Abstract

Drought indices derived from the North American Land Data Assimilation System (NLDAS) Variable Infiltration Capacity (VIC) and Noah models from 1950 to 2000 are intercompared and evaluated for their ability to classify drought across the United States. For meteorological drought, the standardized precipitation index (SPI) is used to measure precipitation deficits. The standardized runoff index (SRI), which is similar to the SPI, is used to classify hydrological drought. Agricultural drought is measured by monthly-mean soil moisture (SM) anomaly percentiles based on probability distributions (PDs). The PDs for total SM are regionally dependent and influenced by the seasonal cycle, but the PDs for SM monthly-mean anomalies are unimodal and Gaussian.

Across the eastern United States (east of 95°W), the indices derived from VIC and Noah are similar, and they are able to detect the same drought events. Indices are also well correlated. For river forecast centers (RFCs) across the eastern United States, different drought indices are likely to detect the same drought events.

The monthly-mean soil moisture (SM) percentiles and runoff indices between VIC and Noah have large differences across the western interior of the United States. For small areas with a horizontal resolution of 0.5° on the time scales of one to three months, the differences of SM percentiles and SRI between VIC and Noah are larger than the thresholds used to classify drought. For the western RFCs, drought events selected according to SM percentiles or SRI derived from different NLDAS systems do not always overlap.

1. Introduction

Droughts collectively affect more people and cause more devastating effects on our society than other forms of disasters. The National Climate Data Center (NCDC) documented the billion-dollar weather disasters for the recent years (Lott and Ross 2006). From 1980 to 2005, the 10 severe drought and flood events across the United States cost 144 billion U.S. dollars (USD) in damages. It is important to have an early warning system to mitigate the affects of drought.

The simplest way to monitor drought is to use drought indices. Two indices commonly used to monitor drought are the standardized precipitation index (SPI) and the Palmer drought severity index (PDSI). The SPI is based on precipitation (P) alone (Hayes et al. 1999; McKee et al. 1993, 1995). It measures the P deficits, but it does not take into account of water supply. The PDSI is based on the water balance between soil moisture supply and demand (Palmer 1965). There are many shortcomings of the PDSI (Alley 1984; Mo and Chelliah 2006; Karl 1983, 1986), for example, soil layers and the fixed value of the available water capacity are arbitrary; the snowmelt and frozen precipitation across the western region are not taken into account. Many parameters used in the PDSI are sensitive to the calibration procedures. These shortcomings make the PDSI less desirable. In addition to precipitation deficits, the depreciation of streamflow and soil moisture deficits also contribute to economic and agricultural losses associated with drought. Keyantash and Dracup (2002) classified droughts into three physical types: meteorological drought results from P deficits, agricultural drought is identified by total soil moisture (SM) deficits, and hydrological drought is related to a shortage of streamflow or runoff. Therefore, different indices based on P, SM, and runoff data are needed to measure different aspects of drought.

The precipitation data coverage is relatively good in comparison to SM and streamflow observations across the United States. However, P data over high mountains are still sparse. There are only limited soil moisture and streamflow data available. For soil moisture, there is the Illinois Climate Network (Hollinger and Isard 1994; Robock et al. 2000), in operation since 1981. There are also limited observations from the Atmospheric Radiation Measurement Program (ARM) Cloud and Radiation Testbed (CART) and the Oklahoma Mesonet (Brock et al. 1995; Basara and Crawford 2000; Robock et al. 2004). Some streamflow data are available from the U.S. Geological Survey, but there is no complete long-term coverage of streamflow across the United States.

Because long-term observations of runoff and soil moisture are scarce, the datasets produced by the North American Land Data Assimilation System (NLDAS) are valuable alternatives. For example, both Scheffield et al. (2004) and Andreadis et al. (2005) used products from the NLDAS Variable Infiltration Capacity (VIC) model to analyze droughts. The horizontal resolution 0.5° is fine enough for regional applications. Because soil moisture and runoff are products of the same land surface model, they are consistent.

The major difficulty is that runoff and soil moisture from the NLDAS depend on model and forcing. Robock et al. (2004) intercompared four NLDAS models and found that soil moisture differs a great deal from one model to another, but anomalies are closer in similarity to each other. In general, soil moisture anomalies or anomaly percentiles are used to monitor drought. Therefore, large differences in the total SM may not be detrimental to drought monitoring. Lohmann et al. (2004) found large regional differences among the four NLDAS models almost by a factor of 4. They also found that most models underestimate runoff in the areas having large snowfall.

The NLDAS products can be used to construct a drought warning system only if the drought classification is not model dependent (Redmond 2002). Datasets should be long enough to cover many drought events, so that the probability distributions are representative. Different indices measure different aspects of droughts, but they should be related to one another (Dracup et al. 1980). All indices should be able to pick up severe drought events. Recently, the long-term NLDAS Noah and VIC model products were made available. This presents an opportunity to assess the possibility to use the NLDAS products for drought monitoring. The goals of this paper are 1) to select a set of indices to monitor different aspects of drought, 2) to determine the uncertainties of drought indices derived from the NLDAS systems, and 3) to examine the relationships among drought indices. Datasets are described in section 2. Drought indices are described in section 3. Properties of probability distributions for soil moisture and soil moisture anomalies are also discussed in section 3. In section 4, uncertainties of indices are discussed. The comparison between two NLDAS systems shows large differences across the western region. The question is whether drought indices derived from two NLDAS systems averaged across large areas are similar enough for drought monitoring. The National Weather Service river forecast centers (RFCs) were chosen for this test because areas within the RFCs have similar hydroclimate. The locations of 12 RFCs are given in Fig. 1c. Conclusions and discussions are given in section 5.

Fig. 1.

(a) Soil moisture probability distribution types based on the nonparametric method for VIC from 1915 to 2003. (b) Difference between SMmax and SMmin from climatological monthly means; contour interval is 50 mm. (c) Locations of the National Weather Service River Forecast Centers.

Fig. 1.

(a) Soil moisture probability distribution types based on the nonparametric method for VIC from 1915 to 2003. (b) Difference between SMmax and SMmin from climatological monthly means; contour interval is 50 mm. (c) Locations of the National Weather Service River Forecast Centers.

2. Data

a. Noah model outputs

The Noah model (Mitchell et al. 2004) of 2007 in cludes the most recent updates (available online at http://www.emc.ncep.noaa.gov/gc_wmb/Documentation). The horizontal resolution is 1/8° and the dataset covers the period 1948–2000. The persistence of SM estimated from the characteristic time T0 (Trenberth 1984) averaged across the United States is approximately 20 months. The quantity T0 has a maximum of about 36 months across the western region. Therefore, correlations and RMS differences were calculated using data from 1952 to 2000 to minimize the spinup. Indices were obtained from 1950 to 2000 to include drought events in the 1950s, but the climatology is based on the period 1952–2000.

The Noah model has four vertical soil layers. The soil depths are 0–10, 10–40, 40–100, and 100–200 cm. Precipitation forcing was derived from the observed gridded precipitation (Higgins et al. 2000) with the Precipitation-elevation Regressions on Independent Slopes Model (PRISM; Daly et al. 1994) correction. The low-level circulation fields were obtained from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) Global Reanalysis 1 (GR-1; Kalnay et al. 1996). Some variables from GR-1 have systematic biases and are less reliable (Scheffield et al. 2006; Kalnay et al. 1996). The big advantage to use GR-1 is that GR-1 data are readily available in near-real time. All forcing terms derived from GR-1 are consistent because they are generated by a frozen version of the model and a frozen assimilation system.

b. VIC model outputs

This version of the VIC model outputs is the same as the one used by Andreadis et al. (2005) to study drought. The early version of VIC was documented by Maurer et al. (2002). Forcing of P was derived from the cooperative observer stations’ meteorological daily data with the PRISM correction. The low-level circulation fields were derived from station data. The horizontal resolution is 0.5°, and it covers the period 1915–2003. The top soil layer is fixed at 10 cm. The soil depths of the second and third layers vary. Across the western region, the routed runoff and simulated snow extent are compared favorably with the observed streamflow and the Northern Hemisphere snow extent data (Maurer et al. 2002). Later, Andreadis et al. (2005) extended the VIC run to include earlier years. They used the NCDC archive of data provided by the Cooperative Observers. The detailed documentation of the VIC model can be found on the University of Washington Web site (available online at http://www.hydro.washington.edu/forecast/monitor).

3. Drought indices

In this paper, the SPI is used to measure the severity of meteorological drought. The standardized runoff index (SRI) is used to monitor hydrological drought. Agricultural drought is measured by the SM anomaly percentiles. They are described below.

a. Standardized precipitation index

The SPI is used to measure a shortage of precipitation P. It is based on the probability of P on different time scales. It was developed by McKee et al. (1993, 1995) at Colorado State University. The detailed description and the computer programs used to calculate SPI can be found at the National Drought Mitigation Center Web site (available online at http://www.drought.unl.edu/monitor). The procedures are briefly summarized below.

To obtain the 3-month SPI (SPI3), 3-month P mean P3 was calculated. The P3(τ) at time τ is the P averaged from the time τ − 2 to τ. Precipitation is not normally distributed. Monthly or seasonal P over the United States typically has a probability distribution similar to a gamma distribution (Wilks and Eggleston 1992; Ropelewski et al. 1985). The P3 distribution was transformed from a gamma distribution to a Gaussian distribution, so that all distributions have a common basis. Then, SPI3(τ) was determined according to the distribution of the transformed dataset (McKee et al. 1993, 1995). The 6-month SPI (SPI6) can be calculated the same way. They represent meteorological droughts on different time scales.

b. Standardized runoff index

Hydrological drought is measured by the streamflow or runoff deficits. Shukla and Wood (2008) applied the same concept of the SPI to analyze runoff data on different time scales. The SRI can be computed the same way as the SPI except it is based on the monthly-mean runoff time series.

c. Soil moisture percentiles

The probability distribution (PD) is needed to calculate soil moisture percentiles. Scheffield et al. (2004) fitted beta distributions to SM data based on three moments of SM. D’Odorico and Porporato (2004) found that the PD for the top 50-cm soil moisture across Illinois from May to September is bimodal. The best way to determine PD is to use a nonparametric method without a priori assumption of the distribution function.

The VIC monthly-mean SM data from 1915 to 2003 were used to analyze PDs because it is the longest dataset available. The PD was determined for each grid point to show the regional characteristics. For each grid point, the PD was determined by pooling together the SM time series of nine grid points in a 1° × 1° box centered at that grid cell. All seasons were pooled together for a total of 9612 points. The SM maximum (SMmax) and minimum (SMmin) were determined, and the histogram was computed. The distribution function was normalized by requiring the integration from SMmin to SMmax to be one. Similarly, PDs can be obtained for a larger area and for any given season by pooling grid points in that region for that season together.

Across the United States, the SM distribution functions can be classified roughly into four categories (Fig. 1a). Two grid points belong to the same category if the correlation between their PDs is greater than 0.85. A slight change of the limit will not change the outcome. Because points in the 1° × 1° box are pooled together, the distributions are not representative for grid points located along the boundary between two categories. These grid points are not colored. From Fig. 1a, four areas were selected to represent four categories of PDs—the Southeast (31°–34°N, 78°–87°W), the mid-Atlantic (38°–42°N, 72°–80°W), Arizona (32°–36°N, 107°–113°W) and the Ohio Valley (37°–42°N, 82°–90°W)—which were obtained for each season and for all seasons together (Figs. 2a–2d).

Fig. 2.

(a) Distribution function D(x) × 100 for the southeastern United States (31°–34°N, 78°–87°W) for winter (January–March; red line), spring (April–June; green line), summer (July–September; blue line) and fall (October–December; purple) and all seasons together (black line and open circles) as an example of type 1 distribution function. The distribution function D(x) is normalized to 1 from SM min to SMmax and is ×100. The x axis is given in millimeters. (b) Same as (a) but for the mid-Atlantic area (38°–42°N, 72°–80°W) as an example of type 2 distribution function. (c) Same as (a) but for Arizona (32°–36°N, 107°–113°W) as an example of type 3 distribution function. (d) Same as (a) but for the Ohio Valley (37°–42°N, 82°–90°W) as an example of type 4 distribution function. (e)–(h) Same as (a)–(d) but for SM anomalies. The x axis is given in standard deviations. Anomalies are defined as departures from monthly-mean climatology from 1915 to 2003.

Fig. 2.

(a) Distribution function D(x) × 100 for the southeastern United States (31°–34°N, 78°–87°W) for winter (January–March; red line), spring (April–June; green line), summer (July–September; blue line) and fall (October–December; purple) and all seasons together (black line and open circles) as an example of type 1 distribution function. The distribution function D(x) is normalized to 1 from SM min to SMmax and is ×100. The x axis is given in millimeters. (b) Same as (a) but for the mid-Atlantic area (38°–42°N, 72°–80°W) as an example of type 2 distribution function. (c) Same as (a) but for Arizona (32°–36°N, 107°–113°W) as an example of type 3 distribution function. (d) Same as (a) but for the Ohio Valley (37°–42°N, 82°–90°W) as an example of type 4 distribution function. (e)–(h) Same as (a)–(d) but for SM anomalies. The x axis is given in standard deviations. Anomalies are defined as departures from monthly-mean climatology from 1915 to 2003.

PD type 1 (Fig. 2a, open circles) and PD type 3 (Fig. 2c, open circles) with all seasons pooling together are unimodal. Type 1 is the most common type. SM across the Southeast and the interior western region (west of 95°W) has unimodal PDs. PD type 2 (Fig. 2b, open circles) and PD type 4 (Fig. 2d, open circles) are bimodal. The type 2 distribution has two peaks on the either side of the median. The type 4 distribution has one prominent peak near SMmax and a broad shoulder. SM for the West Coast and areas east of 95°W except the Southeast has bimodal distribution functions (type 2 and type 4). As noted by D’Odorico and Porporato (2004), the distribution for SM in Illinois is bimodal and belongs to the type 2 distribution.

PDs are strongly modulated by the seasonal cycle, represented by the difference between SMmax and SMmin of the climatological monthly means (Fig. 1b). The bimodal distributions are located over the areas where SM has a strong seasonal cycle. Except for the western mountains, the type 2 and type 4 distributions are located over areas where the differences between SMmax and SMmin are greater than 100 mm. The unimodal distributions are located over the areas where SM has a weak seasonal cycle.

The PDs for individual seasons were presented for the same four regions (Figs. 2a–2c) to study the influence of the seasonal cycle. SM is large during winter because of accumulated rainfall from fall to winter and weak evaporation (E). In spring, E increases and SM depreciates. Summer rainfall is often balanced by E, and SM reaches a minimum in late summer. In the areas with a large seasonal cycle, the PD peaks for winter (red line) and summer (blue line) are far apart (Figs. 2b and 2d). The PDs for all seasons together show a bimodal distribution (dark line and open circles). In the areas that SM has unimodal distribution, SM has a weak seasonal cycle and the PD peaks for different seasons are close together.

Because different PD types are caused by seasonality, the PDs for soil moisture anomalies are unimodal. The PDs for SM anomalies for the four regions are given in Figs. 2e–2h. In this section, monthly-mean anomalies are departures from the monthly-mean climatology from 1915 to 2003. All distributions are unimodal and Gaussian.

The SM percentiles used for drought monitoring can be computed using two different methods. One method is based on the Gaussian distribution function. For each month, monthly-mean SM anomaly at each grid point was computed as the departure from the monthly-mean climatology from 1952 to 2000. The monthly standard deviations were computed from SM anomalies. The Gaussian distribution was determined using the standard deviation as a parameter for each month. Monthly SM percentiles were determined according to the Gaussian distribution. The other method is based on the PDs determined from the nonparametric method described above. The monthly-mean SM anomaly percentiles were obtained according to the PDs of SM anomalies. The root-mean-square (RMS) difference between these two sets of SM percentiles averaged over the period 1952–2000 and averaged across the United States is 4.8%. Therefore, the Gaussian distribution is a good approximation. The percentiles can be calculated the same way for 6-month running mean SM anomalies (SM6).

4. Uncertainties of the drought indices

a. Differences between indices from VIC and Noah

In this section, drought indices based on VIC and Noah are compared. If indices from the NLDAS are used for drought assessment, then they should be independent of the NLDAS systems. Indices derived from VIC and Noah should be similar enough to detect the same severe drought events. The VIC has 0.5° horizontal resolution, so the outputs from Noah were reduced to 0.5° to make them comparable. The comparison will focus on the common period 1952–2000. Monthly-mean anomalies and standard deviations were computed for that base period. To classify drought on the basis of the SM percentiles, the SM percentiles need to be <20% (Svoboda et al. 2002; Andreadis et al. 2005). To classify drought on the basis of SPI and SRI, indices need to be <−0.8 (Svoboda et al. 2002).

Correlations and the RMS differences between the SM percentiles derived from VIC and Noah are given in Figs. 3a and 3d, respectively. Good correlations indicate reliability and similarity of indices. The differences are not seasonally dependent, but they are highly regionally dependent. The differences between SM percentiles derived from these two systems are smaller across the areas east of 95°W. The correlation between them is 0.7 or more, and the RMS difference is <20%–25%. Across the western region, the differences are larger. For most areas across the western mountains, the correlations are below 0.6 and the RMS differences are >20%–25%. For these low-flow cases across the western region with spatial resolution 0.5° and with durations of one month, the SM differences between the two NLDAS systems are too large for drought classification.

Fig. 3.

(a) Correlation between SM percentiles based on VIC and Noah for the period 1952–2000. Contour interval is 0.2; contours ≥0.7 are shaded. (b) Same as (a) but for SPI6. (c) Same as (a) but for SRI6. (d) RMS difference for SM percentiles × 100 between VIC and Noah. Contour interval is 5%; contours ≥20% are shaded. (e) Same as (d) but for SPI6. Contour interval is 0.2; contours ≥0.8 are shaded. (f) Same as (e) but for SRI6.

Fig. 3.

(a) Correlation between SM percentiles based on VIC and Noah for the period 1952–2000. Contour interval is 0.2; contours ≥0.7 are shaded. (b) Same as (a) but for SPI6. (c) Same as (a) but for SRI6. (d) RMS difference for SM percentiles × 100 between VIC and Noah. Contour interval is 5%; contours ≥20% are shaded. (e) Same as (d) but for SPI6. Contour interval is 0.2; contours ≥0.8 are shaded. (f) Same as (e) but for SRI6.

Their differences are caused by both model and forcing differences. Mo and Schemm (2008) reported that drought persists longer over the interior western region west of 95°W. The memory of SM anomalies is located in deeper soil layers, and it depends on the model soil properties. The Noah and VIC have very different soil structure. For spring and early summer, snowmelt and snow depth both contribute to SM across the western mountains, but the two models treat snow differently. Another major contribution to the differences between the two systems is the precipitation forcing. To quantify the P difference, correlation and RMS difference of SPI6 between Noah and VIC are given in Figs. 3b and 3e, respectively. Large P differences are located over the interior west region and the Appalachian Mountains where the data coverage is sparse. Differences can also be caused by whether hourly or daily forcing was used to drive the model. The two systems use different procedures to derive gridded hourly P forcing from daily data.

In comparison with the SPI differences, the SRI6 differences between the two systems are larger (Figs. 3c and 3f), especially across the western region and the Appalachian Mountains. Across the East Coast and the Great Plains, correlations are higher. In addition to the P differences, runoffs in winter and spring are influenced by the timing and amounts of snowmelt (Lohmann et al. 2004).

Even though the NLDAS can produce SM and runoff at 0.125° resolution, the uncertainties between indices may be too large for drought classification across the interior western region. The question is whether the indices from different NLDAS systems averaged across a larger domain will be similar enough for drought monitoring. The National Weather Service RFCs were used for this test because areas within the RFCs have similar hydroclimate. The monthly-mean P for a given RFC is the monthly-mean P averaged over all grid points in the RFC. The monthly-mean runoff and soil moisture for RFCs are defined the same way. The standardized anomalies were calculated and the percentiles were obtained. Table 1 presents the RMS differences and correlations between VIC and Noah for all indices for the RFCs. The SPI6 differences are small. The SM6 between the two NLDAS systems has correlations between 0.71–0.89. Consistent with Fig. 3, the RMS differences for the western RFCs are larger than the eastern RFCs but the differences are still <20%. The RMS differences for both SPI6 and SRI6 are <0.5. Statistically, the differences are within the threshold of drought classification. However, the drought events selected based on the SM percentiles or the SRI derived from the two systems for the western RFCs do not always overlap.

Table 1.

Correlations and RMS differences between indices derived from VIC and Noah.

Correlations and RMS differences between indices derived from VIC and Noah.
Correlations and RMS differences between indices derived from VIC and Noah.

Because the largest differences are located across the interior western region, the monthly-mean SM percentiles for Colorado and Missouri RFCs are given as examples (Fig. 4). SM percentiles based on VIC (blue) have larger month-to-month variations than Noah. The differences are smaller for SM6, but the maxima and minima from VIC are still larger than those from Noah. The differences between the two systems are significant. Both SM6 indices derived from VIC and Noah are able to capture the persistent drought in the 1950s. However, the assessment for the 1988 drought differs. The SM6 index from VIC was <20% from 1988 to 1989, but the SM6 index for the same period from Noah was >20%. Therefore, Colorado and Missouri were classified as under drought for the period 1988–89 by VIC but not by Noah. P forcing may contribute to the large variations of VIC soil moisture. The SPI6 minima from VIC are lower than from Noah (Figs. 4c and 4g). Overall, the SPI6 and SRI6 differences between the two systems are smaller in comparison to the SM6 differences.

Fig. 4.

(a) Mean SM percentile for the Colorado RFC derived from VIC (blue line) and Noah (black line). (b) Same as (a) but for SM6. (c) Same as (a) but for SPI6. (d) Same as (a) but for SRI6. (e)–(h) Same as (a)–(d) but for the Missouri RFC.

Fig. 4.

(a) Mean SM percentile for the Colorado RFC derived from VIC (blue line) and Noah (black line). (b) Same as (a) but for SM6. (c) Same as (a) but for SPI6. (d) Same as (a) but for SRI6. (e)–(h) Same as (a)–(d) but for the Missouri RFC.

The SM criterion used to classify drought is 20%. The question is whether the two systems have more common dry months if the criterion for drought is relaxed to 35%. At each grid point, the number of months (NUMs) that the SM percentiles from either VIC or Noah are below the given threshold was determined. These events can be separated into three cases. These months that the SM percentiles from both VIC and Noah satisfy the criterion belong to case 1. These months that the SM percentiles from Noah (VIC) satisfy the criterion but not VIC (Noah) belong to case 2 (case 3). The ratio between the number of months in each case and NUM is displayed in Fig. 5. Consistent with Fig. 3, there are more common dry months between the two systems across the eastern region (east of 95°W) than the interior western region. If the criterion is relaxed to 35% to include weak drought months, then the two systems have more cases in common across the entire United States (Figs. 5a and 5b). Across the interior western region, VIC has more drought months than Noah because the SM6 minima from VIC are usually lower than those from Noah (Fig. 4).

Fig. 5.

(a) Ratio between the number of months that both VIC and Noah declared under drought and the number of months that either VIC or Noah declared under drought at each grid point. Drought is defined as an SM percentile <20%. Contour interval is 0.1; contours ≥0.3 are shaded according to the color bar. (b) Same as (a) but for number of months that the Noah declared drought but not VIC. (c) Same as (a) but for number of months that the VIC declared drought but not Noah. (d)–(f) Same as (a)–(c) but drought is defined as when the SM percentile is <35%.

Fig. 5.

(a) Ratio between the number of months that both VIC and Noah declared under drought and the number of months that either VIC or Noah declared under drought at each grid point. Drought is defined as an SM percentile <20%. Contour interval is 0.1; contours ≥0.3 are shaded according to the color bar. (b) Same as (a) but for number of months that the Noah declared drought but not VIC. (c) Same as (a) but for number of months that the VIC declared drought but not Noah. (d)–(f) Same as (a)–(c) but drought is defined as when the SM percentile is <35%.

b. Relationships among indices

To investigate relationships among indices, correlations between different indices from the same model were obtained (Fig. 6). Overall, indices derived from VIC are more closely related to each other than Noah and their correlations are higher. Andreadis et al. (2005) found that P has higher correlation with runoff than with SM across the western region during three severe drought events. For VIC, correlations between SPI6 and SRI6 are higher than the correlations between SPI6 and SM6. Correlations between indices are lower and more regionally dependent for Noah. This implies that runoff from VIC responds to P faster than from Noah, especially across the eastern United States. For Noah, SPI and SRI6 are closely related only across the southern Great Plains. For the eastern United States, correlations between SPI and SM6 are higher. SM and runoff from Noah are not well correlated across the interior western region. Their correlations are <0.4. Correlations between SRI6 and SM6 are >0.6 across the western and central United States for both VIC and Noah.

Fig. 6.

(a) Correlation between SPI6 and SRI6 for the period 1952–2000 for Noah. Contour interval is 0.2; light (dark) shading indicates that values are ≥0.6 (0.8). (b) Same as (a) but for correlation between SPI6 and SM6. (c) Same as (a) but for correlation between SRI6 and SM6. (d)–(f) Same as (a)–(c) but for VIC.

Fig. 6.

(a) Correlation between SPI6 and SRI6 for the period 1952–2000 for Noah. Contour interval is 0.2; light (dark) shading indicates that values are ≥0.6 (0.8). (b) Same as (a) but for correlation between SPI6 and SM6. (c) Same as (a) but for correlation between SRI6 and SM6. (d)–(f) Same as (a)–(c) but for VIC.

If larger areas are considered, correlations are higher as expected. Correlations were computed between indices for RFCs for VIC and Noah and their means (Table 2). For SPI6 and SRI6, the differences between VIC and Noah are small, so only the correlations for their means are listed. Correlations between mean SPI6 and SRI6 are >0.76. This suggests that runoff responds to P quickly. The interesting point is that correlations are low between the precipitation index SPI6 and the SM index (SM6), especially for Noah, which is consistent with Fig. 6. For VIC, all correlations are above 0.5 except the Northwest RFC (RFC 1). For Noah, all correlations are <0.55. The change of SM depends on the difference between P and E. In summer, E is large than P across the central and some western states. Therefore, the increases of SM may be small. Evaporation E depends on the model parameterization, soil properties, and vegetation, which may contribute to the differences between VIC and Noah.

Table 2.

Correlation between drought indices.

Correlation between drought indices.
Correlation between drought indices.

The question is whether indices are similar enough to detect the same severe drought events. The mean indices SPI6, SRI6, and SM6 averaged over VIC and Noah were used to classify droughts for each RFC. Figure 7 flags the month that is classified as under drought based on mean SPI6 (black), SRI6 (red), and SM6 (green) indices for each RFC for the period 1950–2000. The salient points are listed below.

  1. The SPI6 index has larger month-to-month variability. Events selected based on SPI6 tend to have shorter durations, and events selected based on SM6 have longer durations. The Colorado RFC (Figs. 8a–8c) is used to illustrate this point. The SM6 was <20% from March 1953 to August 1957. The drought lasted for 51 months. The event was also picked up by the SRI6 index, but it only lasted about 43 months. If SPI6 is used to classify droughts, then the same drought broke into two events: from October 1953 to December 1954 and from July 1956 to January 1957. In addition to the measure of dryness, it is possible to also add persistence to the definition of drought. If persistence of 4 months or longer is added as a condition for drought, then 11 drought events were selected based on SPI6 for the Colorado RFC. The average duration is 8.6 months.

  2. For a given RFC, the events selected based on different indices have overlapping periods, but there are also situation in which only one index satisfies the drought criterion. An RFC under meteorological drought is not always under agricultural or hydrological drought, and vice versa. Events were selected based on the SM percentiles and SPI6 for the Colorado RFC. There were only eight common events. The average duration for these eight events is 15.8 months.

  3. For the Southeast RFC, the mid-Atlantic RFC and the lower Mississippi RFC across the eastern United States, different indices usually detect the same drought events because of strong correlations among indices (Table 2). The periods under meteorological drought overlap considerably with the periods under hydrological or agricultural drought. The duration of drought events across the eastern region is shorter than the western RFCs. The Southeast RFC is used as an example (Figs. 8d–8f). The three indices selected the same six drought events. The mean duration differs slightly. The mean durations for the events selected based on SPI, SRI, and the SM percentiles are 7.9, 9.1 and 12.2 months, respectively.

  4. The indices are noisy. It is difficult to select drought events based on rigid criteria. For example, an index can rise above the threshold for one and two months, and then drop below the threshold again. Subjective decision may be still needed for drought classification.

Fig. 8.

(a) SM6 percentile averaged from VIC and Noah for the Colorado RFC vs year. (b) Same as (a) but for SPI6. (c) Same as (a) but for SRI6. (d)–(f) Same as (a)–(c) but for the Southwest RFC.

Fig. 8.

(a) SM6 percentile averaged from VIC and Noah for the Colorado RFC vs year. (b) Same as (a) but for SPI6. (c) Same as (a) but for SRI6. (d)–(f) Same as (a)–(c) but for the Southwest RFC.

Fig. 7.

Months classified as under drought based on mean SPI6 (black), SRI6 (red), and SM6 (green) indices averaged between VIC and Noah for (a) RFC 1, (b) RFC 2, (c) RFC 3, (d) RFC 4, (e) RFC 5, (f) RFC 6, (g) RFC 7, (h) RFC 8, (i) RFC 9, (j) RFC 10, (k) RFC 11, and (l) RFC 12.

Fig. 7.

Months classified as under drought based on mean SPI6 (black), SRI6 (red), and SM6 (green) indices averaged between VIC and Noah for (a) RFC 1, (b) RFC 2, (c) RFC 3, (d) RFC 4, (e) RFC 5, (f) RFC 6, (g) RFC 7, (h) RFC 8, (i) RFC 9, (j) RFC 10, (k) RFC 11, and (l) RFC 12.

c. Time scales

Results in the previous section suggest that each drought type has its own intrinsic time scales. For example, agricultural drought measured by SM percentiles tends to last longer than the meteorological drought events. To examine the time scales associated with drought indices, the characteristic time T0 was obtained to measure persistence (Fig. 9).

Fig. 9.

(a) The T0 for SM from VIC. Contour interval is 12 months with 6 month contours added. Areas where T0 values ≥12 (24) months are shaded light (dark). (b) Same as (a) but for SPI6. Contour interval is 3 months. (c) Same as (a) but for SRI6. (d) Same as (a) but for SM6. (e)–(g) Same as (a)–(c) but for T0 from Noah.

Fig. 9.

(a) The T0 for SM from VIC. Contour interval is 12 months with 6 month contours added. Areas where T0 values ≥12 (24) months are shaded light (dark). (b) Same as (a) but for SPI6. Contour interval is 3 months. (c) Same as (a) but for SRI6. (d) Same as (a) but for SM6. (e)–(g) Same as (a)–(c) but for T0 from Noah.

The characteristic time T0 (Trenberth 1984) can be calculated from the autocorrelation R(i) at lag i month for i = 1 to 30:

 
formula

SPIs have the shortest time scales. The T0 for SPI6 is about 6–12 months for both VIC and Noah (Figs. 9b and 9f). Across the eastern region, SM and SPI6 have similar time scales independent of the NLDAS systems. The situation is very different across the interior western region where T0 is longer. SM has the longer time scales, but T0 for SM depends on the region and the NLDAS system (Figs. 9a and 9e). The T0 from Noah is about 36 months across the interior western states, and T0 from VIC is about 24 months. SM from VIC has more variability and is less persistent in comparison with Noah. The T0 for SM6 has a similar pattern as SM, but the magnitude is about 12 months longer. The T0 for runoff (SRI6) has a similar pattern and magnitudes as T0 for SM.

d. Spatial extents

Severe droughts are not only characterized by long durations, but they are also characterized by large spatial extents. Figures 10 and 11 display the percentage of area under drought for the western region (31°–48°N, 105°–125°W), the central region (31°–48°N, 85°–105°W), and the eastern region (31°–48°N, 70°–85°W) determined by SM6 (green line), SPI6 (black line), and SRI (red line) for VIC and Noah, respectively. Areas under drought based on different indices from VIC are similar. These differences are larger for Noah because of low correlations among indices (Fig. 6). Across the western region, the differences between drought areas based on different indices can be as large as 20%–30% for Noah. For the eastern region, areas covered under drought have larger month-to-month variations consistent with shorter durations for drought. All indices indicate that the widespread drought in the 1950s covered both the western and central United States for both VIC and Noah.

Fig. 10.

Percentage of areas classified as under drought by SPI6 (black), SRI6 (red), and SM6 (green) based on VIC for the (a) western region (31°–48°N, 105°–125°W), (b) central region (31°–48°N, 85°–105°W) and (c) eastern region (31°–48°N, 70°–85°W) of the United States.

Fig. 10.

Percentage of areas classified as under drought by SPI6 (black), SRI6 (red), and SM6 (green) based on VIC for the (a) western region (31°–48°N, 105°–125°W), (b) central region (31°–48°N, 85°–105°W) and (c) eastern region (31°–48°N, 70°–85°W) of the United States.

Fig. 11.

Same as Fig. 10 but for Noah.

Fig. 11.

Same as Fig. 10 but for Noah.

For Noah, the differences in the early 1950s may be caused by spinup. Noah does not have SM information from the 1940s. The VIC started in 1915, so the spinup is not a problem. For Noah after 1956, areas under drought based on SPI6 (black line) are much larger than areas determined based on runoff and SM6 across the western region, even though they have similar interannual variability. For the western region, the drought areas classified based on the same index may depend on the NLDAS systems. The drought areas are illustrated in Fig. 12.

Fig. 12.

(a) Areas under drought classified based on SM6 from VIC (shaded), and Noah (contoured) for the period 1 Jan 1953–1 Jan 1957. Contour interval is 10% with values ≥20% omitted. (b) Same as (a) but based on mean SRI6. Contour is 0.4 with values ≥0.8 omitted. (c) Same as (a) but for SPI6. (d)–(f) Same as (a)–(c) but for the period 1 May–1 Sep 1988.

Fig. 12.

(a) Areas under drought classified based on SM6 from VIC (shaded), and Noah (contoured) for the period 1 Jan 1953–1 Jan 1957. Contour interval is 10% with values ≥20% omitted. (b) Same as (a) but based on mean SRI6. Contour is 0.4 with values ≥0.8 omitted. (c) Same as (a) but for SPI6. (d)–(f) Same as (a)–(c) but for the period 1 May–1 Sep 1988.

Figure 12 displays the area under drought averaged over the period January 1953–January 1957 based on VIC (shaded) and Noah (contoured). Differences between the VIC and Noah are small and based on SPI6. Both show that drought covered Wyoming and the areas extended from Texas and New Mexico to the northern plains. For VIC, the spatial areas under drought determined by different indices are similar. For Noah, areas under drought shifted westward if SM6 is used to classify drought.

The areas covered under drought derived from the two systems show large differences in the 1980s. For VIC, areas under drought covered more than 30% of the total area across the western region from 1986 to 1989 with a peak in 1988. Figures 12d–12f display the areas under drought for May–September 1988 based on different indices. The drought areas determined based on SPI6 from VIC and Noah are similar (Fig. 12f).They both show that drought extended from Louisiana and Alabama northeastward through the Ohio Valley to the Northeast. Areas under drought also covered the north-central and upper Missouri basin, the Northwest, and a portion of northern California. With SM6 (Fig. 12d) and SRI6 (Fig. 12e), the Noah shows drought over the central–eastern region, but it does not show a coherent spatial pattern for drought over the northwestern region.

5. Conclusions

Drought causes devastating effects on our society. To create a drought early warning system is one of many goals of the National Integrated Drought Information System (NIDIS). One way to integrate data and to provide timely information to decision makers and the general public is to use physically based indices. The commonly used drought indices are the SPI and the PDSI. Many shortcomings of the PDSI make the index less desirable. In addition to precipitation deficits, the socioeconomic affects on agriculture and water supply, which include reservoir storage, streamflow deficits, are also important (Wilhite 2000). Therefore, more than one index is needed to monitor drought. In this paper, SPI, soil moisture percentile, and SRI are used to measure the meteorological, agricultural, and hydrological aspects of drought.

Because long-term observations of runoff and soil moisture are not available, products from the NLDAS become valuable alternatives. To use the NLDAS outputs to analyze droughts, the index based on different NLDAS systems should be similar. They should be able to detect the same drought events. The users of the indices should consider uncertainties in their decision-making process. The relationships between the SPI, SRI, and SM percentiles can give decision makers the linkages among the different aspects of drought.

The indices are designed based on distribution functions and can be used to examine droughts on different time scales. By definition, the distributions for both SRI and SPI are Gaussian. Although the PDs for SM are regionally dependent and are influenced by seasonal cycle, the PDs for SM anomalies obey Gaussian. Therefore, correlations and RMS differences are used for comparison.

The major conclusions are listed below.

  1. Across the eastern region, the indices from VIC and Noah are similar. The RMS differences between indices from Noah and VIC are <20%–25% for SM anomalies and <0.8 for SPI and SRI. The differences are smaller than the thresholds used to classify drought. Both systems are able to detect the same drought events. The correlations among indices are higher than correlations across the western region. For the eastern RFCs such as the Southeast RFC, the mid-Atlantic RFC and the lower Mississippi RFC, different indices tend to select the same drought events.

  2. Across the western interior United States, the situation is very different. For small areas across the western interior region (e.g., 0.5° × 0.5° boxes) on the time scales of one to three months, the RMS differences between Noah and VIC are >20% for SM and 0.8 for SPI and SRI. The differences between the two systems are larger than the thresholds used to classify droughts. With longer spatial and temporal averages, the differences between the two systems are smaller, but there are still situations in which different systems will give different drought assessments. For example, SM and runoff indices based on different NLDAS systems do not always pick up the same drought events for the Colorado and Missouri RFCs, even though most NLDAS systems have the horizontal resolution of 0.125°. Users should proceed with caution when using the NLDAS products to assess drought on fine spatial scales.

  3. Indices from VIC have higher correlations among them than Noah. The correlations between runoff SRI6 and SPI6 are higher than correlations between SM6 and SPI6. Correlations are lower for Noah. This suggests that runoff responds to P quickly in VIC, but less so in Noah. Across the western region, the correlations between SPI and SM or SRI are <0.4 for Noah.

  4. Across the western region, drought classification and durations may depend on the index used because each index has its own intrinsic time scales. If drought events are selected based on SM6, then events tend to last longer because SM anomalies persist longer than precipitation or runoff. This means that agricultural drought tends to last longer because SM takes a long time to refurbish after a long period of dryness.

Precipitation P depends on analyses and data coverage, but it is independent of the NLDAS model used. Therefore, SPI differences between the two systems are smaller in comparison with SM and runoff. Differences still exist over the western high mountains because of sparse data coverage. In the coming years, the improvements of precipitation analyses and the use of radar and satellite measurements may eliminate some of uncertainties in P.

Large differences in SM and runoff between VIC and Noah are located across the western region where droughts last longer (Mo and Schemm 2008). Long memory comes from soil moisture in the deep soil layers. In spring, SM also depends on snowmelt and winter snow coverage. These properties depend on model physics. For VIC, the runoff responds quickly to P. The linkages among different indices are weaker in Noah, as indicated by the low correlations among them. The SM change depends on the difference between E and P. Therefore, the relationship may not be linear and straight forward.

The consolidation of many NLDAS products using different forcing and models may be a way to eliminate uncertainties. Dirmeyer et al. (2006) examined NLDAS outputs from the GSWP-2 and arrived at the conclusion that the ensemble means of soil moisture give the best estimates. In addition to the ensemble mean, the spread should also be given. The spread among the ensemble members indicates the uncertainties among different NLDAS systems, which will assist decision makers in using the information wisely.

Acknowledgments

We wish to thank Drs. Andy Wood and Dennis Lettenmaier for providing VIC data. The Noah data were provided by Drs. Yun Fan and Huug van den Dool. This work was supported by NCPO/CPPA Grant GC06-012.

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Footnotes

Corresponding author address: Kingtse C. Mo, Climate Prediction Center, NOAA/NWS/NCEP, 5200 Auth Rd., Camp Springs, MD 20746. Email: kingtse.mo@noaa.gov