Development and validation of a model to estimate ...

Computers and Electronics in Agriculture 92 (2013) 32–47

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Development and validation of a model to estimate postharvest losses during transport of tomatoes in West Africa V. Venus a,⇑, D.K. Asare-Kyei b, L.M.M. Tijskens c, M.J.C. Weir a, C.A.J.M. de Bie a, S. Ouedraogo d, W. Nieuwenhuis a, S.L.M. Wesselman e, G.A. Cappelli f, E.M.A. Smaling a a Department of Natural Resources, Faculty of Geo-Information Science and Earth Observation (ITC), University of Twente, Hengelosestraat 99, P.O. Box 217, 7500 AE Enschede, The Netherlands b ACDI/VOCA, Ghana ADVANCE Program, A&C Square Jungle Road, Accra, Ghana c WUR, Horticultural Supply Chains, P.O. Box 630, 6708 AP Wageningen, The Netherlands d INERA, BP 7192 Ouagadougou, Burkina Faso e International Centre for Integrated Mountain Development, G.P.O. Box 3226, Khumaltar, Kathmandu, Nepal f Department of Plant Production, University of Milan, Via Festa del Perdono, 7, 20122 Milano, Italy

a r t i c l e

i n f o

Article history: Received 30 September 2011 Received in revised form 30 October 2012 Accepted 16 November 2012

Keywords: Postharvest losses West Africa Transport Satellite meteorology Outside weather condition Cryptoclimate

a b s t r a c t In an effort to better understand postharvest losses associated with low-cost tomato transport in West Africa we present a spatial–temporal simulation model that links the prevailing outside weather conditions, estimated using satellite meteorology, to the microclimate observed inside truck trailers (cryptoclimate) to determine the deterioration in tomato quality during transport. Tomatoes from Burkina Faso are transported under sub-optimal circumstances to important Ghanaian markets; during a number of these transports conditions for the tomato cargo inside trucks were measured while conditions outside the trucks were monitored by means of weather satellites. The presented tomato quality model analytically combines cryptoclimate, duration since harvest, and kinetic modelling to arrive at estimated firmness. Firmness of tomatoes in transport was monitored with a portable penetrometer in selected trucks, augmented with additional (acoustic firmness) data collected in a climate chamber. Half of these observations were used to calibrate a firmness loss model and the other half to validate the simulation results. Our results indicate that outside weather during transport can be reasonably well estimated using satellite meteorology. The model performance for the estimation of outside global radiation (Rg) and land-surface temperature (LST) were found to be satisfactory, with a RMSE = 87.98 W m2; bias = 57.39 W m2 and RMSE = 2.95 °C; bias = 0.91 °C, respectively. Results for the cryptoclimate estimation (conditions inside the trucks) for temperature, relative humidity, and light intensity were as follows: R2 = 0.77, RMSE = 4.18 °C (Tincargo); R2 = 0.84, RMSE = 19.59% (RHincargo); and R2 = 0.9, RMSE = 137.31 lx (LIincargo). The postharvest loss model that relies on these estimates as its input explained on average 77% of the variance in observed tomatoes firmness, with total product losses ranging from 30% to 50% when integrated over the entire transportation period. With the accuracy of the model quantified and the causality of losses partially demonstrated, we argue that the simulation model can be useful as an economic resistor in transport optimization studies to investigate the cost–benefit of various measures to reduce postharvest losses. Such studies could help to illustrate what net gains can be expected if delays along the transportation route are reduced, cargo conditions are semi-controlled (e.g. pre-cooling treatment), or if a different transport schedule is adopted. The model may also be used to show the impact of different climate change scenarios on postharvest losses. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction In West Africa, tomatoes account for around 60 million USD/ year in cross border trade between Burkina Faso and Ghana. Ghana ⇑ Corresponding author. Tel.: +31 (0)53 4874 444. E-mail address: [email protected] (V. Venus). 0168-1699/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.compag.2012.11.011

is the most important destination of the Burkinabe tomato (Ouedraogo et al., 2008) and national agricultural statistics from Burkina Faso (Bakyono, 2007) confirm an increasing trade between the two countries (see Table 1: Tomato trade between Burkina Faso to Ghana). In Ghana, the relative high humidity and rainfall encourages pests and diseases, which hamper tomato production (Asare-Bediako

33

V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47 Table 1 Tomato trade between Burkina to Ghana (tons).

a

MALI

Year

2003

2004

2005

B?G G?B

3306.8 93.0

2420.3 145.2a

4076.0 346.7

Net trade (B ? G)

3213.9

2275.1

3729.3

Bamako

= 4.56 = 25.09 = 38

BURKINA FASO = 2.01 = 8.73 = 21 Ouagadougou

Missing: estimated using linear interpolation.

TOGO

Table 2 Breakdown of transportation margins from farm region to Accra (USD). Source: Adapted from Robinson and Kolavalli (2010).

Distance (km) Fuel Maintenancea Total costs Total cost/kg Revenue Revenue per kg Margin per truck Margin per crate Margin per kg a

Upper East (Ghana)

Brong Ahafo (Ghana)

Yako (Burkina Faso)

785 510 209 719 0.066 1082 0.098 363

442 155 111 266 0.024 618 0.056 352

1065 734 278 1012 0.092 1700 0.155 688

3.63

3.52

6.88

0.033

0.032

0.063

Estimated to be 20% of revenue.

et al., 2007) and, according to Ouedraogo et al. (2008), may cause losses of up to 30–40% in the Ghanaian tomato production. In Burkina Faso, on the other hand, climatic conditions are more favorable for tomato cultivation. Burkinabe tomatoes are considered not only to have a better overall taste and appeal, but also tend to retain these qualities longer during storage. For all of the above reasons they generally tend to attract higher retail prices (Causse et al., 2003). In Ghana, therefore, imported tomatoes are generally more lucrative for traders than those grown by local producers (Robinson and Kolavalli, 2010). Table 2 lists the trading characteristics for three tomato-producing regions as they are transported to markets in Accra (in USD). Generally, the export of tomatoes from Burkina Faso to Accra in the south of Ghana involves a 5 day trip for Ghanaian transporters: 2 days to reach Burkina Faso from Accra, 1 day to load the tomatoes, and 2 days to bring the tomatoes back to Accra. Net revenues comes to $690 per trip, or approximately $140 per day for a 5-day working week (Robinson and Kolavalli, 2010), not taking into account the depreciation of the truck. Transporters are key players in the tomato trade and quality-related marginal differences are essential to keeping these imports attractive. But this potentially viable horticultural value chain is in jeopardy. Not only price fluctuations but also postharvest losses leave traders with uncertain returns, and sometimes losses (The Statesman, 2009). The New Agriculturist (2005) estimated that postharvest losses in West Africa may be anywhere from 20% up to 100%. Reports by FAO (1989, 2004) concur with these data and also state postharvest losses tend to be highest in countries with greatest food shortages. Whilst tomatoes are still on the plant environmental conditions are somewhat controlled as latent energy is expelled from the canopy through the process of evapotranspiration, but once removed they become more vulnerable to direct sources of heat such as incoming solar radiation. This is particularly a problem when tomatoes are transported in trucks that are not climate-controlled (FAO, 2006). Like all fresh produce transport in West Africa, losses in the tomato trade between Burkina Faso and Ghana are further

= 1.50 = 3.33 = 16

LEGEND Police Customs Gendarmerie Others: Transport department, Trade unions, Forestry Department, Health

GHANA = 2.23 = 4.17 = 21

Check points/100 km Value of bribes/100 km Minutes of delay/100 km

Lomé Country borders

Tema

Major cities 100 km (scale bar)

Fig. 1. Road-transport obstacles to regional trade in four (4) West African countries (modified after USAID (2008)).

aggravated by delays at border crossings, (illegal) toll stops, police controls, or poor road and truck conditions. Fig. 1 shows road obstacles and their impact charted for several West African countries (modified after USAID, 2008). Although a variety of quality attributes of fresh produce can be considered, e.g. color as studied by Schouten et al. (2007) and Batu (2004), this study focuses on fruit firmness. This is because firmness is a widely accepted indicator of quality, which can be measured easily and which has direct economic consequences, (Abbott, 1999; Ali, 1998; Auerswald et al., 1999; Lana et al., 2005; Mizrach, 2008). In addition, firmness is highly sensitivity to external environmental conditions such as temperature and relative humidity. Firmness of vegetables describes a textural attribute co-determined by the state of the pericarp, locular tissue, and skin toughness (Ali, 1998). Simulation of vegetable firmness by computer models has been attempted in previous research; examples include De Ketelaere et al. (2004), Ali (1998), Lana et al. (2005), Mizrach (2008), Schouten et al. (2007), and Van Dijk et al. (2006a,b). Applying such postharvest simulation techniques to West African conditions, however, is not straightforward because environmental conditions after harvest are rarely monitored. The climatic conditions inside the cargo (henceforth referred to as cryptoclimate) are co-determined by a number of factors, and in particular by the type of cargo (dry/wet), the way it has been loaded on a trailer (turbulent mixing of inside and outside air), the albedo of the cargo’s cover (amount of solar radiation absorbed), and the ambient weather conditions during transport. In the absence of a reliable and spatially well-distributed network of meteorological stations in most African regions, satellite meteorology offers great promise for the spatial characterization of surface weather conditions during transport (Mueller et al., 2004; Stisen et al., 2007; Yang et al., 2006). Accurate retrieval of land-surface temperature (LST), for example, or global radiation (Rg) using sensors aboard space-born platforms yields an important indicator of this weather variability. Such procedures remain challenging due to the atmospheric attenuation, emission of thermal radiation, and the nonblack-body property of the observed land surface. In the thermal spectral range, the presence of water vapor is considered to be the most important factor driving these processes (Qin et al., 2001). To correct for atmospheric absorption by water vapor, a so-called ‘split-window’ technique is commonly applied using split-data in the far-thermal infrared (10–13 lm)

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V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47

range of the electromagnetic spectrum. Provided satellite sensors have two thermal bands, one centered at 11 lm (T11) and the other at 12 lm (T12), and assuming that surface emissivity is constant over this spectral region, the concept exploits different absorption characteristics of primarily water vapor in the atmosphere within these different, yet close wavelengths (Coll and Caselles, 1997; Sun and Pinker, 2003, 2009). Polar-orbiting, also referred to as sun-synchronous, satellites have the benefit of yielding relatively high spatial resolution (30 m to 1 km) data. However, because of the nature of their orbits, they sample the same spot of the earth surface only once every (other) day. For regions such as West Africa, where cloudiness dominates, polar-orbiting satellite observations therefore tend to yield very few clear-sky observations. This makes their application for the characterization of dynamic surface weather conditions during transport less suitable. In contrast, sunasynchronous, geo-stationary satellites observe diurnal changes in the atmosphere and at the earth’s surface, which makes them an attractive data source for this study. Due to their greater distances from the earth’s surface (approx. 30,000 km), however, geo-stationary satellites record data at a relatively coarse spatial resolution (3.25 km at nadir in the case of MSG/SEVIRI), which allows the sensor to record a full-disk (180 to +180° latitude) within the space of several minutes. The disadvantage of this is that, as the optical path length increases, the atmospheric attenuation also increases, particularly for image-elements that lie further away from the nadir-position at the equator (3.4° longitude). To overcome side effects of this increased attenuation, several authors (McClain et al., 1985; Sun and Pinker, 2003) added a zenith angle correction term to their surface weather estimation algorithms. These authors also showed that by adding a second brightness temperature difference term (T11–T12)2, the effects of atmospheric distortion can be further decreased when applying the split-window algorithm to geo-stationary satellite observations. Finally, Sun and Pinker (2007) developed a multi-channel algorithm to further decrease the effect of atmospheric distortions by applying a second split-window at the 3.9 lm (T3.9) and 8.7 lm (T8.7) bands that are available from more recent sensors. This new 4-channel algorithm was compared to two other algorithms, namely the generalized split-window algorithm proposed by (Becker and Li, 1990; Wan and Dozier, 1996; Sun and Pinker, 2003), and yielded the best retrievals with a maximum bias error of 1.5 K against 3 K produced by the generalized split-window algorithm. All these developments have made the use of satellite meteorology to characterize surface weather conditions possible at reasonable accuracy and applications studies such as the one presented here possible. To transfer the experience gained from one transport operation to another, a better understanding of the interaction between outside and inside climate conditions is essential. Longitudinal data, such as ours, are characterized by the fact that repeated observations for a subject tend to be correlated, which would violate independence assumptions made by most traditional regression procedures, e.g. multiple linear regression. Statistical methods for analyzing longitudinal data where the broad scientific objective is to describe an outcome, yit, for subject i at time t as a function of covariates, xit, are numerous, e.g. the generalized linear models (GLMs) by McCullagh and Nelder (1983) and the quasi-likelihood method as suggested by others (Wedderburn, 1974; McCullagh, 1983). Also a Generalized Estimating Equations (GEEs) model is commonly used as it only assumes that a transformation of the marginal expectation of the response is a linear function of the covariates and that its variance is a known function of its expectation (Zeger and Liang, 1986). As long as the characteristics of truck trailers carrying the tomatoes are comparable between transports, both of these underlying conditions are expected to hold. In other words, the average responses between outside and inside climate

conditions are expected to share the same covariates of outside weather conditions as long as the characteristics of the trailers are comparable, which is largely true in the case of West African transports. Also, the General Estimating Equation (GEE) technique developed by Zeger and Liang (1986), which is an extension of the quasi-likelihood approach (Zeger and Liang, 1986), is insensitive to serial-correlations. GEEs are widely used to analyze longitudinal and correlated data, e.g. Hanley et al. (2003) and Smargiassi et al. (2008) used GEE to predict in-door temperature in an urban setting from highly auto-correlated data. Similarly, Carl and Kühn (2007) used GEE to account for spatial autocorrelation in observations and concluded that it produces more sensible results than the Generalized Linear Models (GLMs). More elaborate descriptions of GEE can be found in Halekoh et al. (2006), Hubbard et al. (2010), Liang and Zeger (1986), and Zeger et al. (1988). For this reason, we opted to use the GEE instead of a basic regression approach in relating the outside weather conditions to the cryptoclimate observed inside the cargo. The un-conditioned means of transport that prevail in West Africa result in a dynamically changing environment during the postharvest lifespan of the fruit. To date, most studies have focused on quantifying postharvest losses under controlled storage conditions (e.g. Lana et al., 2005, 2006; Lukasse and Polderdijk, 2003; Schouten et al., 2007), in which only a few cryptoclimatic conditions vary. These aforementioned authors showed that the firmness of tomatoes decreases exponentially during storage and that it largely depends on temperature (Lana et al., 2005). This is because most metabolic processes, including respiration, transpiration, and ripening, are temperature-dependent, with rates typically increasing according to Arrhenius law roughly by a factor of 2–3 for every 10 °C increase (Beaudry et al., 1992; Exama et al., 1993). Overexposure to sunlight is also known to lead to localized bleaching, necrosis (sunburn or sunscald), or general collapse of vegetables (FAO, 2004). Solar radiation is therefore also considered here as a relevant factor, particularly since trucks in West Africa are open. The effect of wind on vegetables has already been highlighted by FAO (1989): the faster air moves over fresh produce the quicker the vegetables dehydrate. Equally, relative humidity is known to affect water loss, the development of decay, incidence of physiological disorders (e.g. blossom and rot), and the uniformity of fruit ripening (FAO, 2004). Hence we argue that firmness losses in an African transport setting are best described by microclimate conditions including temperature, light intensity, relative humidity, and the duration since harvest, as they all are expected vary between and within transports. Consequently, firmness losses can only be simulated by numerical integration of ordinal differential equations (ODEs) that describe the deterioration of produce on short time steps according to appropriate physical laws. To calibrate and validate such a simulation model, firmness of tomatoes (Lycopersicon esculentum cv.) needs to be continuously measure during transport, which is generally done using a fruit pressure tester because of its portability. A destructive sampling procedure like this, however, introduces noise to a dataset. This noise is caused by a phenomenon referred to as ‘‘sorting bias’’, whereby apparent biological age difference between fruits obscures the effect of storage conditions (Tijskens et al., 2003, 2005, 2006). The biological age is known to vary even if samples are taken from the same production batch. This is because individual fruits are exposed to unique environmental conditions during their pre-harvest lifespan, and depending on their horizontal or vertical position in the field, fruits positioned higher in the plant canopy are generally also exposed to slightly higher temperatures and light intensities and thus tend to age quicker then their neighbors. Sampling new fruits with each firmness measurement, as is the case when using a portable fruit pressure tester, individual fruits are likely to have a unique firmness despite sharing the same

V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47

duration since harvest (t) or even postharvest storage conditions. To correct for this ‘‘sorting bias’’ a non-destructive sampling procedure, e.g. using an AWETAÒ Acoustic Firmness Sensor (AFS), is generally used, but can only be operated in a laboratory environments. Furthermore, in a controlled climate chamber one can continue an experiment indefinitely, well beyond the typical duration of transport (40–48 h), to allow firmness to gradually reach an (asymptotic) end value. Beyond this minimum firmness value, Fmin, further softening is virtually impossible because some firmness generating compounds in the tomato tissue matrix (e.g. cellulose) are not subject to physiological decay. Thus one can only obtain Fmin for a new cultivar under study in a controlled climate chamber where the length of an experiment can be extended. Hence, one can best combine both sampling techniques to overcome each other’s weaknesses. If results based on the above premise are found to be acceptable, i.e. a spatially explicit deterioration in tomato firmness can accurately be simulated as a function of weather and transport conditions, then the resultant postharvest loss model could function as an economic resistor in scenario analysis to estimate the maximum distance that can be travelled to reach potential new markets. This can then help to optimize transport routing by evaluating alternative corridors, or to illustrate possible gains that can be achieved through reducing delays by employing more reliable trucks, improving road conditions, introducing faster procedures at border crossings, and improved security conditions that require less police-presence and road-blocks (see also Table 5). Improved security conditions and a more flexible timetable for border crossings could also make transport during the night a feasible option. In this way, the model could highlight the benefits – in particular, by maintaining cargo quality – that accrues by avoiding the blazing sun during daytime transport reduction. Finally, the model could be used in a cost–benefit analysis to determine if investments to create more favorable cargo conditions (i.e. air conditioning, precooling treatments, etc.) are justifiable. 2. Materials and methods To simulate firmness of tomatoes during non-climate controlled transport, the following three main steps were followed: i. For the estimation of selected outside weather variables along the transportation route, satellite meteorological retrieval algorithms using 1=4 hourly geo-stationary satellite observations (MSG/SEVIRI) were selected and tested. In particular, a 4-channel split-window algorithm as proposed by Sun and Pinker (2007) for the estimation of land-surface temperature (LST) and the HELIOSAT method (Hammer et al., 2003) for the estimation of incident solar radiation (Rg) were used. ii. Then a Generalized Estimating Equations system (GEEs) was developed to relate these remotely sensed variables and other external meteorological observations to the cryptoclimatic conditions of the cargos within the trucks. In this study, cryptoclimate is defined as the microclimate inside a truck trailer with a cargo consisting of stacked, open crates filled with tomatoes. iii. Finally, a tomato firmness simulation model was developed which predicts how tomato quality evolves under dynamic storage conditions over time and space. In this study, firmness of tomatoes is defined as a function of the cryptoclimatic conditions and duration since harvest, where:

Firmness ¼ f ðtemperature; relative humidity; light intensity; duration since harvestÞ

ð1Þ

35

2.1. Materials 2.1.1. Weather data observations HOBO ONSETÒ sensors, which allow the measurement of air temperature (Tair), relative humidity (RH), wind speed (SPD), and global radiation (Rg), were used to obtain independent observations of outside weather conditions during five tomato transports. Ground observations used for the validation of LST were collected at a time interval of 5 min using an IRISYSÒ 1011 Universal Handheld Thermal Imager, which has a reported uncertainty of 0.3 K at 303.15 K. Sensors for measuring ambient air temperature and relative humidity were enclosed in a radiation shield to shield them against direct sunlight. The outside weather conditions were measured by mounting the sensors on a stainless steel pole located at the middle of the truck trailer and sufficiently far away from the cargo as not to be influenced by the environmental conditions prevailing within the truck trailer. On average, the trucks were loaded in nine rows, each with four tomato crates. Each row comprised of three layers of tomato crates stacked on top of each other. This resulted in a total of 108 tomato crates in each truck. The cryptoclimate conditions were recorded using HOBOÒ Pendant light/temperature sensors placed inside the tomato crates, yielding observations of LIincargo and Tincargo respectively. All in situ measurements were recorded at 1 min interval using a HOBOÒ data logger, which automatically handles sensor calibration before data is stored. A HOBOÒ U12-006 4-channel recorder was used to record the tomato-skin temperature (Tskin) and was calibrated once before the start of the experiment. For the1 calibration of these measurements, a mercury thermometer was used to allow conversion from voltage to temperature. This conversion is unique for each thermal contact diode sensor. All measurements for both cryptoclimate and outside weather conditions were subsequently averaged to a 1=4 hourly average to coincide with the satellite sampling frequency. A per-minute track log of GPS points was also collected along the transportation routes by means of a mobile GIS system (HP iPAQ PocketPC equipped with ESRIÒ ArcPad™ 6 software), which automatically converts all geographic coordinates into a common datum (WGS84). In addition, the duration of the transport was extracted from the atomic time field that is provided by the GPS along with the location data. 2.1.2. Tomato firmness data observations Tomato (L. esculentum cv. hybrid ‘‘PETOMECH VF II improved’’) firmness was measured using a fruit pressure tester FT-011 (0– 11 lbs or 0–4.98 N) manufactured by Gullimex at the loading and the offloading points, and also at several other locations along the transportation routes. The sampling procedure as proposed by Schouten et al. (2007) was followed, which involves placing the tomato between the thumb and the forefinger of one hand to keep the tomatoes upright during measurement while being pressed by the Gullimex penetrometer. Firmness is a function of the pressure, measured in Newtons (N), required to force a plunger of specified size into the pulp of the tomato. Two measurements were made on each tomato, diagonally across the fruit. Selection of tomato fruits for sampling was done by randomly selecting four (4) crates in the first and second layers of the cargo. Subsequently, three (3) tomato fruits from each crate were selected at random. During transportation the random selection was done from easily accessible crates only. As a result, a total of twelve (12) fruits were sampled for firmness

1 The calibration was done by placing both the mercury thermometer and the thermal diode sensor in water with an initial temperature of 50 °C. The water was then incrementally cooled by adding ice water each interval. The temperature values were recorded every 30 s and then stored. The polynomial equation with the highest R2 was then used to calibrate the values obtained from the 4-channel sensor. The overall accuracy of these sensors after calibration improved from ±0.65 °C to ±0.11 °C.

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V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47

Table 3 Summary of data sources. Parameter

Institution/vendor

Instrument

Resolution

Period

Radiometric data

EUMETSAT

MSG/SEVIRI

1 and 3.25 km

October– November, 2008

Land cover Air temperature

GLCF Onset Computer Corporation

AVHRR HOBOÒ Weather Station (data loggers) HOBOÒ Pendant light/temperature

1 km 1 min (during transport) and 15 min (as stationary weathers station)

IRISYSÒ

IRI-1011 Handheld Thermal Imager HOBOÒ U12–006 4 channel extensions In trucks: (Penetrometer) model FT-011, and; In climate chamber: Acoustic Firmness Sensor (AFS)

5 min, Field-of-view: 1 m (16  16 pixel array) 1 min (during transport)

As above

Detailed in Section 2.2

As above

Every 3–4 days

November, 2008

Relative humidity Wind speed Global radiation Light intensity Land-surface temperature Tomato-skin temperature Tomato firmness

Onset Computer Corporation Gullimex AWETAÒ

measurement at each sampling moment. Because of the destructive nature of the measuring procedure, the selected tomato fruits were immediately discarded after measurements to avoid sampling the same, already damaged fruit twice. To correct for the ‘‘sorting bias’’ introduced by sampling new fruits with each firmness measurement we acquired additional data by means of a non-destructive sampling procedure in which an AWETAÒ Acoustic Firmness Sensor (AFS) was used to measure the same fruits throughout the experiment under controlled laboratory conditions, every 3–4 days over a total period of 18 days. Each fruit was sampled for weight and acoustic response three times at each time interval. The average reading per sample was retained for further analysis. The AFS yields a response (resonance attenuated vibration) that is characteristic for the overall firmness, juice content, freshness, and the internal structure of the fruit. These acoustic responses were then further analyzed using the AWETAÒ software to yield a firmness index (FI). The FI is high in fresh, juicy fruit and low in soft, ripe fruit. During this additional experiment, a total of 298 tomatoes were stored under three unique environmentally controlled scenarios using a climate chamber. Ceteris paribus, here only temperature was varied (10, 21, and 30 °C) leaving light intensity and relative humidity constant, at 0 lx and 75% RH respectively. Before further analysis, all measured firmness values were re-expressed in Newton (N). Table 3 summarizes the data sources used in this study. 2.2. Methods Data were analyzed using three main steps: (i) select and apply remote sensing algorithms to estimate external environmental (weather) conditions along the transportation route; (ii) train and apply a Generalized Estimating Equation (GEE) technique to estimate the cryptoclimatic (microclimate) conditions of the cargo, and (iii) estimate quality losses of tomatoes in the cargo. 2.2.1. Estimating outside weather conditions In the absence of reliable satellite meteorological estimation algorithms, for this study relative humidity (RH) and wind speed (SPD) were not estimated using satellite data. Instead, they were measured by the sensors mounted on the truck trailer. The other parameters and corresponding retrieval techniques are explained below. 2.2.2. Land-surface temperature retrieval For LST retrieval the 4-channel algorithm as proposed by Sun and Pinker (2007) was used in this study. The algorithm

As above

As above

coefficients used in the retrieval are identical to those presented by Sun and Pinker (2007). Therefore, instead of surface emissivity, surface type information can be used in the 4-channel algorithm. In the present study, a cloud layer mask was produced for cloud screening, in which the average value and the standard deviation of brightness temperature in the infrared channels at 8.7 lm, 9.7 lm, 10.8 lm, 12 lm and 13.4 lm are calculated. If the product of the average value and the standard deviation was found to be less than an empirically determined threshold, the pixel was flagged as cloud-contaminated. Using 1=4 hourly MSG/SEVIRI observations, LST data were retrieved for all clear-sky pixels coinciding with the road network used by the trucks transporting tomatoes. Estimates of LST for cloudy moments were obtained either by a weighted interpolation based in temporally neighboring clear-sky observations or by using physical gap-filling methods such as those presented in Lu et al. (2011). 2.2.3. Global radiation retrieval The global radiation (Rg) retrieval algorithm called HELIOSAT, which was developed by the group of Télédétection et Modélisation, Centre d’Energétique, produces maps of insolation (Rg in W m2) using optical geo-stationary satellite observations. The method assumes a flat surface, and therefore does not account for variations in insolation due to topographical shading or altitude. This assumption is valid for most of the West African topography. The HELIOSAT algorithm analyses the reflectance measured by a sensor to approximate the proportion of cloudiness, expressed as a cloud index value ranging between clear sky and completely overcast [0–1]. This analysis assumes that the difference in solar radiation between two temporally neighboring pixels (i.e. the same image element observed on two unique occasions) can be approximated to the brightness, or appearance, of a cloud. The cloud index, denoted as n, can be written as (Li et al., 1993; Beyer et al., 1996; Dagestad and Olseth, 2007):

n¼

q  qground qcloud  qground

ð2Þ

where q is the reflectance, or apparent albedo, that is observed by the sensor aboard a satellite recording in the visible portion of the electromagnetic spectrum, i.e. HRV channel of the SEVIRI sensor; qground is the reflectance over the ground under clear skies; and qground is the reflectance over the optically brightest clouds. In this study, however, the alternative method proposed by Dagestad and Olseth (2007) was used to calculate the cloud index, in which the term qground is parameterized into a 3rd order polynomial of the co-scattering angle describing the sun–ground–satellite geometry

V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47

(Dagestad, 2004). This compensates for the lower bound of the relative reflectivity of the ground, which can vary with time, largely due to the phenological development of vegetation or to more abrupt land cover changes (e.g. fresh asphalt on roads, rotation of crops, or the presence of burn scars from recent fires). The cloud index is then correlated to the transmissivity of the atmosphere (k) using an empirical relationship (Li et al., 1993; Beyer et al., 1996;). Clear sky irradiance is then corrected using k to arrive at the (shortwave) insolation at the earth’s surface:

Rg ¼ k  Rg clear

ð3Þ 2

where Rgclear is the solar irradiance in W m under clear sky calculated using the Linke turbidity factor (Lefèvre et al., 2002), optionally decoupled for a direct (Page, 1996) and a diffuse irradiance component (Dumortier, 1995) as cited in Hammer et al. (2003). 2.2.4. Estimating cryptoclimatic conditions Although differences in the type, color, and dimension of a truck trailer can all affect crypto heat and moisture retention, for this study their influence on the cryptoclimate could be ignored as all truck trailers were more or less similar. Also differences in the number of tomato crates and the dimensions of the crates may affect the aerodynamic resistance to heat transfer within the cargo and the boundary layer of the atmosphere. Hence, the presented model requires re-calibration if any of these conditions change. To predict the air temperature inside the cargo, Tincargo, a GEE Identity mean link function given as f(x) = x was used (Zeger et al., 1988). The relationship between the Tincargo and its covariates can be written as in

f ðT incargo Þ ¼ T incargo ¼ f ðLST þ T air þ SPDÞ

ð4Þ

Together with Eq. (5) it relates the response variable to the independent variables, the outside weather conditions, as follows:

T incargo ¼ b0 ¼ b1  LST þ b2  T air þ b3  SPD

ð5Þ

where Tincargo is the crypto (air) temperature (°C); LST is the landsurface temperature (°C); Tair represents the ambient air temperature (°C); SPD is the speed of wind blowing over the tomato crates (m s1); b0 is the intercept, and b1, b2 and b3 are the regression coefficients of the covariates. In contrast to the above, the distributions of the cryptoclimatic parameters relative humidity and light intensity were both found to follow the Gamma curve and hence a log mean link function was adopted. The log link function is given as f (x) = log(x). From this, the functional relationship for these cryptoclimatic parameters and their covariates can be characterized as shown in

f ðRHincargo Þ ¼ logðRHincargo Þ ¼ f ðRHout þ T skin þ T air Þ

ð6Þ

and

f ðLIincargo Þ ¼ logðLIincargo Þ ¼ f ðRgÞ:

ð7Þ

Relating the response variables to the independent variables we then obtain:

logðRHincargo Þ ¼ b0 þ b1  RHout þ b2  T skin þ b3  T air

ð8Þ

and

logðLIincargo Þ ¼ b1  Rg

ð9Þ

where RHincargo is the crypto relative humidity (%); RH is the ambient relative humidity (%); LIincargo is the crypto light intensity (lx); Tair represents the ambient air temperature (°C); Rg is the global radiation (W m2); Tskin is the tomato-skin temperature; and b0, b1, b2 and b3 are the regression parameters. A K-fold cross-validation method was used to evaluate the cryptoclimate models. The technique divides the dataset into K subsets, then leaves out one subset and trains the model with the remain-

37

der of the dataset. The one that is left out is used to validate the model. The process is then repeated K times so that all the subsets are used for validation once (Verbyla and Litvaitis, 1989). The model performance was evaluated by the coefficient of determination (R2), Student’s t-test, bias (or accuracy error), and standard error between the observed and estimated values (RMSE). 2.2.5. Estimating tomato firmness Under relatively constant storage or transport conditions, and assuming that relative humidity and light intensity only affect the rate constant of the process, firmness loss by physiology can be written as:

FðtÞ ¼ F 0  ekRH0 L0 t

ð10Þ

where F is the tomato firmness (N) at time t (h); F0 is the initial firmness (N) at t = 0; RH0 is the initial crypto relative humidity (%); k is the rate constant of firmness decay (day1); L0 is the initial crypto light intensity (lx); and, t is the duration since harvest (h). Assuming a linear relation, substituting Eqs. (11) and (12):

RH0 ¼ aR þ bR  RHincargo

ð11Þ

L0 ¼ aL þ bL  LIincargo

ð12Þ

in Eq. (10) yields:

F ¼ F 0  ekðaR þbR RHincargo ÞðaL þbL LIincargo Þt

ð13Þ

where aR and bR are the coefficients in the linear relation between firmness and crypto relative humidity, and aL, bL are in a similar relation between firmness and crypto light intensity. The rate constant of firmness decay, k, depends on temperature according to Arrhenius’ law (Bastin and Dochain, 1990):

k ¼ kref  e

EA R





1  1 T ref þ273 Tþ273

ð14Þ

where kref is the rate of firmness decay at the reference temperature; EA is the activation energy (kJ mol1); R is the universal gas constant (8.314 kJ mol1); Tref is the reference temperature (°C) tentatively set to 10 °C; and, T is the crypto temperature (°C). The above analytical solution works only for tomatoes stored under relatively constant environmental conditions. Furthermore, it assumes all tomatoes share roughly the same age. Even under controlled conditions (e.g. greenhouse environments), this assumption is violated because individual tomatoes tend to differ in their development stage or biological age at harvest. In our case, we are dealing with field grown tomatoes which tend vary even more in their physiological maturity. By assigning a new timecoordinate value to our firmness data, the so-called ‘‘dimensionless biological time’’, this variance in biological maturity can be accounted for. The time difference in the development of produce relative to that chosen reference point is first expressed using the biological shift factor (Dt) following the procedure presented in Tijskens et al. (2003, 2005, 2006). The biological time (t + Dt) is then multiplied by the rate constant k of firmness decay (day1) at the active temperature, yielding the dimensionless biological time. This now expresses the time necessary to place data from successive maturity stages on the same curve of development. This technique is commonly used in engineering and is now increasingly being adopted in postharvest studies to simulate quality behavior of various fruits and vegetables across the whole production chain, irrespective of the phase it resides in, either before or after harvest (Tijskens et al., 2003). Gas exchange in prickly pear cactus stems has been described by Guevara et al. (2006) and is reported to be linearly related to the vapor pressure deficit (VPD) as is also suggested by Lentz and van den Berg (1973). Because of their impermeable skin, weight loss due to vaporization of water is undoubtedly less in tomatoes

38

V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47

than in cactus stems. Nevertheless, the fruits studied here are harvested by picking instead of cutting and have their calyx continuously exposed to ambient conditions during transport. This could cause a measurable, albeit small, amount of water loss. Hence, weight loss (WL) caused by dehydration can be modelled analytically as:

W ¼ WðtÞ ¼ W o  WLrðeðkrtÞ  1Þ þ W o

ð15Þ

where W(t) is the total weight at time t in kg; W0 is the reference weight loss tentatively estimated at 10 (kg); WLr represents the weight fraction that can be lost by dehydration at ambient conditions, and kr is the rate constant. Given the unconditioned means of transport, which induces a dynamically changing environment (with variables T, RH, and LI), firmness losses can only be modelled by numerical integration, which requires the use of ordinal differential equations (ODEs). Differentiating Eq. (15) with respect to time yields:

@ WðtÞ ¼ kr  ðWðtÞ þ W o  WLr  W o Þ @t

ð16Þ

Changes in firmness loss caused by both physiological decay and dehydration can be modelled as the differential of Eqs. (13) and (16):

@ FðtÞ ¼ k  FðtÞ  LðtÞ þ kr  ðFðtÞ  F o þ W o  WLr  W 0 Þ @t

ð17Þ

Substituting Eqs. (11) and (12) in Eq. (17) yields our final estimation equation, whereby the ODE integrator automatically chooses a shorter time-step depending on the dynamics in the cryptoclimatic conditions. To prevent firmness from reducing to zero, which is practically unrealistic because only part of the fruit cells are subject to physiological decay (Lana et al., 2005; Van Dijk and Tijskens, 2000), we substitute F(t) = F(t)  Fmin (21) for F(t) in Eq. (17), where Fmin represents the variety-specific minimum tomato firmness. The tomato firmness, dFtom, can then numerically be approximated by:

@ FðtÞ  F min @t ¼ k  ðFðtÞ  F min Þ  ðaL þ bL  LIincargo Þ þ kr  ðFðtÞ

dF tom :¼

þ F min  F o þ W o  ðaR þ bR  RHincargo Þ  W o Þ

ð22Þ

The unknown parameters then become aR, bR, aL, bL, EA, kw, Fmin, and kref. To obtain values for these unknown parameters, with the exception of Fmin which is discussed in detail separately, a Generalized Reduced Gradient (GRG2) non-linear optimization technique was applied. This uses the computer algebra software system R and follows two steps: 1. Formulation of realistic initial parameter values, and defining their lower and upper limits, based on generally accepted physiological tomato characteristics. This implies that whenever a different cultivar of tomato is studied, this model calibration step should be repeated. 2. Calibration of the model using the GRG2 technique to obtain optimal parameters values, constrained by lower and upper limits defined in step 1, until the absolute total error no longer converges to a smaller value. The absolute total error is defined as:

eABS ¼

X

ðy  wÞ

wobs ¼ f ðX; PÞ

ð23Þ ð24Þ

where eABS is the absolute total error between the simulated (y) and observed (w) firmness (in N), X is a vector of model parameters, and P is a vector of the explanatory variables. Validation was performed using an independent test dataset not used for model calibration by setting aside roughly half of

the total number of observations, i.e. leaving n1 = 22 from the transport data and n2 = 149 from the climate chamber data for performance evaluation. Performance was assessed using a Student’s t-test regression analysis with the observed firmness as the response variable and the model output as the predictor variable. The model output is then assumed to be linearly related to the observed firmness with zero intercept as:

y ¼ a  ðX; PÞ

ð25Þ

where a is the regression coefficient. The model performance was evaluated by the coefficient of determination (R2), Student’s t-test, and standard error between observed and estimated tomato firmness. The relation between data inputs, calculations, and outputs of the various model components are summarized in Fig. 2. 2.2.6. Software Integrating meteorological data, which is distributed in formats such as netCDF, with societal data, i.e. GPS-tracking data from the monitored tomato transports in comma-separated text (csv) format, is far from straightforward. Most GIS tools (e.g., ArcGIS™ by ESRIÒ) do not handle time varying, multidimensional datasets well, nor do they provide full support for temporal or spatial animation. In this study, therefore, the Integrated Data Viewer (IDV) was used. IDV was developed by Unidata (Murray et al., 2003) using the multidimensional VisAD-data model (Hibbard, 1998) that facilitates seamless data integration and allows the evolution of the tomato quality to be geographically presented on a map. The analysis of (satellite) meteorological data and estimation models were implemented in the jython/JAVA™ framework as IDV plug-ins. For the prototyping of the tomato firmness model we used MAPLE™ (Nicolaides and Walkington, 1996). MAPLE is a computer algebra system for symbolic computations, combined with a modified and extended implementation of the biochemical2 kinetic theory library. For estimation of the unknown parameters we preferred R over MAPLE™. R is a language and environment for statistical computing (R Development Core Team, 2011) and offers a broader set of packages for numerical computation. Both symbolic and numerical computations were performed on a PC. 3. Results and discussion 3.1. Estimating outside weather conditions LST estimated from SEVIRI can be larger, close to, or smaller than that obtained from ground observations. The absolute error LST can be as large as 6.86 °C (aside from some outliers). The RMSE of 2.95 °C and bias error of 0.91 °C are encouraging indications of the good overall performance of the algorithm. The scatter plot of LST presented in Fig. 3 shows that the variation is roughly equally distributed around the 1:1 line for the sunlit portion of the day, when most tomatoes are transported, and that the retrieval algorithm overestimates land-surface temperatures during the night. These results concur with the findings of Sun and Pinker (2007) and Lu et al. (2011), who validated the same 4-channel retrieval algorithm for two different locations in Africa (Bias = 0.34 °C, RMSE = 2.49 °C; Bias = 0.85 °C, RMSE = 2.82 °C respectively). Also Rg estimated from SEVIRI is in reasonable agreement with our ground observation data (see Fig. 4), yielding an absolute error that can be as large as 136 W m2 (aside from some outliers). The overall performance, however, is good with an explained 2 For details see Maple Technical Newsletter Vol. 1 No. 2, 1994. AUTHOR: Mark Holmes, [email protected].

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V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47

Satellite observations

In-situ observations

- Transmissivity (aerosol, ozone)

HELIOSAT Rg

- Viewing angles - Solar angles - Cloud cover

Outside weather conditions

Global radiation

- Water vapour

4-channel LST

Outside weather

- Emissivity - Zenith angle

Firmness data

Cryptoclimate

Land-surface temperature

Legend Input Algorithm Output Process Data

Tincargo

RHincargo

Validation

Generalized estimating equations

Cryptoclimate

Calibration (50%)

Firmness model

Calibration (50%)

Firmness

LIincargo

Validation (50%)

Validation (50%)

Fig. 2. Diagram shows the relation between data inputs, calculations, and outputs of the various model components.

58

variance of almost 90% (R2adj ¼ 0:89, RMSE = 87.98 W m2, Bias = 57.39 W m2) and is well within the expected accuracy range 10–100 W m2 (Pinker et al., 1995; Perez et al., 2002; Sßenkal and Kuleli, 2009; Lu et al., 2011).

Bias=0.85, RMSE=2.82, n=393

53

The presented cryptoclimate models yielded accurate and unbiased estimates: explained variance for the crypto temperature was 77% at a RMSE of 4.18 °C, while that of the crypto relative humidity was 84% at a RMSE of 19.59%. The crypto light intensity, LIincargo, also showed a strong positive relationship with the satellite-retrieved solar radiation, with a correlation of 90% and a RMSE of 137.31 lx. In Table 4, the descriptive statistics of the cryptoclimatic and the outside weather conditions are presented for the tomato transports observed. The cryptoclimatic temperature, Tincargo, the air temperature, Tair, and the land-surface temperature, LST, showed an increasing variation, respectively, as was also reported by Parton and Logan (1981). On average, temperatures inside the cargo were higher than external temperatures (i.e. LST and Tair) throughout the transport period. This concurs with the results of Svenson (1985), who found that for a well-ventilated container both the air temperature and the skin temperature of the cargo are, on a daily average, higher than that of the external air. The significance of this was confirmed using the Analysis of Variance (ANOVA) with the null hypothesis stating that the means of the cryptoclimatic temperature, Tincargo, external Tair, and the LST are the same. The alternative hypothesis states that at least one of the means is significantly different:

Estimated LST (ºC)

48

3.2. Estimating cryptoclimatic conditions

43

38

33 nighttime daytime

28

23 23

28

33

38

43

48

53

58

Observed LST (ºC) Fig. 3. In situ measured surface temperature (observed LST) versus surface temperature estimated using the 4-channel method (estimated LST) during tomato transport, Burkina Faso (the thin black line represents the 1:1 line).

Ho: l1 = l2 = l3. Ha: At least one of the means is different. From the ANOVA results follows that the null hypothesis can be rejected and concluded that at least one of the mean temperatures

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V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47

Fig. 4. In situ measured global radiation (observed Rg) versus radiation estimated using the HELIOSAT method (estimated Rg) during tomato transport, Burkina Faso (the thin black line represents the 1:1 line).

Table 4 Descriptive statistics of crypto and outside weather conditions for selecteda transports. Variable

Cryptoclimate Tincargo (°C) RHincargo (%) LIincargo (lx) External climate LST (°C) Tair (°C) Rg (W m2) RH (%) SPD (m s1) a

Transport 1

Transport 2

Transport 3

l

r

l

r

l

r

29.77 85.34 122.36

2.21 4.36 335.65

31.80 78.27 162.55

2.3 7.5 364.14

28.41 77.74 106.37

3.33 9.64 397.78

25.87 24.45 49.21 87.60 4.54

3.21 1.31 128.82 7.70 3.09

24.29 25.59 69.29 89.15 4.05

5.83 3.17 170.28 9.33 6.08

25.01 23.57 52.6 71.79 0.87

4.23 2.25 139.52 11.30 0.79

For briefness only 3 out of the in total 5 transports are here shown.

is significantly different (ANOVA, F = 86.74, df = 150, P-value < 0.001). This outcome is expected because the packaging of the tomatoes in crates limits atmospheric mixing in the truck and leads to a build-up of heat, produced by the respiring produce, which in turn causes the crypto temperature to rise above the external air temperature and land-surface temperature. In a study involving 75 urban dwellings, Smargiassi et al. (2008) found similar results and observed that indoor temperatures were generally higher than outdoor temperatures. Both the land-surface temperature and air temperature rise during the early hours because of increasing strength of incoming solar radiation. The relationship between the Tincargo and LST was, unexpectedly, found to be non-linear. Transforming the cryptoclimatic air temperature values did not change this. LST was, however, found to be strongly positively associated with the Tair with a correlation of 0.70, yet with only 25% of the variability explained (R2 = 0.25). Interestingly, a rather linear relationship was revealed between RH and Tincargo with a strong positive correlation of 0.64. Also a negative linear relationship was found between the wind speed, SPD, and that of the Tincargo. The strength of this relationship, however, is moderate (R2 = 0.36). The cryptoclimatic relative humidity,

RHincargo, has a negative association with the external RH with a correlation of 0.57, probably due to a higher crypto temperature. The global radiation (Rg) estimated from the remote sensing imagery using the HELIOSAT algorithm also shows a strong positive relationship with the crypto light intensity, LIincargo, with a correlation of 90%. These results show that the cryptoclimate, here comprising of Tincargo, and RHincargo, varies linearly with the outside weather conditions. However, the relationship between Tincargo and remotely sensed LST was found to be non-linear. The crypto climatic temperature (Tincargo) does not respond quickly to changes in the outside weather conditions, i.e. LST and Tair. An increasing trend over time is, however, expected because generally colder air from outside only partly mixes with the hotter air inside the trailer, causing a gradual build-up of temperature. The highest temperatures observed during the forward transport (from Accra to Ouagadougou) reached approximately 38 °C, depicted in orange–red colors in Fig. 5. These maximum temperatures coincided with the border crossing, when delays were encountered. Tincargo was significantly lower, by as much as 6 °C, before the crossing at around 12:30 PM when the empty truck was still in northern Ghana (depicted in black on the same figure and super-imposed on the scatter plot). This can be attributed to the longer delay at the border than normal, totalling 4 h (2.30– 6.30 PM), and to the fact that this coincided with the hottest time of the day, which typically occurs around solar noon plus 2 h (Parton and Logan, 1981; Geurts and van Engelen, 1983). For the return trip (not graphically plotted), however, the transporter opted for a next day delivery thus avoiding these drawbacks. They began their southbound trip through Burkina Faso in the afternoon, spending one night at the border, and then entered northern Ghana early in the morning of the following day. It is worth mentioning that we observed a decreasing trend in the temperature of the cargo just after the border crossing at around 7 AM, which reached its lowest value at around 8:00 AM (Tincargo, ±31 °C). The drop observed during this period (3 °C) can largely be attributed to the driving speed of the truck, which picked up in the early morning facilitating the cold, outside air to become well mixed with the warmer air inside the trailer. Vice versa, lower driving speeds would limit this cooling potential and could even result in the opposite, a rise in the in-cargo temperature as during the forward trip. Table 5 details the numerous (partly unofficial) toll stops, police controls, etc. that were encountered as the truck made its way from Burkina Faso to Ghana during the return trip. Delays such as those presented here are typical for West Africa (see also Fig. 1). According to USAID (2008), an average truck driver passing through Ghana encounters 2.23 checkpoints, has to pay 4.17 USD in bribes, causing 21 min of delay for each 100 km of road, which is similar to the situation in Burkina Faso (2.01, 8.73 USD, and 21 min respectively). Although statistical validation failed due to the limited number of transports observed (n = 5), our results suggest that not every delay necessarily has a negative impact on the in-cargo conditions as long as trucks do not have to queue in the blazing sun. If trucks can be parked in the shade or, even better, can be driven at night, Tincargo could remain constant or even drop slightly. 3.2.1. Cryptoclimate model calibration To calibrate the cryptoclimate model, the Generalized Estimating Equations (GEEs) technique was used as introduced earlier. To avoid complexity in the estimation, the cryptoclimate parameters were decoupled and separate estimation procedures were developed for each of the variables. The prediction results are presented in Table 6. Because of the non-linear relation between the cryptoclimatic air temperature and land-surface temperature, the latter was excluded in the GEE model because it violates the fundamental assumption underlying the GEE model as explained in

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V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47

40 38 36 34 32 30 28 Kumasi 26 24 4:48 9:36

Border crossing

Ouagadougou

14:24

19:12

22:00

Fig. 5. Example of observed crypto temperatures (Tincargo, °C) during a forward trip from Ghana to Burkina Faso showing a peak (±38 °C) at the border crossing. On the background: True-colour composite representation of land cover provided by MODIS Blue Marble (Data resolution: 300 arcsec per pixel). On the foreground: The gray, dashed line represents a one-by-one degree latitude/longitude grid (111 km). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Section 3.3.2. Results show that every 1 °C increment in air temperature is associated with 0.42 °C increase in cryptoclimatic air temperature, Tincargo. Also, a 1% increase in the external relative humidity was found to lead to an increase of 0.04 °C in Tincargo while a unit increase in the speed of wind is associated with a 0.17 °C fall in Tincargo. Overall the GEE model explained 77% of the variability of the cryptoclimatic air temperature when all predictor variables were used, against an explanation of only 25% when only

Table 5 Example of delays observed during a return trip from Burkina Faso to Ghana. Time 4:26:47 4:34:21 4:40:30 4:57:39 5:29:41 7:41:09 8:10:40 8:15:13 8:24:16 8:33:17 8:41:34

AM AM AM AM AM AM AM AM AM AM AM

Reason

Time

Reason

Toll Pô Customs Pô Police station Tambolo Dakola Paga (Ghana) Ghana police Gasoline stop Paga Break Paga Police Navrongo Douane – Customs

8:53:03 AM 9:02:18 AM 9:11:05 AM 9:34:49 AM 9:45:20 AM 9:48:18 AM 9:51:38 AM 10:40:11 AM 11:37:19 AM 12:18:34 PM

Break Police Bolgatanga Police Bolgatanga Customs Shia Police Pwalagu Break Pwalagu Toll Pwalagu Customs Ante Customs Savelugu Tamale Station

air temperature is included. The final predictor equation for the cryptoclimatic air temperature is given as:

T incargo ¼ 17:72 þ 0:04  RHout þ 0:42  T air  0:17  SPD

ð26Þ

The slopes of all the predictor variables were significant (P < 0.001). This means that all the parameters were significantly different from zero and that a relationship exists between the crypto temperature and the predictor variables. Table 3 also shows that the estimated parameters have low standard errors and the confidence intervals are within acceptable limits. For the RHincargo prediction, the results showed that for every 1% increase in RH, there is corresponding 0.007% decrease in the logarithm of the RHincargo. A unit rise in the tomato-skin temperature, Tskin, is associated with 0.019% increase in the logarithm of the RHincargo. At a RMSE of 19.59%, the model explained 84% of the variability in the RHincargo. The final predictor equation for the RHincargo is given as:

logðRHincargo Þ ¼ 5:048  0:007  RHout þ 0:019  T skin  0:02  T air

ð27Þ

The GEE prediction model for the RHincargo showed that the determinants of the RHincargo are Tair, RH, and Tskin. All estimated parameters are significant (P < 0.001), have low standard errors and the confidence intervals (CI, between brackets in Table 6) have high

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V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47

Table 6 Parameter estimates and confidence intervals of the cryptoclimate models. Model

Variable estimatesa Tair

RH

SPD

Tskin

Tincargo 95% CI

0.42 (0.02) 0.37–0.47

0.04 (0.006) 0.02–0.05

0.17 (0.02) 0.21 to 0.12

RHincargo 95% CI

0.02 (0.0013) 0.01 to 0.005

0.007 (0.009) 0.001–0.037

Rg

0.019 (0.0093) 0.04 to 0.002

LIincargoc 95% CI a b c

Constant

RMSE

R2

17.72 (0.98) 15.81–19.64

4.18

0.77

5.048 (0.104) 4.85–5.25

19.59

0.8

137.31

0.9

2.29 (0.092) 2.10–2.47

b

All parameters were significant with P < 0.001. Ratio of variance of predicted values to variance of observed values. Model based on simple linear regression. The first two models are based on GEE.

coverage rates, indicating the robustness of the GEE in fitting the model. For the LIincargo, the omission of the intercept term was found to be plausible since light intensity inside the trucks depends solely on the global radiation, Rg. This is because there was no other source of light energy during the transport period than the sun. Since the GEE model does not produce sensible results in the absence of an intercept, a simple linear regression model was used to predict the LIincargo given as:

LIincargo ¼ 2:29  Rg

ð28Þ

For every 1 W m2 increase in Rg, LIincargo increases (as expected) by 2.29 lx. The model confirms that the only determinant of the LIincargo is global radiation. The variance in LIincargo explained by the model is 90% at a RMSE of 137.31 lx. 3.2.2. Cryptoclimate model validation The validity of the cryptoclimate models was tested using the RMSE, Student’s t-test, and R2. The validation procedure followed the procedure of K-fold cross validation, and divided the data from the trucks into two sets. For Tincargo, the averages of the R2 and RMSE of the ‘backward’ and ‘forward’ validations were found to be 77% and 4.18 °C respectively. The Student’s t-test was also used to assess whether the model produces biased estimates. To do this, two null hypotheses were formulated. Ho: intercept = 0 and Ho: slope b1 = b2 = b3 = 1. For which the alternate hypothesis read as: Ha: intercept – 0 and Ha: slope b1 – b2 – b3 – 1. The test results showed that the model did not produce biased estimates and is free from systematic error and therefore both null hypotheses could not be rejected. This means that the model can be used to predict Tincargo reliably (Student’s t-test, T Slopes = 24.8, 270.6, 111.9, T intercept = 18.86, df = 86, a = 5% t = 1.66). Upon validation of the RHincargo model, a relatively high prediction error of 19.59% was found. This error can be attributed to the intercept term in the model. Although the intercept was found to be significant, a Student’s t-test on the validity of the model found a systematic error only in the intercept term. All the slopes of the predictor variables were not significantly different from 1, which implies that the model did not produce biased estimates when the intercept term is dropped (Student’s t-test, T Slope = 774.6, 107.8, 109.6. T intercept = 48.5, df = 86, a = 5% t = 1.66). Whereas both RH and Tair showed a negative association with RHincargo, the tomato skin-temperature was found to be positively associated with RHincargo. Possibly this is because as Tskin increases, there is also an increase in the biochemical reactions of the tomato produce, notably respiration, and consequently more moisture is

released, thereby increasing the RHincargo. At the same time, the loss of moisture induced by the increased biochemical activity leads to a deterioration in the quality of the produce. From literature, this assertion is supported by Yeshida et al. (1984), Beaudry et al. (1992), and Exama et al. (1993) all of whom observed that high temperatures increase enzymatic catalysis, thus leading to increased biochemical breakdown of fruits and vegetables. 3.3. Estimating tomato firmness 3.3.1. Firmness model calibration In Section 3.3.3, a model for tomato firmness loss estimation was proposed that takes into account the dynamically varying transport conditions. For calibration, i.e. the estimation of unknown model parameters, a Generalized Reduced Gradient (GRG) non-linear optimization technique was applied using the R software. The estimated model parameters found for the optimal solution are listed in Table 7. It should be noted that the obtained model calibration is unique for the tomato variety under study, cv. hybrid ‘‘PETOMECH VF II improved’’, and may require re-calibration if the procedure is to be applied to a different cultivar. Based on the climate chamber experiment, the value of the last remaining unknown model parameter Fmin was established at 1(0.9719) N. 3.3.2. Firmness model evaluation The presented model simulations suggested that the firmness of tomatoes decreases exponentially during the course of transportation with a reference rate constant, kref, of 0.0075 ± 0.0003 h1 (0.23 ± 0.0072 day1). This is much higher than the kref reported by Lana et al. (2005) for controlled storage conditions, namely 0.0041 ± 0.00076 h1 (0.0975 ± 0.0183 day1), and that of our climate chamber dataset, which was 0.0043 ± 0.0003 h1 (0.1032 ± 0.0072 day1). In each of these experiments, the reference temperature (Tref) was set at 10 °C. For transport conditions, the model apparently over-fitted the unknown parameters kref,

Table 7 Model calibration, estimated model parameters. Parameter

Trucks

Climate chamber

aR bR aL bL F0 Fmin kr kref EA

0.354 0.002 4.848 0.000015 2.61 N 0.9719 N 2.70E04 0.0075 h1 20.411 kJ mol1

Idem Idem Idem Idem 2.4 N Idem Idem 0.0043 h1 47.423 kJ mol1

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V. Venus et al. / Computers and Electronics in Agriculture 92 (2013) 32–47

2.6 Temperature

2.4 2.2 2.0

Light intensity

10 °C

190 Lux

20 °C

383 Lux

30 °C

575 Lux

40 °C

766 Lux

50 °C

958 Lux

1.8 1.6 1.4

Firmness (N)

1.2 1.0 0.8 2.6 All variables

Relative humidity

2.4 2.2

19 %

Best case

37 %

Worse case

55 %

In situ

75 %

2.0

94 %

1.8 1.6 1.4 1.2 1.0 0.8 0

20

40

60

80

0

20

40

60

80

100

Transportation time (hours since harvest) Fig. 6. Relationships between cryptoclimatic variables and simulated firmness. Superimposed (on all panels): black dashed line (in situ) represents firmness based on observed crypto conditions, green dashed line (Best case) represent firmness assuming favorable crypto conditions (RH = 85%, LI = 0 lx, T = 10 °C), and red dashed line (Worse case) represents firmness assuming unfavorable crypto conditions (RH = 35%, LI = 1000 lx, T = 50 °C), and; Top-left panel: C. paribus, varying crypto temperature alone, Topright panel: C. paribus, varying crypto light intensity alone, Bottom-left panel: C. paribus, varying crypto relative humidity alone, and; Bottom-right panel: all of the above. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

yet still underestimated total losses. Based on the crypto conditions observed during transport, the model outputs suggest that the tomato firmness deteriorates by 37% whereas observations indicate that actual losses are significantly higher (49%, decreasing from 2.61 to 1.32 N). Visual observations at destination points in Accra confirm that losses are indeed in the order of 50%, as half of the transported tomatoes were found to be unacceptable for consumption, either as a result of being too soft or because they lacked some other important quality attribute (e.g. shrivelled skin, discoloration). Underestimation of firmness could be linked to the fact that not all losses in the West African vegetable chain are physiological but also of mechanical nature (van Zeebroeck et al., 2006), a phenomenon that is difficult to quantify and therefore not yet accounted for in this model. These mechanical losses are possibly further aggravated by the numerous transport delays as drivers try to make up for them by speeding (>70 km/h), even when road conditions are not accommodating. C. paribus, results also show that at low temperatures, the loss in firmness tends to be small. Minimal loss at low temperatures was also found by Wu and Abbott (2002) when sliced tomatoes were stored at 5 °C, and again by Lana et al. (2005). At higher temperatures, losses are much more pronounced as is shown by the top-left chart in Fig. 6. This loss is partly related to the

indirect effects of temperature on ripening (Miccolis and Saltveit, 1995). This concurs with the findings of Paull (1999) who showed that storage temperature can significantly affect fruit firmness and when raised above a critical level, i.e. the thermal death point of cells, too hot conditions can even lead to localized bleaching and necrosis (FAO, 2004). The lower-left chart in Fig. 6 shows the relationship between firmness and relative humidity, and illustrates that losses are largely due to the transportation time rather than the effect of relative humidity. This result is supported by a study conducted by Whitelock et al. (1994) who found that the length of the storage period had greater effect on peach quality than a deficit in atmospheric moisture. Paull (1999) also observed that a high relative humidity could not prevent moisture loss in cases where the fruit’s temperature (skin temperature) is not in equilibrium with the surrounding air temperature. Direct sources of heat, e.g. sunlight, also can elevate storage temperatures but when analyzed independently, their effect on firmness is much smaller than that of temperature (topright panel Fig. 6), albeit still stronger than that of relative humidity. Figs. 6 and 7 also show that, as with other climacteric fruits, physiological losses in tomatoes largely depend on time and temperature, whilst other explanatory variables have a modest to small effect.

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Fig. 7. Sensitivity analysis of the tomato firmness model. Ceteris paribus, the various explanatory variables were varied ±30%, while for relative humidity (RH) an increase of +10% and a decrease of 30% was used (to avoid RH > 100%).

To test the sensitivity of the firmness model to the cryptoclimate, an increase and decrease in the various explanatory variables was realized in the model simulation runs (Fig. 7). A range of ±30% and ±30% was used for temperature, time, and light intensity. These percentages were chosen in such a way that the values obtained remain within their practical range. For relative humidity, an increase of 10% and a decrease of 30% were used for the test. This was to guard against a situation where relative humidity will be more than 100%, which in practice is illusory. 3.3.3. Firmness model validation The result of the regression analysis comparing model output with observed firmness is summarized in Table 8 below. The developed quality change model explained 77% of the variability in the observed firmness decay during transport, and 75% if adjusted for the limited number of observations (n1 = 22). The co-efficient of the vector of the explanatory variables was found to be 0.655 with a standard error of 0.057. Eq. (24) can now be reported as:

y ¼ 0:655  ðX; PÞ

ð29Þ

To further test the significance of these results, the Student’s t-test was used. For a perfect predictor, the diagonal in a

Table 8 Firmness model validation. Parameter

Multiple r R2

Trucks

R2adj

0.878 0.771 0.745

Model co-efficient Standard error Observations (n) n for validation

0.655 0.057 40 22

Climate chamber All

10 °C

21 °C

30 °C

0.922 –

0.787 –

0.959 –

0.963 –

100 50

98 49

100 50

regression line should have the mathematical form Y = X. Since the intercept term has already been dropped, the only assessment is whether the slope is indeed equal to 1 for the model to be considered a perfect predictor. The corresponding hypothesis is thus formulated: Ho: b = 1 and Ha: b – 1, where b is the slope of the vector of the model parameters. Since the observed t-value is less than the expected value, we accept the null hypothesis that states the slope is equal to 1 and conclude that the firmness decay model is free from systematic error or bias at a = 0.05 (Student’s t-test (regression slope) 6.05, df = 22, a = 5%, t = 1.73). From Table 8, it also can be noted that the model performs 15% better when applied to the dataset from the controlled climate-chamber experiment compared to the dataset collected during transport, with their coefficients of determination (R2) being 0.92 and 0.77 respectively. The former dataset was collected in the laboratory using an accurate, non-destructive (acoustic) sampling technique. Because some tomatoes had to be assessed while on the road, this dataset could only be collected using a less accurate, destructive, but portable sampling technique using a handheld FT 011 penetrometer. The lower performance of the prediction model can be attributed partly to this. More importantly, tomatoes assessed by means of the penetrometer had to be discarded immediately after being sampled and hence successive information on the same fruit could not be collected. This prevented the use of the biological age correction technique (Tijskens et al., 2003, 2005, 2006) on the transport dataset, thus further aggravating the noise in that dataset. The importance of this correction procedure is further demonstrated by the left panel of Fig. 8, which shows that the spread in measured firmness varies not only with time (horizontally) but also at each moment in time (vertically) because, despite sharing the same harvest date, individual fruits naturally differ in their ripening stage. Finally, maps of the tomato firmness were produced using the same techniques as illustrated in Fig. 5 (output omitted for

45

6 4

Firmness (N)

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30 ºC

30 ºC

21 ºC

21 ºC

12 ºC

2

12 ºC

0

100

200

300

400

-2

0

Time (hours since harvest)

2

4

6

Dimensionless biological time

Fig. 8. Tomato firmness decay in a climate chamber. Ceteris paribus, here temperature was varied alone while leaving light intensity and relative humidity constant, at 0 lx and 75% RH respectively. Left-panel: Relationship between duration since harvest, observed firmness (from successive sampling), and simulated firmness (trend lines in black) for three storage temperature scenarios. Right-panel: As above, the time coordinate-axis re-expressed using the biological shift factor.

briefness). Once charted on a map all transports showed that after high, initial levels of firmness at farm gates, the losses accumulated to roughly 30–40% by the time they arrived at their destination points, with deterioration progressing more quickly where unfavorable climatic conditions were encountered. 4. Conclusions and recommendations Although statistical significance could not be ascertained due to a lack of observations (n = 5, number of transports monitored is five), the tomato firmness loss model seems to underestimate actual losses when integrated over the whole transport. Future studies could attempt to include mechanical losses to explain part of the variance currently not accounted for (23%). This, however, could prove far from being straightforward as, according to Paull (1999), warm fruits are generally more plastic and hence better able to withstand impact injury. Interactions, such as the one highlighted here, call for a careful analysis to compare the physiological and mechanical processes (Kader, 1996). Further, mechanical losses such as impact injury due to inappropriate packaging (wooden crates of variable quality piled on top of each other), rough cargo handling at on- and offloading points, vibration during transport due to poor road and truck conditions may prove difficult to measure and model due to the variable transport and road conditions. With a large part of the variability in firmness loss explained (77%) and causality partially demonstrated, the study presented here provides a mechanism to evaluate more efficient postharvest practices, which will be dealt with in a future study. A possible direction lies in the reduction of the duration of transport, e.g. by making use of faster routes, reducing waiting time at border crossings, minimizing checkpoints along the road corridor, reducing mechanical failure of truck and trailer by better maintenance, etc. Simulation results suggest (Fig. 6, Observed scenario) that losses in firmness could be reduced to 27% if the total transport is reduced from 43 to 24 h, and could be as low as 15% if the produce arrives at the destination points 12 h after harvest. This, however, may not be achieved in the short-term given the lack of cross-border trade policies to regulate the sector and the costs associated with a better

road infrastructure. Another direction to reduce postharvest losses could be through pre-cooling treatment of the produce (Kaynas and Sivritepe, 1995), through the use of Modified Atmosphere Packaging (MAP) (Fonseca et al., 2002), or by semi-controlling the cryptoclimate, particularly around midday (before and after solar noon), using low-cost methods such as hydro cooling. Simulation results indicate (Fig. 6, Best case scenario) that with a similar duration of transport losses in firmness could be limited to ±25% provided fully climate-controlled trailers are used (RH = 85%, LI = 0 lx, T = 10 °C), but again, such measures obviously come at a cost. While it may be uneconomical to control the RH and Tair fully, a better understanding of the behavior of the Tincargo will help to improve the design of any cooling system. In this context, it is worth noting the negative relationship between SPD and Tincargo, which means that if road conditions are improved and truck drivers can drive faster within reasonable limits, Tincargo can also be reduced at no cost. Currently a follow-up study is being conducted which explores how the presented tomato firmness model could function as an economic resistor in a transport optimization model. Finally, the presented model maybe used to illustrate potential gains that can be expected if delays along the transportation route are reduced, if a different transport schedule is adopted, or to model losses under different climate change scenarios. Acknowledgments We gratefully acknowledge the WUR and KNUST for providing access to their climate chamber facilities. A special word of thanks goes to Mr. A. van Embden and Dr. R. Schouten for their help with the acoustic firmness measurements. We thank the Centre for World Food Studies (SOW-VU) and ITC for jointly funding and providing the scientific equipment, assistance, and computer resources. INERA and involved field staff are acknowledged for their help with the data collection during the tomato transports. The West Africa Trade Hub, a USAID funded initiative to increase exports from and within the region, is acknowledged for kindly providing the data they collected since 2006 to help quantify delays during transport.

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