Spatio-temporal drought forecasting within Bayesian networks
Introduction
The National Oceanic and Atmospheric Administration’s (NOAA, 2013) National Climate Data Center reported the year 2012 as the warmest year on record for the United States. Over the entire year of 2012, average temperatures of the contiguous United States were 3.2 °F above that of the 20th century. According to the U.S. Drought Monitor, more than 70% of the contiguous United States experienced some level of dry spells being classified from abnormal to exceptional droughts in 2012. The droughts of 2012 extended to the next year and approximately 58% of the contiguous United States was under drought conditions as of January 29, 2013. Many major rivers in the Western U.S., including the Colorado and the Rio Grande, had below average streamflow in the spring and summer of 2013. The ongoing droughts in the North America and many other regions across the globe are referred to the climate change and global warming effects (Trenberth, 2011, Peterson et al., 2012) and the frequency of future droughts is expected to be increasing, rather than decreasing (Sheffield and Wood, 2008, Dai, 2011). Consequently, a reliable hydrologic forecast for a region has a significant role in the efficient planning of available water resources.
Droughts have strong impacts on the water supply and quality; society and public health; crop production and agriculture; plants, wild fires, and living environments. A variety of studies in the past decades have examined the different aspects of drought events, such as developing different drought indicators (Niemeyer, 2008, Mishra and Singh, 2010), monitoring and characterizing the droughts (Andreadis and Lettenmaier, 2006, Shukla et al., 2011, Shiau, 2006, Dupuis, 2007), climate change impacts on future droughts (Ghosh and Mujumdar, 2007, Sheffield and Wood, 2008, Burke et al., 2010, Moradkhani et al., 2010, Risley et al., 2011, Madadgar and Moradkhani, 2011), and developing early warning systems to survive in drought conditions (Huang and Chou, 2008). There are also a number of studies focused on drought forecasting and estimating the likely drought conditions in the future. In an earlier study, Karl et al. (1987) evaluated the probability of receiving a sufficient amount of precipitation to recover from an ongoing drought over a particular period of time. They rewrote the Palmer Drought Severity Index (PDSI; Palmer, 1965) and utilized the unconditional gamma distribution to obtain the probabilities of future droughts. However, this is disputed for ignoring the dependency and auto-correlation in a precipitation record. Since then, several other methods have been developed and tested in drought forecasting such as Markov Chain model (Lohani and Loganathan, 1997, Steinemann, 2003), stochastic renewal models (Kendall and Dracup, 1992, Loaiciga and Leipnik, 1996), stochastic autoregressive models (Mishra and Desai, 2005), and artificial neural networks (Mishra and Desai, 2006, Barros and Bowden, 2008). Cancelliere et al. (2007) discussed the validity of Markov Chain model for making significant errors in transition probabilities of the Standardized Precipitation Index (SPI; McKee et al., 1993) and then derived the transition probability matrix by an analytical study on the statistics underlying the SPI equations. However, Madadgar and Moradkhani (2013) recently argued, in an analytical framework, that the assumption of independent and normally distributed aggregated precipitation volumes is not always true, especially for other hydrologic variables such as runoff and streamflow. They also discussed that for frequency analysis of different drought states, the intense process of obtaining the transition probability matrix from the index equation could be avoided by using multivariate modeling based on copula functions (Joe, 1997). In several other studies, the climate forecast products of NOAA Climate Prediction Center (CPC) are used for developing probabilistic drought forecasts (Carbone and Dow, 2005, Hwang and Carbone, 2009). However, Steinemann (2006) discussed the poor interpretation of forecast probability and uncertainty information supported by CPC forecast products in real applications.
This study extends the application of the recently developed model in drought forecasting by Madadgar and Moradkhani (2013). In the previous application, the forecast model predicted the future droughts of the Gunnison River Basin (GRB) in Colorado, USA, using the flow volume at the basin outlet. The promising results of that study have encouraged the authors to apply their forecast model in estimating the spatial variation of future droughts using the runoff volume at different grid cells across the basin. Copulas (Joe, 1997, Nelsen, 1999), as the main core of the proposed forecast model, are multivariate distribution functions that join the marginal distributions of the variables with some level of dependency and correlation. According to the existent correlations among the hydrologic variables like runoff, streamflow, groundwater level, and many other variables, the copula functions have been examined in different hydrologic applications over the past few years (e.g. Favre et al., 2004, Bárdossy, 2006, Shiau, 2006, Dupuis, 2007, Zhang and Singh, 2007, Salvadori and De Michele, 2010, Kao and Govindaraju, 2008, Kao and Govindaraju, 2010, Madadgar and Moradkhani, 2011, Madadgar et al., 2012). In drought applications, copulas have been used to characterize the future droughts in terms of estimating the return period of droughts’ severity, intensity, and duration, (Shiau, 2006, Dupuis, 2007, Kao and Govindaraju, 2010, Wong et al., 2010, Madadgar and Moradkhani, 2011). However, in a recent study by Madadgar and Moradkhani (2013), a new application of copula functions in drought forecasting was examined, where instead of analyzing the drought characteristics; they studied the occurrence probability of seasonal droughts regarding streamflow observations. They defined the conditional probability of streamflow via Bayesian networks. According to the correlations among the streamflow of consecutive seasons, the conditional probabilities of seasonal droughts were analyzed using the copula functions adopted in a Bayesian framework. This study aims at extending the application of the proposed copula-based method to estimate the spatial variation of future drought probabilities across the GRB. For this purpose, the runoff generated across the basin is used to evaluate the spatial variation of droughts; while in the previous study, the streamflow observations at a particular point were used for drought forecasting.
The paper is organized as follows. Section 2 explains the drought index to evaluate droughts based on the runoff volume at each spatial unit across the basin. Section 3 describes the hydrologic modeling of GRB and analyzes the historical droughts of the basin. Section 4 elaborates on the probabilistic forecast methodology employed in this study, and is followed by a discussion on the required analyses to apply the forecast model (Section 5). Section 6 demonstrates some forecast products for the study basin and discusses the results. Finally, Section 7 summarizes the major remarks of the study.
Section snippets
Standardized Runoff Index (SRI)
Standardized Runoff Index (SRI; Shukla and Wood, 2008) is used to evaluate the spatial variation of the hydrologic drought across the study area. As with all Standardized Indices (SI), the SRI of each spatial unit reflects the anomalies of surface runoff from its average value generated in the same unit. Mathematically, SRI is defined as the standardized normal variable of the accumulated surface runoff over a specific time period:
Hydrologic modeling of study area
The study basin for the application of drought forecast model is the Gunnison River Basin, one of the headwater sub-basins of the Colorado River Basin (CRB), located in the southwestern United States (DeChant and Moradkhani, 2011a, DeChant and Moradkhani, 2011b). The CRB is divided into upper and lower portions and encompasses parts of seven States: Wyoming, Colorado, Utah, Nevada, California, New Mexico, and Arizona. The GRB consists of seven hydrologic units defined by the U.S. Geological
Probabilistic drought forecast methodology
Drought is an evolving extreme event that occurs over a given period of time. Drought status of a region at any time depends on the water availability (precipitation, soil moisture, runoff, etc.), within the past few months or seasons. In other words, water availability in the past plays a significant role in future drought status. Since drought-related variables (e.g. runoff, streamflow, drought indices, etc.) are statistically dependent on their past status (Madadgar and Moradkhani, 2013),
Correlation analysis and copula fitting
Drought forecasts in the GRB, based on the runoff volume produced in each of the 37 HRUs of the basin (Fig. 1), are examined through the copula-based technique described in the previous section. The runoff of each HRU is accumulated over six months, beginning from different months (January–December) during 32 years from 1979 to 2011. To find the predictor and forecast months with reasonable dependency in associated accumulated runoffs, a correlation analysis is examined for different months (
Drought forecasting products
Future droughts can be analyzed from different perspectives and various products can be generated using the methodology explained in this study. One useful analysis is the forecast of drought-related variables such as runoff, soil moisture, and snow pack across the study area. It would be even more useful to estimate the uncertainty range of forecast variables as well. An advantage of the forecast model proposed in this study is the ability to approximate the forecast uncertainty, via the
Summary and conclusion
Since frequent droughts have recently affected the southwestern U.S. with different water issues, reliable forecast of future droughts are essential for this region of the United States. The historical records across the Colorado River Basin denote the water year 2012 as the 4th driest year of the region in the past century (since 1904), with consequences like insufficient water supply, poor pasture and crop conditions, and region-wide wildfires. Whereas the recent droughts of CRB might be
Acknowledgments
Partial financial support for this study was provided by NOAA-MAPP Grant NA110AR4310140.
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