a markov model projection of soil organic carbon stores following land use changes

Journal of Environmental Management (1995) 45, 287–302

A Markov Model Projection of Soil Organic Carbon StoresFollowing Land Use Changes

D. M. Howard, P. J. A. Howard and D. C. Howard

The Institute of Terrestrial Ecology, Merlewood Research Station,Grange-over-Sands, Cumbria LA11 6JU, U.K.

Received 1 December 1994

Soils are major sinks of carbon, and land use can affect the magnitudes of soilorganic carbon stores and the net flux of carbon between the land andatmosphere. Hence, it is of some interest to have a method for examining thefuture consequences of changes in the patterns of land use for soil organiccarbon stores, and to allow experiments to be carried out to assess the likelyeffects of various policy options. We illustrate the use of a Markov model toproject future areas of land use from land cover transition matrices forEngland, Wales and Scotland, 1984–1990, and by the application of vectors ofsoil organic carbon stores for each land use types to the changes in areas toobtain projected changes in the soil carbon stores. In England and Wales,much depends on whether or not urban land is assumed to store soil carbon.For example, during 1984–1990, there was an overall decrease in potentialorganic carbon store in England and Wales of 32·64 MtC assuming that urbanland stores no soil carbon, but that overall decrease is reduced by 73% if urbanland is assumed to store 26·25×103 tC km−2. For England and Wales, thelimiting probabilities show 37·9% of the land as urban and 15·3% as arable.There would be a decrease in the overall potential soil carbon storage capacityof 610 MtC or 239 MtC, depending on whether or not urban land is assumedto store soil carbon. For Scotland, the limiting probabilities show 53·1% of theland as lowland heath and 16·9% as coniferous forest. There would be adecrease in the overall potential soil carbon storage capacity of 9414 MtC ifurban land is assumed to store no carbon, and 9668 MtC if it is assumed tostore carbon. By changing entries in the land cover transition matrices, theconsequences of different policy options can be examined.

1995 Academic Press Limited

Keywords: soil carbon, land use change, Markov model, policy options.

1. Introduction

The Framework Convention on Climate Change, signed by the U.K. at the EarthSummit in Rio de Janeiro in June 1992, and ratified in 1993, commits all parties toprepare national inventories of emissions and sinks of greenhouse gases, and to takemeasures to preserve and enchance the sinks of greenhouse gases on their land surface.

2870301–4797/95/030287+16 $12.00/0 1995 Academic Press Limited

A Markov model of soil organic carbon288

Government response strategies to counteract anthropogenic global warming aimto moderate the increase in atmospheric greenhouse gases, particularly CO2. Increasingthe size of carbon sinks on land, or “sequestering” carbon, is often proposed as aresponse strategy, but its potential is poorly quantified. Land use can affect themagnitude of soil organic carbon stores and the net flux of carbon between the landand the atmosphere. For example, carbon is released from soils when grassland isbrought under the plough or native forest is cleared for cultivation, and carbon isaccumulated in soils when arable land is converted to grassland or is converted toforest. Hence, it is of interest to use as many methods as possible to simulate futurechanges in soil organic carbon stores following postulated future land use changes.

If a matrix of land use changes over a period of time and a vector of soil organiccarbon stores for the land use types are available, it is possible to use a Markov modelto project future soil organic carbon stores which result from the changes in land use.A first-order Markov model is one in which the future development of a system isdetermined by the present state of the system and is independent of the way in whichthat state has developed. Such a model can be used to project future changes in soilorganic carbon stores given that the trends in the matrix continue in the future. Moreimportantly, by changing the entries in the land use transition matrix, the Markovmodel can be used as an analytical tool for studying the consequences of alternativepolicies which are designed to attain specific land use and carbon sequestrationobjectives.

To illustrate this use of the model, Burnham (1973) suggested three hypotheticalobjectives which planners might attempt to evaluate with respect to the future use ofland in their region:

(i) the retention of the natural forest in the region;(ii) an increase in the rate of development of grassland to accommodate grazing;

(iii) a reduction in the rate of land urbanisation.Four possible ways of attaining these objectives were postulated, and each was analysedin the Markov land use simulation model by means of adjustments in the appropriatecells of the transition probability matrix. Burnham (1973) noted that it was necessaryto determine the extent to which land use transition probabilities change over time andto understand the factors which cause such changes.

The utility of transition matrices in summarising aggregate patterns of change inurban structure, and the analysis of these matrices as Markov chains, was establishedin Canada (Bourne, 1976). Bourne used this method to study the effects of five alternativepolicy options for types of parking in Toronto. He noted that alternative Markovmodels, which relax both the stationary and homogeneity assumptions (Gilbert, 1972;Goldstein, 1973) could be used, but their inclusion in the sample given would simplyadd substantial mathematical complexity and would not enhance the illustrative valueof the example.

Similarly, the Niagara region is the site of an intense land use conflict betweenurban, agricultural and natural uses. Muller and Middleton (1994) used a first-orderMarkov chain to make quantitative comparisons of the land use changes betweendiscrete time periods from 1935–1981. This study led to two main conclusions: (i) thatthe urbanisation of agricultural land was the predominant land use change; and (ii) acontinuous “exchange” of land area between wooded and agricultural land uses haslittle effect on the net amount of wooded land, but could undermine the long-termecological value of remaining natural areas.

Hence, there is reason to suppose that this approach will be of some value in the

D. M. Howard et al. 289

study of land use changes in Great Britain. By a simple extension, the method can alsobe used to study consequent changes in potential soil organic carbon stores. Here, wedescribe such a use of a stationary Markov model to project future changes in soilorganic carbon stores for a range of land use types in England and Wales and inScotland.

2. Methods

The sequence of results generated by a Markov model is called a Markov chain. If thecalculated transition probabilities do not change with time, the Markov chain is saidto be stationary. In land use analysis, “stationary” means that the factors whichinfluence changes in land use over the time period for which the transition probabilitymatrix is constructed remain the same over future time periods. In a dynamic Markovchain, transition probabilities are assumed to change in some sort of regular pattern.A Markov chain is said to be regular if the elements of each row of the transitionmatrix sum to unity and are non-negative. These two assumptions are appropriate forprojecting land uses, as they imply that land is neither created nor destroyed duringthe changes in land use.

The basic requirements of a stationary Markov model are a row vector of initialstates and a transition probability matrix, the entries of which are the probabilities oftransition from one state to another over a specified time period. If we let the rowvector of initial states be v′o and the initial transition probability matrix be P, then thestates after successive time periods are given by:

v′1=v′oP

v′2=v′o[P]2

v′i=v′o[P]i

The mean number of steps required to reach state sj for the first time, starting atstate si, is called the mean first passage time from si to sj.

If a Markov chain is regular, as the transition probability matrix is raised tosuccessively higher powers, all its rows converge to a unique row vector called theequilibrium vector. In terms of land use change, this vector represents the uniqueorganisation of land uses in which net movement from one land use category to anotheris zero. It gives the equilibrium proportions of the various land use types. One methodfor calculating the equilibrium vector would be to multiply matrix P by itself a verylarge number of times until the equilibrium condition is reached. However, this methodwould be very inefficient computationally. A computationally more efficient method isgiven in Kemeny and Kurtz (1971).

Howard and Howard (1994) used a land cover transition matrix for 1984–1990provided by the Merlewood Land Use Section, based on data obtained in countrysidesurveys in 1984 and 1990 (Barr et al., 1990). The soil organic carbon contents for thevarious land cover types for England and Wales were provided by the Soil Survey andLand Research Centre (Silsoe), but no corresponding values were available for Scotland.However, in a separate exercise to produce a map showing the distribution of soilorganic carbon in the 1 km National Grid squares of Great Britain, we noted that soilsunder given broad types of land cover in Scotland have more soil organic carbon thansoils under similar broad types of land cover (e.g. arable, pasture, semi-natural) in


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T 2. Changes in areas of different land cover types in England and Wales, 1984–1990, andcorresponding changes in soil organic carbon stores

Soil Change inorganic Area (km2) Area change soil organic

Land cover carbon (% of total carbon storetype (103 tC km−2) 1984 1990 Change area) (103 tC)

Arable 16·92 43 289·39 43 838·45 +549·06 +0·36 +9292·82Bog 107·41 2650·82 2539·83 −110·99 −0·07 −11 921·02Coniferous 31·80 4812·56 5079·88 +267·32 +0·18 +8499·47Deciduous 26·14 9089·74 9408·80 +319·06 +0·21 +8340·07Horticulture 18·97 974·26 754·40 −219·86 −0·14 −4171·23Ley 19·33 8681·83 5582·74 −3099·09 −2·04 −59 891·25Lowland heath 24·79 594·08 794·32 +200·24 +0·13 +4963·84Orchard 16·97 834·33 634·77 −199·56 −0·13 −3386·65Permanent

grass 23·60 37 614·49 39 469·01 +1854·52 +1·22 +43 759·09Recreation 21·26 3016·56 3068·50 +51·94 +0·03 +1104·14Rough grazing 36·65 10 086·48 10 222·34 +135·86 +0·09 +4979·60Scrub 28·77 794·49 731·99 −62·50 −0·04 −1798·13Upland grass 60·20 1299·87 368·71 −931·16 −0·61 −56 057·46Upland heath 69·85 2725·96 3064·47 +338·51 +0·22 +23 646·09Urban 0·00 25 121·73 26 028·37 +906·64 +0·60 0·00

Total 151 586·60 151 586·60 −32 640·62

T 3. Equilibrium distribution of land cover types in England and Wales from an ergodicMarkov chain, with corresponding changes from 1984

Change inArea change soil carbon

Limiting Area from 1984 storeLand cover type probability (km2) (km2) (103 tC)

Arable 0·153 23 195·75 −20 093·64 −340 084·8Bog 0·008 1170·75 −1480·07 −158 969·4Coniferous 0·063 9542·41 +4729·85 +150 386·1Deciduous 0·080 12 087·29 +2997·55 +78 355·1Horticulture 0·001 218·88 −755·38 −14 331·2Ley 0·019 2853·50 −5828·33 −112 635·1Lowland heath 0·022 3360·51 +2766·43 +68 578·4Orchard 0·001 213·86 −620·47 −10 529·8Permanent grass 0·153 23 191·10 −14 423·39 −340 332·4Recreation 0·027 4109·01 +1092·45 +23 223·4Rough grazing 0·051 7663·76 −2422·72 −88 799·1Scrub 0·004 645·65 −148·84 −4282·0Upland grass 0·001 115·98 −1183·89 −71 272·2Upland heath 0·038 5742·30 +3016·34 +210 701·6Urban 0·379 57 475·86 +32 354·13 0·0

Total 151 586·60 −609 991·6


T 4. Projections of areas of the land cover types of England and Wales (km2) using anergodic Markov chain

No. of transitions 1 2 3 4 5Years 6 12 18 24 30

Arable 43 838·45 43 333·05 42 683·91 42 010·91 41 340·02Bog 2539·83 2415·52 2297·99 2190·47 2092·83Coniferous 5079·88 5329·58 5563·95 5784·66 5992·95Deciduous 9408·80 9692·64 9950·17 10 185·96 10 402·84Horticulture 754·40 617·29 530·11 473·76 436·56Ley 5582·74 5176·03 5061·82 4979·75 4902·71Lowland heath 794·32 986·81 1164·98 1329·05 1480·30Orchard 634·77 515·08 440·59 393·44 363·06Permanent grass 39 469·01 39 246·06 38 765·29 38 252·27 37 739·27Recreation 3068·50 3123·51 3175·55 3224·01 3269·08Rough grazing 10 222·34 10 031·65 9811·01 9615·25 9450·11Scrub 731·99 691·50 665·32 648·94 639·30Upland grass 368·71 179·07 139·37 130·22 127·49Upland heath 3064·47 3331·07 3563·06 3770·57 3957·86Urban 26 028·37 26 917·70 27 773·44 28 597·30 29 392·17


Arable 40 681·57 40 040·79 39 420·21 38 820·92 38 243·14Bog 2004·36 1924·28 1851·85 1786·39 1727·26Coniferous 6189·83 6376·19 6552·79 6720·33 6879·42Deciduous 10 602·91 10 787·86 10 959·05 11 117·67 11 264·72Horticulture 411·27 393·46 380·34 370·21 362·01Ley 4828·19 4756·06 4686·35 4619·06 4554·18Lowland heath 1620·06 1749·52 1869·70 1981·46 2085·56Orchard 342·98 329·27 319·51 312·22 306·48Permanent grass 37 233·48 36 738·05 36 254·95 35 785·47 35 330·44Recreation 3311·01 3350·07 3386·50 3420·52 3452·33Rough grazing 9312·15 9196·81 9099·98 9018·20 8948·65Scrub 634·26 632·31 632·44 633·92 636·27Upland grass 126·27 125·52 125·01 124·65 124·41Upland heath 4127·67 4282·15 4423·09 4551·99 4670·17Urban 30 160·49 30 904·17 31 624·74 32 323·47 33 001·43

England and Wales. Therefore, we used those relationships to calculate soil organiccarbon contents for land cover types in Scotland, and present the results obtained usingseparate land cover transition matrices and their corresponding soil organic carbonstores for England and Wales and for Scotland.

Urban areas present a problem. From one point of view the soil is covered to alarge extent by concrete or tarmac and therefore takes no further part in land usechanges. Furthermore, when land is built upon it is usual for the topsoil to be removedand used elsewhere. From this point of view, the soil organic carbon content of urbanland can be set to zero. Another point of view is that urban land should be consideredto have the organic carbon content of the soil from which it was derived. We examinedthe consequences of using both zero carbon for urban soil and the weighted meancarbon content of the contributing soils.


T 5. Changes in areas of different land cover types of England and Wales (km2) from theprojections in Table 4


Arable +549·06 +43·66 −605·48 −1278·48 −1949·37Bog −110·99 −235·30 −352·83 −460·35 −557·99Coniferous +267·32 +517·02 +751·39 +972·10 +1180·39Deciduous +319·06 +602·90 +860·43 +1096·22 +1313·10Horticulture −219·86 −356·97 −444·15 −500·50 −537·70Ley −3099·09 −3505·79 −3620·01 −3702·08 −3779·12Lowland heath +200·24 +392·73 +570·90 +734·97 +886·22Orchard −199·56 −319·25 −393·74 −440·89 −471·27Permanent grass +1854·52 +1631·57 +1150·80 +637·78 +124·78Recreation +51·94 +106·95 +158·99 +207·45 +252·52Rough grazing +135·86 −54·83 −275·47 −471·23 −636·37Scrub −62·50 −102·99 −129·17 −145·55 −155·19Upland grass −931·16 −1120·80 −1160·50 −1169·65 −1172·38Upland heath +338·51 +605·11 +837·10 +1044·61 +1231·90Urban +906·64 +1795·97 +2651·71 +3475·57 +4270·44


Arable −2607·82 −3248·60 −3869·18 −4468·47 −5046·25Bog −646·46 −726·54 −798·97 −864·43 −923·56Coniferous +1377·27 +1563·63 +1740·23 +1907·77 +2066·86Deciduous +1513·17 +1698·12 +1869·31 +2027·93 +2174·98Horticulture −562·99 −580·80 −593·92 −604·05 −612·25Ley −3853·64 −3925·77 −3995·48 −4062·77 −4127·65Lowland heath +1025·98 +1155·44 +1275·62 +1387·38 +1491·48Orchard −491·35 −505·06 −514·82 −522·11 −527·85Permanent grass −381·01 −876·44 −1359·54 −1829·02 −2284·05Recreation +294·45 +333·51 +369·94 +403·96 +435·77Rough grazing −774·33 −889·67 −986·50 −1068·28 −1137·83Scrub −160·23 −162·18 −162·05 −160·57 −158·22Upland grass −1173·60 −1174·35 −1174·86 −1175·22 −1175·46Upland heath +1401·71 +1556·19 +1697·13 +1826·03 +1944·21Urban +5038·76 +5782·44 +6503·01 +7201·74 +7879·70

3. Results

3.1.

The land cover transition matrix is given in Table 1. The mean first passage times rangefrom 10·5 (63 years), for the conversion of ley to permanent grass, to 1869·1 (11 214years) for the conversion of upland heath to horticulture.

Table 2 shows the actual changes in areas of the land cover types over the period1984–1990 and the corresponding changes in soil organic carbon stores. The largestchanges in area were for ley, which decreased by 3099·09 km2, and permanent grass,which increased by 1854·52 km2. The corresponding changes in soil organic carbonstores were a loss of 59 891·25×103 tC and a gain of 43 759·09×103 tC. The otherlargest changes in soil organic carbon stores were losses of 56 057×103 tC from upland


T 6. Changes in soil organic carbon stores (103 tC) under different land cover types inEngland and Wales calculated from the projected area changes in Table 5


Arable +9292·8 +738·9 −10 247·8 −21 638·3 −32 993·1Bog −11 921·0 −25 272·7 −37 895·9 −49 444·9 −59 931·9Coniferous +8499·5 +16 438·7 +23 890·4 +30 907·9 +37 530·6Deciduous +8340·1 +15 759·6 +22 491·4 +28 654·8 +34 324·0Horticulture −4171·2 −6772·6 −8426·5 −9495·5 −10 201·4Ley −59 891·3 −67 751·0 −69 958·3 −71 544·4 −73 033·2Lowland heath +4963·8 +9735·5 +14 152·4 +18 219·4 +21 968·8Orchard −3386·6 −5417·8 −6682·0 −7482·1 −7997·8Permanent grass +43 759·1 +38 498·3 +27 154·1 +15 049·0 +2944·3Recreation +1104·1 +2273·7 +3379·8 +4410·0 +5368·0Rough grazing +4979·6 −2009·7 −10 096·7 −17 271·8 −23 324·5Scrub −1798·1 −2963·0 −3716·4 −4187·4 −4464·7Upland grass −56 057·5 −67 474·0 −69 864·1 −70 415·2 −70 579·5Upland heath +23 646·1 +42 269·1 +58 474·5 +72 969·8 +86 052·7Urban 0·0 0·0 0·0 0·0 0·0

Total −32 640·6 −51 947·0 −67 345·0 −81 268·6 −94 337·6


Arable −44 137·4 −54 982·6 −65 485·9 −75 628·8 −85 407·8Bog −69 433·8 −78 034·7 −85 814·0 −92 845·2 −99 195·7Coniferous +43 790·6 +49 715·8 +55 330·9 +60 657·9 +65 716·2Deciduous +39 553·8 +44 388·3 +48 863·2 +53 009·5 +56 853·3Horticulture −10 681·1 −11 019·1 −11 268·0 −11 460·2 −11 615·8Ley −74 473·3 −75 867·3 −77 214·4 −78 514·7 −79 768·6Lowland heath +25 433·6 +28 642·8 +31 621·9 +34 392·4 +36 973·1Orchard −8338·4 −8571·1 −8736·8 −8860·6 −8957·9Permanent grass −8990·2 −20 680·3 −32 079·5 −43 157·3 −53 894·1Recreation +6259·4 +7089·8 +7864·3 +8587·5 +9263·6Rough grazing −28 381·2 −32 608·7 −36 157·9 −39 155·1 −41 704·5Scrub −4610·0 −4665·9 −4662·3 −4619·6 −4552·1Upland grass −70 653·0 −70 697·8 −70 728·6 −70 750·1 −70 764·8Upland heath +97 914·5 +108 705·4 +118 550·1 +127 554·8 +135 809·7Urban 0·0 0·0 0·0 0·0 0·0

Total −106 746·5 −118 585·4 −129 917·0 −140 789·7 −151 245·4

grass and 11 921·02×103 tC from bog, and a gain of 23 646·09×103 tC for uplandheath.

Over the period 1984–1990, if urban land is assumed to have a zero organic carbonstore, the recorded land cover changes represented an overall loss in soil organic carbonstores of some 32·64 MtC, an average rate of loss of 5·44 MtC yr−1. However, if urbanland is assumed to have an organic carbon store of 26·25×103 tC km−2, the increaseof 906·64 km2 would represent an increase in the carbon store of 23 799·3×103 tC andthe overall decrease in soil organic carbon stores would be reduced to some 8·84 MtC,an average rate of loss of 1·47 MtC yr−1. Of course, the changes will not be instantaneousbecause it will take some time for a soil to reach its new quasi-steady state organic


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T 8. Changes in areas of different land cover types in Scotland, 1984–1990, and correspondingchanges in soil organic carbon stores

Soil Change inorganic Area (km2) Area change soil organic

Land cover carbon (% of total carbon storetype (103 tC km−2) 1984 1990 Change area) (103 tC)

Arable 37·40 7305·44 6757·27 −548·17 −0·66 −20 503·88Bog 625·10 17 751·51 17 617·40 −134·11 −0·16 −83 832·40Coniferous 82·35 7834·58 8492·83 +658·25 +0·79 +54 206·55Deciduous 67·70 1777·91 1865·33 +87·42 +0·11 +5918·49Horticulture 41·93 25·32 1·79 −23·53 −0·03 −986·58Ley 45·63 2071·15 1586·67 −484·48 −0·58 −22 105·54Lowland heath 64·20 71·42 645·17 +573·75 +0·69 +36 837·46Orchard 40·07 14·63 13·71 −0·92 —0·00 −36·86Permanent

grass 55·71 10 585·60 11 524·73 +939·13 +1·13 +52 318·84Recreation 50·19 194·34 168·27 −26·07 −0·03 −1308·46Rough grazing 94·93 12 773·10 12 254·91 −518·19 −0·63 −49 191·89Scrub 74·51 167·93 140·49 −27·44 −0·03 −2044·68Upland grass 155·92 937·25 354·83 −582·42 −0·70 −90 812·41Upland heath 180·92 8748·78 8730·13 −18·65 −0·02 −3374·24Urban 0·00 12 565·45 12 670·88 +105·43 +0·13 0·00

Total 82 824·41 82 824·41 −124 915·60

T 9. Equilibrium distribution of land cover types in Scotland from an ergodic Markovchain, with corresponding changes from 1984

Change inArea change soil organic carbon

Limiting Area from 1984 storeLand cover type probability (km2) (km2) (103 tC)

Arable 0·025 2087·11 −5218·33 −195 187·6Bog 0·022 1807·48 −15 944·03 −9 966 687·0Coniferous 0·169 14 018·92 +6184·34 +509 276·3Deciduous 0·021 1777·33 −0·58 −39·4Horticulture 0·000 0·47 −24·85 −1042·1Ley 0·006 537·46 −1533·69 −69 978·1Lowland heath 0·531 43 969·12 +43 897·70 +2 818 439·8Orchard 0·000 3·92 −10·71 −429·1Permanent grass 0·055 4514·07 −6071·53 −338 243·9Recreation 0·000 40·46 −153·88 −7723·1Rough grazing 0·042 3498·17 −9274·92 −880 471·5Scrub 0·001 61·32 −106·61 −7944·3Upland grass 0·000 6·69 −930·56 −145 095·3Upland heath 0·030 2508·12 −6240·66 −1 129 062·4Urban 0·097 7993·76 −4571·69 0·0

Total 82 824·41 −9 414 188·0


T 10. Projections of areas of the land cover types in of Scotland (km2) using an ergodicMarkov chain


Arable 6757·27 6337·15 6044·52 5828·08 5655·46Bog 17 617·40 17 465·56 17 307·78 17 148·41 16 989·10Coniferous 8492·83 9091·75 9653·95 10 188·60 10 699·93Deciduous 1865·33 1931·54 1985·90 2032·88 2074·62Horticulture 1·79 1·37 1·32 1·28 1·25Ley 1586·67 1505·73 1466·88 1433·14 1401·26Lowland heath 645·17 1195·94 1720·36 2218·98 2693·42Orchard 13·71 12·55 11·78 11·25 10·86Permanent grass 11 524·73 11 721·73 11 682·80 11 544·19 11 359·53Recreation 168·27 149·56 135·66 125·11 116·94Rough grazing 12 254·91 11 686·77 11 138·74 10 629·88 10 163·97Scrub 140·49 121·98 109·70 101·59 96·18Upland grass 354·83 140·29 61·06 31·61 20·49Upland heath 8730·13 8693·31 8645·24 8589·25 8527·12Urban 12 670·88 12 769·17 12 858·71 12 940·16 13 014·28


Arable 5508·63 5377·66 5257·06 5143·78 5036·12Bog 16 830·46 16 672·73 16 516·02 16 360·37 16 205·83Coniferous 11 190·23 11 661·04 12 113·51 12 548·61 12 967·21Deciduous 2112·30 2146·64 2178·12 2207·09 2233·85Horticulture 1·22 1·19 1·17 1·14 1·12Ley 1370·90 1341·89 1314·06 1287·28 1261·48Lowland heath 3145·55 3577·22 3990·15 4385·92 4765·93Orchard 10·55 10·28 10·04 9·81 9·60Permanent grass 11 154·24 10 941·26 10 727·41 10 516·33 10 309·98Recreation 110·50 105·35 101·16 97·69 94·76Rough grazing 9739·42 9353·04 9001·28 8680·76 8388·35Scrub 92·47 89·84 87·88 86·36 85·11Upland grass 16·15 14·33 13·45 12·94 12·59Upland heath 8459·99 8388·75 8314·10 8236·68 8157·03Urban 13 081·77 13 143·18 13 199·00 13 249·63 13 295·44

carbon content after a change in land cover. Therefore, these organic carbon storesmust be regarded as the potential carbon storage capacities of the soils.

Table 3 shows the equilibrium distribution of land cover types in England andWales which would result if the 1984–1990 trends were to continue. Of the land types,37·9% would be urban (16·6% in 1984), 15·3% would be arable (28·56% in 1984), and15·3% would be permanent grass (24·81% in 1984). Upland grass, bog, horticulture,orchards and scrub would each cover less than 1% of the land (0·86%, 0·77%, 0·64%,0·55%, and 0·42% respectively in 1984).

The largest area changes at equilibrium would be a gain of 32 354·13 km2 for urban,and losses of 20 093·64 km2 for arable and 14 423·39 km2 for permanent grass. Thecorresponding changes in potential soil carbon storage capacity would be zero forurban, and losses of 340·1 MtC for arable and 340·3 MtC for permanent grass. Otherlarge losses would be 159 MtC for bog, 112·6 MtC for ley and 88·8 MtC for rough


T 11. Changes in areas (km2) of different land cover types in Scotland from the projectionsin Table 10


Arable −548·17 −968·29 −1260·92 −1477·36 −1649·98Bog −134·11 −285·95 −443·73 −603·10 −762·41Coniferous +658·25 +1257·17 +1819·37 +2354·02 +2865·35Deciduous +87·42 +153·63 +207·99 +254·96 +296·71Horticulture −23·53 −23·95 −24·00 −24·04 −24·07Ley −484·48 −565·42 −604·27 −638·01 −669·89Lowland heath +573·75 +1124·52 +1648·94 +2147·56 +2622·00Orchard −0·92 −2·08 −2·85 −3·38 −3·77Permanent grass +939·13 +1136·13 +1097·20 +958·59 +773·93Recreation −26·07 −44·78 −58·68 −69·23 −77·40Rough grazing −518·19 −1086·33 −1634·36 −2143·22 −2609·13Scrub −27·44 −45·95 −58·23 −66·34 −71·75Upland grass −582·42 −796·96 −876·19 −905·64 −916·76Upland heath −18·65 −55·47 −103·54 −159·53 −221·66Urban +105·43 +203·72 +293·26 +374·71 +448·83


Arable −1796·81 −1927·78 −2048·38 −2161·66 −2269·32Bog −921·05 −1078·78 −1235·49 −1391·14 −1545·68Coniferous +3355·65 +3826·46 +4278·93 +4714·03 +5132·63Deciduous +334·39 +368·73 +400·21 +429·18 +455·94Horticulture −24·10 −24·13 −24·15 −24·18 −24·20Ley −700·25 −729·26 −757·09 −783·87 −809·67Lowland heath +3074·13 +3505·80 +3918·73 +4314·50 +4694·51Orchard −4·08 −4·35 −4·59 −4·82 −5·03Permanent grass +568·64 +355·66 +141·81 −69·27 −275·62Recreation −83·84 −88·99 −93·18 −96·65 −99·58Rough grazing −3033·68 −3420·06 −3771·82 −4092·34 −4384·75Scrub −75·46 −78·09 −80·05 −81·57 −82·82Upland grass −921·10 −922·92 −923·80 −924·31 −924·66Upland heath −288·79 −360·04 −434·68 −512·10 −591·75Urban +516·32 +577·73 +633·55 +684·18 +729·99

grazing. Large potential gains would be 210·7 MtC for upland heath, 150·4 MtC forconiferous forests and 78·4 MtC for deciduous woodland.

If urban land is assumed to have zero carbon store then, at equilibrium, the totalloss of soil carbon storage capacity would be 610 MtC. However, if urban land isassumed to have a soil carbon store of 26·25×103 tC km−2, then the increase in areaat equilibrium, 32 354·13 km2, would represent an increase of 849·30 MtC in the urbansoil carbon store, and would change the overall loss of some 610 MtC into an increaseof 239·30 MtC.

Projections of the areas of the land cover types in England and Wales for 10transitions (60 years) from 1984 obtained from an ergodic Markov chain are given inTable 4, the corresponding changes in areas are given in Table 5 and the resultingchanges in soil organic carbon storage potential are given in Table 6. If urban land isassumed to have zero soil carbon store, the total soil organic carbon storage potential


T 12. Changes in soil organic carbon stores (103 tC) under different land cover types inScotland calculated from the projected area changes in Table 11


Arable −20 503·9 −36 218·1 −47 163·8 −55 259·5 −61 716·1Bog −83 832·4 −178 748·2 −277 378·0 −377 000·4 −476 586·2Coniferous +54 206·5 +103 526·8 +149 823·6 +193 852·0 +235 959·7Deciduous +5918·5 +10 400·8 +14 081·6 +17 261·6 +20 087·7Horticulture −986·6 −1004·1 −1006·2 −1007·8 −1009·2Ley −22 105·5 −25 798·8 −27 571·2 −29 110·9 −30 565·4Lowland heath +36 837·5 +72 199·8 +105 869·8 +137 883·4 +168 344·5Orchard −36·9 −83·2 −114·0 −135·3 −151·0Permanent grass +52 318·8 +63 293·7 +61 124·9 +53 402·9 +43 115·6Recreation −1308·5 −2247·6 −2945·0 −3474·8 −3884·9Rough grazing −49 191·9 −103 125·7 −155 150·3 −203 456·5 −247 685·5Scrub −2044·7 −3423·7 −4339·1 −4943·4 −5346·8Upland grass −90 812·4 −124 263·2 −136 617·9 −141 210·1 −142 943·0Upland heath −3374·2 −10 036·5 −18 732·5 −28 861·9 −40 103·2Urban 0·0 0·0 0·0 0·0 0·0

Total −124 915·7 −235 528·0 −340 118·2 −442 060·7 −542 483·7


Arable −67 208·3 −72 107·3 −76 618·2 −80 855·2 −84 882·3Bog −575 751·9 −674 350·0 −772 310·8 −869 607·9 −966 211·6Coniferous +276 335·7 +315 106·5 +352 367·1 +388 197·4 +422 668·8Deciduous +22 639·1 +24 964·0 +27 095·0 +29 056·6 +30 867·8Horticulture −1010·4 −1011·6 −1012·7 −1013·7 −1014·7Ley −31 950·4 −33 274·2 −34 544·2 −35 765·9 −36 943·0Lowland heath +197 373·8 +225 089·2 +251 601·3 +277 011·0 +301 409·8Orchard −163·6 −174·4 −184·1 −193·0 −201·4Permanent grass +31 678·9 +19 813·8 +7900·2 −3859·0 −15 354·7Recreation −4207·8 −4466·4 −4676·9 −4851·1 −4997·9Rough grazing −287 988·3 −324 667·8 −358 059·8 −388 487·0 −416 245·9Scrub −5622·8 −5818·9 −5964·7 −6078·4 −6171·4Upland grass −143 619·9 −143 904·5 −144 041·1 −144 120·1 −144 175·1Upland heath −52 247·7 −65 137·7 −78 642·6 −92 649·5 −107 059·6Urban 0·0 0·0 0·0 0·0 0·0

Total −641 743·8 −739 939·3 −837 091·3 −933 215·8 −1 028 311·3

declines by 151·2 MtC after 60 years, an average rate of 2·52 MtC yr−1. On the otherhand, if urban land is assumed to have a soil carbon store of 26·25×103 tC km−2 theincrease in urban land area of 7879·70 km2 after 60 years would represent an increasein the urban soil carbon store of 206·84 MtC. Hence, after 60 years, the overall potentialsoil carbon storage capacity would be 55·60 MtC, an average annual rate of increaseof 0·93 MtC yr−1.

3.2.

The land cover transition matrix is given in Table 7. The mean first passage times range


from 20·5 (123 years) for the conversion of ley to permanent grass, and 181 242(1 087 452 years) for the conversion of lowland heath to horticulture.

Table 8 shows the actual changes in areas of the land cover types over the period1984–1990 and corresponding changes in soil organic carbon stores. The largest increasesin area were for permanent grass (939·13 km2), coniferous forests (658·25 km2) andlowland heath (573·75 km2). The corresponding increases in potential soil organic carbonstores were 52·32 MtC, 54·21 MtC and 36·84 MtC. The largest decreases in area werefor upland grass (582·42 km2), arable (548·17 km2) and rough grazing (518·19 km2).The corresponding decreases in potential soil organic carbon stores were 90·81 MtC,20·50 MtC and 49·19 MtC. The other largest changes in potential soil organic carbonstores were decreases for bog (83·83 MtC) and ley (22·10 MtC).

Overall, if urban land is assumed to have zero organic carbon store, the recordedland cover changes would result in a decrease of 124·92 MtC storage potential. However,if urban land is assumed to have a carbon store of 55·57×103 tC km−2, the increase inarea of 105·43 km2 from 1984–1990 would result in an increase of 5858·74×103 tC inits organic carbon store. Hence, the decrease in the overall carbon store of 124·92 MtCwould be reduced to 119·1 MtC.

Table 9 shows the equilibrium distribution of land cover types in Scotland whichwould result if the 1984–1990 trends were to continue. A total of 53% of the landwould be lowland heath (0·09% in 1984) and nearly 17% would be under conifers(9·46% in 1984). The largest area changes at equilibrium would be a gain of 43 897·70 km2

by lowland heath and a loss of 15 944·03 km2 by bog. The corresponding changes inpotential soil organic carbon storage capacity would be an increase of 2818·44 MtC bylowland heath and a decrease of 9966·69 MtC by bog. Other large changes would bean increase of 509·28 MtC by coniferous forest and decreases of 1129·06 MtC (uplandheath), 880·47 MtC (rough grazing), 338·24 MtC (permanent grass), 195·19 MtC (arable)and 145·09 MtC (upland grass).

At equilibrium, if urban land is assumed to have zero soil carbon store, the overalldecrease on potential soil organic carbon storage capacity would be 9414·19 MtC.However, if urban land is assumed to have a soil carbon store of 55·57×103 tC ha−1,the decrease in area of urban land of 4571·69 km2 would result in a decrease of its soilcarbon store of 254 048·8×103 tC, and the overall decrease on potential carbon storagecapacity would be 9668·24 MtC.

Projections of the areas of the land cover types in Scotland for 10 transitions (60years) from 1984 obtained from an ergodic Markov chain are given in Table 10, thecorresponding changes in areas are given in Table 11, and the resulting changes in soilorganic carbon storage potential are given in Table 12. If urban land is assumed tohave zero soil carbon store, the total soil organic carbon storage potential declines by1028·31 MtC after 60 years, an average rate of 17·14 MtC yr−1. On the other hand, ifurban land is assumed to have a soil carbon store of 55·57×103 tC ha−1, the increasein area of urban land of 729·99 km2 after 60 years would result in an increase in urbansoil carbon store of 40 565·54×103 tC, and the decrease in the overall soil carbonstorage potential would be reduced to 987·75 MtC.

4. Discussion

The patterns of land cover change over the period 1984–1990 differed markedly betweenEngland and Wales and Scotland. The largest percentage changes in England and Waleswere a decrease of 2·04% of land under ley and a gain of 1·22% under permanent grass.


Corresponding changes in Scotland were a loss of 0·58% and a gain of 1·13%,respectively. In Scotland, the greatest decrease was 0·70% for upland grass. Althoughurban land in England and Wales increased by 0·60%, in Scotland the increase wasonly 0·13%. Because of the greater potential organic carbon stores in Scottish soils, thechanges were greater there than in England and Wales. Hence, in terms of conservingor increasing soil organic carbon stores, particular attention needs to be paid to landuse changes in Scotland.

In England and Wales, it makes a great deal of difference to the overall soil carbonstorage potential whether the topsoil is assumed to be removed and used elsewhere inurban areas, i.e. urban soils store no organic carbon, or remain in situ and are covered.In these areas, the overall decrease in potential soil organic carbon store during1984–1992 was reduced by 73% if urban soil was assumed to store 26·25×103 tC km−2.However, the reduction in the decrease for Scotland was only 5% if urban land isassumed to store 55·57×103 tC km−2.

A stationary Markov model should not be regarded as predicting the future, becauseit assumes that the transition probability matrix does not change over time. That is, itassumes that the factors which influence land use changes over the time period forwhich the transition matrix is constructed remain the same over future time periods.The main value of a stationary Markov model is that it allows the future consequencesof a given pattern of land use changes to be studied, and can be used as an analyticaltool for studying the consequences of alternative policies which are designed to attainspecific land use objectives.

The problem of deriving policies for soil organic carbon sequestration is one ofbalancing the socio-economic effects of land use change against the changes in potentialsoil organic carbon stores. The method described here is one way in which plannerscould carry out “experiments” by changing entries in the land use transition matricesand examine their interactive effects on the resulting changes in different types of landuse and the resulting changes in potential soil organic carbon stores. Of course, for themethod to be of practical value better data on potential soil organic carbon stores andrepeated land cover surveys would be needed. The latter might be obtainable fromsatellite data.

The model itself could be used at the degree of complexity required. The simpleversion used here is easy to understand, but it may be considered to be desirable touse a dynamic Markov model, in which the transition probabilities are assumed tochange over time. Such a procedure was given by Vandeveer and Drummond (1978),who compared the use of static and dynamic Markov models in projecting land usechange following the construction of a reservoir. They concluded that perhaps the mostinteresting characteristic of the dynamic land use change estimates was that the amountof estimated change was much less than that estimated by the static transition probabilitymatrices. This was probably a consequence of the geometric adjustment that is used inestimating dynamic transition probabilities.

This research was funded partly by CEC contract EV5V-CT92-0119.

References

Barr, C. J., Bunce, R. G. H., Clarke, R. T., Fuller, R. M., Furse, M. T., Gillespie, M. K., Groom, G. B.,Hallam, C. J., Hornung, M., Howard, D. C. and Ness, M. J. (1990). Countryside survey 1990. Mainreport (Countryside 1990 series, Vol. 2). Eastcote, U.K.: DoE Publication Sales Unit.

Bourne, L. S. (1976). Monitoring change and evaluating the impact of planning policy on urban structure:A Markov chain experiment. Plan Canada 16, 5–14.


Burnham, B. O. (1973). Markov intertemporal land use simulation model. Southern Journal of AgriculturalEconomics 5, 253–258.

Gilbert, G. (1972). Two Markov models of neighbourhood housing turnover. Environment and Planning 4,133–146.

Goldstein, G. S. (1973). Household behavior in the housing market. In Models of residential location andrelocation in the city (E. G. Moore, ed.), pp. 101–118. Evanston, Illinois: Northwestern University.

Howard, P. J. A. and Howard, D. M. (1994). A Markov model simulation of soil organic carbon storesfollowing land use changes. In Carbon sequestration by soils in the UK, pp. 59–76. Contract report to theDepartment of the Environment.

Kemeny, J. G. and Kurtz, T. E. (1971). BASIC programming. New York: Wiley.Muller, M. R. and Middleton, J. (1994). A Markov model of land-use change dynamics in the Niagara

Region, Ontario, Canada. Landscape Ecology 9, 151–157.Vandeveer, L. R. and Drummond, H. E. (1978). The use of Markov processes in estimating land use change.

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a markov model projection of soil organic carbon stores following land use changes

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