Raindrop Size Distribution Prediction by an Improved Long Short-Term Memory Network
<p>The station distribution map, in which the dots are the disdrometers, the triangle in the center is the radar, and the circle is the 230 km detection range of the radar.</p> "> Figure 2
<p>The schematic diagram of RNN network.</p> "> Figure 3
<p>The schematic diagram of LSTM network.</p> "> Figure 4
<p>The schematic diagram of DSDnet network.</p> "> Figure 5
<p>The modeling flow chart.</p> "> Figure 6
<p>The 12-min scatter plot of lgN<sub>w</sub>, Dm, and μ fitted by the observed data and predicted by the model, in which (<b>a</b>–<b>c</b>) are modeled with MLF and (<b>d</b>–<b>f</b>) with SLF. The red line denotes a linear trend line of the scattered points, and the color mark represents the Gaussian kernel density estimation.</p> "> Figure 7
<p>The 30-min scatter plot of lgN<sub>w</sub>, D<sub>m</sub>, and μ fitted by the observed data and predicted by the model, in which (<b>a</b>–<b>c</b>) are modeled with MLF and (<b>d</b>–<b>f</b>) with SLF. The red line denotes a linear trend line of the scattered points, and the color mark represents the Gaussian kernel density estimation.</p> "> Figure 8
<p>The 0.5° PPI of reflectivity of the Hefei radar at 0726 (<b>a</b>), 0127 (<b>b</b>), and 1332 LST (<b>c</b>) on 26 January 2020, in which the red triangle is the location of the disdrometer at Lujiang, and the scale on the coordinate axes represents the distance (km).</p> "> Figure 9
<p>The curve of the 12-min prediction for the stratiform cloud precipitation case, in which the horizontal axes are rainfall duration time (min); vertical axes are (<b>a</b>,<b>d</b>) lgN<sub>w</sub>, (<b>b</b>,<b>e</b>) D<sub>m</sub> (mm), and (<b>c</b>,<b>f</b>) μ; the red and blue curves represent the predicted and actual values; and the vertical dotted line is at the minute of T<sub>step</sub> + M<sub>pred</sub>. Modeling with MLF is shown on the left (<b>a</b>–<b>c</b>), and with SLF on the right (<b>d</b>–<b>f</b>).</p> "> Figure 10
<p>The curve of the 30-min prediction for the stratiform cloud precipitation case, in which the horizontal axes are rainfall duration time (min); vertical axes are (<b>a</b>,<b>d</b>) lgN<sub>w</sub>, (<b>b</b>,<b>e</b>) D<sub>m</sub> (mm), and (<b>c</b>,<b>f</b>) μ; the red and blue curves represent the predicted and actual values; and the vertical dotted line is at the minute of T<sub>step</sub> + M<sub>pred</sub>. Modeling with MLF is shown on the left (<b>a</b>–<b>c</b>), and with SLF on the right (<b>d</b>–<b>f</b>).</p> "> Figure 11
<p>The DSDs of measurement (black solid line), Gamma fitting (blue dotted line), and model prediction (red dotted line, (<b>a</b>) 12-min and (<b>b</b>) 30-min prediction) at the 1063rd min of this stratiform cloud precipitation case.</p> "> Figure 12
<p>The 0.5° PPI of reflectivity of the Hefei radar at 0818 (<b>a</b>), 0914 (<b>b</b>), and 0949 LST (<b>c</b>) on 24 November 2015, in which the red triangle is the location of the disdrometer at ChuZhou.</p> "> Figure 13
<p>The curve of the 30-min prediction for the mixed convective–stratiform cloud precipitation case, in which the horizontal axes are rainfall duration time (min); vertical axes are (<b>a</b>,<b>d</b>) lgN<sub>w</sub>, (<b>b</b>,<b>e</b>) D<sub>m</sub> (mm), and (<b>c</b>,<b>f</b>) μ; the red and blue curves represent the predicted and actual values; and the vertical dotted line is at the minute of T<sub>step</sub> + M<sub>pred</sub>. Modeling with MLF is shown on the left (<b>a</b>–<b>c</b>), and with SLF on the right (<b>d</b>–<b>f</b>).</p> "> Figure 14
<p>The DSDs of measurement (black solid line), Gamma fitting (blue dotted line), and model prediction (red dotted line, (<b>a</b>) 12-min and (<b>b</b>) 30-min prediction) at the 594th min of this mixed convective-stratiform cloud precipitation case.</p> "> Figure 15
<p>The 0.5° PPI of reflectivity of the Hefei radar at 0436 (<b>a</b>), 0522 (<b>b</b>), and 0528 LST (<b>c</b>) on 29 June 2015, in which the red triangle is the location of the disdrometer at Dingyuan.</p> "> Figure 16
<p>The curve of the 30-min prediction for the convective cloud precipitation case, in which the horizontal axes are rainfall duration time (min); vertical axes are (<b>a</b>,<b>d</b>) lgN<sub>w</sub>, (<b>b</b>,<b>e</b>) D<sub>m</sub> (mm), and (<b>c</b>,<b>f</b>) μ; the red and blue curves represent the predicted and actual values; and the vertical dotted line is at the minute of T<sub>step</sub> + M<sub>pred</sub>. Modeling with MLF is shown on the left (<b>a</b>–<b>c</b>), and with SLF on the right (<b>d</b>–<b>f</b>). Results of 30-min Prediction.</p> "> Figure 17
<p>The DSDs of measurement (black solid line), Gamma fitting (blue dotted line), and model prediction (red dotted line, (<b>a</b>) 12-min and (<b>b</b>) 30-min prediction) at the 86th min of this convective cloud precipitation case.</p> ">
Abstract
:1. Introduction
2. Data Source and Preprocessing
2.1. Data Source
2.2. Data Preprocessing
2.3. Normalized Gamma Distribution
3. DSD Prediction Model
3.1. Introduction of the LSTM Algorithm
3.2. DSDnet Design
3.3. Training Dataset Construction
3.4. Self-Defined Loss Function
3.5. Hyperparameter Setting
3.6. Evaluation Indicator
3.7. Modeling Flow Chart
3.8. Model Evaluation by Test Set
4. Model Application
4.1. Stratiform Cloud Precipitation
4.1.1. 12-min Prediction Results
4.1.2. 30-min Prediction Results
4.2. Mixed Convective-Stratiform Clouds
Results of 30-min Prediction
4.3. The Case of Convective Clouds
5. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Gilmore, M.S.; Straka, J.M.; Rasmussen, E.N. Precipitation uncertainty due to variations in precipitation particle parameters within a simple microphysics scheme. Mon. Weather Rev. 2004, 132, 2610–2627. [Google Scholar] [CrossRef]
- Krishna, U.V.M.; Reddy, K.K.; Seela, B.K.; Shirooka, R.; Lin, P.L.; Pan, C.J. Raindrop size distribution of easterly and westerly monsoon precipitation observed over Palau islands in the Western Pacific Ocean. Atmos. Res. 2016, 174, 41–51. [Google Scholar] [CrossRef]
- Marshall, J.S.; Palmer, W.M. The distribution of raindrops with size. J. Meteor. 1948, 5, 165–166. [Google Scholar] [CrossRef]
- Chen, B.J.; Li, Z.H.; Liu, J.C.; Gong, F.J. Model of raindrop size distribution in three types of precipitation. Acta Meteorol. Sin. 1998, 4, 506–512. [Google Scholar]
- Zheng, H.J.; Chen, B.J. Comparative study of exponention and Gamma functional fits to observed raindrop size distribution. Sci. Meteorol. Sin. 2007, 27, 17–23. [Google Scholar]
- Gong, F.J.; He, Y.J.; Wang, J.H. Characteristics of raindrop size distributions of Northeast cold vortex precipitation in China. Sci. Meteorol. Sin. 2007, 4, 365–373. [Google Scholar]
- Ulbrich, C.W. Natural variations in the analytical form of the raindrop size distribution. J. Clim. Appl. Metreor. 1983, 22, 1764–1775. [Google Scholar] [CrossRef]
- Willis, P.T. Functional fits to some observed drop size distributions and parameterization of rain. J. Atmos. Sci. 1984, 41, 1648–1661. [Google Scholar] [CrossRef]
- Kirankumar, N.V.P.; Rao, T.N.; Radhakrishna, B.; Rao, D.N. Statistical characteristics of raindrop size distribution in southwest monsoon season. J. Appl. Meteorol. Climatol. 2008, 47, 576–590. [Google Scholar] [CrossRef]
- Wu, Y.H.; Liu, L.P. Statistical Characteristics of Raindrop Size Distribution in the Tibetan Plateau and Southern China. Adv. Atmos. Sci. 2017, 34, 727–736. [Google Scholar] [CrossRef]
- Wang, G.L.; Li, R.; Sun, J.S.; Xu, X.D.; Zhou, R.R.; Liu, L.P. Comparative Analysis of the Characteristics of Rainy Season Raindrop Size Distributions in Two Typical Regions of the Tibetan Plateau. Adv. Atmos. Sci. 2022, 39, 1062–1078. [Google Scholar] [CrossRef]
- Zeng, G.P.; Zheng, X.Z.; Fang, S.Z. Research on the Method of Evaluating the Efficiency of the Non-Randomized Artificial Pre-cipitation Experiments. Chin. J. Atmos. Sci. 1994, 18, 233–242. [Google Scholar]
- Liu, H.Y.; Lei, H.C. Characteristics of Rain from Stratiform Versus Convective Cloud Based on the Surface Raindrop Data. Chin. J. Atmos. Sci. 2006, 30, 693–702. [Google Scholar]
- Yang, J.M.; Chen, B.J.; Han, Y.X.; Li, P.R. Statistical characteristics of raindrop size distribution in different regions of Shanxi. J. Meteorol. Sci. 2016, 36, 88–95. [Google Scholar]
- Chi, Z.P.; Liu, X.; Chen, J.M. Calculation and Analysis of Z-I Relation among Precipitation Processes Caused by Sheet Cloud in Spring and Autumn. Meteor. Mon. 2000, 26, 35–37. [Google Scholar]
- Graves, A. Long short-term memory. In Supervised Sequence Labelling with Recurrent Neural Networks; Springer: Berlin/Heidelberg, Germany, 2012; pp. 37–45. [Google Scholar]
- Sekertekin, A.; Bilgili, M.; Arslan, N.; Yildirim, A.; Celebi, K.; Ozbek, A. Short-term air temperature prediction by adaptive neu-ro-fuzzy inference system (ANFIS) and long short-term memory (LSTM) network. Meteorol. Atmos. Phys. 2021, 133, 943–959. [Google Scholar] [CrossRef]
- Liu, H.; He, B.; Qin, P.; Zhang, X.; Guo, S.; Mu, X. 2021: Sea level anomaly intelligent inversion model based on LSTM-RBF network. Meteorol. Atmos. Phys. 2021, 133, 245–259. [Google Scholar] [CrossRef]
- Zhang, C.J.; Zeng, J.H.; Wang, Y.; Ma, L.M.; Chu, H. Correction model for rainfall forecasts using the LSTM with multiple meteorological factors. Meteorol. Appl. 2020, 27, e1852. [Google Scholar] [CrossRef] [Green Version]
- Ni, Z.; Liang, P. Fine temperature forecast based on LSTM deep neural network. Comput. Appl. Softw. 2018, 35, 233–236+271. [Google Scholar]
- Yao, W.; Huang, P.; Jia, Z. Multidimensional LSTM networks to predict wind speed. In Proceedings of the 2018 37th Chinese Control Conference (CCC), IEEE 2018, Wuhan, China, 25–27 July 2018; pp. 7493–7497. [Google Scholar]
- Atlas, D.; Srivastava, R.C.; Sekhon, R.S. Doppler radar characteristics of precipitation at vertical incidence. Rev. Geophys. 1973, 11, 1–35. [Google Scholar] [CrossRef]
- Li, H.; Yin, Y.; Shan, Y.P.; Jin, Q. Statistical Characteristics of Raindrop Size Distribution for Stratiform and Convective Precipitation at Different Altitudes in Mt. Huangshan. Chin. J. Atmos. Sci. 2018, 42, 268–280. [Google Scholar]
- Testud, J.; Oury, S.; Black, R.A. The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing. J. Appl. Meteorol. 2001, 40, 1118–1140. [Google Scholar] [CrossRef]
- Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput. 1997, 9, 1735–1780. [Google Scholar] [CrossRef]
- Gers, F.A.; Schmidhuber, J.; Cummins, F. Learning to forget: Continual prediction with LSTM. Neural Comput. 2000, 12, 2451–2471. [Google Scholar] [CrossRef]
Items | Parameters | |
---|---|---|
Average falling speed of channel 1–32 (m/s) | Range | 0.2~20 |
Classification | 0.05, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, | |
0.85, 0.95, 1.10, 1.30, 1.50, 1.70, 1.90, 2.20, | ||
2.60, 3.00, 3.40, 3.80, 4.40, 5.20, 6.00, 6.80, | ||
7.60, 8.80, 10.40, 12.00, 13.60, 15.20, 17.60, | ||
20.80 | ||
Average particle diameter of 1–32 channels (mm) | Range | 0.2~25 |
Classification | 0.062, 0.187, 0.312, 0.437, 0.562, 0.687, 0.812, | |
0.937, 1.062, 1.187, 1.375, 1.625, 1.875, 2.125, | ||
2.375, 2.750, 3.250, 3.750, 4.250, 4.750, 5.500, | ||
6.500, 7.500, 8.500, 9.500, 11.000, 13.000, | ||
15.000, 17.000, 19.000, 21.500, 24.500 | ||
Accuracy | liquid | ±5% |
solid | ±20% | |
Particle level | 32 (size) × 32 (velocity) | |
Differentiation of precipitation types | >97% | |
Measurement interval | 60 s | |
Measuring area | 54 cm2 (18 cm × 3 cm) | |
Wavelength | 780 nm (OTT Parsivel2) | |
650 nm (HSC-OTT Parsivel EF) | ||
Output rating | 0.5 mW (OTT Parsivel2) | |
3 mW (HSC-OTT Parsivel EF) |
Parameter | W | L |
---|---|---|
Nw | 10, 5, 2, 5, 8, 10 | 0.54, 0.63, 0.72, 0.81, 0.90, 1 |
Dm | 10, 5, 2, 5, 8, 10 | 0.14, 0.29, 0.44, 0.74, 0.89, 1 |
μ | 10, 5, 2, 5, 8, 10 | 0.06, 0.16, 0.25, 0.44, 0.64, 1 |
Model | Evaluation Index | lgNw | Dm | μ |
---|---|---|---|---|
MRE | 0.05452 | 0.11925 | 0.16559 | |
With MLF | MAE | 0.23862 | 0.13497 | 1.43105 |
CC | 0.93162 | 0.89621 | 0.87996 | |
MRE | 0.05235 | 0.11561 | 0.15486 | |
With SLF | MAE | 0.23251 | 0.13084 | 1.34834 |
CC | 0.93403 | 0.90934 | 0.89741 |
Model | Evaluation Index | lgNw | Dm | μ |
---|---|---|---|---|
MRE | 0.06867 | 0.17442 | 0.27311 | |
With MLF | MAE | 0.29384 | 0.15411 | 2.36024 |
CC | 0.85564 | 0.83968 | 0.82761 | |
MRE | 0.05983 | 0.16188 | 0.24224 | |
With SLF | MAE | 0.25354 | 0.14287 | 2.01193 |
CC | 0.87599 | 0.85261 | 0.84564 |
Model | Evaluation Index | lgNw | Dm | μ |
---|---|---|---|---|
MRE | 0.02231 | 0.03545 | 0.17484 | |
With MLF | MAE | 0.09959 | 0.03395 | 1.41840 |
CC | 0.88919 | 0.86223 | 0.84995 | |
MRE | 0.02181 | 0.02697 | 0.15086 | |
With SLF | MAE | 0.09739 | 0.02583 | 1.22393 |
CC | 0.90978 | 0.91626 | 0.86207 |
Model | Evaluation Index | lgNw | Dm | μ |
---|---|---|---|---|
MRE | 0.04846 | 0.04277 | 0.22196 | |
With MLF | MAE | 0.21637 | 0.04096 | 1.80071 |
CC | 0.84809 | 0.82457 | 0.79582 | |
MRE | 0.03989 | 0.03633 | 0.17516 | |
With SLF | MAE | 0.18024 | 0.03288 | 1.43994 |
CC | 0.87736 | 0.83032 | 0.84207 |
Model | Evaluation Index | lgNw | Dm | μ |
---|---|---|---|---|
MRE | 0.14235 | 0.08697 | 0.41552 | |
With MLF | MAE | 0.11261 | 0.33545 | 2.63504 |
CC | 0.90904 | 0.89730 | 0.81276 | |
MRE | 0.12532 | 0.06654 | 0.33504 | |
With SLF | MAE | 0.09185 | 0.28565 | 2.43201 |
CC | 0.92786 | 0.91974 | 0.84736 |
Model | Evaluation Index | lgNw | Dm | μ |
---|---|---|---|---|
MRE | 0.08276 | 0.09283 | 0.47653 | |
With MLF | MAE | 0.32051 | 0.15222 | 2.85232 |
CC | 0.74374 | 0.86702 | 0.71285 | |
MRE | 0.06727 | 0.07619 | 0.37871 | |
With SLF | MAE | 0.28180 | 0.13494 | 2.46677 |
CC | 0.79573 | 0.88387 | 0.76503 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2022 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
Zhu, Y.; Hu, Z.; Yuan, S.; Zheng, J.; Lu, D.; Huang, F. Raindrop Size Distribution Prediction by an Improved Long Short-Term Memory Network. Remote Sens. 2022, 14, 4994. https://doi.org/10.3390/rs14194994
Zhu Y, Hu Z, Yuan S, Zheng J, Lu D, Huang F. Raindrop Size Distribution Prediction by an Improved Long Short-Term Memory Network. Remote Sensing. 2022; 14(19):4994. https://doi.org/10.3390/rs14194994
Chicago/Turabian StyleZhu, Yongjie, Zhiqun Hu, Shujie Yuan, Jiafeng Zheng, Dejin Lu, and Fujiang Huang. 2022. "Raindrop Size Distribution Prediction by an Improved Long Short-Term Memory Network" Remote Sensing 14, no. 19: 4994. https://doi.org/10.3390/rs14194994