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There is currently a great deal of interest in estimating crop productivity as a function of climatic factors by means of different crop weather models. In this article, an agrometeorological model based on maximum carbon dioxide assimilation rates for C3 plants, fraction of photosynthetically active radiation, air temperature, photoperiod duration, and crop parameters is assessed as to its performance under tropical conditions. Crop parameters include leaf area, harvest index, dry matter content of potato tubers, and crop cycles to estimate potential potato yields. Productivity obtained with the cultivar Itararé, grown with adequate soil water supply conditions at four different sites in the state of São Paulo (Itararé, Piracicaba, Tatuí, and São Manuel), Brazil, was used to test the model. The results revealed excellent performance of the agrometeorological model proposed here with an underestimation of irrigated potato productivity of less than 10%.
We considered potential yield to be the maximum possible yield of a given species or cultivar achievable under the existing conditions of solar radiation flux density with all the other environmental factors considered to be optimal. Therefore, the potential yield is determined by the biological properties of the cultivar and radiation resources available. Potential yield expresses the solar radiation resources for cultivating a given genotype in yield units, whereas the commercial yield is the yield attainable under existing farm conditions that takes into account all the factors limiting the production process and the crop yield.
Meteorological factors directly influence potential crop productivity, regulating its transpiration, photosynthesis, and respiration processes in such a way as to control the growth and development of the plants throughout their physiological mechanisms at a given site. The interaction of the meteorological factors with the crop responses is complex. However, by assessing physiological crop responses to environmental factors under field conditions, it is possible to derive mathematical models to estimate crop potential production as a function of climatic variables with good precision.
Research has been conducted to quantify the effects of the environment on growth, development, and yield of many agronomic crops. Among the main environmental factors that strongly govern all physiological processes of the plants are global solar radiation flux density, air temperature, and available soil water content (Coelho and Dale, 1980).
Potato yield improvements can be obtained by increasing the net daily photosynthetically radiation (PAR) through higher solar irradiance or longer photoperiod (Stuttle et al., 1996). The photoperiod duration doubles from December to June at 50°N, whereas PAR increases eightfold from 2.11 to 17.01 MJ·m−2·d−1 as a result of higher elevation of the sun above the horizon with lengthening days. Gross carbohydrate production on standard clear days increases from 108 to 529 kg·ha−1·d−1 at 50°N, whereas it remains at ≈420 kg·ha−1·d−1 year-round near the equator. Low solar irradiance is a yield constraint at 30 to 40°N in fall and spring when potatoes are grown to escape the summer heat (Haverkort, 1990).
Sarquis et al. (1996) stated that the magnitude of the effect of elevated temperatures on potato growth and final yield is determined by an intricate interaction among soil temperature, air temperature, solar radiation flux density, and photoperiod duration. Their data extended previous observations of the reduction in photosynthesis rate under elevated temperatures (Manrique and Bartholomew, 1991; Midmore and Prange, 1992). Under field conditions, reduced dioxide carbon assimilation could not explain the yield reduction observed; the temperature effect on assimilation was not as dramatic as it was on growth or yield. Other workers have reported a severe reduction in the rate of assimilation at air temperatures above 30 °C under controlled experimental conditions. In such cases, reductions in CO2 assimilation rate were shown to correlate well with reductions in growth and yield (Ku et al., 1977; Midmore and Prange, 1992). These results reveal the complexity of plant responses to the combined effects of water and temperature stress, which inevitably occur in association under field conditions (Pereira and Shock, 2006).
Knowledge of climatic requirements of potato and its physiological responses to the environment is extremely important to help growers produce high yields with good tuber quality under site-specific atmospheric conditions. The potato growth models included in DSSAT (Decision Support System for Agrotechnology Transfer) are SUBSTOR-POTATO and LINTUL-POTATO (University of Hawaii, Honolulu, Hawaii). The SUBSTOR-Potato crop soil weather model takes into consideration daily air temperature, photoperiod, intercepted solar radiation, soil water, and nitrogen supply. The model simulated fresh tuber yields ranging from 4 t·ha−1 to 56 t·ha−1 resulting from differences in weather patterns, soils, cultivars, and management practices (Bowen, 2003).
Kadaja and Tooming (2004) proposed a relatively simple model, POMOD, to calculate potato yield, which permits integration of the knowledge in different disciplines on the potato crop yield levels using the measured physiological, ecological, agrometeorological, and agronomical parameters of the plant. The input variables of the model can be divided into four groups: daily meteorological information, annual information, location, and cultivar. The first group includes global radiation, air temperature, and precipitation. The location is characterized by geographical latitude and hydrological parameters. As to cultivar, the parameters of gross and net photosynthesis, the coefficients of growth and maintenance respiration, and albedo of the crop are also needed.
The LINTUL-POTATO simulation model (Kooman and Haverkort, 1995) establishes potential yield of a certain cultivar for a determined growing period and plant density and is based on incident PAR, the fraction of PAR intercepted by the crop, and radiation use efficiency to produce dry matter. Phenological crop development is driven by accumulated degree-days, whereas development stage determines dry matter partitioning and the pattern of intercepted PAR is defined through growth. The potential yield established with this simulation model was used by Caldiz and Struit (1999) to perform a preliminary yield gap analysis regarding actual and attainable potato yield in different areas of Argentina.
We tested the performance of a model based on studies of maximum rates of carbon dioxide assimilation for a C3 crop as a function of air temperature, a fraction of global solar radiation flux density (PAR), photoperiod duration, and leaf area index to estimate the potential productivity of potato. To assess the performance of the proposed mathematical model, the estimated values of tuber yield were compared with observed productivity data under irrigation conditions for the studied sites. The present study was similar to the potential productivity estimation model described by Villa Nova et al. (2001) and used by Villa Nova et al. (2005) for sugar cane in Piracicaba, São Paulo, Brazil.
The proposed model for the estimation of potato potential yield (EPY, t·ha−1), expressed by Eq. [1], is based on the concept that the maximum rate of dioxide carbon assimilation by the plants for production of carbohydrate (CH2O) is related to the active photosynthetically fraction of the solar spectrum (PAR) and air temperature:
where CDA is the carbon dioxide assimilation rate (μL·cm−2·h−1), LAI is the maximum leaf area index, GS is the number of days of the crop growing season, N is the mean photoperiod or daylength duration throughout of the crop growing season (hours), C(LAI) is the correction factor for leaf area index variation over time, C(T) is the correction factor for maintenance respiration, HI is the harvest index, and DM is the dry matter content of the potato tubers (%).
Making use of the Clausius-Clapeyron's equation with the masses of CO2 equal to 44 g·mol−1 and of CH2O corresponding to 30 g·mol−1, and considering 1 μL of CO2 at 15 °C (288 K) and 1 atmosphere equal to 1.863*10−6 g CO2, one can infer that the CH2O/CO2 ratio assumes a value of 1.27*10−6 g CH2O/μL CO2 (Villa Nova et al., 2001).
Applying the necessary corrections to the aforementioned equation to express the estimates of potato potential yield in tons per hectare per crop cycle, we have:
Without considering HI, the product of the other terms of the Eq. [2] depicts the estimation of the total dry matter produced by the potato plants, including roots, leaves, and shoots.
Plotted and interpolated values of CDA were obtained from a graph that shows the relation between air temperature and maximum rate of CO2 assimilation for a C3 crop species under controlled conditions (van Heemst, 1986) as a function of the ambient temperature (T) and PAR. However, under field conditions where plants are subjected to fluctuating temperature conditions, there appears to be adaptation of the photosynthetic apparatus. Thus, such plotted and interpolated CDA data are described mathematically by the following equation (Penning de Vries et al., 1989):
where CDAmax is the maximum carbon dioxide assimilation rate of 48 μL·cm−2·h−1.
The PAR, expressed in J·m−2·s−1, was calculated by the equation proposed by Assunção (1994) as a function of the global solar radiation flux density and insolation ratio:
where Qg is the mean global solar radiation flux density throughout the crop growing season (J·m−2·d−1), N is the mean photoperiod during the crop cycle (hours), and n/N is the actual mean insolation ratio of the period.
The global solar radiation flux density (Qg) was estimated taking into account the mean values of a and b Angstrom's coefficients obtained by Cervellini et al. (1966) for the State of São Paulo, Brazil. The equation used for the sites where no radiometric measurements were available for the current study was the following:
where Qo is the extraterrestrial radiation, expressed in J·m−2·d−1, having been determined by the subsequent expression:
where 38.32*106 is the mean value of corrected solar constant converted into J·m−2·d−1, given by Crommelynk and Fichot (1997), H is the semiarc from the meridian crossing of the sun to sunset in degrees, h is the diurnal semiarc in radians, δ is the solar declination in degrees, and ϕ is the local latitude in degrees.
The equations that defined δ, H, and N (Pereira et al., 2003) were:
where DJ is the number of days since the first day of January up to the considered date.
The number of hours of insolation (n) was measured with a Campbell-Stockes sunshine recorder installed at the four weather stations where the studies were carried out.
All the meteorological data used as input variables of the potato potential yield model were obtained from conventional weather stations set up at research locations of the Agronomic Institute of Campinas, IAC, University of São Paulo, ESALQ/USP, and State University of São Paulo, FCA/UNESP. These governmental institutions of the state of São Paulo provided the necessary meteorological data for the municipalities of Itararé, Tatuí, Piracicaba, and São Manuel, São Paulo, Brazil.
The climate of Tatuí (23°22′S, 47°52′W Gr., and 600 m), Piracicaba (22°43′S, 47°25′W Gr., and 580 m), and São Manuel (22°44′S, 48°34′W Gr., and 700 m) is classified as Cwa or subtropical with rains in the summer and dry winter according to the Kőppen System. The climate of Itararé city (24°06′S, 49°20′W Gr., and 1150 m) in the state of São Paulo, Brazil, is classified as Cfb or rainy temperate of altitude, constantly wet throughout the year.
The values of C(T) equal to 0.6 and 0.5 were adopted whenever the mean air temperatures throughout the crop-growing season were below or above 20 °C, respectively, as recommended by Doorenbos and Kassam (1979). The value of C(LAI) was calculated by the equation described by Villa Nova et al. (2001) as follows:
The ratio between harvested yield and net total dry matter is given by the HI for high-producing cultivars under irrigation. For potato, whose commercial product is the tuber, HI varies from 0.55 to 0.65 (Doorenbos and Kassam, 1979). For practical purposes, we adopted the mean value corresponding to 0.6 to calculate the final crop production.
The maximum LAI for the cultivar Itararé (IAC-5986) was determined experimentally in the field by Varillas (1991) and Robles (2003) under the climatic conditions of Itararé and Piracicaba.
The dry matter content of the tubers is intimately related to the tuber-specific gravity. To measure tuber-specific gravity, the weight-in-air/weight-in-water method was used. For that, a random sample of tubers was first weighed in air (Wair) and, after submerging the tubers in water, weighed again (Wwater). Thus, specific gravity (SG) was calculated using the following formula (Stark and Love, 2003):
Dry matter content of the tubers in percentage was determined by the expression described by Ramos (1999) as a function of the specific gravity as follows:
The calculated values of the potential yield obtained by the proposed method were correlated with the observed data from the production fields. Because the coefficients of correlation and determination are not always suitable to evaluate the performance of a model, the agreement index d was also used (Willmott et al., 1985). The index c proposed by Camargo and Sentelhas (1995) was also adopted in this article to indicate the performance of the model, putting together the accuracy R and the exactness d indices, being defined as the product of both indices.
The values of the tuber-specific gravity and dry matter content were obtained by the researchers from the Agronomic Institute of Campinas (IAC) at all the locations where the potato experiments were conducted from 1985 to 2005 (unpublished data).
Potato potential yield for the cultivar Itararé was calculated throughout 15 site years at four different regions of the state of São Paulo, Brazil (Tables 1 and 2) using of the mean values of global solar radiation flux density, photoperiod duration, PAR, air temperature, and the maximum rates of carbon dioxide assimilation obtained from Eq. [3], which are the required input variables of the proposed model.
Tuber potential yields calculated by the agrometeorological model in the study and potential yields harvested from the production fields were highly correlated, because the statistical analysis shows that over 92% of the potential yield variations can be explained by the calculated values. The corresponding values of fresh tuber yields estimated by the model varied from 16.8 to 35.7 t·ha−1, whereas those of fresh tuber yields obtained from the production areas with an adequate soil water supply were within the range varying from 17.5 to 39.0 t·ha−1 (Table 2). The larger difference between measured and estimated tuber yield was observed for the growing period September through January of the years 1998 and 2003 when the model slightly underestimated and overestimated potential yield at 3.3 and 3.5 t·ha−1, respectively.
In the most important potato production areas of Argentina, Caldiz and Struit (1999) reported that actual fresh tuber yields vary from 13 to 30 t·ha−1, whereas potential yields estimated by the LINTUL-POTATO (Research Institute for Agrobiology and Soil Fertilizer, Wageningen, The Netherlands) simulation model ranged from 47 to 126 t·ha−1. Differences between actual and potential yield might be attributed to suboptimal solar radiation interception by the foliage, cultivar, seed management, physiological age of the seed, suboptimal management of water and fertilizer, and inadequate control measures for early blight and late blight.
The potential yield of agronomic crops is dramatically affected by the amount of water applied during the crop-growing season at a given region. Water and temperature are important climatic factors to consider in crop modeling studies. Cooler temperatures result in delayed maturity, which provides more time for the interception of solar radiation and conversion of intercepted radiation into dry matter. Stark and Love (2003) point out that two major factors influence tuber yield: 1) photosynthetic activity and duration of the leaf canopy and 2) the length of the linear tuber growth phase. The longer a canopy is able to produce photosynthate at a relatively high rate, and the longer tubers are bulking at their maximum rate, the higher the yield will be in such a way as to express the productive potentiality of potato crop at a given site.
As to the effect of water application on the productive potentiality expression of potato in a determined climatic locality, Bowen (2003) reported that a reduction of only 62 mm in water applied resulted in a decrease in fresh tuber yield from 38.2 to 30.3 t·ha−1. For the summer potato crop, applied water ranged from 380 to 584 mm and the associated yields ranged from 12.1 to 25.4 t·ha−1. Therefore, approximately half as much water was used during the winter to produce 150% more yield than was obtained throughout the summer crop-growing season.
The differences observed on the dry matter content throughout different years and growth periods of the potato crop (Table 2) might be ascribed to climatic variations on tuber-specific gravity. Apart from the primary environmental factors affecting specific gravity of irrigated potatoes (air and soil temperatures), other weather conditions can also affect tuber-specific gravity.
Stark and Love (2003) state that high evaporative demand caused by low relative humidity, high global solar radiation flux density, or high wind speed can reduce photosynthesis by causing stomata to close with an accompanying restriction of CO2 uptake. Prolonged periods with overcast skies can also reduce light intensity to levels below that required for maximum dry matter production.
The coefficient of determination R2 and correlation R bring information about the degree of accuracy but do not reveal the exactness of the model. The index of agreement d equal to 0.981 reveals a high level of exactness. The index c was 0.945 for the studied sites, showing an excellent model performance according to the interpretation reported by Camargo and Sentelhas (1995). Both the model accuracy, given by the trend line, and the model exactness shown by the dispersion of the data around the fitted 1:1 line were outstanding (Fig. 1). The value of c was higher than 0.93, exceeding, therefore, the values of d considered as satisfactory. The lower limit for the index c recommended by Robinson and Hubbard (1990) is 0.75.
Citation: HortScience horts 43, 5; 10.21273/HORTSCI.43.5.1611
The results showed that the agrometeorological model tested under the climatic conditions of the state of São Paulo, Brazil, in general underestimated irrigated potato yield by less than 10%. This justifies the recommendation to test the performance of the model in other climatic regions for different crops and genotypes under optimal irrigation conditions in further scientific investigations.
Given the excellent performance of the model, we suggest that it can be used to forecast harvest time or be used as an effective tool to predict the suitability of potential regions to the cultivation of potato crops, cultivar Itararé (IAC-5986), in the state of São Paulo, Brazil.
The agrometeorological model taking into account information on LAI, photoperiod duration, PAR, and air temperature is feasible to estimate potential tuber yield at a commercial scale.
Contributor Notes
The access to the meteorological data provided by the Agrometeorology Division of the Instituto Agronômico de Campinas (IAC) by means of Dr. Orivaldo Brunini and Dr. Mario J. Pedro Junior is greatly appreciated. Many thanks are owed to the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for the provision of the productivity scholarship as well as to Sandy Shelton, MSc, from San Francisco, CA, for the thorough revision on the English of this manuscript.
Associate Professor.
Associate Professor and Brazilian Federal Funding Agency Researcher.
To whom reprint requests should be addressed; e-mail andre.pereira@pq.cnpq.br
