Introduction

Future food security is a high priority in the UN Sustainable Development Goals (SDGs). The sustainability of agriculture in a warming climate is vital for food security. As the largest water consumption sector, agriculture heavily relies on stable and consistent water supply. However, being among the costliest natural hazards with disastrous effects1, droughts (i.e., prolonged water deficit) exert devastating impacts on water supply and hence agriculture. Droughts can reduce cereal yield by 10.1%2, and raise the inter-annual variability of agricultural production to be more than 40%3. More seriously, long-lasting extreme droughts can result in massive economic losses and even extensive famine, posing a great challenge for water resource management and food security4,5. Moreover, model-simulations of various hydrological components such as precipitation, streamflow, and soil project an increased risk of droughts under future climate change6,7,8,9,10,11. It is no surprise that the impacts of droughts on agricultural production have attracted widespread concern in recent years12,13.

Well documented have been the impacts of climate extremes on agricultural production (Supplementary Fig. 1). The most commonly used method to analyze the impact of drought on crop yield is to evaluate their statistical relationship, and then to project the yield loss caused by droughts in the future. In this method, the selection of drought index considerably affects the assessment results. In previous studies, the evaluations based on the meteorological drought indices ignored the role of irrigation and other anthropogenic factors in alleviating drought impacts. In other studies, agricultural drought indices defined by soil moisture were used, which could reflect the soil water deficit as the combined results of drought, irrigation, and other factors. Still, it was difficult to separate the impacts of irrigation from other factors to evaluate its effectiveness in alleviating the adverse consequences of droughts. As irrigation is the largest water consumption sector, a deep understanding of the effectiveness of irrigation on agricultural production under different climate scenarios is profound to improve the allocation and management of water resources. Therefore, it is of paramount importance to quantify the impacts of irrigation on crop yield and its effectiveness in agricultural resilience to more frequent and extreme droughts under climate change. The modified Palmer Drought Severity Index (MPDSI), in which irrigation was introduced into the water balance model, has brought new opportunities for improving the scientific understanding of the effectiveness of irrigations in food security under future climate change in different levels10 (more details in Methods). Due to the availability of irrigation data, China was selected as our study area, and the most vulnerable crop, wheat, was investigated. Here, we evaluated the role of irrigation in enhancing the resilience of wheat yields to droughts in a changing climate based on the MPDSI.

Results

Historical and future evolution of droughts in both space and time

Here we used the outputs of four Global Climate Models (GCMs), namely GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR, and MIROC5, from the ISIMIP program (https://www.isimip.org/)14,15,16 to monitor interannual changes of droughts under historical, RCP2.6, RCP6.0, and RCP8.5 scenarios (Fig. 1 and Supplementary Note 3). The negative values of MPDSI mean drought conditions and vice versa. We observed fluctuating droughts from 1860 to 1910 in the historical period. The mean value of MPDSI around 1920 was lower than before (reach -1). And the mean value of MPDSI around 1990 was smaller than 1920, surpassing the lowest point of the previous period (Fig. 1a and Supplementary Fig. 3a). Under RCP2.6 scenario, wet and dry episodes fluctuated without fixed temporal patterns (Fig. 1a and Supplementary Fig. 3b). The RCP6.0 emission scenario shows a dry state, and the drought intensity changes considerably in the 2040s, and the drought intensity after that is significantly stronger (Fig. 1a and Supplementary Fig. 3c). The droughts under the RCP8.5 emission scenario are more severe than the other two scenarios, and the most severe drought events occur in the 2040s and the 2090s, and the severities are close to the most severe drought events in the historical period (Fig. 1a and Supplementary Fig. 3d). In general, droughts in the later period of the historical scenario were stronger than those in the earlier period, and drought intensities in the future scenarios are much more severe. Therefore, considerable attention should be directed to more frequent and extreme droughts as well as the relevant negative impacts in the future.

Fig. 1: Historical and future changes in modified Palmer Drought Severity Index (MPDSI) in China from 1860 to 2099.
figure 1

a Annual-mean MPDSI based on the multiple ISIMIP datasets under historical (1860–2004) and future scenarios (2005–2099). The future scenarios include the Representative Concentration Pathways 2.6 (RCP2.6), RCP6.0, and RCP8.5. The bold curve is the multi-model mean, and the range shows the maximum and minimum values of the four GCMs. b–e Spatial distribution of the Sen’s slope of MPDSI across China in modified Mann-Kendall (MMK). The diagonal line indicates that the trend is significant at the 99% level.

Full size image

Geographically, we observed a drying tendency during 1860–2004 in northwest China (Fig. 1b), especially in Northeast Plain (NCP), northwestern Northern Arid and Semi-arid Region (NASR), and Qinghai-Tibet Plateau (QTP; abbreviated names in Supplementary Table 1). Under RCP2.6 scenario, Huang-Huai-Hai Plain (HHHP) and the Middle and lower reaches of the Yangtze river Plain (MYP) were characterized by intermittent droughts and even wet conditions, while amplifying droughts were detected in NCP, southeastern QTP, and northwestern NASR (Fig. 1c). A drying tendency was observed across China under RCP6.0 and RCP8.5, and the drying trend was more significant under RCP8.5, especially in NCP and southeastern QTP (Fig. 1c, d). The drying tendency in southeastern QTP and northwestern NASR can be attributed to the increased potential evapotranspiration17. In a changing climate, increased potential evapotranspiration exacerbates droughts in areas with sparse precipitation by increasing plant water use and decreasing the recharge of water reserves. Increased potential evapotranspiration also results in a greater risk of droughts over humid areas18,19.

In this study, intensity, affected area, and duration of drought event, which are the determining factors of agricultural yield loss, were represented by the cumulative index value of MPDSI, drought-influenced area, and duration in months of each drought event (Supplementary Note 4). During the historical period, the drought duration was mostly about 0–10 months, the drought-affected area was around 10–20% of the territory of China, and the drought intensity was light in general (Supplementary Fig. 4 and Supplementary Table 4). Under RCP6.0 scenario, the drought-affected area (30%) across China increased significantly compared to that (10–20%) under the historical period but the drought duration and intensity did not change considerably (Supplementary Fig. 6 and Supplementary Table 4). Under RCP2.6 scenario, the duration of most droughts increased to 10–25 months, and the percentage of drought-affected areas was mostly 30–60%. The occurrence probability of mild drought decreased, while the frequency of severe drought increased significantly. The drought duration and the drought-affected area were significantly higher under RCP2.6 scenario than those under RCP6.0 scenario and the historical period (Supplementary Fig. 5 and Supplementary Table 4). The distribution of drought intensity under RCP8.5 scenario was more uneven compared to other scenarios, with much more frequent occurrences of extreme droughts and less occurrences of mild and moderate droughts (Supplementary Fig. 7 and Supplementary Table 4).

Impacts of droughts with different intensities on wheat yield under different scenarios

The Multiple Linear Regression (MLR), Deep Learning (DL), and Erosion-Productivity Impact Calculator (EPIC) crop model were used for the evaluation and projection of wheat yield under the historical and three RCP scenarios20,21 (more details in Methods). MLR represents the traditional statistical model with low requirements on data, while the emerging machine learning algorithm can avoid the disadvantage of MLR, i.e., the yield estimation is linear. The nature of EPIC model is different from MLR and DL. EPIC simulates yield from the physiological process of crop growth and development. The three methods have their own advantages and disadvantages. Therefore, we used these three methods to reduce the uncertainty of yield estimation results. The impacts of droughts with different intensities on wheat yields in the nine agriculture subregions of China during the historical period were shown in Fig. 2. During the historical period, we observed slight decreases or even increases in wheat yield, and the reduction in wheat production was within 15% in general during drought events. The comparison between east and west China revealed that the wheat production reduction during droughts in west China was slightly larger than that in east China. Mild droughts did not significantly affect wheat production, while with increased drought intensity, the production shifted to decrease. Specifically, HHHP, MYP, and South China (SC) were the regions with increasing wheat yield, and the increases were small under severe and extreme drought conditions (Fig. 2d, i, h). The wheat yield changes across the NASR, Loess Plateau (LP), NCP, and QTP were considerably associated with the degree of drought intensity. Wheat yield increased slightly about 1–7% under mild and moderate droughts, and decreased about 3%-9% under severe and extreme droughts (Fig. 2a–c, e). The Sichuan Basin and Surrounding Region (SBSR) and Yunnan-Guizhou Plateau (YGP) were dominated by decreased wheat yield, except that light drought may not pose a threat to the wheat yield of these regions. In these regions, moderate, severe, and extreme droughts reduced wheat yields up to 13% (Fig. 2f, g).

Fig. 2: Impacts of droughts with different intensities on wheat yields in the nine agriculture subregions of China during the historical period (1860–2004).
figure 2

The locations of the agricultural regions are shown in the panel in the center. More details of the agricultural regions can be found in Supplementary Fig. 2 and Supplementary Table 1. a–i The changes in wheat yields in the nine subregions under different drought intensities during the historical period (1860–2004). The y axis in the subplots denotes the percentage of changes in wheat yield, and negative/positive values mean loss/increase of wheat yields. Three colors, including yellow, indigo, and blue, are used to distinguish between three different yield change assessment methods, namely Multiple Linear Regression method (MLR), Deep Learning algorithm (DL), and Erosion-Productivity Impact Calculator model (EPIC), respectively.

Full size image

The drought-induced wheat yield loss in China under RCP2.6 scenario was higher than that during the historical period (Supplementary Fig. 8). The wheat yield across the HHHP and MYP regions under severe and extreme droughts suffered a loss, which is different from the historical period in which slight increases in wheat production were detected. The largest wheat yield reduction was 12% in the HHHP region, and 25% in MYP (Supplementary Fig. 8d and 8i). The wheat yield in other agriculture subregions was more affected by droughts. The wheat yield over the SC region had an increase during the historical period, but under the RCP2.6 scenario, moderate, severe, and extreme droughts reduced the wheat yield by up to 28% (Supplementary Fig. 8h). In QTP, the wheat yield under RCP2.6 increased under mild and moderate droughts, and decreased under the influence of severe and extreme droughts. The maximum yield loss was up to 18% when QTP suffered extreme droughts, which was larger than that during the historical period with the maximum yield loss of 9% (Supplementary Fig. 8e). Wheat yield across the LP and NCP regions decreased regardless of the drought intensity under RCP2.6 scenario, which was different from the changes in wheat yield during the historical period (i.e., increased during mild and moderate droughts but decreased during severe and extreme droughts). The wheat yield loss in the LP region was up to 25%, and that in the NCP region was up to 50% (Supplementary Fig. 8b and 8c). In SBSR and YGP, all drought events resulted in wheat yield loss, and the largest wheat yield loss in the two regions increased sharply from about 10% in the historical period to 35% (SBSR) and 51% (YGP) under RCP2.6 scenario (Supplementary Fig. 8f, Supplementary Fig. 8g).

On the whole, the wheat yield loss under RCP6.0 scenario was less than that under the RCP2.6 scenario but was larger than that during the historical period. Under RCP6.0 scenario, the wheat yield loss in MYP and SC regions increased by about 3–7% compared to the historical period, and decreased by about 4–6% compared to RCP 2.6 (Supplementary Table 5). When extreme droughts occurred, the maximum wheat yield loss in the MYP region was 15% under RCP6.0 and 25% under RCP2.6, respectively (Supplementary Fig. 8i, Supplementary Fig. 9i). The wheat yield loss in the SC sub-region under RCP6.0 scenario (14%) was also less than that under RCP2.6 (28%) (Supplementary Fig. 8h, Supplementary Fig. 9h). Wheat yield loss over the HHHP region exhibited few changes compared to the wheat yield under RCP2.6 scenario, but has more yield loss (about 3%) compared to the historical period (Supplementary Table 5). Wheat yield in NASR increased to 2% under RCP2.6 and 4% under RCP6.0, and decreased under RCP8.5 scenario (Supplementary Fig. 8a, Supplementary Fig. 9a; Fig. 3a). These three regions, LP, NCP, and QTP, were dominated by consistent wheat yield loss under moderate, severe, and extreme droughts. Wheat yield loss in NCP and QTP reached as high as 25% while that in LP was 16% under RCP6.0 scenario (Supplementary Fig. 9b,c, e). Compared to the wheat yield changes during the historical period, the wheat yield in these regions was more vulnerable to droughts under the RCP6.0 scenario. However, compared to RCP2.6 scenario, the wheat yield loss decreased in the LP and NCP regions, but increased in the QTP region under RCP6.0 (Supplementary Figs. 8b, c, e and. 9b, c, e). The wheat yield in the SBSR and YGP regions was dominant by a continuous decline of 7–9% regardless of the intensity of droughts compared to the historical period (Supplementary Table 5), and the largest wheat yield losses during RCP6.0 were 21% in SBSR and 27% in YGP, respectively (Supplementary Fig. 9f, g). Under RCP8.5 scenario, wheat yield across the nine agricultural sub-regions decreased, and the wheat yield loss was significantly higher than that under other scenarios. Specifically, the largest wheat yield loss in NCP and YGP was about 80% (Fig. 3c, g). Wheat yield loss in LP, HHHP, MYP, SC, and SBSR was between 60% and 70% (Fig. 3b, d, i, h, f). The wheat yield loss in the NASR region was the least, being about 17%, followed by 35% in QTP (Fig. 3a, e).

Fig. 3: Impacts of droughts with different intensities on wheat yields in the nine agriculture subregions of China under RCP8.5 (2005–2099).
figure 3

The locations of the agricultural regions are shown in the panel in the center. More details of the agricultural regions can be found in Supplementary Fig. 2 and Supplementary Table 1. a–i The changes in wheat yields in the nine subregions under different drought intensities under RCP8.5 (2005–2099). The y axis in the subplots denotes the percentage of changes in wheat yield, and negative/positive values mean loss/increase of wheat yields. Three colors, including yellow, indigo, and blue, are used to distinguish between three different yield change assessment methods, namely Multiple Linear Regression method (MLR), Deep Learning algorithm (DL), and Erosion-Productivity Impact Calculator model (EPIC), respectively.

Full size image

In order to reflect the differences of drought impacts on wheat yield under different scenarios, the wheat yield loss of the future periods was compared to the historical period (Supplementary Fig. 11 and Supplementary Table 6). We found few changes in drought-induced wheat yield losses from the historical period to RCP2.6 scenario across NASR, HHHP, and QTP (Supplementary Fig. 11d). However, in the LP, SC, and MYP regions, droughts resulted in 10% more wheat loss under RCP2.6 than in the historical scenario (Supplementary Fig. 11d). In the NCP, SBSR and YGP regions, the drought-induced loss under RCP2.6 is quadrupled under the historical period (Supplementary Fig. 11a and 11d). Droughts caused widespread wheat yield loss within the nine agricultural regions under RCP8.5 compared to the historical period (Supplementary Fig. 11c and 11f).

Comparison of wheat yields over irrigated and non-irrigated areas

MPDSI considers irrigation in its water balance model. Therefore, we compared the drought-induced wheat changes in irrigated area and the nearby non-irrigated area to evaluate the effectiveness of irrigation on alleviating drought impacts on wheat production. We found irrigation significantly alleviated drought-induced wheat yield loss under all climate scenarios except the high emission RCP8.5 scenario (Fig. 4b). During the historical period, droughts caused considerable wheat yield reductions up to 15% in the non-irrigated areas. Meanwhile, the wheat yield in the irrigated areas increased by 8%-17% under droughts on average. In other words, irrigation raised wheat yield by 23–32% in irrigated areas compared to non-irrigated areas. Under RCP6.0 scenario, irrigation effectively controlled wheat-yield reduction across the irrigated areas with a decrease rate of 0–10%, while in the non-irrigated areas the average wheat-yield reduction rates were about 2 or even 4 times larger (i.e., 21–44%). Under the RCP2.6 scenario, the wheat-yield loss was prevalent in both irrigated and non-irrigated areas, but the losses in irrigated areas were 10–15% less than that in non-irrigated areas. Under the high-emission RCP8.5 scenario, the wheat-yield reduction rates were larger than those under the other two future scenarios. However, the difference in wheat-yield reduction between the irrigated and non-irrigated areas was not discernible, suggesting that irrigation may not be able to mitigate drought-induced wheat production loss under this high-emission scenario.

Fig. 4: Drought-induced wheat yield change between irrigated and non-irrigated areas.
figure 4

According to the location of irrigated areas shown in Fig. 1, the wheat yield change caused by droughts in irrigated areas was calculated. The equal non-irrigated areas around the irrigated areas were then selected to calculate the wheat yield change. The effect of irrigation on reducing agricultural loss due to droughts in different intensities and under different scenarios was assessed and compared in a and b, respectively. The mean value of wheat yield change calculated by Multiple Linear Regression method (MLR), Deep Learning algorithm (DL), and Erosion-Productivity Impact Calculator model (EPIC) was used for the boxplots. The upper, center, and lower lines of each box show the 75th, 50th, and 25th percentiles of the data, respectively. The upper and lower limits mean the third (i.e., 75th) quartile plus 1.5*Interquartile range (IQR), and the first quartile (i.2., 25th) minus 1.5*IQR, respectively. IQR is the range from the first quartile to the third quartile. If the upper or lower limit exceeds the maximum or minimum value of the data, then the maximum or minimum value is used as the upper or lower boundary of the error bar.

Full size image

Based on the wheat yield estimation in different drought intensities, we found that drought-induced yield losses in irrigated areas were smaller than those in non-irrigated regions (Fig. 4a). Mild and moderate droughts hardly caused grain loss in irrigated areas, while non-irrigated areas were seriously affected by droughts (Fig. 2). Wheat yield in irrigated areas still increased in mild (about 7%) and moderate (1%) droughts. In contrast, wheat yield in non-irrigated areas decreased by 3% in mild droughts and by 13% in moderate droughts. In the face of severe droughts, although both irrigated and non-irrigated areas suffered yield loss, the yield loss in irrigated areas was about 15% lower than that in non-irrigated areas. In extreme drought, irrigation does little to conserve soil moisture and yield, as the yield losses were only about 1–3% different in irrigated and non-irrigated areas. In summary, drought-induced wheat yield reduction in irrigated areas was significantly lower than that in non-irrigated areas, suggesting that irrigated wheat systems are relatively more robust to climate variability than their non-irrigated counterparts. Therefore, irrigation practices are an effective drought-mitigation strategy in maintaining grain yield, but the effectiveness in mitigating drought-induced losses may be significantly reduced under a high-emission scenario and severe droughts.

Discussions

Our study considered irrigation in drought characterization using the MPDSI drought index, and assessed the effectiveness of irrigation on mitigating drought-induced wheat yield losses under historical and three future scenarios. Droughts in future scenarios were likely to be more severe than historical periods, especially under the RCP8.5 scenario. For other future scenarios, a significant increase in area affected by drought events was found in RCP6.0 scenario. Drought-induced wheat yield change was not only influenced by drought intensity and emission scenario, but also affected by irrigation which plays a vital role in ensuring the stability of wheat yield. Irrigation is an effective practice to mitigate yield losses caused by mild, moderate, and severe droughts, and under RCP2.6 and RCP6.0 scenarios. However, irrigation is not a panacea, and its effectiveness is limited under the high emission RCP8.5 scenario.

Although previous studies have investigated the effectiveness of irrigation on soil moisture conservation and yield change, the effectiveness of irrigation measures in the future changing climate has not been well examined. Previous analyses in NCP of China showed that irrigation could enhance the agricultural resilience to droughts and reduce drought-induced wheat yield loss by about a half22. Giving supplementary irrigation after droughts could cut yield reduction by over 80% and crop failure by over 50%23. We here discussed the effectiveness of irrigation when facing different degrees of drought events under different climate scenarios, and found that irrigation is not always effective in mitigating drought. Our results showed that irrigation can mitigate the adverse effects of drought during historical, RCP 2.6 and RCP6.0 scenarios, but not under RCP8.5 scenario. In the historical period, when non-irrigated areas suffered from droughts and yield reduction, the irrigated areas could achieve no yield reduction or even an increase in production due to sufficient water supply. The higher temperature in droughts leads to earlier and faster crop growth and higher biomass accumulation and yield in irrigated areas24,25,26,27. Under the RCP2.6 and RCP6.0 scenarios, the wheat yield in irrigated areas still increased when suffering mild or moderate droughts, and decreased in severe or extreme droughts. Under RCP8.5 scenario, the mitigating effect of irrigation was not significant. Since irrigation is the largest water consumption sector and water availability is a major concern for irrigation in areas such as northern China28,29,30. Therefore, the cost-effectiveness of irrigation in enhancing food security may be low under future high-emission climates.

Methods

The modified palmer drought severity index

The Palmer Drought Severity Index (PDSI) is based on the supply-and-demand concept of the water balance equation31 and is more suitable for agricultural drought monitoring than other drought indices. The modified PDSI (MPDSI) introduced the consideration of irrigation into water balance process10. Besides, the empirical parameters in the MPDSI were estimated and verified in an adaptive way based on regional geographical features of the study regions. Here we assume the future irrigation as a constant variable since that we cannot know the future irrigation and the irrigation is heavily reliant on human irrigation activities. The MPDSI values were classified into various drought levels (e.g., extreme drought, severe drought, moderate drought, mild drought, and slight drought) according to Supplementary Table 3. Drought events were identified on grid cell based on the Run Theory, and the start and end time of drought events and MPDSI values were determined. Then the drought-affected areas were delimited according to the drought duration and cumulative index values of grid cell. Drought duration was expressed by the consecutive months when the drought index MPDSI in this region reached slight drought or above. Drought intensity was defined as the cumulative value of MPDSI during the drought event.

Multiple linear regression (MLR) model

MLR is a statistical technique that builds a linear relationship between explanatory variables and response variables. MLR can predicts the outcome of response variables through several explanatory variables which is commonly used to quantify the relationship between historical drought and wheat yield, and has been widely used for the prediction and evaluation of wheat yield32. We took drought-affected area, drought intensity and drought duration as explanatory variables, and the short-term climate wheat yield as the predicted response variable (More details in Supplementary Method 1). Hodrick-Prescott filter (HP filter) method was used to detrend wheat yield before MLR-based analysis. The wheat yields can be separated to three components: long-term trend yields, short-term climate yields, and random errors33. Trend yields reflect the impact of social productivity factors, such as variety improvement and agricultural technology; climate yields mainly reflect wheat yield changes influenced by climate changes and mainly the agro-meteorological extremes33. Here we detrended the wheat yield data to quantify the wheat yield change due to drought and here we used the HP filter method for detrending analysis.

Deep learning algorithm

Deep learning (DL) has been widely used in data mining, machine learning and relevant applications34,35. The widely-used deep learning algorithms are Artificial Neural Network (ANN), Deep Neural Network (DNN), Convolutional Neural Network (CNN), and Recurrent Neural Network (RNN). Different from Multiple Linear Regression algorithm, Deep Learning algorithms can simulate both linear and nonlinear relationships without making any assumptions in advance. Wheat yield datasets are time series, and the future projection of wheat yield relies heavily on historical data. The advantage of RNN is its ability to process time-series data and predict future yield rather than extract features from images36. LSTM is a special structure type in RNN, which overcomes the deficiency of RNN in predicting long-term sequences. It is more suitable for processing and predicting the impact of important events that last relatively long in time series20,37. The study of Alibabaei et al.36 used LSTM model to estimate tomato and potato yields based on climate data, irrigation amount and soil water content, which shows that analyzing agricultural data with LSTM improves the performance of the model in terms of accuracy. LSTM was chosen as the basis of the calculation model. meteorology data, soil data, the mean MPDSI values, and wheat yield data are used as the input data of LSTM model. Normalization of the input data is conducted to avoid the impact of differences in the order of magnitude of the input variables on LSTM. Then according to the difference between the predicted value calculated by the loss function and the real value, the Back Propagation algorithm (BP) was used to adjust the model parameters until a set of optimal parameters was obtained and saved. More details of DL can be found in Supplementary Method 2.

Erosion-productivity impact calculator (EPIC) crop model

Unlike MLR based on statistics and LSTM based on machine learning, EPIC predicts yield changes by simulating the physiological processes of crop growth and development. The EPIC crop model can model crop growth and development, estimate wheat yield, and evaluate the impact of water stress on wheat yield under different drought conditions21,38. Here, we used the EPIC model to simulate wheat yield under future scenarios. EPIC model can develop its main frame according to the common physiological and ecological processes of various crops, and then simulate the growth of each crop by combining the growth parameters and field management parameters. The EPIC parameters were continuously adjusted by trial and error based on Yue et al.39. And we design two scenarios referring to Jia et al.40 research for EPIC simulations to investigate the wheat yield change caused by drought. Drought intensities characterized by MPDSI were then estimated to analyze the yield changes under different drought intensities. The final yield change of the wheat was calculated for Figs. 2 and 3 and Supplementary Figs. 8-9. More details of EPIC can be found in Supplementary Method 3.

MMK test

The Modified Mann-Kendall trend test (MMK) is a non-parametric method without assuming specific probability distributions41. It can remove the persistence effect in Mann-Kendall trend test with modified variance given the lag-i autocorrelation coefficient was significantly different from zero at the 5% significance level. In general, the pre-whitening procedure is accepted given the lag-1 autocorrelation coefficient, c, is larger than 0.1, and then the time series (x1, x2, …, xn) should be (x2-cx1, …, xn-cxn-1). The Z value of the MMK test greater than zero indicates a positive trend, and vice versa. The absolute Z value greater than 1.96 and 2.58 indicates significant trends at the 95% and 99% confidence level11,42,43.