Green beans have a short growing season so a range of sowing dates result in a long production season with multiple harvests. In South East Queensland (SEQ) there are two sowing seasons: from October to December (‘Spring’), from January to May (‘Autumn’) and in Bowen, North East Queensland (NEQ) a third, ‘Middle’ season occurs from May to October (Table 1).

Examination of the temperatures and vapour pressure data at growing locations across years show an increase in maximum temperature over the last ten years (Fig 2).

Locations in Queensland and northern New South Wales had varied temperature profiles (Fig 3). For each historic sowing the daily weather was extracted and matched to the sowing date and location. Using the crop dates of sowing and petal fall agro-meteorological variables were derived and used in the modelling.

Under well watered conditions intercepted radiation and temperatures are important and so we used these variables in our models. Early emergence and optimum leaf cover in the vegetative period intercepts sunlight for leaf growth, flowering and pod filling. Type I green beans are considered photo period insensitive and there is a simple relationship with thermal time and development [3]. The principles of crop light interception show primary productivity of plant biomass P_n is succinctly described by the following [13, 14]:

Primary production P_n is above ground biomass(dry weight per area) over the growing period for a particular site. It is a function of the annual incident solar radiation S_t which is determined by site and year as solar radiation (MJm⁻²) and varies with latitude and time of year. The efficiency of radiation interception by the crop is denoted by ϵ_i, the efficiency of conversion into biomass ϵ_c and k is the energy content of the plant mass in units of MJg⁻¹. The radiation use efficiency of faba bean was found to be 1.03 to 1.29 gMJ⁻¹ [15].

Yield potential of a crop is a function of interception of light and the transfer of the products of photosynthesis into plant biomass and the component of interest (e.g pods). Yield potential Y_p is defined by Evans [16] as ‘the yield of a cultivar when grown in environments to which it is adapted, with nutrients and water non-limiting, and with pests, diseases, weeds, lodging and other stresses effectively controlled.’

where the harvest index η, (η ≤ 1) is the efficiency with which biomass is partitioned into the harvested product. From these principles, the main factors which influence yield are:

Indices of growth assess the environmental potential for productivity when there is no water limitation [17]. A growth factor to account for the extent of radiation interception RIX (RIX  ≤ 1) was derived from research data on biomass production. Then a growth index I_g which quantifies potential growth per unit of crop development, was calculated for a site using weekly values of daily incident radiation R_i and mean daily temperature T_i are the mean daily solar radiation and the mean daily temperature for week i.

This equation is used for weekly data across the growing period of the crop, and requires Leaf Area Index (LAI) measurements. LAI is a unitless measure of the ratio of the area of green leaf area for a unit land area, and it is required to be over approximately 2 to 3 for full radiation interception (RIX = 1).

In crop studies green leaf area, light interception and biomass (dry weights) of above ground plant parts are measured on several occasions and at key phenological stages throughout the season. Such studies are resource intensive and form part of a research program as several sites and years are required to provide data. As an efficient alternative, our contribution uses statistical modelling with a large data set of bean phenology, derived agro-meteorological variables and fresh yield.

Monteith [14] introduced the concept of thermal time ρ which expresses time on the developmental clock of a plant as the summation of temperature above a threshold. The laying down of the leaf and flower nodes, the plastochron development, is a function of the thermal time and temperatures experienced within the early growth stage. Biomass yield is a function of photo-synthetically active radiation (PAR) interception and yield is improved by early green leaf cover, where water is not limiting.

From the literature, the growth curve for bean dry weight appears as a characteristic logistic curve, which is typical of many plant growth curves under well-watered conditions. Cardinal temperatures (base, optimal and maximum) of the developmental process were found to be 6.8, 24.0 and 34.1∘C, when hourly temperatures, in the phase between emergence and the appearance of the first bean flower, were used [18]. Temperature sensitivity occurs at phenological stages such as petal fall and during pod fill. Partitioning of dry matter studies on beans used a base temperature of 5∘C [3].

Further studies showed bean growth stages had a base temperature of 4.2∘C, an optimum of 24∘C and ceiling of 30∘C, and mild water deficits were not assumed to have any affect on development [19]. The vegetative period ends at petal fall and actual start date of the pod growth will vary with the determinacy of the variety. Across four bean cultivars the mean time required to develop a node was 6.1 days at 18∘C, 3.0 days at 23.3∘C, and 0.91 days at 28.3∘C. Supra-optimal temperatures for a crop either as high day or night temperature can reduce yield. A higher temperature tended to decrease time to flowering by enhancing the rate of vegetative development, while it tended to increase the days to flower by enhancing the photoperiod gene activity. This resulted in a U-shaped curve of time to flowering in response to temperature.[20].

High night temperature is detrimental to growth of many crop species and in particular affects many traits in the reproductive phase [21]. High night-time temperatures appeared to have larger effects than maximum daytime temperatures. High temperatures during pod fill may reduce reproductive performance when tolerance thresholds are exceeded. Bean flowers and developing pods drop in high temperatures thus reducing yield.

Green bean as a C3 warm temperate crop, will lose more biomass in the process of photo-respiration when temperature increases compared to a C4 tropical crop [13]. As climate changes and temperatures increase producers will be looking to better manage these stresses in bean production. The anomaly for Eastern Australia and Queensland temperatures are in the order of a 2∘C for both the minimum and maximum temperature in each of the bean growing seasons [22].

When calculating thermal time, we used a base temperature of 5∘C and a maximum temperature of 30∘C for field grown beans using daily temperatures [7, 23].

The R package cropgrowdays was developed to compute agronomically informative variables using SILO meteorological data [10]. These included agro-meteorological data items such as thermal time (also known as growing degree days) within a period, and mean daily or cumulative radiation within a given period. Currently, functions are provided for calculating growing degree days, stress days, cumulative and daily means of radiation data, and assisting in various day of year units. The package is available under Creative Commons 4.0 licence (see S1 File). Historical meteorological data were extracted from SILO [27] and matched to each sowing and the following agro-meteorological variables were calculated:

The agronomic data consisted of date of sowing, date of petal fall, date of harvest, location and marketable yield. Data were validated, cleaned and vegetative and pod filling growing periods were used to make a range of agro-meteorological variables using cropgrowdays. They were constructed for each observed sowing. The historical dataset of sowing dates and crop phenology was assembled to include a range of derived agro-meteorological variables (S1 Table Derived agro-meteorological variables). Therefore, two datasets were constructed using the cropgrowdays functions to obtain agro-meteorological variables:

We aimed to predict growth periods and fresh green bean yield from combinations of agronomically informed variables developed using sound and practical statistical models. Predominantly, we used growth durations as the focus on predicting durations from localised agro-meterological variables.

Since the 1980s, agro-meteorological variables have been used in predictive plant and crop modelling [17]. The statistical approach employed here balanced the requirement for rigourous and robust statistical modelling while also incorporating the need for practical and readily available agronomic and agro-meteorological variables. (Table 2 and S2 File) outline details of these variables.

Growers are interested in predicting the growing duration given the planting time. Since keeping models as simple and as realistic as possible was one aim of these studies, agronomic variables for inclusion in the initial model were chosen based on informed knowledge of crop growth. For example, sowing day is an important variable for modelling because it is related to whether the plant experienced a declining temperature or an increasing temperature. Since there is little overlap in the two green bean growing seasons in Australia, sowing day also indicates the season. Note also that our data are for the southern hemisphere. We also employed other agronomically useful variables like temperature, degree days and stress days over various periods of growth.

Based on the context, many models may be similar and equally useful. We were conscious of merely using statistical significance and so employed robust statistical procedures and model checking. We used robust statistical modelling, and model simplification based on the principle of parsimony which is when a simpler model with fewer variables is favoured over more complex models with more variables. The iterative statistical process is not trivial, and starts with data validation, model fitting and finally model selection. After data validation, matrix correlation plots were employed to check on linear relationships (correlation). Collinearity was handled by excluding highly correlated variables. Models with a lower Akaike Information Criteria (AIC) indicate a better model fit but, using parsimony, then models with fewer variables are favoured. A final model was determined by stepwise AIC by using groups of variables within relevant growth periods. The final models were obtained using concepts which should prove useful in providing an application for agronomists to replace their complex spreadsheets.

The selected models were based on large datasets and robust statistical methods and, despite the uncertainty of some of the measurements, we were able to fit models useful for prediction. We also provided 80% prediction intervals to assist in capturing the uncertainty for predicting responses.

All data manipulation, wrangling and modelling was completed with R software [28]. The ‘stepAIC’ function from the ‘MASS’ package [29] was employed for robust statistical modelling, and the simplification was based on the principle of parsimony. In essence, as described above, a large number of well chosen agrometerological variables were included in the initial model and the step-wise procedure removed variables which were least related to the outcome variable. This process used a standard, but a well defined, stopping criterion to establish a final model.

Logistic functions are commonly used for describing plant growth. We compared the logistic growth curves of pod fresh weight [6] against thermal time for the seasons. We used the nonlinear least squares function from the nlme R package [30]. The self-starting function ‘SSlogis’ from the ‘nlme’ R package was applied. The parameters are the upper asymptote ‘Asymp,’ a numeric parameter representing the x value at the inflection point of the curve ‘xmid,’ and a numeric scale parameter on the input axis ‘scal.’ In these functions, ‘b’ is replaced by ‘scal’ = -1/b.

Randomly collected samples from a predetermined location at 9 and 14 days prior to actual harvest, were used to determine commercial yield potential and get statistical estimate of pod components. Commercial packets (200g) of locally grown fresh beans had a mean pod bean weight of 4.91 g. We used statistical estimation of components of yield on a fresh weight basis prior to harvest. Components making up fresh pod yield are:

Fresh weight yield = Plants per area x Pods per plant x Pod weight

These statistical estimates required at least 12 to 15 samples to estimate the mean within 10% when simple randomised sampling is used. Due to COVID19 restrictions on travel and field work in Queensland it was not possible to continue sampling in 2021.

Derived agro-meteorological variables considered in models showed cumulative radiation, days of high temperature and thermal time (calculated as growing degree days with base temperature 5∘C and capped at 30∘C) could assist in predicting duration of growth periods and yield.

A selection of agro-meteorological variables found to have value in modelling are named in Table 2. Predictive models and statistical summaries of agro-meteorological variables were found to be useful in modelling (S2 File).

Many models were built and, in general, the derived variables were useful in describing growth and to a lesser extent fresh yield.

Plants and bean pods were counted and weighed from randomly selected samples on a 0.75 m row length. The proportion of pod weight at sampling date was based on a mature marketable pod of 4.9 g. The plant stand from 45 days to 53 days after planting, showed a decline if it was assumed a similar population was planted. This could also be due to a difference in plant population at seeding or plant establishment, although both planting blocks were at the same site. If this is a true decline in plant number it suggests plant competition has occurred within a row and the resulting plant population is adequate for maximum yield. Over seeding at planting, can occur as a strategy to avoid a low or patchy plant population at harvest, and this may lead to a slight decline in plant population from a good emergence. There were an average of 15.6 pods per plant (se 0.83) at 9 days before harvest.

Table 3 shows the components of yield of the sampled fields. At 14 days pre harvest the pod weight was 11% of final fresh yield and at 9 days pre harvest the pod weight was 75.8% of final fresh yield. The pod size was 18.7% and 72.3% respectively of final yield.

The statistical models applied to the data for these seedings were able to accurately predict the vegetative and pod durations within a day of the observed sowing periods for ground-truthed samples. Agronomist visit fields to ascertain when to harvest and modelling total growing duration may assists in focusing when to make field observations.

Models were applied to fields and observed and predicted durations are shown in Table 4 and described in (S2 File).

Interception of PAR radiation by adequate green leaf cover drives biomass production. Early leaf cover assists in accumulation of total biomass when water is not limiting. We have no measure of LAI but we can use some estimates from the literature. At petal fall we can assume full (100%) leaf cover [31, 32]. A LAI of around 2.5 at 50 days after sowing was measured in a bean crop in Florida [33].

Based on Eq 3 we made a simple productivity index for the vegetative (I_veg) and pod fill period (I_pod) respectively. RIX is set to 1 as we are assuming adequate leaf cover.

Where R_i is average daily radiation and T_i − T_b is average temperature over the vegetative period.

Where R_i is average daily radiation T_i − T_b average temperature over the pod filling period.

Indices were derived to act as a proxy of potential productivity for the two periods of growth (vegetative and pod fill) and the three seasons. The seasons differed with the Spring season potentially more productive than the Autumn season (Fig 4) due to a more favourable radiation to temperature balance. The productivity indices do not incorporate temperature stress.

Fresh yield prediction, due to the somewhat imprecise measure of marketable fresh weight, was more difficult to model (S2 File). The R squared for models were low. Fresh weight may vary in water content but the measurement after harvest at the packing shed aimed to minimise such differences. We used actual harvest date as our response variable and bean quality was assumed to be marketable by the producer as poor quality crops were not harvested. Quality is of critical importance for maximising the value of harvested green beans. Commercial harvests are planned to occur within a six day optimum harvest window to maximise quality.

It is documented in the literature that once daily maximum temperature exceeds 30∘C, both plant growth rate and yield declines. High temperatures were observed in the pod fill period and these were also associated with a decline in yield as the number of days over 27.5∘C in the pod fill period increase. Hence, a potential high yielding environment will not reach its yield potential where high temperatures occur. We found that days of temperatures over 27.5∘C or 30∘C occurred frequently in Queensland.

Yield declined as the days of high temperature in the pod fill period increased (Fig 5). The productivity indices are an assessment of potential productivity, however it does not take into account the stress days of temperatures over 27.5∘C or 30∘C.

As the crop has a short season, and is harvested at peak quality, this occurs at about 1050, 1080 and 1010 degree days for Autumn, Middle and Spring seasons, respectively (Table 5).

Using a three parameter logistic functions, to fit the increase in pod fresh weight from petal fall to harvest, the two seasons had a significantly different growth curve. We fitted thermal times using less than 1080 ∘C d, as above this thermal time pods become stringy and thus fresh weight is past its optimum.

The fitted parameters varied significantly by season (p<0.001). The coefficients are shown in Table 6. The best model has separate asymptote, and separate ‘xmid’ but a common ‘scal.’ In Fig 6, there is a large variation in the fresh weight. Quality is not assessed in the field and can reduce the yield by up to 20%. Conditions in transport and at the delivery shed may influence water content and thus weight of fresh beans.

Agro-meteorological variables plotted for observed historic bean pod filling periods allow insight on temperature stress that may be experienced. The median of a ten year period of maximum temperature of the sites during the pod filling period was plotted. For the sites of bean production in SE Queensland the maximum temperature of over 27.5∘C frequently occurs in each season (Fig 7).