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column_water_vapor.py
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column_water_vapor.py
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#!/usr/bin/python
# -*- coding: utf-8 -*-
"""
Determining atmospheric column water vapor based on
Huazhong Ren, Chen Du, Qiming Qin, Rongyuan Liu, Jinjie Meng, Jing Li
@author nik | Created on 2015-04-18 03:48:20 | Updated on June 2020
"""
from citations import CITATION_COLUMN_WATER_VAPOR
from constants import DUMMY_Ti_MEAN
from constants import DUMMY_Tj_MEAN
from constants import DUMMY_Ti_MEDIAN
from constants import DUMMY_Tj_MEDIAN
from constants import DUMMY_Rji
from constants import EQUATION
from constants import NUMERATOR
from constants import DENOMINATOR_Ti
from constants import DENOMINATOR_Tj
from randomness import random_adjacent_pixel_values
from grass.pygrass.modules.shortcuts import general as g
from dummy_mapcalc_strings import replace_dummies
import grass.script as grass
from helpers import run
class Column_Water_Vapor():
"""
Retrieving atmospheric column water vapor from Landsat8 TIRS data based on
the modified split-window covariance and variance ratio (MSWCVR).
-------------------------------------------------------------------------
*Note,* this class produces valid expressions for GRASS GIS' mapcalc raster
processing module and does not directly compute column water vapor
estimations.
-------------------------------------------------------------------------
With a vital assumption that the atmosphere is unchanged over the
neighboring pixels, the MSWCVR method relates the atmospheric CWV to the
ratio of the upward transmittances in two thermal infrared bands, whereas
the transmittance ratio can be calculated based on the TOA brightness
temperatures of the two bands.
Considering N adjacent pixels, the CWV in the MSWCVR method is estimated
as:
- cwv = c0 + c1 * (tj / ti) + c2 * (tj / ti)^2
- tj/ti ~ Rji = SUM [ ( Tik - Ti_mean ) * ( Tjk - Tj_mean ) ] /
SUM [ ( Tik - Ti_mean )^2 ]
In Equation (3a):
- c0, c1 and c2 are coefficients obtained from simulated data;
- τ is the band effective atmospheric transmittance;
- N is the number of adjacent pixels (excluding water and cloud pixels)
in a spatial window of size n (i.e., N = n × n);
- Ti,k and Tj,k are Top of Atmosphere brightness temperatures (K) of
bands i and j for the kth pixel;
- mean(Ti) and mean(Tj) or median(Ti) and median(Tj) are the mean or median
brightness temperatures of the N pixels for the two bands
The regression coefficients:
==================================================================
* NOTE, there is a typo in the paper!
[0] Du, Chen; Ren, Huazhong; Qin, Qiming; Meng, Jinjie; Zhao,
Shaohua. 2015. "A Practical Split-Window Algorithm for Estimating
Land Surface Temperature from Landsat 8 Data." Remote Sens. 7, no.
1: 647-665.
http://www.mdpi.com/2072-4292/7/1/647/htm\#sthash.ba1pt9hj.dpuf
from which the equation's coefficients are (also) published.
The correct order of constants is as below, source from the
referenced paper below.
==================================================================
- c2 = -9.674
- c1 = 0.653
- c0 = 9.087
where obtained by:
- 946 cloud-free TIGR atmospheric profiles,
- the new high accurate atmospheric radiative transfer model MODTRAN 5.2
- simulating the band effective atmospheric transmittance
Model analysis indicated that this method will obtain a CWV RMSE of about
0.5 g/cm2. Details about the CWV retrieval can be found in:
Ren, H., Du, C., Liu, R., Qin, Q., Yan, G., Li, Z. L., & Meng, J. (2015).
Atmospheric water vapor retrieval from Landsat 8 thermal infrared images.
Journal of Geophysical Research: Atmospheres, 120(5), 1723-1738.
Old reference:
Ren, H.; Du, C.; Qin, Q.; Liu, R.; Meng, J.; Li, J. Atmospheric water vapor
retrieval from landsat 8 and its validation. In Proceedings of the IEEE
International Geosciene and Remote Sensing Symposium (IGARSS), Quebec, QC,
Canada, July 2014; pp. 3045–3048.
"""
def __init__(self, window_size, ti, tj):
"""
"""
# citation
self.citation = CITATION_COLUMN_WATER_VAPOR
# model constants
self.c2 = -9.674
self.c1 = 0.653
self.c0 = 9.087
self._equation = ('c0 + '
'c1 * (tj / ti) + '
'c2 * (tj / ti)^2')
self._model = ('{c0} + '
'{c1} * ({tj} / {ti}) + '
'{c2} * ({tj} / {ti})^2')
# window of N (= n by n) pixels, adjacent pixels
assert window_size % 2 != 0, "Window size should be an even number!"
assert window_size >= 7, "Window size should be equal to/larger than 7."
self.window_size = window_size
self.window_height = self.window_size
self.window_width = self.window_size
self.adjacent_pixels = self._derive_adjacent_pixels()
# maps for transmittance
self.ti = ti
self.tj = tj
# mapcalc modifiers to access neighborhood pixels
self.modifiers_ti = self._derive_modifiers(self.ti)
self.modifiers_tj = self._derive_modifiers(self.tj)
self.modifiers = list(zip(self.modifiers_ti, self.modifiers_tj))
# mapcalc expression for means; medians
self.mean_ti_expression = self._mean_tirs_expression(self.modifiers_ti)
self.mean_tj_expression = self._mean_tirs_expression(self.modifiers_tj)
self.median_ti_expression = self._median_tirs_expression(self.modifiers_ti)
self.median_tj_expression = self._median_tirs_expression(self.modifiers_tj)
# mapcalc expression for ratio ji
self.ratio_ji_expression = str()
self.ratio_ij_expression = str()
self.retrieval_accuracy = float()
def __str__(self):
"""
The object's self string
"""
msg = (f'- Window size: {self.window_size} by + {self.window_size}'
'- Expression for r.mapcalc to determine column water vapor: ')
return msg + str(self.column_water_vapor_expression)
# def compute_column_water_vapor(self, tik, tjk):
# """
# Compute the column water vapor based on lists of input Ti and Tj
# values.
# This is a single value production function. It does not read or return
# a map.
# """
# # feed with N pixels
# ti_mean = sum(tik) / len(tik)
# tj_mean = sum(tjk) / len(tjk)
# # numerator: sum of all (Tik - Ti_mean) * (Tjk - Tj_mean)
# numerator_ji_terms = []
# for ti, tj in zip(tik, tjk):
# numerator_ji_terms.append((ti - ti_mean) * (tj - tj_mean))
# numerator_ji = sum(numerator_ji_terms) * 1.0
# # denominator: sum of all (Tik - Ti_mean)^2
# denominator_ji_terms = []
# for ti in tik:
# term = (ti - ti_mean)**2
# denominator_ji_terms.append(term)
# denominator_ji = sum(denominator_ji_terms) * 1.0
# ratio_ji = numerator_ji / denominator_ji
# cwv = self.c0 + self.c1 * (ratio_ji) + self.c2 * ((ratio_ji) ** 2)
# return cwv
def _derive_adjacent_pixels(self):
"""
Derive a window/grid of "adjacent" pixels:
[-1, -1] [-1, 0] [-1, 1]
[ 0, -1] [ 0, 0] [ 0, 1]
[ 1, -1] [ 1, 0] [ 1, 1]
"""
# center row indexing
half_height = (self.window_height - 1) // 2
# center col indexing
half_width = (self.window_width - 1) // 2
return [[col, row]
for col in range(-half_width + 1, half_width)
for row in range(-half_height + 1, half_height)]
def _derive_modifiers(self, tx):
"""
Return mapcalc map modifiers for adjacent pixels for the input map tx
"""
return [tx + str(pixel)
for pixel
in self.adjacent_pixels]
def _mean_tirs_expression(self, modifiers):
"""
Return mapcalc expression for window means based on the given mapcalc
pixel modifiers.
"""
tx_sum = '(' + ' + '.join(modifiers) + ')'
tx_length = len(modifiers)
tx_mean_expression = f'{tx_sum} / {tx_length}'
return tx_mean_expression
def _median_tirs_expression(self, modifiers):
"""
Parameters
----------
modifiers
Pixel modifiers to access adjacent pixels using GRASS GIS' mapcalc
syntax
Returns
-------
tx_mean_expression
A mapcalc expression for window medians based on the given mapcalc
pixel modifiers.
"""
modifiers = ', '.join(modifiers)
tx_median_expression = f'median({modifiers})'
return tx_median_expression
def _numerator_for_ratio(self, ti_m, tj_m):
"""
Build the numerator for Ratio ji or ij which is:
Sum( (Tik - Ti_mean) * (Tjk - Tj_mean) )
Note that 'Ratio_ji' =~ 'Ratio_ij'.
Use this function for building GRASS GIS mapcalc expression.
Parameters
----------
modifiers
Not explicitly needed as an input since it is sourced from the
objects attribute self.modifiers
ti_m
Either of mean(Ti) or median(Ti)
tj_m
Either of mean(Tj) or median(Tj)
Returns
-------
numerator
The numerator expression for Ratio ji or ij
Examples
--------
>>> numerator = self._numerator_for_ratio(
ti_m = mean_ti,
tj_m = mean_tj,
)
>>> numerator = self._numerator_for_ratio(
ti_m = median_ti,
tj_m = median_tj,
)
"""
numerator = ' + '.join([NUMERATOR.format(Ti=modifier_ti,
Tim=ti_m,
Tj=modifier_tj,
Tjm=tj_m)
for modifier_ti, modifier_tj
in self.modifiers])
return numerator
def _denominator_for_ratio_ji(self, ti_m):
"""
Denominator for Ratio ji which is:
Sum ( (Tik - Ti_mean)^2 )
"""
denominator_ji = ' + '.join([DENOMINATOR_Ti.format(Ti=modifier_ti,
Tim=ti_m)
for modifier_ti
in self.modifiers_ti])
return denominator_ji
def _denominator_for_ratio_ij(self, tj_m):
"""
Denominator for Ratio ij.
"""
denominator_ij = ' + '.join([DENOMINATOR_Tj.format(Tj=modifier_tj,
Tjm=tj_m)
for modifier_tj
in self.modifiers_tj])
return denominator_ij
def _ratio_ji_expression(self, statistic):
"""
Returns a mapcalc expression for the Ratio ji, part of the column water
vapor retrieval model.
"""
if 'mean' in statistic:
rji_numerator = self._numerator_for_ratio(
ti_m=DUMMY_Ti_MEAN,
tj_m=DUMMY_Tj_MEAN,
)
rji_denominator = self._denominator_for_ratio_ji(ti_m=DUMMY_Ti_MEAN)
if 'median' in statistic:
rji_numerator = self._numerator_for_ratio(
ti_m=DUMMY_Ti_MEDIAN,
tj_m=DUMMY_Tj_MEDIAN,
)
rji_denominator = self._denominator_for_ratio_ji(ti_m=DUMMY_Ti_MEDIAN)
rji = f'( {rji_numerator} ) / ( {rji_denominator} )'
self.ratio_ji_expression = rji
return rji
def _ratio_ij_expression(self, statistic):
"""
Returns a mapcalc expression for the Ratio ij, part of the column water
vapor retrieval model.
"""
if 'mean' in statistic:
rij_numerator = self._numerator_for_ratio(
ti_m=DUMMY_Ti_MEAN,
tj_m=DUMMY_Tj_MEAN,
)
rij_denominator = self._denominator_for_ratio_ij(tj_m=DUMMY_Tj_MEAN)
if 'median' in statistic:
rij_numerator = self._numerator_for_ratio(
ti_m=DUMMY_Ti_MEDIAN,
tj_m=DUMMY_Tj_MEDIAN,
)
rij_denominator = self._denominator_for_ratio_ij(tj_m=DUMMY_Tj_MEDIAN)
rij = f'( {rij_numerator} ) / ( {rij_denominator} )'
self.ratio_ij_expression = rij
return rij
def _cwv_expression_mean(self):
"""
Build and return a valid mapcalc expression for deriving a Column
Water Vapor map from Landsat8's brightness temperature channels
B10, B11 based on the MSWCVM method (see citation).
"""
modifiers_ti = self._derive_modifiers(self.ti)
ti_mean = self._mean_tirs_expression(modifiers_ti)
modifiers_tj = self._derive_modifiers(self.tj)
tj_mean = self._mean_tirs_expression(modifiers_tj)
numerator = self._numerator_for_ratio(
ti_m=DUMMY_Ti_MEAN,
tj_m=DUMMY_Tj_MEAN,
)
denominator = self._denominator_for_ratio_ji(ti_m=DUMMY_Ti_MEAN)
cwv_expression = ('eval('
f'\ \n ti_mean = {ti_mean},'
f'\ \n tj_mean = {tj_mean},'
f'\ \n numerator = {numerator},'
f'\ \n denominator = {denominator},'
'\ \n rji = numerator / denominator,'
f'\ \n {self.c0} + {self.c1} * (rji) + {self.c2} * (rji)^2)')
return cwv_expression
def _cwv_expression_mean_ij(self):
"""
Build and return a valid mapcalc expression for deriving a Column
Water Vapor map from Landsat8's brightness temperature channels
B10, B11 based on the MSWCVM method (see citation).
"""
modifiers_ti = self._derive_modifiers(self.ti)
ti_mean = self._mean_tirs_expression(modifiers_ti)
modifiers_tj = self._derive_modifiers(self.tj)
tj_mean = self._mean_tirs_expression(modifiers_tj)
numerator = self._numerator_for_ratio(
ti_m=DUMMY_Ti_MEAN,
tj_m=DUMMY_Tj_MEAN,
)
denominator = self._denominator_for_ratio_ij(tj_m=DUMMY_Tj_MEAN)
cwv_expression = ('eval('
f'\ \n ti_mean = {ti_mean},'
f'\ \n tj_mean = {tj_mean},'
f'\ \n numerator = {numerator},'
f'\ \n denominator = {denominator},'
'\ \n rji = numerator / denominator,'
f'\ \n {self.c0} + {self.c1} * (rji) + {self.c2} * (rji)^2)')
return cwv_expression
def _cwv_expression_median(self):
"""
Build and return a valid mapcalc expression for deriving a Column
Water Vapor map from Landsat8's brightness temperature channels
B10, B11 based on the MSWCVM method (see citation).
"""
modifiers_ti = self._derive_modifiers(self.ti)
ti_median = self._median_tirs_expression(modifiers_ti)
modifiers_tj = self._derive_modifiers(self.tj)
tj_median = self._median_tirs_expression(modifiers_tj)
numerator = self._numerator_for_ratio(
ti_m=DUMMY_Ti_MEDIAN,
tj_m=DUMMY_Tj_MEDIAN,
)
denominator = self._denominator_for_ratio_ji(ti_m=DUMMY_Ti_MEDIAN)
cwv_expression = ('eval('
f'\ \n ti_median = {ti_median},'
f'\ \n tj_median = {tj_median},'
f'\ \n numerator = {numerator},'
f'\ \n denominator = {denominator},'
'\ \n rji = numerator / denominator,'
f'\ \n {self.c0} + {self.c1} * (rji) + {self.c2} * (rji)^2)')
return cwv_expression
def _cwv_expression_median_ij(self):
"""
Build and return a valid mapcalc expression for deriving a Column
Water Vapor map from Landsat8's brightness temperature channels
B10, B11 based on the MSWCVM method (see citation).
"""
modifiers_ti = self._derive_modifiers(self.ti)
ti_median = self._median_tirs_expression(modifiers_ti)
modifiers_tj = self._derive_modifiers(self.tj)
tj_median = self._median_tirs_expression(modifiers_tj)
numerator = self._numerator_for_ratio(
ti_m=DUMMY_Ti_MEDIAN,
tj_m=DUMMY_Tj_MEDIAN,
)
denominator = self._denominator_for_ratio_ij(tj_m=DUMMY_Tj_MEDIAN)
cwv_expression = ('eval('
f'\ \n ti_median = {ti_median},'
f'\ \n tj_median = {tj_median},'
f'\ \n numerator = {numerator},'
f'\ \n denominator = {denominator},'
'\ \n rji = numerator / denominator,'
f'\ \n {self.c0} + {self.c1} * (rji) + {self.c2} * (rji)^2)')
return cwv_expression
def _compute_retrieval_accuracy(self, **kwargs):
"""
"""
if 'mean' in kwargs:
numerator_ji = self._numerator_for_ratio(
ti_m=DUMMY_Ti_MEAN,
tj_m=DUMMY_Tj_MEAN,
)
numerator_ij = numerator_ji
denominator_ji = self._denominator_for_ratio_ji(ti_m=DUMMY_Ti_MEAN)
denominator_ij = self._denominator_for_ratio_ij(tj_m=DUMMY_Tj_MEAN)
if 'median' in kwargs:
numerator_ji = self._numerator_for_ratio(
ti_m=DUMMY_Ti_MEDIAN,
tj_m=DUMMY_Tj_MEDIAN,
)
numerator_ij = numerator_ji
denominator_ji = self._denominator_for_ratio_ji(ti_m=DUMMY_Ti_MEDIAN)
denominator_ij = self._denominator_for_ratio_ij(tj_m=DUMMY_Tj_MEDIAN)
ratio_ji = numerator_ji / denominator_ji
ratio_ij = numerator_ij / denominator_ij
x2 = ratio_ji * ratio_ij
self.retrieval_accuracy = x2
return ratio_ji * ratio_ij
def _retrieval_accuracy_expression_mean():
"""
"""
ratio_ji = self._cwv_expression_mean()
ratio_ij = self._cwv_expression_mean_ij
return ratio_ji * ratio_ij
def _retrieval_accuracy_expression_median():
"""
"""
ratio_ji = self._cwv_expression_median()
ratio_ij = self._cwv_expression_median_ij
return ratio_ji * ratio_ij
def estimate_cwv(
temporary_map,
cwv_map,
t10,
t11,
window_size,
median=False,
info=False,
):
"""
Derive a column water vapor map using a single mapcalc expression based on
eval.
*** To Do: evaluate -- does it work correctly? *** !
"""
msg = "\n|i Estimating atmospheric column water vapor"
cwv = Column_Water_Vapor(window_size, t10, t11)
if median:
msg += f'\n|! Computing median value in a {window_size}^2 pixel neighborhood'
cwv_expression = cwv._cwv_expression_median()
else:
cwv_expression = cwv._cwv_expression_mean()
# if accuracy:
# if median:
# accuracy_expression = cwv._accuracy_expression_median()
# else:
# accuracy_expression = cwv._accuracy_expression_mean()
# else:
# accuracy_expression = str()
if info:
msg += '\n Expression:\n'
msg = replace_dummies(
cwv_expression,
in_ti=t10, out_ti='T10',
in_tj=t11, out_tj='T11',
)
g.message(msg)
cwv_equation = EQUATION.format(
result=temporary_map,
expression=cwv_expression,
)
grass.mapcalc(cwv_equation, overwrite=True)
# accuracy_equation = EQUATION.format(result=outname, expression=accuracy_expression)
# grass.mapcalc(accuracy_equation, overwrite=True)
if info:
run('r.info', map=temporary_map, flags='r')
if cwv_map:
history_cwv = f'\nColumn Water Vapor = {cwv._equation}'
history_cwv += f'\nSpatial window size: {cwv.window_size}^2'
title_cwv = 'Column Water Vapor'
description_cwv = 'Column Water Vapor based on MSWVCM'
units_cwv = 'g/cm^2'
source1_cwv = cwv.citation
source2_cwv = 'FixMe'
run("r.support",
map=temporary_map,
title=title_cwv,
units=units_cwv,
description=description_cwv,
source1=source1_cwv,
source2=source2_cwv,
history=history_cwv,
)
run('g.rename', raster=(temporary_map, cwv_map))
# reusable & stand-alone
if __name__ == "__main__":
print ('Atmpspheric column water vapor retrieval '
'from Landsat 8 TIRS data.'
' (Running as stand-alone tool?)')