Nonlinear Multivariate Prediction Model of ‘Kyoho’ Grape Full Bloom Dates in Japan

Abstract

In this study, after developing a method for predicting full bloom dates of ‘Kyoho’ grape by incorporating ‘Kyoho’ growth characteristics at multiple sites in Japan into one model, we evaluated the prediction accuracy of the model. Using data of bud break dates and full bloom dates of ‘Kyoho’ at 14 public test sites from 2000–2018, we investigated the grape development characteristics at the sites. The conventional effective accumulated temperature model relies on the assumption of a linear relation between temperature and grape development. However, based on results of grape development characteristic analyses, we formulated new prediction models that include the following considerations: 1) a nonlinear relation between temperature and grape development, 2) effects of solar radiation on grape development, and 3) relations between Day of Year (DOY) of bud break date and grape development. Prediction analyses of two types were applied to full bloom dates at the 14 sites using the effective accumulated temperature model and our model, which includes the three considerations above simultaneously. For the first analysis, after estimating the model parameters for each site using data observed at that site, we predicted full bloom dates there. Evaluation of the prediction accuracy using leave-one-out cross validation revealed that the average root mean square error (RMSE) for all sites was 2.24 days for the effective accumulated temperature model. For our model, it was 2.06 days. The model had higher prediction accuracy at multiple sites. For the second analysis, we used the model parameters for each site based on data collected at all sites except the site in question. The average RMSE for all sites was 2.76 days for the effective accumulated temperature model and 2.54 days for our model. These results suggest that our model of ‘Kyoho’ growth characteristics at multiple sites can predict full bloom dates with higher accuracy than the effective accumulated temperature model.

Introduction

In grape cultivation management, work including gibberellin and shoot treatments is concentrated in the days near full bloom dates. Therefore, predicting the full bloom date supports the creation of a work plan. However, many cases in which developmental processes of fruit crops have been affected by global warming have been reported (Sugiura and Yokozawa, 2004; Honjo, 2007; Sugiura et al., 2007, 2012; Adachi et al., 2018; Kamimori et al., 2019). One example is early grape blooming (Sugiura et al., 2007; Kamimori et al., 2019). Consequently, it is becoming increasingly important to predict full bloom dates of grapes accurately.

The developmental stages of various plants, including grapes, have been predicted using development prediction models that represent development of plants in terms of meteorological elements. Classic and basic methods represent development by accumulated temperature or effective accumulated temperature assuming a linear relation between temperature and development (Hanyu and Uchijima, 1962; Noro et al., 1986; Kubota et al., 2009; Sato and Takezawa, 2014; Kamimori et al., 2020). The DeVelopmental Rate (DVR) model has also been proposed (de Wit et al., 1970). The DVR model is based on the idea that the developmental stage of plants can be represented as an integral of the developmental rate, mainly expressed as a function of temperature. In the model, both linear and nonlinear relations between temperature and development can be considered in the calculation of the developmental rate. The DVR model has been applied to predict the developmental stages of grapes (Motonaga et al., 2000; Sato and Takezawa, 2014; Kamimori et al., 2020).

To predict grape full bloom dates, earlier studies targeted one site and certified the prediction accuracy at that site. However, prediction accuracy at multiple sites has not been clarified. To elucidate the usefulness of prediction models over a wide area, investigating prediction accuracy at multiple sites is important. Furthermore, development of a general model that can represent characteristics of grape development at multiple sites is important for use as a model over a wide area (Parker et al., 2011; Pereira et al., 2018). The general model is also applicable to prediction in places where grapes have not been cultivated. Moreover, it can help people to formulate a work plan and start growing grapes at different places. In fact, grape development was represented as a function of air temperature in many earlier studies, but it is now possible to use various long-term meteorological data and grape-development data at multiple sites. Therefore, attempting more accurate predictions using a multivariate model presents a new challenge. Given such motivations, the purpose of this study was to make a general model to predict grape full bloom dates while considering the relation between grape development and various factors at multiple sites. We also tried to systematically clarify the prediction accuracies achieved at various sites in Japan.

The most cultivated grape variety in Japan is ‘Kyoho’. For this study, we analyzed data of bud break dates and full bloom dates of ‘Kyoho’ grapes at multiple sites in Japan. These data are useful to elucidate characteristics of ‘Kyoho’ development over a wide area. Based on characteristic analysis results, we advanced the effective accumulated temperature model to a nonlinear multivariate model by considering the nonlinear relation between temperature and grape development and by considering some other factors that affect grape development. Then, the conventional effective accumulated temperature model and our models were applied to predict the full bloom date of ‘Kyoho’ at multiple sites in Japan. In this study, we conducted two types of prediction analyses. For the first analysis, we built a model for each site using data observed at the site and predicted full bloom dates there. In the second analysis, for each site we built a model based on data collected at all sites, except the site in question, and then predicted full bloom dates at that site. Based on results obtained from the second analysis, we evaluated the usefulness of our model for places at which no grape-development data had been collected.

Materials and Methods

1.  Data used for this study

1)  Data of bud break dates and full bloom dates

Characteristic grape tests to investigate vigor, bud break dates, full bloom dates, fruit characteristics, etc. have been conducted at various public test sites in Japan in recent decades. For this study, we used data of bud break dates and full bloom dates of ‘Kyoho’ grapes under open field conditions at 14 sites for which the number of data points was greater than or equal to 4 between 2000 and 2018. Full-flowering date is defined as the date when more than 80% of all florets were open in more than 80% of all flower clusters. Bud break date is defined as the date when more than 50% of all second buds of the fruiting mother shoot treated by the long-cane pruning method, or more than 50% of all spur buds trained by the spur pruning method appeared. One data point was used for one year. Table 1 presents details of the sites and the data used for this study. Symbol N represents the number of data points between 2000 and 2018; D_MEAN is the mean value of the number of days from the bud break date to the full bloom date for all years; D_STD is its standard deviation. The respective ranges of D_MEAN and D_STD at the 14 sites were 41.6–53.1 days and 1.2–6.2 days. Figure 1 shows the location of the 14 sites. Numbers adjacent to each dot represent the site number in Table 1.

Table 1

Details on the 14 sites and data of bud break date and full bloom date at each site used in this study. The sites are listed in ascending order of latitude. The symbol N represents the number of data points between 2000 and 2018; D_MEAN denotes the mean value of the number of days from bud break date to full bloom date; D_STD denotes the standard deviation. One data point was used for one year in this table.

Fig. 1

Locations of the14 sites. Numbers adjacent to each dot represent the site number in Table 1.

2)  Meteorological data

We used Agro-Meteorological Grid Square Data, NARO from the National Agriculture and Food Research Organization (NARO) (hereinafter, the data are designated as AMGD–NARO) (Ohno et al., 2016; Kominami et al., 2019) <https://amu.rd.naro.go.jp/>. Data on the daily mean air temperature and daily integrated global solar radiation of AMGD–NARO were used for this study. The data units were degrees Celsius (°C) and megaJoules per square meter (MJ·m⁻²). The average values of parameter above in 1 km × 1 km mesh were used, including the latitude and longitude of the respective sites.

2.  Proposed Models

This section first presents a description of a conventional model for predicting grape full bloom dates and problems posed by the model. Then, we introduce new models addressing these shortcomings.

Here, we introduce five models (Models 1–5) to calculate the effective accumulated temperature necessary for full bloom after bud break using various models. Model 1 is a conventional model assuming a linear relation between temperature and grape development. Based on results of characteristic analysis of grape development at multiple sites, we formulated Models 2, 3, and 4 by adding the following considerations to Model 1, respectively; 1) the nonlinear relation between temperature and grape development, 2) the effects of solar radiation on grape development, and 3) the relation between the Day of Year (DOY) of the bud break date and grape development. Model 5 is a combined model of Models 2, 3, and 4, which includes the three considerations above simultaneously.

1)  Model 1: An effective accumulated temperature model incorporating a linear relation between temperature and grape development

The conventional model assumes that temperatures under a certain base value (denoted by T₀) do not contribute to grape development and that the relation between temperature over T₀ and grape development is linear. Let T_i be the daily mean air temperature at day i and let D be the number of days from bud break date to the full bloom date. The effective accumulated temperature from the day after bud break date to the full bloom date EAT^(D) can be represented as a function of D with the following equation.   

$${\mathit{\text{EAT}}}^{\left(D\right)}={\sum }_{i=1}^D\left(T_i-T_0\right)$$Eq. 1

where   

$$T_i-T_0=0\text{if}{T}_i<T_0\text{.}$$

For this study, D is estimated according to   

$$\widehat{D}=\arg \underset{\mathrm{D}}{\min }\left|{\widehat{\mathit{EAT}}}^{\left(D\right)}-{\mathit{EAT}}^{\left(D\right)}\right|$$Eq. 2

where $\widehat{D}$ is the estimated D and ${\widehat{\mathit{EAT}}}^{\left(D\right)}$ is the estimated EAT^(D).

In the following section, we refer to this model as Model 1. Let a be EAT^(D). Model 1 has two parameters: T₀ and a. The units of the parameters are, respectively, degrees Celsius (°C) and degrees Celsius·day (°C·day). We determine T₀ and a in the following manner: we assume that we have the number of days from bud break date to the full bloom date D^(j) in year j, where j = 1, ..., and n and n represent the numbers of years. We also have daily mean air temperatures T₁^(j), ..., T_D(j)^(j) observed between the day after bud break date and the full bloom date in year j. To estimate the full bloom date, T₀ is calculated as the solution of the minimization problem of   

$$\underset{6\le {\mathrm{T}}_0\le 12}{\min }{\sum }_{j=1}^n{\left(D^{\left(j\right)}-{\widehat{D}}^{\left(j\right)}\right)}^2$$Eq. 3

using the method developed by Brent (1973). Also, a is estimated simultaneously according to the following.   

$$a=\frac{1}{n}{\sum }_{j=1}^n{\sum }_{i=1}^{D^{\left(j\right)}}\left(T_i^{\left(j\right)}-T_0\right)$$Eq. 4

The initial value of T₀ is 7–11°C (δT₀=1°C). The optimal value of T₀ is derived in the range of 6–12°C as described in Eq. 3.

2)  Model 2: A model incorporating the nonlinear relation between temperature and grape development

We next describe our motivation to extend Model 1. Model 1 has two parameters, T₀ and a, which means that the base temperature T₀ and the effective accumulated temperature EAT^(D) calculated using Eq. 1 are constant for each year. To investigate the validity of the assumption, we calculated EAT^(D) by changing T₀ by 1°C for each year. Figure 2 shows the calculated EAT^(D) at Ibaraki, Hiroshima, and Nagano. As the figure shows, it is apparent that EAT^(D) for each T₀ differed depending on the year and we could not find a T₀ at which EAT^(D) was equal for all years. Consequently, T₀ and EAT^(D) by Eq. 1 were not constant for each year. Therefore, the model setting in Model 1 can cause an error in the model parameters, which can introduce a prediction error of the full bloom dates.

Fig. 2

Calculated effective accumulated temperature from the day after bud break date to the full bloom date ${\mathit{\text{EAT}}}^{\left(D\right)}={\sum }_{i=1}^D\left(T_i-T_0\right)$ (T_i − T₀ = 0 if T_i < T₀) changing base temperature T₀ by 1°C at Ibaraki, Hiroshima, and Nagano, where D stands for the number of days from the day after bud break date to the full bloom date; T_i expresses daily mean temperature at day i. Plot type represents the year.

We first re-examined Eq. 1, which includes the assumption of a linear relation between temperature and grape development. In Model 2, to suppress EAT^(D) fluctuation by Eq. 1 for one T₀, we extended Eq. 1 by consideration of the nonlinear relation between temperature and grape development. Many earlier studies have also presented the relation nonlinearly using DVR models and have clarified the usefulness of the representation. For this model, the effective accumulated temperature is calculated as   

$${\mathit{EAT}}^{\left(D\right)}={\sum }_{i=1}^D{\left(T_i-T_0\right)}^b$$Eq. 5

where   

$$T_i-T_0=0\text{if}{T}_i<T_0\text{,}$$

and b represents the nonlinearity of the relation between temperature and grape development.

Model 2 has three parameters: T₀, a, and b. We determined the parameters in the following manner: parameter T₀ was calculated using Eq. 3 with the method developed by Nelder and Mead (1965); b was derived at the same time in the calculation. Parameter a was also estimated simultaneously with other parameters in the same way as Eq. 4, but according to Eq. 5. The initial value of b is 1.0. The optimal value of b is derived in the range of 1.0–1.3. The initial and optimal values of T₀ are the same as those in Model 1.

3)  Model 3: A prediction model incorporating effects of solar radiation on grape development

In Model 1, it is assumed that base temperature T₀ and the effective accumulated temperature EAT^(D) calculated using Eq. 1 are constant for all years. However, as described above, no value of T₀ can be found at which values of EAT^(D) are equal for all years (Fig. 2). Therefore, we next dropped the assumption that T₀ is constant and introduced a model in which T₀ can change. Here, we extended Model 1 by modeling the base temperature as a decreasing function of solar radiation in Model 3, because it is possible that solar radiation can affect grape development via the trunk body temperature (Landsberg et al., 1974).

In Model 3, the effective accumulated temperature is calculated as   

$${\mathit{EAT}}^{\left(D\right)}={\sum }_{i=1}^D\left\{T_i-\left(T_0-c\times S_i\right)\right\}$$Eq. 6

where   

$$T_i-\left(T_0-c\times S_i\right)=0\text{if}{T}_i<\left(T_0-c\times S_i\right)\text{,}$$

and S_i stands for the daily integrated global solar radiation at day i. Also, c represents the contribution of solar radiation to T₀.

Model 3 has three parameters: T₀, a, and c. We determined the parameters in the following manner: parameter T₀ is calculated using Eq. 3 and the method developed in Nelder and Mead (1965); c is derived simultaneously in the calculation. Parameter a is also estimated simultaneously with other parameters similar to Eq. 4, but according to Eq. 6. The initial value of c is 0.0. The optimal value of c is derived in the ranges of 0.0–0.25. The initial and optimal values of T₀ are the same as those in Model 1.

4)  Model 4: A prediction model incorporating the relation between the bud break date day each year and grape development

We investigated the relation between the DOY of bud break date x and the accumulated temperature ${\mathit{AT}}^{\left(D\right)}={\sum }_{i=1}^D{T}_i$ from the day after bud break date to the full bloom date for each year at each site. Results indicated a negative relation between x and AT^(D) at seven sites: a larger x tended to be associated with smaller AT^(D). Figure 3 presents examples at Saitama, Hiroshima, and Nagano. The correlation coefficient between x and AT^(D) by Pearson’s product-moment correlation analysis (r) and its p-value (P) are also shown in this figure. The negative relation tends to be eliminated by introducing the effective accumulated temperature EAT^(D) by Eq. 1 with T₀ = 6–12°C, but a negative relation between x and EAT^(D) is observed at several sites.

Fig. 3

Relation between Day of Year (DOY) of bud break date x and accumulated temperature ${\mathit{\text{AT}}}^{\left(D\right)}={\sum }_{i=1}^D{T}_i$ at Saitama, Hiroshima, and Nagano. The solid line represents the regression line. Correlation coefficient between x and AT^(D) by Pearson’s product-moment correlation analysis (r) and its P-value (P) are also presented in this figure.

In this model, the effective accumulated temperature is calculated as   

$${\mathit{EAT}}^{\left(D\right)}={\sum }_{i=1}^D\left(T_i-T_0\right)\times f\left(x\right)$$Eq. 7

where   

$$T_i-T_0=0\text{if}{T}_i<T_0\text{.}$$

In Eq. 7, T_i−T₀ is multiplied by a function of x, f(x), to explain the negative relation between x and EAT^(D). Experimenting with various f(x), such as multiplying x and exponentiation of x, we found f(x)=(x/80)^d to be suitable. The minimum value of x among the data used for this study was 84 at Hiroshima in 2000, so a value of 80 was introduced as a reference value of x.

Model 4 has three parameters: T₀, a, and d. We determined the parameters in the following manner: parameter T₀ was calculated using Eq. 3 using the method developed in Nelder and Mead (1965); d was derived at the same time in the calculation. Parameter a was also estimated simultaneously with other parameters in the same way as Eq. 4, but according to Eq. 7. The initial value of d was 0.1. The optimal value of d is derived in the range of 0.0–1.0. The initial and optimal values of T₀ are the same as those in Model 1.

5)  Model 5: A prediction model incorporating the nonlinear relation between temperature and grape development, solar radiation effects on grape development and the relation between bud break date each year and grape development

Model 5 is a combined model of Models 2, 3, and 4, which simultaneously incorporates the nonlinear relation between temperature and grape development, solar radiation effects on grape development, and the relation between DOY bud break and grape development. In this model, the effective accumulated temperature is calculated as   

$${\mathit{EAT}}^{\left(D\right)}={\sum }_{i=1}^D{\left\{T_i-\left(T_0-c\times S_i\right)\right\}}^b\times f\left(x\right)$$Eq. 8

where   

$$T_i-\left(T_0-c\times S_i\right)=0\text{if}{T}_i<\left(T_0-c\times S_i\right)\text{,}$$

and f(x)=(x/80)^d as Eq. 7.

Model 5 has five parameters: T₀, a, b, c, and d. We determined the parameters in the following manner: parameter T₀ was calculated using Eq. 3 with the method developed by Nelder and Mead (1965); b, c, and d were derived at the same time in the calculation. Parameter a was also estimated simultaneously with other parameters in the same way as Eq. 4, but according to Eq. 8. The initial and optimal values of T₀, b, c, and d are the same as those in Models 2, 3, and 4.

3.  Methods for predicting full bloom dates of ‘Kyoho’ grapes

We conducted two types of prediction analyses using data described in Section 1 and the models formulated in Section 2. In the first analysis, for each of the 14 sites in Japan (Table 1; Fig. 1), we estimated the model parameters using meteorological and grape-developmental data at the site. We then predicted the full bloom dates at the site. Next, we evaluated the prediction accuracy of each model using a Leave-One-Out Cross Validation (LOOCV) at each site, assuming that the data were collected for n_i years at each site i = 1, ..., 14. In the LOOCV, for each year j = 1, ..., n_i at each site, we estimated the model parameters using data at the site except the data at year j, and predicted the full bloom date in year j.

In the second analysis, for each of the 14 sites, we estimated the model parameters using data at the 13 sites other than the site under analysis. Then, we predicted the full bloom dates at the site. This represents an original prediction analysis used in this study. The aims of the analysis were as follows: to build a general model representing characteristics of ‘Kyoho’ grapes at multiple sites in Japan, and to evaluate the usefulness of the obtained model for prediction in places where grape-development data have not been collected.

In both analyses, the number of days from bud break date to full bloom date was predicted as D. We defined the prediction error as D_PRED−D_OBS, where D_OBS denotes the observed D and D_PRED stands for the predicted D. The suitability of the predictions for the observations of D was evaluated by the root mean square error (RMSE) of the predictions generated by the following equation at each site;   

$$\mathit{\text{RMSE}}=\sqrt{\frac{{\sum }_{j=1}^{n_i}{\left(D_{\mathit{\text{PRED}}}^{\left(j\right)}-D_{\mathit{\text{OBS}}}^{\left(j\right)}\right)}^2}{n_i}}$$Eq. 9

where $D_{\mathit{\text{PRED}}}^{\left(j\right)}$ and $D_{\mathit{\text{OBS}}}^{\left(j\right)}$ are D_PRED and D_OBS at year j, respectively, and n_i is the number of data points at site i. The unit of RMSE is days.

Results

1.  Prediction of full bloom dates at each site using data at the site

For these analyses, for each site, we estimated the model parameters using data observed at the site and the predicted full bloom dates there. Table 2 shows RMSE of the predictions in results obtained using Models 1–5 at each site and the average RMSE for all sites on the “All” line. For Models 1–5, RMSE varied from site to site, which means the models are site-specific. Therefore, we calculated the average RMSE for all sites by simply averaging the RMSE for each site.

Table 2

Root mean square error (RMSE) of the predictions by Models 1–5 which were built at each site using data at that site. The average RMSE for all sites is shown on the “All” line. The average RMSE for all sites was calculated by simply averaging the RMSE for each site. The unit of RMSE is days.

First, we compare result obtained using Model 1 and results of Models 2, 3, and 4. Table 2 shows that one of Models 2, 3, and 4 had smaller RMSEs than Model 1 at all sites. Therefore, each consideration in Models 2, 3, and 4 can improve the prediction accuracy of the full bloom date of ‘Kyoho’. However, the model yielding the highest accuracy varied among sites. Particularly, it was improved greatly in Niigata by Model 2, in Tokushima, Kanagawa, Tokyo, and Ibaraki by Model 3, and in Saitama by Model 4. In Kyoto, Models 2, 3, and 4 similarly improved the accuracy. However, the accuracy was particularly reduced at Saitama and Yamagata by Model 3. The average RMSE for all sites of Models 2, 3, and 4 were, respectively, 2.11, 2.17, and 2.17 days; this means they were smaller than the 2.24 days of Model 1.

Next, we give the results of Model 5, which is a combined model of Models 2, 3, and 4. RMSE of Model 5 was smaller in Tokushima, Kanagawa, Kyoto, Tokyo, Saitama, Ibaraki, Niigata, and Yamagata than that obtained using Model 1. However, RMSEs of Model 5 were much larger in Aichi, Nagano, Toyama, and Iwate than those obtained using Model 1. The average RMSE for all sites was 2.06 days for Model 5, which was the smallest among all models.

Model 5 is useful for predicting full bloom dates of ‘Kyoho’ according to the results presented above. The results of Models 1 and 5 are presented below. Figure 4 shows a histogram of the prediction errors; Figure 5 presents a comparison of D_OBS and D_PRED for each model. The solid line in Figure 5 shows the 1:1 relation. The set of D_PRED by both Models 1 and 5 indicates good correlation with the D_OBS set (Fig. 5), but the prediction errors were more concentrated near 0 in Model 5 than in Model 1 (Fig. 4). The range of errors was from −7 to 7 days for Model 1 and from −7 to 6 days for Model 5.

Fig. 4

Histogram of prediction errors by Models 1 and 5, which are built at each site using data at the site in question.

Fig. 5

Comparison of observed value (D_OBS) and predicted value (D_PRED) of number of days from the day after bud break date to the full bloom date (D) by Models 1 and 5 which were built at each site using data at the site in question. The solid line shows the 1:1 relation.

We estimated the model parameters of Models 1 and 5 for each site using meteorological and grape-development data for all years at the site. Table 3 presents the results. For example, the parameters in Hiroshima were derived using all data obtained at Hiroshima from 2000–2018. We also calculated the estimation error by D_EST−D_OBS, where D_EST is the estimated D obtained using all data at each site. Table 3 also shows the estimation errors at each site and the average RMSE for all sites on the “All” line. The average RMSE for all sites was calculated by simply averaging the RMSE for each site. Each estimated model parameter was site-specific for both Models 1 and 5. For Model 5, a parameter b greater than 1 produces stronger nonlinearity of the temperature-development relation. Also, a parameter c larger than 0 yields stronger effects of solar radiation on grape development. A parameter d greater than 0 gives a stronger relation between DOY of bud break date and grape development. Results demonstrated that the estimated b, c, and d in Model 5 were, respectively, greater than 1, larger than 0 and greater than 0 at almost all sites. Therefore, Model 5 can represent the nonlinearity, solar radiation effects, and the relation with DOY of bud break for grape development in many places. RMSE of the estimations at each site was 0.9–3.5 days for Model 1 and 0.6–2.9 days for Model 5. The average values for all sites were, respectively, 1.82 and 1.48 days.

Table 3

Estimated model parameters of Models 1 and 5 for each site using all data at the site. Root mean square error (RMSE) values of the estimations at each site are also shown. The average RMSE for all sites is shown on the “All” line. The average RMSE for all sites was calculated by simply averaging the RMSE for each site.

To visualize the grape development represented by Models 1 and 5, we calculated the developmental rate DVR for each model. Figure 6 presents the DVR in Ibaraki as an example. Here, DVR is calculated by dividing both sides of Eqs. 1 and 8 by parameter a (the estimated value of the effective accumulated temperature) in Ibaraki shown in Table 3. Then, the following values were substituted for meteorological factors and the model parameters on the right side of Eqs. 1 and 8: to Eqs. 1 and 8, the amplitude of 7–25°C for T and the values of each model parameter in Ibaraki shown in Table 3 for each parameter; to Eq. 8, the amplitudes of 5, 15, and 25 MJ·m⁻² for S and 116 for DOY of bud break date x. The value of 116 was derived by averaging x in Ibaraki for all years. The unit of DVR is 1/day. From Figure 6, it is apparent that the DVR in Model 1 represents the linear relation between temperature and grape development, and DVR in Model 5 represents the nonlinear relation. It is also apparent that DVRs at S = 15 and 25 MJ·m⁻² in Model 5 are shifted to the left for the entire DVR at S = 5 MJ·m⁻². By letting DVR(T,S) be the DVR at T and S, then Figure 6 shows that DVR(14.5,5) = DVR(12,15) = DVR(9.5,25) = 0.01. Therefore, in Model 5, for the average x at Ibaraki, 116, the level of the effect by increasing T by 2.5°C on grape development is identical to that by increasing S by 10 MJ·m⁻².

Fig. 6

Calculated developmental rate DVR in Models 1 and 5 at Ibaraki. Here, DVR is calculated by dividing both sides of Eqs. 1 and 8 by the parameter a (the estimated value of the effective accumulated temperature) at Ibaraki presented in Table 3. Then, the following values were substituted for the meteorological factors and the model parameters on the right side of Eqs. 1 and 8: to Eqs. 1 and 8, the amplitude of 7–25°C for daily mean temperature T and the values of each model parameter at Ibaraki shown in Table 3 for each parameter; to Eq. 8, the amplitude of 5, 15, and 25 MJ·m⁻² for daily integrated global solar radiation S and 116 for DOY of bud break date x. The unit of DVR is 1/day.

2.  Prediction of full bloom dates at each site using data at all sites except for the site being analyzed

In this analysis, for each site, we determined the model parameters based on data collected at all sites except the site in question and predicted full bloom dates at the site. As shown in the previous section, Model 5 was found to be useful for predicting full bloom dates of ‘Kyoho’; predictions were made using Models 1 and 5 in this analysis. Table 4 shows RMSE of the predictions produced by Models 1 and 5 at each site and the average RMSE for all sites on the “All” line. The average RMSE for all sites was calculated by simply averaging the RMSE for each site. The sites RMSE in Model 5 were smaller at nine sites, equivalent at three sites and larger at two sites compared with those of Model 1. The average RMSE for all sites was 2.76 days for Model 1 and 2.54 days for Model 5. It was smaller for Model 5 than at Model 1. However, the average RMSE of Model 5 that was built in this analysis (2.54 days as shown in Table 4) was larger than that for Model 5, which was built using data at each site (2.06 days, as presented in Table 2).

Table 4

Root mean square error (RMSE) of the predictions by Models 1 and 5, which were built for each site using data at all sites except the site in question. The average RMSE for all sites is shown on the “All” line. The average RMSE for all sites is calculated by simply averaging the RMSE for each site. The unit of RMSE is days.

Figure 7 presents a histogram of prediction errors. Figure 8 presents a comparison of D_OBS and D_PRED. The prediction errors obtained using Model 5 were more concentrated near 0 compared than those found using Model 1, but the range of prediction errors was from −7 to 6 days for Model 1 and from −7 to 8 days for Model 5 (Fig. 7). For both models, for cases in which D_OBS was above 57 and below 40, the prediction errors in this analysis were greater than those for Models 1 and 5, which were built using data at each site (Figs. 5 and 8). The larger errors for the range of D_OBS in this study are described in Section 3 of Discussion.

Fig. 7

Histogram of the prediction errors by Models 1 and 5, which were built at each site using data at all sites except the site in question.

Fig. 8

Comparison of observed value (D_OBS) and predicted value (D_PRED) of number of days from the day after bud break date to the full bloom date (D) by Models 1 and 5 which were built at each site using data at all sites except the site in question. The solid line shows the 1:1 relation.

Table 5 presents the estimated model parameters of Models 1 and 5 obtained using all data at all sites. Table 5 also shows the RMSE of estimation errors at each site and the average RMSE for all sites on the “All” line. In this analysis, the RMSE for each site was derived from the same model, so we calculated the average RMSE for all sites by weighted averaging the RMSE for each site by the number of data points at each site. Results show that the estimated b, c, and d were, respectively, 1.11, 0.16, and 0.24 for all sites. Therefore, Model 5 can represent nonlinearity, the effects of solar radiation, and the relation with DOY of bud break of grape development for many sites. In fact, the RMSE of the estimations at the sites were 1.6–3.6 days for Model 1 and 1.0–3.5 days for Model 5. The average values for all sites were 2.64 and 2.41 days, respectively.

Table 5

Estimated model parameters of Models 1 and 5 using all data at all sites. Root mean square error (RMSE) values of the estimations at each site are also shown. The average RMSE for all sites is shown on the “All” line. The average RMSE for all sites is calculated by weighted averaging the RMSE for each site by the number of data points at each site.

Figure 9 shows the calculated developmental rate DVR in Models 1 and 5 using all data at all sites. The DVR was calculated by dividing both sides of Eqs. 1 and 8 by a for all sites shown in Table 5. Then, the following values were substituted for the meteorological factors and the model parameters on the right side of Eqs. 1 and 8: to Eqs. 1 and 8, the amplitude of 7–25°C for daily mean air temperature T and the values of each model parameter for all sites are shown in Table 5 for each parameter; to Eq. 8, the amplitude of 5, 15, and 25 MJ·m⁻² for global solar radiation S and 108 for DOY of the bud break date x. The value of 108 was derived by averaging x at all sites for all years. From Figure 9, it is apparent that this was almost identical to that in Figure 6, but DVR(13.9,5) = DVR(12.3,15) = DVR(10.7,25) = 0.01. It means that, in Model 5, for the average x for all sites, 108, the amount of the effect by increasing T by 1.6°C on grape development was almost identical to that by increasing S by 10 MJ·m⁻².

Fig. 9

Calculated developmental rate, DVR, in Models 1 and 5 using all data at all sites. The DVR is calculated by dividing both sides of Eqs. 1 and 8 by a for all sites shown in Table 5. Then, the following values are substituted for the meteorological factors and the model parameters on the right side of Eqs. 1 and 8: to Eqs. 1 and 8, the amplitude of 7–25°C for daily mean temperature T and the value of each model parameter for all sites shown in Table 5 for each parameter; to Eq. 8, the amplitude of 5, 15, and 25 MJ·m⁻² for daily integrated global solar radiation S and 108 for DOY of the bud break date x. The unit of DVR is 1/day.

Discussion

1.  Model validity

In Models 1–5, we introduced the effective accumulated temperature needed for full blooming after bud break to represent grape development. Because the growth rate of plants is strongly dependent on temperature, the growth amount has been expressed in many studies by the accumulated temperature or effective accumulated temperature. For this study, we assumed that factors other than air temperature, such as solar radiation and DOY of bud break date, affect grape development indirectly through the effective accumulated temperature.

The nonlinear relation between temperature and grape development, the effect of solar radiation on grape development and the relation between DOY of bud break date and grape development are considered respectively in Models 2, 3, and 4. Here, we discuss the validities of Models 2, 3, and 4.

For Model 2, it was assumed that higher temperatures result in a greater degree of grape development (Eq. 5), but the upper limit of temperature for grape development is around 25°C at the foliage stage (Buttrose, 1969). However, for temperature data used in this study, the temperature during bud break to full bloom was almost always 7–25°C. On a few days, the daily mean air temperature was higher than or equal to 25°C. Therefore, the assumption that grape development progresses at higher temperatures is introduced into this model.

Model 3 incorporates the effects of solar radiation on grape development. Few earlier studies have considered solar radiation in grape full bloom prediction. Sugiura et al. (1995) compared the number of days from bud break to full blooming D of six trees of ‘Kyoho’ grapes in an open field for one year for an untreated environment and those for an environment in which the upper part of the vines were covered with a sheet with a transmittance of about 40%. Results showed no difference in D between the two environments and showed that direct effects of solar radiation on D were small. However, Oikawa and Kikuchi (1997) predicted apple full bloom dates in an open field for 16 years and reported that the prediction accuracy was improved by considering not only temperature, but also solar radiation. Furthermore, Anderson et al. (1986) introduced a model incorporating air temperature and bud temperature to predict cherry development. Landsberg et al. (1974) pointed out that apple bud and flower temperatures differ from air temperature because of radiation and wind effects. It is assumed that as solar radiation increases, vine trunk temperature such including the bud temperature, leaf temperature, and branch temperature increase. Therefore, we considered the possibility that solar radiation can affect grape development through vine trunk temperature in Model 3.

In Model 4, the relation between DOY of bud break date and grape development was considered. Many earlier studies included the assumption that grape growth progress after bud break is independent of time. However, Takagi and Tamura (1987) reported the relation between development and time for completion of the grape dormancy process. Their study investigated the bud break process of ‘Muscat of Alexandria’ grapes planted in a greenhouse. Results showed that a later heating start date was associated with a smaller accumulated temperature necessary for bud break. Takagi and Tamura (1987) reported that this result may be related to the degree of the dormancy completion and that the degree of dormancy completion was determined by the degree of low temperature to which the grapes were exposed as well as the time of exposure. However, we investigated the relation between the accumulated temperature from the day after bud break to the full bloom date, ${\mathit{\text{AT}}}^{\left(D\right)}\left(=\mathrm{ }{\sum }_{i=1}^D{T}_i\right)$, and DOY of the bud break date x in this study. Similar to results reported by Takagi and Tamura (1987), the larger x becomes, the smaller AT^(D) tended to be at several sites (Fig. 3), suggesting that the growth rate of grapes after bud break is dependent on time. It can also be inferred that the growth rate of grapes after bud break can be affected by development at the growth stage before bud break in some way. These possibilities must be investigated in future studies. In this study, based on the obtained results, we used a function that represents the negative relation between x and AT^(D) in Eq. 7 in Model 4.

2.  Prediction of full bloom dates at each site using data at the site

As described in Table 2, RMSEs of Models 1–5 were smaller than D_STD (shown in Table 1) at 13 sites other than Kyoto. For Kyoto, RMSEs of Models 1–5 were larger than D_STD at Kyoto, but the value was sufficiently small to use in the models. Therefore, rather than averaging D_OBS at each site, using Models 1–5 is useful for predicting the full bloom dates of ‘Kyoho’ grapes. A large RMSE was found at Niigata, details of which must be investigated in future studies.

Kamimori et al. (2020) predicted full bloom dates of ‘Delaware’ grapes in Osaka after bud break. The prediction was made using an accumulated temperature model and two DVR models based on the effective accumulated temperature and a logistic curve of grape development. For that study, meteorological data observed at the cultivation field were used. The reported RMSEs of the models were 2.4, 2.1, and 2.3 days, respectively. Because of the differences in data used for each study, it is not possible to compare the results described above with our results directly. However, the results of the model obtained using effective accumulated temperature suggest that Model 1 (the effective accumulated temperature model in this study) using AMGD–NARO data has the same prediction accuracy (the average RMSE for 14 sites was 2.24 days, as presented in Table 2) with that of Kamimori et al. (2020) (RMSE is 2.1 days), even without using meteorological observations at the cultivation fields. Actually, AMGD–NARO are meteorological grid data provided for the whole area of Japan. Therefore, prediction with high accuracy can be expected using our Models 1–5 with meteorological grid data, even for places where meteorological data have not been collected before.

Sato and Takezawa (2014) predicted full bloom dates of ‘Azumashizuku’ grapes in Fukushima not after bud break, but after leafing. The prediction was made using various models including an effective accumulated temperature model. The reported RMSEs of each model were all about 1.0 day. It is not possible to compare the results described above with our obtained results directly, but our prediction accuracy may be lower when considering the results of the effective accumulated temperature model, which suggests that full bloom dates of grape can be predicted more accurately after leafing rather than after bud break.

From the Section 1 Results, the findings show that the following considerations can improve the suitability of predictions for observations of ‘Kyoho’ full bloom dates: 1) the nonlinear relation between temperature and grape development; 2) the effect of solar radiation on grape development; and 3) the relation between DOY of bud break date and grape development. Model 5, with all considerations, showed the smallest average RMSE value for predictions for all sites among all models (Table 2). However, at several sites, RMSE was smaller with Models 2, 3, or 4 than with Model 5. Also, the model that most improved the prediction accuracy varied from site to site (Table 2). Future studies must set criteria for model selection by investigating the relation between the three considerations presented earlier and regional characteristics of grape development.

3.  Prediction of full bloom dates at each site using data at all sites except the site under analysis

From Table 4, we found that RMSE of the predictions by each model was smaller than D_STD (Table 1) at 12 sites other than Tokushima and Kyoto. Therefore, using the models, rather than averaging D_OBS, a more accurate prediction could be achieved at many sites.

We also found that the average RMSE of the predictions for all sites with Model 5 was smaller than that with Model 1 (Table 4), suggesting that it is useful to consider nonlinearity, solar radiation effects, and the relation with DOY of grape bud break development for predicting full bloom dates of ‘Kyoho’ grapes over a wide area. Model 5, which was built using data at various sites, is expected to be useful for predictions in places where grape-development data have not been collected. However, the average RMSE for all sites in Model 5 used for prediction at each site using data from all sites except the site in question (2.54 days, as shown in Table 4) was larger than that obtained using Model 5 built using data at each site (2.06 days, as shown in Table 2). Therefore, if grape-development data are observed at the target site, then it is better to build a prediction model using data at the target site.

To describe characteristics of the prediction errors with Model 5 built using data at multiple sites except the target site, we investigated the distribution prediction errors. For the grape-development data used in this study, D_OBS takes a value between 35 and 66. Therefore, we divided the set of D_OBS into six ranges (D_OBS ≤ 40, 41 ≤ D_OBS ≤ 45, 46 ≤ D_OBS ≤ 50, 51 ≤ D_OBS ≤ 55, 56 ≤ D_OBS ≤ 60, 61 ≤ D_OBS) and investigated the error histogram for each range of D_OBS. The results are presented in Figure 10. The figure shows the following characteristics: 1) D_OBS is concentrated in the range of 41–50, with a median error of almost 0 for the range; 2) D_OBS larger (smaller) than the values in the above range tend to be underestimated (overestimated). Underestimation for large D_OBS can result from incorrect estimation of the model parameters. With such incorrect estimation, parameter a, which represents the estimated EAT^(D), can be smaller than the true EAT^(D). This may occur because parameter a estimated from a large amount of data of the average D_OBS can show a value close to the average EAT^(D). Then, parameter a can be smaller than the EAT^(D) actually needed for a large D_OBS. The opposite result may be obtained for small D_OBS. We also found underestimation and overestimation using Model 1. A small error for the average D_OBS, and overestimation or underestimation for D_OBS far from the average D_OBS are valid results of a statistical model. Therefore, for Tokushima and Hiroshima, the large RMSE of Models 1 and 5, which were built using data at multiple sites except for the target site (Table 4) is attributable to the nature of the statistical model.

Fig. 10. 

Histograms of prediction errors by Model 5 built at each site using data at all sites except the site in question for the following six ranges of D_OBS; (a) D_OBS ≤ 40, (b) 41 ≤ D_OBS ≤ 45, (c) 46 ≤ D_OBS ≤ 50, (d) 51 ≤ D_OBS ≤ 55, (e) 56 ≤ D_OBS ≤ 60, and (f) 61 ≤ D_OBS.

Based on these overall results, we were able to build a general prediction model that is applicable for various sites with higher accuracy than the conventional effective accumulated temperature model. Model 5 that summarizes the growth characteristics of ‘Kyoho’ at multiple sites can also help people to start growing grapes in places where grapes have not been cultivated. To use Model 5 at such places, bud break date data at the nearest public test site to the target area will be helpful. It is also possible to back-calculate the bud break date from the desired full bloom date. Furthermore, the model can be used easily because it uses AMGD–NARO data, which are meteorological grid data provided for all areas of Japan, and which do not entail any costs unlike meteorological observations at cultivation fields. It is expected that the forecast values of the Japan Meteorological Agency will be used after the bud break date. However, after predicting the full bloom date at the bud break date, the actual values of AMGD–NARO data for the last few days after the bud break date will be available and then the prediction can be revised.

4.  Importance of using data at multiple sites over a wide area

In summary, based on results of the characteristic analysis of grape development conducted at multiple sites over a wide area in Japan, we were able to build a prediction model for the full bloom date of ‘Kyoho’ grapes that is applicable to many places. Results of this study suggest the importance of using data at multiple sites to build a general model. Further improvements in prediction accuracy are expected by referring to grape development processes that cannot be considered in this study. Further improvements can be achieved by performing additional laboratory experiments and by comparing the results to grape development characteristics found over a wide area. From analyses of other grape characteristics over a wide area, it is also expected that extensive prediction of fruit quality such as soluble solids content and acidity will be useful as indices for judging the harvest time of grape at many places.

Acknowledgements

‘Kyoho’ grape development data were provided by public test sites in Tokushima, Hiroshima, Aichi, Kanagawa, Kyoto, Tokyo, Yamanashi, Saitama, Ibaraki, Nagano, Toyama, Niigata, Yamagata, and Iwate. We received generous support from Dr. Masahiro Yano and Dr. Hiromi Kanegae at the Research Center for Agricultural Information Technology, National Agriculture and Food Research Organization.

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