An experimental, district-level system was developed to forecast droughts and floods over South Korea to properly represent local precipitation extremes. The system is based on the Asia-Pacific Economic Cooperation (APEC) Climate Center (APCC) multimodel ensemble (MME) seasonal prediction products. Three-month lead precipitation forecasts for 60 stations in South Korea for the season of March to May are first obtained from the coarse-scale MME prediction using statistical downscaling. Owing to the relatively small variance of the MME and regression-based downscaling outputs, the downscaled MME (DMME) products need to be subsequently inflated. The final station-scale precipitation predictions are then used to produce drought and flood forecasts on the basis of the Standardized Precipitation Index (SPI).
Extreme droughts and floods result in tremendous economical, social, and environmental losses. Overall, drought is one of the costliest types of natural disasters and affects many people every year (Wilhite, 2000). The 1994–1995 drought in South Korea, caused by a large-scale circulation system rather than local factors (Park and Schubert, 1997), affected an area of 173 269 ha (MCT, 1995). During 2011, 86 cities and approximately 300 000 people were affected by the most severe drought (KWRA, 2002) to have struck South Korea during the last 100 years ('Seoul, 10 June 2011 (Agence France-Press)', available at http://reliefweb.int/node/81 940; Min et al., 2003; Sohn et al., 2011b). The drought was induced by an anomalous high at the centre of the Eurasian continent (Lee et al., 2001). In July 2011, an extremely severe flood event hit South Korea, with Seoul recording the heaviest single-day rainfall since 1907 (available at www.ncdc.noaa.gov/climate-monitoring). El Niño and Southern Oscillation (ENSO) events, including its recently discovered flavour called, ENSO Modoki, also strongly influence the hydrological cycle in many Asia-Pacific locations (Ashok et al., 2007, 2009; Weng et al., 2007; Zhang et al., 2007; Feng et al., 2010; Pradhan et al., 2011; Sohn et al., 2012). Moreover, flood frequency can be quite sensitive to modest changes in climate (Knox, 1993). Developing a reliable prediction system for hydrological extremes is essential to the preparedness of stakeholders and policy makers in agricultural planning, water management, and so forth. However, there are still very few studies on seasonal predictions of extreme droughts and floods across South Korea.
In recent decades, climate and weather forecast skill has increased drastically (Goddard et al., 2001), and it is worthwhile to explore the potential of extreme drought and flood forecasts derived from general circulation model (GCM)-based seasonal prediction systems. GCM products have been adapted to assess potential climatic impacts on water resources at the district level (Vidal and Wade, 2009; Vosin et al., 2010; Kim et al., 2011), using bias-corrected local scaling (BLS) methods (Wood et al., 2002). The procedure involves a bias correction of GCM outputs using a probability-mapping approach, before the use of simple spatial interpolation.
Recently, multimodel ensemble (MME) prediction products have also been statistically downscaled to improve the skill of local precipitation predictions at the seasonal time scale (Kang et al., 2007, 2009; Chu et al., 2008). There are two major advantages of using such a method to forecast local precipitation. One is that the MME approach can usually lead to more accurate forecasts owing to the better sampling of uncertainties related to model formulations (Krishnamurti et al., 1999, 2000; Doblas-Reyes et al., 2000; Palmer et al., 2000; Shukla et al., 2000). In addition, statistical post processing can lead to further reduction of model biases, and in many cases, can tap into the predictability of some local variable if the latter is related to the large-scale circulation patterns that are well resolved by GCMs (Karl et al., 1990). However, there is often relatively low variance in the MME (Yoo and Kang, 2005) and regression-based downscaling prediction products (Feddersen et al., 1999; von Storch, 1999; Kang et al., 2004; Feddersen and Andersen, 2005). Therefore, there is a need for methods for correcting low variance such that local-level drought and flood forecasts can be realistic in both their temporal fluctuations and absolute magnitudes (Klein et al., 1959; Huth, 1999; Kang et al., 2004).
In this study, we seek to develop a reliable long lead, district-level MME-based prediction system for droughts and floods, using the downscaled MME (DMME) method and the inflation of the variance of the prediction products. One novelty of this approach is a more physically meaningful downscaling compared to BLS, combined with the merits of MME; another is the inflation of low variance originating from both downscaling and MME. The goal is to accurately predict springtime droughts and floods over South Korea, which comprises the southern part of the Korean Peninsula, between 33°N and 39°N and from 124°E to 130°E (Figure 1(a)). In the boreal spring, South Korea is susceptible to abnormal aridity, droughts, and dust storms. Moreover, rainfall deficiency accumulated from the previous winter can greatly impact agriculture practices such as irrigation and seeding. Thus, for mitigation and preparedness purposes, accurate forecasting of seasonal disparities (particularly extremes) in local rainfall has become an important topic for South Korea. In this article, we implement a three-step procedure to produce a long lead, district-level MME-based prediction for extreme drought and flood events: The first step is spatial downscaling of precipitation data from multiple global models to stations across South Korea. Next, variance inflation is applied, as necessary, to calibrate the amplitude of the downscaling prediction. Three different approaches to correcting the variance of the Asia-Pacific Economic Cooperation (APEC) APEC Climate Center (APCC) 3-month DMME precipitation forecasts are evaluated (an alternative method, which will not be considered in this study, is to add a stochastic noise term to the forecasts; Hewitson, 1998; Kilsby et al., 1998; von Storch, 1999; Min et al., 2011). The final step is to produce drought or flood forecasts on the basis of the Standardized Precipitation Index (SPI; McKee et al., 1993, 1995) for each station location.
The rest of the article is organized as follows: Section 2 describes the forecast procedure and datasets used and Section 3 presents the results of downscaling, variance correction methods, and extreme drought and flood predictions across South Korea. A summary and discussion of the results are presented in Section 4.
2. Data and prediction procedure
In this study, the prediction period of interest is the three months during the March–April–May (MAM) season. The retrospective forecast (hindcast) datasets span a period of 21 years, from 1983 to 2003, for the same season. Particular attention is paid to 3-month accumulated precipitation anomalies later used to calculate SPI.
These datasets are obtained from ten operational seasonal prediction models participating in the APCC MME seasonal forecast (Kang et al., 2007, 2009; Lee et al., 2011; Min et al., 2011; Sohn et al., 2011). The hindcast data generation methods examined in this study follow the guidelines of the Seasonal Model Intercomparison Project/Historical Forecast Project (Kang and Shukla, 2006) or Coupled Model Intercomparison Project (Covey et al., 2003) typed experiments, with 1-month lead time, issued on 1 February. The ten prediction systems used are listed in Table I. These forecasts are used to derive a statistical relationship between the observed local-scale precipitation (i.e. predictand) and the models' behaviour on large-scale circulation (predictor) in the cross-validated mode (Michaelsen, 1987). Potential predictors include upper-air variables such as temperature at 850 hPa (T850), winds at 850/200 hPa (UV850/200), and the geopotential height at 500 hPa (Z500), as well as air temperature at 2 m (T2M), and sea-level pressure (SLP).
Table I. Description of the general circulation models used in this study
Model experiment for hindcast generation
CMIP, Coupled Model Intercomparison Project; SMIP/HFP, Seasonal Model Intercomparison Project/Historical Forecast Project
The baseline reference precipitation data was obtained from 60 stations in South Korea, shown in Figure 1(b); the data were used to calibrate and validate the precipitation predictions at the target locations (for more information, Table AI). In South Korea, there are two main ridges, namely, the Taebaek and Sobaek Mountains. The Taebaek Mountains are located along the eastern edge of the peninsula and run along the East Sea (average elevation approximately 1000 m). The Sobaek Mountains cut across the southern Korean Peninsula, diverge from the Taebaek Mountains, and trend southwest across the centre of the peninsula.
2.2. Hydrological extreme forecast system
2.2.1. Statistical downscaling
Local precipitation forecasts at 60 stations in South Korea are produced using statistical downscaling, which is a regression-based method with multimodel output variables as predictors (Kang et al., 2009). This method consists of the following steps: (1) coupled pattern selection and projection (Kang et al., 2007; Kug et al., 2007), (2) selection of optimal multipredictors, and (3) multimodel averaging. A downscaled retrospective prediction by (1) and (2) is produced separately for each model on the basis of a leave-one-out cross-validation framework. The pattern projection method selects the optimal predictor for each station by performing global scanning of different variables. The final forecast obtained from (3) is then the simple average of downscaled precipitation forecasts of the ten models using their respective optimal predictors.
2.2.2. Variance inflation
At time ‘t’, the DMME prediction at a particular station ‘k’, denoted by Y(t, k), is inflated to Z(t, k) according to the following formula:
where IF(k) represents the inflation factor. Three possible methods of variance correction, i.e. ways to define the inflation factor IF, were tested in predicting extreme hydrological events over South Korea. Along with the original non-inflated DMME precipitation forecast, we tested four different methods for predicting hydrological extremes. The formulas of the various inflation schemes are listed in Table II.
Table II. Variance correction methods
Y(t, k) and Z(t, k) are, respectively, the original and calibrated monthly mean anomalies, for station k at time t, where IF(k) represents the inflation factor
The first method of correcting variance, hereafter referred to as M1, is to inflate the forecast by a factor that is inversely proportional to the correlation between the original and downscaled time series (Klein et al., 1959; Karl et al., 1990; Huth, 1999). The second method (referred to as M2) is to multiply the adjusted values by the ratio between the standard deviation (SD) of the observations and that of the adjusted values (Leung et al., 1999). The third way (referred to as M3) to introduce an inflation factor is by combining the common method of inflation with a weighting factor (Kang et al., 2004), which depends on the magnitude of local variability of the adjusted field (Feddersen et al., 1999). This approach leaves points of small variability, which usually have little skill, non-inflated while concentrating on locations with large variability.
2.2.3. Calculation of SPI
Hydrological extremes are indentified on the basis of SPI, which is a widely used index adopted by the World Meteorological Organization (WMO) for drought monitoring (WMO Press Release No. 872; Sohn et al., 2011b). It can be used to detect drought over a variety of time scales and can distinguish regions with persistent or emerging hydrological extremes. SPI has the following properties (Vidal and Wade, 2009): SPI calculation is more flexible and efficient than calculations using other indices (Hayes et al., 1999), and the required data are easily available (Paulo and Pereira, 2006) for achieving skill comparable with that achieved with other indices (Morid et al., 2006). It can accommodate different time scales (McKee et al., 1995) and tends to provide reasonable spatial consistency (Loukas and Vasiliades, 2004). It was also successfully tested in many regions (Ntale and Gan, 2003; Sonmez et al., 2005; Vicente-Serrano and Lopez-Moreno, 2005; Wu et al., 2007).
The value of SPI is estimated by transforming the observed rainfall distribution for the most recent 30 years (here, 21 years), usually fitted to a gamma distribution, into a standardized normal distribution on an equal-probability basis (McKee et al., 1993; Edwards, 1997). The two-parameter gamma distribution is defined by its frequency or probability density function:
Here, α and β, both being non-negative, are the shape and scale parameters, respectively; x is the precipitation amount; and is the gamma function. The obtained parameters are then used to find the cumulative probability of an observed precipitation event for the given month and time scale for the region in question. The cumulative probability is given by the following:
Setting gives the incomplete gamma function . Since the gamma function is undefined for x = 0 and a precipitation distribution may contain zeros, the cumulative probability is given by H(x) = q+ (1—q)G(x), where q is the probability of a zero. The cumulative probability, H(x), is then transformed to the standard normal random variable Z with mean of zero and variance of one, where Z represents the value of SPI.
The advantage of using the SPI is that it recognizes a variety of time scales and provides information on precipitation deficit, precipitation percent of average, and probability. Since the SPI is normalized, wetter and drier climates can be represented in the same way. Depending on the purpose, the SPI can also be computed in a similar way with different inputs such as snowpack, stream flow, reservoir storage, soil moisture, and ground water.
On the basis of this index, extreme droughts and floods can be categorized accordingly (Table III). In particular, SPI values in the ranges of − 1.0 to − 1.49, − 1.5 to − 2.0, and less than -2.0 indicate moderate, severe, and extreme drought conditions, respectively. This study considers SPI computed for a 3-month period (hereafter referred to as SPI3) since this represents the typical time scale for precipitation deficits to affect usable water sources and soil moisture important for agriculture (McKee et al., 1993).
Table III. Flood/drought conditions categorized according to the Standardized Precipitation Index (SPI) value and corresponding class probabilities
1.5 to 1.99
1.0 to 1.49
− 0.99 to 0.99
− 1.0 to − 1.49
− 1.5 to − 1.99
< − 2.0
2.2.4. Forecast quality measures
The basic statistics of seasonal precipitation predictions for extreme droughts and floods were compared with those from observations. The forecast quality measures used include the temporal correlation coefficient (TCC), pattern correlation, SDs, probability distribution functions (PDFs), cumulative density functions (CDFs), and the interquartile range (IQR; Wilks, 1995). TCC is a skill score commonly used to assess seasonal predictive skill (Barnston, 1994). For the computation of PDFs and CDFs, we use the 3-month accumulated precipitation aggregated for 60 stations, based on a 21-year record to include more samples (Min et al., 2011). IQR is defined as the difference between the upper and lower quartiles; it is the simplest, most common, and robust measure of the spread of data. Since the ultimate goal is to predict SPI3, we only consider 3-month accumulated precipitation during MAM as inputs for SPI calculations.
3.1. Statistical downscaling
Figure 2 compares TCC between observations and the MME average of raw GCM prediction, and that based on DMME prediction, for 3-month accumulated rainfall at each station in MAM. MME products are spatially interpolated onto the 60 station locations for comparison (very similar to the BLS method). From Figure 2(a), it can be seen that the MME forecast error is particularly large in two main areas. One region is near the rim of the Taebaek Mountains (hence, the low skill corresponding to stations along the eastern coastline and just to the south of the mountain range), whereas the other is to the southeast of the Sobaek Mountains, at the southern tip of the Korean Peninsula (location shown in Figure 1). The low skill corresponding to these two regions can be attributed to the relatively coarse resolutions of GCMs (Table I), as the Korean Peninsula is only two grid points wide on a 2.5°× 2.5 grid. Interpolation of GCM products to station locations can also introduce large errors. The above suggests that simple spatial interpolation of MME seasonal prediction cannot always provide reliable station-based information for users.
On the other hand, statistical downscaling can correct a large proportion of the systematic error over South Korea, even for locations over which the rainfall is strongly influenced by local topography (Kang et al., 2009). This is evidenced by the downscaling results in Figure 2(b). The 60-station-averaged TCC value is 0.37 based on raw MME, while it is 0.49 based on DMME. In particular, the skill corresponding to the two regions mentioned in the previous paragraph was improved by the downscaling method. Overall, DMME can significantly improve the prediction skill, as measured by the temporal correlation.
Figure 3 shows SDs of 3-month accumulated precipitation for MAM. The average accumulated spring rainfall in South Korea is approximately 80–440 mm (KMA, 2010), with some regional variations; the mean accumulated rainfall is about 300–400 mm on the southern coast, with Jeju Island receiving more than 400 mm in spring. Figure 3(a) shows that the largest variability is found in the southern coastal locations, including Jeju Island, consistent with the mean rainfall distribution. The springtime precipitation is also influenced by the local terrain, resulting in large variability in the northeastern part of South Korea. Compared with observations, the MME average gives very low variance in precipitation (Figure 3(b)). Moreover, there is very little regional variation. For DMME, it gives larger variability in southern regions; nevertheless, the variance of the downscaling product is much less than the observed interannual variability. It is well known that the regression-based downscaling prediction tends to yield low variance (Feddersen et al., 1999; Kang et al., 2004), but this can be remedied by means of various inflation methods.
The 1983–2003 rainfall time series during spring for the whole of South Korea (i.e. averaged over 60 stations) from observations, MME, and DMME are further compared in Figure 4. It can be seen that DMME has generally better skill than MME in predicting the MAM precipitation. The observed rainfall variability is the largest, whereas both the MME and DMME give very low variance. Consistent with previous analyses, this suggests that the DMME needs to be further inflated even though it is able to capture the historical large-scale drought and flood events over South Korea.
3.2. Variance inflation
To compensate for the low variance of the seasonal prediction results, inflation methods are employed to adjust the amplitudes of the DMME products. Figure 5 shows the PDFs and CDFs for the 3-month accumulated precipitation aggregated for 60 stations, based on a 21-year record, for both the observations and DMME prediction results. For DMME, PDFs are computed by adding the observed climatological mean to the (inflated) downscaling station rainfall anomaly prediction. It is noteworthy that, the inflated DMMEs all give Gaussian-like PDFs that are right skewed, consistent with observations (Figure 5(a)). Although M1 is one of the most common inflation methods, its performance in this study is worse than M2, although better than the non-inflated DMME result and M3. This may be because the variance inflation implicitly assumes that all local variability is related to large-scale variability, which is not the case (von Storch, 1999). Alternatively, it could be that the inflation factor is not a reciprocal of the correlation between observations and DMME prediction, especially since precipitation is not one of the potential predictors. M2 gives the best PDF and is able to reproduce extremely intensive as well as rare rainfall events. M3 gives almost the same PDF as the non-inflated method. Similar to the non-inflated prediction, most values from the M3 distribution are clustered around the climatological mean value. On the basis of the CDF plots (Figure 5(b)), it can be seen that M2 gives a distribution closest to observations. In other words, the M2-inflated DMME prediction can best characterize extreme precipitation events. In comparison, M3 and non-inflated DMME have a tendency to overestimate flood events (i.e. to give false alarms) (for reference, cumulative frequencies less than 0.159 and more than 0.841 indicate moderately dry and wet conditions, respectively; see Table III).
The spatial distributions of the DMME variance inflated by various schemes are also investigated. Figure 6 shows IQR maps for different inflation schemes. It can be seen that M2, which rescales the DMME variance directly based on observations, shows a comparable spread to the observed data. The method also tends to slightly overestimate IQR in some locations. On the other hand, the non-inflated as well as the M1- and M3-inflated DMMEs tend to give smaller spreads and all give relatively large root mean square differences (about 2.3–2.8, compared to 1.6 given by M2). However, it is interesting to note that M3 shows the best spatial consistency with observations, as indicated by the high spatial correlation of 0.72. This may be because M3 leaves stations of small variability, which usually have little skill, non-inflated, while concentrating the inflation on stations with large amplitudes (Kang et al., 2004). It is also seen that at least M3 is good for stations with very large variability (e.g. the southern coast). Further inspection shows that the PDF of M3 in these locations is comparable with those from the other schemes, supporting the idea that M3 works better when the variance to be fitted is large (figure not shown).
3.3. Extreme drought and flood predictions
We now assess the impact of various calibrations of DMME precipitation forecasts on extreme drought and flood predictions. TCCs between the observed and predicted SPI3, ending in May, are given in Figure 7. SPI3 based on non-inflated DMME is moderately skilful in the northern part and the southern coastal region of South Korea (including Jeju Island). Due to its inflation method, SPI3 based on the M1 scheme actually shows a decrease in skill at some inland stations where there is a high correlation between observations and DMME (Figure 2(b)). M2 gives the best overall skill of the three schemes (based on the 60-station-averaged result), while the performance of M3 is almost the same as the non-inflated products. Overall, it appears that M2 is the best inflation method for predicting extreme drought and flood events. It is worth noting that all the schemes considered are also likely to inflate the accurate as well as inaccurate forecasts. Therefore, stations with low skill become more inaccurate when inflated by either M1, M2, or M3 (e.g. at Daegu in the southern-central part of South Korea and at Pohang near the southeastern coast).
The previous discussion focused on the average performance of different inflated DMME products over the entire period. However, it is also of interests to see how well they capture individual drought or flood episodes. Figure 8 compares the SPI maps from observations and predictions for the drought of May 2001. Most stations shows severe to extreme drought conditions, except in a few places (Figure 8(a)). A few locations also indicate moderate drought conditions. There is broad agreement between model predictions and observed conditions over the northern region of South Korea, even though the predicted signals are not as strong as the observed data. However, dry features in more southerly stations are not well captured. These systematic biases cannot be solved through simple inflation. Again, the M2-inflated prediction shows the best performance of all the inflated DMME products. Finally, we also assessed the extent to which our method can predict wet episodes in South Korea. During the anomalously wet boreal spring season of 1998, the inflated DMME also give more reasonable SPI maps compared with the non-inflated prediction. In this case, the non-inflated DMME overestimated SPI values due to its smaller interannual range; the variance-corrected prediction based on M2 is seen to give more realistic SPI predictions (figure not shown).
A long lead, district-level MME-based hydrological extreme prediction system was developed to facilitate early warning of droughts and floods. Hydrological extremes are identified based on SPI maps for the preceding 3-month period using monthly precipitation at 60 south Korean stations. First, the skill of 3-month lead precipitation forecasts for each station, based on DMME, is compared with predictions interpolated from coarse-scale MME products (similar to BSL). Statistical downscaling is found to be more skilful than the raw MME, suggesting that it can be applied to more accurately assess climatic impact on water resources at the district level than the BLS method. Moreover, statistical downscaling can correct a large proportion of the systematic bias over South Korea, even for locations at which rainfall is strongly influenced by local topography.
Methods for correcting the interannual variability of DMME precipitation forecasts have also been investigated to accurately predict hydrological extreme events. In particular, the performances of three different inflation schemes were compared in improving DMME prediction. It was found that a simple rescaling of variance according to the observational record gives the best overall performance in terms of both the amplitude of precipitation variance and SPI predictions.
However, systematic biases cannot be eliminated through simple inflation itself; the application of such inflation often increases the mean square error of the estimate (Karl et al., 1990). The results indicate that further work is required to improve the quality of DMME forecasts of drought/flood events. For example, the improvement provided by the multimodel method is robust in regions where individual models are relatively skilful (Yoo and Kang, 2005). In general, the internal variability of the climate system, the choice of models, and the statistical downscaling models can give rise to uncertainties in model output statistics-based forecasts (Benestad, 2001; Chen et al., 2006). Therefore, different combinations of models and alternative downscaling methodologies should also be explored. For instance, pattern-based statistical methods, such as those using empirical orthogonal function and singular value decomposition techniques, can also be applied.
Overall, the use of DMME, in conjunction with inflation, gives very promising results in predicting extreme droughts and floods over South Korea. Our results suggest that well-designed downscaling and variance inflation could be one method of utilizing meteorological forecasting to reliably predict extreme hydrological events, thereby allowing policy makers and stakeholders in the agricultural and water management sectors to develop more effective mitigation and adaption strategies. In this study, we use only the 3-month lead precipitation to represent extreme droughts and floods. Further investigations of extreme drought and flood predictions, based on longer lead times and multiple variables, will be carried out in the near future.
We would like to thank two anonymous reviewers. Their comments resulted in significant improvements to this article. Chi-Yung Tam acknowledges the support from the City University of Hong Kong (grant no. 9360126).
Table AI. List of the synoptic stations used for the study (KMA, 2010). Height is the station elevation about mean sea level.