A distributed eco-hydrological model and its application

Zong-xue Xu*,Lei Li,Jie Zhao

aCollege of Water Sciences,Beijing Normal University,Beijing 100875,China

bBeijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology,Beijing 100875,China

cBureau of Hydrology,Ministry of Water Resources of China,Beijing 100053,China

1.Introduction

Eco-hydrology was described as an independent discipline for thefirst time at the International Conference on Water and the Environment in Dublin,Ireland,held from January 26 to 31,1992.Studies on eco-hydrological processes in arid regions,whose spatial heterogeneity leads to complex and little described eco-hydrological processes,have received broad attention in thefields of hydrology and water resources recently(Vertessy et al.,1996;Moret et al.,2007).The ecological and hydrological characteristics of arid and semiarid areas have changed due to fragile ecological environments,water resources shortages,and intense disturbance by human activities.

However,the interplay between vegetation and water is insufficient in hydrological models,and most previous studies have only emphasized the importance ofhydrological processes or ecosystems independently,while the connection between ecological systems and hydrological processes has been neglected.In the traditional hydrological models,the effects of vegetation ecosystems on hydrological processes are usually generalized as an empirical parameter,the value of which isfixed at spatial and temporal scales.In the current ecological models,hydrological processes are mainlyconceptualized in terms of vertical processes of the soilvegetation-atmosphere continuum(SPAC)and water movement in the soil,and the water interaction between plant roots and soil zone interface cannot be described in detail(Xu and Zhao,2016;Zhao et al.,2015).For soil water simulation,the unsaturated zone is generally conceptualized as a reservoir,and water is generally simulated according to the principle of the water balance.In fact,hydrological processes in nature are closely related to the ecological processes of the land,while most hydrological models or ecological models are used to simulate hydrological and ecological processes independently.

With the development of computer science,remote sensing,and geographic information systems,and especially the improvement of earth observation system technology and digital simulation technology,eco-hydrological models have received more attention recently.At present,eco-hydrological models can be divided into two categories:loosely coupled models with ecological and hydrological simulation results,and one-way coupling models of the hydrological or ecological system.In order to reflect the relationship between water and ecology as a whole,two-way coupling of the water cycle and plant growth was realized in this study using a distributed eco-hydrological model,the ecology module for a grid-based integrated surface and groundwater model(Eco-GISMOD),which was developed to simulate eco-hydrological processes by considering the interaction between vegetation and water in different soil layers.Ecological and hydrological processes are synchronized in Eco-GISMOD through a series of processes of exchanges of water and energy between vegetation and soil,providing a new method for investigating eco-hydrological processes at the river basin scale.

2.Model description

Based on Eco-GISMOD,a new distributed ecohydrological simulation system with a three-soil layer structure was developed using modular technology and distributed data management.It includesfive modules:preprocessing,interpolation,evapotranspiration estimation,runoff simulation,and eco-simulation(including natural plants and crops).The model can be executed independently without another platform.Basic data of runoff generation,such asflow direction,simulation sequence,and potential evapotranspiration,are identified in the preprocessing and interpolation modules first.Then,the water allocation and movement of each layer are estimated on the basis of plant transpiration,ground evaporation,and precipitation intercepted by plants.Correspondingly,the dynamic characteristics of leaf area index for different natural vegetation types are computed according to the water requirements and water consumption for each type of vegetation in Eco-GISMOD.

2.1.Preprocessing

The pre-processing module is used to delineate the river basin and to extract the drainage networks automatically from the digital elevation model(DEM)data(Li et al.,2013).This module has various functions,such as flow direction definition,flow accumulation calculation,and drainage network generation,and the order of runoff simulation can be analyzed conveniently using a special approach(Xu,2009).

2.2.Interpolation

The Thiessen method,gradient plus inverse distance squared method(GIDS),and inverse distance squared method(IDS)were used in the model for spatial interpolation(Nalder and Wein,1998;Teegavarapu and Chandramouli,2005).

2.3.Evapotranspiration estimation

Eco-GISMOD integrates eight methods(Allen et al.,1998;Hargreaves and Samani,1985;Priestley and Taylor,1972;Turc,1961)to estimate potential evapotranspiration(PET)and also to enable users to import their own PET data.

Actual evapotranspiration(AET)can be assumed to be present,depleting water in the root zone of the soil(Beven et al.,1995;Kennen et al.,2008),and is expressed as a simple function of PET and the water content of the surface layer.

2.4.Runoff simulation

There are two types of grids in the runoff simulation module:the ordinary grid,which is vertically discretized into three layers:the surface layer,soil layer,and groundwater layer;and the river grid,which looks like a single reservoir for channel routing.In an ordinary grid,each portion of the outflow pours into its corresponding parts when the downstream grid is also an ordinary grid.Otherwise,yielding water will come together as streamflow into the river grid,then move among these river grids and eventually drain out of the watershed(Fig.1).In Fig.1,R is the daily precipitation,E is evapotranspiration,Qr0is the inflow from the upstream neighboring surface layer,Qr1is the inflow from the soil layer,Qr2is the inflow from the groundwater layer,Qr3is the inflow of river grid,Qs1is the saturation excessflow,Qs2is the infiltration excessflow,Qb0is the recharge flow from the soil layer,Qb1is rechargeflow from the groundwater layer,Qc0is the lateral outflow of the surface layer,Qc1is the lateral outflow of the soil layer,Qc2is unconfined groundwater flow,Qc3is confined groundwaterflow,Qx0is the infiltration flow of the surface layer,Qx1is the infiltration flow of the soil layer,Qout0is the outflow of surface layer,Qout1is the outflow of the soil layer,Qout2is the outflow of the groundwater layer,and Qout3is the discharge of river grid.

Fig.1.Runoff generation structure.

It is assumed that evapotranspirationfirst takes place in the surface layer.The amount of water used for evapotranspiration is mainly dependent upon the water content of the surface layer.If there is no water in the surface layer,water from the soil layer will be supplied to the surface layer.

2.5.Eco-simulation

Plants are crucial in terrestrial hydrological cycles,with their leaves playing key roles during plant development in terms of their functions of photosynthesis and transpiration,but soil moisture,solar radiation,and nutrient elements restrain the plant growth.

In Eco-GISMOD,the simplified crop growth modules of the environmental policy impact climate(EPIC)model,which was developed by Jimmy Williams from Texas A&M University(Williams et al.,1989),is coupled with a new kind of distributed hydrological model(Li et al.,2015)through two key parameters:leaf area index and soil moisture.It is assumed that the concentration of carbon dioxide in the air is constant,and the plant growth is not restricted by the root system and nutrient substance.The main limiting factors of plant growth are temperature and soil moisture in the model.Suitable temperature and rainfall promote plant growth and development,which increase the leaf area,leading to a larger amount of precipitation interception,leaf evaporation,and transpiration,and a decrease in the soil infiltration.Conversely,the deficiency of soil water restricts plant growth and yield.

2.5.1.Natural plants

There are two kinds of natural plants in the model,forest and grass.Their plant roots absorption is different from one another due to the root distribution functions.Forests can fully use the water in the soil with a developed root system,but grass can only uptake water from the surface soil.

First,the daily cumulative effective heat(heat unit,simplified as N)is computed according to the daily maximum and minimum temperature,and the plant growth reference temperature.

Then,the possible daily increase of biomass is estimated based on energy-biomass conversion parameters,the day length,latitude and longitude,and effective photosynthesis radiation,which are obtained from the relationship between solar radiation and the leaf area index.

Third,the impact of soil moisture and temperature is considered,and the greatest impact factor is selected as the plant growth-limiting factor.

The heat unit formula is as follows:

where i is number of days;j is the plant type;Tmaxand Tminare the daily maximum temperature and minimum temperature,respectively;and Tbaseis the minimum temperature required for plant growth.

The heat unit index(Z),which reflects the status of plant development throughout the growing season,can be obtained by comparing N and the total heat for plant needs from growth to maturity(M).The formula is as follows:

Plant growth is also closely related to solar radiation.The photosyntheticallyactiveradiation(X,MJ·m-2·d-1)intercepted byplantscanbecalculatedfromsolarradiation(S,MJ·m-2·d-1)and leaf area index(I)according to Beer's Law:

Daily increased biomass(ΔB,kg·d-1)is affected by X,and the energy-biomass conversion parameter(E,kg·MJ-1):

where D is day length(h)and ΔD is the change in day length(h·d-1),which is computed as

where L is the latitude(o)and V is the daily solar elevation angle(o):

The final increased daily biomass(ΔF,kg·d-1)is mainly affected by the daily plant stress index(G)and ΔB:

2.5.1.1.Leaf area index

Leaf surface is the most direct and rapid channel for changing the substance and energy between plants and the environment,and is involved in ecosystem water circulation through evapotranspiration and interception(Running and Coughlan,1988;Tian et al.,2003;Wasseige et al.,2003).In Eco-GISMOD,rainfall is divided into two parts.One part is net rainfall that falls into the soil,and the other part is what is intercepted on the leaf surface,and will evaporate quickly.Therefore,leaf area index is a very important indicator for estimating and evaluating the water consumption of vegetation.The leaf area index is estimated for growing and declining periods individually.

(1)Growing period:

Plants are considered in the growing period when the heat unit is less than or equal to 1(Zi≤ 1）,the leaf area index of which is computed as

where Iiis the leaf area index of day i,Imaxis the maximum leaf area index,ΔI is the variation of the leaf area index,and ΔU is the variation of the heat unit factor(U),which is calculated as follows:

The default values of θ1and θ2are set as 6.5 and 10 in this formula,respectively,which can be modified under different situations.

G ranges between 0 and 1 in the model,which considers the effect of soil moisture and temperature on plant growth,but ignores the impact of nitrogen,phosphorus,and root development.The formula is as follows:

where Ws，iis the water stress factor of day i,and Ts，iis the temperature factor of day i.

As one of the key limiting factors in the vegetation,Ts，iis obtained from the following formula:

where Tg，jis the average temperature required for the growth of plant j(°C),Tb，jis the basic temperature for the growth of plant j(°C),and To，jis the optimum temperature for the growth of plant j(°C).

Another limiting factor,Ws，i,is determined by the relationship between the available water supply from the soil layer(Wsupply，i）and the water requirement of the plant(Wdemand，i）.Wswill be 0 if Wsupply，iis greater than Wdemand，i.Otherwise,Ws，iis computed as follows:

where h0is the height of the soil layer(m);Agis grid area(m2);Sais the actual water content of soil;k0is the hydraulic conductivity of the soil layer(m3·d-1);Peis the potential evaporation;and j0is a factor that depends on the relationships between Sa,the critical soil water content(Sc),and the wilting point of the soil water content(Sw):

where v is an empirical coefficient,the value of which is between 0.80 and 0.95.The available water supply comes mainly from the soil layer when the plant type is forest,and from the surface layer when the plant type is grass.(2)Declining period:

Plants are regarded as in the declining period when the heat unit index is greater than 1(Zi＞1）,the leaf area index of which is computed as

where I0and Z0are the corresponding values of leaf area index and heat unit index when plants begin declining,and Cjis the fading rate of plant j.

2.5.1.2.Dry matter

The quality of dry matter from growth to maturity is determined by the plant harvest index of day i(Ai):

(1)Without considering water shortage:

where Hjis the harvest index of plant j during the whole growth period,and Ukis the heat unit factor of day k.

(2)Considering water shortage:

where Yjis the drought sensitivity index of plant j and Wirepresents the water consumption on day i:

Finally,the harvested dry matter from growth to maturity Ydis obtained as follows:

where n is the total number of days.

2.5.2.Crops

In contrast to natural plants,crops mainly depend on irrigation,and their growth and development have regularity.For instance,spring wheat is sown in the middle of March,and harvested in May or June.The water consumption of summer corn from jointing to heading periods accounts for 65%of the whole growth period.However,summer corn is usually sown in May and harvested in September or October.The water consumption of each growth stage is not very different.

According to the characteristics of different crop types,the crop water consumption is estimated by combining the crop coefficient method and potential evapotranspiration method.The crop growth period is divided into four stages(seeding,jointing,heading,and maturity),and the water consumption of each stage can be obtained by multiplying the potential evapotranspiration by the crop coefficient.

2.5.2.1.Leaf area index

Variation of the crop leaf area is simulated by the photosynthesis module of the crop,which is a kind of terrestrial net primary productivity(NPP)estimation model developed by Huang et al.(2006).The formula is as follows:

where Jiis the ratio of yellow leaves to green leaves on day i,Kiis the transfer coefficient of photosynthetic products(0-0.48 for spring wheat,and 0-0.54 for corn)on day i,Pn，iis the net photosynthesis on day i,and Slis specific leaf area(m2/g).

The photosynthetic products are not transferred to the leaf surface during the heading and maturity period.The leaf area index can be computed as follows:

where δ and ε are key parameters that are determined by crop type and soil moisture,with values ranging from 0 to 8 and 0.5 to 1.0,respectively;and O is the standard fertility index:

where Atis the effective accumulated temperature from planting to harvesting(°C),B is the initial air temperature of crop growth(°C),Tiis daily mean temperature on day i(°C),and x is the cumulative number of days from sowing.

2.5.2.2.Actual water consumption

Water consumption of crop j on day i(Wi，j）is determined by the following formula:

where Ks，jis the coefficient of crop j in the growing stage s;and efis the irrigation efficiency,the value of which can be as low as 0.4 to 0.5 withflood irrigation,but as high as 0.6 to 0.8 with micro-sprinkle irrigation and drip irrigation.

Irrigation water is assumed mainly to be taken from rivers.Therefore,the model requires some water intakes(also called control points),which can be used to calculate the total amount of water consumption in the watershed.

where t is the number of crop types and m is the total number of days of crop growth.

2.5.2.3.Dry matter

Crop dry matter can be obtained without considering water shortage(setting Wsas 0),using the same formula as that of natural plants.

3.Case study

In order to evaluate the performance of Eco-GISMOD,the upper and middle parts of the Heihe River Basin were selected as the study area,where plant growth is severely restricted by seasonaldroughtand watershortage.The period of 1990-1993 was chosen for the case study.The calibration period was set from 1990 to 1992,and 1993 was selected for validation.Observed precipitation and discharge data were provided by the Cold and Arid Regions Environmental and Engineering Research Institute(CAREER)of the Chinese Academy of Sciences.DEM data with 1 km×1 km horizontal resolution was used and other spatial distribution data with the same resolution,such as land use data,soil data,and geological data,were all obtained from the Environmental and Ecological Science Data Center for West China.

3.1.Parameter setting

Requirements for air temperature,solar radiation,and soil moisture vary according to vegetation type and the spatial distribution of each kind of plant.The vegetation was divided intofive types(coniferous forest,broad-leaved forest,shrub,farmland,and grass)from mountainous areas to plains in the Heihe River Basin.The initial values of plant growth parameters were chosen according to the parameters recommended in the EPIC model(Table 1).The values of parameters in the hydrological module were obtained from the results of previous studies(Li et al.,2015).

3.2.Results and discussion

3.2.1.Runoff

The accuracy of runoff simulation plays an important role in plant growth and the development of the eco-hydrological model.Therefore,a river grid near the Yingluoxia Hydrological Station was used to make a comparison with the measured runoff in this study.It can be seen from Fig.2 that Eco-GISMOD reproduces the monthly runoff series with Nash-Sutcliffe efficiency coefficient(NSE)values between 0.88 and 0.93,the corresponding deviation of which ranges from-2.1%to 2.3%.The performances of Eco-GISMOD at theYingluoxia Hydrological Station are acceptable in both the calibration and validation periods.

Table 1 Initial values of plant growth parameters.

3.2.2.NPP

The totalbiomass amountconverted from energy throughout the growth period is calculated by considering the limit factor of plant growth and potential biomass,through subtraction of the self-energy consumption of vegetation.NPP cannot only reflect the production capacity of ecosystems in the natural environment,but is also the key factor in evaluating the quality of the terrestrial ecosystem.

For the purpose of comparison with other study results,we assume that the daily increased biomass is only used for plant growth,development,and reproduction.Other energy consumption was not considered in this study.Therefore,a comparative analysis of the results of Eco-GISMOD,the data obtained from high-resolution Satellite Pour l’Observation de la Terre(SPOT)remote sensing images using the C-FIX model(Lu et al.,2005),and the data calculated from the TESim model(Peng,2007)was used for model validation in this study(Fig.3).In general,results show that the NPP values of shrub, grass, and farmland (223.2, 246.4, and 394.6 g·m-2·year-1)from Eco-GISMOD are close to those of the C-FIX model(268,244,and 364 g·m-2·year-1),but the NPP values of coniferous forest and broad-leaved forest from Eco-GISMOD(29.2 and 91.8 g·m-2·year-1)are much smaller than those calculated by the C-FIX model(266 and 184 g·m-2·year-1).For the TESim model,in addition to the simulated NPP of broad-leaved forest that is close to the result of the C-FIX model(266.7 g·m-2·year-1),there are signifi-cant differences between the C-FIX model and Eco-GISMOD with the other four vegetation types.

Fig.2.Comparison between simulated and observed monthly streamflow at Yingluoxia Hydrological Station.

Fig.3.Comparison of simulated net primary productivity from three models.

Although the results of these three models are different from one another,Eco-GISMOD shows a strong performance of plant growth,especially for shrub,grass,and farmland.For instance,Hu et al.(1994)and Wang et al.(1988)found that the value of NPP of high mountain meadows from the Qilian Mountains varies from 150 to 240 g·m-2·year-1,which is consistent with the results of Eco-GISMOD.Chen et al.(2008)showed that the value of grass NPP ranges from 128 to 370 g·m-2·year-1,based on statisticsofaboveground biomass obtained using the harvesting method.According to the estimation of farmland biomass in arid areas of western China from 1992 to 1998,some studies have pointed out that the value of farmland NPP is about 390.42 g·m-2·year-1(Zhang et al.,2006),which is in accordance with the simulated results of Eco-GISMOD.

Fig.4.Spatial distribution of annual average net primary productivity(units:g·m-2·year-1).

Table 2 Variation of net primary productivity with different simulation conditions.

Spatial distribution of annual average NPP was analyzed in detail(Fig.4).There was a strong relationship between NPP and topography.A high value of NPP is mainly distributed in the middle part of the agricultural oasis.The lower values are mainly found at the southern part of the Qilian Mountains.Without consideration of water stress,the increase of NPP mainly occurs in the middle part of the Heihe River Basin,where it is dominated by grass and shrub(Table 2).The value of NPP of grassland increases significantly,with a range from 41 to 57 g·m-2·year-1,and the NPP increase for shrub is between 6.9 and 17.4 g·m-2·year-1.The broad-leaved forest and coniferous forest experience less water stress,and the values of NPP of these two types of plants change within 3 g·m-2·year-1.

3.2.3.Water productivity

Thewaterproductivitiesofthesefivetypesofvegetationwere compared with those of previous studies,in order to assess the performance of Eco-GISMOD in the simulation of plant growth.Inviewoftheoverallsimulationresults,thewaterproductivityof farmlandishighest,ranging from1.04to1.44kg/m3andwithan average annual value of 1.23 kg/m3.Wu and Hu(2009)also found that the water productivity of crops is between 0.93 and 1.53 kg/m3,based on research in Gansu Province from 1995 to 2007.The water productivity of coniferous forest ranks second,as simulated by Eco-GISMOD,with values changing between 0.19 and 0.41 kg/m3.Through the analysis of a forest plantation in Qinghai Province,Liu et al.(2006)pointed out that the water productivity of Qinghai spruce and larch coniferous forest varies from 0.19 to 0.26 kg/m3,as estimated according to the water efficiency rate(about 44%)and water potential productivity(0.44-0.58 kg/m3).Water productivity of shrub and grassland simulatedbyEco-GISMODisthelowestamongthesevegetation types,with annual mean values of 0.016 and 0.014 kg/m3,respectively.Chen et al.(2006)simulated the water productivity ofartificialgrasslandontheLoessPlateauusingtheEPICmodel.Results show that the water potential productivity of alfalfa and other pasture vegetation is between 0.05 and 0.58 and kg/m3.These facts illustrate that Eco-GISMOD performs well with regard to water productivity simulation,especially for the simulation of crops and coniferous forests.

4.Conclusions

In orderto evaluate the eco-hydrologicalprocesses focusing on water exchange between plants and the surrounding natural environment at a catchment scale,Eco-GISMOD,anew kind ofeco-hydrologicalmodelis proposed.It combines the simplified EPIC model and a new kindofdistributedhydrologicalmodelGISMOD.The advantage of this model is that water interaction between plants and soil water can be simply described by a generalized physical process in various situations.Eco-GISMOD can reflect the plant growth status through leaf area index.Dry matter and the spatial and temporal variations of water exchange can also be estimated using this model.

A case study was carried out in the Heihe River Basin in northwestern China to evaluate the system's performance.The results show that forest and crops generally grow well with enough water supply,but water shortages,especially in summer,inhibit the growth of grass and cause grass degradation.This demonstrates that the simulation system is appropriate for eco-hydrological study in arid and semi-arid areas and will be helpful for the planning and management of water resources in the future.

Allen,R.G.,Pereira,L.S.,Raes,D.,Smith,M.,1998.Crop evapotranspiration:guidelines for computing crop water requirements-FAO Irrigation and Drainage Paper 56.Food and Agriculture Organization(FAO),Rome.

Beven,K.J.,Lamb,R.,Quinn,P.F.,Romanowicz,R.,Freer,J.,1995.TOPMODEL.In:Singh,V.P.(Ed.),Computer models of watershed hydrology.Water Resources Publications,Highlands Ranch,pp.627-668.

Chen,B.,Li,J.,Li,X.F.,2006.Long term simulation of water potential productivity of alfalfa on rain fed highland in south of Loess Plateau.Agric.Res.Arid Areas 24(3),31-35.https://doi.org/10.3321/j.issn:1000-7601.2006.03.006(in Chinese).

Chen,Z.H.,Ma,Q.Y.,Wang,J.,Qi,Y.,Li,J.,Huang,C.L.,Ma,M.G.,Yang,G.J.,2008.Estimation of Heihe Basin net primary productivity using the CASA model.J.Nat.Resour.23(2),263-273.https://doi.org/10.11849/zrzyxb.2008.02.011(in Chinese).

Hargreaves,G.H.,Samani,Z.A.,1985.Reference crop evapotranspiration from temperature.Appl.Eng.Agric.1(2),96-99.https://doi.org/10.13031/2013.26773.

Hu,Z.Z.,Sun,J.X.,Li,Y.,Long,R.J.,Yang,F.L.,1994.The characteristics of biomass and conversion efficiency of solar radiation for principal types of alpine grasslands in Tianzhu,Gansu Province,China.Chin.J.Plant Ecol.18(2),121-131(in Chinese).

Huang,Y.,Wang,Y.,Zhang,W.,Yu,Y.Q.,Wang,P.,2006.Simulating net primary production of agricultural vegetation in China(I):Model establishment and sensitivity analysis.J.Nat.Resour.21(5),790-801.https://doi.org/10.11849/zrzyxb.2006.05.013(in Chinese).

Kennen,J.G.,Kauffman,L.J.,Ayers,M.A.,Wolock,D.M.,Colarullo,S.J.,2008.Use of an integratedflow model to estimate ecologically relevant hydrologic characteristics at stream biomonitoring sites.Ecol.Model.211(1-2),57-76.https://doi.org/10.1016/j.ecolmodel.2007.08.014.

Li,L.,Xu,Z.X.,Li,Y.L.,Liu,W.F.,Zhang,L.Y.,2013.A preprocessing program for a distributed hydrological model:Development and application.J.Hydroinf.15(4),1258-1275.https://doi.org/10.2166/hydro.2013.140.

Li,L.,Xu,Z.X.,Zuo,D.P.,Zhao,J.,2015.A grid-based integrated surfacegroundwater model(GISMOD).J.Water Clim.Change 7(2),296-320.https://doi.org/10.2166/wcc.2015.006.

Liu,S.,He,K.N.,Wang,Z.N.,Chang,G.L.,Li,S.R.,2006.Extinction characteristics of artificial forest in removal lands in Datong of Qinghai Province.Sci.Soil Water Conserv.4(3),59-64.https://doi.org/10.3969/j.issn.1672-3007.2006.03.012(in Chinese).

Lu,L.,Li,X.,Frank,V.,2005.Estimation of net primary productivity of Heihe River Basin using remote sensing.J.Desert Res.25(6),823-830(in Chinese).

Moret,D.,Braud,I.,Arru′e,J.L.,2007.Water balance simulation of a dryland soil during fallow under conventional and conservation tillage in semiarid Aragon,Northeast Spain.Soil Tillage Res.92(1-2),251-263.https://doi.org/10.1016/j.still.2006.03.012.

Nalder,I.A.,Wein,R.W.,1998.Spatial interpolation of climate normals:Test of a new method in the Canadian boreal forest.Agric.For.Meteorol.92(4),211-225.https://doi.org/10.1016/S0168-1923(98)00102-6.

Peng,H.C.,2007.Study on Dynamic Simulation of Ecosystem in Heihe River Basin.Ph.D.Dissertation.Chinese Academy of Sciences,Lanzhou(in Chinese).

Priestley,C.H.B.,Taylor,R.J.,1972.On the assessment of surface heatflux and evaporation using large scale parameters.Mon.Weather Rev.100(2),81-92.https://doi.org/10.1175/1520-0493(1972)100＜0081:OTAOSH＞2.3.CO;2.

Running,S.W.,Coughlan,J.C.,1988.A general model of forest ecosystem processes for regional applications,I:Hydrologic balance,canopy gas exchange and primary production processes.Ecol.Model.42(2),125-154.https://doi.org/10.1016/0304-3800(88)90112-3.

Teegavarapu,R.S.V.,Chandramouli,V.,2005.Improved weighting methods,deterministic and stochastic data-driven models for estimation of missing precipitation records.J.Hydrol.312(1-4),191-206.https://doi.org/10.1016/j.jhydrol.2005.02.015.

Tian,Y.H.,Wang,Y.J.,Zhang,Y.,Knyazikhin,Y.,Bogaert,J.,Myneni,R.B.,2003.Radiative transfer based scaling of LAI retrievals from reflectance data of different resolutions.Rem.Sens.Environ.84(1),143-159.https://doi.org/10.1016/S0034-4257(02)00102-5.

Turc,L.,1961.Estimation of irrigation water requirements,potential evapotranspiration:A simple climatic formula evolved up to date.Ann.Agron.12(1),13-49.

Vertessy,R.A.,Hatton,T.J.,Benyon,R.G.,Dawes,W.R.,1996.Long-term growth and water balance predictions for a mountain ash(Eucalyptus regnans)for catchment subject to clear-felling and regeneration.Tree Physiol.16(1-2),221-232.https://doi.org/10.1093/treephys/16.1-2.221.

Wang,Q.J.,Yang,F.T.,Shi,S.H.,1988.A preliminary study on the formation of underground biomass in alpine meadow.In:Proceedings of the International Symposium Alpine Meadow Ecosystem,pp.73-80(in Chinese).

Wasseige,C.D.,Bastin,D.,Defourny,P.,2003.Seasonal variation of tropical forest LAI based onfield measurements in Central African Republic.Agric.For.Meteorol.119(3-4),181-194.https://doi.org/10.1016/S0168-1923(03)00138-2.

Williams,J.R.,Jones,C.A.,Kiniry,J.R.,Spanel,D.A.,1989.The EPIC crop growth model.Transactions of the ASABE 32(2),497-511.https://doi.org/10.13031/2013.31032.

Wu,J.X.,Hu,G.L.,2009.Interannual change on water productivity of crop irrigation in Gaotai County.Developing(8),116-117(in Chinese).

Xu,Z.X.,2009.Hydrological Models.Science Press,Beijing(in Chinese).

Xu,Z.X.,Zhao,J.,2016.Development and applications of eco-hydrological models:Past and future.J.Hydraul.Eng.47(3),346-354.https://doi.org/10.13243/j.cnki.slxb.20151160(in Chinese).

Zhang,J.,Pan,X.L.,Gao,Z.Q.,Shi,Q.D.,Lu¨,G.H.,2006.Satellite estimates and change detection of net primary productivity of oasis-desert based on ecosystem process with remotely sensed forcing in arid western China.Acta Geograph.Sin.61(1),15-25.https://doi.org/10.11821/xb200601002(in Chinese).

Zhao,J.,Xu,Z.X.,Zuo,D.P.,Wang,X.M.,2015.Temporal variations of reference evapotranspiration and its sensitivity to meteorological factors in Heihe River Basin,China.Water Sci.Eng.8(1),1-8.https://doi.org/10.1016/j.wse.2015.01.004.