The use of series of at least 30 years as a reference for the calculation of climatic anomalies, under the assumption of stationary conditions, has been reported in several studies [10, 11, 12]. In this sense, the three databases considered in this study (summarized in Table 1) were accumulated in monthly time steps for the period 1980-2010 (31 years), since it corresponds to the current period of the climatological normal, defined by the WMO [13].

Table 1

Source: The Authors.

Gridded population data for the MCRB were created by extrapolating the raw census of the target years 1993, 2005, and the projections for 2010, from the public information of the Department of Statistics in Colombia (DANE, for its acronym in Spanish) [23].

First, we created a base map for the 2005 population, by interpolating the census values and incorporating additional geographic data, in order to produce weighting matrices for determining how to apportion population by pixel. Then, assuming that the population is growing with an exponential model, the rates of growth were calculated by municipality using the 1993, 2005 and 2010 data. Finally, maps of annual population were projected throughout the study period, from 1981 to 2010.

Drought indicators simplify information about meteorological phenomena as precipitation to understand its change over a time period [24]. These indicators assess whether a region is experiencing a drought and quantify its severity. They are also useful for monitoring and mapping regional water supply trends, both temporal and spatial in two dimensions.

Although no indicator is better than another, some indices are more appropriate, depending on the region, the type of drought to analyze, the available information and the objective of the study. The indicators chosen to describe the drought at the regional level in the MCRB are described below.

The main characteristic of the SPI is that it only requires precipitation data to identify different types of droughts (depending on the temporal scale used). This can be an advantage due to its practicality, but without considering the temperature, the results may not correctly represent the water balance in a region. In order to have a more robust indicator, Vicente-Serrano et al. [26] modified the SPI, by switching the precipitation information with the water balance (B = P - PET) time series, thus creating the SPEI.

Instead of analyzing the precipitation series, the SPEI evaluates the water balance, understood as the difference between precipitation and potential evapotranspiration. Compared to the SPI estimation, the SPEI calculations require additional information on climatic variables such as temperature, radiation, vapor pressure, wind velocity, among others, for the calculation of potential evapotranspiration, depending on the equation chosen. The SPI and SPEI are classified using the ranges shown in Table 2.

Table 2

Source: Adapted from [20, 21]

To define the hydrological drought (as an alteration in the water availability), some authors have focused on the quantification of the scarcity of water for human consumption generated by drought events. Thus, Malin Falkenmark has developed a series of analysis of scarcity from a hydrological perspective [27], defining the WCI according to eq. (1).

WCI is calculated as the ratio between the population in a region (demand) and the annual volume of available water (supply), where the availability of water is understood as the precipitation that does not return to the atmosphere, e.g. surface runoff, available flow in a channel or aquifers’ recharge, depending on the scale of analysis [28]. In this study, runoff (R) represents the water available, calculated as precipitation (P) minus actual evapotranspiration (AET): R = P - AET. The AET has been estimated with the Budyko equation [29].

WCI classification (Table 3) evaluates how many people can benefit from each unit of available water, understanding a unit of water as one million cubic meters per year.

Table 3

Source: Adapted from [27]

To evaluate the eartH2Observe reanalysis products, for the drought analysis in the MCRB, the P and PET daily distributed data were re-gridded using bilinear interpolation to a 0.1° spatial resolution and accumulated monthly. Then, the distributed monthly values of AET and B were calculated.

Once the meteorological and demographic inputs were produced on the same spatial scale, the next phase consisted in calculating the three drought indicators with the three input databases (in-situ, WFDEI, and MSWEP). SPI and SPEI were calculated at 1, 3, 12 and 24 months, while the WCI was annually estimated. With these results, we characterize the dry events that the in-situ data set identifies and compare their correlation with the WFDEI and MSWEP results, using the Root-mean-square error (RMSE) and the Spearman correlation (ρ).

The last methodological phase of the study was to evaluate the uncertainty of the results, due to the use of several different meteorological information sources, applying the methodology proposed by Hu et al. [30]. This methodology quantifies the uncertainty of the results in terms of the bias and confidence intervals (CI), considering the impact of the uncertainty associated with the nature of the sample, on the uncertainty of the estimated values of the indicator.

For this purpose, we conducted a seasonal re-sampling of the meteorological series (P for the SPI, B for the SPEI and R for the WCI). This process starts by creating 1,000 random subsets from the original series (observed, WFDEI or MSWEP), i.e. a random selection of the data of a month (e.g Jan ₁₉₈₀ , Jan ₁₉₈₁ …, Jan ₂₀₁₀ ) that comprises a new sample of the original size. Then, we calculated the indicators (SPI, SPEI or WCI) for each sample, and its results are associated with a probability distribution function (DESPI, DESPEI or DEWCI). Based on this distribution, the 90% confidence interval (CI) of the indicator is estimated.

At last, we evaluated the CI through the containing ratio (CR) indicator [31], which is a ratio expressed as a percentage, between the number of observed values within the limits of the 90% IC and the total length of the observed variable, as shown in eq. (2).

In this section, we discuss the results for the SPI and the SPEI indices in the MCRB at temporal scales of 1, 3, 12 and 24 months, as well as the annual results for the WCI. All of them were calculated first with the in-situ series, to identify the most important drought events that have affected the MCRB during the analysis period (1980-2010).

Ten events were identified as those with the largest incidence throughout the MCRB and correspond to the years 1980, 1982-1983, 1985-1986, 1988, 1990-1992, 1995, 1997, 2001-2002, 2007 and 2009-2010 (representative months for these events are shown in Fig.5). These events were selected with a spatial affectation threshold of 40%, that is, when 40% of the basin or more had moderate, severe or extreme drought conditions (SPI, SPEI ≤ -1.00), according to the national recommendations for drought evaluations [32].

Figure 5 Source: The Authors.

These results are consistent with the historical records of hydropower and irrigation affectations associated with droughts, which affected the levels of reservoirs and the general availability of water in the country. For example, the production of hydraulic electricity in the country is affected by droughts. The 1992 energy crisis forced the national government to take rationing measures with power cuts, and even to adopt a daylight-saving time, which is a rare measure in countries on the equatorial line [33]. Likewise, there was also a reduction in energy production during 1997-1998, although there was no need for electricity rationing.

Fig. 6 shows the SPI and SPEI indices, compared to the Oceanic Niño Index values (ONI) [34], where it is clear that seven, out of the ten drought events identified, correspond to a warm “El Niño” phase of the El Niño-Southern Oscillation (ENSO). In Fig. 6, the panels corresponding to the small temporal accumulations (i.e. 1 and 3 months) show dry oscillating periods (SPI or SPEI below -1), which do not always coincide with a period of “El Niño” or negative values of the ONI, as in the case of the 1985 and 2001 events. This indicates that other climatic phenomena can generate droughts in the MCRB as strong as the ENSO does.

Figure 6 Source: The Authors.

Likewise, the 12 and 24 months panels in Fig. 6 indicate that periods with precipitation deficit are continuous, in such a way that their effects are aggregated in an annual trend that could affect river flows, reservoir levels, and even groundwater. Therefore, all periods with dry tendencies are consistent with an “El Niño” event. However, despite no apparent relationship with the ENSO, the 1985 and 2001 events continue to be relevant for the 12-month scale. These droughts are usually associated with the natural climatic variability in the country and effects from a rapid change from “El Niño” to “La Niña” phase [35, 36].

Due to the annual scale of the WCI, it was necessary to average the monthly values of the ONI series. The results identify years with warm (“El Niño”) or cold (“La Niña”) trends depending on the average temperature of the Pacific Ocean. This limits the analysis of the WCI results and their comparison with meteorological drought indicators. Nevertheless, Fig. 7 shows a clear correspondence between the warm years (ONI > 0) and the increase in the value of the hydrological drought indicator averaged within the MCRB, mainly for the years 1990-1992, 1997, 2001- 2002 and 2009.

Figure Source: The Authors.

We also made the calculations presented in section 4.1 with the two reanalysis datasets: WFDEI and MSWEP. The quantification of the efficiency of the reanalysis for reproducing the results of the indices calculated with the in-situ database is described below.

Through a cross-validation analysis between the distributed in-situ indices and the same indicators calculated with the two reanalysis datasets for the entire basin, we obtained maps of the Spearman correlation coefficient (ρ) and for the Root mean square error (RMSE). However, only the average values are analyzed below.

The Spearman coefficient describes the relationship between two variables using a monotonic function. For the two meteorological drought indicators, SPI and SPEI, the MSWEP shows a stronger correlation than the WFDEI (see Figs. 8, 9), in all the temporal scales analyzed. None of the scales evaluated shows a correlation smaller than 0.5 for any of the two products analyzed. The largest correlations are mainly located on the south of the MCRB, on the mountain areas, and along the three branches of the Colombian Andes, which can affect the flows in the lower part of the basin. Likewise, both products decrease their performance in the middle and lower part of the basin, in the areas of flat slopes and upstream of the mouth of the Magdalena River. This may be due to the spatial scale used.

Figure 8 Source: The Authors.

Figure 9 Source: The Authors.

Although both reanalysis datasets have errors with respect to the in-situ indicators, Figs. 10 and 11 show that the RMSE of the MSWEP (mean 0.61) is much lower than that of the WFDEI (mean 0.83). Moreover, the SPEI differences are slightly larger than the SPI ones, regardless of the reanalysis dataset used. This may be due to the choice of the equations for potential and actual evapotranspiration, and the regional scale of the analysis. Thus, it is recommended to perform further analyses for hydrological droughts with more equations for evapotranspiration and with other indices based on runoff and streamflow.

Figure 10 Source: The Authors.

Figure 11 Source: The Authors.

Due to the annual scale of the WCI, it was necessary to average the monthly values of the ONI series. The results identify years with warm (“El Niño”) or cold (“La Niña”) trends depending on the average temperature of the Pacific Ocean. This limits the analysis of the WCI results and their comparison with meteorological drought indicators, but identify the years in which the effects of the drought could affect the water supply, according to domestic demand. Fig. 7 shows a clear correspondence between the warm years (ONI > 0) and the increase in the value of the hydrological drought indicator averaged within the MCRB, mainly for the years 1990-1992, 1997, 2001- 2002 and 2009.

Likewise, in some years in Fig. 7, there are differences in the occurrence of “El Niño” and the peaks of the WCI. This can be associated with the annual analysis scale, the magnitude and duration of the event. For example, although the droughts of 1980 and 1988 affected more than 40% of the basin, it was for a shorter period than three months, which is why the annual average does not reflect an extreme condition.

Regardless of the reanalysis dataset considered, the large differences identified in the WCI calculations are not equally found in the meteorological drought indicators. This is due to the order of magnitude of the WCI, since it is not standardized, and it magnifies the differences where the largest population is concentrated.

Thus, the analysis confirms that the reanalysis WFDEI and MSWEP adequately identify the drought events in the MCRB. For the meteorological drought indicators, the performance of the products improves as the time scale of analysis increases, with an optimum close to the 12 months-scale of accumulation. In addition, the MSWEP can predict correctly temporal and spatial trends of droughts in the MCRB, with consistently better correlations and minor mean errors than the WFDEI product. Similarly, for hydrological droughts, Fig. 12 depicts a better performance for the MSWEP, with mean values of the Spearman correlation (ρ) around 0.82, a bias below 40% in contrast with the 0.67 and 45% values of the WFDEI.

Figure 12 Source: The Authors.

Once the results were analyzed with the original inputs, we applied in both, the WFDEI and MSWEP products, the uncertainty analysis procedure proposed by Hu et al. [30]. The precipitation, balance, and runoff distributed time series were sampled 1,000 times, calculating the three drought indices with each of the Bootstrap sets.

Fig. 13 shows the containing ratio (CR) maps for the nine drought indices evaluated in this study. The top panels present the results for the WFDEI and the lower panels, the indicators calculated with the MSWEP. These values represent the relationship between the number of values of the in-situ indicators within the 90% confidence interval (CI) limits of the reanalysis indices.

Figure 13 Source: The Authors.

In general terms, for the SPI and SPEI, the CI calculated with the MSWEP contains about 15% more in-situ values than the WFDEI, with an average close to 45% of the values derived from observations. In the same way, the CR increases with the scale of the temporary accumulation for the two reanalysis databases, with an optimal value for the 12-month accumulation period. This occurs due to the typical periodic variability of precipitation and temperature in the MCRB.

Unlike meteorological drought indices, the WCI confidence intervals are highly variable, due to the differences in magnitude of populated and rural areas. With this condition, the WFDEI confidence bands contain about 73% of the in-situ values, having better performance in areas of low population density. Meanwhile, the MSWEP has a CR of 52%, maintaining the trend of better performance in rural areas.

Although there were relatively high values of CR, the CI for the WCI are very wide. This hides the real divergence between the observed values and the prediction limits of the reanalysis. In rural areas for the WFDEI and the MSWEP, the CR is up to 45% and 47% higher with respect to the reference values, respectively, and in the main cities is up to 81% and 91%.