KR102677271B1 - How to predict leaf water vapor pressure difference (VPD) using meteorological data - Google Patents

Abstract

The present technology relates to a technology for predicting the appropriate water vapor pressure difference of the leaves of crops to create optimal growth conditions for crops in smart farms, and more specifically, to a technology for optimizing the growth of crops. The method for predicting the water vapor pressure difference of leaves using weather data including air temperature and air humidity includes a learning data preparation step (SB1) for preparing measurement values measured at a weather station installed in a farm, leaf temperature prediction data, and water vapor pressure difference values of crop leaves; a learning model generation step (SB2) for generating a multilayer neural network learning model; and a learning step (SB3) for learning the data prepared at the learning data preparation step into the learning model generated in the learning model generation step. The data obtainable from the weather station installed in the farm is input into the artificial neural network learning model that has completed the learning step to predict the water vapor pressure difference value of crop leaves. According to the present invention, by predicting the water vapor pressure difference value of crop leaves grown in a farm using only weather data provided in the farm and controlling the ground and underground environments inside the smart farm, there is an effect in which crops inside the smart farm can grow well without stress.

Description

Leaf vapor pressure difference (VPD) prediction method using meteorological data{.}

This technology is about predicting the appropriate water vapor pressure difference between crop leaves to create optimal growth conditions for crops in smart farms. More specifically, it concerns technology for optimizing crop growth.

Prior art prior to the application of the present invention discloses a device for collecting plant growth environment data by measuring the temperature of plants. This technology is about an image processing system that can recognize the location of plants and a technology that can automatically measure the temperature value of the exact location using this.

Another prior technology is a technology that measures the temperature of leaves in a non-contact manner using color images and thermal images taken of plants. In this technology, the first step is to calculate mapping parameters between color images and thermal images using captured images of the same shot taken through a color camera and a thermal camera, and to target plants photographed through the color camera and thermal camera. A second step of acquiring a color image and a thermal image respectively, a third step of separating a leaf area with the corresponding color based on the color of the plant's leaf in the color image obtained in the second step, calculated in the first step A fourth step of setting an area corresponding to the leaf area in the color image in the thermal image based on the mapping parameters, and calculating the average temperature value for each pixel for the leaf area in the thermal image set in the fourth step. Thus, a technology including a fifth step of obtaining the leaf temperature of the plant is disclosed.

Public Patent Publication No. 10-2013-0035816 Public Patent Publication No. 10-2016-0145319

In existing smart farms, leaf temperature has been measured and used to determine whether photosynthesis and transpiration are occurring well. However, leaf temperature is only one of the indicators that can confirm whether photosynthesis is occurring well and is not a value that directly represents the amount of transpiration occurring inside the plant's leaves.

For this reason, accurate prediction of leaf VPD values is important. Depending on the value of Leaf VPD, the temperature and humidity inside the smart farm can be controlled, and the supply and irrigation of nutrient solution can be precisely controlled.

Leaf VPD to VPD (Vapor Pressure Deficit) Leaf VPD is the water vapor pressure difference of the leaves. Leaf VPD is an indicator of the transpiration state of the leaf. Leaf VPD is directly or indirectly related to leaf stomata opening, carbon dioxide absorption, water vapor evaporation, nutrient absorption in roots, and heat stress of crops.

As Leaf VPD increases, leaf stomata become smaller. As the pores become smaller, the absorption of carbon dioxide decreases and the amount of photosynthesis also decreases. As Leaf VPD increases, the crop absorbs more nutrients from the roots due to faster evaporation from the leaves due to the greater difference in vapor pressure between the leaves and the air, and the crop absorbs more nutrients from the leaves to the roots due to faster evaporation. This increases crop stress.

Therefore, if the water vapor pressure difference between leaves is accurately measured, the environment inside the smart farm can be adjusted at each stage of crop growth to control the water vapor pressure difference between crop leaves, thereby promoting crop growth more quickly.

Calculation of the water vapor pressure difference (Leaf VPD) of crop leaves is calculated in the following order, and air temperature, air humidity, and leaf temperature data are required.

- ASVP (Air Saturation Vapor Pressure) calculation

ASVP(kPa) = 0.61078 x e^( Ta / ( Ta + 233.3) x 17.2694 ) )

※ Ta(℃): Ambient temperature

- LSVP (Leaf Saturation Vapor Pressure) calculation

LSVP(kPa) = 0.61078 x e^( Tc / ( Tc + 233.3) x 17.2694 ) )

※ Tc(℃): Leaf temperature

- LVPD calculation

LVPD(kPa) = LSVP - (ASVP * RH/100)

※ RH(%): Atmospheric humidity

In the above calculation process, a measured value of leaf temperature is required, but measuring leaf temperature is not easy. In the present application, the results of predicting the water vapor pressure difference (Leaf VPD) of crop leaves using the MLP model using leaf temperature data and the results of predicting the water vapor pressure difference (Leaf VPD) of crop leaves without leaf temperature data are provided in smart farms. We aim to precisely control the temperature, humidity, and nutrient solution supply inside the smart farm by predicting the water vapor pressure difference (Leaf VPD) of crop leaves using only environmental measurement data that is constantly being measured.

The means to solve the above problems are as follows.

In the method of predicting the difference in water vapor pressure of leaves using meteorological data,

A learning data preparation step (S1) that prepares measurements from a weather station installed on the farm, leaf temperature data, and water vapor pressure difference values of crop leaves; and

Learning model generation step (S2) to generate a multi-layer neural network learning model; and

A learning step (S3) of learning the data prepared in the learning data preparation step with the learning model created in the learning model generation step; and

A method for predicting the water vapor pressure difference of leaves using meteorological data is provided, which involves predicting the water vapor pressure difference value of crop leaves by inputting data obtainable from a weather station installed on the farm to the artificial neural network learning model that has completed the learning step.

In addition, the learning model creation step provides a method of predicting the water vapor pressure difference of leaves using meteorological data, which means setting model hyperparameters.

In addition, the model hyperparameters include a loss function, activation function, learning rate, and number of hidden layers. A method for predicting the water vapor pressure difference of leaves using meteorological data is provided.

In addition, a method for predicting the difference in water vapor pressure of leaves using meteorological data is provided, wherein the meteorological data are atmospheric temperature and atmospheric humidity.

In addition, in another embodiment

In the method of predicting the difference in water vapor pressure of leaves using meteorological data,

A learning data preparation step (SA1) that prepares measured values from a weather station installed on the farm and water vapor pressure difference values of crop leaves; and

Learning model generation step (SA2) to generate a multi-layer neural network learning model; and

A learning step (SA3) of learning the data prepared in the learning data preparation step with the learning model created in the learning model generation step; and

A method for predicting the water vapor pressure difference of leaves using meteorological data is provided, which involves predicting the water vapor pressure difference value of crop leaves by inputting data obtainable from a weather station installed on the farm to the artificial neural network learning model that has completed the learning step.

In addition, in another embodiment

In the method of predicting the difference in water vapor pressure of leaves using meteorological data,

Learning data preparation step (SB1), which prepares measured values from a weather station installed on the farm, leaf temperature prediction data, and water vapor pressure difference values of crop leaves; and

Learning model generation step (SB2) to generate a multi-layer neural network learning model; and

A learning step (SB3) of learning the data prepared in the learning data preparation step with the learning model created in the learning model generation step; and

A method for predicting the water vapor pressure difference of leaves using meteorological data is provided, which involves predicting the water vapor pressure difference value of crop leaves by inputting data obtainable from a weather station installed on the farm to the artificial neural network learning model that has completed the learning step.

In addition, the leaf temperature prediction data uses air temperature, solar radiation, and leaf temperature measurement data as input variables, and uses the following leaf temperature prediction regression equation to calculate leaf temperature as a function of air temperature and solar radiation. The air temperature measured at the weather station installed on the farm is Provides a method for predicting the water vapor pressure difference in leaves using meteorological data, which is calculated from solar radiation (leaf temperature prediction regression equation = 9.651772156859273 + (0.46214678+0.08514499 ) * air_temp (air temperature) + 0.00351328 * solar_radiation (solar radiation))

In addition, the leaf temperature prediction data is an MLP model created as a result of learning an MLP artificial intelligence learning model using air temperature, air humidity, solar radiation, and leaf temperature measurement data as input variables, and the air temperature and air temperature measured at the weather station installed on the farm. A method for predicting the water vapor pressure difference of leaves using meteorological data is provided, which uses predicted leaf temperature values calculated as output by inputting humidity and solar radiation.

According to the above-mentioned configuration of the present application, the water vapor pressure difference value of the leaves of crops grown on the farm is predicted using only the weather data provided on the farm, and the above-ground and underground environments inside the smart farm are controlled, so that the crops inside the smart farm are stress-free. It is an invention that is effective in growing well.

In addition, considering the weak or strong characteristics depending on the condition or cultivation stage of the crop or the characteristics of the crop, the above-ground part and It has the effect of creating an underground environment. In other words, depending on the crop, the above-ground and below-ground environments are adjusted to be slightly higher for crops that can tolerate high water vapor pressure differences between plant leaves, and slightly lower for crops that can tolerate low water vapor pressure differences between plant leaves, and depending on the cultivation stage, the water vapor pressure of crop leaves is adjusted appropriately. By controlling the car, a healthy smart farm above-ground and underground cultivation environment can be created.

Figure 1 shows the Leaf VPD (water vapor pressure difference of crop leaves) calculation formula of the present invention.
Figure 2 is a VPD chart when the temperature difference between the plant and the air is 0 in relation to the Leaf VPD of the present invention.
Figure 3 shows the results of predicting the water vapor pressure difference of crop leaves using the MLP learned model for predicting water vapor pressure difference of crop leaves, which was learned using the air temperature, atmospheric humidity, solar radiation, and leaf temperature of the present invention as learning data.
Figure 4 shows the results of predicting the water vapor pressure difference of crop leaves using the MLP learned model for predicting water vapor pressure difference of crop leaves, which was learned using the air temperature, atmospheric humidity, and solar radiation of the present invention as learning data.
Figure 5 shows the results of predicting the water vapor pressure difference of crop leaves using the MLP learned model for predicting water vapor pressure difference of crop leaves, which was learned using the air temperature, atmospheric humidity, solar radiation, and leaf temperature prediction data of the present invention as learning data.
Figure 6 shows the results of predicting the leaf temperature of crops using the MLP learned model for predicting leaf temperature of crops, which was learned using the air temperature, atmospheric humidity, and leaf temperature data of the present invention as input.

The effects of the invention of this application are explained using the drawings as follows.

Figure 1 shows the Leaf VPD (water vapor pressure difference of crop leaves) calculation formula of the present invention. The method is to first calculate the atmospheric saturated vapor pressure (ASVP), then calculate the leaf saturated vapor pressure, and then calculate the difference. At this time, calculation is possible only if you know the leaf temperature.

Leaf VPD to VPD (Vapor Pressure Deficit) Leaf VPD is the water vapor pressure difference of the leaves. Leaf VPD is an indicator of the transpiration state of the leaf. Leaf VPD is directly or indirectly related to leaf stomata opening, carbon dioxide absorption, water vapor evaporation, nutrient absorption in roots, and heat stress of crops.

As Leaf VPD increases, leaf stomata become smaller. As the pores become smaller, the absorption of carbon dioxide decreases and the amount of photosynthesis also decreases. As Leaf VPD increases, the crop absorbs more nutrients from the roots due to faster evaporation from the leaves due to the greater difference in vapor pressure between the leaves and the air, and the crop absorbs more nutrients from the leaves to the roots due to faster evaporation. This increases crop stress.

Therefore, if the water vapor pressure difference between leaves is accurately measured, the environment inside the smart farm can be adjusted at each stage of crop growth to control the water vapor pressure difference between crop leaves, thereby promoting crop growth more quickly.

In order to calculate the water vapor pressure difference of the leaf, the leaf temperature must be measured. Methods for measuring leaf temperature include contact measurement using a temperature sensor, and recently, remote measurement technologies such as infrared thermometry or thermal imaging have been used. However, in order to measure the leaf temperature that represents the cultivation state, the crop at the representative location must be measured in an appropriate manner using a thermometer or thermal imaging camera to measure the accurate leaf temperature. Therefore, it is necessary to purchase equipment for measurement and install the equipment. It can be said that it is a costly measurement that requires a lot of manpower to measure the leaves used. However, if the water vapor pressure difference between crop leaves can be accurately measured using the leaf temperature measured at such a cost, environmental control of the above-ground and underground parts of the smart farm can be optimized.

It is not desirable for the water vapor pressure difference between the crop leaves to be maintained constant, but it is helpful for the healthy growth of the crop to be appropriately adjusted depending on the growth stage of the crop.

Generally, about 0.8 to 1.2 kPa (kilopascals) is good for crop growth. However, maintaining a slightly different water vapor pressure difference between crop leaves depending on the growth stage may be better for crop growth.

After germination, the early crop cannot handle much stress as the plant struggles to take root during the clone stage, which is also known as the baby plant stage. In other words, the low water vapor pressure difference between plant leaves required for survival is appropriate (0.8 kPa).

Additionally, crops in the growth stage are larger and stronger than baby plants, so they can withstand a relatively high difference in water vapor pressure between the crop leaves. Nevertheless, at high water vapor pressure differences in crop leaves, the plant's stomata may close, reducing the absorption of carbon dioxide, making photosynthesis difficult. This is because carbon dioxide absorption plays an important role in the growth stage, and the water vapor pressure difference between crop leaves is 1.0 kPa to maintain stomata opening.

During the flowering period, the plants are strong enough, but since the flowers are sensitive, it is not good to have too much humidity. The appropriate water vapor pressure difference between crop leaves at this time is 1.2 to 1.5 kPa. In other words, 1kPa is appropriate when photosynthesis is required, and around 1.5kPa is appropriate during the flowering period because the moisture around the crop must be low.

Figure 2 is a VPD chart when the temperature difference between the plant and the air is 0 in relation to the Leaf VPD of the present invention.

This table calculates the difference in water vapor pressure between crop leaves according to relative humidity and temperature when there is no temperature difference between the crop and the atmosphere.

Figure 3 shows the results of predicting the water vapor pressure difference of crop leaves using the MLP learned model for predicting water vapor pressure difference of crop leaves, which was learned using the air temperature, atmospheric humidity, solar radiation, and leaf temperature of the present invention as learning data.

The data used to create the model were temperature, humidity, and leaf temperature values from the moisture stress index (CWSI) data (2021.07.19 ~ 2021.07.30) provided by the Rural Development Administration. This is the result of comparing the predicted and true values of the model created by learning the MLP learning model to predict the water vapor pressure difference of crop leaves using air temperature, atmospheric humidity, and leaf temperature as input data. The RMSE value is 0.05, showing very accurate results.

The RMSE is called Root Mean Squared Error (RMSE), and measures the average difference between the value predicted by the prediction model and the actual value. It is a representative value that estimates how well a prediction model can predict the target value (accuracy). It can be said that the smaller the error, the better the prediction model predicts the target value.

In the invention of this application, MLP was used as a learning model. MLP (Multi-Layer Perceptron) is a type of artificial neural network used in supervised learning. MLP typically includes at least one nonlinear hidden layer, and these layers help extract complex patterns from training data. MLP is mainly applied to classification and regression problems, and the backpropagation learning method is mainly used as its learning algorithm.

Recently, due to the influence of deep learning, the number of nonlinear hidden layers tends to increase, and the input of nonlinear hidden layers also tends to increase. As the number of hidden layers and the number of nodes in each hidden layer increases, the amount of data required to learn the node must also sufficiently increase to accurately learn the node. In other words, the deeper the deep learning module, the more big data is needed. However, because the amount of data used in the invention of this application was not large, the number or number of nodes in the hidden layer could not be increased as much as in deep learning. Nevertheless, optimal learning results were obtained through simulation.

The learning model in FIG. 3 used air temperature, atmospheric humidity, leaf temperature, and water vapor pressure difference values of crop leaves calculated using the equation shown in FIG. 1 as learning data. The artificial intelligence learning model used the MLP model, and the above learning data was preprocessed to normalize the mean and standard deviation so that there was no difference in the learning results based on the data. Model hyperparameters for model learning: adam, relu, lr = 0.01, layers = (6, 6, 3).

Here, adam represents the optimization parameter, relu represents the activation function, Ir represents the learning rate, layers represent the hidden layer, and (6,6,3) represents the first hidden layer with 6 nodes and the second hidden layer with 6 nodes. It indicates that the node and the third hidden layer are an artificial neural network model structure with three nodes.

Figure 4 shows the results of predicting the water vapor pressure difference of crop leaves using the MLP learned model for predicting water vapor pressure difference of crop leaves, which was learned using the air temperature, atmospheric humidity, and solar radiation as learning data of the present invention.

It differs from the model in Figure 3 in that it uses the learning results by subtracting the leaf-on data from the learning data. This model has an RMSE of 0.15, which is about 0.1 different from the model in Figure 3.

The learning model in FIG. 4 used air temperature, atmospheric humidity, and water vapor pressure difference values of crop leaves calculated using the formula shown in FIG. 1 as learning data. The artificial intelligence learning model used the MLP model, and the above learning data was preprocessed to normalize the mean and standard deviation so that there was no difference in the learning results based on the data. Model hyperparameters for model learning: adam, relu, lr = 0.01, layers = (2, 4, 4, 4).

Here, adam represents the optimization parameter, relu represents the activation function, Ir represents the learning rate, layers represent the hidden layer, (2, 4, 4, 4) represents 2 nodes for the first hidden layer, and 2 nodes for the second to fourth hidden layers. It indicates that the layers are an artificial neural network model structure with four nodes each. You can see that the predicted value appears slightly lower in the peak value compared to the true value.

Figure 5 shows the results of predicting the water vapor pressure difference of crop leaves using the MLP learned model for predicting water vapor pressure difference of crop leaves, which was learned using the air temperature, atmospheric humidity, solar radiation, and leaf temperature prediction data of the present invention as learning data.

There is a difference from the models in FIGS. 3 and 4 in that the leaf temperature is not a measured value, but a value predicted by the leaf temperature using a leaf temperature prediction model. This model has an RMSE of 0.1, which is about 0.05 larger in error compared to the model in Figure 3, and has a smaller error of about 0.05 compared to the model in Figure 4.

Figure 6 shows the results of predicting the leaf temperature of crops using the MLP learned model for predicting leaf temperature of crops, which was learned using the air temperature, atmospheric humidity, and leaf temperature data of the present invention as input. As mentioned above, it is most accurate to measure the leaf temperature of a crop using a measuring device, but even in specific cases, there may be measurement errors depending on who measures which leaf of the crop is located at which location in the smart farm, so the actual leaf temperature cannot be measured. This may not necessarily be the best way to calculate the exact water vapor pressure difference between crop leaves.

In the invention of this application, the temperature of the leaves of crops was created by using a regression equation using the air temperature and solar radiation, which can affect the leaf temperature. This regression equation is

Crop leaf temperature = 9.651772156859273 + (0.46214678+0.08514499 ) * air_temp

+ 0.00351328 * solar_radiation

It is displayed as The regression equation obtained in this way was used to learn the model in Figure 5.

In addition, as can be seen from the above, since air temperature and solar radiation are variables, an MLP model for predicting leaf temperature was also obtained using air temperature, solar radiation, and actually measured leaf temperature. This model used air temperature, atmospheric humidity, and solar radiation as input data for learning, and the model hyperparameters used for model learning were adam, relu, lr = 0.01, layers = (9, 9, 9).

The prediction error of the model was RMSE = 0.776. Very highly accurate results were obtained. The peak value appeared slightly lower than the true value. It can be seen that this is very similar to the result in which the model in FIG. 5 inputs the leaf temperature prediction result value and the predicted value is slightly lower compared to the true value.

The difference in water vapor pressure between crop leaves is an indicator that is related to the amount of photosynthesis of cultivated crops and also affects the absorption of nutrients and moisture by roots. Since the ultimate goal of smart farms is to create optimal growth conditions for each stage of crop growth, the water vapor pressure difference between crop leaves can be said to be an essential growth measurement indicator to achieve this goal. Being able to predict the difference in water vapor pressure of the crop leaves using only air temperature, atmospheric humidity, and solar radiation, which is essential for smart farms or farms, can be evaluated as a very groundbreaking technology.

This is a technology that previously could only be calculated by measuring leaf temperature, but was modeled using an artificial intelligence MLP learning model to model a non-linear relationship. This is a technology that provides differentiation in composition and remarkable effectiveness in a way that was completely unexpected by a person in the field. no see.

The composition of the invention having the above excellent effects is as follows.

In the method of predicting the difference in water vapor pressure of leaves using meteorological data,

A learning data preparation step (S1) that prepares measurements from a weather station installed on the farm, leaf temperature data, and water vapor pressure difference values of crop leaves; and

A learning model creation step (S2) that generates a multi-layer neural network learning model; and

A learning step (S3) of learning the data prepared in the learning data preparation step with the learning model created in the learning model generation step; and

A method for predicting the water vapor pressure difference of leaves using meteorological data is provided, which involves predicting the water vapor pressure difference value of crop leaves by inputting data obtainable from a weather station installed on the farm to the artificial neural network learning model that has completed the learning step.

In addition, the learning model creation step provides a method of predicting the water vapor pressure difference of leaves using meteorological data, which means setting model hyperparameters.

In addition, the model hyperparameters include a loss function, activation function, learning rate, and number of hidden layers. A method for predicting the water vapor pressure difference of leaves using meteorological data is provided.

In addition, a method for predicting the difference in water vapor pressure of leaves using meteorological data is provided, wherein the meteorological data are atmospheric temperature and atmospheric humidity.

In addition, in another embodiment

In the method of predicting the difference in water vapor pressure of leaves using meteorological data,

A learning data preparation step (SA1) that prepares measured values from a weather station installed on the farm and water vapor pressure difference values of crop leaves; and

Learning model generation step (SA2) to generate a multi-layer neural network learning model; and

A learning step (SA3) of learning the data prepared in the learning data preparation step with the learning model created in the learning model generation step; and

A method for predicting the water vapor pressure difference of leaves using meteorological data is provided, which involves predicting the water vapor pressure difference value of crop leaves by inputting data obtainable from a weather station installed on the farm to the artificial neural network learning model that has completed the learning step.

In addition, in another embodiment

In the method of predicting the difference in water vapor pressure of leaves using meteorological data,

Learning data preparation step (SB1), which prepares measured values from a weather station installed on the farm, leaf temperature prediction data, and water vapor pressure difference values of crop leaves; and

Learning model generation step (SB2) to generate a multi-layer neural network learning model; and

A learning step (SB3) of learning the data prepared in the learning data preparation step with the learning model created in the learning model generation step; and

A method for predicting the water vapor pressure difference of leaves using meteorological data is provided, which involves predicting the water vapor pressure difference value of crop leaves by inputting data obtainable from a weather station installed on the farm to the artificial neural network learning model that has completed the learning step.

In addition, the leaf temperature prediction data uses air temperature, solar radiation, and leaf temperature measurement data as input variables, and uses the following leaf temperature prediction regression equation to calculate leaf temperature as a function of air temperature and solar radiation. The air temperature measured at the weather station installed on the farm is Provides a method for predicting the water vapor pressure difference in leaves using meteorological data, which is calculated from solar radiation (leaf temperature prediction regression equation = 9.651772156859273 + (0.46214678+0.08514499 ) * air_temp (air temperature) + 0.00351328 * solar_radiation (solar radiation))

In addition, the leaf temperature prediction data is an MLP model created as a result of learning an MLP artificial intelligence learning model using air temperature, air humidity, solar radiation, and leaf temperature measurement data as input variables, and the air temperature and air temperature measured at the weather station installed on the farm. A method for predicting the water vapor pressure difference of leaves using meteorological data is provided, which uses predicted leaf temperature values calculated as output by inputting humidity and solar radiation.

Claims (8)

delete delete delete delete delete In the method of predicting the difference in water vapor pressure of leaves using meteorological data including air temperature and atmospheric humidity,
Learning data preparation step (SB1), which prepares measured values from a weather station installed on the farm, leaf temperature prediction data, and water vapor pressure difference values of crop leaves; and
Learning model generation step (SB2) to generate a multi-layer neural network learning model; and
A learning step (SB3) of learning the data prepared in the learning data preparation step with the learning model created in the learning model generation step; and
The water vapor pressure difference value of crop leaves is predicted by inputting data that can be obtained from a weather station installed on the farm into the artificial neural network learning model that has completed the learning step above,
The leaf temperature prediction data uses air temperature, solar radiation, and leaf temperature measurement data as input variables, and uses the following leaf temperature prediction regression equation to calculate leaf temperature as a function of air temperature and solar radiation. The air temperature measured at the weather station installed on the farm is Calculated from solar radiation,
The learning model creation step means setting model hyperparameters, and the model hyperparameters include a loss function, activation function, learning rate, and number of hidden layers. A method for predicting water vapor pressure difference in leaves using meteorological data.
(Leaf temperature prediction regression equation = 9.651772156859273 + (0.46214678+0.08514499 ) * air_temp (air temperature) + 0.00351328 * solar_radiation (solar radiation)) delete delete