**1. Introduction**

Drought is a natural hazard related to a deficiency of precipitation for an extended period that results in water shortage for some activities or for some economic sectors [1]. The meanings of "drought" depend on different perspectives of stakeholders from farmers to meteorologists [2]. Commonly, according to the studies of droughts [3–5], the concept of drought is clustered into four types consisting of meteorological, agricultural, hydrological and socioeconomic types. The Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report [6] emphasizes that the world indeed has become more drought-prone during the past 25 years. Drought-affected areas will likely increase in frequency and severity, with implications for sustainable development (e.g., agriculture and forestry production or land degradation). Observed changes in characteristics of droughts (i.e., more intense and longer duration droughts) are widely documented for a variety of regional and ocean basin scales since the 1970s with the emphasis on tropics and substropics [6]. In comparison to the Medieval Climate Anomaly (950–1250), more megadroughts appeared in monsoon Asia and wetter conditions became dominant in arid Central Asia and the South American monsoon region during the Little Ice Age (1450–1850) [7]. Over a global scale, it is observed that the intensity and/or duration of droughts likely increase in the Mediterranean and West Africa and decrease in central North America and north-west Australia [6]. Increased drying is directly linked to higher temperatures and decreased precipitation. It is noteworthy that the palaeoclimate records show that droughts prolonging with a scale of decades or longer have been very likely a repetitive feature of the climate in several regions over the last 2000 years [6].Overall, these studies show that several

extreme droughts occured in the last millennium. Moreover, it poses questions about the uncertainty of calculated results as well as how the projected droughts express their footprint on a local scale under different scenarios of climate change. There is an urgent need to find away to evaluate the droughts. This plays a central role in drought management strategies, and social responses to manage the risks and mitigate the drought impacts.

To evaluate the impacts of droughts on different fields (e.g., water shortages, concomitant shortages, crop growth), many drought indices have been developed and applied under timescales of short- or long-term. These indices widely vary from simple indices (e.g., percentage of normal precipitation) to sophisticated indices (e.g., Palmer drought severity index). Obviously, no drought index is suitable for all circumstances of a specific region. Some indices can be better suited than others for certain regional applications. Svoboda and Brian [8] showed some disadvantages of the standardized precipitation index (SPI) such as an assumption of distribution that can bias the results, particularly when examining short-duration events. In this study, however, the SPI index is still selected to calculate the drought-related components for numerous reasons: (1) the SPI index has been suggested and highlighted by the World Meteorological Organization [5], and nowadays many national meteorological services and drought monitoring centers use it (e.g., in the US [9]; in Europea [10]; and in Canada [11]); (2) the SPI is a powerful, flexible indicator based on robust underlying probability functions and it has high spatial coherence. Moreover, it is simple to calculate and needs only the required input parameter of precipitation. More importantly, Salehnia et al. [12] showed that eight precipitation-based drought indices, namely SPI, PNI (percent of normal index), DI (deciles index), EDI (effective drought index), CZI (China-Z index), MCZI (modified CZI), RAI (rainfall anomaly index), and ZSI (Z-score index) have similar trends; (3) lots of publications illustrated that precipitation data alone could explain most of the variability of drought (e.g., [13]). Furthermore, some indices (i.e., SPI, the standardized precipitation evapotranspiration index (SPEI: [14]), the Palmer drought severity index (PDSI: [15]); the self-calibrated PDSI [16] and the reconnaissance drought index (RDI: [17])) have been tested on a global scale by Spinoni et al. [18]. They showed that these indices have more difficulties than the SPI with possible error values such as a heat wave for a meteorological drought for the SPEI index or unrealistic extreme values for the RDI index; (4) the SPI index is designed to quantify the precipitation deficit for multiple timescales, reflecting the impact of drought on the water availability. For example, shorter SPI timescales (from 1 to 6 months) mainly indicate the drought index for agriculture practices like soil moisture conditions, whereas longer SPI timescales (from 12 to 48 months) indicate the drought index for hydrology like groundwater, streamflow and reservoir [5]. In this study, multiple timescales of the SPI index (1-, 3-, 6-, 9-, 12- and 24-month SPI) are considered using multiple climate models. The reason for this is that Vietnam is an agricultural country and has nearly 7000 reservoirs over the whole country. VG-TB has 6 reservoirs including the A Vuong, DakMi 4, Song Tranh 2, Song Bung 4, Song Bung 4A and Song Bung 5 reservoirs.

For climate projections, strictly speaking, the understanding of nature and its representation in climate models is mostly incomplete with sources of uncertainty (e.g., emissions of greenhouse gases, parameterization schemes of convective cloud and land surface, grid systems, map projections and climatic forcing factors). Thus, to be more reliable and accurate for climate projections, a combination of multiple climate models is widely applied. This pragmatic approach has received much attention over the availability of numerical weather and climate forecasts from institutions and centers of weather and climate research. To date, the metadata has been constructed such as the Ensemble-Based Predictions of Climate Changes and Their Impacts (ENSEMBLES) project [19] and phase 3, phase 5 and phase 6 of the Coupled Model Intercomparison Project (CMIP3, CMIP5 and CMIP6) using multiple climate models. Usually, the simplest method of constructing a multiple climate model is used with "equal weighting" in which weights equal 1/M, where M is the number of models. In a more sophisticated manner, the approach of "unequal weighting" or "optimum weighting" is voted. Weigel et al. [1] discussed two ways of "equal weighting" and "unequal weighting". The study showed that "equal weighting" from multiple models perform better than the single models. Furthermore, the projection errors can

be further eliminated by using "unequal weighting". To get this, however, single model skills and relative contributions of the joint model error are required. More importantly, Timothy et al. [20] used a statistical test to define whether an ensembles of multi models with "unequal weighting" is significantly better than without "unequal weighting". The study showed that a value for the relatively small global fraction is illustrated with the method of "unequal weighting". Sanderson et al. [18] suggested a weighting scheme to eliminate some aspects of model codependency in the ensemble. Also, a weighting strategy for an ensemble of CMIP5 was presented by Sanderson et al. [21] in the fourth National Climate Assessment. In general, these studies use a distance metric of models to observations and the distance metric of a pair of models i and j, and a relationship to convert those into a weight. The equal weighting is, remarkably, often used to develop the global ensemble scenarios as a safer and more transparent way to combine models [1], but unequal weights can be better for some areas of the global [20]. In most cases of existing ensemble members, the application of any kind of weighting to ensemble variance is mostly discarded, but only considered the weighted mean [1,22,23]. This can ignore the intermodel relationships and unexpected values, as extreme weather variables can potentially be more sensitive to changes in the variance [24]. In addition, ensemble members typically come from the same model.

In the context of changing climate, studies in drought events at scales of region and basin are valuable for understanding their evolution and impacts on a wide range of fields (e.g., agriculture, socio-economic, environment and natural resources) that occur over certain areas. In this sense, the present study aims to evaluate the wet and drought events in the 21stcentury using multiple climate models for multiple timescales. The precipitation projections from multiple regional climate models driven by multiple global climate models are separately corrected using the method of delta change factor. In addition, an unequal weight method is proposed in the expectation of a better performance of multiple climate projections of precipitation at basin scale in Vietnam as a case study. Weights for each climate simulation are calculated on the basic of rank sum metric of each climate simulation. The rank sum is defined from statistical indices of each climate simulation in comparison with observation. In comparison with the existing methods mentioned above, this approach can measure not only the absolute performance of each model, but the performance compared with the other models in the ensemble with its ranks. The methods of the non-parametric Mann–Kendall (MK) test [25,26] and Sen's slope [27] are then applied to detect the projection trends in meteorological drought for multiple timescales at a significance level of 0.05. The reason for this is that the MK test is widely applied [28–30] with advantages of a rank correlation without any request of a particular distribution of data and not affected by the data errors and outliers.

#### **2. Materials and Methodology**

### *2.1. Description of the Case Study Area: Vu Gia-Thu Bon Basin*

A plot basin, Vu Gia-Thu Bon (VG-TB), is selected in this study. It is located in central Vietnam, elongating from 16◦55 through 14◦55 and from 107◦15 through 108◦24 and covers a total of area of approximately 12,577 km2. The VG-TB basin is surrounded by two main provincial administrative territories Quang Nam and Da Nang. The basin is characterized by a steep topography and the altitude ranging from 0 m at the coast to 2567 m in elevation above sea level (m.a.s.l) in the west (Figure 1).

**Figure 1.** Network of hydro-meteorological stations at Vu Gia-Thu Bon (VG-TB) basin.

#### *2.2. Data*

#### 2.2.1. Observational Data

The monthly precipitation records are obtained from the Vietnam HydroMeteorological Data Center of the Ministry of National Resources and Environment of Vietnam (MONRE). They are aggregated from the daily series of data. There are two national rain gauge stations (i.e., Danang and Tramy). Other stations including Ainghia, Camle, Giaothuy, Caulau, Hien, Hiepduc, Hoian, Khamduc, Nongson, Queson, Thanhmy and Tienphuoc are popular rain gauge stations which operate manually on the base of volunteers. The location of these stations is displayed on Figure 1. The data is available from 1986–2015.

#### 2.2.2. Gridded Data

The precipitation products are from different assembliese of regional models: (1) The Regional Climate Model version 4 (RegCM4), developed by the International Centre for Theoretical Physics (ICTP). The dynamical structure of RegCM4 firstly developed at the National Center of Atmosphere Research (NCAR) and Penn State University (PSU) for a hydrostatic version of the Meso-scale Model (MM5). A detailed description of RegCM4 can be found in Giorgi et al. [31]. The model output of HadGEM2-AO produced by the National Institute of Meteorological Research (NIMR)/Korea Meteorological Administration (KMA) are used as an initial and boundary conditions, referred to REG/HadGEM. Details of HadGEM2-AO are given by Collins et al. [32]; (2) The model of SNU-MM5(Seoul National University Meso-scale Model version 5) [33] is based on a hydrostatic version of the Meso-scale Model and the community land model version 3 (CLM3). The future climatic projections are produced with the HadGEM2-AO, referred to SNU/HadGEM; (3) A regional spectral model, which is also known as Regional Model Program (RMP) of the Global/Regional Integrated Model System (GRIMs) [34] is used in this study. The dynamic frame of RMP is rooted in the National Center for Environmental Prediction (NCEP) RSM. More detailed information about the GRIMs-RMP is provided by Hong et al. [34]. This model is driven by the HadGEM2-AO, referred to RSM/HadGEM; (4) The RegCM4 is forced by the model of Max Planck Institute for Meteorology Earth System Model MR (MPI-ESM-MR), which has an ocean horizontal resolution of 0.4◦ × 0.4◦ and atmosphere horizontal resolution of 1.9◦ × 1.9◦. It is written under a short symbol of REG/MPI; (5) The RegCM4 is forced by the model of Institut Pierre Simon Laplace CM5A-LR (IPSL-CM5A-LR), which is the low-resolution version of the IPSL-CM5A Earth system model. It has a horizontal resolution of 1.875◦ × 3.75◦ with 39 vertical level for the atmosphere and about 2◦ (with a meridional increased resolution of 0.5◦ near the equator) and with 31 vertical levels for the ocean. In this study, it implies to REG/IPSL; (6) The RegCM4 is forced by the model of Irish Centre for High-End Computing European community Earth-System (ICHEC-EC-EARTH), which is a new Earth system model on the basic of the operational seasonal forecast system of the European Centre for Medium-Range Weather Forecasts (ECMWF). This case is written with a short symbol of the REG/ICHEC. More importantly, all simulations and projections of climatic are run under two IPCC RCP4.5/8.5 scenarios. The RCP4.5 is a stabilization scenario where total radiative forcing is stabilized before 2100 by employment of a range of technologies and strategies for reducing greenhouse gas emissions. Meanwhile, the RCP8.5 is characterized by increasing greenhouse gas emissions over time representative for scenarios in the literature leading to high greenhouse gas concentration. Table 1 lists the name of the models and the number of runs of historical control and RCPs as well as the considered periods. A total of 18 climatic simulations and projections are considered in this study as shown in Table 1.


