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5026 B. J. Dermody et al.: A virtual water network of the Roman world

forcings and crop response to climate change make futurepredictions on VW trade and VW content highly uncertain(Fader et al., 2010; Konar et al., 2013; Zhao et al., 2014).

Sivapalan et al. (2012) recommend studying past soci-etys relations with water, a term they refer to as historicalsocio-hydrology, to understand fundamental processes link-ing humans and water resources. They propose that waterhas played a role in the growth, evolution and eventual col-lapse of many past societies. Therefore by studying the re-lation of past societies with water we can illuminate fac-tors that are also relevant in the present day, such as howclose we are to reaching the planetary boundaries of currentfreshwater resources (Bogardi et al., 2013; Rockstrm et al.,2009). Historical socio-hydrology principles were applied inan analysis of the coevolution of society and water resourcesover the last 2000 years in the Tarim river basin of north-west China (Liu et al., 2014). Based on historical reconstruc-tions, Liu et al. (2014) developed a conceptual model whichidentied a positive, destructive feedback loop related to eco-nomic gains from water resources and a negative, restorativefeedback loop related to the impacts of exploitation of wa-ter resources. That same model was shown to be representa-tive of the changes in the Murrumbidgee catchment in Aus-traliaover the last 100 years indicating that an historical basisfor understanding socio-hydrological systems shows promise(van Emmerik et al., 2014). In a modelling context, one of the principal advantages of using historical data is that itis possible to constrain simulations based on historical re-constructions and compare model output with what actuallyhappened (given the inherent uncertainties of historical re-constructions) (Cornell et al., 2010; van der Leeuw et al.,

2011). Such an approach can indicate if the assumptions andprocesses incorporated in models are valid. A modelling ap-proach can also be revealing in an historical context (Cornellet al., 2010). For example, the use of physically basedmodelsin an historical context facilitates the renement of theoriesabout past human relations with their environment based onwhat was physically possible given the constraints of the en-vironment.

In the preindustrial period, the Roman Empire was likelythe greatest exponent of virtual water trade as evidencedby the widespread trade in water resources, and particularlygrain, throughout the Mediterranean and Black Sea region(Erdkamp, 2005; Kessler and Temin, 2007; Rickman, 1980;Scheidel, 2010). Supplying the main cities of the Empirewith sufcient grain was one of the principal preoccupationsof the ruling elite throughout the lifetime of the Republicand Empire, to the extent that a stable supply of grain to thecity of Rome became personied by the deity Anonna (Ma-zoyer and Roudart, 2006; Rickman, 1980). In a close parallelto current demographic trends (Chen, 2007; United Nations,2012), an explosion in urban populations during the Late Re-publican era (Bowman and Wilson, 2011) led many citiesto overshoot their local ecohydrological carrying capacitiesbringing about an increased reliance on imports of VW (Erd-

kamp, 2005). Similar trends, but of a much greater magtude, are seen in the present day across the globe in countrsuch as China where rapid urbanization, increased afuenand relaxing of trade restrictions have brought about a 2fold increase in VW imports in less than a quarter of a ctury (Hubacek et al., 2009; Shi et al., 2014).

As with current society, the Romans sought to secure fosecurity in two principal ways: through in situ water rsource management using rainfed agriculture and irrigati(Fader et al., 2010; Torell et al., 1990; Wada et al., 201and through VW trade (Barnaby, 2009; Shi et al., 2014; Yaand Zehnder, 2001). Irrigation enabled the Romans to maimize exploitation of local water resources whilst VW traallowed them to inhabit regions where local water resourwere insufcient for the resident population (Garnsey, 19DOdorico et al., 2010). The Romans also made use of lamunicipalgrain stores which were replenished after each havest owing to spoilage. These municipal stores acted abuffer for when imports became disrupted (Erdkamp, 200Temporal market speculation on grain through hoardingthought to have been limited in the Roman period, hoever. Market speculation was a high-risk venture owingthe loss in value of grain as a result of storage and the huncertainty associated with predicting surpluses or decitsubsequent years (Erdkamp, 2005). As a result VW distribtion predominantly responded directly to yield surpluses adecits integrated over a short number of years rather thcomplex economic dynamics arising from speculation (Ekamp, 2005; Horden and Purcell, 2000).

In terms of in situ water resource management the Rommade use of a wealth irrigation technologies such as dam

aqueducts, canals, cisterns, water wheels and qanats (Bark1996; Wilson, 1997). The maintenance and operation of igation infrastructure was tightly controlled with users taxon the extent of land they irrigated in regions such as Egor on the magnitude of their harvest in Spain, Sicily and Sdinia (Beltrn Lloris, 2006; Erdkamp, 2005). The Romawere far from the rst Mediterranean civilization to use suwater management practices but the extent and organizatiwas unprecedented andenabled them to achieve high agricutural yields throughout their Empire (Barker, 1996). Not odid irrigation increase grain production but surface water wa far more reliable source of water compared with precipition, particularly in large river basins such as the Nile Dethe Po Valley and the Orontes, Ebro and Vera catchmentspresent-day Syria and Spain (Beltrn Lloris, 2006; Butzeral., 1985; van der Leeuw, 1998).

VW redistribution during the Roman period was compatively simple compared with present-day global trade in wter resources (Erdkamp, 2005; Konar et al., 2011). Withthe Roman Empire few articial trade barriers existed, stead the redistribution of VW was driven by satisfying mand of urban centres from regions with a surplus prinpally by means of tributary donations (tax-in-kind in the forof grain) (Erdkamp, 2005; Scheidel, 2010; Temin, 201

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B. J. Dermody et al.: A virtual water network of the Roman world 5027

There was a parallel free market, however it was thoughtthat the urban grain supply was too important to be riskedon the free market and was ensured by hierarchical methods(Rickman, 1980). The principal constraint on VW redistri-bution in the Roman period was the struggle against dis-tance (Braudel, 1995). However, advanced shipping tech-nology during the Roman period combined with the relativesafety of summer maritime travel within the Mediterraneanfacilitated unprecedented trade in bulk goods such as grain(Houston, 1988). As with the present day, trade costs of thesebulk goods co-varied with distance (Hummels, 2007). How-ever, transport by ship was signicantly cheaper comparedwith overland transport owing to the difcultly in land-basedtransport of bulk goods by horseand cart (Jones, 1986; Schei-del, 2013) a feature of trade in bulk goods that remains de-spite modern advancements in transport technology (Limoand Venables, 2001).

In this paper we set out to examine how irrigation and VWtrade contributed to Roman resilience against the twin pres-sures of urbanization and climate variability. In order to un-derstand this we have developed a Virtual Water Networkof the Roman World. Our VW network contains two princi-pal components: a hydrological model and a dynamic, agent-based VW redistribution network. We simulate yields undervariable climate conditions using the hydrological model PCRaster Global Water Balance Model (PCR-GLOBWB) (vanBeek and Bierkens, 2009; van Beek et al., 2011). VW tradeis simulated using Orbis, the Stanford Geospatial Network of the Roman World (Scheidel, 2013) as our network structure,with link weights reecting transport costs at AD 200 associ-ated with the struggle against distance (Braudel, 1995). We

do not model the feedbacks between the trade dynamics andhydrology (similar to the socio-hydrological approach pro-posed by Liu et al. (2014) and Elshafei et al. (2014) for ex-ample); rather we apply a scenario-based approach using his-torical reconstructions and the physical hydrological modelas constraints. Our analysis of the Roman water resourcemanagement not only adds to our understanding of that civi-lization but also helps us to understand the fundamental pro-cesses underpinning VW trade in the present day (Sivapalanet al., 2012).

2 Methods

The schematic of our Virtual Water Network of the RomanWorld is shown in Fig. 1. To summarize our methodology;we calculated yields using the global hydrological modelPCR-GLOBWB based on estimates of the extent of Romancropland in AD200 from the History Database of the GlobalEnvironment (HYDE) (Klein Goldewijk et al., 2011). Landwith a potential for irrigation was assigned within HYDEcropland regions based on the MIRCA data set of Portmannet al. (2008). Natural land cover was assigned based on theOlson classication (Olson, 1994a, b). The yield response

Figure 1. Schematic of our virtual water network of the Romaworld. (a) The overlay of the History Database of the Global Envronment (HYDE) cropland reconstructions for AD200, monthlyrigated and rainfed crop areas (MIRCA) and global land cover chacterization (GLCC) forms the land cover attributes in our modRegions are only assigned as irrigated where MIRCA irrigatedgions overlap with historical cropland regions. (b) Grain yields inirrigated and rainfed agricultural regions are simulated in PC RaGlobal Water Balance model (PCR-GLOBWB) based on 52 yeof spatially and temporally variable temperature and precipitatforcing. (c) Regions are dened based on a Thiessen polygon o

eration between network nodes (Fig. S1). Virtual water surpluand decits are calculated for each region based on HYDE recstructions of Roman population distribution and grain yields callated in PCR-GLOBWB. We x the annual grain consumption200kg per person. (d) The virtual water surpluses and decits areabstracted to the Orbis network and virtual water redistributionsimulated. Decit nodes import virtual water from surplus nodalong the minimum cost path. Imports continue until the demanddecit nodes is met. See Fig. S2 for a spatially explicit schematiour virtual water network of the Roman world.

to climate variability was calculated in PCR-GLOBWB wclimate prescribed using meteorological observations ovthe period 19492000 (Ngo-Duc et al., 2005). VW surpluand decits were calculated with VW demand based HYDE gridded population estimates. Yearly VW surplusand decits were abstracted to Orbis and the redistributionVW from VW-rich to VW-poor regions of the Roman Epire was simulated. A detailed description of our methodogy follows.

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2.1 Simulating cereal yields under variable climate

We computed VW based on cereals at 5 minute spatialresolution under rainfed and irrigated cultivation using theGlobal Hydrological model PCR-GLOBWB (see van Beeket al. (2011) and van Beek and Bierkens (2009) for a de-tailed description of the model). PCR-GLOBWB is a spa-tially explicit three-layer (two soil layers and one groundwa-ter reservoir) hydrological model that computes the verticalwater balance for different land cover types under prescribedmeteorological conditions and routes the specic runoff toobtain discharge elds. One of the outputs of the vertical wa-ter balance is the actual transpiration (so-called green wa-ter) which was used here to estimate grain yields (Dooren-bos and A.H. Kassam, 1979). When soil moisture is limiting,yield may be maximized for a healthy and fertilized crop if the crop water requirements are met by irrigation (blue wa-ter) and the crop transpires at the potential rate sustained bythe atmospheric demand (Allen et al., 1998). Following thisprinciple, yield can be taken to be proportional to the wateruseefciency multiplied by transpiration (Zwartet al., 2010).The crop water requirements equal the difference betweenpotential and actual evapotranspiration for the cropped areaand correspond to the irrigation water demand when dividedby the irrigation efciency that accounts for conveyance andapplication losses. Using these principles, irrigation waterdemand and the realized yield were evaluated on a monthlyscale with consideration of climate variability. To this end,the potential and actual evapotranspiration rates of croppedareas when fed by rainfall only were used to compute the ir-rigation water demand (see Wada et al., 2011 for details) and

to ascertain what proportion of the irrigation water demandcan be satised with the available discharge.PCR-GLOBWB requires meteorological and land cover

data as input. As meteorological forcing we used the Na-tional Center for Environmental Prediction/National Centerfor Atmospheric Research (NCEP/NCAR) corrected by theClimate Research Unit (CRU) climate reanalysis data setover the period 19492000 (Ngo-Duc et al., 2005), whichdownscales NCEP/NCAR data to a regular 1-degree globalgrid with a daily resolution. Using current reanalysis datafor the Roman period was deemed acceptable as the recon-structed Roman climate optimum was estimated to be com-parable with the mean Northern Hemisphere temperature be-tween 1961 and 1990 (Ljungqvist, 2010). In terms of pre-cipitation, early modelling studies had suggested that greaterforest cover in the Roman period maintained a wetter cli-mate (Reale and Dirmeyer, 2000; Reale and Shukla, 2000).However,historical, archaeologicaland palaeoclimatologicalevidence indicates that the mean background climate in theMediterranean during the Roman period was broadly simi-lar to the present day although there were likely centennialmillennial shifts in synoptic climate systems which wouldhave made certain regions relatively drier or wetter on av-erage at different times during the Roman period (Bntgen

et al., 2011; Dermody et al., 2012). The impacts of longterm shifts in the synoptic climate systems on Roman wter resource management will be assessed in a follow-up per. The CRU TS 2.1 data set only species variables for global land mass, so as to ensure global coverage, the orinal NCEP/NCAR values were inserted if no values wespecied. From this data set, daily precipitation totals athe average temperature were used directly as model inpThe model also requires reference potential evapotranspition as direct input which was computed using the Hammethod (Allen et al., 1998), which only requires temperatas meteorological input compared to more complex equtions. Monthly climatologys of wind speed and relative hmidity were used indirectly to estimate the crop factors (below).

To partition precipitation (rainfall, snow) into intercetion and throughfall and to prescribe the crop-specic ptential evapotranspiration, PCR-GLOBWB requires the terception capacity, ground cover and the crop coefcient each land cover type. The natural land cover parametriztion is based on the Global Land Cover Characterizati(GLCC) at 30 second spatial resolution with the Olson clsication (Olson, 1994a, b) and the parameter set of Hagmann et al. (1999). Irrigated areas were inserted using tMIRCA data set of Portmann et al. (2008) (see van Beet al., 2011; Wada et al., 2011 for details). The fraction each cell assigned as crop and pasture land was dened baon History Database of the Global Environment (HYDE) constructions for AD 200 at 5horizontal resolution (KleinGoldewijk et al., 2011) (Fig. S3). HYDE does not explitly account for crop rotation and the issue of crop rotat

in the Roman period remains controversial, with some athors claiming that no rotation was practised in Roman timwhereas others claim two-eld rotation was practised wone half of elds laying fallow at any one time (Fox, 198Based on White (1970), we adopt an intermediate valuecontinual three-eld cropping with 2 years of a cereal crand 1 year of fallow assigned as sparse grassland accordto GLCC. In irrigated regions we employ multi-season cercropping based on the crop calendars from the MIRCA dset (Portmann et al., 2008).

The land cover parametrization is derived from the 3distribution of the GLCC (Olson, 1994a, b). In order to corporate the information on cultivated area for the Romperiod from the HYDE data set, having a spatial resolutof 5, the distribution of cultivated and pasture areas was constructed at the resolution of 30. Within each 5cell, all30 cells were ranked on suitability; using the GLCC clasication at 30, areas were delineated to represent respectively the presently cultivated areas and those under pastuWithin these areas, each cell was assigned a decreasing suability with increasing slope owing to the Romans prefence for low-lying, gently sloping land for agriculture (vder Leeuw, 1998). Outside the presently exploited areas, suability was ranked using the slope-parallel cumulative d



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tance from the boundaries of these areas outwards. Suitabil-ity was then scaled between the minimum and maximum val-ues to yield a range between 0 and 1. This suitability was thenused to iteratively select the most suitable cells until the de-sired area was met. Precedence was rst given to cultivatedarea, followed by pasture. The remaining area was lled withthe reconstructed natural vegetation from the GLCC data set.The resulting mosaic at 30was consecutively used to com-pute the effective values of the land cover parametrizationper land use type at 5. Any remaining cells were assignedas semi-natural land cover types that were extrapolated spa-tially on the basis of the Holdridge life zones (Leemans,1990, 1992). For the semi-natural vegetation, a subdivisionbetween short and tall natural vegetation was made on thebasis of forest fraction.

Cropland was subdivided proportionally into irrigated andrainfed land on the basis of the MIRCA data set, giving,with pasture, a total of ve land cover classes within eachcell. Monthly characteristics were prescribed to account forseasonal growth changes in cereals and natural vegetation.For short-natural, tall-natural and pasture land cover types,these values were based on the original Olson classica-tion and the corresponding parametrization of Hagemann etal. (1999). For the irrigated and rainfed cropland, the cropfactors and calendars were taken directly from the MIRCAdata set (Portmann et al., 2008) for cereals under rainfedand irrigated conditions and weighted by area. Water useefciency for all cereals was assigned the value for winterwheat and crop yield taken to be equivalent to 25 % of thetotal above-ground biomass compared to the 35 % used byZwart et al. (2010) for present-day crops, in line with esti-

mates from Roman and pre-agricultural revolution sources(Erdkamp, 2005; Goodchild, 2007). It is important to high-light that we only calculated yields based on cereal cropswhereas large portions of land would have also been givenover to viticulture, olives, market gardens and so forth (Col-umella, 70AD; Erdkamp, 2005).

HYDE population values were used to calculate VW wa-ter demand as well as the workforce available for harvest. Inaddition to water availability, labour availability constrainsthe area that can be cultivated. The labouring population wascalculated based on the grid-based population estimates fromthe HYDE data set (Klein Goldewijk et al., 2011). We esti-mated a harvesting period of 1 month with an average har-vest area per person per day of 0.2 ha which equates to 6 haper person per year. We restricted harvesting to the able-bodied population aged between 12 and 55. Based on demo-graphic life tables from Roman Egypt, this equated to 55 %of the population that were capable of helping with the har-vest (Frier, 1982). HYDE population values were also usedto calculate VW demand based on a consumption of 200 kgof grain per person per year (Erdkamp, 2005). For the 20most populous cities in the Empire, the grid-based popula-tion values of HYDE were corrected using Chandlers (1987)estimates of Roman urban population. For each cell we sub-

tracted the population demand from the realized yield pviding yearly maps of surplus and decit VW (Fig. S4).

2.2 Simulating virtual water redistribution

Orbis, the Stanford Geospatial Network of the Roman Woforms the basis for our VW redistribution network of tRoman world (Meeks, 2013; Scheidel, 2013). Orbis broareects the transport network in the Roman Empire arouAD200 with all links conrmed as Roman era transproutes although we cannot be certain that all were activeAD 200. Orbis should be taken in the spirit for which it wintended, which is to outline the dramatic contrasts betweterrestrial, uvial and maritime transportation expenses athe patterns they imposed on the ow of goods within tRoman Empire (Scheidel, 2013). Orbis contains a databaof 751 roman towns and cities that form the nodes withour network. These cities are linked by (1371 2) directededge segments that represent the cost to transport a kilogrof grain in denarii along Roman roads, rivers and over sea ieach month of the year based on Diocletians Edict on Mimum Prices and physical cost distance calculations (Schdel, 2013). The links between each node have a cost reresenting transport in each direction. For example, up-rivtransport is more costly compared with down-river transpWe used transport costs for the month of June because tmajority of grain was transported during summer montwhen sea conditions were calm (Erdkamp, 2005; Horden aPurcell, 2000).

We collapsed nodes within 10 km of each other into onode owing to the resolution of the underlying gridded da

leaving us with 649 nodes. To simplify calculations in odynamic redistribution model, we converted the directed nwork of Orbis into an undirected network by taking the avage cost of the directed links between nodes resulting in atal of 1371 undirected links. As we are interested in Mediranean climate variability, we restricted our analysis to tpart of the network that extends from 10 W to 45 E and 25to 46 N, however all simulations were carried out for the etire Empire. In order to convert grid-based surplus and dedata to the Orbis network structure we assigned city regiousing a Thiessen polygon operation between our city nod(see Fig. S1 for city regions). All gridded data within thregions were summed and applied to the relevant city or tonode. Therefore certain nodes in the network were either Vrich or VW poor based on the total grain yield minus tograin demand within that city region. The VW surplus adecits in each node changed each year based on changesyield owing to climate variability. We represent VW watimports and exports in tonnes of grain year 1 rather than cu-bic metres of water to make our ndings more accessiblenon-specialists in hydrology.

Our VW redistribution network operates as a dynamicagent-based network (Wilensky, 1999). In line with our uderstanding of the Roman grain economy (Erdkamp, 200



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Scheidel, 2010), our network is demand driven with eachVW-poor node (nodes with a VW decit) individually de-manding VW from linked VW-rich nodes. That is to say,our network simulates a hierarchical grain supply systemwhereby urban centres ensure supplies through taxation inkind, constrained by the struggle against distance (Braudel,1995). Although much of the evidence on which we base ourtrade rules pertain to the city of Rome, it is likely that othermajor cities used similar methods to ensure grain supplies.Similarly to DOdorico et al. (2010), we do not simulate VWtrade between VW-rich nodes although this may have oc-curred. Since the links in our network are undirected, owdirection is dictated by the VW potential among VW-richand VW-poor nodes. Thus, VW ow in our network respondsdirectly to changes in yields arising from climate variabil-ity. VW redistribution is simulated over 52 years of climatevariability (Ngo-Duc et al., 2005), with a year ending whendemand at all decit nodes has been satised or all surplusnodes are depleted. We quantify the stress on the system interms of the cost to import VW with costs measured at allVW-poor nodes.

3 Results and discussion

3.1 Yield response to climate variability

The yearly average simulated yield for cereals per 5cell isshown in Fig. 2a with the contribution to the total from rain-fed (Fig. 2b) and irrigated (Fig. 2c) land shown separately.The yields in kgha 1 are shown in Fig. S5, however since

HYDE cropland fractions vary per cell, the yield per 5cellgives a clearer impression of spatial variability in total yieldamount. Rather than reporting VW partitioned into its greenand blue component sources we partitioned VW into VWderived from rainfed and irrigated land. Yields from rainfedland derive only from green water whereas yields from irri-gated land incorporate blue water where there is a shortfallin green water to meet the evaporative demand (van Beek etal., 2011). Our simulations indicate that the most productiverainfed agricultural regions are located in present-day Spain,France, the Po Valley, western Turkey and the Fertile Cres-cent (present-day Syria, Iraq and Israel) (Fig. 2b). Irrigationagriculture is also widespread (Fig. 2c), with the largest ar-eas of irrigated agriculture located in Egypt, the Po Valley,southeastern Turkey, the Fertile Crescent and Spain. Rainfedagriculture accounts for 71.5 % of the total yield in the re-gion with irrigation accounting for the remaining28.5 %. Thekgha 1 yields (Fig. S5) are consistent with yield estimatesbased on Roman sources and yields prior to the agriculturalrevolution in Europe (Erdkamp, 2005; Goodchild, 2007).

Lower than expected yields are calculated for Sicily andpresent-day Algeria and Tunisia related to what is knownfrom historical sources about the productivity of these re-gions (Erdkamp, 2005). The low yields in these regions are

Figure 2. Average cerealyield (tonne per5cell).(a) Average cerealyield in tonnes per 5cell, calculated in PCR-GLOBWB and basedon 52 years of climate forcing. The yields from rainfed (b) and ir-rigated (c) agriculture are shown separately. See Fig. S5 for yiein kgha 1. Yields are highest in irrigated regions where year-rounsupply of surface water allows for multi-cropping, which can tadvantage of the seasons when temperatures for growth are optim

due to a probable underestimation of cropland fractionsthe HYDE data set (Fig. S3b). HYDE provides estimatescropland fractions and population concentration at 5spa-tial resolution globally for the entire Holocene using lasuitability algorithms and back-calculating from current pulation and cropland distributions (Klein Goldewijk et a2011). Thus, it is not surprising that for certain regions crland fractions are inconsistentwith historicalaccounts for tspecic date of AD 200 (Fig. S3) (Klein Goldewijk and Vburg, 2013). For the purposes of this paper it was decidto use unadjusted HYDE grid-based estimates of croplandtransparently show our methodology.

Proxy reconstructions indicate anomalously warm climconditions during the Roman period owing to warm tempatures of the North Atlantic Ocean at the time (Bond et 2001; Desprat et al., 2003; McDermott et al., 2001). Fiure 3 shows the correlation between grain yield with te



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Figure 3. Yield plotted against temperature andprecipitation. Total yield (a andb) in theMediterranean increases with increasingtemperatuand decreases with increasing precipitation. The trend is strongest in regions where agriculture is rainfed (c and d). Irrigated regions (e andf ) also exhibit increased yields with increasing temperature whereas the impact of precipitation is negligible. The reduced higher precipitation is likely related to decreased temperatures under increased precipitation in most of the Mediterranean andevapotranspiration (Fig. S6). This indicates that the majority of the Mediterranean is temperature-limited for cereals.

perature and precipitation averaged over land cells in the

Mediterranean region (25

N, 46

N and 10

W, 45

E). Eachpoint represents a single year of climate forcing with tem-perature and precipitation plotted on the x -axis and yield onthe y-axis. Under warmer temperatures, grain yield signif-icantly increased in both rainfed (p = 0.001) and irrigated(p = 0.001) regions (Fig. 3a, c, e). Somewhat counterintu-itively, yield signicantly decreased in rainfed regions un-der increased precipitation (p = 0.008) (Fig. 3d). No sig-nicant relation was found between precipitation and yieldsin irrigated regions (p = 0.62) (Fig. 3f). Yield is calculatedbased on evapotranspiration, with warmer conditions bring-

ing about higher evapotranspiration and thus higher yiel

where water is not limiting (van Beek et al., 2011). Yield creases under increased precipitation owing to the negatrelation between temperature and precipitation in most of Mediterranean for the predominantly winterspring growseason (Fig. S6) (Portmann, 2008). Additionally, dependion soil type and average rainfall, transpiration can be liited in PCR-GLOBWB by oxygen stress in the soil causby water logging (van Beek and Bierkens, 2009). In irrigaregions there is no relation with precipitation because muof the growing period in irrigated regions occurs during sumer when rainfall in the Mediterranean region is very lo



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Added to this, many of the regions with large-scale irrigationhave very dry climates (Lionello, 2012) with the vast propor-tion of water resources coming from surface water sources.

Increased yield under warmer temperatures and decreasedprecipitation indicate that in most of the Mediterranean,grain yields are temperature limited and not water lim-ited. The spatial distribution of the correlation between cli-mate during the growing season and yield indicates that wa-ter is limiting only in very dry regions such as the south-ern Fertile Crescent, parts of North Africa and coastal re-gions (Fig. S7). Increased grain yields under higher tem-peratures were also found for Mediterranean climate con-ditions in Western Australia in simulations using the Agri-cultural Production Systems Simulator (APSIM)-N wheatmodel to predict the impact of changing temperature, pre-cipitation and CO2 on yield (van Ittersum et al., 2003; Keat-ing et al., 2003; Ludwig and Asseng, 2006). In the southernpart of the study area (> 500 mm precipitation), wheat yieldswere predicted to increase with increasing temperature irre-spective of predicted changes in rainfall, whilst in the driernorth (< 350mm precipitation) rainfall reduction was par-tially counteracted by increased temperatures (Ludwig andAsseng, 2006). It should be stressed that the response to cli-mate is very heterogeneous throughout the Mediterranean(Fig. S7). Nonetheless, as we will show, Mediterranean-scalechanges are highly relevant at the smaller city-region scale inan integrated network such as the Virtual Water network of the Roman world.

3.2 Virtual water redistribution

Rome is the largest importer of VW in our network withimports averaging 92313 tonnes year 1 (Fig. 4a). Egypt isthe largest exporter of virtual water, however much of thisexport is local with large quantities owing to the denselypopulated Egyptian cities of Alexandria and Memphis witha proportion also owing towards Italy (Fig. 4b). The largestows of VW occur between eastern and southern Spain andRome. There are also large ows between southeastern Italyand the densely populated region around the Bay of Naples.Other large ows occur along the Turkish Aegean Coast,within the Po Valley and locally in the region around An-tioch in present-day southeast Turkey. Although only 28.5 %of yield is from irrigated land, VW from irrigated agricultureaccounts for 34% of VW ow among nodes. The dispro-portionately large exports from irrigated land are owing tothe location of irrigated cropland close to the coast or alongrivers where transport is less costly compared with transportover land. Indeed, all large VW ows originate in areas closeto the coast or a large river. Rome has by far the biggestVW demand followed by other large coastal cities such asAlexandria, Ephesus and Antioch (Fig. 4a).

The node degree distribution of the VW redistribution net-work is shown in Fig. 5a. As with many real-world net-works the node degree distribution of our network exhibits a

Figure 4. Virtual water imports and exports (tonne grain year 1).The relative amount of VW imported (a) and exported (b) fromeach node is illustrated by the size of the nodes, whilst the assated numbers show the average VW imported or exported each yexpressed in tonnes of grain. The edge colour and thickness incates the relative volume of VW ow between nodes. The largows are between eastern and southern Spain and Italy, locawithin Egypt, from south-eastern Italy to western Italy and alothe Aegean coast of Turkey. Rome is by far the largest imporof VW, followed by Alexandria and Memphis in Egypt, Epheon the west coast of Turkey, Antioch in south-eastern Turkey aCorinth in Greece.

skewed distribution meaning that most nodes are connecto a few edges (low degree nodes) whilst there are a liminumber of nodes that are highly connected (high degreehub nodes) (Konar et al., 2011; Lewis, 2011; Suweis et 2011). The correspondence of the node degree distributto a real-world network gives us condence that Orbis faifully captures the network structure of the principal Romtrade routes (Scheidel, 2013). Figure 5b shows the costimport VW as a function of node degree. Our analysis incates that low-degree nodes incur the highest import costsour network (Fig. 5b), consistent with the nding that poinfrastructure increases import costs (Limo and Venabl2001). However in Orbis, lower-degree nodes are generalocated inland where import costs are also higher owingthe difculties in transporting large quantities of grain ovland by horse and cart compared with ship (Braudel, 199Limo and Venables, 2001; Meeks, 2013; Scheidel, 201To isolate the effect of node degree from edge cost we simlated VW redistribution with the same network structure reassigned edge costs and VW values at nodes randomlyeach simulation year (Fig. S8a). This analysis demonstra



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Figure 5. Cost to import VW in relation to node degree. (a) Thenode degree distribution of the virtual water redistribution network.(b) Lower-degree nodes generally have higher costs to import VW

compared with high-degree nodes. For thehighest-degree nodes, thecost to import is higher than nodes with an intermediate number of links as many of the highly connected nodes in our network are alsoports or urban centres with high demand. Therefore nearby nodesare often depleted leading to the need to import from further awaywith an associated increase in cost. (c) For nodes with 14 links,import costs remain high irrespective of the level of demand. How-ever, for nodes with 58 links and 912 links, costs increase underincreasing demand. 100 % demand represents the standard modelsimulations presented elsewhere in the paper.

that import cost is closely related to node degree, indepdent of the transport costs of edges connected to that node

In a network where costs co-vary with distance, higher iport costs for low-degree nodes arise because a node wfew transport links has a higher chance of depleting neigbouring nodes compared with a high-degree node, assuing equal demand. Once neighbouring nodes are depletedVW-poor node must import from further away, thus increing cost. However, as node degree increases it is less likthat all neighbouring nodes become depleted, which on aerage will reduce import distance and costs. It is notable tfor the highest-degree nodes, import costs are higher on erage (Fig. 5b). In network theory, highly connected nodare known as hubs. Hub nodes are mostly located along Mediterranean coast in our network (Scheidel, 2013). Konet al. (2011) and Suweis et al. (2011) demonstrated that thhub nodes play a critical role in providing access for pooconnected nodes to the larger VW network. In Orbis, hnodes are usually ports (for example the port node at Osnear Rome) or urban centres. Thus the demand of hub nois in reality the sum of demand from many inland nodeslarge local populations. Owing to the high demand levof these hub nodes they often deplete all their neighbourVW-rich nodes and must import from further away, thus creasing import costs.

Changes in import costs indicate how stressed our Vnetwork of the Roman world is. For example, if total nwork cost is 0, then all regions have sufcient local waresources to meet the demands of the local population. If tal network cost > 0 then local water resources in at least oncity region are insufcient to meet the local population d

mand, meaning that VW import is required. To investigathe impact of increased stress on our network, we simulaVW redistribution across a stress gradient based on increaor decreases in population at each VW-poor node. We choto only change populations at VW-poor nodes as these agenerally representative of urban regions and therefore ect urban population growth during the late Republican aearly Imperial era (Scheidel, 2001). Our analysis indicathat lower-degree nodes exhibit a negligible increase in cas a result of increased demand (Fig. 5c). However, higdegree hub nodes exhibit an incremental increase in cost increasing demand.

In all cases, as demand increases, a VW-poor node muimport from further away in the network. For low-degrnodes, most of which are inland, the largest costs are volved in bridging the gap to coastal hub nodes. Once a hnode is reached import costs increase relatively slowly owto the increased number of coastal import routes that canselected. For high-degree nodes, the increased number of port routes that can be selected means that costs begin velow when demand is low and increase incrementally as dmand increases and nearby nodes are depleted (Fig. 5c). Toutcome of this is that although import costs in poorly conected, inland regions of the network are high, they do



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Figure 6. Cost of imports in relation to temperature. There is a neg-ative relation between the cost to import VW and temperature be-cause yields increase on average in the Mediterranean with increas-ing temperature. Therefore competition for VW resources reduces

and as a result, import distances decrease.

increase substantially for increases in demand. However, forhub nodes that are adapted to low costs, increases in demandcan cause substantial increases in import cost. This pattern isonly applicable in a network such as our VW network of theRoman world, where lower-degree nodes tend to be locatedinland (Fig. S8b) (Scheidel, 2013), which is also typical of the present-day global trade network for bulk goods (Limoand Venables, 2001).

We nd that the total import cost of our water redistribu-tion network is closely linked to climate, in particular tem-perature (Fig. 6). During warm years, increased yields meanthat many regions have sufcient local VW to meet demandso imports are unnecessary. However, even in the case whereimport is required, total demand will drop with the resultthat a VW-poor node competes with fewer VW-poor nodesfor increased VW resources. Consequently, nearby surplusnodes are less likely to become depleted and imports oc-cur over shorter average distances. As stated, reconstructionsof climate during the Roman period indicate that tempera-tures were anomalously warm (Chen et al., 2011; Davis et al.,2003; Ljungqvist, 2010; Wang et al., 2012), creating optimalconditions for the growth of grain. Therefore, the averagetransport distance of VW in the Empire was likely reduced(Fig. 6) compared with the subsequent, cooler Dark Agescold period beginning around AD 400 (Bond et al., 2001; De-sprat et al., 2003; McDermott et al., 2001).

3.3 Roman water resource management

Taking Rome as an example, our simulations indicate thatthe majority of its VW was imported from Spain with Sar-dinia, southern France and Egypt also contributing substan-tial quantities (Fig. 4). However, historical sources indicate

that Egypt, North Africa and Sicily were the dominant eport regions of VW to Rome (Bransbourg, 2012; Erdkam2005). As previously stated, grain yields are underestimain HYDE for North Africa and Sicily, thus Spain supplathese regions as the primary exporters of VW to Romethe western Mediterranean in our network. Additionally, onetwork solves VW transport along the most efcient rouwith VW-poor nodes having perfect knowledge of the Vstatus of the closest VW-rich node. Thus import routes aconstantly adapted to keep cost to a minimum. However, the Roman period this is an unrealistic scenario as the eciency of knowledge transfer varied based on distance, fquency of trade relations and so forth (Kessler and Tem2007). Probably Romans had little knowledge of yieldsremote regions of the Empire until grain ships arrived in p(Rickman, 1980). If the cargo on incoming ships was belexpectations then cities risked famine and potential violunrest (Erdkamp, 2005). Therefore stable yields in exportregions were particularly important to the Romans.

Examining the year-to-year variability in yield we csee that much of the eastern Empire likely had highly sble yields, in particular Egypt. In the western Empire NoAfrica, Sicily and the Po Valley exhibited the most stabgrain production (Fig. 7). The stability of yields in irrigaregions such as Egypt and the Po Valley was borne out a year-round supply of surface water so that multi-croppcould take advantage of the seasons when temperatures growth were optimal. Yields from rainfed agriculture wprobably most stable in southwestern Turkey, the westeFertile Crescent, North Africa and Sicily. In these regiowinter climate is relatively warm compared with Spain, It

France and the eastern Adriatic coast (Lionello, 2012). In dition, winter climate in the eastern Mediterranean was qustable owing to the reduced inuence of Atlantic storm tracompared with the northwestern Mediterranean (Lionel2012; Xoplaki et al., 2004).Although Spain andFrancecouexport large quantities of VW in many years, the reliabilof yields were much less compared with the aforementionregions, a disadvantage that was unacceptable in an erainefcient information transfer (Kessler and Temin, 200The high productivity of Spain but low stability in yieldprobably why its main exports during the Roman period wnon-staple foods such as olive oil (Blzquez, 1992; Woo1992).

Our analysis highlights that the heterogeneity of tMediterranean environment was important for providing Romans with resilience to interannual climate variabiliAs we mentioned, a widespread use of irrigation as welwarm winter temperatures meant that the eastern Empire hwarmer and more stable winter temperatures compared wthe west. Topographical variations also played an importrole with grain yields limited by temperature at higher evations whereas they were water limited at lower elevatioand in more arid environments (Fig. S7). It was the Romaability to link these environmentally heterogeneous regio



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Figure 7. The stability of yields over time. The map shows in how many years the total annual yield in each cell remains within average yield for the same cell calculated over 52 years of climate forcing. In the Nile Valley, yields remain within 10% of the ain all years, meaning that yields are exceptionally stable. Regions of northern Spain and northern France are relatively unstabledropping below 10% in at least 40 out of 52 years.

through trade that provided them with a stable food sup-ply despite the variable climate of the Mediterranean region.However, VW redistribution during the Roman period alsofacilitated populations in VW-poor regions, in particular ur-ban areas, to overshoot their ecohydrological carrying ca-pacities (Erdkamp, 2005; Garnsey, 1988; Rickman, 1980).The population growth and increased urbanization duringthe Late Republican and Early Imperial periods (Bowmanand Wilson, 2011; Scheidel, 2001) likely pushed the Em-pire closer to the limits of available freshwater resourcesand reduced resilience to climatic variability (DOdorico etal., 2010; Garnsey, 1988). In addition, our simulations usinga costdistance-based network show that increased demandarising from urbanization caused an increase in average im-port distance and an associated increase in import costs. Itis plausible that lower water resource redundancy and in-creased import costs may have been a contributing factor tothe third century crisis which followed a period of popula-tion growth, urbanization and trade in the second century AD(Parker, 1992; Scheidel, 2010).

3.4 Present-day implications

Our analysis uncovered a number of important featuresthat have general implications for virtual water trade un-der spatially and temporally variable environmental condi-tions. For example, provided there are enough trading re-gions with temporally heterogeneous yields, virtual watertrade increases carrying capacity without an increase in wa-ter resource use in any of the trading regions (Fig. 8). Vir-tual water trade is therefore a highly efcient method of providing resilience to interannual climate variability. How-ever, by increasing the carrying capacity of trading regionsas well as allowing VW-poor regions to overshoot their lo-

cal ecohydrological carrying capacities (Fig. 8) (Barnab2009; DOdorico et al., 2010), virtual water trade promopopulation growth and urbanization (Hubacek et al., 200Therefore, the short-term resilience that VW trade providis eroded in the long term as population growth and urbantion pushes trading societies towards a global carrying capity. The present-day trend of urbanization (United Natio2012) means that the global society is becoming increaingly dependent on trade to ensure food supplies. As poulation continues to grow there is less space to adapt to yiperturbations that may arise owing to anthropogenic climchange (DOdorico et al., 2010). The globalized populatiis therefore in danger of becoming vulnerable to climate pturbations in the same way that an isolated population However, unlike an isolated population, the globalized cilization is also vulnerable to perturbations in the trade nwork itself (De Benedictis and Tajoli, 2011; Grubesic et a2008).

In our study we used a costdistance network to invesgate VW trade. However, the majority of studies analysiVW trade use socioeconomic trade relations to dene tnetwork structure (Hanasaki et al., 2010; Konar et al., 20Suweis et al., 2013). Socioeconomic-based trade networ

are highly changeable over time with projections of fture network structure highly uncertain (Carr et al., 2012though evolutionary approaches do show promise (Dalinal., 2012a). In contrast, costdistance-based networks amuch more stable through time. As with the Roman priod, present-day transport costs continue to co-vary wdistance, particularly for bulk, staple foods such as gra(Hummels, 2007). Just as in the Roman period, presenday land-based transport of bulk goods is considerably mcostly compared with sea-based transport (Limo and Veables, 2001). Indeed, it has been found that trade costs



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Figure 8. Conceptualgure illustrating the impactof trade on carry-ing capacity in a variable environment. Carrying capacities are vari-able over time owing to the impact of interannual climate variability

on yields. In an isolated society populations must remain below theclimate-forced carrying capacity to avoid famine. In societies withtrade, the carrying capacity becomes the average carrying capacityof all trading regions. Thus, where there is a sufcient number of trading regions with heterogeneous environments, carrying capacityis increased without an increase in resource use in any of the tradingsocieties. Trade even allows certain regions to attain carrying capac-ities well above their local ecohydrological constraints, thus facil-itating urbanization. However, under continued population growth,the resilience to climate variability provided by trade is eroded aspopulations approach a new global carrying capacity. In addition,urbanization means that regions become vulnerable to perturbationsin the trade network as well as perturbations arising from crop fail-ure. Carrying capacities are smoothed to illustrate the dampeningeffect of food storage.

bulk goods have become increasingly distance sensitive inthe latter part of the 20th and early 21st century with approx-imately half of world trade occurring between trade partnersless than 3000 km apart (Berthelon and Freund, 2008). Thereasons for a stronger relation between cost and distance inrecent decades are not straightforward (Berthelon and Fre-und, 2008), but it is likely that future increases in fuel costswill strengthen the trend further (Curtis, 2009). Therefore,the struggle against distance (Braudel, 1995) which wasa characteristic of preindustrial trade remains a central con-straint for present-day VW redistribution.

As population growth and urbanization (United Na-tions, 2012) continues to reduce water resource redundancy(DOdorico et al., 2010), our analysis demonstrates that anassociated increase in import distance will be unevenly dis-tributed throughout the global VW network, with hub nodesexperiencing the greatest increases in import cost. How suchcosts will actually be distributed throughout the global tradenetwork are complicated by socioeconomic factors such asprotectionism (Carr et al., 2012b; Messerlin, 2011). There-

fore, research on VW trade should continue to explore ttwo-way feedbacks between society and their environme(Sivapalan et al., 2012) because socioeconomic forcings perhaps the primary driving force of VW trade (Hoekstra aChapagain, 2008). However, costdistance-based networprovide an additional avenue for understanding the undering physical and environmental constraints inuencing Vtrade. In addition, the stability of costdistance relations ctributes to improving projections as well as identifying most economical VW trade routes, not just in terms of sing water but also in terms of fossil fuel use.

4 Conclusions

The question of what brought about the fall of the RomEmpire is one that has occupied Roman scholars for ceturies (Gibbon, 1776). However, an equally relevant questis what enabled the Roman civilization to persist for so loin a region of highly variable climate (Lionello, 2012) aassociated variability in agricultural yields upon which theconomy and survival depended (Erdkamp, 2005; Garns1988; Rickman, 1980). Our ndings show that the majorof the Mediterranean is temperature limited for the growof grain. Given that the height of the Roman civilization incided with centuries of anomalously warm climate (Boet al., 2001; Desprat et al., 2003; Ljungqvist, 2010), coditions for the growth of grain were likely optimal. Hoever, higher-frequency climate variability has been demostrated to have catastrophic impacts for other past civilitions where water resources were not spatially integrated

the extent of the Roman Empire (de Menocal, 2001; Weet al., 1993). The Romans ability to link heterogeneous vironments of the Mediterranean using VW trade meant tthey could offset decits in one region with surpluses in other (Kessler and Temin, 2007). In an era before the invtion of the combustion engine, the Mediterranean playecritical role because it enabled the spatial integration of Empire through shipping (Braudel,1995; Jones,1986; Schdel, 2013). The linked-heterogeneity of the Roman Empundoubtedly increased their resilience to climate variabiland contributed to the longevity of their civilization (Gibb1776; Scheidel, 2013). The importance of VW redistributin the Mediterranean as a buffer to climate variability is illtrated in the writings of Pliny the Younger (AD98AD 1in Erdkamp (2005): Even the heavens can never provekind as to enrich and favour every land alike. But he [the eperor] can so join east and west by convoys that those pple who offer and those who need supplies . . . appreciatehaving one master to serve.

However, although VW redistribution increased resiliento shorter-term climate variability, it was also central to faitating the population growth and urbanization that occurduring the Late Republican and Early Imperial period (Riman, 1980). VW trade facilitated urbanization because it



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abled regions to overshoot their local ecohydrological carry-ing capacities (Barnaby, 2009; DOdorico et al., 2010). Theassociated increase in water resource exploitation pushed theEmpire closer to the boundary of its freshwater resources,thus eroding its long-term resilience to crop failures. In ad-dition, growing urban demand led to an increased relianceon VW trade, an increase in average import distances and anassociated increase in import costs. The combination of re-duced resilience to crop failures and increased import costsmay have contributed to the third century crisis following apeak in population and urbanization in the second centuryAD. Given that present-day trade costs in bulk, staple foodscontinue to co-vary with distance, the struggle against dis-tance that typied preindustrial trade will continue to be aconstraint on future VW trade. Just as with the Roman Em-pire, present-day population growth continues to push civi-lization closer to the boundary of our global water resourcesand erode our resilience to crop failure (Bogardi et al., 2013).In addition, rapid urbanization means we are becoming in-creasingly reliant on VW trade, meaning that we are not justvulnerable to crop failures but perturbations in the VW tradenetwork itself.

The Supplement related to this article is available onlineat doi:10.5194/hess-11-5025-2014-supplement.

Author contributions. B. J. Dermody, R. P. H. van Beek, E. Meeks,K. K. Goldewijk, W. Scheidel, Y. van der Velde, M. F. P. Bierkens,M. J. Wassen, S. C. Dekker wrote the paper. B. J. Dermody,R. P. H. van Beek, E. Meeks, K. K. Goldewijk, Y. van der Velde,M. F. P. Bierkens, S. C. Dekker designed the experiments. W. Schei-del, E. Meeks and K. K. Goldewijk contributed data. B. J. Dermodyand R. P. H. van Beek carried out the experiments. B. J. Dermodyprepared the paper with contributions from all co-authors.

Acknowledgements. Thanks to David Bijl and Gurvan Cabon forthought-provoking discussions. The authors would also like tothank the anonymous reviewers for their valuable comments andsuggestions to improve the manuscript.

Edited by: J. Liu

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