Probabilistic Seasonal Prediction of Meteorological Drought Using the Bootstrap and Multivariate Information

Ali Behrangi Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

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Hai Nguyen Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

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Stephanie Granger Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

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Abstract

In the present work, a probabilistic ensemble method using the bootstrap is developed to predict the future state of the standard precipitation index (SPI) commonly used for drought monitoring. The methodology is data driven and has the advantage of being easily extended to use more than one variable as predictors. Using 110 years of monthly observations of precipitaton, surface air temperature, and the Niño-3.4 index, the method was employed to assess the impact of the different variables in enhancing the prediction skill. A predictive probability density function (PDF) is produced for future 6-month SPI, and a log-likelihood skill score is used to cross compare various combination scenarios using the entire predictive PDF and with reference to the observed values set aside for validation. The results suggest that the multivariate prediction using complementary information from 3- and 6-month SPI and initial surface air temperature significantly improves seasonal prediction skills for capturing drought severity and delineation of drought areas based on observed 6-month SPI. The improvement is observed across all seasons and regions over the continental United States relative to other prediction scenarios that ignore the surface air temperature information.

Corresponding author address: Ali Behrangi, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, MS 233-304, Pasadena, CA 91109. E-mail: ali.behrangi@jpl.nasa.gov

Abstract

In the present work, a probabilistic ensemble method using the bootstrap is developed to predict the future state of the standard precipitation index (SPI) commonly used for drought monitoring. The methodology is data driven and has the advantage of being easily extended to use more than one variable as predictors. Using 110 years of monthly observations of precipitaton, surface air temperature, and the Niño-3.4 index, the method was employed to assess the impact of the different variables in enhancing the prediction skill. A predictive probability density function (PDF) is produced for future 6-month SPI, and a log-likelihood skill score is used to cross compare various combination scenarios using the entire predictive PDF and with reference to the observed values set aside for validation. The results suggest that the multivariate prediction using complementary information from 3- and 6-month SPI and initial surface air temperature significantly improves seasonal prediction skills for capturing drought severity and delineation of drought areas based on observed 6-month SPI. The improvement is observed across all seasons and regions over the continental United States relative to other prediction scenarios that ignore the surface air temperature information.

Corresponding author address: Ali Behrangi, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, MS 233-304, Pasadena, CA 91109. E-mail: ali.behrangi@jpl.nasa.gov

1. Introduction

Drought is one of the costliest natural hazards worldwide. A 2012 drought in the United States extended over 20% of the country (Folger et al. 2013), cost more than $35 billion in the Midwest alone, and was predicted to reduce the gross domestic product with an overall loss of $75–$150 billion (Masters 2013). Shortly before the U.S. drought, one of the worst droughts in 60 years affected the entire East Africa region, causing a severe food crisis and famine in several East African countries (OCHA 2011). Clearly, improving seasonal climate forecasts has significant socioeconomic benefits in informing proper decision-making from the government level down to local people for ameliorating the effects of drought. For example, if ranchers and farmers know a severe drought is forming they can minimize potential economic losses by purchasing crop insurance or adjusting their planting or grazing strategy. While there is no unique definition for drought, the absence or deficit of precipitation relative to the expected climate is an essential driver. When precipitation variability is integrated over a range of time periods (e.g., from one month to more than a year) it can capture multiple aspects of water resources and hydrologic processes (e.g., soil moisture at different depths, river discharge, reservoir storage, crop production), because the response of hydrological systems to precipitation is time dependent (Changnon and Easterling 1989; Eltahir and Yeh 1999; Pandey and Ramasastri 2001; Krishna et al. 2012). This feature of precipitation has formed the basis for the development of the standard precipitation index (SPI), which is comparable in time and space (Hayes et al. 1999) and is commonly used as a robust indicator for general drought.

With the higher temperatures due to warming climate, the moisture-holding capacity of the atmosphere increases, and this can lead to a greater atmospheric demand for evapotranspiration. The increase in temperature-induced evapotranspiration demand, especially when the region experiences low precipitation and low atmospheric humidity, can intensify droughts and exacerbate their impact (Breshears et al. 2005; Weiss et al. 2009). The warmer climate can thus reduce the frequency of rain (longer dry spells), but when rainfall occurs it is expected to be more intense (Trenberth et al. 2013). Drought is thus expected to occur more often and be more intense in the future as a result of climate change, although the magnitude of the trends has been debated (Sheffield et al. 2012; Trenberth et al. 2013). Several studies have shown that drought and heat go together; therefore, considering both of them in drought monitoring and prediction is important (e.g., Nicholls 2004; van Dijk et al. 2013; Lewis and Karoly 2013). Furthermore, temperature and precipitation can impact soil moisture, which in part can affect the rate and distribution of precipitation through regulating the amount of energy absorbed from the sun. In other words, soil moisture can affect atmospheric convection, clouds, and precipitation formation through a feedback loop (Taylor et al. 2013). This suggests that the previous and current statuses of temperature and soil wetness are linked with future precipitation, especially over semiarid regions, and thus information on temperature and soil wetness of the region can potentially be useful for drought prediction.

It has also been recognized that natural oscillations in areas of the Pacific Ocean, especially El Niño–Southern Oscillation (ENSO), have a substantial impact on the weather and climate patterns worldwide (e.g., Andrews et al. 2004; Amarasekera et al. 1997; Zaroug et al. 2013). Indeed, ENSO is known to be the most common source of episodic droughts around the world (Trenberth et al. 2013). Given that the timing of El Niño and La Niña is generally predictable few months in advance (Barnett et al. 1988; Latif et al. 1998; Chen et al. 2004; Chen and Cane 2008), it can potentially provide useful information to enhance the drought prediction skill, especially over regions more impacted by ENSO, including the western United States (Dai 2013). Studies of the influence of ENSO on precipitation suggest that precipitation on land is controlled to a large degree by ENSO and, in general, with more El Niño phases less overland precipitation is expected globally (Dai 2011).

Probabilistic drought forecasting is an important and active area of research. Kim et al. (2003) derived estimates of return periods of droughts in arid regions using weighted moving averages of the data in a small neighborhood around the point of estimation. Cancelliere et al. (2007) proposed probabilistic predictions of SPI using temporal autocorrelation and using the empirical conditional distribution as a function of past precipitation values. Yuan et al. (2013) used a dynamical forecast system based on the Climate Forecast System and the Variable Infiltration Capacity land surface model to make probabilistic drought forecasts. Madadgar and Moradkhani (2014) developed a probabilistic forecast model that applies a family of multivariate distribution functions to forecast future drought conditions from past conditions.

In this paper, a probabilistic ensemble method similar to the approach of Cancelliere et al. (2007) is developed using the bootstrap for seasonal drought prediction. This method is used to assess if and to what extent various long-term observed variables (e.g., precipitation, surface air temperature, and ENSO index) can enhance meteorological drought prediction. The study is designed to address the goals of the National Integrated Drought Information System implementation plan, which expresses the need for development of a more objective-based drought prediction approach that is transparent to the users and can generate probabilistic drought-related information for specific decision-making needs. Detailed analysis is performed through development and cross comparison of several representative scenarios, inspired from the theoretical background gained from previous studies, and by assessing their skill for seasonal drought prediction.

The dataset used in this work is described in section 2. The prediction method, skill scores, and combination scenarios are discussed in section 3. Section 4 provides the results and cross-comparison analysis followed by concluding remarks in section 5.

2. Dataset

The datasets used in this study are described below. The long-term datasets are available globally so the analysis can potentially be extended worldwide.

a. Surface air temperature

Observations of surface air temperature (at 2 m above surface) T2m are obtained from the University of Delaware Air Temperature dataset (Willmott and Matsuura 2011), which provides monthly global gridded high-resolution station (land) data from the period 1901–2010. A large number of stations from the Global Historical Climate Network (GHCN2; Lawrimore et al. 2011) and various other sources are used in production of this dataset and, if needed, careful interpolation was made using digital-elevation-model-assisted interpolation, traditional interpolation, and climatologically aided interpolation.

b. Surface precipitation rate

Precipitation observation is obtained from the Global Precipitation Climatology Centre (GPCC; Schneider et al. 2011, 2014) monthly global gridded analyses (version 6) at 0.5° longitude × 0.5° latitude spatial resolution (1901–2010). The dataset is based on quality-controlled data from 67 200 stations worldwide. GPCC employs a variety of sources including the World Meteorological Organization Global Telecommunication System and rain gauge data from the national meteorological and/or hydrological services of 190 countries worldwide and from research projects. Quality control and harmonization of the station metadata are employed to detect errors in the station metadata and ensure consistency in merging the data from different sources (Schneider et al. 2014).

c. ENSO

The commonly used Niño-3.4 index—the average sea surface temperature anomaly in the region bounded from 5°N to 5°S and from 170° to 120°W—is utilized. Niño-3.4 data were obtained from the Climate Prediction Center (http://www.esrl.noaa.gov/psd/data/correlation/nina34.data), providing monthly data since 1950. Monthly Niño-3.4 data for 1901–49 were obtained online (http://www.cgd.ucar.edu/cas/catalog/climind/TNI_N34/index.html#Sec5).

3. Method

The prediction method is based on construction of probability density function (PDF) for the predicted 6-month SPI (SPI6) using long-term precipitation, surface air temperature, and ENSO data. Different combination scenarios are developed and cross compared to study the impact of individual and combination of the variables on the predictive skill. A log-likelihood-based skill score is employed to perform the comparative analysis based on the entire PDF.

a. Calculation of SPI

The monthly GPCC data are used to calculate the SPI (McKee et al. 1993) based on a precipitation probabilistic approach. SPI is negative for drought and positive for wet conditions with absolute values greater than 0.8, which are usually referred to as moderately to extremely wet or dry events. SPI can be used to monitor conditions on a variety of time scales, making it a very useful indicator for both short- and long-term applications (Karavitis et al. 2011). The multiscalar SPI can thus respond to soil moisture, river discharge, reservoir storage, vegetation activity, and crop production and distinguish hydrological, environmental, and agricultural droughts occurring at different time scales (e.g., Sims et al. 2002; Ji and Peters 2003; Patel et al. 2007; Vicente-Serrano 2007).

The focus of this study is on seasonal drought predictability; similar to previous studies (Quan et al. 2012; Yuan and Wood 2013), the SPI is calculated for 6-month time scales for seasonal prediction, and it is a compromise between the short- and long-term drought indices (e.g., SPI3 and SPI12). SPI6 is also used as one of the major metrics for Drought Monitor (Svoboda et al. 2002). The time series of 6-month accumulated precipitation for 1901–2010 is transformed into a normal distribution so that the mean SPI6 for any grid point is zero. The normalization allows SPI to be compared across regions with different climates. In the present study the SPI6 from the interval 1901–90 is used to create the training sample and the time interval 1991–2010 is used for prediction and cross comparison of different scenarios. The SPI6 values are assigned to the ending month. That is, the SPI6 value for December is constructed from precipitation for December and the preceding 5 months (July–November). SPI was constructed by fitting a gamma distribution on the precipitation on monthly scales. For instance, gamma parameters for SPI6 ending in January are estimated using all 6-month blocks that end in January.

b. Development of prediction scenarios

Precipitation, temperature, soil moisture, and ENSO at any time point can potentially provide predictive information regarding future meteorological drought. This could be through drought persistency (e.g., shown by analysis of precipitation; Lyon et al. 2012), feedbacks (e.g., between soil moisture, temperature, and precipitation), SST (e.g., through ENSO index), or some combination thereof. In this study different scenarios are designed and cross compared to investigate how such information can enhance climatology-based drought prediction. The scenarios include seasonal prediction using only SPI6 (scenario 1: S1), and when SPI6 is used with other variables such as ENSO index (scenario 2: S2), the month of year (scenario 3: S3), SPI3 (scenario 4: S4), and surface air temperature (scenario 5: S5). Potentially these indicators should help refine the selection of ensembles used to predict future probability of SPI6. SPI3 provides recent conditions of precipitation that could be inferred as a long-term proxy for soil moisture (e.g., Mueller and Seneviratne 2012) that otherwise will be limited to a relatively short record of satellite-based soil observations to fully cover the entire region of study. Note that the intention of this study is not necessarily to develop the best climatology-based drought prediction method, but to gain more insight on predictive information contained in different variables that potentially can be used in regional and seasonal drought prediction. Note that analysis of the results, discussed in section 4, suggests development of another scenario (S6) that collects information from SPI6, SPI3, and surface air temperature.

c. Ensemble prediction using bootstrap

The nature of prediction based on past information allows probabilistic prediction through construction of a PDF for the predicted variable (e.g., seasonal prediction of SPI). In practice, there are many ways of capitalizing on the autocorrelation of a single variable to estimate the predictive distribution for some future time. Lyon et al. (2012) discussed a parametric methodology for estimating a Gaussian predictive distribution using observed climatology data for the predictive mean and the autocorrelation for the predictive standard deviation. An alternative approach, given an initial value of the variable, is to use historical observations to empirically find pairs of observations separated by the desired prediction length where the first value belongs within some small range of desired initial value (Day 1985). The empirical methodology has attractive properties in that it is data dependent and does not assume a particular parametric class for the predictive distribution. However, building a robust predictive PDF requires a substantial number of observations, and this is a disadvantage of the empirical methodology in Day (1985). This shortcoming is addressed here by using a statistical resampling method called the bootstrap, which is the practice of estimating properties of an estimator (e.g., mean, median, variance, autocorrelation) via resampled data constructed from the observed data. If we consider the observed data to be a single realization of some process, then the bootstrap allows us to construct many realizations of the same process. The ensemble of bootstrap realizations would then allow us to construct a more accurate and more robust predictive PDF.

The method is as follows. Given a detrended N-dimensional vector of data that is regularly spaced in time called ,
e1
a resampled dataset is constructed by taking randomly sampled “blocks” (with replacement) of the original data to construct M new datasets . For instance, using 100 years of monthly SPI data, new resampled datasets can be generated by choosing a block length of n consecutive data points (here n = 24, or 2 yr). A 2-yr block of consecutive data is chosen randomly from , and it is then put at the start of our resampled vector . Similarly, another 2-yr block of consecutive data from is sampled from the original randomly and independently of the previous blocks and is appended to . The procedure is repeated until has the same length as .

Because 2-yr blocks of data are sampled from the original , most of the temporal correlation should still be captured in the resampled datasets , which can improve the predictive skill. Note this method can easily be extended to multivariate inputs, which makes it attractive for exploring the interactions between different geophysical processes for drought prediction. For example, in a bivariate case, such as predicting SPI6 3 months in the future using current SPI6 and surface temperature, the data at each time point would be a bivariate vector (e.g., SPI6 and surface air temperature), and the resampling process would be exactly the same as in the univariate case.

The construction of the predictive PDF can be done similarly by selecting pairs of elements for which the initial condition x0 and historical data are similar (i.e., for some distance d and some vector norm g). For instance, to make prediction of SPI6 at a 3-month lag, we take the condition of the current month, x0, and search for all months in the resampled datasets yi where the conditions are similar to the current month (call this similar set of months S). By including all months that follow from S by 3 months, an empirical predictive distribution is constructed. Once such an empirical dataset of the predictive distribution is obtained, it is straightforward to construct a continuous PDF using a probability density kernel smoother, which estimates the probability density function of a random variable from finite data samples using nonparametric methods (Wand and Jones 1995).

Choosing an optimal block length is an area of active research, but in general the block length should be larger than the temporal correlation range within the data (e.g., Hall et al. 1995). At one extreme, if we choose the block length to be n = 100 × 12 = 1200, then we are essentially exactly duplicating the entire time series dataset M times. Since the observed time series is limited in size, PDF estimates made from this extreme case would likely be overly optimistic, especially when the input condition has only a few similar realizations in y0. At the other extreme, if we set n = 1, then we are completely destroying the temporal correlation between the consecutive months, which would lead to poor predictive PDFs.

Lowering the block length n essentially introduces additional variability (informed by the overall training data variability or climatology) to the predictive PDFs, and ideally the additional variability that we introduce approximates the natural variability in the drought process that is only partially captured by the time series y0. Essentially the block length that we choose is controlling the degree of climatological information in the prediction. A shorter block length will allow more climatological information to come through, while a longer block length will give more weight to the past data. The ideal block length is one that produces the highest skill score (see section 3d below) when applied to validation data. For this particular application, we found that block length to be about 2 years.

For scenario m, the smoothed predictive PDF given the initial data is denoted as . In the following section, a skill score based on the log-likelihood is described to assess the predictive skills of these smoothed predictive PDFs.

d. Log-likelihood skill score

Because a predictive PDF is produced for every scenario m and every initial condition , it is useful to construct a metric for assessing the overall skill or the accuracy of the scenarios (listed in section 3b) when compared with actual observations. Without lack of generality, one can consider the case of predicting a single variable given a univariate input (e.g., S1: estimating SPI6 in the future given current SPI6). We first set aside the validation data where we actually know the variable of interest for consecutive time periods. The validation vector is denoted as , and the goal is to test the accuracy of the predicted PDF against the actual observed value , where i is the index of the current month and L is the temporal prediction range.

The problem of assessing the accuracy of probabilistic predictions in comparison with actual observed data is well developed in information theory and decision theory under scoring rules (Bickel 2007; Bröcker 2009). We choose to use the logarithmic scoring rule (LSS), which has the following form:
e2
The logarithmic skill score is simply the sum of the log of the probability density of the observed data from the predictive PDF (see Fig. 1). From (2) it is straightforward to compute the predictive skill of forecast scenario m and compare it with the corresponding skill score for other scenarios. The advantage of LSS is that it evaluates the entire continuous predictive PDF against the actual observed value and produces a quantitative assessment of the prediction accuracy. This makes LSS a good choice for comparing predictive PDFs against the observed data and evaluating the relative predictive ranks for the various methods.
Fig. 1.
Fig. 1.

Schematic display of the LSS.

Citation: Journal of Applied Meteorology and Climatology 54, 7; 10.1175/JAMC-D-14-0162.1

The logarithmic skill score is consistent with the likelihood principle and has strong information theory foundation (Bickel 2007). It is also a proper scoring rule, which means that it reports the highest score when the predictive distribution is exactly the same as the distribution being predicted. The LSS is also, up to a multiplicative constant, identical to the ignorance index, which evaluates probabilistic forecasts in a data compression framework (Roulston and Smith 2002).

We note that the popular Brier score and the ranked probability skill scores (RPSS) are also scoring rules (albeit quadratic rather than logarithmic; Bickel 2007), and the prevalent Brier skill score (BSS) is a modified version of the Brier score, normalized by a reference or climatological forecast. These two scores are designed for categorical predictive PDFs, while our forecast PDFs are continuous. For this reason, we opted to use the LSS instead of BSS or RPSS. In Fig. 2 the relative performance of LSS and BSS is shown, and for the most part the two scores agree with one another.

Fig. 2.
Fig. 2.

Cross comparison of the prediction skills of the five studied scenarios as a function of the prediction time interval for two grids in (a),(c) California (35°N, 118°W) and (b),(d) New York (41°N, 74°W) and using the entire evaluation datasets. Panels (a) and (b) compare scenarios using the LSS, while (c) and (d) compare scenarios using the BSS (with a threshold of −0.8 for converting the continuous PDFs into binary categorical predictions).

Citation: Journal of Applied Meteorology and Climatology 54, 7; 10.1175/JAMC-D-14-0162.1

The principle behind our skill score is shown in Fig. 1, which displays three predictive PDFs from three models (or scenarios) for a single month. The actual observed value (e.g., SPI = −1.3) is plotted as a thick vertical line that intersects the predictive PDFs. The intersection values from the y axis denote the probability density, and the higher the probability density is, the more skill the model has in its prediction. From the hypothetical case below, we can rank the predictive skill of the three models according to their probability density values at the intersections. LSS simply aggregates this probability density metric over many different predictive PDFs as described in (2).

The method described above is applied to all of the scenarios described in section 3b. The PDFs for each scenario are constructed using the entire dataset, but the last 20 years (1991–2010) were used for evaluation.

4. Results

Figure 2 cross compares the prediction skills of the 5 studied scenarios as a function of the prediction time interval for two grids in California (35°N, 118°W) and New York (41°N, 74°W). The skill scores are calculated using the entire monthly SPI6 predictions made during the evaluation period (1991–2010). To illustrate the difference between the LSS and BSS, the LSS in Figs. 2a and 2b and the BSS (after converting the continuous predictive PDFs into binary PDFs) in Figs. 2c and 2d were calculated. Overall, the LSS and BSS indicate that the predictive performance generally degrades in proportion to the lag time. This is expected because predictions further into the future should be less accurate. The scoring rules clearly rank the different scenarios in order of predictive accuracy (e.g., S5 is the best, while S1 is the worst), and both the LSS and BSS tend to agree on the same rankings.

It should be noted that the BSS depends upon a somewhat arbitrary choice of threshold (−0.8) to convert the continuous PDFs into binary PDFs. The LSS operates directly on the continuous predictive PDFs, hence our decision to make use of them to assess the accuracy of the predictive PDFs in this particular application. Figure 2 shows that scenario 4 (SPI6 + SPI3) and scenario 5 (SPI6 + 2-m surface air temperature) have overall better performance than the other scenarios. Scenario 2 (SPI6 + ENSO) is also effective when compared with using only SPI6 or combination of SPI6 and month. Figure 2, however, suggests that the performance of the scenarios is regionally dependent, and therefore for a thorough analysis, a spatial map of the LSS has to be constructed. We used 90-yr (1901–90) datasets for training and the rest (1901–2010) for testing and comparison of the scenarios.

The relationship between the skill and prediction time can be better understood using Fig. 3, which displays a SPI6 value from January 2001 for Reno, Nevada, and the corresponding predictive PDFs using scenario 5 for four different monthly lags. Note that our empirical predictive PDFs are unimodal but slightly nonsymmetric. The current SPI6 has a value of about −1.35 (heavy drought), and the predictive PDFs have heavier tails toward positive values (wetter conditions), which is consistent with the typical “regression toward the mean” behavior of climate. The predictive PDFs also widen as the predictive lag increases; the 1-month-lag PDF is tightly clustered around the current observed value, indicating a high degree of temporal correlation, while the 6-month-lag PDF is much wider (indicating less confidence in our prediction) and more skewed toward the mean 0.

Fig. 3.
Fig. 3.

An illustration of an observed SPI6 value (vertical line) and the corresponding predictive PDFs.

Citation: Journal of Applied Meteorology and Climatology 54, 7; 10.1175/JAMC-D-14-0162.1

Figure 4 extends the analysis shown in Fig. 2 by constructing spatial maps of LSSs for 2-month-lead seasonal prediction of SPI6. The analysis is performed for the four seasons and for every 1° × 1° grid in the contiguous United States (CONUS) using the entire evaluation dataset. The seasons are defined as December–February (DJF), March–May (MAM), June–August (JJA), and September–November (SON), where the named month is the ending month of an SPI6 value (e.g., for DJF, we select SPI6 values that end during December, January, or February). A strong seasonality in the skill can be observed for most of the scenarios. For instance, during spring, LSS of S1 is greatest along the West Coast but lowest over the Great Plains. This is also the case for the other scenarios. Conversely, during fall, LSS is higher over the Great Plains and lower along the West Coast.

Fig. 4.
Fig. 4.

Geographical maps of LSS for 2-month-lead seasonal prediction of SPI6. LSS is calculated for every 1° × 1° grid in CONUS using the entire evaluation dataset.

Citation: Journal of Applied Meteorology and Climatology 54, 7; 10.1175/JAMC-D-14-0162.1

The first two columns in Fig. 4 suggest that by adding the Niño-3.4 index to SPI6 (S2), LSS is generally increased relative to S1 (baseline scenario), especially over the western and northeastern United States in winter, the West Coast in spring, and the central United States in summer and fall. By including month-of-year information in the predictions (S3), LSS is increased relative to both S1 and S2. Further analysis (not shown here) suggests that a combination of the two (month of year and Niño-3.4) provides superior skill relative to that obtained from the individual ones, although when compared with S3 the observed improvement is relatively minor. The seasonal predictions using a combination of SPI3 and SPI6 (S4), however, result in significant improvement in LSS relative to the first three scenarios. The improvement is observed across the four seasons but is more pronounced over the Great Plains in winter and fall and along the West Coast in spring and summer, which is consistent with that observed by Quan et al. (2012) using a different prediction method.

The improvement along the Gulf of Mexico and along the East Coast is also remarkable during winter. Note that SPI3 provides more recent conditions of precipitation and can be considered as a proxy for soil moisture (e.g., Mueller and Seneviratne 2012), which can be related to the improved prediction skill of S4. This could be through the soil moisture precipitation feedback loop discussed by Taylor et al. (2013). As discussed in section 1, drought and heat usually tend to go together, and there is a strong link between them. S5 shows that seasonal predictions using both T2m and SPI6 results in significant improvement relative to the other scenarios (S1–S4).

The LSS patterns of S5 are also very different from the other combination scenarios. For example, in contrast to S4 for JJA prediction, S5 shows higher LSS over the central United States than surrounding coastal regions. Furthermore, S4 provides higher LSS for winter prediction over the Great Plains and along the Gulf of Mexico, while S5 shows higher LSS over the northeastern CONUS. Comparison of the prediction skills for S4 and S5 suggests that the two scenarios can likely complement each other to improve the drought prediction score. This motivated the authors to investigate an additional scenario (S6) in which a combination of SPI6, SPI3, and T2m is used as predictor. The results (S6, shown in the last row of Fig. 4) show a significant improvement compared to all other scenarios across all seasons and regions, confirming that SPI6, SPI3, and T2m data provide complementary information, and S6 is able to take advantage of this complementary information to improve upon both S4 and S5.

Figure 5 shows a typical case study in which observed (Fig. 5a) and predicted SPI6 using S1 (Fig. 5b), S4 (Fig. 5c), S5 (Fig. 5d), and S6 (Fig. 5e) are compared for a severe drought in May 2002. The predictions are based on initial conditions in February 2002 (3 months earlier). While none of the predictions can capture the actual severity of the observed drought, the combined prediction based on S6 is clearly superior to the other scenarios in capturing both the severity and extent of the drought. This indicates that the three predictors (i.e., T2m and SPI3 when added to SPI6) can collectively yield complementary information that can result in an enhanced prediction skill as shown with the aid of solid and dotted circles in Fig. 5. The boxes in the top-right corners of the panels of Fig. 5 show that the addition of T2m is also useful in reducing the false alarms in the prediction of drought. Nonetheless, the severity of drought remains as a prediction weakness that is related to the typical problem with ensemble prediction and the inherent averaging effect that depresses the extremes, even after refining the ensemble members through more informed scenarios (e.g., Fig. 5e). Note that in producing the predictions shown in Fig. 5, the modes of the predicted PDFs are used to represent the entire PDF. The use of the mean or median of the PDFs does not impact the results considerably (not shown).

Fig. 5.
Fig. 5.

A typical case study in which (a) observed and predicted SPI6 using (b) S1, (c) S4, (d) S5, and (e) S6 are compared for a severe drought in May 2002. The predictions are based on initial conditions in February 2002 (3 months earlier).

Citation: Journal of Applied Meteorology and Climatology 54, 7; 10.1175/JAMC-D-14-0162.1

Figure 6 shows maps of predicted probability of SPI6 < −0.8 for the same drought case study shown in Fig. 5 and using the four scenarios: S1, S4, S5, and S6. The threshold of −0.8 is used to delineate drought regions in the observed SPI6 map (Fig. 6a) and calculate the probability of drought occurrence (the area below −0.8 using predicted PDFs) from the studied scenarios. Cleary, S6 outperforms the other scenarios by capturing drought areas with fairly high probabilities. While the result shown in Fig. 6 is consistent with that observed in Fig. 5, analysis based on probability of drought occurrence allows more efficient use of the predicted PDFs and is likely more suitable for decision-making. In other words, maps of probability of drought can be produced for any given threshold allowing more detailed study of the extremes that otherwise cannot be captured through the mean, mode, or median of the PDFs.

Fig. 6.
Fig. 6.

Maps of predicted probability of SPI6 < −0.8 for a severe drought in May 2002. The predictions are based on initial conditions in February 2002 (3 months earlier).

Citation: Journal of Applied Meteorology and Climatology 54, 7; 10.1175/JAMC-D-14-0162.1

Figure 7 compares the performance of the six studied scenarios for drought detection using the entire evaluation datasets for 3-month-lead predictions. The skill scores are derived from the contingency table (Wilks 2011) constructed by converting the predicted probability of SPI6 to binary (yes/no) drought occurrence using a SPI6 threshold of −0.6 and a range of probability thresholds. For example, grids with probability P(future SPI < −0.6) > 0.5 (or 50%) are flagged as drought and are compared with the observed binary drought maps. The probability of detection (POD), false alarm ratio (FAR), bias, and Heidke skill score (HSS) are used to investigate the binary prediction skills.

Fig. 7.
Fig. 7.

Comparison of drought detection skill of the studied scenarios using skills scores derived from the contingency table constructed from the entire evaluation datasets. The contingency table is constructed by converting the predicted probability of SPI6 to binary (yes/no) drought occurrence using a SPI6 threshold of −0.6 and a range of probability thresholds.

Citation: Journal of Applied Meteorology and Climatology 54, 7; 10.1175/JAMC-D-14-0162.1

POD and FAR range from 0 to 1, with perfection represented by 1 for POD and 0 for FAR. POD is sensitive to the number of hits, but it ignores false alarms; FAR, on the other hand, is sensitive to false alarms, but it ignores misses. A bias value of 1 indicates that the total number of predicted occurrences (hits + false alarms) is equal to the total number of observed occurrences (hits + misses). HSS measures the fraction of correct prediction by excluding those predictions that would be correct by random chance. HSS is a commonly used score and ranges between −∞ and 1; negative values indicate that the chance prediction is better, 0 means no skill, and 1 is a perfect prediction.

Consistent with previous results, Fig. 7 confirms that S6, followed by S4 and S5, outperforms other scenarios for drought prediction for 3-month-lead predictions (the results for other lead times are largely consistent with those described herein). Figure 7 also shows that there is an inverse relationship between the predicted probability of drought occurrence and POD, FAR, and bias scores. In other words higher confidence for drought prediction is obtained at the expense of a smaller number of hits as can also be inferred from Fig. 6. Figure 7d shows that the HSS value is largest for the detection probability of 0.4, which also corresponds to a bias value of 1 (Fig. 7c). This means that if grids with predicted probability of drought >0.4 are selected as drought, the overall area of predicted drought occurrences is equal to the area of observed drought, although a perfect bias score of 1 does not necessarily indicate that the prediction model is perfect. Therefore, one can use a combination of HSS and bias to identify the best probability threshold. Nevertheless, representation of predicted drought area versus probability, as a proxy for confidence, seems to be an invaluable feature for decision making.

5. Concluding remarks

Drought is one of the costliest natural hazards worldwide and improving its seasonal prediction has significant socioeconomic benefits for proper decision-making and managing properties from the government level down to local residents. Using 110 years of surface precipitation and air temperature data, a probabilistic ensemble method using the bootstrap is developed to predict the future state of the standard precipitation index commonly used for drought monitoring. Various combination scenarios based on observed climatology of precipitation, surface air temperature, and ENSO index are constructed, and their prediction skills are cross compared using a logarithmic skill score and the commonly used detection indices.

It is found that seasonal drought prediction using combination of SPI6, SPI3, and surface air temperature outperforms other scenarios, across almost all seasons and regions over the continental United States. The improvement suggests that the three predictors collectively yield complementary information that can result in an enhanced prediction skill in capturing drought severity and delineation of drought areas with fairly high probability compared to the other studied scenarios. Nonetheless, as shown with a case study, the severity of drought remains as a prediction weakness that is related to the typical problem with ensemble prediction and the inherent averaging effect that depresses the extremes, even after refining the ensemble members through more informed scenarios.

Although the presented approach can potentially be extended and used for global drought prediction, several issues have to be considered in a future work. Most of the current climate-quality observations of surface temperature and precipitation come with a few months’ delay, hampering a short-term observation-driven prediction. One solution is to use various near-real-time sources (e.g., remotely sensed data) after adjusting them with respect to the long-term observed climatology (e.g., Quan et al. 2012). However, a robust procedure has to be implemented for the adjustment because initial condition is a key to the prediction. Furthermore, it is important to note that there is no unique definition for drought, and its definition depends on the end user’s needs. Therefore, a comprehensive drought prediction system should be able to utilize various predictors and have flexibility to predict different types of drought indicators. In other words, in the present study a focus has been on meteorological drought by accounting for the absence or deficit of precipitation relative to the expected climate. It is important to also investigate the predictability of other drought indicators (such as the standardized precipitation evapotranspiration index) that can be more important than SPI under warming climate conditions (Vicente-Serrano et al. 2010). Efforts are also underway to investigate the role of other predictors such as soil moisture, evapotranspiration, and vegetation indices in the prediction process.

Although the presented analysis demonstrates that the combination of historical temperature and precipitation can yield improved skill for drought prediction, one has to recognize that numerical models will also continue to play a critical role in seasonal drought prediction, especially when an ensemble of model predictions is used effectively (Yuan and Wood 2013). However, the history of performance has shown that they are not always reliable. For example, such operational seasonal forecasts have shown little skill for U.S. summer rainfall since the mid-1990s (Hoerling et al. 2014). This was also noticed by Quan et al. (2012), where they showed that dynamical seasonal predictions may not materially increase summer skill over the Great Plains relative to a persistence-forecast baseline that could be related to the small SST sensitivity of the region’s rainfall. In addition to the efforts for improving numerical models, identifying robust procedures for utilizing multimodel outputs is another challenging yet important area of research that is being investigated.

Acknowledgments

The research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Government sponsorship is acknowledged.

REFERENCES

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    • Export Citation
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    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Bröcker, J., 2009: Reliability, sufficiency, and the decomposition of proper scores. Quart. J. Roy. Meteor. Soc., 135, 15121519, doi:10.1002/qj.456.

    • Search Google Scholar
    • Export Citation
  • Cancelliere, A., G. D. Mauro, B. Bonaccorso, and G. Rossi, 2007: Drought forecasting using the standardized precipitation index. Water Resour. Manage., 21, 801819, doi:10.1007/s11269-006-9062-y.

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    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Eltahir, E. A. B., and P. J.-F. Yeh, 1999: On the asymmetric response of aquifer water level to floods and droughts in Illinois. Water Resour. Res., 35, 11991217, doi:10.1029/1998WR900071.

    • Search Google Scholar
    • Export Citation
  • Folger, P., B. A. Cody, and N. T. Carter, 2013: Drought in the United States: Causes and issues for Congress. Congressional Research Service Rep. RL34580, 32 pp. [Available online at http://www.fas.org/sgp/crs/misc/RL34580.pdf.]

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    • Search Google Scholar
    • Export Citation
  • Hayes, M. J., M. D. Svoboda, D. A. Wilhite, and O. V. Vanyarkho, 1999: Monitoring the 1996 drought using the standardized precipitation index. Bull. Amer. Meteor. Soc., 80, 429438, doi:10.1175/1520-0477(1999)080<0429:MTDUTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoerling, M., J. Eischeid, A. Kumar, R. Leung, A. Mariotti, K. Mo, S. Schubert, and R. Seager, 2014: Causes and predictability of the 2012 Great Plains drought. Bull. Amer. Meteor. Soc., 95, 269282, doi:10.1175/BAMS-D-13-00055.1.

    • Search Google Scholar
    • Export Citation
  • Ji, L., and A. J. Peters, 2003: Assessing vegetation response to drought in the northern Great Plains using vegetation and drought indices. Remote Sens. Environ., 87, 8598, doi:10.1016/S0034-4257(03)00174-3.

    • Search Google Scholar
    • Export Citation
  • Karavitis, C. A., S. Alexandris, D. E. Tsesmelis, and G. Athanasopoulos, 2011: Application of the standardized precipitation index (SPI) in Greece. Water, 3, 787805, doi:10.3390/w3030787.

    • Search Google Scholar
    • Export Citation
  • Kim, T., J. Valdés, and C. Yoo, 2003: Nonparametric approach for estimating return periods of droughts in arid regions. J. Hydrol. Eng., 8, 237246, doi:10.1061/(ASCE)1084-0699(2003)8:5(237).

    • Search Google Scholar
    • Export Citation
  • Krishna, T. M., G. Ravikumar, and M. Krishnaveni, 2012: Meteorological drought severity assessment for Vellore District, Tamil Nadu State, India. Int. J. Civ. Eng. Res., 3, 115120.

    • Search Google Scholar
    • Export Citation
  • Latif, M., and Coauthors, 1998: A review of the predictability and prediction of ENSO. J. Geophys. Res., 103, 14 37514 393, doi:10.1029/97JC03413.

    • Search Google Scholar
    • Export Citation
  • Lawrimore, J. H., M. J. Menne, B. E. Gleason, C. N. Williams, D. B. Wuertz, R. S. Vose, and J. Rennie, 2011: Global Historical Climatology Network–Monthly (GHCN-M), version 3. NOAA National Climatic Data Center, accessed 20 June 2012, doi:10.7289/V5X34VDR.

  • Lewis, S. C., and D. J. Karoly, 2013: Anthropogenic contributions to Australia’s record summer temperatures of 2013. Geophys. Res. Lett., 40, 37053709, doi:10.1002/grl.50673.

    • Search Google Scholar
    • Export Citation
  • Lyon, B., M. A. Bell, M. K. Tippett, A. Kumar, M. P. Hoerling, X.-W. Quan, and H. Wang, 2012: Baseline probabilities for the seasonal prediction of meteorological drought. J. Appl. Meteor. Climatol., 51, 12221237, doi:10.1175/JAMC-D-11-0132.1.

    • Search Google Scholar
    • Export Citation
  • Madadgar, S., and H. Moradkhani, 2014: Spatio-temporal drought forecasting within Bayesian networks. J. Hydrol., 512, 134146, doi:10.1016/j.jhydrol.2014.02.039.

    • Search Google Scholar
    • Export Citation
  • Masters, J., 2013: Top ten global weather events of 2012. Weather Underground. [Available online at http://www.wunderground.com/blog/JeffMasters/article.html?entrynum=2326.]

  • McKee, T. B., N. J. Doesken, and J. Kliest, 1993: The relationship of drought frequency and duration to time scales. Preprints, Eighth Conf. on Applied Climatology, Anaheim, CA, Amer. Meteor. Soc., 179–184.

  • Mueller, B., and S. I. Seneviratne, 2012: Hot days induced by precipitation deficits at the global scale. Proc. Natl. Acad. Sci. USA, 109, 12 39812 403, doi:10.1073/pnas.1204330109.

    • Search Google Scholar
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  • Fig. 1.

    Schematic display of the LSS.

  • Fig. 2.

    Cross comparison of the prediction skills of the five studied scenarios as a function of the prediction time interval for two grids in (a),(c) California (35°N, 118°W) and (b),(d) New York (41°N, 74°W) and using the entire evaluation datasets. Panels (a) and (b) compare scenarios using the LSS, while (c) and (d) compare scenarios using the BSS (with a threshold of −0.8 for converting the continuous PDFs into binary categorical predictions).

  • Fig. 3.

    An illustration of an observed SPI6 value (vertical line) and the corresponding predictive PDFs.

  • Fig. 4.

    Geographical maps of LSS for 2-month-lead seasonal prediction of SPI6. LSS is calculated for every 1° × 1° grid in CONUS using the entire evaluation dataset.

  • Fig. 5.

    A typical case study in which (a) observed and predicted SPI6 using (b) S1, (c) S4, (d) S5, and (e) S6 are compared for a severe drought in May 2002. The predictions are based on initial conditions in February 2002 (3 months earlier).

  • Fig. 6.

    Maps of predicted probability of SPI6 < −0.8 for a severe drought in May 2002. The predictions are based on initial conditions in February 2002 (3 months earlier).

  • Fig. 7.

    Comparison of drought detection skill of the studied scenarios using skills scores derived from the contingency table constructed from the entire evaluation datasets. The contingency table is constructed by converting the predicted probability of SPI6 to binary (yes/no) drought occurrence using a SPI6 threshold of −0.6 and a range of probability thresholds.

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