# Radar Technology for River Flow Monitoring: Assessment of the Current Status and Future Challenges

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Principle of Velocity Estimation

#### 1.3. Outline

## 2. The Challenges of Processing River Flow from Raw Radar Data

#### 2.1. Signal Sampling

#### 2.2. Doppler Spectrum Estimation

#### 2.3. Signal Processing

#### 2.4. Flow Calculation

## 3. State-of-the-Art

#### 3.1. Sampling Methods

_{n}(t) is multiplied with the impulse function p(t) to obtain the discrete signal x(nT

_{s}), which realizes the conversion from analog to digital. The period of the impulse function in the time domain is T

_{s}, while its period in the frequency domain is f

_{s}. The frequency spectrum of x(nT

_{s}) will likewise exhibit periodicity after being sampled. If f

_{s}is less than twice the maximum frequency f

_{max}of the discrete signal spectrum, then the sampled spectrum appears to exhibit an aliasing phenomenon. The Nyquist theorem states that in order to recover the continuous signal x

_{n}(t) from the discrete signal without distortion, the sampling frequency f

_{s}must be at least twice the maximum frequency f

_{max}of the discrete signal spectrum, f

_{s}≥ 2f

_{max}[80,81].

#### 3.2. Spectrum Estimation Methods

#### 3.2.1. Classical Spectrum Estimation

^{2}-th multiplication and addition, which is a complex and computationally intensive process. Considering the portability and cost of a fixed-point radar, the Fast Fourier transform (FFT) is mostly used. Alimenti et al. designed a low-cost radar based on the FFT algorithm, and the results showed that the accuracy of this radar was comparable to that of a high-precision commercial radar flowmeter [89]. The FFT algorithm’s basic idea is to continually split the discrete signal ${x}_{N}(n)$ by using the symmetry and periodicity of ${e}^{-j\frac{2\pi}{N}nk}$. This reduces the computational steps to (n/2)log

_{2}n times multiplication and nlog

_{2}n times addition while maintaining the precision of the results.

#### 3.2.2. Modern Spectrum Estimation

_{i}and incidences on the array:

_{1},…, λ

_{M}) is the eigenvalue matrix, U

_{S}is the signal subspace, and U

_{N}is the noise subspace. The spectrum function is denoted as:

#### 3.3. Target Detection Methods

#### 3.3.1. MTI and MTD

_{c}is frequently larger than the average power of noise P

_{s}.

_{r}is the radar repetition period, N is the number of accumulated pulses, and w

_{i}are the weighting coefficients. The weighting coefficients are transformed as follows:

#### 3.3.2. CFAR

#### 3.4. Flow Calculation Methods

#### 3.4.1. Index-Velocity Method

- Single point velocity, which measures the velocity at a single point in a river section.
- Depth averaged velocity, which takes into account the river’s average velocity in a vertical direction.
- Horizontal average velocity, which utilizes a certain water layer’s average velocity.

_{m}and the index-velocity V

_{index}are obtained:

#### 3.4.2. Probability Concept Method

_{0}, and the maximum flow velocity is reached when ξ = ξ

_{max}= 1. If h > 0, it indicates that the maximum flow velocity occurs below the water surface, if h < 0, it is meaningless. The relationship between y and ξ can be expressed as:

#### 3.4.3. Surface Velocity Coefficients Method

_{s}. Then, as illustrated in Figure 2d, the river flow can be computed using the velocity-area method. Commonly used flow distribution models include logarithmic distribution, exponential distribution, parabolic distribution, and elliptical distribution, etc. The most usually used exponential distributions is taken as an example below [122].

_{s}are:

_{s}in the range of 0.80–0.85 for natural channels. In Japan, η

_{s}= 0.85 is used as the reference value. In France, Hauet et al. came to the following conclusions after analyzing 3611 stations on 176 channels: (1) The relationship between the surface velocity coefficient and roughness is complex and still unknown. (2) The average value of the surface velocity coefficient for natural rivers (with a sand, cobble, or boulder bed) is 0.80. (3) The average value of the surface velocity coefficient for artificial concrete channels is 0.90 [124].

## 4. Discussion

#### 4.1. Current and Future Limitations

#### 4.2. Future Potentials

#### 4.3. Future Challenges

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Principle sketch of the measurement setup from side (

**left**) and top view (

**right**), the observation area (marked in yellow) depends on the height of radar and the beam width in elevation θ

_{el}and azimuth θ

_{az}.

**Figure 2.**Illustration of a typical workflow, starting from sampling raw signal data to having the river flow. (

**a**) Raw data obtained from radar equipment. (

**b**) Doppler estimation using spectrum methods. (

**c**) Signal processing, including clutter removal and target identification. (

**d**) Converting surface velocity to flow.

**Figure 3.**A streamlined signal sampling procedure in the time domain (

**a**) and in the frequency domain (

**b**).

**Figure 6.**Schematic diagram of the probability concept-based velocity distribution calculation method. (

**a**) Iso-velocity coordinate system for h < 0. (

**b**) Iso-velocity coordinate system for h > 0.

Algorithm | Advantages | Disadvantages |
---|---|---|

CA-CFAR | High detection performance in the case of uniform clutter background. | The detection performance degrades in multiple targets and the clutter edge condition. |

SO-CFAR | Good detection performance in the case of multiple targets | The probability of false alarm rises in the clutter edge condition. |

GO-CFAR | Robust edge clutter resistance. | Multiple targets increase the likelihood of false alarms and decrease the detection performance. |

OS-CFAR | Great detection performance in multiple targets circumstances. Good anti-clutter edge capabilities. | High false alarm loss due to the influence of k-value. Time-consuming process, and high hardware requirements. |

Pretty Coarse | Coarse | Normal | Smooth | |

m | 1–2 | 3–4 | 5–7 | 8–10 |

η_{s} | 0.50–0.67 | 0.75–0.80 | 0.83–0.88 | 0.89–0.91 |

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## Share and Cite

**MDPI and ACS Style**

Huang, Y.; Chen, H.; Liu, B.; Huang, K.; Wu, Z.; Yan, K.
Radar Technology for River Flow Monitoring: Assessment of the Current Status and Future Challenges. *Water* **2023**, *15*, 1904.
https://doi.org/10.3390/w15101904

**AMA Style**

Huang Y, Chen H, Liu B, Huang K, Wu Z, Yan K.
Radar Technology for River Flow Monitoring: Assessment of the Current Status and Future Challenges. *Water*. 2023; 15(10):1904.
https://doi.org/10.3390/w15101904

**Chicago/Turabian Style**

Huang, Yu, Hua Chen, Bingyi Liu, Kailin Huang, Zeheng Wu, and Kang Yan.
2023. "Radar Technology for River Flow Monitoring: Assessment of the Current Status and Future Challenges" *Water* 15, no. 10: 1904.
https://doi.org/10.3390/w15101904