# Machine Learning Approach to Classify Rain Type Based on Thies Disdrometers and Cloud Observations

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- How do classification methods designed for other disdrometer types perform when applied to Thies disdrometer measurements?
- Can we achieve better classification performance by tuning the decision boundary for each method?
- Which rain microstructure parameters are superior as rain type classifiers?
- Do machine-learning techniques support a better classification?

## 2. Materials and Methods

#### 2.1. Data Sources and Tools

#### 2.2. Cloud Observations

#### 2.3. Thies Disdrometer and Extraction of Rain DSD

#### 2.4. Prior Rain Type Classification

#### 2.5. Rain Microstructure-Based Classification Methods

#### 2.6. Indicators of the Classification Performance

#### 2.7. Advanced Predictive Models

#### 2.7.1. Linear Discriminate Analysis (LDA)

#### 2.7.2. K Nearest Neighbor (KNN)

#### 2.7.3. Naïve Bayes (NB)

#### 2.7.4. Conditional Trees (Ctree)

#### 2.7.5. Random Forests (RF)

#### 2.8. Selecting Rain DSD Parameters

- High computational costs,
- The risk of overfitting the training set,
- Non-informative features that negatively affect some models [60], and
- Constructed models that are difficult to interpret.

- 1-
- The features are clustered into X groups (hierarchal clustering). Each group contains a few correlated features.
- 2-
- One feature is chosen out of each cluster. The chosen feature is the one with the highest AUC value, where AUC is the area under the receiver operating characteristic curve [67]. The AUC value is a measure of the capability of each feature to separate the classes.

## 3. Results

#### 3.1. Performance of the Classification Methods from the Literature

#### 3.2. Feature Selection

#### 3.3. Performance of the ML Methods

## 4. Discussion

_{10}(Nw) to classify rain type is superior to any other combination suggested in the literature. This is in agreement with the findings of Thurai et al. [24] and explains the good performance reported in various papers despite the different geographical locations and use of different devices. However, after adjusting the decision boundary, TS_a and TS_b revealed very similar values for the three performance indicators, i.e., accuracy, F-measure, and Kappa. This strongly suggests that the parameters used in TS_a, TS_b, and Br_09 carry a sensitive signal that can successfully be used in classifying the rain type.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Rain intensity variations for selected events with convective clouds at Fürstenzell. Rain intervals classified as stratiform by Bringi et al. [9] (blue points) were removed from the reference dataset.

**Figure 2.**Rain intensity variation for selected events with stratiform clouds at Fürstenzell. Rain events that are marked with an asterisk in the upper left corner of the panel were removed from the reference dataset due to sub-periods with convective rain type.

**Figure 3.**Performance of the classification methods from the literature (columns) using different performance indicators. The box plots represent the performance of a linear discriminant model (LDA) using the same parameters suggested by each model and a cross validation with 200 repetitions of stratified sampling.

**Figure 4.**Correlation matrix of the rain microstructure parameters. Blank cells represent insignificant correlation with confidence level of 0.95.

**Figure 5.**Relative importance of the rain microstructure parameters expressed by the area under the receiver operating characteristic curve (AUC) [67].

**Figure 6.**(

**a**) Correlation matrix where blank cells represent insignificant correlation with confidence level of 0.95. (

**b**) AUC values of the final list of selected features.

**Figure 7.**Performance of the machine-learning classification methods with different numbers of features. Each point is produced by taking the mean value of 200 repetitions of stratified cross validation performed on the Fürstenzell dataset. The red point represents the performance of the Bu_15 method with four parameters.

**Figure 8.**Performance of the machine-learning classification methods with different numbers of features. Each model was trained on the Fürstenzell dataset and tested on the Regensburg dataset. The red point represents the performance of the Bu_15 method with four parameters.

Cloud Type (Genera) | Abbreviation | Expected Rain Type |
---|---|---|

Cirrus | CI | - |

Cirrocumulus | CC | - |

Cirrostratus | CS | - |

Altocumulus | AC | - |

Altostratus | AS | - |

Nimbostratus | NS | Stratiform |

Stratocumulus | SC | - |

Stratus | ST | Stratiform |

Cumulus | CU | Convective |

Cumulonimbus | CB | Convective |

Abbreviation | Unit | Parameter Name and Relevant Reference ^{1} | |
---|---|---|---|

R | mm·h^{−1} | rain intensity [8] | |

Z | dBZ | reflectivity [8] | |

Dm | mm | mass weighted diameter [55] | |

D0 | mm | median volume diameter [56] | |

sd_D | mm | instantaneous (1 min) standard deviation of drop size [2] | |

sd_V | m·h^{−1} | instantaneous standard deviation of drop velocities [2] | |

Nt | drop·m^{−3} | total number of drops per cubic meter [57] | |

Nw_Tes | mm^{−1}·m^{−3} | normalized number of drops [58] | |

Nw_Br | mm^{−1}·m^{−3} | normalized number of drops [28] | |

logNw | Nw: mm^{−1}·m^{−3} | logNw = log_{10}(NW_Br) | |

D0_Nt | mm.m^{3}·drop^{−1} | D0/Nt [59] | |

Lambda_TS | mm^{−1} | slope of fitted gamma distribution [25] | |

logLambda | Lambda: mm^{−1} | logLambda = log_{10}(Lambda_TS) [25] | |

mu_TS | - | shape of fitted gamma distribution [25] | |

N0_TS | mm^{−1−m}·m^{−3} | intercept of fitted gamma distribution [25] | |

logN0 | N0_TS: mm^{−1−m}·m^{−3} | logN0 = log_{10}(N0_TS) [25] | |

Lambda_Ca06 | mm^{−1} | slope of fitted gamma distribution [26] | |

mu_Ca06 | - | shape of fitted gamma distribution [26] | |

N0_Ca06 | mm^{−1−m}·m^{−3} | intercept of fitted gamma distribution [26] | |

Lambda_Ca08 | mm^{−1} | slope of fitted gamma distribution [27] | |

N0_Ca08 | mm^{−1−m}·m^{−3} | intercept of fitted gamma distribution [27] | |

Nt_4R | (Drop·m^{−3})^{0.25} | 4th root of Nt [11] | |

sd_R_10 | mm·h^{−1} | sd_XX_YY: standard deviations of XX over YY minutes [11] | |

sd_Dm_10 | mm | ||

sd_D0_10 | mm | ||

sd_Nt_10 | drop | ||

sd_R_30 | mm·h^{−1} | ||

sd_Dm_30 | mm | ||

sd_D0_30 | mm | ||

sd_Nt_30 | drop | ||

sd_log_{10}(Nt)_30 | - | ||

sd_log_{10}(R)_30 | - | ||

sd_log_{10}(Nt)_10 | - | ||

sd_log_{10}(R)_10 | - |

^{1}The parameter was used in (or motivated by) the associated reference.

Method | Reference | Parameters: y ~ x | Decision Boundary |
---|---|---|---|

TS_a | [25] | N0_TS ~ R | $\mathrm{N}0\_\mathrm{TS}=4\times {10}^{9}\times {\mathrm{R}}^{-4.3}$ convective region above the decision boundary |

TS_b | [25] | Lambda_TS ~ R | $\mathrm{Lambda}\_\mathrm{TS}=17\times {\mathrm{R}}^{-0.37}$ convective region above the decision boundary |

Ca_06 | [26] | Lambda_Ca06 ~ mu_Ca06 | $\left(1.635\times \mathrm{Lambda}\_\mathrm{Ca}06-\mathrm{mu}\_\mathrm{Ca}06\right)=1$ convective region below the decision boundary |

Ca_08 | [27] | Lambda_Ca08 ~ N0_Ca08 | $\mathrm{Lambda}\_\mathrm{Ca}08+4.17=1.92\mathrm{log}\left(\mathrm{N}0\_\mathrm{Ca}08\right)$ convective region below the decision boundary |

Br_09 | [28] | Nw_Br ~ D0 | ${\mathrm{log}}_{10}\left(\mathrm{Nw}\_\mathrm{Br}\right)=-1.6{\mathrm{D}}_{0}+6.3$ convective region above the decision boundary |

You_16 | [30] | Nw_Br ~ D0 | >${\mathrm{log}}_{10}\left(\mathrm{Nw}\_\mathrm{Br}\right)=-9.6{\mathrm{D}}_{0}+5.3$ convective region above the decision boundary |

Bu_15 | [11] | Z, Nt_4R, sd_log10(Nt)_30, sd_log10(R)_30 | - |

Prediction of Rain Type | Observed Rain Type * | |
---|---|---|

Convective | Stratiform | |

Convective | True Positive (TP) | False Positive (FP) |

Stratiform | False Negative (FN) | True Negative (TN) |

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**MDPI and ACS Style**

Ghada, W.; Estrella, N.; Menzel, A.
Machine Learning Approach to Classify Rain Type Based on Thies Disdrometers and Cloud Observations. *Atmosphere* **2019**, *10*, 251.
https://doi.org/10.3390/atmos10050251

**AMA Style**

Ghada W, Estrella N, Menzel A.
Machine Learning Approach to Classify Rain Type Based on Thies Disdrometers and Cloud Observations. *Atmosphere*. 2019; 10(5):251.
https://doi.org/10.3390/atmos10050251

**Chicago/Turabian Style**

Ghada, Wael, Nicole Estrella, and Annette Menzel.
2019. "Machine Learning Approach to Classify Rain Type Based on Thies Disdrometers and Cloud Observations" *Atmosphere* 10, no. 5: 251.
https://doi.org/10.3390/atmos10050251