Research paper for Expert system(AI) for decision making support

Expert Systems With Applications 83 (2017) 145–163

Contents lists available at ScienceDirect

Expert Systems With Applications

journal homepage: www.elsevier.com/locate/eswa

Developing an intelligent expert system for streamflow prediction,

integrated in a dynamic decision support system for managing

multiple reservoirs: A case study

Hamed Zamani Sabzi a , ∗, James Phillip King a , 1 , Shalamu Abudu b

a Department of Civil Engineering, New Mexico State University, MSC 3CE, PO Box 30 0 01, Las Cruces, NM, USA, 88003 b Texas AgriLife Research & Extension Center at El Paso, Texas A&M University System, 1380 A&M Circle, El Paso, TX 79927, USA

a r t i c l e i n f o

Article history:

Received 23 June 2016

Revised 18 April 2017

Accepted 18 April 2017

Available online 19 April 2017

Keywords:

ANFIS

ARIMA

ANN

Hybrid model of ANN-ARIMA

Data mining

Streamflow prediction

a b s t r a c t

Since fresh water is limited while agricultural and human water demands are continuously increasing,

optimal prediction and management of streamflows as a source of fresh water is crucially important. This

study investigates and demonstrates how data preprocessing and data mining techniques would improve

the accuracy of streamflow predictive models. Based on easily accessible Snow Telemetry data (SNOTEL),

four streamflow prediction models – autoregressive integrated moving average (ARIMA), artificial neural

networks (ANNs), a hybrid-model of ANN and ARIMA (ANN-ARIMA), and an adaptive neuro fuzzy infer-

ence system (ANFIS) – were developed and utilized in a streamflow prediction process on Elephant Butte

Reservoir. Utilizing the statistical correlation analysis and the extracting importance degrees of predic-

tors led to efficiently select the most effective predictors for daily and monthly streamflow to Elephant

Butte Reservoir. For the daily prediction time step, by preprocessing the historical data and extracting

and utilizing the extracted climate variability indices through data mining techniques, the ANFIS model

achieved a superior streamflow prediction performance for Elephant Butte Reservoir compared to the

other three evaluated prediction models. Additionally, for predicting monthly streamflow to the Elephant

Butte Reservoir, ANFIS showed significantly higher accuracy than the ANNs. As an optimal application of

the developed predictive expert systems, successful integrating the prediction models in integrated reser-

voir operations balanced the need for a reliable supply of irrigation water against losses through evapo-

ration. The optimal operation plan significantly minimizes the total evaporation loss from both reservoirs

by providing the optimal storage levels in both reservoirs. This study provides the conceptual procedures

of non-seasonal (ARIMA) model, and since the model is univariate, it demonstrates a strongly-reliable

inflow prediction when existing information is limited to streamflow data as a predictor.

© 2017 Elsevier Ltd. All rights reserved.

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. Introduction

Multi-objective reservoirs play a critical role in providing a re-

iable source of fresh water for domestic human needs, agricul-

ural water demands, hydroelectricity production, and environmen-

al purposes. Therefore, to adequately meet these needs, multi-

bjective reservoirs should be operated optimally. Elephant Butte

eservoir is a multi-objective reservoir that produces electrical

ower and provides water for south-central New Mexico and west

exas. For irrigation, it provides water for about 170,0 0 0 acres of

∗ Corresponding author. E-mail addresses: [email protected] (H. Zamani Sabzi),

[email protected] (J.P. King), [email protected] (S. Abudu). 1 Member of the Engineering Research Center for Re-inventing Urban Water In-

rastructure, Stanford University.

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ttp://dx.doi.org/10.1016/j.eswa.2017.04.039

957-4174/© 2017 Elsevier Ltd. All rights reserved.

gricultural lands. Elephant Butte Reservoir releases water to Ca-

allo Reservoir, 25 mi downstream of Elephant Butte Reservoir. Di-

ect water release from Caballo Reservoir provides water for irriga-

ion downstream in the Rio Grande Project.

The two reservoirs of Elephant Butte and Caballo are considered

s an integrated system whose streamflow values, outflows, and

torage volumes can be simulated. A reliable release plan from Ca-

allo directly relates to the storage levels at Caballo Reservoir. The

arger of the two reservoirs, Elephant Butte, retains water across a

ength of 40 mi, and the total surface area of that water can reach

7 mi 2 . Although retaining such high levels of water would in-

rease the likelihood of meeting the area’s water needs, this prac-

ice can cause significant water losses to evaporation: during the

ummer, evaporation rates in the area can reach 1 cm per day,

nd the historical evaporation rates are measured as pan evapo-

ation rates in each specific region. Therefore, a decision support

146 H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163

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system that balances the need for reliable water supplies against

evaporation loss, under realistic conditions that are uncertain and

dynamic, can provide significant benefits. The optimal operation

policy critically depends on accurately estimating the streamflow

to Elephant Butte Reservoir. Depending on the forecasting condi-

tion and availability of the utilized data, different forecast models

would be appropriate for different forecasting conditions. Although

some forecast models in many cases have better prediction perfor-

mances, but appropriateness of any specific streamflow forecasting

model is not universal. Therefore, it is crucially important to in-

vestigate the appropriateness of several streamflow forecast mod-

els for a specific prediction condition, and select the most reli-

able streamflow forecast model. As a result, considering the sev-

eral previously developed studies on streamflow forecasting, four

categories of the forecast models of time series models (ARIMA),

ANNs, hybrid models of ANN and ARIMA (ANN-ARIMA), and AN-

FIS applied in predicting hydrologic parameters were investigated

through this study. Then considering the accuracy performances,

the most accurate forecast model is introduced for this study case

along with introducing an efficient approach in selecting the ef-

fective predictors. Previously, many researchers have studied ap-

plications of those forecast models in diverse engineering predic-

tions including streamflow forecasting. Cumulatively, the two ma-

jor artificial-intelligence-based prediction models of ANN and AN-

FIS have been widely used to estimate diverse hydrologic objec-

tives such as the dispersion coefficient of natural streams, earth-

quake probability, global solar radiation, daily pan evaporation,

fishing rate, and lake level fluctuations.

In several of the previous studies such as study that was de-

veloped by Adamowski (2008) , accuracy performances of differ-

ent models were compared. Adamowski (2008) investigated sev-

eral prediction models including multiple linear regression models,

time series, and ANNs to forecast the peak water daily demand in

the city of Ottawa, Canada for the summer period of May to Au-

gust. He utilized historical data of 10 years on peak daily water de-

mand and meteorological variables of the maximum daily temper-

ature and daily rainfall. His accuracy performance analysis showed

that ANNs predicted the peak daily water demand with higher ac-

curacy compared to the other multiple linear regression and time

series based models. Basically, in majority of prediction cases a

structure of ANNs based forecast model is utilized to map the ex-

isting nonlinear relationships between the predictors and predicted

values. Therefore, observing higher accuracy for ANNs would be

due to the existing non-linear relationships between the mete-

orological variables and peak daily water demands ( Adamowski,

2008 ).

Basically, developing an accurate and efficient ANNs based fore-

cast model relies on two factors of correct election of the pre-

dictors and designing an efficient ANN along with efficient train-

ing and validation techniques. Some of previous researchers such

as Coulibaly, Anctil, and Bobée (20 0 0) studied accuracy perfor-

mance of utilizing various techniques for training the defined

ANNs. Findings indicates that obtaining a higher accuracy by uti-

lizing specific training and validation techniques is not a univer-

sal expectation and it might be different case by case ( Coulibaly

et al., 20 0 0 ). However, in majority of the evaluated previous stud-

ies through this work such as studies developed by Imrie, Duru-

can, and Korre (20 0 0) and Othman and Naseri (2011) , a typical

feed-forward network with Levenberg–Marquart Back Propagation

(LMBP) structure and algorithm were utilized ( Imrie et al., 20 0 0 ).

The same approach in searching for an optimal structure of the

ANNs for streamflow prediction was followed by other researchers.

Valipour, Banihabib, and Behbahani (2012) specifically investigated

the searching procedure to find the near-optimal structure of the

developed ANNs that was used to predict monthly streamflow to

the Dez Reservoir in Iran ( Valipour et al., 2012 ). Some studies

uch as the study developed by Wu, Chau, and Li (2009) indicate

hat simultaneously utilizing the effective streamflow lagged val-

es along with the other effective predictors would improve the

rediction accuracy. In more details, Wu et al. (2009) examined

sing different hybrid models of moving average (MA), wavelet

ulti-resolution analysis (WMRA), and singular spectrum analysis

SSA) coupled with an ANNs model to improve the daily stream-

ow prediction accuracy based on data from different watersheds

n China. Their numerical results of accuracy performance analysis

f developed hybrid models showed that utilizing effective stream-

ow lagged values from moving average analysis along with the

NNs (ANN-MA) provided the most accurate model compared to

he other developed hybrid models of ANN-SSA and ANN-WMRA

Wu et al., 2009 )

ANFIS, too, has been used by several researchers to develop

treamflow and runoff forecast models. Majority of the previously

eveloped studies on hydrologic forecast models such as stud-

es developed by Atsalakis and Minoudaki (2007) and El-Shafie,

aha, and Noureldin (2007) reported that utilizing ANFIS as a fore-

ast model provides higher accuracy compared to the time series

nd ANNs based models. Atsalakis and Minoudaki (2007) utilized

NFIS to predict daily irrigation water demand, and compared

heir results with ARIMA based predicted values. Their results

howed that ANFIS is more accurate model than ARIMA in predict-

ng the water demand values ( Atsalakis & Minoudaki, 2007 ). El-

hafie et al. (2007) used ANFIS as a technique to predict monthly

treamflow for the Nile River inflowing to the Aswan High Dam

AHD). They used 130 years gathered historical data to develop

he ANFIS-based forecast model. The prediction accuracy perfor-

ance of their model indicates higher prediction accuracy for AN-

IS based forecast model compared to the previously developed

NNs-based forecast model ( El-Shafie et al., 2007 ). Pramanik and

anda (2009) utilized ANN and ANFIS to develop a forecast model

o predict the daily outflow from a barrage located on the Ma-

anadi River Basin, India based on flow data upstream of the bar-

age. Their accuracy performance of the developed forecast mod-

ls indicate that ANFIS based models provide higher prediction ac-

uracy compared to the ANN based models ( Pramanik & Panda,

009 ). Talebizadeh and Moridnejad (2011) used ANN and ANFIS

odels to predict the lake level fluctuations in Urmia Lake located

n northwest of Iran. In developing the lake level fluctuations, they

tilized time series of lake levels, rainfall magnitudes, evaporation

ates, and inflow to the lake as predictors ( Talebizadeh & Morid-

ejad, 2011 ). Similar to the several other researches’ studies that

ere considered as literature review, wherever ANNs and ANFIS

tilize the same sort of the predictors, in most cases ANFIS pro-

ided accurate data compared to the ANNs. Although in the major-

ty of the previous researches, ANFIS provided better prediction ac-

uracy, still there are some cases such as study that was developed

y Karimi-Googhari and Lee (2011) report that ANNs-based fore-

ast model provided better prediction accuracy compared to the

NFIS. As a results, expecting the higher prediction accuracy from

NFIS based forecast models compared to the ANNs-based models

s not an universal fact ( Karimi-Googhari & Lee, 2011 ).

The following material details some of the other previous

tudies in using ANNs, ARIMA, and hybrid models for predict-

ng streamflow. Jain, Das, and Srivastava (1999) utilized ANN and

RIMA models to predict the monthly streamflow to the Indravati

ultipurpose reservoir in Orissa, India; then. they utilized the pre-

icted values to optimize the reservoir operation policies (monthly

elease plans) ( Jain et al., 1999 ). Mohammadi, Eslami, and Dayyani-

ardashi (2005) studied the similarities and dissimilarities of the

egression-based model, ARIMA, and ANNs in forecasting reser-

oir streamflow in Karaj, Iran ( Mohammadi et al., 2005 ). Some

esearchers such as Muluye and Coulibaly (2007) in order to im-

rove the prediction accuracy, utilized climate variability indices

H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163 147

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long with historical time series of streamflow data to forecast the

easonal streamflow from a watershed to the reservoir ( Muluye &

oulibaly, 2007 ).

In this study, runoff regime in the region of the study area

s snowmelt dominated which led us to select and include the

ost effective physical predictors through forecasting model de-

elopment procedure. Shukla, Sheffield, Wood, and Lettenmaier

2013) investigated various physical parameters that affect global

and surface hydrologic predictability ( Shukla et al., 2013 ). There-

ore, considering the physical characteristics of the study area can

ead to appropriately selecting the optimal hydrologic prediction

odel.

So far, most of the previous studies show that the optimal oper-

tion of a reservoir depends on the accurate estimation of stream-

ow values. Since most models have different levels of predic-

ion accuracy when they are applied on different case studies, it

s significantly important to select the most appropriate predic-

ion models. Therefore, to optimize the operation of the Elephant

utte and Caballo reservoirs, the present study investigates sev-

ral prediction models to accurately estimate the streamflow to

lephant Butte Reservoir. The accurately predicted values are uti-

ized in a multi-objective decision support system that minimizes

otal evaporation loss by providing the optimal storage levels on

oth reservoirs. Simultaneously, release reliability from the Caballo

eservoir is maximized. In more details, based on the accuracy per-

ormances, the most accurate model was introduced. Then, values

or one specific month predicted through the utilized prediction

odels were incorporated in the operation policy for one month to

djust the storage levels on Elephant Butte and Caballo reservoirs.

he extended processes of developing the procedures of ARIMA,

NN, and ANN-ARIMA have been described through two indepen-

ent studies that are in the publication process. Two indepen-

ent studies have been developed by authors of this study to pro-

ide comprehensive details regarding the development of optimal

treamflow prediction models focusing on ANNs and ARIMA mod-

ls ( Zamani Sabzi, King, & Abudu, 2017a, 2017b ).

The following sections describe the study area, utilized data,

treamflow prediction models, mass balance concept (control vol-

me), and the optimal choice of reservoir for storing a specific

mount of streamflow for a specific prediction period. The adap-

ive reservoir operation model will support daily operations when

hort-term predicted values are utilized in providing the optimal

peration plans and daily observed values are fed to the predic-

ion model to update the prediction model’s accuracy.

. Study area and data used

The required data include the recorded historical streamflow

ata measured at San Marcial gauges from 1961 to 2015, histori-

al agricultural water demand, rainfall rates, and measured evap-

ration rates. These data sources were used to estimate the agri-

ultural water demand and evaporation loss from both Elephant

utte and Caballo reservoirs. Physical characteristics of the reser-

oirs and recorded bathymetry data by USGS were utilized to de-

elop the stage-surface area and stage-storage relationships for

oth Elephant Butte and Caballo reservoirs. Fig. 1 shows the de-

eloped watershed area above the Elephant Butte Reservoir in

his study. The digital elevation model (DEM) maps were obtained

hrough USGS website and GIS software (Arc Map 10.1) was uti-

ized to develop the watershed boundary and its sub-basins. The

tudy area as shown in Fig. 1 is the Rio Grande watershed lo-

ated in Colorado and New Mexico upstream of the Elephant Butte

eservoir in New Mexico. Two US geological survey gaging sta-

ions are utilized to measure the flow at San Marcial, New Mex-

co at the upstream of the reservoir. Two measurement sites in-

lude: the Rio Grande Floodway at San Marcial, NM (USGS Sta-

ion no: 08358400), which located in the river channel, and the

io Grande Conveyance Channel at San Marcial, NM (USGS Station

o. 08358300), a developed channel parallels the Rio Grande. The

um of the streamflows in these two channels are considered as

otal streamflow at San Marcial inflowing to the Elephant Butte

eservoir. All data utilized as model inputs were easily accessi-

le online from Natural Resources Conservation Center (NRCS), Na-

ional Weather Service (NWS) websites, and United States Geol-

gy Service (USGS). Specifically, the snow water equivalent (SWE)

ata were obtained through the Natural Resources Conservation

ervice (NRCS) website: http://www.wcc.nrcs.usda.gov/snow/ . The

NOTEL precipitation (PRCP) data were obtained from NRCS web-

ite: http://www.wcc.nrcs.usda.gov/snow/ . In addition, the monthly

recipitation data for weather stations were obtained through the

estern Region Climate Center (WRCC) website: http://www.wrcc.

ri.edu/ . Considering the physical characteristics of the study area,

he major portion of the streamflow is from snowmelt, therefore,

nowpack related data were the most effective selected predictors

hrough the developed prediction models.

The snowpack related historical data have been obtained from

2 snow telemetry sites in upper side of the Elephant Butte’s wa-

ershed region.

Regarding the data sources for the SNOTEL sites where the data

ave been obtained, Table 1 . Represents the names, locations, geo-

raphical coordinates, and the elevations of the selected sites.

Twelve SNOTEL sites were chosen for this study. In addition, the

orrelation analysis indicated that the SNOTEL sites located in west

f Rio Grande in New Mexico and Colorado have stronger correla-

ions than the SNOTEL sites located in east of Rio Grande in New

exico and Colorado, although three SNOTEL sites were selected

orm the east sides, since the selected sites located in the positions

hat affects the total streamflow in the Rio Grande.

Historical precipitation record indicates that the average of to-

al annual based on the gathered information precipitation amount

easured on the 12 SNOTEL sites was 189.1 in. The total SWE

mount for the six-month period of the available snowpack on the

atershed based on the gathered information measured on the 12

NOTEL sites was 65.6 inches. The minimum, maximum and aver-

ge of annual temperatures from the 12 weather station sites on

he watershed are −8 °C, 12 °C, and 1 °C respectively. Total water- hed area above the Elephant Butte Reservoir is about 29,0 0 0 mi 2 .

he total capacities of the Elephant Butte and Caballo reservoirs

re about 2.5 billion m 3 and 424 million m 3 , respectively.

. Methodology

Fig. 2 shows the schematic diagram of the integrated reservoirs’

peration model. The operation model includes a prediction en-

ine with four prediction models, a control volume concept, and

n optimization process. The historical recorded data are utilized

hrough streamflow prediction models. Considering the accuracy

erformance of the developed models, the most accurate model is

sed to provide the daily predicted values. The predicted values are

tilized in the mass balance calculation process. Finally, the opti-

al storage strategy on the two reservoirs is obtained.

This study utilized the ANFIS, ANN, and the hybrid model of

NN and ARIMA as multivariate models and ARIMA as a univari-

te streamflow prediction model. The accuracy performances and

he availability of data on the predictors identified the appropriate

treamflow prediction model.

.1. ARIMA model

ARIMA models are stochastic univariate time series models that

ere developed by Box and Jenkins (1976) . Generally, the ARIMA

odels are the generalized forms of the auto regressive moving

148 H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163

Fig. 1. Study area showing the locations of Elephant Butte and Caballo reservoirs, the watershed area above Elephant Butte Reservoir, and the Rio Grande above Caballo

Reservoir.

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d

average (ARMA) models ( Box & Jenkins, 1976 ). ARIMA as non-

seasonal univariate model is applicable prediction technique when

existing information is limited to streamflow data as a predictor.

The nonseasonal form of ARIMA models is defined as:

ARIMA ( p , d, q ), in which parameters p , d , and q are the number of

autoregressive lags, order of differencing, and number of moving

average lags through the ARIMA model, respectively. In this work,

he three stages of identification, estimation, and diagnostic check

efined by Box and Jenkins were followed and examined to find

he most accurate ARIMA model for daily streamflow prediction.

he appropriate parameters of ( p and q ) were obtained by inves-

igating autocorrelation (ACF) and partial autocorrelation functions

PACF). The parameters of ( p and q ) demonstrate the time depen-

ency of the time series values. Abudu (2009 ) and Abudu, King,

H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163 149

Table 1

SNOTEL Sites used in the study of Rio Grande Basin above the Elephant Butte Reservoir, New Mexico.

SNOTEL SITES Location Elevation (feet)

West longitude North latitude Region

Bateman 106.32 36.51 Rio Grande west in New Mexico 9300

Chamita 106.66 36.96 Rio Grande west in New Mexico 8400

Culbera#2 105.2 37.21 Rio Grande east in New Mexico 10,500

Cumbres Trestle 106.45 37.02 Rio Grande west in Colorado 10,040

Gallegos PEAK 105.56 36.19 Rio Grande east in New Mexico 9800

Hopewell 106.26 36.72 Rio Grande west in New Mexico 10,0 0 0

Lily Pond 106.55 37.38 Rio Grande west in Colorado 11,0 0 0

Middle Greek 107.03 37.62 Rio Grande west in Colorado 11,250

Quemazon 106.39 35.92 Rio Grande west in New Mexico 9500

Red River Pass#2 105.34 36.7 Rio Grande east in New Mexico 9850

Upper San Juan 106.84 37.49 Rio Grande west in Colorado 10,200

Wolf Greek 106.8 37.48 Rio Grande west in Colorado 11,0 0 0

a

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nd Bawazir (2011 ) utilized a seasonal ARIMA (SARIMA) model to

redict the monthly streamflow to the Elephant Butte Reservoir

Abudu, 2009; Abudu et al., 2011 ).

The ARIMA model was developed and examined through data

reprocessing, processing, and programming in Statistical Analysis

oftware (SAS).

Generally, a non-seasonal ARIMA model is defined through

qs. (1) –(6) as follows:

( B ) x t = θ ( B ) a t (1)

here x t = 1 − B d X t , as stationary series after differencing, and d is the number of non-seasonal differencing. (2)

ϕ ( B ) = 1 − ϕ 1 B − ϕ 2 B 2 − · · · − ϕ p B p , as nonseasonal autoregressive polynomial

(3)

( B ) = 1 − θ1 − θ2 B 2 − · · · − θq B q , as nonseasonal moving average polynomial,

q indicates the order of moving average polynomial.

(4)

here p indicates the order of autoregressive polynomial, q indi-

ates the order of moving average polynomial, a t represents the

hite noise, X t represents a dependent variable, and B is backward

hift operator (lag operator). The backward shift operator B is cal-

ulated via Eq. (5 ) as follows:

X t = X t−1 (5) Since the mean and variance of non-seasonal daily streamflow

ata are not constant, the data are non-stationary. In utilizing the

RIMA model for daily prediction, the data are stabilized as sta-

ionary (having constant means and variance on time series data)

ondition by applying the required order of differencing, such as

rder of differencing applied on the square roots of data. The opti-

al values of the parameters of p and q orders were obtained con-

idering the covariance values observed through plotting the PACF

nd ACF, respectively. Based on the utilized data, the ARIMA model

30,1,1) was obtained as the most accurate non-seasonal univari-

te model. The lags of 1, 2, 7, 8, 24, and 30 were extracted as

ignificant autoregressive factors and passed all required diagnos-

ic checks. The primary daily ARIMA model was obtained as: (1-

.05209 B ∗∗ (1) + 0.23324 B ∗∗ (2) - 0.0213 B ∗∗ (7) + 0.02406 B ∗∗ (8) 0.00835 B ∗∗ (24) + 0.01832 B ∗∗ (30)) W t = (1-0.85063 B ∗∗ (1)) ∗A t in which is transferred to the usable predictive model through

he Eq. (6) as follows ( Zamani Sabzi, King, & Abudu, 2017b ):

t = (√

x t−1 + 1 . 05209 (√

x t−1 − √

x t−2 )

− 0 . 23324 (√

x t−2 − √

x t−3 )

+ 0 . 0213 (√

x t−7 − √

x t−8 )

− 0 . 02406 (√

x t−8 − √

x t−9 )

+ 0 . 00835 (√

x t−24 − √

x t−25 )

− 0 . 01832 (√

x t−30 − √

x t−31 )

+ A t − 0 . 85063 A t−1 ) 2 (6) here W t = Z t − Z t−1 , Z t =

√ x t , x t represents the daily stream-

ow data to the reservoir (acre-ft), Z t represents the trans-

ormed daily streamflow data, W t is the differenced time series

ata, A t = error term on √ x t ( considere d white noise on √ x t ) , and t−1 = error term on √ x t−1 = actu al √ x t−1 − pred icted √ x t−1 .

.2. Artificial neural networks

Basically, ANNs are computational models that were developed

hrough inspiration from the human brain. ANNs can identify the

xisting complex relationships and patterns between input and

utput values. Generally, neural networks are formed through in-

erconnected neurons, which are computed by using historical data

nd future values. The most accurate models are made by using

he most meaningful information. Considering the simplicity and

omplexity of the existing relationships, the best models are ob-

ained by examining both simple and complex models and evalu-

ting the accuracy performances of the constructed models. Feed-

orward neural networks (FFNNs), the most commonly used ANNs

odels, were utilized in this study. Fig. 3 shows a typical structure

f an ANN model with one input layer, one hidden layer, and one

utput layer.

In a three-layered FFNN, the outputs are computed through the

onlinear transformation of linear combinations of input variables.

he output values are explicitly expressed and calculated through

q. (7) as follows:

ˆ k = f 0

[ M ∑

j=1 w k j . f h

( N ∑

i =1 w ji x i + w j0

) + w k 0

] (7)

here the parameter of w ji represents the optimal assigned weight

hat connects the i th neuron of the input layer to the j th neuron on

he hidden layer, w j 0 is the considered bias value assigned to the

th neuron on the hidden layer, f h is the taken activation function

pplied on the neurons in the hidden layer, w kj is the considered

eight that relates the j th neuron on the hidden layer to the k th

euron on the output layer, w k 0 is the bias value assigned to the

th neuron on the output layer, and f 0 is the taken activation func-

ion applied on the output neurons:

150 H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163

Accuracy Performance Inflow es�ma�on using Univariate and

Mul�-Variate Predic�on Models

Find the op�mal storage levels on Elephant Bu�e and Caballo

U�lize historical data and update predic�on models with observed data

Rio G rande

Rio G rande

Seepage and groundwater interac�on

Elephant Bu�e Reservoir

Tributary streamflow

Evapora�on from Elephant Bu�e

Tributary streamflow

Seepage to the groundwater

Direct precipita�on on the reservoir

)e muloV lortnoC( l ortnoC ecnala B s sa

M

Evapora�on from Caballo Reservoir

Seepage and groundwater

Direct precipita�on on the reservoir

Subject to:

� Minimize evapora�on loss � Maximize the release reliability � Maximize the hydropower electricity produc�on

Caballo Reservoir

ANN Hybrid model of ANN and ARIMA ANFIS ARIMA

St re

am flo

w P

re di

c� on

E ng

in e

R es

er vo

irs O

p� m

iz a�

on M

od el

Fig. 2. Optimization process in the developed dynamic model.

w

s

o

w

S

m

t

t

p

d

E(n ) = 1 2

N ∑ p=1

L ∑ k =1

[ y pk (n ) − ˆ y pk (n )

]2 (8)

where N represents the number of observations (inputs), L repre-

sents the number of predicted output values, y pk ( n ) represents the

observed values (desired target values), and ˆ y pk (n ) represents the

value simulated by the network for the k th neuron by n th iteration.

One of the optimal models obtained through accuracy perfor-

mances of developed ANNS is formed as follows:

I t +1 ,t +2 ,t +3 ,t +4 ,t +5 ,t +6 ,t +7 = f ( I t , SW E t ∗ , SW E E t ∗ , P M−2 , M i ) (9)

here I t+1 , t +2 , t +3 , t +4 , t +5 , t +6 , t +7 are the predicted daily treamflows at 1, 2, 3, 4, 5, 6, and 7 days ahead; I t defines the

bserved daily value at an assumed day I t ; SW E t ∗ is the snow ater equivalent recorded at the first day of the prediction month;

W E E t ∗ defines the snow water equivalent at the first day of the onth that has higher correlation between the recorded SWE and

he streamflow values ate the prediction month; and P M−2 defines he precipitation index recorded in the two months preceding the

redicted month, and M i is the month index (month number).

Eq. (10) represents the model of Eq. (9) along with utilized time

ependent trend indices as other effective predictors.

H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163 151

wk0 Bias values

wj0 Bias values

1

L M-1

M

1

N-1

N

2

1

Output 1

Output L

Input layer

Output layer

Hidden layer

kth

Input 1

Input 2

Input N-1

Input N

ith jth

Weights wji

Weights wkj

Fig. 3. Typical structure of an FFNN model with one input layer, one hidden layer, and one output layer.

I

fl

a

p

s

t

3

a

A

I

w

fl

t

I

1

d

h

d

a

f

3

w

e

o

i

f

fi

p

t

a

S

3

o

2

a

fl

p

w

m

t

I

I

w

m

d

e

o

m

f

t

d

r

b

n

P

y

4

4

p

d

(

T

o

t +1 ,t +2 ,t +3 ,t +4 ,t +5 ,t +6 ,t +7 = f ( I t , SW E t ∗ , SW E E t ∗ , P M−2 , M i , P 5 Y i , P 2 Y i , P Y i ) (10) Where P 5 Y i represents the average value of annual stream in-

ow in the 5 years before the predicted year, P 2 Y i represents the

verage value of annual stream inflow in the 2 years before the

redicted year, and PY i represents the average value of annual

tream inflow in the year before the predicted year. The rest of

he utilized predictors are the same as explained through Eq. (9) .

.3. The hybrid model of the ANN-ARIMA

The hybrid model is defined by utilizing the most significant

utoregressive lags and the meaningful predictors of developed

NN models.

t +1 ,t +2 ,t +3 ,t +4 ,t +5 ,t +6 ,t +7 = f ( I t , I t−1 , I t−2 , I t−7 , I t−8 , I t−24 , I t−30 , SW E t ∗ , P M−2 , M i ) (11) here I t−1 , I t−2 , I t−7 , I t−8 , I t−24 , I t−30 are the lagged daily stream- ow values at 1, 2, 7, 8, 24, and 30 days in the past. The rest of

he utilized predictors are the same as explained through Eq. (9) .

Since, in the developed daily ARIMA model, we utilize

t−1 , I t−2 , I t−7 , I t−8 , I t−24 , I t−30 as lagged daily streamflow values at , 2, 7, 8, 24, and 30 days in the past, therefore for predicting 2

ays ahead, we will need I t , which we do not have it yet and we

ave to observe it. As a result, when the closest effective lagged

ata is I t−1 , we can predict the streamflow value for just one day, nd if the closest effective lagged data was I t−2 , we could predict or 2 days ahead.

.4. Adaptive network based fuzzy inference system (ANFIS)

As another prediction model, a fuzzy inference system (FIS)

ith a Takagi–Sugeno inference system was utilized as an infer-

nce system to estimate the streamflow values as output values

f the inference system. ANFIS was utilized as a hybrid learn-

ng method to find the optimal parameters of the membership

unctions of the Takagi–Sugeno system. The Takagi–Sugeno FIS de-

nes the input variables through Gaussian distribution, and out-

ut variables are defined as constant output values or linear in-

ervals. Then, the parameters of the utilized membership functions

re tuned using ANFIS. Fig. 4 illustrates the schematic of a Takagi–

ugeno FIS. ( Jang, 1993 )

.5. Monthly streamflow prediction models

Monthly streamflow prediction models were developed based

n the same data set available from January 1961 to August

015. Physical parameters (snowpack data, precipitation indices,

nd streamflow values), time indices, and time dependent stream-

ow trend indices were utilized to develop monthly streamflow

rediction models. The time dependent stream flow trend indices

ere obtained through supervised data mining techniques.

Conceptually, importance degrees along with accuracy perfor-

ance analysis led us to develop monthly prediction models

hrough Eqs. (12) and (13) .

m = f ( I m −1 , SW E Em , SW E m , P m −1 , P m −2 , S i , M i , P 5 Y i , P 2 Y i , P Y i ) (12)

m = f ( I m −1 , SW E Em , SW E m , P m −1 , P m −2 , M i , ) (13) here I m −1 indicates the observed monthly value at a specific onth, SWE represents the snow water equivalent at the first

ay of the prediction month, SWE Em represents the snow water

quivalent at the first day of the month with higher correlation

f the SWE and predicted stream inflow values in the prediction

onth, P m −1 represents the precipitation index in the month be- ore the predicted month, P M−2 represents the precipitation index wo months before the predicted month, S i represents season in-

ex, M i stands for the number of the predicted month, P 5 Y i rep-

esents the average value of annual stream inflow in the 5 years

efore the predicted year, P 2 Y i represents the average value of an-

ual stream inflow in the 2 years before the predicted year, and

Y i represents the average value of annual stream inflow in the

ear before the predicted year.

. Results and discussion

.1. Accuracy performance analysis on developed daily streamflow

rediction models

To compare the accuracy performance of the four utilized pre-

iction models, the last 25% of the test data from 1961 to 2015

from January 2002 to August 2015) was used as a test data set.

ables 2 and 3 represent the accuracy performance of the devel-

ped models along with the correlation coefficient fitted between

1 5

2

H . Z

a m

a n

i Sa

b zi et

a l. / E

xp ert

Sy stem

s W

ith A

p p

lica tio

n s 8

3 (2

0 17

) 14

5 –

16 3

Table 2

Numerical results of the developed networks for prediction models through different periods of the year.

Input variables (Predictors) Correlation coefficient (r) between predicted

and observed daily streamflow values

MI P M-2 SWE EM SWE t I t Climate variability indices No. of Month Prediction period I t+1 I t+2 I t+3 I t+4 I t+5 I t+6 I t+7 ( P 5 Y i , P 2 Y i , PY i )

- - - - ∗ - ARIMA (Model 1) 1 day 0.97 - - - - - - ∗ ∗ ∗ ∗ ∗ ∗ 12 Month (ANN) 7 days 0.982 0.965 0.948 0.929 0.911 0.897 0.884 ∗ ∗ ∗ ∗ I t, t-1, t-2, t-7, t-8, t-24, t-30 - 12 month Hybrid ANN_ARIMA

(Model 2)

7 days 0.977 0.961 0.943 0.926 0.907 0.892 0.877

∗ ∗ - ∗ ∗ - 12 Month (ANN) 15 days, (first 7 days from 15 days prediction period)

0.984 0.963 0.946 0.927 0.908 0.892 0.879

∗ ∗ ∗ ∗ ∗ - 12 Month (ANN) (Model 3) 7 days 0.983 0.964 0.945 0.925 0.908 0.893 0.878 ∗ ∗ ∗ ∗ ∗ - 12 Month (ANFIS) (Model 4) 7 days 0.987 0.984 0.978 0.973 0.967 0.956 0.950

Note : the star sign ( ∗) indicates that the related parameter has been considered as a predictor and the hyphen ( −) sign indicates that the related parameter has not been used as a predictor in the developed prediction model. The bold values represent the parameters of the selected models.

H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163 153

Fig. 4. Typical structure of ANFIS model with five predictors and one output.

Table 3

Accuracy of the utilized prediction models in different prediction periods.

Accuracy performance I t+1 I t+2 I t+3 I t+4 I t+5 I t+6 I t+7

MSE (ARIMA), Model 1 76,437.3 - - - - - -

MSE (ANN_ARIMA), Model 2 110,775.3 192,241.2 279,312.5 352,262.5 434,890.2 499,070.6 566,679.2

MSE (ANN), Model 3 77,628.1 164,806.7 250,180.5 338,942.4 412,681.4 476,938.0 543,114.5

MSE (ANFIS), Model 4 62,553.1 138,206.5 201,320.2 270,732.2 336,255.4 370,526 419,128

The bold values represent the parameters of the selected models.

t

e

i

r

t

I

p

m

fl

o

t

u

t

B

o

p

p

2

l

b

u

c

m

v

t

2

a

t

r

m

u

F

o

A

o

p

a

d

f

p

he predicted and observed daily streamflow values through differ-

nt predicted future periods.

Four models of ARIMA , ANN_ARIMA , ANN, and ANFIS as bolded

n Table 2 were selected and compared for their prediction accu-

acy performances. Three models of ANN-ARIMA, ANN, and ANFIS

hat utilize the same sort of predictors (MI, P M-2 , SWE EM , SWE t ,

t ) along with ARIMA model (four models) were selected and com-

ared for their prediction accuracy performances. Since the ARIMA

odel predicts only for one time step ahead, and just utilizes in-

ow data ( I t ), as shown in Table 2 , provides the predicted value

nly for I t+1 . For ARIMA model, the correlation coefficient between he predicted and observed daily values was 0.97.

Figs. 5 –8 illustrate the predicted values versus the observed val-

es. As shown in Table 3 , ANFIS is significantly more accurate than

he other three models in estimating the streamflow to Elephant

utte Reservoir. After ANFIS, the ARIMA model accurately predicts

ne day ahead compared to ANN and ANN-ARIMA. To extend the

rediction period to more than one day ahead, the one-day-ahead

redicted value should be used as another observed value. Tables

and 3 represent the prediction accuracy performances for the se-

ected four models. In order to accuracy performance comparison,

oth correlation coefficient and MSE (Mean of Squared Error) val-

es are considered, Therefore, Table 2 represents the correlation

oefficient and Tables 3 for the selected models (for the selected

odels, the correlation coefficient have been highlighted as bold

alues), the related MSE values have been represented. Although,

he daily prediction model (the ANN model as shown in Table

, fourth row of the numerical results) that predicts for 15 days

head has slightly higher correlation coefficient value compared to

he selected ANN model (the ANN model as shown in Table 2 , fifth

ow of the numerical results), it was not selected as an optimal

odel due to its high MSE values for the predicted streamflow val-

es. In addition, the selected models of ANN-ARIMA, ANN, and AN-

IS predict for the 7 days ahead, and only ARIMA model predicts

nly one day ahead on daily streamflow prediction models. For the

RIMA model, the correlation coefficient between predicted and

bserved daily values was 0.97, indicating that the daily ARIMA

rediction model was significantly accurate just only for one day

head. Since this produces a higher error value for extended pre-

ictions, ARIMA is not considered an appropriate model to predict

or more than one day ahead. The values predicted by the most ap-

ropriate prediction model would be incorporated in the mass bal-

154 H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163

Fig. 5. Output values (predicted) versus Target values (observed) using ANFIS. 25% of the data from 1961 to 2015 was used as a test data set.

0

5000

10000

15000

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Ta rg

et s a

nd O

ut pu

ts Targets Outputs

-4000

-2000

0

2000

4000

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Er ro

r

MSE=77628.1, RMSE=278.618

, A cr

e- fe

et

, A cr

e- fe

et

Number of u�lized daily data

Number of u�lized daily data

Fig. 6. Output values (predicted) versus target values (observed) using ANN. 25% of the data from 1961 to 2015 was used as a test data set.

a

o

a

s

w

i

s

t

a

p

a

t

l

ance (volume balance) law to investigate the two integrated reser-

voirs’ operation optimization. In addition, because of the differ-

ent physical characteristics of the two reservoirs, the evaporation

rates in different times of the year are different at each reservoir,

and these differences are considered to calculate the evaporation

loss from each reservoir. The observed timely evaporation rates are

shown in Fig. 9 . The average annual evaporation rates from Ele-

phant Butte and Caballo reservoirs are 112.8 inch/year and 107.6

inch/year respectively.

Considering the numerical results in Table 4 , in order to

demonstrate the application of the most appropriate prediction

model, ANFIS was successfully used to predict the streamflow for a

specific period. Since the Elephant Butte Reservoir is connected to

the existing aquifer, there is interaction between the groundwater

nd surface water in this reservoir. When the surface water level

n the reservoir rises, it charges the groundwater (existing aquifer),

nd when surface water levels falls, the groundwater charges the

urface water level. The historical recorded data on both surface

ater level and groundwater level in the Elephant Butte Reservoir

ndicates that the interactions between these two water levels are

ignificantly non-linear. As a result, it is recommended to consider

he daily existing water level on the Elephant Butte Reservoir as

reliable parameter in finding the optimal operation plan (release

lan) from this reservoir.

Because of the existing interaction between the groundwater

nd surface water in Elephant Butte Reservoir, mass balance equa-

ion cannot be used deterministically to find the water levels for a

ong period ahead. In more details, it is not deterministic that for a

H . Z

a m

a n

i Sa

b zi et

a l. / E

xp ert

Sy stem

s W

ith A

p p

lica tio

n s 8

3 (2

0 17

) 14

5 –

16 3

1 5

5

Table 4

Incorporating the daily streamflow values predicted by four prediction models in estimating the surface increments in both Elephant Butte (EB) and Caballo (Ca) reservoirs per acre-feet.

Date Actual Stream-flow Pred. Streamflow Pred. Stream-flow Pred. Stream-flow Pred. Stream-flow Storage level at Release from EB, Storage level at Release from Ca, dS/dV at EB, dS/dV at Ca,

to EB, acre-ft (acre-ft)/day, ARIMA (acre-ft)/day, Hybrid (acre-ft)/day, ANN (acre-ft)/day, ANFIS EB, (acre-ft) (acre-ft) Ca, (acre-ft) (acre-ft) ac/(acre-ft) ac/(acre-ft)

6/1/2015 2235.40 2637.46 1631.86 2001.03 2192.16 342,023 3828.10 42,629 5373.22 0.0157 0.0629

6/2/2015 1763.33 2193.99 1377.32 1562.66 1744.24 345,365 3828.10 40,999 5032.07 0.0157 0.0629

6/3/2015 1610.58 1739.87 1387.54 1423.33 1591.83 348,407 3788.43 39,611 4952.73 0.0157 0.0545

6/4/2015 1560.96 1647.28 1404.90 1378.38 1542.30 351,357 3768.60 38,191 4911.07 0.0157 0.0545

6/5/2015 1509.40 1595.05 1352.02 1331.78 1491.04 353,578 3768.60 36,997 4748.43 0.0157 0.0577

6/6/2015 1281.28 1515.01 1116.91 1127.60 1271.48 355,699 3768.60 36,080 4540.17 0.0157 0.0577

6/7/2015 1271.42 1247.55 1058.73 1118.79 1262.29 357,720 3788.43 35,179 4464.79 0.0157 0.0577

6/8/2015 1390.39 1288.19 1089.36 1224.85 1374.66 359,747 3788.43 34,203 4839.67 0.0157 0.0577

6/9/2015 1261.53 1439.96 944.59 1110.00 1253.13 361,672 3788.43 33,011 5137.19 0.0157 0.0612

6/10/2015 1267.43 1256.74 933.83 1115.27 1258.62 363,066 3808.26 31,850 5008.26 0.0157 0.0612

6/11/2015 1237.70 1304.93 904.18 1088.91 1231.29 364,355 3828.10 30,859 4863.47 0.0157 0.0612

6/12/2015 1192.11 1262.23 870.78 1048.59 1189.93 365,108 3828.10 29,892 4762.31 0.0157 0.0652

6/13/2015 1715.70 1207.07 1285.40 1519.09 1696.91 365,431 3828.10 28,895 4724.63 0.0157 0.0652

6/14/2015 3945.10 1852.06 3651.48 3657.50 3862.80 366,724 3808.26 27,973 4700.83 0.0157 0.0652

6/15/2015 4821.77 4517.17 4277.03 4527.70 4575.30 367,587 3728.93 27,299 4502.48 0.0179 0.0697

6/16/2015 4242.57 4818.95 3309.39 3952.12 4127.49 368,452 3689.26 26,633 4462.81 0.0179 0.0697

6/17/2015 3193.38 3923.91 2154.55 2919.28 3097.77 369,317 3709.09 25,977 4556.03 0.0179 0.0697

6/18/2015 3159.68 2896.78 2332.50 2886.45 3060.92 371,051 3709.09 25,405 4536.20 0.0179 0.0697

6/19/2015 3058.53 3103.60 2262.55 2788.16 2954.43 374,095 3709.09 24,595 4625.45 0.0179 0.0521

6/20/2015 2959.25 3065.42 2179.02 2692.08 2855.70 376,718 3728.93 23,944 4686.94 0.0179 0.0521

6/21/2015 2834.39 3024.20 2106.18 2571.45 2736.91 379,574 3728.93 23,208 4655.21 0.0179 0.0521

6/22/2015 3151.70 2840.57 2693.39 2878.73 3052.34 382,001 3728.93 22,555 4637.36 0.0179 0.0521

6/23/2015 3322.25 3168.16 2925.95 3045.05 3242.42 384,661 3728.93 21,618 4730.58 0.0179 0.0550

6/24/2015 3254.93 3209.88 2743.98 2979.21 3166.31 386,775 3709.09 20,791 4790.08 0.0179 0.0550

6/25/2015 2423.79 3122.77 1746.71 2178.93 2362.81 389,345 3689.26 20,091 4677.02 0.0179 0.0582

6/26/2015 1644.30 2199.28 1159.77 1453.98 1625.56 391,701 3709.09 19,511 4595.70 0.0179 0.0582

6/27/2015 1301.12 1491.38 997.20 1145.23 1289.95 393,841 3669.42 18,774 4651.24 0.0179 0.0582

6/28/2015 1053.20 1268.24 860.28 926.72 1067.16 395,876 3649.59 18,115 4669.09 0.0179 0.0582

6/29/2015 954.01 1064.73 813.76 840.46 980.27 397,463 3649.59 17,609 4526.28 0.0179 0.0618

6/30/2015 1297.22 1005.13 1099.24 1141.70 1286.25 399,054 3649.59 17,310 4270.41 0.0179 0.0618

156 H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163

0

5000

10000

15000

0 1000 2000 3000 4000 5000

Ta rg

et s a

nd O

ut pu

ts Targets Outputs

-4000

-2000

0

2000

4000

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Er ro

r

MSE=110775.3, RMSE=332.829 Number of u�lized daily data

Number of u�lized daily data

, A cr

e- fe

et

, A cr

e- fe

et

Fig. 7. Output values (predicted) versus Target values (observed) using Hybrid model of ANN-ARIMA. 25% of data from 1961 to 2015 were used as test data set.

0

5000

10000

15000

0 1000 2000 3000 4000 5000

Ta rg

et s a

nd O

ut pu

ts

Targets Outputs

-4000

-2000

0

2000

4000

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Er ro

r

MSE=76437.329, RMSE=276.473

Number of u�lized daily data

Number of u�lized daily data

, A cr

e- fe

et

, A cr

e- fe

et

Fig. 8. Output values (predicted) versus target values (observed) using ARIMA. 25% of the data from 1961 to 2015 was used as a test data set.

a

b

v

d

f

F

v

O

l

s

long prediction period how much reservoir can discharge water to

the groundwater or being recharged from the groundwater. There-

fore, it would be a rational decision to plan for a short prediction

period (for example, only one day ahead). As a result, for each in-

dividual one day ahead, daily observed storage levels is considered

for the mass balance calculation; then, considering the observed

storage levels on both reservoirs and bathymetry data as shown

in Figs. 9 and 11 , the evaporation loss rates from both reservoirs

can led us to select the optimal storage levels, which simultane-

ously minimize the evaporation loss and maximize the release reli-

bility to meet the agricultural water demands downstream of Ca-

allo Reservoir. Fig. 10 illustrates the surface area versus storage

olumes in both Elephant Butte and Caballo reservoirs. Table 4 in-

icates the integration of the predicted streamflow values through

our developed prediction models through this study including AN-

IS, ANN, ARIMA, and Hybrid model of ANN-ARIMA. The predicted

alues were successfully utilized in the mass balance calculation.

f course, some error are observed through mass balance calcu-

ation because of existing interaction between the surface water

torage and groundwater level behind the Elephant Butte Reser-

H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163 157

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

1 2 3 4 5 6 7 8 9 10 11 12

A ve

ra ge

E va

po ra

tio n,

in ch

/m on

th

Month

Average eveporation from Elephant Butte Reservoir, inch/month

Average eveporation from Caballo Reservoir, inch/month

Fig. 9. Monthly average evaporation from Elephant Butte and Caballo reservoirs.

0

5000

10000

15000

20000

25000

30000

35000

0 500000 1000000 1500000 2000000

Su rf

ac e

ar ea

, a cr

es (a

c)

Storage volume, ac-ft

Elephant Bu�e Reservoir Caballo Reservoir

Fig. 10. Surface area versus storage volumes in both Elephant Butte and Caballo reservoirs.

0

0.2

0.4

0.6

0.8

1

1.2

0 250000 500000 750000 1000000 1250000 1500000 1750000 2000000

D ai

ly e

va po

ra tio

n vo

lu m

e in

cr em

en t,

ac -ft

Storage Volume, ac-ft

Caballo Elephant Butte

Fig. 11. Evaporation volume from Elephant Butte and Caballo reservoirs considering different surface area increments in different storage volumes of the reservoirs.

v

a

a

r

b

R

b

v

t

s

d

i

u

m

s

v

s

fl

a

m

i

p

oir. Last two columns in Table 4 shows the surface increment per

cre-feet estimated through bathymetry data of stage-surface area

nd stage-storage relationships for both Elephant Butte and Caballo

eservoirs.

In Table 4 , column 7, considering the existing interaction

etween the surface and groundwater in the Elephant Butte

eservoir, utilizing the observed storage volumes obtained from

athymetry data (storage levels-volumes relationships) would pro-

ide accurate data compared to the storage volumes obtained

hrough the mass balance. Therefore, both mass balance and ob-

erved storage levels would be considered, however, utilizing the

aily observed storage volume would be significantly reliable. But,

n planning for more than one day ahead, the predicted values are

tilized.

Fig. 12 shows the numerical results of sensitivity about the

ean. In order to analyze the importance degrees of variables, the

ensitivity about the mean was determined. Additionally, the de-

eloped pre-trained network was batch tested for another type of

ensitivity analysis for the predictors on the average monthly in-

ow; the first input variable was changed by ± one standard devi- tion, while the rest of the variables were fixed by their respective

eans. Then, the output of the network was computed for lim-

ted steps (usually 50 steps) above and below the mean. The same

rocess was done for the rest of the variables. Sensitivity analy-

158 H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163

0

10000

20000

30000

40000

50000

60000

N or

m al

iz ed

s en

sit iv

ity a

bo ut

th e

m ea

n of

o ut

pu ts

(p re

di ct

ed v

al ue

s)

Input variavles (predictors)

Fig. 12. Sensitivity analysis of effective parameters on monthly inflow prediction (April to September).

Fig. 13. Output values (simulated) versus target values (observed) using ANFIS. The data set from 1961 to 2015 was used to tune the model based on the 10 most effective

selected predictors.

o

p

I

i

p

t

p

d

o

p

t

4

m

m

b

d

sis results, as shown in Fig. 12 , represent the variation of output

values against variation of each individual input variable. Finally,

in order to rank the impacts of the input variables on the outputs

(predicted values), relative importance indices were developed by

normalizing the sensitivity of the variables ( Cheung, Fung, & Cof-

fey, 2006; Cheung, Tam, & Harris, 2012 ).

4.2. Accuracy performance analysis on developed monthly streamflow

prediction models

Figs. 13 and 15 illustrate simulated monthly streamflows ver-

sus target values (observed) using ANFIS by utilizing Eqs. (12) and

(13) . Eqs. (12) and (13) , which utilized the data set from 1961

to 2015, were used to tune the model based on the 10 and

6 most effective selected predictors, respectively. Figs. 14 and

16 graphically represent the monthly simulated streamflows ver-

sus the observed monthly historical streamflows, and the mod-

els were developed based on the 10 and 6 most effective se-

lected predictors, respectively. Comparing the 6 most effective

parameters, P m −1 is the least sensitive variable. Although based

n importance degree analysis, P m −1 has significantly lower im- ortance degree compared to the other utilized predictors of

m −1 , SW E Em , SW E m , P m −2 , S i , M i , P 5 Y i , P 2 Y i , and P Y i , but including t in the model improves a little bit the prediction accuracy com-

ared to the model that we did not utilize P m −1 . The significance of he selected predictors was statistically analyzed, and all included

redictors are statistically significant and effective, but they have

ifferent degrees of importance ( Zamani Sabzi et al., 2017a ).

As illustrated in Figs. 13–16 , utilizing time-dependent indices

f PY i , P 2 Y i , and P 5 Y i obtained through historical data clustering im-

roved the prediction accuracy (lower RMSE) and coefficient of de-

ermination ( R 2 ).

.3. Numerical analysis on saved water volume due to considering

ore efficient management based on the daily streamflow prediction

odels

The release from Elephant Butte Reservoir inflows to the Ca-

allo Reservoir, and release from Caballo Reservoir goes to the

ownstream agricultural lands. Since these two reservoirs have dif-

H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163 159

y = 0.8161x + 11404 R² = 0.8219

0

50000

100000

150000

200000

250000

300000

350000

400000

0 50000 100000 150000 200000 250000 300000 350000 400000

Pr ed

ic te

d M

on th

ly S

tr ea

m flo

w , a

c- �

Monthly Streamflow, ac-� Fig. 14. Monthly simulated streamflows versus observed monthly historical streamflow, model developed based on the 10 most effective selected predictors.

Fig. 15. Output values (simulated) versus target values (observed) using ANFIS. The data set from 1961 to 2015 was used to tune the model based on the 6 most effective

selected predictors.

1 6

0

H . Z

a m

a n

i Sa

b zi et

a l. / E

xp ert

Sy stem

s W

ith A

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5 –

16 3

Table 5

The operation policies for both Elephant Butte (EB) and Caballo (Ca) reservoirs considering the daily predicted inflows.

Date Pred.

Streamflow

(acre-ft)/day,

ARIMA

Pred.

Stream-flow

(acre-ft)/day,

Hybrid

Pred.

Stream-flow

(acre-ft)/day,

ANN

Pred.

Stream-flow

(acre-ft)/day,

ANFIS

Storage

Volume at

EB, (acre-ft)

Storage

Volume at

Ca, (acre-ft)

dS/dV at EB,

ac/(acre-ft)

dS/dV at Ca,

ac/(acre-ft)

Correct

Choice for

Storing

Saved

Volume

Actual

stream flow

(acre-ft)

Saved

Volume

ARIMA

stream flow

(acre-ft)

Saved

Volume

Hybrid

stream flow

(acre-ft)

Saved

Volume ANN

stream flow

(acre-ft)

Saved

Volume

ANFIS stream

flow (acre-ft)

6/1/2015 2637.46 1631.86 2001.03 2192.16 342,023 42,629 0.0157 0.0629 EB 97.7 115.3 71.3 87.5 95.8

6/2/2015 2193.99 1377.32 1562.66 1744.24 345,365 40,999 0.0157 0.0629 EB 77.1 95.9 60.2 68.3 76.2

6/3/2015 1739.87 1387.54 1423.33 1591.83 348,407 39,611 0.0157 0.0545 EB 57.9 62.5 49.9 51.1 57.2

6/4/2015 1647.28 1404.90 1378.38 1542.30 351,357 38,191 0.0157 0.0545 EB 56.1 59.2 50.5 49.5 55.4

6/5/2015 1595.05 1352.02 1331.78 1491.04 353,578 36,997 0.0157 0.0577 EB 58.7 62.0 52.6 51.8 58.0

6/6/2015 1515.01 1116.91 1127.60 1271.48 355,699 36,080 0.0157 0.0577 EB 49.8 58.9 43.4 43.9 49.5

6/7/2015 1247.55 1058.73 1118.79 1262.29 357,720 35,179 0.0157 0.0577 EB 49.4 48.5 41.2 43.5 49.1

6/8/2015 1288.19 1089.36 1224.85 1374.66 359,747 34,203 0.0157 0.0577 EB 54.1 50.1 42.4 47.6 53.5

6/9/2015 1439.96 944.59 1110.00 1253.13 361,672 33,011 0.0157 0.0612 EB 53.2 60.7 39.8 46.8 52.8

6/10/2015 1256.74 933.83 1115.27 1258.62 363,066 31,850 0.0157 0.0612 EB 53.4 52.9 39.3 47.0 53.0

6/11/2015 1304.93 904.18 1088.91 1231.29 364,355 30,859 0.0157 0.0612 EB 52.1 55.0 38.1 45.9 51.9

6/12/2015 1262.23 870.78 1048.59 1189.93 365,108 29,892 0.0157 0.0652 EB 54.6 57.9 39.9 48.1 54.5

6/13/2015 1207.07 1285.40 1519.09 1696.91 365,431 28,895 0.0157 0.0652 EB 78.6 55.3 58.9 69.6 77.8

6/14/2015 1852.06 3651.48 3657.50 3862.80 366,724 27,973 0.0157 0.0652 EB 180.8 84.9 167.4 167.6 177.1

6/15/2015 4517.17 4277.03 4527.70 4575.30 367,587 27,299 0.0179 0.0697 EB 231.3 216.7 205.2 217.2 219.5

6/16/2015 4818.95 3309.39 3952.12 4127.49 368,452 26,633 0.0179 0.0697 EB 203.5 231.1 158.7 189.6 198.0

6/17/2015 3923.91 2154.55 2919.28 3097.77 369,317 25,977 0.0179 0.0697 EB 153.2 188.2 103.3 140.0 148.6

6/18/2015 2896.78 2332.50 2886.45 3060.92 371,051 25,405 0.0179 0.0697 EB 151.6 138.9 111.9 138.5 146.8

6/19/2015 3103.60 2262.55 2788.16 2954.43 374,095 24,595 0.0179 0.0521 EB 96.9 98.3 71.7 88.3 93.6

6/20/2015 3065.42 2179.02 2692.08 2855.70 376,718 23,944 0.0179 0.0521 EB 93.7 97.1 69.0 85.3 90.4

6/21/2015 3024.20 2106.18 2571.45 2736.91 379,574 23,208 0.0179 0.0521 EB 89.8 95.8 66.7 81.4 86.7

6/22/2015 2840.57 2693.39 2878.73 3052.34 382,001 22,555 0.0179 0.0521 EB 99.8 90.0 85.3 91.2 96.7

6/23/2015 3168.16 2925.95 3045.05 3242.42 384,661 21,618 0.0179 0.0550 EB 114.1 108.8 100.5 104.6 111.4

6/24/2015 3209.88 2743.98 2979.21 3166.31 386,775 20,791 0.0179 0.0550 EB 111.8 110.3 94.3 102.3 108.8

6/25/2015 3122.77 1746.71 2178.93 2362.81 389,345 20,091 0.0179 0.0582 EB 90.4 116.5 65.2 81.3 88.2

6/26/2015 2199.28 1159.77 1453.98 1625.56 391,701 19,511 0.0179 0.0582 EB 61.4 82.1 43.3 54.3 60.7

6/27/2015 1491.38 997.20 1145.23 1289.95 393,841 18,774 0.0179 0.0582 EB 48.6 55.7 37.2 42.7 48.1

6/28/2015 1268.24 860.28 926.72 1067.16 395,876 18,115 0.0179 0.0582 EB 39.3 47.3 32.1 34.6 39.8

6/29/2015 1064.73 813.76 840.46 980.27 397,463 17,609 0.0179 0.0618 EB 38.8 43.3 33.1 34.2 39.8

6/30/2015 1005.13 1099.24 1141.70 1286.25 399,054 17,310 0.0179 0.0618 EB 52.7 40.9 44.7 46.4 52.3

The bold values were used to emphasize on the selected reservoir and the saved water through considering different forecast models.

H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163 161

y = 0.8068x + 11904 R² = 0.8061

0

50000

100000

150000

200000

250000

300000

350000

400000

0 50000 100000 150000 200000 250000 300000 350000 400000

Pr ed

ic te

d M

on th

ly S

tr ea

m flo

w , a

c- �

Monthly Streamflow, ac-� Fig. 16. Monthly simulated streamflows versus observed monthly historical streamflow, model developed based on the 6 most effective selected predictors.

Table 6

Total saved volume based on correct choice of reservoir for storing through the same prediction period of the June 2015 (the same prediction period through Table 5 ).

Date Saved volume considering Saved volume, Saved volume hybrid Saved volume, Saved volume,

the actual streamflow ARIMA streamflow streamflow ANN streamflow ANFIS s

(acre-ft) (acre-ft) (acre-ft) (acre-ft) treamflow (acre-ft)

Total saved volume, acre-ft 2650.4 2680.0 2117.0 2400.0 2591.0

Total saved volume, m 3 3,269,188 3,305,751 2,611,216 2,960,334 3,195,956

The bold values were used to emphasize on the selected reservoir and the saved water through considering different forecast models.

f

t

t

E

u

R

o

d

l

e

c

n

a

r

u

c

i

t

c

t

i 5)

t

e

p

o

i

t

m

5

fl

erent evaporation losses for different storage levels, the baseline is

o select the reservoir that would have lower amount of evapora-

ion loss. In other words, considering the existing storage levels, if

lephant Butte has lower evaporation loss for storing specific vol-

me, in time of demand, the required demand from Elephant Butte

eservoir would be released to the Caballo Reservoir and with-

ut keeping in Caballo Reservoir, simultaneously be release to the

ownstream; In other words, the baseline is adjusting the storage

evels on both reservoir to save more amount of water due to the

vaporation loss and provide required water to downstream agri-

ultural lands.

As shown in Fig. 9 , evaporation rates in these two reservoirs are

ot equal and vary thorough the year, different evaporation rates

re considered in determining the total loss from each individual

eservoir. Total evaporation loss for storing specific amount of vol-

me in each individual reservoir of Elephant Butte and Caballo is

alculated through Eq. (14) as follows:

( Total added surf ace area for spec ific amou nt of volu me in each

indi vidu al rese rvoir ) ∗ Evap orat ion rate each indi vidu al rese rvoir n the cons ider ed time peri od = Total Evap orat ion Loss in that ime peri od

(14)

Therefore, the total saved evaporation loss because of correct

hoice of reservoir to store specific amount of volume is calculated

hrough Eq. (15) as follows:

( Differen ce of total added surf ace area for spec ific amou nt of

volu me in each indi vidu al rese rvoir ) ∗ Evap orat ion rate each ndi vidu al rese rvoir in the cons ider ed time peri od = Total sava ble water from mini mizi ng evap orat ion loss in that time peri od

(1

Table 5 indicates the saved amount of water volume obtained

hrough correct taken decision on choosing the reservoir with less

vaporation loss. Total saved volume of evaporation loss for the

rovided example in Table 5 through month of June is the sum

f daily saved evaporation loss in month of June, which is a signif-

cant amount of 2680 acre-ft (3,305,750.52 m 3 ).

The numerical results in Table 6 represents the total saved wa-

er volume through utilizing the different streamflow prediction

odels

. Conclusion

Our findings through comparison of four categories of stream-

ow forecast models revealed the importance of appropriate se-

162 H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163

w

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o

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A

t

t

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t

a

m

t

o

s

w

v

t

d

a

d

g

t

u

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5

t

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T

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t

(

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o

lecting the effective predictors on the prediction accuracy per-

formances. Although, similar to most of the previous studies in

comparing the ANNs and ANFIS based streamflow forecast mod-

els, in our case study, ANFIS performed better than ANNs and hy-

brid models of ANNs-ARIMA, still the superiority of the ANFIS to

other forecast models is not a universal conclusion, but its supe-

riority can be considered as an expectation. Therefore, in most of

the river or reservoir management that optimal operation relies on

the accuracy of the streamflow prediction, different forecast mod-

els should be examined to get the most accurate model.

In our case study, prediction accuracy performances for daily

streamflow prediction models showed that utilizing ANFIS led

to a superior prediction performance compared to the other

three selected prediction models. In addition, extracting and uti-

lizing the climate variability indices (time-dependent indices of

PY i , P 2 Y i , and P 5 Y i ) through utilizing ANFIS led us to a superior pre-

diction performance for monthly streamflow prediction. For daily

streamflow prediction, utilizing time dependent trend indices did

not change the prediction accuracy as significantly as monthly pre-

diction. Rationally it is expected that the effect of a historical ex-

isting trend would be more sensible on the longer prediction pe-

riod. Therefore, for prediction cases that computational procedure

to extract the time dependent trend indices are costly and timely

significant, the prediction model can be developed only based on

other physical effective predictors. Accuracy performance indicated

that, for this case study, the use of more information through hy-

brid models did not improve the prediction performance.

Although the ARIMA based univariate streamflow prediction

models are significantly simple to use, but most of the univari-

ate forecast models utilize only previous observed values for pre-

diction. As an example of a univariate ARIMA model, for predict-

ing four time steps ahead ( I t+4 ) , if effective lags are 1, 2, and 3, it means observing streamflow values for 1, 2, and 3 days ahead

( I t+1 , I t+2 , and I t+3 ) are required. Therefore, extending the predic- tion period for ARIMA would not be as reliable as ANFIS and ANNs.

The non-seasonal ARIMA and seasonal ARIMA (SARIMA) mod-

els are univariate and only utilize the observed past streamflow

values. Conceptually, the univariate models do not utilize the exist-

ing information from other prediction variables, such as snowpack

and precipitation data; therefore, the prediction accuracy of those

models rationally are considered less than the ANNs and ANFIS

based forecast models. As a results, ARIMA as non-seasonal uni-

variate model demonstrates an approach for a strongly-reliable in-

flow prediction when existing information is limited to streamflow

data as a predictor.

ANFIS as a powerful fuzzy logic based neural network by apply-

ing fuzzy inference approach between input and output datasets

provides significantly reliable forecast models. In this study, the

applicability of the ANFIS was investigated, and the comparison of

the prediction accuracy performances proved its significant relia-

bility compared to the other models of ANNs and hybrid models

of ANNs-ARIMA. Of course, this cannot be considered as a univer-

sal conclusion since in most of the forecast models designing the

structure of the prediction networks and selecting the most effec-

tive predictors are considered as other significantly important fac-

tors.

The data in Table 4 indicate that the streamflow values pre-

dicted by ANFIS and the other three prediction models were suc-

cessfully incorporated in the mass balance calculation along with

optimization process. This achievement will support the daily oper-

ation and short-term forecasting for the reservoirs and provide the

operation managers with clearer and more detailed hydrology. The

developed management model, as shown in Fig. 2 , and the predic-

tion model present a foundation for an analysis of water manager

values and an assessment of the interaction between conflicting

criteria, such as maximizing the reliability of the Caballo release

hile minimizing the net evaporation loss to the system by adjust-

ng the appropriate storage levels in both reservoirs. Optimal man-

gement of integrated reservoirs would save fresh water sources

nd bring significant hydrological and environmental impacts and

enefits.

The approach used through this study is extendable to similar

ater resource projects, enabling reservoir operators to save wa-

er as the major source for meeting agricultural demands, environ-

ental demands, and hydropower energy production.

Cumulatively, preprocessing monthly historical data through

lustering historical data and adding the time-dependent stream-

ow trend indices improved the prediction accuracy of the devel-

ped models. This suggests that prediction accuracy in both ANNs

nd ANFIS significantly depends on optimal structure design, intel-

igent selection of the predictors, and preprocessing of the selected

redictors.

Superior prediction performances were achieved by preprocess-

ng historical data through data mining techniques and the intel-

igent selection of the predictors based on their developed im-

ortance degrees, and the employment of several developed pre-

iction models including ANFIS, ANNs, hybrid model of ARIMA-

NN, and univariate time series model of ARIMA. Specifically, on

he monthly model, utilizing ANFIS along with the time dependent

rend indices significantly improved the prediction accuracy.

As such, the results of this study would serve to prediction

odel developers; those interested in applying time series and ar-

ificial intelligence based prediction models; and the profession-

ls interested in applying those intelligent models in real environ-

ents, particularly those involved in diverse engineering applica-

ions of intelligent prediction expert systems such as policy-makers

n water and energy resources.

The numerical example represented in Table 5 indicates the

uccessful application of the developed prediction models along

ith the developed dynamic operation model. The daily observed

alues were successfully incorporated in the estimation process of

he daily inflow values to the Elephant Butte Reservoir and in up-

ating the utilized parameters in Eqs. (14) and (15) as mass bal-

nce law in the dynamic model.

The developed management approach, along with accurate

aily predicted values, provided a sound basis for the optimal inte-

rated operation of Elephant Butte and Caballo Reservoirs and led

o minimum evaporation loss by selecting appropriate storage vol-

mes in both reservoirs, minimizing total surface area, and there-

ore minimizing the evaporation amount. As presented in Tables

and 6 , according to the optimal reservoir operation strategy, the

otal saved volume of evaporation loss for a single month (June)

onsidering different prediction methods are significant amounts.

he accuracy performances of the developed prediction models

hrough Table 3 and numerical results through Tables 5 and 6 rep-

esents that ANFIS and ARIMA provided more reliable with higher

ccuracy compared to the other models. In addition, utilizing this

wo models led us to save significant amounts of 2591 acre-ft

3,195,956 m 3 ) and 2680 acre-ft (3,305,750.52 m 3 ) respectively. The

aved amounts of water due to utilizing the developed prediction

odels in this study led us to save significant amount of fresh-

ater through the integrated optimal management these two Ele-

hant Butte and Caballo reservoirs, in which considering the fresh-

ater shortage in this region, is a significantly critical value.

Since the area of this study is a snowmelt dominated region,

he developed streamflow prediction models through this study

ould be more appropriate for specific regions that are considered

nowmelt dominated regions, and it would be less effective in the

ainfall dominated regions.

As a future direction of this study, in order to show the effect

f one-unit increment or decrement of each individual predictors

n the streamflow magnitude, multiple logistic regression models

H. Zamani Sabzi et al. / Expert Systems With Applications 83 (2017) 145–163 163

w

m

(

B

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fl

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r

i

b

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c

s

s

A

U

f

R

A

A

A

A

B

C

C

C

E

I

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J

K

M

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O

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Z

ould be developed. In addition, those multiple logistic regression

odels would be used to quantify and predict streamflow drought

in term of hydrologic drought) on the Rio Grande above Elephant

utte Reservoir, New Mexico. Those models would provide a basis

or quantifying how significant each individual predictor of stream-

ow value is for quantifying the probability of hydrologic (stream-

ow) drought one year ahead. This study comparatively investi-

ated the applicability of several forecast models on Rio Grande

nflow, and led to integrating those models in successful multiple

eservoirs’ optimal operation. Along with this study, a comparative

eview study on the accuracies and capabilities of numerous ex-

sting forecast models based on artificial intelligence or regression-

ased models would be done to introduce the applicability of those

odels, in which it would provide a basis for categorizing the fore-

ast models and recommend the best forecast model to select con-

idering the existing prediction conditions in regional and global

cales.

cknowledgment

The authors would like to thank the Reinventing the Nation’s

rban Water Infrastructure Engineering Research Center at Stan-

ord University for partially funding this research project.

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