# Regional Climate Models Validation for Agroclimatology in Romania

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Used

#### 2.2. Methods Used

#### 2.2.1. Evaluation Metrics for Validation

- i.
- Mean absolute error (MAE) was used to calculate the absolute value of the difference between modeled and observed data (Equation (1)):$$MAE=\frac{{{\displaystyle \sum}}_{i=1}^{n}\left|{y}_{i}-{x}_{i}\right|}{n},$$
- ii.
- Root mean squared error (RMSE) detects the effect of the outliers in the difference between modeled and observation-derived values (Equation (2))$$RMSE=\sqrt{\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({y}_{i}-{x}_{i}\right)}^{2}}{n}}$$
- iii.
- Pearson’s Correlation Coefficient (Corr) helped to measure the linear correlation between modeled and observation-derived values.

#### 2.2.2. Algorithm for RCMs Ranking

**Step 1.**Based on the 3 validation metrics (MAE, RMSE, Corr), a d performance score was assigned to simulations in the case of the variables tasmax, tasmax 95th percentile, tasmin, tasmin 5th percentile, pr, and pr 95th percentile (Table S2). The scoring procedure is adapted after Bartok et al., 2019 [29]. The scores are calculated as described in Equation (3) for MAE and RMSE and Equation (4) for Corr.

**Step 2.**The d performance scores for each variable and evaluation metric were turned into an initial ranking between 1 and 15 (position

_{n}) since we have 15 models. The highest d score (the model that best fit the observation-derived data) was assigned to 1 (position

_{1}in the ranking), and the lowest d score (the model with the lowest performance against the observation-derived data) was assigned to 15 (position

_{15}in the hierarchy). In this way, a uniform initial ranking was obtained (instead of the relative d performance scores, which vary among variables and metrics).

**Step 3.**The initial ranking (1 to 15) was converted into a weighted scale to assign values with different orders of magnitude for various positions. In this way, the final step summing up of weights is relevant, where models performing mostly well will have a score much higher than the models performing relatively weakly. The weighted ranking is elaborated based on a non-linear series which starts at 3 (1st initial position receives the value of 3) and is growing as presented in Equation (5):

_{n}—the weighted rank of the model on a given position; x

_{n−}

_{1}is the weighted rank obtained by the model on the previous position; position

_{n}is the number of the position in the initial ranking (e.g., an x

_{n}score of 9 is assigned to the model ranked in position 2 in the initial order: 3 + 2 × 3, where 3 is the rank for the model in position 1 in the initial ranking, 2 is the position of the model for which the weighted rank is calculated; similarly, a score of 18 is assigned to the model ranked in position 3 in the initial ranking (9 + 3 × 3), etc.). The series was introduced in reverse order to set the highest value (360) to the highest initial position (rank1).

**Step 4.**We developed the final ranking of the models based on a final score (FS) obtained by summing up the weighted ranks calculated in Step 3 for each variable and evaluation metric. The higher the final score, the better the simulation performs compared to the others. Since temperature and precipitation act differently on cereal crops, for the final score, we applied weight for the three climatic parameters as follows: tasmin—40%; tasmax—30%, and pr—30% (Equation (6)).

- x
_{n}tasmin_{MAE}—weighted rank obtained by the model n for tasmin for the MAE metric; - x
_{n}tasmin_{RMSE}—weighted rank obtained by the model n for tasmin for the RMSR metric; - x
_{n}tasmin_{Corr}—weighted rank obtained by the model n for tasmin for the Pearson Correlation metric; - x
_{n}tasmin5p_{MAE}—weighted rank obtained by the model n for 5th percentile of tasmin for the MAE metric; - x
_{n}tasmin5p_{RMSE}—weighted rank obtained by the model n for 5th percentile of tasmin for the RMSR metric; - x
_{n}tasmin5p_{Corr}—weighted rank obtained by the model n for 5th percentile of tasmin for the Pearson Correlation metric; - x
_{n}tasmax_{MAE}—weighted rank obtained by the model n for tasmax for the MAE metric; - x
_{n}tasmax_{RMSE}—weighted rank obtained by the model n for tasmax for the RMSR metric; - x
_{n}tasmax_{Corr}—weighted rank obtained by the model n for tasmax for the Pearson Correlation metric; - x
_{n}tasmax95p_{MAE}—weighted rank obtained by the model n for 95th percentile of tasmax for the MAE metric; - x
_{n}tasmax95p_{RMSE}—weighted rank obtained by the model n for 95th percentile of tasmax for the RMSR metric; - x
_{n}tasmax95p_{Corr}—weighted rank obtained by the model n for 95th percentile of tasmax for the Pearson Correlation metric; - x
_{n}pr_{MAE}—weighted rank obtained by the model n for pr for the MAE metric; - x
_{n}pr_{RMSE}—weighted rank obtained by the model n for pr for the RMSR metric; - x
_{n}pr_{Corr}—weighted rank obtained by the model n for pr for the Pearson Correlation metric; - x
_{n}pr95p_{MAE}—weighted rank obtained by the model n for 95th percentile of pr for the MAE metric; - x
_{n}pr95p_{RMSE}—weighted rank obtained by the model n for 95th percentile of pr for the RMSR metric; - x
_{n}pr95p_{Corr}—weighted rank obtained by the model n for 95th percentile of pr for the Pearson Correlation metric;

#### 2.2.3. Area Analysis

## 3. Results

#### 3.1. Model Performance on Temperature

#### 3.2. Model Performance on Precipitation

#### 3.3. Model Selection Procedure

## 4. Conclusions and Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Validation metrics for tasmax (

**upper left**and

**right**) and tasmin (

**bottom left**and

**right**), EURO-CORDEX simulations (full name of individual models are given in Table 1) against ROCADA observation-derived datasets, over the period 1971–2000.

**Figure 3.**Validation of tasmax and tasmin for 15 EURO-CORDEX simulations against ROCADA observation-derived datasets over the period 1971–2000 (full names of the individual model are given in Table 1) for vegetation periods of maize (April–October) and winter wheat (October–June). In the diagram, the circle on the Ox-axis represents the observation, and the colored plots represent the different models. Three statistics determine the relative places of the models: the Pearson correlation coefficient (curved axes), the centered RMS error (grey contours), and the standard deviation (Oy-axis). The model fitting best with observations will lie the nearest to the Ox-axis.

**Figure 4.**Mean absolute error (MAE) for the 5th and 95th percentiles in case of daily tasmax and tasmin, EURO-CORDEX simulations (full names of individual models are given in Table 1) against ROCADA observation-derived datasets, over the period 1971–2000.

**Figure 5.**Pearson correlation for tasmin (

**left**) and tasmax (

**right**) between EURO-CORDEX simulations (full names of individual models are given in Table 1) and ROCADA observation-derived datasets over the period 1971–2000.

**Figure 6.**Validation metrics for precipitation, EURO-CORDEX simulations (full names of individual models are given in Table 1) against ROCADA observation-derived data, over the period 1971–2000.

**Figure 7.**Validation of pr in 15 EURO-CORDEX simulations against ROCADA observation-derived data, over the period 1971–2000 (full names of individual models are given in Table 1) for vegetation periods of maize (April–October) and winter wheat (October–June). In the diagram, the circle on Ox-axis represents the observation, and the colored plots represent the different models. Three statistics determine the relative places of the models: the Pearson correlation coefficient (curved axes), the centered RMS error (grey contours), and the standard deviation (Oy-axis). The model best fitting with observations will lie the nearest to the Ox-axis.

Domain | EUR-11 | ||
---|---|---|---|

EURO-CORDEX Simulation | Driving Model | Regional Climate Model | No. |

CNRM-CM5 | CLMcom-CCLM4-8-17_v1 IPSL-WRF381P_v2 KNMI-RACMO22E_v2 SMHI-RCA4_v1 | M1 M2 M3 M4 | |

ICHEC-EC-EARTH | KNMI-RACMO22E_v1 SMHI-RCA4_v1 | M5 M6 | |

IPSL-CM5A-MR | IPSL-WRF381P_v1 | M7 | |

MOHC-HadGEM2-ES | CLMcom-CCLM4-8-17_v1 IPSL-WRF381P_v1 KNMI-RACMO22E_v2 SMHI-RCA4_v1 | M8 M9 M10 M11 | |

MPI-M-MPI-ESM-LR | KNMI-RACMO22E_v1 CLMcom-CCLM4-8-17_v MPI-CSC-REMO2009_v1 SMHI-RCA4_v1a | M12 M13 M14 M15 | |

Experiment | historical | ||

Ensemble * | r1i1p1 | ||

Time Frequency | Daily | ||

Variable ** | tasmax tasmin pr |

**Table 2.**Validation metrics for tasmax, tasmin, and pr: multimodel mean of 15 EURO-CORDEX simulations against ROCADA observation-derived datasets, over the period 1971–2000.

Variable/Metric | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Annual | MVP * | WWVP ** | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

tasmax | MAE | 1.46 | 1.85 | 2.42 | 2.22 | 2.34 | 1.77 | 2.17 | 2.24 | 1.57 | 1.27 | 1.25 | 1.28 | 1.29 | 1.40 | 1.44 | |

RMSE | 1.79 | 2.27 | 2.86 | 2.57 | 2.60 | 2.06 | 2.44 | 2.50 | 1.83 | 1.55 | 1.51 | 1.58 | 1.60 | 1.70 | 1.78 | ||

Corr | 0.78 | 0.78 | 0.81 | 0.89 | 0.90 | 0.91 | 0.92 | 0.91 | 0.92 | 0.91 | 0.89 | 0.83 | 0.90 | 0.91 | 0.89 | ||

tasmin | MAE | 1.84 | 2.21 | 2.35 | 2.19 | 1.96 | 1.63 | 1.80 | 1.74 | 1.51 | 1.36 | 1.42 | 1.59 | 1.52 | 1.47 | 1.62 | |

RMSE | 2.07 | 2.48 | 2.61 | 2.39 | 2.13 | 1.84 | 2.06 | 2.02 | 1.77 | 1.57 | 1.60 | 1.80 | 1.73 | 1.70 | 1.83 | ||

Corr | 0.87 | 0.89 | 0.90 | 0.91 | 0.91 | 0.90 | 0.89 | 0.87 | 0.89 | 0.89 | 0.89 | 0.87 | 0.92 | 0.91 | 0.91 | ||

pr | MAE | 25.25 | 22.64 | 24.26 | 15.89 | 21.38 | 23.64 | 24.67 | 22.74 | 11.28 | 15.48 | 21.70 | 22.23 | 144.1 | 155.9 | 88.68 | |

RMSE | 32.28 | 29.56 | 29.52 | 21.48 | 28.33 | 29.92 | 29.16 | 25.51 | 14.00 | 19.69 | 27.75 | 29.26 | 208.3 | 207.0 | 118.8 | ||

Corr | 0.73 | 0.58 | 0.61 | 0.70 | 0.72 | 0.73 | 0.75 | 0.74 | 0.71 | 0.72 | 0.59 | 0.71 | 0.80 | 0.77 | 0.79 | ||

tasmax | 5th percentile | MAE | 2.37 | 2.79 | 2.49 | 2.35 | 1.65 | 1.62 | 1.83 | 1.98 | 1.34 | 1.21 | 1.61 | 1.99 | 1.31 | 1.22 | 1.63 |

RMSE | 2.78 | 3.25 | 2.87 | 2.70 | 1.99 | 1.89 | 2.11 | 2.26 | 1.63 | 1.54 | 1.89 | 2.32 | 1.62 | 1.50 | 1.95 | ||

Corr | 0.77 | 0.75 | 0.80 | 0.88 | 0.89 | 0.92 | 0.93 | 0.93 | 0.92 | 0.87 | 0.83 | 0.78 | 0.91 | 0.92 | 0.89 | ||

95th percentile | MAE | 1.83 | 2.36 | 3.19 | 2.78 | 2.48 | 1.96 | 2.51 | 2.39 | 1.85 | 1.53 | 1.45 | 1.57 | 1.46 | 1.51 | 1.76 | |

RMSE | 2.30 | 2.94 | 3.69 | 3.11 | 2.74 | 2.27 | 2.79 | 2.65 | 2.12 | 1.81 | 1.76 | 1.92 | 1.81 | 1.83 | 2.14 | ||

Corr | 0.78 | 0.83 | 0.83 | 0.85 | 0.89 | 0.90 | 0.90 | 0.89 | 0.89 | 0.88 | 0.85 | 0.83 | 0.89 | 0.90 | 0.88 | ||

tasmin | 5th percentile | MAE | 2.66 | 2.99 | 3.93 | 2.98 | 2.20 | 1.64 | 1.76 | 1.65 | 1.43 | 1.52 | 2.80 | 2.68 | 1.89 | 1.47 | 2.19 |

RMSE | 3.09 | 3.43 | 4.28 | 3.39 | 2.38 | 1.86 | 2.01 | 1.92 | 1.67 | 1.77 | 3.04 | 3.06 | 2.14 | 1.70 | 2.45 | ||

Corr | 0.76 | 0.82 | 0.88 | 0.87 | 0.90 | 0.91 | 0.91 | 0.89 | 0.89 | 0.85 | 0.86 | 0.78 | 0.91 | 0.92 | 0.90 | ||

95th percentile | MAE | 1.40 | 1.58 | 1.87 | 1.88 | 1.74 | 1.69 | 2.04 | 2.19 | 1.78 | 1.53 | 1.36 | 1.42 | 1.42 | 1.55 | 1.40 | |

RMSE | 1.64 | 1.79 | 2.11 | 2.10 | 1.93 | 1.90 | 2.30 | 2.48 | 2.06 | 1.77 | 1.59 | 1.67 | 1.63 | 1.78 | 1.59 | ||

Corr | 0.79 | 0.86 | 0.85 | 0.89 | 0.88 | 0.87 | 0.85 | 0.82 | 0.83 | 0.86 | 0.86 | 0.83 | 0.90 | 0.88 | 0.89 | ||

pr | 95th percentile | MAE | 3.21 | 3.20 | 3.43 | 1.95 | 2.20 | 3.11 | 3.88 | 4.10 | 2.52 | 2.26 | 3.10 | 2.89 | 1.44 | 1.85 | 2.04 |

RMSE | 4.11 | 4.11 | 4.15 | 2.68 | 2.93 | 3.78 | 4.43 | 4.48 | 2.99 | 2.90 | 4.12 | 3.85 | 2.09 | 2.30 | 2.80 | ||

Corr | 0.65 | 0.50 | 0.48 | 0.60 | 0.61 | 0.59 | 0.63 | 0.70 | 0.58 | 0.65 | 0.45 | 0.60 | 0.73 | 0.74 | 0.69 |

**Table 3.**Regional climate model ranking for months, for annual, and for vegetation periods of maize (April–October) and winter wheat (October–June) (full names of individual models are given in Table 1).

Final Rank | Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Annual | MVP * | WWVP ** |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | M5 | M1 | M8 | M8 | M1 | M13 | M3 | M3 | M12 | M12 | M12 | M12 | M9 | M12 | M1 |

2 | M1 | M9 | M9 | M1 | M13 | M2 | M12 | M12 | M10 | M2 | M6 | M5 | M1 | M2 | M9 |

3 | M12 | M8 | M1 | M10 | M8 | M10 | M10 | M10 | M3 | M5 | M3 | M1 | M2 | M15 | M10 |

4 | M9 | M2 | M5 | M13 | M12 | M1 | M2 | M15 | M4 | M7 | M2 | M3 | M10 | M9 | M8 |

5 | M8 | M12 | M2 | M15 | M14 | M14 | M4 | M13 | M2 | M11 | M10 | M4 | M12 | M10 | M12 |

6 | M11 | M6 | M11 | M14 | M10 | M12 | M5 | M14 | M11 | M15 | M1 | M7 | M11 | M11 | M11 |

7 | M6 | M5 | M3 | M12 | M3 | M9 | M15 | M4 | M5 | M3 | M9 | M6 | M5 | M7 | M5 |

8 | M2 | M3 | M4 | M9 | M9 | M5 | M7 | M2 | M13 | M10 | M4 | M11 | M8 | M5 | M2 |

9 | M10 | M4 | M12 | M11 | M5 | M3 | M13 | M5 | M1 | M4 | M11 | M8 | M15 | M4 | M3 |

10 | M4 | M11 | M13 | M2 | M15 | M7 | M14 | M9 | M15 | M9 | M15 | M13 | M3 | M13 | M13 |

11 | M3 | M7 | M6 | M5 | M2 | M11 | M6 | M7 | M9 | M6 | M5 | M14 | M13 | M3 | M6 |

12 | M7 | M15 | M7 | M4 | M11 | M15 | M1 | M6 | M7 | M13 | M8 | M2 | M4 | M1 | M15 |

13 | M14 | M13 | M10 | M3 | M6 | M6 | M9 | M11 | M8 | M1 | M7 | M10 | M6 | M8 | M4 |

14 | M13 | M10 | M14 | M6 | M4 | M4 | M11 | M1 | M6 | M14 | M13 | M9 | M14 | M14 | M14 |

15 | M15 | M14 | M15 | M7 | M7 | M8 | M8 | M8 | M14 | M8 | M14 | M15 | M7 | M6 | M7 |

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**MDPI and ACS Style**

Bartok, B.; Telcian, A.-S.; Săcărea, C.; Horvath, C.; Croitoru, A.-E.; Stoian, V. Regional Climate Models Validation for Agroclimatology in Romania. *Atmosphere* **2021**, *12*, 978.
https://doi.org/10.3390/atmos12080978

**AMA Style**

Bartok B, Telcian A-S, Săcărea C, Horvath C, Croitoru A-E, Stoian V. Regional Climate Models Validation for Agroclimatology in Romania. *Atmosphere*. 2021; 12(8):978.
https://doi.org/10.3390/atmos12080978

**Chicago/Turabian Style**

Bartok, Blanka, Adrian-Sorin Telcian, Christian Săcărea, Csaba Horvath, Adina-Eliza Croitoru, and Vlad Stoian. 2021. "Regional Climate Models Validation for Agroclimatology in Romania" *Atmosphere* 12, no. 8: 978.
https://doi.org/10.3390/atmos12080978