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Proceedings of The Fourth International Iran & Russia Conference 1165

Water Deficit and Drought Forecast by a Markov-Chain Model:

Case Study in Central Iran

Peyman Daneshkar Arasteh1

and Masoomeh Mianehrow2

1- Hydrology Department, Soil Conservation and Watershed Management Research Institute (SCWMRI),Tehran, Iran. P.O.Box: 13445-1136, Tehran, Iran Phone: 0098-21-4901240 ~ 47 Fax: 0098-21-4905709 E-mail:

[email protected]; 2- Former graduate student of Climatology E-mail: [email protected]

Abstract

Deserts emerge and expand as a result of destruction of vegetation cover. If the plant is

watered and irrigated enough, in the proper time and place, the vegetation cover is firmed and

desertification is stopped. If the time and magnitude of watering with the peak of water

consumption of plant are unbalanced, the vegetation cover is weakened and if this shortage

continues, the vegetation will be destroyed. Water deficit due to drought accelerates this

vegetative destruction.

In this research the Thornthwait Moisture Index (TMI) is used to foresee the drought.

According to run theory, a threshold was determined and on the basis of this threshold, in

respect to the gained index, the system is divided into three conditions: normal, water excess

and water shortage. In addition to have a quantity, the above-mentioned threshold, needs a

definition of a period of continuation. In this research, a band with a width of two times of

standard deviation as threshold and a three-year continuation period are used. On this basis, if

the TMI is in this band, the region is in normal condition, if not, provided that the index is out

of the band for three years, depending on the absolute value of the index, the system is either

improving or being destroyed. Using the achieved definitions of the system’s condition on the

basis of the TMI and mentioned continuation period, the transition and static probability

matrices were calculated according to forecast the long time probability of regional

desertification as normal, excessive or short, is represented in this paper. The research wascarried out on the Central Basin of Iran (CBI) and iso-probability maps of water deficit are

provided. The maps show that the study area will be in normal condition with a probability of

50 to 60 percent and dry out with probability of 38 to 50 percent in future. Only with a

maximum probability of 2 percent state of the CBI changes to improve. Drying gradually

increases and is fixed after 25 to 40 months.

Key Words: Iran, Markov Chain, Thornthwait Moisture Index, TPSS, Water Deficit

Introduction

Desertification is the degradation of drylands. It involves the loss of biological or economical

productivity and complexity in croplands, pastures, and woodlands. If the time of wateringand peak of water consumption of plant are unbalanced, the vegetation cover is weakened

and if this water shortage continues, the vegetation will be destroyed. It is due mainly to

climate variability and unsustainable human activities.

Drylands respond quickly to climatic fluctuations and have limited freshwater supplies.

Precipitation can vary greatly during the year. In addition to this seasonal variability, wide

rainfall depth fluctuations occur over years and decades, frequently leading to drought. In the

other hand, land degradation affects the quantity and quality of freshwater supplies too.

Drought and desertification are associated with low water levels in rivers, lakes, and aquifers.

Success in combating desertification will require an improved understanding of its causes and

impacts. There is still much to learn about the linkages between desertification and climate,

soils, water, plants, animals, and, in particular, people.

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Drought is an environmental phenomenon and an integrated part of climate variability. It is

also an inherent, normal, recurrent feature of climate (Wilhite, 1997; Dupigny-Giroux, 2001).

Drought occurs everywhere and causes intense water shortage but its characteristics vary

significantly from one region to another (Baren, 1985). There are several classifications of

drought among different disciplines. A popular and world-wide accepted disciplinary

perspective classification, classifies droughts into meteorological, hydrological, agriculturaland socio-economical drought (Dracup et al. 1980a).

In order to analyze drought, an index is required to determine wet and dry spells clearly.

Many researchers have proposed several drought indices. Among these indices, the most

commonly used are Bhalme and Mooley Drought Index, BMDI (Bhalme and Mooley 1980),

Crop Moisture Index, CMI (Palmer, 1968), Deciles (Gibbs and Maher 1967), Palmer Drought

Severity Index, PDSI (Palmer 1965), Percent of Normal, PN (Willke et al. 1994),

Reclamation Drought Index, RDI (Weghorst 1996), Standardized Precipitation Index, SPI

(Makee et al. 1993,1995), Surface Water Supply Index, SWSI (Shafer and Dezman 1982),

Thornthwait Moisture Index, TMI (Subrahmanyam, 1985).

In this paper, how the climate causes desertification in Central Basin of Iran (CBI) and how

desertification border by climatic factors fluctuations could be predicted, is represented. In

this regard, Thornthwait Moisture Index (TMI) was used. It is the algebraic sum of humidity

and aridity indices that both are the ratio of available water (precipitation) to consumptive

water (potential evaporation), respectively in two periods of wetness and dryness (water

excess and shortage durations). Also, a linear Markov’s process was applied to forecast the

situation of CBI in future.

Materials and Methods

Study Area

The study area has been located between 48o

27’ to 61o

29’ eastern longitudes and between

27

o

12’ to 36

o

41’ northern latitudes including all or some parts of 14 provinces of Iran. Theseprovinces are Zanjan, Hamadan, Qazvin, Tehran, Semnan, Khorasan, Isfahan, Yazd, Fars,

Hormozgan, Sistan and Baloochestan, Kerman, Qom and Central Province. The CBI is the

largest watershed of Iran with an area about 50% of the area of the country. Lack of

precipitation causes few permanent rivers in this watershed. River flow regime in high lands

is snowy and in low land is rainy. Climate of CBI in Thornthwait classification varies form

EB’2c’1d in high lands of northwest to EA’b’1d in low lands of southeast of CBI

(Mianehrow, 2002).

Several investigations about drought extend zonation has been carried out in CBI. Mianehrow

(2002) and Mianehrow et al. (2003) studied the drought, spatially in CBI by time series

modeling and Razi et al. (2003) determined the SPI distribution over Yazd Province in

central part of CBI. Also, Shokoohi et al. (2002) studied drought occurrence in southeast of Iran by Z-score.

In this research to study the climatic behavior of the CBI, 29 synoptic stations of National

Weather Organization (Fig. 1) with data length of 30 years from 1971 to 2000 were used.

Ambrothermic diagrams show large temporal variation in temperature and rainfall in the

study area. For example Fig. 2 shows one of these diagrams for Yazd synoptic station. As this

diagram shows, seasonal variation of temperature is large and precipitation concentrates in a

period from late autumn to early spring. CBI is a sensitive watershed and is under

desertification and dryland degradation impacts. Across the CBI, these diagrams show

different spatial behavior of temperature and rainfall.

Methodology

In this research, it was assumed that water shortage investigation could be used to predictsensitivity of vegetation cover to water deficit and to forecast desertification extend. To study

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the trend of desertification and vegetation destruction, Thornthwait Moisture Index (TMI)

was used and required data was achieved from synoptic stations spread over CBI. TMI as

Thornthwait defined in 1948 (Subrahmanyam, 1985) is the difference between humidity and

aridity indices, which are defined as the ratios of excess and deficit in annual water supply

(i.e. difference between precipitation and evaporation to annual potential evaporation).

Bearing the run theory in mind, a threshold was determined and on the basis of this threshold,in respect to the gained index, the system is divided into three conditions: normal, water

excess and water shortage. In addition to have a quantitative magnitude, the above-mentioned

threshold, needs a definition of a period of continuation. In principle, the threshold and its

continuation must be determined in respect to the dominant type of the regional vegetation

cover and the representative types’ tolerance against water deficit. For all stations, TMI time

series was derived and a band of normality was defined about the mean as truncation level on

the base of run theory (Sharma, 2000, Moye et al., 1988). Outside this band (threshold) water

excess or shortage situations are specified. Width of this band was selected two times of

standard deviation of TMIs for each station as Shokoohi et al. (2002) and Razi et al. (2002)

introduced for drought indices for east and southeast of Iran and a three-year continuation

period, are used, without considering the biological factors and with reliance on statistical

deductions. To predict the future situation of CBI a stochastic modeling was conducted. As

shokoohi et al. (2002) confirmed, a first order Markov-chain was used to predict the

probability of occurrence of each state on a stepwise manner.

Results

After forming TMIs time series on monthly basis and considering the state of each month

according to the normal band and recognizing its state, probability of moving from each state

to others (water shortage to normal and excess, normal state to shortage and excess states and

excess to shortage and normal states) was determined. To form the Markov-chains, transition

probability matrices (TPMs) must be computed as mentioned above.The TPMs and initial state probability vectors (ISPVs) for each time series was determined.

Table 1 and Fig. 3 show TPM and TMI time series diagram for Yazd, respectively.

Discussion

Observation of time series shows normal state for all regions of CBI in 1997. So the ISPV for

all time series was considered as [0 1 0]. It means the state of CBI has been normal before

starting the modeling.

The TPMs show that in most regions of CBI like Yazd, there are only two states of shortage

and normal and in western and northwestern parts of CBI, the TPM is a trapping one. A

trapping TPM causes the steady state probability vector (SSPV) becomes similar to ISPV. It

means for every ISPV, the given ISPV repeats for SSPV. For example if ISPV in a region isnormal, its SSPV will also be in normal condition. Stochastic modeling with linear Markov-

chain was carried out for all 29 stations until 2005. It was shown that steady state or

smoothing condition accurse after 25 to 40 months. Table 2 and Fig. 4 show this smoothness

for Yazd station.

After forecasting SSPVs for all stations, interpolation procedure was done to map the

sensitive area to water deficit. On the base of Mahdian et al. (2001) investigation, a thin plate

smoothing spline interpolator (TPSS) with a weight of two was applied to interpolate point

SSPVs to an aerial extend raster map by ArcView GIS. Three contour maps of different states

were inferred (Figs. 5 to 7). They showed normal state is the major condition of CBI and its

occurrence probability is between 50 to 60 percent (Fig. 6). Water shortage state occurs with

probability of 38 to 50 percent (Fig. 5) and occurrence of less water deficit, which was calledexcess state in this paper, has a probability less than 2 percent (Fig. 7).

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Conclusion

Central Basin of Iran (CBI) is a sensitive region and desertification in this area is active now.

A study was conducted to show if desertification has a climatological cause or another factors

cause this phenomenon. In this regard, Thornthwait Moisture Index (TMI) and its temporal

variations were selected as time series. On the base of run theory three states of water

shortage and excess, and normal were recognized. A linear Markov process was applied toforecast the steady state probability of each state in long times. It was shown that steady

states would occur after 25 to 40 months. And aridity is the nature of CBI and occurrence of

water deficit in 50 to 60 percent of times is normal and in 38 to 50 percent of times, water

deficit is drought and is not a normal event. Only less than 2 percent, it is expected to

improve the state and less water deficit takes place. Also, spatial distribution of steady state

probability (iso-probability maps) showed that central parts of CBI are in high risk of

drylands degradation. So the climatic parameters are principle factors of desertification in

long time and some other factors like human activities increase the speed of desert

development and have short time impacts.

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Weather Review 108: 1197-1211

2. Baren MA (1985) Hydrological aspects of droughts. UNESCO/WMO London UK

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climatological perspective. Journal of America Water Resources Association 37(3): 505-525

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Conference on Applied Climatology 15-20 January Dallas TX USA 233-236

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indices and mathematical modeling. MSc. Thesis Free University Rey Branch Tehran Iran

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by time series analysis in Central Watershed of Iran. Proceeding of the 7th

International Conference

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drought prediction. Journal of Hydrology 103: 127-137

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Commerce Weather Bureau Washington D.C. USA

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Moisture Index. Weatherwise 21: 156-161

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index. Proceeding of the 7th

International Conference on Development of Dry Lands Tehran Iran

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16. Shafer BA, Dezman LE (1982) Development of a Surface Water Supply Index (SWSI) to assess

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Conference 164-175

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Table 1. Transition probability matrix Yazd (%).Station State Shortage Normal Excess

Shortage 78.1 21.9 0.0

Normal 22.6 77.4 0.0Yazd

Excess 0.0 0.0 0.0

Table 2. Smoothness of state probability vector in Yazd station.Month 1 2 3 4 5 6 7 8 9 10

S 0.1421 0.23516 0.29611 0.33602 0.36216 0.37928 0.39049 0.39783 0.40264 0.40579

N 0.8579 0.76484 0.70389 0.66398 0.63784 0.62072 0.60951 0.60217 0.59736 0.59421

Month 11 12 13 14 15 16 17 18 19 20

S 0.40785 0.4092 0.41009 0.41067 0.41105 0.4113 0.41146 0.41157 0.41164 0.41168N 0.59215 0.5908 0.58991 0.58933 0.58895 0.5887 0.58854 0.58843 0.58836 0.58832

Month 21 22 23 24 25 26 27 28 29 30

S 0.41171 0.41173 0.41174 0.41175 0.41176 0.41176 0.41176 0.41176 0.41176 0.41176

N 0.58829 0.58827 0.58826 0.58825 0.58824 0.58824 0.58824 0.58824 0.58824 0.58824

r

r

r

r

rr

r

r

rr

r

r

r

r

r

r

r

r

r

r

r

r

r

r

r

r

r

r

r

Bam

Arak

Yazd

Baft

Anar

Tabas

Zabol

Khash

Khoor-e-Biabanak

Semnan

Qazvin

Kashan

Kerman

Zanjan

Shiraz

Abadeh

Sirjan

Esfehan Birjand

Hamedan

Zahedan

Kahnooj

Torbat-e-Heydarieh

Tehran

Sabzevar

Shahrood

Iranshahr

Nehbandan

Shahr-e-Kord

400 0 400 800 Kilometers

Fig. 1. Central Watershed of Iran and location of synoptic stations.

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Fig. 2. Ambrothermic diagram for Yazd.

Fig. 3. TMI time series of Yazd.

Fig. 4. Smoothness of state probability vector in Yazd.

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Fig. 5. Spatial distribution of SSPVs of water shortage state across CBI (%).

Fig. 6. Spatial distribution of SSPVs of normal state across CBI (%).

Fig. 7. Spatial distribution of SSPVs of less water deficit (excess) across CBI (%).

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