Flash drought fades away under the effect of accumulated water deficits: the persistence and transition to conventional drought

Flash drought typically refers to the rapid intensification process that would only persist for a certain amount of time. In spite of short duration, flash drought may cause destructive impacts on agricultural and ecological sectors due to the sustained drought severity during or after the rapid intensification period. Understanding the persistence of flash drought, its regional patterns, and to what extent a transition from rapid intensification to conventional drought occurs is beneficial for drought monitoring and drought management. Employing surface and root-zone soil moisture reanalysis datasets, the notion of accumulated water deficits over varying time scales (can be detected by the moving averages of daily soil moisture series from 1 to 300 d) was introduced to explore how the signal of flash drought fades away over China during the period of 1950–2021. Results show that the flash drought signal gradually attenuates under the increased time scales of water deficits. With significant spatial differences, more than 50% of flash drought on average would be lost at a 10 d time scale, and the attenuation ratio may reach 90% when the time scale increases to 100 d. Under the effects of accumulated water deficits, the majority of flash drought events may evolve into conventional drought before dissipating completely. Soil moisture memory has a finite effect on the attenuation of flash drought signal. Flash drought signal dissipates slowly in areas with strong soil moisture memory. As time scale increases, both flash drought signal and the memory of soil moisture decrease, and their correlation also weakens.


Introduction
Flash drought, characterized by both rapid onset and intensification rate, is one kind of drought distinguished from the four traditional types (i.e.meteorological, agricultural, hydrological, and socioeconomical; Mishra and Singh 2010).Under the combined effects of high temperature and moisture deficit conditions (Mo and Lettenmaier 2015, Basara et al 2019, Mukherjee and Mishra 2022), the formation of flash drought is typically recognized to be as short as two weeks (Ford and Labosier 2017), which breaks the understanding of conventional drought as creeping, and slowly developed over one month or longer time periods (Yuan et al 2019, Mahto and Mishra 2020, Zhang et al 2021, Tyagi et al 2022).In spite of the distinctions for the physical driving mechanisms and the speed of drought development, several studies suggested a close relationship exists between flash drought and conventional drought (Otkin et al 2018, Osman et al 2021).The devastating impacts caused by flash drought on agricultural lands, vegetation health, and economy were usually the results of the sustained development of actual drought severity during or after the rapid intensification period, such as the 2021 and 2017 flash droughts in the U.S. (Otkin et al 2021).Several studies also identified the cases that flash drought transitioned to conventional drought after the rapid intensification period terminated (Christian et al 2019, Liu et al 2020).And a natural question is how long would flash drought persist, and to what extent a transition from rapid intensification to conventional drought occurs.
The fact that drought may transform from one type to another has been well recognized in literature, however, most of them were focused on the relationship among the four traditional drought types (Mishra and Singh 2010), while knowledge of the transformation mechanism from flash drought to conventional is generally rare.For example, starting from atmospheric dryness, a variety of studies analyzed the subsequent process for arousing negative anomalies in soil moisture or streamflow under prolonged moisture deficit conditions (Peña-Gallardo et al 2019, Apurv and Cai 2020, Zhu et al 2021, Shi et al 2022).With the shifts of affected water bodies, changes of drought characteristics are also apparent during the propagation process, manifested as extended drought duration and enhanced drought severity (Van Loon 2015, Hao et al 2018, Zhang et al 2022a, 2022b).This shows how the evolution of drought can be affected by the accumulated water deficits over time.Due to this reason, the water deficits accumulated over different time scales were commonly employed as indicators to distinguish and characterize droughts of different types, and were also effective tools for interpreting the transition of drought signal among different droughts (Vicente-Serrano and López-Moreno 2005, Liu et al 2017, Manning et al 2018, Zhang et al 2019).
Similar to conventional drought, we also introduce the notion of accumulated water deficits over different time scales for investigating how flash drought signal dissipates and its potential of transferring into conventional drought.The changes of drought signal (i.e.flash drought or conventional drought) can be detected according to the intensification rate of drought condition represented by water deficits over different time scales.Given the close relationship between soil moisture and vegetation condition, we use soil moisture data at surface and root-zone layers, respectively, to identify flash drought events under varying time scales, and address several questions: (1) how long does flash drought persist?(2) Where does the signal of flash drought go with gradually extended time scales, and the effects of accumulated water deficits on the persistence of flash drought signal?In the context of climate change, flash drought may become more frequent (Pendergrass et al 2020, Qing et al 2022), and knowledge on the persistence of flash drought and their ongoing impacts on the hydrological system is essential for drought monitoring and management.This study is structured as follows.Section 2 describes data and methodology used in the study.Section 3 provides results, followed by discussion and conclusions in section 4.

Data
Soil moisture data from the enhanced version of the fifth generation of the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (hereafter referred to as ERA5-Land) was employed for analysis.Compared to ERA5 and the older ERAinterim datasets, the estimation of soil moisture in ERA5-Land has improved accuracy both for the surface layer and root zone (Muñoz-Sabater et al 2021).The horizontal resolution of ERA5-Land is 9 km, and the temporal resolution is hourly.The ERA5-Land also provides integrated products of varied spatial and temporal resolutions.We selected the daily data at a spatial resolution of 0.25 • , and the periods were from 1950 to 2021.The ERA5-Land provides soil moisture estimates for four layers (i.e.0 ∼ 7 cm, 7 ∼ 28 cm, 28 ∼ 100 cm, and 100 ∼ 289 cm).In this study, the values for the top layer, and the averages of the top three layers (0-100 cm) were used to analyze the behavior of surface and root zone soil moisture, respectively.We also used in-situ soil moisture data from the International Soil Moisture Network (ISMN), which contains 40 stations (see figure S1 in supporting information for the spatial distribution, and the observational data of one site was chosen as an example to show how the onset of flash drought changes under extended time scales in the following section) over China with measurements up to 1 m depth, which are available from January 1981 to December 1999 (Liu et al 2001, Dorigo et al 2021).

Flash drought identification
Flash drought events were identified based on the intensification rate of soil moisture percentile (SMP).Daily soil moisture series were classified into 12 groups according to their calendar month.For each month, 13 candidate theoretical probability distributions (including beta, gamma, log-logistic, generalized extreme value, loglog, Weibull, exponential, generalized Pareto, Nakagami, Birnbaum-Saunders, normal, Ray, and Rici distributions) were employed to fit the samples of each grid cell, respectively, and the best fit was chosen as the one that passed the Kolmogorov-Smirnov test at the 95% significance level, along with the minimum root-meansquare error.The derived cumulative probabilities were assigned to each calendar day to constitute a SMP series.Then we use the consecutive SMP series to identify drought events.In this study, drought events are identified when the following three criteria are met: (i) the SMP is below 40%, and the first time that SMP falls below 40% represents the onset time of drought, and a drought event terminates when SMP exceeds 40%; (ii) there should contain at least one time interval that SMP falls below 20% to ensure the event really falls into drought; and (iii) the duration of drought events should be no less than one week.The above three criteria are also used for flash drought identification.On this basis, one more criterion was added, that is 'flash droughts' to be situations when SMP drops from above 40% to below 20% within 20 d (to ensure the event has the rapid intensification process) (Ford andLabosier 2017, Otkin et al 2018).For cases that a drought event has a sudden onset (fulfilling the criteria of flash onset) and lasted for a long period, the term 'flash drought' should be reserved for the time period during which the rapid intensification occurred (Otkin et al 2018).
To explore how the dry signal (the signal here includes both the strictly intensification process and the drought component) attenuates during the development process, the notion of accumulated water deficits at varied time scales is introduced.Following the mathematical method of the standardized precipitation index (McKee et al 1993), a moving average window is implemented to soil moisture series to generate SMP at different time scales.For example, SMP at a k-day time scale (denoted as SMP-k, and k represent the window size and can be any positive integer) can be generated on the basis of k-day moving average of daily soil moisture series, then transformed into standardized index values through the theoretical probability distribution as aforementioned for calculating SMP.In this study, the moving window k ranged from 1 to 300 d, and for SMP generated under varied window size, the corresponding characteristics such as the number of drought events, and drought duration (denoted as T dur ) were extracted.Flash drought onset (denoted as T onset ) is recognized as the first time that SMP falls below 40%, while the drought duration measures the temporal length from drought onset to the termination of a drought event (the time when SMP exceeds 40%).The lagging of drought is measured as the difference of drought initiation time indicated by SMP at varying time scales.In addition, the attenuation rate of flash drought signal was also introduced to measure the changes of flash drought events over varying time scales.In this study, the attenuation rate is computed as the ratio of the number of flash drought events indicated by SMP-k (namely how many events could be retained under a k-day time scale, and can be viewed as the intensity of flash drought signal) to those of SMP-1.Values of the attenuation rate over 100% indicates the increased number of flash drought events (also enhanced signal of flash drought) under SMP-k, while 0% of the attenuation rate represents the total loss of flash drought signal.

Attenuation of flash drought signal under prolonged time scale
The observational soil moisture data from ISMN was first used to generate SMP at different time scales to show the variation of flash drought and the compositing drought over time.Figure 1 shows the time series of SMP-10, SMP-20, SMP-50, and SMP-100 of the Nanchong site (106.1 • E, 30.68 • N; data are from ISMN) for the 1985-1986 drought event.For SMP-10, the soil moisture took 3 three days (i.e.T onset = 3 d) to drop from above 40th percentile to 20th percentile, which is a typical rapid intensification process.With increased time scales, the onset stage of drought also increased, and T onset for SMP-20, SMP-50, and SMP-100 were 10 d, 20 d, and 31 d, respectively.According to the criterion of flash drought proposed by Ford and Labosier (2017), a rapid intensification process can be recognized with drought onset of no more than 20 d.In other words, for the Nanchong site, the flash drought signal would be lost at a compositing time scale of 50 d, while the drying process would follow the way of the traditional slowly-evolved drought at lengthened time scales.It is worth mentioning that although the initiation time of droughts indicated by SMP-10, SMP-20, SMP-50, and SMP-100 are different, more than 50% of their drought duration were overlapped.For instance, figure 1 shows that both SMP-10 and SMP-100 suggested the Nanchang site were under drought status during January 1986 and March 1986, and the overlapping time period accounts for approximately two thirds of drought duration.In this sense, droughts at 10 d and 100 d scales could be recognized as the same drought event.This shows the superiority of short time scales in providing the precursor signal of drought, which is also crucial for improving drought early warning techniques.In addition, drought propagation features, such as lagging and lengthened duration (Van Loon 2015), can also be found under extended time scales.For instance, comparison of the onset time of SMP-10, SMP-50 and SMP-100 presented lagged response of 12 d and 35 d, respectively.The duration of drought corresponding to SMP-10, SMP-20, SMP-50, and SMP-100 were 96 d, 103 d, 116 d, and 92 d.Based on the surface soil moisture of the ERA5-Land, figure 2(a) shows the attenuation rate of flash drought signal at varying time scales for all grid cells over China.The attenuation rate is computed as the ratio of the number of flash drought events indicated by SMP-k to those of SMP-1.In other words, the percentages in figure 2(a) represent how many events can be captured under a k-day moving window.It can be seen that the number of flash drought events  decreased as the time scale increased.For example, the attenuation rate of flash drought signal ranged between 45% and 73% (corresponding to the 10% and 90% of the attenuation rate of all grid cells in China), with a mean of 59% at a 10 d time scale, and the attenuation rate falls below 50% at a 30 d time scale, meaning that more than half of the flash drought events would be missed.When the time scale increased to 100 d, 90% of flash drought signal would be lost in most regions of China.Figure 2(b) shows the spatial distribution of the time scales corresponding to 90% losses of flash drought events.With significant regional differences, Northeast China (NE), Central China (CEN), and western Tibet Plateau exhibited the lowest values of moving days, where 90% losses of flash drought may occur at time scales of no more than 50 d.For Huang-Huai-Hai (HHH) Plain, Northwest China (NW), and South China (SOU), the time scale ranged between 60 and 100 d.The longest time scales were found in the eastern Tibet Plateau (TibE) and southwest China (SW), ranging between 200 and 300 d.Cases of the root-zone soil moisture are shown in figure S2 in supporting information.Generally, in most regions of China, the time scales corresponding to 90% losses of flash drought signal ranged between 30 and 40 d, which were lower than cases of the surface soil moisture.
Figure 3 compares the attenuation rates of flash drought indicated by surface soil moisture and rootzone soil moisture of 10th ∼ 90th percentile for all grid cells in each sub-region over time.Generally, the amounts of flash drought events for the surface layer were two to three folds of those identified by the rootzone layer according to the bar plots in each panel in figure 3. Significant regional differences were found in seven typical sub-regions of China.In CEN, NE, and central Tibet Plateau, the patterns of attenuation curves for surface soil moisture were generally similar to those of the root-zone soil moisture.In NW and HHH, the curves of root-zone soil moisture overall presented a phase shifting pattern (with lagging behind by 15 d for NW, and by 8 d for HHH on average) compared to that of the surface soil moisture, implying that the attenuation rate of root-zone soil moisture was lower than of the surface.In SOU and TibE, the curves both showed a crossed pattern, where the signal of surface soil moisture attenuated more slowly than the root-zone soil moisture before the cross point.After that, the attenuation rates of the two layers were generally comparable in SOU, while for TibE, the root-zone soil moisture attenuated more slowly than did the surface.

Transition of flash drought to conventional drought
To explore how the signal of flash drought attenuated over time and their relation with traditional slowlyevolved droughts, a Sankey diagram was introduced to depict the transformation of drought events at a 30 d, 60 d, 90 d, 120 d, and 300 d time scales, respectively.Based on the flash drought identification method in section 2.2, these events were classified into five categories according to their onset time and the duration of drought, i.e. flash drought with long duration (FDLD; T dur ⩾ 30 d, and T onset ⩽ 20 d), flash drought with short duration (FDSD; 7 d ⩽ T dur < 30 d, and T onset ⩽ 20 d), slowly-evolved droughts with short duration (SDSD; 7 d ⩽ T dur < 30 d, and T onset > 20 d), slowly-evolved droughts with long duration (SDLD; T dur ⩾ 30 d, and T onset > 20 d), and non-droughts (NON, i.e. the moisture condition indicated by SMP does not satisfy all three thresholds of identifying drought events mentioned in section 2.2).In this study, traditional drought refers to the drought events that do not have the rapid drought onset, i.e.SDSD and SDLD. Figure 4 exhibits the proportion of each drought category generated from millions of drought events of all grid cells over China.The percentage in the figure represents the ratio of five each drought category to the number of all drought events for the current moving window.In other words, the sum of percentages in each column equals to 100%.At a 30 d time scale, the FDSD accounted for the highest proportion (35.75%), while FDLD accounted for the lowest proportion (10.49%), and proportions of other three categories were generally comparable.As the time scale increased, the proportion of SDLD and NON also increased, and 35.61% of drought events were classified into NON at a 300 d scale.This suggests the vanishing signal of flash drought (particularly for FDLD) may not necessarily signify the termination of drought, instead, flash drought may first transform into SDLD, and terminate as NON over time.In this sense, SDLD acts more like a medium linking flash drought and non-drought.In addition, considerable non-drought events at a 30 d time scale may also evolve into droughts as the time scale increases, under the cumulative effects of prolonged water deficits conditions.Similar phenomenon can be found for the root-zone soil moisture in figure S3 in the Supporting Information.

Relationship with the memory of soil moisture
The memory of soil moisture is a rough measurement on the time taken for the soil column to dissipate an imposed positive or negative anomaly (Ghannam et al 2016, McColl et al 2017).Given its indicative role on the persistence of soil moisture state, we explored its influence on the attenuation of flash drought signal over time.Taking the grid cell where the Beijing city is located as an example, both the attenuation rate of flash drought signal and the autocorrelation coefficient of soil moisture (indicating strong memory of soil moisture when the coefficient value is high) showed a decreasing pattern over extend days, and a good synchronization between the two factors was apparent within the time scale of 30 d (see supporting information in figure S4). Figure 5 displays the scatterplots of the attenuation rate of flash drought and the memory of surface soil moisture under varied time scales moving at a time interval of 2 d (i.e.panels from (a) to (p) corresponding to results at 1 d-31 d time scales, respectively).The colors in the figure represent the density of points, and the density decreases from red to blue.It is worth mentioning that the attenuation rate above 100% in figure 5 suggests the increased number of flash drought events at k-day moving time scales comparing to those of SMP-1.Such phenomenon represents the rare condition and mostly occurs at short moving time scales (i.e.k is of low value).For instance, some events (especially those very approaching to but not meet the critical thresholds of flash drought identification) were filtered out under 1 d time scale, but may satisfy the criterion of flash drought identification as a result of k-day moving treatments, leading to the attenuation ratio slightly higher than 100%.The x-axis in each panel shows the strength of the memory effect, where higher values of the correlation coefficients correspond to stronger memory effect of the surface soil.It can be seen that the attenuation of flash drought signal was negatively correlated with the memory of soil moisture at short time scales (figures 5(a)-(d)), that is, flash drought attenuated more slowly in areas with strong soil moisture memory.With extended time scales (approximately 11 d of lagging time or more, figures 5(f)-(p)), both the number of flash drought events and the memory effect of soil moisture decreased, meanwhile, their correlation also weakened according to the discretely distributed scatters.This suggests the soil moisture memory has a finite effect on the attenuation of flash drought, and such influence may gradually weaken over time.

Discussion
Some uncertainty may exist for the derived results regarding how we define flash drought events.Among the diverse definition of flash drought, we use the definition that 'the decline of SMP from above 40% to below 20% within 20 days' as the criterion, which is also a common selection in recent flash drought related researches (e.g.Ford and Labosier 2017, Otkin et al 2018, Yuan et al 2019).One major reason for choosing this definition lies in that it is suggested to perform better in capturing the onset of flash drought (Osman et al 2021).Given the objective of this study, accurate recognition of flash drought onset is particularly important for distinguishing the variation of flash drought characteristics (e.g. the onset time, the transition to conventional drought) under the accumulated effects of water deficits over time.In addition, according to the sensitivity tests of thresholds by Liu et al (2020), the definition that 'the decline of SMP from above 40% to below 20% within 20 days' was also capable of generating rational results of flash drought frequency in China.This is quite relevant to the attenuation rate of flash drought signal which is computed as the ratio of the flash drought events under k-day moving window to those of SMP-1.For instance, alteration of the upper or lower limits (i.e.thresholds of 40% and 20%) of the definition may increase/decrease the number of identified flash drought events, leading to a potential change for the specific values of the attenuate rate of flash drought signal.Nonetheless, the overall downward pattern of flash drought signal under extended time scales (figures 2 and 3) would not be influenced a lot.The rational choice of flash drought definition is necessary for acquiring more accurate and reliable results.
From the perspective of flash drought motoring and forecasting, the results may provide some implications on the selection of an optimal time scale for flash drought identification.According to figures 2 and 3, SMP at short time scales are capable of capturing more flash drought events.The huge massive information provides sufficient samples for understanding the diverse patters of flash droughts.Moreover, the precursor signal of drought especially those develop in strong intensity within one week, also provides valuable information for strategies of drought adaption and management.It is worth mentioning that the actual impacts should also be considered when using indicators at very short time scales.For instance, the drought indicated by SMP-1 to SMP-4 with duration less than week, may impose negligible impacts on the environment.Accordingly, such minor events could be filtered out before analyzing drought trend or evaluating their ecological impacts.As the time scale increases, the signal of flash drought dissipates gradually (figure 2).This suggests considerable flash drought events could be lost by using SMP at long time scales.For the purpose of improving drought monitoring and forecasting techniques, the indicator should be capable of capturing at least 80% of flash drought events so as to contain effective and timely information of drought.For the case of China, a time scale ranging between 5 and 15 d is recommended (figure 3).Regional differences also exist regarding the patterns of the attenuation rate of flash drought.Overall, the signal of flash drought in SOU and TibE dissipates slowly than in other regions, accordingly SMP at slightly long time scales can be used in these regions.Reasons for the diverse patterns of the attenuation rate are complicated, and a variety of factors, such as the climate conditions (both moisture and energy conditions), soil type and properties, and vegetation type and densities, are suggested to have substantial influences on the evaporative rate of moisture from soil profile (Seneviratne et al 2010).These further determine the time period consumed for flash drought to initiate and the magnitude of water deficits may intensity (Koster et al 2019).The soil moisture memory to some extent represents the comprehensive effects of such factors, and is also suggested to have a finite influence on the attenuate rate of flash drought (figure 5).In future researches, a quantitative evaluation framework is necessary to quantify the specific role of each affecting factor on Y Liu et al the attenuation pattern of flash drought, which is also conductive to the understanding the formation and development mechanism of flash drought.

Conclusions
The time scale over which water deficits are accumulated is an important metric to distinguish and characterize drought with varied features (Zhu et al 2021).Focusing on flash drought, the reanalysis soil moisture datasets at the surface and root-zone layers during 1950-2021 were employed to investigate the effect of accumulated water deficits on the onset time of flash drought, the attenuation rate of flash drought signal, and the transformation mechanism among droughts with varied characteristics.Similar to conventional drought, drought propagation features such as the lagging and lengthened duration were also found for flash drought under extended time scales.The onset time of flash drought, which is typically employed as an essential metric for judging the 'flash' characteristic of drought events (Ford and Labosier 2017), showed a gradually lengthened pattern as the time scale increased (figure 1).This leads to considerable drought events that no longer have the characteristic of 'flash' due to the extended time period for drought initiation.The likelihood of flash drought signal to transform into conventional droughts under the effect of time scale was further supported by the Sankey diagram in figure 4, where the proportion of flash droughts decreased as the time scale increased, along with enlarged proportions for slowly-evolving droughts and non-drought conditions.The results highlight the transition from flash drought to conventional drought before dissipating a negative anomaly completely (Otkin et al 2018).Spatially, the flash drought signal attenuated more quickly in NE China, CEN China, and western Tibet Plateau, followed by the HHH Plain, NW China, and SOU China.In contrast, much more time was consumed (ranging between 200 and 300 d) in the TibE Plateau and SW China to dissipate a flash drought signal.Such a spatial difference may partially be related to the memory effect of soil moisture, where flash drought attenuates more slowly in areas with strong soil moisture memory at short time scales (Ghannam et al 2016).With extended time scales, both the amount of flash drought events and the memory effect of soil moisture decrease, and their correlation also weakens, that is, the soil moisture memory has a finite influence on the attenuation of flash drought (figure 5).
From a perspective of time scale, results of this study illustrate how the signal of flash drought changes and transitioned into conventional drought over time, which has potential implications for drought monitoring and management in a warming world.

Figure 1 .
Figure 1.The onset time (Tonset), drought duration (T dur ), and lagging time of flash drought at different time scales for the Nanchong site (106.1 • E, 30.68 • N, located in central China).The yellow and red solid lines represent the 40th (representing mild drought) and 20th (representing severe drought) percentile of soil moisture.Data are from the ISMN during 1985-1986.

Figure 2 .
Figure 2. (a) The attenuation rate of flash drought signal (indicated by surface soil moisture) at varying time scales for all grid cells over China.The yellow and orange shades show the 10th ∼ 90th, and 25th ∼ 75th percentiles of grid cell values, respectively, and the dashed line show the areal means.(b) Spatial distribution of the time scales for 90% losses of flash drought signal.Data are from ERA5-Land.

Figure 3 .
Figure 3.As in figure 2 but for the patterns of surface soil moisture and root-zone soil moisture in different regions in China.The boxplots show the moving days corresponding to 90% losses of flash drought signal in each region for surface soil moisture and root-zone soil moisture.

Figure 4 .
Figure 4. Sankey diagram showing the transformation process among different drought types under extended time scales.The percentage in the figure represents the ratio of five drought categories to the number of all drought events for the current time scale.

Figure 5 .
Figure 5. Scatterplots of the attenuation rate of flash drought signal and the memory of surface soil moisture for all grid cells over China.(a)-(p) show the relationships of varied time scales moving at a time interval of two days, and higher values of correlation coefficients (x-axis) represent stronger memory of the surface soil moisture.The colors in the figure represent the density of points, and the density decreases from red to blue.