# Seasonal Drought Forecasting for Latin America Using the ECMWF S4 Forecast System

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area, Datasets and Methods

#### 2.1. Forecasts: The ECMWF Seasonal Forecast System (S4)

#### 2.2. Observations: The GPCC Full Data Reanalysis Version 6.0

#### 2.3. Drought Indicator: The Standardized Precipitation Index (SPI)

#### 2.4. Drought Detection and Verification Methods

## 3. Results and Discussion

#### 3.1. Non-Probabilistic Forecasts of Continuous SPI Values

#### 3.2. Non-Probabilistic Forecasts of Categorical SPI Values

#### 3.3. Probabilistic Forecasts of Categorical SPI Values

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Description of the Validation Metrics

#### Appendix A.1. Nonprobabilistic Forecasts of Continuous SPI Values

_{years}= 29 observations (i.e., after subtracting 1 year from the total number of available years in the dataset).

_{1}, that exceed the expected correlation of the same observations with the climatological SPI baseline value (0), r

_{2}. Under the assumption that the sets of forecasts are normally distributed, to assess the statistical significance of the difference between two correlations r

_{1}and r

_{2}, we used Fisher’s Z transformation, as explained in [49]. We define Z

_{i}as

_{1}and r

_{2}to Z

_{1}and Z

_{2}, and computed the statistical significance for the difference in correlations using the Z statistics:

_{1}− 3 and N

_{2}− 3 are the degrees of freedom for r

_{1}and r

_{2}, respectively. Using a null hypothesis of equal correlation and a non-directional alternative hypothesis of unequal correlation, if Z is greater than 1.96, the difference in correlations is statistically significant at the 5% confidence level.

_{Clim}is an estimate of the sample variance of the predictand. For the RMSE using climatology as the control forecasts, the skill score becomes

_{Clim}based on RMSE is sometimes called the reduction of variance (RV), because the quotient being subtracted is the average squared error (or residual, in the nomenclature of regression) divided by the climatological variance.

#### Appendix A.2. Nonprobabilistic Forecasts of Categorical SPI Values

**Table A1.**SPI classification following McKee et al. [8].

SPI Value | Class | Cumulative Probability | Probability of Event [%] |
---|---|---|---|

SPI > 2.00 | Extreme wet | 0.977–1.000 | 2.3% |

1.50 < SPI < 2.00 | Severe wet | 0.933–0.977 | 4.4% |

1.00 < SPI < 1.50 | Moderate wet | 0.841–0.933 | 9.2% |

−1.00 < SPI < 1.00 | Near normal | 0.159–0.841 | 68.2% |

−1.50 < SPI < −1.00 | Moderate dry | 0.067–0.159 | 9.2% |

−2.00 < SPI < −1.50 | Severe dry | 0.023–0.067 | 4.4% |

SPI < −2.00 | Extreme dry | 0.000–0.023 | 2.3% |

**Table A2.**Methods to detect drought events from the S4 ensemble system. Adapted from [40].

Name | Definition | Type |
---|---|---|

13th percentile (Q13) | Member located at the 13% of the CDF | Individual |

23th percentile (Q23) | Member located at the 23% of the CDF | Individual |

Median (MED) | Member located at the 50% of the CDF | Individual |

77th percentile (Q77) | Member located at the 77% of the CDF | Individual |

88th percentile (Q88) | Member located at the 88% of the CDF | Individual |

Large spread (SpL) | Sum of the extreme members (Q13 + Q88) | Partially integrative |

Low spread (Spl) | Sum of the members (Q23 + Q78) | Partially integrative |

Dry spread (SpD) | Sum of the dry members (Q13 + Q23) | Partially integrative |

Flood spread (SpF) | Sum of the wet members (Q77 + Q88) | Partially integrative |

Mean (EM_RES) | Ensemble mean | Integrative |

#### Appendix A.3. Probabilistic Forecast of Categorical SPI Values

_{k}= 1 if a drought event occurs (i.e., SPI ≤ −1), and that the GPCC observation at time k is o

_{k}= 0 if a drought event does not occur (i.e., SPI > −1). The BS averages the squared differences between pairs of forecast probabilities, fcst

_{k}, and the subsequent binary reference observations,

_{clim}are also often computed for the BS, yielding the Brier Skill Score (BSS):

_{perf}= 1. Similarly ROC curves for random forecasts lie along the 45° diagonal of the unit square, yielding the area A

_{rand}= 0.5. The area A under a ROC curve of interest can also be expressed in standard skill-score form SS

_{ROC}, as

_{ROC}is a reasonably good discriminator among relatively low-quality forecasts, but that relatively good forecasts tend to be characterized by quite similar (near-unit) areas under their ROC curves. The SS

_{ROC}ranges between 0 and 1; 0.5 indicates no skill, while the perfect score is 1.

**Figure A1.**Monthly correlation of the observed and forecast SPI at 6-months lead time (SPI6) (using the mean of the ensemble) for the hindcast period (1981–2010). Values are indicated in the color bar: 0.31 (0.37) is statistical significant at 10% (5%) significance level.

**Figure A2.**Monthly difference in forecast skill (Pearson correlation) between the forecast SPI6 at 6-month lead time (using the mean of the ensemble) and climatological SPI for the hindcast period (1981–2010). Values are indicated in the color bar: 1.96 is the statistical significant at the 5% significance level.

**Figure A3.**RMSE between the observed and forecast SPI6 at 6-month lead time (mean of the ensemble) for the hindcast period (1981–2010). Values in difference of percentile magnitude are indicated in the color bar.

**Figure A4.**Skill Score of the SPI6 at 6-month lead time forecast measured in terms of the RMSE relative to climatological RMSE for the hindcast period (1981–2010).

**Figure A5.**Verification measures of categorical drought forecasts (i.e., below the SPI6 “-1” threshold) estimated with the methods described in Table A2.

## References

- Carrão, H.; Singleton, A.; Naumann, G.; Barbosa, P.; Vogt, J. An optimized system for the classification of meteorological drought intensity with applications in frequency analysis. J. Appl. Meteorol. Climatol.
**2014**, 53, 1943–1960. [Google Scholar] [CrossRef] - Goddard, S.; Harms, S.K.; Reichenbach, S.E.; Tadesse, T.; Waltman, W.J. Geospatial decision support for drought risk management. Commun. ACM
**2003**, 46, 35–37. [Google Scholar] [CrossRef] - Dai, A. Drought under global Warming: A review. Wiley Interdiscip. Rev. Clim. Chang.
**2011**, 2, 45–65. [Google Scholar] [CrossRef] - Lloyd-Hughes, B. The impracticality of a universal drought definition. Theor. Appl. Climatol.
**2014**, 117, 607–611. [Google Scholar] [CrossRef] - Steinemann, A.C.; Cavalcanti, L.F. Developing multiple indicators and triggers for drought plans. J. Water Res. Plan. Manag.
**2006**, 132, 164–174. [Google Scholar] [CrossRef] - Heim, R.R. A review of twentieth-century drought indices used in the United States. Bull. Am. Meteorol. Soc.
**2002**, 83, 1149–1165. [Google Scholar] [CrossRef] - Vicente-Serrano, S.M.; Beguerıa, S.; Lopez-Moreno, J.I. A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index. J. Clim.
**2010**, 23, 1696–1718. [Google Scholar] [CrossRef] - McKee, T.B.; Doeskin, N.J.; Kleist, J. The relationship of drought frequency and duration to time scales. In Proceedings of the 8th Conference on Applied Climatology, American Meteorological Society, Anaheim, CA, USA, 17–22 January 1993; pp. 179–184. [Google Scholar]
- Svoboda, M.; Hayes, M.; Wood, D. Standardized Precipitation Index User Guide; WMO-No. 1090; World Meteorological Organization (WMO): Geneva, Switzerland, 2012. [Google Scholar]
- Mishra, A.K.; Singh, V.P. A review of drought concepts. J. Hydrol.
**2010**, 391, 202–216. [Google Scholar] [CrossRef] - Kim, T.-W.; Valds, J.B. Nonlinear model for drought forecasting based on a conjunction of wavelet transforms and neural networks. J. Hydrol. Eng.
**2003**, 8, 319–328. [Google Scholar] [CrossRef] - Mishra, A.K.; Desai, V.R.; Singh, V.P. Drought forecasting using a hybrid stochastic and neural network model. J. Hydrol. Eng.
**2007**, 12, 626–638. [Google Scholar] [CrossRef] - Mishra, A.K.; Desai, V.R. Drought forecasting using stochastic models. Stoch. Environ. Res. Risk Assess.
**2005**, 19, 326–339. [Google Scholar] [CrossRef] - Vitart, F.; Buizza, R.; Alonso Balmaseda, M.; Balsamo, G.; Bidlot, J.-R.; Bonet, A.; Fuentes, M.; Hofstadler, A.; Molteni, F.; Palmer, T.N. The new VAREPS-monthly forecasting system: A first step towards seamless prediction. Q. J. R. Meteorol. Soc.
**2008**, 134, 1789–1799. [Google Scholar] [CrossRef] - Nijssen, B.; Shukla, S.; Lin, C.; Gao, H.; Zhou, T.; Ishottama; Sheffield, J.; Wood, E.F.; Lettenmaier, D.P. A prototype global drought information system based on multiple land surface models. J. Hydrometeorol.
**2014**, 15, 1661–1676. [Google Scholar] [CrossRef] - Yuan, X.; Wood, E.F. Multimodel seasonal forecasting of global drought onset. Geophys. Res. Lett.
**2013**, 40, 4900–4905. [Google Scholar] [CrossRef][Green Version] - Hao, Z.; AghaKouchak, A.; Nakhjiri, N.; Farahmand, A. Global integrated drought monitoring and prediction system. Sci. Data
**2014**, 1, 140001. [Google Scholar] [CrossRef] [PubMed] - Dutra, E.; Wetterhall, F.; Di Giuseppe, F.; Naumann, G.; Barbosa, P.; Vogt, J.; Pozzi, W.; Pappenberger, F. Global meteorological drought Part 1: Probabilistic monitoring. Hydrol. Earth Syst. Sci.
**2014**, 18, 2657–2667. [Google Scholar] [CrossRef] - Dutra, E.; Pozzi, W.; Wetterhall, F.; Di Giuseppe, F.; Magnusson, L.; Naumann, G.; Barbosa, P.; Vogt, J.; Pappenberger, F. Global meteorological drought Part 2: Seasonal forecasts. Hydrol. Earth Syst. Sci.
**2014**, 18, 2669–2678. [Google Scholar] [CrossRef][Green Version] - Spennemann, P.C.; Rivera, J.A.; Osman, M.; Saulo, A.C.; Penalba, O.C. Assessment of seasonal soil moisture forecasts over Southern South America with emphasis on dry and wet events. J. Hydrometeorol.
**2017**, 18, 2297–2311. [Google Scholar] [CrossRef] - Sheffield, J.; Andreadis, K.M.; Wood, E.F.; Lettenmaier, D.P. Global and continental drought in the second half of the twentieth century: Severity–area–duration analysis and temporal variability of large-scale events. J. Clim.
**2009**, 22, 1962–1981. [Google Scholar] [CrossRef] - Zhao, M.; Running, S.W. Drought-induced reduction in global terrestrial net primary production from 2000 through 2009. Science
**2010**, 329, 940–943. [Google Scholar] [CrossRef] [PubMed] - Vargas, W.M.; Naumann, G.; Minetti, J.L. Dry spells in the river Plata Basin: An approximation of the diagnosis of droughts using daily data. Theor. Appl. Climatol.
**2011**, 104, 159–173. [Google Scholar] [CrossRef] - Field, C.B.; Barros, V.; Stocker, T.F.; Qin, D.; Dokken, D.J.; Ebi, K.L.; Mastrandrea, M.D.; Mach, K.J.; Plattner, G.-K.; Allen, S.K.; et al. (Eds.) Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation; Cambridge University Press: New York, NY, USA, 2012; pp. 1–19. [Google Scholar]
- Penalba, O.C.; Rivera, J.A. Future changes in drought characteristics over Southern South America projected by a CMIP5 multi-model ensemble. Am. J. Clim. Chang.
**2013**, 2, 173–182. [Google Scholar] [CrossRef] - Trenberth, K.E.; Stepaniak, D. Indices of El Niño evolution. J. Clim.
**2011**, 14, 1697–1701. [Google Scholar] [CrossRef] - FAO. Aquastat Database. Food and Agriculture Organization of the United Nations (FAO). 2017. Available online: http://www.fao.org/nr/water/aquastat/main/index.stm (accessed on 15 October 2017).
- Magrin, G.; Garcia, C.G.; Choque, D.C.; Gimenez, J.C.; Moreno, A.R.; Nagy, G.J.; Nobre, C.; Villamizar, A. Climate change, Impacts, adaptation and vulnerability. In Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change; Parry, M.L., Canziani, O.F., Palutikof, J.P., van der Linden, P., Hanson, C.E., Eds.; Cambridge University Press: Cambridge, UK, 2007; pp. 581–615. [Google Scholar]
- Llano, M.P.; Vargas, W.; Naumann, G. Climate variability in areas of the world with high production of soya beans and Corn: Its relationship to crop yields. Meteorol. Appl.
**2012**, 19, 385–396. [Google Scholar] [CrossRef] - Molteni, F.; Stockdale, T.; Balmaseda, M.; Balsamo, G.; Buizza, R.; Ferranti, L.; Magnunson, L.; Mogensen, K.; Palmer, T.; Vitart, F. The new ECMWF seasonal forecast system (System 4). In Technical Memorandum No. 656; European Centre for Medium Range Weather Forecasts: Berkshire, UK, 2011. [Google Scholar]
- Rudolf, B.; Becker, A.; Schneider, U.; Meyer-Christoffer, A.; Ziese, M. New full data reanalysis version 5 provides high-quality gridded monthly precipitation data. GEWEX News
**2011**, 21, 4–5. [Google Scholar] - Naumann, G.; Barbosa, P.; Carrão, H.; Singleton, A.; Vogt, J. Monitoring drought conditions and their uncertainties in Africa using TRMM data. J. Appl. Meteorol. Climatol.
**2012**, 51, 1867–1874. [Google Scholar] [CrossRef] - Svoboda, M.; LeComte, D.; Hayes, M.; Heim, R.; Gleason, K.; Angel, J.; Rippey, B.; Tinker, R.; Palecki, M.; Stooksbury, D.; et al. The drought monitor. Bull. Am. Meteorol. Soc.
**2002**, 83, 1181–1190. [Google Scholar] [CrossRef] - Steinemann, A. Drought indicators and Triggers: A stochastic approach to evaluation. JAWRA
**2003**, 39, 1217–1233. [Google Scholar] [CrossRef] - Hayes, M.J.; Svoboda, M.D.; Wilhite, D.A.; Vanyarkho, O.V. Monitoring the 1996 drought using the standardized precipitation index. Bull. Am. Meteorol. Soc.
**1999**, 80, 429–438. [Google Scholar] [CrossRef] - Wu, H.; Hayes, M.J.; Wilhite, D.A.; Svoboda, M.D. The effect of the length of record on the standardized precipitation index calculation. Int. J. Climatol.
**2005**, 25, 505–520. [Google Scholar] [CrossRef][Green Version] - Sepulcre-Canto, G.; Horion, S.; Singleton, A.; Carrão, H.; Vogt, J. Development of a combined drought indicator to detect agricultural drought in Europe. Earth Syst. Sci.
**2012**, 12, 3519–3531. [Google Scholar] [CrossRef] - Ntale, H.K.; Gan, T.Y. Drought indices and their application to east Africa. Int. J. Climatol.
**2003**, 23, 1335–1357. [Google Scholar] [CrossRef] - Hofer, B.; Carrao, H.; Mcinerney, D. Multi-disciplinary forest fire danger assessment in Europe: The potential to integrate long-term drought information. IJSDIR
**2012**, 7, 300–322. [Google Scholar] - Lavaysse, C.; Vogt, J.; Pappenberger, F. Early warning of drought in Europe using the monthly ensemble system from ECMWF. Hydrol. Earth Syst. Sci.
**2015**, 19, 3273–3286. [Google Scholar] [CrossRef][Green Version] - Mo, K.C.; Lyon, B. Global meteorological drought prediction using the North American multi-model ensemble. J. Hydrometeorol.
**2015**, 16, 1409–1424. [Google Scholar] [CrossRef] - Vera, C.S.; Alvarez, M.S.; Gonzalez, P.L.; Liebmann, B.; Kiladis, G.N. Seasonal cycle of precipitation variability in South America on intraseasonal timescales. Clim. Dyn.
**2017**, 1–11. [Google Scholar] [CrossRef] - González, P.L.; Vera, C.S. Summer precipitation variability over South America on long and short intraseasonal timescales. Clim. Dyn.
**2014**, 43, 1993–2007. [Google Scholar] [CrossRef] - González, P.L.; Vera, C.S.; Liebmann, B.; Kiladis, G. Intraseasonal variability in subtropical South America as depicted by precipitation data. Clim. Dyn.
**2008**, 30, 727–744. [Google Scholar] [CrossRef] - Ghelli, A.; Primo, C. On the use of the extreme dependency score to investigate the performance of an NWP model for rare events. Meteorol. Appl.
**2009**, 16, 537–544. [Google Scholar] [CrossRef][Green Version] - Ruscica, R.C.; Sörensson, A.A.; Menéndez, C.G. Pathways between soil moisture and precipitation in southeastern South America. Atmos. Sci. Lett.
**2015**, 16, 267–272. [Google Scholar] [CrossRef][Green Version] - Spennemann, P.C.; Saulo, A.C. An estimation of the land–atmosphere coupling strength in South America using the Global Land Data Assimilation System. Int. J. Climatol.
**2015**, 35, 4151–4166. [Google Scholar] [CrossRef] - Wilks, D.S. Statistical Methods in the Atmospheric Sciences, 2nd ed.; Academic Press: Amsterdam, The Netherlands, 2005. [Google Scholar]
- Quan, X.W.; Hoerling, M.P.; Lyon, B.; Kumar, A.; Bell, M.A.; Tippett, M.K.; Wang, H. Prospects for dynamical prediction of meteorological drought. J. Appl. Meteorol. Climatol.
**2012**, 51, 1238–1252. [Google Scholar] [CrossRef] - Lavaysse, C.; Carrera, M.; Blair, S.; Gagnon, N.; Frenette, R.; Charron, M.; Yau, M.K. Impact of surface parameter uncertainties within the Canadian regional ensemble prediction system. Mon. Weather Rev.
**2013**, 141, 1506–1526. [Google Scholar] [CrossRef] - Stephenson, D.B.; Casati, B.; Ferro, C.A.T.; Wilson, C.A. The extreme dependency Score: A non-vanishing measure for forecasts of rare events. Meteorol. Appl.
**2008**, 15, 41–50. [Google Scholar] [CrossRef]

**Figure 1.**Monthly correlation of the observed and forecast standardized precipitation index (SPI) at 3-months lead time (SPI3) (using the mean of the ensemble) for the hindcast period (1981–2010). Values are indicated in the color bar: 0.31 (0.37) is statistical significant at 10% (5%) significance level.

**Figure 2.**Monthly difference in forecast skill (Pearson correlation) between the forecast SPI3 at 3-month lead time (using the mean of the ensemble) and climatological SPI for the hindcast period (1981–2010). Values are indicated in the color bar: 1.96 is the statistical significance at the 5% significance level.

**Figure 3.**Root Mean Squared Error (RMSE) between the observed and forecast SPI3 at 3-month lead time (mean of the ensemble) for the hindcast period (1981–2010). Values in difference of percentile magnitude are indicated in the color bar.

**Figure 4.**Skill Score of the SPI3 at 3-month lead time forecast measured in terms of the RMSE relative to climatological RMSE for the hindcast period (1981–2010).

**Figure 5.**Verification measures of categorical drought forecasts (i.e., below the SPI3 “-1” threshold) estimated with the methods described in Table A2.

**Figure 6.**Brier Skill Score (BSS) of the European Centre for Medium Range Weather (ECMWF) S4 SPI-3 forecast for different probabilities of SPI occurrence, at a lead time of 3 months for the hindcast period 1981–2010. Values are indicated in the color bar; land grid points colored in white indicate that the forecasting system is no more skillful than the climatology.

**Figure 7.**Brier Skill Score (BSS) of the ECMWF S4 SPI-6 forecast for different probabilities of SPI occurrence, at a lead time of 3 months for the hindcast period 1981–2010. Values are indicated in the color bar; land grid points colored in white indicate that the forecasting system is no more skillful than the climatology.

**Figure 8.**Area under the Relative Operating Characteristic (ROC) curve for the probability of drought detection at different SPI3 frequencies. Values indicated in the color bar are estimated at lead time of 3 months for the hindcast period 1981–2010.

**Figure 9.**Area under the ROC curve for the probability of drought detection at different SPI6 frequencies. Values indicated in the color bar are estimated at lead time of 6 months for the hindcast period 1981–2010.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Carrão, H.; Naumann, G.; Dutra, E.; Lavaysse, C.; Barbosa, P. Seasonal Drought Forecasting for Latin America Using the ECMWF S4 Forecast System. *Climate* **2018**, *6*, 48.
https://doi.org/10.3390/cli6020048

**AMA Style**

Carrão H, Naumann G, Dutra E, Lavaysse C, Barbosa P. Seasonal Drought Forecasting for Latin America Using the ECMWF S4 Forecast System. *Climate*. 2018; 6(2):48.
https://doi.org/10.3390/cli6020048

**Chicago/Turabian Style**

Carrão, Hugo, Gustavo Naumann, Emanuel Dutra, Christophe Lavaysse, and Paulo Barbosa. 2018. "Seasonal Drought Forecasting for Latin America Using the ECMWF S4 Forecast System" *Climate* 6, no. 2: 48.
https://doi.org/10.3390/cli6020048