Where does Oxygen Extinction Occur in a Soil Profile?

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1 2st Interntion Congress on Modeing nd Simution, God Cost, Austri, 29 Nov to 4 ec 25 Where does Oxygen Extinction Occur in Soi Profie? Freemn J Cook nd John H Knightb Freemn Cook nd Assocites, The University of Queensnd nd Griffith University b The University of Sydney Emi: freemn@freemncook.com.u Abstrct: The probem of where nd under wht circumstnces oxygen extinction (concentrtion in gs phse, C =) in soi profie is of incresing interest, due to the effect of nitrous oxide nd methne fuxes on tmospheric chemistry (Rvishnkr et., 29) cimte chnge (Forster et., 27). The oxygen concentrtion profie is so of importnce s the biogeochemic processes in sois re miny medited by oxidtion/reduction rections. In soi there re two min sinks for oxygen (O2), microbes nd pnt roots. Cook nd Knight (23) deveoped n nytic mode for the stedy-stte trnsport of oxygen into uniform soi by use of trnsformtions of the independent vribes, the concentrtion (C) nd spti dimension (z). The trnsformed concentrtion is C ' = C Cr / α ; Cr is the critic concentrtion in the wter phse t the root surfce nd α is the Bunsen coefficient. The spti trnsform is = 2 r exp( z / 2 r ) g with g = 2πα L / [ n( R / )], r the scing depth for n exponentiy decresing root ength density with z, is the diffusion of O2 in soi wter, is the diffusion of O2 in soi ir, R is the rdius of the root pus sturted soi round the root, is the root rdius nd L is the root ength density t z =. This mode coud not ccute the depth t which either C or C ' went to extinction. A subsequent extension ws be to ccute the depth () when C ' = nd the ir-fied porosity (θ) ws ess thn critic vue (θc) but with =. Here we remove this restriction nd by couping with mode of Cook (995) where the ony O2 sink is microbes re be to determine the depth () t which C =. This requires soving set of five boundry condition equtions nd recursive method is presented. The extension to '/ d < resuts , (m) the restriction tht '/ d.5, '/d =, '/d <, < infinity, '/d <, = infinity θc θ..5 in essentiy the sme critic ir-fied. porosity (θc) beow which C ' = t finite depth. When θ < θc the recursive method cn be used to determine nd θ from this. Couping this with the Cook (995) soution so tht C = Cr/α t the Figure. The depth t which or occurs s function reminder of the O2 profie cn be obtined. of θ for different modes for cy soi (Tbe ). The When θ is ess thn further critic vue critic vues of θ re shown. (θz) then C = t finite depth nd cn be determined. An exmpe of typic resut for sit om soi is shown in figure. This shows the rpid increse in nd tht occurs s θ pproches the critic vue. The mode of Cook nd Knight (23) where '/ d = (soid circes) overestimtes the depth of compred to the new mode given here which removes this restriction. There is not perfect mtch in round θz, this is ikey due to difficuties with computtion imittions. This suggests tht nitrous oxide genertion in prticur is ikey to occur cose to the soi surfce in ccord with mesurements (Cough et. 24). Keywords: Oxygen trnsport, soi ertion, nitrous oxide, methne 87

2 Freemn J Cook nd John H Knight, Where does oxygen extinction occur in soi profie?. INTROUCTION Oxygen is one of the driving forces for biogeochemic processes in sois nd understnding the controing fctors in its distribution within soi is importnt. The min process for oxygen trnsport into soi is due to diffusion s resut of the sinks for oxygen within the soi. The min sinks re microbi respirtion nd pnt root uptke. Microbi respirtion cn be described s distributed sink with decresing sink strength with incresing soi depth. Uptke by pnt roots occurs s ocized trnsport to the root surfce vi zone of sturted soi (Cook nd Knight 23, b). Vi the root ength density distribution of the soi this cn be converted to distributed sink, but this sink term now so contins the oxygen concentrtion (C). The stedy-stte oxygen concentrtion s function of depth ws soved by Cook nd Knight (23,b) using trnsforms for both the oxygen concentrtion C' = C Cr / α nd the spti dimension = 2r exp( z/ r) g. The ower boundry conditions nd trnsformed oxygen concentrtion ment tht the depth t which either C = or C ' = coud not be ccuted. This ws ter remedied for C'( ) = by Cook et. (23), but this mode coud sti not find the depth t which C = nd required '/ d = s one of the boundry conditions. Here we wi present further extension tht removes this boundry condition restriction nd by couping with the mode deveoped by Cook (995) for ony microbi sink ows the depth t which C = ( ) to be obtined. We wi then show the effect of these chnges on critic ir-fied porosity vues nd... Theory Ony imited deveopment of the theory wi be given here s the fu deveopment hs redy been pubished. Using the trnsforms, the stedy-stte oxygen trnsport into soi by diffusion cn be described by: 2( p ) ' C ' β = C + p r d d d d g 2 where β = M /, M is the microbi respirtion sink strength t z =, p = r / m is the rtio of exponenti scing depths for the root ength density ( r ) nd microbi sink strength ( m ). For p = we obtin the soution: where β = + (2) g ' C ( ) I( ) bk ( ), /2 = 2 r g, K is modified Besse functions of second kind nd zero order, I is modified Besse functions of first kind nd zero order, is the vue of where prmeters tht need to be determined. At the depth ( ) cn be determined from the definition of. At the concentrtion of oxygen must be C r /α from definition of the trnsformed concentrtion nd further reduction in oxygen concentrtion cn ony occur due to microbi respirtion. Thus we cn now coupe the soution from Cook (995) to give C for z > (fter Cook, 995): () C'( ) = nd nd b re 2 2 mm z z mm Cz ( ) = Cr / α exp exp, Cr / α <, z m m m 2 2 mm z mm = Cr / α exp, Cr / α, z m where z = z nd M M ( ) = exp / m. From the boundry conditions for eqns (2) nd (3) we cn get five simutneous eqns: (3) 88

3 Freemn J Cook nd John H Knight, Where does oxygen extinction occur in soi profie? ( ) ( ) ( ) ( ) A= I + bk β / g = I + bk β / g ' d =. = I ( ) bk ( ) g exp d /2 2 r mm = exp, = < m mm = =, = 2 mm = Cr / α + exp, < m m 2 mm = Cr / α, = where A is the tmospheric concentrtion of oxygen, K is modified Besse functions of second kind nd first order, I is modified Besse functions of first kind nd first order. These set of equtions cn be soved recursivey obtin, b, nd using the methodoogy given beow. 2. METHOS In order to obtin vues of nd scheme to sove the set of constrints in eqn (4). The foowing schem ws devised:. Ccute zero estimte for using (Cook nd Knight, 23): g I( ) K( ) + K( ) I( ) = ( A Cr / α ) nd soving itertivey. The vue of wi ie in the rnge ( r ) = 2 n / 2 g. /2 r β < <, so the first estimte is (4) = ( + )/2 nd 2. The vues of nd b cn now be ccuted from the first two constrints in eqn (4) by ( ( r α) β ) ( ) ( / α) β / ( ) / = K ( ) A C / + / g K ( ) / ( r ) b = I A C + g I = I ( ) K ( ) I ( ) K ( ) 3. The vue of of ' d d cn be ccuted with the third constrint in eqn (4) nd first estimte is mde by equting the third nd fourth constrints of eqn (4) 2 ' d mm ' d = m Cr / α + m / + m. d d 4. The vue of cn be ccuted from the fourth constrint in eqn (4). 89

4 Freemn J Cook nd John H Knight, Where does oxygen extinction occur in soi profie? 5. If < ' ( ) d d or 2 = H + L. /2 > then H = ese L= nd This procedure is repeted unti used in ccuting < T, with T = -2. If the vue of < then constrint 5 is i i nd =. The vues of nd re ccuted from nd respectivey. A MtLb computer progrm ws written tht soved the bove schem for rnge of ir-fied porosity vues. The critic wter contents t which C = t infinity is estimted with this procedure from the vue of by (Cook et., 23; Modrup et. 2): 2+ 3/ λ 3 θ = ( 2θ +.4θ) θ (5) where is the oxygen diffusion in ir, θ is θ t mtric potenti of - m nd λ is Cmpbe (974) soi wter retention prmeter. This mends the diffusion in ir to tht in soi ir which is ess due to some of the voume being wter nd soids nd the pthwy being tortuous. Simiry, the diffusion in the wter ws ccuted with (Osen et. 2): where ( λ ) = f f 2..2 (6) is the oxygen diffusion in wter nd f is the soi porosity. Vues of the nd cn be found in Cook et. (23) nd the vues t 2 C re used in ccutions here. The other prmeters for the ccutions cn be found in Cook et. (23) 3. RESULTS AN ISCUSSION For sndy om soi prmeters (Tbe ) t temperture of 2 the oxygen concentrtion profies with depth for different vues of ir-fied were ccuted with the pproprite mode depending on the vue of θ for sndy om soi t 2 C (figure 2). The extension to vues of C < Cr/α using the mode deveoped here is shown for θ =. where = nd for θ =.75 where =.36 m. A comprison for between the Cook et. (23) nd eqns (2) nd (3) shows tht Cook et. (23) overestimtes the depth t which C ' = (figure 3). Eqn (3) wi give more ccurte resuts s it wi represent more cosey the ctu grdients nd sinks in the soi. A comprison of the concentrtion profies ccuted with Cook et C (kg m -3 ) z (m) θ =.2 θ =.24 C = C r /α θ =., eqn (2) θ =., eqn (3) θ =.75, eqn (2) θ =.75, eqn (3) Figure 2. Oxygen concentrtion (C) with depth for sndy om soi t 2 C for different vues of θ. The vue of C = C r /α is shown to indicte where C =. (m) Cook et. 23 Eqn (2) Figure 3. Comprison of versus θ for sndy om soi t 2 C ccuted with Cook et. (23) nd eqns (2) nd (3). θ 8

5 Freemn J Cook nd John H Knight, Where does oxygen extinction occur in soi profie?. (23) nd eqns (2) nd (3) show how the oxygen profie gets distorted to meet the condition tht '/ d = with oxygen penetrting to deeper in the soi profie (figure 4). This occurs becuse in order to meet the boundry conditions oxygen must be consumed so tht C'( ) = nd '/ d = must be greter thn for eqn (2). This mens tht for soi biochemic processes such s denitrifiction nd nitrous oxide production the depth t which oxygen concentrtions ssocited with the required redox potenti wi be cose to the soi surfce (<.2 m) when θ <.6θ c. This is consistent with mesurements of nitrous oxide fuxes to the tmosphere (Cough et. 24). C (kg m -3 ) z (m) Cook et. (23) Eqn (2) nd (3) C = C r /α Figure 4. Comprison of oxygen profies for sndy om soi t 2 C ccuted with Cook et. (23) nd eqns (2) nd (3) with θ =.. The fct tht the depth of oxygen extinction ( ) cn now be determined with this retivey simpe mode shoud so ssist in estimting when nd where methne fuxes re ikey to occur in soi profies. The increse with increse in θ is retivey sow unti θ pproches θ z (figure ). Agin this suggests tht the methne genertion wi be cose to the soi surfce which wi enhnce its biity to escpe into the tmosphere. Tbe. Soi properties (fter Cook et., 23) nd critic ir-fied porosities (θ c nd θ z ) t 2 C. Soi f (m 3 m -3 ) θ (m 3 m -3 ) λ θ c (m 3 m -3 ) θ z (m 3 m -3 ) Snd Lomy snd Sndy om Lom Sit Lom Sndy cy om Cy om Sity cy om Sndy cy Sity cy Cy Thus the critic ir-fied porosities tht cn be ccuted with eqns (2) nd (3) re importnt in being be to understnd soi conditions tht coud resut in nitrous oxide nd methne production in sois. The fct tht eqns (2) nd (3) provide retivey simpe mens of ccuting soi oxygen concentrtions wi ssist in providing better understnding of mny soi biogeochemic processes nd hep with modes tht use redox potenti s the driver of these processes (Grnt, 999). Critic vues for θ for vrious sois t temperture of 2 C re presented in Tbe. These resuts show the gener trend of decresing critic irfied porosities from snd to cy. This my seem t first surprising s snds re genery considered not to hve ertion probems. The vues need to be considered compred to the θ vue. This is the vue tht the sois wi drin to. The rtio of θ c /θ for the snd is.39 whie for the cy is.47. This mens tht the snd wi drin to ess thn θ c whie the cy wi require further drying by evpotrnspirtion before θ c is reched. Thus these vues re consistent with wht is common knowedge of soi behvior. 4. CONCLUSIONS A mode for oxygen trnsport nd consumption in soi is present which hs two sinks, pnt roots nd microbi respirtion nd is be to compute oxygen extinction for trnsformed nd oxygen concentrtions. This requires soution of the mode of Cook et. (23) but without the constrint on the bottom boundry tht the grdient in the trnsformed oxygen concentrtion ( C ' ) is zero when C'( ) = ong with couping the concentrtion (C) to the soution of Cook (995) where microbi respirtion is the ony sink. A 8

6 Freemn J Cook nd John H Knight, Where does oxygen extinction occur in soi profie? soution scheme is proposed for the five constrints ssocited with the boundry conditions nd it is shown to work. The oxygen concentrtion for the compete rnge of oxygen concentrtions cn now be ccuted with this new mode. The depth t which C'( ) =, ( ) is ess with the new mode thn tht previousy ccuted with the mode of Cook et. (23). This mens tht oxygen concentrtions re ower deeper in the soi nd this hs impictions for soi biogeochemic process such s denitrifiction nd methnogenesis. A critic vue for the ir-fied porosity (θ c ) cn be ccuted nd is essentiy the sme s tht ccuted with the Cook et. (23) mode. The depth t which C = ( ) cn now be ccuted nd resuts show tht this, though greter thn, occurs t retivey show depths for most the reevnt ir-fied porosity rnge. A critic vue for the irfied porosity θ z cn be ccuted bove which is infinite nd C is greter thn zero for depths. REFERENCES Cough, T.J., Keiher, F.M., Sherock, R.R. nd Ford, C.. (24) Lime nd soi moisture effects on nitrous oxide emissions from urine ptch. Soi Science Society of Americ Journ, 68(5), Cook, F.J. (995). One-dimension oxygen diffusion into soi with exponenti respirtion: nytic nd numeric soutions. Ecoogic Modeing, 78, Cook, F.J. nd Knight, J.H. (23). Oxygen trnsport to pnt roots: Modeing for physic understnding of soi ertion. Soi Science Society of Americ Journ, 67, 2-3. Cook, F.J. nd Knight, J.H. (23b). Errtum, Oxygen trnsport to pnt roots: Modeing for physic understnding of soi ertion. Soi Science Society of Americ Journ, 67,964. Cook, F.J., Knight, J.H. nd Keiher, F.M. (23). Modeing oxygen trnsport in soi with pnt root nd microbi oxygen consumption: epth of oxygen penetrtion. Soi Reserch, 5, Forster, P., Rmswmy, V., Artxo, P., Berntsen, T., Betts, R., Fhey,.W., Hywood, J., Len, J., Lowe,.C., Myhre, G., Ngng, J., Prinn, R., Rg, G., Schuz, M. nd Vn ornd, R., (27). Chnges in Atmospheric Constituents nd in Rditive Forcing. In: Cimte Chnge 27: The Physic Science Bsis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernment Pne on Cimte Chnge, Soomon, S., Qin,., Mnning, M., Chen,., Mrquis, M., Averyt, K.B., Tignor, M. nd Mier, H.L. (eds.). Cmbridge University Press, Cmbridge, United Kingdom nd New York, NY, USA. Grnt, R.F. (999). Simution of methnotrophy in the mthemtic mode ecosys. Soi Bioogy & Biochemistry, 3, Modrup, P., Oesen, T., Schjønning, P., Ymguchi, T. nd Roston,.E. (2). Predicting gs diffusion coefficient in unsturted soi from soi wter chrcteristics. Soi Science Society of Americ Journ, 64, 94. Oesen, T., Modrup, P., Ymguchi, T. nd Roston,.E. (2). Constnt sope impednce fctor mode for predicting the soute diffusion in unsturted soi. Soi Science, 66, Rvishnkr AR, nie JS nd Portmnn RW (29). Nitrous oxide (N2O): the dominnt ozone-depeting substnce emitted in the 2st century. Science 326:

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