*3.2. Methods*

3.2.1. Established SMAP Training Samples for Winter Wheat and Rainfed Crops

The selection of training samples is important before establishing a model of irrigation signal detection. Since the SMAP data have a low spatial resolution, the training samples should be selected to ensure that the surrounding crops are consistent. In this paper, samples were selected using a combination of MODIS NDVI and MODIS ET. Since the winter wheat (WW) NDVI in the NCP was significantly higher than other crop in March, the spatial distribution of WW can be extracted based on the March NDVI data. However, this spatial distribution may include other vegetation with a higher NDVI (such as landscape forest), and ET is needed to improve the extraction accuracy of WW. Since March to April is the main irrigation period for WW, the cumulative ET value of WW is significantly higher than that of other vegetation during this period [48]. This indicates that the extraction accuracy of WW can be improved by adding ET as a limiting condition. Using these two features (NDVI and ET), the WW pixels can be extracted more accurately. WW and rainfed crop pixels were extracted by the decision tree model in Figure 3.

**Figure 3.** Winter wheat and rainfed crops planting area extraction model. Where March NDVI and Mar-May ET represent the NDVI in March (May NDVI is similar to March NDVI) and cumulative amount of ET from March to May, respectively; DEM is the elevation information; and T is the threshold in different conditions. If the pixel value (such as NDVI and ET) satisfies the threshold, the pixel value is 1, and if it is not satisfied, the pixel value is 0.

The selection of WW samples should be based on SM sites, and more irrigation information can be obtained. Rainfed crop samples should ensure that there are no irrigated crops nearby as much as possible, which can reduce the influence of surrounding crop irrigation on SM. Finally, 11 WW samples and 7 rainfed crop samples were established in the study area, 7 WW samples and 4 rainfed crop samples were used as training samples, and the remaining samples were used as validation samples. These samples are distributed from north to south and can reflect the difference in irrigation time of winter wheat under different latitude conditions.

#### 3.2.2. Irrigation Information Detection and Irrigated Area Downscaling

Extracting the precipitation and SMAP time series data of the meteorological site spatial location can not only be used to evaluate the sensitivity of the SMAP data to the precipitation response but also to support the threshold setting of the irrigation signal detection. The irrigation signal detection is based on the SMAP SM variation. It can be assumed that if the SM of SMAP is increased and the grid has no significant precipitation, the increase in SMAP SM is caused by irrigation. Since the amplitude increase in the SMAP original SM signal is significant, it is difficult to detect irrigation by threshold segmentation and the original signal needs to be processed using the moving average method. In the original SMAP data, due to the existence of signal noise, the SM is may be suddenly reduced (previously without precipitation and irrigation), if this value is calculated with the SM at the latter time, the identified irrigation signal is invalid. SM Value in that time need to be corrected. To reduce the influence of SMAP SM data amplitude on the irrigation signal detection, a 5-point moving average method is used to process the SMAP SM original signal. The 5-point moving average not only ensures the amplitude of the original but also reduces the frequent fluctuations in the original

signal. Sun et al. [49] compiled the water requirement for di fferent growth stages of WW in the NCP. In this paper, the daily precipitation of >4 mm was used as the threshold for e ffective precipitation (referenced by Sun et al.). In this study, the irrigation identification results of the grid were binarized (irrigation is 1, no irrigation is 0).

By accumulating the binarized daily irrigation identification results, the frequency of irrigation in the WW planting region can be obtained. Notably, the irrigation frequency of a grid may be higher than 6 times because the grid (9 km × 9 km) cannot be completed irrigated in one day. After integrating the spatial distribution of the irrigation intensity and the WW planting area, the irrigated area with the irrigation intensity identification was finally obtained. However, the accuracy of the irrigated area recognition results based on a single SMAP data source does not meet the general application requirements. By introducing the previously extracted WW spatial distribution, the downscaled results of irrigation intensity were obtained from the SMAP irrigation intensity results without the influence of non-irrigation pixels (such as rainfed crops and city). The mathematical expression of the method in this section is as follows:

$$IS\_{i,j} = SM\_{i,j} \succ T\_6 \text{ and } Pre\_{i,j} \prec EPre \tag{4}$$

$$II\_{i,j} = \frac{\sum\_{1}^{t} IS\_{i,j}}{\max\left(\sum\_{1}^{t} IS\_{\text{w,ft}}\right)}\tag{5}$$

$$II\_{downscale} = \begin{cases} \begin{array}{c} II\_{i,j\_\prime} \ W W = 1 \\ 0 \end{array} \\ \end{cases} \tag{6}$$

where *i* and *j* represent the pixels of the ith row and jth column, respectively; *IS* is the irrigation signal; *SM* is the soil moisture derived from SMAP; *T6* is the threshold for soil moisture increase; *Pre* and *EPre* represent precipitation and e ffective precipitation, respectively; *II* is the irrigation intensity; *t* is the total number of days in the study period; max*<sup>t</sup>* 1 *ISm*,*<sup>n</sup>* represents the maximum value of the accumulated value of the irrigation signal over the entire event range; and *IIdownscale* is the downscaled irrigation intensity. In equation 6, the WW spatial distribution and the irrigation intensity image need to be calculated. If the WW spatial distribution image pixel value is 1, the *IIdownscale* pixel value is assigned as the irrigation intensity value. The irrigated area is calculated as the area of the pixel where the irrigation intensity is greater than zero. The algorithm implementation in this section still needs to use the arcpy function based on python 2.7.

#### 3.2.3. Validation and Consistency Analysis

The results of the irrigation signal detection have been validated, and the uncertainty in the irrigated area downscaling has also been analyzed. First, the detection results of the irrigation signal are based on the irrigation record. Since the SMAP SM time series data in this paper used the 5-point moving average method, if the detected WW irrigation signal is di fferent from the irrigation record in three days, the result is correct. Simultaneously, if the non-WW planting area also detects the irrigation signal, it is necessary to reset the irrigation signal detection threshold according to the irrigation signal frequency. The equation for the validation of irrigation timing is as follows:

$$Accuracy = \left(\frac{\text{CDet}}{ADet + \text{VRac}}\right) \* 100\% \tag{7}$$

$$OA = \text{avg}(Accuracy\_1 + Accuracy\_2 + \dots + Accuracy\_l) \tag{8}$$

where *Accuracy* is the sample validation accuracy; *OA* is the overall accuracy and *l* indicates the total number of validation samples; *CDet* indicates the number of days that were correctly detected in the irrigation record; *ADet* represents the number of days for all irrigation detected results; and *WRec* is the number of days that have not been detected in the irrigation record.

Second, when using the WW data extracted by MODIS to downscale the SMAP irrigation signal detection results, whether the growth of WW covered by one SMAP pixel is consistent must be considered. The selection strategy for the consistent analysis of WW growth is to establish samples in four corners and center points covered by one SMAP pixel as shown in Figure 4. The NDVI daily signal extracted from the samples was subjected to upper envelope processing [23], and the signal was divided according to the growth stage of WW and the change in SM. By counting the number of samples from the consistent growth of WW, the consistency analysis results of WW growth covered by one SMAP pixel were obtained. The consistency analysis results are calculated as follows:

$$P = \left(\frac{RG+f}{10}\right) \ast 100\% \tag{9}$$

where *P* is the percentage of growth consistency of WW; *RG* and *J* are the number of consistent samples of WW growth in the returning green and jointing stages, respectively; and 10 is the number of samples for all these two stages. Five growth consistency samples can be obtained for each growth stage (corresponding to the red sample point), and 10 consistency analysis samples can be obtained for the two stages of the returning green and jointing stages.

**Figure 4.** Sample maps. Red triangles and blue points are used to extract the SMAP SM time series signals from di fferent crops; red points are used to extract the winter wheat NDVI time series signal and then compare the consistency of winter wheat growth covered by one SMAP pixel.

#### **4. Results and Validation**

#### *4.1. Irrigation Signal Detection*

Taking four meteorological stations as examples, the time series of NDVI (8-day maximum synthesis), ET (8-day), precipitation and SM from 2015 to 2017 were plotted in Figure 5. Comparing the time series data of the four meteorological stations, it was found that the vegetation coverage of the Baoding and Nangong stations were rainfed crops and those of the Botou and Raoyang stations were WW. An analysis of the time series changes of NDVI and ET showed that the meteorological stations with WW vegetation cover (Botou and Raoyang) not only had more NDVI peaks than rainfed crop stations (Baoding and Nangong) but also significantly higher ET from March to May. Time series changes of precipitation and SM provide an important basis for irrigation signal detection. During the main growth period of WW (March to May), Botou and Raoyang stations were a ffected by irrigation and still maintained high SM without precipitation. Simultaneously, the SM observed in the WW growing season was more stable and higher than that of the non-irrigated crops.

**Figure 5.** NDVI (8-day maximum synthesis), ET (8-day), precipitation (daily) and SM (daily) time series variations. (**a**) Nangong, (**b**) Baoding, (**c**) Botou and (**d**) Raoyang meteorological stations; and VSM means volume of soil moisture. The land cover at Nangong and Baoding stations was rainfed crops, and the land cover at Botou and Raoyang was winter wheat.

Using the 5-point moving average method for statistical time series SM results, which can reduce the influence of abnormal points on the irrigation signal detection. The smoothed SM results are shown in Figure 6. Figure 6a Changes in SM (blue lines) and effective precipitation events (green lines) in WW samples, and the statistical WW irrigation time is also plotted (Triangle point). Figure 6b Changes in SM and effective precipitation events for rainfed crops. The figure can reflect the response relationship between SM and precipitation, at the same time, by comparing the SM curves of different crops, it can be found that show the WW pixels have a more obvious SM increase than rainfed crop pixels. Comparing WW samples with rainfed crop samples, it was found that both had an increasing trend in SM before the first recorded irrigation. The slowly increasing trend in SM under no precipitation conditions may be caused by seasonal and vegetation water content changes [31]. However, the increasing trend in WW samples with different spatial locations was different before the first irrigation stage. Due to the difference in temperature, the irrigation time was different. The SM of the WW sample in the southern region increased significantly compared to the WW samples in the northern region (top line in Figure 6a is the southern region WW sample, and the bottom is the northern region). Both WW samples and rainfed crop samples have significant SM increase feedbacks under effective rainfall events. The difference is that irrigation events will also significantly increase SM without effective rainfall, which is shown in Figure 6. Setting the threshold for SM increase without an effective rainfall event can be used to detect irrigation signals in the WW region.

**Figure 6.** Training samples of irrigation signal detection. (**a**) Winter wheat training samples, and (**b**) rainfed crop training samples. The irrigation record is a summary of the irrigation records of the main irrigation region in the study area and used as a reference for the water supply time for winter wheat.

The irrigation signal detection results of WW and rainfed crops are shown in Figure 7a,b, respectively. By setting the SM change threshold, the time when the SM was significantly increased without effective precipitation is detected as the irrigation time (square point in Figure 7). In the rainfed crop region, only one irrigation signal was detected in this region due to the setting of the SM increase threshold. By comparing the SM trend of WW and rainfed crops, the SM trend in the WW region was more obvious, and there was also a significant increase (it is affected by irrigation) in SM when there was no precipitation. The SM trend in the rainfed crop region is more stable. Under the same precipitation conditions, the SM increase in the rainfed crop region is lower than that in the WW region. According to the results of WW irrigation signal detection, the irrigation frequency was higher from mid-February to mid-March. Due to the high frequency of precipitation in April and May, the irrigation frequency is lower than in February and March. Additionally, in the early WW growth stage (turning green and jointing), the main irrigation water source in the study area is surface water, and the amount of irrigation water will be more than that in the middle and late growth stages of WW. For different study areas, the setting of effective precipitation can be stricter, which may reduce the false detection of irrigation signals. Notably, the results of irrigation signal detection in this paper were large-scale surface water irrigation signals. Due to the small amount of irrigation water and the dispersion of irrigation areas, SMAP pixels do not easily reflect changes in SM amplitude caused by groundwater irrigation.

**Figure 7.** Irrigation signal detection results. (**a**) WW sample detection result and (**b**) RF samples detection result. The time corresponding to the square mark is the irrigation time, and the time corresponding to the circle mark is the effective rain time.

#### *4.2. WW Extraction Results and Irrigated Area*

In this paper, irrigation signal detection training samples must refer to both WW and rainfed crops. Figure 8a,b were obtained by daily NDVI using an 8-day maximum synthesis process, and Figure 8c was the cumulative ET from early March to early May. According to the crop growth phenology of the study area, only the WW crop in the study area showed obvious vegetation characteristics in March and early April. Therefore, most of the green areas in Figure 8a characterize the spatial distribution of WW. Since WW is already irrigated, the cumulative ET is significantly higher than that of other crops. Combined with the cumulative ET in Figure 8c, WW pixels with higher precision can be extracted. The vegetation characteristics of rainfed crop pixels appeared later than that of WW, and the cumulative ET was significantly lower than that of WW.

The normalized results of the cumulative irrigation detection signal are downscaled as shown in Figure 9a, wherein all blue areas indicate the spatial distribution of irrigated WW and blue shades indicate the intensity of irrigation. Downscaling normalization results eliminates the effects of non-irrigated pixels and directly expresses the spatial distribution of WW. Figure 9b,c are the results of the irrigated area provided by GIAM and GRIPC, respectively. The largest irrigated area is shown in Figure 9c because the data are classified into only four categories for agricultural areas, and the irrigation area cannot be effectively distinguished, whereas the irrigation area of the two crop rotations is shown in Figure 9b, which is close to the irrigation area identified in this paper. In recent years, due to the problem of overexploitation of groundwater in the NCP, many regions no longer plant high-water-consumption crops, such as WW, which results in Figure 9a irrigated areas being less than that of the GIAM data. Compared with the traditional irrigated area identification results, the proposed method can also reflect the irrigation intensity of the study area.

**Figure 8.** Sample selection based on MODIS NDVI and ET: (**a**) MODIS NDVI of DOY (day of year) 89-97, (**b**) MODIS NDVI of DOY 116-124, (**c**) MODIS ET accumulate from DOY 65-129.

**Figure 9.** Irrigated area distribution in the study area. (**a**) shows the downscaled irrigated area and irrigation intensity results, (**b**) shows the irrigated area from GIAM, and (**c**) shows the irrigated area from GRIPC.

#### *4.3. Validation and Growth Consistency Analysis*

The detection results of irrigation signals in this paper will be validated from two aspects: 1) Validate the time of irrigation according to irrigation record; 2) count the consistent samples of WW growth and validate the effectiveness of the irrigation signal detection result.

In Table 2, the timing of the irrigation signal detection is compared to the timing of the irrigation records. The irrigation detection accuracy of the WW samples WW 1, WW 2, WW 3, and WW 4 used for validation were 50.00%, 100.00%, 75.00%, and 83.33%, respectively. It should be noted this irrigation record corresponds to two detection dates, with the irrigation record recorded for two days to calculate the single sample accuracy validation. Irrigation signals were also detected in the rainfed crop samples, which were added as errors to the calculation of the overall irrigation signal detection accuracy. The overall accuracy of the irrigation timing detection in this paper was 77.08%. The calculation of overall accuracy must consider the detection error of the rainfed crop region.

Since WW presents significant NDVI changes in the returning green and jointing stages and less precipitation during this period, little effect on WW growth is observed. Therefore, the returning green and jointing stages of WW are selected as the key period of growth consistency analysis. WW showed more significant growth consistency in the early stage of returning green and jointing than in other growing stages. The irrigation records show that the irrigation water used in the returning green and jointing stages is surface water, and the irrigation water in other growth stages is irrigated groundwater. Surface water irrigation is a unified supply for water resource managemen<sup>t</sup> departments, and groundwater irrigation is privately accessible to farmers. Different irrigation times are the main reason for the inconsistency in WW growth. WW is irrigated by surface water during these two growth stages, and surface water irrigation can cover a wide range of WW regions. Irrigation caused an increase in the SMAP pixel value (SM), which was used to identify an irrigation pixel. Due to the low spatial resolution of SMAP data, the consistency of WW growth under the coverage of one SMAP pixel in this study area must be discussed. If most of the WW covered by one SMAP pixel shows a consistent increase in the NDVI, then the spatial distribution of WW is effective for downscaling the irrigation signal. Conversely, if the increase in the NDVI for most WW (covered by one SMAP pixel) is inconsistent, then the irrigation signal identified by the SMAP pixel cannot effectively express WW growth. In Figure 10, SM, NDVI changes (after upper envelop) and irrigation time for different SMAP samples were plotted. Figure 10a–d correspond to Validate WW1, Validate WW2, Validate WW3 and Validate WW4 in Figure 7a, respectively.



Det: irrigation detection result. Rec: irrigation records. Units marked in green indicate that the detected irrigation date matches the recorded irrigation date, and units marked in orange indicate the detection irrigation date does not match the recorded irrigation date.

**Figure 10.** SM, NDVI changes (after upper envelop) and irrigation time for different SMAP samples.

According to the NDVI variation treatment method shown in Figure 10, 55 NDVI samples covered by 11 SMAP WW samples were validated for WW growth consistency. The number of samples with same increase trend of WW NDVI in the returning green and jointing stages was counted separately. For example, at the time of the returning green stage, the simultaneous increase in the NDVI indicates

consistency among the WW growth samples, and vice versa. By counting the number of consistent WW samples covered by di fferent SMAP pixels, the percentage of WW growth consistency covered by SMAP pixels can be calculated, and the results are shown in Table 3. In Table 3, the ratio of the consistent growth of WW covered by SMAP pixels is greater 70%, and in some regions, it can reach 100%. The overall consistency result reached 83%, and the results show that the irrigated area after downscaling can e ffectively express the true WW irrigation situation.


**Table 3.** Statistical results of the winter wheat sample consistencies.

RG: returning green stage; J: jointing stage; P: percentage; OA: overall accuracy.
