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Chilean journal of agricultural research

On-line version ISSN 0718-5839

Chilean J. Agric. Res. vol.72 no.1 Chillán Mar. 2012 

Chilean Journal of Agricultural Research 72(1) January - March


Assessing the Transferability of Transpiration-use Efficiency Models of Biomass Production

Comprobando la Transferibilidad de Modelos para la Producción de Biomasa basados en la Eficiencia del uso de la Transpiración

Cristián Kremer1,2*, and Claudio Stöckle1

1Washington State University, Biological Systems Engineering Department, Pullman, Washington, 99163, USA.
2Universidad de Chile, Facultad de Ciencias Agronómicas, Av. Santa Rosa 11315, Santiago, Chile. "Corresponding author (

Transpiration-use efficiency (w), defined as the ratio of biomass produced per unit water transpired, has been used to evaluate crop performance under limited water supply. However, the lack of consistency of w values through different environmental conditions has not allowed, using it as a transferable parameter. Thus, simple approaches have been developed, including: 1) w = kDa Da1 and; 2) w = kEto ETo'1 where kDa and kETo are crop-dependent parameters, with the underlying concept that normalization by Da or ET0 would accounts for the effects of climate variations on w, while these parameters would be reasonably constant across diverse environments. The objective of this study was to assess the transferability of kDa and kET^0 for wheat (Triticum aestivum L.) and maize (Zea mays L.). The scarcity of experimental information and discrepancy of the methodology used, justified the use of a canopy transpiration and photosynthesis model which was developed, tested, and fitted with weather data from eight environmentally different locations to simulate values of w, kDa and kETOo. The results indicated that kDa and kET^0 were more variable than expected; suggesting that calibration would be desirable. A consistent trend of change of the parameter values as function of Da or ET0 was found, which can be represented by mathematical functions, allowing transferring w, kDa and kET^0 (maize). In contrast, the kETOo for wheat correlated weakly with Da and ET0, but a low overall coefficient of variation (10%) allowed using an average value as a reasonable predictor of w.

Key words: Transpiration-use efficiency, models of biomass production.

Eficiencia del uso de la transpiración (w), definida como la relación entre biomasa producida por unidad de agua transpirada, se ha utilizado para evaluar productividad bajo condiciones limitadas de agua. Sin embargo, la falta de consistencia de valores w bajo condiciones climáticas distintas no ha permitido su uso como parámetro transferible. Consecuentemente, aproximaciones simples han sido desarrolladas, incluyendo: 1) w = kDa Da1 y; 2) w = kETo ET0-1 donde kDa y kETo son parámetros dependientes del cultivo, y sustentado en que la normalización por Da o ETo absorbería el efecto del clima en la determinación de w, mientras que estos parámetros se mantendrían razonablemente constantes. El objetivo de este estudio fue determinar la transferibilidad de kDa y kETo para su uso en trigo (Triticum aestivum L.) y maíz (Zea mays L.). La escasez de información experimental y metodologías usadas, justificó el uso de un modelo para estimar transpiración y fotosíntesis, el cual fue desarrollado y probado con datos de ocho regiones climáticamente distintas para simular valores de kDa y kETo. Los resultados indicaron que estos parámetros poseían mayor variabilidad de la esperada, sugiriendo que una calibración previa sería necesaria. Además, el cambio de estos parámetros como función de Da o ET0 tiene una tendencia consistente, representable por funciones matemáticas, permitiendo transferir w, kDa y kETo (maíz). Por otro lado, valores de kETo en trigo se correlacionaron débilmente con Da y ET0, pero un bajo coeficiente de variación (10%) permitiría el uso de un valor promedio como un predictor razonable de w.

Palabras clave: eficiencia en el uso de la transpiración, modelos de producción de biomasa.

Agriculture is challenged by the scarcity of water resources in many regions of the world, problem that is compounded by climate variability and expected to worsen in the future. There is a raising need for tools to evaluate crop productivity as a function of water to better guide development policies and field management practices aimed at producing "more crop per drop".

Mechanistic simulation models of canopy photosynthesis and transpiration appear as suitable tools to evaluate the effect of interacting factors on water-use efficiency and productivity of crops. However, demanding parameterization and computing requirements of these models limit their applicability for long-term analysis that includes multiple species across the globe. As a result, there is a renewed interest in simple, transpiration-based models of crop productivity that can be readily applied to a large number of crop species across the range of climatic conditions where these crops are grown. Although these models were introduced as early as the beginning of the previous century, the experimental determination of the parameters (typically just one parameter) used in the models has been relatively scarce, probably due to the need of measuring crop transpiration for their determination. As a result of scarce experimental information, it is not easy to assess the variability and transferability among locations of the parameters of these simple transpiration-based models.

Attempts to develop simple relationships to predict w for different crops and climates can be traced back to the early 20th century and later (Brigss and Shantz, 1914; Shantz and Piemeisel, 1927; de Witt, 1958; Arkley, 1963; Bierhuizen and Slatyer, 1965; Tanner, 1981; Ritchie, 1983; Tanner and Sinclair, 1983; Steduto and Albrizio, 2005). The underlying assumption has been that the parameters of these relationships are relatively constant across diverse climatic conditions, and assumption that has not been well evaluated.

Early work by Bierhuizen and Slatyer (1965) led the way to the development of a comprehensive physiologically-based description of transpiration use efficiency as follows:


where Nl is the net leaf photosynthesis, Tl is the leaf transpiration, ΔC is the CO2 concentration difference between the atmosphere and the CO2 compensation point, rCO2 is the leaf resistance to CO2 diffusion from the surrounding air into the leaf and into the cells of the chloroplasts, ρ is the density of the air, e is the vapor to air molecular weight ratio, Dl is the vapor pressure difference between the leaf and the surrounding air, Pa is the atmospheric pressure, and rv is the summation of the partial resistances to water vapor flux from the leaf. Bierhuizen and Slatyer (1965) showed that the ratio Ni Tl'1 is determined largely by Dl based on the following assumptions: (1) ΔC is a relatively constant crop-dependent parameter, and (2) the rv rCO2-1 ratio is fairly constant in active leaves when the water stress is not severe. The authors redefined Equation [1] in a simpler expression:

here kl is considered constant for leaves in a given crop. The authors also argued that Nl Tl'1 should be proportional to canopy B T -1 (where B is canopy dry matter and T is canopy transpiration) and, therefore, kl could be scaled up to the entire canopy kDa and that Dl could be well represented by the air vapor pressure deficit Da since the leaf temperature appear to be within ± 2-3 °C of air temperature. Hence:

w = BT -1= kDa Da-1 [4]

where kDa is obtained experimentally as the slope of the linear regression between cumulative biomass and the daily integration of the quotient TDa-1.

Tanner and Sinclair (1983) extended the work initiated by Bierhuizen and Slatyer (1965) and Tanner (1981), developing equations to represent biomass production and transpiration of the sunlit and shaded fractions of the canopy, essentially leading to a re-derivation of Equation [4].

Although Equation [4] has been adopted as a reasonable predictor of biomass accumulation (Stòckle et ai., 1994; Sinclair and Seligman, 1995), concerns have been raised about the transferability of kDa (Kemanian et ai., 2005). These authors argued that kDa is not a "constant" for a crop, but it rather changes with environmental conditions, most noticeable Da.

Steduto and Albrizio (2005) presented field data and a discussion of the concept and mechanism of determination of kDa, including C3: chickpea (Cicer arietinum L.), sunflower (Heiianthus annuus L.), wheat (Triticum aestivum L.), and C4: sorghum (Sorghum bicoior (L.) Moench subsp. bicoior) species in one location (Bari, Italy; 41o03' N, 16o52' E, 72 m a.s.l.). They found that their kDa values had large variability among species and did not match data for the same species from literature. Two explanations to their findings were mentioned: 1) the error introduced by scaling Di to Da, especially in low Da conditions where leaf temperature can be several degrees larger than air temperature, and 2) the effectiveness of Da normalization to represent Di since the latter is defined by the transpiration flux, which changes as the physiological stage of the crop changes. They proposed an alternative methodology, similar to the original work by de Witt (1958), where w is a function of the evaporation rate of a reference condition as:

w = BT -1= kETo ET0 -1 [5]

where ET0 is the reference crop evaporation computed as proposed by Allen et ai. (1998) and kETo is the slope of the linear regression between cumulative biomass and the daily integration of the quotient TET0-1. Steduto and Albrizio (2005) claim that this method would work better than Equation [4] and that kETo appeared transferable among different climatic zones. However, this claim was based on limited data and has not been verified.

The main objective of this work was to evaluate the transferability across diverse climatic condition of kDa and kETo of wheat and maize. However, experimental data allowing the calculation of kDa and kETo is scarce and does not cover well the wide array of environmental conditions where wheat and maize are grown. In addition, the available data include differences in cultivars, crop management, methods to estimate transpiration, sampling methods for biomass, and other sources of variability and experimental error, making it difficult to evaluate the constancy of the parameters. For that reason, a canopy transpiration and photosynthesis (CTP) model was developed and tested (Kremer, 2006), and used as reference to obtain simulated values of w, kDa, and kETo under variable climatic conditions while crop and soil characteristic were held constant, allowing a more consistent evaluation of the transferability of these parameters.


The model
An hourly time step canopy transpiration and photosynthesis (CTP) model, separating sunlit and shaded fractions of the canopy, was developed as a tool to obtain simulated values of kDa and kETo. The model simulates C assimilation (g CO2 m-2 ground area), and crop transpiration (kg H2O m-2 ground area) in response to climatic conditions, soil and plant water status, and atmospheric CO2 concentration. Transpiration, photosynthesis, stomatal conductance, and plant water uptake are solved simultaneously through an iterative numerical procedure. Daily measurements of global solar radiation, air temperature, air humidity, and wind speed are inputs to the model. Additional inputs include green leaf area index (LAI), maximum crop height, maximum LAI, assimilation rate as a function of intercellular CO2 concentration, stomatal conductance response to air vapor pressure deficit and leaf water potential, and soil characteristics (hydraulic parameters, bulk density, depth, and number and thickness of soil layers). Model performance was tested using meteorological and crop data (wheat and maize) collected at the Conservation and Production Research Laboratory, Bushland (35°11' N, 102°06' W; elevation 1170 m a.s.l.), Texas, USA, indicating the suitability of the model for the application presented in this research. A more detailed description of the CTP model and parameters for the simulation of wheat and maize transpiration-use efficiency is presented in Kremer (2006). For this study, soil water content, LAI, crop height, and crop parameters for photosynthesis and stomatal conductance were held constant during the entire simulation period at all the locations. Thus, only daily weather was variable.

Meteorological data
To generate a highly diverse set of conditions, daily weather data from eight locations were selected. The data were composed of daily measurements of global solar radiation (MJ m-2 d-1), maximum and minimum air temperature (oC), maximum and minimum air relative humidity, and average wind speed (m s-1), encompassing the period day of the year (DOY) 120 through 239 for a year selected at random in the following locations: Concepcion del Uruguay (32°28' S, 58°16' W; elevation 20 m a.s.l.), Argentina; Landriano (45°18' N, 9°15' E; elevation 78 m a.s.l.), Italy; Temple (31°7' N, 97°4' W; elevation 208 m a.s.l.), Texas, USA; Pullman (46°45' N, 117°1' W; elevation 756 m a.s.l.), Washington, USA; Prosser (46° N, 119°7' W; elevation 380 m a.s.l.), Washington, USA; Ankara (40°7' N, 32°59' E; elevation 948 m a.s.l.), Turkey; Aleppo (36°1' N,37°18' E; elevation 430 m a.s.l.), Syria; and DOY 166 through 239 for Maricopa (33°49' N, 112°1' W; elevation 359 m a.s.l.), Arizona, USA. The main climatic characteristics of the selected period in the eight locations are presented in Table 1.

Table 1. Mean (x) and standard deviation (sd) of weather data from eight locations and selected periods.


Tmax and Tmn: maximum and minimum ir temperatures (°C), Sr: global solar radiation (MJ m-2 d-1), RHmax and RHmrl: maximum and: minimum relative humidity, ETo: reference evapotranspiration (mm d-1), Da: day time air vapor pressure deficit (kPa) estimated as: Da = 2/3 es(Tmax), (1 - Rmin). where es (Tmax) is the saturation vapor pressure of the air in kPa at maximum.

Determination of kDa and kETo
Daily transpiration and photosynthesis for wheat and maize were simulated for all locations using the CTP model and assuming well-developed and unstressed crops. The parameters kDa (g CO2 kg-1 H2O kPa) and kETo (g CO2m-2) were estimated as the slope of the linear regression between cumulative photosynthesis and the accumulation of the transpiration to daytime Da quotient (Tanner, 1981; Condon et al., 1993) and transpiration to ET0 quotient (Steduto and Albrizio, 2005), respectively. Calculations of the parameters were done for moving 15-d intervals, shifted by 5 d throughout the 120-d period. Daily ET0 calculation was carried out as proposed by Allen et al. (1998).


As was expected simulated w values for 15-d periods across eight locations were highly variable (Table 2), with coefficient of variation of 25% and 18% for wheat and maize, respectively, with the known implication that w values determined experimentally in one location may not be readily transferable to another. Normalization of w by Da Equation [4] or ET0 Equation [5] is expected to account for weather variability, with the parameters kDa or kETo remaining reasonable constant. However, as shown in Table 2 kDa and kETo (maize) present more variability than desirable for transferring values derived in one location to another with kDa variability being greater than that of kETo.

Table 2. Mean (x), standard deviation (sd), number of data (n), and coefficient of variation (CV) for simulated values of transpiration-use efficiency (w), and the crop parameters kDa and kETo from eight locations.


As pointed out by Tanner (1981) and Steduto and Albrizio (2005), a drawback associated with Da normalization is usually related to the degree of error introduced on the assumption that Da is a fair representation of Dl, especially in humid environments. In these environments, transpiration rate is expected to be lower, and as a result leaf temperature should increasingly depart from air temperature making Dl larger than Da. To test this assumption, the values of kDa obtained in environments with Da less than 1 kPa were not included in the coefficient of variation (CV) analysis. Some improvement on CV was obtained for both crops however the variability still remained (wheat: 18.75%, and maize: 26.18%).

Figures 1 and 2 present w as a function of the average Da and ET0 of each corresponding 15-d interval. Both figures show that w is not constant across environments characterized by Da and ET0, and has an important non-linear response to Da and ET0 (Abbate et al., 2004; Kemanian et al., 2005). Fitted power equations appear good estimators of w, with Da explaining 94% and 90% of the w variability for wheat and maize, respectively, and ET0 explaining 89% and 72%, respectively. The dispersion around the fitted lines represents variability due to climate that is not accounted for Da or ET0. This effect of other weather variables is less important with Da and ET0 greater than 2 kPa and 7 mm d-1, respectively.

Figure 1. Transpiration use efficiency (w, g CO2 kg-1 H2O) as a function of the air water vapor pressure deficit (daytime, kPa) for wheat and maize.

Figure 2. Transpiration use efficiency (w, g CO2 kg-1 H2O) as a function of reference evapotranspiration ((ET0 mm d-1) for wheat and maize.



Figure 3 reaffirms that the variability in Table 2 is not random, but can be explained to a large extent when kDa values are plotted vs. Da or ET0. A linear equation was fitted to the kDa values and included in the figure. It seems that Da was able to explain kDa variability better than ET0, which presented a larger scattering, particularly for wheat. These results confirm that: 1) kDa is not a constant value and, 2) kDa increases when Da and ET0 increases.


Figure 3. Variability of the crop dependant parameter koa (g CO2 kg1 H2O kPa) as a function of the daytime vapor pressure deficit (Da; kPa), and the reference evapotranspiration (ETo, mm d1) for wheat and maize.


The significant conclusion is that the use of Equation [4] to estimate w has to considerer local calibration of kDa to be transferable. The linear response obtained for kDa should facilitate transferability through field calibration based on a few points across the environmental range. The fitted linear equations included in each figure, can be used as kDa estimators for climatic conditions characterized by different Da or ET0.

In an attempt to explain kETo variability, kETo values were plotted vs. Da and ET0 (Figure 4). Fitted linear equations are included in the Figure 4, which shows that kETo variation in wheat does not correlate well with variations in climatic conditions represented by Da or ET0. However the relatively low CV and standard deviation (sd) determined that a mean value of 55.87 (g CO2 m-2) can be used as a constant regardless of the climatic environment, supporting the view of Steduto and Albrizio (2005). Nevertheless, some response of kETo for wheat when the ET0 gradient is increasing was observed (Figure 4), suggesting some benefit of using the fitted equation in situations with high evaporative demand.


Figure 4. Variability of the crop dependant parameter kETo (g CO2 m2) as a function of the daytime vapor pressure deficit (Da; kPa), and the reference evapotranspiration (ETo, mm d-1) for wheat and maize.

A different scenario was found in maize (Table 2). Figure 4 shows that kETo (maize) did not correlate well with variations in Da, and that the variability was better explained by ET0, although ET0 alone was not able to account for the entire variability due to weather. It can be concluded that kETo is not a constant and, therefore, experimental values cannot be transferred among locations with different climate. The linear equation presented here to estimate kETo as function of ET0 for maize should be taken as first approximation to overcome the transferability problem.


The simulation results showed as was expected that w is not constant across climatic environments, so that values determined in one location cannot be readily transferred to another. However, w as a function of Da and ET0 was well described by a power function, with Da explaining 94% and 90% of the w variability for wheat and maize, respectively, and ET0 explaining 89% and 72%, respectively. The dispersion around the fitted lines was much lower with Da and ET0 greater than 2 kPa and 7 mm d-1 , respectively.

Normalization of the kDa and kETo parameters of two simple transpiration-use efficiency models by Da and ET0 was not able to properly account for the effect of weather variability, resulting in parameters still too variable to be readily transferred across locations for both wheat and maize.

It was found that the transferability of these parameters can be dramatically improved when they are plotted against Da (in the case of kDa) or ET0 (in the case of kETo), with linear functions describing well the relations and explaining 79% and 91% of kDa variability for wheat and maize, and 71% of kETo variability for maize. The kETo for wheat correlated weakly with ET0, explaining only 25% of its variability. However, the overall coefficient of variation of this parameter across eight locations was about 10%, so that the use of a constant kETo value is not unreasonably, although is not a perfect solution.

The simulation-based equations presented here are offered as a first approximation to overcome the spatial transferability of w, kDa, and kETo, but field validation will be required before adoption is recommended.


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Received: 18 April 2011.
Accepted: 4 January 2012.