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Modelling uncertainty in field grown iceberg lettuce production for decision support
Computers and Electronics in Agriculture 71 (2010) 57–63
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Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag
Modelling uncertainty in field grown iceberg lettuce production for decision support T.D. Harwood a,∗ , F.A. Al Said b , S. Pearson a , S.J. Houghton a , P. Hadley a a b
School of Biological Sciences, University of Reading, Reading RG6 2SA, UK Department of Crop Sciences, Sultan Qaboos University, Alkhod 123, Oman
a r t i c l e
i n f o
Article history: Received 3 September 2008 Received in revised form 26 November 2009 Accepted 9 December 2009 Keywords: Crop forecasting Stochastic model Lettuce Uncertainty Weather generator Variability
a b s t r a c t Uncertainty in terms of input parameters, particularly weather variables, has implications for the results of a deterministic crop prediction model. This manuscript describes the development of the Iceberg Predictor decision support system which uses a stochastic weather generator to provide three alternative scenarios for future weather. These are used to drive a mechanistic model which provides posterior distributions of potential crop outcomes including within-field variability, which are summarised for grower interpretation. Multiple crops can be simulated allowing improved management of uncertainty at the whole enterprise scale. Experimental work demonstrated that variation in transplant size is a major contributor to variability in the final harvest. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The accurate prediction of harvest dates is critical to the minimisation of profit loss for both growers and retailers (D. May personal communication, 1999). Both the supply (e.g. Thompson and Knott, 1934; Scaife, 1973; Wurr and Fellows, 1991; Al Said, 2000) and demand (Borg, 1998) of iceberg lettuce (Lactuca sativa L.) are sensitive to changes in weather, often resulting in shortage or surplus in the supply chain. Prediction of these phenomena can reduce their economic impact (Ryder, 1999). The Iceberg Predictor software described in this paper explicitly deals with the uncertainty of future weather, presenting results as posterior distributions which describe the resultant uncertainty in model predictions to assist growers in maintaining a continuous supply to meet a flexible demand. A typical field grown iceberg lettuce grower in the UK (industrial partners personal communication, 1999) will plant a number of different batches throughout the season, timed to produce a continuous supply. The crop usually takes between 40 and 80 days to mature. Retailers will normally specify a narrow range of acceptable head weights between 400 and 700 g. Managers can make accurate harvest predictions up to 2 weeks in advance, but the quality of prediction decreases beyond this due to the variability of
∗ Corresponding author at: CSIRO Entomology, Black Mountain, Clunies Ross St., Canberra, ACT 2601, Australia. Tel.: +61 (0)2 6246 4018. E-mail address: [email protected] (T.D. Harwood). 0168-1699/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.compag.2009.12.003
future weather. Supply forecasts can be used to help growers prearrange promotions with supermarkets or to buy in products from other suppliers to fulfil contracts. This latter aspect is important at the extremes of the season, since accurate crop forecasts will allow growers (and supermarkets) to decide when to stop/start importing overseas product. This project was developed with a multiple retailer and six growers (representing the majority of field grown lettuce suppliers in Great Britain) in order to improve predictions 3 or 4 weeks from harvest date, to increase the possibilities for remedial action. Continuing improvements in long-term weather forecasting provide a potential source of inputs to further improve predictions (Semenov and Doblas-Reyes, 2007). Crop forecasting models are typically deterministic, providing output in terms of a predicted day of harvest for a given simulation (e.g. Pearson et al., 1997). The rate of development of iceberg lettuce is sensitive to temperature and radiation (Dullforce, 1963; Wurr and Fellows, 1991; Wheeler et al., 1993), and variable weather will cause variation both within the crop and in the timing of harvest. This manuscript describes the development and application of a generic approach to the incorporation of uncertainty in model predictions due to weather into crop scheduling software incorporating growth models. By combining model predictions based on up to date weather records with future predictions based on simulated local weather, the range of expected variation in harvest date can be described. In addition, we deal explicitly with the interaction between uncertain weather and within-crop variation in progress to harvest. Whilst in this example, the approach is applied to field grown iceberg lettuce production using a specific growth model,
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and a specific weather generator, it has generic application to most crop systems where the weather is the main source of uncertainty. 2. Methods Six commercial growers distributed across the UK in the 2000 season contributed to the development of the model. These were located as follows in (a) Fife, 56◦ N, (b) Lancashire, 53.5◦ N, (c) Norfolk, 52.5◦ N, (d) Cambridgeshire, 52.5◦ N, (e) Berkshire, 51.5◦ N, and (f) West Sussex, 51◦ N. Sites c and d were within 40 km of each other, allowing a trivial examination of site-to-site variation in similar weather conditions. 2.1. Experiment 1: within-field variation If variability changes systematically across a field then it is due to changes in the state of the soil and/or microclimate. This is superimposed on top of the variability caused by the plants themselves (plant to plant variability). Six transects of >200 heads were sampled across an area of 30 m at five different grower sites (b–f) in England. Head weights and location were measured on the day of crop harvest. 2.2. Experiment 2: effects of temperature on iceberg lettuce growth and variability Plants (cv. Calgary) were grown from three planting dates (17 March, 25 June and 28 August), at each of six different temperatures (8, 10, 14, 18, 22, and 26 ◦ C) in factorial glasshouses at the University of Reading. Plants were grown semi-hydroponically in a mixture of vermiculite, sand and gravel. Head and total plant weight of 30 plants were measured on five occasions.
Fig. 1. Typical variogram showing iceberg head weight across a field (i.e. lag distance) for site d. There is no systematic increase in variability with lag distance indicating a lack of field variability.
to plant to plant rather than field variability. Head weight varied insignificantly according to position in the bed. 3.2. Experiment 2: effects of temperature on iceberg lettuce growth and variability Overall, plant growth in terms of fresh weight increased with temperature up to an optimum of 18 ◦ C as observed in previous studies on iceberg lettuce. No evidence was found to show that plant-to-plant variability was significantly affected by temperature, or solar radiation. The coefficient of variation showed no consistent response to temperature or planting date, remaining broadly at the same scale (approximately 15%) over time, suggesting that plant-to-plant variability within a field may be inherent at the planting stage. 3.3. Experiment 3: variability within transplants
2.3. Experiment 3: variability within transplants To test whether plant to plant variability was inherent within the transplants used by growers (and to generate a series of data for model parameterization) a series of on farm trials at each of the participating growers were conducted. The aim was to establish the extent to which variability at the transplant stage accounts for variability within a harvest. If field conditions introduce further variation, this will increase the coefficient of variation over time. This information is crucial to the model representation of variability. Externally raised plugs (dry weight 1–2 g) are planted 3–4 weeks after germination in commercial production (Ryder, 1999). For each trial run, each site was supplied with identical batches of 2500 plants of each of two cultivars (Diamond and Calgary), treated with GAUCHO at a standard rate. Transplants were grown by the same company from the same seed stock to minimise variability. Plugs were planted within a standard block by each grower and grown under typical conditions. This experiment was repeated on 6 occasions over two seasons. Twenty plants were sampled from each run at weekly intervals and total above ground plant fresh weight and head weight (when present) measured. Weather data were recorded by each site’s monitoring system. 3. Results 3.1. Experiment 1: within-field variation Variograms were plotted for each field in GENSTAT (e.g. Fig. 1). There was no systematic change in variability across the field in five of the transects (excepting one atypical field which was waterlogged), indicating that much of the variability within crops is due
All sites showed a nearly normal distribution in fresh weight for both transplants and final harvest in both years. In most cases this was a symmetrical distribution, although there was some skewness evident towards heavier heads for some of the harvest data. The coefficients of variation at transplanting showed a range of 0.10–0.35. The coefficients of variation in head weight at harvest ranged from 0.10 to 0.25, with a mean 0.18 with no consistent interim pattern, providing no evidence for an increase in variability as a result of field conditions. Analysis of variance was then conducted using GENSTAT to test for differences between growers, but revealed no significant differences. This indicates that variance in final head weight is largely generated at transplanting. 4. Deterministic lettuce model The data from the controlled environment experiments and data from Al Said (2000) were used to parameterize a mechanistic model of iceberg lettuce growth on a daily timestep. The model was adapted from that developed by Pearson et al. (1997) for butterhead lettuce. The model predicts canopy photosynthesis, light interception, losses from respiration and partitions a fixed proportion into the head. Equations are presented using the discrete difference form of the equations. The original model form is outlined in Fig. 2a. Net photosynthesis as a function of temperature and radiation is input into the plant storage compartment (Ws). Separate respiration rates are applied to all material converted to structural matter in proportion to temperature. This model was modified to include a term for whole plant respiration which was originally grouped with net photosynthesis. Whole plant structural mass was added to the mass of material being converted to give an independent respiration term
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Fig. 2. Basic model structure. (a) Pearson et al. (1997) and (b) new model.
(Fig. 2b). Whole plant respiration was then estimated as a function of temperature and plant dry weight. It was assumed that the rate of growth of structural matter is proportional to the contents of the storage compartment at a given temperature. Available assimilates were converted into structural dry matter as a linear response to temperature.
for respiration (30 ◦ C) and Ta is the mean daily temperature (◦ C)), Tmin is the minimum temperature required for respiration (0 ◦ C), is the rate constant for the effect of temperature on respiration in ◦ C−1 (taken as 1/Tos − Tmin ) dWgi is the daily increase in structural matter (g), and Wg is the current structural mass (g). The rate of conversion of storage (Ws) to structural (Wg) (where Ws > dWg) is given by:
4.1. Model definition dWg = Wg KTes Three daily flows operate: the inflow into the storage compartment; outflow due to respiration (Rtotal ) during conversion of storage material (Rd ), maintenance respiration of the whole plant; and the flow of carbohydrate from the storage compartment to the structural compartment (dWg). Loss through respiration of structural material is taken from the inflow into the storage compartment such that dWs represents the net result of both flows. Thermal time, i (◦ C) is accumulated for the growth of the plant, assuming an initial value of 50 degree days above base temperature of 0 ◦ C for transplants, and adding the daily temperature each day. Daily inputs are daily temperature, Ta (◦ C), taken as (max. temp. + min. temp)/2, and total daily radiation, Itotal (MJ m−2 ). The increment in storage compartment: dWs = daily photsynthesis(Pg ) − daily respiration(Rtotal ) where daily photosynthesis is calculated as: Pg = ˛m Itotal ˚(1 − e(−FG Wg ) )(m − i )(Tep −Tbase )(1−ˇ/(C))/m where is a factor to convert CO2 to dry weight (30/44), ˛m is the leaf light utilisation efficiency in kg (CO2 ) J−1 (12.87 × 10−9 ), Itotal is the total daily radiation in MJ m−2 , ˚ is the rate constant for the effect of temperature on photosynthesis in ◦ C−1 (0.0537: from 1/(Top − Tbase ) to give 0 at Tbase and 1 at Top ), FG is the leaf area ratio in m−2 kg−1 (50), is the spacing density of the crop in plants per m2 , m is the thermal time for the cessation of photosynthesis (1600), i is the thermal time on the current day (i), Tep is the effective temperature for photosynthesis, (taken as: Tep = Top − |Top − Ta | where Top is the optimum temperature for photosynthesis (22.6 ◦ C) and Ta is the mean daily temperature (◦ C)), Tbase is the minimum temperature required for photosynthesis (4 ◦ C), ˇ is the photo-respiration constant in kg (CO2 ) m−2 s−1 (1.0 × 10−7 ), is the leaf conductance in m s−1 (0.002) and C is the atmospheric CO2 concentration in kg (CO2 ) m−2 (0.00075); and daily respiration is calculated as: Rtotal = RG (m − (i / )/m )(Tes − Tmin )(dWg + Wg ) where RG is the rate constant for the effect of temperature on respiration in gWs, gWg (0.4), is the ontogenetic respiration rate constant (3.0), Tes is the effective temperature for photosynthesis, (taken as: Tes = Tos − |Tos − Ta | where Tos is the optimum temperature
where dWg (kg) is the daily increment in structural growth, Wg the total structural dry weight (kg) and Tes the effective temperature (◦ C) for respiration. dWg is set to zero where Ws is limiting.
4.2. Parameterization Where possible parameter values were left unchanged from those used for butterhead lettuce in Pearson et al. (1997). Values for ˛m , Top , m and K were taken from the model parameterization in Al Said (2000) for controlled environment studies. In order to improve the model fit for field conditions, a grid search was conducted, minimising the total sum of the least square deviations to optimise the model fit to the data. It was considered that only two model parameters could reasonably be altered within a small range without violating the model assumptions. These were K, the rate of unrestricted linear growth (how fast the plant grows in non-limiting conditions) and rg, the respiration rate for unit dry weight. The original values in the model for these constants were 0.009 and 0.3 for K and rg, respectively. Increasing K increases the simulated plant growth of the model, particularly in mid-season, where light and temperature are not limiting. Increasing rg has the effect of slowing down growth in early and particularly late season, by altering the balance between energy input (photosynthesis) and output (respiration) in the model. A grid search was then performed, for the 72 batches in Experiment 3. K was varied from 0.0086 to 0.0098 at a 0.0002 step, and rg from 0.3 to 0.46 at a 0.02 step. For each of these combinations, the sum of square deviations (actual–predicted harvest date) for all sample points at all sites was calculated. There were inconsistencies between sites, in particular one grower in East Anglia where faster growth rates (approximately 5 days) converged at an optimum of K = 0.0098, and rg = 0.3, which disagreed with the optima for the other sites, including the other East Anglian site. At the more northerly sites, an early drop off in late season skewed the correlation towards slower combinations, but these tended to produce unrealistic model behaviour, giving poor correlations in early and mid-season, and with late season at other sites. Despite these conflicts, a clear optimal area within the grid search was revealed.
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Fig. 3. Performance of the deterministic model using actual site weather records (䊉) against dates of commercial harvest () for the whole 2000 season for the six enterprises (a) Fife, 56◦ N, (b) Lancashire, 53.5◦ N, (c) Norfolk, 52.5◦ N, (d) Cambridgeshire, 52.5◦ N, (e) Berkshire, 51.5◦ N, and (f) West Sussex, 51◦ N. Pearson rank correlation coefficients () for each site are shown, giving a scale-independent indication of the degree to which deviations in actual times to harvest are reflected in the model data.
At the lower K value of 0.0088, the annual curve was less realistic for most sites, due to the deviation between model output and actual maturity in Scotland during late season. It was decided to use the original K value of 0.009, with an rg value of 0.4, giving the joint lowest sum of square deviation for all sites, and the most even spread of deviations between sites. 4.3. Validation The validation data set consisted of all crop records for field grown iceberg lettuce for a single season from each of the six grower sites. The time from planting to actual harvest varied with time of year, with the minimum time to harvest towards the end of the season, followed by a rapid increase in time to harvest with decreasing daylength in later season. Even for the same site, there was considerable variation in time to harvest for a particular transplanting date, and in most cases this was independent of cultivar. For all sites weather data comprising daily maximum and minimum temperatures and solar radiation was recorded. The deterministic model was run with this data and results are shown in Fig. 3. Whilst the model described the main features of the annual curve for most sites, there was considerably more variation in the actual harvest dates. Predictions for site c are consistent overestimates. However, it should be noted that the nearest site d which is within 40 km and experienced similar weather conditions was much better predicted. For the more northerly sites, a and b a systematic deviation is evident towards the end of the season, with the model underestimating time to harvest. This was also evident in previous seasons. Early season deviation at site e was found to be due to a specific waterlogging issue which delayed harvests in a number of fields. Whilst the deviation could result from parameterization data from a latitude of 51.5◦ N (Reading), manual manipulation of the parameters failed to produce a more consistent model fit, which may point to a deficiency in the model formulation. The deterministic model appears to describe the main features of iceberg lettuce growth, for a range of latitudes 51◦ N–52.5◦ N. For more northerly latitudes other models may prove more reliable for the full season. The deterministic model was then incorporated
into a system describing variation in plant size within the crop and weather conditions. 5. Application description Software was designed to provide a site-specific decision support tool, giving predictions of harvest statistics (head weight and shape) up to 5 weeks in advance, whilst providing estimates of uncertainty of prediction. It was developed using Borland Delphi 4, to run on 32-bit Windows and is available from the corresponding author. 5.1. The size cohort model The experimental work and Al Said (2000) indicate that coefficients of variation of size in iceberg remained constant between transplanting and harvesting in most cases at around 18%. A single model crop is therefore divided into 14 distinct, normally distributed size cohorts at transplanting, each represented by a single plant object (mean starting weight: 1.5 g coefficient of variance: 0.18 ± 0.2 depending on site variability). Each size cohort represents a 0.5 SD range, with the 3.5 and 4 SD range being grouped. As the crop reaches maturity, the size cohorts pass sequentially through the window of marketable sizes defined by the minimum and maximum head weight. Fig. 4 shows how the key crop statistics are recorded. Since some cohorts may reach maturity on the same day, the number of columns in the histograms may be less than 14. 5.2. Weather recording and generation A simple weather generator was used to capture the variation in crop timing due to weather conditions. The growth model receives inputs in terms of daily max. and min. temperatures (◦ C) and solar radiation (mJ m−2 ) from a Weather class within the software which deals with all aspects of weather generation and history. Where possible actual site weather records are uploaded into the software. Data from multiple sites can be stored. These only cover the past, and future weather is required for predictive simulations. When site records run out, or for any days where site weather data is miss-
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Fig. 4. Recording of harvest statistics as the crop passes through the window of marketable size. For each single simulation, for each of these days, the total, mean and standard deviation of head numbers and head weight are recorded. These results are summarised for multiple simulations for each scenario.
ing, stochastically generated weather values are used. To capture the range of expected future weather, 100 runs for each scenario are simulated, and the results summarised. This approach parallels the Model Output Statistics approach in weather forecasting (Wilks, 1995). Three future scenarios are presented by altering the mean of the expected distributions of future temperature; Normal, Warm (+2 ◦ C) and Cool (−2 ◦ C). As site records represent more of the total simulation, the difference between these scenarios becomes smaller. Ideally, site records are used up to the present date, so that all variation in the model outputs can be attributed to uncertainty in future weather. Forecast estimates can be entered to further reduce the period of generated weather. The weather generator used was of the simple form used by Strandman et al. (1993), Harwood (1996) and Harwood et al. (1996), where daily values are randomly generated from normal distributions (specified by mean and variance) based on historical site records for each month. These statistics can usually be obtained from meteorological records at or near the site location. An index of periodicity (Harwood, 1996) is used to determine whether any autocorrelation will occur between days in order to represent the weather groupings which are associated with particular air masses (Lamb, 1950). A Poisson generated deviate of expected value 7 is used to define the length of periods of similar weather. During a period of similar weather, each new value is averaged with the previous day’s value. When a new air mass arrives, the daily value is generated independently. Actual site records are exempt from the autocorrelation process. As for the deterministic growth model, an alternative weather generator could be substituted. For each of the days for which predictions are made by the model (peak day for head numbers, peak day for weight and first and last possible days) and for each of the values associated with that day (mean number of heads, mean head weight, variation in head weight, total batch weight mean stem length) a distribution of output statistics for all the model runs is produced. These are used to generate mean values for all runs, and to assess the variation due to weather. Estimates of the model internal confidence in terms of an estimate of the expected range is generated from the output probability distribution. A threshold of 2 standard deviations was used to define an estimated 95.44% range, assuming a normal distribution of output statistics. This range relates to the results generated, and in no way reflects confidence in the accuracy of the model itself. Consequently, when the same actual weather records are used, the range will be zero. 5.3. Validation of weather generator in context An analysis of the predictions generated using actual data and generated data for the 2000 season is presented to describe internal model consistency. The weather generator was provided with accu-
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Fig. 5. A comparison of the 95% range against deviations from the predicted value when recorded weather data is used, showing the deviation between the growth model prediction from recorded weather and the prediction from generated weather (bold line) plotted against the predicted 95% range which changes over time (thin lines).
rate monthly site statistics based on over 10 years on site recording. Actual daily max. and min. temperatures and total daily radiation were recorded for the season. The model was run for the duration of the recorded data, using exclusively either the recorded data or the generated data. As such this represents an extreme test of the approach, since in practice, a combination of actual and predicted records would be used to make a prediction. The predicted day of peak head numbers, and the 95% range was recorded for each model prediction. For the recorded data, the range was 0. Fig. 5 shows the difference between the two predictions, plotted against the range for the 2000 season at site e. Whilst the deviations lie broadly within the range, the estimates seem to be slightly conservative. Only 75% of the predictions made based on actual weather data lay within the range estimated, although those which lay outside were mainly within 1 day of the estimated deviation. It would appear that the model range could be increased to provide a better coverage of results. A 98.8% range based on 2.5 standard deviations would include all but one (96%) of the data points. This approach provides a flexible alternative to the use of historical weather records or long-term forecasts, and presents a practical solution to the problems of forecasting, where future weather is a great element of uncertainty. The dynamically generated range provides an indication of the internal certainty of the model. 5.4. Model outputs For each field, transplanting details (date, number, variety), harvesting specifications (min. and max. head weight, min. harvest numbers), and site-specific weather file are specified by the user. Actual weather records are entered as available. The crop details are used to generate the initial 14 size cohorts, and the daily growth for each of these is calculated using inputs from the Weather class. The daily head weight (0.8 fresh weight) of each cohort is checked against the marketable range of head weights. Each cohort will meet the harvesting criteria for a given period, and a variable number of heads will be marketable on a given date. The period for which the number of available heads exceeds the minimum harvest numbers defines the start and end of the viable harvesting period for each simulation (Fig. 4). Within this period, the number of heads and the distribution of head sizes will vary. Results are presented for the three future weather scenarios, labeled Cool, Normal and Warm and summarise each set of runs. Fig. 6 shows the main results page for a single batch simulation, summarising the output for 100 simulations. All graphs have a horizontal date axis, and display the daily number of heads or total marketable head weight for each field, and enterprise wide weekly
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Fig. 6. Summary panel for a single batch, showing the passage of the crop through the window of marketable size. Results for the three weather scenarios are displayed, as the mean results for the 100 simulations. The graph shows a single simulation that most closely fits the presented output statistics. The peak day and total are given for both heads and fresh weight. Stem length and head density are calculated from a head development model (Harwood, 2001) which is outside the scope of this paper.
totals. For each of the scenarios, the predicted first and last days meeting the harvest criteria, and the day of peak heads and the day of peak total weight are presented, along with estimates of accuracy on the Batch Harvesting panel. For each of these 4 days, the predicted number and mean weight of marketable heads and the coefficient of variation in head weight of harvestable heads are presented, along with a qualitative estimate of head quality based on the rate of stem elongation during heading (Harwood, 2001). Before results in terms of the optimum predicted harvest date for each batch are collated for whole enterprise predictions, the facility is provided for managers to override the model recommendations and make up to three separate cuts from a single field. It is hoped therefore that at this stage, the batch predictions will represent the best available estimate. 6. Discussion The mechanistic growth model described goes some way towards capturing the characteristics of commercial field grown iceberg lettuce. However, validation against data from a range of latitudes reveals a shortcoming in the model in that it fails to capture late season trends at higher latitudes. Since the physiological responses of iceberg lettuce will be independent of latitude per se, the problem may be attributed to model structure rather than parameterization. As such, it seems inappropriate to use the model outside the range for which it has been validated. Further to this, wide variation in harvest timing was evident both within and between enterprises experiencing similar conditions. This could not be attributed to differences in cultivar. Economic considerations, such as meeting specific orders can result in sub optimal harvesting. At one grower site, the majority of harvests were made on the same day of the week prior to dispatch. A further source of error was noticed when a period of consistent rain produced waterlogging at one site, slowing the growth rate to the extent that the crops fell behind subsequently transplanted batches. Uncommon and field specific phenomena of this type are unlikely to merit explicit modelling. By allowing the manager to override the model predictions in such cases, accuracy can be maintained at whole enterprise level.
The deterministic model has also been successfully applied to glasshouse grown lettuce (Al Said, 2000), although in this more controlled environment with its own product specifications, specifically designed models (e.g. Seginer, 2003; Incrocci et al., 2006) are likely to be more useful, and a weather generator would be of little value. Taking the variation in size within the crop into account allows better characterization of the harvest period for a given deterministic model, providing growers with information to make decisions about, for example, the effect of delaying harvest. At the margins of the growing season this can be of particular value, where the potential harvest period is longer, and some plants may not reach a harvestable size. The presentation of the summary statistics and graphs for the posterior distributions of results was considered straightforward by the growers initially supplied by the model. However, it is possible that the software provides more information than is easy to assimilate. Managing uncertainty due to weather is critical for field grown crops, where little control can be exerted to meet specific orders. Generating weather from site statistics allows reasoned decision making. The simple weather generator has been previously validated for temperature and solar radiation but is not appropriate for aspects of the weather (e.g. rainfall) which do not conform to the normal model. If the growth model required such, an alternative algorithm for weather generation e.g. time-series algorithms such as LARS-WG (Racsko et al., 1991; Barrow and Semenov, 1995) may be useful. However, it is essential that any approach is easily parameterized from local weather data. Weather generators have been used as inputs for models, including crop models (Hansen and Indeje, 2004; Semenov and Doblas-Reyes, 2007) and erosion models (Williams et al., 1992). Where actual crop records are incomplete, or where the period of simulation extends beyond the present, they are used to fill gaps. In this respect the software described here does not represent a methodological advance. However, in terms of practical application, the incorporation of the whole process within the software frees growers from the requirement to use a weather generator in a statistically appropriate manner. Such use is unlikely to represent an efficient use of a technical manager’s time, and is unlikely to be adopted. As such the software overcomes a major barrier to the uptake of this technology. Research has been conducted into the incorporation of seasonal forecasts into models (Hansen and Indeje, 2004; Hansen et al., 2004; Semenov and Doblas-Reyes, 2007), showing success in more predictable equatorial climates. However, for the UK, the accuracy of long-term weather forecasts is likely only to be as accurate a predictor of weather as site records up to 72 h (Murphy et al., 1989). This is borne out by the modelling studies of Semenov and Doblas-Reyes (2007), which show little advantage to the use of weather generated data based on seasonal forecasts. The approach of generating three sets of scenarios for future weather, based on expected, expected +2 ◦ C and expected −2 ◦ C offers a simple alternative. Whilst possibly misleading when predicting long periods of weather, this approach allows the manager to reason using linguistically meaningful scenarios over the critical period approaching harvest. The size cohort model indicates that the response of crops to weather is complex, particularly at either end of the growing season. The optimal harvest date is not necessarily best represented by a single average plant, due to the movement of growing plants of different sizes through the marketable range. For example, at the tail end of the season, some of the smaller plants may not reach a marketable weight. When part of the crop is reaching maturity, decisions will need to be made as to when to harvest, according to the expected growth of the smaller plants. In mid-season, growth of the larger plants may move them out of the marketable range, and an assessment of the period for which the crop will provide
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a certain number of marketable heads will allow a more flexible approach harvesting. The approach represents a simple extension to any deterministic model which is straightforward to implement and of wide applicability. Alternative models and weather generators could be effectively combined to improve management of uncertainty. However, treatment of the effects of weather variation on a variable crop is important to avoid inappropriate advice. Acknowledgement Funding for this work was provided by a UK MAFFlink Consortium. References Al Said, F., 2000. The effect of temperature and photoperiod on growth and development of iceberg lettuce (Lactuca sativa L.). PhD thesis. University of Reading. Barrow, E.M., Semenov, M.A., 1995. Climate change scenarios with high spatial and temporal resolution for agricultural applications. Forestry 68, 349– 360. Borg, M., 1998. Getting Ready For Summer’ Tesco Internal Report. Dullforce, W.M., 1963. Analysis of the growth of winter glasshouse lettuce varieties. In: Proceedings of the 16th International Horticultural Congress 2, pp. 496–501. Hansen, J.W., Indeje, M., 2004. Linking dynamic seasonal climate forecasts with crop simulation for maize yield prediction in semi-arid Kenya. Agric. For. Meteorol. 125, 143–157. Hansen, J.W., Potgieter, A., Tippett, M.K., 2004. Using a general circulation model to forecast regional wheat yields in northeast Australia. Agric. For. Meteorol. 127, 77–92. Harwood, T.D., 1996. A dynamic three-dimensional plant-microclimate model, “Ecospace”. PhD thesis. University of Edinburgh. Harwood, T.D., Russell, G., Muetzelfeldt, R.I., 1996. A dynamic three-dimensional plant-microclimate model “Ecospace”. Aspects Appl. Biol. 46, 159–164.
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Harwood, T.D., 2001. The development of a new generation of horticultural crop forecasting techniques. MAFF Link project: CSA 4283: Final Report. MAFF, UK. Incrocci, L., Fila, G., Bellocchi, G., Pardossi, A., Campiotti, C.A., Balducchi, R., 2006. Soil-less indoor-grown lettuce (Lactuca sativa L.): approaching the modelling task. Environ. Model. Softw. 21 (1), 121–126. Lamb, H.H., 1950. Types and spells of weather around the year in the British Isles: annual trends, seasonal structure of the year, singularities. Q. J. Roy. Meteorol. Soc. 76, 343–348. Murphy, A.H., Brown, B.G., Chen, Y.-S., 1989. Diagnostic verification of weather forecasts. Weather Forecast. 4, 485–501. Pearson, S., Wheeler, T.R., Hadley, P., Wheldon, A.E., 1997. A validated model to predict the effects of environment on the growth of lettuce (Lactuca sativa, L.): implications for climate change. J. Hortic. Sci. 72 (3). Racsko, P., Szeidl, L., Semenov, M., 1991. A serial approach to local stochastic weather models. Ecol. Model. 57, 27–41. Ryder, E.J., 1999. Lettuce Endive and Chicory. CABI Publishing, Wallingford and New York. Scaife, M.A., 1973. The early relative growth rates of six lettuce cultivars as affected by temperature. Ann. Appl. Biol. 74, 119–128. Seginer, I., 2003. A dynamic model for nitrogen stressed lettuce. Ann. Bot. 91, 623, 635. Semenov, M.A., Doblas-Reyes, F.J., 2007. Utility of dynamic seasonal forecasts in predicting crop yield. Clim. Res. 34, 71–81. Strandman, H., Vaisanen, H., Kellomaki, S., 1993. A procedure for generating synthetic weather records in conjunction of climatic scenario for modelling of ecological impacts of changing climate in boreal conditions. Ecol. Model. 70, 195–220. Thompson, R.C., Knott, J.E., 1934. The effect of temperature and photoperiod on the growth of lettuce. Proc. Am. Soc. Hortic. Sci. 30, 507–509. Wheeler, T.R., Hadley, P., Morison, J.I.L., Ellis, R.H., 1993. Effects of temperature on the growth of lettuce (Lactuca sativa L.) and the implications for assessing the impacts of potential climate change. Eur. J. Agron. 2, 305–311. Wilks, D.S., 1995. Statistical Methods in the Atmospheric Sciences. Academic Press, San Diego. Williams, J.R., Richardson, C.W., Griggs, R.H., 1992. The weather factor: incorporating weather variance into computer simulation. Weed Technol. 6, 731–735. Wurr, D.C.E., Fellows, J.R., 1991. The influence of solar radiation and temperature on the head weight of crisp lettuce. J. Hortic. Sci. 66 (2), 183–190.
Contents lists available at ScienceDirect
Computers and Electronics in Agriculture journal homepage: www.elsevier.com/locate/compag
Modelling uncertainty in field grown iceberg lettuce production for decision support T.D. Harwood a,∗ , F.A. Al Said b , S. Pearson a , S.J. Houghton a , P. Hadley a a b
School of Biological Sciences, University of Reading, Reading RG6 2SA, UK Department of Crop Sciences, Sultan Qaboos University, Alkhod 123, Oman
a r t i c l e
i n f o
Article history: Received 3 September 2008 Received in revised form 26 November 2009 Accepted 9 December 2009 Keywords: Crop forecasting Stochastic model Lettuce Uncertainty Weather generator Variability
a b s t r a c t Uncertainty in terms of input parameters, particularly weather variables, has implications for the results of a deterministic crop prediction model. This manuscript describes the development of the Iceberg Predictor decision support system which uses a stochastic weather generator to provide three alternative scenarios for future weather. These are used to drive a mechanistic model which provides posterior distributions of potential crop outcomes including within-field variability, which are summarised for grower interpretation. Multiple crops can be simulated allowing improved management of uncertainty at the whole enterprise scale. Experimental work demonstrated that variation in transplant size is a major contributor to variability in the final harvest. © 2009 Elsevier B.V. All rights reserved.
1. Introduction The accurate prediction of harvest dates is critical to the minimisation of profit loss for both growers and retailers (D. May personal communication, 1999). Both the supply (e.g. Thompson and Knott, 1934; Scaife, 1973; Wurr and Fellows, 1991; Al Said, 2000) and demand (Borg, 1998) of iceberg lettuce (Lactuca sativa L.) are sensitive to changes in weather, often resulting in shortage or surplus in the supply chain. Prediction of these phenomena can reduce their economic impact (Ryder, 1999). The Iceberg Predictor software described in this paper explicitly deals with the uncertainty of future weather, presenting results as posterior distributions which describe the resultant uncertainty in model predictions to assist growers in maintaining a continuous supply to meet a flexible demand. A typical field grown iceberg lettuce grower in the UK (industrial partners personal communication, 1999) will plant a number of different batches throughout the season, timed to produce a continuous supply. The crop usually takes between 40 and 80 days to mature. Retailers will normally specify a narrow range of acceptable head weights between 400 and 700 g. Managers can make accurate harvest predictions up to 2 weeks in advance, but the quality of prediction decreases beyond this due to the variability of
∗ Corresponding author at: CSIRO Entomology, Black Mountain, Clunies Ross St., Canberra, ACT 2601, Australia. Tel.: +61 (0)2 6246 4018. E-mail address: [email protected] (T.D. Harwood). 0168-1699/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.compag.2009.12.003
future weather. Supply forecasts can be used to help growers prearrange promotions with supermarkets or to buy in products from other suppliers to fulfil contracts. This latter aspect is important at the extremes of the season, since accurate crop forecasts will allow growers (and supermarkets) to decide when to stop/start importing overseas product. This project was developed with a multiple retailer and six growers (representing the majority of field grown lettuce suppliers in Great Britain) in order to improve predictions 3 or 4 weeks from harvest date, to increase the possibilities for remedial action. Continuing improvements in long-term weather forecasting provide a potential source of inputs to further improve predictions (Semenov and Doblas-Reyes, 2007). Crop forecasting models are typically deterministic, providing output in terms of a predicted day of harvest for a given simulation (e.g. Pearson et al., 1997). The rate of development of iceberg lettuce is sensitive to temperature and radiation (Dullforce, 1963; Wurr and Fellows, 1991; Wheeler et al., 1993), and variable weather will cause variation both within the crop and in the timing of harvest. This manuscript describes the development and application of a generic approach to the incorporation of uncertainty in model predictions due to weather into crop scheduling software incorporating growth models. By combining model predictions based on up to date weather records with future predictions based on simulated local weather, the range of expected variation in harvest date can be described. In addition, we deal explicitly with the interaction between uncertain weather and within-crop variation in progress to harvest. Whilst in this example, the approach is applied to field grown iceberg lettuce production using a specific growth model,
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and a specific weather generator, it has generic application to most crop systems where the weather is the main source of uncertainty. 2. Methods Six commercial growers distributed across the UK in the 2000 season contributed to the development of the model. These were located as follows in (a) Fife, 56◦ N, (b) Lancashire, 53.5◦ N, (c) Norfolk, 52.5◦ N, (d) Cambridgeshire, 52.5◦ N, (e) Berkshire, 51.5◦ N, and (f) West Sussex, 51◦ N. Sites c and d were within 40 km of each other, allowing a trivial examination of site-to-site variation in similar weather conditions. 2.1. Experiment 1: within-field variation If variability changes systematically across a field then it is due to changes in the state of the soil and/or microclimate. This is superimposed on top of the variability caused by the plants themselves (plant to plant variability). Six transects of >200 heads were sampled across an area of 30 m at five different grower sites (b–f) in England. Head weights and location were measured on the day of crop harvest. 2.2. Experiment 2: effects of temperature on iceberg lettuce growth and variability Plants (cv. Calgary) were grown from three planting dates (17 March, 25 June and 28 August), at each of six different temperatures (8, 10, 14, 18, 22, and 26 ◦ C) in factorial glasshouses at the University of Reading. Plants were grown semi-hydroponically in a mixture of vermiculite, sand and gravel. Head and total plant weight of 30 plants were measured on five occasions.
Fig. 1. Typical variogram showing iceberg head weight across a field (i.e. lag distance) for site d. There is no systematic increase in variability with lag distance indicating a lack of field variability.
to plant to plant rather than field variability. Head weight varied insignificantly according to position in the bed. 3.2. Experiment 2: effects of temperature on iceberg lettuce growth and variability Overall, plant growth in terms of fresh weight increased with temperature up to an optimum of 18 ◦ C as observed in previous studies on iceberg lettuce. No evidence was found to show that plant-to-plant variability was significantly affected by temperature, or solar radiation. The coefficient of variation showed no consistent response to temperature or planting date, remaining broadly at the same scale (approximately 15%) over time, suggesting that plant-to-plant variability within a field may be inherent at the planting stage. 3.3. Experiment 3: variability within transplants
2.3. Experiment 3: variability within transplants To test whether plant to plant variability was inherent within the transplants used by growers (and to generate a series of data for model parameterization) a series of on farm trials at each of the participating growers were conducted. The aim was to establish the extent to which variability at the transplant stage accounts for variability within a harvest. If field conditions introduce further variation, this will increase the coefficient of variation over time. This information is crucial to the model representation of variability. Externally raised plugs (dry weight 1–2 g) are planted 3–4 weeks after germination in commercial production (Ryder, 1999). For each trial run, each site was supplied with identical batches of 2500 plants of each of two cultivars (Diamond and Calgary), treated with GAUCHO at a standard rate. Transplants were grown by the same company from the same seed stock to minimise variability. Plugs were planted within a standard block by each grower and grown under typical conditions. This experiment was repeated on 6 occasions over two seasons. Twenty plants were sampled from each run at weekly intervals and total above ground plant fresh weight and head weight (when present) measured. Weather data were recorded by each site’s monitoring system. 3. Results 3.1. Experiment 1: within-field variation Variograms were plotted for each field in GENSTAT (e.g. Fig. 1). There was no systematic change in variability across the field in five of the transects (excepting one atypical field which was waterlogged), indicating that much of the variability within crops is due
All sites showed a nearly normal distribution in fresh weight for both transplants and final harvest in both years. In most cases this was a symmetrical distribution, although there was some skewness evident towards heavier heads for some of the harvest data. The coefficients of variation at transplanting showed a range of 0.10–0.35. The coefficients of variation in head weight at harvest ranged from 0.10 to 0.25, with a mean 0.18 with no consistent interim pattern, providing no evidence for an increase in variability as a result of field conditions. Analysis of variance was then conducted using GENSTAT to test for differences between growers, but revealed no significant differences. This indicates that variance in final head weight is largely generated at transplanting. 4. Deterministic lettuce model The data from the controlled environment experiments and data from Al Said (2000) were used to parameterize a mechanistic model of iceberg lettuce growth on a daily timestep. The model was adapted from that developed by Pearson et al. (1997) for butterhead lettuce. The model predicts canopy photosynthesis, light interception, losses from respiration and partitions a fixed proportion into the head. Equations are presented using the discrete difference form of the equations. The original model form is outlined in Fig. 2a. Net photosynthesis as a function of temperature and radiation is input into the plant storage compartment (Ws). Separate respiration rates are applied to all material converted to structural matter in proportion to temperature. This model was modified to include a term for whole plant respiration which was originally grouped with net photosynthesis. Whole plant structural mass was added to the mass of material being converted to give an independent respiration term
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Fig. 2. Basic model structure. (a) Pearson et al. (1997) and (b) new model.
(Fig. 2b). Whole plant respiration was then estimated as a function of temperature and plant dry weight. It was assumed that the rate of growth of structural matter is proportional to the contents of the storage compartment at a given temperature. Available assimilates were converted into structural dry matter as a linear response to temperature.
for respiration (30 ◦ C) and Ta is the mean daily temperature (◦ C)), Tmin is the minimum temperature required for respiration (0 ◦ C), is the rate constant for the effect of temperature on respiration in ◦ C−1 (taken as 1/Tos − Tmin ) dWgi is the daily increase in structural matter (g), and Wg is the current structural mass (g). The rate of conversion of storage (Ws) to structural (Wg) (where Ws > dWg) is given by:
4.1. Model definition dWg = Wg KTes Three daily flows operate: the inflow into the storage compartment; outflow due to respiration (Rtotal ) during conversion of storage material (Rd ), maintenance respiration of the whole plant; and the flow of carbohydrate from the storage compartment to the structural compartment (dWg). Loss through respiration of structural material is taken from the inflow into the storage compartment such that dWs represents the net result of both flows. Thermal time, i (◦ C) is accumulated for the growth of the plant, assuming an initial value of 50 degree days above base temperature of 0 ◦ C for transplants, and adding the daily temperature each day. Daily inputs are daily temperature, Ta (◦ C), taken as (max. temp. + min. temp)/2, and total daily radiation, Itotal (MJ m−2 ). The increment in storage compartment: dWs = daily photsynthesis(Pg ) − daily respiration(Rtotal ) where daily photosynthesis is calculated as: Pg = ˛m Itotal ˚(1 − e(−FG Wg ) )(m − i )(Tep −Tbase )(1−ˇ/(C))/m where is a factor to convert CO2 to dry weight (30/44), ˛m is the leaf light utilisation efficiency in kg (CO2 ) J−1 (12.87 × 10−9 ), Itotal is the total daily radiation in MJ m−2 , ˚ is the rate constant for the effect of temperature on photosynthesis in ◦ C−1 (0.0537: from 1/(Top − Tbase ) to give 0 at Tbase and 1 at Top ), FG is the leaf area ratio in m−2 kg−1 (50), is the spacing density of the crop in plants per m2 , m is the thermal time for the cessation of photosynthesis (1600), i is the thermal time on the current day (i), Tep is the effective temperature for photosynthesis, (taken as: Tep = Top − |Top − Ta | where Top is the optimum temperature for photosynthesis (22.6 ◦ C) and Ta is the mean daily temperature (◦ C)), Tbase is the minimum temperature required for photosynthesis (4 ◦ C), ˇ is the photo-respiration constant in kg (CO2 ) m−2 s−1 (1.0 × 10−7 ), is the leaf conductance in m s−1 (0.002) and C is the atmospheric CO2 concentration in kg (CO2 ) m−2 (0.00075); and daily respiration is calculated as: Rtotal = RG (m − (i / )/m )(Tes − Tmin )(dWg + Wg ) where RG is the rate constant for the effect of temperature on respiration in gWs, gWg (0.4), is the ontogenetic respiration rate constant (3.0), Tes is the effective temperature for photosynthesis, (taken as: Tes = Tos − |Tos − Ta | where Tos is the optimum temperature
where dWg (kg) is the daily increment in structural growth, Wg the total structural dry weight (kg) and Tes the effective temperature (◦ C) for respiration. dWg is set to zero where Ws is limiting.
4.2. Parameterization Where possible parameter values were left unchanged from those used for butterhead lettuce in Pearson et al. (1997). Values for ˛m , Top , m and K were taken from the model parameterization in Al Said (2000) for controlled environment studies. In order to improve the model fit for field conditions, a grid search was conducted, minimising the total sum of the least square deviations to optimise the model fit to the data. It was considered that only two model parameters could reasonably be altered within a small range without violating the model assumptions. These were K, the rate of unrestricted linear growth (how fast the plant grows in non-limiting conditions) and rg, the respiration rate for unit dry weight. The original values in the model for these constants were 0.009 and 0.3 for K and rg, respectively. Increasing K increases the simulated plant growth of the model, particularly in mid-season, where light and temperature are not limiting. Increasing rg has the effect of slowing down growth in early and particularly late season, by altering the balance between energy input (photosynthesis) and output (respiration) in the model. A grid search was then performed, for the 72 batches in Experiment 3. K was varied from 0.0086 to 0.0098 at a 0.0002 step, and rg from 0.3 to 0.46 at a 0.02 step. For each of these combinations, the sum of square deviations (actual–predicted harvest date) for all sample points at all sites was calculated. There were inconsistencies between sites, in particular one grower in East Anglia where faster growth rates (approximately 5 days) converged at an optimum of K = 0.0098, and rg = 0.3, which disagreed with the optima for the other sites, including the other East Anglian site. At the more northerly sites, an early drop off in late season skewed the correlation towards slower combinations, but these tended to produce unrealistic model behaviour, giving poor correlations in early and mid-season, and with late season at other sites. Despite these conflicts, a clear optimal area within the grid search was revealed.
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Fig. 3. Performance of the deterministic model using actual site weather records (䊉) against dates of commercial harvest () for the whole 2000 season for the six enterprises (a) Fife, 56◦ N, (b) Lancashire, 53.5◦ N, (c) Norfolk, 52.5◦ N, (d) Cambridgeshire, 52.5◦ N, (e) Berkshire, 51.5◦ N, and (f) West Sussex, 51◦ N. Pearson rank correlation coefficients () for each site are shown, giving a scale-independent indication of the degree to which deviations in actual times to harvest are reflected in the model data.
At the lower K value of 0.0088, the annual curve was less realistic for most sites, due to the deviation between model output and actual maturity in Scotland during late season. It was decided to use the original K value of 0.009, with an rg value of 0.4, giving the joint lowest sum of square deviation for all sites, and the most even spread of deviations between sites. 4.3. Validation The validation data set consisted of all crop records for field grown iceberg lettuce for a single season from each of the six grower sites. The time from planting to actual harvest varied with time of year, with the minimum time to harvest towards the end of the season, followed by a rapid increase in time to harvest with decreasing daylength in later season. Even for the same site, there was considerable variation in time to harvest for a particular transplanting date, and in most cases this was independent of cultivar. For all sites weather data comprising daily maximum and minimum temperatures and solar radiation was recorded. The deterministic model was run with this data and results are shown in Fig. 3. Whilst the model described the main features of the annual curve for most sites, there was considerably more variation in the actual harvest dates. Predictions for site c are consistent overestimates. However, it should be noted that the nearest site d which is within 40 km and experienced similar weather conditions was much better predicted. For the more northerly sites, a and b a systematic deviation is evident towards the end of the season, with the model underestimating time to harvest. This was also evident in previous seasons. Early season deviation at site e was found to be due to a specific waterlogging issue which delayed harvests in a number of fields. Whilst the deviation could result from parameterization data from a latitude of 51.5◦ N (Reading), manual manipulation of the parameters failed to produce a more consistent model fit, which may point to a deficiency in the model formulation. The deterministic model appears to describe the main features of iceberg lettuce growth, for a range of latitudes 51◦ N–52.5◦ N. For more northerly latitudes other models may prove more reliable for the full season. The deterministic model was then incorporated
into a system describing variation in plant size within the crop and weather conditions. 5. Application description Software was designed to provide a site-specific decision support tool, giving predictions of harvest statistics (head weight and shape) up to 5 weeks in advance, whilst providing estimates of uncertainty of prediction. It was developed using Borland Delphi 4, to run on 32-bit Windows and is available from the corresponding author. 5.1. The size cohort model The experimental work and Al Said (2000) indicate that coefficients of variation of size in iceberg remained constant between transplanting and harvesting in most cases at around 18%. A single model crop is therefore divided into 14 distinct, normally distributed size cohorts at transplanting, each represented by a single plant object (mean starting weight: 1.5 g coefficient of variance: 0.18 ± 0.2 depending on site variability). Each size cohort represents a 0.5 SD range, with the 3.5 and 4 SD range being grouped. As the crop reaches maturity, the size cohorts pass sequentially through the window of marketable sizes defined by the minimum and maximum head weight. Fig. 4 shows how the key crop statistics are recorded. Since some cohorts may reach maturity on the same day, the number of columns in the histograms may be less than 14. 5.2. Weather recording and generation A simple weather generator was used to capture the variation in crop timing due to weather conditions. The growth model receives inputs in terms of daily max. and min. temperatures (◦ C) and solar radiation (mJ m−2 ) from a Weather class within the software which deals with all aspects of weather generation and history. Where possible actual site weather records are uploaded into the software. Data from multiple sites can be stored. These only cover the past, and future weather is required for predictive simulations. When site records run out, or for any days where site weather data is miss-
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Fig. 4. Recording of harvest statistics as the crop passes through the window of marketable size. For each single simulation, for each of these days, the total, mean and standard deviation of head numbers and head weight are recorded. These results are summarised for multiple simulations for each scenario.
ing, stochastically generated weather values are used. To capture the range of expected future weather, 100 runs for each scenario are simulated, and the results summarised. This approach parallels the Model Output Statistics approach in weather forecasting (Wilks, 1995). Three future scenarios are presented by altering the mean of the expected distributions of future temperature; Normal, Warm (+2 ◦ C) and Cool (−2 ◦ C). As site records represent more of the total simulation, the difference between these scenarios becomes smaller. Ideally, site records are used up to the present date, so that all variation in the model outputs can be attributed to uncertainty in future weather. Forecast estimates can be entered to further reduce the period of generated weather. The weather generator used was of the simple form used by Strandman et al. (1993), Harwood (1996) and Harwood et al. (1996), where daily values are randomly generated from normal distributions (specified by mean and variance) based on historical site records for each month. These statistics can usually be obtained from meteorological records at or near the site location. An index of periodicity (Harwood, 1996) is used to determine whether any autocorrelation will occur between days in order to represent the weather groupings which are associated with particular air masses (Lamb, 1950). A Poisson generated deviate of expected value 7 is used to define the length of periods of similar weather. During a period of similar weather, each new value is averaged with the previous day’s value. When a new air mass arrives, the daily value is generated independently. Actual site records are exempt from the autocorrelation process. As for the deterministic growth model, an alternative weather generator could be substituted. For each of the days for which predictions are made by the model (peak day for head numbers, peak day for weight and first and last possible days) and for each of the values associated with that day (mean number of heads, mean head weight, variation in head weight, total batch weight mean stem length) a distribution of output statistics for all the model runs is produced. These are used to generate mean values for all runs, and to assess the variation due to weather. Estimates of the model internal confidence in terms of an estimate of the expected range is generated from the output probability distribution. A threshold of 2 standard deviations was used to define an estimated 95.44% range, assuming a normal distribution of output statistics. This range relates to the results generated, and in no way reflects confidence in the accuracy of the model itself. Consequently, when the same actual weather records are used, the range will be zero. 5.3. Validation of weather generator in context An analysis of the predictions generated using actual data and generated data for the 2000 season is presented to describe internal model consistency. The weather generator was provided with accu-
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Fig. 5. A comparison of the 95% range against deviations from the predicted value when recorded weather data is used, showing the deviation between the growth model prediction from recorded weather and the prediction from generated weather (bold line) plotted against the predicted 95% range which changes over time (thin lines).
rate monthly site statistics based on over 10 years on site recording. Actual daily max. and min. temperatures and total daily radiation were recorded for the season. The model was run for the duration of the recorded data, using exclusively either the recorded data or the generated data. As such this represents an extreme test of the approach, since in practice, a combination of actual and predicted records would be used to make a prediction. The predicted day of peak head numbers, and the 95% range was recorded for each model prediction. For the recorded data, the range was 0. Fig. 5 shows the difference between the two predictions, plotted against the range for the 2000 season at site e. Whilst the deviations lie broadly within the range, the estimates seem to be slightly conservative. Only 75% of the predictions made based on actual weather data lay within the range estimated, although those which lay outside were mainly within 1 day of the estimated deviation. It would appear that the model range could be increased to provide a better coverage of results. A 98.8% range based on 2.5 standard deviations would include all but one (96%) of the data points. This approach provides a flexible alternative to the use of historical weather records or long-term forecasts, and presents a practical solution to the problems of forecasting, where future weather is a great element of uncertainty. The dynamically generated range provides an indication of the internal certainty of the model. 5.4. Model outputs For each field, transplanting details (date, number, variety), harvesting specifications (min. and max. head weight, min. harvest numbers), and site-specific weather file are specified by the user. Actual weather records are entered as available. The crop details are used to generate the initial 14 size cohorts, and the daily growth for each of these is calculated using inputs from the Weather class. The daily head weight (0.8 fresh weight) of each cohort is checked against the marketable range of head weights. Each cohort will meet the harvesting criteria for a given period, and a variable number of heads will be marketable on a given date. The period for which the number of available heads exceeds the minimum harvest numbers defines the start and end of the viable harvesting period for each simulation (Fig. 4). Within this period, the number of heads and the distribution of head sizes will vary. Results are presented for the three future weather scenarios, labeled Cool, Normal and Warm and summarise each set of runs. Fig. 6 shows the main results page for a single batch simulation, summarising the output for 100 simulations. All graphs have a horizontal date axis, and display the daily number of heads or total marketable head weight for each field, and enterprise wide weekly
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Fig. 6. Summary panel for a single batch, showing the passage of the crop through the window of marketable size. Results for the three weather scenarios are displayed, as the mean results for the 100 simulations. The graph shows a single simulation that most closely fits the presented output statistics. The peak day and total are given for both heads and fresh weight. Stem length and head density are calculated from a head development model (Harwood, 2001) which is outside the scope of this paper.
totals. For each of the scenarios, the predicted first and last days meeting the harvest criteria, and the day of peak heads and the day of peak total weight are presented, along with estimates of accuracy on the Batch Harvesting panel. For each of these 4 days, the predicted number and mean weight of marketable heads and the coefficient of variation in head weight of harvestable heads are presented, along with a qualitative estimate of head quality based on the rate of stem elongation during heading (Harwood, 2001). Before results in terms of the optimum predicted harvest date for each batch are collated for whole enterprise predictions, the facility is provided for managers to override the model recommendations and make up to three separate cuts from a single field. It is hoped therefore that at this stage, the batch predictions will represent the best available estimate. 6. Discussion The mechanistic growth model described goes some way towards capturing the characteristics of commercial field grown iceberg lettuce. However, validation against data from a range of latitudes reveals a shortcoming in the model in that it fails to capture late season trends at higher latitudes. Since the physiological responses of iceberg lettuce will be independent of latitude per se, the problem may be attributed to model structure rather than parameterization. As such, it seems inappropriate to use the model outside the range for which it has been validated. Further to this, wide variation in harvest timing was evident both within and between enterprises experiencing similar conditions. This could not be attributed to differences in cultivar. Economic considerations, such as meeting specific orders can result in sub optimal harvesting. At one grower site, the majority of harvests were made on the same day of the week prior to dispatch. A further source of error was noticed when a period of consistent rain produced waterlogging at one site, slowing the growth rate to the extent that the crops fell behind subsequently transplanted batches. Uncommon and field specific phenomena of this type are unlikely to merit explicit modelling. By allowing the manager to override the model predictions in such cases, accuracy can be maintained at whole enterprise level.
The deterministic model has also been successfully applied to glasshouse grown lettuce (Al Said, 2000), although in this more controlled environment with its own product specifications, specifically designed models (e.g. Seginer, 2003; Incrocci et al., 2006) are likely to be more useful, and a weather generator would be of little value. Taking the variation in size within the crop into account allows better characterization of the harvest period for a given deterministic model, providing growers with information to make decisions about, for example, the effect of delaying harvest. At the margins of the growing season this can be of particular value, where the potential harvest period is longer, and some plants may not reach a harvestable size. The presentation of the summary statistics and graphs for the posterior distributions of results was considered straightforward by the growers initially supplied by the model. However, it is possible that the software provides more information than is easy to assimilate. Managing uncertainty due to weather is critical for field grown crops, where little control can be exerted to meet specific orders. Generating weather from site statistics allows reasoned decision making. The simple weather generator has been previously validated for temperature and solar radiation but is not appropriate for aspects of the weather (e.g. rainfall) which do not conform to the normal model. If the growth model required such, an alternative algorithm for weather generation e.g. time-series algorithms such as LARS-WG (Racsko et al., 1991; Barrow and Semenov, 1995) may be useful. However, it is essential that any approach is easily parameterized from local weather data. Weather generators have been used as inputs for models, including crop models (Hansen and Indeje, 2004; Semenov and Doblas-Reyes, 2007) and erosion models (Williams et al., 1992). Where actual crop records are incomplete, or where the period of simulation extends beyond the present, they are used to fill gaps. In this respect the software described here does not represent a methodological advance. However, in terms of practical application, the incorporation of the whole process within the software frees growers from the requirement to use a weather generator in a statistically appropriate manner. Such use is unlikely to represent an efficient use of a technical manager’s time, and is unlikely to be adopted. As such the software overcomes a major barrier to the uptake of this technology. Research has been conducted into the incorporation of seasonal forecasts into models (Hansen and Indeje, 2004; Hansen et al., 2004; Semenov and Doblas-Reyes, 2007), showing success in more predictable equatorial climates. However, for the UK, the accuracy of long-term weather forecasts is likely only to be as accurate a predictor of weather as site records up to 72 h (Murphy et al., 1989). This is borne out by the modelling studies of Semenov and Doblas-Reyes (2007), which show little advantage to the use of weather generated data based on seasonal forecasts. The approach of generating three sets of scenarios for future weather, based on expected, expected +2 ◦ C and expected −2 ◦ C offers a simple alternative. Whilst possibly misleading when predicting long periods of weather, this approach allows the manager to reason using linguistically meaningful scenarios over the critical period approaching harvest. The size cohort model indicates that the response of crops to weather is complex, particularly at either end of the growing season. The optimal harvest date is not necessarily best represented by a single average plant, due to the movement of growing plants of different sizes through the marketable range. For example, at the tail end of the season, some of the smaller plants may not reach a marketable weight. When part of the crop is reaching maturity, decisions will need to be made as to when to harvest, according to the expected growth of the smaller plants. In mid-season, growth of the larger plants may move them out of the marketable range, and an assessment of the period for which the crop will provide
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a certain number of marketable heads will allow a more flexible approach harvesting. The approach represents a simple extension to any deterministic model which is straightforward to implement and of wide applicability. Alternative models and weather generators could be effectively combined to improve management of uncertainty. However, treatment of the effects of weather variation on a variable crop is important to avoid inappropriate advice. Acknowledgement Funding for this work was provided by a UK MAFFlink Consortium. References Al Said, F., 2000. The effect of temperature and photoperiod on growth and development of iceberg lettuce (Lactuca sativa L.). PhD thesis. University of Reading. Barrow, E.M., Semenov, M.A., 1995. Climate change scenarios with high spatial and temporal resolution for agricultural applications. Forestry 68, 349– 360. Borg, M., 1998. Getting Ready For Summer’ Tesco Internal Report. Dullforce, W.M., 1963. Analysis of the growth of winter glasshouse lettuce varieties. In: Proceedings of the 16th International Horticultural Congress 2, pp. 496–501. Hansen, J.W., Indeje, M., 2004. Linking dynamic seasonal climate forecasts with crop simulation for maize yield prediction in semi-arid Kenya. Agric. For. Meteorol. 125, 143–157. Hansen, J.W., Potgieter, A., Tippett, M.K., 2004. Using a general circulation model to forecast regional wheat yields in northeast Australia. Agric. For. Meteorol. 127, 77–92. Harwood, T.D., 1996. A dynamic three-dimensional plant-microclimate model, “Ecospace”. PhD thesis. University of Edinburgh. Harwood, T.D., Russell, G., Muetzelfeldt, R.I., 1996. A dynamic three-dimensional plant-microclimate model “Ecospace”. Aspects Appl. Biol. 46, 159–164.
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Harwood, T.D., 2001. The development of a new generation of horticultural crop forecasting techniques. MAFF Link project: CSA 4283: Final Report. MAFF, UK. Incrocci, L., Fila, G., Bellocchi, G., Pardossi, A., Campiotti, C.A., Balducchi, R., 2006. Soil-less indoor-grown lettuce (Lactuca sativa L.): approaching the modelling task. Environ. Model. Softw. 21 (1), 121–126. Lamb, H.H., 1950. Types and spells of weather around the year in the British Isles: annual trends, seasonal structure of the year, singularities. Q. J. Roy. Meteorol. Soc. 76, 343–348. Murphy, A.H., Brown, B.G., Chen, Y.-S., 1989. Diagnostic verification of weather forecasts. Weather Forecast. 4, 485–501. Pearson, S., Wheeler, T.R., Hadley, P., Wheldon, A.E., 1997. A validated model to predict the effects of environment on the growth of lettuce (Lactuca sativa, L.): implications for climate change. J. Hortic. Sci. 72 (3). Racsko, P., Szeidl, L., Semenov, M., 1991. A serial approach to local stochastic weather models. Ecol. Model. 57, 27–41. Ryder, E.J., 1999. Lettuce Endive and Chicory. CABI Publishing, Wallingford and New York. Scaife, M.A., 1973. The early relative growth rates of six lettuce cultivars as affected by temperature. Ann. Appl. Biol. 74, 119–128. Seginer, I., 2003. A dynamic model for nitrogen stressed lettuce. Ann. Bot. 91, 623, 635. Semenov, M.A., Doblas-Reyes, F.J., 2007. Utility of dynamic seasonal forecasts in predicting crop yield. Clim. Res. 34, 71–81. Strandman, H., Vaisanen, H., Kellomaki, S., 1993. A procedure for generating synthetic weather records in conjunction of climatic scenario for modelling of ecological impacts of changing climate in boreal conditions. Ecol. Model. 70, 195–220. Thompson, R.C., Knott, J.E., 1934. The effect of temperature and photoperiod on the growth of lettuce. Proc. Am. Soc. Hortic. Sci. 30, 507–509. Wheeler, T.R., Hadley, P., Morison, J.I.L., Ellis, R.H., 1993. Effects of temperature on the growth of lettuce (Lactuca sativa L.) and the implications for assessing the impacts of potential climate change. Eur. J. Agron. 2, 305–311. Wilks, D.S., 1995. Statistical Methods in the Atmospheric Sciences. Academic Press, San Diego. Williams, J.R., Richardson, C.W., Griggs, R.H., 1992. The weather factor: incorporating weather variance into computer simulation. Weed Technol. 6, 731–735. Wurr, D.C.E., Fellows, J.R., 1991. The influence of solar radiation and temperature on the head weight of crisp lettuce. J. Hortic. Sci. 66 (2), 183–190.