# Spatiotemporal Kriging for Days without Rainfall in a Region of Northeastern Brazil

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}of 71%, indicating a good performance of spatiotemporal kriging for predicting DWRs. The results indicate a spatial dependence for a radius of up to 39 km and that the DWR observations in a certain location influence its estimates in the next 2.8 years. The projection maps from 2021 to 2030 identified a growing trend in the DWRs. With the results presented in our study, it is expected that they can be used by government agencies for the adoption of public policies aiming to minimize the possible damage caused by long periods of drought.

## 1. Introduction

## 2. Materials and Methods

^{2}, which corresponds to 0.664% of the entire territory of Brazil [17]. To obtain an idea of the extent of this region, countries on the European continent, such as Slovakia (48,845 km

^{2}), Denmark (43,094 km

^{2}) and Switzerland (41,290 km

^{2}) have areas smaller than the State of Paraíba. The state is divided into four mesoregions (Sertão Paraibano, Borborema, Agreste Paraibano and Mata Paraibana) with different climatic and environmental conditions (Figure 1).

^{2}) was calculated to determine how much of the variability in the DWR is explained by the tendency.

^{2}.

## 3. Results and Discussion

^{2}of 29% [18].

^{2}of 85% in the “leave-one-out” cross-validation. Research on the space–time distribution of pests and predators in maize production used the generalized product-sum model. However, they only verified the adequacy of this model to the point cloud of the empirical variogram, not using cross-validation to verify the predictive quality of the fit [28].

## 4. Final Remarks

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Map of South America (

**left side**) with details for the region under study (

**right side**) accompanied by the location of the 238 rainfall stations in the state of Paraíba.

**Figure 2.**Average annual number of days without rain (DWR) for the State of Paraíba in the period from 1994 to 2020.

**Figure 3.**Density of the annual number of days without rain (DWR) for the Paraíba mesoregions from 1994 to 2020.

**Figure 4.**Analysis of the trend between the annual number of days without rain (DWR) and the geographic coordinates longitude (

**a**) and latitude (

**b**) in the state of Paraíba.

**Figure 5.**Experimental variograms (

**left side**) and the theoretical generalized product-sum (

**right side**) for the number of days without rain in the year after removing the tendency.

**Figure 6.**Leave-one-out cross-validation results for the annual number of days without rain (DWR) for the State of Paraíba. Figure (

**a**) is the mean absolute error (abs(error)) at each station, and Figure (

**b**) represents the relationship between the observed and predicted DWR data.

**Figure 7.**Spatiotemporal kriging for the annual number of days without rain (DWR) in the State of Paraíba.

**Figure 8.**Spatial distribution of the Spearman correlation between the annual number of days without rain and the annual accumulated rainfall in the State of Paraíba.

**Table 1.**Descriptive measures for the number of days without rain in the state of Paraíba from 1994 to 2020.

Mesoregions | N Station | Mean | Median | SD | CV (%) |
---|---|---|---|---|---|

Zona da Mata | 33 | 240.32 | 234.00 | 38.11 | 15.86% |

Agreste | 71 | 288.84 | 283.00 | 33.67 | 11.99% |

Borborema | 48 | 324.88 | 327.00 | 18.58 | 5.72% |

Sertão | 86 | 313.53 | 315.00 | 17.71 | 5.65% |

**Table 2.**Results of the multiple regression adjustment for the number of days without rain in the State of Paraíba in the period from 1994 to 2020.

Variable | Estimate | Std. Error | t Value | p Value | R^{2} |
---|---|---|---|---|---|

Intercept | −354.895 | 13.919 | −25.497 | <0.01 | 54.64% |

Longitude | 1.985 | 0.038 | 52.002 | <0.01 | |

Longitude^{2} | −0.001 | 0.000 | −56.499 | <0.01 |

**Table 3.**Estimates of the generalized product-sum theoretical model adjusted to the number of days without rain per year in the State of Paraíba.

Component | Variogram | Nugget | Sill | Range | k |
---|---|---|---|---|---|

Spatial | Exponential | 140.043 | 272.274 | 39.145 km | 0.545 |

Temporal | Exponential | 1.505 | 3.176 | 2.757 years |

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**MDPI and ACS Style**

Medeiros, E.S.d.; Lima, R.R.d.; Santos, C.A.C.d.
Spatiotemporal Kriging for Days without Rainfall in a Region of Northeastern Brazil. *Climate* **2023**, *11*, 21.
https://doi.org/10.3390/cli11010021

**AMA Style**

Medeiros ESd, Lima RRd, Santos CACd.
Spatiotemporal Kriging for Days without Rainfall in a Region of Northeastern Brazil. *Climate*. 2023; 11(1):21.
https://doi.org/10.3390/cli11010021

**Chicago/Turabian Style**

Medeiros, Elias Silva de, Renato Ribeiro de Lima, and Carlos Antonio Costa dos Santos.
2023. "Spatiotemporal Kriging for Days without Rainfall in a Region of Northeastern Brazil" *Climate* 11, no. 1: 21.
https://doi.org/10.3390/cli11010021