# Drought Model DISS Based on the Fusion of Satellite and Meteorological Data under Variable Climatic Conditions

^{*}

## Abstract

**:**

## 1. Introduction

- HTC is adequate for stratifying the water deficit regions;
- TCI with lag steps characterizes the thermal conditions of the area;
- fusion of meteorological and satellite data is cardinal in the drought detection model.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Meteorological Data

#### 2.3. Hydrothermal Coefficient

**[37,38]**. HTC is included in the Handbook of Drought Indicator and Indices [39] as one of the indices useful for defining atmospheric drought. The accumulation period of precipitation and air temperature is usually assumed for drought assessment as multiples of ten days; such a principle was applied in the present work.

#### 2.4. Satellite Data

- LST
_{max}—maximum LST from the multiannual period; - LST
_{min}—minimum LST from the multiannual period; - LST
_{i}—LST for the particular eight-day period.

#### 2.5. Approach for Drought Assessment Using Satellite and Meteorological Data

#### 2.5.1. Panel Data and Fixed Effect Model

_{i,t-k}, k = 0,…,m;

- $\widehat{{Y}_{i}}$, $\widehat{{X}_{i}}$—the fixed-in-time expected values of variables X and Y;
- $\widehat{{\epsilon}_{i}}$ = 0, because the mean of the residuum is zero by assumption of the least mean squares method (LMSQ) method.

#### 2.5.2. Design of the Drought Index Based on the TCI under Different Climatic Areas

- $HTC{30}_{i,t}$—HTC30 coefficient of station i at time point t (eight-day step in the growing season);
- $MedHTC{30}_{i}$—median of all HTC30 observations at station i;
- $TC{I}_{i,t}$—TCI for the area close to station i at time point t;
- 0.5—the expected mean of the TCI variable for every station at every time point;
- ${\epsilon}_{i,t}$—the error for station i at time point t;
- ${\beta}_{0}$, ${\beta}_{1},$${\beta}_{2}$—the parameters to estimate.

_{i,t}= log(HTC30

_{i,t}) – log(MedHTC30

_{i}). The mean subtraction results in the dependent variable becoming free from the atmospheric characteristics represented by the median MedHTC30 of each station. The learning sample was limited to such cases where the number of agricultural pixels within 10 km of the meteorological station exceeded 200. Such a choice provides more averaging of area in the agricultural cover class, which is advantageous for modeling. TCI data come from the aggregation of 1 km

^{2}pixel values for the sample area. A histogram of the dependent variable, called YHTC30, presented in Figure 10, shows the normal distribution necessary for using the LMSQ regression method.

- Drought—when DISS < 0.5
- Drying—when DISS ≥ 0.5 and DISS < 0.8
- Average conditions—when DISS ≥ 0.8 and DISS < 1.5
- Good conditions—when DISS ≥ 1.5 and DISS < 3.0
- Wet/cold conditions—when DISS ≥ 3.0

#### 2.6. Areas of Drought versus Yield Reduction

## 3. Results

#### 3.1. Comparison of the Spatial Patterns of the HTC and DISS Indices

#### 3.2. Temporal Analysis of the Occurrence of Drought in Poland

## 4. Discussion

#### 4.1. Verification of Drought Maps

#### 4.2. Spatial Analysis of the Occurrence of Drought in Poland

#### 4.3. General Discussion

## 5. Conclusions

^{2}, which is very important for the agriculture sector. In the future, the model will be tested for the global scale with the use of gridded meteorological data from models. Strong discussions are taking place in regional governments regarding the building of irrigation systems and the provision of capacity for local retention. Local retention is very important, as Poland is exposed to climate changes when drought frequently occurs.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Changes in hydrothermal coefficient (HTC) for growing seasons 2015 and 2017—meteorological station Smolice.

**Figure 4.**Precipitation (PP) and temperature (T) for growing seasons 2015 and 2017—meteorological station Smolice.

**Figure 11.**Comparison of Drought Information Satellite System (DISS) values for different MedHTC conditions.

**Figure 14.**Comparison of the DISS index (

**a**,

**b**) and the corresponding HTC (

**c**,

**d**) across Poland. (

**a**) DOY 149, 2015 and (

**b**) DOY 171, 2018—DISS, (

**c**) DOY 149, 2015 and (

**d**) DOY 171, 2018—HTC.

**Figure 15.**Distribution of the DISS Moderate-resolution Imaging Spectroradiometer (MODIS) drought index in the 2015 growing season.

**Figure 18.**Percentage of drought area in Poland for the years 2002, 2003, 2006, 2012, 2015, and 2018.

Obs. | i | t | HTC30 d | TCI d | TCI d-1 | TCI d-2 | |
---|---|---|---|---|---|---|---|

Year | d | ||||||

1 | 1 | 2001 | 112 | HTC(82..112) | TCI 112 | TCI 94 | TCI 86 |

2 | 1 | 2001 | 120 | HTC(90..120) | TCI 120 | TCI 112 | TCI 104 |

… | … | … | … | … | … | … | … |

418 | 1 | 2019 | 280 | HTC(250..280) | TCI 280 | TCI 272 | TCI 264 |

419 | 2 | 2001 | 112 | HTC(82..112) | TCI 112 | TCI 94 | TCI 86 |

… | … | … | … | … | … | … | … |

836 | 2 | 2019 | 280 | HTC(250..280) | TCI 280 | TCI 272 | TCI 264 |

… | … | … | … | … | … | … | … |

97 394 | 233 | 2019 | 280 | HTC(250..280) | TCI 280 | TCI 272 | TCI 264 |

**Table 2.**Results of multivariate regression (Equation (4)) in three versions of HTC accumulation (i.e., 30, 40, and 50 days) for agricultural area.

TCI Lag | HTC Accumulation Period in Days | Pearson’s R Coefficient | Standard Error | Number of Observations | Range of R for Meteo Stations |
---|---|---|---|---|---|

3 | 30 | 0.63 | 0.34 | 8492 | 0.48–0.74 |

4 | 40 | 0.63 | 0.30 | 7702 | 0.49–0.72 |

5 | 50 | 0.64 | 0.26 | 7692 | 0.50–0.74 |

DISS Range | Water Deficit Probability | ||
---|---|---|---|

3 Time Steps | 4 Time Steps | 5 Time Steps | |

Below 0.5 | 81% | 83% | 88% |

0.5–0.8 | 58% | 61% | 65% |

0.8–1.5 | 36% | 34% | 32% |

1.5–3.0 | 15% | 10% | 8% |

Above 3.0 | 3% | 1% | 1% |

No. obs. | 57,638 | 50,267 | 47,352 |

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**MDPI and ACS Style**

Dabrowska-Zielinska, K.; Malinska, A.; Bochenek, Z.; Bartold, M.; Gurdak, R.; Paradowski, K.; Lagiewska, M.
Drought Model DISS Based on the Fusion of Satellite and Meteorological Data under Variable Climatic Conditions. *Remote Sens.* **2020**, *12*, 2944.
https://doi.org/10.3390/rs12182944

**AMA Style**

Dabrowska-Zielinska K, Malinska A, Bochenek Z, Bartold M, Gurdak R, Paradowski K, Lagiewska M.
Drought Model DISS Based on the Fusion of Satellite and Meteorological Data under Variable Climatic Conditions. *Remote Sensing*. 2020; 12(18):2944.
https://doi.org/10.3390/rs12182944

**Chicago/Turabian Style**

Dabrowska-Zielinska, Katarzyna, Alicja Malinska, Zbigniew Bochenek, Maciej Bartold, Radoslaw Gurdak, Karol Paradowski, and Magdalena Lagiewska.
2020. "Drought Model DISS Based on the Fusion of Satellite and Meteorological Data under Variable Climatic Conditions" *Remote Sensing* 12, no. 18: 2944.
https://doi.org/10.3390/rs12182944