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304 Agronomy Journa l • Volume103 , I s sue2 • 2011

Biom

etrics, Modeling, and Statistics

ParameterizationandEvaluationofPredictionsofDSSAT/CANEGROforBrazilianSugarcane

FabioR.Marin,*JamesW.Jones,FrederickRoyce,CarlosSuguitani,JorgeL.Donzeli,WanderJ.PalloneFilho,andDanielS.P.Nassif

Published in Agron. J. 103:304–315 (2011)Published online 15 Dec 2010doi:10.2134/agronj2010.0302Copyright © 2011 by the American Society of Agronomy, 5585 Guilford Road, Madison, WI 53711. All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

Sugarcane is of major social and economic impor-tance in Brazil. It is one of the most important commodities

in Brazilian agribusiness, contributing to the energy and food security of the country, as sugar, ethanol, and biomass for energy are produced from sugarcane (Goldemberg, 2007). Brazilian pro-duction of sugarcane has been expanding since the early 2000s, now reaching areas where it has never been planted, mainly driven by the rise in ethanol consumption in the internal market. The coefficient of variation of annual national production was 7.2% from 1990 to 2008, ranging from 5 to 12% among different regions. The new production areas, mainly located in Central and Northeast regions are more often subject to higher risk.

Crop simulation models may contribute to improved crop monitoring and yield forecasting, while enhancing our under-standing of sugarcane growth and yield. Worldwide, there are several models dedicated to sugarcane crop simulation: AUSCANE (Jones et al., 1989), CANEGRO (Inman-Bamber, 1991; Singels et al., 2008), QCANE (Liu and Kingston, 1995), APSIM (Keating et al., 1999), MOSICAS (Martiné, 2003), and CASUPRO (Villegas et al., 2005). The CANEGRO

model was shown to accurately simulate sugarcane yield when compared to South African sugar industry data by Bezuiden-hout and Singels (2007a, 2007b). A new version of CANE-GRO (Singels et al., 2008) has been included with version 4.5 of the DSSAT environment (Jones et al., 2003; Hoogenboom et al., 2010) replacing an earlier version (Inman-Bamber and Kiker, 1997) available in DSSAT version 3.5.

These efforts to model the sugarcane crop reflect the fact that simulated processes often have to be modified to adapt models to specific environments, supporting the idea that there is no uni-versal crop model (Sinclair and Seligman, 1996) even for a single crop such as sugarcane. These authors emphasized the benefit for a group of researchers to build their own model appropriate to their specific purpose, with the possible use of formalisms from existing models. However, there are also advantages to adapting an existing model compared to developing a new one in terms of cost and time. To use an existing model for a particular crop, nevertheless, the main physiological parameters controlling the growth and development of that crop must be known, the model must be parameterized, and its predictions evaluated.

This paper has three major goals: (i) characterize the physi-ological parameters controlling growth and development of two of the most important Brazilian sugarcane cultivars; (ii) param-eterize the DSSAT/CANEGRO model for southern Brazilian production systems using an objective and automatic procedure; and (iii) evaluate the predictions of stalk mass and sucrose accu-mulation using a cross-validation computer experiment.

These goals emerged from several discussions in the litera-ture, regarding the relatively little work on parameter estima-tion for crop models (Makowski et al., 2006, p.101–103), the increasing importance of mechanistic crop models, and the

ABStrActThe DSSAT/CANEGRO model was parameterized and its predictions evaluated using data from five sugarcane (Saccharum spp.) experiments conducted in southern Brazil. The data used are from two of the most important Brazilian cultivars. Some param-eters whose values were either directly measured or considered to be well known were not adjusted. Ten of the 20 parameters were optimized using a Generalized Likelihood Uncertainty Estimation (GLUE) algorithm using the leave-one-out cross-validation technique. Model predictions were evaluated using measured data of leaf area index (LAI), stalk and aerial dry mass, sucrose content, and soil water content, using bias, root mean squared error (RMSE), modeling efficiency (Eff), correlation coefficient, and agreement index. The Decision Support System for Agrotechnology Transfer (DSSAT)/CANEGRO model simulated the sugarcane crop in southern Brazil well, using the parameterization reported here. The soil water content predictions were better for rainfed (mean RMSE = 0.122mm) than for irrigated treatment (mean RMSE = 0.214mm). Predictions were best for aerial dry mass (Eff = 0.850), followed by stalk dry mass (Eff = 0.765) and then sucrose mass (Eff = 0.170). Number of green leaves showed the worst fit (Eff = –2.300).The cross-validation technique permits using multiple datasets that would have limited use if used independently because of the heterogeneity of measures and measurement strategies.

F.R. Marin, Embrapa Agriculture Informatics, Av. André Tosello, 209- Barão Geraldo, CP 6041-13083-886- Campinas, SP; J.W. Jones and F. Royce, Dep. of Agricultural and Biological Engineering, Museum Rd., P.O. Box 110570, Univ. of Florida, Gainesville, FL 32611; C. Suguitani, J.L. Donzeli, and W.J. Pallone Filho, Sugarcane Technology Center, Fazenda Santo Antônio S/N, Bairro Santo Antônio, Piracicaba–SP, Brazil, CEP 13400-970, Cp. 162; D.S.P. Nassif, 4 University of Sao Paulo, College of Agriculture “Luiz de Queiroz”, Piracicaba, SP, Av.: Pádua Dias, 11 CP 9, Piracicaba–SP, Brazil, 13418-900. Received 9 July 2010. *Corresponding author ([email protected]).

Abbreviations: DAP, days after planting; DSSAT, Decision Support System for Agrotechnology Transfer; Eff, modeling efficiency; GLUE, Generalized Likelihood Uncertainty Estimation; PTF, pedotransfer functions; RMSE, root mean squared error; RWF, root weighting factor; SRL, specific root length.

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nonstandard nature of sugarcane crop experiments. First, the literature has stressed the importance of raising the quality of parameterization in crop simulation models by replacing the common trial-and-error approach by an automatic procedure for parameter adjustment, which would ensure that the data are always used in the same way for parameter estimation (Wal-lach et al., 2001). Second, the use of data not specifically col-lected for modeling studies requires skill to deal with different types of data, different measurement frequencies, inadequate site details, and lack of suitable measurements due to inherent difficulties in the production of the sugarcane crop. Third, to include both parameterization and evaluation steps dealing with small datasets, common methods of estimating prediction error are by cross-validation or bootstrap techniques.

MAteriAlS And MethodSModel description

CANEGRO simulates sugarcane growth using climate and water inputs (Singels et al., 2008), based on process-based models of sugarcane growth and development including phenology, canopy development, tillering, biomass accumulation and par-titioning, root growth, water stress, and lodging. It uses a daily time-step and is designed to simulate the whole plant, stalk and root biomass, sucrose concentration, plant phenology and other variables. The model requires as an input data soil parameters that regulate the soil water balance (field capacity, wilting point, water saturation, and soil depth) and also daily weather variables (solar radiation, maximum and minimum temperatures, precipi-tation) and irrigation. Relative humidity and wind speed are not essential but are recommended whenever available.

An overall description of the CANEGRO model can be found in Singels et al. (2008) and only its main features are briefly described here. The model simulates the development of individual leaves and shoots, and then scales up to per unit of area by multiplying leaf area per shoot and number of shoots per unit area. Radiation interception is calculated by Beer’s law and tiller development is based on thermal time functions which describe the rate of tillering, maximum tiller population and senescence. Leaf emergence is based on a phyllocron interval concept divided into two periods in the crop cycle. Biomass accumulation and partitioning are based on a radiation use efficiency algorithm that is modified by air temperature, water stress, and growth respiration (Singels and Bezuidenhout, 2002). Stalk elongation is a function of thermal time, and partitioning to stalk is regulated by sink capacity for stalk structural growth and the source-to-sink ratio. Root growth is expressed in terms

of the extension of the rooting depth and root length in each soil layer. CANEGRO was designed to simulate the effects of water stress on photosynthesis and leaf growth using two variables, which in turn are dependent on the ratio of transpiration rate to root water uptake. The soil-water balance in DSSAT follows the algorithm described by Ritchie (1998). The lodging stress effect is simulated by comparing the aerial biomass with a cultivar-specific threshold, above which lodging will begin.

In the DSSAT environment, the model has three types of genetic parameters, divided into cultivar, ecotype, and species, which are designed to represent the genetic characteristics at different levels of crop specificity. This means that each cultivar characteristic is specific, representing a single cultivar, while eco-type parameters can be identical across more than one cultivar. Species parameters are expected not to vary among different cultivars and are assumed to be fully stable, describing some characteristics of sugarcane such as: photosynthesis, respiration, partitioning, root growth, and plant response to water stress.

data Sources

CANEGRO was parameterized and evaluated using data from two Brazilian cultivars, collected in four locations in Brazil (Suguitani, 2006; Laclau and Laclau, 2009; Tasso, 2007; Santos, 2008) (Table 1). All experiments received adequate N, P, and K fertilization and regular weed control and were planted using healthy cuttings with 13 to 15 buds m−2. Row spacing varied from 1.4 to 1.5 m. One of the datasets had two treatments (irrigated and rainfed), and all the remaining data were for rainfed. The irrigated treatment received water by sprinkling and the irrigation schedule was determined by tensiometer monitoring to maintain the soil layers close to field capacity down to a depth of at least 1 m. Three replicates of ten-siometers were set up in the irrigated and rainfed plots at the depths of 0.1, 0.3, 0.5, 0.8, and 1.5 m at a distance of 0.12, 0.35, and 0.70 m from the planting row. Soil water potential was measured every 2 to 3 d (before 0800 h) over the study period (Laclau and Laclau, 2009). These data were used to evaluate the model’s soil water balance algorithm.

Matric potential tensiometer measurements were converted to soil water content using the van Genuchten (1980) equa-tion for soil water retention curve and values of water content at −10 kPa (UWL), at −1500kPa (LWL), and at saturation (SWL). As soil water parameters were not measured, the values of UWL, LWL, and SWL were defined using the pedotransfer functions (PTF) provided by Tomasella et al. (2000) (Table 2). The estimated values were checked against measured pressure

table 1. Sources of experimental data used and main soil and climate characteristics of each site.

dataset

Site

Planting andharvest dates

cultivars

crop cycle†

climate‡

treatments

1 Piracicaba/SP,22°52´S,47°30´W,560masml 29Oct.2004and26Sept.2005

RB72-454SP83-2847NCo376

PC 21.6°C,1230mm,CWa

1.Irrigated,2.Rainfed

2 AparecidadoTaboado/MS,20°05´19˝S,51°17´59˝W,335masml

1July2006and8Sept.2007

SP83-2847 R1 23,5°C,1560,Aw 3.Rainfed

3 Colina/SP,20°25´S48°19´W,590masml

2Feb.2004and15June2005

RB72-454SP83-2847

PC 22.8°C,1363mm,Aw

4.Rainfed

4 Olimpia/SP,20°26´S,48°32´W,500masml 10Feb.2004and15June2005

RB72-454SP83-2847

PC 23.3°C,1349mm,Aw

5.Rainfed

†PC-Plantcanecrop;R-ratooncropandfollowingnumberistheratoonrank.‡Respectively:meanannualtemperature,annualtotalrainfall,KoeppenClassification.

306 Agronomy Journa l • Volume103, Issue2 • 2011

plate data from Embrapa (1981) and Radambrasil Project (1973–1986) from multiple locations at each site, with good agreement. The input data for PTF were provided by Suguitani (2006), Laclau and Laclau (2009), Tasso (2007), and Santos (2008). The hydraulic conductivity at saturation (KSat) was estimated based on (Poulsen et al., 1999) (Table 2), whose method produced a good fit with Brazilian field data mea-sured in similar soils (Ribeiro et al., 2007). A location <5 km from the site 1 that had the same soil classification (Carvalho and Libardi, 2009) showed KSat data based on hydraulic

conductivity measurements using neutron probes which were compared with estimated KSat data for this site (Fig. 1).

The DSSAT Soil water balance also requires input of a root weighting factor (RWF), a relative variable ranging from 1—a soil most hospitable to root growth—to near 0—soil inhospi-table to roots (Ritchie, 1998). Since the distribution of sugarcane root length is similar to an exponential pattern (Ball-Coelho et al., 1992; Laclau and Laclau, 2009) RWF values were estimated using the approach proposed by Jones et al. (1991) using the exponential geotropism constant equal to 2, which gave the best fitting with root length density profile (R2 = 0.94) among values

table 3. dSSAt/cAneGro cultivar parameters, descriptions, and units.

Parameter description UnitsParcemax Maximum(nostress)radiationconversionefficiencyexpressedasassimilateproducedbeforerespiration,perunitofPAR gMJ–1

Apfmx Maximumfractionofdrymassincrementsthatcanbeallocatedtoaerialdrymass tt–1

Stkpfmax Fractionofdailyaerialdrymassincrementspartitionedtostalkathightemperaturesinamaturecrop tt–1

Suca Maximumsucrosecontentsinthebaseofstalk tt–1

Tbft Temperatureatwhichpartitioningofunstressedstalkmassincrementstosucroseis50%ofthemaximumvalue °CTthalfo Thermaltimetohalfcanopy °CdTbase Basetemperatureforcanopydevelopment °CLfmax Maximumnumberofgreenleavesahealthy,adequately-wateredplantwillhaveafteritisoldenoughtolosesomeleaves leavesMxlfarea MaximumleafareaassignedtoallleavesaboveleafnumberMXLFARNO cm2

Mxlfarno LeafnumberabovewhichleafareaislimitedtoMXLFAREA leafPI1 Phyllocroninterval1forleafnumbersbelowPswitch °CdPI2 Phyllocroninterval2forleafnumbersabovePswitch °CdPswitch Leafnumberatwhichthephyllocronchanges. leafTtplntem Thermaltimetoemergenceforaplantcrop °CdTtratnem Thermaltimetoemergenceforaratooncrop °CdChupibase Thermaltimefromemergencetostartofstalkgrowth °CdTt_Popgrowth Thermaltimetopeaktillerpopulation °CdMax_Pop Maximumtillerpopulation stalksm–2

Poptt16 Stalkpopulationat/after1600°Cd–1 stalksm–2

Lg_Ambase Aerialmass(freshmassofstalks,leaves,andmoisture)atwhichlodgingstarts tha–1

table 2. Soil properties input for dSSAt/cAneGro model each dataset.

layerdepth

lowerlimit

Upperlimit drain.

Upperlimit sat.

root growth factor

Sat. hyd. cond.

Bulkdensity

organic carbon

clay

Silt

ph water

cationexchange capacity

cm3cm–3 cmh–1 gcm–3 % cmolckg–1

Dataset1–LatossoloVermelho-Amarelo(TypicHapludox)†20 0.200 0.310 0.480 0.956 0.380 1.37 1.24 48.5 4.5 4.1 4.540 0.225 0.330 0.480 0.913 0.390 1.36 0.90 52.0 4.5 4.1 3.2100 0.238 0.338 0.485 0.751 0.400 1.19 0.45 59.8 4.0 4.4 2.7450 0.250 0.350 0.490 0.049 0.360 1.13 0.10 59.0 10.0 4.6 2.1

Dataset2–LatossoloVermelho-Amarelo(TypicHapludox)†20 0.220 0.360 0.520 0.956 0.390 1.34 1.70 50.0 8.5 4.6 5.040 0.235 0.355 0.495 0.913 0.385 1.29 0.81 54.0 9.0 4.6 3.2100 0.240 0.343 0.473 0.751 0.373 1.25 0.05 57.0 8.0 4.2 2.7450 0.250 0.335 0.470 0.049 0.370 1.22 0.05 57.0 8.0 4.2 2.7

Dataset3–LatossoloVermelho-Escuro(TypicHapludox)†20 0.115 0.210 0.440 0.956 0.850 1.31 0.81 18.5 6.5 5.5 5.940 0.120 0.220 0.440 0.913 0.745 1.22 0.59 21.0 8.5 4.7 3.9100 0.120 0.210 0.420 0.751 0.715 1.21 0.06 21.0 8.0 5.3 2.8450 0.120 0.210 0.420 0.049 0.700 1.21 0.06 21.0 8.0 5.3 2.8

Dataset4–LatossoloVermelho-Escuro(TypicHapludox)†20 0.115 0.215 0.440 0.956 0.795 1.32 0.75 19.0 5.5 5.9 4.340 0.120 0.220 0.440 0.913 0.710 1.25 0.57 22.0 8.5 5.2 4.4100 0.120 0.210 0.420 0.751 0.680 1.22 0.05 22.0 8.0 4.8 4.7450 0.120 0.210 0.420 0.049 0.680 1.22 0.05 22.0 8.0 4.8 4.7†SoilClassificationbyBrazilianSoilClassificationSystem(Embrapa,1999)andtheirnearestU.S.SoilTaxonomyequivalent(inbrackets).


tested ranging from 1.5 to 4. Soil depths were set up to allow roots to reach 4.5 m in all locations, as this was the maximum root depth found by Laclau and Laclau (2009). The soils in the experi-ments used in this paper did not have any impediments to root growth such as soil compaction or high water tables. The low pH values (Table 2) observed in this soil seemed to not affect the root development. There was no information if those pH values were measured before the soil pH correction and fertilization.

For Site 1, daily solar radiation, maximum and minimum air temperature, rainfall, wind speed, and relative air humidity were collected adjacent to the experiment site using an automatic weather station. For Site 2, air temperature, wind speed, rela-tive humidity, and solar radiation were collected by automatic weather station positioned about 15 km from the experiment. A flat terrain minimized the error associated with this procedure. Sites 3 and 4 are about 30 km from each other in a flat terrain. For both, maximum and minimum air temperature data were collected daily at the same weather station about 15 km from the experiments. Wind speed and relative air humidity were not measured for these sites. Since there was no solar radiation mea-surement available daily data were estimated using an empirical equation (R2 = 0.82), as a function of latitude, longitude, extra-terrestrial radiation, air temperature and rainfall, generated using regional data from two weather stations about 70 km from the experiment site. For all datasets, rainfall data were recorded at a distance <100 m from the experimental fields.

The cultivars RB72-454 and SP83-2847 were among the five most commonly planted in Brazil. Both are late maturing with high cane and sucrose yields when grown either as a plant crop or ratoon. They are able to produce high yields even in poor soils and diverse climates. The cultivar RB72-454 is typically used as the standard cultivar in biometric and yield trials in Brazil and is found in sugarcane collections around the world.

For Dataset 1, detailed crop growth variables including green LAI, stalk population, stalk and aerial dry mass; and number of green leaves were collected at 4 to 5 wk intervals over the cycle (Suguitani, 2006). Root length density, root depth, and root mass were also collected, for cultivar RB72-454 (Laclau and Laclau, 2009), using the experimental procedures described in Laclau and Laclau (2009). For Dataset 2, LAI, stalk population, sucrose concentration, and stalk mass three to seven samples were collected for each variable at different intervals. For datasets 3 and 4, stalk population, stalk mass, and stalk height were col-lect just one time during the cycle, while sucrose dry mass was collected 13 times from the mid-season through harvest.

Parameterization and evaluating Predictions

Considering the cultivar of measurements taken and differ-ent measurement strategies in each dataset, the leave-one-out cross-validation method (Wallach, 2006) of data splitting was used to simultaneously include all the variability of conditions and measurements in the parameter estimation and evaluation of the model predictions.

The leave-one-out cross-validation procedure had a factorial design in which each run missed one treatment each time. So, five simulation combinations were performed for cultivar SP83-2847 and four for RB72-454. The parameters sets derived from these cross-validation runs were used one at a time to evaluate the predictions for the treatment left out. In addition, two other

optimizing runs were done to estimate a set of parameters using all treatments for each cultivar. These sets are shown as the final optimized parameters for each cultivar. Root data were not used in the parameter estimation procedure.

To determine which parameters to estimate, a targeted sensi-tivity analysis was first performed to determine the dependency of simulated variables on changes in key parameters. In addi-tion, a major decision about what parameters to optimize was based on available measured data, to avoid adjusting parameters that were not related to available data. We also did not adjust other parameters whose values could be measured directly or were considered to be well-known, such as base temperature for canopy development (Tbase), maximum leaf area (Mxlfarea), leaf number at which maximum leaf area occurs (Mxlfarno), maximum number of green leaves (Lfmax), leaf phyllocron inter-vals (PI1 and PI2), leaf number at which leaf phyllocron changes (Pswitch) (see Table 3). These were derived from experimental data as discussed in section 3.1. The idea in this strategy was to minimize the number of parameters to be optimized, keeping the ratio of the number of adjusted parameters to the number of measurements at a reasonably low level (Refsgaard 1997).

Ten of the 20 CANEGRO model cultivar parameters were optimized (Table 3), including those related to leaf and tiller phenology (Ttplntem, Ttratnem, Chupibase, Tt_Popgrowth, Max_Pop, and Poptt16), radiation conversion efficiency, sucrose accumulation and partitioning coefficients (Parce-max, Apfmx, Stkpfmax, and Suca). Parameters regarding temperature at which partitioning of unstressed stalk mass increments to sucrose in 50% of its maximum value (Tbft) and aerial mass at which lodging starts (Lg_Ambase) were kept at default values due the lack of relevant experimental data. The ecotype parameter dPERdT (change in plant extension rate, mm h−1 ºC d−1) was adjusted to fit the simulated stalk height to the observed data, using a visual trial and error procedure.

For all coefficients, the range of variation was defined based on field data, the sugarcane literature and model

Fig. 1. hydraulic conductivity at saturation (KSat) observed by carvalho and libardi (2009) (candl) and estimated using the Poulsen method for dataset 1 site.


documentation (Singels et al., 2008). Since the DSSAT/CANEGRO model has a well-tested set of default values for cultivar NCo376 in South Africa, that set was used as a source of nominal values within a range defined from observed data.

A DSSAT v4.5 built-in algorithm (Jones et al., 2010) of the Generalized Likelihood Uncertainty Estimation (GLUE) method (Mertens et al., 2004) was used for estimating the 10 CANEGRO cultivar parameters. GLUE is a Bayesian estimation method that uses Monte Carlo sampling from distributions (assumed to be uni-form) generated by combinations of the coefficients and evaluated by a Gaussian likelihood function to determine the best coefficient set based on the observed data used in the estimation process. The GLUE algorithm was set up to generate at least 6000 random samples of parameters (3000 for phenological parameters plus 3000 for growth) for each simulation combination. This number of samples represents a compromise between the required comput-ing time and the stability of estimated parameters.

Model predictions were evaluated using the following out-puts: LAI, stalk and aerial dry mass, sucrose content, and soil water content for datasets 1 and 2. The quality of predictions were computed using bias, root mean squared error, modeling efficiency, correlation coefficient (Wallach, 2006), and agree-ment index (Willmott, 1981) as agreement measures.

reSUltS And diScUSSioncharacterizing Physiological Parameters

controlling Growth and developmentcanopy development and Phenology data

The scatter values and regression line for the cultivars (Fig. 2) indicated that maximum leaf size differed little among Brazil-ian cultivars, being as large as 796 cm2 for RB72-454 and 733cm2 for SP83-2847, representing nearly the double of the default Mxlfarea value available in DSSAT/CANEGRO, for cultivar NCo376 (Table 4).

For both cultivars, maximum leaf size (Mxlfarno) was reached around 25th leaf (Fig. 2), which is similar to results of Sinclair et al. (2004) for cultivar CP72-2086 in Florida, but substantially different from the values obtained and for cultivars in South Africa and Australia (Cheeroo-Nayamuth et al., 2000, Inman-Bamber, 1994). The 18th leaf as the default Mxlfarno value in DSSAT/CANEGRO may be related to the lower phyllocron values (PI2) found for Brazilian cultivars, as discussed below.

Comparing the effect of irrigated and rainfed treatments, both Brazilian cultivars showed <5% difference in terms of leaf size due water stress. For the conditions of Dataset 1, Suguitani (2006) showed differences of 22% (464 ± 44 cm2 for irrigated and 363 ± 34 cm2 for rainfed treatment) for cultivar NCo376, suggesting some greater tolerance to drought in the Brazilian cultivars compared to NCo376.

The mean value for the maximum green leaf number per stalk for all three cultivars was approximately 9 (Table 4). For both cultivars in Dataset 1 the peak and stable stalk popula-tions were almost the same for both irrigated and rainfed treatments. Both cultivars also showed similar tillering rates, regardless of water treatment and experiment site (Fig. 3 and Table 4). The tillering pattern is similar to that described by Bezuidenhout et al. (2003), but with a lower tiller density than reported there, at 12 and 14 tiller m−2 in the tillering peak, respectively for cultivar RB72-454 and SP83-2847. After the senescence phase, tiller density stabilized at 7 tiller m−2 regard-less of water source (rain or irrigation) or planting site. Stalk growth began about 500 to 700ºC d−1 after planting, with peak tillering at about 900ºC d−1 after planting.

The lower tillering rate and number of final tillers observed in Brazilian compared to South African cultivars (Table 4), seems to be related to quicker initial development and greater leaf area causing higher levels of light interception and early shadowing of the stalk base. This implies that tillering rate is related to canopy light interception (van Dillewijn, 1952; Inman-Bamber, 1994,

Fig. 2. Size and number of leaves for rB72-454 and SP83-2847 cultivars during the crop cycle for the conditions of dataset 1.

table 4. Maximum leaf size, number of leaves and green leaves, maximum leaf area index and mean stalk population at peak of til-lering and at maturing observed for both cultivars.

cultivar leaf† size no. of leaves† Max. number green leaves† Population at peak tillering Population at maturing Green lAi cm2 stalkm–2

SP83-2847 733.9 33.8 8.8 14.1 8.3 4.7RB72-454 796.0 34.7 9.3 12.7 9.7 5.2†OnlydatafromDataset1.


and Bezuidenhout et al., 2003) and not simply a fixed response to temperature as calculated by DSSAT/CANEGRO.

The leaf appearance algorithm in DSSAT/CANEGRO is based on phyllocron interval concept (Inman-Bamber, 1994), representing the thermal time elapsed between the emergence of subsequent leaves on a tiller (Singels et al., 2008). The plant cycle is divided in two phases (PI1 and PI2), whose transition is controlled by a cultivar specific threshold (Pswitch). The values obtained from Brazilian data (Table 5), were derived from linear equations shown in Fig. 4. The base temperature for leaf development of Brazilian cultivars ranged from 14.4 to 14.6ºC, slightly lower than the 16ºC obtained for the standard NCo376 in DSSAT/CANEGRO (Table 5).

The range of PI1 values (104–113ºC d−1 leaf−1) was higher for both Brazilian cultivars tested than the DSSAT/CANE-GRO default values corresponding to NCo376. However, at

116 to 122ºC d−1 leaf−1, PI2 was smaller than the default. This suggests that use of the two-phyllocron approach does not seem to be as important for Brazilian cultivars as for South Africa, where the results of Inman-Bamber (1994), Bonnett (1998), and Robertson et al. (1998) showed differences between PI1 and PI2 ranging from 14 to 69%. Results from Sinclair et al., (2004) were closer to those observed in this paper, with only 6% difference between PI1 and PI2. Those authors hypothesized that the smaller-than-expected difference in leaf appearance rate between early and late leaves might owe to higher evaporative cooling in fully developed canopies than in younger, more open canopies. This assumption seems to be related to the vegetation-atmosphere decoupling approach (McNaughton and Jarvis, 1983), from which one can derive another assumption, that the two phyllocron approach would be observed only under highly coupled conditions. Based on this, one could infer that the use of two phyllocrons as being not cultivar specific, but rather an ecotype characteristic. Of course, further studies will be needed to better understand this issue.

Biomass PartitioningThe observed accumulation of biomass in the millable stalks

closely mirrored the accumulation of aboveground biomass for the two Brazilian cultivars, starting with 9% at 129 days after planting (DAP) to reach a maximum of 61 and 70% after 330 DAP for RB72-454 in irrigated and rainfed treatments, respectively. Cultivar SP83-2847 showed a maximum stalk/aboveground biomass ratio of 0.66 for both treatments (Fig. 5,

Fig. 3. tillering rate during the crop cycle, expressed in term of cumulative degree-days, using base temperature of 10ºc, for cultivars SP83-2847 and rB72-454.

table 5. Base temperature for leaf development, the single, full-season phyllocron value (Pi), the two-phase phyllocron intervals (Pi1 and Pi2), and leaf number range at which Pi1 switches to Pi2.

Parameter SP83-2847 rB72-454 Standard nco376Tb,ºC 14.6 14.4 16PI,ºCd 118.2 114.9 –PI1,ºCd 113.0 112.8 69PI2,ºCd 122.2 116.6 169Pswitch(leafno.) 20–25 20–24 18

Fig. 4. leaf development rate vs. temperature for cultivars (a) rB72-454and (b) SP. 83-2847 for base temperature of 10ºc.


Table 6). In South Africa, Singels and Bezuidenhout (2002) found values around 0.60 for measurements up to 120 DAP, while Simões et al. (2005) found ratios of around 0.80 in the southern Brazil region at 140 to 400 DAP. Muchow et al. (1994) found stalk-to-aboveground biomass values ranging from 0.6 at 300 DAP to 0.8 at 450 DAP, in Australia.

The measured root biomass for cultivar RB72-454 shown here (Laclau and Laclau, 2009) corresponds only the first meter of soil depth, so the ratios presented are somewhat underes-timated. The root/shoot ratio decreased from 0.61 kg kg−1 at 42 DAP, which is comparable to 0.42 kg kg−1 at 50 d age as reported by Smith el al. (2005), to 0.09 kg kg−1 at the harvest.

The leaf/aboveground biomass ratio decreased during the crop cycle from 0.26 to 0.10 kg kg−1 and 0.18 to 0.09 kg kg−1 for irrigated and rainfed RB72-454, respectively, and from 0.21 to 0.11 kg kg−1 for both treatments of SP83-2847. These results suggest a direct relationship between the stalk/aboveground biomass ratios and crop age that should be taken into account during the parameterization process.

Specific root lengthLaclau and Laclau (2009) have a detailed description of root

development in treatments 1 and 2 for cultivar RB72-454, here only the aspects relevant for sugarcane modeling are emphasized. First, the specific root length (SRL) (m g−1) was consistent over time despite the large variation in total root lengths within the upper 1 m of soil. The SLR ranges from 16 to 18 m g−1 and 19 to 22 m g−1 on average from 125 DAP onward, in the rainfed

and the irrigated treatments, respectively. Mean SRL down to the depth of 1 m was 17.6 m g−1 for rainfed and 19.1 m g−1 for irrigated crops. Chopart et al. (2008) found a large range of SRL’s (from 7–91 m g−1) measured at 45 and 113 DAP down to a depth of 1.1 m in Ivory Coast. Ball-Coelho et al. (1992) found SRLs near 16.5 m g−1 in northeastern Brazil through the plant and first ratoon crop cycles. So, the default value of 5 m g−1 used in DSSAT/CANEGRO seems very conservative and easily could be increased to as high as 16 m g−1. The simulations reported in this paper used the default values to be comparable to previous papers.

Parameterization of dSSAt/cAneGro

The range of values obtained in the cross validation are sum-marized in Table 7. Some of the parameters values obtained were considerably different from the NCo376 values. In general, parameters related to growth tended to increase compared to default values, while parameters controlling phenology decreased compared to defaults, for both cultivars (Table 7). For example, MaxParce increased about 50% compared to NCo376 values, while Maxpop and Poptt16 showed large decreases. Simulations using the MaxParce NCo376 value resulted in underestimation of all plant components for both Brazilian cultivars.

Values of Suca were slightly higher than the default ones, being out of range proposed by Singels and Bezuidenhout (2002) and Robertson et al. (1996). A previous attempt to opti-mize SUCA constrained to the boundaries provided by these authors resulted in severe underestimation of sucrose content and led to increasing the upper limit to 0.75 (Table 7).

table 6. ratio between root (r) (up to 1-m depth), stalk (S), and green leaf (l) dry mass and total dry mass (t) for cultivar rB72-454, and ratio between stalk and green leaves and aerial biomass (A) for cultivar SP83-2847.

cultivar

treatment

r/t S/t l/tMean Maximum Minimum Mean Maximum Minimum Mean Maximum Minimum

RB72-454 Irrigated 0.35±0.37 0.61 0.09 0.65±0.01 0.66 0.63 0.15±0.07 0.26 0.10Rainfed 0.43±0.38 0.70 0.16 0.62±0.03 0.65 0.58 0.14±0.04 0.18 0.09

S/A L/AMean Max. Min. Mean Max. Min.

SP83-2847 Irrigated 0.60±0.08 0.66 0.46 0.15±0.04 0.21 0.11Rainfed 0.60±0.09 0.66 0.44 0.15±0.05 0.21 0.11

Fig. 5. time series of root, stalk, aboveground and green leaves dry mass for three cultivars in Piracicaba, SP.


Parameters regarding tillering (Maxpop and Poptt16) decreased to nearly half of NCo376 values based on experimental data.

Model evaluationSoil Water and Plant Water Stress

Water content, as measured by tensiometers in soil layers cen-tered at 10, 30, 50, and 80 cm, was reasonably accounted for by the model (Table 8). Since tensiometer measurements reflect the matric potential rather than water content, this comparison may not be strictly valid and does not warrant statistical treatment. Better agreement was achieved in the first half of the crop cycle for both treatments, while the rainfed simulations showed better overall agreement (Table 8) in part due the greater oscillations of matric potential during the crop cycle (Fig. 6b).

For both treatments, the model overestimated soil water content in all layers (Table 8), with the exception of the 21- to 40-cm layer in the rainfed treatment. This trend is the inverse of that observed by Inman-Bamber (1991) in South African using an early version of the CANEGRO model. This result may be due the underestimation of soil Ksat reducing the water flow to lower layers and/or the underestimation of root water uptake in deeper layers, leaving more water available in those horizons. The top layers showed better agreement than deeper ones, as was observed by Inman-Bamber (1991). This may also be a consequence of errors in root simulation in deeper layers.

From the 160th to 210th DAP it is possible to observe a drought period in the rainfed treatment (Fig. 6b) during which the model simulated the observed values well. At 211 DAP a heavy rain event was observed and soon after the model’s soil-water simulation deviate more from the observed value than in the previous period. Laclau and Laclau (2009) reported considerable root mortality in the 0- to 0.2-m soil layer from 179 to 241 DAP (Fig. 5a) in the

rainfed crop. This was mostly due to water stress, and was followed by some recovery of root dry mass afterward.

Those observations from Laclau and Laclau (2009) may explain the consistent underestimation trend after 250 DAP, since the model did not compute any root loss during the mentioned drought period, implying a root water uptake capacity greater than the observed one, and explaining the model’s lack of fit after 179 DAP (Fig. 6b). The water content peak simulated near 211 DAP could be interpreted as an effect of the lower KSsat for this site (Fig. 1), retaining water after rainfall and releasing it slowly.

Predictions of Plant development and Growth Variables

Because DSSAT/CANEGRO is intended to simulate the partitioning among plant components, including stalk dry mass and sucrose, comparison of model predictions to these two frequently-available field measurements is particularly important (Tables 9 and 10). The RMSEP of 9.8 and 9.6 t ha−1 for RB72-454 and SP83-2847, respectively are higher than

table 7. optimized parameters values of dSSAt/cAneGroparameters for two Brazilian cultivars and default nco376 values.

Parameter Units rB72-454 SP83-2847 Standard nco376 ranges for optimizationParcemax gMJ–1 14.86 14.86 9.9 9–15†Apfmx tt–1 0.904 0.904 0.88 0.84–0.92†Stkpfmax tt–1 0.642 0.655 0.65 0.6–0.9†Suca tt–1 0.565 0.65 0.58 0.48–0.75‡Tbft ºC 25 25 25 §Tthalfo ºCd–1 285.9 193.7 250.0 180–300†Tbase ºC 14.4 14.6‡ 16.0 ¶Lfmax leaves 292.1 297.4 428.0 ¶Mxlfarea cm2 796.0 734.0‡ 360.0 ¶Mxlfarno leaf 23 23 23 ¶PI1 ºCd–1 112.8 113.0‡ 69 ¶PI2 ºCd–1 116.6 122.2‡ 169 ¶Pswitch leaf 18 18 14 ¶Ttplntem ºCd–1 292.1 297.4 203.0 428–588†Ttratnem ºCd–1 448.0 486.69 1050 203–303†Chupibase ºCd–1 628.3 628.1 600 400–1050†Tt_Popgrowth ºCd–1 11.82 12.62 30 400–700†Max_Pop stalksm–2 8.4 8.0 30 10–13†Poptt16 stalksm–2 18.4 18.9 13.3 5–10†Lg_Ambase tha–1 220 220 220 §†RangeoptimizedusingGLUEalgorithminDSSAT(Jonesetal.,2010).Upperandlowerlimitwerederivedfromliteratureandexperimentaldata.‡ValuesdefinedafterafirstparameterizationattemptshowingtherangesproposedbySingelsandBezuidenhout(2002)andRobertson(1998)seemedtoonarrowtoparameterizeCANEGROforBraziliancultivars.§Valuesneitheroptimizednorderivedfromexperimentaldata.KeptdefaultvaluesfollowingSingelsetal.(2008).¶Valuesderivedfromexperimentaldata,asdiscussedinsection3.1.

table 8. Statistical comparison of observed and modeled soil water content data for treatments 1 and 2, for four soil layers comprising top 90 cm soil.

Soil

layer†

irrigated rainfed d

rMSe

Modeling efficiency

Bias

d

rMSe

Modeling efficiency

Bias

mm mm mm mm0–20cm 0.78 0.46 0.09 –0.24 0.89 0.14 0.53 –0.0921–40cm 0.82 0.17 0.24 –0.10 0.84 0.04 0.21 0.0441–60cm 0.69 0.20 0.24 –0.13 0.79 0.10 0.17 –0.2070–90cm 0.46 0.11 –1.94 –0.25 0.59 0.30 –0.48 –0.440–90cm 0.82 0.13 0.47 –0.10 0.93 0.03 0.68 –0.64†Tensiometermeasurementsweremadeatthecenterofeachsoillayer.


either the values obtained by Singels and Bezuidenhout (2002) (RMSE = 5.48 t ha−1) in CANEGRO simulations of the NCo376 cultivar in South Africa, or values from Cheeroo-Nayamuth et al. (2000) using APSIM model to simulate sug-arcane growth in Mauritius (RMSEP = 6.0 t ha−1). However, these RMSE are lower than those values obtained by O´Leary (2000) using an older version of CANEGRO, without the modifications of the photosynthesis algorithm proposed by Singels and Bezuidenhout (2002), which was incorporated in the version DSSAT/CANEGRO used here.

Agreement measures for sucrose content showed low predic-tive skills relative to the other variables, with model efficiency for sucrose content ranging from 0.23 to 0.11 for RB72-454 and SP83-2847, respectively. The values of r and d-index were slight

lower than observed by Singels and Bezuidenhout (2002) and by Singels et al. (2008), with a tendency to underestimate sucrose content mainly very late in the crop cycle for both cultivars (Fig. 7b). Results presented by Singels et al. (2008) for experi-ments in South Africa showed the same shape as observed here, overestimating sucrose content under conditions of low sucrose concentration, and the opposite as the sucrose content increased.

Part of these sucrose results might be attributed to the sucrose measurements only during the late season, which reduced the range of variation of values analyzed (Fig. 7b). In general, modeling sucrose accumulation remains a challenge, due a weak understanding of this at the whole-plant level (Inman-Bamber et al., 2009).

The RMSEP obtained for aboveground biomass, ranging from 9.9 to 8.5 t ha−1, may also be regarded as satisfactory, with the highest model efficiency coefficients (over 0.8) among the variables analyzed (Tables 9 and 10). The RMSEP values for aboveground biomass were also higher than those observed by Singels et al. (2008).

The very low agreement obtained for the number of green leaves (Tables 9 and 10) may be mostly due the characteristic of measured data rather than a weakness of model algorithms. Those observations were concentrated in the middle of the crop cycle, and hence had a low range of variation. As modeling efficiency represents how much better the model is compared to the average of observed values, the negative modeling efficiency values for leaf number are due mainly to the stable measure-ments of green leaf number This is, in turn, a consequence of the concentration of measurements during a short period of time, compared to the full-season range of simulated values.

Laclau and Laclau (2009) observed a constant rate of deep-ening of the root front (0.53 cm d−1 or 0.048 cm ºC−1 d−1) over the first 4 mo after planting, and an increase thereafter to 1.75 cm d−1 (0.22 cm ºC−1 d−1) in the irrigated crop and 1.86 cm d−1 (0.24 cm ºC−1 d−1) in the rainfed crop up to harvest. The root front velocity simulated was much higher than the observed one, as deeper roots reached the 4.5 m depth at about 50 DAP, which means a root front velocity of about 6.5 cm d−1. For the rainfed treatment, the observed root length density was 0.265 cm cm−3 in the 0.6 to 1.0 m layer, while the irrigated treatment had as low as 0.059 cm cm−3 in the same layer during the same period (Laclau and Laclau, 2009). The maximum root densities found by Laclau and Laclau (2009)

Fig. 6. Simulated and measured soil water content to 90-cm soil depth.

table 9. Agreement measures of cross-validated predictions for cultivar rB72-454, for stalk dry mass (StKh), aerial dry mass (Aelh), sucrose content (SUch), leaf area index (lAi), number of green leaves (leaf no.), root dry mass (rdM), and root length density (rde).

Measures of agreement StKh SUch lAi Aelh leaf no. rdM rdet(DM)ha–1 tt(WM)–1 t(DM)ha–1 t(DM)ha–1 cmcm–3

Meanobservation 26.9 14.1 2.1 29.0 6.8 1.25 0.167SDobservation 12.7 1.7 1.2 24.4 1.2 0.94 0.154Meansimululation 24.7 12.8 1.6 25.0 7.5 2.71 0.091SDsimulation 17.4 0.8 1.4 21.7 2.3 2.35 0.064RMSEP 9.8 2.0 1.0 9.9 2.4 2.06 0.127Modeff. 0.72 0.23 0.24 0.82 –3.4 –4.27 0.311r 0.83 0.72 0.78 0.92 0.15 0.92 0.880d-index 0.88 0.68 0.84 0.95 0.45 0.64 0.709Bias –2.2 –1.3 –0.54 –3.9 0.70 1.46 –0.076n 12.0 27.0 10.0 12.0 16.0 12.00 70.000


were 0.450 and 0.457 cm cm−3 at 322 DAP in the first 20-cm layer for rainfed and irrigated crops, respectively. Van Antwer-pen (1998) and Smith et al. (2005) reported maximum root length densities of between 0.5 and 2.7 cm cm−3 for several South African cultivars ranging in age from 87 to 238 d after planting. In Australia, Reghenzani (1993) found maximum length densities of 1.3 cm cm−3, and (Ball-Coelho et al., 1992) found roots fully extended into the interrow 4 mo after plant-ing, with maximum length densities as high as 5.3 cm cm−3 in northeastern Brazil. The large differences observed in these studies may be partially due the inherent difficulties to measure the root length density.

The simulations underestimated root length density (Fig. 7e, Table 9). The simulated root dry mass values were always higher than observed throughout the crop cycle, despite the

table 10. Agreement measures of cross-validated predictions for cultivar SP83-2847, for stalk dry mass (StKh), aerial dry mass (Aelh), sucrose content (SUch), leaf area index (lAi), number of green leaves (leaf no.).

Measures of agreement

StKh

SUch

lAi

Aelh

leaf no.

Meanobservation 26.4 13.8 2.1 27.8 8.2SDobservation 13.2 1.9 1.3 24.2 1.4Meansimulation 23.5 12.6 1.6 24.1 6.8SDsimulation 17.8 1.0 1.5 20.8 1.1RMSEP 9.6 1.8 1.1 8.5 2.0Modefficiency 0.81 0.11 0.27 0.87 –1.2r 0.83 0.81 0.72 0.95 0.35d-index 0.91 0.72 0.82 0.96 0.53Bias –2.6 –1.2 –0.44 –3.7 –1.39n 13 30 10 12 14

Fig. 7. Simulated values (based on cross-validation) vs. observed for (a) stalk dry mass, (b) sucrose content, (c) aerial dry mass, (d) number of green leaves, and (e) root length density for both cultivars in all treatments.


high partitioning coefficient (parameter APFMX) which drives synthesized biomass to aboveground parts. The negative bias shown by simulated root length density (Table 9) may be also a consequence of the low specific root length used in the DSSAT/CANEGRO species file, as mentioned above.

conclUSionSThe DSSAT/CANEGRO model, using the described param-

eterization, simulated the sugarcane crop in southern Brazil well. The cross-validation technique permits the use of diverse datasets that would be difficult to use separately because of the heterogeneity of measurements and measurement strategies. In contrast, this technique allowed the richness of this variability to contribute to parameterization. This provides the opportunity to use large amounts of existing data, which is typically under-used in modeling studies, and allows faster progress in countries like Brazil, where the crop has been studied with other objectives.

The simulation errors were comparable with those found in other models, and reported in the literature. Limitations include the tiller algorithm that was based on an assumed fixed response to temperature, and the root algorithm that did not give realistic values of root front velocity, root dry mass, and root length density. The model predictions were best for stalk and aboveground mass. Sucrose accumulation prediction was less accurate. Leaf area index was realistically simulated. DSSAT/CANEGRO reasonably simulated sugarcane growth and development in the Brazilian conditions.

AcKnoWledGMentS

We are grateful to Professor Dr. Francisco Maximino Fernandes and to Dra. Patricia Battie Laclau, who kindly allowed the use of data from Dataset 2 and for root data from Dataset 1, respectively. We also thank Dr. Abraham Singels for his suggestions for improving the paper. This research was partially supported by Brazilian Council for Scientific and Technological Development (CNPq) through the proj-ects 478744/2008-0 and 0303417/2009-9.

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