# Calibration of X-Band Radar for Extreme Events in a Spatially Complex Precipitation Region in North Peru: Machine Learning vs. Empirical Approach

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}. Calibration schemes developed for the systems in Ecuador shall now be adapted to the operational conditions of the Piura system.

^{b}, where A and b are empirical parameters largely adjusted for the particular site and rainfall type [23]. From the studies addressed in the tropics and in deserts, a limited number of parameters A and b have been documented. Orellana-Alvear et al. [24] summarized varied contributions in the tropics, particularly in mountain regions. On the other hand, Z–R relations used in arid regions are even more scarce and highly variable among different sites and rainfall types as in [25,26] (78 < A < 190; 1.4 < b < 2.1). Due to the spatial variability of Z–R, different approaches that allow for a definition of Z–R relations according to the proper characteristics of terrain and rainfall classification are needed, also distinguishing convective and stratiform rainfall formation. Typically, a fixed set of the parameters A and b is employed, which is sometimes modified on an event basis or depending on rain rate or other observations regarding the atmospheric conditions. Then, further corrections are applied to the derived QPE (quantitative precipitation estimate) as post-processing, frequently using multiplicative and additive error models [27]. Here, we propose a new empirical approach, using the parameters of the Z–R relation to integrate post-processing steps in the initial calibration for each time step and each detected reflectivity value.

## 2. Materials and Methods

#### 2.1. Study Area

^{2}(2.4% of the Peruvian territory) and has a population of around 1.8 million. The coastline of 382 km length is the most western part of South America and as such is particularly exposed to the cold Humboldt current and the Pacific equatorial counter current. The coastal plain in Piura is the widest in all of Peru (120 km); its eastern border is formed by the Andes Cordillera with peak elevations beyond 3000 m. Both of the main rivers in the region are diarheic: The Chira originates from the humid south Ecuadorian Andes and is the source for Peru’s largest man-made water reservoir, the Poechos dam, which is an important part of water management in the desert zone of north Peru. The second main river Piura has its sources in the Andes of Piura in Peru and forms the northern limit of the tropical desert Sechura.

#### 2.2. Radar Data Preprocessing

#### 2.3. Rain Gauge Data

#### 2.4. Empirical Calibration Approach

^{2}possible (Figure 3). The selection criteria for the validation sites were to have at least five days of gauge and reflectivity data while maintaining a large enough spatial coverage. Optimization runs found the best values for the linear variogram to be slope = 0.5 and nugget = 0.1 with the r

^{2}value between 0.42 and 0.91 for the different stations.

^{(1/b)}is employed (Figure 4), resulting in a parameter set of A = 40 and b = 1.6 albeit with a very low coefficient of correlation, which is later addressed by modifying A and b to daily conditions. As rain gauge data are available as daily totals, the daily mean of Z is related to the daily rain total, although the averaging of Z may violate the equality of the Z–R-relation. As the internal software from the manufacturer already applies averaging on dBZ, the equality assumption can be discarded anyway [45]. So, a further transformation is required to linearize the final values for QPE. The median b0 of parameter b is used as a starting point for the daily calibration, and from iterative validation runs, a general empirical relation between b and Z at coordinates i,j is determined:

_{i,j}is the reflectivity-dependent pixel-wise value for b. The constant 2 scales b′ to a range of 1.0 to 4.5 with a median of 1.6. Higher values of b′ are theoretically possible but will yield QPE values below the detection threshold of the radars (<0.08 mm per day). In effect, this is just a range compression for Z, which is required for highly sensitive X-band microwaves. Then, QPE values are calculated by using this variable exponent in the Z–R relation.

^{−1}.

^{1/b′}.

#### 2.5. Machine Learning Approach: Random Forest

#### 2.6. Input Features

#### 2.7. Statistical Metrics

^{2}, the Spearman rank correlation coefficient, root mean squared error (RMSE), mean absolute error (MAE), and percentage bias are chosen as diagnostic variables for the parameter optimization.

## 3. Results

#### 3.1. Validation of the Empirical Method

#### 3.2. Results Machine Learning Approach

#### 3.3. Precipitation Climatology and Case Studies

## 4. Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- WMO. 2021. Available online: https://public.wmo.int/en/media/press-release/water-related-hazards-dominate-disasters-past-50-years (accessed on 1 September 2021).
- Rodríguez-Morata, C.; Díaz, H.F.; Ballesteros-Canovas, J.A.; Rohrer, M.; Stoffel, M. The anomalous 2017 coastal El Niño event in Peru. Clim. Dyn.
**2019**, 52, 5605–5622. [Google Scholar] [CrossRef] - Son, R.; Wang, S.-Y.S.; Tseng, W.-L.; Schuler, C.W.B.; Becker, E.; Yoon, J.-H. Climate diagnostics of the extreme floods in Peru during early 2017. Clim. Dyn.
**2020**, 54, 935–945. [Google Scholar] [CrossRef][Green Version] - Bendix, J.; Fries, A.; Zárate, J.; Trachte, K.; Rollenbeck, R.; Pucha-Cofrep, F.; Paladines, R.; Palacios, I.; Orellana, J.; Oñate-Valdivieso, F.; et al. Radarnet-Sur First Weather Radar Network in Tropical High Mountains. Bull. Am. Meteorol. Soc.
**2017**, 98, 1235–1254. [Google Scholar] [CrossRef] - Hitschfeld, W.; Bordan, J. Errors inherent in the radar measurement of rainfall at attenuating wavelengths. J. Meteorol.
**1954**, 11, 58–67. [Google Scholar] [CrossRef][Green Version] - Joss, J.; Waldvogel, A. Raindrop size distribution and Doppler velocities. In Proceeding of the 14th Meteorology Conference, Boston, MA, USA, 17–20 November 1970; pp. 153–156. [Google Scholar]
- Battan, L.J. Radar Observation of the Atmosphere; University of Chicago Press: Chicago, IL, USA, 1973; p. 323. [Google Scholar]
- Collier, C.G. Applications of Weather Radar Systems: A Guide to Uses of Radar Data in Meteorology and Hydrology; Ellis Horwood—University of Michigan: Ann Arbor, MI, USA, 1996. [Google Scholar]
- Skolnik, M. Radar Handbook, 2nd ed.; McGraw-Hill Publishing Company: London, UK, 1990. [Google Scholar]
- Andrieu, H.; Creutin, J.D.; Delrieu, G.; Faure, D. Use of weather radar for the hydrology of a mountainous area. Part I: Radar measurement interpretation. J. Hidrol.
**1997**, 193, 1–25. [Google Scholar] [CrossRef] - Amitai, E. Systematic Variation of Observed Radar Reflectivity-Rainfall Rate Relations in the Tropics. J. Appl. Meteorol.
**2000**, 39, 2198–2208. [Google Scholar] [CrossRef] - Kumar, S.; Castillo-Velarde, C.D.; Valdivia Prado, J.M.; Flores Rojas, J.L.; Callañaupa Gutierrez, S.M.; Moya Alvarez, A.S.; Martine-Castro, D.; Silva, Y. Rainfall Characteristics in the Mantaro Basin over Tropical Andes from a Vertically Pointed Profile Rain Radar and In-Situ Field Campaign. Atmosphere
**2020**, 11, 248. [Google Scholar] [CrossRef][Green Version] - Manz, A.; Smith, A.H.; Hardaker, P.J. Comparison of different methods of end to end calibration of the U.K. weather radar network. Phys. Chem. Earth Part B Hydrol. Oceans Atmos.
**2000**, 25, 1157–1162. [Google Scholar] [CrossRef] - Lang, P.; Deutscher, W. KONRAD: Ein Operationelles Verfahren zur Analyse von Gewitterzellen und Deren Zugbahnen, Basieren auf Wetterradarprodukten; Deutscher Wetterdienst: Frankfurt, Germany, 2003. [Google Scholar]
- Ventura, J.F.; Lainer, M.; Schauwecker, Z.; Grazioli, J.; Germann, U. Pyrad: A Real-Time Weather Radar Data Processing Framework Based on Py-ART. J. Open Res. Softw.
**2020**, 8, 28. [Google Scholar] [CrossRef] - Heistermann, M.; Jacobi, S.; Pfaff, T. Technical Note: An open source library for processing weather radar data (wradlib). Hydrol. Earth Syst. Sci.
**2013**, 17, 863–871. [Google Scholar] [CrossRef][Green Version] - Flores-Rojas, J.L.S.; Silva, Y.; Suárez-Salas, L.; Estevan, R.; Valdivia-Prado, J.; Saavedra, M.; Giraldez, L.; Piñas-Laura, M.; Scipión, D.; Milla, M.; et al. Analysis of Extreme Meteorological Events in the Central Andes of Peru Using a Set of Specialized Instruments. Atmosphere
**2021**, 12, 408. [Google Scholar] [CrossRef] - Pegram, G.; Llort, X.; Sempere-Torres, D. Radar rainfall: Separating signal and noise fields to generate meaningful ensembles. Atmos. Res.
**2011**, 100, 226–236. [Google Scholar] [CrossRef] - Gabella, M.; Notarpietro, R. Ground clutter characterization and elimination in mountainous terrain. In Proceeding of the 2nd European Conference on Radar Meteorology (ERAD) 2002, Delft, The Netherlands, 18–22 November 2002; pp. 305–311. [Google Scholar]
- Jacobi, S.; Heistermann, M. Benchmarking attenuation correction procedures for six years of single-polarized C-band weather radar observations in South-West Germany. Geomat. Nat. Hazards Risk
**2016**, 7, 1785–1799. [Google Scholar] [CrossRef][Green Version] - Rollenbeck, R.; Bendix, J. Experimental calibration of a cost-effective X-band weather radar for climate ecological studies in southern Ecuador. Atmos. Res.
**2006**, 79, 296–316. [Google Scholar] [CrossRef] - Rollenbeck, R.; Bendix, J. Rainfall distribution in the Andes of southern Ecuador derived from blending weather radar data and meteorological field observations. Atmos. Res.
**2011**, 99, 277–289. [Google Scholar] [CrossRef] - Ignaccolo, M.; De Michele, C. One, No One, and One Hundred Thousand: The Paradigm of the Z–R Relationship. J. Hydrometeorol.
**2020**, 21, 1161–1169. [Google Scholar] [CrossRef] - Orellana-Alvear, J.; Célleri, R.; Rollenbeck, R.; Bendix, J. Analysis of Rain Types and Their Z–R Relationships at Different Locations in the High Andes of Southern Ecuador. J. Appl. Meteorol. Climatol.
**2017**, 56, 3065–3080. [Google Scholar] [CrossRef] - Xie, H.; Pan, P.; Shi, H.; Chen, J.; Wang, J. Observed Microphysical Characteristics of Stratiform and Convective Precipitation over an Inland Arid Region of the Qinghai–Tibet Plateau. Water
**2020**, 12, 2300. [Google Scholar] [CrossRef] - Xie, Z.; Yang, H.; Lv, H.; Hu, Q. Seasonal Characteristics of Disdrometer-Observed Raindrop Size Distributions and Their Applications on Radar Calibration and Erosion Mechanism in a Semi-Arid Area of China. Remote Sens.
**2020**, 12, 262. [Google Scholar] [CrossRef][Green Version] - Goudenhoofdt, E.; Delobbe, L. Evaluation of radar-gauge merging methods for quantitative precipitation estimates. Hydrol. Earth Syst. Sci.
**2009**, 13, 195–203. [Google Scholar] [CrossRef][Green Version] - Orlandini, S.; Morlini, I. Artificial neural networks estimation of rainfall intensity from radar observations. J. Geophys. Res.
**2000**, 105, 849–861. [Google Scholar] [CrossRef] - Teschl, R.; Randeu, W.L.; Teschl, F. Improving weather radar estimates of rainfall using feed-forward neural networks. Neural Netw.
**2007**, 20, 519–527. [Google Scholar] [CrossRef] - Orellana-Alvear, J.; Célleri, R.; Rollenbeck, R.; Bendix, J. Optimization of X-band radar rainfall retrieval in the southern Andes of Ecuador using a random forest model. Remote Sens.
**2019**, 11, 1632. [Google Scholar] [CrossRef][Green Version] - Wolfensberger, D.; Gabella, M.; Boscacci, M.; German, U.; Berne, A. RainForest: A random forest algorithm for quantitative precipitation estimation over Switzerland. Atmos. Meas. Tech.
**2021**, 14, 3169–3193. [Google Scholar] [CrossRef] - Yang, X.; Kuang, Q.; Zhang, W.; Zhang, G. A terrain-based weighted random forests method for radar quantitative precipitation estimation. Meteorol. Appl.
**2017**, 24, 404–414. [Google Scholar] [CrossRef][Green Version] - Yu, P.S.; Yang, T.C.; Chen, S.Y.; Kuo, C.M.; Tseng, H.W. Comparison of random forests and support vector machine for real-time radar-derived rainfall forecasting. J. Hydrol.
**2017**, 552, 92–104. [Google Scholar] [CrossRef] - Mao, Y.; Sorteberg, A. Improving radar-based precipitation nowcasts with machine learning using an approach based on random forest. Weather. Forecast.
**2020**, 35, 2461–2478. [Google Scholar] [CrossRef] - Shin, K.; Song, J.J.; Bang, W.; Lee, G. Approaches with Operational Dual-Polarization Radar Data. Remote. Sens.
**2021**, 13, 694. [Google Scholar] [CrossRef] - Hengl, T.; Nussbaum, M.; Wright, M.N.; Heuvelink, G.B.; Gräler, B. Random Forest as a generic framework for predictive modeling of spatial and spatio-temporal variables. PeerJ
**2018**, 6, e5518. [Google Scholar] [CrossRef][Green Version] - Breiman, L. Random forests. Mach. Learn.
**2001**, 45, 5–32. [Google Scholar] [CrossRef][Green Version] - Natekin, A.; Knoll, A. Gradient boosting machines, a tutorial. Front. Neurorobot.
**2013**, 7, 1–21. [Google Scholar] [CrossRef][Green Version] - Khan, R.S.; Bhuiyan, M.A.E. Artificial intelligence-based techniques for rainfall estimation integrating multisource precipitation datasets. Atmosphere
**2021**, 12, 1239. [Google Scholar] [CrossRef] - Probst, P.; Wright, M.N.; Boulesteix, A.L. Hyperparameters and tuning strategies for random forest. Wiley Interdiscip. Rev. Data Min. Knowl. Discov.
**2019**, 9, e1301. [Google Scholar] [CrossRef][Green Version] - SENAMHI—Portal de Transparencia-Datos/Datos Hidrometeorológicos. Available online: https://www.senamhi.gob.pe/?&p=estaciones (accessed on 6 May 2021).
- Rollenbeck, R.; Trachte, K.; Bendix, J. A New Class of Quality Controls for Micrometeorological Data in Complex Tropical Enviroments. J. Atmos. Ocean. Technol.
**2015**, 33, 169–183. [Google Scholar] [CrossRef] - Aslantaş, P.; Heuvelink, G.; Akyürek, Z. Comparison of regression and kriging techniques for mapping the average annual precipitation of Turkey. Int. J. Appl. Earth Obs. Geoinf.
**2012**, 19, 115–126. [Google Scholar] [CrossRef] - Smith, J.A.; Krajewski, W.F. Estimation of mean field bias of Radar rainfall estimates. J. Appl. Meteorol.
**1991**, 30, 397–412. [Google Scholar] [CrossRef][Green Version] - Warren, R.A.; Protat, A. Should interpolation of Radar Reflectivity be Performed in Z or dBZ? J. Atmos. Ocean. Technol.
**2019**, 36, 1143–1156. [Google Scholar] [CrossRef][Green Version] - Contreras, P.; Orellana-Alvear, J.; Muñoz, P.; Bendix, J.; Célleri, R. Influence of random forest hyperparameterization on short-term runoff forecasting in an andean mountain catchment. Atmosphere
**2021**, 12, 238. [Google Scholar] [CrossRef] - Zach, C.; Pock, T.; Bischof, H. A Duality Based Approach for Realtime TV-L1 Optical Flow. In Pattern Recognition, Proceedings of the Joint Pattern Recognition DAGM-Symposium, Heidelberg, Germany, 12–14 September 2007; Lecture Notes in Computer Science; Hamprecht, F.A., Schnörr, C., Jähne, B., Eds.; Springer: Berlin/Heidelberg, Germany, 2007; Volume 4713, Chapter 22; pp. 214–223. [Google Scholar] [CrossRef]
- Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michael, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; et al. Scikit-learn: Machine Learning in Python. J. Mach. Learn. Res.
**2011**, 12, 2825–2830. [Google Scholar] - Muñoz, P.; Célleri, R.; Feyen, J. Effect of the Resolution of Tipping-Bucket Rain Gauge and Calculation Method on Rainfall Intensities in an Andean Mountain Gradient. Water
**2016**, 8, 534. [Google Scholar] [CrossRef][Green Version] - Ryzhkov, A.; Zrnić, D.; Atlas, D. Polarimetrically Tuned R(Z) Relations and Comparison of Radar Rainfall Methods. J. Appl. Meteorol.
**1997**, 36, 340–349. [Google Scholar] [CrossRef] - Rosenfeld, D.; Amitai, E. Comparison of WPMM versus Regression for Evaluating Z-R Relationships. J. Appl. Meteorol. Climatol.
**1998**, 37, 1241–1249. [Google Scholar] [CrossRef] - Stout, G.E.; Mueller, E.A. Survey of Relationships between Rainfall Rate and Radar Reflectivity in the Measurement of Precipitation. J. Appl. Meteorol.
**1968**, 7, 465–474. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**(

**a**) Overview map of the Piura region showing the available rain gauge sites and the maximum radar range of 100 km. (

**b**) The 12 m tower of PIUXX with the radar antenna installed (Photo: Rollenbeck).

**Figure 2.**Maximum (red) and mean (green) dBZ profile along the radar beam for all radar images. Black lines show the fitted correction curves.

**Figure 3.**Validation of the interpolated rainfall map. Station codes are resolved in Supplementary Materials. The regression line is illustrated in red while the bisector line is shown in gray.

**Figure 4.**Daily mean reflectivity vs. mean rain rate and fitted conversion functions for the range of values of the A parameter. MP denotes the widely used Marshall–Palmer parametrization with A = 200 and b = 1.6. The outliers below the lower black line can be attributed to uncompensated noise in the first 200 range gates around the radar caused by episodic reflections from the side lobes.

**Figure 6.**Validation results for daily totals of rain gauges and QPE (empirical). Scatter plot and linear regression (

**left**), Box–Violin plot with scatter of residuals (blue dots,

**right**).

**Figure 8.**Feature importance and its standard deviation of the RF model. Out-of-bag (OOB) error was used to rank the features in the training stage.

**Figure 9.**Correlation of observed and estimated daily rainfall using the QPE random forest model on the entire test dataset (104 samples) is illustrated. Scatter plot and linear regression (

**left**), Box–Violin plot with scatter of residuals (blue dots,

**right**).

**Figure 10.**Mean annual total for 2019–2021: Interpolated station data from 53 rain gauge sites (

**a**), empirically calibrated radar map (QPE) (

**b**,

**c**) radar map (QPE) from the machine learning approach, and (

**d**) absolute difference between (

**b**,

**c**).

**Figure 12.**Case studies for extreme events for the full radar domain: interpolated station data empirical calibrated radar map (QPE) of the daily total and radar map (QPE) from the machine learning approach.

Manufacturer | Country: Germany Brand: Selex (Now: LEONARDO) Model: RS120 Range: 100 km |

Antenna | Diameter: 1.2 m Gain: 38.5 dB Side lobe elevation: −27 dBc Beam width (azimuth): 2° Beam width (elevation): 2° Rotation: 12 r.p.m. Azimuth tolerance: ±0.5° |

Emitter | Peak power: 25 kW Frequency: 9410 (±30 MHz) Pulse repetition frequency (PRF): 833–1500 Hz Pulse duration: 500–1200 ns Pulse length (range resolution): 75–180 m |

Receiver | Band width (1200 ns/500 ns): 3 MHz/7 MHz Minimum detectable signal: −100 dBm Dynamic range: 70 dB Noise figure: 6 dB |

Signal processor | CPU: Intel Pentium Dual Core, Operating System: SuSe LINUX Radar A/D converter: 14 bit, 20 MS/s |

Power supply | Radar: 100 VA/70 W Signal Processor: 100 VA/90 W Total system requirement incl. climatization and UPS: Max 500 VA |

Station Type | n | Source |
---|---|---|

Conventional rain gauge (manual readout) | 20 | SENAMHI |

Registering rain gauge (hourly data) | 24 | SENAMHI |

Registering rain gauge (10-min data) | 8 | UDEP |

Conventional rain gauge (manual readout) | 1 | UDEP |

**Table 3.**Description of Rf hyperparameters defined in the implementation of the scikit-learn library (version 0.21).

Hyperparameter | Description | Default Value |
---|---|---|

criterion | Metric used to evaluate the quality of a split. | mean squared error |

max_depth | Maximum depth of a tree. | ‘none’ (until all leaves are pure) |

max_features | Maximum number of random features to be used while building an individual tree. | total number of features |

max_leaf_nodes | Maximum number of leaf nodes. | unlimited number of leaf nodes |

max_samples | Maximum number of samples for training each tree. | all samples |

min_samples_leaf | Minimum number of samples that belong to a leaf node. | 1 |

min_samples_split | Minimum number of samples allowed to split an internal node. | 2 |

n_estimators | The total number of trees in the forest. | 100 |

Feature Name | Description |
---|---|

Longitude | Longitude |

Latitude | Latitude |

Altitude | Altitude |

Distance | Distance from radar |

Avg Z temporal | 5-min temporal average reflectivity (1-day window) |

Std Z temporal | 5-min temporal standard deviation reflectivity (1-day window) |

Max Z temporal | 5-min temporal maximum reflectivity (1-day window) |

Sum Z temporal | 5-min temporal accumulation of reflectivity (1-day window) |

Avg u component temporal | 5-min temporal average u component (1-day window) |

Std u component temporal | 5-min temporal standard deviation u component (1-day window) |

Avg v component temporal | 5-min temporal average v component (1-day window) |

Std v component temporal | 5-min temporal standard deviation v component (1-day window) |

Avg Z temporal/Altitude | Quotient of 5-min temporal average reflectivity (1-day window) and altitude |

**Table 5.**Comparison of detection rate for rainfall. Radar reflectivity is submitted to a 3 × 3 median filter to compensate for small errors in pixel location caused by the polar–Cartesian conversion.

Radar > 0 | Radar = 0 | |
---|---|---|

Rain gauge > 0 | 1383 (6%) | 2134 (9%) |

Rain gauge = 0 | 8103 (34%) | 6702 (28%) |

Metric | All Data | Validation Data |
---|---|---|

Correlation coefficient | 0.78 | 0.82 |

r^{2} Coefficient of determination | 0.61 | 0.67 |

Spearman rank correlation coefficient | 0.77 | 0.69 |

Mean absolute error | 5.75 | 7.25 |

Percent bias | 34.4 | −13.8 |

Metric | Training Data | Test Data |
---|---|---|

Correlation coefficient | 0.94 | 0.65 |

r^{2} Coefficient of determination | 0.89 | 0.42 |

Spearman rank correlation coefficient | 0.78 | 0.56 |

RMSE | 5.01 | 12.87 |

Mean absolute error | 3.28 | 9.01 |

Mean error | 0.03 | 1.08 |

Percent bias | 0.3 | 6.8 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Rollenbeck, R.; Orellana-Alvear, J.; Rodriguez, R.; Macalupu, S.; Nolasco, P. Calibration of X-Band Radar for Extreme Events in a Spatially Complex Precipitation Region in North Peru: Machine Learning vs. Empirical Approach. *Atmosphere* **2021**, *12*, 1561.
https://doi.org/10.3390/atmos12121561

**AMA Style**

Rollenbeck R, Orellana-Alvear J, Rodriguez R, Macalupu S, Nolasco P. Calibration of X-Band Radar for Extreme Events in a Spatially Complex Precipitation Region in North Peru: Machine Learning vs. Empirical Approach. *Atmosphere*. 2021; 12(12):1561.
https://doi.org/10.3390/atmos12121561

**Chicago/Turabian Style**

Rollenbeck, Rütger, Johanna Orellana-Alvear, Rodolfo Rodriguez, Simon Macalupu, and Pool Nolasco. 2021. "Calibration of X-Band Radar for Extreme Events in a Spatially Complex Precipitation Region in North Peru: Machine Learning vs. Empirical Approach" *Atmosphere* 12, no. 12: 1561.
https://doi.org/10.3390/atmos12121561