# The Role of Weather Radar in Rainfall Estimation and Its Application in Meteorological and Hydrological Modelling—A Review

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## Abstract

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## 1. Introduction

## 2. The Importance of Rainfall Input for Hydrological Modelling

#### 2.1. Spatial and Temporal Resolution of Weather Radar and Rain Gauge Data

^{2}for a standard C-band radar, a rain gauge typically collects rainfall at ground level over a circular area with a diameter of 20 cm. Hence, observation scales differ dramatically between these two devices. As a consequence, direct comparison of the outputs of a rain gauge and weather radar is problematic at least [12].

#### 2.2. Needs of Urban Hydrology in Terms of Resolution of Precipitation Data

_{l}is the characteristic time of the system [min]. The factor f (Berne et al. [15] suggested f = 4 in their study) is an order of magnitude and depends on a given catchment and expected accuracy.

_{l})—the time difference between the gravity center of the mean rainfall over the catchment and the gravity center of the generated hydrograph—is often selected.

_{l}(min) and a catchment area A (km

^{2}) can be estimated. According to Berne et al. [15]:

## 3. High-Resolution Techniques for Precipitation Measurement and Estimation

#### 3.1. Rain Gauge Networks

#### 3.2. Weather Radar Networks

#### 3.2.1. Introduction

- S-band (2.7–2.9 GHz) is well suited for detecting heavy rain at very long ranges (up to 300 km), as it is least affected by attenuation. However, quantitative precipitation estimation observations are reliable up to ranges of about 200 km, as a larger beam width brings limitations. Data corrections are most robust and easiest to implement for S-band weather radars; however, they are also the most expensive.
- C-band (5.6–5.65 GHz) represents a compromise between range and reliability of reflectivity measurements and cost. A C-band weather radar can provide rain detection up to a range of 200 km, but it is less expensive than an S-band radar. Attenuation of the received signal is significantly stronger than in case of an S-band radar. Thus, the attenuation limits the QPE to ranges of about 100–150 km.
- X-band (9.3–9.5 GHz) weather radars are more sensitive to hydrometeors than S- or C-band weather radars when measuring up to a range of 50 km. Attenuation of the signal by rain is strongest in the case of X-band radars (compared to S- and C-band radars) and strongly limits the QPE. Accurate QPE is usually possible up to ranges of about 30 km. On the other hand, X-band weather radars are the least expensive.

#### 3.2.2. Sources of Errors in Weather Radar Data

#### 3.2.3. Dual-Polarization Weather Radars

_{H}and Z

_{V}, respectively). As a consequence, information on horizontal and vertical dimensions of meteorological targets, such as their shape and size, may be inferred from dual-pol radar measurements. They also give the radar reflectivity and Doppler velocity, just like single polarimetric radars.

_{DR}), specific differential phase shift (K

_{DP}), and sometimes correlation coefficient (ρ

_{HV}). Since the advent of dual-pol radar technology, many studies have been conducted to determine the extent to which the dual-pol products add benefits to estimating R as compared to Z alone [6].

_{DR}allows for the discrimination of hydrometeor types. When the hydrometeor is a sphere, it is assumed that it is either a hail stone or a small rain drop. When the hydrometeor is vertically orientated, it is typically an ice crystal, while when the hydrometeor is orientated horizontally, it indicates a medium to large rain drop. The ρ

_{HV}helps in the identification of the type of hydrometeor, and it suggests how similar hydrometeors are to each other (the hydrometeor type and its horizontal and vertical drop size distribution). For example, a ρ

_{HV}value close to 1 indicates a uniform drop size and shape distributions. Thus, ρ

_{HV}is useful for determining locations where different types of precipitation occur. The K

_{DP}, which reduces the effect of radar signal attenuation in rainfall, indicates where the heaviest rainfall is likely occurring. Thereby, the K

_{DP}can help in predicting locations in storms where high precipitation intensities are expected to occur [53].

_{H}), R(Z

_{H}, Z

_{DR}), R(K

_{DP}), and R(K

_{DP}, Z

_{DR}), are proposed for dual-pol C-band and S-band weather radars [54,55,56]. Algorithms used for radar rainfall estimation are based on different combinations of the above-listed products. The comparison of QPE derived from dual-pol radar data with rain gauge accumulations by Montopoli et al. [54] indicates that a combined algorithm that merges different dual-pol parameters through a weight factor performs better in most cases than if a single radar product is used.

#### 3.2.4. Radar-Based Precipitation Estimates

#### 3.2.5. Machine Learning for Radar-Based Precipitation Estimates

#### 3.2.6. Weather Radar Composites

_{i}is the single radar reflectivity, ${w}_{i}$ is the weight of the i–th radar, i is the radar number, and n is the number of radars covering a given pixel.

#### 3.3. Multi-Source Precipitation Estimation

## 4. Techniques for High-Resolution Nowcasting

#### 4.1. Extrapolation Methods

#### 4.1.1. Motion Field

#### 4.1.2. Quantitative Precipitation Forecast

#### 4.1.3. Probabilistic and Ensemble Forecasts

#### 4.2. Blending Methods

#### 4.3. Artificial Intelligence-Based Methods

#### 4.4. Conceptual Models

## 5. Using Radar Data in NWP Modeling: Radar Data Assimilation

#### 5.1. Methods of Assimilation of Radar Reflectivity Data into a NWP

#### 5.1.1. Latent Heat Nudging (LHN)

#### 5.1.2. Water Vapor Correction Method

#### 5.1.3. Inverse Modelling Technique

#### 5.2. Assimilation of Doppler Radial Velocity into a NWP

## 6. Using Radar Rainfall Data in Flash Flood Modeling

#### 6.1. Flash Flood Modelling Approaches Using Radar Data

#### 6.2. Uncertainty in Radar Estimates for Hydrological Modeling

#### 6.3. Radar Spatial Resolution and Catchment Scale

^{2}) close to Paris. Results pointed to a better representation of X-band radar rainfall with a spatial resolution of 250 × 250 m

^{2}at 3.41 min frequency in contrast to the 1 × 1 km

^{2}spatial resolution of the C-band radar data at 5 min frequency. Evaluation on a small (64 km

^{2}) mountainous catchment in the Italian Alps confirmed the benefits on X-band spatial resolution data for peak simulation [199]. A review paper of the effects of spatial and temporal variability on hydrological response in urban areas was performed by Cristiano et al. [200]. The authors concluded from the literature that physically-based models have become more specialized, and high-resolution spatial rainfall data is of utmost need to take advantage of the models.

#### 6.4. Usefulness of Blending Data and Ancillary Data

#### 6.5. Post-Event Flash Flood Analyses

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**The relationship between required temporal resolution of precipitation data and catchment area (based on Berne et al. [15] et de Vos [14]). The light blue rectangle represents the required resolution for urban catchments, while the dark blue squares represent the most common resolutions of standard measurement techniques: R—weather radar network; G—recording rain gauge network; and C—manual rain gauge network. The blue arrows indicate the actual positions of the blue squares, symbolizing the particular measurement techniques in relation to the diagram scale.

**Figure 2.**Precipitation fields aggregated for August 2017 resulting from weather radar compositing from 10-min accumulations using (

**a**) the maximum value, (

**b**) the value from the nearest radar, and (

**c**) the quality index QI. Data from the POLRAD radar network consisting of eight radars are displayed (based on Jurczyk et al. [64]).

**Figure 3.**Comparison of daily accumulation of radar composites of POLRAD radar network with rain gauge accumulations in August 2017 in terms of RMSE using: 1—the maximum value, 2—the value from the nearest radar, and 3—the quality index QI (based on Jurczyk et al. [64]).

**Figure 4.**Precipitation fields (10-min. accumulations) in Poland, 22 May 2019, 14:20 UTC, RainGRS multi-source QPE model [25]. In the upper row from left to the right—results provided by (

**a**) rain gauges, (

**b**) weather radars, and (

**c**) Meteosat satellite; at the bottom (

**d**) combined precipitation field as a result of conditional merging (based on Jurczyk et al. [25]).

**Figure 5.**Mean bias (

**a**) and root mean square error RMSE (

**b**) of different radar–gauge merging methods based on four-year verification (2005–2008) in the gauge locations with gauge data as reference (adapted from Goudenhoofdt and Delobbe [60]). The investigated precipitation estimates are 1—radar-based precipitation, 2—radar-based precipitation after mean field bias correction, 3—radar-based precipitation after range-dependent adjustment, 4—radar-based precipitation after static local bias correction and range dependent adjustment, 5—radar-based precipitation after Brandes’s [87] spatial adjustment, 6—rain gauge data interpolated using ordinary Kriging, 7—radar–gauge combination using Sinclair’s and Pegram’s technique [78], and 8—radar–gauge combination using Kriging with an external drift.

**Figure 6.**Monthly values of root relative squared error (RRSE) for precipitation fields using gauge data in the gauge locations as reference, obtained by: 1—interpolation of rain gauge data, 2—raw radar data, 3—unbiased radar data, 4—satellite data, and 5—conditional merging. The values are obtained for winter (December 2018;

**a**) and summer (July 2019;

**b**), based on Jurczyk et al. [25].

**Figure 7.**(adapted from Pop et al. [111]). Probabilistic forecast of exceeding a precipitation threshold tr = 0.1 mm for a convective event on 28 July 2012 (first two rows) and a stratiform event on 17 July 2012 (third and fourth row) for a lead time T (from left to the right) of 0, 60, and 120 min. The forecasted probability p (tr > 0.1 mm) is depicted by color scale. Displayed forecasts represent results of an Ensemble Tree Model (first and third row) and a Linear Regression Model (second and fourth row). Note that the grey hatched area corresponds to observed precipitation field, derived from a C-band weather radar data.

**Table 1.**Most frequent operational parameters of basic measurement techniques applied for the estimation of a precipitation field.

Measurement Technique | Spatial Resolution | Temporal Resolution | The Most Important Properties for Combination |
---|---|---|---|

Recording rain gauge network | Point measurements interpolated spatially | 1 min–1 h | Measurements considered of relatively high quality at gauge locations. |

Weather radar network | 0.5–2.0 km | 5–15 min | Numerous measurement errors. Good high-resolution reproduction of spatial distribution of precipitation field. |

Meteorological satellite Meteosat or GOES (VIS and IR channels) | About 4–6 km (depending on latitude) | 5–15 min | Low spatial resolution and approximate measurements. Good reproduction of location of clouds and convective phenomena. High data availability. |

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## Share and Cite

**MDPI and ACS Style**

Sokol, Z.; Szturc, J.; Orellana-Alvear, J.; Popová, J.; Jurczyk, A.; Célleri, R. The Role of Weather Radar in Rainfall Estimation and Its Application in Meteorological and Hydrological Modelling—A Review. *Remote Sens.* **2021**, *13*, 351.
https://doi.org/10.3390/rs13030351

**AMA Style**

Sokol Z, Szturc J, Orellana-Alvear J, Popová J, Jurczyk A, Célleri R. The Role of Weather Radar in Rainfall Estimation and Its Application in Meteorological and Hydrological Modelling—A Review. *Remote Sensing*. 2021; 13(3):351.
https://doi.org/10.3390/rs13030351

**Chicago/Turabian Style**

Sokol, Zbyněk, Jan Szturc, Johanna Orellana-Alvear, Jana Popová, Anna Jurczyk, and Rolando Célleri. 2021. "The Role of Weather Radar in Rainfall Estimation and Its Application in Meteorological and Hydrological Modelling—A Review" *Remote Sensing* 13, no. 3: 351.
https://doi.org/10.3390/rs13030351