Optimal Reservoir Operations using Long Short-Term Memory

Network
Asha Devi Singha,∗, Anurag Singhb
a
G.B Pant Institute of Technology, New Delhi, India
b
Netaji Subhas Institute of Technology, University of Delhi,India

Abstract
arXiv:2109.04255v1 [cs.LG] 7 Sep 2021

Reliable forecast of inflows to the reservoir is a key factor in the optimal operation of
reservoirs. Real-time operation of the reservoir based on forecasts of inflows can lead to
substantial economic gains. However, the forecast of inflow is an intricate task as it has to
incorporate impacts of climate and hydrological changes. Therefore, the major objective of
the present work is to develop a novel approach based on long short-term memory (LSTM)
for the forecast of inflows. Real-time inflow forecast, in other words, daily inflow at the
reservoir helps in efficient operation of water resources. Also, daily variations in the release
can be monitored efficiently and reliability of operation is improved. This work proposes
a naive anomaly detection algorithm baseline based on LSTM. In other words, a strong
baseline to forecast flood and drought for any deep learning-based prediction model. The
practicality of the approach has been demonstrated using the observed daily data of the past
20 years from Bhakra Dam in India. The results of the simulations conducted herein clearly
indicate the supremacy of the LSTM approach over the traditional methods of forecasting.
Although, experiments are run on data from Bhakra Dam Reservoir in India, LSTM model
and anomaly detection algorithm are general purpose and can be applied to any basin with
minimal changes. A distinct practical advantage of the LSTM method presented herein is
that it can adequately simulate non-stationarity and non-linearity in the historical data.
Keywords: LSTM, Thomas-Fiering model, Inflow forecasting, RMSE

1. Introduction
All forms of life on earth depend on water. The distribution of water is, however, not
uniform. It varies both spatially and temporally across regions. At certain locations, ample
water is available, whereas some areas face scarcity of water and are frequently subjected to
drought. Areas having abundant water face challenges of managing it and preventing the
area from flood. For efficient use of river water, dams are built and management of water

∗
Corresponding Author: Asha Devi Singh
Email addresses: adsingh@gbpit.ac.in (Asha Devi Singh), anurags.it@nsit.net.in (Anurag
Singh)
Preprint submitted to Elsevier September 10, 2021
resource is carried out. Due to climate change exhaustive planning of water resource is
required to meet the water demands in the dry season and firm power demand under stress
of increased climate variability.
Optimal operation of reservoir system is essential to meet competing water demands.
Various techniques to achieve optimal operation of reservoir system have been used to
treat non-convex, non-linear behavior of reservoir systems. Dynamic Programming (DP)
[1](Bellman, 1966) is the widely accepted technique for optimization of reservoir system as
these are characterized by a large number of non-linear and stochastic features that can be
translated into DP formulation. Thomas-Fiering model is a widely used technique to forecast
inflows, and can be effectively used for deciding reservoir release policies. [2](Sargent,1979)
used transition probabilities to generate sequences of daily stream flows while preserving
the important characteristics of the daily inflow hydrograph. In the past a wide variety of
approaches have been used to forecast inflows. In this paper a novel long short-term memory
(LSTM) based neural network architecture has been developed for inflow forecasting.
The use of LSTM to forecast inflows has not been attempted to the best of our knowl-
edge. Considerable success has been achieved with the use of machine learning techniques
which are able to solve wide range of problems in optimization and operations research
[3, 4](Singh, 2019, 2020) [5, 6](dutta 2020). Recently attempts have been made for success-
ful determination of precipitation but naive deep learning based architectures are difficult
to train them to learn and investigate temporal correlation over arbitrary length. Artificial
Neural Networks (ANN) are essentially functions that consist of large set of parameters i.e.
weights that try to fit the data by tuning them. ANNs does not have any consideration
of the temporal sequence within the data. Several applications of ANNs to water resource
management problems have been reported in the literature [7] (Zealand et.al,1999). On the
other hand, recurrent neural networks (RNNS) have self referencing feedback loop in their
architecture. The use of recurrent neural networks has been proposed by several researchers
[8] (Coulibaly et.al, 2017). When considered theoretically, RNNs are capable of learning to
track relationships for arbitrary lengths in temporal input. However, it becomes intractable
to keep account of learning for arbitrary length. RNN fails as gradients being used for
computation cannot keep values for arbitrary precision which then turn to zero or explode.
Precipitation and inflow prediction are essentially time series problems and have a tem-
poral correlation in the data. Since the approximate period for such repetition will be no
less than an year based upon first principles. We can safely conclude that remembering
gradients for such long iterations to take into account data for last year can cause problems
in case of RNNs due to their limitations of vanishing gradients. RNN could be employed
for cases when month wise average inflow needs to be computed for the reservoir system.
Monthly average inflow predictions cannot reveal much significant information for design
of strategies for daily operation of reservoir, therefore not serving much fruition in real use
case. The Long Short Term network is a recurrent neural network which is trained using
back propagation through time and also overcomes problem of vanishing gradient.
Anomaly in daily inflow prediction by LSTM will also help in prediction of drought and
flood. Result obtained using LSTM network reveals that model is satisfactorily able to
stimulate non stationary and non- linear inflow trends.
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2. Literature Review
Hydrological process are intricate as it is difficult to understand the complex underlying
process that generate the observed system dynamics. [9](Thomas, H.A et.al 1962) made
use of Auto regressive model to generate inflow assuming hydrological data as time series
and stochastic in nature. [10](M.Singhal, et.al,1980) developed a mathematical model using
Thomas-Fiering model suggest that inflow in any month is dependent on previous month and
also depends on the inflow of the previous year of same month. Model was used for Matatila
dam on river Betwa [11](D.O Faruk,2010) has developed a model combining ARIMA and
neural network. ARIMA model is unable to deal with non-linear relationship where as neural
network model alone is incapable of handling linear and non-linear pattern for accurate
estimation of time series data. The hybrid model was tested for 108-month observations of
water quality and the results obtained were promising. In [12] (I. Khandelwal et. al, 2015)
proposed a novel technique of forecasting by segregating a time series dataset into linear
and non-linear components. Thereafter, the Autoregressive Integrated Moving Average
(ARIMA) was used to predict linear component and the ANN model was used to predict
non linear components. Authors have used the strength of Discrete wavelet Transform,
ARIMA, and ANN to improve the accuracy of forecasts.
In water resource planning and management streamflow forecasting plays critical role.
[13] (Sun et.al, 2015) described a streamflow forecasting approach using Gaussian Process
Regression (GPR), which is an effective kernel-based machine learning algorithm. Re-
sults obtained using GPR are more promising when compared to linear regression and
artificial neural network models. [14](J.R.Stedinger et.al,1984) developed a stochastic dy-
namic programming model to forecast the current period inflow for devising reservoir re-
lease policy. Expected benefits from future operations using forecast inflows are also esti-
mated. [15](Mujumdar et.al,2007) developed an operating policy for the Kalindi Hydroelec-
tric Project Stage-1 of the state of Karnataka in India using a Bayesian stochastic dynamic
programming model. The performance of the model is measured by estimating its devia-
tion from the total firm power. [16](Raso et.al,2007) developed a stochastic dual dynamic
programming model for the determination of stream flows. Based on generated streamflow,
reservoir operating rules were decided for Menantali Reservoir located on the river Senegal,
West Africa. [17](Li et.al. 2010) used dynamic programming to estimate stochastic inflows
considering its uncertainty. The authors have estimated future inflows from the available
records with an assumption that the inflow forecasting error has a normal distribution.
[18](Philbrick et.al, 1999) proposed the application of deterministic optimization for de-
vising reservoir operating policies. The authors concluded that it is possible to solve large
scale problems without much simplification when a reliable forecast of inflow is available.
[19](Naadimuthu et.al, 1982) demonstrated the application of two nonlinear programming
techniques – a generalized reduced gradient technique and a gradient projection technique.
Each of these techniques was used in conjunction with a Markovian decision process to
solve the problem of multipurpose reservoir systems operation. [20](Fayaed et.al. 2013)
proposed the integration of stochastic dynamic programming and artificial neural network
for optimization of reservoir operation. [21](Rashid et.al. 2007) used stochastic dynamic

3
programming to obtain optimal operating decisions for Dokan reservoir in Iraq.
Due to the large availability of hydrological data and increase of computational capacity,
the statistical models are generally developed to estimate the behavior of observed data. Lot
of seminal work involving solutions to the problems in different areas is now being powered
by deep learning. For prediction of nonlinear hydrologic processes, ANNs are widely used
now days. Using ANNs, forecasting of stream flow for short term time horizons is feasible.
[22][20](Castelletti et.al. 2007) used neuro-dynamic programming for management of multi-
purpose reservoir instead of stochastic dynamic programming. [7](Zealand.et.al,1999) com-
pared the performance of ANN with the conventional methods of streamflow forecasting.
[8](Coulibaly et.al, (2017) investigated the performance of three different types of temporal
neural networks for reservoir operations. The best results were provided by the recurrent
neural network.
[23](Duong,et.al. 2019) used long short term memory recurrent neural network tech-
nique for determination of monthly rainfall predictions. Based upon the predicted rainfall,
the inflows to the reservoir were estimated. [24](Le et al, 2019) suggested a use of Long
Short-Term Memory (LSTM) neural network model for flood forecasting, used daily dis-
charge and rainfall as input data. Findings of his study were implemented to forecast flood
on the Da River in Vietnam, where the river flow through many countries and downstream
flows (Vietnam) may fluctuate suddenly due to flood discharge from upstream hydroelectric
reservoirs. [25](Yutao et al, 2019) used LSTM to forecast inflow and the results obtained
illustrate superiority the average absolute percentage error is reduced to 13.11%, and the nor-
malized mean square error is reduced by 4%, the coefficient of determination was increased
by 5%. Model is experimented on the Ankang reservoir in China.

3. Study Area
Bhakra Dam is located on river Satluj which originates from Mansarowar lake in Tibet at
an approximate elevation of 4572 m. The Satluj basin extends from 30◦ N to 33◦ N latitudes
and 76◦ E to 83◦ E longitudes. The length of the river is approximately about 1,448 km. River
Satluj which originates from Himalayan region provides the critical source of water and is
also considered one of the most sensitive area to global warming. Due to change in climate,
precipitation pattern changes, causes variation in stream flow. Changes in timing of stream
flow even without change in magnitude of stream flows also poses a serious implication
for water management. Figure 1 explains in two different sections various observed trends
within the last 20 years of operations in Bhakra Nangal Dam. The first figure explains the
relationship between Inflow and discharge in last 20 years using a time series. Second Figure
shows trend in reservoir levels on which the dam operates notice the crests and troughs of
each year throughout 20 years, which are spaced evenly indicating strong correlation in
months and reservoir levels. Reservoir levels in Figure 1 indicate at the end of filling period
reservoir level is El. 1680(Ft).
A major reservoir of Satluj River basin is located at Bhakra. The operation is becoming
a complex process due to the large number of uncertainties associated with it, particularly
under the influence of climatic changes that have altered precipitation and streamflow pat-
4
 Figure 1: Inflow, Discharge and reservoir levels stats for Bhakra Reservoir.

terns in the basin as described by [26] (Sharif et al. 2013). In general, the reservoir operation
strategies consist of controlled release of water downstream considering the inflow and the
available storage in the reservoir. The objective of operation is to fulfill the demand with
respect to power, irrigation, water supply and flood control among other demands.
For the purpose of reservoir operation at Bhakra, an year is divided into two parts. The
filling period is from 21st May to 20th September, whereas the depletion period is from 21st
September to 20th May of the next year. The water accounts are prepared separately for
the filling and depletion period. The excess/shortages of one period are not carried over to
the next period. The present procedure of meeting the water indents require to supply full
water requirements during filling period irrespective of the type of the year (above or below
average) expected to encountered.
Depending upon whether the year is going to be wet or a dry one, a suitable reservoir
factor is estimated for the depletion period and releases are made accordingly till the reservoir
touches down the dead storage level after which only the runoff of the river is passed down.
For the above purposes the reservoir factor is defined as a factor by which indents are to be

5
reduced before making the releases and is equal to the ratio:
Available storage + T otal inf low during remaining year
ReservoirF actor = (1)
T otal water indent during remaining year
where ’Available storage’ is water available at the end of filling period, it also considers the
reservoir losses during the remaining period of year. Total river flow during the remaining
period of the year is calculated for average 10 daily discharges obtained from the discharge
observations for the corresponding 10 day periods for various years for which the discharge
record is available, it also includes the effect of losses or gains during the remaining period of
the year. The reservoir factor is effective only when its value is 1 or less than 1. Estimating
the reservoir factor according to above definition requires estimating the likely inflow during
the depletion period. The accuracy of the reservoir factor would thus depend upon the
degree of accuracy to which likely inflow during the depletion period can be estimated.
Current operational strategies for inflow determination in remaining period depends upon
averages 10 daily of historical data. The rule curve of Bhakra Dam enumerated below shows
that filling of dam is correlated with levels to be attained by certain dates. The RMSE of
current strategies is 29.4% and R2 is 0.6571 . The results clearly indicate variation persists
between actual inflow and predicted inflow.

• The reservoir should not be filled beyond El. 1650 ft by 31st July

• Reservoir level El. 1670 ft should be filled by 15 August not beyond it.

• The reservoir level El. 1680 ft should not fill earlier than 31st August.

The reservoir should not be filled beyond El. 512.06. (1680ft ) and also this level should
not reach earlier than 31st August and filling above this elevation should be attempted after
ensuring due safeguards.

4. Dataset
The observed daily inflow for the period 1999 - 2018 at Bhakra is available on the website
of Bhakra Beas Management board (BBMB). The Table 1 shows the statistics of the observed
daily inflow data at Bhakra for three periods. It is subdivided into Training set, Testing set
and validation set as provided in Table 1. It includes minimum, maximum, mean, standard
deviation, Kurtosis, Skewness and auto correlation for 1 day lag to 3 day lag( R1, R2, R3)
of daily inflow data. Auto correlation indicates high degree of dependency on previous day
inflow.

5. Flow Forecasting Models

Streamflow forecasting techniques are an integral part of real time operation models.
Stochastic streamflow models are generally used in simulation studies to assess the response
of the water resource systems to future scenarios. The development and implementation
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 Parameters Training Set Validation Set Testing Set
Minimum 3101 4471 2767
Maximum 149075 92890 131488
Mean 19226.518 18079.232 19754.6
Standard Deviation 17161.079 16353.411 16957.402
Kurtosis 2.314 1.875 1.334
Skewness 1.486 1.526 1.314
R1 0.974 0.969 0.955
R2 0.945 0.951 0.936
R3 0.926 0.946 0.918
Table 1: Statistics for Training Set ,Validation Set and Testing Set of observed daily inflow data

of such models require the historical record of flows. Based upon the historical record, the
parameters of the rainfall or streamflow forecasting model are generated. The verification
of the model is then carried out by comparing the statistics of the generated sequences
with the historical sequences. Results indicate relatively strong persistence of streamflow
predictability.

5.1. The Thomas- Fiering Model (TFM)

The Thomas-Fiering model (TFM)[9](Thomas, 1962); [27] (Fiering, 1967) is a lag -one
Markov model. In most streamflow generation techniques it is sufficient to assume that a
first order Markov structure exists. The Thomas Fiering model is fitted to the standardized
monthly flows.
(xi,j − x¯j )
yi,j = (2)
σj
where xi ,j is the original flow for year i and month j , x¯j and σj are sample estimates of the
month and standard deviation respectively, for month j. The model is based on a lag-one
auto-regressive Markov process, and the standardized generated flow is given by

yi,j = βj yi−1,j−1 + i,j (3)

where i is the random component as described by

q
 = 1 − βj2 × Zi,j (4)

and Zi,j is the randomly generated normal variate with zero mean and unit variance, βj is
the lag-one serial correlation between month j and j − 1 given by
P
dx dy
βj = qP P (5)
d2x × d2y

where dx and dy are the derivatives of inflows in month j and j − 1 from their respective
means. A suitable starting value and the sample estimates of monthly parameters x¯j and
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Figure 2: 20 years of month wise prediction of inflow using Thomas Fiering model on Bhakra Nangal data
from year 2017-2037

σj are required to generate a continuous of T years of synthesized monthly flows,xi ,j where

i = 1, T and j = 1, 12 for monthly flows, Since the next period’s inflow can be estimated
from the previous period inflow , (9) can be used recursively to generate synthetic sequence
of desired duration but it is highly dependent upon the random seed that is used to initialize
set of random number in a form of pseudo random sequence. The choice of the seed might
leave the Markov Chain non- stationary in some cases, which means that the reproducibility
of the results obtained from Thomas Fiering Model is less likely on day today basis. Seed
given in this model is 9001.

6. Long Short term Memory (LSTM)

The Long Short Term Memory [28] (Hochreiter et al, 1997) is a recurrent neural network
that is trained using back propagation through time and overcomes vanishing gradient prob-
lem. LSTM networks follow the standard computation graph model for processing continual
input streams that are not a prior segmented into sub sequences. The network consists of
several gates ”forget gate”, ”input gate” and ”output gate” and also in that sequence. The
Equations (6-11) represent the order in which computation for each gate is done within a
LSTM cell. The key to LSTM is that it contains a cell state ct which maintains the state of
each cell and it’s update is shown in Equation (9).
Also, it can be noticed the cell state runs through the LSTM in Fig 3b on top and has
minimal interaction with rest of the cell. The forget is described as ft which is a number in
0 to 1 and is multiplied to cell state to regulate how much of information does it need to

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(a) Recurrent Neural Networks consist of the loop within the network and is unwrapped through time in the above figure to
explain the flow of input and gradients in the model. The simple model consists of an tanh activation at heart that takes
current input and output.

(b) LSTM unwrapped through time shows how the model is designed differently from a RNN model which consists of two
different loops acting as an input an output at each time step. One is the output from ”output gate” and other is output from
the ”forget gate”.

Figure 3: Architectural Differences of RNN and LSTM

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keep. The input gate and output gate along with hidden layer computation are defined in
Equations (5),(8) and (9) respectively.

ft = σ(Wf · [ht−1 , xt ] + bf ) (6)

it = σ(Wi · [ht−1 , xt ] + bi ) (7)

ĉt = σ(Wĉ · [ht−1 , xt ] + bĉ ) (8)
ct = f t ct − 1 + it ĉt (9)
ot = σ(Wo · [ht−1 , xt ] + bo ) (10)
ht = ot φ(ct ) (11)
Its design is such that it enables an LSTM cell to learn to reset itself at appropriate times,
thus releasing internal resources or gradients. The novelty of ”forget gate” is that it locks the
gradient which helps in remembering long term dependencies of the input data. Therefore
the information from the forget gate is not propagated back in time. Thus it helps to remove
the vanishing gradient descent problem that the Recurrent Neural Networks(RNNs) faces
and is the reason why RNNs tend to perform poorly to keep in memory and exploit temporal
relationships that extend over large time steps.LSTM with forget gates, however, easily solve
them in an elegant way as compared to other sequential models such as RNNs and Hidden
Markov models.

7. Experiments
To test the efficacy of the proposed model multiple experiments are run for evaluation at
training and testing time. An effort is made to keep the empirical evidence transparent and
reproducible, implementation details i.e. code and data are made public1 . Figure4 describes
visualization of the network with the help of open libraries(keras and graph viz). We use a
variant of LSTM with two densely packed layers. The first entry i.e. 15 in each of tuples
across all the layers of network denotes the batch size. It is the size of input data for which
network runs predictions in parallel. It helps in leveraging graphic processing unit (GPU)
for faster computations and training of network. Network can be designed with different
batch sizes ranging from 1 to length of data. We use batch size of 15 because it perfectly
divides both our train and test datasets and helps us in faster computation by leveraging
GPU. The second number in the tuple i.e. 3 in input is look back. In other words, it is
the number of past days needed to make prediction for coming day. Similar to batch size,
look back can be adjusted in the parameters fed to the LSTM while training. For all the
experiments and results obtained in the given section look back of 3 days was considered.

1
https://github.com/Anurag14/Inflow-Prediction-Bhakra

10
Figure 4: Architecture of Stacked LSTM network used in experiments with input batch size of 15. The
respective layers have 96, 144 and 5 trainable parameters including both weights and biases. There are total
of 245 trainable and 0 non trainable parameters in the network.

7.0.1. Training and RMSE

The Stacked LSTM is trained using tensorflow framework[29] on a NVIDIA 920 M GPU
for 100 epochs with batch size of 15 throughout. Standard Mean square Error(MSE) is
used as a loss to train the model to fit the data. The model is trained on past data of
20 years of inflow data at Bhakra Dam obtained from Bhakra Beas Management Board.
Precisely two thirds of which, i.e. first 13 years of data is used for training. One tenth of the
data from first 13 years of training set i.e. last one year is kept aside as validation set for
validation after every 5 epochs. The rest of data is never shown to the model — 7 years of
latest data upon which we make inference and test our model. Model is constantly tested on
test data after every 10 epoch, however, it doesn’t learn from test data. Figure 6 describes
the time series view of observed data in blue vs predictions on training data in orange and
test data in green. It can be observed that the predictions of the model after 100 epochs
tightly follow the trends observed in original data making the time series generated by the
model. To quantify the difference between predictions made by the model and to compare
with existing methods of inflow prediction we use Root Mean Square Error(RMSE) and R2
as a metrics to evaluate the error correlation of predictions made by the model with ground
truth. The input inflow time series that is fed to the LSTM network is first normalized
between 0 to 1. The standard normalization is done using min max normalization.
Xi − min Xi
∀i
X̂i = (12)
max Xi − min Xi
∀i ∀i

The root mean squared values are also calculated for the normalized input throughout in
the experiments. The mean squared error also acts as the loss for the training of model. The
loss on training and validation set vs the number of epochs is shown in Figure 5. In table
2 the RMSE and (R2 ) for train set and test set is given. It can be noticed that the RMSE
performance for both test and train set improves as the model learns. Where it can also
be observed that the model learns decent parameters and after one full epoch of learning is
able to make predictions on trains set with RMSE of 0.11 and on test set with RMSE 0.11.
The learnable parameters are kept simple in the LSTM model, explained in Figure 4 i.e.
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 (a) Train Loss (b) Validation Loss

Figure 5: Training and Validation loss plots for 100 epochs

Epochs
Dataset 1 10 20 30 40 50 100
RMSE 0.11 0.04 0.04 0.03 0.03 0.03 0.03
Test 2
R 0.9165 0.9256 0.9215 0.9193 0.9170 0.9140 0.9053
RMSE 0.11 0.04 0.03 0.03 0.03 0.03 0.03
Train 2
R 0.9027 0.9520 0.9507 0.9489 0.9487 0.9492 0.9434
Table 2: Epoch wise RMSE and R2 of stacked LSTM Model for train and test data

245 total parameters, which shows that if more powerful network along with more data can
result in even better predictions. LSTM based neural network architecture proposed in this
paper is shown to have RMSE of 0.03 on test and train sets from the daily inflow data of
20 years. Table 3 is comparison of our approach with other acceptable baselines on recently
sourced inflow data of 2018-2019.
Thomas Fiering model is a the standard model which is used for inflow determination
and is used as the baseline for comparison in our further experiments. Since Thomas Fiering
model just uses lag-1 auto-correlation it tends to estimate the presence of any trend based on
observation of just one previous entry. In table 3 it can be observed that the monthly average
estimates made using Thomas-Fiering model tend to give a RMSE of 0.1207 and (R2 ) 0.8933.
The Thomas-Fiering model is also extended to give daily predictions for comparisons. When
compared for one year duration it gives RMSE value 0.1420 and (R2 ) value 0.6766. LSTM

Metrics
Evaluation for 1st May, 2018 to 30th April, 2019
RMSE R2
Thomas Fiering Monthly 0.1207 0.8933
Thomas Fiering Daily 0.1420 0.6766
LSTM Daily 0.0503 0.9389
10 Daily 0.2940 0.6571
Table 3: RMSE and R2 Values for Monthly and Daily Inflow forecast results

12
 Figure 6: Time series plot of original dataset and train and test

give RMSE 0.0503 and (R2 ) 0.9389. It can therefore be concluded that the Thomas Fiering
model is not very suitable for very accurate daily predictions of inflow in a reservoir. The
daily inflow bears more significance for real time operations of the reservoir and its strategies
as compared to monthly average inflow.

8. Anomaly Detection
Inflow prediction for reservoir operations helps in making better and more sound real
time micro management strategies. Daily inflow prediction with certain accuracy can help
in creating better awareness regarding what inflow to expect on normal days. However, in
certain scenarios there might be instances where the predictions are very different from the
observed values. The model is trained on cases borrowing data from large corpus of past
it learns parameters and generalizes. It has to be robust to anomalies or outliers to be
good at making general predictions. There are several techniques of regularization used in
machine learning community to prevent the model from over-fitting to such anomalies as it
leads to poorer predictions in real world. Having said that, there are sometimes cases where
detection of anomalies is also of great significance. One such use case is flood and drought
prediction.
The below Algorithm tries to describe the proposed naive algorithm baseline using LSTM
models. This naive algorithm baseline can be extended to any deep learning model in future
as in nutshell the algorithm compares the predictions on previous k days with the observed
inflow values. Before that, the ground truth that is the absolute observed values are first
normalized using min max normalization. The comparison is based upon the RMSE values
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Algorithm 1 Naive Anomaly Detection based on LSTM
1: procedure PredictFloodOrDrought(LST M ,lookback,groundtruth,k,ρ,τ = 0.03)
2: Observations ← N ormalizeObservations(groundtruth)[−k :] . last k days
3: input ← Observations[−(k + lookback) : −k] . Take lookback entries before k
4: P redictions ← null
5: for k iterations do
6: P rediction ← LST M (input)
7: Input ← Input[1 :] . Remove of last entry
8: Input.append(P rediction) . Insert Prediction
9: P redictions.append(P rediction)
10: ObservedRM SE ← RM SE(P redictions, Observations)
11: if ObserverdRM SE > τ ρ then
12: Anomaly is observed
13: ObservedInf low, P redictedInf low ← sum(observations), sum(predictions)
14: if P redictedInf low < ObservedInf low then
15: return Flood
16: else
17: return Drought

obtained upon the normalized data. Predicted values give a ball park figure of what the
normal inflow should have been. τ is the empirical RMSE value that is derived using
the experiments of training LSTM model on past 20 years of data. Hence, it is safely
assumed that the RMSE of the observed value with current prediction must remain in
certain tolerance with the empirical RMSE value i.e. τ . Now, that tolerance is defined as
τ ρ where ρ is a multiplier and ρ > 1. For safely concluding that the observed inflow trend
is anomalous ρ = 2 can be taken but in general ρ must be a linear multiplier i.e. tolerance
must be O(τ ).

9. Major contributions of this paper are:

A LSTM based deep neural network architecture has been used for reservoir daily inflow
forecasts.

• Multiple experiments are conducted to prove efficacy of LSTM in calculating daily in-
flow levels both by qualitative measure such as Figure 6 and quantitatively as compar-
ison of Root Mean Square Errors and coefficient of determination R2 between ground
truth and daily predictions from LSTM, Thomas-Fiering and 10 Daily procedure.

• RSME and R2 for widely accepted Thomas-Fiering model for monthly average inflow
prediction with monthly average observed inflow are also provided as reference.

• A naive algorithm baseline for anomaly detection i.e. flood and drought prediction
based upon LSTM is also proposed.
14
It is suggested release policy can be more robust if they operate dam considering LSTM
daily inflow predictions into account.
Available storage
Daily release f rom storage = (13)
T otal water indent during remaining year

T otal Daily release = Daily release f rom storage + Inf low predicted using LST M (14)

Quantity of water available for daily discharge depends upon:

• Daily release possible from available storage depends on the storage in the reservoir
at the end of filling period.

• Daily inflow forecasted using LSTM with 3% RMSE.

Use of above criteria for release of water will reduce the error for inflow determination
currently followed from 29.4% to 3% using LSTM code, providing better decision policy for
reservoir operation

10. Conclusion
With population growth increase in requirement of power and reliable water supply
increases. With increase in demand, more clever reservoir operation is needed to meet power
demands and provide reliable water supply. With the use of machine learning techniques
wide range of problems in optimization and operations research are being solved. Deep
learning has become ubiquitous in recent state of art solutions that are being employed to
wide array of tasks. An attempt has been made in this study for determination of inflow at
Bhakra Dam. Daily inflow predictions using LSTM will enhance operational performance
of reservoir. Model is able to predict daily inflow with Root Mean Square error of 3%
and R2 value 0.9389. Thomas-Fiering model is also extended from monthly prediction to
daily prediction. The Root Mean Square error is 14.20% and R2 value is 0.6766 compared
to observed values. Using Thomas- Fiering Model monthly prediction were also made and
results when compared with observed monthly resulted in Root Mean Square error as 12.07%
and R2 value as 0.8923. RMSE and R2 values clearly indicate that application of LSTM
in reservoir operation and daily prediction of inflow performs best compared to prevailing
technique followed at Bhakra dam and Thomas- Fiering Model predictions. Using LSTM
release from the reservoir can be monitored efficiently. Use of daily inflow prediction in
estimating the release will reduce the complexities of reservoir operation. Use of monthly
inflow overlooks daily variation of inflow in making decision regarding releases which can be
avoided. Naive Anomaly detection based on LSTM will be able to warn water management
regarding flood and drought. If the value of RMSE shows large variation between observed
inflow and LSTM predicted inflow, it is clear indication of flood or drought. Operational
release policy can be updated accordingly in order to have efficient operation. Daily inflow
determination modeling technique is expected to improve the reservoir operational strategies
15
under changing climatic conditions. Streamflow generation model are used to synthesize
daily inflow sequences considering previous inflow. Comparison between synthetic data
from these models and observed data in terms of RMSE can help evaluate climate change.

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