
new variable in the original dataset.
Last modified: July 2022
Parameters
----------
ds : xarray Dataset
A two-dimensional or multi-dimensional array with containing the
spectral bands required to calculate the index. These bands are
used as inputs to calculate the selected water index.
index : str or list of strs
A string giving the name of the index to calculate or a list of
strings giving the names of the indices to calculate:
* ``'ASI'`` (Artificial Surface Index, Yongquan Zhao & Zhe Zhu 2022)
* ``'AWEI_ns'`` (Automated Water Extraction Index, no shadows, Feyisa 2014)
* ``'AWEI_sh'`` (Automated Water Extraction Index, shadows, Feyisa 2014)
* ``'BAEI'`` (Built-Up Area Extraction Index, Bouzekri et al. 2015)
* ``'BAI'`` (Burn Area Index, Martin 1998)
* ``'BSI'`` (Bare Soil Index, Rikimaru et al. 2002)
* ``'BUI'`` (Built-Up Index, He et al. 2010)
* ``'CMR'`` (Clay Minerals Ratio, Drury 1987)
* ``'ENDISI'`` (Enhanced Normalised Difference for Impervious Surfaces Index, Chen et al. 2019)
* ``'EVI'`` (Enhanced Vegetation Index, Huete 2002)
* ``'FMR'`` (Ferrous Minerals Ratio, Segal 1982)
* ``'IOR'`` (Iron Oxide Ratio, Segal 1982)
* ``'LAI'`` (Leaf Area Index, Boegh 2002)
* ``'MBI'`` (Modified Bare Soil Index, Nguyen et al. 2021)
* ``'MNDWI'`` (Modified Normalised Difference Water Index, Xu 1996)
* ``'MSAVI'`` (Modified Soil Adjusted Vegetation Index, Qi et al. 1994)
* ``'NBI'`` (New Built-Up Index, Jieli et al. 2010)
* ``'NBR'`` (Normalised Burn Ratio, Lopez Garcia 1991)
* ``'NDBI'`` (Normalised Difference Built-Up Index, Zha 2003)
* ``'NDCI'`` (Normalised Difference Chlorophyll Index, Mishra & Mishra, 2012)
* ``'NDMI'`` (Normalised Difference Moisture Index, Gao 1996)
* ``'NDSI'`` (Normalised Difference Snow Index, Hall 1995)
* ``'NDTI'`` (Normalised Difference Turbidity Index, Lacaux et al. 2007)
* ``'NDVI'`` (Normalised Difference Vegetation Index, Rouse 1973)
* ``'NDWI'`` (Normalised Difference Water Index, McFeeters 1996)
* ``'SAVI'`` (Soil Adjusted Vegetation Index, Huete 1988)
* ``'TCB'`` (Tasseled Cap Brightness, Crist 1985)
* ``'TCG'`` (Tasseled Cap Greeness, Crist 1985)
* ``'TCW'`` (Tasseled Cap Wetness, Crist 1985)
* ``'WI'`` (Water Index, Fisher 2016)
collection : str
Deprecated in version 0.1.7. Use `satellite_mission` instead.
Valid options are:
* ``'c2'`` (for USGS Landsat Collection 2)
If 'c2', then `satellite_mission='ls'`.
* ``'s2'`` (for Sentinel-2)
If 's2', then `satellite_mission='s2'`.
satellite_mission : str
An string that tells the function which satellite mission's data is
being used to calculate the index. This is necessary because
different satellite missions use different names for bands covering
a similar spectra.
Valid options are:
* ``'ls'`` (for USGS Landsat)
* ``'s2'`` (for Copernicus Sentinel-2)
custom_varname : str, optional
By default, the original dataset will be returned with
a new index variable named after `index` (e.g. 'NDVI'). To
specify a custom name instead, you can supply e.g.
`custom_varname='custom_name'`. Defaults to None, which uses
`index` to name the variable.
normalise : bool, optional
Some coefficient-based indices (e.g. ``'WI'``, ``'BAEI'``,
``'AWEI_ns'``, ``'AWEI_sh'``, ``'TCW'``, ``'TCG'``, ``'TCB'``,
``'EVI'``, ``'LAI'``, ``'SAVI'``, ``'MSAVI'``)
produce different results if surface reflectance values are not
scaled between 0.0 and 1.0 prior to calculating the index.
Setting `normalise=True` first scales values to a 0.0-1.0 range
by dividing by 10000.0. Defaults to True.
drop : bool, optional
Provides the option to drop the original input data, thus saving
space. If `drop=True`, returns only the index and its values.
deep_copy: bool, optional
If `deep_copy=False`, calculate_indices will modify the original
array, adding bands to the input dataset and not removing them.
If the calculate_indices function is run more than once, variables
may be dropped incorrectly producing unexpected behaviour. This is
a bug and may be fixed in future releases. This is only a problem
when `drop=True`.
Returns
-------
ds : xarray Dataset
The original xarray Dataset inputted into the function, with a
new varible containing the remote sensing index as a DataArray.
If drop = True, the new variable/s as DataArrays in the
original Dataset.
"""
# Set ds equal to a copy of itself in order to prevent the function
# from editing the input dataset. This is to prevent unexpected
# behaviour though it uses twice as much memory.
if deep_copy:
ds = ds.copy(deep=True)
# Capture input band names in order to drop these if drop=True
if drop:
bands_to_drop = list(ds.data_vars)
print(f"Dropping bands {bands_to_drop}")
# Dictionary containing remote sensing index band recipes
index_dict = {
# Normalised Difference Vegation Index, Rouse 1973
"NDVI": lambda ds: (ds.nir - ds.red) / (ds.nir + ds.red),
# Enhanced Vegetation Index, Huete 2002
"EVI": lambda ds: (
2.5 * ((ds.nir - ds.red) / (ds.nir + 6 * ds.red - 7.5 * ds.blue + 1))
),
# Leaf Area Index, Boegh 2002
"LAI": lambda ds: (
3.618
* ((2.5 * (ds.nir - ds.red)) / (ds.nir + (6 * ds.red) - (7.5 * ds.blue) + 1))
- 0.118
),
# Soil Adjusted Vegetation Index, Huete 1988
"SAVI": lambda ds: ((1.5 * (ds.nir - ds.red)) / (ds.nir + ds.red + 0.5)),
# Mod. Soil Adjusted Vegetation Index, Qi et al. 1994
"MSAVI": lambda ds: (
(2 * ds.nir + 1 - ((2 * ds.nir + 1) ** 2 - 8 * (ds.nir - ds.red)) ** 0.5)
/ 2
),
# Normalised Difference Moisture Index, Gao 1996
"NDMI": lambda ds: (ds.nir - ds.swir_1) / (ds.nir + ds.swir_1),
# Normalised Burn Ratio, Lopez Garcia 1991
"NBR": lambda ds: (ds.nir - ds.swir_2) / (ds.nir + ds.swir_2),
# Burn Area Index, Martin 1998
"BAI": lambda ds: (1.0 / ((0.10 - ds.red) ** 2 + (0.06 - ds.nir) ** 2)),
# Normalised Difference Chlorophyll Index,
# (Mishra & Mishra, 2012)
"NDCI": lambda ds: (ds.red_edge_1 - ds.red) / (ds.red_edge_1 + ds.red),
# Normalised Difference Snow Index, Hall 1995
"NDSI": lambda ds: (ds.green - ds.swir_1) / (ds.green + ds.swir_1),
# Normalised Difference Water Index, McFeeters 1996
"NDWI": lambda ds: (ds.green - ds.nir) / (ds.green + ds.nir),
# Modified Normalised Difference Water Index, Xu 2006
"MNDWI": lambda ds: (ds.green - ds.swir_1) / (ds.green + ds.swir_1),
# Normalised Difference Built-Up Index, Zha 2003
"NDBI": lambda ds: (ds.swir_1 - ds.nir) / (ds.swir_1 + ds.nir),
# Built-Up Index, He et al. 2010
"BUI": lambda ds: ((ds.swir_1 - ds.nir) / (ds.swir_1 + ds.nir))
- ((ds.nir - ds.red) / (ds.nir + ds.red)),
# Built-up Area Extraction Index, Bouzekri et al. 2015
"BAEI": lambda ds: (ds.red + 0.3) / (ds.green + ds.swir_1),
# New Built-up Index, Jieli et al. 2010
"NBI": lambda ds: (ds.swir_1 + ds.red) / ds.nir,
# Bare Soil Index, Rikimaru et al. 2002
"BSI": lambda ds: ((ds.swir_1 + ds.red) - (ds.nir + ds.blue))
/ ((ds.swir_1 + ds.red) + (ds.nir + ds.blue)),
# Automated Water Extraction Index (no shadows), Feyisa 2014
"AWEI_ns": lambda ds: (
4 * (ds.green - ds.swir_1) - (0.25 * ds.nir * +2.75 * ds.swir_2)
),
# Automated Water Extraction Index (shadows), Feyisa 2014
"AWEI_sh": lambda ds: (
ds.blue + 2.5 * ds.green - 1.5 * (ds.nir + ds.swir_1) - 0.25 * ds.swir_2
),
# Water Index, Fisher 2016
"WI": lambda ds: (
1.7204
+ 171 * ds.green
+ 3 * ds.red
- 70 * ds.nir
- 45 * ds.swir_1
- 71 * ds.swir_2
),
# Tasseled Cap Wetness, Crist 1985
"TCW": lambda ds: (
0.0315 * ds.blue
+ 0.2021 * ds.green
+ 0.3102 * ds.red
+ 0.1594 * ds.nir
+ -0.6806 * ds.swir_1
+ -0.6109 * ds.swir_2
),
# Tasseled Cap Greeness, Crist 1985
"TCG": lambda ds: (
-0.1603 * ds.blue
+ -0.2819 * ds.green
+ -0.4934 * ds.red
+ 0.7940 * ds.nir
+ -0.0002 * ds.swir_1
+ -0.1446 * ds.swir_2
),
# Tasseled Cap Brightness, Crist 1985
"TCB": lambda ds: (
0.2043 * ds.blue
+ 0.4158 * ds.green
+ 0.5524 * ds.red
+ 0.5741 * ds.nir
+ 0.3124 * ds.swir_1
+ -0.2303 * ds.swir_2
),
# Clay Minerals Ratio, Drury 1987
"CMR": lambda ds: (ds.swir_1 / ds.swir_2),
# Ferrous Minerals Ratio, Segal 1982
"FMR": lambda ds: (ds.swir_1 / ds.nir),
# Iron Oxide Ratio, Segal 1982
"IOR": lambda ds: (ds.red / ds.blue),
# Normalized Difference Turbidity Index, Lacaux, J.P. et al. 2007
"NDTI": lambda ds: (ds.red - ds.green) / (ds.red + ds.green),
# Modified Bare Soil Index, Nguyen et al. 2021
"MBI": lambda ds: ((ds.swir_1 - ds.swir_2 - ds.nir) / (ds.swir_1 + ds.swir_2 + ds.nir)) + 0.5,
}
# Enhanced Normalised Difference Impervious Surfaces Index, Chen et al. 2019
def mndwi(ds):
return (ds.green - ds.swir_1) / (ds.green + ds.swir_1)
def swir_diff(ds):
return ds.swir_1/ds.swir_2
def alpha(ds):
return (2*(np.mean(ds.blue)))/(np.mean(swir_diff(ds)) + np.mean(mndwi(ds)**2))
def ENDISI(ds):
m = mndwi(ds)
s = swir_diff(ds)
a = alpha(ds)
return (ds.blue - (a)*(s + m**2))/(ds.blue + (a)*(s + m**2))
index_dict["ENDISI"] = ENDISI
## Artificial Surface Index, Yongquan Zhao & Zhe Zhu 2022
def af(ds):
AF = (ds.nir - ds.blue) / (ds.nir + ds.blue)
AF_norm = (AF - AF.min(dim=["y","x"]))/(AF.max(dim=["y","x"]) - AF.min(dim=["y","x"]))
return AF_norm
def ndvi(ds):
return (ds.nir - ds.red) / (ds.nir + ds.red)
def msavi(ds):
return ((2 * ds.nir + 1 - ((2 * ds.nir + 1) ** 2 - 8 * (ds.nir - ds.red)) ** 0.5) / 2 )
def vsf(ds):
NDVI = ndvi(ds)
MSAVI = msavi(ds)
VSF = 1 - NDVI * MSAVI
VSF_norm = (VSF - VSF.min(dim=["y","x"]))/(VSF.max(dim=["y","x"]) - VSF.min(dim=["y","x"]))
return VSF_norm
def mbi(ds):
return ((ds.swir_1 - ds.swir_2 - ds.nir) / (ds.swir_1 + ds.swir_2 + ds.nir)) + 0.5
def embi(ds):
MBI = mbi(ds)
MNDWI = mndwi(ds)
return (MBI - MNDWI - 0.5) / (MBI + MNDWI + 1.5)
def ssf(ds):
EMBI = embi(ds)
SSF = 1 - EMBI
SSF_norm = (SSF - SSF.min(dim=["y","x"]))/(SSF.max(dim=["y","x"]) - SSF.min(dim=["y","x"]))
return SSF_norm
# Overall modulation using the Modulation Factor (MF).
def mf(ds):
MF = ((ds.blue + ds.green) - (ds.nir + ds.swir_1)) / ((ds.blue + ds.green) + (ds.nir + ds.swir_1))
MF_norm = (MF - MF.min(dim=["y","x"]))/(MF.max(dim=["y","x"]) - MF.min(dim=["y","x"]))
return MF_norm
def ASI(ds):
AF = af(ds)
VSF = vsf(ds)
SSF = ssf(ds)
MF = mf(ds)
return AF * VSF * SSF * MF
index_dict["ASI"] = ASI
# If index supplied is not a list, convert to list. This allows us to
# iterate through either multiple or single indices in the loop below
indices = index if isinstance(index, list) else [index]
# calculate for each index in the list of indices supplied (indexes)
for index in indices:
# Select an index function from the dictionary
index_func = index_dict.get(str(index))
# If no index is provided or if no function is returned due to an
# invalid option being provided, raise an exception informing user to
# choose from the list of valid options
if index is None:
raise ValueError(
f"No remote sensing `index` was provided. Please "
"refer to the function \ndocumentation for a full "
"list of valid options for `index` (e.g. 'NDVI')"
)
elif (
index
in [
"WI",
"BAEI",
"AWEI_ns",
"AWEI_sh",
"EVI",
"LAI",
"SAVI",
"MSAVI",
]
and not normalise
):
warnings.warn(
f"\nA coefficient-based index ('{index}') normally "
"applied to surface reflectance values in the \n"
"0.0-1.0 range was applied to values in the 0-10000 "
"range. This can produce unexpected results; \nif "
"required, resolve this by setting `normalise=True`"
)
elif index_func is None:
raise ValueError(
f"The selected index '{index}' is not one of the "
"valid remote sensing index options. \nPlease "
"refer to the function documentation for a full "
"list of valid options for `index`"
)
# Deprecation warning if `collection` is specified instead of `satellite_mission`.
if collection is not None:
warnings.warn('`collection` was deprecated in version 0.1.7. Use `satelite_mission` instead.',
DeprecationWarning,
stacklevel=2)
# Map the collection values to the valid satellite_mission values.
if collection == "c2":
satellite_mission = "ls"
elif collection == "s2":
satellite_mission = "s2"
# Raise error if no valid collection name is provided:
else:
raise ValueError(
f"'{collection}' is not a valid option for "
"`collection`. Please specify either \n"
"'c2' or 's2'.")
# Rename bands to a consistent format if depending on what satellite mission
# is specified in `satellite_mission`. This allows the same index calculations
# to be applied to all satellite missions. If no satellite mission was provided,
# raise an exception.
if satellite_mission is None:
raise ValueError(
"No `satellite_mission` was provided. Please specify "
"either 'ls' or 's2' to ensure the \nfunction "
"calculates indices using the correct spectral "
"bands."
)
elif satellite_mission == "ls":
sr_max = 1.0
# Dictionary mapping full data names to simpler alias names
# This only applies to properly-scaled "ls" data i.e. from
# the Landsat geomedians. calculate_indices will not show
# correct output for raw (unscaled) Landsat data (i.e. default
# outputs from dc.load)
bandnames_dict = {
"SR_B1": "blue",
"SR_B2": "green",
"SR_B3": "red",
"SR_B4": "nir",
"SR_B5": "swir_1",
"SR_B7": "swir_2",
}
# Rename bands in dataset to use simple names (e.g. 'red')
bands_to_rename = {
a: b for a, b in bandnames_dict.items() if a in ds.variables
}
elif satellite_mission == "s2":
sr_max = 10000
# Dictionary mapping full data names to simpler alias names
bandnames_dict = {
"nir_1": "nir",
"B02": "blue",
"B03": "green",
"B04": "red",
"B05": "red_edge_1",
"B06": "red_edge_2",
"B07": "red_edge_3",
"B08": "nir",
"B11": "swir_1",
"B12": "swir_2",
}
# Rename bands in dataset to use simple names (e.g. 'red')
bands_to_rename = {
a: b for a, b in bandnames_dict.items() if a in ds.variables
}
# Raise error if no valid satellite_mission name is provided:
else:
raise ValueError(
f"'{satellite_mission}' is not a valid option for "
"`satellite_mission`. Please specify either \n"
"'ls' or 's2'"
)
# Apply index function
try:
# If normalised=True, divide data by 10,000 before applying func
mult = sr_max if normalise else 1.0
index_array = index_func(ds.rename(bands_to_rename) / mult)
except AttributeError:
raise ValueError(
f"Please verify that all bands required to "
f"compute {index} are present in `ds`."
)
# Add as a new variable in dataset
output_band_name = custom_varname if custom_varname else index
ds[output_band_name] = index_array
# Once all indexes are calculated, drop input bands if drop=True
if drop:
ds = ds.drop(bands_to_drop)
# Return input dataset with added water index variable
return ds
def dualpol_indices(
ds,
co_pol='vv',
cross_pol='vh',
index=None,
custom_varname=None,
drop=False,
deep_copy=True,
):
"""
Takes an xarray dataset containing dual-polarization radar backscatter,
calculates one or a set of indices, and adds the resulting array as a
new variable in the original dataset.
Last modified: July 2021
Parameters
----------
ds : xarray Dataset
A two-dimensional or multi-dimensional array containing the
two polarization bands.
co_pol: str
Measurement name for the co-polarization band.
Default is 'vv' for Sentinel-1.
cross_pol: str
Measurement name for the cross-polarization band.
Default is 'vh' for Sentinel-1.
index : str or list of strs
A string giving the name of the index to calculate or a list of
strings giving the names of the indices to calculate:
* ``'RVI'`` (Radar Vegetation Index for dual-pol, Trudel et al. 2012; Nasirzadehdizaji et al., 2019; Gururaj et al., 2019)
* ``'VDDPI'`` (Vertical dual depolarization index, Periasamy 2018)
* ``'theta'`` (pseudo scattering-type, Bhogapurapu et al. 2021)
* ``'entropy'`` (pseudo scattering entropy, Bhogapurapu et al. 2021)
* ``'purity'`` (co-pol purity, Bhogapurapu et al. 2021)
* ``'ratio'`` (cross-pol/co-pol ratio)
custom_varname : str, optional
By default, the original dataset will be returned with
a new index variable named after `index` (e.g. 'RVI'). To
specify a custom name instead, you can supply e.g.
`custom_varname='custom_name'`. Defaults to None, which uses
`index` to name the variable.
drop : bool, optional
Provides the option to drop the original input data, thus saving
space. If `drop=True`, returns only the index and its values.
deep_copy: bool, optional
If `deep_copy=False`, calculate_indices will modify the original
array, adding bands to the input dataset and not removing them.
If the calculate_indices function is run more than once, variables
may be dropped incorrectly producing unexpected behaviour. This is
a bug and may be fixed in future releases. This is only a problem
when `drop=True`.
Returns
-------
ds : xarray Dataset
The original xarray Dataset inputted into the function, with a
new varible containing the remote sensing index as a DataArray.
If drop = True, the new variable/s as DataArrays in the
original Dataset.
"""
if not co_pol in list(ds.data_vars):
raise ValueError(f"{co_pol} measurement is not in the dataset")
if not cross_pol in list(ds.data_vars):
raise ValueError(f"{cross_pol} measurement is not in the dataset")
# Set ds equal to a copy of itself in order to prevent the function
# from editing the input dataset. This is to prevent unexpected
# behaviour though it uses twice as much memory.
if deep_copy:
ds = ds.copy(deep=True)
# Capture input band names in order to drop these if drop=True
if drop:
bands_to_drop = list(ds.data_vars)
print(f"Dropping bands {bands_to_drop}")
def ratio(ds):
return ds[cross_pol] / ds[co_pol]
def purity(ds):
return (1 - ratio(ds)) / (1 + ratio(ds))
def theta(ds):
return np.arctan((1 - ratio(ds))**2 / (1 + ratio(ds)**2 - ratio(ds)))
def P1(ds):
return 1 / (1 + ratio(ds))
def P2(ds):
return 1 - P1(ds)
def entropy(ds):
return P1(ds)*np.log2(P1(ds)) + P2(ds)*np.log2(P2(ds))
# Dictionary containing remote sensing index band recipes
index_dict = {
# Radar Vegetation Index for dual-pol, Trudel et al. 2012
"RVI": lambda ds: 4*ds[cross_pol] / (ds[co_pol] + ds[cross_pol]),
# Vertical dual depolarization index, Periasamy 2018
"VDDPI": lambda ds: (ds[co_pol] + ds[cross_pol]) / ds[co_pol],
# cross-pol/co-pol ratio
"ratio": ratio,
# co-pol purity, Bhogapurapu et al. 2021
"purity": purity,
# pseudo scattering-type, Bhogapurapu et al. 2021
"theta": theta,
# pseudo scattering entropy, Bhogapurapu et al. 2021
"entropy": entropy,
}
# If index supplied is not a list, convert to list. This allows us to
# iterate through either multiple or single indices in the loop below
indices = index if isinstance(index, list) else [index]
# calculate for each index in the list of indices supplied (indexes)
for index in indices:
# Select an index function from the dictionary
index_func = index_dict.get(str(index))
# If no index is provided or if no function is returned due to an
# invalid option being provided, raise an exception informing user to
# choose from the list of valid options
if index is None:
raise ValueError(
f"No radar `index` was provided. Please "
"refer to the function \ndocumentation for a full "
"list of valid options for `index` (e.g. 'RVI')"
)
elif index_func is None:
raise ValueError(
f"The selected index '{index}' is not one of the "
"valid remote sensing index options. \nPlease "
"refer to the function documentation for a full "
"list of valid options for `index`"
)
# Apply index function
index_array = index_func(ds)
# Add as a new variable in dataset
output_band_name = custom_varname if custom_varname else index
ds[output_band_name] = index_array
# Once all indexes are calculated, drop input bands if drop=True
if drop:
ds = ds.drop(bands_to_drop)
# Return input dataset with added water index variable
return ds