Further author information: (Send correspondence to Satish Kumar, Rui Kou,
Vikram Jayaram)
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Rui Kou: E-mail<EMAIL_ADDRESS>
Vikram Jayaram<EMAIL_ADDRESS>
# In-situ Water quality monitoring in Oil and Gas operations

Satish Kumar  University of California, Santa Barbara  Rui Kou  Pioneer
Natural Resources, Irving, Texas  Henry Hill  Pioneer Natural Resources,
Irving, Texas  Jake Lempges  Pioneer Natural Resources, Irving, Texas  Eric
Qian  Pioneer Natural Resources, Irving, Texas  Vikram Jayaram  Pioneer
Natural Resources, Irving, Texas

###### Abstract

From agriculture to mining, to energy, surface water quality monitoring is an
essential task. As oil and gas operators work to reduce the consumption of
freshwater, it is increasingly important to actively manage fresh and non-
fresh water resources over the long term. For large-scale monitoring, manual
sampling at many sites has become too time-consuming and unsustainable, given
the sheer number of dispersed ponds, small lakes, playas, and wetlands over a
large area. Therefore, satellite-based environmental monitoring presents great
potential. Many existing satellite-based monitoring studies utilize index-
based methods to monitor large water bodies such as rivers and oceans.
However, these existing methods fail when monitoring small ponds–the
reflectance signal received from small water bodies is too weak to detect. To
address this challenge, we propose a new Water Quality Enhanced Index (WQEI)
Model, which is designed to enable users to determine contamination levels in
water bodies with weak reflectance patterns. Our results show that 1) WQEI is
a good indicator of water turbidity validated with 1200 water samples measured
in the laboratory, and 2) by applying our method to commonly available
satellite data (e.g. LandSat8), one can achieve high accuracy water quality
monitoring efficiently in large regions. This provides a tool for operators to
optimize the quality of water stored within surface storage ponds and
increasing the readiness and availability of non-fresh water. The code-base is
publicly available at Github: https://github.com/satish1901/In-situ-Water-
quality-monitoring-in-Oil-and-Gas-operations

##  1 Introduction

Water is one of the most abundant and most essential resources on earth. Not
only does water sustain all life on Earth, but it is also requisite to
industrial processes such as fabrication, washing, cooling, and fuel
generation [1, 2]. Particularly in the oilfield, the average frac job uses 4
million gallons of water, and availability becomes a key logistical issue in
high activity basins such as the Permian [3]. The industry addresses this
necessity with efficient storage of water, particularly in networks of open
body ponds down to the frac site [4]. However, new challenges arise from even
this, such as monitoring, sourcing, transportation, and treatment.

The monitoring and maintenance of these water bodies is crucial. Monitoring is
usually done manually: water samples are collected from different points in
the pond (as impurities can vary spatially) and sent off to a lab to be
tested. Tests include checking for types of impurities, sediment
concentration, algae growth, turbidity of the water, and chloride
concentration changes over time. The amount of manual field work needed to
collect samples from multiple points and multiple water bodies across a large
distance is almost infeasible. Due to the logistical challenges testing
presents, sampling and testing is conducted at extremely infrequent intervals.
To make matters worse, tests done on water samples do not produce in-situ
results.

To overcome these major limitations, we propose our novel Water Quality
Enhanced Index ($WQEI$) to detect the turbidity and salinity in water ponds,
open tanks, water storage ponds for irrigation, playas, etc using
multispectral satellite images [5, 6]. Remote Sensing has been used in
multiple domains [7, 8, 9], often to create spectral indexes. Spectral indexes
are combinations of spectral reflectance from two or more wavelengths that
indicate the relative abundance of features of interest [10, 11, 12].
Vegetation indices are the most popular of these, derived using the
reflectance properties of vegetation [13, 14, 15, 12, 16]. The most popular
vegetation index is NDVI (Normalized, Difference Vegetation Index) [13, 14].

The question of water quality detection using satellite imagery has seen much
scientific inquiry already [17, 18, 19, 20, 21, 22, 23, 24, 25].However most
of this work detects water quality in large water bodies with substantial
depth($\geq\sim 100$ft) and size($\geq 100$ acres). The reflectance signals
recorded in such cases have a high Signal-to-Noise Ratio (SNR). There is
minimal interference from surrounding confounding elements like the bottom of
the water body and pixels with low SNR. Small-sized water bodies present
unique challenges and prevent the translation of existing methods directly to
monitor small ponds, shallow lakes, storage tanks, playas, etc. The small size
($\sim 2$ acres) causes the pixels representing surface reflectance in the
satellite image to be very noisy due to interference from surroundings(soil,
rocks, bushes, and other potentially confusing elements on the ground).
Shallowness($\sim 30$ ft) of the water body also adds noise to reflectance
values: the earth below has a different surface reflectance than the water
above. In this study, we focus on the following areas:

  * •

We propose a novel Water Quality Enhanced Index ($WQEI$) for detecting the
turbidity, and salinity in very small and shallow water tanks, ponds, playas
using satellite images.

  * •

The proposed index improves the SNR of the weak signal received from the
ground. It is robust to changing conditions in the surroundings. e.g. changes
in the vegetation type, in soil salinity, etc.

  * •

We verified the output of our estimation index against lab tests done on 49
water ponds for hydraulic fracturing purposes. This data was collected over a
2-year time period for each pond at variable frequency, totaling $\sim 1200$
samples.

  * •

We tested our index on multi-spectral data from two different sources of
satellite imagery: commercial satellite (private) and LandSat8 (public).

  * •

We developed an end-to-end pipeline that pulls data from LandSat8 periodically
every week. This allows us to monitor any water body anywhere on earth.

  * •

We also developed and trained a neural network to check the effectiveness of
machine learning models for such problems.

Overall we developed a cost-effective and efficient technique for monitoring
small water bodies’ turbidity and salinity. These small sources of water can
thus become usable to prevent wildlife from consuming polluted water, and in
the restoration of natural playas and a healthier ecosystem.

##  2 Related Works

Our method draws from numerous areas of remote sensing, utility of spectral
signatures, and information capture from the landscape. In this section, we
discuss the key relevant areas of existing works that motivated our work and
contributions.
Deterministic and Semi-empirical methods: There have been many studies done on
detecting different types of impurities in water [18, 19, 20, 21, 26, 22, 23,
24, 25, 17], these studies are often designed for a specific water body in a
specific region. For example, [17] took the data from a 1978 Malaysian water
monitoring program and developed estimation methods for suspended matter [27],
phytoplankton growth [28] and turbidity [29], using multi-spectral data from
LandSat5 satellite. That monitoring program had created data for only two
similar rivers within Malaysia, which greatly limits its generalizability.
[24] used multi-spectral data from LandSat5 (TM) to analyze the presence of
suspended sediments and chlorophyll in Lake Chicot, Arkansas. [23] took a
different approach and proposed the importance of detecting landscape features
while assessing the impurities in a water body. [23] analysed the relationship
of landscape pattern ecological processes. For example, environmental
attributes and processes like water quality, nutrient flow, and population
dynamics are correlated with landscape spatial patterns using different
indexes. [26] studied the attenuation coefficient of water by mixing different
types of impurities in it and analyzed the relationship between spectral
reflectance and different level of depth of water. This study was conducted on
432 acres of Loosdrecht lakes in the Netherlands.
Regression and Neural Networks based methods: Regression analysis is the most
common data-driven approach in remote sensing. [30] mentioned the requirement
of comparing multiple approaches e.g. deterministic, semi-empirical, and
empirical, data-driven regression analysis methods when computing the water
quality index. [24, 31, 32, 30, 33, 34] mentioned different data-driven
approaches. [31, 30] for the first time mentioned that water quality
measurement methods were dependent on the water body classification (i.e,
lake, pond, playa, tank, etc) and water depth that needs multiple bands
information. [32, 30] calibrated empirical relation between different bands in
LandSat8-OLI/TRS imagery to detect chlorophyll present in the water body. [24]
evaluated the possibility of a nonlinear relationship model by checking the
water bodies in Arkansas and Mississippi, USA. [24] claim was supported by
[34] of using regression analysis. [34] evaluated the combination of multiple
bands and proved that no single band combination has uniqueness, thereby
implying the use of information from all the bands to make any kind of
decision.

Figure 1: Image “a”shows data sample from private source at 2m per pixel
resolution, the marked regions are frac ponds. Image “b” shows data from
LandSat8 satellite at 30m per pixel resolution, it shows different types of
water storage ponds. It can be seen that at 30m resolution the ponds
contribute only few pixel in the image that makes the problem more challenging
to detect $WQEI$.

Neural Network approaches have been proven to be better than traditional
methods [35, 36]. The usefulness of the neural networks was tested by [37] to
compute the water quality index. [37]’s use case proved that neural network
captures all the vital, non-computable by regression methods relations like
atmospheric disturbance, non-ideal contextual uncertainties, etc. The
McCulloch and Pitt model [33] is the widely used network. It consists of a
simple multi-layer neural network with convolution layers and non-linear
activation functions in between batch normalization. With all the benefits and
flexibility of neural networks, the major limitation is that the convergence
of neural networks is very difficult with less amount of data. The curse of
dimensionality if a huge issue in neural networks. Since the multispectral
data is very high in dimension with very small numbers of pixels of interest.
It needs a large amount of clean training data and big compute power(GPUs) to
train a neural network. This was one of the motivations for our work of
selecting simple nonlinear regression methods for creating the water quality
index explained in detail in the next section.

##  3 Approach

In this section, we describe the technical approach for our Water Quality
Enhanced Index (WQEI) in detail, we will also talk about the study area,
details about the dataset used, and satellite information.

###  3.1 Study Area

The area selected for the development, analysis, and evaluation of $WQEI$ in
Midland, Texas, USA. This region uniquely contains a large number of frac
ponds closer to the oil drilling sites along with a large number of playas in
the same region. Right next to the Midland region, there are many ponds for
irrigation purposes in Stanton, Texas, USA. Along with these, there are many
small natural water bodies in the Permian basin, Texas region, that appears
during the monsoon season and disappear over the year as summer progresses.
This region uniquely contains water bodies of different sizes, shapes, and
depths. Another major benefit of these sites is that they have different use
cases (i.e. fracing job in oil well drilling, irritation purpose, industrial
use, drinking purposes, etc). That adds a different types of sediments and
impurities, this made our $WQEI$ more robust and generic to be used for
different types of water bodies. Figure 3 shows few samples of different types
of water bodies tested in our case. The water stored in frac ponds is built to
store fresh water or flowback water from the well, or a mixture during the
course of well-site development. It is most important to monitor frac ponds as
the water which flows back from wells may contain some dangerous substances,
and should be monitored for those according to federal, state, and local laws
[38]. Usually this water becomes unusable overtime, and it adds a huge
economic burden on the oil & gas companies and damage to environment. Some of
the irrigation ponds are retention ponds that capture stormwater. Texas alone
has more than one million ponds and small farming lakes [39]. This is an
extremely large number to be monitored manually, which is where remote sensing
is the most effective. The variety of sizes, shapes, depths uses and
seasonalities make this region an ideal environment for a monitoring study.

###  3.2 Dataset curation

We used satellite data from 2 different sources i.e. Commercial satellite
dataset (private data repository) and LandSat8 satellite data (public data).
Both the datasets have multispectral bands. The initial development and
analysis were done using the data from commercial Pleiades-1B Satellite Sensor
(AIRBUS Defence & Space). It covers a few sections of Midland, Texas region.
The spatial resolution of this data is $\sim 2m$ per pixel and 4 spectral
bands. 3 of the spectral bands are in visible spectrum (Blue: $430-550\mu m$,
Green: $490-610\mu m$, Red: $600-720\mu m$) and 1 in Near Infrared spectrum
($750-950\mu m$). All the data files are geo-tagged for each pixel. This
dataset covered 17 frac pond sites with less than $10\%$ cloud cover. Sample
from it dataset is shown in Figure 3a.

To make our model more effective and useful, we used LandSat8 satellite -OLI
[5] to have a continuous stream of multispectral images from anywhere on the
earth at a frequency of 2 weeks. LandSat8 orbits the earth every $99\;minutes$
in a sun-synchronous orbit at an altitude of $705\;kms$. LandSat8 acquires 740
scenes a day where each scene is $185\times 180\;kms$. LandSat8 have 11
spectral bands information. The 3 bands in visible spectrum lies in the range
$0.43-0.67\;\mu m$ with $30m$ resolution. The 4 bands in infrared regions lies
in the range $0.85-1.38\;\mu m$ with $30m$ resolution. LandSat8 also have 2
thermal bands in wavelength range $10.6-12.51\;\mu m$ at $100m$ resolution.
Along with these, LandSat8 data have a Panchromatic (PAN) band for visible
spectrum ($0.50-0.68\;\mu m$) at resolution of $15m$. The data is captured by
the sensor in 12-bit dynamic range. We downloaded data for 2 years
(2018-2020), to do the initial development, analysis and evaluation of our
$WQEI$. We manually downloaded the initial data from Midland and Permian basin
in Texas. For later stage, we developed an end-to-end pipeline to pull data
from LandSat8 and run $WQEI$ and create analysis report along with
visualization

Figure 2: The image shows the improvement in quality of $WQEI$ output by up-
sampling the image using panchromatic band information. The shown sample is an
irrigation pond.

###  3.3 Pre-processing

LandSat8 satellite data is at $30m$ resolution, small ponds constitute very
few pixels in the image. This way we does not have enough information to make
a pixel level prediction. To overcome this issue, we used the panchromatic
band data which is at higher resolution of $15m$ to improve the resolution of
all visible and short infrared bands. First we normalize each band using mean
($\mu$) and standard deviation ($\sigma$) computed from the whole dataset
downloaded. Then a high resolution image is created by up-sampling the visible
bands using bi-linear interpolation method. The distribution ratio is then
computed using Brovey transform [40]. The decision for choosing Brovey
transform over others is motivated because of its simplicity and analysis by
[41]. Brovey transform is based on spectral modelling and increase the visual
contrast in the high and low ends of the data’s histogram. Each up-sampled
band is multiplied by ratio of corresponding panchromatic pixel intensity to
weighted sum of all multispectral bands [40].
Lab reports of water quality testing from frac ponds and other sources were
organized to be in syn with satellite data. To minimize outliers, we selected
only those sample which have atleast 20 test samples collected per pond over
the span of 2 years. Since water sample collection for lab testing have
different frequency, we shortlist only those were collected with 5 days window
of LandSat8 satellite passing that location. We also normalized all the
reading and unified the measuring scale of all the parameters measured in the
lab reports (“pH”, “conductivity”, “temperature”, “algae”, “dissolved oxygen”,
etc).

###  3.4 Water Quality Enhanced Index (WQEI)

With the motivation insight mentioned in previous sections, we propose a novel
Water Quality Enhanced Index. It is a new, invariant to spatial extent, robust
analytical approach for characterizing the level of impurity spatially. We can
map each and every section of the given water body to generate a spatial
visual color-coded output representing the water quality. The $WQEI$ is
developed in the following steps:

First a generic scan is done in the whole area, that scans for moisture
content in the whole image, covers water body as well as soil around. Now we
remove the potential confusers due to sand/soil/rocks or dust that settles on
water temporarily, this is done by second term in equation 1. The overall
water impurity detector developed so far is as shown below

$imp\\_detected=\frac{(R-NIR)}{R+NIR}-(\sqrt{B}+R)$ (1)

where $R$ is red band ($0.65\mu m$), $G$ is green band ($0.55\mu m$), $B$ is
expected value of (B1 ($0.44\mu m$), B2 ($0.48\mu m$)) i.e. blue band, $NIR$
is near infrared band ($0.86\mu m$).
Next we observed that algae have a similar spectral signature to the index
computed in equation 1, and most of the algae growth is in or around the water
body. We compute a similarity index with algae detection index, the intuition
behind that is it will further remove the confuser element from the site. This
increases the strength of the spectral signal representing water impurity.
This step also ensures that algae growth on general vegetation around the
water body or somewhere else in the area is removed. This is shown as below:

$amp\\_sig=imp\\_detected\;\circ\;\frac{G-R}{G+R}$ (2)

where $imp\\_detected$ is from equation 1. Now we normalize this
$amp\\_signal$ with the sum of red and near infrared signal. This is a
standard practice in literature as it scales the values in the range $-1$ to
$+1$ [42]. Now to have a better fit according to the settings of the
environment, we made the numerator and denominator differentiable function. We
used regression-based approaches to estimate the values of variable
parameters. The final estimated function is:

$WQEI_{1}=\frac{\\{\frac{(R-NIR)}{R+NIR}-(\sqrt{B}+R)\\}\;\circ\;\frac{G-R}{G+R}}{\sum_{i}^{h\times
w}\alpha\times G-\beta\times(R+NIR)},$ (3)

here $h$ and $w$ are the spatial dimension (height and width) of the image
(water body) respectively, $\alpha$=2.74 and $\beta$=4.89 are the estimated
values. Equation 3 is the final estimation index for water quality detection.

Figure 3: This plot shows the dependence of reflectance of light at different
wavelength versus temperature. The reflectance of water decreases are the
temperature increases. Also, lower wavelengths have higher reflectance and
wavelengths in near infrared region have lower reflectance

Next, we analyzed the water quality for the presence of chlorides, fluorides,
and other salts. Our lab reports did not have direct tests for the presence of
salts in the water. Salt level monitoring is also a very important factor when
it comes to water quality. Specially used water pumped back into frac ponds
from wells, or water discharged into natural playas for wildlife. Maintaining
the level of salinity is very crucial in such cases. Our engineers performed
tests for the conductivity of water samples collected from the ponds. Our
basic assumption is here is that conductivity has a high correlation with the
salinity of water [43, 44]. [45, 46] derived an approximate relation between
the temperature of the water and its reflectance pattern. According to [45],
in the wavelength range $200\mu m-1000\mu m$ as the temperature of water
increases, the reflectance of water reduces as shown in figure 3. This study
was done on clean water. A scientific report from NASA [46], further backed
this claim, on studying the reflectance pattern of different types of water
bodies, e.g. salt water bodies, and clear water bodies at different
temperatures.

We further study the behavior of certain types of salt when they are mixed
with water. Most of the saltwater mixture reactions as endothermic reactions
[47], which include, sodium chloride, phosphates, magnesium salts, etc. So we
used the above two properties of water to propose a novel index to estimate
the salinity in very small and shallow bodies of water. Most of the standard
salinity indexes like normalized difference salinity index (NDSI) are not
effective because they are designed to study the soil salinity or salinity of
arid or semi-arid vegetation. The reflectance property of salts present in the
soil is totally different from salts mixed in water.

We start with the prior knowledge that water has a strong absorption towards
red ($0.65\mu m$), near-infrared bands ($0.86\mu m$) and higher reflectance
towards green ($0.55\mu m$), blue ($0.44\mu m$) bands [45]. As the number of
soluble impurities in water increases, its reflectance increase [48]. There is
a shift in the reflectance and absorption pattern of water towards red bands.
The base salinity/impurity level detection of the water body is computed as:

$sal\\_detect=(G+B)-\gamma(R+NIR),$ (4)

where $R$ is red band ($0.65\mu m$), $G$ is green band ($0.55\mu m$), $B$ is
expected value of (B1 ($0.44\mu m$), B2 ($0.48\mu m$)) i.e. blue band, $NIR$
is near infrared band ($0.86\mu m$) and $\gamma$ is a learnable coefficient.
Next we explore the dependence on temperature, using the prior knowledge of
[43, 44, 45, 46] salt-water reaction being endothermic and temperate-
reflectance relationship. Since temperature has a inverse relation with
reflectance and variations in temperature are directly visible in the thermal
bands ($10.8\mu m$) of LandSat8.

$sal\\_detect=(G+B)-(\gamma(R+NIR))^{(\frac{\theta}{T})}$ (5)

here $T$ is the thermal band ($10.8\mu m$) and $\theta$ is learnable
coefficient. This boost the weak signal from the from the small and shallow
water pond as there is a shift towards the $R$ and $NIR$ bands with increase
in impurity. Next we normalize equation 5. The final Water Quality Enhanced
Index is as shown below

$WQEI_{2}=\frac{(G+B)-(\gamma(R+NIR))^{(\frac{\theta}{T})}}{NIR+R+G+B}$ (6)

Equation 6 is the another estimated index for detection salinity of water. The
final estimated/learnred values of $\gamma$=1.8 and $\theta$=2. The output
($WQEI_{2}$) of equation 6 is in range $-1$ to $+1$.

##  4 Verification of Indexes

Figure 4: Row 1 : Plot of $WQEI_{C}$ over 4 different ponds over the time
period of one year, it shows the strong correlation of $WEQI_{C}$ with Lab
reports for $Conductivity$. Row 2: Plot of $WQEI_{T}$ over 4 different ponds
for 1 year and its strong correlation with Lab report of Conductivity
computation.

In this section, we will discuss the experiments that verified our created
indexes and validation for our design choices. The validation tests are
performed against the test done on water samples collected from the 49 frac
ponds/irrigation ponds/playas. Here we will discuss in detail the types of
tests and how we estimated the correlation between various tests and both the
indexes created.
Satellites: We used the multispectral images (remote sensing data) from two
different satellites to ensure the generality of our methods. The
multispectral data from commercial source has $\sim 2m$ per pixel spatial
resolution and 4 spectral bands, covering the visible and near-infrared
regions. The spatial resolution is good enough for our small water ponds, we
directly computed $WQEI_{1}$ and $WQEI_{2}$ for all the satellite images. In
$11$ multispectral images, we have $17$ ponds sites. Since the output of each
index is of the size of the input image ($H=20kms\times W=18kms$). The maximum
size of any frac pond is $70m\times 70m$, we cropped size of $100m\times 100m$
(expected to cover the whole pond) around the $lat,\;long$ (approximate center
of the pond) from the indexes output. Next, we compute the mean
($\mu^{1}_{i},\mu^{2}_{i}$) and standard deviation
($\sigma^{1}_{i},\sigma^{2}_{i}$) for each of the cropped outputs of indexes.

$\mu^{1}_{i},\sigma^{1}_{i}=\sum_{k=0}^{h\times
w}P^{1}_{k},\;\frac{1}{n}\sum_{k=0}^{h\times
w}P^{1}_{k}-\mu^{1}_{i}\;\;\forall\;(WQEI_{1})$ (7)
$\mu^{2}_{i},\sigma^{2}_{i}=\sum_{k=0}^{h\times
w}P^{2}_{k},\;\frac{1}{n}\sum_{k=0}^{h\times
w}P^{2}_{k}-\mu^{2}_{i}\;\;\forall\;(WQEI_{2})$ (8)

where $\mu_{i}$ and $\sigma_{i}$ are mean and std of $i_{th}$ cropped output
of indexes respectively, $P_{k}$ is the $k_{th}$ pixel in the cropped output.
LandSat8 has spatial image resolution is $30m$ per pixel, we used panchromatic
band information to up-sample the spatial resolution to $15m$ per pixel.
Details about up-sampling transform are discussed in section 3.3. On the up-
sampled multispectral image, we compute both $WQEI_{1}$ and $WQEI_{2}$ for all
the 49 ponds where each pond have approximately 18 images over the span of 2
years. Then we compute the mean ($\mu^{1}_{i},\mu^{2}_{i}$) and standard
deviation ($\sigma^{1}_{i},\sigma^{2}_{i}$) of all images. In total
(commercial satellite and LandSat8) we have approximately 1200 images taken at
different time intervals.
Lab test reports data is cleaned and formatted to be compared directly with
outputs ($WQEI_{1},WQEI_{2}$) from satellite data. Each pond water sample is
tested for the following parameters: $pH$, $Conductivity$, $Turbidity$,
$Dissolved\;Oxygen$, $Temperature$, $H_{2}S$, $Depth$. To find out the
relation of our indexes ($WQEI_{1},WQEI_{2}$) with lab test parameters, we
match each index with each of the test parameters recording using a matching
criterion.

Figure 5: Row 1& 2: shows qualitative results of computing the $WQEI_{C}$ for
a irrigation field and natural playas. The data is observed over 8 months and
compared with Lab test also. Row 3 & 4: shows qualitative results for
computing the $WQEI_{T}$ for the same water bodies, and the data is observed
over same time interval. We can see, towards the months of summer, the natural
playa dries up and water is very saline and turbid, while the irrigation water
pond was filled up from the near by canal in the month of july, showing less
saline and more turbid, as turbidity increases temporarily as water is
discharged in from canal

###  4.1 Matching Criterion:

The first matching criterion used our case is Pearson Correlation (PC). The
reason for using it is that, Pearson Correlation coefficients are used in
statistics to measure how strong a relationship is between two signals
irrespective of the amplitude. It is defined as the covariance of the two
signals divided by the product of their standard deviations.

$\rho_{indexes,lab\\_test}=\frac{cov(indexes,lab\\_test)}{\sigma_{indexes}\;\circ\;\sigma_{lab\\_test}},$
(9)

here $\sigma_{indexes}$ is $(\sigma^{1}_{i},\sigma^{2}_{i})$ and
$\sigma_{lab\\_test}$ is $(\sigma_{pH},\sigma_{conductivity},..etc)$, $cov$ is
covariance. PC shows how significantly the shape of the curve plotted for
indexes output readings ($\mu^{1}_{i},\mu^{1}_{i}$) correlates well with each
lab test parameter ($pH,Conductivity,..etc$) over the time span of 2 years.
For the PC, we are ignoring the magnitude because the signals (indexes v/s lab
test) are from 2 totally different domain spaces. Magnitude optimization may
lead to incorrect matching or no matching at all. So we started with curve
shape matching first.

First we set all the learnable parameters ($\alpha,\beta,\gamma,\theta$) to 1
in equation 3 & 6. Next for each pond over the time span of 2 years ($\sim 18$
readings), we compute PC for each index ($WQEI_{1},WQEI_{2}$) with each lab
test parameter ($pH,Conductivity,Turbidity,..etc$). And picks the best match
lab test parameter for each of our indexes. We found out that $WQEI_{1}$ has
the highest correlation with $Turbidity$ and $WQEI_{2}$ has $Conductivity$.

$\begin{split}\begin{cases}\rho_{1}=argmax(\textbf{PC}\;(WQEI_{1},\;lab\\_test))\\\
\rho_{2}=argmax(\textbf{PC}\;(WQEI_{2},\;lab\\_test))\end{cases}\\\
\forall\;\;lab\\_test\in(pH,Conductivity,..),\end{split}$ (10)

where PC is Pearson Correlation. We observed that $\rho_{1}$ points to
$Turbidity$ and $\rho_{2}$ to $Conductivity$. Hence we found that our
$WQEI_{1}$ is a measure of $Turbidity$ of water in the pond and $WQEI_{2}$ is
a measure of $Conductivity$ of water estimated using satellite imagery. For
the sake of simplicity now on, we will use $WQEI_{T},WQEI_{C}$ for $WQEI_{1}$
and $WQEI_{2}$ respectively. Next we find the optimum value for out learnable
coefficients ($\alpha,\beta,\gamma,\theta$) of indexes ($WQEI_{T},WQEI_{C}$).
For this we used second matching criterion using simple regression methods.

Mean Square Error (MSE) is used to estimate the right values of learnable
coefficients. MSE is a model evaluation metric used for regression tasks. The
main reason for using MSE as an evaluation/matching criterion is to estimate
as precise as possible values for $Turbidity$ and $Conductivity$ of water in
small ponds using satellite imagery. We used simple regression to estimate
those values and optimized on minimizing the MSE for both the $WQEI_{T}$ and
$WQEI_{C}$. The final indexes are as follows:

$WQEI_{T}=\frac{\\{\frac{(R-NIR)}{R+NIR}-(\sqrt{B}+R)\\}\;\circ\;\frac{G-R}{G+R}}{\sum_{i}^{h\times
w}2.74\times G-4.89\times(R+NIR)},$ (11)
$WQEI_{C}=\frac{(G+B)-(1.8(R+NIR))^{(\frac{2}{T})}}{NIR+R+G+B}$ (12)

With the help of our very simple and novel indexes, we can monitor the quality
of water in small ponds, tanks, playas, etc using satellite imagery in the
remotest section of the world. We can reuse the wastewater to recharge the
natural playas. We can point out the location where the water is unfit for
drinking by the wildlife, provide alternate sources and block the unfit pond,
or tank.

| Ponds (MSE) - Turbidity
---|---
Methods | P1 | P2 | P3 | P4 | P5
TI1 [49] | 0.955 | 0.880 | 0.861 | 0.797 | 0.862
TD2 [50] | 0.768 | 0.724 | 0.736 | 0.777 | 0.779
MLR [51] | 0.645 | 0.655 | 0.588 | 0.511 | 0.680
GEP [51] | 0.563 | 0.541 | 0.581 | 0.410 | 0.471
| Reg
---
Model [52]
0.157 | 0.243 | 0.159 | 0.151 | 0.140
| Neural
---
Net (Ours)
0.218 | 0.245 | 0.273 | 0.395 | 0.206
WQEIT | 0.097 | 0.028 | 0.017 | 0.040 | 0.035
Table 1: Comparison of $WQEI_{T}$ with the popular methods of detecting water
turbidity. $WQEI_{T}$ have lower MSE than other methods when tested on 5
randomly selected ponds.

| Ponds (MSE) - Salinity
---|---
Methods | P1 | P2 | P3 | P4 | P5
SI4 [53] | 0.757 | 0.997 | 0.892 | 0.704 | 0.932
SI6 [54] | 0.799 | 0.655 | 0.618 | 0.890 | 0.860
SI7 [55] | 0.508 | 0.648 | 0.669 | 0.669 | 0.550
SAVI [56] | 0.444 | 0.545 | 0.497 | 0.589 | 0.633
NDSI [57] | 0.358 | 0.466 | 0.341 | 0.438 | 0.353
VSSI [58] | 0.165 | 0.179 | 0.177 | 0.165 | 0.177
MSAVI [59] | 0.106 | 0.175 | 0.298 | 0.217 | 0.131
| Neural
---
Net (Ours)
0.254 | 0.137 | 0.141 | 0.196 | 0.256
WQEIC | 0.082 | 0.068 | 0.099 | 0.063 | 0.081
Table 2: Comparison of $WQEI_{C}$ to detect salinity with the most popular
indexes that exists in literature. It can be seen $WQEI_{C}$ have lower mean
square error as compared with other methods. We performed it on 5 randomly
selected ponds and computed the salinity using each index listed from
satellite images and the corresponding lab report.

###  4.2 Estimation with Neural Networks:

In this section we will discuss the neural network architecture we designed to
estimate $Turbidity$ and $Conductivity$. We started with a small VGG16 [60]
network pre-trained on natural images dataset (imageNet) [61]. We used
convolutional layers only of the VGG16 as feature extractor, appended 2 Fully
Connected (FC) layers initialized randomly. The final layer has 2 output
neurons. The training data used is 1200 satellite images cropped out for each
pond at different timestamps. The ground truth are the lab test reports
discussed in section 3.3. We created a 80-10-10% train-val-test split of the
dataset.
Loss function used is inspired from [62, 63]. Since we are directly predicting
a value for $Turbidity$ and $Conductivity$, the output of last layer is passed
through a softmax function. The loss function used is simple MSE for
optimization. Each input image is of size $100\times 100$ with 12 bit depth
information per pixel. The batch size is 32 images with a learning rate of
0.005 at starting and reduces by a factor of 0.5 after every 10 epochs.
Stochastic Gradient Descent is used as optimizer for the network. The network
is trained for 30 epochs.

##  5 Results and Conclusions

In this study, we utilize multi-spectral data (LandSat8) to monitor water
bodies that are dispersed in a large region. By creating the Water Quality
Enhanced Index ($WQEI_{T},WQEI_{C}$), we show:

  * •

Comparing our $WQEI_{T},WQEI_{C}$ model prediction with laboratory water
quality measurements, our results show that applying our model can achieve
frequent water body monitoring with sufficient accuracy.

  * •

The time series plot (Figure 5) shows that $WQEI$ is a good indicator of water
quality. More specifically, $WQEI_{C}$ shows a strong correlation with water
conductivity and $WQEI_{T}$ with water turbidity.

  * •

Compared with traditional water quality index models, the $WQEI$ formulation
includes a water impurity term (Equation 1, a signal amplification term
(Equation 2) and a normalization term (Equation 3). The combination of
multiple terms we introduced leads to better performance, especially for
small-sized water bodies.

The proposed methods are evaluated on the criterion of Mean Squared Error
(MSE). They are also compared to standard indices for detecting $Turbidity$
and $Conductivity/Salinity$. As shown in table 1&2, $WQEI_{T}$ and $WQEI_{C}$
performs better than most existing methods [53, 57, 54, 55, 56, 59, 58] & [49,
50, 51, 52]. Even with limited data, our proposed neural network accurately
detects water salinity and turbidity. Further research is needed to stabilize
these results: the neural network proposed here primarily functions as
validation of the feasibility of this idea.

###  5.1 Industrial Deployment

We deployed a fully function model of our detection methods in industrial
application for monitoring and maintaining water quality at independent oil
and gas organization. We will release the complete source code and details in
the final publication and plan to present these findings to several oil and
gas trade associations.

##  6 APPENDIX A: Additional Experimental Results Visualizations

Figure 6: Pearson correlation plot of $WQEI_{C}$ & $WQEI_{T}$ with lab test
parameters. The oval marks shows the strongest correlation.

###  6.1 Pearson Correlation plots

As discussed in section 4.1 in the main paper, the correlation plots for for
equation 10 are shown in figure 6. Figure 6a shows the Pearson correlation
coefficient plot for $WQEI_{C}$ with each of the lab test parameter
($pH,Conductivity,Turbidity,etc$). As shown with orange oval mark in figure
6a, $Conductivity$ has highest correlation with $WQET_{C}$. Similary figure 6b
shows the Pearson correlation coefficient plot for $WQEI_{T}$ with each of the
lab test parameter ($pH,Conductivity,Turbidity,etc$). The green oval mark
shows a strong correlation of $WQEI_{T}$ with Turbidity. We also observed that
it has significant correlation with volumne of water too in the pond. This
way, using $WQEI_{T}$, we can make a relative estimate of volumne of water in
the water body using satellite imagery only.

###  6.2 Qualitative results

Figure 8 shows some of the qualitative results on very small frac ponds in
Midland, Texas region. The indexes are computed on images from LandSat8
satellite. We picked a mixture of ponds, the ones from which, water is used
very frequently and refilled frequently and the ones from which, water is used
only once in 3-4 months. Row 1 and 2 (Turbidity ($WQEI_{T}$)) shows the ponds
which are used very frequently (almost every 3 weeks) and refilled very
frequently. We can see, most of the time the water stays turbid. Row 3
(Turbidity ($WQEI_{T}$)) shows very less used pond (3-4 months, the water
stays calm and idle but the pond starts to dry up over time. We can see for
the month of march, april, june of row 3, the turbidity is low and the pond
starts to dry up, refilled back in next months, based on usage, we can see the
increase in turbidity.

Figure 7: Neural Network architecture used for detecting water turbidity and
conductivity/salinity.

Row 4,5,6 (Salinity/Conductivity ($WQEI_{C}$)) shows how the salinity of the
frac pond changes over time. We observed that the salinity is very high in the
months towards the end of summer, as the fracturing process is at higher rate
and a lot of water is pumped back from the well back to the pond. Salinity is
very high also in those cases when the water in the pond has almost dried up.
As we can see in row 5 in month is September (this pond was unused), towards
the end of summer, almost all the water in the pond dries up and we can see
high concentration of salts in the ponds before it dries up completely.

Figure 8: Qualitative results on frac ponds from LandSat8 satellite for
turbidity and salinity detection using $WQEI_{T}$ & $WQEI_{C}$ respectively.
The results are shown from the start of summer in midland, Texas region until
start of winter.

###  6.3 Neural Network Architecture

As mentioned in the main paper we tested a simple VGG16 [60]. Here we will add
more details about the architecture and the observations on training a neural
network on remote sensing data for our problem set. The input image size is
$100\times 100\times 3$. We used pre-trained VGG16(pre-trained on imagenet
dataset [61]) for input image feature extraction to a feature map of size
$7\times 7\times 512$. Fully connected layer with ReLu activation are
initialized randomly. The output is passed through a softmax function to
predict score of turbidity and salinity/conductivity. The architecture diagram
is shown in Figure 7.

Limitations: The training data used is very limited in our case and the
predictions are only the score of $Turbidity$ and $Conductivity/Salinity$ of
the whole pond. Limited data problem arises in almost all the fields when it
comes to remote sensing. As the terrain covered to do any kind of anomaly
detection (e.g. water quality, sand quality, GHG emissions, etc) is extremely
large ( 1000s of miles) and it is very challenging to generate ground truth
information in such cases. For example in our case only, the data from 49
ponds only was a major challenge, our team spent 2 years of time and millions
of dollars just to monitor such a small number of ponds. Unlike natural images
object detection where simple objects (e.g. car, truck, animal, person) seen
in surroundings can be annotated with very minimal amount of knowledge. We
need specialized equipments and expertise in the subject matter (e.g. chemical
engineering, hydrologist, geologist, etc) to check presence of certain types
of impurities. And after that the next challenge is understanding of
multispectral data.

Index creation [53, 57, 54, 55, 56, 59, 58, 49, 50, 51, 52] is one way where
people have done analysis of multispectral data from satellites using remote
sensing. Index creation needs expertise in both the multispectral imagery from
satellite and chemical properties of object of interest. Indexes are very much
prone to change in environmental conditions and the change in terrain. The
simplistic neural network used for the problem gives green light to
application of machine learning in remote sensing. We can predict different
kind of impurities score by just using one neural network, instead of using a
specialized index for each one. Our future work in this domain is to work
towards using an encoder-decoder network architecture, so that we can generate
a spatial map of impurities in the whole water body instead of a single score.
But that is also going to need lab test on water samples collected from
different sections of same water body.

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