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Global pattern for the effect of climate and land cover on water yield (1)(1)

ARTICLE

Received8Apr2014|Accepted20Nov2014|Published9Jan2015

DOI:10.1038/ncomms6918

Global pattern for the effect of climate

and land cover on water yield

Guoyi Zhou1,Xiaohua Wei2,*,Xiuzhi Chen1,*,Ping Zhou3,Xiaodong Liu1,Yin Xiao1,Ge Sun4,

David F.Scott2,Shuyidan Zhou5,Liusheng Han6&Yongxian Su6

Research results on the effects of land cover change on water resources vary greatly and the

topic remains controversial.Here we use published data worldwide to examine the validity of

Fuh’s equation,which relates annual water yield(R)to a wetness index(precipitation/

potential evapotranspiration;P/PET)and watershed characteristics(m).We identify two

critical values at P/PET?1and m?2.m plays a more important role than P/PET when m o2,

and a lesser role when m42.When P/PET o1,the relative water yield(R/P)is more

responsive to changes in m than it is when P/PET41,suggesting that any land cover changes

in non-humid regions(P/PET o1)or in watersheds of low water retention capacity(m o2)can

lead to greater hydrological responses.m signi?cantly correlates with forest coverage,

watershed slope and watershed area.This global pattern has far-reaching signi?cance in

studying and managing hydrological responses to land cover and climate changes.

1South China Botanical Garden,Chinese Academy of Sciences,Guangzhou510650,China.2Earth&Environmental Sciences and Physical Geography, University of British Columbia(Okanagan campus),Kelowna,British Columbia,Canada V1V1V7.3Department of Forest Ecology,Guangdong Academy of Forestry,Guangzhou510520,China.4Eastern Forest Environment Threat Assessment Center,USDA Forest Service,Raleigh,North Carolina27606,USA. 5Beijing Institute of T echnology,Zhuhai Campus,Zhuhai519088,China.6Guangzhou Institute of Geography,Guangzhou510070,China.*These authors contributed equally to this work.Correspondence and requests for materials should be addressed to G.Z.(email:gyzhou@https://www.sodocs.net/doc/c213923869.html,).

T he effects of land cover changes on water resources have been debated for many years.Numerous studies have been

conducted throughout the world to address this concern. The paired-watershed experiment(PWE)method1,which is believed to accurately quantify the change in water yield caused by vegetation changes,has been widely used in the past century2,3.Several reviews of these experiences involving more than250PWEs from around the globe have reported that, although forest changes signi?cantly affect the water yield3–5,the magnitude of any change varies greatly from one watershed to another6,7.Some studies,especially in large watersheds,found that forest changes have limited effects8,no effects9,10or even positive effects11,12on water yield.These highly variable and apparently inconsistent results have led to debates in both research and resource management communities,especially when another catastrophic?ood or drought occurs somewhere in the world13.Clearly,a unifying theory describing the in?uence of climate and land cover on water yield,and which is validated by global experimental studies,would improve our understanding on the underlying mechanisms and support natural resource management.

Along with‘bottom-up’experimental approaches,energy-based theoretical equations describing climate and water balance have been developed and applied in what is often called a top-down approach14–16.Among them,frameworks by Budyko17and Fuh18have received the most attention and application19.Both frameworks consider climate as well as a watershed-speci?c parameter.Recently,the two frameworks were shown to be virtually identical20,with the Fuh’s equation being a more generalized form19.However,neither framework has been comprehensively analysed using a global data set nor have possible mechanisms to explain emerging patterns been offered.

A universal model that incorporates precipitation(P),potential evapotranspiration(PET)and watershed characteristics to explain the variable hydrological responses to land cover changes is needed.

In this study,a theoretical pattern on the dependence of the ratio of annual water yield to precipitation on wetness index (P/PET)and watershed characteristics(m)based on Fuh’s equation18is analysed and validated using the globally published data.We con?rm that the Fuh’s theoretical equation is a valid and useful framework for studying land cover changes and hydrological responses.Theoretical analyses identify two critical values at P/PET?1and m?2.P/PET plays a more important role than m when m42,and less when m o2.When P/PET o1,the sensitivities of R/P to m values are more dramatic and multi-directional than those when P/PET41,suggesting that any land cover changes in non-humid regions(P/PET o1)can lead to greater and more sensitive hydrological responses.Relative contributions of P/PET and m to annual water yield at a large spatial scale are mapped out globally.The m values are signi?cantly correlated with forest coverage or treated area in PWE,watershed area and slope.The pattern explains the great variability in the effect of forest cover changes on water yield and implies that the effect can be negative,neutral or even positive, depending on the P/PET and m values of a watershed.

Results

Performance and validation of the pattern.Equation(1)depicts the dependence of the ratio(R/P)of annual water yield(R)to precipitation(P)on P and PET(see Methods):

R P ?1t

PET

àm

PET

à1

e1T

where R/P is a dimensionless annual water yield coef?cient;P/PET is a dimensionless variable often called wetness index that differs by region and year,with its reciprocal(PET/P)often called dryness index;and m(1,N)is an integration constant that is dimensionless and independent of P and PET,and represents watershed characteristic18,21.One extreme case occurs when m?1,R/P?1,where all precipitation becomes stream?ow and residence time is0.The opposite extreme case occurs when m-in?nity,R/P?0(PET4P)or R/P?1à(P/PET)à1(PET o P), where all precipitation remains in the watershed and residence time equals the time for all precipitation to evaporate.Thus,m indicates the ability for a watershed to retain water for evapotranspiration;larger m values mean larger and longer water retention capacities.The variable m can be used to denote watershed characteristics,including watershed area,slope,land cover and other characteristics(for example,soil texture,depth). From the equation(1),the sensitivity functions of R/P to P/PET@R

PET

àá

and m@R

àá

are given as:

PET

à2

àmà1

?1t

àm!1àm m

e2T

P?à1t

àm

ln1t

PET

àm

PET

àm ln P

PET

àá

1tP

PET

àáàm

e3TThe results of equations(1)–(3)are illustrated in Fig.1. According to equation(1),R/P changes with P/PET and m within the theoretical range de?ned by the?ve boundaries of P/ PET?0,P/PET?N,R/P?1(m?1),R/P?0(P/PET o1and m-N)and R/P?1à(P/PET)à1(P/PET41and m-N), which are shown in Fig.1a.We veri?ed equation(1)with the globally published data(Supplementary Data1for time-trend studies and Supplementary Data2for PWE studies.The time-trend studies are de?ned as those that provide circumstantial evidence of the in?uence of watershed management on water yield3).First,this hypothetical universal pattern captured the majority of the data regarding the changes in R/P with P/PET for four land cover types(forest,shrub,grass/crop and mixed lands). More than90%of the data on R/P with P/PET,as shown in Fig.2a and listed in Supplementary Data1,and more than88%of the data on R/P with P/PET,as shown in Fig.2b and listed in Supplementary Data2,?t within the theoretical range.Second, the curves in Fig.2a,b are all statistically signi?cant(p o0.001). The one-way analysis of variance shows that the differences in m values between any two of the four land cover types and between the forested and non-forested watersheds were all signi?cant (p o0.001).This suggests that land cover changes signi?cantly modify m values,and an increase in forest coverage indeed reduces R/P,which is consistent with the general conclusions from PWE studies3,5,13.

Theoretically,R/P increases with P/PET for all m(1,N)and decreases with m for all P/PET(0,N)(Fig.1a).Correspondingly, the sensitivities of R/P to P/PET are above0(Fig.1b),while these to m are below0(Fig.1c).

Our theoretical analysis from equations(1)–(3)identi?ed two critical values m?2and P/PET?1(see Methods).When 1o m r2,e@R

@PTdecreases rapidly and monotonically with increasing P/PET.In contrast,when m42,e@R

PET

Tchanges with P/PET as unimodal curves(Fig.1b),with the P/PET values of in?ection points increasing with m from the starting point m?2and P/PET?0.The critical value of m?2is also supported by the published data as shown in Fig.2c where there are two different patterns of R/P in response to P/PET for m o2

and m 42.Thus,our theoretical analyses and global data indicate that hydrological responses to land cover changes are more sensitive when watersheds have lower water retention capacity (1o m o 2),probably due to the dominance of low water retention land types (for example,open or sparsely vegetated natural land cover types or disturbed land cover types)or other watershed characteristics of low water retention capacity (for example,small watershed area,thin soils,shallow bedrocks,low in?ltration capacities,steep watershed slopes).

The sensitivity of R /P to m varies with P /PET in unimodal curves for all m values (1,N ),but they are not symmetrical to P /PET (Fig.1c).When P /PET 41,the absolute values of @R P @m àádecrease smoothly and monotonically with P /PET for all m values (1,N ).In extremely wet environments (P /PET 441),hydro-logical responses are neither sensitive to m nor sensitive to P /PET (Fig.1c).When 0o P /PET r 1,the absolute values of @R P

@m àá

change with P /PET in unimodal curves for all m values (1,N ),with the P /PET values of in?ection points increasing mono-tonically from 0to 1when m changes from 1to N .For any given m value,the highest sensitivity of R /P to m occurs at 0o P /PET o 1.In extremely dry environments (P /PET o o 1),the smaller the m is,the greater the sensitivity of R /P to m and P /PET will be,and vice versa (Fig.1c).Theoretically,all D R /P values between any two different m values,including the maximum D R /P between m ?1and m ?N ,change with P /PET in unimodal curves with the peak values falling in the P /PET range of 0to 1(Fig.1a).Clearly,the P /PET values of in?ection points lie between 0and 1with their actual values varied by m .

The global data set shows that D R /P values between forest cover and any one of the other three land covers in the time-trend studies (with m values ranging from 2.12to 2.83as shown in Fig.2a)and between the forested and non-forested types of PWE studies (with m values ranging from 2.05to 2.32as shown in Fig.2b)change with P /PET as unimodal curves with their peak values at the P /PET values of 0.5–0.7(Fig.2a,b),which are within the theoretical P /PET range of (0,1).In addition,much higher coef?cients of variation (CV)in the globally published R /P also fall in the P /PET range of (0,1)(Fig.3).Thus,any land cover changes in the regions with P /PET o 1(non-humid regions)can potentially cause higher and more sensitive impacts on water yields.

In summary,we conclude that equation (1)and its derived equations (2)and (3)are a robust framework for studying global land cover patterns and water yields,and two critical values (m ?2and P /PET ?1)exist for de?ning hydrological sensitivities.

1.0m =1

m =1.05

m =1.1

m =1.18m =1.3m =1.5m =3.0

m =4.0m →∞

m =2.0 1.01.21.41.61.80.8

0.8

0.6R /P

0.60.40.40.20.20.0

0–1

–2–3–2R P m –4

–7.2–7.4

–4–5–6–7–8

0.00.00.00

m =1m =1m =1.05m =1.05m =1.1m =1.1m =1.3m =1.3m =1.5m =1.5m =2m =2m =2.5m =2.5m =3m =3m =4

m =4

0.08

0.16

1.60E–007

8.00E–0080.00E+0000.0

0.50.51.5 1.52.0 2.0

P /PET

P /PET P /PET P /PET

2.0R

P PET 2.5 2.53.0 3.03.5 3.54.0

4.0

1.0 1.00.0

0.5

1.5

2.0 2.5

3.0

3.5

4.0

1.0

P m R

P Figure 1|Theoretical distributions of the pattern and two sensitivity functions.(a )Distribution of the pattern,red line is the curve m (watershed characteristics)?2and dashed line is the curve of maximum D R /P (difference in R /P (water yield coef?cient)between m ?1and m ?N )with P /PET

(wetness index).(b )Distribution of the sensitivity function of R/P to P/PET ,green line is the curve m ?2;when 1o m r 2,@R P @P PET àá

decreases rapidly and monotonically with P /PET ,while when m 42@R P @P PET àá

changes with P /PET in unimodal curves.(c )Distribution of the sensitivity function of R/P to m ,

dashed line is P /PET ?1,the two small panels showing ?ner scale of P /PET ;when 0o P /PET r 1,@R P @m àá

changes with P /PET dramatically with multiple directions,while when P /PET 41@R P @m àá

changes smoothly and monotonically with P /PET .

The factors in?uencing m and changed water yield in PWEs .We further related the m values to various watershed variables given in Supplementary Data 1and 2.The m values were

positively related to forest coverage (or treated forested area for the PWE studies;p o 0.001)and watershed area (p o 0.001)and negatively to watershed slope (p o 0.001).In addition,we related the change in water yield coef?cient (D R /P )to the land cover changes,watershed area and watershed slope for the PWE stu-dies.While D R /P increased signi?cantly with treated area per-centages (Fig.4a)as previously reported 3,D R /P also increased (p o 0.001)with watershed slope (Fig.4b)but decreased (p o 0.001)with watershed area (Fig.4c).Thus,R /P is not only affected by P /PET ,but also by changes in land cover and difference in the watershed parameter,which highlights the fact that the effects of land cover changes on water yield are in?uenced by watershed characteristics and thus are watershed speci?c 22.

Relative contributions of P /PET and m to R /P .The global distributions of P /PET and m values are shown in Fig.5(see Methods).Percentages of the global areas with P /PET o 1and m 42are 68.9and 74.1%,respectively.

To quantify the relative roles of P /PET and m in R /P ,we estimated their relative contributions,C P /PET and C m ,respectively (Fig.6).When m 42,P /PET has a larger role in R /P than m ,while when m o 2,m becomes more important.This theoretical result is

1.0m =1Shrub Shrub

Forest Forest

Shrub-forest

ΔR /P :

Total

Grass or crop Grass or crop Grass & crop-forest Mixed land

Control-treated

Control

Treated

m =1Mixed land

Mixed land-forest

0.8

0.6

R /P

ΔR /P

R /P

0.4

0.2

0.0

1.00.80.80.60.40.20.0

0.0

0.5 1.0

1.5

2.0

3.0

0.000.04

0.080.120.16ΔR /P

ΔR /P :0.240.20

0.28 1.0

0.6m =1m <2m <2

m =2m >2m >20.40.00.0

0.22.5

0.5 1.0

1.5

2.0

3.0 3.5

2.50.5

1.0

P /PET

1.5

2.0

2.5

3.5

3.0

0.00

0.020.04

0.06

0.08

0.100.12m →∞m →∞m ∞Figure 2|Validation of the pattern using global observed water yield coef?cient.(a )Ninety percent of Supplementary Data 1fall within the theoretical range;the ?ve coloured lines:forest (n ?1,187,m ?2.83,p o 0.001),shrub (n ?271,m ?2.33,p o 0.001),grassland or cropland (n ?233,m ?2.28,p o 0.001),mixed land (n ?237,m ?2.12,p o 0.001)and the total (n ?1,928,m ?2.54,p o 0.001);the three dashed lines are the D R /P s (differences in R /P (water yield coef?cient)between forest and the other three respective land covers).(b )Eighty-eight percent of Supplementary Data 2fall within the theoretical range;the two coloured lines:forested (n ?234,m ?2.32,p o 0.001)and non-forested (n ?234,m ?2.05,p o 0.001);the dashed line is the D R /P (difference in R /P between forested and non-forested).(c )The critical value m (watershed characteristics)?2(red line)dividing the changes of R /P with P /PET (wetness index)into two apparently different patterns (m o 2(blue line)and m 42(green line)).

120Coefficient of variation

80100C o e f f i c i e n t o f v a r i a t i o n

604000

201

P /PET

Figure 3|Changes in coef?cient of variation of globally observed water yield coef?cient with wetness index.For all the gathered data in

Supplementary Data 1,we calculated the CV (coef?cient of variation)in every sub-range (0–0.2,0.2–0.4,0.4–0.6y ,)of P/PET (wetness index)according to CV i ?S i /X i (CV i is the CV of the sub-range;S i is the standard deviation;X i is the mean value)(see Methods).

0.35R 2=0.1392; p <0.001

R 2=0.2203; p <0.001

R 2=0.1320; p <0.001

0.300.250.20I n c r e a s e d R /P

I n c r e a s e d R /P

0.150.100.050.00

0.350.30

0.250.20I n c r e a s e d R /P

0.150.100.050.00

0.00.40.20.8

Watershed area (km 2)

8,000

6,0004,0002,0001,0000.60.350.300.250.200.150.100.050.00

20406080100Treated forest area (%)

020405060

1030Slope (%)

Figure 4|Relationships of the change in water yield coef?cient with various factors in PWE.(a )Relationship with the percentage of treated area (n ?181,p o 0.001);(b )relationship with the watershed slope (n ?70,p o 0.001);(c )relationship with the watershed area (n ?214,p o 0.001).

<0.03 (5.0%)

P /PET index m value

0.03–0.20 (12.8%)0.20–0.50 (15.8%)

0.50–0.65 (10.3%)0.65–0.75 (8.0%)0.75–1.00 (17.0%) 1.00–1.15 (8.2%)1.15–1.50 (11.0%)>1.50 (11.9%)

1.0–1.5 (9.49%)1.5–

2.0 (16.45%) 2.0–

3.0 (19.73%)3.0–

4.0 (10.69%)

>4 (43.64%)

Figure 5|Global distributions of wetness index and watershed characteristic values.(a )P /PET (wetness index)values;(b )m (watershed characteristics)values.

10080R e l a t i v e c o n t r i b u t i o n o f P /P E T (%)

604020010080R e l a t i v e c o n t r i b u t i o n o f m (%)

60402000

P /PET

m =1.0m =1.2m =1.4m =1.6m =1.8m =2.0m =2.5m =3.0m =4.0

P /

PET

Figure 6|Relative contributions of wetness index and watershed characteristics to water yield coef?cient.(a )Relative contributions of P /PET (wetness index)to R /P (water yield coef?cient);(b )relative contributions of m (watershed characteristics)to R /P .

congruent with the global published data where the averaged relative contributions of m are72and15%for1o m o2and m42,respectively,with28and85%for their corresponding P/PET values.

On the basis of the distributions of P/PET and m values shown in Fig.5,the worldwide C P/PET and C m in percentages as well as the patterns of m-dominated and P/PET-dominated zones are mapped in Fig.7.The P/PET-dominated zones(C P/PET460%or C m o40%)amount to70.4%,while m-dominated zones (C m460%or C P/PET o40%)are13.8%,and the rest are15.8% where both P/PET and m have a similar role in runoff.This result is consistent with the case study in Murray–Darling basin, Australia19,where the C P/PET and C m,according to Fig.6,are75.4 and24.6%,respectively,with its m being2.465and P/PET being 0.287.The two percentages are close to our corresponding values of76.1and23.9%in Fig.7a.In addition,the result from Fig.7a is strongly supported by the data in Supplementary Data1,as there were signi?cant correlations between them (n?19,R2?0.74,p o0.001for large watersheds(42,500km2 comparable to0.5°(lat.)?0.5°(long.)grid pixel)and n?125, R2?0.085,p o0.001for all watersheds).

Discussion

Using the globally published data,this study con?rms that equation(1)derived from Fuh’s equation is a valid framework for the effects of climate and land cover on hydrology.More importantly,we clari?ed the relative roles of climate and watershed characteristics on hydrological response.When interpreting various Budyko-based coupled curves or equations2,14,20,23,the common perception is that hydrological responses are mainly driven by precipitation(climate)and PET(energy)with the watershed parameter playing a secondary role14,24.However,the relative contributions of the watershed parameter and climate to hydrological responses have never been fully examined and quanti?ed.Without those quanti?cations,the above perception is questionable.Our theoretical analysis shows that m can play a more important role in hydrological responses than P/PET when m o2,while m plays a lesser role when m42.This result is supported by empirical analysis of the globally published data where the averaged relative contributions of m are72and15%for 1o m o2and m42,respectively.Clearly,both our theoretical and empirical analyses demonstrate that the role of m can be larger than P/PET in hydrological responses,even though P/PET plays a dominant role in most of the regions of the world.This conclusion is different from the commonly held perception that climate plays the dominant role and watershed characteristics(m)are secondary. The critical value of m?2de?nes the high(1o m o2)and low (m42)sensitivity ranges for hydrological response(R/P)to changes in m.Zhang et al.14also noted the different hydrological responses with respect to various values of the watershed parameter,but failed to?nd the critical value.When m42,the water retention capacity in a watershed is high,probably due to the combination of high vegetation cover,mixed forest type25, large watershed area,gentle slopes and high soil in?ltration capacity.In this case,the hydrological effects of any land cover change in m(for example,deforestation,urbanization)will likely be buffered.In contrast,when m o2,the water retention capacity in a watershed is low,probably due to the combination of poorer vegetation cover,simpli?ed forest type25,small watershed area, steeper slopes and lower soil in?ltration capacity.Under this situation,the hydrological responses are more sensitive to any land cover-induced change in m.

The large role of m in hydrological responses is supported by published studies26–28,which shows that land cover change can signi?cantly alter m values and lead to a larger role in hydrological responses than climate(P/PET).

Climatic variability and land cover/land-use changes are commonly recognized as two major drivers for hydrological variations,and consequently their strengths,directions and interactions control future water supply and?ow regimes. Unfortunately,current climate change impact studies predict future water supply based only on various climate change scenarios without speci?c consideration of land cover or land-use changes,which may either underestimate or overestimate the impacts of climate change on water resources.In contrast,the majority of PWE studies exclude the impacts of climatic variability so that the impacts of forest changes on hydrology can be determined.This approach may not provide a full picture on how climate and forest change interactively affect hydrology. Therefore,inclusion of both m and P/PET in future water resource assessment is critical for understanding and managing water resources.

Our results show that annual water yield is more sensitive to land cover change(m)in water-limited regions(P/PET o1),as indicated by higher CV,non-symmetrical shapes and multiple changing directions in R/P,as compared with those when P/PET41(Figs1b,c and3).In water-limited environments (P/PET o1),forests normally develop deeper and larger root systems to access more soil water.This strategy allows forests to survive.Conversely,any changes to forests(for example, deforestation or conversion to other land-use types)can lead to larger hydrological responses(for example,larger water yields). The above conclusion is supported by various case studies.For example,the relative contribution of m to R/P in the Yellow River basin,China,was estimated as89.1%(ref.29),which is much higher than that estimated41.9%response in the Miramichi River basin in Canada30,when their P/PET were markedly different

<10 (23.24%)P/PET-dominated zones (70.39%)

P/PET and m-similar zones (15.80%) m-dominated zones (13.81%)

10 – 25 (32.00%)

25 –40 (15.15%)

40 –50 (8.69%)

50 – 60 (7.12%)

60 – 75 (7.25%)

>75 (6.55%)

Relative contribution of m Global patterns of dominant zones

Figure7|Global patterns for the contributions of wetness index and watershed characteristics to water yield coef?cient.(a)Relative contributions of m(watershed characteristics)or P/PET(wetness index)to R/P(water yield coef?cient);(b)global patterns of m-and P/PET-dominated zones(P/PET-dominated zones:C m o40%or C P/PET460%;P/PET and m-equal zone:C m or C P/PET?40–60%;m-dominated zones:C m460%or C P/PET o40%;C m and C P/PET are the relative contributions of m and P/PET,respectively;C P/PET?100àC m).

(0.51and1.91,respectively)and their m values were similar(1.51 and 1.40,respectively).Another useful comparison is that between Manuel Diaz basin in Uruguay31and Lookout Creek watershed,near Eugene,Oregon,USA32where their relative contributions were86.9and34.1%,when their P/PET were markedly different(0.95and 2.91,respectively)and their m values were similar(1.68and1.53,respectively).

Zhang et al.14showed that E/P is most sensitive to changes in watershed characteristics for the regions with the dryness index (PET/P)around1.However,our theoretical analysis(Fig.1c) showed that the greatest sensitivities fall in the regions of P/ PET o1,the P/PET value at which the greatest sensitivity of R/P to m is reached increases from0to1with m changing from1to N.Our analysis from the globally published data(Fig.2a,b)also shows that the P/PET values of maximum D R/P fall in the range of0.5–0.7for the averaged m values varying from2.05to2.83. According to our framework,the water yield coef?cient(R/P) is determined by just three variables(P,PET and m)or even two independent ones(P/PET and m).Using the globally published data from time-trend studies and PWE studies,this paper shows that the m values and change in water yield coef?cient(D R/P)are signi?cantly correlated with proportion of forest coverage, watershed area and slope,although each coef?cient of determina-tion is relatively low.The reason for the low coef?cients of determination may be that m or D R/P is in?uenced by many factors and thus the contribution of each single factor is small.In this study,we identi?ed three key variables in?uencing m values and D R/P based on the limited data we have.It is likely that many other variables may also contribute to water yields33–36. Nevertheless,the signi?cant relationship between m and the three identi?ed key variables indicated that any changes in those variables can alter m values and consequently lead to changes in D R/P.

Deforestation may decrease water retention ability or m values and thus increase water yield due to accelerating water movement as a result of fewer obstacles and surface soil compaction37.In contrast,reforestation may increase water retention ability or m values and thus decrease water yield through decelerating water movement as a result of more obstacles,longer?ow paths and poriferous surface soils.With respect to slope,the watersheds with steeper slopes normally have lower water retention ability or smaller m values and thus higher water yields due to its faster water movement and consequently shorter residence time of liquid water.Watershed area can be an important variable for hydrological https://www.sodocs.net/doc/c213923869.html,pared with small-sized watersheds, large ones tend to have higher water retention capacities(greater m values)and consequently lower hydrological responses mainly due to their more complex landforms(for example,lakes, wetlands),greater buffering capacities and longer residence times. Changes in forest cover have been shown to in?uence water yield in small watersheds,but it is unclear if this result holds for large basins38.Researchers have showed that forest changes in large watersheds have limited effects8,no effects9,10or even positive effects11,12on water yield.The inconsistency may be explained through our https://www.sodocs.net/doc/c213923869.html,pared with small watersheds,large ones usually have higher m values due to greater areas and gentler slopes8.Thus,it is expected that the same forest changes in large watersheds will cause less change in m values,with the result that there is less effect on water yield than in small watersheds.If m values of some large watersheds are much higher than two(m442),forest changes will have no effects on water yield.In humid regions(P/PET41)where PET plays a dominant role in water yield or evapotranspiration,a decrease in PET will likely cause a signi?cant increase in water yield.This is consistent with the?ndings that afforestation can increase water yield in large watersheds of humid regions11,12because afforestation cools local land surface temperature39and thus decreases PET.

Our results on the unifying framework and the relationship between m and watershed characteristics have far-reaching implications for scienti?c research and natural resource manage-ment.First,the veri?ed Fuh’s equation can be used as a top-down framework for studying and managing the effects of climate and land cover changes on water resources.It also opens up new research opportunities for studying how climate and watershed characteristics interactively affect hydrology,and what hydro-logical responses might occur under speci?c m and P/PET values. Second,we have clari?ed and quanti?ed the relative roles of climate and watershed characteristics in hydrological response and challenged the commonly held perception that climate plays a dominant role while watershed characteristic is secondary. Correctly understanding the relative roles and possible interac-tions of watershed condition(m)and climate(P/PET)in hydrological response is crucial for predicting and managing future water resources and their associated ecological services under climate and land cover changes.Third,the critical values (m?2and P/PET?1)we identi?ed can provide important guides for determining hydrological sensitivities to any changes in climate and land cover.Speci?cally,the most sensitive regions in the world are those where m is o2and P/PET o1.Finally,large variations in hydrological response suggest that any extrapolation of research results from one watershed to others must be done with caution.

This study has made incremental advancement on several important aspects of the energy framework(namely,Budyko and Fuh’s equations or curves),but like all studies there are some uncertainties in this research.The uncertainties come from several sources.First,the global published data used in this study are from various case studies where different methods(for example,PWE,time-trend studies)are applied,which may cause a level of uncertainty in our data.Second,the time period over which the data were collected may not include all representative responses of water yields to P/PET and m.Third,the data are mainly from the regions where the research is concentrated because of management concerns,suggesting that our data set may not well cover the regions where there are no or less management interests or concerns(for example,extremely arid areas).Each of these aspects may create uncertainties,which calls for the need for both empirical and modelling studies using comparable methods in all representative parts of the world.

Methods

Derivation of equation(1).Fuh’s model18can be written as:

E?P1t

PET

à1

à1t

PET

àm!1m

()

e4T

where E is evapotranspiration from a watershed and the other variables have the same meanings as those in equation(1).

Both P/PET and PET/P have been used as the surrogate of climate in various water–energy equations2,23,40,41.In this study,we used P/PET instead of PET/P as the former offers several important advantages.First,PET is always larger than0 and relatively stable in a given region as it is determined by available energy.In contrast,P may be0in some extremely arid areas(for example,deserts),which can lead to in?nite values of PET/P.Therefore,P/PET falls in clearly de?ned and limited boundary ranges in any given region(for example,0–4in our study),while PET/P may have in?nite boundary ranges(for example,from0.25to in?nite in our study)that make analysis more dif?cult.Second,because of the difference in the boundary ranges,using P/PET allows more effective quanti?cations on the hydrological sensitivity of R/P to P/PET than using PET/P,especially for the areas with P/PET o1in which R/P is more sensitive to P/PET and m values.

The general water balance equation for a watershed can be written as:

P?EtRtD We5Twhere R is total water yield including surface runoff,inter?ow and base?ow and D W is change of watershed water storage.For a whole water year,D W E0,there

will be equation (6):

R =P ?1àE =P

e6T

Equation (1)can be derived by substituting E in equation (6)with equation (4).Estimation of yearly PET .Yearly PET was estimated using Hamon’s method 42,43.

PET ?0:1651?D ?V d ?K ?365

e7T

where D is the time from sunrise to sunset in multiples of 12h,varies with

date,latitude,slope and aspect of a watershed (if the in?uences of slope and aspect are not considered,the average daily D of an entire year is 1).V d is the saturated vapour density (g m à3)at the annual mean temperature (T ,°C),V d ?216.7?V s /(T t273.3);V s is the saturated vapour pressure (mb),V s ?

6.108?exp[1

7.26939?T/(T t237.3)].K is the correction coef?cient to adjust PET calculated using Hamon’s method to realistic https://www.sodocs.net/doc/c213923869.html,paring the reported PET s with the calculated PET s for some PWE and time-trend studies,we found that the K values to adjust the two types of PET s ranged from 1.2to 1.4.Thus,to keep consistency,we used K ?1.3to calculate the PET s of all PWE and time-trend studies in Supplementary Data 1and 2,even for those studies that had PET s reported.

Determination of the two critical values P /PET ?1and m ?2.The second derivatives of equation (1)or the ?rst derivatives of equations (2)and (3)are given as follows:

@2R P ?A tB e8T

A ?1tP àm 1m à1ln 1tP àm àP PET àáàm ln

P PET àám 1tP PET

àáàm àá

e9T

B ?1tP àm 1m 2ln 1tP àm t2P PET àáàm ln

P PET m 1tP PET àáàm àá

tP PET àáàm ln P PET àá2m 1tP PET àáàm àáàP PET àáà2m ln P PET àá2m 1tP PET

àáàm àá2

e10T

@2R P @eP PET T

2?1àm eTP PET

à2m à21tP PET àm 1m à2

t1tm eTP PET àm à21tP PET àm 1m à1à2

P PET

à3

e11T

@2R P @P PET @m ?@2R P @m @P PET ?P PET àm à11tP PET

àm 1m

à1

ln P PET t

1àm m P PET àm ln P

PET 1tP PET

àáàm t1m 2ln 1tP PET àm

!e12T

e@2R P =@m 2

Tis above 0for all P /PET (0,N )and m (1,N )values,showing that

the e@R P =@m Tis increasing with m (1,N ).When m o 2,@2R P @eP PET T2àá

is below 0for all P /PET (0,N ),showing that the @R P @P PET àáis decreasing with P /PET (0,N ).When m ?2,@2R P @eP PET T

2àá!0at P /PET -0.When m 42,for any given m value (2,N ),there is an in?ection point at which the @2R P @eP PET T2

àáchanges with P /PET from above 0to below 0,and

correspondingly,@R @P àá

changes with P /PET from uptrend to downtrend.

A mathematical theorem guarantees the correctness of the claim @2R P @P PET @m àá?@2R P @m @P

PET àá.We have also demonstrated the conclusion through respective derivatives.When P /PET 41,@2R P @m @P

PET àáis above 0for all m (1,N ),showing that the @R P @m àáis increasing with P /PET (1,N ).When P /PET ?1,@2R P @m @P PET àá!0at m -N .When P /PET o 1,for any given m value (1,N ),there is an in?ection point at which the @2R P @m @P PET àáchanges with P /PET from below 0to above 0,

and correspondingly,@R P @m àá

changes with P /PET (0,1)from downtrend to uptrend.

We summarized the above analyses in Table 1.

CV of globally published R /P data .For all the gathered data in Supplementary

Data 1,we calculated the CV in every sub-range (0–0.2,0.2–0.4,0.4–0.6,y )of P /

PET according to CV i ?S i

X i (CV i is the CV of the sub-range;S i is the standard

deviation; X i is the mean value).

The relative contributions of P /PET (C P /PET )and m (C m ).On the basis of equations (2)and (3),we calculated the ratio (a )of @R P @P PET àá=@R

@m àá.C P /PET

and C m were calculated according to:

C P =PET ?

100?a j j 1ta j j

e13TC m ?

1001ta j j

e14T

Global distributions for various parameters .Using data on global annual runoff

(R )and precipitation (P )(https://www.sodocs.net/doc/c213923869.html,/atlas/maps.php?datase-tid=41&includerelatedlinks=1&dataset=41)and PET (https://www.sodocs.net/doc/c213923869.html,/data/global-aridity-and-PET-database),we calculated the global P /PET and hence estimated global m values according to equation (1).The estimated global m values and global wetness index (P /PET )were then used as inputs to equations (2)and (3)to calculate the global sensitivities of R /P to P /PET and m .Finally,the global sensitivities of R /P to P /PET and m were used to calculate the relative contributions

Table 1|Changes of the two sensitivity functions with wetness index and watershed characteristics.

Sensitivity functions Variables

Change in trends with variables

Variable ranges for the trends

IP Second derivatives @R P @m

àám m m (1,N )and P /PET (0,N )No IP

MM 40

P /PET

From k to m

m (1,N )and P /PET (0,1)For each m (1,N ),

an IP exists in P /PET (0,1)From MP o 0to MP 40B P /PET ?1and m -N

B MP -0m

m (1,N )and P /PET (1,N )No IP

MP 40

@R P @P PET

àám

From m to k

m (1,N )and P /PET (0,1)For each P /PET (0,1),an IP exists in m (1,N )From PM 40to PM o 0B P /PET ?1and m -N

B PM -0m

m (1,N )and P /PET (1,N )No IP

PM 40

P /PET

k m (1,2)and P /PET (0,N )No IP PP o 0B

m ?2and P /PET -0

PP -0

From m to k

m (2,N )and P /PET (0,N )

For each m (2,N ),

an IP exists in P /PET (0,N )

From PP 40to PP o 0

IP,in?ection points;m ,watershed characteristics;P/PET ,wetness index.m ,uptrend;k ,downtrend;B ,non-trends.

MM !@2R P @m 2;MP !@2R P @m @P PET

;PM !@2R P @P PET

@m ;PP !@2R

@eP PET

;MP ?PM.

of P/PET and m to R/P according to equations(13)and(14).All the above results were integrated to develop the world maps at the grid size of0.5°(latitude)?0.5°(longitude).

Statistic analysis.Correlations between any two parameters are calculated using OriginLab OriginPro9.0.0.All recorded forest coverage(or treated forest area), watershed slope and watershed area in Supplementary Data1and2are used to calculate the relationship between m values(or D R/P)and any one of the watershed characteristics.The C m for large watersheds(42,500km2)in Supplementary Data 1and2were directly related to the C m in Fig.7a.However,the C m for smaller watersheds were averaged in each pixel(2,500km2)and then related to the C m in Fig.7a.

References

1.Bates,C.G.&Henry,A.J.Forest and stream?ow experiment at Wagon Wheel

Gap,Colorado.Mon.Weather Rev.Supplement30,1–79(1928).

2.Zhang,L.,Dawes,W.R.&Walker,G.R.Response of mean annual

evapotranspiration to vegetation changes at catchment scale.Water Resour.

Res.37,701–708(2001).

3.Brown,A.E.,Zhang,L.,McMahon,T.A.,Western,A.W.&Vertessy,R.A.A

review of paired catchment studies for determining changes in water yield resulting from alterations in vegetation.J.Hydrol.310,26–61(2005).

4.Hibbert,A.R.in Proceedings of International Symposium on Forest Hydrology,

Penn State University1965,527–543(Pergamon Press,1967).

5.Bosch,J.M.&Hewlett,J.D.A review of catchment experiments to determine

the effect of vegetation changes on water yield and evapotranspiration.

J.Hydrol.55,3–23(1982).

6.Bruijnzeel,L.A.Hydrological functions of tropical forests:not seeing the soils

for the trees.Agric.Ecosyst.Environ.104,185–228(2004).

7.Sun,G.et al.Potential water yield reduction due to forestation across China.

J.Hydrol.328,548–558(2006).

8.Buttle,J.M.&Metcalfe,R.A.Boreal forest disturbance and stream?ow

response,northeastern Ontario.Can.J.Fish.Aquat.Sci.57,5–18(2000). 9.Dyhr-Nielsen,M.in International Symposium on Tropical Forest Hydrology

and Application12(World Bank,1986).

10.Antonio,C.B.,Enrique,M.T.,Miguel,A.L.U.&Jose,M.L.P.Water

resources and environmental change in a Mediterranean environment:the south-west sector of the Duero river basin(Spain).J.Hydrol.351,126–138 (2008).

11.Zhou,G.Y.et al.Forest recovery and river discharge at the regional scale of

Guangdong Province,China.Water Resour.Res.46,W09503(2010).

12.Wang,S.,Fu,B.J.,He,C.S.,Sun,G.&Gao,G.Y.A comparative analysis of

forest cover and catchment water yield relationships in northern China.For.

Ecol.Manage.262,1189–1198(2011).

13.Andre′assian,V.Waters and forests:from historical controversy to scienti?c

debate.J.Hydrol.291,1–27(2004).

14.Zhang,L.,Hickel,K.&Dawes.,W.R.A rational function approach for

estimating mean annual evapotranspiration.Water Resour.Res.40,1–14

(2004).

15.Oudin,L.,Andre′assian,V.,Lerat,J.&Michel,C.Has land cover a signi?cant

impact on mean annual stream?ow?An international assessment using1508 catchments.J.Hydrol.357,303–316(2008).

16.Andre′assian,V.&Perrin,C.On the ambiguous interpretation of the

Turc-Budyko non-dimensional graph.Water Resour.Res.48,W10601(2012).

17.Budyko,M.I.in Climate and Life.(https://www.sodocs.net/doc/c213923869.html,ler,D.H.)(Academic Press,1974).

18.Fuh,B.P.On the calculation of the evaporation from land surface.Sci.Atmos.

Sin.5,23–31(in Chinese with English abstract)(1981).

19.Roderick,M.L.&Farquhar,G.D.A simple framework for relating variations

in runoff to variations in climatic conditions and catchment properties.Water Resour.Res.47,W00G07(2011).

20.Yang,H.,Yang,D.,Lei,Z.&Sun,F.New analytical derivation of the mean

annual water-energy balance equation.Water Resour.Res.44,W03410(2008).

21.Zhou,G.Y.et al.Estimating forest ecosystem evapotranspiration at multiple

temporal scales with a dimension analysis approach.J.Am.Water Resour.

Assoc.44,208–221(2008).

22.Troch,P.A.,Carrillo,G.,Sivapalan,M.,Wagener,T.&Sawicz,K.Climate-

vegetation-soil interactions and long-term hydrologic partitioning:signatures of catchment co-evolution.Hydrol.Earth Syst.Sci.17,2209–2217(2013). 23.Choudhury,B.J.Evaluation of an empirical equation for annual evaporation

using?eld observations and results from a biophysical model.J.Hydrol.216, 99–110(1999).

24.Budyko,M.I.The Heat Balance of the Earth’s Surface(National Weather

Service,U.S.Department of Commerce,1958).

25.Creed,I.F.et al.Changing forest water yields in response to climate warming:

results from long-term experimental watershed sites across North America.

Glob.Change Biol.20,3191–3208(2014).26.Zhang,M.&Wei,X.The effects of cumulative forest disturbance on stream?ow

in a large watershed in the central interior of British Columbia,Canada.Hydrol.

Earth Syst.Sci.16,2021–2034(2012).

27.Zhao,F.F.,Xu,Z.X.,Zhang,L.&Zuo,D.P.Stream?ow response to climate

variability and human activities in the upper catchment of the Yellow River Basin.Sci.China Ser.E Tech.Sci.52,3249–3256(2009).

28.Coe,M.T.,Latrubesse,E.M.,Ferreira,M.E.&Amsler,M.L.The effects of

deforestation and climate variability on the stream?ow of the Araguaia River, Brazil.Biogeochemistry105,119–131(2011).

29.Yang,Z.,Yan,Y.&Liu,Q.Assessment of the?ow regime alterations in the

Lower Yellow River,https://www.sodocs.net/doc/c213923869.html,rm.10,56–64(2012).

30.Caissie,D.,Jolicoeur,S.,Bouchard,M.&Poncet,https://www.sodocs.net/doc/c213923869.html,parison of stream?ow

between pre and post timber harvesting in Catamaran Brook(Canada).

J.Hydrol.258,232–248(2002).

31.Silveira,L.&Alonso,J.Runoff modi?cations due to the conversion of natural

grasslands to forests in a large basin in Uruguay.Hydrol.Process.23,320–329 (2009).

32.Harr,R.D.,Levno,A.&Mersereau,R.Stream?ow changes after logging

130-year-old Douglas?r in two small watersheds.Water Resour.Res.18,

637–644(1982).

33.Yang,D.et al.Analyzing spatial and temporal variability of annual water-

energy balance in nonhumid regions of China using the Budyko hypothesis.

Water Resour.Res.43,W04426(2007).

34.Shao,Q.,Traylen,A.&Zhang,L.Nonparametric method for estimating the

effects of climatic and catchment characteristics on mean annual

evapotranspiration.Water Resour.Res.48,W03517(2012).

35.Xu,X.,Liu,W.,Scanlon,B.R.,Zhang,L.&Pan,M.Local and global factors

controlling water-energy balances within the Budyko framework.Geophys.Res.

Lett.40,6123–6129(2013).

36.Devito,K.et al.A framework for broad-scale classi?cation of hydrologic

response units on the Boreal Plain:is topography the last thing to consider?

Hydrol.Process.19,1705–1714(2005).

37.Zhou,G.Y.,Wei,X.H.&Yan,J.H.Impacts of eucalyptus(Eucalyptus exserta)

plantation on sediment yield in Guangdong province,southern China-a kinetic energy approach.Catena49,231–251(2002).

38.Wilk,J.,Andersson,L.&Plermkamon,V.Hydrological impacts of forest

conversion to agriculture in a large river basin in northeastThailand.Hydrol.

Process.15,2729–2748(2001).

39.Peng,S.S.et al.Afforestation in China cools local land surface temperature.

Proc.Natl https://www.sodocs.net/doc/c213923869.html,A111,2915–2919(2014).

40.Oldekop,E.M.On the evaporation from the surface of river basins.Trans.

Meteorol.Obs.Univ.Tartu4,200(1911).

41.Pike,J.G.The estimation of annual runoff from meteorological data in a

tropical climate.J.Hydrol.12,2116–2123(1964).

42.Federer,C.A.&Lash,D.Brook:A Hydrologic Simulation Model for Eastern

Forests.NH,Research Report19,84(Water Resources Research Center,

University of New Hampshire,1978).

43.Vo¨ro¨smarty,C.J.,Federer,C.A.&Schloss,A.L.Potential evaporation

functions compared on US watersheds:possible implications for global-scale water balance and terrestrial ecosystem.J.Hydrol.207,147–169(1998). Acknowledgements

Funding for the study was provided by the projects of NSFC41430529and

XDA05050200.The study was administrated by CERN(Chinese Ecosystem Research Network).

Author contributions

G.Z.designed the study,proposed the scienti?c hypothesis,analysed the formula and wrote the paper.X.W.proposed the scienti?c hypothesis and wrote the paper.X.C. discussed the scienti?c hypothesis,collected and analysed the data and drew the?gures. P.Z.analysed the formula and discussed the scienti?c hypothesis.X.L.and Y.X.collected and analysed the data.G.S.and D.F.S.reviewed the manuscript and gave some com-ments.S.Z.calculated the performance data of the formula.L.H.calculated the global-based m values.Y.S.collected the global in situ time-trends’hydrological data. Additional information

Supplementary Information accompanies this paper at https://www.sodocs.net/doc/c213923869.html,/ naturecommunications

Competing?nancial interests:The authors declare no com PET ing?nancial interests. Reprints and permission information is available online at https://www.sodocs.net/doc/c213923869.html,/ reprintsandpermissions/

How to cite this article:Zhou,G.et al.Global pattern for the effect of climate and land cover on water https://www.sodocs.net/doc/c213923869.html,mun.6:5918doi:10.1038/ncomms6918(2015).

Global pattern for the effect of climate and land cover on water yield (1)(1)

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