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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 30, 2016

A hybrid downscaling approach for the estimation of climate change effects on droughts using a geo-information tool. Case study: Thessaly, Central Greece

  • John Tzabiras EMAIL logo , Athanasios Loukas and Lampros Vasiliades
From the journal Open Geosciences

Abstract

Multiple linear regression is used to downscale large-scale outputs from CGCM2 (second generation CGCM of Canadian centre for climate monitoring and analysis) and ECHAM5 (developed at the Max Planck Institute for Meteorology), statistically to regional precipitation over the Thessaly region, Greece. Mean monthly precipitation data for the historical period Oct.1960-Sep.2002 derived from 79 rain gauges were spatially interpolated using a geostatistical approach over the region of Thessaly, which was divided into 128 grid cells of 10 km × 10 km. The methodology is based on multiple regression of large scale GCM predictant variables with observed precipitation and the application of a stochastic time series model for precipitation residuals simulation (white noise). The methodology was developed for historical period (Oct.1960–Sep.1990) and validated against observed monthly precipitation for period (Oct.1990–Sep.2002). The downscaled proposed methodology was used to calculate the standardized precipitation index (SPI) at various timescales (3-month, 6-month, 9-month, 12-month, 24-month) in order to estimate climate change effects on droughts. Various evaluation statistics were calculated in order to validate the process and the results showed that the method is efficient in SPI reproduction but the level of uncertainty is quite high due to its stochastic component.

1 Introduction

It is generally accepted that the increasing concentrarion of greenhouse gases in the atmosphere will very likely lead to the change of climate. Globally averaged mean evaporation, temperature, and rainfall intensity will likely increase in response to increased concentration of greenhouse gases [13]. This shift toward higher global temperature and more intense rainfall is of great concern for assesing climate change impacts on water resources due to potential effects on extreme events such as floods and droughts. The risk of increase in the frequency of extremes is clear but the potential consequenses in particular regions need to be assessed [46]. This is required because such information may lead to practices that should be taken in order to protect local societies from such probable catastrophic environmental changes.

In the case of drought, despite the extended research in the context of hydrology and water resources, this water shortage is still major issue in many regions around the world. Generally, drought is related with a prolonged period of low soil water content and low water supply relative to the normal levels that human societies are used. Especially for hydrological drought, there is abundant evidence that water streams are inadequate to supply specific water uses within the boundaries of an existing water resources management system. Consequently, climate change impact studies should provide a reliable estimation of droughts in a manner that can be used to decision makers to develop emergency plans or other measures for the confrontation of this phenomenon.

General circulation models (GCMs) are the main tools today for simulating present and future climate conditions. These models have shown their efficiency to simulate the large-scale variables of historical climate which is why they are widely employed to study the impacts of greenhouse gases increasing concentration on the global climate. GCMs include representations of surface hydrology, sea ice, cloudiness, convection, atmospheric radiation and other processes [7]. Though differences between model formations may exist, most models project relevant results on a global extent. However, in regional climate schemes, restrictions and large discrepancies are detected among models.

A common approach for bridging the scale gap is downscaling, both statistical and dynamical. Statistical downscaling is based on the use of observed relationships between the global-scale climate variable (predictor) and the local-scale climate variable (predictand) for a projection of GCM output on a regional scale. However, dynamical downscaling is mainly based on the development of regional climatic models (RCMs) with resolution finer than that of GCMs in order to have a much more representative view of regional climate conditions. RCMs usually have 25 × 25 km or 50 × 50 km grid-scale and therefore are not recommended for accurate analysis at lower scales. Although there are applications related criteria that contribute to an appropriate choice of downscaling method in a certain context [7, 8], the advantages of the statistical approaches are that they are easy to implement, computionally costless and calibration to the local extent is a basic part of the procedure [9].

Most general circulation models predict a significant change in precipitation and observations of precipitation shifts indicate reduced winter rainfall and increased variability [10, 11]. There is evidence that such changes are now obvious in low flows and hydrologic droughts. Limited research has been conducted on drought based on meteorological drought indices, which require less input data when compared to weather, soil and land use information needed by meteorological, hydrologic, agrohydrologic and water management models, have been performed [1218]. In this paper a statistical downscaling methodology was applied to CGCM2 and ECHAM5 outputs in order to achieve a reliable way of projecting droughts at local extent and particularly over the region of Thessally, Greece. Multiple linear regression (MLR) models were calibrated and verified for the periods 1960–1990 and 1990–2002 with 10 × 10 km grid resolution. Indeed, the MLR models were improved by use of multivariate autoregressive models for simulation of the residuals (white noise), thereby developing a new hybrid technique based on stochastic hydrology [18]. The novelty of the paper lies on the combinational use of MLR models and multivariate models for the treatment of the residuals to spatially downscale the precipitation. This study also targets in the estimation of drought characteristics at a grid 10 × 10 km, which is considered adequate for the estimation of the spatial variation of the phenomenon of drought because it captures the micro-climatic variations. The downscaled precipitation was used to calculate the standardized precipitation index (SPI) at various timescales (3-month, 6-month, 9-month, 12-month, 24-month) for the estimation of climate change effects on droughts.

2 Study area and data base

Thessaly is a plain region located in Central Greece (Figure 1a). surrounded by Mount Kisavos and Mount Pelion in the east, along the coast of the Aegean Sea, Mount Olympus in the north, the Pindus Mountain Range in the west, and the Othrys Mountain Range in the south. Thessaly’s total area is about 13 700 km2. The elevation ranges from sea level at the eastern coastal area to more than 2800 m. Thessaly lies between latitude 400941 to 385840 N and longitude 211219′′ to 232219′′. Mean annual precipitation over the whole Thessaly region is about 700 mm and it is distributed unevenly in space and time. The mean annual precipitation varies from about 400 mm at the central plain area to more than 1850 mm at the western mountain peaks. Generally, rainfall is rare from June to August and temperature is extremely high, making Thessaly one of hottest regions all over Greece. The Thessaly plain is the most productive agricultural region of Greece with an area of about 4000 km2 (Figure 1a). The main crops cultivated in the plain area are cotton, wheat and maize whereas apples, apricots, cherries, grapes and olives are cultivated at the foothills of the eastern mountains. The Pinios River and its tributaries traverse the plain area and the basin total drainage area is about 9500 km2 (Figure 1b). Thessaly experienced severe, extreme and persistent droughts during the period from mid to late 1970s and the period from late 1980s to early 1990s and the first years of 2000s. The prolonged and significant decrease of monthly and annual precipitation has had a dramatic impact on water resources of the region. Usually, the dry periods are accompanied with high temperatures, which lead to higher evapotranspiration rates and dry soils. These conditions inversely affect both the natural vegetation and the agriculture of the region as well as the water resources. Severe and extremely dry conditions result in irrigation cutbacks, overexploitation of groundwater and significant losses of crop yields [19].

Figure 1 a) Digital elevation model (DEM) of Thessaly region b) Locations of precipitation stations
Figure 1

a) Digital elevation model (DEM) of Thessaly region b) Locations of precipitation stations

In Greece, especially in Central Thessaly, the major methodological drawback for a long-term assessment of regional climate and its variability results from the lack of suitable observations or simulated data. Although global reanalyses have been created to overcome this obstacle (e.g. CORDEX and others) [3,4], the coarse spatial resolution of global reanalysis make these data sets inadequate tool to characterize regional, prevailing atmospheric conditions over areas where orography and land-sea contrasts are valuable [5]. Hence, the database in this study consisted of observed monthly precipitation values from 78 rain gauges from the Greek National Meteorological Agency and other governmental organizations for 42 hydrological years located across the region of Thessaly (October 1960 to September 2002). The data were processed and homogenised.

3 Methods

In this study, the second generation GCM (CGCM2) of the Canadian centre for Climate Monitoring and Analysis was one of the GCMs that were used for the choice of predictor variables in downscaling procedure, with a spectral model with resolution 3.75 latitude and 3.75 longitude with a global grid box size approximately 300 × 400 km, or 120,000 km2 [2022]. The model has10 atmospheric layers and is based on improvements of the former generation model CGCM1. The ocean component is based on the Geophysical Fluid Dynamics Laboratory MOM 1.1 model and has a resolution of roughly 1.8 of latitude by 1.8 of longitude and 29 vertical levels. The second GCM used in this study was the fifth-generation atmospheric general circulation model (ECHAM5) developed at the Max Planck Institute for Meteorology and is a relatively recent version in a series of ECHAM models evolving originally from the spectral weather prediction model of the European Centre for Medium Range Weather Forecasts [23]. ECHAM5 was run at T63 spectral resolution, which corresponds to a horizontal grid spacing of approximately 140 × 210 km grid spacing at mid-latitudes. Compared to the previous version, a number of substantial changes have been done in both the numerics and physics of the ECHAM4 model. These include denite positive variables like water components and chemical tracers, a new longwave radiation scheme, separate prognostic equations for cloud liquid water and cloud ice, a new cloud microphysical scheme and a prognosticstatistical cloud cover parameterization.

The methodology proposed in this paper and applied to Thessaly region consisted of the spatial distribution of the observed precipitation values into 128 grid cells of 10 × 10 km using ordinary Kriging, cluster analysis of gridded precipitation data, development of statistical downscaling model for mean monthly precipitation and the simulation of the residuals by a hydrological stochastic model.

3.1 Spatial distribution of observed precipitation

Observed monthly precipitation data from 78 rain gauges for 42 hydrological years (October 1960 to September 2002) were spatially distributed into 128 grids of 10 × 10 km using a geostatistical technique. An ordinary Kriging based model was applied to the rainfall data as it is described by the formula below:

(1)Pso=i=1NλiPsi

where P(si ) is the measured precipitation value at the rain gauge ith, λi an unknown weight for the measured precipitation value at the ith rain gauge, so is the prediction grid cell, P (so) is the predicted precipitation at so grid cell and N is the number of observed values [24]. Observation data were transformed into normal distribution using Box-Cox transformation:

(2)Ps=psλ1λ,λ0

where p (s) is the observed precipitation value and P (s) is the tranformed value.

Precipitation data are measurements of a variable for a given study area. In such data samples there is a strong relation between mean values and variation. Consequently, when values in a region are quite low, variability will be smaller compared to another region where precipitation values are higher. In these cases, it is well known that when λ = 1/2, fluctuations become more constants for the whole region of interest [25]. A geographical information system was used for the spatial distribution of observation data per month of each year for the hydrological period October1960- September 2002 and Gaussian models were used for the semi-variogram development. It should be mentioned that box-cox transformation allowed variances between data to become more constant throughout the study area and the data closer to normal distribution. This smoothing of the data set enhanced the use of isotropic semi-variograms. The spatial variation is quantified by the semivariogram. The semivariogram is estimated by the sample semivariogram, which is computed from the input point dataset. The value of the sample semivariogram for a separation distance of h (referred to as the lag) is the average squared difference in z-value between pairs of the input sample points separated by h. The sample semivariogram was calculated from the sample data with the equation (3):

(3)γh=c0+c1eh2r2

where c0 is the sum of observation errors and low scale variation while both is likely to be zero, so the c0 value may be exported completely from one or another, especially where c is the point on y-axis in which the semivariogram is stabilized. Every model that was applied for each month of each year was calibrated separately and c0, c parameters were estimated in respect to the verification results of each model.

Semi-variograms portray spatial autocorrelation of an observation sample. In order to develop an empirical semivariogram, one should define the square difference of values in all pairs. Spatial autocorrelation quantifies the hypothesis that things which are close to one another present similar characteristics, contrary to those that are found at a longer distance. This can be shown on a semi-variogram with values approaching axis y and present resemblances or equivalent with values that are removed at axis x and indicate large square difference. During semi-variogram development, many points that exist should be grouped into pairs of points and then the groups of pairs with similar distance must be formated. In semi-variogram map charts, these groups may be grid cells that represent points with common characteristics and which are used for the calculation of empirical semi-variograms. In this study, semivariogram map charts were developed where each group was a grid cell of 10 × 10 km that covered the wider region influenced by the rain gauges and each grid cell had a value of precipitation. However, the geographical data base is supported by the digital elevation model of the study area at 10 × 10 km grid resolution and a modification of the method was adopted in order to obtain a rank of 128 grid cells – subareas.

The results showed that for the period October 1960-September 1990, the driest month that the Thessaly region experienced was August 1985 while the wettest was November 1979. However, during the period October 1990-September 2002, the driest month was July 1993 and the wettest was November 1998. Figure 2a and Figure 2b illustrate that during the mean months for both periods, precipitation had similar spatial distribution. On the contrary, Figure 2c and Figure 2d indicated that during November 1979, rainfall oscillated from 100 until 250 mm in Thessaly region grid cells and central grid cells accepted smaller amounts of precipitation than those found at north-eastern as well as some western grid cells with high altitude. November 1998 precipitation variability was higher and the western grid cells accepted the highest amounts of precipitation exceeding 250 mm. Furthermore, for the eastern grid cells, precipitation amounts were between 100–200 mm. In the case of driest month of the period October 1960-September 1990 (August 1985), precipitation oscillated from 0 until 10 mm and it is evident that the north-eastern grid cells experienced the highest quantities of precipitation in opposition to those in the centre where precipitation was quite low. Figure 2f illustrates the spatial distribution of precipitation during July 1993 where the south-western grid cells of Thessaly region experienced precipitation amounts that exceeded 5 mm.

Figure 2 Spatial distribution of observed mean precipitation during a) mean month of development period (Oct.1960-Sep.1990) b) mean month for validation period (Oct.1990-Sep.2002) c) wettest month of development period (Oct.1960-Sep.1990) d) wettest month of validation period (Oct.1990-Sep.2002) e) driest month of development period (Oct.1960-Sep.1990) f) driest month of validation period (Oct.1990-Sep.2002).
Figure 2

Spatial distribution of observed mean precipitation during a) mean month of development period (Oct.1960-Sep.1990) b) mean month for validation period (Oct.1990-Sep.2002) c) wettest month of development period (Oct.1960-Sep.1990) d) wettest month of validation period (Oct.1990-Sep.2002) e) driest month of development period (Oct.1960-Sep.1990) f) driest month of validation period (Oct.1990-Sep.2002).

The purpose of this study is the verification of a hybrid downscaling methodology based on statistical downscaling and stochastic hydrology in order to propose new ways of capturing the global climate signal by downscaling it to the local extent and overcoming uncertainty obstacles. Furthermore, the aim was to investigate if this method is efficient in estimating droughts at local extent. This statistical downscaling methodology was developed using the outputs of the Canadian Centre for Climate Modeling Analysis (CCCma) General Circulation Model (CGCMa2) and the Max-Plank Institute for Meteorology (MPIM) General Circulation Model (ECHAM5) for the base historical period (1960–1990) and validated against observed precipitation for the period 1990–2002. The methodology applied in this study is presented in the next paragraphs.

3.2 Cluster analysis

It is acknowledged that cluster analysis is the procedure where the initial data are being separated into clusters in a way that data which are part of the same cluster present similar characteristics in oppotition to data that are part of another cluster [26]. As mentioned, the historical precipitation data were spatially distributed into 128 grids of 10 × 10 km over the study area by use of ordinary Kriging. The development of a statistical downscaling model in each grid is computationally expensive, therefore cluster analysis was applied to the gridded precipitation data. Principal components (PCs) analysis was used for factors or variables which can explain why the variance’s formula may be found in the data sets. Generally, principal components analysis (PCA) is applied for the reduction of data size and for detection of a small number of factors that have almost the same variance with a much larger number of variables. In this method, a formulation of linear combinations of variables is employed in a way that the first extracted component explains the main percentage of variance while those that follow explain gradually smaller variance. Six PCs were retained for the precipitation data, which explained a total variance of at least 91.2% and four PCs were extracted for the temperature data, which explained variance of 93.8%. However, a different selection of variables may lead to diffirent number of ‘statistically significant’ factors. Hence, the PCs were retained by the conjuction of the ‘eigenvalue-greater-than-one’ rule with a ‘scree plot’ (eigen values versus the PCs number). The extracted PCs were rotated using the ‘Varimax Criterion’, which is an orthogonal rotation method minimizing the number of variables that are of great weight on the factors, which allows the simpler explaining of total variance across the data set.

Although the number of clusters in each data set was identified, k-means clustering was employed for the classification of all grid cells. The restraint is that the exact number of clusters must be determined before the algorithm procedure [27]. The algorithm starts by choosing K random grids as centers of the clusters and classifies each grid to the cluster with the nearest (smaller distance) center. Hence, for all clusters the average of grids is computed and the new center of the cluster is formed. The two last steps are used for a pre-defined number of steps or until no change appears in the division of grids into clusters. In this way, six clusters for the rainfall data set were formed consisting of 128 grids of the Thessaly region. In Figure 3a, the spatial distribution of precipitation clusters is presented. It is evident that the results of cluster analysis appeared in rational form if the geomorphology of Thessaly region is taken into consideration. The northern part of Thessaly is known as an area with high altitude and microclimatic shceme far too different than the north-eastern and eastern part which are saturated by the Aegean Sea. However, in the central part where the main agricultural plain is located, the elevation is much lower and weather conditions are drier. In the southern and western part of Thessaly, which consists of mountains and areas with high altitude zones, two separate clusters were rationally formed.

Figure 3 Spatial presentation of six formed clusters (cluster analysis) for Thessaly region (the colors of the clusters follow the logical assumption of the altitude and the variation of precipitation in each cluster. Hence the darker cluster has the highest altitudes and precipitation variations).
Figure 3

Spatial presentation of six formed clusters (cluster analysis) for Thessaly region (the colors of the clusters follow the logical assumption of the altitude and the variation of precipitation in each cluster. Hence the darker cluster has the highest altitudes and precipitation variations).

3.3 Proposed downscaling methodology

The procedure is based on the development of empirical relationships between the large-scale climatic variables, the predictors and local scale mean monthly precipitation, the predictand. In this study, the CGCM2 and ECHAM5 outputs were downscaled using multiple regression equations between GCM predictor output variables and the monthly precipitation average in each of the formed clusters. The historical data were divided into a development set and an independent validation set. The equations were developed using the 1960-1990 period and a validation period for years 1990–2002 was used to test the results against the observed data. The predictors used in such analyses should be: a) well simulated by the GCM, b) strongly correlated with the predictand variable (precipitation), and c) available. The above criteria and forward selection stepwise regression were used in order to determine the predictor variables [28, 29]. Geopotential thickness between 500 and 1000 hpa (GZ500-1000) and the mimimum daily surface temperature (Stmin) were the predictor variables choosen for precipitation downscaling. This means that from all the accessible variables (namely all the variables provided from the model institute), two were finally chosen for CGCM2 output. In order to obtain comparable results for ECHAM5 output, the same two variables cited were used. These are some of the most commonly used predictors in statistical downscaling of precipitation and temperature [30]. In addition, dummy variables (a set of twelve categorical variables assigned to the 12 months of the year) were used to account for the effect of the “month” on precipitation.

A major issue during this study was whether to develop one regression model for each cluster and have six downscaling models for precipitation data, or a single generalized multiple linear regression (GMLR) model that could perform the same in all clusters. Table 1 illustrates there are no ‘statistical significant’ descrepancies for the correlation coeficient when the downscaling procedure is based on one general model for all the clusters or when one model for each cluster is used. Hence, one (GMLR) downscaling model containing monthly dummy variables was employed and it is expressed as:

(4)PGMLR=a1b1+a2b2+a3b3++a12b12+a13GZ5001000+a14STmin+c

Table 1

Correlation Coefficients of (MLR) downscaling models and (GMLR) downscaling model for precipitation data compared with observed values at development and validation periods by use of CGCM2 and ECHAM5 outputs.

ClusterCorrelation Coefficient
Multiple linear Regression (MLR) modelGeneralized Multiple

Linear Regression

(GMLR) model
Multiple linear Regression (MLR) modelGeneralized Multiple

Linear Regression

(GMLR) model
a)CGCM2b)ECHAM5a)CGCM2b)ECHAM5
Development period Oct 1960 - Sep 1990
10.310.310.300.30
20.40.410.400.40
30.420.420.410.41
40.430.420.420.42
50.590.590.580.58
60.520.520.510.51
Validation period Oct 1990 - Sep 2002
10.290.290.280.31
20.430.450.450.44
30.470.480.480.47
40.440.440.430.44
50.580.560.560.58
60.490.50.490.49

Where PGMLR is the logarithmically transformed monthly precipitation, b1, b2, b3, . . . , b12 are the monthly weighting dummy variables for precipitation. The regression coefficients are a1, a2, a3, . . . , a12 and c is the regression constant. Dummy variables, b1b12 are assigned binary values, 0 or 1, depending on the month in which precipitation is referred. For example, if the month is October, then, b1 take the value of 1 and all the other dummy variables, b2-b12 take the value of 0. Similarly, if the month is November, then, b1 take the value of 0, b2 take the value of 1 and all the other dummy variables, b3b12 take the value of 0 and so on.

GMLR model mean cluster projections and observed mean cluster values were different and this error was defined as residual (Pres). In this study, to preserve the observed time series pattern, the estimated precipitation was combined with the residual values of the regression. In many climate impact assessments, the variance of the downscaled time series should be the same with the variance of the observed values. However, in order to estimate the uncertainty of the downscaling method stochastic time series modelling was applied for the treatment of the residuals.

Stochastic simulation of precipitation is based mainly on mathematical models. For this purpose, several stochastic models have been proposed [31, 32]. Application of one type of model or different for a case study depends on various factors as physical and statistical characteristics of the process taking place, system’s complexity and naturally the aim of the study [33, 34]. For historical periods reproduction of historical statistics is a crucial issue. For this reason, a basic step in such simulations is time-series analysis. Since the model is selected, model parameters are being calibrated and finally the model is being tested [35].

The basic steps of the process are defined as follows:

  1. PGMLR refers to mean cluster precipitation described by the equation below:

    (5)Pcluster=1ni=1nPgridi,gridiisthegridnumber

    (number of classification in each cluster)

  2. Calculation of cluster precipitation residuals based on following equation:

    (6)Pres,cluster=PclusterPGMLR,cluster
  3. Calculation of gridded precipitation residuals according to equation:

    (7)Pres,grid=PgridPcluster
  4. Simulation of Pres,cluster using a stochastic model. Given that in Thessaly region six clusters were extracted a main issue lied in whether to use six different stochastic models or one for all clusters. Consequently, due to practical reasons and calculation economy a type MPAR (p) model (Multivariate Periodic Autoregressive Model) was employed. The best fitted model, according to Akaike Information Criterion (AIC), was the Multivariate Periodic Autoregressive Model of order two (2), MPAR(2) defined for 6 points (clusters) as:

    (8)Pres,u,t=i=12Φι,τPu,t1+Eu,t

    where Pres,u,t is a 6 × 1 matrix that represents the mean cluster precipitation for year u and period t. Factor Φι,τ, is the 6 × 6 periodical matrix of autoregressive parameters and Eu,tis the matrix 6 × 1 of normally distributed noise with mean zero and variance στ2.

  5. Several statistics were estimated to evaluate Eq. (8) in simulating residual monthly precipitation for development and validation periods and then Eq. (8) was applied stochastically to generate 100 time series of the Pres,cluster.

    The calculated cluster residual precipitation time series were added to the downscaled PGMLR to reproduce the observed monthly cluster precipitation pattern according to equation (9):

    (9)Pcluster=PGMLR+Pres,cluster

    Finally, the gridded precipitation residuals were added to Pcluster using Eq. (10), assuming that they retain in the future the same statistical characteristics of the historical period.

    (10)Pgrid=Pcluster+Pres,grid

3.4 Standardized Precipitation Index (SPI)

Many indices have been used for the identification of more than one type of drought [36, 37] and their categorization may not be appropriate, although it is widely used [38, 39]. The Standardized Precipitation Index (SPI) has been developed by McKee and his associates (1993) for defining and monitoring droughts [40]. It is used, among others, by the U.S. Colorado Climate Center, the U.S. Western Regional Climate Center, and the U.S. National Drought Mitigation Center to monitor drought in the United States. The main advantage of the SPI is that can be calculated for multiple time-scales. This is very important because the timescale over which precipitation deficits accumulate functionally separates different types of drought [41] and, therefore, allows to quantify the natural lags between precipitation and other water usable sources such as river discharge, soil moisture and reservoir storage. Recent studies have used SPI as indicator of hydrological and water resources variables, like soil moisture, surface runoff and reservoir storage [4244]. The U.S. National Drought Mitigation Center computes the SPI with five running time intervals, i.e. 1-, 3-, 6-, 9-, and 12-months, but the index is flexible with respect to the period chosen. This powerful feature can provide an overwhelming amount of information unless researchers have a clear idea of the desired intervals [43].

Computation of the SPI involves fitting a Gamma probability density function to a given frequency distribution of precipitation totals for a station, area or a watershed. The alpha and beta parameters of the Gamma probability density function are estimated for each station, for each timescale of interest (1, 3, 6, 9, 12 months, etc.), and for each month of the year. Table 2 contains the corresponding probabilities of occurrence of each severity arising naturally from the Normal probability density function. Thus, at a given location for an individual month, moderate dry periods (SPI ≤ -1) have an occurrence probability of 15.9%, whereas extreme dry periods (SPI ≤ -2) have an event probability of 2.3%. Extreme values in the SPI will, by definition, occur with the same frequency at all locations. Negative SPI values indicate droughts and positive SPI values denote wet weather conditions (Table 2).

Table 2

Drought classification by SPI values and corresponding event probabilities.

SPI valueCategoryProbability (%)
2.00 or moreExtremely wet2.3
1.50 to 1.99Severely wet4.4
1.00 to 1.49Moderately wet9.2
-0.99 to 0.99Near normal68.2
-1.49 to -1.00Moderately dry9.2
-1.99 to -1.50Severely dry4.4
-2 or lessExtremely dry2.3

In this study, the gridded observed monthly precipitation was used for the estimation of the monthly SPI for 1-month, 3-month, 6-month, 9-month, 12-month, and 24-month timescales, during the development and validation period over Thessaly region. As mentioned, Greece, and especially Thessaly, experienced severe, extreme and persistent droughts during the periods from mid to late 1970s, from late 1980s to early 1990s and the first years of 2000s. These three drought periods were quite remarkable and affected large areas. The first drought episode (1976–1977) affected southern and western Europe, the second drought episode (1988–1991) affected the whole Mediterranean Region with an estimated economic cost lager than 2.1 billion Euros, whereas the third drought episode(2000–2001) affected Central Europe and the Balkans with total damage of 0.5 billion Euros [44]. During these three periods monthly and annual precipitation was significantly below normal in Thessaly. The prolonged and significant decrease of monthly and annual precipitation has a dramatic impact on natural vegetation, agricultural production and the water resources of the region.

Figure 4 shows the spatial distribution of the SPI index during a selected period (May 1977–August 1977) of the 1976–1977 drought episode. It is obvious that for May 1977 the south-eastern part of Thessaly was affected with an extreme way (SPI values < -2) while for the north-western part which is characterized by higher altitudes and lower temperatures this drought event was severe (-1.5 > SPI values > -1.99). During June 1977 the SPI spatial distribution was the opposite, since the north-western part experienced extreme drought while the south-eastern severe. As for July 1977, the situation resembled June 1977 with an exception of a small part located between central and coastal Thessaly in which the drought episode was moderate (-1 > SPI values > -1.49). The north-western part of Thessaly region experienced extreme drought during August 1977 as well, but for the central part the drought event was severe while for the coastal part near Pagasitikos bay was moderate. On the other hand, a selected period (March 1990– June 1990) of 1988–1991 drought episode shows that during March 1990 the north-western part of Thessaly experienced extreme drought events (SPI values < -2) whilst for the south-eastern part of the region the episode was severe (-1.5 > SPI values > -1.99). April 1990 was quite the same to March 1990 with the difference that the area affected by extreme drought event was extended to some grid-cells. As for May 1990, the drought episode climbed down since only a restricted number of grid-cells (some located at the north-eastern part and some at the western part of Thessaly) experienced extreme drought. For the rest of the north-western part of Thessaly the drought event was severe (-1.5 > SPI values > -1.99) whereas for the south-eastern part the episode was moderate (-1 > SPI values > -1.49). Regarding June 1990 extreme drought (SPI values < -2) was confined at a few grid-cells (some located at the north-eastern part and some at the western part of Thessaly) while most of the Thessaly region experienced severe drought events.

Figure 4 Spatial distribution of the observed 6-month SPI index over the region of Thessaly for a) May 1977 b) June 1977 c) July 1977 and d) August 1977.
Figure 4

Spatial distribution of the observed 6-month SPI index over the region of Thessaly for a) May 1977 b) June 1977 c) July 1977 and d) August 1977.

In this paper, the statistically downscaled from the two GCMs (CGCM2 and ECHAM5) and stochastically generated precipitation was used for the reproduction of SPI index both for development and validation period. In this way observed and downscaled SPI time series can be compared and the proposed downscaling methodology may be evaluated in the context of SPI calculation, as well for drought estimation.

4 Results and discussion

In this work mean monthly precipitation was reproduced in 128 grid cells of Thessaly region of 10 km × 10 km resolution by use of Ordinary Kriging for the whole data record of Oct.1960-Sep.2002 period. Spatial analysis of precipitation in the region of Thessaly illustrated dry and wet months and determined grid cell resemblances and descrepancies. These grid cells were grouped by application of cluster analysis and six subareas (clusters) were defined. The proposed method described previously was used, firstly, to downscale the monthly precipitation using information from the two mentioned GCMs (CGCM2 and ECHAM5) and secondly to estimate the standardized precipitation index both for development (1960–1990) and validation period (1990–2002).

4.1 Evaluation of the statistical downscaling procedure

This downscaling method is a combination of generelized multiple linear regression (Eq. 4) and stochastic treatment of the residuals derived from GMLR (Eq. 8). The analysis of the results for the GMLR and MLR has shown that the correlation coefficient, r, between the logarithmically transformed estimated downscaled monthly precipitation and the logarithmically transformed observed monthly clustered precipitation both for development and validation periods has no statistical significant differences. Hence a GMLR model was used where the correlation coefficient was between 0.3 and 0.58 depended on the cluster. These results are comparable with the results of previous studies on statistical monthly precipitation downscaling with more analytical methodologies [45,46] and the results obtained by Loukas et al. (2008) and Vasilliades et al. (2009) with a similar MLR statistical downscaling method for Lake Karla watershed. However, this regression model (Eq. 8) failed to reproduce the variance of precipitation, although simulated quite well the mean monthly precipitation for historical (Table 3) and validation period (Table 4).

Table 3

Evaluation statistics of proposed downscaling method in reproducing the observed historical precipitation for development period (Oct.1960-Sep.1990) based on CGCM2 and ECHAM5 outputs.

ClusterMAE(mm)MAPE(%)RMSE(mm)RMSE(%)CEIAPI
Development period Oct.1960-Sep.1990
CGCM2
10.56810.0120.7850.0960.9980.9990.998
20.85030.0221.3220.1680.9950.9980.996
30.67850.0160.9050.1050.9970.9990.998
40.85330.0201.0970.1290.9910.9970.992
51.4860.0131.8490.1620.9980.9990.998
60.6090.0110.8490.0790.9990.9990.999
ECHAM5
11.1440.0211.5340.1840.9930.9980.995
21.3090.0291.6870.1990.9910.9970.994
31.3790.0361.6360.1940.9920.9980.995
41.2570.0261.5040.1740.9940.9980.996
51.5450.0262.0080.1940.9950.9990.996
61.4020.0281.5750.1670.9960.9990.996

Table 4

Evaluation statistics of proposed downscaling method in reproducing the observed historical precipitation for validation period (Oct.1990-Sep.2002) based on CGCM2 and ECHAM5 outputs.

ClusterMAE(mm)MAPE(%)RMSE(mm)RMSE(%)CEIAPI
Validation period Oct.1990-Sep.2002
CGCM2
10.56810.0120.7850.0960.9980.9990.998
20.85030.0221.3220.1680.9950.9980.996
30.67850.0160.9050.1050.9970.9990.998
40.85330.0201.0970.1290.9910.9970.992
51.4860.0131.8490.1620.9980.9990.998
60.60970.0110.8490.0790.9990.9990.999
ECHAM5
11.1440.0211.5340.1840.9930.9980.995
21.3090.0291.6870.1990.9910.9970.994
31.3790.0361.6360.1940.9920.9980.995
41.2570.0261.5040.1740.9940.9980.996
51.5450.0262.0080.1940.9950.9990.996
61.4020.0281.5750.1670.9960.9990.996

Several evaluation statistics were calculated in order to verify the process. Mean Average Error (MAE), Root Mean Square Error (RMSE), the Coefficient of Efficiency (CE), the Index of Agreement (IA) and the Persistence Index (PI) are described by equations (11), (12), (13), (14) and (15). These statistics were calculated for each cluster in order to examine model efficiency through different geomorphological clusters. On the other hand, a calculation in space meaning the whole study area (Thessaly region) which consists of 128 grid cells would be usefull for a more spherical model evaluation. Hence, MAE and RMSE are statistical criteria that measure the error in real value, in this case milimetres for precipitation. MAE concretely measures the error of estimation while RMSE measures error of variation. The coefficient of efficiency is an estimate of how good a model or a methodology is compared to mean model and if it’s value is negative this means that mean projections are better while zero value means model and mean have the same efficiency and finally, model projections are more accurate when CE has a positive value with the perfect model reaching the value of one. IA is a measure of agreement between observations and model projections while PI is a comparison between proposed and persistense model.

(11)MAE=k=1qPgridPgrid
(12)RMSE=k=1qPgridPgrid2q
(13)CE=1k=1qPgridPgrid2k=1pPgridP¯grid2
(14)IA=1k=1qPgridPgrid2k=1qPgridP¯grid+PgridP¯grid2
(15)PI=1k=1qPgridPgrid2k=1qPgrid,kPgrid,k12

where Pgrid the observed values of precipitation in each grid while where Pgrid are model estimations. P¯grid are mean grid values of observed precipitation though q is the number of monthly values,meaning 360 months for development period nad 144 months for validation period. Foe calculation in space the sum 1ni=1n is added in order to define the number of grids in a cluster (where n is the number of clusters).

(16)MAEspace=1ni=1n1mj=1mk=1q1qPgridPgrid
(17)RMSEspace=1ni=1n1mj=1mk=1qPgridPgrid2q
(18)CEspace=1ni=1n1mj=1m1k=1qPgridPgrid2k=1pPgridP¯grid2
(19)IAspace=1ni=1n1mj=1m1k=1qPgridPgrid2k=1qPgridP¯grid+PgridP¯grid2
(20)PIspace=1ni=1n1mj=1m1k=1qPgridPgrid2k=1qPgrid,kPgrid,k12

Tables 3 and 4 indicate that the process based on CGCM2 output presents slightly higher evaluation statistics compared to that employing ECHAM5 output. Furthrmore an interior analysis among clusters shows that in the case of CGCM2 the method simulates with a better way clusters 1,3 and 6 while for ECHAM5 the results are better in clusters 1,2 and 4. However these divergences are quite low, of 0.1% or less and rationally they may be consired negligible. Particularly, for the development period MAPE (Mean Average Percentage Error) is 1.2% for cluster 1 and RMSPE (Root Mean Error Percentage Error) reaches 9.6% for CGCM2 while for the second GCM (ECHAM5) used these statistics are 2.1% and 18% respectivelly. Cluster 1 consists of grid cells with relativelly high altitude and typical variation of precipitation. At the same period MAPE and RMSPE for cluster 2 which contains grids neighbouring Aegean Sea, reach for CGCM2 up to 2.2% and 16.8% while for ECHAM5 they are slightly higher up to 2.9% and 19.9%. Cluster 3 is a subarea surrounded by sea and these two statistics drop down to 16% and 10.5% for CGCM2 while for ECHAM5 model they maintain higher values of 3.6% and 19.4%. The percentages for cluster 4, where the main cultivating plain lies, were calculated to 2% and 12.9% for CGCM2 while for ECHAM5 2.6% and 17.4%. Cluster 5 contains the grids with the highest altitude and the largest variation of precipitation. In this subarea MAPE and RMSPE were 1.3% and 16.2% for CGCM2 whilst for ECHAM5 they were 2.6% and 19.4% respectivelly. These two criteria for cluster 6 were calculated at 1.1% and 1.9% for CGCM2 and 2.8% and 16.7% for ECHAM5. On the other hand, for validation period the results presented at Table 4 have similar evaluation statistics. MAPE and RMSPE at cluster 1 for CGCM2 are 1.2% and 9.6% while for ECHAM5 they were calculated 2.1% and 18.4%. For cluster 2 they reached 2.2% and 16.8% concerning CGCM2 case whilst for ECHAM5 case they were slightly higher up to 2.9% and 19.9% respectivelly. Similarlly in cluster 3 MAPE is 1.6% andRMSPE 10.5% for CGCM2 model, and for ECHAM5 they were calculated at 3.6% and 19.4%. In cluster 4, these statistics are2% and 12.9% for CGCM2 wlile 2.6% and 17.4% for ECHAM5 model. For cluster 5 they drop down at 1.3% and 16.2% for the first GCM whilst for ECHA% they rise to 2.6% and 19.4% respectively. Finally, for cluster 6 MAPE was calculated at 1.1% and RMSPE at 7.9% for CGCM2 while 2.8% and 16.7% for ECHAM5. Generally, the proposed method has reliable results in all clusters for both GCMs adopted.

As mentioned, stochastic time series methodology was employed for the simulation of the residuals to maintain the variance of observed monthly precipitation. The method of moments (MOM) have been used to estimate the model parameters of the MPAR(2) model. Stocahstic models are considered reliable when they can reproduce the statistical properties of historical time series. These properties may be the mean, standard deviation, skewness, kyrtosis, correlation and extreme values. After the fitting of MPAR(2) model, generated residual time series illustrated that the stochastic models for both cases of CGCM2 and ECHAM5 were slightly underestimating the residual precipitation at summer months (June, July and August). This can be explained rationally by the smaller variaton of precipitation values during summer months. The stochastically generated time series were produced to evaluate the results of the process, and the uncertainty introduced for the historical period. Furthermore, the synthetic residual time series were generated to verify the methodology for the period 1990–2002. These stochastically generated residual precipitation time series for every cluster were added to downscaled PGMLR in order to reproduce the observed monthly cluster precipitation pattern. Figure 5 shows the statistical properties (mean and standard deviation) of the generated sample for the development period (1960–1990) for a random grid cell. Clearly the method is able to reproduce the statistical properties of historical monthly precipitation for historical period. As can be seen the GMLR model failed to generate the standard deviation of observed time series for both cases of CGCM2 and ECHAM either for development period or for validation period. However, the model simulated precipitation satifactorally in most of the months. The use of the stochastic method improved the process by accessing the observed time series uncertainty and in this way the results were remarkable. We can easily assume that these results are presented only for a random grid, and we can have scepticisms about the efficiency of the process when it is applied for all the 128 grid cells of 10 km × 10 km (Thessaly region); for this reason, the evaluation statistics were calculated for each grid separately. Table 2 indicates the calculated evaluation statistics according to equations(16), (17), (18), (19) and (20), for the region of Thessaly. As can be seen, for the development period MAE is 0.84 mm for CGCM2 and 1.34 mm for ECHAM5, while for validation period is higher up to 8.29 mm for CGCM2 and 6.90mm for ECHAM5 (Table 5). Furthermore, RMSE for development period is 1.14 mm for CGCM2 and 1.66 mm for ECHAM5, whereas for validation period reached 10.45 mm for CGCM2 and 8.79 mm for ECHAM5. The rest of the statistics were quite high especially for the development period approaching the value of one but for validation period downscaling proccedure based on the CGCM2 output presented lower statistics in opposition to the grid resolution analysis. This can be explained by the stochastic generation of residual precipitation time series based on MPAR(2) model which was validated for this period and the GMLR model.

Figure 5 Statistical properties of the statistical downscaling procedure for the development period Oct.1960–Sep.1990 at a random grid cell for (a) average monthly precipitation based on CGCM2 output (b) average monthly precipitation based on ECHAM5 output (c) standard deviation of monthly precipitation based on CGCM2 output (d) standard deviation of monthly precipitation based on ECHAM5 output (Note: Box-Whisker plots and average refers to stochastic simulation results. while GMLR are the results from generalized multiple linear regression).
Figure 5

Statistical properties of the statistical downscaling procedure for the development period Oct.1960–Sep.1990 at a random grid cell for (a) average monthly precipitation based on CGCM2 output (b) average monthly precipitation based on ECHAM5 output (c) standard deviation of monthly precipitation based on CGCM2 output (d) standard deviation of monthly precipitation based on ECHAM5 output (Note: Box-Whisker plots and average refers to stochastic simulation results. while GMLR are the results from generalized multiple linear regression).

Table 5

Calculated evaluation statistics for Thessaly region during development period Oct.1960-Sep.1990 and validation period Oct.1990-Sep.2002.

GCMMAERMSECEIAPI
Development period Oct.1960-Sep.1990
CGCM20.841.140.990.990.99
ECHAM51.341.660.990.990.99
Validation period Oct.1990-Sep.2002
CGCM28.2910.450.860.960.87
ECHAM56.908.790.900.970.90

4.2 Reproduction of the standardized precipitation index (SPI)

The 100 synthetically generated monthly precipitation time series were used for the estimation of SPI time series at multiple timescales. The parameters of the gamma distribution, α and β, were assumed unchanged for validation period and their respective values for the development period have been used. Figure 6 shows the comparison of the 3-month, 6-month and 12-month SPI, according to the GCM (CGCM2 or ECHAM5) at hand for a random grid-cell. SPI was calculated for the median and mean of the 100 stochastic time series. The use of average values for Gamma parameters of the 100 generated SPI time series failed to reproduce the observed drought pattern for historical and validation periods (Figure 6) due to the nonlinearity of the accumulated precipitation which increases as timescale increases. However, the use of median values in α and β parameters of the gamma distribution is able to reproduce the historical temporal evolution of SPI time series for all timescales (Figure 6). Indeed, for 3-month timescales the divergence between the median and the mean is not clearly identified but as the timescale rises from 3-month to 6-month or more (9-month, 12-month, 24-month) this difference is magnified.

Figure 6 Comparison of observed SPI time series with simulated SPI time series for a random grid-cell using median and average values of the Gamma distribution parameters. α and β. of stochastically generated SPI time series in reproducing the observed historical precipitation for timescales: a) 3-month. b) 6-month and c) 12-month.
Figure 6

Comparison of observed SPI time series with simulated SPI time series for a random grid-cell using median and average values of the Gamma distribution parameters. α and β. of stochastically generated SPI time series in reproducing the observed historical precipitation for timescales: a) 3-month. b) 6-month and c) 12-month.

The deterministic approach for SPI calculation for a random grid-cell (meaning the observed SPI time series) identifies for the 3-month timescale total number of dry months (SPI < -1) equal to 108 (25 extreme, 24 severe and 59 moderate according to SPI drought categorization) while the mean stochastic approach in the case of CGCM2 indicates 365 dry months (190 extreme, 95 severe and 80 moderate). Median stochastic approach estimates SPI index of 3-month timescale with a more efficient way since the total number of dry months reaches 93 (13 extreme, 24 severe and 56 moderate) and approximates the observed 3-monthtimescale index. As for ECHAM5, the mean stochastic approach presents 371 dry months (198 extreme, 91 severe and 82 moderate according to SPI categorization) while the median stochastic 90 dry months (13 extreme, 27 severe and 50 moderate). Regarding the 6-month SPI, the deterministic approach estimated 85 dry months (16 extreme, 19 severe and 50 moderate) whilst the mean stochastic for the case of CGCM2 indicates 456 dry months (296 extreme, 107 severe and 53 moderate) and the median stochastic 87 dry months (16 extreme, 23 severe and 48 moderate). As for ECHAM5 case, the mean stochastic approach illustrates 464 dry months (313 extreme, 100 severe and 51 moderate) while the median stochastic identified 91 dry months (14 extreme, 24 severe and 53 moderate). Concerning the 12-month SPI, the deterministic approach illustrates 71 dry months (16 extreme, 22 severe and 33 moderate) whereas the mean stochastic approach for the CGCM2 case indicates 474 dry months (401 extreme, 38 severe and 35 moderate) while for the median stochastic 87 dry months (16 extreme, 22 severe and 33 moderate) were estimated. For the ECHAM5 case, mean stochastic approach identified 480 dry months (410 extreme, 39 severe and 31 moderate) while the median stochastic approach illustrated 90 dry months (31 extreme, 29 severe and 30 moderate). It is obvious that the mean stochastic approach underestimates SPI at multiple timescales and as the timescale gets larger, the divergence is getting higher. On the other hand, the median stochastic approach approximates the deterministic approach and we can assume that this process is appropriate for drought estimation. The above analysis was conducted for a random gridcell of Thessaly region, however it would be of great interest to investigate how this method corresponds in space (namely, for all the grid-cells of Thessaly region).

As mentioned, Thessaly experienced severe, extreme and persistent droughts during the period from mid to late 1970s and the period from late 1980s to early 1990s and the first years of 2000s. The spatial distribution of the 6-month SPI for two representative months (July 1988 and June 2001) of the corresponding two drought episodes (1988-1991, 2000-2001) are presented in Figures 7 and 8. Regarding July 1988, it is clearly noted that mean stochastic approach fails to reproduce the spatial distribution of SPI for both GCMs (CGCM2 and ECHAM5). This approach estimates lower SPI values for all the grid cells Thessaly region. However, median stochastic approach reproduces the spatial distribution of the 6-month SPI with a satisfactory way. Indeed, the spatial distribution for both GCMs approximates the deterministic approach with some exceptions (divergences in some grid-cells where higher or lower SPI values have been estimated). The results are similar for June 2001 spatial distribution of the 6-month SPI.

Figure 7 Comparison of observed SPI time series with simulated SPI time series for Thessaly region using median and average values of the Gamma distribution parameters. α and β. of stochastically generated SPI time series in reproducing the observed historical precipitation for 6-month timescale and for July 1988.
Figure 7

Comparison of observed SPI time series with simulated SPI time series for Thessaly region using median and average values of the Gamma distribution parameters. α and β. of stochastically generated SPI time series in reproducing the observed historical precipitation for 6-month timescale and for July 1988.

Figure 8 Comparison of observed SPI time series with simulated SPI time series for Thessaly region using median and average values of the Gamma distribution parameters. α and β. of stochastically generated SPI time series in reproducing the observed historical precipitation for 6-month timescale and for June 2001.
Figure 8

Comparison of observed SPI time series with simulated SPI time series for Thessaly region using median and average values of the Gamma distribution parameters. α and β. of stochastically generated SPI time series in reproducing the observed historical precipitation for 6-month timescale and for June 2001.

5 Conlusions

Present work was focused in downscaling precipitation over the region of Thessaly with 10 km × 10 km grid resolution and in estimating standardized precipitation index (SPI). The original data were extracted from 79 precipitation stations located in the study region. In order to create a gridded data base ordinary Kriging was used for this spatial distribution. The outputs of two GCMs, CGCM2 and ECHAM5 were used for the downscaling process, which was applied in to six clusters developed from an adjusted cluster analysis. The result of a multiple linear regression with the use of independent variables from the two GCMs showed that correlation coefficients do not variate if a generalized model of multiple linear regression is used. The analysis showed that models simulate in a satisfying way mean monthly precipitation in each cluster, whereas projections deviate considerably from observations. The actual divergences between GMLR model and observed precipitation values were calculated and simulated by use of a stochastic model MPAR(2) and this way the uncertainty of the GCMs was accounted. Finally, 100 synthetic time series of residuals were generated and were added in the GMLR model estimations. Hence, 100 synthetic time series of mean monthly precipitation were developed in each grid of 10 km × 10 km and the estimation of SPI at multiple timescales became a feasible process. In this way precipitation spatial variability was maintained among the grids of the study area. The basic stage of process constitutes the assumption that the actual residuals in each grid remain unchanged for every future or synthetic period. Various evaluation statistics were used for the verification of the results and these criteria were calculated for every grid.

The present study developed a statistical downscaling method with a stochastic component to account the variability of descriptors with climate change, and to evaluate the uncertainty introduced on climate change impact on droughts. The method showed satisfactory efficiency in SPI calculation and the results are comparable to a previous study [46] where a similar method was applied in Lake Karla basin and the output of one GCM was used. Future work will be focused in the use of this process in climate change impact assessments concerning droughts with employment of a larger number of GCMs and drought indices. The outputs of the CORDEX program (http://www.cordex.org/) and especially the Med-CORDEX experiments (https://www.medcordex.eu/) will be used for comparison purposes and the validation of the methodology. Furthermore, the process should be further modified in a way that actual residuals will not remain unchanged but they would be simulated with other methods (Kriging, IDW, Spline).

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Received: 2015-9-30
Accepted: 2016-9-5
Published Online: 2016-12-30
Published in Print: 2016-1-1

© 2016 J. Tzabiras et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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