Assessment and Prediction of Maize Production Considering Climate Change by Extreme Learning Machine in Czechia

Abstract

Machine learning algorithms have been applied in the agriculture field to forecast crop productivity. Previous studies mainly focused on the whole crop growth period while different time windows on yield prediction were still unknown. The entire growth period was separated into each month to assess their corresponding predictive ability by taking maize production (silage and grain) in Czechia. We present a thorough assessment of county-level maize yield prediction in Czechia using a machine learning algorithm (extreme learning machine (ELM)) and an extensive set of weather data and maize yields from 2002 to 2018. Results show that sunshine in June and water deficit in July were vastly influential factors for silage maize yield. The two primary climate parameters for grain maize yield are minimum temperature in September and water deficit in May. The average absolute relative deviation (AARD), root mean square error (RMSE), and coefficient (R2) of the proposed models are 6.565–32.148%, 1.006–1.071%, 0.641–0.716, respectively. Based on the results, silage yield will decrease by 1.367 t/ha (3.826% loss), and grain yield will increase by 0.337 t/ha (5.394% increase) when the max temperature in May increases by 2 °C. In conclusion, ELM models show a great potential application for predicting maize yield.

1. Introduction

Climate change has established its reality on affecting temperatures and precipitation, with much evidence confirming the increase of global temperature and change in the rainfall rates. The changes in the temperature and precipitation often come in the form of heat waves, changes in frequency and intensity of precipitation, or other extreme events. Over the last century, studies have shown an increase in global temperatures [1] and alterations in rainfall patterns. The precipitation shifts are twofold: first is “wet get wetter, dry get drier,” and the second is a change in storms that should move away from the equator toward the poles [2].

Climate change is causing an impact on food production, and maize is no exception [3]. Temperature and precipitation are the two main climate factors influencing maize productivity. It will be reduced when extreme temperature events occur during pollination and are further exaggerated when there are water deficits. During the grain-filling period, warm temperatures above the upper threshold cause a reduction in yield. Model estimates suggest that for every 1 °C increase in temperature, there is nearly a 10% yield reduction [3]. Tigchelaar et al. (2018) predicted maize production under the climate change scenarios, and found that maize yields will decrease about 20–40% and 40–60% if a temperature increase of 2 and 4 °C, respectively [4]. According to the employed statistical model heat stress and lack of participation can cause the observed global variability from 50% in 1980–2010. Observed and predicted extreme climate events would bring losses to world maize production (ten years return in the given period), with 1.5 °C global warming levels (the 2020s). The scenario with a 2 °C temperature increase (the late 2030s) shows that maize production will suffer from heat stress and drought with no historical parallel [5].

Machine learning (ML) allows independent learning and improves from experience via iterative training [6]. It has been applied in the agriculture field to increase the quality and productivity of the crops. It has been proved that ML has powerful performance in data mining and agricultural analyses, such as classifying crop types and yield prediction [7,8,9,10]. Crop yield can be predicted based on different historical available data, including weather parameters, soil parameters, and historical crop yield [11], as well as optical, fluorescence, thermal satellite data [12] and nitrogen loss [13]. Recently, different ML models for crop yield prediction have been developed with various input parameters. Mainly, three ML approaches (decision tree, Naïve Bayes Classifier, and K-nearest neighbor) were used to classify the soils and estimate rice yield by Singh et al. [14]. They also proposed the support vector machine and rule-based induction have the potential application to obtain better accuracy. Panda et al. [15] initially constructed predictive models for agriculture crop yield through Back-propagation Neural Network models combined with four vegetation indices. Sharifi [16] established a model for integrating field data, remote sensing data and meteorological data using four machine learning methods to predict barley production in Iran, and found that the gaussian process regression algorithm performed the best results. What’s more, Sharifi [17] reported the use of Sentinel-2 data for predicting maize nitrogen update in three different farms to develop an array of precision agriculture applications. However, Mupangwa et al. [18] found that linear discriminant analysis algorithm was the best tool, and SVM was the worst algorithm in maize yield prediction under conservation agriculture in Eastern and Southern Africa. Abbas et al. [19] employed four ML algorithms, including linear regression (LR), support vector regression (SVR), k-nearest neighbor (k-NN), elastic net (EN), to forecast the yield of potato tuber based on the soil data and crop properties from proximal sensing. Among the ML techniques, extreme learning machine (ELM), a novel type of learning algorithm with exceptional speed and excellent generalization abilities [20], has been increasingly considered by researchers in various fields.

Besides, some researchers also implemented various ML approaches for crop yield forecasting by climate variables in recent years. In 2014, Veenadhari et al. [21] applied a kind of decision tree technique to find out the dominant climate parameter for crop yields, and the incredible accuracy of predictions showed the potential power of the algorithm in forecasting the crop yield. In 2018, the deep neural network was utilized for crop yield prediction underlying the climate data by Crane-Droesch A. [22], and results showed that climate change has considerable negative impacts on corn yield. Hoffman et al. [23] explored the relation between crop yields and scale-compatible climate data for the 1962–2014 period using Random Forest from sub-Saharan Africa. Vogel et al. [24] studied the impacts of climate extremes on yield anomalies of maize, soybeans, rice, and spring wheat at the global scale using sub-national yield data and applying a machine-learning algorithm. Chemura et al. [25] used extreme gradient boosting, a machine learning approach to model the current climatic suitability for maize, sorghum, cassava and groundnut in Ghana using yield data and agronomically important variables. Fan et al. [26] provided an alternative tool for prefecture level users using an aggregate Z-index which uses precipitation as an input in random forest to predict rice and maize yield in Sichuan Province, China.

In the recent decade (2011–2019), the average temperature increased by 0.7 °C, and the average precipitation decreased by 88 mm compared to the last decade (2001–2010) in Czechia. Meanwhile, the maize yield rate slightly decreased from 7.73 t/ha (2001–2010) to 7.67 t/ha (2011–2019). This decrease can be significant when considering the improvement of technological and management of maize production. Therefore, the objectives of this study were (1) to assess the influence of climate factors on maize yield (both grain and silage) by ELM in Czechia; (2) to establish a predictive model for maize prediction using the ELM algorithm considering various climate parameters.

2. Materials and Methods

2.1. Data Collection

We selected nine regions for a detailed study on maize production (both grain and silage) from 2002–2018: Liberec, Moravian-Silesian, South Moravian, Usti nad Labem, Vysočina, Plzen, South Bohemia, Central Bohemia, and Prague. The data of maize yields for maize production (both for grain and silage) of the nine selected regions from 2002 to 2018 were obtained from the Institute of Agricultural Economics and Information (IAEI, http://www.iaei.cz (accessed on 1 July 2021)). The temperatures and rainfall data from 2002 to 2018 come from the Czech Hydrometeorological Institute (CHMI, http://portal.chmi.cz/historicka-data/pocasi/uzemni-srazky?l=en (accessed on 1 July 2021)). The data on daily average, maximum and minimum air temperature, relative humidity, daily total precipitation, and duration of sunshine cover from 2002 to 2018 were collected from the nine selected stations for the nine studied regions. The maize yield from 2002–2018 was collected from the Czech Statistical Office (https://www.czso.cz (accessed on 1 July 2021)) The water deficit data was calculated based on the Czech technical norm (ČSN 750434), which uses standardized temperatures (ST) according to the long-term averages. Detailed calculation of water deficit was provided in Supporting Information 1.

2.2. Theory of Extreme Learning Machine (ELM)

The ELM is a novel evolutionary machine learning technique coined by Huang et al. [27]. It overcomes the shortcomings of traditional neural networks, particularly, slow learning rate and easy to fall into local minima [28]. In the learning procedure, the weights between the input layer and the hidden layer as well as the bias between different hidden layer neurons can be randomly generated without iterative adjustments, and then the optimal global solution can be gained by setting the number of hidden layer neurons [29,30]. Figure 1 described the network structure of ELM, including three layers which are input, hidden, and output layers, respectively. The input layer has l input variables (x₁, x₂, …, x_l,), and m neurons in the hidden layer; the output layer has one desired variable (y). The specific steps of the ELM algorithm are expressed as follows:

Randomly generated the input weights (w_ij) between the input layer and hidden layer and the bias (b_m) between hidden neurons;

Confirm the number of hidden layer neurons and activation function g(x) and calculate the connection weights (βjk) for the hidden and output layer as well as the output matrix of hidden layer H (Equation (1)). The connection weights matrix is β (Equation (2)), and the desired matrix notes y. Then the ELM network with m neurons can be expressed as Equation (3)

$$\begin{gathered} \mathrm{H} = (w_1,\dots ,w_m,x_1,\dots ,x_l,b_1,\dots ,b_m) = \\ {\left[\begin{array}{c}g\left(w_1\times x_1+b_1\right), g\left(w_2\times x_1+b_2\right)\dots \dots g\left(w_m\times x_1+b_m\right)\\ \dots \dots \dots \\ g\left(w_1\times x_l+b_1\right), g\left(w_2\times x_1+b_2\right)\dots \dots g\left(w_m\times x_l+b_m\right)\end{array}\right]}_{l\times m} \end{gathered}$$

(1)

$$\mathrm{B}=[{\beta }_1^T,\dots ,{\beta }_l^T]$$

(2)

Hβ = y

(3)

Calculate the output weights matrix ($\widehat{\beta }$) of output layer: $\widehat{\beta }=H^{+}y,$ where $H^{+}$ is the Moore–Penrose generalized inverse matrix of H.

2.3. Description of Selected Descriptors and Data Analysis

It is known that the silage and grain maize have different growing seasons in the Czech Republic, where the growing season for silage maize contains four months, from May to August, while five months for grain maize between May and September. Therefore, the climate indexes of each month in their growing seasons were employed to build predictive models. The average values of each month were calculated by the collected data of daily average, maximum and minimum air temperature, relative humidity, daily total precipitation, duration of sunshine. As a result, seven types of descriptors, namely water deficit, precipitation, average temperature (Temp. Mean), maximal temperature (Temp. Max), minimal temperature (Temp. Min), humidity, and sunshine of each month during the growing seasons of silage and grain maize were obtained. In summary, the descriptors for modeling the silage and grain maize yields are 28 and 35, respectively.

The specific data information of the climate indexes and maize yields were given in Supporting Information 2. The first dataset (dataset 1, Table S1) for silage maize includes 153 data points. In contrast, there are 152 samples in the second dataset (dataset 2, Table S2) for grain maize as the observed yield data of South Bohemia in 2015 is missing. Besides, six data points about the grain maize yields are less than 2 t/ha, probably unreasonable. Hence, the unreliable values were removed, and the remaining data points in the second dataset were assembled as the third dataset (dataset 3, Table S3) for building models. The datasets were arbitrarily divided into two subsets, containing the training set (80%) for modeling and the test set (20%) for validating, respectively.

2.4. Model Validation

To assess the performance of the predictive models, the metrics of determination coefficient (R²), relative deviation (RD), average absolute relative deviation (AARD), and the root mean square error (RMSE) are employed. The equations of them are presented as follows:

$$R^2=\frac{{{\displaystyle \sum }}_{i=1}^{N_p}{\left(y_i^{pre}-{\overline{y}}_m\right)}^2-{{\displaystyle \sum }}_{i=1}^{N_p}{\left(y_i^{pre}-y_i^{obs}\right)}^2}{{{\displaystyle \sum }}_{i=1}^{N_p}{\left(y_i^{pre}-{\overline{y}}_m\right)}^2}$$

(4)

$$\mathrm{AARD}(\%)=100\times {{\displaystyle \sum }}_{i=1}^{N_p}\left|\frac{y_i^{pre}-y_i^{obs}}{y_i^{obs}}\right|/N_p$$

(5)

$$\mathrm{RD}(\%)=100\times \frac{y_i^{pre}-y_i^{obs}}{y_i^{exp}}$$

(6)

$$\mathrm{RMSE}=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^{N_p}{\left(y_i^{pre}-y_i^{obs}\right)}^2}{N_p}}$$

(7)

where $y_i^{pre}$ means the predicted yield of corn, while $y_i^{obs}$ notes the observed yield of corn; ${\overline{y}}_m$ stands for the average data of the training or test dataset, and Np is the sample number of the corresponding dataset.

2.5. Software

The SPSS software performed the significance of climate parameters on silage and grain maize yields based on the multiple linear regression (MLR) input method. The software Matlab 2018a was utilized to build and train ELM models and calculate the application domain of the developed models. The significant level was set as Sig. < 0.05.

3. Results and Discussion

3.1. Impact Analysis of Descriptors

As mentioned in 2.5, the input method of MLR was utilized to analyze the influence of climate factors on silage and grain maize yields. The “t” and “Sig.” values were calculated and listed in

Table 1. Climate parameters for silage maize yields of the 9 selected regions in Czechia (dataset 1).

No.	Parameters		t	Sig.
	Climate Factors	Month
1	Water deficit	05	1.279	0.203
2	Water deficit	06	−0.322	0.748
3	Water deficit	07	−2.118	0.036
4	Water deficit	08	−0.443	0.658
5	Temp. Mean	05	0.700	0.485
6	Temp. Mean	06	−0.659	0.511
7	Temp. Mean	07	0.110	0.912
8	Temp. Mean	08	1.020	0.310
9	Temp. Max	05	−1.726	0.087
10	Temp. Max	06	1.356	0.177
11	Temp. Max	07	0.039	0.969
12	Temp. Max	08	−0.963	0.337
13	Temp. Min	05	1.039	0.301
14	Temp. Min	06	−0.868	0.387
15	Temp. Min	07	1.639	0.104
16	Temp. Min	08	−1.261	0.210
17	Humidity	05	1.007	0.316
18	Humidity	06	−1.108	0.270
19	Humidity	07	−0.476	0.635
20	Humidity	08	0.266	0.791
21	Precipitation	05	−0.135	0.893
22	Precipitation	06	0.595	0.553
23	Precipitation	07	−0.768	0.444
24	Precipitation	08	0.186	0.853
25	Sunshine	05	2.158	0.033
26	Sunshine	06	−2.955	0.004
27	Sunshine	07	−2.194	0.030
28	Sunshine	08	0.744	0.458
29	(Constant)		3.239	0.002

,

Table 2. Descriptors of climate for predicting grain yields in the nine selected regions of Czechia (dataset 2).

No.	Parameters		t	Sig.
	Climate Factors	Month
1	Water deficit	05	2.971	0.004
2	Water deficit	06	0.834	0.406
3	Water deficit	07	−0.958	0.340
4	Water deficit	08	−0.308	0.759
5	Water deficit	09	−0.327	0.744
6	Temp. Mean	05	0.603	0.548
7	Temp. Mean	06	−0.505	0.614
8	Temp. Mean	07	0.654	0.514
9	Temp. Mean	08	1.405	0.163
10	Temp. Mean	09	1.185	0.238
11	Temp. Max	05	1.458	0.148
12	Temp. Max	06	0.314	0.754
13	Temp. Max	07	−1.263	0.209
14	Temp. Max	08	−0.355	0.723
15	Temp. Max	09	−1.622	0.108
16	Temp. Min	05	−1.609	0.110
17	Temp. Min	06	0.134	0.894
18	Temp. Min	07	1.610	0.110
19	Temp. Min	08	−0.739	0.462
20	Temp. Min	09	3.134	0.002
21	Humidity	05	1.334	0.185
22	Humidity	06	1.641	0.103
23	Humidity	07	1.456	0.148
24	Humidity	08	−0.281	0.779
25	Humidity	09	−1.059	0.292
26	Precipitation	05	2.074	0.040
27	Precipitation	06	−0.860	0.392
28	Precipitation	07	−0.341	0.734
29	Precipitation	08	0.578	0.565
30	Precipitation	09	−0.973	0.333
31	Sunshine	05	−1.433	0.154
32	Sunshine	06	1.525	0.130
33	Sunshine	07	−0.633	0.528
34	Sunshine	08	−1.909	0.059
35	Sunshine	09	0.179	0.858
36	(Constant)		−1.507	0.134

and

Table 3. Descriptors of climate for grain maize yields in the nine selected regions of Czechia (dataset 3).

No.	Parameters		t	Sig.
	Climate Factors	Month
1	Water deficit	05	2.643	0.009
2	Water deficit	06	0.686	0.494
3	Water deficit	07	−0.509	0.612
4	Water deficit	08	−0.153	0.879
5	Water deficit	09	0.485	0.628
6	Temp. Mean	05	0.002	0.999
7	Temp. Mean	06	−0.186	0.853
8	Temp. Mean	07	1.107	0.271
9	Temp. Mean	08	1.804	0.074
10	Temp. Mean	09	0.293	0.770
11	Temp. Max	05	1.934	0.056
12	Temp. Max	06	−0.126	0.900
13	Temp. Max	07	−1.923	0.057
14	Temp. Max	08	−0.090	0.929
15	Temp. Max	09	−1.393	0.166
16	Temp. Min	05	−1.360	0.177
17	Temp. Min	06	−0.195	0.846
18	Temp. Min	07	1.718	0.089
19	Temp. Min	08	−0.753	0.453
20	Temp. Min	09	3.439	0.001
21	Humidity	05	0.320	0.749
22	Humidity	06	2.033	0.044
23	Humidity	07	0.655	0.514
24	Humidity	08	−0.273	0.785
25	Humidity	09	−0.310	0.757
26	Precipitation	05	1.784	0.077
27	Precipitation	06	−1.095	0.276
28	Precipitation	07	−0.173	0.863
29	Precipitation	08	0.517	0.606
30	Precipitation	09	−0.895	0.373
31	Sunshine	05	−2.216	0.029
32	Sunshine	06	2.069	0.041
33	Sunshine	07	−1.029	0.306
34	Sunshine	08	−2.517	0.013
35	Sunshine	09	0.234	0.815
36	(Constant)		−0.817	0.416

. The significance of the climate parameter grows as the increasing absolute values of t and the declining Sig. values. It should be noted that the “-” in front of t values symbolize the corresponding parameters that negatively influence the maize yields and vice versa.

The descriptor of sunshine in June (Sig. = 0.004) is the most important for the silage maize yield in Czechia, and then the sun of May and July and water deficit of July with the Sig. < 0.05 are also of great significance (Table 1). The minimum temperature (Temp. Min) in September and the water deficit in May are the first and second most significant factors for the grain maize yield in Czechia (Table 2 and Table 3), while the following crucial descriptors (Sig. < 0.05) are different since the datasets have a bit different.

3.1.1. Temperature

Temperature is an essential factor influencing maize yield. As shown in Table 1, Temp. Max of May and June and the Temp. Min of July with lower Sig. values and higher absolute t values are more crucial than other temperature descriptors for the silage maize. However, for the grain maize, the enormously influential temperature indexes include Temp. Min of September (Sig. = 0.002), July (Sig. = 0.110), and May (Sig. = 0.110). When it turns to the third dataset, the three most crucial factors for grain maize are the Temp. Min of September (Sig. = 0.001) and Temp. Max of May (Sig. = 0.056) and July (Sig. = 0.057). Overall, the Temp. Max of May is significant for both silage and grain maize, but it is negative for silage and positive for grain maize. The most critical temperature factor is Temp. Min of July for silage maize while that is Temp. Min of September for grain maize. Generally, the maize yields typically decrease with increasing temperature because of the shorter phenological phases [31]. In United State, Hoffman et al. [32] reported that maize yield decrease sharply when maximum temperature exceed 29 °C.

3.1.2. Precipitation

Precipitation is another critical factor influencing the maize yield. According to the t and Sig. values of precipitation parameters from Table 1, Table 2 and Table 3, it has a more significant influence on grain maize than silage maize. It also can be observed that the precipitation of May and September has a positive influence on grain maize, but the precipitation of other months presents a negative impact. Besides, the greatest precipitation month is May (Sig. = 0.040 or 0.077) for grain maize, but that is July (Sig. = 0.444) for silage maize. In principle, the effect of precipitation may be either positive or negative. A positive correlation may happen if precipitation reduces the existing water stress, and a negative correlation maybe because of the intensified nitrogen leaching by the excessive precipitation [31]. Meanwhile, Fan et al. [26] also reported a negative effect of precipitation on maize yield in Mianyang, China.

3.1.3. Water Deficit

Compared with the water deficit of other months, the water deficit of July has the most significant impact on silage maize yield. Still, the water deficit of May is the most influential parameter for the grain maize. Based on the t values of water deficit descriptors, we can deduce that the water deficit in May has a positive influence while June, July, and August show a converse effect. As for grain maize, the water deficit of May and June is positive, while that of July, August, and September is negative. In Peru, Laudien et al. found that a higher water availability of 77 mm in the growing season would have regionally different effects, ranging from an increase of 20% to a decrease of 17% in maize yields [33].

3.1.4. Sunshine

Sunshine hours are significant for crop growth. In our study, the sunshine hours of May with Sig. = 0.004 are highly significant for silage maize yields, and then the sunshine hours of June (Sig. = 0.033) are also quite influential (Table 1, Table 2 and Table 3). In terms of grain maize yields, the sunshine hour of August with Sig.= 0.059 or 0.013 is still a crucial parameter, while others are relatively less important. It has been reported that long hours of sunshine in spring (April to June) increased maize yield in Czechia [34].

3.1.5. Humidity

The humidity of June has the lowest Sig. value for both silage and grain maize among their whole growth seasons (Table 1, Table 2 and Table 3). Thus, the descriptor of June’s humidity has greater importance for them than other months. This is consistent with a previous report on maize yield response to climate using ML (Random Forest) in the US, in which maize yield showed a negative response to low atmospheric humidity during the critical phase that encompasses flowering [32].

3.2. Extreme Learning Machine (ELM) Model Establishment

To develop effective models in this work, the collected data of climate indices during the growing season of silage and grain maize were used as the input descriptors as previously mentioned in the Section 2.3. The number of hidden neurons m was set as 40, and activation function g(x) was determined as “sigmoid” for all the training datasets. Then three ELM models were constructed to predict silage and grain maize in Czechia, and the test sets were used to verify the properties of the models.

Figure 2a shows the predicted yields compared with observed yields for silage maize. Figure 2b,c show the predicted yields compared with observed yields for grain maize using different datasets. The data points located in the vicinity of the diagonal demonstrate the excellent performance of the proposed models.

Figure 3a shows the RD% of ELM1 for silage maize in different regions of Czechia, with 93.4% of RD% values for the data points in the range of ±15%. Only one predictive data has the RD value of over 20%, which is 20.79% for the maize yield from Moravian-Silesian in 2004. The RD% values of ELM2 and grain maize in different regions of Czechia are presented in Figure 3b,c. As for the ELM2 model, around 69.1% of RD values are between −20% and 20%, and the percent of RD within ±40% is 93.4%. However, there are four RD% exceed 100%, which corresponds to the maize yields from Liberec in 2005 (113.8%), from Vysočina in 2015 (2062.2%), from Plzen in 2015 (267.5%), from South Bohemia in 2013 (121.0%). Nevertheless, after removing the yields below 2 t/ha from the training and test datasets, the percent of RD in the range of ±20% and ±40% are 74.7% and 94.5%, respectively. Additionally, there was only one data from Plzen in 2013 with the RD over 100%, which is 129.8%.

It can be observed that the AARD value of the ELM1 model for the total datasets is 6.565%, illustrating the incredible precision of the model for predicting silage maize yields (

Table 4. The statistical parameters of ELM models built in this study.

No.	Models	Datasets	Number of Datasets	AARD %	RMSE	R2
1	ELM1	Train	123	6.200	2.675	0.674
		test	30	8.062	3.307	0.560
		total	153	6.565	2.810	0.641
2	ELM2	Train	122	35.791	1.052	0.746
		test	30	17.335	1.145	0.754
		total	152	32.148	1.071	0.741
3	ELM3	Train	117	15.126	1.013	0.705
		test	29	15.193	0.981	0.773
		total	146	15.139	1.006	0.716

). The AARD% values of the ELM3 model for different datasets are lower than those of the ELM2 model (Table 4). Therefore, the accuracy of the ELM3 model is better than the ELM2 model for grain maize. Our models are comparable regarding accuracy and stability with other ML algorithms applied for maize prediction in the US, in which the best algorithm and inputs improves the prediction accuracy by 5% when compared to a baseline statistical model (Lasso) using only basic climatic and satellite observations [35]. Besides, all the values of RMSE for various models in our study are relatively low (0.981–3.307%), which performs better than other ML algorithms (random forests) used for maize yield prediction with an RMSE of 14% [13]. The determination coefficient (R²) values in our study are above 0.7 (Table 4), this is comparable to the R² of 0.77 using Bayesian Neural Network for the late-season prediction across the U.S. Corn Belt in testing years 2010–2019 [36], and R² of 0.78 using boosted regression tree model to predicting life cycle global warming on corn production under four emissions scenarios for years 2022–2100 [37].

3.3. The Application Domain (AD) of ELM Models

Defining the application domain of a model is essential to verify individual data, which may be far from the majority of data in a dataset [38]. A well-known approach to detect the outlier of a model is the leverage approach presented by William plot, consisting of the standardized residual (σ) as y-axis and leverage value (h) as the x-axis. The leverage values are obtained through Hat matrix (H) expressed as follows (Equation (8)) [39,40,41]:

$$H=X{\left(X^{t}X\right)}^{-1}{X}^t$$

(8)

where X is the input descriptor matrix of the training set and t means the transpose matrix. The critical leverage value is described as h* = 3 p/n, where p is the number of input variables plus one and n stands for the number of training samples. The points located in the domain of 0 ≤ h ≤ h* and −3 ≤ σ ≤ 3 illustrate that the predictions locate in the application domain. The points located in the range of h* ≤ h and −3 ≤ σ ≤ 3 can be considered the points outside the AD of the implemented model. Nevertheless, the points situated in the domain of 3 ≤ σ and σ≤ −3 are regarded as outliers of the predictive model [42].

Figure 4a shows that all the predictions of the ELM1 model for silage maize yield are reliable data though there is one point in the range of Good High Leverage. As for the ELM2 model (Figure 4b), two outliers are probably attributed to the doubtful data [42,43], but the majority of the data points are still in the AD of the model demonstrating that the model is valid. It can be seen from Figure 4c that all the points are located in the AD of the ELM3 model. Therefore, the ELM3 model for grain maize yields has better performance than the ELM3 model for predicting the grain maize in Czechia.

3.4. Prediction of Maize Yield under Various Climate Factors

By analyzing the climate descriptors in Section 3.3, the temperature and water deficit can be considered the most critical parameters for the silage and grain maize yields. To predict the silage and grain maize using our models, we first calculated the average of different climate parameters from 2002 to 2018; then under the precondition that the average values of other parameters remain the same, the values of temperature and water deficit were adjusted. Specifically, two groups of parameters, one is water deficit (05) and Temp. Max (05) and the other is water deficit (07) and Temp. Min (07) was designed to forecast the maize yields by ELM1 and ELM2 models. Specifically, 11 data points (including the average) were taken within the range of plus or minus one degree of the average temperature, and 11 data points were used within the range of plus or minus 50 of the average water deficit. Finally, 242 new climate data points as input descriptors are used to predict the silage and grain maize yields by the two proposed models separately, and the detailed results were provided in the supplementary information (Tables S4 and S5).

It should be noticed that although the developed models are nonlinear, i.e., the relationships between the grain maize yields and the climate factors are nonlinear, the increased or decreased rate can be obtained. For the forecasted grain maize yields, approximately 0.356 t/ha will be decreased when the water deficit (07) value adds by 10, and around 0.137 t/ha will be dropped when the Temp. Max (05) rises by 0.2 °C, with a growing proportion of −1.002% and −0.389%, respectively. In contrast, when the water deficit (05) value grows by 10 and the Temp. Min (07) by 0.2 °C, the maize yields of the silage will add about 0.510 t/ha and 0.181 t/ha, respectively, and the growth rates are 1.467% and 0.511%, respectively. Regardless of the new grain maize yields predicted by the ELM2 model, every 10 mm increase of water deficit (05) and water deficit (07) will cause a roughly 2.995% (0.194 t/ha) and −0.962% (−0.059 t/ha) increment, respectively. On the other hand, when the Temp. Max (05) and Temp. Min (07) go up by 0.2 °C, the yields increase rate of grain maize will be around 0.527% (0.034 t/ha) and 0.277% (0.018 t/ha). Obviously, water deficit (05) has a greater influence on grain maize yields than silage maize yields, but the Temp. Min (07) is more influential for silage than grain maize yields. In the case of Temp. Max (05) increase 2 °C, silage yield will decrease 1.367 t/ha and is about 3.826% loss, while grain yield will increase 0.337 t/ha and is about 5.394% increase. This means our results on maize yield considering climate change by ELMs is not so pessimistic compared to other models (combined empirical models of maize production with future warming scenarios) that maize yields are foreseen to decline by 20–40% and 40–60% with a temperature increase of 2 and 4 °C, respectively [4]. Furthermore, Crane-Droesch found that negative impacts of climate change on corn yield by semiparametric neural networks (one of ML methods), but less severe than impacts projected using classical statistical methods, especially in warmest regions [22]. Fan et al. found −0.58% to −0.75% maize yield by precipitation [26]. However, Su et al. estimated that under future climate conditions, the performance of conservation agriculture is expected to mostly increase for maize over its tropical areas [44]. In sub-Saharan Africa, technology could steadily increase maize yields by about 1% (13 kg/ha) per year while increasing temperatures decreased yields by 0.8% (10 kg/ha) per °C. That means although we should expect increases in future crop yields due to improving technology, the potential yields could be progressively reduced due to warmer and drier climates [23].

4. Conclusions

The current work collected the climate data of nine regions in Czechia between 2002 and 2018, and the influences of climate indexes on the silage and grain maize yields in Czechia were analyzed. Results show that the most significant two climate parameters are sunshine in June and water deficit in July for the silage maize yield, while those are the Temp. Min of September and the water deficit in May for grain maize yield in Czechia. There ELM models were obtained to predict the silage (ELM1) and grain (ELM2 and ELM3) maize yields in Czechia. The R2 values of the models for the total datasets are 0.641, 0.741, and 0.716, while the AARD values are 6.565%, 32.148%, and 15.139%, respectively, presenting their robustness and accuracy. The application domain was also defined to detect the reliability of the predictions. The majority of predictions are situated in the AD of models showing the reliability of these models. Based on our ELM models, silage yield will decrease by 1.367 t/ha (3.8% loss), and grain yield will increase by 0.337 t/ha (5.4% increase) when the max temperature in May increases by 2 °C. In conclusion, the proposed models show a potential application for predicting maize yield.