Evaluation of Drought Severity with a Bayesian Network Analysis of Multiple Drought Indices

Kim, Soojun; Parhi, Pradipta; Jun, Hwandon; Lee, Jiho

doi:10.1061/(ASCE)WR.1943-5452.0000804

Open access

Case Studies

Nov 1, 2017

Evaluation of Drought Severity with a Bayesian Network Analysis of Multiple Drought Indices

Authors: Soojun Kim [email protected], Pradipta Parhi [email protected], Hwandon Jun [email protected], and Jiho Lee [email protected]Author Affiliations

Publication: Journal of Water Resources Planning and Management

Volume 144, Issue 1

https://doi.org/10.1061/(ASCE)WR.1943-5452.0000804

PDF

Abstract

Drought indices assimilate meteorological and/or hydrological information to come up with a comprehensible index. Over the last few decades, hundreds of drought indices have been developed in order to improve monitoring and impact assessment. For a particular drought event, these multiple indices sometimes indicate different levels of drought severity, creating confusion among stakeholders and posing challenges for decision making. To overcome the problem, this study suggests a novel methodology using a Bayesian network. There are several advantages of this proposed method: (1) it pools information from multiple drought indices and comes up with a better estimate for drought severity; (2) instead of a deterministic drought-severity outcome from the individual indices, it offers probabilistic estimates for drought severity; and (3) it reduces the uncertainty of the individual drought indices. The robustness of the methodology is further checked with a case study of an actual drought event in South Korea.

Introduction

A broad definition of drought is a deficiency of precipitation over an extended period of time, usually a season or more, which results in a water shortage for some activity, group, or environmental sectors. However, in terms of typologies, droughts are classified as meteorological, agricultural, hydrological, and socioeconomic. To analyze droughts, multiple methods and indices exist in the literature. These methods typically measure different factors and identify and classify a drought accordingly (Bhuiyan 2004). For example, representative drought indices include the Palmer drought-severity index (PDSI) (Palmer 1965), rainfall anomaly index (RAI) (van Rooy 1965), surface water supply index (SWSI) (Shafer and Dezman 1982), standardized precipitation index (SPI) (McKee et al. 1993, 1995), Deciles (Gibbs and Maher 1967), crop moisture index (CMI) (Palmer 1968), Bhalme and Mooley drought index (BMDI) (Bhalme and Mooley 1980), effective drought index (EDI) (Byun and Wilhite 1999), standardized runoff index (SRI) (Shukla and Wood 2008), soil-moisture deficit index (SMDI) (Narasimhan and Srinivasan 2005), and reconnaissance drought index (RDI) (Tsakiris et al. 2007).

Among existing drought indices, SPI is likely the simplest drought index because it can be compared across different climatic regions. It is designed to be a spatially invariant quantity that can be computed to give precipitation excesses and deficits at multiple timescales (Guttman 1999). It gives a better representation of the abnormal wetness and dryness than the PDSI. Furthermore, SPI can provide an early warning of a drought with a longer lead-time compared with other indices (Zargar et al. 2011). Thus, SPI is a well-accepted index by the water management community (Khedun et al. 2011) in various parts of the world (e.g., Guttman 1999; Keyantash and Dracup 2002; Ntale and Gan 2003; Vicente-Serrano et al. 2004; Patel et al. 2007; Pandey et al. 2008; Mishra and Singh 2009; Edossa et al. 2010; Roudier and Mahe 2010; Stricevic et al. 2011; Zhai et al. 2010; Kim et al. 2011). A natural extension of SPI is the SRI, which has more appeal than SPI because it incorporates hydrological and meteorological processes that influence the volume and timing of streamflow (Shukla and Wood 2008).

Droughts are typically categorized into four major classes: meteorological, hydrological, agricultural, and socioeconomic (Anderson et al. 2011; Wilhite and Glantz 1985). They cater to different objectives using different hydrometeorological data. Sometimes, the results of assessed drought are totally different in an area. For example, in an area that has a good irrigation system, agricultural drought might not be of serious concern, even though meteorological drought is severe. When multiple stakeholders are involved in a decision-making process (e.g., water allocation), such differences in drought-severity assessment can create confusion, making it difficult to manage droughts effectively. A methodology for estimating drought severity by combining multiple drought indices is needed to reconcile the outcomes of different drought indices and foster better understanding among different stakeholders (Kallis 2008; Niemeyer 2008; Sivakumar et al. 2011).

This study introduces a novel methodology that estimates a drought severity from three drought indices using a Bayesian network. The three drought indices, namely SPI, SRI, and standardized storage volume index (SSVI) (Gusyev et al. 2015), were selected because despite using different types of hydrological variables—precipitation, discharge, and storage volume, respectively—they use a similar methodology to estimate drought severity. A Bayesian network is a potential method to integrate these indices and determine the value of information from each information source. An actual drought deficit measure was used as a benchmark to compare and assess the skill of the proposed Bayesian-network-based method. The actual drought severity in a basin was estimated by rainfall-runoff modeling and water-balance analysis.

The rest of this paper is organized as follows. The “Materials and Methodology” section presents the basic theory and application methodology. The “Application and Results” section describes the observed data from the study basin and applies the proposed method to estimate the correlations between the multiple drought indices and the composite drought severity as estimated by the Bayesian network. Finally, in the “Summary and Conclusions” section, the findings in this study are summarized, and conclusions offered.

Materials and Methodology

This study collects precipitation, discharge, and storage volume in a basin and estimates the drought indices from the different data sources. The actual drought severity is estimated with a water-balance model considering water supply, water demand, and water transfer in the subbasins. The water supply is estimated from the discharge by a rainfall-runoff model that uses weather data series, digital elevation model (DEM), land-use map, and soil-type map of the basin. The demand and transfer of water are estimated based on data from the Water Management Information System (WAMIS 2015). A Bayesian network (BN) is used to integrate the multiple drought indices and suggest a composite drought severity (CDS). Finally, its applicability in case of a real drought event in a basin is assessed (Fig. 1).

Fig. 1. Schematic drawing of the analysis procedures in this study

Drought Indices

McKee et al. (1993) developed the SPI for the purpose of defining and monitoring a drought event. SPI is computed as follows (Guttman 1999; Mishra and Desai 2005). First, a probability density function that describes the long-term time series of precipitation is determined. The base time of rainfall observation series can be any, depending on the timescale of interest. In the present study, running series of total precipitation corresponding to 1, 3, 6, 9, 12, and 24 months were used. Once the probability density function is determined, the cumulative probability of an observed precipitation amount is computed. The inverse normal function, with mean as 0 and variance as 1, is then applied to the cumulative probability distribution function, which results in SPI. In the present study, all the different accumulated monthly rainfall series followed a gamma distribution based on the Kolgomorov-Smirnov (K-S) and chi-square test statistics as follows:

g (x; α, β) = \frac{β^{α} x^{α - 1} e^{- x β}}{Γ (α)} for x \geq 0 and α, β > 0

(1)

where

α

= shape parameter;

β

= scale parameter; and

Γ (α)

= gamma function.

The use of different timescales allows an assessment of the effects of a precipitation deficit on different water-resource components (e.g., groundwater, reservoir storage, soil moisture, and streamflow). The SPI can be used for monitoring both dry and wet conditions because a positive (negative) SPI value indicates greater (less) than mean precipitation (Table 1). The procedures for computing SRI and SSVI are the same as used for SPI in this study.

Table 1. SPI, SRI, and SSVI Ranges

Range	SPI, SRI, and SSVI values
[2.0, $+ \infty$ ]	Extremely wet
[1.5, 2.0)	Very wet
[1.0, 1.5)	Moderately wet
( $- 1.0$ , 1.0)	Normal
( $- 1.5$ , $- 1.0$ ]	Moderately dry
( $- 2.0$ , $- 1.5$ ]	Severely dry
[ $- \infty$ , $- 2.0$ ]	Extremely dry

Bayesian Networks

Bayes’ theorem provides a formula for updating the prior belief about a hypothesis

H

in the light of observing the evidence

E

and can be expressed

p (H | E) = \frac{p (E | H) p (H)}{p (E)}

(2)

where

p (H)

= prior probability distribution;

p (H | E)

= posterior probability distribution;

p (E | H)

= likelihood function; and

p (E)

= normalizing or scaling factor.

The BN is a probabilistic graphical model that can represent relationships between variables even if the relationships involve uncertainty. The BN consists of a directed acyclic graph of nodes and links and can integrate different types of variables from various sources into a single framework (Jensen 1996; Pearl 2014). The relationships among nodes are described by conditional probability distributions that capture the dependences between variables.

A formal definition of a BN is given by Eq. (3). In a BN,

B

is an annotated acyclic graph that represents a joint probability distribution over a set of random variable. The network is defined by a pair

B = < G, Θ >

, where

G

is the directed acyclic graph whose nodes

X_{1}, X_{2}, \dots, X_{N}

represent random variables, and whose edges represent the direct dependencies between these variables. The graph

G

encodes independence assumptions by which each variable

X_{i}

is independent of its nondescendents given its parents in

G

. The second component,

Θ

, denotes the set of parameters of the network. This set contains the parameter

θ_{x_{i} | π_{i}} = P_{B} (x_{i} | π_{i})

for each realization

x_{i}

of

X_{i}

conditioned on

π_{i}

, the set of parents of

X_{i}

in

G

. Accordingly,

P_{B}

is defined in Eq. (3)

P_{B} (X_{1}, X_{2}, \dots, X_{n}) = \prod_{i = 1}^{n} P_{B} (X_{i} | π_{i}) = \prod_{i = 1}^{n} (θ_{X_{i} | π_{i}})

(3)

For simplicity of representation, the subscript

B

is omitted henceforth. If

X_{i}

has no parents, its local probability distribution is said to be unconditional; otherwise, it is conditional. If the variable represented by a node is observed, then the node is said to be an evidence node; otherwise, the node is said to be hidden or latent (Ben-Gal 2007; Pearl 2014).

Application and Results

Study Basin and Materials

The present study was conducted on the Chungju Dam. It is one of the two largest multipurpose dams tasked with water-use and flood-control functions in the Korean peninsula. The Chungju Dam is located in the upper region of the Han River basin. The length and height of the dam are 464 and 97.5 m, respectively. It is equipped with a water-storage capacity of approximately

2.75 \times 10^{9} m^{3}

to

supply \times 10^{9} m^{3}

of water per year for various usages, and has a storage volume of

616 \times 10^{6} m^{3}

for flood control. The basin area of the Chungju Dam is approximately

6,648 {km}^{2}

, and the length of the feeding upstream river is approximately 280 km. The average, maximum, minimum, and standard deviation of the altitude of the basin calculated using

50 \times 50 m

grids are 610, 1,560, 105, and 261 m, respectively. The daily gauging time-series data from one runoff, one storage volume, and three weather stations were collected for 1986–2014 (Fig. 2 and Table 2).

Table 2. Hydrologic Gauging Stations in Chungju Dam Basin

Station	Name	Latitude (°N)	Longitude (°E)	Elevation (m)	Period (years)
Weather	Daegoanryung	37.68	128.82	772.4	1986–2014
	Jecheon	37.16	128.19	263.1	1986–2014
	Chungju	36.97	127.95	113.7	1986–2014
Runoff	Chungju	36.99	127.93	141.0	1986–2014
Storage volume	Chungju	36.99	127.93	141.0	1986–2014

Drought Indices

The SPI, SRI, and SSVI in the Chungju Dam basin were estimated for 1, 3, 6, and 12 months of total precipitation, runoff, and storage volume, respectively. The drought indices for the years 1987–2014 are shown in Fig. 3. The three indices show similar patterns, especially for the 12-month total. However, the specific years in which a moderate or higher-severity drought occurs vary across the indices [e.g., SPI in Fig. 3(a) suggests 1988–1989, 1992–1993, 1995, 1997, 2001–2002, and 2014, SRI in Fig. 3(b) suggests 1994–1995, 1996–1997, 2001–2002, 2009, and 2014, and SSVI in Fig. 3(c) suggests 1996–1997 and 2001–2002 as drought years]. For example, for the 12-month total in 1992, the SPI value of

- 1.8

suggests a severely dry type, whereas the SRI value of

- 1.1

shows a moderately dry type and the SSVI value of 0.1 shows a near-normal type drought. Furthermore, the variability decreases in the cases of SRI and SSVI compared with that in the case of SPI. The lack of clear agreement on the drought-severity classification by multiple indices creates confusion and makes it harder to manage drought risk.

Fig. 3. Monthly time series of the estimated drought indices: (a) SPI; (b) SRI; (c) SSVI

Estimation of Actual Drought

Hydrological Modeling

The soil and water assessment tool (SWAT) is a physically based, distributed, agrohydrological model that operates on a daily time step at the watershed scale. SWAT is designed to predict the impact of change in management on water, sediment, and agricultural chemical yields in ungauged catchments (Arnold et al. 1998). The model is capable of continuous simulation of dissolved and particulate elements in large complex catchments with varying weather, soil, and management conditions over long time periods. SWAT can analyze small or large catchments by discretizing them into subbasins, which are then further subdivided into hydrologic response units (HRUs) with homogeneous land use, soil type, and slope. When embedded within a geographical information system (GIS), SWAT can integrate various spatial environmental data including soil, land cover, climate, and topographical features. The theory and details on the hydrological and sediment transport processes integrated in SWAT are available from the website of the Texas A&M University System (SWAT 2015).

The HRUs in the SWAT were analyzed using the DEM and land-use data of Chungju Dam basin. The basin was divided into three subbasins (Fig. 4), and geomorphological parameters of each subbasin were extracted. The weather stations (Fig. 2) located in Chungju Dam basin were applied to the model to simulate the runoff. The calibration and validation periods were classified as 1986–2000 and 2001–2006, respectively (Table 3). The evaluation results of the calibration [Fig. 5(a)] and validation [Fig. 5(b)] confirmed that the model can properly represent the runoff characteristics of the Chungju Dam basin based on multiple criteria: coefficient of correlation (CC), coefficient of determination (

R^{2}

), model efficiency (ME), and root-mean squared error (RMSE).

Fig. 4. Three subbasins with land-use map in Chungju Dam basin

Table 3. Calibration and Verification of Runoff (or Inflow) Series at Chungju Dam

Evaluation function	Calibration	Verification
Coefficient of correlation (CC)	0.87	0.84
Coefficient of determination ( $R^{2}$ )	0.76	0.71
Model efficiency (ME)	0.80	0.77
Root-mean squared error (RMSE)	$88.92 m^{3} / s$	$92.61 m^{3} / s$

Fig. 5. Calibration and verification results of monthly runoff series at Chungju Dam: (a) calibration (1986–2000); (b) verification (2001–2006)

Water-Balance Analysis

The relevant data for 37 years (1973–2014) were collected from WAMIS, which maintains South Korean water-resources data related to hydrometeorology, basins, rivers, dams, groundwater, water use, etc.

The water demand (

D_{j, t}

) can be largely classified into household (

H_{j, t}

), industrial (

I n_{j, t}

), and agricultural (

A g_{j, t}

) for geographical location

j

and day

t

D_{j, t} = H_{j, t} + I n_{j, t} + A g_{j, t}

(4)

Household and industrial water demand do not show significant seasonality (Kim et al. 2014), and thus can be assumed to be a fixed amount every day. For household water use, annual population data were collected for each basin, and 359 L per capita per day (LPCD) (Ministry of Environment, Water Supply Statistics 2004) was assumed. The industrial water use for each basin was taken from WAMIS. In the case of agricultural water use, the daily deviation in water demand is large in connection with the growth of the crops. To assess the daily demand of the agricultural water, daily potential evapotranspiration calculated using the Penman-Monteith method and the crop coefficient recommended by the food and agriculture organization of the United Nations (FAO) (Richard et al. 1998) were used.

The most important source of water supply in all the regions is precipitation. In some regions, however, water resources such as reservoirs and underground water have been developed for active use. Thus, water supply (

S_{j, t}

) can be classified into what is available as a fraction of the net precipitation supply (

{NPS}_{j, t}

) and transfer water supply (

T S_{j, t}

) in each unit basin [Fig. 6(b)] as indicated in Eq. (5). The relevant data were collected from WAMIS

S_{j, t} = {NPS}_{j, t} + T S_{j, t}

(5)

where

{NPS}_{j, t}

= difference between precipitation (

P S_{j, t}

) and simulated natural streamflow (

S S_{j, t}

) from the SWAT.

Fig. 6. Water demand and transfer in Chungju Dam basin: (a) monthly water demand; (b) water transfer in each subbasin

The water deficit was calculated by the difference between water demand and water supply for the period between 1987 and 2014 in the basin as follows:

W D_{t} = \sum_{1}^{j} (D_{j, t} - S_{j, t}); D_{j, t} - S_{j, t} = 0 (if D_{j, t} - S_{j, t} < 0)

(6)

The water deficits were estimated for the timescales of 1, 3, 6, and 12 months in each subbasin, and the results are shown in Fig. 7. There were six extreme drought events between 1987 and 2014, based on the water deficit of the timescale of 12 months. During the worst drought of 2001–2002, water deficit was over

90 \times 10^{6} m^{3}

.

Fig. 7. Water deficit for 1987–2014 in Chungju Dam basin from the WBA

The linear correlations between the water deficit and drought indices SPI, SRI and SSVI for the timescale of 1 month shows that the correlation was the highest (0.61) with the SPI and the lowest (0.1) with the SSVI as shown in Fig. 8. However, the correlation increased to approximately 0.5 with SSVI for the timescale of 12 months. In contrast, the correlation with SPI decreased to 0.5 for the longer timescale of 12 months. The correlation with the SRI index was relatively constant (0.43–0.5). Thus, drought severity may vary significantly depending on the timescale used to calculate the drought index.

Fig. 8. Correlations between water deficit from the WBA and drought indices

Application of Bayesian Networks and Discussion

In the situation of making a decision to manage drought, many drought indices, such the SPI, SRI, and SSVI, can be estimated in a basin. If the indices provide same drought severity, they will be very good for making a decision. However, if they show different severities, for example when SPI was severe, SRI was moderate, and SSVI was normal in 1992, as shown in Fig. 3, it will be very difficult to make a decision. In this respect, a BN is powerful for incorporating data and knowledge from different sources and domains (Castelletti and Soncini-Sessa 2007; Henriksen and Barlebo 2008).

In this study, a simple BN was developed considering the hydrological causality between the drought indices of SPI, SRI, and SSVI using four nodes and five links (Fig. 9). The node SPI is a root node, and its prior probability distribution can be inferred directly from the histogram depending on the ranges in Table 1. The probability distribution for SRI (where the underlying variable is streamflow) depends on the SPI values (where the underlying variable is precipitation); the distribution for SSVI (where the underlying variable is water storage) depends on the SRI values. Similarly, the conditional probability distribution for actual drought severity depends on the SPI, SRI, and SSVI values. The unidirection or acyclic property of the BN nodes is an important assumption. Here, it is less likely that the water storage can affect the streamflow or that precipitation or streamflow can influence rainfall. Furthermore, rainfall does not affect the storage volume significantly because the direct contribution of precipitation to storage volume is very small compared to rainfall over the total catchment area.

Fig. 9. Bayesian networks for integrating drought indices

Each node has seven categories as indicated in Table 1. The estimated water deficit from the water-balance model is assumed to indicate the actual drought severity in the basin. Drought severity is classified based on timescale into four categories: (1) normal (less than 2 years), (2) moderately dry (2–5 years), (3) severely dry (5–10 years), and (4) extremely dry (over 10 years) based on return periods of 2, 5, and 10 years in each timescale (Table 4). The estimated probability density functions (PDFs) and water deficits for each timescale case are shown in Fig. 10 and Table 4.

Table 4. Water Deficit in Each Return Period (

\times 10^{6} m^{3}

)

Timescale	Return periods: normal ( $< 2 year$ ), moderate (2–5 years), severe (5–10 years), and extremely dry ( $> 10 years$ )
Timescale	2 years	5 years	10 years
1 month	15.6	20.5	23.5
3 months	24.0	31.7	36.3
6 months	35.8	46.1	52.2
12 months	57.7	74.3	84.2

Fig. 10. PDFs and categories of drought severity for each timescale case

For BN construction and modeling, AgenaRisk 6.2 (Fenton and Neil 2014) was used in this study. The conditional probability in each node of BN was input as shown in Fig. 11. To illustrate in detail, the BN on a drought timescale of 12 months and probability results are shown in Fig. 11. The SPI, SRI, and SSVI nodes have seven discrete probabilities, and the water-deficit node has four discrete probabilities.

Fig. 11. Initial probability of Bayesian networks on a drought timescale of 12 months

A sensitivity analysis was performed to assess the impact of different nodes (SPI, SRI, and SSVI) on the consolidated drought severity. The inferred probability from BN analysis of the drought-severity node depended on drought ranges given the parent nodes; the calculated results are provided in Table 5. For example (in case of extremely dry range of SPI index in Table 5), when the SPI is extreme dry, the probability that the CDS will be extreme is 0.337, the probability it will be severe is 0.372, the probability it will be moderate is 0.169, and the probability it will be normal is 0.121.

Table 5. Sensitivity Analysis of Composite Drought Severity (12-Month Timescale)

Indices	Drought ranges	Composite drought severity (CDS) (probabilistic drought inferred from BN)
Indices	Drought ranges	Extreme	Severe	Moderate	Normal
SPI P(RDS \| SPI)	Extremely dry	0.337	0.372	0.169	0.121
	Severely dry	0.067	0.44	0.31	0.184
	Moderately dry	0.019	0.155	0.537	0.289
	Normal	0.001	0.019	0.109	0.871
	Moderately wet	0.002	0.028	0.056	0.915
	Very wet	0	0.001	0.01	0.989
	Extremely wet	0	0	0.001	0.999
SRI P(RDS \| SRI)	Extremely dry	0.665	0.298	0.035	0.002
	Severely dry	0.109	0.57	0.271	0.051
	Moderately dry	0.017	0.16	0.634	0.189
	Normal	0.001	0.013	0.106	0.88
	Moderately wet	0	0.002	0.034	0.964
	Very wet	0	0	0.009	0.991
	Extremely wet	0	0	0	1
SSVI P(RDS \| SSVI)	Extremely dry	0.693	0.234	0.064	0.009
	Severely dry	0.144	0.489	0.233	0.135
	Moderately dry	0.033	0.207	0.493	0.266
	Normal	0.001	0.013	0.111	0.875
	Moderately wet	0	0.003	0.031	0.966
	Very wet	0	0	0.006	0.993
	Extremely wet	0	0	0	1

The BN framework was applied to assess the particular drought in 2014 because it was the highest drought year in recent years, as shown in Fig. 3. The SPI estimated severely dry and the SRI estimated extremely dry for all timescales. The SSVI estimated severely dry for the timescales of 1 and 3 months and moderately dry for the timescales of 6 and 12 months. The actual drought represented by the result of the water-balance analysis (WBA) indicated extremely dry for a 1-month timescale and severely dry for the other timescales. The BN using the aforementioned information to estimate the severity probabilities are summarized in Fig. 12. The estimated first and second highest probabilities by the BN are given in Table 6. When the results are compared between WBA-based and BN-based CDS estimates for the highest probability values, the outcomes from the BN analysis matches very well with the actual drought severity for the basin, although there is some difference for the 3-month-timescale case.

Fig. 12. Estimated probability of drought severity for each timescale in 2014

Table 6. Assessment of Drought Severity in 2014

Timescale	SPI	SRI	SSVI	WBA (actual drought, $10^{6} m^{3}$ )	CDS from BN (highest/second highest)
1 month	$- 1.89$ [S]	$- 2.49$ [E]	$- 1.71$ [S]	24.1 [E]	[E] (51.1%)	[S] (45.1%)
3 months	$- 1.92$ [S]	$- 2.37$ [E]	$- 1.58$ [S]	35.3 [S]	[E] (41.9%)	[S] (36.8%)
6 months	$- 1.83$ [S]	$- 2.21$ [E]	$- 1.4$ [M]	47.8 [S]	[S] (63.1%)	[E] (31.1%)
12 months	$- 1.86$ [S]	$- 2.28$ [E]	$- 1.1$ [M]	75.3 [S]	[S] (52.6%)	[E] (25.0%)

Note: E = extremely dry; M = moderately dry; S = severely dry.

Summary and Conclusions

This study used BNs to estimate a composite drought-severity index using different drought indices. BNs provide a powerful modeling framework and have been applied to many real-world problems involving uncertainty. They are applicable to evaluating the improvement of a system’s performance with indices based on the probability in the case of using restricted observations in the evidence. Fig. 13 shows the estimated CDS in various situations with restricted evidence (if one of the variables, e.g., precipitation, streamflow, or storage volume, is not available). Fig. 13(a) is the case when only SPI evidence is available, and it shows extremely dry conditions. The CDS shows a drought severity of extreme with a probability of 33.7%, severe with a probability of 37.2%, moderate with a probability of 16.9%, and normal with a probability of 12.1%. Fig. 13(d) is the case when SPI and SRI are both available with an extremely dry outcome. The probability of the CDS suggesting an extreme outcome increases up to 75.7%. Fig. 13(f) is the case when all indices are available with an extremely dry outcome. The probability with SPI, SRI, and SSVI increases up to 90.4% and the uncertainty decreases significantly compared with the case in Fig. 13(a).

Fig. 13. Probabilities of the estimated CDS depending on restricted evidence of extremely dry at a timescale of 12 months: (a) SPI; (b) SRI; (c) SSVI; (d) SPI and SRI; (e) SRI and SSVI; (f) SPI, SRI, and SSVI

These results show that more reliable information provides much stronger evidence and also reduces uncertainty. In other words, the drought severity in a basin can be estimated more accurately by integrating drought indices using information on precipitation, runoff, and storage volume.

The proposed method helps to integrate three specific drought indices to suggest a probabilistic outcome for a drought occurrence that is closer to the real outcome. But the ways in which this method could be beneficial to different stakeholders and water-resource managers will depend on the specific situation. To begin with, the three indices were created assuming different definitions of drought so as to have different sets of actions or decision making by different stakeholders. So long as the success or failure of a decision is strictly based on a particular definition of drought, there is no issue. But there are emerging issues around water resources that have multiple dimensions (such as water allocation), and a decision based a single index might not be useful. Furthermore, the existing indices are deterministic, whereas for risk-based decision making, probabilistic estimates are more relevant.

Drought index outcomes can differ and are sensitive to the methods used. This can create conflict of interest among multiple stakeholders. An advantage of the proposed method is that it can reconcile different drought indices and help multiple stakeholders better understand the drought occurrence uncertainty. For example, an insurance company might be paying compensation to a farmer based on a particular drought index. But a farmer using a different drought index might not be satisfied if outcomes differ between the two indices and compensation is not paid. The proposed method can be seen as a calibration exercise of these two indices to inform both farmer and insurance company regarding the uncertainty, which might improve their cooperation and trust.

It has been assumed that an actual drought can be determined by summing up all the water deficits from agricultural, industrial, and household sectors. The economic weightings of the water sources or deficits were not determined given limited data availability. In total deficit, agricultural water’s contribution is the biggest.

The three indices were chosen because they have similar methods. However, the critical point is that the acyclic property has to be adhered to when the nodes and information flow direction are designed in a BN. It might be difficult to satisfy the one-way causal direction for some indices. For example, the normalized difference vegetation index (NDVI) can replace SRI, but sufficient caution should be applied because some studies show that vegetation can affect rainfall (land–atmospheric feedback). Other methods, such as system dynamics, agent-based models, and discrete-event models, are being actively researched to address the cyclic nature of some networks.

Acknowledgments

This research was supported by a grant (No. 13SCIPS04) from the Smart Civil Infrastructure Research Program funded by the Ministry of Land, Infrastructure and Transport (MOLIT) of the Korean Government and the Korea Agency for Infrastructure Technology Advancement (KAIA).

References

AgenaRisk version 6.2 [Computer software]. Agena Ltd., Cambridge, U.K.

Abstract

Introduction

Materials and Methodology

Drought Indices

Bayesian Networks

Application and Results

Study Basin and Materials

Drought Indices

Estimation of Actual Drought

Hydrological Modeling

Water-Balance Analysis

Application of Bayesian Networks and Discussion

Summary and Conclusions

Acknowledgments

References

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