# Meteorological and Hydrological Drought Risk Assessment Using Multi-Dimensional Copulas in the Wadi Ouahrane Basin in Algeria

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Collection

^{2}, with a maximum altitude of 991 m a.s.l. and a minimum altitude of 165 m a.s.l.

#### 2.2. Analysis Methods

#### 2.2.1. Univariate Indices in Monitoring of Meteorological and Hydrological Drought

_{w}represents the total precipitation (runoff) over a period of w previous months, by fitting a suitable distribution such as the gamma distribution of the X

_{w}time series, ${u}_{w}={F}_{{x}_{w}\left({x}_{w}\right)}$, a marginal cumulative distribution function (CDF) is obtained. Then the SPI (SRI) is transformed to normality by applying the inverse CDF for the standard normal distribution or ${\phi}^{-1}\left({u}_{w}\right)$. In other words, the distribution of the SPI or SRI time series at any timescale w is described by a standard normal variable (mean zero and standard deviation of 1).

_{w}is grouped by its ending month to create a new dataset ${X}_{w}^{\mathrm{month}}$, in which month represents one of the months of January, February, …December. In this way, ${X}_{1}^{\mathrm{Jan}}$ represents January rainfall and ${X}_{5}^{\mathrm{Aug}}$ represents the total five-month rainfall from April to August, and thus samples in each ${X}_{w}^{\mathrm{month}}$ dataset are collected annually without overlapping as long as w ≤ 12. By fitting the distribution function to each group separately, SPI

^{mod}was calculated similarly to the original SPI from the following equation:

^{mod}method. u

_{1}shows last month’s rainfall status (u

_{1}is important for detecting the onset of drought) and u

_{12}represents last year’s rainfall status (important for diagnosing long-term droughts). It should be noted that none of the u

_{i}can completely reflect the information of the other u

_{j}, and each single u

_{i}can only reflect a partial view of the meteorological drought as a cross-timescale phenomenon. The same process can be applied to generate runoff indices based on 1 to 12 month timescale modified SRI, {v

_{1}, v

_{2}, …, v

_{12}}, which each give a partial representation of hydrological drought.

#### 2.2.2. Drought Definition and Characteristics

#### 2.2.3. Copula Functions

#### 2.2.4. Joint Deficit Index (JDI)

_{1}, u

_{2}, …, u

_{12}(or v

_{1}, v

_{2}, …, v

_{12}) set. However, due to the mathematical complexity of 12-dimensional parametric copulas, Kao and Govindaraju [36] used empirical joints for this purpose. To specify the dependence structure encoded in a copula, either parametric or non-parametric approaches can be used. However, in a higher-dimensional setting, the non-parametric approach has an advantage over the parametric one, given the complexity of parameter estimation as well as the strong assumptions that have to be made in the parametric approach. Empirical Copula [45] with dependence structure defined by independent rank transformations of the samples in each of the dimensions of the multivariate data space, provides a non-parametric alternative to circumvent the above issues associated with the parametric approach. According to the definition of Empirical Copula, if two multivariate samples have identical rank structures, their Empirical Copulas are the same [46]. The choice of u

_{1}, u

_{2}, …, u

_{12}in forming high-dimensional copulas increases the complexity of the dependency model [47]. However, because the duration of droughts shows wide time variations, droughts can only be well described by considering different periods (from 1 to 12 months). In addition, this structure allows for a month-by-month assessment of future conditions. Kao and Govindaraju [36] did not consider timescales longer than 12 months (w > 12) because they observed that the samples used will overlap, and even after applying the modified SPI process, the results could be distorted. Therefore, in this study, only 12 modified SPIs were considered to create the joint deficit meteorological index (JDMI), and the corresponding modified SRIs were used to create the joint deficit hydrological index (JDHI), both special cases of the JDI concept.

_{1}, u

_{2}, …, u

_{12}sample. As each margin indicates the conditions of moisture deficiency for each given period of time, the conditions of joint deficit are determined by t. Clearly, a smaller cumulative probability indicates drier conditions (drought on different time scales), and a larger value indicates wetter conditions. Assuming t reflects the severity of the combined drought, knowing the probability of events occurring with joint values less than or equal to t (i.e., events drier than a certain threshold) will be very beneficial. For this purpose, the definition of the joint distribution function is used, because the joint distribution function is in fact the cumulative probability ${K}_{C}\left(t\right)=P\left[{C}_{{U}_{1},{U}_{2},\dots ,{U}_{12}}\left({u}_{1},{u}_{2},\dots ,{u}_{12}\right)\right]t$. The special advantage of using K

_{C}is that it allows a single probabilistic criterion for joint deficit conditions to be calculated, which can be interpreted as an indicator of combined drought. In fact, K

_{C}is the joint CDF. Figure 3 shows the distribution function of K

_{C}in different values of ${C}_{{U}_{1},{U}_{2},\dots ,{U}_{12}}$ joints for the rainfall (Figure 3a) and runoff (Figure 3b) of the study area.

_{C}> 0.5) indicates a general wet condition, a negative JDI (K

_{C}< 0.5) indicates a general dry condition, and JDI = 0 (K

_{C}= 0.5) indicates a normal condition. Since JDI is inverted on a normal scale (similar to SPI (SRI)), the classification of droughts based on the SPI (SRI) (Table 3) can also be applied to the JDMI (JDHI). The most important character of JDI is the evaluation of general joint conditions based on the structure of dependence of deficiency indices with different time periods.

#### 2.3. Parametric Copula

#### 2.4. Estimation of Parameters and Goodness of Fit Test

#### 2.5. Conditional Return Period

## 3. Results

#### 3.1. Calculation of Univariate Drought Indices and Fitting of Marginal Distribution Functions

#### 3.2. Correlation Analysis of Two Variables of Modified Rainfall and Runoff Indices

_{ij}) are shown in pairs for the marginal distribution functions ${\mathrm{SPI}}_{W}^{\mathrm{mod}}$ and ${\mathrm{SRI}}_{W}^{\mathrm{mod}}$ for w = 1, 2, …, 12. For precipitation marginal distributions as shown in Table 5, the short-term marginals ${u}_{1}^{\mathrm{mod}}$ have a high correlation with ${u}_{2}^{\mathrm{mod}}$, which is equal to 0.84. The correlation coefficient decreases with increasing time window i (when i ≥ 6, the correlation between ${u}_{1}^{\mathrm{mod}}$ and ${u}_{i}^{\mathrm{mod}}$ becomes less than 0.13). The long-term margin distribution function ${u}_{12}^{\mathrm{mod}}$ has a high correlation with ${u}_{j}^{\mathrm{mod}}$ at j > 5, and the correlation coefficient decreases when the time window is shorter (less than 5). These findings are consistent with the results of Kao and Govindaraju [55] for calculating the joint deficit index using precipitation and runoff data. ${u}_{1}^{\mathrm{mod}}$ shows last month’s rainfall status (important for identifying ongoing droughts), and ${u}_{12}^{\mathrm{mod}}$ shows last year’s rainfall status (important for identifying long-term droughts). Although not well correlated with each other, none of them can be ignored.

#### 3.3. Comparison of Multivariate Indices with Univariate Indices

^{mod}, and JDMI for precipitation and SRI, SRI

^{mod}, and JDHI for runoff in October 1982 as examples. The rate of change in precipitation during this period (October 1982 in the past 12 months) varies from 0 mm to 88 mm, and runoff from 0 to 0.392 m

^{3}/s. This month was selected because, in this period, the joint deficit indices (JDHI, JDMI) showed severe and extreme drought, and thus it is a good example to show the efficiency of hydrometeorological indices.

_{1}, w

_{2}, …, w

_{9}) was so severe that it negatively affected the JDMI index (severe drought). The case for hydrological drought is similar to that for meteorological drought. Thus, the SRI value in October 1982 was 0.62, indicating wet conditions, while the calculated JDHI value was −1.19, indicating drought.

#### 3.4. Hydro-Meteorological Joint Deficit Drought Index

^{mod}of all SPI

^{mod}s and SRI

^{mod}s and provides a comprehensive overview of drought conditions. JDHMI fluctuations are similar to those of JDMI and JDHI when these are the same sign, but mediates between them during some transition periods when they have opposite signs. For JDMI or JDHI individually, which use SPI

^{mod}or SRI

^{mod}alone, a comprehensive view of the prevailing hydro-meteorological situation in the region cannot be achieved, due to not considering the simultaneous effects of precipitation and runoff in a drought. Therefore, the composite index is able to reflect the simultaneous hydrological and meteorological behavior well, and it can be inferred that JDHMI can present the probability of a common hydrological and meteorological deficit situation more accurately and realistically than univariate and multivariate precipitation-based indicators or runoff alone.

#### 3.5. Correlation between Composite, Multivariate, and Univariate Indices

#### 3.6. Correlation Structures of Drought Variables and Fitting of Marginal Functions

#### 3.7. Fitting of Copula Functions to a Pair of Hydro-Meteorological Drought Variables

#### 3.8. Conditional Trivariate Return Period and Risk Analysis

## 4. Discussion

^{mod}and SRI

^{mod}, the cumulated rainfall and runoff values of 1 to 12 months based on the moving time window were averaged; then, marginal distribution functions were fitted. The results showed that the gamma function has the best fit for precipitation and the log normal function has the best fit on the runoff. Shukla and Wood [35] showed that in small watersheds, the runoff variable is often a normal function, and in large watersheds, the gamma function is best. Results of our study are confirmed by Yusof et al. [58], who found log-normal distribution as the best fitting distribution for drought severity.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location, topographic characteristics, and pluviometric and hydrometric network of the study area.

**Figure 3.**The distribution function of Kc in different values of ${C}_{{U}_{1},{U}_{2},\dots ,{U}_{12}}$ joints for the rainfall (

**a**) and runoff (

**b**) of the study area.

**Figure 5.**Comparison of univariate (SPI, SRI) and multivariate (JDMI, JDHI) drought indices in October 1982.

**Figure 6.**Time series of univariate (SPI-12, SRI-12) (

**a**) and multivariate (JDHI, JDMI) (

**b**) with composite index (JDHMI).

**Figure 7.**Time series of cumulative of univariate (SPI-12, SRI-12) (

**a**) and composite (JDHMI) and multivariate (JDHI, JDMI) indices (

**b**) in the study area.

**Figure 9.**Graph of goodness of fit test for the marginal distribution functions to drought characteristics.

Stations | Type | ID | Name | Longitude | Latitude | Elevation (m) |
---|---|---|---|---|---|---|

S1 | H | 012201 | LARBAT OULED FARES | 01°13′56″ | 36°14′14″ | 173 |

S1 | R | 012201 | LARBAT OULED FARES | 01°09′18″ | 36°16′20″ | 116 |

S2 | R | 012224 | BOUZGHAIA | 01°14′27″ | 36°20′15″ | 217 |

S3 | R | 012205 | BENAIRIA | 01°22′28″ | 36°21′04″ | 320 |

S4 | R | 012221 | MEDJAJA | 01°20′53″ | 36°16′39″ | 487 |

S5 | R | 012209 | CHETIA | 01°15′53″ | 36°12′56″ | 108 |

S6 | R | NMO | Airport, Chlef | 01°19′28″ | 36°13′31″ | 158 |

Soil Occupation | 1979 | 1989 | 1999 | 2009 | 2017 | |||||
---|---|---|---|---|---|---|---|---|---|---|

Area (km ^{2}) | Area (%) | Area (km ^{2}) | Area (%) | Area (km ^{2}) | Area (%) | Area (km ^{2}) | Area (%) | Area (km ^{2}) | Area (%) | |

Dense vegetation | 0.00 | 0.00 | 0.25 | 0.09 | 1.30 | 0.48 | 0.17 | 0.06 | 0.24 | 0.09 |

Moderate vegetation | 10.46 | 3.87 | 39.87 | 14.77 | 56.48 | 20.92 | 93.08 | 34.47 | 187.80 | 69.56 |

Sparse vegetation | 86.68 | 32.10 | 94.73 | 35.08 | 72.52 | 26.86 | 96.85 | 35.87 | 77.00 | 28.52 |

Bare soil | 172.86 | 64.02 | 135.05 | 50.02 | 139.68 | 51.73 | 79.90 | 29.59 | 4.90 | 1.81 |

Water surface | 0.00 | 0.00 | 0.10 | 0.04 | 0.02 | 0.01 | 0.00 | 0.00 | 0.06 | 0.02 |

Total | 270 | 100 | 270 | 100 | 270 | 100 | 270 | 100 | 270 | 100 |

SPI Values | Drought Category |
---|---|

2.00 or more | Extremely wet |

1.50 to 1.99 | Very wet |

1.00 to 1.49 | Moderately wet |

0 to 0.99 | Near normal |

−0.99 to 0 | Mild drought |

−1.00 to −1.49 | Moderate drought |

−1.50 to −1.99 | Severe drought |

−2.00 or less | Extreme drought |

Copulas | Bivariate Copula C (u, v) | Parameters |
---|---|---|

Elliptical copulas | ||

Student’s t | ${{\displaystyle \int}}_{-\infty}^{{t}_{\theta}^{-1}\left(u\right)}{{\displaystyle \int}}_{-\infty}^{{t}_{\theta}^{-1}\left(v\right)}\frac{1}{2\pi \sqrt{1-{r}^{2}}}{\left\{1+\frac{{x}^{2}-2rxy+{y}^{2}}{\theta \left(1-{r}^{2}\right)}\right\}}^{\frac{-\theta +2}{2}}\mathrm{dxdy}$ ${t}_{\theta}\left(x\right)={{\displaystyle \int}}_{-\infty}^{x}\frac{\Gamma \left(\frac{\theta +1}{2}\right)}{\sqrt{\pi \theta}\Gamma \left(\theta /2\right)}{\left(1+{y}^{2}/\theta \right)}^{\frac{-\theta +1}{2}}dy$ | $\theta >2,r\in \left(0,1\right]$ |

Gaussian | ${\Phi}_{2}\left({\Phi}^{-1}\left(u\right),{\Phi}^{-1}\left(v\right),\rho \right)$ | $-1\le \rho \le 1$ |

Archimedean copulas | ||

Clayton | ${\left({u}^{-\theta}+{v}^{-\theta}-1\right)}^{-1/\theta}$ | $\theta \in {\displaystyle \cup}\left(0,\infty \right)$ |

Frank | $\frac{-1}{\theta}\mathrm{log}\left[1+\frac{\left({e}^{-\theta u}-1\right)\left({e}^{-\theta v}-1\right)}{{e}^{-\theta}-1}\right]$ | $\theta \in {\displaystyle \cup}\left(0,\infty \right)$ |

Joe | $1-{\left[{\left(1-u\right)}^{\theta}+{\left(1-v\right)}^{\theta}-{\left(1-u\right)}^{\theta}{\left(1-v\right)}^{\theta}\right]}^{1/\theta}$ | $\theta \in {\displaystyle \cup}\left(0,\infty \right)$ |

Distribution | Statistics | Evaluation Index | |
---|---|---|---|

SPI^{mod} (1,2, …, 12) | Gamma | K–S = 0.16; CM = 4.79; A–D = 27.37 | AIC = 4656; BIC = 4665 |

SRI^{mod} (1,2, …, 12) | Log-normal | K–S = 0.15; CM = 1.26; A–D = 7.83 | AIC = −788; BIC = −780 |

**Table 6.**Spearman correlation coefficient between u

_{i}, u

_{j}(upper triangle) for precipitation marginal and v

_{i}, v

_{j}(lower triangle) for runoff marginal cumulative distribution functions (r

_{ij}= r

_{ji}).

i | $\mathrm{Spearman}\prime \mathrm{s}{r}_{ij}\mathrm{between}{u}_{i}^{\mathrm{mod}}$$\mathrm{and}{u}_{j}^{\mathrm{mod}}$ | ||||||||||||

j | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |

Spearman’s r_{i,j} between v_{i}^{mod} and v_{j}^{mod} | 1 | 0.84 | 0.70 | 0.57 | 0.42 | 0.28 | 0.17 | 0.07 | 0.00 | 0.00 | 0.08 | 0.19 | |

2 | 0.87 | 0.90 | 0.77 | 0.64 | 0.49 | 0.35 | 0.24 | 0.15 | 0.11 | 0.16 | 0.26 | ||

3 | 0.76 | 0.92 | 0.92 | 0.81 | 0.68 | 0.53 | 0.41 | 0.30 | 0.24 | 0.24 | 0.32 | ||

4 | 0.65 | 0.83 | 0.94 | 0.93 | 0.83 | 0.70 | 0.56 | 0.44 | 0.36 | 0.33 | 0.35 | ||

5 | 0.53 | 0.71 | 0.84 | 0.94 | 0.94 | 0.83 | 0.71 | 0.58 | 0.47 | 0.41 | 0.40 | ||

6 | 0.42 | 0.58 | 0.72 | 0.85 | 0.94 | 0.94 | 0.84 | 0.71 | 0.58 | 0.49 | 0.45 | ||

7 | 0.34 | 0.48 | 0.62 | 0.75 | 0.86 | 0.95 | 0.94 | 0.83 | 0.71 | 0.59 | 0.51 | ||

8 | 0.28 | 0.40 | 0.52 | 0.65 | 0.77 | 0.87 | 0.95 | 0.94 | 0.82 | 0.70 | 0.60 | ||

9 | 0.25 | 0.35 | 0.46 | 0.56 | 0.68 | 0.79 | 0.88 | 0.96 | 0.93 | 0.81 | 0.70 | ||

10 | 0.24 | 0.33 | 0.41 | 0.50 | 0.61 | 0.71 | 0.81 | 0.90 | 0.96 | 0.93 | 0.82 | ||

11 | 0.26 | 0.33 | 0.40 | 0.47 | 0.56 | 0.65 | 0.74 | 0.83 | 0.91 | 0.97 | 0.93 | ||

12 | 0.31 | 0.36 | 0.41 | 0.47 | 0.54 | 0.62 | 0.70 | 0.79 | 0.86 | 0.93 | 0.97 |

Indices | SPI-12 | SRI-12 | JDMI | JDHI | JDHMI |
---|---|---|---|---|---|

SPI-12 | 1.00 | 0.52 | 0.60 | 0.32 | 0.51 |

SRI-12 | 0.52 | 1.00 | 0.28 | 0.52 | 0.58 |

JDMI | 0.60 | 0.28 | 1.00 | 0.61 | 0.89 |

JDHI | 0.32 | 0.52 | 0.61 | 1.00 | 0.86 |

JDHMI | 0.51 | 0.58 | 0.89 | 0.86 | 1.00 |

Characteristics | Value | |
---|---|---|

Number of months less than zero | 261 | |

Maximum
| severity | 65.19 |

duration | 45 | |

magnitude | 1.57 | |

Average
| severity | 10.19 |

duration | 9.65 | |

magnitude | 0.93 | |

Minimum
| severity | 0.88 |

duration | 2 | |

magnitude | 0.41 |

**Table 9.**Goodness of fit test of marginal distribution function on hydro-meteorological drought characteristics.

Indices | Functions | Parameters | K–S Test | Evaluation Index | |
---|---|---|---|---|---|

S | p | ||||

Severity | Weibull | λ = 0.95, k = 9.88 | 0.05 | 0.15 | AIC = 249.55; BIC = 252.77 |

Gamma | α = 1.05; β = 0.10 | 0.07 | 0.17 | AIC = 249.72; BIC = 252.94 | |

Log-normal | µ = 1.77; σ = 0.99 | 0.06 | 0.10 | AIC = 239.85; BIC = 243.07 | |

Normal | µ = 10.19; σ = 13.80 | 0.02 | 0.28 | AIC = 303.27; BIC = 306.49 | |

Logistic | λ = 7.40; k = 5.40 | 0.05 | 0.23 | AIC = 285.31; BIC = 288.53 | |

Exponential | λ = 0.098 | 0.08 | 0.17 | AIC = 247.78; BIC = 249.39 | |

Duration | Weibull | λ = 1.1, k = 10.30 | 0.08 | 0.21 | AIC = 243.96; BIC = 247.19 |

Gamma | α = 1.61; β = 0.17 | 0.06 | 0.22 | AIC = 241.30; BIC = 244.52 | |

Log-normal | µ = 1.92; σ = 0.77 | 0.14 | 0.17 | AIC = 231.80; BIC = 235.02 | |

Normal | µ = 9.64; σ = 9.98 | 0.15 | 0.31 | AIC = 143.86; BIC = 146.38 | |

Logistic | λ = 7.52; k = 4.31 | 0.11 | 0.22 | AIC = 267.30; BIC = 270.52 | |

Exponential | λ = 0.10 | 0.09 | 0.19 | AIC = 243.74; BIC = 245.35 | |

Magnitude | Weibull | λ = 2.94, k = 1.04 | 0.09 | 0.14 | AIC = 28.48; BIC = 31.70 |

Gamma | α = 7.01; β = 7.67 | 0.091 | 0.14 | AIC = 27.19; BIC = 30.42 | |

Log-normal | µ = −0.14; σ = 0.38 | 0.11 | 0.14 | AIC = 27.32; BIC = 30.54 | |

Normal | µ = 0.93; σ = 0.34 | 0.09 | 0.14 | AIC = 30.36; BIC = 33.58 | |

Logistic | λ = 0.90; k = 0.21 | 0.08 | 0.15 | AIC = 33.42; BIC = 36.65 | |

Exponential | λ = 1.08 | 0.05 | 0.35 | AIC = 70.32; BIC = 71.93 |

Variables | Function | Sn | Parameter | p-Value | ML |
---|---|---|---|---|---|

Severity-Duration | Frank | 0.03 | 13.93 | 0.76 | 33.59 |

Joe | 0.022 | 5.30 | 0.95 | 34.83 | |

Clayton | 0.060 | 3.65 | 0.053 | 26.25 | |

Normal | 0.081 | 0.94 | 0.011 | 38.59 | |

T | 0.080 | 0.94 | 0.01 | 38.59 | |

Gumbel | 0.048 | 4.05 | 0.95 | 38.63 | |

Severity-Magnitude | Frank | 0.064 | 5.67 | 0.015 | 12.3 |

Joe | 0.049 | 1.64 | 0.22 | 4.54 | |

Clayton | 0.04 | 2.19 | 0.78 | 17.22 | |

Normal | 0.08 | 0.70 | 0.019 | 12.46 | |

T | 0.04 | 0.70 | 0.08 | 12.52 | |

Gumbel | 0.04 | 1.66 | 0.55 | 8.14 | |

Duration-Magnitude | Frank | 0.04 | 2.51 | 0.67 | 3.18 |

Joe | 0.10 | 1.20 | 0.01 | 0.99 | |

Clayton | 0.10 | 0.89 | 0.461 | 4.58 | |

Normal | 0.032 | 0.40 | 0.12 | 3.30 | |

T | 0.038 | 0.41 | 0.11 | 3.40 | |

Gumbel | 0.039 | 1.22 | 0.29 | 1.85 | |

Severity-Duration-Magnitude | Frank | 0.046 | 5.30 | 0.18 | 25.04 |

Joe | 0.04 | 1.63 | 0.27 | 12.53 | |

Clayton | 0.032 | 1.77 | 0.83 | 29.28 | |

Normal | 0.02 | 0.68 | 0.22 | 26.28 | |

T | 0.050 | 0.67 | 0.97 | 30.42 | |

Gumbel | 0.081 | 1.62 | 0.03 | 18.98 |

Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | |
---|---|---|---|---|

S | 50.00 | 50.00 | 50.00 | 50.00 |

D | 45.00 | 45.00 | 45.00 | 45.00 |

M | 0.30 | 0.90 | 1.30 | 1.90 |

Return Period conditional | 10.00 | 6.60 | 5.26 | 4.16 |

Risk conditional (N = 10 years) | 0.65 | 0.81 | 0.88 | 0.94 |

Risk conditional (N = 20 years) | 0.88 | 0.96 | 0.99 | 1.00 |

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**MDPI and ACS Style**

Achite, M.; Bazrafshan, O.; Wałęga, A.; Azhdari, Z.; Krakauer, N.; Caloiero, T. Meteorological and Hydrological Drought Risk Assessment Using Multi-Dimensional Copulas in the Wadi Ouahrane Basin in Algeria. *Water* **2022**, *14*, 653.
https://doi.org/10.3390/w14040653

**AMA Style**

Achite M, Bazrafshan O, Wałęga A, Azhdari Z, Krakauer N, Caloiero T. Meteorological and Hydrological Drought Risk Assessment Using Multi-Dimensional Copulas in the Wadi Ouahrane Basin in Algeria. *Water*. 2022; 14(4):653.
https://doi.org/10.3390/w14040653

**Chicago/Turabian Style**

Achite, Mohammed, Ommolbanin Bazrafshan, Andrzej Wałęga, Zahra Azhdari, Nir Krakauer, and Tommaso Caloiero. 2022. "Meteorological and Hydrological Drought Risk Assessment Using Multi-Dimensional Copulas in the Wadi Ouahrane Basin in Algeria" *Water* 14, no. 4: 653.
https://doi.org/10.3390/w14040653