An improved nonnegative matrix factorization with the imputation method model for pollution source apportionment during rainstorm events

Data scarcity caused by extreme conditions during storms adds difficulties in performing pollution source apportionment. This study integrated nonnegative matrix factorization with the imputation method (NMF-IM) to fill in missing data (NAs) and conduct source apportionment. A total of 367 river samples and 35 runoff samples were taken from the Banqiao and Nanfei River basins located in Hefei, China, during four rainfall events from June to August 2020. Sixteen indicators were quantified and used for source diagnostics using NMF-IM. The results showed that total phosphorus (TP) had higher concentrations and more violent fluctuations than total nitrogen (TN) in river samples taken from rain. NMF-IM was shown to recover the value distribution of NAs approximately. The source profiles and contribution rates calculated by NMF-IM with NAs were close to the original results calculated by NMF without NAs, with root mean square error of less than 2.3% and differences less than 9.5%. Multiple forms of nitrogen and phosphorus indicators benefit reaching reasonable source diagnostics results. At least four indicators were needed to reach the same contribution rates as 16 indicator diagnostics. The two good indicator combination groups are nitrate (NO3-N), nitrite (NO2-N), ammonia nitrogen (NH3-N), and total suspended solids (TSS) and NO3-N, NO2-N, phosphorus (PO4-P), and TSS. The pollution source contributions changed with the Antecedent dry period (ADPs) of rain events. Treated tailwater and untreated sewage were major sources, contributing more than 80% of the total pollution of the rainstorm events with short ADPs. Dust wash became the dominant contributor after 60 min and contributed 36% of the total pollution of rainstorm events with long ADPs. The average source contribution rates for rainfall events in the Banqiao River were treated tailwater (41%) > untreated sewage (27%) > dust wash (19%) > other sources (16%). The pollution source diagnostics results were verified to be reasonable by simulation using tested run-off data and literature results.