Background

Before we started our wet lab experiments with the hydroponic system, we wanted to know how different plants, especially crops, grow in different pH environments. Therefore, we used a model to fit crop yield under different pH. We found data of 7 different crops, where each crop was tested in 5 different pH.

Objective

The purpose of our project is to increase the hydroponic system's effectiveness. We built a model to predict the varying yield of plants in different pH conditions by analyzing how different plants grow in different pH situations, with pH being one of the key factors.

Model’s assumptions

1. pH influences plant growth in hydroponic systems the same way it does in soil

2. The pH influence can be fitted by a quadratic model (with one turning point)

3. The data collected with pH 4.7-7.5 is representative and the range is adequate for the model

4. No factors other than pH level is influencing the plant growth in the data set

Data

Relative yield of crops under different pH, from Simth and Doran 1996

Crop	pH
	4.7	5	5.7	6.8	7.5
	Releative Average Yield
Corn	34	73	83	100	85
Wheat	68	78	89	100	99
Oat	77	93	99	98	100
Barley	0	23	80	95	100
Alfalfa	2	9	42	100	100
Soybean	65	79	80	100	93
Timothy	31	47	66	100	95

Methods & parameters

Data was fitted with Matlab Polynomial Models tools (polynomial regression model):

In relation to the value of an independent variable x(pH value), it uses the predicted value of a dependent variable y(yield). Meanwhile, p is the multinomial coefficient, n represents the degree and the i represents the number samples.

To avoid overfitting of the result, we here fit our model with only 2nd degree polynomial model:

where y represents the plant's yield and x represents the pH values. By having this linear relationship, we could make a curve to clearly see the result.

Data was fitted to a polynomial, and estimated the 95% prediction intervals and the roots of the fitted polynomial (Polynomial confidence intervals model):

When the p represents the unknown mean function estimated by the fit, l lower confidence bound and u represents the upper confidence bound.

By default, the interval [ln+1(xn+1), un+1(xn+1)] is a 95% confidence bound on yn+1(xn+1). Where x represents the crops yield and y represents the pH values.

Result

As shown in the results (Fig. 1), we found that most of the major crops have a better yield when pH is around 6-7 (neutral). Some crops, such as barley and alfalfa are more sensitive to the acidic pH and thereby could be more beneficial with our genetic pH shooting (adjusting) system.

Looking at the graph (Fig. 2), we could also see the trends of the yields of different crops. Although the range of the confidence intervals is not so thin, but the total trend shows a clear linear relationship between the different pH evironment.

Conclusion

This model supports the concept of using pH shooting systems to adjust the pH in the hydroponic system. By introducing genetic modified bacteria to adjust the pH automatically, we can hopefully increase the yield of the hydroponics.

Reference

1. South Dakota Soil Health Coalition Soil pH
2. The MathWorks Polynomial Models
3. The MathWorks Polyconf

Objective

Our modelling goal is to calculate how much carbon emissions from imported vegetables could be reduced by our project, which is a hydroponic system specially designed for plant growth and carbon reduction, if our project is implemented for our home city of Macau. By comparing the carbon emissions from imported vegetables by Macau including the factors of planting with soil and the transportation with those from locally grown vegetables using hydroponics only considers the factor of planting with hydroponics) and assuming the percentage of different Macau commercial, residential sites agreeing to use our hydroponics machine, we can reach the goal and let the citizens, society and even the government of Macau realize the importance of carbon reduction, and contribute to Macau's environmental protection.

Assumptions

1. The percentage of Macau commercial, residential sites agreeing to use the hydroponics machines of our project is 5%, 10%, 25%, 50% respectively.
2. The land occupation rate of the original installation of our hydroponic system is 50%.
3. The success rate of growing vegetables in hydroponics is 50%.
4. The varieties of all grown vegetables are with a weight of 10g and a growth cycle of one month.
5. The data on imported vegetables of Macau can be extrapolated from Hong Kong's data.

Modelling Process

1. Data Integration of imported vegetables

Because the Macau government hasn't presented data on imported goods to the public, at this time, the data from Hong Kong, which is adjacent to Macau and is also a special administrative region, will serve as a reference.

According to the import merchandise trade statistics of the Hong Kong Census and Statistics Department for February 2010, the following chart about Hong Kong’s imported vegetables per two months can be drawn (Figure 1):

Imported From	Quantity(two months)
Mainland China	630622
Turkey	19925
Taiwan	10901
Total	661448

Figure 1: Vegetable products used for human foods per two months in Hong Kong (kg)

Comparing the population of Hong Kong, 7,401,500, with the population of Macau, 682,070, and by halving the data above, the amount the imported vegetables of Macau per one month can be estimated(Figure 2):

Imported From	Quantity(one month)
Mainland China	29056.8
Turkey	918.1
Taiwan	502.3
Total	30477.2

Figure 2: Estimated vegetable products used for human foods per one month in Macau (kg)

By measuring the distances between the three importing places and Macau and multiplying them by the carbon emissions of 435g CO2/ton-km from transportation, the transportation carbon emissions of the three places per month can be obtained, as shown in Figure 3.

Imported From	Carbon Emissions
Mainland China	1415.6
Turkey	2992.4
Taiwan	168.1
Total	4576.1

Figure 3: Carbon emissions of vegetable transportation to Macau per month (kg)

The carbon emission of producing one kilogram of vegetables is 0.7kg. By multiplying this by the weight of imported vegetables, we can obtain the carbon emissions from the cultivation of imported vegetables in the three places. Then, adding the carbon emissions of planting to the carbon emissions of transportation, we obtained the total carbon emissions of imported vegetables. As shown in Figure 4 and 5.

Imported From	Carbon Emissions
Mainland China	21755.4
Turkey	3635.1
Taiwan	519.7
Total	25910.2

Figure 4: The total Carbon Emissions per month(kg)

2. Data Integration of hydroponics (our project)

According to the information of the Macau Cartography and Cadastre Bureau, the existing commercial and residential land in Macau is 3.1 square kilometers. We multiplied this by the different estimated percentages of households that would agree to use our hydroponics home kit. As shown in the figure 6.

Agreed Percentage(assume)	Area
5%	0.2
10%	0.3
25%	0.8
50%	1.6

Figure 6: the Available Area (km2)

Model building

The monthly demand for vegetables in Macau is 30477.2kg and all of them are imported. Therefore, to calculate the carbon emission from hydroponics planting enough to supply Macau's daily needs, it can be obtained by multiplying the carbon emission of one kilogram of vegetables by hydroponic cultivation, 0.158kg by 30477.2kg, which equals 4815.4kg.

Our hydroponic machine takes up an area of 168cm^2 to grow one vegetable plant. By combining the occupancy rate of the original device, the success rate of hydroponics and the weight of a vegetable, it can be obtained how many kilograms of vegetables can be grown in different areas, as shown in Figure 7.

By multiplying the data shown in Figure 7 with the carbon emission 0.158kg required to grow one kilogram of vegetables in hydroponics, excluding the influence of the success rate, the carbon emission under different consent rates can be obtained, and figure 8 is established.

Results

From figure 7, it can be seen that when the approval rate is 10%, the quantity of vegetables grown by hydroponic method is 46131kg, which can fully meet the needs of Macau, and even 15654kg more. At this time, it can be seen from Figure 8 that the carbon emissions, 14,577kg, are nearly 12,000 kg less than those of imported vegetables. When consent rate is 25% or 50%, carbon emissions exceed the carbon emissions of imported vegetables, but at the same time their output far exceeds the imported. This proves that Macau can easily reduce carbon emissions by deploying our hydroponics in a very small area without much difficulty in implementation and promotion. This shows that our project can definitely effectively establish a green Macau, and even a green earth, and contribute to all mankind.

References

1. Cartography and Cadastre Bureau
2. Hong Kong Merchandise Trade Statistics Imports
3. A roadmap for decarbonizing logistics?
4. The Carbon Footprint of Food