Fungicides, either preventative or eradicative, are used to manage cucumber powdery mildew (Ni and Punja, 2020). An accurate forecasting model is essential to prevent overuse of fungicides and improve their efficiency (Mahal et al., 2012). Temperature has been considered a key factor for disease forecasting, and it is often introduced in models as a thermal unit called “growing degree-day” (GDD), which provides an improved description of phenological events compared to calendar dates or day counts (Mahal et al., 2012; McMaster and Wilhelm, 1997). GDD is estimated by calculating the difference between the average daily temperature and the base temperature (or lowest temperature threshold) below which a particular biological phenomenon does not occur (McMaster and Wilhelm, 1997). Another key factor for disease forecasting is leaf wetness duration (LWD) (Magarey et al., 2005). LWD is the period of visible water on plant tissues (Wang et al., 2019), and it is often estimated from relative humidity (Sentelhas et al., 2008). The relationship between LWD and the severity of cucumber powdery mildew has been previously studied (Granke et al., 2012; Mieslerová et al., 2022; Milod et al., 2021). These studies found that moisture directly or indirectly affects the infection and disease progression of cucumber powdery mildew. Additionally, drought may accelerate the onset of the disease by hindering plant growth and development (Mieslerová et al., 2022).

Considering these observations, in this study, we developed a model to simulate the onset of cucumber powdery mildew using GDD and LWD. A successful model should predict the first onset date with a margin of error under 10 days, which is a conventional fungicide spraying interval considering decay rates, as shown on most fungicide labels and in the literature (Quesada-Ocampo, 2023). Therefore, this study aims to assess the effectiveness of GDD and LWD in forecasting the onset date of cucumber powdery mildew.

Four field experiments were conducted at Suncheon, Republic of Korea, from 2022 to 2024 in the same greenhouse, where hourly weather data were measured inside and outside the greenhouse using appropriate sensors (Woosung Hitec Co., Yangsan, Korea): inside air temperature and relative humidity, and outside air temperature, relative humidity, wind speed and direction, and rainfall. The results from two initial experiments in spring and autumn of 2022 were used to calibrate the model, while two experiments in the springs of 2023 and 2024 were used to validate the model. No fungicides for powdery mildew were applied to allow the disease to occur naturally in the greenhouse. The plants were drip-irrigated every three days in the morning. Plants were observed on less than a weekly basis, and the disease onset dates were recorded when the first symptom appeared on a leaf. Air temperature (hereafter, temperature) and relative humidity inside and outside the greenhouse during the cultivation period were used in the study. Right after each trial, the greenhouse was thoroughly cleaned of all plant debris and heavily sprayed with pesticides, kresoxim-methyl, and triflumezole (Dream Heart, Hanearl Science Ltd.). This practice is recommended for farmers growing cucumbers in greenhouses to eliminate potential inoculum sources (Badgery-Parker et al., 2019).

Temperatures inside and outside the greenhouse were converted into GDD: GDD_in and GDD_out for the GDD inside and outside, respectively. GDD_in and GDD_out were defined as the accumulated degree days since the planting date of cucumber in the study. It was assumed that cucumber growth and primary infection are related to GDD_in (Wang et al., 2022), whereas pathogen inoculum transmission from outside into the greenhouse is affected by GDD_out (Sapak et al., 2023). The disease will occur when the host tissues have grown enough to be infected and the environmental conditions are favorable for the disease (Scholthof, 2007). The base temperature and ceiling temperature (or upper threshold) for both GDD_in and GDD_out were determined based on the literature and are presented in Table 1 (Sapak et al., 2023; Wang et al., 2022). The reference GDD inside (rGDD_in) and outside (rGDD_out) were determined by averaging the actual GDD_in and GDD_out values, respectively, on the observed onset dates of two calibration trials in 2022. The rGDD_in was higher than rGDD_out, as the temperature inside the greenhouse is generally higher than the temperature outside in spring and autumn. GDD_d on a given day were scaled between 0 and 1 based on the rGDD as follows:

, where GDD_d is the scaled GDD and is set to 1 when GDD exceeds the rGDD. The disease onset risk was then calculated by multiplying GDD_d inside (GDD_din) and GDD_d outside (GDD_dout).

The simulated onset date is the day when the disease onset risk first reaches 1, which is the threshold for disease occurrence (Fig. 1). In the calibration trials in 2022, the model with GDD simulated the onset date with an average margin of error of 8 days (Table 2). The difference in the autumn of 2022 was 14 days, which is unacceptable as it is longer than the recommended fungicide interval of 10 days. The deviations were 9 days and 5 days for the validation trials in the spring of 2023 and 2024, respectively.

To further improve the model performance, LWD was introduced as additional input to the model to factor in the biophysical interaction of temperature and leaf wetness (humidity) resulting in disease onset. LWD was estimated using a simple empirical method with a constant relative humidity threshold (relative humidity ≥ 90%) (Sentelhas et al., 2008). An exponential function to represent the decreasing risk of disease with increasing LWD was adopted to estimate the LWD index on a given day (L_d) (Fig. 2). L_d was calculated as follows:

, where LWD_d is the LWD (h) of the past 6 days, K is the maximum L_d, and r is the rate of risk decrease for powdery mildew development. The parameters in the exponential function were calibrated using two calibration trials in 2022 by utilizing the optim function of R (R Development Core Team, 2011) (Table 1). As shown in Fig. 2, the calculated L_d with the parameterized exponential function ranges from 0.5 to 1.5, acting as a correction factor for the disease onset risk with GDD.

Using the GDD and LWD index, the disease onset risk was calculated as:

The first symptom of cucumber powdery mildew occurs when the disease onset risk of the model reaches 1 (Fig. 1).

In all calibration and validation trials, the simulated dates with the model using GDD and LWD were earlier than those with GDD alone (Table 2). As a result, the absolute values of the errors decreased in two trials in autumn, 2022 and spring, 2023. For the calibration trials in 2022, the model simulated the onset date with an average margin of error of 4 days. Although the error between the simulated and observed dates increased from 2 days (by the model with GDD) to 5 days (by the model with GDD and LWD) in spring, 2022, the error was reduced from 14 days to 3 days in autumn, 2022. For the validation trial in spring, 2023, the error also decreased from 9 days to 2 days when LWD was considered. For spring, 2024, the deviation between the observed and simulated dates increased from 5 days to 9 days.

Comparing the outside temperatures, the spring of 2024 showed substantially higher accumulated GDD (132.8 degree days) than the other trials (38.0 for the spring of 2022, 41.1 for the autumn of 2022, and 32.2 for the spring of 2023). This indicates that the higher GDD_dout in Spring, 2024 might abnormally increase pathogen propagation outside and thus advance transmission inside the greenhouse, resulting in an onset of powdery mildew 9 days earlier than observed. With this simplified equation—assuming a linear relationship between the disease onset risk and the outside GDD—the model may have inherent limitations, especially in dealing with extreme conditions affecting inoculum availability (timing and amount) from outside sources such as collateral hosts or nearby greenhouses. Therefore, further study should be conducted to address such unusual cases in the near future. Additional data collection is essential because the current model was calibrated using only two trials, which may create bias. Increasing the data size through trials in different environmental conditions will improve the model’s performance.

To understand the relative contribution of each factor in determining the onset date, whether delayed or advanced, we analyzed the average values of GDD_din, GDD_dout, and L_d for the period from planting to onset dates in four trials. Based on the average value of each factor used to calculate the disease onset risk, we can infer the relative contribution of each factor, although it is not quantitative (Fig. 3). First, when comparing the contributions of GDD_din and GDD_dout, GDD_dout contributed more to advancing the disease onset date in autumn, 2022 and spring, 2024, while GDD_din contributed more in spring, 2022, and both showed similar contributions in spring, 2023. As a correction factor derived from LWD inside the greenhouse, L_d amplified the effects of GDD in spring and autumn, 2022 and spring, 2023, while it had a minimum effect in spring, 2024. This result further supports our hypothesis that the abnormally high GDD_dout in Spring 2024 was the main contributor to significantly advancing disease onset (Table 2).

Forecasting disease onset is crucial for integrated disease management, as it enables the optimization of fungicide spraying programs. However, there have been few successful attempts to predict disease onset. Salotti et al. (2023) recently developed a universal model for Colletotrichum diseases, in which primary inoculum build-up was calculated based on temperature and wet periods as one of several modules within a complex model. Nettleton et al. (2019) predicted the onset of rice blast disease using machine learning and process-based models, demonstrating that when a sufficient amount of data is available, machine learning models can provide accurate predictions. In contrast, the simple framework presented in this study focuses solely on disease onset, offering a practical solution when the dataset size is limited.

Precise disease onset prediction can help prevent fungicide overuse by reducing unnecessary early sprays before symptoms appear. While the recommended first spray is 40 days after planting, many farmers begin much earlier—15 days or even sooner (personal communications). This discrepancy underscores the potential of a disease onset prediction model to improve spray decision-making. If farmers were to follow the model’s predictions, fungicide applications could be reduced by 1.8 times compared to conventional programs starting at 15 days after planting. By integrating a model-based approach, fungicide applications can be more efficiently timed, reducing chemical inputs while maintaining effective disease control and supporting sustainable farming practices.