*3.1. Calculation of Remote Sensing Nine Indices:*

Crop yield is markedly influenced by the growth conditions in each crop stage. Nine typical vegetation and drought indices were computed and compared with spring wheat yield. These indices are commonly used for crop yield estimation, drought monitoring, and only require optical spectral bands for calculation. For example, the NDVI has been most commonly used for vegetation monitoring, crop yield assessment and forecasting [27,49,50]. Kogan [51] has been developed the VCI to study the response of vegetation to drought conditions worldwide. Unganai et al. [52] conducted that the vegetation condition index (VCI) derived from AVHHR-NDVI correlated significantly with maize yield in Zimbabwe. The growth condition and crop yield are strongly correlated at the pixel level. Each pixel's value of remote sensing indices was directly taken at point locations of the eight stations. We examined the relationship between NDVI, NDWI, NMDI, TCI, VCI, VHI, NDDI, VSDI, and VSWI with actual spring wheat yield during the growing season (June–August) for 2000–2017 across Northern Mongolia. The 10 day and monthly nine remote sensing indices (NDVI, NMDI, NDWI, VCI, TCI, VHI, NDDI, VSDI, and VSWI), which are derived from transformations of the red, NIR, blue, and SWIR spectral bands, was used to continuous time series of data the represented the spring wheat growth indices temporal curve for each pixel in the study area. We used Table 2 for remote sensing indices calculation. Active plants are intensely absorbed by red and blue bands and reflected by the near-infrared band (NIR) [53]. Depending on the type of plant and the crop yield stage, the absorption of red and blue bands and the degree of the NIR band is different. When vegetation is stressed by lack of water, and also at the end of the growing period, the chlorophyll absorption declines and the ratio of NIR to RED or visible reflectance decreases. Therefore, vegetation index can be defined as the difference between RED and NIR bands reflections measured from satellites. The SWIR-1 and SWIR-2 bands are sensitive to the soil and vegetation moisture content. Hence, we calculated nine remote sensing indices utilized NIR, red, blue, and SWIR bands for spring wheat yield monitoring. Furthermore, we determined which indices from nine remotely sensed indices were more suitable to estimate spring wheat yields. To reduce the impact of atmosphere and cloud, the 10-day remote sensing-based indices derived from the daily data using maximum value composition (MVC) [54] were considered. Besides, we have retrieved monthly remote sensing indices from 10 days MVC indices by a simple moving average method. Particularly, each monthly remote sensing index was calculated by averaging three temporally 10 days MVC indices.


**Table 2.** Equations of tested nine remote sensing indices.

NIR-near-infrared band, Band2 (841–876 nm); RED-red band, Band1 (620–670 nm); SWIR1 - shortwave infrared band, Band6 (1628–1652 nm); SWIR2-shortwave infrared band, Band7 (2105–2155 nm); Blue–Band 3 (459–479 nm); Tj, Tmax and Tmin–surface temperature (current, maximum, and minimum).

#### *3.2. Sensitive Analysis between Remote Sensing Indicators and Crop Yield*

In this study, Pearson's correlation coefficient (R) between remote sensing indices and spring wheat yield was calculated for every 10 days and every month of the growing season from June to August for the northern part of Mongolia for 2000–2017 using following (Equation (1)). Pearson's correlation coefficient (R) represents the degree and direction of the linear regression between two continuous variables that are measured on the equal interval. The range of values for the R is from −1 to 1 (R > 0 it is a positive linear relationship, R = 0 it is indicated that there is no relationship and R < 0 it is a negative linear relationship).

$$R = \frac{\sum\_{i=1}^{n} (\mathbf{x}\_i - \overline{\mathbf{x}})(y\_i - \overline{y})}{\sqrt{\sum\_{i=1}^{n} (\mathbf{x}\_i - \overline{\mathbf{x}})^2 \sum\_{i=1}^{n} (y\_i - \overline{y})^2}},\tag{1}$$

where *xi* and *yi* presents remote sensing indices and the value of spring wheat yield at different time periods, n is the number of samples, *x* and *y* are the average values of *xi* and *yi*.

#### 3.2.1. Crop Yield Estimation Model

The process of crop production is directly influenced by many biological, physiological and biophysical laws that are directly responsible for plants, and theoretically, it is possible to model the whole process of vegetative growth by mathematically describing the physical processes of these processes. Nowadays, dynamic modeling techniques are based on simple statistical equations, based on complex differential equations systems, in modeling the events of agroecosystems. In this study, using the remote sensing nine indices, we tested and attempted to develop the spring wheat yield estimation model. The relationship between spring wheat yield and remote sensing indices was observed through the linear regression model, where the independent variable was represented by remote sensing nine indices and the dependent variable was spring wheat. The estimation model is multilinear and includes slope and an interception constant coefficient. The empirical regression methods based on spectral indices have commonly used for modeling crop yield in many studies [49,60,61]. Bolton et al. [62] found a good linear correlation between different crop yields with MODIS-NDVI, EVI, and NDWI data at the county levels. Sui et al. [11] developed the estimation model for winter wheat production based on the environmental factors derived from satellite at a regional level, with errors of <12% for winter wheat yield, respectively. To determine when the correlation between remote sensing indices and spring wheat yield is strongest, we estimated the coefficient of determination (R2) using data from every 10 days and monthly in the growing period of spring wheat. In order to make the final predicted results more accurate and stable, we considered it necessary to select the critical growth stage and remote sensing indices from all indices. We used a stepwise regression model in order to select the best candidate indices for yield estimation using SPSS 12 software. Stepwise regression provides a strong mean between the one or more independent variables and a dependent variable that conforms to the general equation for a multidimensional flat.

$$\hat{Y} = \mathbf{b}\_0 + \mathbf{b}\_1 \boldsymbol{\chi}\_1 + \mathbf{b}\_2 \boldsymbol{\chi}\_2 + \dots + \mathbf{b}\_n \boldsymbol{\chi}\_n \tag{2}$$

where, Yˆ is the dependent variable and predicted spring wheat yield, X1, X2... Xn are the independent variables and MODIS remote sensing indices, and b0, b1, b2 ... bn are the regression coefficients and n is the number of independent variables.

#### 3.2.2. Model Performance Evaluation

Then we selected the month that produced the highest coefficients to the determination to develop multilinear regression models based on all 18 years of data. Generally, the comprehensive method to validate models is to correlate the measured values against the predicted values [48]. We used model fitting and performance statistics such as the coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), bias and an index of agreement (d) agreement.

$$\text{RMSE} = \sqrt{\frac{\sum\_{i=1}^{n} \left(\hat{\mathbf{Y}} - \mathbf{Y}\right)^{2}}{n}},\tag{3}$$

$$\text{MAE} = \frac{1}{n} \sum\_{i=1}^{n} \left| \hat{\mathbf{Y}} - \mathbf{Y} \right|, \tag{4}$$

$$d = 1 - \frac{\sum\_{i=1}^{n} \left(\mathbf{Y}\_i - \mathbf{Y}\_i\right)^2}{\sum\_{i=1}^{n} \left( \left|\mathbf{Y}\_i - \overline{\mathbf{Y}}\right| + \left|\mathbf{Y}\_i - \overline{\mathbf{Y}}\right| \right)^2},\tag{5}$$

where Y is observed values, Yˆ is modeled values, Y is an average of observed values, and n is a number of yield and RS data.

#### **4. Results**

#### *4.1. Temporal Climate Variables and Remote Sensing Indices Profiles for Spring Wheat*

Figure 5 describes annual spring wheat yield with the amount of precipitation and average temperature throughout each growing season from 2000 to 2017. The temperature change, precipitation, and soil moisture have a significant impact on wheat yield. Mainly in the period May–September which accounts for 85% of annual precipitation. Especially in June–August, about 50%–60% of the annual precipitation occurs in Mongolia [63]. According to the [64] results show that the break of rainy season caused a similar reduction in soil moisture around mid-July in Mongolia. The highest mean precipitation of the growing months at the eight meteorological stations was 352 mm in 2013, 309 mm in 2009, 293 mm in 2008, 290 mm in 2012 and lowest annual precipitation occurred in 143 mm in 2002, 172 mm in 2001, and 199 mm in 2005 for the study area. In summer, especially growing season temperature and precipitation were negatively correlated. From (Figure 5) the lowest yield of spring wheat harvested in 2002(4.2kg ha<sup>−</sup>1) and the highest yield in 2014(21.9kg ha<sup>−</sup>1) in these two provinces. The main reason is that high temperatures and low precipitation led to soil moisture deficits, which is a significant impact on wheat yield. The climate of Mongolia is dry and semi-arid, and the growing vegetation cover and crop yields and development are highly dependent on the amount of precipitation and the related soil moisture [7,8].

Processed growing season (June–August) Moderate Resolution Imaging Spectroradiometer (MODIS-Terra) daily reflectance bands for study area for the years to 2000 to 2017. Based on the corrected surface reflectance NIR, red, blue, SWIR bands and LST of MODIS data, we have computed nine remote sensing indices and listed in (Table 2). We extracted time series values of NDVI, NDVI, NMDI, NDWI, VCI, TCI, VHI, NDDI, VSDI, and VSWI interpolated 10 day and monthly intervals in growing season (June–August) from 2000 to 2017. As shown in (Figure 6), the long-term annual remote sensing nine indices variables for spring wheat yield in Northern Mongolia.

**Figure 5.** Long-term trend of average spring wheat yield and climate variables (2000–2017).
