As the source and main producing area of tea in the world, China has formed unique tea culture, and achieved remarkable economic benefits. However, frequent meteorological disasters, particularly low temperature frost damage in late spring has seriously threatened the growth status of tea trees and caused quality and yield reduction of tea industry. Thus, timely and accurate early warning of frost damage occurrence in specific tea garden is very important for tea plantation management and economic values. Aiming at the problems existing in current meteorological disaster forecasting methods, such as difficulty in obtaining massive meteorological data, large amount of calculation for predicted models and incomplete information on frost damage occurrence, this paper proposed a two-fold algorithm for short-term and real-time prediction of temperature using field environmental data, and temperature trend results from a nearest local weather station for accurate frost damage occurrence level determination, so as to achieve a specific tea garden frost damage occurrence prediction in a microclimate. Time-series meteorological data collected from a small weather station was used for testing and parameterization of a two-fold method, and another dataset acquired from Tea Experimental Base of Zhejiang University was further used to validate the capability of a two-fold model for frost damage forecasting. Results showed that compared with the results of autoregressive integrated moving average (ARIMA) and multiple linear regression (MLR), the proposed two-fold method using a second order Furrier fitting model and a K-Nearest Neighbor model (K = 3) with three days historical temperature data exhibited excellent accuracy for frost damage occurrence prediction on consideration of both model accuracy and computation (98.46% forecasted duration of frost damage, and 95.38% for forecasted temperature at the onset time). For field test in a tea garden, the proposed method accurately predicted three times frost damage occurrences, including onset time, duration and occurrence level. These results suggested the newly-proposed two-fold method was suitable for tea plantation frost damage occurrence forecasting.

China is the first country to discover and use tea, and thus form unique tea culture [

Early warning and prediction of frost damage had been conducted in China as early as the agrarian age. However, most of these warnings were at relatively large scale and not practical. With the advancement of agricultural modernization, more and more attention has been paid to prediction of frost damage in microclimate environment. Wu et al. [

Since predicted temperature is a key indicator for frost damage warning, abundant attentions had been focused on accurate temperature forecasting in varied application scenarios. Jin et al. [

Fourier fitting is one of the important algorithms for signal processing and data analysis. Owning to its high efficiency, fast speed, and suitable for small sample modeling, it had been extensively used in various researches. Gao et al. [

At present, tea plantation frost damage early warning mostly relied on information released by meteorological department. These warnings were generally about tendency of temperature variations or predicted damage levels at a large regional level. While temperature in mountainous areas is affected by terrain fluctuation, vegetation coverage and other factors, thus predicted temperature or damage levels in regional scale could not fully represent the real situation of tea garden in mountainous and hilly areas. With the advancement of internet of things (IOT) techniques, some tea gardens are equipped with sensors for temperature monitoring. However, these sensors were unable to predict temperature and forecast frost damage, thus could not provide timely warnings. The effective combination of real-time temperature acquired by IOT sensors with forecasted temperature provided by meteorological department to analyze the mechanism of frost damage early warning in mountain tea garden region is of great significance for providing crucial information on guiding forewarning measures. Hence, aiming at problems mentioned in current meteorological disaster forecasting methods, such as difficulty in obtaining massive meteorological data, large amount of calculation for predicted models and incomplete information on frost damage occurrence, this paper tried to propose a two-fold algorithm for short-term and real-time prediction of temperature using field environmental data, and temperature tendency results from a nearest local weather station for accurate frost damage occurrence information determination, including occurrence time, duration and occurrence level, so as to achieve a specific tea garden frost damage occurrence prediction in a microclimate.

The criteria (^{st} November 2018 to 31^{st} March 2019, and from 1^{st} November 2019 to 30^{th} March 2020, were used to train and validate the feasibility of building a model for predicting frost damage according to information listed in ^{st} March to 29^{th} April 2021. During this period, cold spell in later spring happened frequently. These data were further used to validate model’s capability of for frost damage forecasting.

Level | Meteorological index | Symptom | Shoot damage rate |
---|---|---|---|

Mild | 0 ≤ _{min} < 2 and 2 ≤ H < 4;_{min} < 4 and H > 4 |
Bud leaves turned brown, slightly damaged, young leaves appeared ‘hemp point’, the edge became purplish red, remanent leaves were yellow brown. | <20% |

Moderate | −2 ≤ _{min} < 0 and 2 ≤ H < 4;_{min} < 2 and H > 4 |
Bud leaves become brown, then withered and shrank. and it spread from edge to middle of leaves. buds could not expand, and young leaves tarnished. | ≥20% and <50% |

Severe | _{min} < −2 and H < 4;_{min}< 0 and H ≥ 4 |
Bud leaves became dark brown, young leaves curled, dried and were vulnerable to shedding. | ≥50% and <80% |

Extra severe | _{min} < −2 and H ≥ 4 |
Bud leaves exhibited brown and scorched, new shoot and upper shoot withered, branch cuticles appeared chapped. | ≥80% |

Note: _{min} (°C) is the lowest hourly temperature, and H (h) is the number of _{min} duration in tea garden.

Generally, results of forecasted frost damage contain four parts: start time, onset temperature, duration and occurrence level, among which, onset temperature and duration are important meteorological indicators for assessment of frost damage occurrence level. Based on damage levels information (

The first step of a two-fold method was to use a fitting curve to predict the lowest temperature within a 24-h period. Considering the real-time performance of calculation of temperature prediction, it is necessary to reduce the amount of calculated data as much as possible and improve computation speed of forecasting while ensuring the accuracy of prediction. Thus, a Fourier fitting model with relatively few data orders was selected to build a first step model, i.e.,

where values of _{0}, _{j}, _{j},

Predicted temperatures obtained from a 24-h temperature fitting model were then compared with actual temperatures acquired from observations at the same time, and the minimum temperature from a fitting model was modified to achieve the lowest temperature prediction in 24 h (

where _{1} is a modified lowest prediction of temperature, _{0} is a predicted lowest temperature by a 24-h temperature fitting model. _{mi} is a set model temperature at each hourly time, while _{ri} is the corresponding observed temperature before _{0} and _{1}.

Although modified lowest prediction of temperature could be achieved through a process of the first step of a two-fold method. Information on specific onset time, duration, and accurate disaster occurrence level of frost damage could not be accurately provided. Here, the second step of a two-fold method (

where _{2} is a predicted temperature for 2 h later by using the slop method, _{t} is an actual temperature measured at the current time node, _{t−1} is an actual temperature measured at the previous time node, n is the number of time node intervals for prediction (

where,

After the process of two-fold method, environmental predicted temperature at a certain time could be accurately derived. Nevertheless, confirmation of frost damage occurrence level includes two aspects: environmental predicted temperature and duration of low temperature. Firstly, it is necessary to determine the onset time of frost damage. Here, a K-Nearest Neighbor method was chosen to predict onset time of frost damage. The method referred to collect three values of predicted temperature continuously in the form of a queue. If the second value of predicted temperature was lower than the threshold, frost damage was deemed to occur only at the time.

Apart from forecasting of frost damage onset time, it is still necessary to predict specific duration of low temperature to comprehensively determine frost damage occurrence level. Here, real-time weather forecast of temperature trends over next 24 h from a nearest local weather station were used to predict duration of low temperature, and thus to predict frost damage level. The prediction process was shown in

To investigate and compare the capability and potentiality of a proposed two-fold method for frost damage predicting, two reference methods that widely used in previous studies were selected, i.e., autoregressive integrated moving average (ARIMA) and multiple linear regression (MLR).

(1) ARIMA is a commonly used forecasting model for time series data. Which needs to transform non-stationary time series into stationary time series firstly. Combination of temperature variations and time exhibits a relatively obvious periodicity; thus, the model has been extensively used in applications of temperature prediction. Implementation of the model is mainly based on a batch of existing data to predict the next N unknown data. The larger N value is, the worse the prediction result is. this might suggest that the model is suitable for short-term prediction rather than long-time temperature forecasting.

(2) MLR is also frequently considered in temperature prediction researches. The premise of the method for tea plantation frost damage predicting is that environmental temperature in tea plantation area is influenced by many factors, such as air humidity, atmospheric pressure, precipitation, wind direction, wind speed and other meteorological factors. Through analyzing correlation between meteorological factors apart from temperature at a certain time and forecasted temperature at another moment, in order to predict frost damage. The formula was listed as follows:

where _{i} is temperature at current time, _{0}, _{1}, …, _{n} are coefficients calculated from historical data, _{1i}, _{2i}, …, _{ni} represent different meteorological factors corresponded to these coefficients.

In order to verify prediction accuracy under the effect of different factors, predicted and measured data and frost damage information were compared and analyzed. Differences between predicted temperature at the onset time of frost damage and actual temperature at the time (∆T), differences between predicted onset time of frost damage and the actual occurrence time (∆t), and differences between predicted frost damage duration time and duration of the actual damage occurrence (∆D), were selected as indicators to evaluate the capability of the mentioned methods:

where _{a}(_{p}) represents actual temperature at a predicted time of frost damage, _{f}(_{p}) stands for forecasted temperature at a predicted time of frost damage. _{a} and _{p} refer to actual time and predicted time when frost damage occurred, respectively. _{a} and _{p} denote number of days of actual frost damage, and number of days of predicted frost damage, respectively. If the error of predicted onset temperature is within ±1°C, the prediction of the onset temperature of frost damage could be considered accurate. If the error of predicted onset time is within ±2 h, the onset time prediction of frost damage could be acceptable. Specific number of days of frost damage occurrence depends on actual situation of environmental temperature.

Since detailed process of a two-fold method for tea plantation frost damage prediction were presented in

The proposed two-fold method needed to conduct temperature prediction firstly through modelling, so as to reduce the influence of temperature fluctuation on the process of temperature prediction, and eliminate the influence of temperature rapid variations on forecasted temperature when actual minimum temperature did not reach the threshold value of temperature. Therefore, whether the first step of a two-fold method was accord with actual temperature variation trend could great affect the overall temperature prediction. Here, effects of different values of Fourier fitting order on prediction accuracy were investigated. Furthermore, polynomial fitting method was tested and compared using the same data size and same criteria. Owning to its characteristic that higher fitting order could result in better precision, high-order polynomial fitting modelling was tested. With regard to Fourier fitting, increase of fitting order did not significantly improve fitting accuracy according to our analysis, thus low-order Fourier fitting was used. Partial results of both two methods are presented in

Method | Fitting order | Forecasted temperature at the onset time | Forecasted duration of frost damage | Forecasted number of days of frost damage |
---|---|---|---|---|

Furrier fitting | Second-order | 95.38% | 98.46% | 71 |

Third-order | 95.38% | 96.92% | 70 | |

Polynomial fitting | Eighth-order | 84.62% | 63.08% | 86 |

Ninth-order | 89.23% | 73.85% | 83 |

Results show that prediction accuracy of forecasted temperature at the onset time are higher than 80% for different orders of both Fourier and polynomial fitting methods. Nevertheless, values of polynomial fitting order are much higher than that of Fourier fitting. Furthermore, it is obvious that the prediction accuracy of forecasted duration of frost damage by Fourier fitting exceed the results obtained by polynomial fitting. Results of forecasted number of days of frost damage also show similar tendency, which suggesting that Furrier fitting is much more accurate than polynomial fitting in temperature prediction, even though complicated and high-order polynomial fitting methods are adopted. As for Furrier fitting, results of varied values of Furrier fitting order do not show significant differences in prediction accuracy. Considering that high-order Furrier fitting needs much computation, a second-order Fourier fitting model was selected for calculation and prediction in subsequent experiments.

Since a two-fold method required a certain amount of temperature data to establish a tendency model which reflected actual temperature variation for short-term temperature forecasting, data size that used in the model could directly affect prediction accuracy. Here, the influence of different data size on model prediction was analyzed. Datasets consisted of 3, 7, 15 and 30 days historical temperature data were compared and analyzed for modeling analysis. A second-order Fourier fitting model was employed, K-value of K-Nearest Neighbor was initially set as 3, and threshold temperature value was set as 4°C. Detailed results are shown in

Data size | Forecasted temperature at the onset time | Forecasted duration of frost damage | Forecasted number of days of frost damage |
---|---|---|---|

3 days dataset | 95.38% | 98.46% | 71 |

7 days dataset | 96.68% | 96.92% | 70 |

15 days dataset | 95.38% | 98.46% | 70 |

30 days dataset | 95.38% | 98.46% | 71 |

For a two-fold method, K-Nearest Neighbor method was a crucial process to determine occurrence and specific time of frost damage. Nevertheless, different K-values affected the performance of K-Nearest Neighbor method. Here, influence of varied K-values (i.e., K = 3, 5, and 7) for K-Nearest Neighbor model on prediction accuracy was investigated, and results are shown in

K-value | Forecasted temperature at the onset time | Forecasted duration of frost damage | Forecasted number of days of frost damage |
---|---|---|---|

3 | 95.38% | 98.46% | 71 |

5 | 93.84% | 81.54% | 67 |

7 | 86.15% | 72.31% | 62 |

In order to test the capability of the above proposed method for tea plantation frost damage prediction, performance of ARIMA and MLA methods for temperature forecasting and frost damage prediction were investigated and compared based on measured data acquired from Xiaotangshan Meteorological Station. For temperature prediction, a time series dataset containing continuous 120 h of temperature data, collected from 1^{st} November 2019 to 30^{th} March 2020, was used for these two methods. The first 100 h data were used for forecasting models building, and then the established models were used to predict temperature and frost damage occurrence of next 20 h. Predicted temperature results with ARIMA model was presented in

Regarding to MLR methods, temperature forecasting results for next 20 h were rather poor, so results for the next 2 h were investigated. For MLR models, different meteorological factors were randomly combined for predicting temperature. top rank three combinations for MLR models that showed the highest predicted accuracy are presented in

No. | Variables | Prediction accuracy |
---|---|---|

1 | humidity, air pressure, wind direction, wind speed | 71.52% |

2 | humidity, air pressure, wind speed | 72.84% |

3 | humidity, air pressure | 69.08% |

Note: Prediction accuracy was obtained from comparison between predictions for the next 2 h and its actual temperature. Since precipitation value was zero, so it was not included in MLR models.

Method | Forecasted temperature at the onset time | Forecasted duration of frost damage | Forecasted number of days of frost damage |
---|---|---|---|

ARIMA | 72.84% | 66.15% | 46 |

MLR with four variables | 66.23% | 30.78% | 34 |

Proposed two-fold method |

According to the above-mentioned parameterization of a two-fold method, a second-order Fourier Fitting model was established based on 3 days temperature datasets. Threshold temperature for determining frost damage was set at 4°C, and K-value for K-Nearest Neighbor was set at 3. The method was then used for frost damage prediction in Tea Experimental Base of Zhejiang University. During the field test, Actual frost damage occurred on 22^{nd} and 23^{rd} March 2021, which were mainly due to the influence of cold air moving southward. Also, a frost damage occurred on 11^{th} April due to the affection of precipitation. As for forecasting of these three frost damage occurrences with the parameterized two-fold method, results are presented in ^{nd} and 23^{rd} March are accorded with the actual situations. While, forecasted results for 10^{th} April regarding to predicted occurrence time and duration show an obvious difference with actual scenario. According to our analysis, we found that there could be an error in the judgment of frost damage in second step of a two-fold method when actual temperature was very close to the threshold temperature at the time when frost damage occurrence was predicted. This might be largely explained for the difference in occurrence time and duration of frost damage on 10^{th} April. Since the method could provide slight early predictions compared with actual situations, which indicating its fast and good response in advance, and it could be very effective for early frost prevention. Thus, we suggest that the proposed two-fold method is suitable for accurate prediction of tea plantation frost damage occurrence.

Frost damage occurrence date | 22^{nd} March |
23^{rd} March |
10^{th} April |
---|---|---|---|

Actual occurrence time | 5:19 | 22:32 | 4:50 |

Predicted occurrence time | 5:00 | 22:30 | 3:00 |

Actual temperature at predicted occurrence time (°C) | 5.1 | 5.7 | 4.3 |

Predicted temperature at predicted occurrence time (°C) | 4.2 | 3.7 | 3.9 |

Actual duration (h) | 1.38 | 7.00 | 1.37 |

Predicted duration (h) | 1.50 | 7.50 | 3.00 |

Actual damage level | Mild | Moderate | Mild |

Predicted damage level | Mild | Moderate | Mild |

In this paper, a two-fold method was proposed and tested to establish a scheme for short-term and real-time tea plant frost damage prediction. First, a Fourier fitting method was selected for predicting of temperature and its change trend, then combining with weather forecast temperature variation trend of next 24 h from a nearest local weather station, a K-Nearest Neighbor method was used to predict frost damage occurrence level, so as to achieve tea plantation frost damage early warning. Comparison with the performance of ARIMA and MLA models, a parameterized two-fold method showed good accuracy for prediction of duration and temperature at the onset time of frost damage (>95%), with a historical temperature dataset acquired from a meteorological station. For field test in Tea Experimental Base of Zhejiang University, the proposed method accurately predicted three times frost damage occurrences, including occurrence time, duration and occurrence level. These results suggested the capability and potentiality of newly proposed two-fold method for frost damage occurrence forecasting.

For modelling process, the method used a small amount of temperature data, which reduced the dependence of prediction scheme on the amount of historical data. Moreover, the approach adopted next 24 h temperature forecasting information from a nearest local weather station for frost damage level determination, which further improved the adaptability of prediction scheme. Nevertheless, the method also has its drawbacks, since an error could occur in the judgment of frost damage in second step of a two-fold method when actual temperature was very close to the threshold temperature at the time when frost damage occurrence was predicted. In addition, the model was just tested on a specific tea plantation area, the applicability of the method to other tea area locations and prediction accuracy of frost damage in these areas need to be further verified. Thus, more work is still needed in the future to optimize the two-fold model and improve its capability for accurate and robust forecasting of frost damage occurrence.

The authors are grateful to Jiaju Li, Panpan Zhao and Qiaowei Li for their assistance in experimental design and data collection.