*4.2. Sensitivity Analysis between Remote Sensing Indicators and Crop Yield*

The Pearson's correlation analysis examined between multi-year spring wheat yield data of eight stations and NDVI, NMDI, NDWI, TCI, VCI, VHI, NDDI, VSDI, and VSWI for June-August from 2000 to 2017, for a total of about 135 data points. To test the regional effectiveness of remote sensing indices and determine the best index during the growing period (June to August) for spring wheat yield estimation, we compared the 10 days and monthly remote sensing indices with the spring wheat yield. In general, in terms of the sown stage in the middle of May, emergency in early June, flowering in late June and early July, milk, and dough in August, maturity in early September, and harvesting in late September in the study area (each growing stage shown in Figure 3). For each of the remote sensing indices, the correlation values and significant *p*-values were produced by eight stations from 2000 to 2017 (Table 3).

The results show that most of the indices had found a higher correlation with spring wheat yield in June and July. This period covers the heading and flowering phenological stage of spring wheat. To see all of the correlations between June remote sensing indices and spring wheat yield in more detail, refer to Figure 7. About 50–60% of the annual precipitation occurred in the growing period, especially most of the precipitation occurred in June and the beginning of July. Because of that reason, there is sufficient moisture and suitable weather condition. Slightly lower correlation was found in August since crops are harvested in September. We can see that results of correlation (R) among the nine indices, NDDI, VSDI, VSWI, and crop yield were negatively correlated with spring wheat yield, while other NDVI, VCI, TCI, VHI, NDWI, and NMDI were positively correlated. The highest correlation coefficient (R) values of between 10 day remote sensing 9 indices with spring wheat yield were NDVI

(0.51) in first 10 days of July, NMDI (0.18) in first 10 days of August, NDWI (0.48) in first 10 days of June, TCI (0.57) in third 10 days of June, VCI (0.31) in first 10 days of July, VHI (0.46) in third 10 days of June, NDDI (−0.38) in second 10 days of July, VSDI (−0.56) in first 10 days of July and August, and VSWI (−0.36) in first 10 days of June, respectively. These were statistically significant values with a yield of *p* < 0.05. Indices including NDDI, VSDI, and VSWI were negatively correlated with spring wheat yield, this implies when the values of these indices increase, the spring wheat yield decreased.

**Figure 6.** Annual growth season (June–August) average VSWI (**a**), VSDI (**b**), NDDI (**c**), VHI (**d**), VCI (**e**), TCI (**f**), NDWI (**g**), NMDI (**h**), NDVI (**i**), and Spring wheat yield (**j**).


**Table 3.** Multi-year correlation between 10-day indices and spring wheat yield in June to August (2000–2017).

Significant at highlighted values = *p* < 0.05, Number of samples = 126 − 134 ((Due to the clouds or error data of satellite images there were some 10days of some indices are missed).

**Figure 7.** The correlations between spring wheat yield with June (**a**) NDVI, (**b**) NDWI, (**c**) NMDI, (**d**) TCI, (**e**) VCI, (**f**) VHI, (**g**) NDDI, (**h**) VSDI, and (**i**)VSWI. Number of samples N = 135.

Also, we did a correlation between monthly nine remote sensing indices and spring wheat yield at each station in the monitoring period. The results show that the absolute value of correlation coefficients (R) of each month as shown in Table 4. These were statistically significant *p* < 0.01 with yield, except NMDI.


**Table 4.** Multi-year correlation between monthly indices and spring wheat yield in June- August (2000–2017).

Significant at \*= *p* < 0.05, \*\* = *p* < 0.01, \*\*\* = *p* < 0.001; Number of samples=134.

The relationship between NMDI and spring wheat yield showed was the lowest results (0.10–0.15), which is indicating that this index not suitable for spring wheat yield estimation in this region. From Table 4 we can see that monthly NDWI was the highest correlated indices with yield in June (0.51) and monthly VSDI was the highest correlated with yield in July (−0.57) and these were statistically significant *p* < 0.001, respectively. It indicates the soil and crops moisture and water content are most important for crop yield.

#### *4.3. Yield Estimation Model*

In this study, we tested nine remote sensing indices to develop the best and most accurate estimation models for spring wheat yield for Northern Mongolia. The yield was estimated at station level based on remote sensing indices for the spring wheat-growing season (June to August) and ground crop yield data. Each model has used eight stations crop yield data and nine remote sensing indices (10 daily and monthly) from 2000 to 2017. We used stepwise regression as a technique for choosing independent nine remote sensing indices for a multiple linear regression equation from a list of candidate indices. The results of regression analysis and best-fitted models are summarized in (Table 5).


**Table 5.** Best-fit estimation models for spring wheat yield during the growing period (June–August).

Number of samples (N = 135), VSDI63-third 10 days of June, VSDI; NDWI6–June, NDWI; VSDI7–July, VSDI; NDVI71-first 10 days, NDVI; VSDI81, NDWI81, and NDVI81- first 10 days of August, VSDI, NDWI, and NDVI.

The models had R<sup>2</sup> values ranging from 0.39 to 0.57 and all models had statistically significant *p* < 0.001, respectively. The models with high R2 values, low RMSE, and MAE values indicate the best model for spring wheat yield estimation. The highest R<sup>2</sup> values were 0.57 in June and 0.55 in July. Final all models include NDWI and VSDI (VHI and NDVI in some models) from June to August were good predictors of spring wheat yield.

In order to test the estimate performance of the method, we used the coefficient of determination (R2), root means square error (RMSE), mean absolute error (MAE), bias and index of agreement (d) to evaluate the estimated spring wheat yield in regional level. We compared the predicted yield with the actual yield of eight stations for 2000–2017, the results showed in (Figure 8).

**Figure 8.** Comparison between actual spring wheat yield with estimated spring wheat yield for each model; model 1 (**a**), model 2 (**b**), model 3 (**c**), model 4 (**d**), model 5 (**e**), model 6 (**f**). Each point indicates the estimated yield versus the actual yield for a single station and year.

The best timing and more accurate model for spring wheat yield estimation was found at the end of June and beginning of July. Model 4 was selected as the best estimation model for spring wheat in Northern Mongolia. Model 4 has combined variables of VSDI, NDWI, and NDVI, and index of agreement (d) value was 0.84, the relationship between estimated and actual yield was R2 = 0.55, mean absolute error was MAE = 3.3 and root mean square error was RMSE = 4.1(100 kg ha<sup>−</sup>1), respectively.
