2009 Annual Report for FNC08-746
Winter Greenhouse
Summary
I received partial payment for instruments on 10/29/09. I immediately placed an order for the instruments that I had previously decided upon. They arrived by the middle of November. I began setting up the instruments on 11/23/09, and began taking data on 11/29/09.
Initially, I collected, every ten minutes, six datasets: water temperature, internal air temperature, external air temperature, soil temperature, internal solar irradiance, and external solar irradiance. On the northern wall in the greenhouse, there are sixteen (16) 55-gallon barrels filled with water. Twelve of these are directly in contact with the north wall and stacked in two rows of six, one on top of the other. The last four barrels are located directly to the south and in near contact with the barrels along the north wall. The water barrels serve as the principal means of storing heat energy. It is the temperature of these water barrels that I was measuring. Also located in the greenhouse are two cement planters, each about 2 feet wide, eight feet long and two feet deep. Each of these cement planters (constructed of cinder blocks) are filled with soil. It is the soil temperature of these planters that I was initially measuring. The internal temperature sensor was shielded inside a 1.25 inch PVC pipe; and a pyranometer was initially mounted horizontally and placed atop the most southern planter. The shielded external temperature, a horizontally mounted pyranometer, and a solar panel were mounted on a two meter tripod, which was secured to the ground by three guy wires. A data logger, located in the south east corner of the greenhouse, collected data from all six sensors.
For much of the month of December, until around Christmas time, I became familiar with the instruments, and the collection and downloading of data. Several features of the data became clear early on. First, the water temperatures were far from uniform. There was a several degree variation from top to bottom of a particular barrel, and between barrels centrally located to those at the eastern or western walls. Because the two rows of barrels along the north wall locates one row on top of the other, I cannot get a sensor into the water on the lower level. Were I able to do so, I would expect another variation in the temperature profile since these barrels are shadowed by the four barrels in front of them and to the south. Thermodynamically, this made sense, but was disturbing nonetheless. I was thinking at this time of developing a simple model relating external inputs (solar and thermal) to internal parameters (e.g., soil and water temperature). But if water temperature, and one might suspect, soil temperatures as well, were to be significantly non-uniform, I would have to start thinking of average water temperatures. How was I to assess average water (or soil) temperatures with but one or two sensors when there was so much variation?
It was during this time, during the month of December, that I spent a significant amount of time trying to understand the pyranometer results. Examining the external pyranometer results it soon became clear that I had a distinct loss of expected radiation during the middle part of the day, apparently due to shadowing in the low lying winter sun.
The initial theoretical template I used was an energy balance equation suggested by Beshada, et al., whereby the solar energy was absorbed by massive bodies (e.g., water, soil, cement flooring and cinder blocks), and lost by either thermal conduction or air infiltration. The amount of energy stored in the water could be computed by the knowing the heat capacity of the water, the amount of water, and the temperature change of the water. But with significant water temperature inhomogeneity this became problematic. A similar problem developed with regard to the total solar energy input into the greenhouse.
Objectives/Performance Targets
For several weeks I attempted to understand the relationship between the external pyranometer and internal pyranometer results. I was expecting to obtain, due to transmission losses, internal readings that were a nearly constant fraction of those obtained outside. However, this proved difficult to obtain. The internal pyranometer results were lower than the external, as expected, but the ratio of the two varied between about 0.2 to 0.9. It seemed possible that I was having some difficulty getting radiation into the greenhouse. Since the east and west walls of the greenhouse are windowless, insulated walls, it seemed possible that there was significant shadowing of the diffuse component of the solar radiation inside the greenhouse, as opposed to that received externally. In order to investigate this possibility more closely, I attached the external and internal pyranometers to the outside surface and inside surface of the greenhouse window, respectively. The results obtained were by far the most satisfactory. Aside from results during the early morning or late evening hours, where there might be significant shadowing effects, I obtained a ratio of internal to external irradiance of between 0.86 and 0.65, with an average of about 0.78, which is the rated transmission of the 8 mm. twin walled polycarbonate sheets being used for the solar window.
Believing that I had a better understanding of the pyranometer reading still did not solve the problem of knowing what exactly to use in the energy balance equation for the solar irradiance into the greenhouse. Moreover, there was the additional problem of attempting to estimate the losses due to infiltration. Beshada used a “conservative”; estimate of the rate of exchange. I looked into measuring the rate of air exchange in the greenhouse. It could be estimated with a “blower door”; measurement, wherein a fan is used to produce a pressure differential of 50 Pascal between the air inside and outside the greenhouse. At this pressure difference there exists an empirically approximate relationship between the area A of the fan, velocity V of the air being expelled by the fan and the volume of air being exchanged per unit time. With all these difficulties frustrating progress, I began to re-evaluate my approach.
One of the principal goals of this study is to be able to unambiguously evaluate various winter greenhouse strategies. It may be asking too much to hope that we could instrumentally make unambiguous assessments, but we surely could hope to be able to make more precise and less ambiguous assessments. With this in mind, I especially wanted to evaluate a number of winter greenhouse strategies, including the effect of mulches on soil temperatures, the effect of interior canopies on soil temperatures, the effect of the timing of watering on soil temperatures, the efficacy of buried insulation around the greenhouse perimeter, and the efficacy of solar curtains. It is the last that I particularly wanted to evaluate this winter.
I began design of a solar curtain just before Christmas. The purpose of the solar curtain is to increase the R-value of the solar window at night. Hence, its principal purpose is to reduce conductive heat losses at night, although it would also reduce radiative heat losses through the solar window. I initially tried using insulated foam board. But these proved too difficult and clumsy to maneuver. Ultimately, I settled on using Reflectix 174. Reflectix 174 is a fairly thin sheet of something like bubble wrap, covered on both sides by a highly reflective layer. If the curtain sufficiently covered the entire window, it would significantly reduce direct air contact with the solar window, thereby reducing conduction losses. It would also help produce an air gap between the outward facing side of the curtain and the solar window. After a number of unsatisfactory designs, I settled upon hoisting the curtain in two phases using pulleys. In the first phase the end of the curtain that had been secured to the bottom of the solar window was lifted to the top of the solar window using two pulleys. In the second phase, the middle of the solar curtain, that was after the first phase hanging from the top of the solar window, was hoisted using one pulley to the top of the solar window. In this way, the solar curtain was folded twice, raising the solar curtain sufficiently high that solar irradiance could directly irradiate the water barrels located on the northern wall of the greenhouse. The solar curtain was completed and ready to be tested on 11/15/10, after a prolonged cold period, where wind chills dropped to -40 degrees Fahrenheit.
Testing the efficacy of the solar curtain is somewhat challenging. Direct comparisons are not possible since the solar curtain, when in use, would be in use for the entire greenhouse. The situation, for example, is different from testing the effect of internal canopies on soil temperatures. One can place internal canopies above soil, while simultaneously having soil that is not covered by a canopy. Not only are direct comparisons not possible with the solar curtain, the variation in external conditions makes easy comparisons over different days difficult. External air temperatures and solar irradiance varies considerably from day to day. How is one to know how to account for differences in soil and water temperatures? How will we be able to distinguish differences due to changes in environmental parameters from those due to the solar curtain?
First, some preliminary analysis is appropriate. What expectation might we have that a solar curtain would be effective? How effective? The answer to these kinds of questions would ultimately be folded into a cost/benefit analysis. That, however, is beyond the scope of this' present project.
In order to evaluate the effectiveness of a solar curtain, we will compare the heat losses associated with the solar window due to conduction losses and radiative heat losses. We have where 0 is the heat loss per unit area per unit time, T; and To are the internal and external temperatures in degrees Kelvin, R is the total R value of the solar window (i.e., the total thermal resistance and not an R value per unit length), fp is the emissivity of the solar window, and If 1s the Stefan-Boltzmann constant. The first term is the heat loss clue to conduction losses through the solar window, and the second term is that due to radiative cooling through the solar window.
A number of simplifying assumptions are implied by this equation for the rate of heat loss. The radiative cooling term presumes that the greenhouse can be treated as a black body. The emissivity is the ratio of radiated energy of a body to that of a black body at the same temperature as the body. A black body absorbs all the radiation that is incident upon it. Typically, this is pictured as a cavity into which radiation is incident. The exit hole is sufficiently small that all the incident radiation is absorbed in the walls of the cavity; and then re-radiated at the temperature of the cavity. Hence, a true black body has zero reflectance. Clearly, if significant fraction of the incident radiation is reflected, the radiative energy emitted from the body will not be a function only of the temperature of the body. Whether the greenhouse approximates a black body is not clear. It is something like a cavity, but the walls are reflective, and radiation is reflected from the window. Nonetheless, we will presume that the greenhouse is sufficiently like a black body for our purposes.
The greenhouse will absorb and store radiation in the visible and re-radiate it in the infrared. The emissivity of the greenhouse that is most relevant is that in the infrared regime. The lower the amount of radiation reflected by a body, generally the higher the emissivity, and the closer is the spectral emissivity of the body to that of a black body. Generally, this kind of data is unavailable. We know that the transmission of visible light through the greenhouse window is approximately 0.78. If the emissivity of the greenhouse window is constant across all wavelengths (i.e., the emissivity is gray), then we can approximate the emissivity as the same as that of the transmission.
The solar curtain would only be employed at night since during the day we would want to collect solar radiation. Hence, we are primarily interested in heat losses at night. We approximate in the radiative cooling formula that both the night sky and the greenhouse are black bodies radiating at their respective temperatures.
In order to approximate the relative effects of conductive and radiative losses, we also need an approximate value for the total R value of the solar window. The 8 mm twin walled polycarbonate has a R-value of about 1.7 BTU I hr ft 2 F. Using these nominal values of emissivity and R value, and temperature of 40 deg F inside the greenhouse and I 0 deg F outside the greenhouse, we find that the ratio is very close to one. We can reasonably expect the solar curtain to influence both the emissivity and the R-value of the solar window. Because the solar curtain is highly reflective, we expect the transmission of the infrared radiation to be significantly reduced from that of a curtain-less window. Additionally, the solar curtain will establish something of an air gap behind the Reflectix 174, which itself has an R-value of about I. The curtain, as designed, is not air tight, but it will nonetheless impede air flow and contact with the window. For this reasm1, we expect the R-value of the solar window plus solar curtain to be significantly higher than that of the solar window by itself.
If the ratio of the emissivity with the solar curtain to that without the solar curtain is 12 the ratio of the R-value of the solar window plus curtain to that for the window alone is 1%, and the ratio of the conduction heat loss to that of the radiative heat loss without the curtain is f , then the ratio of the heat loss with the solar curtain 01 to that without the solar curtain 02 is given by. For small differential changes in 12 and 1 percent, it can be shown that where 1 = d1 ij{j ( d12 ) • Moreover, considering only the effect of the solar curtain upon the stored energy in the soil and water, we have at night (when there is no solar irradiance) the energy balance equation where, for simplicity, we have assumed that the change in temperature of both the soil and water was identical or nearly so. Here the variables I' OV,C represent the material density, volume, and heat capacity of their respective materials. The subscripts 'w' and ‘s’ indicate the respective values of water or soil.
So that with 1 T1 being the change in temperature without the solar curtain and 1 T 2 the change in temperature with the solar curtain, we have for small changes in emissivity and R-value.
So if the R-value of the combined solar window and solar curtain increases over that of the solar window alone, and the emissivity of the combined solar window and solar curtain is less than that for the solar window alone, there will be a fractional change in both the heat loss and temperature change of the storage elements that equals the fractional change in the emissivity and R-value, for all values of the ratio j of the heat conduction losses to the radiative losses.
With the solar curtain up, the reflectivity of the solar window in conjunction with the solar curtain will be quite high. The reflectivity of Reflectix 174; is listed at 96 percent and its emissivity at 4%. While it is not specified what the emissivity is in the infrared, we can assume that it is quite low. As a result, with the curtain covering generally quite well the entire solar window, we can safely presume that the emissivity of the solar window with the curtain up will be somewhere around 4%, about 5% of the curtain-less solar window. If we can reasonably presume that the R value of the solar window and solar curtain combination is at least twice of that without the solar curtain, we find (with/presumed to be I) that the heat loss with the curtain is only about 28% of that without the curtain. Because of the approximate equality of the fractional heat loss change and the fractional change in temperature of the storage elements in the greenhouse, the change of temperature of the greenhouse storage elements over night with the solar curtain up (i.e., soil and water) will likewise be about 28% of that without the solar curtain. Since one of the primary purposes of a winter greenhouse is to keep soil temperatures sufficiently high to encourage plant growth, it appears prima facie that the use of solar curtain will be a very effective means of serving that purpose.
Having now established good reasons to pursue the installation of a solar curtain, we face now the problem of how to empirically confirm the efficacy of the specific implementation. There are good reasons to doubt that the particular implementation in my winter greenhouse might not live up to our expectations. The solar curtain is not sealed to convective flow along the edges. Such a deficit might significantly reduce the potential R value of a solar curtain. Still we would be very surprised if the R-value were not greater than that without the solar curtain. Even if f% equals 1, the heat loss with the curtain would be about half of that without the curtain (assuming f equals 1). Nonetheless, such considerations ought to serve to warn us of the destiny of mice and men's best laid plans. All the scribbling in the world cannot replace the proof the pudding provides.
Classical statistical analysis would treat the curtain-less solar window as the control, and the solar window with the solar curtain as the variation on the control to be tested. We would examine a certain set of variables in both cases. In this case, we might wish to examine soil and water temperatures. We would then compute the sample means and variances for the two cases, i.e., with and without the solar curtain. Having done that, we need to be able to assess with some probability the difference between the actual and true means, and not simply between the two sample means, which are themselves random variables. In order to make progress we would usually presume that the true variances (as opposed to the sample variances) are equal. While this is likely not exactly true, it likely that they are close to each other. With this assumption it is now possible to employ what is called the Student T probability distribution. This probability distribution is derived on the assumption that the random variables (soil and water temperatures) are normally distributed. It is then possible to form a random variable, using the sample means and variances, that is independent of the actual variances (presumed equal), but dependent upon the true and actual means. Having gotten this far, one then arbitrarily establishes a confidence limit. The confidence limit establishes the probability of a false negative that you are prepared to accept. A false negative is what happens when one uses some criterion to decide when the probability of a certain event is too low to believe it would happen and yet it does and you are wrong. The confidence limit is established by choosing the total probability of a false negative that one is willing to bear. Once this confidence limit is established, one can determine, using the Student T distribution, for the two sets of data (e.g., soil temperatures with and without the solar canopy) a confidence limit for the difference between the actual means. The result will be a ce1tain confidence that the difference between the two actual means is between two values. In the case of the solar canopy, we would hope that the lower bound of that difference between the actual means is greater than zero, perhaps even greater than 2 degrees F.
What is outlined above is the normal statistical approach to evaluating statistically the efficacy of a certain difference from the control. There are, however, problems with this approach. What we want to test is just the effect due to a change in whether we use the solar canopy or not. The problem is that there are a number of other factors that significantly affect the soil and water temperatures, including the solar irradiance, external temperature, and wind velocity. It may even be that cloud cover affects the results since more cloud cover will increase the diffuse component of the solar irradiance and that might influence the amount of radiation that gets into the greenhouse. All of these other independent variables have a significant effect upon the soil and water temperature history. How can we be certain, then, that we are actually measuring the effect of the solar canopy and not some other variable? The traditional means of dealing with this problem is tem1ed randomization. By including in both datasets a wide range of these uncontrolled variables, we hope that their effect will average out. Ideally, we would like to have the same kind of variability in the uncontrolled variables in both datasets. Perhaps the best way to ensure this is by having large datasets. Taking datasets over the course of a year, or even longer, would provide some confidence that the rich effects of these diverse uncontrolled variables have been sufficiently averaged out.
Roberts 2 in their paper, Movable Thermal Insulation for Greenhouses, say: In evaluating the thermal performance of the various curtain materials, it has been found that there is a significant variation in the heat loss coefficient from hour to hour or night to night. These variations are caused by changes in cloud cover, wind velocity, precipitation, and amount of condensation within the greenhouse and the mechanical performance of the pulling system, i.e., how well each curtain edge seals each night and the presence of ponds of water on top of the curtain or unrepaired tears. Therefore, it is necessary to evaluate a curtain and determine its total energy savings over an entire cropping system in order to be certain of the systems effectiveness (emphasis added). It is our intention to try to find a way around this expensive and time consuming assessment method.
Metric of Efficacy
Because of the statistical difficulties associated with assessing the efficacy of the solar curtain in the presence of large number of richly varying uncontrolled variables, a different assessment method was sought. What we seek in our analysis is a metric that is independent or nearly independent of the various uncontrolled environmental variables, but, nonetheless, reflects a dependence upon the changes engendered by the solar curtain. With this intention in mind, we begin with the energy balance equation for the greenhouse.
For solar energy input Qin , area A, overall thermal resistance R, inside temperature T1 , external temperature To , air infiltration rate V; , volume of the greenhouse v, density of air roa 'air heat capacity ca' emissivity ffJ , Stefan Boltzmann constant if , density of water i'Dw, volume of water V w, heat capacity of water C w, water temperature T w, soil density ro s' volume of soil versus soil heat capacity c s' and soil temperature Ts we have, following Beshada, the greenhouse energy balance equation.
Here the first three terms are the right hand side of the equation is the heat loss due to conduction, heat loss due to air infiltration, and radiative heat loss. This last term is not included by Beshada but with our preliminary calculations indicating the relative importance of radiative cooling, it seems wise to include it. The last two terms are the greenhouse storage terms, that stored in the water and that stored in the soil.
For our purposes we will consider the situation at night, when the solar energy input is zero. When there is no solar energy input, there are heat losses due to conduction, air infiltration, and radiative cooling, and the temperatures of the energy stored elements decrease as they release thermal energy.
In order to make progress, one additional approximation is necessary. The radiative term in the energy balance equation involves temperatures, measured in degrees Kelvin, raised to the fourth power. This kind of dependency is inconvenient for our analysis. We rely then upon the following expansion of the radiative.
Since this analysis must serve the purposes of our experimental setup, we must bear in mind that the number of temperature measurements is significantly limited. This would not be a significant deficit were it not for the observed inhomogeneity of those temperatures, at least for the case of water temperatures. With this in mind, we have to find a way to speak of the water temperature in a particular water barrel, or the soil temperature in a particular location in a particular planter. Consider first the case of water temperature. Let the thermal gain or release in a particular water barrel to be equal to a fraction F of the total thermal gain or release of all storage elements. With this assignment, using the greenhouse energy balance equation at night (when there is no solar input).
I have learned how to use the Hobo data logger, in conjunction with the sensor instruments that was purchased with the SARE grant money I have additionally learned how to download the data and manipulate it in many and various ways by the use of FORTRAN codes that I have written.
I had hoped to be able to confirm empirically that the use of a solar curtain is a cost efficient addition to any winter greenhouse. I don't believe that I am able to say that unambiguously at this time. But I do believe that I have the tools, both instrumentally and theoretically, to address the question.
I plan to continue a more careful analysis of the efficacy of the solar curtain. I will examine, as promised above, to examine the reliability of the carefully selecting the observation time period. We need to demonstrate that it is neutral with regard to datasets with the same conditions with regard to the solar curtain, and that it demonstrates reliable indicators when compared to datasets differing in the use of the solar curtain.
I intend to, in some sense, go back to square one. I will try to find time periods over which the uncontrolled environmental variables are sufficiently close to each other that I can be confident that differences observed in water and soil temperatures can be attributed to the effect of the solar curtain. These periods will be chosen such that the wind conditions are generally quiet, in order to hopefully reduce the influence of air infiltration. I will also attempt a more conventional analysis of the greenhouse, relying upon longer time series data for randomization of enviro1m1ental inputs. In this way, by using a number of different evaluation techniques we can gain confidence in any or all of them.
Moreover, even given the value of the metric RG to assess the efficacy of the solar curtain, what is lacking is some estimation of how this metric would be associated with a particular temperature differential in the soil or water temperatures. After all, it is the soil temperature that is most important for plant growth, and just what we would need to know in order to assess the cost-effectiveness of installing a solar curtain, even one as crude as the one described here.
I also plan to examine a number of strategies, perhaps even before the close of the winter season, now rapidly coming to an end. These include the use of mulches, perhaps of different colors, of plastic coverings, and of watering schedule on soil temperatures.
Roberts indicates that sealing the thermal curtain to prevent air infiltration is important. My solar curtain is not sealed at any of its borders. If the insulating quality of the solar curtain is particularly sensitive to this feature, then my solar curtain might prove much better. What is unclear how I would go about sealing the borders and still be able to readily take the curtain up and down? Putting it on tracks is a possibility, but likely too expensive. It is also interesting to note that Roberts had apparently experimented with foam board, as I have. Their assessment is that it could be an effective means of reducing conduction losses. But they also found the board too difficult to work with.
Next winter I hope to be able to examine the influence of burying foam insulation around the perimeter of the greenhouse. The hope is that sun insulation will reduce of the rate of heat loss to the ground. In many ways the analysis of the effectiveness of such ground insulation depends critically upon the success of my analysis of the solar curtain. The difficulty associated with analyzing the efficacy of the solar curtain is that its effect upon soil and water temperatures is not observed simultaneously with those results without the solar curtain. Hence, the number of uncontrolled variables is significant. The situation is even more difficult in examining the efficacy of ground insulation. For in this case we are examining results not a few days apart, but a year apart. It is critical; it seems to me, to be able to somehow diminish the influence of the uncontrolled variables, e.g., external temperature, solar irradiation, and wind conditions.
IMPACTS AND CONTRIBUTIONS
I may attempt, perhaps over the summer months, to develop a “blower door” instrument, using it to estimate the infiltration rate. At present, the peak of the greenhouse is not sealed tightly. I may seal it and then measure the effect engendered upon the infiltration rate. Having hopefully decreased the air infiltration rate, I might next winter re-examine the efficacy of the solar curtain, in this way getting some handle on why the metric suggested in equation (2) is not working as well as I had hoped.
At some point, I am still hoping to be able to compare growth rates of various winter greens under varying conditions. Such experiments will be take place on the scale of months.
At present, I have dedicated little time to sharing what I've learned. I've told a few people involved in high tunnels about the work I am doing, but I've shared nothing of my results. It seems too early and preliminary to do that. I am planning, perhaps next year, to share the ability provided by the instruments in hand to evaluate other winter greenhouses. The unit was chosen with portability in mind. Lastly, if all goes well, I intend to publish the results in a scientific journal and to report on the more practical aspects at either a MOSES or a NPSAS (N01them Plains Sustainable Agriculture Society) conference.