# An Integrated Statistical Method to Generate Potential Future Climate Scenarios to Analyse Droughts

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## Abstract

**:**

## 1. Introduction

## 2. Method

#### 2.1. Generation of Future Individual Projections

- (1)
- For each RCM model, we can represent the differences between the statistics (basic and drought statistics) of the control scenarios simulations and the “historical” values. These usually reveal significant bias, which justifies correcting them. The set of techniques to address this issue are known as bias correction approaches, since they apply a perturbation to the control series with the aim of forcing some of their statistics to get closer to the historical ones. In order to generate future series, they assume that the bias between the statistics of real data and model scenarios (control scenarios) will remain invariant into the future (e.g., [22,32]).
- (2)
- We can also represent and analyse the relative differences between control and future scenario statistics for the climatic model simulation for specific emission scenarios. Based on this information, future scenarios can be also generated by assuming that the RCMs provide accurate assessment of the relative changes in the statistics between present and future scenarios, but that they do not adequately assess the absolute values. These approaches, known as delta change solutions, use the relative difference in the statistics of control and future simulations to create a perturbation in the historical series, in accordance with these estimated changes (e.g., [25,26,27]).

#### 2.2. Multi-Objective Analysis of the Main Statistics (Basic and Drought Statistics)

#### 2.3. Ensembles of Predictions to Define More Representative Future Climate Scenarios

## 3. Study Area: Description and Available Data

#### 3.1. Location and Description of the Alto Genil Basin

#### 3.2. Historical Climate Data

#### 3.3. Climate Model Simulation Data. Control and Future Scenarios

## 4. Results and Discussion

#### 4.1. Application of Different Correction Techniques

#### 4.2. Multi-Objective Analysis of Basic and Drought Statistics

#### 4.3. Ensembles of Predictions to Define More Representative Future Climate Scenarios

#### 4.4. Sensitivity of Results to Spatial Scale

## 5. Limitations and Future Research Works

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Historical precipitation and temperature in Alto Genil basin. Above: Monthly precipitation and temperature time series. Below: Spatial distribution of mean precipitation and temperature.

**Figure 4.**Monthly mean and standard deviation for the historical and control series (precipitation and temperature) for the mean year in the period 1971–2000—lumped approaches.

**Figure 5.**Drought statistics for the historical and control series in the period 1971–2000—lumped approaches.

**Figure 6.**Dimensionless relative monthly change in mean and standard deviation of the future P and T series (2071–2100) with respect to the control series (1971–2000)—lumped approaches. Relative changes calculated as (F − C)/C where F stands for future model projections and C control model simulations.

**Figure 7.**Mean, standard deviation, and asymmetry coefficients of the corrected control scenario (1971–2000) for precipitation (left column) and temperature (right column). Average year for HIRHAM5 RCM model nested inside EC-EARTH GCM—lumped approaches.

**Figure 8.**Drought statistics of the corrected precipitation control scenario (1971–2000) for the HIRHAM5 RCM model nested inside EC-EARTHGCM—lumped approaches.

**Figure 9.**Mean, standard deviation and asymmetry coefficients of future precipitation (

**left**column) and temperature series (

**right**column). Average year for HIRHAM5 RCM model nested inside EC-EARTH GCM—lumped approaches.

**Figure 10.**Drought statistics of future precipitation series for the HIRHAM5 RCM model nested inside EC-EARTH GCM—lumped approaches.

**Figure 11.**(

**A**) Times that the techniques are not eliminated in the multi-objective analysis (bias correction approach); (

**B**) Times that the RCMs are not eliminated in the multi-objective analysis (bias correction change approach).

**Figure 12.**Mean and standard deviation of future precipitation and temperature series obtained by the four ensemble options (E1, E2, E3, and E4)—lumped approaches.

**Figure 13.**Drought statistics of future precipitation series obtained by the four ensemble options (E1, E2, E3, and E4)—lumped approaches.

**Figure 14.**Spatial distribution of the mean relative change (expressed in %) in precipitation and temperature obtained by the four ensemble options (E1, E2, E3, and E4)—distributed approaches.

**Figure 15.**Monthly differences in mean and standard deviation in an average year between distributed (D) and lumped (L) approaches ((L − D)/D) × 100) for the four ensembles scenarios (E1, E2, E3 and E4).

**Table 1.**Summary of advantages and disadvantages of each correction technique (P stands for precipitation).

Correction Technique | Pros | Cons |
---|---|---|

First-moment correction | - Does not generate negative values for P | - Only preserve the mean |

Second-moment correction | - Preserve mean and standard deviation | - Generates some negative values for P |

Regression | - Allow to use different regression models - Preserve mean and standard deviation | - Generates some negative values for P |

Quantile mapping | - Preserve mean and standard deviation - No generates negative values of P - Variety of methods (theoretical distribution, parametric, non-parametric, empirical, splines) | - Required more complex transformations (application to the probability distribution of data) |

GCM | CNRM-CM5 | EC-EARTH | MPI-ESM-LR | IPSL-CM5A-MR | |

RCM | |||||

CCLM4-8-17 | X | X | X | ||

RCA4 | X | X | X | ||

HIRHAM5 | X | ||||

RACMO22E | X | ||||

WRF331F | X |

**Table 3.**Eliminated and uneliminated models in the multi-objective analysis of the delta change approaches for the lumped and distributed cases.

RCM | GCM | Eliminated | |
---|---|---|---|

Lumped Cases | Distributed Case | ||

CCLM4-8-17 | CNRM-CM5 | NO | NO |

CCLM4-8-17 | EC-EARTH | NO | NO |

CCLM4-8-17 | MPI-ESM-LR | NO | NO |

HIRHAM5 | EC-EARTH | NO | YES |

RACMO22E | EC-EARTH | NO | NO |

RCA4 | CNRM-CM5 | NO | NO |

RCA4 | EC-EARTH | NO | YES |

RCA4 | MPI-ESM-LR | YES | NO |

WRF331F | IPSL-CM5A-MR | NO | NO |

CCLM4-8-17 | CNRM-CM5 | NO | NO |

**Table 4.**Eliminated and uneliminated combinations of model and bias correction technique for the lumped and distributed cases.

RCM | GCM | Technique | Lumped Case | Distributed Case |
---|---|---|---|---|

CCLM4-8-17 | CNRM-CM5 | 1st moment correc. | YES | YES |

CCLM4-8-18 | CNRM-CM6 | 2nd moment correc. | NO | YES |

CCLM4-8-19 | CNRM-CM7 | Regression | YES | YES |

CCLM4-8-20 | CNRM-CM8 | QM Parametric dist. | NO | YES |

CCLM4-8-21 | CNRM-CM9 | QM Empirical quant. | YES | NO |

CCLM4-8-17 | EC-EARTH | 1st moment correc. | YES | YES |

CCLM4-8-18 | EC-EARTH | 2nd moment correc. | YES | YES |

CCLM4-8-19 | EC-EARTH | Regression | NO | YES |

CCLM4-8-20 | EC-EARTH | QM Parametric dist. | YES | YES |

CCLM4-8-21 | EC-EARTH | QM Empirical quant. | NO | NO |

CCLM4-8-17 | MPI-ESM-LR | 1st moment correc. | YES | YES |

CCLM4-8-17 | MPI-ESM-LR | 2nd moment correc. | NO | NO |

CCLM4-8-17 | MPI-ESM-LR | Regression | NO | NO |

CCLM4-8-17 | MPI-ESM-LR | QM Parametric dist. | NO | NO |

CCLM4-8-17 | MPI-ESM-LR | QM Empirical quant. | NO | NO |

HIRHAM5 | EC-EARTH | 1st moment correc. | YES | YES |

HIRHAM5 | EC-EARTH | 2nd moment correc. | NO | NO |

HIRHAM5 | EC-EARTH | Regression | NO | NO |

HIRHAM5 | EC-EARTH | QM Parametric dist. | NO | YES |

HIRHAM5 | EC-EARTH | QM Empirical quant. | NO | YES |

RACMO22E | EC-EARTH | 1st moment correc. | YES | YES |

RACMO22E | EC-EARTH | 2nd moment correc. | YES | YES |

RACMO22E | EC-EARTH | Regression | NO | YES |

RACMO22E | EC-EARTH | QM Parametric dist. | YES | YES |

RACMO22E | EC-EARTH | QM Empirical quant. | YES | YES |

RCA4 | CNRM-CM5 | 1st moment correc. | YES | YES |

RCA4 | CNRM-CM5 | 2nd moment correc. | NO | YES |

RCA4 | CNRM-CM5 | Regression | NO | YES |

RCA4 | CNRM-CM5 | QM Parametric dist. | YES | YES |

RCA4 | CNRM-CM5 | QM Empirical quant. | NO | NO |

RCA4 | EC-EARTH | 1st moment correc. | YES | YES |

RCA4 | EC-EARTH | 2nd moment correc. | YES | YES |

RCA4 | EC-EARTH | Regression | YES | YES |

RCA4 | EC-EARTH | QM Parametric dist. | YES | YES |

RCA4 | EC-EARTH | QM Empirical quant. | YES | YES |

RCA4 | MPI-ESM-LR | 1st moment correc. | YES | YES |

RCA4 | MPI-ESM-LR | 2nd moment correc. | YES | YES |

RCA4 | MPI-ESM-LR | Regression | YES | NO |

RCA4 | MPI-ESM-LR | QM Parametric dist. | NO | NO |

RCA4 | MPI-ESM-LR | QM Empirical quant. | YES | YES |

WRF331F | IPSL-CM5A-MR | 1st moment correc. | YES | YES |

WRF331F | IPSL-CM5A-MR | 2nd moment correc. | YES | YES |

WRF331F | IPSL-CM5A-MR | Regression | YES | YES |

WRF331F | IPSL-CM5A-MR | QM Parametric dist. | YES | YES |

WRF331F | IPSL-CM5A-MR | QM Empirical quant. | NO | NO |

**Table 5.**Changes of overall mean values for precipitation and temperature scenarios compared to historical data.

Scenario | Lumped Case | Distributed Case | ||
---|---|---|---|---|

P | T | P | T | |

Absolute Changes (mm or °C) | ||||

E1 | −147.9 | 4.5 | −142.4 | 4.5 |

E2 | −139.0 | 4.5 | −131.9 | 4.6 |

E3 | −143.4 | 4.5 | −149.4 | 4.5 |

E4 | −139.1 | 4.4 | −141.9 | 4.6 |

Relative Changes (%) | ||||

E1 | −28.21 | 31.94 | −27.16 | 31.66 |

E2 | −26.51 | 31.59 | −25.16 | 32.05 |

E3 | −27.35 | 31.74 | −28.50 | 31.79 |

E4 | −26.53 | 30.99 | −27.06 | 32.49 |

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**MDPI and ACS Style**

Collados-Lara, A.-J.; Pulido-Velazquez, D.; Pardo-Igúzquiza, E.
An Integrated Statistical Method to Generate Potential Future Climate Scenarios to Analyse Droughts. *Water* **2018**, *10*, 1224.
https://doi.org/10.3390/w10091224

**AMA Style**

Collados-Lara A-J, Pulido-Velazquez D, Pardo-Igúzquiza E.
An Integrated Statistical Method to Generate Potential Future Climate Scenarios to Analyse Droughts. *Water*. 2018; 10(9):1224.
https://doi.org/10.3390/w10091224

**Chicago/Turabian Style**

Collados-Lara, Antonio-Juan, David Pulido-Velazquez, and Eulogio Pardo-Igúzquiza.
2018. "An Integrated Statistical Method to Generate Potential Future Climate Scenarios to Analyse Droughts" *Water* 10, no. 9: 1224.
https://doi.org/10.3390/w10091224