Real-time flood forecasting updating is essential in improving the forecasting performance and preventing flood damages. The advanced dynamic system response curve (DSRC) method has been validated to be effective by adjusting precipitation based on simulated streamflow errors. However, the time lag between input-output signals is not explicitly considered in the original DSRC, resulting in the problem that the most recent precipitation information is not utilized in updating the forecasting. Moreover, regularization techniques are normally introduced in DSRC to ensure the numerical stability of error estimation, however, the commonly used Ridge estimator can result in excessive adjustment of precipitation. To address these critical issues, we proposed an improved precipitation adjustment framework (DSRC-ARMA) that integrated the DSRC method and the autoregressive-moving average (ARMA) model, such that the most recent precipitation information can be used for a complete precipitation adjustment. Moreover, alternative regularized estimators (i.e., the Lasso and Elastic Net estimators) were introduced and cross-compared to prevent the excessive adjustment issue. The performance of the proposed framework was evaluated in two basins in China. The results showed that the DSRC-ARMA method outperformed the original DSRC method in terms of overall goodness-of-fit (e.g., Nash-Sutcliffe efficiency improved from 0.94 f 0.03 to 0.95 f 0.04 and 0.89 f 0.05 to 0.91 f 0.05, respectively in Dapoling (DPL) and Jianyang (JY) basin) and particularly capturing the peak flows (relative error of peak flow decreased from 13.6 f 7.3 % to 5.2 f 3.7 % and from 10.1 f 7.8 % to 5.9 f 3.5 % in DPL and JY, respectively). For different regularized estimators, the Ridge estimator was most suitable for the rainfall events without intermittent non-rainfall time segments (due to its veracity feature); while the Lasso estimator performed better for intermittent rainfall events, due to its feature of sparsity that can confine non-rainfall period errors to be zeros and thus avoid excessive adjustment. Overall, the proposed precipitation adjustment framework holds the potential to enhance the real-time flood forecasting accuracy, thereby offering a valuable approach for flood mitigation.

Flash droughts tend to cause severe damage to agriculture due to their characteristics of sudden onset and rapid intensification. Early detection of the response of vegetation to flash droughts is of utmost importance in mitigating the effects of flash droughts, as it can provide a scientific basis for establishing an early warning system. The commonly used method of determining the response time of vegetation to flash drought, based on the response time index or the correlation between the precipitation anomaly and vegetation growth anomaly, leads to the late detection of irreversible drought effects on vegetation, which may not be sufficient for use in analyzing the response of vegetation to flash drought for early earning. The evapotranspiration-based (ET-based) drought indices are an effective indicator for identifying and monitoring flash drought. This study proposes a novel approach that applies cross-spectral analysis to an ET-based drought index, i.e., Evaporative Stress Anomaly Index (ESAI), as the forcing and a vegetation-based drought index, i.e., Normalized Vegetation Anomaly Index (NVAI), as the response, both from medium-resolution remote sensing data, to estimate the time lag of the response of vegetation vitality status to flash drought. An experiment on the novel method was carried out in North China during March-September for the period of 2001-2020 using remote sensing products at 1 km spatial resolution. The results show that the average time lag of the response of vegetation to water availability during flash droughts estimated by the cross-spectral analysis over North China in 2001-2020 was 5.9 days, which is shorter than the results measured by the widely used response time index (26.5 days). The main difference between the phase lag from the cross-spectral analysis method and the response time from the response time index method lies in the fundamental processes behind the definitions of the vegetation response in the two methods, i.e., a subtle and dynamic fluctuation signature in the response signal (vegetation-based drought index) that correlates with the fluctuation in the forcing signal (ET-based drought index) versus an irreversible impact indicated by a negative NDVI anomaly. The time lag of the response of vegetation to flash droughts varied with vegetation types and irrigation conditions. The average time lag for rainfed cropland, irrigated cropland, grassland, and forest in North China was 5.4, 5.8, 6.1, and 6.9 days, respectively. Forests have a longer response time to flash droughts than grasses and crops due to their deeper root systems, and irrigation can mitigate the impacts of flash droughts. Our method, based on cross-spectral analysis and the ET-based drought index, is innovative and can provide an earlier warning of impending drought impacts, rather than waiting for the irreversible impacts to occur. The information detected at an earlier stage of flash droughts can help decision makers in developing more effective and timely strategies to mitigate the impact of flash droughts on ecosystems.