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MBW:Crop Production Modeling for Bio-regenerative Space Life Support Systems

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Executive Summary

An Environmental Control and Life Support System (ECLSS) for human spaceflight provides the basic conditions necessary to support human life (atmospheric management, food and water provision, and waste removal) in an environment where those functions are not naturally available like they are on Earth. An ECLSS must provide adequate oxygen to the human crew, remove excess carbon dioxide (CO2) from the air, maintain adequate temperature and relative humidity for metabolic processes and comfort, provide food for nutrition, provide potable water for drinking, remove (or store) crew metabolic wastes, and remove trace contaminants from the air, food, and water supply.

Bioregenerative life support is the use of regenerative technology (which continuously renews resources) that is biological in origin (uses living components). Plants fill many roles in space life support. They can recycle carbon dioxide back into oxygen, treat organic waste, provide food, and recycle clean water for drinking. The question remains as to whether higher plants in a controlled environment would provide the most cost effective means of filling these functions though, as opposed to alternative physicochemical means. That cost effectiveness is a function of number of crew, distance from Earth, and mission duration.

One way to compare cost effectiveness and feasibility of a given technology for a space mission is to evaluate the equivalent system mass efficiency[1], (ESM), which is a measure of resources produced over system cost (in terms of mass, volume, energy consumption and required crew time). In order to make such an estimate for a crop production system, one must be able to predict the quantity of food produced, oxygen produced, carbon dioxide removed, and water recycled, as well as the cost of doing so (the resources required). Through modeling, we can better understand and predict the response of a crop to a set of controlled environmental conditions and resource provisions. To optimize crop production in a controlled environment predictive models of plant response to the environment are needed.

Herein an overview of crop production modeling methods and their potential applicability to predict and/or control system performance in space is presented. A simplified explanatory model called the Energy Cascade will then be discussed in detail that has been used to evaluate and predict the potential performance of crop production systems for space life support.

Photosynthesis and Plant Growth, The Basics

The three major processes of plant growth and development are:

  • Photosynthesis: The process of using light energy to convert CO2 and water into sugar.
  • Respiration: The process of metabolizing sugars for energy for life processes (e.g., growth and reproduction).
  • Transpiration: The loss of water vapor through the stomata of leaves.

Similar to animals, plants oxidize (or burn) sugars for energy through the process of respiration. They use this energy for their growth, reproduction, and other biological maintenance processes. They take up oxygen for respiration through stomata in their leaves and through their roots. However, unlike animals, plants produce their own food (sugars) through a process called photosynthesis. In photosynthesis, captured radiation (light) energy is used to convert carbon dioxide (CO2) and water (H2O) into food products called photosynthates (sugars, starches, carbohydrates, and proteins). Photosynthesis occurs in the day when there is radiant light, while respiration can occur throughout the day and night. The absorption of light energy is made possible and controlled by a green pigment called chlorophyll. Carbon dioxide is taken up through stomata in the leaves and water is taken up through the plant’s roots. Water then flows from the roots, through the plant, and out through the stomata where it evaporates into water vapor. This water transport process is called transpiration. About 90% of the water taken up through a plants roots is lost to the atmosphere through transpiration. The other 10% is used by the plant for plant tissues and chemical reactions. Transpiration is vital for delivering nutrients from the roots to the rest of the plant, for evaporative cooling, and to maintain turgor pressure (keeping cells stiff and giving the plant strength). In addition to transpiration, osmotic pressure and capillary action also drive water through the plant.

Figure 1 Plant Metabolic Inputs and Outputs

The primary environmental factors that affect plant growth are temperature, light (intensity, spectrum, and photoperiod), humidity, water availability, and nutrition (macro and micronutrients, including CO2).

Light Effects: Photosynthesis generally increases with increasing light intensity. Red and blue light have the greatest effect on plant growth since it is absorbed by chlorophyll. Different intensities at different wavelengths drive different stages of plant development. For example, blue light is primarily used in growing leaves, while red light combined with blue encourages flowering. The effect of different wavelengths of light on the growth and morphology of the plant is called photomorphogenesis. Photoperiod, or more precisely the length of uninterrupted dark periods, also controls plant flowering.

Temperature Effects: Rates of both photosynthesis and respiration are regulated by temperature, and plant response to temperature depends on the plant variety or species. Temperatures that are too high or too low for too long can prevent flowering, fruiting, and pollination, and can also decrease both growth rates and quality (such as taste). Therefore by manipulating temperature, one can manipulate the life cycle stages of the plant (like flowering). Thermo-period (the daily change in temperature) can also affect growth rates. Maximum growth occurs when plants are exposed to a day temperature that is about 10 to 15° F (5.5 to 8°C) higher than that at night[2] , allowing for reduced respiration rates at night. If temperatures get too high, respiration rates can rise above photosynthesis rates, such that no growth can occur (products are being used faster than they are being produced). But on the other hand, if temperatures are too low, photosynthesis for growth slows down. The optimal temperature ranges for a plant differ amongst varieties. Water temperature effects the ability to uptake water through the plant roots and to dissolve nutrients in the water solution.

Relative Humidity Effects: Water vapor moves from high relative humidity to low relative humidity, and the greater that difference, the faster the water moves. An increase in temperature or air movement (convection) decreases relative humidity, increasing evaporation of water through the stomata, causing leaf guard cells to shrink, which then opens the stomata and further increases transportation. Hence, decreased relative humidity in the air leads to increased water loss through transpiration and increased water uptake at the plant roots.

Oxygen Effects: Oxygen is taken up from the soil by the plant roots for respiration. If oxygen is limited or not present, anaerobic respiration occurs, which produce ethyl alcohol and CO2[2]. Respiration is needed for cell growth and maintenance, and for nutrient absorption across root cell membranes.

Nutrition and Water Effects: Plants need 18 elements for normal growth[2]. In addition to carbon, hydrogen, and oxygen provided by air and water, nitrogen, phosphorus, potassium, magnesium, calcium, and sulfur are needed and acquired from the soil. These six elements, used in large amounts, are called macronutrients. Other nutrients acquired from the soil that are used in small quantities (iron, zinc, molybdenum, nickel, manganese, boron, copper, cobalt, and chlorine) are also essential for growth. Most are delivered to the plant by being dissolved in water that is taken up through the roots. Nutrient solutions are then effected by the chemical characteristics of the water such as its temperature, pH, and salinity.

For a more detailed overview of basic botany and plant physiology, see the Arizona Master Gardener Manual, Chapter 1 or the Colorado Master Gardener Program Garden Notes.

Environmentally Controlled Growth Chambers for Crop Model Development

Plant growth chambers have been used for decades in botanical, agricultural or other plant science research. Growth chambers can control the temperature, light, and atmospheric conditions that plants are exposed to, as well, as the delivery of water and nutrients. For detailed information on growth chamber requirements and considerations for chamber design, see the Growth Chamber Handbook. Another use of plant growth chambers is in horticulture and controlled environment agriculture, where precise control of a crop’s environment allows for improved crop yield and quality.

Sealed growth chambers have been the primary research facility for space crop studies allowing precise measurement of radiation and CO2 fluxes. “Measurements and models of short term (minutes to hours) and long term (days to weeks) plant metabolic rates have enormously improved our understanding of plant environment interactions in ground based growth chambers and are critical to understanding plant responses to the space environment.” Ultimately, the objective of crop production in a CELSS is to maximize production efficiency. This is the ratio of energy captured in biomass produced per energy input.[3] Real time measurement of production efficiency can be achieved by measuring CO2 fluxes in a sealed growth chamber[3]. The three primary determinants of growth (absorption of photosynthetic photons, photosynthetic efficiency, and carbon use efficiency) can also be calculated through gas exchange measurements in sealed chambers. Several parameters must be measured simultaneously.

For detailed review of the photosynthetic gas-exchange measurement and calculation techniques, see:

  • Field, C. B., et al. "Measuring photosynthesis under field conditions: past and present approaches." Measurement techniques in plant science. (1990): 185-205.
  • Field, Christopher B., J. Timothy Ball, and Joseph A. Berry. "Photosynthesis: principles and field techniques." Plant physiological ecology. Springer Netherlands, 2000. 209-253.
  • Garcia, Richard L., John M. Norman, and Dayle K. McDermitt. "Measurements of canopy gas exchange using an open chamber system."Remote Sensing Reviews 5.1 (1990): 141-162.
  • Reicosky, Donald C. "Canopy gas exchange in the field: closed chambers."Remote sensing reviews 5.1 (1990): 163-177.

Overview of Crop Production Modeling Methods for Horticulture

Crop models have both scientific and operational value. They are utilized to make decisions in agricultural production, in agricultural teaching, in agricultural policy development, and in the climate control of greenhouses.[4] In an operational context, yield prediction is necessary for growers with market deadlines to meet, while models are also needed to provide the right conditions (nutrients, water, and climate) for high yield, similar to industrial production, where automatic control systems can be used.[5]

Scientifically, horticulture crops have been considered lab tools to study and model plant processes. Controlled cultivation systems allow study of environmental effects on physiology. There have been significant advances in the modeling of leaf and canopy photosynthesis with tomato and chrysanthemum plants; analysis of growth with lettuce and tomato cops; and the modeling of developmental phases, like fruiting or dormancy.[5] Even models of the entire plant canopy have been developed that couple micrometeorological models with crop physiology models.[5]

Typically models can be based on statistical analysis of experimental data (descriptive) or based on a set of physical laws or mechanistic processes (explanatory). Descriptive models can include any mathematical relationship without being restricted to physical law, while mechanistic models might be more robust to extrapolation outside of sampled data conditions. Two other families of crop models include:[4]

  • Teleonomic: those built in terms of goals (processes oriented with a guiding objective)
  • Functional structural: those that merge geometrical models of plant visualization with process based models in order to control the whole plant development

Explanatory models can be preliminary (containing just the basic features of the system), comprehensive (detailed mechanistic models), or summary (simplifying comprehensive models to make them more accessible and practical for use).[5] While preliminary models might be of limited value in their simplicity, comprehensive models might be limited in practical application. The appropriate modeling complexity and approach depends on the intended purpose or problem to be solved.

Most explanatory models developed for plant growth aim to predict biomass production (or crop yield), characterized by dry matter (DM) production, DM distribution, and DM content of harvestable organs, relating not only volume produced but the quality of the product. Explanatory models of yield are typically based on the plants primary physiological growth processes of light interception, photosynthesis, respiration, and leaf area development. Models of these four processes, though an abstraction of reality, can be useful in predicting and understanding the effects of the plant’s environment and resources on its growth over time.

Greenhouse climate control is of particular interest in crop modeling for spacecraft life support systems. The main climate elements that affect a plants physiological growth processes are radiation, CO2 concentration, temperature, and relative humidity (or the water vapor pressure). Other non-climatic factors that affect yield are salinity (measured as electrical conductivity in the water), nutrient uptake, and water uptake.

There is a wealth of research in the mechanistic modeling of plant growth as a function of environmental conditions, at the cell, leaf, plant, and whole canopy level. There is also a wealth of literature reviewing and summarizing the history of this field.

In the 1970s, preliminary (functional) models of relative growth rate (RGR in g g-1 d-1) based on leaf area ratio (LAR in m2 g-1) and the net assimilation rate (NAR, in g m-2 d-1), representing canopy size and activity were developed: RGR = LARxNAR.[5] Other preliminary models were developed based on light interception and rate of conversion into biomass. In Figure 3 below, the functional approach describes the very basic processes that may limit yield based on empirical data, while the more detailed mechanistic approach provides a more realistic description, provided the parameters can be estimated.[5]

In 1980’s, more process oriented ‘photosynthesis-driven’ models were the dominant strategy,[5] that track the fate of carbon in the crop to predict yield. Mercelis et al. (1998) presents a detailed review of these models.[6] In photosynthesis based models, the interception of light by the plants leaf area is first calculated, then the production of photosynthates is simulated. Finally, the use of photosynthates for respiration, conversion into structural dry mass, and the partitioning of that dry mass amongst the plant organs is calculated. Each process might be integrated over different time scales. Most process based models developed are deterministic, ignoring variability of real systems, but some attempts at stochastic model development have been made.[5] To simulate light interception and subsequent photosynthesis, models of plant morphology are also used as in input to photosynthetic models.[5]

Figure 3 Comparison of Functional (A) and Mechanistic (B) Approaches of Yield Prediction. [7]

Tomgro is a well-established photosynthetic and morphological model for tomato crop development. It includes differential equations that describe changes in the number and weight of leaves, fruites, stems, leaf area, and new organ growth that approximate the carbohydrate distribution throughout the plant.[4] Rodríguez, Francisco, et al. (2015) present a detailed description of a simplified Tomgro model. Simplification allows its use in greenhouse control systems.

There are two other processes that strongly influence plant growth: water balance and nutrient uptake. Models of transpiration have been used for irrigation management and can include interactions between water availability, stomatal conductance, and gas (CO2 and water vapor) exchange.[5] Other models have been developed of the water storage and growth processes. Rodríguez, Francisco, et al. (2015)[4] present a detailed description of plant water dynamics and provide an example of an integrated water balance model. Jones and Tardieu (1998) [8] provide a review of the basic principles of plant water relations modeling as a determinant of growth, productivity, and quality. Mechanistic models of nutrient uptake have lagged behind the other processes, but those developed include simulated partitioning and dilution of nitrogen amongst organ classes.[5]

Diversity of Species:[5] Most crop models have focused on common crop species, but models will be needed that can be adapted to a variety of species. Photosynthetic metabolisms are fairly generic to species, but developmental phases and partitioning of dry matter amongst organs is species specific. Crop modelers advocate generic modular model structures that allow a user to parameterize a range of species, with a limited number of inputs and outputs that are measurable for model calibration.

Heterogeneity of Plant Response:[5] Though most mechanistic models are deterministic, they only represent the average plant, while plant responses may differ stochastically due to genetic variability, variability in the shoot/root environment, or variability in plant management (like pruning). Accounting for variability through stochastic modeling requires more experimental data to establish (non-mechanistic) probability distributions around mechanistic model parameters. This process tends to add unrealistic noise that would be homeostatically dampened in nature.

Despite a lot of advances in explanatory crop growth models, there is much room for improvement in the simulation of leaf area development, maintenance respiration, organ abortion, dry matter content, and product quality.[4]

For crop production systems used in space life support, it may be advantageous to apply mechanistic growth models to optimal control processes that determine the best environmental set points for maximizing plant yield or other outputs. Another objective is to estimate direction and magnitude of changes in canopy gas-exchange and production under off-nominal conditions. For use in optimization algorithms and for quick predictions, models must be quantitative, but with a limited number of variables. Research based photosynthetic models may be too complex for this purpose. Methods to reduce complexity have include aggregation or reduction of parameters in mechanistic yield models, the creation of simplified ‘black box’ models (which lose process rationale), and simulation via neural networks. The challenge is to derive simple models that maintain sufficient functionality to be robust and realistic.

Objectives of Crop Production Modeling for Spacecraft Life Support

When producing crops for space life support resources are very limited (like power and space available for equipment and time). Crop production research for space life support seeks to maximize plant production with limited resources, including time. We want to provide the maximum amount of food for the crew, and hence the biomass production rate (grams m-2 d-1). Therefore, an objective might be to maximize the slope of growth versus development time.

Figure 4 Objective of Space Life Support Crop Production

To increase the growth versus development slope, one can increase growth rate, or decrease development time. Growth can be increased by increasing light or CO2 inputs. Development can be driven by photoperiod and temperature.[3]

Another objective of crop production in a CELSS is to maximize production efficiency. This is the ratio of energy captured in biomass produced per energy input. The numerator can be expressed as the total biomass at the end of the life cycle, and the denominator as the integrated energy used over the life cycle. One can also look at normalized production efficiency per growing area and per day.

There are three determinants of production efficiency, and hence plant growth:[3]

  • Radiation absorption: The absorption of photosynthetic photons by green tissue is calculated by subtracting the transmitted and reflected photons from the incident photons and photons reflected from the ground surface.
  • Photosynthetic efficiency (or quantum yield): The moles of CO2 fixed per mole of photons absorbed by the entire canopy, is calculated as the gross photosynthesis per absorbed photon. Gross photosynthesis is the net photosynthetic rate during light periods plus respiration.
  • Respiration efficiency (or carbon use efficiency): Respiration efficiency is measured as the moles of carbon retained in biomass (net photosynthesis) per mole of carbon fixed (gross photosynthesis).

Maximum values for each can be derived from underlying biochemistry and each can be measured in laboratory growth chambers. Continuously measuring these parameters over a growth cycle allows estimation of daily growth rates and is the basis for modeling plant productivity based on metabolic processes (photosynthesis, respiration, transpiration).[3] By understanding the effects of environmental conditions on plant metabolism, one can control those conditions to optimize productivity under constrained resources, like space for growing area, or power for light. In addition to predicting crop biomass production, it will also be beneficial to predict associated gas exchange rates (CO2 uptake, O2 production, water uptake, water vapor production, and production of organic volatiles.)

The Energy Cascade (EC) Model: Description, Analysis, and Interpretation

EC Model Development:

Tyler Volk at New York University in collaboration with Bruce Bugbee at Utah State University, and Ray Wheeler at Kennedy Space Center (1995) developed a biomass productivity model, called the Energy Cascade based on the three determinants of plant growth described above: [9]

  1. Photosynthetic photon flux (PPF) absorption
  2. Canopy quantum yield (or conversion of absorbed photon energy into sucrose during photosynthesis), and
  3. Carbon use efficiency (conversion of the carbohydrate into structural and enzyme portions of plant biomass).

This energy cascade sequence represents the primary steps to convert photon energy into biomass. The initial model was presented as a ‘basic skeleton’ to be improved upon as needed. Models parameters were derived from experimental data from Utah State University and Kennedy Space Center for wheat crops grown in hydroponics growth chambers. Net canopy CO2 uptake during light hours, canopy respiration during dark hours and root respiration were continuously measured for four cases: low CO2, high CO2, and two different light treatments. As opposed to the detailed mechanistic models of photosynthesis previously developed for plant science research this model is extremely simplified in attempt to increase the immediate and practical utility for engineering analysis, design, and real time environmental optimization. The authors state that the system is probably at the ‘lower limit of simplicity’ to which a model can be reduced and yet still provide utility. It is intended to be adaptable to a variety of crops grown in controlled environments as a ‘generic tool’ for life support system design.

The model parameters are defined as follows:

Pn: Net photosynthesis, measured as the net canopy uptake of CO2 during light hours. R: Respiration, measured as the rate of CO2 release during dark hours Pg: Gross photosynthesis, the actual fixation of carbon into primary sugars through the Calvin cycle, requiring light (specifically photosynthetically active radiation, or PAR).

Sugars are then converted into plant components through biosynthesis, also known as dark respiration transferring carbon into new molecules and also oxidizing sugars into energy. This oxidation process creates CO2 as a byproduct.

Assuming respiration rates are equal during light and dark hours, than Pg = Pn + R.

In the energy cascade, a fraction of the PPF is absorbed by the leaf canopy. Next, a fraction of this absorbed energy is converted into carbohydrates via photosynthesis, and finally a fraction of the quantum yield is turned into new biomass through dark respiration.

(1) C = Pn/Pg

(2) Pg = Q*A*PPF

(3) Pn = PgR = C*Pg = C*Q*A*PPF

(4) R = PgPn = (1-C)*Pg (1-C)*Q*A*PPF

(5) CGR = k [H*Pn – (24-H)R] = K[H*Pg – 24R]

(6) B = ∫CGR dt

Where A is the fraction PPF absorbed by canopy (non-dimensional), B is the total accumulated biomass over a growth cycle (g m-2), C is the carbon use efficiency (mol carbon/mol carbon), CGR is the crop growth rate (g biomass m-2 d-1), H is the photoperiod in hours, k is a constant for unit conversion of μmol CO2 to grams of biomass (0.098), PPF is the photosynthetic photon flux (μmol m-2 s-1), and Q is the canopy quantum yield (mol carbon/mol PPF).

Figure 5 PPF Absorption, Quantum Yield, and Carbon Use Efficiency (measured versus modeled) for Utah State University Data [9]

Through analysis of experimental wheat growth data, time dependent trends in parameters A, Q, and C were identified.

  • A increases linearly from zero to maximum Amax until time of canopy closure (ta), due to increasing leaf area index.
  • A remains constant throughout the rest of the life cycle after canopy closure.
  • Q starts at a high constant value (Qmax), until flowering (anthesis) and then declines steadily until the end of the life cycle towards Qmin.
  • C remains constant throughout the life cycle (with a sudden decrease at the very end, ignored as a second order effect)

These observations resulted in a set of equations for A, Q, and C:

(7) A = (Amax/ta)t (for t≤ ta)

(8) A = Amax (for t≥ta)

(9) Q = Qmax (for t≤ tq)

(10) Q = Qmax – (Qmax – Qmin)/(tm – tq) * (t-tq) (for t>tq)

(11) C = Constant

Model Validation:[9] Data from the first set of wheat growth data (USU1) was used to tune the model parameters, and then those parameters were validated on the second set of wheat growth data USU2. All parameters were directly applied with the exception of Q which was multiplied by a factor of 1.25 to account for high CO2 levels. To test the model on data from experiments at KSC, model parameters for Amax, Qmin, Qmax, and C were carried from the USU parameters, while the development parameters tq (time of anthesis, or senescence) and tm (the time of maturity, or the end of the life cycle), were derived based on known development equations for wheat cultivars. The time of canopy closure ta was fit from KSC experimental data. Overall the model was successful, predicting Pn and CGR within about 10% of peak values, while for all experiments, the total biomass B was predicted within 6% of actual values.

Model Analysis:[10]

Figure 6 Time Profile for Pg, Pn, and R[10]

1) Since C is treated as a constant over time than outputs Pg, Pn, and R are proportional to A*Q*PPF. If PPF is held constant, then outputs are proportional to the time profile shape of A*Q, shown in Figure 6.

2) The definition for CGR allow for negative growth for short photoperiods. Since CGR – (H-24*R/Pg)*Pg*k, then CGR (growth) is negative if H is less than 24*(R/Pg) = 24*(1-C). This would typically occur for photoperiods less than 8 hours. This issue is addressed in the TLEC model variation described in a later section.

Important Assumptions:

  • Respiration rates are equal during light and dark periods (common assumption for most crop models)
  • Water and nutrients do not limit crop productivity

Model Weaknesses:

  • Model is restricted to the environmental regime in which photosynthesis is a linear function of PPF, and in a standard, ideal temperature regime of 19-23° Celsius, for a static photoperiod.[9]
  • Parameters are derived from empirical data and treated as constants, with light level and photoperiod being the only environmental independent variables that might affect plant growth and development.
  • Time to senescence (tq) and time to maturity (tm) are modelled as constant cultivar specific parameters, which are in reality affected by environmental conditions, like light level and photoperiod.
  • Senescence for the KSC experiments came earlier than predicted, possibly due to the build-up of toxic ethylene levels in the closed growing chamber.

Model Strengths:[9]

  • Original EC model is simple with parts representative of physiological processes, conducive to elaboration.
  • Model provides a useful approximation for gas exchange during the life cycle.
  • Model allows assumptions about the underlying processes of the energy cascade to be tested through experimentation.
  • Experiment validation highlights areas of uncertainty in the life cycle that need further investigation.

TLEC Model Development:

The next stage of development for the Energy Cascade was the Top Level Energy Cascade (TLEC) model, developed by James Cavazzoni at Rutgers University and Harry Jones at NASA Ames Research Center.[10] The original model was modified to simulate the effect of temperature, carbon dioxide level, planting density and relative humidity on canopy gas exchange.

  • Model was extended to predict the times of canopy closure, senescence, and maturity as functions of environmental conditions (light temperature, dark temperature, PPF, carbon dioxide level, planting density and photoperiod), using existing explanatory models.
  • C (carbon use efficiency) was redefined as varying rather than constant for legumes (starting high as a constant and then decreasing linearly to zero after senescence.)
  • C' was changed to a 24 hour parameter rather than one computed only during light periods:
- C24 = 24 hour net photosynthesis/24 hour gross photosynthesis = (H*'Pg-24*R)/(H*Pg) => CGR = (H*Pg – 24*R)*k = C24*H*Pg*k = C24*H*A*Q*PPF*k
- C24 can be computed from the original C parameter as C24 = 1-(24/H)*(1-C)
- This allows C to be computed as a function of H, which is more realistic and allows the possibility of positive growth for short photoperiods (a limitation of the original model).
  • The definition of Pn was changed to incorporated the new C24:
- Pn24 = (H*Pg – 24*R)/24 = C24*(H/24)*Pg = C24*(H/24)*A*Q*PPF
  • Dependence of Qmax (maximum canopy quantum yield) on constant carbon dioxide and PPF level was also incorporated, with function parameters derived from explanatory crop models.
  • Transpiration simulation, as a function of light temperature, photo-period, relative humidity, and carbon dioxide level was added to the model, but not validated with experimental data.
  • Daily crop growth and development is calculated to quantify leaf area index, which is then used to calculate light absorption (A), allowing non-linear canopy closure.
  • Crops modeled included other cultivars (bean, lettuce, peanut, white potato, sweet potato, rice, soybean, tomato and wheat).

Important Assumptions:[10]

  • Respiration rates are equal during light and dark periods (common assumption for most crop models)
  • Water and nutrients do not limit crop productivity
  • There is no dark period transpiration (stomata are closed)
  • Environmental input parameters are constant throughout growth cycle (except PPF*H)
  • Relative humidity only effects transpiration and no other growth parameters.

Model Strengths: The TLEC model can simulate growth for different levels of environmental control: nominal fixed conditions, off-nominal fixed conditions, and variable daily conditions (PPF*H only). Observing predicted growth under off-nominal conditions allows analysis of the effects of changing growth parameters, which might occur due to system operation decisions, or power shortages.[10]

Model Weaknesses:

  • Modeling Pn24 rather than instantaneous Pn using C prevents gas exchange simulation at time scales smaller than a day.
  • Crop growth parameters may not be independent of relative humidity (RH), as RH effects stomatal closure and therefore canopy conductance of CO2, and the evaporative cooling mechanism.
  • Even though PPF*H can change daily, ta (canopy closure date) is fixed and cannot respond to changes in PPF, H, or CO2

MEC Model Development:

In a third generation of the EC model, Harry Jones (NASA Ames), James Cavazzoni (Rutgers University), and Paul Keas (Orbital Sciences Corporation) developed the Modified Energy Cascade (MEC) model.[11], [12]

Improvements over the TLEC were to

  • Allow setting the time for seed emergence
  • Incorporate more realistic, crop specific exponential canopy growth: A = Amax * (t/ta)n for t<ta; A = Amax for t>ta, where n varies per crop type (wheat, lettuce, potato, etc).
  • Calculate canopy closure time, ta, and Qmax (maximum canopy quantum yield) as a differential function of light integral (PPF*H) and CO2 level, using empirical models developed by Vaccari and Levri (1999).[13] These functions are 6th order non-linear equations with a set of 25 coefficients who’s values were derived through multiple regression data fitting.
  • Add corrected harvest dates for potato and tomato
  • Add crop specific biomass partitioning into edible/inedible components (defined by coefficient XFRT) to allow edible biomass simulation rather than just applying a fixed ‘harvest index’ at the end.
  • Add daily oxygen production (DOP, in mol O2 m-2 d-1) as a model output:
DOP = OPF * DCG, where OPF is the crop specific oxygen production fraction (mol O2 mol-1 C) and DCG is the daily carbon gain (mol C m-2 d-1).

Model Validation: Model results fit Utah University and KSC experimental growth data very well.

Figure 7 MEC Model Simulations of Daily Carbon Content with Utah University (a – Low Temp; b – High Temp) and Kennedy Space Center Experimental Data[12]

Model Analysis and Simulation Results:[12]

  • Maximum edible biomass per meter squared per day is produced at the maximum allowed carbon dioxide level, nominal temperatures, and maximum light input.
  • Increasing temperature decreases production more than it decreases time to harvest (speeding development), hence productivity is greater at nominal rather than maximum temperatures.
  • Though productivity is greatest at maximum light inputs, reducing light increases use efficiency (edible biomass produced per light energy input)
  • PPF fluctuations that average out over a few days do not greatly affect crop productivity, meaning that a production chamber can tolerate some level of power fluctuations and brief outages.

Model Strengths:

  • Differential calculation of canopy closure (A) allows response to changing PPF, H, or CO2 levels.
  • All environmental inputs can be varied from one day to the next.

Model Weaknesses:

  • Parameters must be fixed throughout the day and remain in an allowable range. In order to simulate a range of temperatures over the life cycle, leaf area growth would need to be simulated adding considerable detail. Simplified models with this capability (for variable temperature, photoperiod, and planting density) have been developed but found too detailed to be readily incorporated into advance life support system models.[12]
  • The authors state that the model indicates maximum edible biomass per meter squared per day is produced at the maximum allowed carbon dioxide level, nominal temperatures, and maximum light input.[11] While this is true for the CO2 conditions tested, other growth chamber studies have shown a negative effect of extremely high CO2 levels on growth. Hence, this relationship may not be a linear.
  • The calculation for ta and Qmax is based on a 25 coefficient linear regression model empirically fit to experimental time dependent data. This seems like a fairly high number of coefficients without basis in physiological processes, presenting a risk that the model that is over-fit to the data from which it is produced such that it could be less robust to other applications and environments.

Implications for Model Enhancement for BLSS Design and Control

There are numerous benefits of applying simplified explanatory crop models to the design and operation of crop production systems for space life support systems. Simplified yet physiologically based models of crop growth and development and of canopy gas exchange are valuable tools in predicting the reliability, robustness, adaptability, and cost of biological life support. Also, the ability to predict optimal environmental conditions, as well as tolerable limits for those conditions, enables better definition of performance and sizing requirements for environmental control and support equipment. Set points for environmental control algorithms can be optimized (initially or in real time) to optimize growth and gas exchange for specific crops. And finally, model driven adaptive environmental control optimization becomes feasible, where environmental set points can be automatically adapted to changes in mission objectives, constraints, or other external perturbations, like power loss.

However, after this brief review of the development and evolution of the very useful Energy Cascade model, it is clear that there is still much room for improvement.

  • To predict reliability and adaptability, there needs to be a better understanding of what will happen on a ‘bad day’ and what extremes can be tolerated before losing a crop. In other words, models should incorporate plant response to unallowable parameter ranges as well as the ‘allowable’ ranges.
  • Some assumptions used in the EC models may not be valid. For instance respiration may not be equal during light and dark periods. Also the models assume that RH does not impact quantum yield when in fact this also may not be true.
  • Water and nutrient availability may indeed be a limiting factor during operation, so these factors should be considered for incorporation.
  • The conclusion that production maximizes at maximum allowable CO2 level implies that one can amp up CO2 to increase production. After a certain point this relationship does not hold, and this CO2 saturation point could be incorporated into the model to investigate effects of extremely elevated CO2 levels (>5000 ppm).
  • The model can only be used to evaluate daily growth, when operationally, growth conditions may change minute by minute, or hour by hour. It would be advantageous to adjust the model algorithm to allow finer resolution in time.

It is interesting to note that the original EC model, where Pg = Q*A*PPF, is not very different than the preliminary functional models developed in the 1970’s where relative growth rate (RGR) was calculated as Leaf Area Ratio (LAR) times an assimilation rate (NAR). The original EC simply allows the incorporation of the dependent variable PPF into the equation. As can be seen from the evolution of the EC model, its complexity grew very quickly to make it more adaptable to a range of crop types and environmental conditions, showing that a balance between the simple, functional model and the complex biochemical photosynthetic models must be reached for practical utility in predicting and controlling crop production systems.


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