Influence of Vertical Resolution on the Validation of Atmospheric Chemistry Instruments

A large number of valida tion campaigns for atm ospheric che mistry instruments are being carried out and more such st udies will be performed in the future. The aims of validation are to confirm the accuracy and precision of the measurement of a new instrument. There are many factors that may deteriorate the validation results and one of them is the vertical resolution of instruments when using the profiles intercomparison approach. The influence from the vertical resolution can be eliminated by using the averaging kernel m ethod but it is necessary to find the conditions for using the method. This study simulated the influence of vertical resolution for a cert ain curvature. The results show t hat both the curvature of a profile and th e difference of vertical resolution between two instruments have pos itive correlation with the differences between their measurements. The quanti tative estim ations of influ ence for some practical vertical resolu tions were obtained. The combined error of two instruments was defined as the criteria to judge the significance of influence. A c ase study based on the sim ulated results was demonstrated to show wh en the influence from the vertical resolution should be considered and when such influence can be omitted in order to avoid some unnecessary works in validation.


Introduction
Limb-scanning remote-sounding atmospheric chemistry instruments onboard satellit es are w idely used t o measure atmospheric parameters like the density of g ases, temperature and pressu re at di fferent altit udes, thus forming profiles of par ameters.For the validation of a new rem ote sounder, it is necessary to compare its measurements with the observ ations of o ther proved instruments at the same time and location.There are many factors that can deteriorate the validation results, for example, measuring different air masses be cause of a tmospheric f luidity, the che mical reaction in the atmo sphere, the different char acteristics of instruments like the vertical and horizontal resolution, etc. [1,2].The ver tical r esolution shoul d be especially concerned during the validation for limb-scan remote sounders which usually present their output data with profile form of atmospheric parameters.Figure 1 shows an intercomparison of t emperature prof iles d uring t he v alidation for M I-PAS/ENVISAT, Michelson Inte rferometer for Pas sive Atmospheric Sounding aboard t he Environmental Satellite of European Space Agen cy [3,4] (this instrument is named MIPAS-E hereafter) by using the data from MIPAS-B -a remote sounder t hat is si milar t o M IPAS-E but aboard a large Balloo n [5][6][7].Bo th instruments adopted limb-sounding geo metry and can m easure t ens of atmospheric par ameters prof iles like pressure and tem perature profiles, mixing vol ume rati o profi les of O 3 , H 2 O, HNO 3 , N 2 O, CH 4 and NO 2 etc. within a short period of time.In the figure, t he r ight pan el g ives t he temperature profile of MIPAS-E with vertical resolution 3 k m, the profile of t he same parameter from MIPAS-B but with vertical resolution 1 km which is the nominal resolution of the instrument.An additional r etrieved temperature profile fro m MIPAS-B with v ertical r esolution 3 k m was also presented.Th e left panel g ives t he di fferences of profi les bet ween M IPAS-E and MIPAS-B with vertical resolution 3 k m, 1 km and its smoothed profile (details in section 3.3), resp ectively.The agreements between t he MIPAS-E and M IPAS-B profiles are generally good in the whole altitude range of comparison.However, in the range of 169 -126 hPa (11 -15 km ), the d ifferences are obvi ously larger when u sing the MI-PAS-B p rofile with v ertical re solution 1 k m than the d ifferences when using another MIPAS-B profile w ith ver ti- cal resolution 3 km.This indicates that if th e vertical resolution of an instrument used for validation is different from that of the instrument to be validated, the validation results may be incorrect.Ther efore, the ver tical resol ution of all instruments that involved in v alidation should be equal in principle.However, because of t he limitation of char acteristics of each instrument, this requi rement w ill not be always sa tisfied.In th is c ase, fo r el iminating the influence due to ver tical reso lution, the method usi ng aver ageing kernel matrix to sm ooth the profile with fine vertical resolution may b e performed [8,9] .Howev er, so metimes this step will not be carried out i f the influence can be ignored based on empirical knowledge of validation [10][11][12].However, this kind of empirical judgment is not always correct.Hence, it is worth to evaluate the condition that what difference of vertical resolution bet ween t i nstruments i nvolved in validation is acceptable or unacceptable since it is beneficial t o sci entist for redu cing t he computational burden, financial cost and saving time in validation.

Reasons of Vertical Resolution Influencing Validation
In general, th e atm ospheric parameters lik e temperature and density of gases are variables with respect to altitude.As a re sult, t he pr ofiles of a tmospheric pa rameters are smoothly continuous curves which have different curvature at d ifferent lev el of altitu de.However, in struments can only measure atmospheric parameters at certain altitude levels.Then the measured profiles form the broken lines as the temperature profiles shown in Figure 1.Vertical resolutions may be tens of meters (in situ measurement), several kilometers (limb-viewing remote sensing), and more than ten kilometers (nadir remote sensing).
In th e valid ation when u sing a m ethod of profiles in -tercomparison, th e first step should be to in terpolate all the profiles o nto a defined vertical g rid ( represented by altitude levels or pressure levels) b y using logarithm, or linear, or sp line algo rithms.The in terpolation algorith m may introduce extra errors to the intercomparison and the errors h ave positive co rrelation to th e d ifference of v ertical resolution am ong t he profiles.This is because that the profile which has ro ugh v ertical r esolution can no t resolve the fine structure of atmospheric parameter field.Obviously, if t he profiles are straigh t lines, the extra errors disappear an d t he vertical res olution has no i nfluence on intercomparisons.Therefore, in order to evaluate the e rrors i ntroduced by t he v ertical grid, two factors should be considered simultaneously the vertical resolution and the curvature of profile.

Curvature in a Profile
In general, there are many different values of curvature for a prof ile of atm ospheric parameters.See Figure 1, for the MIPAS-B measured temperature profile at 1 km vertical grid, between the height region 126 -231 hPa, the profile has relative large curvatures, i.e. small radii of curva ture co mparing with the seg ments which are nearly straight lines in regions of 360 -26 8 hPa, 109 -28.6 hPa and 25 -4 hPa.For perfor ming sim ulation and assuming a segment of a profile, which represents the true values of an atmospheric parameter at different altitude levels, has a radi us of curvat ure r.The arb itrary unit of at mospheric parameter is used w ithout incur an y wron g conclusion.Sm all r rep resents that th e profile has fine structure.Further, it is assumed that all instruments that adop t di fferent ver tical gr id measure the true val ue of atmospheric parameters.Some of atmospheric chemistry instruments used to adop t one of the following vertical resolutions [0.5, 1, 2, 3, 4, 5, 6] km.The choosed curvature radius of the profile for simulation shou ld not be less than 1 k m in order to ensure that at least two points can be ex tracted fro m the profile.In order to ensure t hat t he sim ulation can be carried out for all t he verti cal reso lutions just mentioned above, we choose a curv e w ith a curv ature r adius 4 k m to r epresent the true profil e of an atm ospheric parameter.

The Profile Number for Intercomparison
For validation of instruments, a definite conclusion should depend on statistical results of intercomparisons.Figure 2 gi ves t he si mulation res ults fo r t he i nfluence o f t he number of profiles i nvolved i n i ntercomparison t o t he comparison results, i.e. the measurement difference of a proved i nstrument and a n u nproved one.I t i s cl ear t hat the differences vary with th e n umber of p rofiles es pecially when the number is less tha n 20.However, the differences approach a constant with the increasing of profile number.This actually indicates the changing trend of the standard error of comparison with the number of intercomparisons.Here, 70 simu lated profiles will be used during the simulation comparisons.

Simulation Comparison
The sim ulation procedure inclu des th e fo llowing step s.Firstly, let the cu rve ) represents th e true profile of an atm ospheric p arameter.Here, h is the altitude, and r is the cu rvature radius.Parameter x has an arbitrary unit.Secondly, for each vertical grid given above, 70 p rofiles were p roduced by extracting a point from the true profile at each level of altitude.These 70 simulated profiles represent the measured profiles of an instrument without any errors.Thirdly, for each c omparison, t he values of t he parameter at eac h level of altitude were calculated by interpol ating all the profiles linearly into the vertical grid with the vertical resolution 0.5 km.Finally, the calculations for the a verage difference at each level of altitude in the comparison for the two kinds of p rofile were carried out.For eliminating the influence of the absolute value of parameter to conclusions, the a verage difference i n percentage wa s used.The standard deviations of each average were also calculated to denote the dispersing extent of average difference.
There a re m any different c ombinations o f i ntercomparison according to the given vertical resolutions.Here, the vertical resolutions w hich are fre quently appeared during practical validation activities were considered.Figure 3 shows t he sim ulation results for the com parisons between vertical res olutions of 0 .5 -1 km, 0.5 -2 km, 0.5 -3 km, 0.5 -4 km, 0.5 -5 km, 0.5 -6 km, and 1 -3 km.The results clearly show s that the vertical resolution of instruments has influence on intercomparison, i.e. the differences of com parisons have positive correlation with the diffe rence of verti cal resolution betwee n two kinds of pro files ev en if both in struments measured th e true value of atmospheric parameters.The averaged standard deviation ba rs in dicate that with inc reasing o f difference of vertical resolution the precision of comparison decreases.This may lead to an underestimation of precision of a n in strument.Eve n if the dif ference of vertical resolution is equal for eac h comparison ( Figure 4), the influence to comparison is not the sam e.This is beca use the influence of vertical resolution is related with the curvature of the true profile.For a fixed curvature, the larger vertical res olution o f instr uments incurs larger differences between their measurements.
In fact, the tr ue p rofile of a ny atmospheric parameter is unavailable.Fortunately, for most of the cases of validation, th e profiles fr om th ose pr oved in struments h ave finer ve rtical resol ution tha n the profiles from the instruments whi ch need t o be validated .T hus, t hese profiles with fine vertical resolution can be regarded as true profiles.The curvature of a profile can be d educed from the fitted curve of the profile.Generally, t he curvature varies with point of t he fitted curve.Theref ore, the curvature of the c urve (or a se gment of cu rve) nee ds t o be determined?For estim ating the i nfluence o f vertical resolution, th e a veraged c urvature of th e cur ve (or a segment of a curve) can be regarded as the curvature of the whole curve.In Figure 1, the fitted curve of MIPAS-B te mperature pr ofile in th e r ange of 11 -15 km is a polynomial curve.And the averaged curvature radius of the curve around the peak point is about 1 km.
The c riteria whether the in fluence of ve rtical res olution can be omitted depend on the measurement errors of two i nstruments w hich are in volved in inter comparison.Assuming two instruments have measurement errors 1  , 2  , respectively, the combined error is If th e di fferences of sim ulated c omparison are lar ger than the combined e rrors, th en the in fluence of vertical resolution to validation s hould not be neglected.Figure 3 shows that the differences between profiles of vertical resolution 1 k m and 3 km are 2 -1 6% when the curvature radius is 4 km.This is ju st the case in term s of vertical resolutio n fo r the validation o f M IPAS-E by usi ng MIPAS-B data.In the range of 11 -15 km, the maximum of t he c ombined e rror of te mperature di fferences be -tween MIPAS-E a nd M IPAS-B is 1.7% .Since t he c urvature radius around the peak point of the fitted curve is about 1 km, the simulation can not be carried out because the inter polation al gorithm is invalid for t he M PAS-E profile which has a vertical resolution of 3 km (> 1 km).However, it is clear that the simulated differences in this case will be la rger t han 2 -16% because t he c urvature radius 1 km is less than 4 km and it is de finitely larger than the m aximum of the c ombined e rror 1.7% .T herefore, in the range of 11 -15 km, the results of direct comparison between t he m easurements of M IPAS-E a nd MIPAS-B (Figure 1) doesn't give the true differences of th e m easurements betwee n the tw o inst ruments, i.e. the differences of comparison in 11 -15 km may include significant co ntribution f rom the influen ce of vertical resolution.T herefore, f or t his case the in fluence of ve rtical resolution should be considered.For the segments  of temperature pr ofiles a bove 15 km and below 11 km, since their c urvatures are very sm all, the influe nce of vertical resolution can be omitted.
If the influence of vertical resolution can not be omitted and there fore direct comparison is unacceptable, the following t wo ap proaches for im proving validation ca n be adopted.One is to retrieve the profiles of atmospheric parameter with the sam e vertical resolution for both instruments.As an example, the result fr om this kin d of approach is shown in Figure 1.This approach, however, is often li mited by the characteristics of instrum ent, retrieval algorithm, etc., and not always feasible.The second approach is the m ethod to use the averaging kernel.This ap proach was d escribed by Rodg ers and C onnor [14].B efore performing th e com parison, the p rofiles with higher v ertical resol ution need to be smoothed.I f disregarding n oise, t he retrieved profile X re is a wei ghted average of the "true" profile X true and the a priori profile X a in the form of ( ) where A is th e a veraging kernel m atrix and I denotes the i dentity matrix.Th e higher-resolved profiles B X of instrument B are sm oothed by ap plying the averaging kernel m atrix of the low-resol ved profiles E X of instrument E. And the profile smoothing is done by where Ea X denotes the a pr iori profile of in strument E. Comparing equation (3) with equation (2), i t is clear that B X  is the res ult derived from the instr ument E inve rse mode, if B X is assumed to be the tr ue profile.Thus, in the difference of B X  -E X the contributions originating from different vertical resolution are reduced.Figure 1 als o p resents the difference p rofile between smoothed MIPAS-B temperature and MIPAS-E measurements (for clarity, the sm oothed MIPAS-B tem perature profile was not plotted).Above 15 km and below 11 km, the dif ference profile is very close to the one of direct comparison.This i ndicates that t he vertical res olution influences o n the validation are very small and consistent with the simulation results mentioned here.However, the improvement of com parison between altitudes 11 -15 km is obvious.It indicates that a fter adopting t he averaging ke rnel approach to smoothing the higher-resolved MIPAS-B profile, the i nfluence o f vertical resol ution to the comparisons was reduced.

Conclusions and Outlook
For t he validation of a n atm ospheric c hemistry instrument by c omparison with t he p rofiles f rom prove d i nstruments, vertical res olution o f p rofiles ca n deteriorate the validation results.The quantitative simulation results show the extent of deterioration due to the difference of vertical res olution bet ween the profiles fo r comparison for a certain c urvature of profile.T he re sults also show that when the difference of vertical resolution is equal for each pair of c omparison, t he larger ve rtical resolutions have more influence on comparison for a given curvature.The influence of vertical resolution on a validation has to be considered if its caused difference is beyond the combined errors of two instruments.In general, this kind of influence can be eliminated or reduced by using the averaging kernel of profile with rough vertical resolution to smooth the profile with fine vertical resolution.
Since the number of validation activities will increase in the future, it is useful to simulate the influence of vertical resoluti on o n validatio n f or different combinations of vertical reso lution and d ifferent cu rvatures of pro file.Our ne xt aim is to establish a datab ase based o n the complete simulation results.The database will be freely accessible for all scientists engaging in validation.

Figure 2 .
Figure 2. Influence of the profile number to the comparison between profiles with different vertical resolution.

Figure 3 .
Figure 3. Simulated comparisons between two profiles with different vertical resolution.

Figure 4 .
Figure 4. Simulated comparisons between two profiles with different vertical resolution where the difference of vertical resolution is equal for each comparison.