In this paper, we consider an unknown source problem for the modified Helmholtz equation. The Tikhonov regularization method in Hilbert scales is extended to deal with ill-posedness of the problem. An a priori strateg...In this paper, we consider an unknown source problem for the modified Helmholtz equation. The Tikhonov regularization method in Hilbert scales is extended to deal with ill-posedness of the problem. An a priori strategy and an a posteriori choice rule have been present to obtain the regularization parameter and corresponding error estimates have been obtained. The smoothness parameter and the a priori bound of exact solution are not needed for the a posteriori choice rule. Numerical results are presented to show the stability and effectiveness of the method.展开更多
HONO is a critical precursor of•OH,but its sources are controversial due to its complex formation mechanism.This study conducted comprehensive observations in Zhengzhou from April 26 to May 11,2022.Low NO_(x)concentra...HONO is a critical precursor of•OH,but its sources are controversial due to its complex formation mechanism.This study conducted comprehensive observations in Zhengzhou from April 26 to May 11,2022.Low NO_(x)concentrations were observed during the Covid epidemic period(EP)(10.4±3.0 ppb),compared to the pre-epidemic period(PEP)(12.5±3.8 ppb).The mean HONO concentration during EP(0.53±0.34 ppb)was 0.09 ppb lower than that during PEP(0.62±0.53 ppb).The decrease in HONO concentration during EP came mainly at night due to the reduction in the direct emission(P_(emi))(0.03 ppb/hr),the homogeneous reaction between•OHandNO(P_(OH+NO))(0.02 ppb/hr),and the heterogeneous conversion of NO_(2)on the ground(0.01 ppb/hr).Notably,there was no significant change in daytime HONO concentration.The daytime HONO budget indicated that the primary HONO sources during PEP were the nitrate photolysis(P_(nitrate)),followed by the P_(OH+NO),Pemi,the photo-enhanced reaction of NO_(2)on the ground(P_(ground+hv))and aerosol surface(Paerosol+hv).The primary HONO sources were Pnitrate,POH+NO,P_(emi),and_(Paerosol+hv)during EP,respectively.The missing source has a high correlation with solar radiation,there might be other photo-related HONO sources or the contributions of photosensitized reactions were underestimated.In the extremely underestimated cases,HONO production rates fromthe P_(nitrate),P_(ground+hv),and Paerosol+hv increased by 0.17,0.10,and 0.10 ppb/hr during PEP,0.23,0.13,and 0.16 ppb/hr during EP,and P_(nitrate)was still the primary source during both PEP and EP.展开更多
Nitrous acid （HONO）, as a primary precursor of OH radicals, has been considered one of the most important nitrogencontaining species in the atmosphere. Up to 30% of primary OH radical production is attributed to the...Nitrous acid （HONO）, as a primary precursor of OH radicals, has been considered one of the most important nitrogencontaining species in the atmosphere. Up to 30% of primary OH radical production is attributed to the photolysis of HONO. However, the major HONO formation mechanisms are still under discussion. During the Campaigns of Air Quality Research in Beijing and Surrounding Region （CAREBeijing2006） campaign, comprehensive measurements were carried out in the megacity Beijing, where the chemical budget of HONO was fully constrained. The average diurnal HONO concentration varied from 0.33 to 1.2 ppbv. The net OH production rate from HONO, Pon（HONO）net, was on average （from 05：00 to 19：00） 7.1 × 10^6 molecule/（cm^3 s）, 2.7 times higher than from 03 photolysis. This production rate demonstrates the important role of HONO in the atmospheric chemistry of megacity Beijing. An unknown HONO source （Punknown） with an average of 7.3 × 10^6 molecule/（cm^3 s） was derived from the budget analysis during daytime. Punknown provided four times more HONO than the reaction of NO with OH did. The diurnal variation of Punknown showed an apparent photo-enhanced feature with a maximum around 12：00, which was consistent with previous studies at forest and rural sites. Laboratory studies proposed new mechanisms to recruit NO2 and J（NO2） in order to explain a photo-enhancement of of Puknown. In this study, these mechanisms were validated against the observation-constraint Punknown. The reaction of exited NO2 accounted for only 6% of Puknown, and Punk poorly correlated with [NO2] （R = 0.26） and J（NO2）[NO2] （R = 0.35）. These results challenged the role of NO2 as a major precursor of the missing HONO source.展开更多
文摘In this paper, we consider an unknown source problem for the modified Helmholtz equation. The Tikhonov regularization method in Hilbert scales is extended to deal with ill-posedness of the problem. An a priori strategy and an a posteriori choice rule have been present to obtain the regularization parameter and corresponding error estimates have been obtained. The smoothness parameter and the a priori bound of exact solution are not needed for the a posteriori choice rule. Numerical results are presented to show the stability and effectiveness of the method.
基金supported by China Postdoctoral Science Foundation(2023M733220)Zhengzhou PM_(2.5)and O_(3)Collaborative Control and Monitoring Project(20220347A)the National Key Research and Development Program of China(No.2017YFC0212403).
文摘HONO is a critical precursor of•OH,but its sources are controversial due to its complex formation mechanism.This study conducted comprehensive observations in Zhengzhou from April 26 to May 11,2022.Low NO_(x)concentrations were observed during the Covid epidemic period(EP)(10.4±3.0 ppb),compared to the pre-epidemic period(PEP)(12.5±3.8 ppb).The mean HONO concentration during EP(0.53±0.34 ppb)was 0.09 ppb lower than that during PEP(0.62±0.53 ppb).The decrease in HONO concentration during EP came mainly at night due to the reduction in the direct emission(P_(emi))(0.03 ppb/hr),the homogeneous reaction between•OHandNO(P_(OH+NO))(0.02 ppb/hr),and the heterogeneous conversion of NO_(2)on the ground(0.01 ppb/hr).Notably,there was no significant change in daytime HONO concentration.The daytime HONO budget indicated that the primary HONO sources during PEP were the nitrate photolysis(P_(nitrate)),followed by the P_(OH+NO),Pemi,the photo-enhanced reaction of NO_(2)on the ground(P_(ground+hv))and aerosol surface(Paerosol+hv).The primary HONO sources were Pnitrate,POH+NO,P_(emi),and_(Paerosol+hv)during EP,respectively.The missing source has a high correlation with solar radiation,there might be other photo-related HONO sources or the contributions of photosensitized reactions were underestimated.In the extremely underestimated cases,HONO production rates fromthe P_(nitrate),P_(ground+hv),and Paerosol+hv increased by 0.17,0.10,and 0.10 ppb/hr during PEP,0.23,0.13,and 0.16 ppb/hr during EP,and P_(nitrate)was still the primary source during both PEP and EP.
基金supported by the National Natural Science Foundation of China(21190052,40675072,41121004)the Ministry of Science and Technology of China(2002CB410801)the Beijing Council of Science and Technology(HB200504-6,HB200504-2)
文摘Nitrous acid （HONO）, as a primary precursor of OH radicals, has been considered one of the most important nitrogencontaining species in the atmosphere. Up to 30% of primary OH radical production is attributed to the photolysis of HONO. However, the major HONO formation mechanisms are still under discussion. During the Campaigns of Air Quality Research in Beijing and Surrounding Region （CAREBeijing2006） campaign, comprehensive measurements were carried out in the megacity Beijing, where the chemical budget of HONO was fully constrained. The average diurnal HONO concentration varied from 0.33 to 1.2 ppbv. The net OH production rate from HONO, Pon（HONO）net, was on average （from 05：00 to 19：00） 7.1 × 10^6 molecule/（cm^3 s）, 2.7 times higher than from 03 photolysis. This production rate demonstrates the important role of HONO in the atmospheric chemistry of megacity Beijing. An unknown HONO source （Punknown） with an average of 7.3 × 10^6 molecule/（cm^3 s） was derived from the budget analysis during daytime. Punknown provided four times more HONO than the reaction of NO with OH did. The diurnal variation of Punknown showed an apparent photo-enhanced feature with a maximum around 12：00, which was consistent with previous studies at forest and rural sites. Laboratory studies proposed new mechanisms to recruit NO2 and J（NO2） in order to explain a photo-enhancement of of Puknown. In this study, these mechanisms were validated against the observation-constraint Punknown. The reaction of exited NO2 accounted for only 6% of Puknown, and Punk poorly correlated with [NO2] （R = 0.26） and J（NO2）[NO2] （R = 0.35）. These results challenged the role of NO2 as a major precursor of the missing HONO source.
