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Research Fund of CAMS","award":["2021L3019"],"award-info":[{"award-number":["2021L3019"]}]},{"name":"Science &amp; Technology Plan Project of Fujian Province","award":["2021YJ0280"],"award-info":[{"award-number":["2021YJ0280"]}]},{"name":"Science &amp; Technology Plan Project of Fujian Province","award":["2019YFC1510304"],"award-info":[{"award-number":["2019YFC1510304"]}]},{"name":"Science &amp; Technology Plan Project of Fujian Province","award":["2020B1111200001"],"award-info":[{"award-number":["2020B1111200001"]}]},{"name":"Science &amp; Technology Plan Project of Fujian Province","award":["U2021Z05"],"award-info":[{"award-number":["U2021Z05"]}]},{"name":"Science &amp; Technology Plan Project of Fujian Province","award":["42105141"],"award-info":[{"award-number":["42105141"]}]},{"name":"Science &amp; Technology Plan Project of Fujian Province","award":["2020Y017"],"award-info":[{"award-number":["2020Y017"]}]},{"name":"Science &amp; Technology Plan Project of Fujian Province","award":["2021L3019"],"award-info":[{"award-number":["2021L3019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The observation of and research on raindrop size distribution (DSD) is important for mastering and understanding the mutual restriction relationship between cloud dynamics and cloud microphysics in a process of precipitation; it also plays an irreplaceable role in many fields, such as radar meteorology, weather modification, boundary layer land surface processes, aerosols, etc. Using more than 1.7 million minutes of raindrop data observed with 17 laser disdrometers at 17 stations in Anhui Province, China, from 7 August 2009 to 30 April 2020, a DSD training dataset was constructed. Furthermore, the data are fitted to a normalized Gamma function and used to obtain its three parameters, i.e., the normalized intercept Nw, the mass weighted average diameter Dm, and the shape factor \u03bc. Based on the long short-term memory network (LSTM), a DSD Gamma distribution prediction network (DSDnet) was designed. In the process of modeling based on DSDnet, a self-defined loss function (SLF) was proposed in order to improve the DSD prediction by increasing the weight values in the poor fitting regions according to the common mean square error loss function (MLF). By means of the training dataset, a DSDnet-based model was trained to realize the prediction of Nw, Dm, and \u03bc minute-to-minute over the course of 30 min, and then was evaluated by the test dataset according to three indicators, namely, mean relative error (MRE), mean absolute error (MAE), and correlation coefficient (CC). The CC of lgNw, Dm, and \u03bc can reach 0.93403, 0.90934, and 0.89741 for 12-min predictions, and 0.87559, 0.85261, and 0.84564 for 30-min predictions, respectively, which means that the DSD prediction accuracy within 30 min can basically reach the application level. Furthermore, the 12- and 30-min predictions of 3 precipitation processes were taken as examples to fully demonstrate the application effect of model. The prediction effects of Nw and Dm are better than that of \u03bc, and the stratiform precipitation is better than the convective and convective-stratiform mixed cloud precipitation.<\/jats:p>","DOI":"10.3390\/rs14194994","type":"journal-article","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T03:07:28Z","timestamp":1665371248000},"page":"4994","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Raindrop Size Distribution Prediction by an Improved Long Short-Term Memory Network"],"prefix":"10.3390","volume":"14","author":[{"given":"Yongjie","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Atmospheric Sciences, Chengdu University of Information Technology, Chendu 610225, China"},{"name":"State Key Lab of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China"},{"name":"Key Laboratory of Atmospheric Sounding, China Meteorological Administration, Chengdu 610225, China"},{"name":"Research Centre on Meteorological Observation Engineering Technology, China Meteorological Administration, Beijing 100081, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4991-3647","authenticated-orcid":false,"given":"Zhiqun","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Atmospheric Sciences, Chengdu University of Information Technology, Chendu 610225, China"},{"name":"State Key Lab of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China"},{"name":"Key Laboratory of Atmospheric Sounding, China Meteorological Administration, Chengdu 610225, China"},{"name":"Research Centre on Meteorological Observation Engineering Technology, China Meteorological Administration, Beijing 100081, China"}]},{"given":"Shujie","family":"Yuan","sequence":"additional","affiliation":[{"name":"School of Atmospheric Sciences, Chengdu University of Information Technology, Chendu 610225, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5836-6839","authenticated-orcid":false,"given":"Jiafeng","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Atmospheric Sciences, Chengdu University of Information Technology, Chendu 610225, China"}]},{"given":"Dejin","family":"Lu","sequence":"additional","affiliation":[{"name":"Weather Modification Office of Anhui, Hefei 230031, China"}]},{"given":"Fujiang","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Atmospheric Sciences, Chengdu University of Information Technology, Chendu 610225, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2610","DOI":"10.1175\/MWR2810.1","article-title":"Precipitation uncertainty due to variations in precipitation particle parameters within a simple microphysics scheme","volume":"132","author":"Gilmore","year":"2004","journal-title":"Mon. Weather Rev."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.atmosres.2016.01.013","article-title":"Raindrop size distribution of easterly and westerly monsoon precipitation observed over Palau islands in the Western Pacific Ocean","volume":"174","author":"Krishna","year":"2016","journal-title":"Atmos. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1175\/1520-0469(1948)005<0165:TDORWS>2.0.CO;2","article-title":"The distribution of raindrops with size","volume":"5","author":"Marshall","year":"1948","journal-title":"J. Meteor."},{"key":"ref_4","first-page":"506","article-title":"Model of raindrop size distribution in three types of precipitation","volume":"4","author":"Chen","year":"1998","journal-title":"Acta Meteorol. Sin."},{"key":"ref_5","first-page":"17","article-title":"Comparative study of exponention and Gamma functional fits to observed raindrop size distribution","volume":"27","author":"Zheng","year":"2007","journal-title":"Sci. Meteorol. Sin."},{"key":"ref_6","first-page":"365","article-title":"Characteristics of raindrop size distributions of Northeast cold vortex precipitation in China","volume":"4","author":"Gong","year":"2007","journal-title":"Sci. Meteorol. Sin."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1764","DOI":"10.1175\/1520-0450(1983)022<1764:NVITAF>2.0.CO;2","article-title":"Natural variations in the analytical form of the raindrop size distribution","volume":"22","author":"Ulbrich","year":"1983","journal-title":"J. Clim. Appl. Metreor."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1648","DOI":"10.1175\/1520-0469(1984)041<1648:FFTSOD>2.0.CO;2","article-title":"Functional fits to some observed drop size distributions and parameterization of rain","volume":"41","author":"Willis","year":"1984","journal-title":"J. Atmos. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1175\/2007JAMC1610.1","article-title":"Statistical characteristics of raindrop size distribution in southwest monsoon season","volume":"47","author":"Kirankumar","year":"2008","journal-title":"J. Appl. Meteorol. Climatol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1007\/s00376-016-5235-7","article-title":"Statistical Characteristics of Raindrop Size Distribution in the Tibetan Plateau and Southern China","volume":"34","author":"Wu","year":"2017","journal-title":"Adv. Atmos. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1007\/s00376-021-1135-6","article-title":"Comparative Analysis of the Characteristics of Rainy Season Raindrop Size Distributions in Two Typical Regions of the Tibetan Plateau","volume":"39","author":"Wang","year":"2022","journal-title":"Adv. Atmos. Sci."},{"key":"ref_12","first-page":"233","article-title":"Research on the Method of Evaluating the Efficiency of the Non-Randomized Artificial Pre-cipitation Experiments","volume":"18","author":"Zeng","year":"1994","journal-title":"Chin. J. Atmos. Sci."},{"key":"ref_13","first-page":"693","article-title":"Characteristics of Rain from Stratiform Versus Convective Cloud Based on the Surface Raindrop Data","volume":"30","author":"Liu","year":"2006","journal-title":"Chin. J. Atmos. Sci."},{"key":"ref_14","first-page":"88","article-title":"Statistical characteristics of raindrop size distribution in different regions of Shanxi","volume":"36","author":"Yang","year":"2016","journal-title":"J. Meteorol. Sci."},{"key":"ref_15","first-page":"35","article-title":"Calculation and Analysis of Z-I Relation among Precipitation Processes Caused by Sheet Cloud in Spring and Autumn","volume":"26","author":"Chi","year":"2000","journal-title":"Meteor. Mon."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Graves, A. (2012). Long short-term memory. Supervised Sequence Labelling with Recurrent Neural Networks, Springer.","DOI":"10.1007\/978-3-642-24797-2"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1007\/s00703-021-00791-4","article-title":"Short-term air temperature prediction by adaptive neu-ro-fuzzy inference system (ANFIS) and long short-term memory (LSTM) network","volume":"133","author":"Sekertekin","year":"2021","journal-title":"Meteorol. Atmos. Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s00703-020-00745-2","article-title":"2021: Sea level anomaly intelligent inversion model based on LSTM-RBF network","volume":"133","author":"Liu","year":"2021","journal-title":"Meteorol. Atmos. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"e1852","DOI":"10.1002\/met.1852","article-title":"Correction model for rainfall forecasts using the LSTM with multiple meteorological factors","volume":"27","author":"Zhang","year":"2020","journal-title":"Meteorol. Appl."},{"key":"ref_20","first-page":"233","article-title":"Fine temperature forecast based on LSTM deep neural network","volume":"35","author":"Ni","year":"2018","journal-title":"Comput. Appl. Softw."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Yao, W., Huang, P., and Jia, Z. (2018, January 25\u201327). Multidimensional LSTM networks to predict wind speed. Proceedings of the 2018 37th Chinese Control Conference (CCC), IEEE 2018, Wuhan, China.","DOI":"10.23919\/ChiCC.2018.8484017"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/RG011i001p00001","article-title":"Doppler radar characteristics of precipitation at vertical incidence","volume":"11","author":"Atlas","year":"1973","journal-title":"Rev. Geophys."},{"key":"ref_23","first-page":"268","article-title":"Statistical Characteristics of Raindrop Size Distribution for Stratiform and Convective Precipitation at Different Altitudes in Mt. Huangshan","volume":"42","author":"Li","year":"2018","journal-title":"Chin. J. Atmos. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1175\/1520-0450(2001)040<1118:TCONDT>2.0.CO;2","article-title":"The concept of \u201cnormalized\u201d distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing","volume":"40","author":"Testud","year":"2001","journal-title":"J. Appl. Meteorol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1162\/089976600300015015","article-title":"Learning to forget: Continual prediction with LSTM","volume":"12","author":"Gers","year":"2000","journal-title":"Neural Comput."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/19\/4994\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:47:56Z","timestamp":1760143676000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/19\/4994"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,7]]},"references-count":26,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["rs14194994"],"URL":"https:\/\/doi.org\/10.3390\/rs14194994","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,7]]}}}