Towards Improving Drought Forecasts Across Different Spatial and Temporal Scales

Recent water scarcities across the southwestern U.S. with severe effects on the living environment inspire the development of new methodologies to achieve reliable drought forecasting in seasonal scale. Reliable forecast of hydrologic variables, in general, is a preliminary requirement for appropriate planning of water resources and developing effective allocation policies. This study aims at developing new techniques with specific probabilistic features to improve the reliability of hydrologic forecasts, particularly the drought forecasts. The drought status in the future is determined by certain hydrologic variables that are basically estimated by the hydrologic models with rather simple to complex structures. Since the predictions of hydrologic models are prone to different sources of uncertainties, there have been several techniques examined during past several years which generally attempt to combine the predictions of single (multiple) hydrologic models to generate an ensemble of hydrologic forecasts addressing the inherent uncertainties. However, the imperfect structure of hydrologic models usually lead to systematic bias of hydrologic predictions that further appears in the forecast ensembles. This study proposes a post-processing method that is applied to the raw forecast of hydrologic variables and can develop the entire distribution of forecast around the initial single-value prediction. To establish the probability density function (PDF) of the forecast, a group of multivariate distribution functions, the so-called copula functions, are incorporated in the post-processing procedure. The performance of the new post-processing technique is tested on 2500 hypothetical case studies and the streamflow forecast of Sprague River Basin in southern Oregon. Verified by some deterministic and probabilistic verification measures, the method of Quantile Mapping as a traditional post-processing technique cannot generate the qualified forecasts as comparing with the copula-based method. The post-processing technique is then expanded to exclusively study the drought forecasts across the different spatial and temporal scales. In the proposed drought forecasting model, the drought status in the future is evaluated based on the drought status of the past seasons while the correlations between the drought variables of consecutive seasons are preserved by copula functions. The main benefit of the new forecast model is its probabilistic features in analyzing future droughts. It develops conditional probability of drought status in the forecast season and generates the PDF and cumulative distribution function (CDF) of future droughts given the past status. The conditional PDF can return the highest probable drought in the future along with an assessment of the uncertainty around that value. Using the conditional CDF for forecast season, the model can generate the maps of drought status across the basin with particular chance of occurrence in the future. In a different analysis of the conditional CDF developed for the forecast season, the chance of a particular drought in the forecast period can be approximated given the drought status of earlier seasons. The forecast methodology developed in this study shows promising results in hydrologic forecasts and its particular probabilistic features are inspiring for future studies

Improved Bayesian Multi-Modeling: Integration of Copulas and Bayesian Model Averaging

Bayesian Model Averaging (BMA) is a popular approach to combine hydrologic forecasts from individual models, and characterize the uncertainty induced by model structure. In the original form of BMA, the conditional probability density function (PDF) of each model is assumed to be a particular probability distribution (e.g. Gaussian, gamma, etc.). If the predictions of any hydrologic model do not follow certain distribution, a data transformation procedure is required prior to model averaging. Moreover, it is strongly recommended to apply BMA on unbiased forecasts, whereas it is sometimes difficult to effectively remove bias from the predictions of complex hydrologic models. To overcome these limitations, we develop an approach to integrate a group of multivariate functions, the so-called copula functions, into BMA. Here, we introduce a copula-embedded BMA (Cop-BMA) method that relaxes any assumption on the shape of conditional PDFs. Copula functions have a flexible structure and do not restrict the shape of posterior distributions. Furthermore, copulas are effective tools in removing bias from hydrologic forecasts. To compare the performance of BMA with Cop-BMA, they are applied to hydrologic forecasts from different rainfall-runoff and land-surface models. We consider the streamflow observation and simulations for ten river basins provided by the Model Parameter Estimation Experiment (MOPEX) project. Results demonstrate that the predictive distributions are more accurate and reliable, less biased, and more confident with small uncertainty after Cop-BMA application. It is also shown that the post-processed forecasts have better correlation with observation after Cop-BMA application

Improved Bayesian multimodeling: Integration of copulas and Bayesian model averaging

Bayesian Model Averaging (BMA) is a popular approach to combine hydrologic forecasts from individual models, and characterize the uncertainty induced by model structure. In the original form of BMA, the conditional probability density function (PDF) of each model is assumed to be a particular probability distribution (e.g. Gaussian, gamma, etc.). If the predictions of any hydrologic model do not follow certain distribution, a data transformation procedure is required prior to model averaging. Moreover, it is strongly recommended to apply BMA on unbiased forecasts, whereas it is sometimes difficult to effectively remove bias from the predictions of complex hydrologic models. To overcome these limitations, we develop an approach to integrate a group of multivariate functions, the so-called copula functions, into BMA. Here, we introduce a copula-embedded BMA (Cop-BMA) method that relaxes any assumption on the shape of conditional PDFs. Copula functions have a flexible structure and do not restrict the shape of posterior distributions. Furthermore, copulas are effective tools in removing bias from hydrologic forecasts. To compare the performance of BMA with Cop-BMA, they are applied to hydrologic forecasts from different rainfall-runoff and land-surface models. We consider the streamflow observation and simulations for ten river basins provided by the Model Parameter Estimation Experiment (MOPEX) project. Results demonstrate that the predictive distributions are more accurate and reliable, less biased, and more confident with small uncertainty after Cop-BMA application. It is also shown that the post-processed forecasts have better correlation with observation after Cop-BMA application

Assessment of Climate Change Impacts on Drought Return Periods Using Copula Functions

Drought events are usually characterized by their duration, severity, and intensity which are calculated based on different indices for drought recognition. Streamflow Drought Index (SDI) used in hydrological droughts is applied in this study to calculate drought variables of historical events in Upper Klamath River basin in Oregon. Historical extreme events in this area necessitate studies on possible potentials of future droughts in the region. While the return period of drought variables are mostly studied by separate probability distributions modeling individual variables, this study employs Copula functions as multivariate probability distributions to model correlated drought variables altogether within a single function. The analysis follows by development of trivariate return periods and conditional probabilities to assess drought occurrence based on joint behavior of its variables. The trivariate return period is developed for two different cases: either 1) all the variables exceed particular values or 2) each variable does. Furthermore, the impacts of climate change are investigated by application of six GCMs and one emission scenario for the future time period of 2020-2090. The results indicate less severe droughts with smaller duration in future for Upper Klamath River basin comparing to historical events which generally implies wetter climate for the region. Maximum duration of 8 months for historical droughts shrinks to 6 months for future droughts, and the maximum severity is reduced from 12 to 8 for employed index. Moreover, the GCM IPSL-CM4 predicts the most water availability in the region among other applied GCMs.Presented at The Oregon Water Conference, May 24-25, 2011, Corvallis, OR

Assessment of Climate Change Impacts on Drought Returns Periods Using Copula

Joint behavior of drought characteristics under climate change is evaluated using copula method which has recently attained popularity in analysis of complex hydrologic systems with correlated variables. Trivariate copulas are applied in this study to analyze the major drought variables; duration, severity, and intensity in the Upper Klamath River basin in Oregon. Results show that, among the variables, duration-severity is the most correlated pair whereas duration-intensity is the least correlated one. The impact of climate change on future droughts is evaluated using five Global Climate Models (GCMs) under one emission scenario. Comparing to the historical events, an overall decrease in drought duration and severity is estimated for the time period of 2020-2090 and the maximum duration is shown a decrease from 8 months to 5 months. Among the five GCMs employed in this study, GFDL-CM2.1 and CSIRO-MK3.0 are recognized as the wettest and driest projections, respectively. High uncertainty associated with GCM products is demonstrated in the analysis of return period by means of bivariate copulas; however, all projections result in larger return periods; i.e., less frequent droughts comparing to historical droughts during the reference period

Quantifying Increased Fire Risk in California in Response to Different Levels of Warming and Drying

Warming temperatures and severe droughts have contributed to increasing fire activity in California. Decadal average summer temperature in California has increased by 0.8 °C during 1984–2014, while the decadal total size of large fires has expanded by a factor of 2.5. This study proposes a multivariate probabilistic approach for quantifying changes to fire risk given different climatic conditions. Our results indicate that the risk of large fires in California increases substantially in response to unit degree changes in summer temperature. The probability of annual mean fire size exceeding its long-term average increases by 30% when summer temperature anomaly increases by 1 °C (from −0.5 °C to + 0.5 °C). Furthermore, the probability of annual average fire size exceeding its long-term average doubles when the annual precipitation decreases from the 75th (wet) to the 25th (dry) percentile. The proposed model can help manage fire-prone regions where fire activity is expected to intensify under projected global warming

Increasing probability of mortality during Indian heat waves.

Rising global temperatures are causing increases in the frequency and severity of extreme climatic events, such as floods, droughts, and heat waves. We analyze changes in summer temperatures, the frequency, severity, and duration of heat waves, and heat-related mortality in India between 1960 and 2009 using data from the India Meteorological Department. Mean temperatures across India have risen by more than 0.5°C over this period, with statistically significant increases in heat waves. Using a novel probabilistic model, we further show that the increase in summer mean temperatures in India over this period corresponds to a 146% increase in the probability of heat-related mortality events of more than 100 people. In turn, our results suggest that future climate warming will lead to substantial increases in heat-related mortality, particularly in developing low-latitude countries, such as India, where heat waves will become more frequent and populations are especially vulnerable to these extreme temperatures. Our findings indicate that even moderate increases in mean temperatures may cause great increases in heat-related mortality and support the efforts of governments and international organizations to build up the resilience of these vulnerable regions to more severe heat waves