Agroforestry Systems 60: 277–289, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands.
277
Modelling species and spacing effects on root zone water dynamics using Hydrus-2D in an Amazonian agroforestry system P. Schlegel1, B. Huwe1,* and W.G. Teixeira2 1
Soil Physics Group, Universität Bayreuth, 95440 Bayreuth, Germany; 2Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA) – Amazonia Occidental, Manaus, Caixa Postal 319, 69011-970-Manaus, Brazil; *Author for correspondence (e-mail:
[email protected]) Received 15 november 2003; accepted in revised form 17 september 2003
Key words: Bactris gasipaes, Model scenarios, Plant spacing, Pueraria phaseoloides, Root distribution, Theobroma grandiflorum
Abstract Modelling the root zone water dynamics in a tree crop agroforestry system is a useful approach to understanding small-scale effects in tree crop systems and may be helpful for optimizing tree spacing in agroforestry system planning. The agroforestry system in this study consists of the species Theobroma grandiflorum 共Willd ex Spreng兲 Schum 共Cupuaçu兲, Bactris gasipaes H.B.K. 共peach palm兲 and the cover crop Pueraria phaseoloides 共Roxb.兲 Benth 共Pueraria兲. The soiltype is an oxisol. Calibration was conducted for each of the three species separately. Calibration results show good conformity between simulated and measured data. Simulated scenarios examine the influence of different spacing between trees on root water uptake, evaporation and drainage. Mean interception and crop factors of the whole flow region vary with spacing or are held constant to examine below-ground effects only. Also a fictitious scenario of an older agroforestry system with deeper roots is calculated. In order to overcome restrictions of the computer program Hydrus-2D, correction factors in the root zone were introduced and a calculation scheme for root water uptake of a flow subregion was developped. Below-ground effects of spacing between trees are not or almost not present, but the depth of the tree roots has a significant influence on root water uptake, evaporation and drainage. When mean interception and crop factor vary, drainage increases and root water uptake decreases slightly with spacing. The modelling approach has been found promising for optimizing agroforestry systems although it can only be seen as a first beginning. In an agroforestry systems under drier conditions differences in results will probably be larger.
Introduction The Amazon region still contains the world’s largest area of tropical rain-forest 共Klinge et al. 1981兲, although it is constantly reduced by deforestation 共Ministery of Science and Technology, 2001; Nepstad 1999兲. This is in a large part due to the establishment of pastures and shifting cultivation by small farmers 共Diegues 1992兲. The destruction of rain forest has many adverse effects on the environment among which are disturbances of the regional and continental water balance, but also a contribution to
the global greenhouse effect 共Fearnside 1985; Fearnside 1988兲 and loss of biodiversity. The Amazon rain forest is rich of biomass and species, but stands mainly on extremely poor soils, which are not able to store large amounts of nutrients 共Fittkau 1990兲. A large part of nutrients is stored in the biomass of the tropical forest and are lost to a great extent when plants are removed to give way to agricultural land use systems 共Fearnside 1985兲. Agroforestry systems are closer to the rain forest than conventional agriculture or pasture systems with respect to their structure and ability to store nutrients in
278 biomass and therefore are a promising form of land use in the Amazon region 共Diegues 1992兲. Some important institutions working intensively with agroforestry modelling are the Cranfield University Silsoe 共models CUPPA-Tea 共Matthews 2001a兲 and HyCAS 共Matthews 2001b兲兲, the Centre for Ecology and Hydrology Edinburgh 共Simile 共Muetzelfeldt 2001兲 and HyPAR 共Matthews and Hunt 2002兲兲 and the International Centre for Research in Agroforestry 共SeXI-FS 共Vincent 2001兲 and WaNuLCas 共Noordwijk and Lusiana 2000兲兲. Moreover there exist the widelyapplicable hydrological models like Hydrus-2D 共Simunek et al. 1999兲 or WaSim water balance model 共Hess and Angood 2002兲 which focus on belowground interactions. In the following study data from SHIFT 共Studies on Human Impact on Forest and Floodplains in the Tropics兲 are used to model the water dynamics in an agroforestry system near Manaus with help of the computer program Hydrus-2D 共Simunek et al. 1999兲. Performing a water balance simulation is of special interest as water is the most important growth factor in any agroforestry system and as nutrient uptake is directly linked to it. Water fluxes in the root zone are examined putting special emphasis on the influence of spacing on the water balance. It is a modelling approach towards better understanding of root zone interactions and improved agroforestry experiment design, which in the end should lead to better water use and corresponding nutrient use efficiency in agroforestry systems under use and derivation of optimal spacing between trees.
Material and Methods Field studies The study site was cleared of primary forest in 1980 and an experiment with rubber tree conducted until 1986. The then developping secondary vegetation was cleared in 1992 and the actual experimental plot consisting of agroforestry systems and monocultures established hereafter. We focused in our simulations exemplary on an agroforestry system consisting of Theobroma grandiflorum (Willd ex Spreng) Schum 共Cupuaçu兲 and Pueraria phaseoloides (Roxb.) Benth. 共Pueraria or tropical kudzu兲. Calibration for the model was conducted with data from the monocultures of Cupuaçu and Bactris gasipaes H.B.K. 共Pupunha or peach palm兲 with pueraria growing between trees.
Planting density were 7 ⫻ 6.4 m for Cupuaçu and 2 ⫻ 2 m for Pupunha. Weather and soil data were obtained from the research station of EMBRAPA 共Empresa Brasileira de Pesquisa Agropecuária兲 – Amazonia Ocidental 共38' S, 5952' W, 40 to 50 m a.s.l.兲 near Manaus. The site is characterized as hot, tropical rain forest with more than 60 mm rain per month during all seasons 共after Köppen as presented in Critchfield, 1983兲. Mean annual precipitation of the years 1971 to 1997 is 2530 mm 共Correia and Lieberei 1998兲. The soil is a Xanthic Ferralsol 共FAO兲 with a clay content of upto 80 % 共Schroth et al. 2000兲. Solar radiation, net radiation, dry and wet temperature, soil temperature in three depths, humididty, wind speed, wind direction and precipitation were monitored by an automated station 共Didcot UK兲 on at least hourly interval. Additionally daily minimum, mean and maximum temperature, relative humidity, mean wind speed and precipitation were provided from a conventional weather station. Selected parameters both from conventional and automated weather station were used, whereby preference was given to the automated station as it was nearer to the plot. Implausible values of the automated station were filtered. Data gaps due to device problems were filled by either using the values of the previous or following year or by periods of the same year with similar weather. Evapotranspiration was calculated using FAO-Penman-Monteith: 0.408 䉭 共Rn ⫺ G兲 ⫹ ␥ ET0 ⫽
900 T ⫹ 273
䉭 ⫹ ␥共1 ⫹ 0.34u2兲
u2共es ⫺ ea兲 共1兲
Soil water content was measured using TDR-technique in the according monocultures for Theobroma grandiflorum 共Willd ex Spreng兲 Schum and Bactris gasipaes H.B.K. and for Pueraria phaseoloides 共Roxb.兲 Benth. in an agroforestry system and in the said monocultures. Out of six measurements for each species mean values were calculated in the case that not more than three values were missing. Modelling Water flow in Hydrus-2D is considered to be a twodimensional isothermal Darcian flow in a variably saturated medium, and it is assumed that the air phase
279 Table 1. Particle size distribution 共for the particle classes sand, silt and clay percentage兲 and bulk density 共bd兲1, used as input parameters for the soil hydraulic properties prediction tool Rosetta2 in an agroforestry system near Manaus, Brasil. depth
sand
silt
clay
bd
0-20 20-40 40-90 90-
23.7 15.2 12.5 11.8
11.8 11.9 11.0 17.3
64.5 73.0 76.6 70.9
1.04 1.02 0.98 1.00
1
Modified from Teixeira, 2001;2Source: Schaap, 2001.
plays an insignificant role. The governing flow equation is given by the modified Richard’s equation, wherein the root water uptake is specified as a sink term 共Simunek et al. 1999兲. ⭸ ⭸t
⫽
⭸ ⭸xi
冋冉
K KAij
⭸h ⭸x j
⫹ KizA
冊册
⫺S
共2兲
The partial differential equation is solved by a finite element method. The discretization of the model area is done by a triangular grid; the intersections of adjoined triangles are referred to as nodes. Soil heterogeneity was modelled implementing four layers with different soil hydraulic parameters. These parameters are part of the applied soil hydraulic function of van Genuchten 共1980兲 关in Simunek et al. 1999兴 for the calculation of water content at a given pressure head. Starting from soil particle size analysis conducted by Teixeira, 2001 the coarse and fine sand fractions were combined and original discontinous data were smoothed in order to get a continuous depth profile and to avoid numerical problems. Out of these aggregated data, groups with similar particle size distribution and bulk density were made up 共Table 1兲. Out of these texture data, van Genuchten parameters and Ks were calculated with the network prediction tool Rosetta 共Schaap 2001兲. Initial conditions of water content were set to 0.36 at the top and 0.54 at the bottom with a linear depth distribution. Upper boundary was specified as atmospheric, lower boundary as free drainage. Atmospheric boundary conditions are daily values of precipitation, evaporation and transpiration rate. Precipitation is rain as measured by the weather station reduced by water interception percentage. Evapotranspiration is split into evaporation 共20%兲 and transpiration 共80%兲. Hints for this assumption gave FAO56, who stated that the evaporation of an annual
crop lies between 100% at the beginning of the growing period and 10% at the stage of fullest leaf development. The leaf area index 共LAI兲, which highly influences the ratio between evaporation and transpiration, varies according to Allen et al., 1998 between 0 and 4.5 dependent on season in an annual crop. The LAI for decidous trees varied in experiments of Martens et al., 1993 between 2.1 and 6.6 共with a mean of 3.8兲 dependent on applied method. As the leaf area index of the agroforestry system in this study is likely to be in the same order as the LAI of the annual crop in Allen et al., 1998 and as the optimum of fully developed leafs probably is not given throughout the whole year, 20% evaporation was assumed to be a reasonable number. Transpiration 共as calculated from evapotranspiration兲 is multiplied with the crop factor before application in Hydrus-2D. Observation nodes were set at 10, 30, 90 and 150 cm depth as for these depths water contents were measured. At observation nodes simulated water content per time step is given out by Hydrus-2D. Soil profile depth was chosen 160 cm to exclude bottom boundary effects; profile width was 10 cm. Calibration was done for each of the three plants separately starting with Pueraria 共Pueraria phaseoloides兲 and using the described soil and boundary conditions as well as the following plant parameters. Plant and soil parameters are adjusted during the calibration process. The influence of different discretization schemes on simulated water content was checked examplary with Pueraria. Hints for a possible root density distribution were given by measurements from Haag, 1997. He examined root dry matter concentration of live and dead fine roots for Cupuaçu 共Theobroma grandiflorum兲 and Pupunha 共Bactris gasipaes兲. As the root water uptake is directly linked to the absorbing surface of the root system 共Larcher 1994兲, which is mainly constituted by living fine roots, weighting factors proportional to root dry matter concentration could be extracted 共see Table 2兲. Weighting factors are only in order to weight between different root zones of different water uptake activity and cannot be compared between species; they are dimensionless. For Pueraria rooting depth is assumed to be 10 cm. As discretization is chosen to be 10 cm, a homogenous root density distribution with the factor b⫽1 is assumed for Pueraria. Vo et al., 1998 examined the spatial root distribution of four tropical tree plant species including Cupuaçu, but not Pupunha. Table 3 shows observed
280 Table 2. Root weighting factors between depth increments for the three sprecies Cupuaçu 共Theobroma grandiflorum兲, Pupunha 共Bactris gasipaes兲 and Pueraria 共Pueraria phaseoloides兲 in an agroforestry system near Manaus, Brazil. depth
Cupuaçu
Pupunha
Pueraria
0-10 10-20 20-30 ⬎ 30
3.2 0.5 0.5 ⬍ 0.1
3.4 0.7 0.7 ⬍ 0.3
1
Deductions for enhancements of Hydrus-2D
Table 3. Root geometry for Cupuaçu 共Theobroma grandiflorum兲 in an agroforestry system near Manaus, Brazil: Mean maximal root extension from the stem to the left and right side1, herof calculated mean diameter and rounded values for depth increments with a root density factor ⬎ 0.1. depth
left 共cm兲 right 共cm兲 sum 共cm兲 rounded 共cm兲 factor
0-10 10-20 20-30 30-40 40-50 ⬎ 50
26 38 28 15 16 9
34 23 16 20 6 0
60 61 44 34 22 9
60 60 40
10 to 20 %. Parameters governing the ratio actual to potential root water uptake in dependence on soil pressure head were accepted as suggested by Hydrus2D.
3.2 0.5 0.5 ⬍ 0.1 ⬍ 0.1 ⬍ 0.1
Plant Transpiration for different crops within one simulation As in Hydrus-2D there does not exist the possibility to define different crop factors within one flow region, a mean transpiration rate was calculated and applied and correction factors in the root zone, which account for this deficit, introduced. There exist n subregions ⍀i on which different crops with different crop factors cfi are grown 共see Figure 1兲. The length of the transpiring surface for each subregion is Lti The transpiration rate Tpi of each subregion and the transpiration of the whole flow region Vtot are related by: Tpi ⫽ c fiTp
共3兲
1
Source: Voß et al., 1998.
Vtot ⫽ horizontal root extension from the stem, total extension and rounded numbers in order to make data fit into the discretization scheme. As below 30 cm depth the amount of living fine roots was small, root geometry of Cupuaçu was reduced to 30 cm depth. Rooting depths of Pupunha were adjusted within calibration. The crop factor 共cf兲 for cacao 共Theobroma cacao L.兲, a close relative to Cupuaçu, lies according to Allen et al., 1998 between 1.00 and 1.05; 共cf兲 for the other two species are not listed. The crop factor for Pueraria was estimated to be 1. The crop factor indicates the difference in evapotranspiration between a special crop and the reference evapotranspiration 共defined as a surface of green grass兲 共Allen et al. 1998兲. Schroth et al., 1999 examined rain water partitioning in the SHIFT agroforestry systems and monocultures by substracting measured throughfall from open rainfall. Throughfall as percentage of open was measured at 40 and 150 cm from stems for Cupuaçu and Pupunha 共Table 4兲. As soil water contents were measured at 40 cm, interception values of the same distance are used. According to Table 4 Pupunha has an interception of 40 to 50 %, but has a relatively high stemflow contributing to plant rain water supply. Cupuaçu intercepts
n
兺 cfiLtiTP
or
i⫽1
Vtot ⫽ c fmLtTP
共4兲 共5兲
A mean crop factor cfm is determined and used for calculation of the transpiration rate Tp, which is input parameter for the simulations. cfm ⫽
1
n
兺 c f Lt Lt i⫽1 i
i
共6兲
Deduction of the correction factors r1 and r2 is given in the appendix. Also the calculation scheme for root water uptake of a subregion can be found there. Scenarios Different scenarios were established to examine the influence of different plant spacing on water dynamics. Plant spacing in our study refers to spacing between root bodies and can be compared to the free inter-row width. These scenarios consist of deeprooted Cupuaçu trees and the cover crop Pueraria with its relatively shallow roots. Spacings were 30 cm, 50 cm and 90 cm.
281 Table 4. Throughfall of Pupunha 共Bactris gasipaes兲 and Cupuaçu 共Theobroma grandiflorum兲 in poly- and monoculture as percentage of open rainfall in an agroforestry system near Manaus, Brazil, in 40 and 150 cm distance from the stem and stemflow1.
Pupunha fruit
polyculture monoculture polyculture monoculture
Cupuaçu
40 cm 共% of open兲
150 cm 共% of open兲
stemflow 共l/mm兲
61.9 50.3 95.4 82.1
90.5 63.0 97.4 98.5
1.80 1.48 0.13 0.12
1
Source: Schroth et al., 1999.
Figure 1. Subregions of the flow domain in an agroforestry system near Manaus, Brazil: Theobroma grandiflorum 共index ⫽ 1兲 and Pueraria phaseoloides 共index ⫽ 2兲, corresponding depth increments di,j and subsubregions ⍀i,j.
Interception and crop factor, which influence rain and transpiration rate, should be unique for each crop, but in Hydrus-2D it is only possible to implement one set of atmospheric boundary conditions in which rain, evaporation and transpiration rate are defined. Thus a mean interception percentage was calculated as a weighted mean value according to
Im
n 兺 i L t Ii ⫽ i
Lt
共7兲
Also correction factors to account for different crop factors were introduced in the root zone and their value derived 共see ‘Deductions for Enhancements of Hydrus-2D’ and appendix兲. In order to calculate the actual and cumulated root water uptake per plant, which is not given by Hydrus-2D, a method to calculate the root water uptake of a subregion was developped 共see appendix兲. With increasing distance between Cupuaçu trees, the rain reaching the soil surface is increasing and the potential transpiration is decreasing. The question is now whether the reduced amount of water in a system with narrow spacing can be made up for by a possible better soil water use efficiency through higher amount of deep roots in the system. Four blocks with different assumptions are simulated for the spacings 10, 30, 50, 70 and 90 cm: In Block 1 共‘Real’ Agroforestry System兲 the agroforestry system in its actual 共⫽initial兲 state is mod-
elled as close to reality as possible; mean interception and mean crop factor vary according to spacing. In Block 2 共‘Real’ Agroforestry System Subregion兲 the root water uptake of the middle Cupuaçu tree of Block 1 is calculated 共only spacings 10, 50, 90 cm兲. In Block 3 共‘Only-Root-Effects’ System兲 interception and crop factor are held constant in order to separate the below-ground from the above-ground interactions and root water uptake is simulated. It means that atmospheric conditions remain constant and only spacing between root bodies varies. If the model output shows differences in this block, spacing has an influence on root water uptake already by root effects. In Block 4 共‘Deep-Roots’ System兲 Cupuaçu roots of the ‘Only-Root-Effects’ System are enlarged into depth to see how water dynamics of the agroforestry system, which is in its initial stage, might develop 共only spacings 10 and 90 cm兲. Atmospheric conditions were held constant at the same values as in block 3. Soil layers are defined according to calibration results. Initial and boundary conditions as well as Feddes-Parameter and potential evaporation are set as described in Modelling. For the ‘Real’ Agroforestry System a mean precipitation, respectively interception is calculated according to 共7兲. A mean crop factor is calculated analogous to 共7兲. For the ‘Only-RootEffects’ System and the ‘Deep-Roots’ System the reduced rain 共1 minus interception兲 is 0.8 and the crop factor is 1.1. Root density factors for the systems with shallow roots are applied as shown in Table 5 where
282 Table 5. Root density factors for Cupuaçu 共Theobroma grandiflorum兲 and weighting factor for Pueraria 共Pueraria phaseoloides兲 in an agroforestry system near Manaus, Brazil, root geometry for Cupuaçu as diameter in cm and number of nodes in the discretization scheme for the scenarios, whereby spacing refers to the spacing between Cupuaçu trees. density factors
root geometry 共cm兲 共nodes兲
depth
Cupuaçu
Pueraria
Cupuaçu
0 10 20 30
3.2 3.2 0.5 0.5
3.1 3.1
60 60 60 40
共70兲 共7兲 共7兲 共5兲
Pueraria spacing spacing
a correction factor of 3.1 is already applied to Pueraria. For Cupuaçu, root density factors of the ‘DeepRoots’ System were set to 3.2 down to a depth of 10 cm and 1.0 for the rest of the profile 共depth ⫽ 110 cm兲. For Pueraria it was set to 5.5 down to 10 cm. Root geometry of Cupuaçu was decreasing with depth in four steps. Time integral of actual and potential root water uptake and drainage for each simulated spacing are provided by Hydrus-2D, actual and potential evaporation can be obtained by a simple calculation. The total of actual root water uptake, actual evaporation and drainage is the volume of water that left the flow domain and is referred to as “outflow total”. The ratios between actual and potential root water uptake and actual and potential evaporation and drainage to rain are plotted to reveal relative changes. In order to see different behaviour between rainy season, the time period was divided into three nearly equal periods: days 1-210, 211-420 and 421-627. The first represents the end of a rainy season and a mild dry season, the second the rainy season and the third the second, more severe dry period. Additionally, values for the whole period 共days 1-627兲 are shown. In order to make comparison between the four periods easier, values are divided by the number of days so that simulated fluxes are given as cm/day. Results refer to the whole flow region except in block 2, where the subregion of one Cupuaçu tree is compared to the entire flow region.
Results Field studies There is a rain season between December 96 and May 96. The dry period of 96 is less severe than the dry season of 97. Mean annual precipitation of the years 1971 to 1997 is 2530 mm 共Correia and Lieberei 1998兲. Total of precipitation in 1996 is 2585 mm and 2243 mm in 1997, which indicates that 1996 is an average year and 1997 a dry year. The monthly mean air temperature lies between 23.6 and 27.0 °C and has with 3.4 °C only few seasonal variations. The lowest mean daily temperature in the observed period was in July 1997 共19.6 °C兲 and the highest in September 1997 共35.2 °C兲. The difference between minimum and maximum air temperature is higher in the dry season than in the rainy season because of higher net radiation and reduced cloud cover. Net radiation lies between 50 and 110 W/m2 Relative humidity is high throughout the year 共75 to 90%兲. Wind speed shows few seasonal variations and lies between 0.55 and 0.85 m/s. Under prevailing conditions, radiation is the main factor influencing evapotranspiration. A regression between net radiation and evapotranspiration 共ET兲 reveals a linear connection with a high coefficient of determinacy of 0.97. The comparison of monthly precipitation and evapotranspiration shows that ET lies beneath rain in most months 共humid兲 and only has higher values than rainfall in June, July, September and October 1997 共arid兲. Soil moisture lies between approx. 0.25 and 0.55 for all three plants and increases with depth. Variation is greatest 10 cm below the surface and least in 150 cm depth, because of an decreasing atmospherical influence of dry and rainy season with depth. Modelling Rosetta parameters proved to not suit field data. Thus soil physical parameters were altered until simulated and measured data reached highest similarity. Inverse simulation was not used because of long calculation time and instability of the algorithm. After pinning down soil parameters for Pueraria, Cupuaçu and Pupunha were calibrated. Interception rates and crop factors from the literature were used, but fitted to suit measured data. Only slight alterations of soil parameters were done and counterchecked with Pueraria.
283
Figure 2. Calibration results for Pueraria 共Pueraria phaseoloides兲 in an agroforestry system near Manaus, Brazil: Measured and observed soil water content in 30 and 150 cm depth for the years 1996 and 1997 共day 1 ⫽ 1 Jan 1996兲.
Calibration results generally exhibit good conformity between simulated and measured data. Order of values as well as dynamics are well met. Results for Pueraria are shown in Figure 2. Vertical node spacing of 5 cm showed distinct differences to spacing of 10 cm, but discretization of 2.5 cm showed only slight variations in contrast to 5 cm. Because of undramatic effects of discretization and in order to minimize calculation times discretization of 10 cm was chosen for scenarios. Scenarios ‘Real’ agroforestry system In the second dry period 共days 421-627兲 as well as in the rain season 共days 211-420兲 the root water uptake is lower than in the first dry season 共days 1-210兲. A very slight decrease of root water uptake with spacing can be observed. Drainage is highest in the rain season, lower in the first dry period and lowest in the second dry period. Drainage is increasing with spacing on days 1-210 and 211-420, but not on days 421627. Actual evaporation is as high as potential in the first dry period and in the rainy season and slightly lower than potential in the second dry season. Potential evaporation is not dependent on spacing per definition, rain is increasing due to decreased interception and potential root water uptake is decreasing as the mean crop factor of the flow region is decreasing with spacing. Outflow total lies above rain
in the first dry period and in the second dry period, indicating that the profile gets drier; in the rain season it is more or less the same as the incoming rain. The ratio of actual to potential root water uptake is about 0.9 in the first dry period, between 0.8 and 0.9 in the rain seaon and with 0.7 lowest in the second dry period. In the first dry season and in the rainy season actual evaporation is 100% of potential evaporation; in the second dry period it is only about 80%. The ratio drainage/rain is higher in the rain season than in the first dry season. In the second dry period the ratio drainage/rain is with approx. 0.2 very low. On days 1-210 and 211-420 more water per unit rain might be drained with increased spacing, but on days 421-627 it remains more or less constant. ‘Real’ agroforestry system subregion The water uptake of Cupuaçu remains more or less constant for all four periods 共Figure 3兲, whereas the water uptake of the whole region decreases slightly in most cases. Only in the dry season 共days 421-627兲 root water uptake for Cupuaçu is increasing whereas root water uptake for the whole region is more or less constant. ‘Only-Root-Effects’ system Neither in the whole period nor in the period from days 421-627 any distinct influence of spacing on output parameters can be observed. Differences might
284
Figure 3. Modelled Scenario ‘Real’ Agroforestry System in an agroforestry system near Manaus, Brazil: root water uptake of the subregion 共Cupuaçu 共Theobroma grandiflorum兲兲 and entire region in dependence on spacing for the four periods first dry season 共days 1-210兲, rainy season 共days 211-420兲, second dry season 共days 421-627兲 and entire period 共days 1-627兲兲.
Figure 4. Modelled Scenario ‘Deep-Roots’ System in an agroforestry system near Manaus, Brazil: Mean daily fluxes of actual and potential root water uptake, actual and potential evaporation, drainage, rain and outflow total for the spacing 10 and 90 cm for the days 421-627.
be due to numeric error, as potential evaporation as calculated from Hydrus-2D output varies, but should remain constant in theory. ‘Deep-Roots’ system In the dry period differences between spacings are more expressed than in the other periods. Actual root water uptake and actual evaporation are slightly lower, drainage slightly higher at 90 cm than at 10 cm 共Figure 4兲. The comparison of mean daily fluxes between ‘Only-Root-Effects’ System and ‘Deep-Roots’ Sys-
tem reveals greater differences and here also the greatest on days 421-627. Potential root water uptake, potential evaporation and rain are identical for both systems 共see Figure 5兲 as atmospheric conditions were held constant for both scenarios. Actual root water uptake in the system with deeper roots is higher than in the system with shallow roots, actual evaporation is only slightly higher. Drainage is lower in the ‘Deep-Roots’ System than in the ‘Only-Root-Effects’ System.
285
Figure 5. Mean daily fluxes of actual and potential root water uptake, actual and potential evaporation, drainage, rain and outflow total for the modelled ‘Only-Root-Effects’ System and ‘Deep-Roots’ System in an agroforestry system near Manaus, Brazil for the spacing 10 cm for the days 421-627.
Discussion and conclusions In the examined initital stage of the agroforestry system 共Block 1 ‘Real’ Agroforestry System兲 Cupuaçu and Pueraria root interactions show no or only minimal differences in dependence on spacing. The observed increase in drainage and slight decrease of root water uptake with increased distance between trees are mainly the consequence of reduced mean water interception and mean crop factor. This can be seen from results of Block 3 共‘Only-Root-Effects’ System兲, where values are more or less constant for all spacings indicating that differences in the ‘Real’ Agroforestry System are only caused by different mean interception and crop factor, respectively effective rain and potential root water uptake. But there occur distinct differences between the examined periods, which represent the first dry period, the rainy season, the second dry season and the entire simulation time. Spacing has no influence on the single tree plant 共Block 2 ‘Real’ Agroforestry System Subregion兲 except for the dry season 共days 421-627兲, where root water uptake for Cupuaçu is increasing with spacing. If this increase is not due to numeric error in Hydrus-2D calculations it can be stated that the tree crop profits from wider spacing in the more severe dry period. In the fictitious more developped agroforestry system 共Block 4 ‘Deep-Roots’ System兲, where Cupuaçu roots are considerably deeper than in the inital stage, there occur slight differences between spacing in the second dry period. These are namely a
decrease of root water uptake, an increase in drainage and possibly a decrease of evaporation. Differences in the entire period can be observed, but are rather small. But there is a significant effect between a system with shallow roots 共‘Only-Root-Effects’ System兲 and one with deep roots 共‘Deep-Roots’ System兲. Thus it can be concluded that for maximizing root water uptake plants with deep roots are more suitable than plants with shallow roots. For maximizing production, which is linked to root water uptake, it can be recommended that plants which develop deep roots within a short time should be preferred to species with shallow roots. Spacing between trees under the studied climate should be chosen in consideration of practical reasons and the estimated crown size in mature state. Yet it must be regarded that the danger of leaching of e.g., fertilizer gets higher with increased spacing as the effective rain of the system increases. In contrast to the studied agroforestry system, which is in a humid climate, agroforestry systems in semiarid regions encounter water stress more often and thus the effects of spacing will probably be bigger. While examining scenarios with identical atmospheric conditions there seemed to arise some problems in numerical calculations in Hydrus-2D. These occur namely in the variables potential root water uptake and potential evaporation. Simulations suggest that this numeric error might occur due to different sizes of the flow domains for different spacing. When spacing is constant, numeric error for the mentioned
286 parameters is zero, when spacing varies there occurs numeric error. Numeric errors are typical for numeric models due to the necessary discretization and can not be avoided. If differences between results are larger than in our study, numeric error will be less important. Yet Hydrus-2D may be regarded as a reliable and tested tool for system analysis and optimization of agronomic measures 共spacing, crop selection, fertilization, irrigation兲. Nevertheless results of this study are only a beginning and should be regarded as a conceptional approach rather than a realistic one. In future studies it should be possible to obtain more realistic output based on improved data basis. But still it will never be possible to model an agroforestry system, which indeed is a very complex system, in each detail and with values identical to reality, because heterogeneities in soil and plant behaviour will be an unavoidable source of uncertainty. Thus experimental approaches will always remain important in the future. Hydrus-2D itself is a well-known Windows program with a user-friendly interface and can serve as a suitable tool for our modelling approach. As it is physically based, there is the possibility to model interactions close to reality. Yet some improvements could be introduced in Hydrus-2D to facilitate the incorporation of different plant species. Advantages of the conducted modelling approach are, that the procedures for simulating the agroforestry system under study can be used to calculate any other agroforestry system, if root distribution and the other necessary site-specific data are known. If further tested with other data sets, it might be sufficient to know soil parameters, which can easily be derived by the relatively simple soil texture analysis. Then it might also be possible to conduct to a certain degree system analysis and system design without site-specific calibration or develop a reliable automated calibration. Our modelling approach puts special emphasis on roots and soil water dynamics, which are according to our experience often the crucial and sensitive factors in such a system. As a disadvantage it could be seen that root data are needed, which are not easily obtained. Also tree growth is not yet considered, but in the future it should be possible to extend Hydrus-2D by a module for crop and root growth. Another disadvantage could be that practitions might rely too much on model results, as they regard the model as too realistic. But this danger
could easily be compensated by appropriate courses and exercises.
Acknowledgements The Brazilian-German cooperation SHIFT 共Studies on Human Impact on Forest and Floodplains in the Tropics兲 examines the recultivation of degraded monoculture sites of the terra firme 共the land not inundated by the Amazon river兲 near Manaus in the project “Water and nutrient fluxes as inidcators for sustainability”. Our gratitude goes to all the researchers and field staff, who were involved in providing weather and soil data at Manaus, Brazil. Among them special thanks goes to Götz Schroth. We are also indebted to Jirka Simunek, who always provided quick help for specific problems with Hydrus-2D. Furthermore we thank the collegues of the department of soil physics and helpful students of the University Bayreuth.
Appendix Correction factors in the root region For each node within the root region the equalities for the actual S共h兲 and potential sink term Sp hold:
b共x, z兲 ⫽
S共h兲 ⫽ a共h兲Sp
共8兲
Sp ⫽ b共x, z兲LtTp
共9兲
b ⬘ 共x, z兲
兰
⍀
b ⬘ 共x, z兲d⍀
兰
b共x, z兲 ⫽ 1
⍀
,
thus
共10兲
共11兲
The root weighting factor b共x,z兲 is introduced into Equation 共5兲 using 共11兲 and 共10兲: Vtot ⫽ c f mLtTP ⫽ c f mLtTP Let
兰
⍀
兰
兰
⍀
⍀
b共x, z兲d⍀
b ⬘ 共x, z兲 b ⬘ 共x, z兲d⍀
d⍀
共12兲 共13兲
287 b ⬘ 共x, z兲 ⫽ r共x, z兲b ⬙ 共x, z兲
共14兲
where b⬙共x,z兲 is a root density function and r共x,z兲 a correction factor, which varies according to crop factors c f i. The correction factor is constant for each subregion, i.e. bi共x, z兲 ⫽ rib ⬙ 共x, z兲
Root water uptake of a subregion The flow region can be divided into a number of subregions ⍀i with a width of Lti. Transpiration of the flow region is made up of the transpiration volumes of the subregions.
共15兲
Vtot ⫽
n
n
n
兺 Vi ⫽ i⫽1 兺 Lt Tp ⫽ Tpi⫽1 兺 Lt ⫽ TpLt i⫽1 i
i
After various mathematical modifications: r2 ⫽
A1c f 2Lt2
共16兲
c f 1Lt1A2
where: A1 ⫽ A2 ⫽
m
b⬙1,j⍀1,j 兺 j⫽1
共17兲
b⬙2,j⍀2,j 兺 j⫽1
共19兲
m
b⬙2,jd2,jLt ⫽ Lt f 兺 j⫽1 f ⫽ constant
Tp ⫽ c f mTP
共25兲
兰
⍀
S共h, x, z兲d⍀ ⫽ LtTp
兰
⍀
a共h兲b共x, z兲d⍀ 共26兲
For each node within a subregion respectively:
A1 ⫽ constant
2
共24兲
共18兲
A1 and A2 are just summary variables and serve the purpose of simplifying equations. In the applied case of the modelled agroforestry system of the tree Cupuaçu and the cover crop Pueraria, the index 1 should stand for Cupuaçu and the index 2 for Pueraria 共see fig 1兲. Pueraria has for each depth increment the same width Lt2. When the root weighting factors b⬙i,j and root geometry for the tree species remain constant, it can be demonstrated that r2 is not dependent on tree plant spacing Lt. Then
A2 ⫽
Vi ⫽ LtiTp
For each node in the root zone root water uptake is calculated with 共8兲, 共9兲, 共10兲 and Vtot ⫽
m
共23兲
2
共20兲
Si共h, x, z兲 ⫽ a共h, x, z兲Spi共x, z兲
共27兲
Spi共x, z兲 ⫽ bi共x, z兲LtiTp
共28兲
bi共x, z兲 ⫽
兰
⍀i
Vi ⫽
兰
⍀i
b⬘i 共x, z兲 b⬘i 共x, z兲d⍀
Si共h, x, z兲d⍀ ⫽ LtiTp
兰
⍀i
共29兲
a共h, x, z兲bi共x, z兲d⍀ 共30兲
The root region is composed of a number m of elements e j:
共21兲
Vi ⫽
m
Se 共h兲Ae 兺 j⫽1 j
j
共31兲
Then r2 ⫽
A1c f 2 c f 1Lt1 f
For each grid element in the root subregion it follows: 共22兲 Se j ⫽
Sa j共h兲 ⫹ Sb j共h兲 ⫹ Sc j共h兲 3
共32兲
288 where a, b and c are indices indicating the nodes of each triangular element. Let x⫽1,2,3 be one of the indices a, b or c and X j represent the coordinates of the according node, then Sx j ⫽ LtiTpa共h, X j兲bi共X j兲
共33兲
An average value of is calculated for each triangular element e. ¯e ⫽ b⬘ j
b⬘a j ⫹ b⬘b j ⫹ b⬘c j
共34兲
3
From Equation 共29兲 and the concept of grid elements it follows bi共X j兲 ⫽
b⬘i 共X j兲
¯ A e e 兺mj⫽1 b⬘ j
共35兲 j
共34兲 and 共32兲 in 共31兲: Vi ⫽
Vi ⫽
m
兺 j⫽1
m
兺 j⫽1
3 Sx 兺x⫽1 A
共36兲
j
ej
3
3 Lt Tpa共h, X j兲 兺x⫽1 i
bi⬘共X j兲 ¯ A b⬘
兺mj⫽1
ej ej
3
Ae j 共37兲
It can be seen that Ae j is redundant under the circumstance of triangular elements of the same area, which is true. Thus the area can be set Ae⫽1 leading to
Vi ⫽
m
兺 j⫽1
3 Lt Tpa共h, X j兲 兺x⫽1 i
3
bi⬘共X j兲 ¯ 兺mj⫽1 b⬘
ej
共38兲
The transpiration or root water uptake of the subregion is calculated according to 共38兲, wherein b⬘e j is gained through 共34兲. Pressure head h for each node is calculated by Hydrus-2D at observation nodes. Dependent on Feddesparameter and according reduction function a共h兲 is calculated. It is zero below h4 or over h1, 1 between h2 and h3 and a linear function in the remaining regions.
Notation ET0⫽reference evapotranspiration 关mm day⫺1兴 Rn⫽net radiation at the crop surface 关MJ m⫺2 day⫺1兴 G⫽soil heat flux density 关MJ m⫺2 day⫺1兴 T⫽mean daily air temperature at 2 m height 关C兴 u2⫽wind speed at 2m height 关m s⫺1兴 es⫽saturation vapour pressure 关kPa兴 ea⫽actual vapour pressure 关kPa兴 es⫺ea⫽saturation vapour deficit 关kPa兴 ⌬⫽slope vapour pressure curve 关kPa C⫺1兴 ␥⫽psychometric constant 关kPa C⫺1]兴 ⫽volumetric water content 关L3L–3兴 h⫽pressure head 关L兴 S⫽sink term 关T⫺1兴 xi 共i⫽1,2兲⫽spatial coordinates 关L兴 t⫽time 关T兴 KAij⫽components of a dimensionless anisotropy tensor K⫽unsaturated hydraulic conductivity function 关LT⫺1兴 Tp⫽transpiration rate 关LT⫺1兴 Tpi⫽transpiration rate for the subregion 关LT⫺1兴 TP⫽reference transpiration rate 关LT⫺1兴 c f i⫽crop factor for the subregion c f m⫽mean crop factor Vtot⫽transpiration of the whole flow region 关L2T⫺1兴 Vi⫽transpiration of the subregion i 关L2T⫺1兴 n⫽number of subregions Lt⫽width of soil surface associated with transpiration 关L兴 Lti⫽Lt for the subregion 关L兴 Im⫽mean interception 关%兴 Ii⫽interception of each subregion, i.e crop关%兴 S共h兲⫽sink term 共root water uptake兲 关T⫺1兴 a共h兲⫽water stress response function 共Feddes function兲 Sp⫽potential root water uptake 关T⫺1兴 b共x,z兲⫽standardized root weighting factor 共function of spatial coordinates兲 关L⫺2兴 b⬘共x,z兲⫽user-specified root weighting factor 共function of spatial coordinates兲 关L⫺2兴 b⬙共x,z兲⫽root density function for the subregion before correction by ri 关L⫺2兴 ri⫽correction factor for each subregion ⍀⫽root region 关L2兴 A1⫽transitory variable A2⫽transitory variable f⫽transitory variable
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