Materials and methods

Data.

Yield data from 118 planting dates spanning the years from 2002 to 2007 were compiled into a single database (GDDLA-Y). Storage roots were graded according to USDA standards (USDA, 2005): US #1 grade = 2 to 3-1/2 inches in diameter, 3 to 9 inches in length, maximum weight not more than 20 oz; canner = 1 to 2 inches in diameter, 2 to 7 inches in length; jumbo = larger versus the others, but marketable. These tests represented various planting times (May to July), cultural practices (irrigation regimes, weed control, and cropping patterns), management regimes (experimental station and on-farm replicated trials), and locations [northern and south central Louisiana (Table 1)]. The yield data were obtained from plots that were planted with ‘Beauregard’ and no significant year × US#1 yield interaction was detected. Yield in the US #1 grade ranged from 38 to 617 50-lb bushels per acre (mean = 306 bushels/acre). Days to harvest ranged from 83 to 166 DAT.

Table 1.Location of experimental test sites for ‘Beauregard’ sweetpotato in Louisiana.

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Sampling.

Agrometeorological data were collected from the following Louisiana Agriclimatic Information System (LAIS) weather network stations (Louisiana Agriclimatic Information, 2008): Burden Center, Baton Rouge (BTR), R & D Research Farm, Port Barre (SC), Sweet Potato Research Station, Chase (CHS, NE10), and University of Louisiana at Monroe (NE). Values enclosed in parentheses represent location of test sites as defined in Table 1. Daily agrometeorological variables included maximum air temperature (MAXAIR), minimum air temperature (MINAIR), mean air temperature (MEANAIR), maximum soil temperature (MAXSOIL), minimum soil temperature (MINSOIL), mean soil temperature (MEANSOIL), radiation (RAD), maximum relative humidity (MAXRH), minimum relative humidity (MINRH), mean RH (MEANRH), and total rainfall (RAIN). Means (MAXAIR, MINAIR, MEANAIR, MAXSOIL, MINSOIL, MEANSOIL, RAD, MAXRH, MINRH, and MEANRH) or totals (RAIN) were calculated for the following periods: 5, 10, 20, and 30 DAT for each planting date. Normality analysis was performed on the combined yield and agrometeorological data set using SAS Analyst (version 9.2; SAS Institute, Cary, NC). Outliers were identified using the “filter outliers” node in SAS Enterprise Miner (version 4.5). Only the following climate-related variables met the Kolmogorov-Smirnov (K-S) test for normality: MAXSOIL 5 DAT (MAXSOIL5), RH 5 DAT (RH5, log 10 transformed), MINSOIL 30 DAT (MINSOIL30), MINRH30, MAXSOIL10 (log 10 transformed), MEANSOIL30, MAXAIR20, MINSOIL20, MINRH10, RH10, MINRH20, and RH20. Following tests for normality, we performed correlation and variance inflation factor analyses in SPSS (version 15; SPSS Inc., Chicago) to test for variable independence. The following variables were identified to be independent and were used in all subsequent multiple variable LR experiments (forward stepwise selection, criterion for inclusion P = 0.05): RH20, MAXSOIL10, and MAXAIR20. Subsequent modeling experiments were performed on this reduced database, GDDLA-YMET (n = 116). RH20 ranged from 69% to 92% (mean = 79%, sd = 5.5), MAXSOIL10 ranged from 76 to 107 °F (mean = 89 °F, sd = 6.75), and MAXAIR20 ranged from 83 to 94 °F (mean = 89 °F, sd = 2.11).

Methods for calculating accumulated GDD.

Eight methods for calculating GDD were used (Table 2). The following base (B) temperatures were used: 60, 65, and 70 °F. The following ceiling (C) temperatures were used: 80, 85, 90, 95, and 100 °F. For the purpose of this study, we used this notation (xx-XX) where xx = B and XX = C. GDD coefficients of variation were calculated using all combinations of methods (M), B, and C for each planting × harvest date (PH) combination.

Table 2.Methods used to calculate accumulated growing degree days (GDD) for ‘Beauregard’ sweetpotato grown in Louisiana.

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LR modeling.

Single-variable LR analysis (criterion for inclusion P = 0.05) was performed using US#1 as the dependent variable (DV) and GDD as the predictor variable. Subsequent multiple LR experiments (forward stepwise selection, criterion for inclusion P = 0.05) were performed using GDD, RH20, MAXSOIL10, and MAXAIR20 as predictor variables. SAS Analyst (version 9.2) was used to run the LR modeling experiments. Partial residual plots were generated using Statistica (version 8; Statsoft, Tulsa, OK).

DM methods.

Insightful Data Miner (version 8; Insightul Corp., Seattle) was used to randomly generate five unique sets (five pseudoreplications) of training and testing data partitions from GDDLA-YMET. Each pseudoreplication was generated by specifying a unique number to “seed” the random sampling-based partitioning process. The proportion of training to testing data was 50%:50% (50% training:50% testing). Statistica Data Miner (version 8, Statsoft) was used to develop models from the training partition and measure predictive accuracy on testing partition. An overview of the DM-based model development (“DM mode”) and testing is summarized in Fig. 1. The following algorithms were used: LR, SVM, NN, RT, MARS, and GLM. In most cases, the default software settings were used performing the DM algorithms. SVM: regression type 1, kernel = RBF, v-fold cross validation = 10, training = 1000 iterations. NN: training sample size = 80%; network = MLP, maximum hidden units = 13; minimum hidden units = 4; hidden neurons = identity, logistic, Tanh; output neurons = identity, logistic, Tanh. RT: stopping option for pruning = prune on variance, minimum n per node = 5, maximum number of nodes = 1000, v-fold cross validation = 10, standard error rule = 1. MARS: maximum number of basis functions = 21, degree of interactions = 1. GLM: model building method = forward stepwise, stepwise selection criterion = probability, criterion for best subset selection = r². Statistica Data Miner automatically generated and exported the “trained” model, applied it to the testing data set, and generated the measurements of predictive accuracy (Fig. 1). Several measurements of predictive accuracy were generated, but we only used mean square error (MSE) for comparing model performance where

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where E_i = predicted value of case i, O_i = observed value of case i, and N = number of observations. The exported model was in a predictive markup modeling language (PMML) format (Data Mining Group, 2008). To investigate the effect of the training sample size on model performance, new paired training and data sets were generated from GDDLA-YMET (5 pseudoreplications) with the following proportion of training and testing data: 50%:50%, 70%:30%, and 90%:10%. DM experiments were performed with each set of training and testing data, along with evaluation of prediction accuracy.

Results

M1 [(Tmax + tmin)/2) − B] has been considered as the standard method for calculating GDD and is frequently used for identifying alternative GDD models (Dufault, 1997). The cv values calculated for each M × C × B × PH ranged from 12.48 (SINE, 60–85) to 54.45 (M6, 70–80) (Table 3). The lowest cv for M1 was 17.35 (B = 60 °F). The adjusted r² values of single-variable LR models ranged from 0.01 (M5, 65–100) to 0.13 (M4, 60–85) (Table 3). The lowest overall MSE using the DM approach was 15208 calculated using REG (TRI, 65–95). The lowest observed MSE for M1 was 16298 (SINE). To investigate if further improvement in model accuracy (increased adjusted r², decreased MSE) was possible, we used SINE (60–80, 60–85), M4 (60–85, 60–80, 60–90), and TRI (60–80, 65–95) in multiple LR and DM experiments that included agrometeorological predictor variables (Table 4). These methods and combinations of B × C represented the three best-performing models in each approach (i.e., minimum cv, LR, and DM). Multiple variable LR models showed an improvement in adjusted r² values when agroclimatic variables (MAXSOIL10 log 10 transformed, RH20, and MAXAIR20) were used along with candidate GDD methods (Table 4). The M4 (60–90)-based multivariable model ranked first in terms of adjusted r² value at 0.42, had the lowest MSE (DM mode), and represents the best candidate for predicting US#1 yield for the current data set. M4 (60–85) was ranked second in LR and DM.

Table 3.Coefficients of variation (normal font), adjusted r² (bold), and mean square errors (italics) for eight methods of calculating accumulated growing degree days (GDD) from transplanting to harvest in ‘Beauregard’ sweetpotato grown in Louisiana.

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Table 4.Linear regression equations, adjusted r² values, and mean square errors (MSE) of data mining models describing US#1 yield based on various growing degree day (GDD) methods and agrometeorological factors for ‘Beauregard’ sweetpotato grown in Louisiana.

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Partial residual plots summarized the effect of each predictor variable after factoring out the effects of other covariables (Fig. 2). In DM mode, SVM (M4, 60–90), REG (M4, 60–90), and REG (SINE, 60–85) were the best-performing models for predicting US#1 yield using GDD and agrometeorological variables (Table 5). RT and NN models were ranked near the bottom in terms of predictive accuracy. Increasing the size of the training data set (with a consequent decrease in the size of the testing data set) did not result in significant increase of predictive accuracy for any model except for NN (Fig. 3). While the other models showed a slight and gradual decrease in MSE, the NN MSE showed instability over the various training sample sizes [i.e., MSE increased from 50%:50% to 70%:30%, and then decreased at 90%:10% (Fig. 3)]. The relationship between GDD, harvest dates, climatic variables, and actual and predicted US#1 yield for 2007 field trials are presented in Table 6. The accumulated GDD at harvest ranged from 2774 (214.97 bushels/acre) to 3389 (477.05 bushels/acre). Based on yield and GDD estimates of GDDLA-YMET, GDD = 2600 appears to be the suitable GDD-based scheduling of test harvest. In GDDLA-YMET, nine of 10 harvest dates before GDD = 2600 resulted in US#1 yield below 300 bushels/acre (data not shown). This yield level has been suggested by growers in Louisiana as the “break even point” (K. Thornhill, personal communication).

Table 5.Mean square error (MSE) of data mining models describing the relationship between US#1 yield and various growing degree day (GDD) methods and agrometeorological factors for ‘Beauregard’ sweetpotato grown in Louisiana.

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Table 6.Agrometeorological variables, accumulated growing degree days (GDD) to test harvest and harvest, and actual and predicted US#1 storage root yields of ‘Beauregard’ sweetpotato grown in Louisiana.^z

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Discussion

Our results indicate that alternative methods of calculating accumulated GDD lowered cvs, increased LR-adjusted r² values, and reduced MSE relative to M1. Several candidate models were identified using multiple approaches (i.e., minimum cv, LR, and DM). Inclusion of agrometeorological predictor variables in single-variable GDD models increased model goodness-of-fit (as measured by adjusted r²) and predictive ability (as measured by MSE) and helped to identify the best candidate for calculating GDD. The use of DM methods helped to quantify predictive accuracy of the candidate models. MSE is generally considered the most robust measure of overall predictive model performance (Schwartz et al., 1997). Our results are consistent with previous reports that heat units alone cannot explain the entire development of a crop (Arnold, 1960; Perry and Wehner, 1996). Our data also suggested a ceiling temperature of 90 °F for computing accumulated GDD for ‘Beauregard’ sweetpotato grown in Louisiana. Using a different method for calculating accumulated GDD may introduce more variation, thereby reducing prediction precision (Dufault, 1997). Regardless of the calculation method, Higley et al. (1986) emphasized that degree days are never more than estimates of developmental time. Although Arnold (1959) has suggested that a base temperature for a linear heat unit system may not be identical with all of the physiological requirements of the plant, the empirically derived base and ceiling values were consistent with known optimal temperature ranges in sweetpotato growth and yield. For example, in a review of the effect of atmospheric and soil factors that influenced sweetpotato growth and yield, Ravi and Indira (1999) noted that night air temperature below 59 °F suppressed storage root formation while promoting shoot growth. At air temperatures greater than 86 °F, an increase in indole acetic acid oxidase activity caused reduction in storage root formation and growth (Ravi and Indira, 1999). Taking all of these into consideration, using a different method for calculating GDD for ‘Beauregard’ sweetpotato in Louisiana might lead to less precise scheduling of time-critical management activities (e.g., test harvest and harvest). For example, prevailing temperatures are generally lower in “early” planting dates in May [5-year mean Tmax = 84.1 °F, mean minimum temperature (Tmin) = 62.4 °F] compared with “late” planting dates in July (5-year mean Tmax = 88.4 °F, mean Tmin = 70.5 °F) in two northeast Louisiana locations (CHS, NE10). If M1 or M2 (both methods do not require a ceiling temperature) were used to calculate GDD, an earlier harvest date for “late” planted sweetpotato would have been predicted due to rapid accumulation of GDD associated with higher Tmax compared with the “early” planting date. When the negative effect of high temperature (greater than 86 °F) on storage root initiation is considered (Ravi and Indira, 1999), it is apparent that rapid accumulation of GDD due to high Tmax does not translate to an early harvest or higher potential yield. This is in part demonstrated in Table 6 where the 28 June planting date achieved GDD = 2600 at 89 d (compared with 91 d for the 22 May planting date). Even when harvested at a comparatively later date (106 DAT), the US#1 storage root yield of the “late” planting was similar to the 22 May planting (92 DAT).

The application of DM to agricultural field data has previously been described (Frank et al., 2004; Witten and Frank, 2005), and several examples exist in the scientific literature (Bui et al., 2006; Ekasingh et al., 2005). As scientific instruments continue to generate massive data sets, the KDD approach and, in particular DM methods, play important and enabling roles (Fayyad et al., 1996). We used DM methodology to provide estimates of predictive accuracy wherein “trained models” were applied on “test (nontraining) data.” In the DM mode, the best LR model (M4, 60–90) was ranked second in terms of predictive ability (Table 5). The best-performing DM model used SVM (M4, 60–90) (Table 5). SVMs are a set of unsupervised learning methods originally developed to solve classification problems, but were later extended to the domain of regression problems (Vapnik et al., 1997). SVMs have been used in agricultural research to predict soil moisture (Gill et al., 2006) and maize hybrid performance (Maenhout et al., 2007). Several studies have demonstrated that DM-based techniques, especially NN and RT, matched or exceeded the predictive accuracy of LR-derived models (Clapham and Fedders, 2004; Park et al., 2005). In our work, the predictive accuracy of NN and RT models were ranked lowest (high MSE), suggesting that the trained models likely overfit the training data, leading to high MSE estimates. Overfitting pertains to cases where the model gives good results when applied to the training data, but yields poor results when applied to a new set of observations [i.e., testing data (Levin and Zahavi, 2005)]. RT- and NN-based models have been documented as prone to produce models that overfit data (Khoshgoftaar and Allen, 2001; Zhang, 2005). The relatively small sample size of the modeling database likely contributed to the instability of the NN-derived models. While a data set of 100 to 10,000 records is considered “large” in traditional statistics, in DM, 10⁴ may be considered a small sample size (Benjamini and Leshno, 2005). During model development, NN further splits the training data into the actual training sample and a validation sample. Thus, the actual sample size used in NN model building is smaller than the initial sample size (Zhang, 2005). A sample size of 40 and 74 is considered sufficient for classification and time series problems, respectively (Zhang, 2005). However, Kim (2008) reported that LR techniques were superior to DM regardless of the number of variables and sample size when continuous independent variables were used, and that NN were better when categorical variables were involved. This information can be used for future studies where categorical variables are involved. Our results underscore the necessity of comparing the results derived from DM-oriented methodology with traditional LR approaches to verify the suitability or advantages of using one method or the other (Zhang, 2005). The DM approach can be used in conducting preliminary assessment for the presence of nonlinear relationships, especially in large data sets. Current DM software applications have built-in functions that automate this procedure. DM software applications also include tools that are potentially useful in crop growth modeling work. For example, various DM software feature “deployment” modules that automatically generate computer programming code (e.g., C and C++) so that “trained” models can be incorporated into compiled programs that underlie deterministic growth models or decision support systems.

The main premise of using nonlinear methods in modeling plant development is that growth response to temperature is often nonlinear (Clapham and Fedders, 2004; Park et al., 2005). Our experimental results indicate that the variables used in this study failed to show nonlinearity, and various DM algorithms that fit nonlinear functions or interactions did not contribute to increased predictive accuracy. The partial residual plots (Fig. 2) help to show the linear relationship of these predictor variables. It is possible that certain growth stages of the sweetpotato may respond nonlinearly to temperature or that certain other variables may demonstrate nonlinear relationship to covariables and yield. Kays (1985) cited studies that documented that early in the growing season, crop growth rate (CGR) was initially slow; highest CGR was achieved 70 to 98 DAT, after which it decreased. Kays (1985) also noted that for a planting date of 16 June, net photosynthesis tended to increase until the middle of September (about 87 DAT), and then gradually decreased as harvest approached. This decline was attributed to a decline in gross photosynthesis rather than an increase in respiration. It appears that sweetpotato respond linearly to temperature for most of the growing season, but this response becomes less linear as the harvest approaches. At this time, we are unable to account for the existence of this nonlinear relationship due to the experimental limitations imposed by our modeling data set.

The empirically derived models in this study were specific to the range of environments where the yield trials were conducted. To some extent, such models can be calibrated for use in other locations outside of Louisiana. Empirical models can be used as explanatory tools for identifying the hidden structure of crop growth processes (Park et al., 2005). Results from this work have practical implications for the sweetpotato harvest scheduling in Louisiana. One direct application of our work would be to schedule test harvests using GDD = 2600 instead of using calendar days. Based on 2007 planting dates, the number of days required to reach GDD = 2600 ranged from 69 to 91 d. Scheduling a test harvest and the ability to forecast yield can help commercial growers and crop consultants to further fine tune decisions concerning harvest dates based on a target yield level. For example, the harvest can be scheduled based on yield potential of fields (planting dates) if a threat of extended severe weather emerges during this period. Seem et al. (2003) also proposed using GDD as a method for ‘Beauregard’ to better compete with weeds if it is planted during periods where maximum GDD is accumulated rapidly. The GDD model can be incorporated into predictive models of sweetpotato crop phenology. To our knowledge, a well-defined phenological model does not exist for the species, and past reviews of sweetpotato yield physiology (Kays, 1985; Ravi and Indira, 1999) do not mention the development or existence of such models. Such models can open areas for further investigation, including the role of accumulated GDD in scheduling herbicide application, fertilizer application, irrigation, and pest management.

Currently, some commercial weather monitoring stations include software that calculates GDD using specific preprogrammed methods (i.e., triangle, sine, and modifications of these basic methods). Our results indicate that the SINE method (60–85) can be used with a very slight reduction in model accuracy. This will allow growers and crop consultants to use such software without further modification. This research represents a preliminary step toward helping to account for field-level yield variability in sweetpotato. Future studies should be able to improve the predictive performance of current models through the addition of other soil- and plant-related predictor variables. Rainfall-related variables were excluded from the current modeling experiments due to violation of normality assumptions. Even when all agrometeorological variables were included in DM mode, none of the rainfall-related measurements were included as predictor variables in the best-performing models (data not shown). Soil moisture and nutrient measurements were available for some locations for the current study, but were excluded in the analysis because this would have reduced the size of the modeling database.

Conclusions

This research indicates the potential for using GDD-based models to help predict sweetpotato harvest dates in Louisiana. Several methods and combinations of B and C showed better goodness-of-fit and predictive accuracy when compared with the standard method of calculating GDD. In addition to the conventional methods of identifying candidate GDD methods, we also considered using adaptive algorithms associated with DM methodology. LR- and DM-based regression approaches identified similar candidate models. Using accumulated GDD, our results suggest that test harvests can be done at about GDD = 2600 and harvesting can start shortly thereafter. Further calibration is necessary to improve the predictive ability of the current model. Future studies will likely investigate the potential modulating effect of moisture stress and other management variables.