Sign up & Download
Sign in

Box model studies of ClOx deactivation and ozone loss during the 1991/92 northern hemisphere winter

by E R Lutman, R Toumi, R L Jones, D J Lary, J A Pyle
Geophysical Research Letters (1994)

Abstract

Calculations using a photochemical box model from mid-January to early March 1992 show the return from perturbed levels of ClO(x) to near background levels, and the associated rise of ClONO2. The calculated values of ClONO2 in an in-vortex, background aerosol scenario are in good agreement with those observed by the balloon borne MIPAS-B limb sounder. Implications for ozone loss are discussed.

Cite this document (BETA)

Available from David Lary's profile on Mendeley.
Page 1
hidden

Box model studies of ClOx deactivation and ozone loss during the 1991/92 northern hemisphere winter

GEOPHYSICAL RESEARCH LETTERS, VOL. 21, NO. 13, PAGES 1415-1418, JUNE 22, 1994
Box model studies of CIOx deactivation and ozone loss
during the 1991/92 northern hemisphere winter
E. R. Lutman, R. Toumi, R. L. Jones, D. J. Lary, J. A. Pyle
Centre for Atmospheric Science, Department of Chemistry, University of Cambridge, United Kingdom
Abstract. Calculations using a photochemical box model from
mid-January to early March 1992 show the return from perturbed
levels of C10 x to near background levels, and the associated rise of
C1ONO2. The calculated values of C1ONO 2 in an in-vortex,
background aerosol scenario are in good agreement with those
observed by the balloon borne MIPAS-B limb sounder.
Implications for ozone loss are discussed.
Introduction
The chemical evolution of the vortex from late November 1991
until January 1992 has previously been discussed (Lutman et al.,
this issue). In that paper, the activation of chlorine by polar
stratospheric louds (PSCs) on the 475K potential temperature
surface was studied using a trajectory model. It was found that by
early January large amounts of active chlorine (ClOx = C10 +
2xC1202), over 2ppbv, were produced throughout the vortex by
heterogeneous reactions on PSCs. During the second half of
January the vortex became more disturbed (Naujokat et al., 1992).
When temperatures rose in late January and large scale PSC
processing stopped, C1Ox levels began to relax back to background
levels through reformation of reservoir species. When chlorine
levels were at their peak in mid-January there was not enough
sunlight present for appreciable ozone loss to occur. Balloon
measurements carried out in early March showed that most ClOy
(HCl+C1ONO2+HOCl+C1Ox) was in the form of C1ONO 2 (Oelhaf
et al., this issue). By performing photochemical box model runs for
mid-January to March a number of problems may be addressed:
whether the rapid increase of chlorine nitrate shown by the MIPAS
measurements is consistent with known photochemistry, the role
the Mt. Pinatubo aerosol played in determining the timescale for
C10 x recovery and the implications of the speed of C10 x recovery
for ozone destruction.
Model Description
The photochemical box model used is described in Lutman et al.,
(this issue). It includes a full gas phase chemistry scheme and
heterogeneous reactions on sulphuric acid aerosol and polar
stratospheric louds (PSCs). For the period from mid-January 1992,
the temperature is constrained to be above the critical temperature
for PSC formation so only heterogeneous reactions on sulphate
aerosols need be considered. The model includes the following two
reactions on sulphate aerosol:
CIONO 2(g) + H20 (l) --> HOCI (g) + HNO 3 (g) (1)
N20 5 (g) + H20 (l) --> 2HNO 3(g) (¾ = 0.1 ) (2)
A sticking probability, ¾, calculated as a function of temperature
and reaching a maximum value of 0.1 at around 195K, is used for
reaction 1 (Hanson and Ravishankara, 1991). Sulphate aerosol
Copyright 1994 by the American Geophysical Union.
Paper number 93GL03046
0094-8534/94/93GL-03046503.00
surface areas available for heterogeneous chemical reactions are
calculated in this study for two cases. Firsfly ordinary background (surface area - 0.5-0.75 gm2cm -3)were used which compare well
with in-vortex measurements of aerosol on January 18 (Deshler et
al., 1993) over Kiruna as described later. Secondly volcanic (i.e.
Pinatubo influenced) conditions were used (~ 10-15 Ixm2cm-3).
These are somewhat lower than measurements by Deshler et al.,
(1992) at Laramie, Wyoming between 26 July and 29 August 1991
of between 9 and 84gm2cm -3. However as will be seen this does
not affect our argument.
The recently determined temperature dependence of the HNO 3
photolysis cross section (Rattigan et al., 1992) is included in the
model. The effect of the temperature dependence of the HNO 3
photolysis rate on the chlorine relaxation in the model is discussed
below.
Method
We follow a different approach to the companion study (Lutman
et al., this issue) where chlorine activation was investigated. Here,
in order to study the chemical behaviour of the polar vortex after
PSC activation has ceased, integrations coveting 55 days were
performed from 20 January to 5 March 1992 at 50mb. The model
was initialised assuming apre-processed, i.e. high C1Ox atmosphere
(see Table 1). Other species take values suitable for winter/spring
high latitudes with a background aerosol. The air parcel follows an
idealised temperature history which rises linearly from 198K to
213K at the end of the run. This approach does not reproduce
periods when temperatures may again have dropped below the
critical temperature for PSC formation in late January or early
February (Naujokat et al., 1992) or when oscillations in temperature
caused by transport around the vortex may have lowered the
temperature. These temperature changes will make litfie difference
to the gas phase chemistry. However if the temperature dropped
below 195K levels of C1ONO 2 would have been lowered due to
heterogeneous reactions. Again this strengthens our conclusions as
shall be discussed later. However for the purposes of this study the
idealised model temperatures were in broad agreement with the
general temperature trend of this period. Thus the temperature
dependent reaction I is only effective for approximately the first 10
days of the runs in which sulphate aerosol reactions are included,
while reaction 2 is effective throughout hese runs.
By performing box model runs at 65øN a picture can be
developed of chlorine relaxation inside, and on the edge of the polar
vortex from late January to mid March 1992. Since the effects of
excursions to lower latitudes, namely greater insolation, will be
omitted by taking this approach, the results from 55øN and 75øN
are also discussed.
TABLE 1. Chemical Initialisations / ppbv for 55øN-75øN.
Latitude C10 x CIONO 2 HCI
75/65øN 2.0 0.3 0.4
55øN 1.0 1.1 0.2
(At all latitudes HOC1 = 0.2, HNO 3 = 10.5, NO x = 0.24, N205 =
0.4, O x = 3.5E+3, Br x = 8.0E-3 ppbv.)
1415
Page 2
hidden
1416 Lutman et al.: Box Model Studies
Results
In figure 1 are shown nitric acid concentrations a a function of
day of run, where day 1 is January 20 1992 for 65øN. Three cases
are shown, perturbed aerosol similar to a Mt. Pinatubo scenario
(case A), background aerosol, (case B), and only gas phase
chemistry, (case C) for both temperature dependent and room
temperature nitric acid photolysis rates. Using the older room
temperature cross-sections compared to cross-sections calculated at
200K resulted in a doubling of the nitric acid photolysis rate at
20kin, 0 ø solar zenith angle. The relative effect increases with solar
zenith angle and is therefore of great importance at high latitudes.
In the cases including heterogeneous chemistry there is clearly
some immediate adjustment to the initialisation during the first 3
days, greatest in the case of the large aerosol oading. In all three
cases there is then a rather slow photolyric loss of HNO 3 (and an
associated increase in NOx, see figure 3). The difference in day 55
values arises from the increased rate of formation of HNO 3 in
heterogeneous cases A and B and in the slower nitric acid
photolysis rate when using temperature dependent cross-sections
(Toumi et al. 1993a).
Figure 2 shows midnight values of chlorine nitrate for the same 3
cases. In case A (volcanic aerosol) C1ONO2 decays initially
following reaction 1. Levels of C1ONO 2 then rise as the
recombination reaction of CIO and NO 2, arising from nitric acid
photolysis, is faster than the loss of CIONO2 due to its photolysis.
In case A around l ppbv is formed by the end of the run. The
reformation is controlled by the levels of NO2, which as can be seen
from figure 3 are lowest in case A.
12 I I I 12
,,- '\"\"'\"'--...., '%.,..,.,.. \"' ^]
 9- -\",._.,;. \"\"'\"\",. [b] -9 \"'--
8- - -8
- [c]
7 7
0 10 20 30 40 50 60
DAY OF RUN
Fig. I HNO 3 (ppbv) as a function of day of run, at 50rob. Volcanic
aerosol (A), background aerosol (B), pure gas phase chemistry (C).
Effect of temperature dependent [capita]s] and room temperature
[lower case] absorption cross-sections for nitric acid photo]ysis
shown.
3.01 I I I 3.0 2.5 - 2.5
,,,, ..... 20- ,\"
. ,,, . ,' ,' -2.0
./-/,,,,' / ,.,,\"
O ,,,.,,.\" - 1.5 /;\" .,::\"/ .,,\"
0'5 -- r:' :' / .[.a.]/'\" ../ -0.5
ß 0 10 20 30 40 50 60 0.0
DAY OF RUN
Fig. 2 As in Fig. I but œor midnight values of CIONO2 (ppbv).
In case B, with background levels of sulphate aerosol, the levels
of NO x are somewhat higher than in case A. Even at the beginning
of the run, formation of CIONO2 is faster than its destruction on
aerosol and it rises slowly, peaking at 2.3 ppbv at day 50. It is then
destroyed slowly by photolysis.
In case C (pure gas phase chemistry) the C1ONO2 rises most
steeply at first since there is more NO x available and there is no
heterogeneous destruction. CIONO 2 peaks on day 37 at 2.35 ppbv
before declining gently throughout the rest of the run.
A key test of our understanding of the chemical processes
controlling chlorine deactivation is how well chlorine nitrate
concentrations are calculated. Observations by Oelhaf et al., (this
issue) showed high C1ONO 2 at 50mb in March 1992 in the centre
of the vortex. We have run three cases, volcanic aerosol (run A),
background aerosol (run B) and gas phase (run C). The results show
that the background aerosol and gas phase cases are consistent with
the C1ONO 2 measurements of Oelhaf et al. In contrast by running
with volcanic aerosol we cannot produce sufficient C1ONO2 by mid
March. Thus our background aerosol runs are consistent with the
low aerosol measured by Deshler et al. (1993) on January 18 1992
inside the vortex at Kiruna which indicated that at 50mb
(approximately 19 km) background values of 0.7pm2cm -3 were
present, and also with the high CIONO 2 values observed in March
by Oelhaf et al. (this issue).
Temperature dependent nitric acid photolysis rates.
The background aerosol case agrees best with the data whether
using room temperature or temperature dependent nitric acid
absorption cross-sections. Clearly with the larger (room
temperature) photolysis rates there is more NOx available to reform
C1ONO2. However no difference is made to the day 55 values of
C1ONO 2 using room temperature cross-sections for cases B and C
even though the peak in C1ONO 2 occurs approximately 12 days
earlier in case B when using room temperature cross-sections.
However in the volcanic aerosol case run, A, ClONO2 is produced
more rapidly with the faster photolysis rates but still only reaches
1.8ppbv by the end of the run, i.e. much less than the background
aerosol case.
The latest evaluation of the temperature dependence of nitric
acid absorption cross-sections (R.A. Cox, pets. comm.) results in a
small increase in the 200K photolysis rates. This does not alter our
conclusions ince this increase in photolysis rates would speed up
the formation of C1ONO2 in our background run. However on day
55 of the volcanic run, values of CIONO2 would still be much
lower than measurements.
The evolution of HCI is considered using the temperature
dependent nitric acid photolysis rates in figure 3. HCI is produced
mainly via the reactions
o 7 0.6 I I 0.6
o s- ///[B]
 0.4- ' / -0.4
0.3- -0.3
o o .... '\"- - . ' '' ..... 0.0
0 10     60
DAY OF RUN
Fig. 3 HC1 and noon vues of NO 2 (ppbv) as a nction of day of
ran. Temmmm deandent JHNO 3 am used.
Page 3
hidden
Lutman et al.: Box Model Studies 1417
ClO + NO --) Cl + NO 2 (3)
Cl + CH 4 --) CH 3 + HCI (4)
In case A, where C1ONO 2values are lowest, HCI values increase
very slightly during the run. In case C, where NO values are higher,
HC1 concentrations rise to a value of 0.6 ppbv by the end of the run.
Case B lies between the other cases.
End point values of C1ONO2 and HCI may be compared to those
at 55øN and 75øN in Table 2.
TABLE 2. Volume mixing ratios in ppbv of C1ONO 2 and HCI after
55 day integrations for various scenarios.
Lat. Species Vole. (A) Backgr. (B) Gas ph. (C)
75øN C1ONO 2 0.64 1.3 2.1
HC1 0.46 0.47 0.47
65øN C1ONO 2 1.1 2.2 2.2
HCI 0.47 0.55 0.60
65øN ' C1ONO 2 1.9 2.2 2.2
HC1 0.53 0.57 0.61
55øN C1ONO 2 1.4 1.8 1.8
HC1 0.34 0.46 0.65
65øNf -using room temperature photolysis rates.
The dependence of the removal of CIO x on the sulphate aerosol
concentration and the nitric acid photolysis rate is shown in figure
4. In the gas phase chemistry case (C), CIO x returns to steady state
levels of around 0.2ppbv in 35 days. In case B the decay takes 50
days before CIOx comes to steady state. In the volcanic case, (A),
there are still high concentrations of CIO x of 0.7ppbv remaining by
day 55.
High values of HOCI (not shown) are calculated in case A,
peaking at 0.95ppbv, produced by reaction 1. These values are
higher than those indicated by column measurements inside and
outside the vortex during EASOE (Toon et al., 1992a). A possible
problem is thus indicated in our understanding of reaction I as
discussed in Lutman et al., (this issue), this reaction may either be
slower than currently thought or may not even occur on aerosol at
all. In the background aerosol case (B), HOC1 values peak at
0.45ppbv which compares well with 1989 values of HOC1 inferred
by Toon et al., (1992b) which peaked around 0.4ppbv at 70øN.
Although by day 55 in the background aerosol run, values of
C10 x have dropped to less than 500pptv, the vortex still contains
high amounts of CIONO 2 as previously discussed. The implications
for ozone loss in the springtime due to a cycle involving C1ONO2
photolysis are discussed by Toumi et al., (1993b).
In summary, recovery depends on available NOx, and hence
aerosol amount, and also latitude (i.e. zenith angle); at 75øN, 55
days is not long enough for recovery in cases A and B, this is
0 0 0.0
0 10  0 40  
OAY  N
Fi. 4 s in Fi. 1 but for noon values of OOx {ppbv}.
especially true in the runs performed using the new temperature
dependent nitric acid photolysis rate. At 65øN our run B
(background aerosol) results compare best with C1ONO2
observations. This is supported by in-vortex measurements of
aerosol on January 18 over Kiruna. However at lower altitudes
aerosol surface areas rose from background values of 0.7 to 10
ixm2cm '3 at 16.5km (Deshler t al., 1993). Our calculations show
that March chlorine nitrate measurements are inconsistent with
volcanic aerosol.
Absolute values of C1ONO2 in March will depend in part on our
total chlorine content. MLS measured a maximum of 2ppbv of CIO
at 46mb in January (Waters et al., 1993) suggesting that our total
chlorine values are on the low side. However in-vortex
measurements of ClOy in January 1992 by Schmidt et al. (this
issue) gave values of under 3.0ppbv at 475K.
Note that over a period of 2 months an air parcel would be likely
to experience many latitudinal excursions, producing increased
solar radiation - particularly, in the case of in-vortex air, when the
vortex is distorted by tropospheric weather systems and warmings.
This may have the effect of accelerating the formation of chlorine
nitrate as is indicated by our 55øN runs. However this may be
counterbalanced by the reactivation of C1Ox caused if temperatures
dropped again below the threshold temperature for type 1 PSC
which would delay the reformation of C1ONO 2, again suggesting
that only our background aerosol runs could be comparable to
measurements of C1ONO2.
Ozone Loss.
The various catalytic cycles which deplete ozone are described,
for example in Wayne (1991). In figure 5 the noon rates of ozone
loss due to the well known cycles and also the direct ozone loss
from the cycle involving CIONO 2 photolysis (see Toumi et al.,
(1993b) for derivation) are presented. Since C1ONO 2 calculations
in run B (background aerosol case) compare best with CIONO 2
observations, the respective cycles are presented only for the
background aerosol case (run B).
The chlorine and bromine cycles dominate ozone destruction
over the classic O+NO 2 and O+HO 2 cycles (not shown) during late
winter and early spring in the background aerosol case. The largest
contributors to ozone loss in the model are the cycles C10+O,
C10+BrO and C10+HO 2. The noon loss rates due to cycles C10+O
and C10+BrO peak near the beginning of the nm at 0.8 and
0.7ppbvhr '1 espectively. At this time the highest C10 levels are
present. These two cycles then decay throughout the run as CIO
o
1.o
0.8-
0.0
0
I .0 1.0
, JCI202
co../\"'\"* .... ___.% o.
,\" 0.4
,,
,,' ClO+HO2
,.:
/ 0.2
JClON
10   40   0.0
Fig. 5 Noon 03 destruction rates / v.m.r. per hour as a function of
day of run, at 50mb, for background aerosol case only. E.g. rate of
ozone loss due to reaction C10 + BrO --) C1 + Br + 0 2 is calculated
as 2kx[BrO]xC10]x[M]x3600.0 The cycle involving JCIONO 2 is
included. Temperature dependent JHNO 3 are used.
Page 4
hidden
1418 Lutman et al.: Box Model Studies
concentrations are depleted. The effectiveness of the CIO+BrO
cycle is limited by our relatively low initialisation of Br x.
The loss rate due to CIO+HO 2 peaks on day 27 at 0.6ppbv hr -1.
In the model, levels of NO 2 are rising with the increasing photolysis
of nitric acid as solar zenith angles decrease during the spring. This
loss rate then drops off slowly towards the end of the run.
The rate of the dimer cycle, initially larger at 1 ppbv hr -1, decays
rapidly and is the least important of the chlorine loss rates by day
55. This cycle is evidently not so important with the higher
temperatures used in the model. This model uses the most recent
evaluation of the CIO dimer photolysis rate (Burkholder et al.,
1990).
The cycle involving CIONO 2 photolysis which was shown to be
important later in the year by Toumi et al., (1993b) is unimportant
during the period of this run due to the low levels of CIONO 2
present at this time of year. However, this loss rate can be seen to be
rising steadily throughout he run as levels of CIONO2 and solar
radiation increase.
The chlorine and bromine cycles are more effective in the
volcanic runs (case A) due to more available CIO x and Br x. The
cycle C10+HO 2 is more effective in the volcanic run due to larger
levels of C10 caused by the production and subsequent photolysis
of large amounts of HOC1. In the gas phase chemistry run (case C),
the chlorine and bromine cycles are less effective, e.g. the cycle
involving C120 2 photolysis rates drops off by day 10. The effects of
the NO2+O cycle is however larger in the gas phase run.
A local net percentage ozone destruction (not shown) is implied
of between 14% and 20% in 1991-92 and 27% to 35% in a winter
with volcanic sulphate aerosol, such as 1992-93. However the
observed ozone loss will be expected to be smaller since the effects
of mixing will dilute concentrations of CIO x and latitudinal
excursions will increase NO x concentrations through photolysis of
HNO 3 thus speeding its relaxation to reservoir species.
Conclusions
The relaxation of highly perturbed levels of chlorine in the polar
vortex from mid-January to early March has been modelled using a
photochemical box model. Using a background aerosol scenario,
C10 x is observed to have fallen to near background levels by early
March. Chlorine nitrate levels are found to have risen to over
2ppbv, consistent with levels measured balloon borne MIPAS-B
limb sounder, and levels of HOC1 of around 0.4ppbv were
calculated, consistent with the inferred levels in March. In contrast,
when using a volcanic aerosol scenario, lower values of chlorine
nitrate and high levels of HOCI were calculated, inconsistent with
measurements. It is noted that 03 loss is expected to continue well
after the time when high CIO ceases, and that in 1992/3, when more
volcanic aerosol was present, larger 03 losses might be expected.
Acknowledgements. This work was funded by DG X ll of the
CEC under contract no. STEP-CT91-0139 for the support of
EASOE. ERL was supported by a Gassiot Award from the
Meteorological Office. The modelling work described here is part
of our NERC supported UGAMP effort.
References
Burkholder J.B., J.J. Orlando, and C.J. Howard, Ultraviolet
absorption cross-sections of C120 2 between 210 and 410nm, J.
Phys. Chem., 94, 687, 1990.
Deshler T., In situ measurements of the size distribution of the
Pinatubo aerosol over Kiruna, on four days between 18 January -
13 February 1992, Geophys Res. Lett., this issue, 1993.
Deshler T., D.J. Hoffman, B.J. Johnson, W.R. Rozier, 1992,
Balloonbome Measurements of the Pinatubo Aerosol Size
Distribution and Volatility at Laramie, Wyoming during the
summer of 1991, Geophys Res. Lett., 19, 199-202, 1992.
Hanson D.R. and A.R. Ravishankara, The reaction probabilities of
C1ONO 2 and N205 in 40 to 75% sulphuric acid solutions,
J. Geophys. Res., 96, 17307-17314, 1991.
Lutman E.R., J.A.Pyle, R.L. Jones, D.J. Lary, A.R. MacKenzie, I.
Kilbane-Dawe, N. Larsen, B. Knudsen, Trajectory model studies
of C10 x activation and ozone loss during the 1991/92 northem
hemispheric winter, Geophys Res. Lett., this issue, 1993.
McElroy M.B., R.J. Salawitch, S.C. Wofsy and J.A. Logan,
Antarctic ozone: Reductions due to synergetic interactions of
chlorine and bromine, Nature, 321,759, 1986.
Molina M.J. and L.T. Molina, Production of C120 2 from the self
reacti'on of the C10 radical, J. Phys. Chem., 91,433-436, 1987.
Molina, M.J. and F.S. Rowland, Stratospheric sink for
chlorofluoromethanes: chlorine-atom catalysed destruction of
ozone, Nature, 249, 810, 1974.
Naujokat B. et al., The stratospheric winter 1991/92, Bedage zur
Berliner Wetterkarte, SO 18/92, 1992.
Oelhaf H., T. v. Clarmann, H. Fisher, F. Friedl-Vallon, Ch.
Fritzsche, A. Linden, Ch. Piesch, M. Seefeldner, W. Volker,
Stratospheric C1ONO 2, and HNO 3 profiles inside the Arctic
vortex from MIPAS-B limb emission spectra obtained during
EASOE, Geophys Res. Lett., this issue, 1993.
Rattigan O., E.R. Lutman, R.L. Jones, R.A. Cox, K. Clemitshaw,
and J. Williams, Corrections to 'Temperature dependent
absorption cross-sections of gaseous nitric acid and methyl
nitrate', J. Photochem. Photobiol., 69, 125-126, 1992.
Solomon S., R.R. Garcia, F.S. Rowland and D.J. Wuebbles, On the
depletion of Antarctic Ozone, Nature, 321,755, 1986.
Toon, G.C., J.-F. Blavier, J.N. Solario, J.T. Szeto, Airborne
Observations of the 1992 Arctic winter stratosphere by FTIR
solar absorption spectroscopy, SPIE Vol. 1715 Optical Methods
in Atmospheric Chemistry, 457-467, 1992a.
Toon, G.C., C.B. Farmer, P.W. Schaper, L.L. Lowes and R.H.
Norton, Composition measurements of the 1989 Arctic winter
stratosphere by airborne infrared solar absorption spectroscopy,
J.Geophys. Res., 97, 7939-7961, 1992b.
Toumi R., S. Bekki and R. Cox, A Model Study of ATMOS
Observations and the Heterogeneous Loss of N205 by the
Sulphate Aerosol Layer, J. Atmos Chem. 115, 135-144, 1993a.
Toumi R., R.L. Jones, J.A. Pyle, Stratospheric ozone depletion by
CIONO2 photolysis, Nature, 365,37-39, 1993b.
Waters J.W., L. Froidevaux, W.G. Read, G.L. Manhey, L.S. Elson,
D.A. Flower, R.E Jamot, R.S. Harwood, Stratospheric C10 and
ozone from the Microwave Limb sounder on the Upper
Atmosphere Research Satellite, Nature, 362,597-602, 1993.
Wayne R.P. Chemistry of the Atmospheres, Oxford Science
Publications, 1991.
R.L. Jones, D.J. Lary, E.R. Lutman, J.A. Pyle, R.Toumi, Centre
for Atmospheric Science, Dept. of Chemistry, University of
Cambridge, Lensfield Rd., Cambridge, CB2 1EW, U.K.
(Received: December 11, 1992
Revised: May 6, 1993
Accepted: October 29, 1993.)

Sign up today - FREE

Mendeley saves you time finding and organizing research. Learn more

  • All your research in one place
  • Add and import papers easily
  • Access it anywhere, anytime

Start using Mendeley in seconds!

Already have an account? Sign in

Readership Statistics

2 Readers on Mendeley
by Discipline
 
by Academic Status
 
50% Professor
 
50% Assistant Professor
by Country
 
100% United States