MLP-based drought forecasting in different climatic

MLP-based drought forecasting in different climatic regions

Mehdi Rezaeian-Zadeh & Hossein Tabari

Theoretical and Applied Climatology ISSN 0177-798X Volume 109 Combined 3-4 Theor Appl Climatol (2012) 109:407-414 DOI 10.1007/s00704-012-0592-3

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Author's personal copy Theor Appl Climatol (2012) 109:407–414 DOI 10.1007/s00704-012-0592-3

ORIGINAL PAPER

MLP-based drought forecasting in different climatic regions Mehdi Rezaeian-Zadeh & Hossein Tabari

Received: 28 November 2011 / Accepted: 18 January 2012 / Published online: 31 January 2012 # Springer-Verlag 2012

Abstract Water resources management is a complex task and is further compounded by droughts. This study applies a multilayer perceptron network optimized using Levenberg– Marquardt (MLP) training algorithm with a tangent sigmoid activation function to forecast quantitative values of standardized precipitation index (SPI) of drought at five synoptic stations in Iran. The study stations are located in different climatic regions based on De Martonne aridity index. In this study, running series of total precipitation corresponding to 3, 6, 9, 12, and 24 months were used and the corresponding SPIs were calculated: SPI3, SPI6, SPI9, SPI12, and SPI24. The multilayer perceptrons (MLPs) for SPIs with the 1-month lead time forecasting, were tested and validated. Four different input vectors were considered during network development. In the first model, MLP constructed by importing antecedent SPI with 1-, 2-, 3-, and 4-month time lags and antecedent precipitation with 1- and 2-month time lags (MLP1). Addition of antecedent North Atlantic Oscillation or antecedent Southern Oscillation Index with 1-month time lag or both of them to MLP1 led to MLP2, MLP3, and MLP4, respectively. The MLP models were evaluated using the root mean square error (RMSE) and the coefficient of determination (R2). The results showed that MLP4 had a higher prediction efficiency than the other MLPs. The more satisfactory results of RMSE and R2 values of MLP4 for 1-month lead time for validation phase were M. Rezaeian-Zadeh Young Researchers Club, Shiraz Branch, Islamic Azad University, Shiraz, Iran H. Tabari (*) Department of Water Engineering, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran e-mail: [email protected]

equal to 0.35 and 0.92, respectively. Also, results indicated that MLPs can forecast SPI24 and SPI12 more accurately than the other SPIs.

1 Introduction Drought is one of climatic phenomena that its occurrence is inevitable. The term meteorological drought is used to identify those situations with precipitation amounts falling short of the long-term average values. The consequential impacts of a meteorological drought may over time lead to other drought categories, i.e., agricultural, hydrological, or socio/economic droughts (Dracup et al. 1980). Then, depending on the type of problem at hand, proper definition, and application of relevant drought category must be realized. Furthermore, occurrence of drought events can have economical impacts far beyond the affected area (Mishra et al. 2007). Drought events are usually explained by drought indicators, as variables that identify drought characteristics, i.e., the magnitude, duration, severity, and spatial extent. In addition, over the years, several indices have been proposed to detect and monitor droughts. As a common practice, drought indices are used to investigate occurrence and extent of drought events. One of the well-known meteorological drought indices is the Standardized Precipitation Index (SPI), originally suggested by McKee et al. (1993). Some of the recent researches on drought evaluation include Edossa et al. (2010), Pandey et al. (2010), Vangelis et al. (2010), and Vasiliades et al. (2011). The SPI has been used quite extensively, addressing a variety of drought related issues worldwide. Some of the more recent research efforts on SPI in Iran include and are not limited to: Morid et al. (2006), Modarres (2010), Abolverdi and Khalili (2010), Tabrizi et al. (2010), and Khalili et al. (2010). Mishra and

Author's personal copy 408 Table 1 The SPI drought category classification (Mckee et al. 1993)

M. Rezaeian-Zadeh, H. Tabari

SPI

Category

2.0 and above

Extremely wet

1.5 to 1.99 1.00 to 1.49

Very wet Moderately wet

−0.99 to 0.99

Near normal

−1.0 to −1.49

Moderately dry

−1.5 to −1.99 −2.0 and less

Severely dry Extremely dry

forecast streamflow in Aspas Watershed in Fars province in southwestern Iran. Owing to the importance of drought forecasting in water resources planning and management and the stochastic behavior of drought, this study evaluated the capability of ANNs in forecasting of the SPI in different time scales based on the data from selected stations in Iran, representing a variety of climatic zones.

2 Materials and methods Desai (2006) implemented feed-forward recursive neural networks to forecast drought using SPI series. The results were obtained from three models and their potential to forecast drought over different lead times were discussed. Recently, Keskin et al. (2011) applied artificial neural networks (ANNs) to analyze meteorological drought based on SPI. During the last decades, new techniques such as ANN have been applied as efficient alternative tool for modeling of complex water resources systems and widely used for forecasting (Rahimikhoob 2009, 2010; Tabari et al. 2010a, b, 2011b; Marofi et al. 2011; Hosseinzadeh Talaee et al. 2011; Goyal and Ojha 2011; Rezaeian-Zadeh et al. 2011). Mishra et al. (2007) used a hybrid model with ANN model for drought forecasting in the Kansabati River basin in India. They found the model hybrid to forecast droughts with greater accuracy. Morid et al. (2007) employed different ANN models for the Effective Drought Index and SPI to forecast drought at several rainfall stations in the Tehran province of Iran. Jamshidi et al. (2009) applied multilayer perceptron (MLP) networks optimized with three different training algorithms, including resilient back propagation, variable learning rate, and Levenberg–Marquardt, to Fig. 1 The location of the studied stations

2.1 The SPI drought index The standardized precipitation index (SPI) was developed by McKee et al. (1993), as a means to define and monitor drought events. Computation of the SPI involves fitting a probability density function (PDF) to total precipitations for the stations of interest. Typically, the gamma distribution is applied, which requires an estimation of its corresponding α, β parameters, to each time scale of interest (1, 2, 3… months) and for each month of the year. The gamma distribution is defined by its frequency or PDF: Zx GðxÞ ¼ 0

1 gðxÞdx ¼ a b Γ ðaÞ

Zx

xa1 e b dx x

for x > 0

0

ð1Þ where α and β are shape and scale parameters, x is the precipitation amount and Г(α) is the gamma function. Maximum likelihood solutions are used to estimate α and β. The resulting parameters are used to find the cumulative probability of an observed precipitation event for the given

Author's personal copy MLP-based drought forecasting in different climatic regions Table 2 Geographical location and related information of the studied stations

409

Synoptic station

Latitude

Longitude

30°22′

48°15′

6.6

168.6

Arid

37°28′

49°28′

−26.2

1,779.1

Very humid

Kermanshah Mashhad

34°17′ 36°16′

47°07′ 59°38′

1,322 999.2

462.4 264

Semi-arid Semi-arid

Iran Shahr

27°12′

60°42′

591.1

111.6

Arid

ð2Þ

where, q represents the probability of zero precipitation. The calculated precipitation probabilities are transformed into the corresponding standard normal values, from which the SPI values are calculated. Additional descriptions can be found in the several available texts, i.e., Edwards and McKee (1997). A discussion of the advantages and disadvantages of using the SPI to characterize drought severity has been provided by Hayes et al. (1999). Table 1 provides a drought classification based on the SPI (McKee et al. 1993). 2.2 Neural network training algorithms The ANN algorithms, including Levenberg–Marquardt, were first trained by minimizing the global error E defined as: p X

Climate type (De Martonne 1942)

Abadan

HðxÞ ¼ q þ ð1  qÞ  GðxÞ

1 p

Mean annual rainfall (mm)

Bandar anzali

month and the timescale in the given station, which is then used to obtain the SPI values. The developed SPI values are then classified into different ranges of above and below normal values, indicating the severity of drought or nondrought events. Several characteristics of droughts such as magnitude, duration, or intensity can follow based on the SPI values. It is possible to have several zero values in a sample set. In order to account for zero value probability, the CDF for gamma distribution is modified as:

E¼

Altitude (m a.s.l)

ð3Þ

Ep

where n0the total number of output nodes; ok 0the network output at the kth output node; and tk 0the target output at the kth output node. In every training algorithm described in the next section, an attempt was made to reduce the global error by adjusting weights and biases (Kisi 2007). Levenberg–Marquardt algorithm The Levenberg–Marquardt algorithm was designed to approach the second-order training speed without having to compute the Hessian matrix (More 1977). When the performance function has the form of a sum of squares (as is typical in training feedforward networks), then the Hessian matrix can be approximated as: H ¼ JTJ

ð5Þ

and the gradient can be computed as: ð6Þ

g ¼ JTe

where J0the Jacobian matrix that contains first derivatives of the network errors with respect to weights and biases, and e0the vector of network errors. The Jacobian matrix can be computed through a standard back-propagation technique that is much less complex than computing the Hessian matrix. The Levenberg–Marquardt algorithm uses this approximation to the Hessian matrix in the following Newton-like update:

p¼1

where P0the total number of training patterns and EP 0the error for training pattern p. EP was calculated as: Ep ¼

1 2

n X

ðok  tk Þ2

ð4Þ

k¼1

Table 3 The performance of all the MLP models in validation phase for Abadan station

Station

MLP1 MLP2 MLP3 MLP4

SPI3

xkþ1 ¼ xk  ½J T J þ μI1 J T e

ð7Þ

where scalar μ is zero, this becomes just Newton's method, using the approximate Hessian matrix. When μ is large, this becomes a gradient descent with a small step size. Newton's method is faster and more accurate near an error minimum,

SPI6

SPI9

SPI12

SPI24

R2

RMSE

R2

RMSE

R2

RMSE

R2

RMSE

R2

RMSE

0.095 0.095 0.088 0.126

0.932 0.919 0.923 0.904

0.219 0.206 0.257 0.293

0.816 0.803 0.799 0.792

0.325 0.353 0.378 0.381

0.742 0.727 0.718 0.711

0.411 0.607 0.622 0.629

0.662 0.545 0.530 0.525

0.637 0.625 0.644 0.667

0.483 0.491 0.479 0.463

Author's personal copy 410 Table 4 The performance of all the MLP models in validation phase for Bandar Anzali station

M. Rezaeian-Zadeh, H. Tabari

Station

SPI3

SPI6

SPI12

SPI24

R2

RMSE

R2

RMSE

R2

RMSE

R2

RMSE

R2

RMSE

MLP1 MLP2

0.141 0.167

0.909 0.895

0.325 0.298

0.805 0.821

0.445 0.496

0.702 0.682

0.603 0.607

0.594 0.576

0.632 0.696

0.473 0.431

MLP3

0.236

0.857

0.338

0.805

0.495

0.679

0.611

0.572

0.703

0.426

MLP4

0.252

0.848

0.353

0.789

0.508

0.661

0.618

0.568

0.715

0.414

so the aim is to shift towards Newton's method as quickly as possible. Thus, μ is decreased after each successful step (reduction in performance function) and is increased only when a tentative step would increase the performance function. In this way, the performance function will always be reduced at any iteration of the algorithm (Kisi 2007).

3 The case study and relevant data Iran is located in the Middle East, between Iraq and Pakistan. Iran lies between 45–63° East longitude and 25–40° North latitude and is surrounded by the Caspian Sea in North, the Oman Sea, and the Persian Gulf in South. Similar with the other Middle East countries, droughts are also common in Iran. More than 75% of the country's area has been classified as arid or semi-arid (Tabari et al. 2011a). It must be noted that there is variation in the quantity of precipitation in Iran. The mean annual rainfall for Iran is less than one third of the world average. The long-term mean annual rainfall in the country ranges from below 100 mm to exceeding 1000 mm. For this purpose, five synoptic stations located in different climatic regions were selected (Fig. 1). These stations are among the official sites maintained by the Iranian Meteorological Organization, and all necessary data can be accessed via http://www.weather.ir site. The selected stations for this study mostly have 39- to 53-year records and represent a very good spatial distribution over the region (Fig. 1). Also, geographical location and relevant information pertaining to each station are given in Table 2. As noted in Table 2, the De Martonne aridity index (De Martonne 1942) was used to classify climatic conditions of the stations. Table 5 The performance of all the MLP models in validation phase for Iran Shahr station

SPI9

Station

MLP1 MLP2 MLP3 MLP4

SPI3

Because the signature of the North Atlantic Oscillation (NAO) is strongly regional, a simple NAO index has been defined as the difference between the normalized mean sealevel pressure anomalies at locations representative of the relative strengths of the Azores High (AH) and Icelandic Low (IL). A lower-than-normal (higher-than-normal) IL and higher-than-normal (lower-than-normal) AH result in an enhanced (reduced) pressure gradient and a positive (negative) NAO index (Cullen et al. 2002). The Southern Oscillation Index (SOI) is an index which is used to quantify the strength of an El Nino Southern Oscillation (ENSO) event. It is calculated as the difference between the sealevel pressure at Tahiti and Darwin, Australia (Philander 1990). The monthly values of the SOI and NAO have been obtained from the Internet at www.cru.uea.ac.uk/cru/data.

4 Results and discussion 4.1 Development of drought forecasting models Establishing the appropriate ANN architecture is the main issue in setting up the ANN. There exists no systematic way by which to establish a suitable ANN architecture. Networks that are too small and simple can lead to the under-fitting, while networks that are too complex tend to over-fit the training pattern (Dawson and Wilby 1998). In this study, in order to determine the optimum input combination to the network, various epochs and neuron numbers are examined. Through this process, extracted training and testing records with various proportions are used. The architecture that produced the smallest error is used for the development of networks employed to perform drought forecasting. For cases 1 through 4 (MLP1 to MLP4), the neuron numbers

SPI6

SPI9

SPI12

SPI24

R2

RMSE

R2

RMSE

R2

RMSE

R2

RMSE

R2

RMSE

0.155 0.163 0.184 0.242

0.947 0.943 0.931 0.898

0.447 0.549 0.481 0.519

0.881 0.862 0.854 0.823

0.545 0.669 0.688 0.764

0.875 0.745 0.725 0.630

0.798 0.827 0.814 0.870

0.613 0.567 0.588 0.493

0.830 0.908 0.913 0.920

0.577 0.425 0.413 0.397

Author's personal copy MLP-based drought forecasting in different climatic regions Table 6 The performance of all the MLP models in validation phase for Kermanshah station

Station

SPI3

411

SPI6

SPI9

SPI12

R2

RMSE

R2

RMSE

R2

RMSE

R2

RMSE

R2

RMSE

MLP1 MLP2

0.111 0.144

0.986 0.967

0.266 0.338

0.831 0.789

0.317 0.421

0.765 0.704

0.365 0.615

0.696 0.543

0.459 0.628

0.471 0.389

MLP3

0.147

0.965

0.318

0.802

0. 395

0.725

0.562

0.579

0.629

0.389

MLP4

0.195

0.939

0.404

0.749

0.440

0.693

0.656

0.512

0.708

0.346

in input layer are 6, 7, 7, and 8, respectively. Furthermore, the optimum numbers of neuron in hidden layer for all models are 10. Finally, one neuron in the output layer is selected to train and test the models. The target error for the training of networks is set to 0.0001, with 50 iterations for all of four models. The training of the networks is stopped when their performances reached the target error. The best proportion of data was 70% for training and 30% for validation. It should be noted that tansig and purelin activation functions were used in hidden and output layers, respectively. The normalized data are employed to train each of the four MLP models, all of which being three-layered networks.

In this study, drought (SPI values) forecasting by using MLPs is considered. Four different cases are constructed using the SPI values with time lags, precipitation (P) data, and their lag, NAO and SOI values. The SOI and NAO indices are two predictants most commonly used in mediumrange climate forecasting (Hurrell 1995; Nicholson and Selato 2000; Trenberth and Caron 2000). The ENSO is an anomalous large-scale ocean–atmosphere system associated with strong fluctuations in ocean currents and surface temperatures. NAO is the dominant mode of winter climate variability in the North Atlantic region ranging from central North America to Europe and much into Northern Asia. ENSO and NAO have different impacts on climate throughout the globe (Morid et al. 2007). The models used in this study are listed below:

SPIðt þ 1Þ ¼ f ðSPIðtÞ; SPIðt  1Þ; SPIðt  2Þ; SPIðt  3Þ; PðtÞ; Pðt  1ÞÞ SPIðt þ 1Þ ¼ f ðSPIðtÞ; SPIðt  1Þ; SPIðt  2Þ; SPIðt  3Þ; PðtÞ; Pðt  1Þ; NAOÞ SPIðt þ 1Þ ¼ f ðSPIðtÞ; SPIðt  1Þ; SPIðt  2Þ; SPIðt  3Þ; PðtÞ; Pðt  1Þ; SOIÞ SPIðt þ 1Þ ¼ f ðSPIðtÞ; SPIðt  1Þ; SPIðt  2Þ; SPIðt  3Þ; PðtÞ; Pðt  1Þ; NAO; SOIÞ The performance of each of these input vectors is evaluated using the root mean square error (RMSE) and coefficient of determination (R2). Before applying the ANN algorithm, the data is normalized to [0.05, 0.95] using the following transformation function (Soroosh et al. 2005; Rezaeian-Zadeh et al. 2010): r Xmin Xn ¼ 0:05 þ 0:9 XXmax Xmin

ð8Þ

where, Xn and Xr are the normalized input and the original input; Xmin and Xmax are the minimum and maximum of input data, respectively. Table 7 The performance of all the MLP models in validation phase for Mashhad station

SPI24

Station

MLP1 MLP2 MLP3 MLP4

SPI3

ðCase 1Þ ðCase 2Þ ðCase 3Þ ðCase 4Þ

A related subject is the choice of transfer function. The most commonly used transfer functions are the logistic sigmoid and tangent functions. Wang et al. (2006) pointed out that the training of ANNs with the logistic sigmoid function is more difficult than that of ANNs with the tangent function. Maier and Dandy (1998) also showed that not only is the training with the tangent function faster than the training with the logistic sigmoid transfer function, but the predictions obtained using networks with the tangent are slightly better than those with the logistic sigmoid transfer functions. Kalman and Kwasny (1992) indicated mathematically that the tangent function possesses particular properties that make it appealing for use while training. Therefore,

SPI6

SPI9

SPI12

SPI24

R2

RMSE

R2

RMSE

R2

RMSE

R2

RMSE

R2

RMSE

0.089 0.123 0.133 0.137

0.937 0.919 0.914 0.912

0.189 0.235 0.217 0.237

0.845 0.821 0.834 0.820

0.409 0.495 0.499 0.585

0.687 0.635 0.632 0.576

0.653 0.716 0.699 0.730

0.532 0.481 0.496 0.469

0.693 0.774 0.760 0.802

0.531 0.456 0.469 0.427

Author's personal copy 412

M. Rezaeian-Zadeh, H. Tabari

Fig. 2 The observed and predicted values of SPI12 using MLP4 in the validation phase for Iran Shahr station

single hidden layer with tangent sigmoid function was used in the current study. 4.2 Drought forecasting The results of the MLPs models for the climatic regions are presented in Tables 3, 4, 5, 6, and 7. The evaluation of constructed models showed that the prediction results related to case 4 (MLP4) had the lowest error (higher R2 values and lower RMSE values) among the entire models. It's interesting to express that addition of NAO and SOI as input variable to the MLPs improved the prediction efficiency of the models so that in the fourth model (MLP4) the best results were obtained. So, in this study, the results of MLP4 are discussed. As it is obvious from the obtained results, the prediction efficiency of the SPI12 and also the SPI24 are higher than the other SPIs. For SPI24 and in the whole surveyed stations, the RMSE values are less than 0.5 showing that the MLPs can predict the SPI24 superior to the other SPIs. The related values of R2 confirm this achievement. The achieved results indicated that the MLP4 for all of the stations was applicable and it would recommend for new researches in the same climatic conditions. Evaluation of SPI12 expressed that Iran Shahr (Arid region) and Mashhad (Semi-Arid

region) stations had more satisfactory results in comparison to the other stations (Tables 3, 4, 5, 6, and 7). On the other hand, Bandar Anzali with a very humid climatic condition had the highest RMSE value (equal to 0.568) and it showed that MLPs in arid and semi-arid regions had better results in the predictions but there were no noticeable differences between the results and generally, the MLPs depicted their abilities to capture the SPI variations. For SPI24, Kermanshah and Iran Shahr stations are predicted superior to the others by using the developed MLPs. It should be noted that the RMSE values of Kermanshah was equal to 0.346 and it was lower than 0.397 (for Iran Shahr) while R2 value of Iran Shahr was higher than the other one. In the mentioned time scale (SPI24), the prediction results related to Bandar Anzali (very humid region) is better than Abadan (arid region) station. So, there is no significant improvement in the application of MLPs for drought forecasting when studying the stations located in different climatic regions. Figures 2 and 3 display the variations of observed and predicted values related to SPI12 for the validation phase of MLP4. Based on the findings related to this study, ANNs have the strong ability to capture the variations of SPIs in different time series especially in SPI12 and SPI24.

Fig. 3 The observed and predicted values of SPI12 using MLP4 in the validation phase for Mashhad station

Author's personal copy MLP-based drought forecasting in different climatic regions

5 Conclusions In this study, four MLPs are applied and optimized using Levenberg–Marquardt training algorithm with a tangent sigmoid activation function to forecast quantitative values of SPI of drought at five synoptic stations in Iran located in different climatic regions. The MLPs for SPIs with the one month lead time forecasting, were tested and validated. Four different input vectors were considered during network development. In the first model, MLP constructed by importing antecedent SPI with 1-, 2-, 3-, and 4-month time lags and antecedent precipitation with 1- and 2-month time lags (MLP1). Addition of antecedent NAO or antecedent SOI with 1-month time lag or both of them to MLP1 led to MLP2, MLP3, and MLP4, respectively. It's interesting to express that addition of NAO and SOI as input variable to the MLPs improved the prediction efficiency of the models so that in the fourth model (MLP4) the best results were obtained. The prediction efficiency of the SPI12 and also the SPI24 are higher than the other SPIs. For SPI24 and in the whole surveyed stations, the RMSE values are less than 0.5 and it's expressing this issue that the MLPs can predict the SPI24 superior to the other SPIs. Based on the findings related to this study, ANNs have the strong ability to capture the variations of SPIs in different time scales especially SPI12 and SPI24.

Acknowledgments The authors wish to express a gratitude to the Islamic Republic of Iran Meteorological Organization (IRIMO) for access to the weather station data.

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