Abstract

The ability to use in situ soil moisture for large-scale soil moisture monitoring, model and satellite validation, and climate investigations is contingent on properly standardizing soil moisture observations. Percentiles are a useful method for homogenizing in situ soil moisture. However, very few stations have been continuously monitoring in situ soil moisture for 20 years or more. Therefore, one challenge in evaluating soil moisture is determining whether the period of record is sufficient to produce a stable distribution from which to generate percentiles. In this study daily in situ soil moisture observations, measured at three separate depths in the soil column at 15 stations in the United States and Canada, are used to determine the record length that is necessary to generate a stable soil moisture distribution. The Anderson–Darling test is implemented, both with and without a Bonferroni adjustment, to quantify the necessary record length. The authors evaluate how the necessary record length varies by location, measurement depth, and month. They find that between 3 and 15 years of data are required to produce stable distributions, with the majority of stations requiring only 3–6 years of data. Not surprisingly, more years of data are required to obtain stable estimates of the 5th and 95th percentiles than of the first, second, and third quartiles of the soil moisture distribution. Overall these results suggest that 6 years of continuous, daily in situ soil moisture data will be sufficient in most conditions to create stable and robust percentiles.

1. Introduction

The role of soil moisture in the climate system has been thoroughly investigated over the last two decades (Legates et al. 2011). Soil moisture modifies energy and moisture flux into the boundary layer (Guo and Dirmeyer 2013) thereby influencing near-surface air temperature (Hirschi et al. 2011; Miralles et al. 2012), humidity (Ek and Holtslag 2004; Ford et al. 2015b), and boundary layer instability (Myoung and Nielsen-Gammon 2010; Gentine et al. 2013) and in some cases determining if, where, or when precipitation occurs (Findell and Eltahir 2003; Taylor et al. 2011, 2012). Soil moisture anomalies, forced by the interplay between precipitation and evapotranspiration, can exhibit monthly-to-seasonal persistence, causing similarly persistent surface heat flux and air temperature anomalies (Delworth and Manabe 1988). Persistence of extreme temperatures over much of the world’s land surface can be partially attributed to land–atmosphere interactions and soil moisture memory (Kohler et al. 2010; Mueller and Seneviratne 2012). Precipitation deficits caused by persistent atmospheric circulation patterns diminish soil moisture, which can increase near-surface air temperature through enhanced sensible heating (Vautard et al. 2007; Gallego-Elvira et al. 2016). Mueller and Seneviratne (2012) demonstrate the strong coupling between soil moisture and subsequent extreme heat over large regions of Europe, Australia, and North and South America, corroborated by subsequent studies using both models (Stéfanon et al. 2014; Hirsch et al. 2014) and observations (Meng and Shen 2014). Understanding these land–atmosphere interactions driven by soil moisture anomalies is crucial for subseasonal-to-seasonal climate prediction as well as forecasting of extreme climatic events (Koster et al. 2010; Guo et al. 2012).

In addition to playing an integral role in the global climate system, soil moisture is typically used as an indicator of moisture stress and agricultural drought (Quiring and Papakryiakou 2003). Because of its importance for water resource management and drought monitoring/forecasting, numerous soil moisture products are available for monitoring purposes, but most are based on models. These include the University of Washington Experimental Surface Water Monitor (Wood 2008), the NOAA Climate Prediction Center soil moisture product (Fan and van den Dool 2004), the North American Land Data Assimilation (NLDAS) Drought Monitor soil moisture output (Mitchell et al. 2004), and the Princeton Drought Monitoring and Forecasting project (Luo et al. 2007; Sheffield et al. 2014). These products are invaluable for drought monitoring, flood forecasting, and seasonal climate prediction. Indeed the U.S. Drought Monitor (Svoboda et al. 2002) uses these soil moisture datasets to generate weekly, nationwide drought maps.

The temporal variability of soil moisture is a strong function of both small-scale features such as soil texture and topography and large-scale atmospheric circulation (Entin et al. 2000). Therefore mapping soil moisture conditions across an entire nation or continent using volumetric water content (cm3 cm−3), percent of field capacity (%), or total soil water content (mm) will not accurately capture moisture surplus or deficit with respect to a region’s normal conditions. Accordingly, many of the aforementioned model-based soil moisture products are available in standardized units such as volumetric water content anomalies or volumetric water content percentiles. Using soil moisture percentiles is a simple, robust way of placing the current soil moisture conditions in the context of both average soil moisture and the variability of soil moisture at that particular location. However, it should be noted that percentiles of absolute soil moisture do not provide a physical indication of drought severity, such as plant moisture stress or available well water. When representing drought severity statistically with soil moisture percentiles, one disadvantage is the necessity of a robust probability density function on which to base the percentiles. For example, if one were to generate soil moisture percentiles from one year’s worth of observations, depending on the soil moisture conditions during that year, the percentiles may or may not actually capture the true distribution of soil moisture at that location. This is not an issue for soil moisture datasets based on 30+-yr model simulations; however, it is an issue for shorter-term observational records.

Despite the importance of in situ soil moisture for model calibration and validation, there are relatively few sites that measure soil moisture. However, as our understanding of the importance of soil moisture to both the climate system and to extreme climatic events advances, the quantity and quality of in situ soil moisture monitoring stations has increased. Efforts to assemble and homogenize in situ records are important for making these data more useful for the scientific community. For example, Robock et al. (2000) developed the Global Soil Moisture Data Bank, providing soil moisture observations from several hundred stations globally. The Global Soil Moisture Data Bank was incorporated into the International Soil Moisture Network (ISMN; Dorigo et al. 2011). The ISMN is a global database of in situ soil moisture observations from 47 networks containing 1900 stations around the world. More recently, the North American Soil Moisture Database (NASMD; Quiring et al. 2016) was developed to provide harmonized and quality-controlled soil moisture data from stations across the United States, Canada, and Mexico. The NASMD integrates daily soil moisture observations from over 1800 stations throughout all 50 U.S. states and 6 Canadian provinces.

Unlike the model-simulated soil moisture products, the observation datasets incorporated in the ISMN and NASMD do not have a consistent record length. The NASMD in particular includes both a nearly 50-yr record of Iowa soil moisture and a <2-yr record of soil moisture from nearby Indiana (Khong et al. 2015; Quiring et al. 2016). The ability to use these databases for large-scale soil moisture monitoring, model and satellite validation, or land–atmosphere interaction investigations is contingent on standardizing properly soil moisture observations from a variety of in situ sources. Generating soil moisture percentiles from daily measurements is a useful method for homogenizing these data. However, very few stations have been continuously monitoring in situ soil moisture for 20 years or more. Therefore, one challenge in using in situ soil moisture is determining whether the period of record is sufficient to produce a stable distribution from which to generate percentiles. Stability, in this case refers to the relative change in the soil moisture distribution as the data record length increases, such that the (e.g.) median, first quartile, or 5th percentile of a stable distribution does not change significantly as data record years are added.

Indeed record length has a large influence on the robustness and reproducibility of observation-based climate analyses (Findell et al. 2015). Despite this, very few studies have attempted to determine the requisite observation record length to understand the anomaly of one observation. Numerous studies have focused on the time stability of soil moisture over a relatively small spatial area and short (subdaily to daily) time scale (Martínez-Fernández and Ceballos 2003; Cosh et al. 2006; Brocca et al. 2009). In these cases, soil moisture spatial variability can be estimated accurately using the known temporal stability of soil moisture at a few discrete points. However, we are interested in the temporal stability of soil moisture on interannual time scales. In this study we seek to determine the record length necessary to generate stable soil moisture percentiles from daily in situ soil moisture observations.

2. Data

Daily volumetric water content (cm3 cm−3) observations taken from the NASMD (soilmoisture.tamu.edu; Quiring et al. 2016) were the primary data used in this study. The NASMD contains daily soil moisture observations from over 1800 stations in North America; however, many of these stations have record lengths of five years or less. Our priorities for selecting stations to include in our analysis were as follows: 1) the station had a data record length of no less than 13 years, 2) the time series of observations was complete such that no more than 10 daily observations were missing from any month, and 3) the stations chosen span a diverse set of soil texture and climate conditions. Based on these priorities we selected 13 stations with a 15-yr record and 2 stations with a 13-yr record from the NASMD to include in the analysis. Unfortunately, soil moisture monitoring stations are not distributed equally over the United States and Canada. This is particularly the case for those stations with a 13+-yr observation record. Namely, 7 of the 15 stations that were used in this study are located in Oklahoma. With that being said, the location of the 15 monitoring stations ranged from 31° to 53°N latitude and 109°W to 76°W longitude (Fig. 1), ensuring that our results were representative of a variety of climatic and edaphic conditions. The stations used in this study are from four networks: Atmospheric Radiation Measurement (ARM) Climate Research Facility, Oklahoma Mesonet, Fluxnet Canada, and Soil Climate Analysis Network (SCAN).

Fig. 1.

Soil moisture monitoring stations are symbolized in accord with the network to which they belong. Soil moisture data for all 15 stations were provided by NASMD (http://soilmoisture.tamu.edu).

Fig. 1.

Soil moisture monitoring stations are symbolized in accord with the network to which they belong. Soil moisture data for all 15 stations were provided by NASMD (http://soilmoisture.tamu.edu).

Two stations from ARM, operated by the U.S. Department of Energy, were used in our analysis: Lamont and Pawhuska, Oklahoma. The ARM stations monitor soil moisture as well as several other meteorological variables at a variety of subhourly time scales (all of which are available from http://www.arm.gov/.) The ARM data provided by the NASMD were quality controlled (see Quiring et al. 2016) and aggregated to the daily time scale. Volumetric water content at each of the ARM sites is measured using the Soil Water and Temperature System (SWATS). Specifically, volumetric water content is calculated from a thermal matric potential measured using a model 229-L heat dissipation sensor (Campbell Scientific, Inc.), and is provided at 5, 15, 25, 35, 60, 85, 125, and 175 cm (Cook 2016). The ARM Lamont site is located in a cattle pasture in north-central Oklahoma with mostly clay soils ranging from 54% to 43% clay content (Table 1). The ARM Pawhuska site is located in grazed pasture in northeast Oklahoma and exhibits sandy loam soils ranging from 61% to 68% sand content. We use daily soil moisture observations from Lamont and Pawhuska spanning the time period 1997–2012.

Table 1.

Soil moisture station information. Data from the various networks were provided by the NASMD (soilmoisture.tamu.edu).

Soil moisture station information. Data from the various networks were provided by the NASMD (soilmoisture.tamu.edu).
Soil moisture station information. Data from the various networks were provided by the NASMD (soilmoisture.tamu.edu).

The Oklahoma Mesonet (http://www.mesonet.org/; Illston et al. 2008) is a statewide monitoring network with over 120 stations. The Oklahoma Mesonet is unique in that the majority of its stations have been monitoring soil moisture at subdaily intervals, continuously for 15+ years. Similar to the ARM network, volumetric water content of the soil is estimated at Oklahoma Mesonet stations using the thermal matric potential measured by the 229-L heat dissipation sensor at 5-, 25-, 60-, and 75-cm depths. The NASMD provides daily averaged soil volumetric water content data from 120 of the Oklahoma Mesonet stations. We selected five of these stations for our analysis, choosing those with relatively long and serially complete observation records. Soil textures at these five sites include sandy loam, loam, and clay loam; three sites are located in grassland and the two sites in the Oklahoma Panhandle are sited in scrubland. Daily soil moisture observations from each of the Oklahoma Mesonet sites are available over the period 1998–2013.

The Fluxnet Canada Research Network, operated by Environment Canada, was developed to investigate the influence of climate and disturbances on carbon cycling in Canadian forests and peatlands (Margolis et al. 2006). Fluxnet Canada stations employ both the 615-L water content reflectometer (Campbell Scientific) and time-domain reflectometer (TDR; Campbell Scientific) sensors for soil moisture measurements at various depths throughout the soil column. We select two Fluxnet Canada stations, Borden (Ontario) and Old Aspen (Saskatchewan), for our analysis as these stations have the longest, most complete observation records. The Borden site is located in southern Ontario in a large mixed hardwood forest and has soil moisture observations from the 615-L sensor at 2, 5, 10, 20, 50, and 100 cm. Unfortunately, we were unable to find soil texture information for the Borden site. The Old Aspen site is located in an Aspen forest in central Saskatchewan and has soil moisture observations at 2.5 and 7.5 cm with the 615-L sensor and at 7.5, 15, 30, 60, and 90 cm with the TDR sensor. Soils at the Old Aspen site range from loam near the surface to sandy clay loam deeper in the soil column. The two Fluxnet Canada stations are the stations with the shorter 13-yr record; Borden and Old Aspen records span the periods 1998–2011 and 1997–2009, respectively.

The SCAN network is operated by the U.S. Department of Agriculture Natural Resources Conservation Service and contains over 200 stations in all 50 states continuously monitoring soil moisture, some for more than 20 years. Soil moisture observations are taken at most SCAN stations at 5-, 10-, 20-, 50-, and 100-cm depths using the Hydraprobe sensor (Stevens Water Monitoring Systems, Inc.). The national extent of the SCAN network allows us to select long-running stations experiencing a variety of regional climates. In all we use six SCAN stations for our analysis, located in Georgia, Pennsylvania, North Dakota, Montana, Colorado, and Nevada. Soil textures at the SCAN sites range from loamy sand with more than 88% sand content to silty clay loam with more than 27% clay content. Similarly land cover at SCAN sites ranges from mowed grass to pasture and scrubland. Daily soil moisture observation records at SCAN stations begin between 1997 and 2000 and we used data through the end of 2014 for this study.

Table 1 displays the variety of environmental conditions in which the 15 sites are located. The measurement depths at each station are also provided. Soil texture and land-cover information were provided by the individual networks. We expect that the number of years necessary to generate stable percentiles will vary quite strongly as a function of soil depth, and therefore our analysis will only use soil moisture observations from three depth ranges: 5–10, 20–30, and 50–60 cm. These depths were chosen to include observations from all 15 sites, and generally represent near-surface, middle, and deeper soil. Therefore, the 5-, 25-, and 60-cm measurements were used for the ARM and Oklahoma Mesonet stations; the 5-, 20-, and 50-cm measurements were used for SCAN stations; the 5-, 20-, and 50-cm measurements were used for Borden; and the 7.5-, 30-, and 60-cm measurements were used for Old Aspen. Analyzing soil moisture observations from the similar depths in the soil column ensures internally consistent comparison between sites.

3. Methodology

The primary purpose of the study is to determine the necessary observation record length to generate stable percentiles of volumetric water content. The stability of soil moisture distributions is quantified by measuring the distribution change (or lack of change) as the data record length increases. We expect that the necessary record length will vary as a function of the depth at which the measurements are taken and, particularly for stations in the midlatitudes, the time of the year in which the measurements are taken. Therefore, for each station we separate the daily soil moisture observations by measurement depth and month. We then select n number of years from an individual depth–month combination at an individual station. A soil moisture distribution is then generated based on just these n observation years, and the first, second, and third quartiles as well as the 5th and 95th percentiles of this distribution are noted. Therefore, using only n = 2 years of data, there are only, at most, 62 data points (31 days in the month × 2 years) from which to build the distribution and compute the quartiles and percentiles. In contrast, when using n = 10 years, there are up to 310 days from which to build the distribution. The process of selecting n years of data, generating a distribution, and noting the first, second, and third quartiles and 5th and 95th percentiles of the distribution is repeated 300 times using a bootstrapping procedure that randomly resamples with replacement. The number of iterations necessary to generate a stable, normally distributed data population was determined through an analysis of variance (see the online supplemental material). We repeated our analysis using 150, 500, 700, and 1000 iterations, with no noticeable difference in results. This could be partly attributed to the limited number of permutations of randomly selected years out of the relatively short 15-yr record. Once the procedure had completed 300 iterations, the value of n was increased by 1 year and the entire process was repeated. For our analysis, the number of years (n) varied from 2 to N − 1 where N was the total number of years of data available at each station. We initially generated distributions based on only one year of data; however, we found that only a single year of data was not sufficient to represent the entire 15-yr record at any of the stations and therefore the N = 1 results are not reported. Our analysis produced a distribution of 300 first quartiles, second quartiles, third quartiles, 5th percentiles, and 95th percentiles for each value of n; a unique solution was generated for each combination of calendar month and measurement depth.

Figure 2 shows an example of these distributions generated using data from July for the middle depth (20 cm) at the SCAN station in Little River, Georgia. The blue area at the top of each plot and the first box plot immediately below represent the probability distribution of the entire Little River 20-cm dataset for July, and the series of gray box plots show the distributions of the 300 estimated first-quartile values (Fig. 2, top), second-quartile values (Fig. 2, middle), and third-quartile values (Fig. 2, bottom), output from the bootstrapping procedure. Each of these box plots is labeled on the y axis according to the number of years n that were used to generate the distribution (n varies from 2 to 14). In each box plot, the distribution median is shown with a black line, the dark gray area represents the interquartile range, and the area between the 5th and 95th percentile are shown in light gray. The red lines running from top to bottom through the entire plot represents the first quartile, second quartile, and third quartile of the population, based on the entire record at Little River. Figure 2 illustrates how the possible range of estimated values narrows and converges near the actual population quartiles as more years of data are used. The simulated population converges rapidly between 2, 3, and 4 years but then changes more slowly as more years of data are included.

Fig. 2.

The entire distribution of July 20-cm soil moisture observations at Little River is represented as the blue density plot and the first box plot. The following 13 box plots show the distributions of (top) first quartiles, (middle) second quartiles, and (bottom) third quartiles generated with the bootstrapping resampling process. Each sequential box plot shows a distribution generated with n data record years, as n varies from 2 to 14. The median of each distribution is represented with a black line, the interquartile range is shown in dark gray, and the 5th–95th-percentile range is shown in light gray. The red line extending through the entire panel represents the first quartile, second quartile, and third quartile, respectively, of the entire 15-yr soil moisture distribution.

Fig. 2.

The entire distribution of July 20-cm soil moisture observations at Little River is represented as the blue density plot and the first box plot. The following 13 box plots show the distributions of (top) first quartiles, (middle) second quartiles, and (bottom) third quartiles generated with the bootstrapping resampling process. Each sequential box plot shows a distribution generated with n data record years, as n varies from 2 to 14. The median of each distribution is represented with a black line, the interquartile range is shown in dark gray, and the 5th–95th-percentile range is shown in light gray. The red line extending through the entire panel represents the first quartile, second quartile, and third quartile, respectively, of the entire 15-yr soil moisture distribution.

Based on this consistent pattern of convergence, we can estimate the minimum record length (in years) required to generate stable percentiles representative of the actual population distribution. The range of estimates for each bootstrapping simulation exhibits rapid convergence toward the population and then flattens out beyond a certain record length. It is this “flattening out” point that we argue is the minimum record length necessary to generate a stable distribution. To quantitatively determine at what record length this point occurs, we use the Anderson–Darling (A-D) test to measure how different one simulated population is from the next simulated population. Given n number of years of data distributions, where n ranges from 2 to N − 1 (N = full observation record length in years), we use the A-D test to determine significant differences between the distribution of 5th percentiles, first/second/third quartiles, and 95th percentiles generated using n years to the distribution generated using n + 1 years. For example, we test for significant differences between the distribution of 300 first quartiles generated using 3 years of data and the distribution of 300 first quartiles generated using 4 years of data. Then we repeat this test for significant differences between the 4-yr distribution and 5-yr distribution, and so on. The distribution after which no significant differences exist is assumed to be the sufficient number of years to ensure a stable distribution from which to generate a robust percentile estimate. Any additional years of data beyond this point do not significantly change the soil moisture distribution. Therefore a stable distribution is one in which no significant change occurs as a result of an increase in record length. More specifically, a distribution is determined to be stable if it is not significantly different (based on the A-D test) than the distribution based on the entire 15-yr record. The two-sample A-D test, similar to the Kolmogorov–Smirnoff test, assesses the hypothesis that the populations from which two groups of data were drawn are identical. Based on Engmann and Cousineau (2011), the two-sample A-D test is generalized as

 
formula

where Z(n+m) is the combined and ordered samples X(n) and Y(m), of size n and m, and Ni is the number of observations in X(n) equal to or less than the ith observation in Z(n+m). The two-sample A-D test assesses the null hypothesis that samples X(n) and Y(m) come from the same continuous distribution. We selected the A-D test over the two-sample Kolmogorov–Smirnov test because it considers the shape and symmetry of the distributions tested (Anderson and Darling 1954; Engmann and Cousineau 2011). In addition, the A-D test is nonparametric, which is an advantage when working with soil moisture because these data are often not normally distributed. The A-D test has been similarly used for climate applications in lieu of the Kolmogorov–Smirnov test because of its nonparametric advantages and higher sensitivity to the distribution tails (Viglione et al. 2007; Russo and Sterl 2012).

Testing distributions iteratively using the A-D test increases the likelihood of a type I error, and in this case a potential inflation of the number of years necessary to generate stable percentiles. However, using an overly conservative method for adjusting p values, such as the Bonferroni adjustment, can result in an increased likelihood of type II error and, in many cases, it may not be necessary (Perneger 1998; Morgan 2007). Since the results of this study are highly dependent on the outcome of the A-D tests, we include results obtained using both a Bonferroni adjustment and those obtained without any p-value adjustment. In both cases the initial p value was set as 0.01 (99% confidence level). The Bonferroni adjustment calls for the division of the critical p value (in this case 0.01) by the number of comparisons being made, and although overly conservative, it has been applied previously to multiple comparison tests (Gamache and Payette 2004). We apply the methods to the bootstrapped distributions for each of the 15 stations and separately for each calendar month and measurement depth.

4. Results

a. First, second, and third quartiles

The A-D test was used to determine if significant differences exist between distributions using n and n + 1 record years, where n ranged from 2 to one less than the total observation record years available. We report the value of n beyond which no significant differences exist between distributions. These values are used to identify the minimum number of years that are necessary to generate stable soil moisture percentiles. Our results show that the minimum number of years ranges from 3 to 9; however, the majority cases required only 3–5 years (Table 2). In general, employing the A-D test with a Bonferroni adjustment tends to reduce the number of years that are required to obtain a stable distribution (Table 3). However, even without the adjustment, over 80% of the cases require 5 years or less to obtain a stable distribution. The number of cases requiring 5 or more years of data tends to increase as the measurement depth increases; however, even for the deepest measurements (50–60 cm), only 10% of the cases required 6 or more years of data to obtain stable percentiles (Table 2). The statistics reported in Tables 2 and 3 (and later in Tables 4 and 5) are based on all calendar months at a particular station. For example, the mean for each station in Table 2 represents the average of the first, second, and third quartiles, over all calendar months at each station.

Table 2.

Descriptive statistics of the necessary observation record length (years) for each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth and are generated using the Anderson–Darling test with no adjustment. The mean for each station represents the necessary observation record length averaged between the first, second, and third quartile, over all calendar months at that particular station.

Descriptive statistics of the necessary observation record length (years) for each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth and are generated using the Anderson–Darling test with no adjustment. The mean for each station represents the necessary observation record length averaged between the first, second, and third quartile, over all calendar months at that particular station.
Descriptive statistics of the necessary observation record length (years) for each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth and are generated using the Anderson–Darling test with no adjustment. The mean for each station represents the necessary observation record length averaged between the first, second, and third quartile, over all calendar months at that particular station.
Table 3.

Descriptive statistics of the necessary observation record length (years) for each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth, and are generated using the Anderson–Darling test with a Bonferroni adjustment. The mean for each station represents the necessary observation record length averaged between the first, second, and third quartile, over all calendar months at that particular station.

Descriptive statistics of the necessary observation record length (years) for each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth, and are generated using the Anderson–Darling test with a Bonferroni adjustment. The mean for each station represents the necessary observation record length averaged between the first, second, and third quartile, over all calendar months at that particular station.
Descriptive statistics of the necessary observation record length (years) for each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth, and are generated using the Anderson–Darling test with a Bonferroni adjustment. The mean for each station represents the necessary observation record length averaged between the first, second, and third quartile, over all calendar months at that particular station.
Table 4.

Descriptive statistics of the necessary observation record length (years) for the 5th percentile at each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth, and are generated using the Anderson––Darling test without adjustment. The mean for each station represents the necessary observation record length averaged over all calendar months at that particular station.

Descriptive statistics of the necessary observation record length (years) for the 5th percentile at each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth, and are generated using the Anderson––Darling test without adjustment. The mean for each station represents the necessary observation record length averaged over all calendar months at that particular station.
Descriptive statistics of the necessary observation record length (years) for the 5th percentile at each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth, and are generated using the Anderson––Darling test without adjustment. The mean for each station represents the necessary observation record length averaged over all calendar months at that particular station.
Table 5.

Descriptive statistics of the necessary observation record length (years) for the 95th percentile at each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth, and are generated using the Anderson–Darling test without adjustment. The mean for each station represents the necessary observation record length averaged over all calendar months at that particular station.

Descriptive statistics of the necessary observation record length (years) for the 95th percentile at each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth, and are generated using the Anderson–Darling test without adjustment. The mean for each station represents the necessary observation record length averaged over all calendar months at that particular station.
Descriptive statistics of the necessary observation record length (years) for the 95th percentile at each of the 15 stations assessed. Statistics are separated by the soil moisture measurement depth, and are generated using the Anderson–Darling test without adjustment. The mean for each station represents the necessary observation record length averaged over all calendar months at that particular station.

Figure 3 shows box plots of the distribution of the number of observation record years necessary for generating a stable distribution, by calendar month. In both panels, the box plots are grouped (left to right) by quartile and (top to bottom) by measurement depth. Therefore, each individual box shows the distribution of sufficient record length for all stations combined. The blue box represents the interquartile range, the red line is the median, and the black plus symbols are statistical outliers. Record length thresholds are determined using the Anderson–Darling test with (Fig. 3a) and without (Fig. 3b) a Bonferroni adjustment. Both panels in Fig. 3 show a consistent pattern of a longer observation record necessary to capture the first and third quartiles than the median. Indeed the average record length required for the first, second, and third quartiles was determined as 3.36, 3.11, and 3.28 years, respectively, when using the Bonferroni adjustment and 4.00, 3.36, and 3.87 years, respectively, without the Bonferroni adjustment. One would expect the first quartile, third quartile, and the interquartile range to change as observations are added, while concurrent changes in the median would be relatively small. A similar increase in the necessary record length with depth is demonstrated, as the average record length required for the shallow, middle, and deep measurement depths were 3.25, 3.39, and 3.57 years, respectively, with the adjustment and 3.74, 3.91, and 4.18 years, respectively, without the adjustment. Analyses of both modeled and observed soil moisture show that spectral frequency decreases with depth (Wu et al. 2002; Wu and Dickinson 2004). Therefore, it is not surprising that a longer observation record is necessary to generate stable 50–60-cm soil moisture percentiles than for 5–10-cm soil moisture percentiles.

Fig. 3.

Box plots representing the distribution of the number of observation record years sufficient for generating a stable distribution, by calendar month. Each individual box shows the distribution of sufficient record length for all stations put together. The blue box represents the interquartile range, the red line is the median, and the plus symbols are statistical outliers. Record length thresholds are determined using the Anderson–Darling test (a) with and (b) without a Bonferroni adjustment.

Fig. 3.

Box plots representing the distribution of the number of observation record years sufficient for generating a stable distribution, by calendar month. Each individual box shows the distribution of sufficient record length for all stations put together. The blue box represents the interquartile range, the red line is the median, and the plus symbols are statistical outliers. Record length thresholds are determined using the Anderson–Darling test (a) with and (b) without a Bonferroni adjustment.

We use maps of the average number of years necessary to generate stable soil moisture percentiles to illustrate the spatial variations (Figs. 4 and 5). Figure 4 displays this information from top to bottom for the shallow, middle, and deep measurement levels, and left to right for the first, second, and third quartiles. Results generated from the A-D test with and without adjustment are shown in Figs. 4a and 4b, respectively. The patterns in Fig. 4a show that a longer observation record is necessary for the first and third quartiles than for the second quartile and that the necessary record length increases as depth increases, both in agreement with patterns in Fig. 3. However, this pattern is not entirely consistent among all stations, even in a particular region. For example, the westernmost station in the Oklahoma Panhandle, Goodwell, exhibits a large increase in necessary record length between the middle and deepest depths (based on the first quartile). The soil textures of the middle and deepest depths at Goodwell are nearly identical. In addition, a similar pattern is not evident at the closest station, Beaver, which is approximately 100 km away and has similar soil, land cover, and climate conditions. Since it does not appear that differences in land cover, soil, or climate characteristics can account for these differences, we believe that these differences may be due to microscale differences in vegetation (e.g., vegetation density or health), topography (e.g., slope or aspect), or soil conditions. They may also be due to data quality issues at one of these stations. The same general spatial characteristics are shared between Figs. 4a and 4b; however, they are somewhat dampened in the former. The relative lack of interstation variation in Fig. 4a is a result of using a Bonferroni adjustment with the A-D test. The required record length is between 3 and 4 years at the majority of stations.

Fig. 4.

Depth of measurement variations: the average number of years of data that are necessary to generate stable soil moisture percentiles at each station. The record length thresholds are determined using the Anderson–Darling test (a) with and (b) without a Bonferroni adjustment. In (a) and (b), the results are presented for the first, second, and third quartiles from left to right and for the 5–10-, 20–30-, and 50–60-cm measurement depths from top to bottom.

Fig. 4.

Depth of measurement variations: the average number of years of data that are necessary to generate stable soil moisture percentiles at each station. The record length thresholds are determined using the Anderson–Darling test (a) with and (b) without a Bonferroni adjustment. In (a) and (b), the results are presented for the first, second, and third quartiles from left to right and for the 5–10-, 20–30-, and 50–60-cm measurement depths from top to bottom.

Fig. 5.

Seasonal variations: the average number of years of data that are necessary to generate stable soil moisture percentiles at each station. The record length thresholds are determined using the Anderson–Darling test (a) with and (b) without a Bonferroni adjustment. In (a) and (b), the results are presented for winter (Dec–Feb), spring (Mar–May), summer (Jun–Aug), and autumn (Sep–Nov) from left to right and for the 5–10-, 20–30-, and 50–60-cm measurement depths from top to bottom.

Fig. 5.

Seasonal variations: the average number of years of data that are necessary to generate stable soil moisture percentiles at each station. The record length thresholds are determined using the Anderson–Darling test (a) with and (b) without a Bonferroni adjustment. In (a) and (b), the results are presented for winter (Dec–Feb), spring (Mar–May), summer (Jun–Aug), and autumn (Sep–Nov) from left to right and for the 5–10-, 20–30-, and 50–60-cm measurement depths from top to bottom.

Along with variations by depth and quartile, seasonal variability in the necessary record length is also examined (Fig. 5). For the majority of stations, a longer observation record length is necessary to generate stable wintertime (December–February) soil moisture percentiles than in the spring (March–May) or summer (June–August) seasons. This result is not surprising as most of these stations experience a summer dry down of soils as evapotranspiration and vegetation root uptake are maximized (e.g., Hollinger and Isard 1994; Illston et al. 2004; Khong et al. 2015). In addition, CS-616 and CS-615 sensors do not measure frozen water content, and are prone to error when soils are frozen. The maps in Fig. 5a show patterns that are similar to those in Fig. 5b, but there is less interseasonal variation. Analogous to Fig. 4a, the dampening of seasonal variations in Fig. 5a is a result of adjusting the p-value threshold of the A-D test and the required record length is between 3 and 4 years at the majority of stations.

b. Extremes

In addition to testing the first, second, and third quartiles of the soil moisture distribution, we examine the extremes of the distribution (i.e., 5th and 95th percentiles). Changes in the 5th percentile as a function of record length are of particular interest in the context of drought monitoring. In situ soil moisture stations can potentially be used for drought monitoring (Schaefer et al. 2007; Illston et al. 2008; Diamond et al. 2013), and indeed the addition of in situ soil moisture to multi-index monitoring products has resulted in improved accuracy (Ford et al. 2015a). With that being said, a percentile-based drought classification presumes a certain frequency of drought events of a given intensity. For example, the U.S. Drought Monitor (http://droughtmonitor.unl.edu/) includes percentiles of the Climate Prediction Center’s soil moisture model in its drought classification, such that soil moisture conditions below (drier than) the 5th percentile are considered “extreme drought.” This means that if we classify drought using daily soil moisture observations, approximately 5% of the days will be classified as extreme drought, no matter the record length. In this case, days that are classified as extreme drought using only one or two years of soil moisture observations may be well above or below the true 5th percentile of soil moisture (i.e., where the true 5th percentile is based on the entire population) and would therefore not actually represent extreme drought conditions. In addition, this method does not account for consistently wet locations, where the 5th percentile of soil moisture may not cause significant drought impacts.

The same methodology is used to determine the necessary record length to represent the 5th and 95th percentiles. The results from the A-D test without adjustment for the 5th- and 95th-percentile estimates are shown in Tables 4 and 5, respectively. The mean values in Table 4, for example, represent the necessary observation record length for the 5th percentile, averaged over all calendar months at that particular station. The mean record years necessary for convergence of the population’s 5th and 95th percentiles is larger than for the first, second, and third quartiles at virtually every station. The overall average required record length to represent the population’s 5th percentile was 4.9, 5.5, and 5.2 years at the shallow, middle, and deep depths, respectively. The average record lengths to represent the 95th percentile were less, at 3.7, 4.4, and 5.1 years at the shallow, middle, and deep depths, respectively. Six or more years of data are necessary to represent the population’s 5th percentile for over 30% of conditions tested, while a record length of six or more years was only required in 15% of conditions tested for the 95th percentile. At the Lamont site in Oklahoma the mean required record length increased from 3.6 for the first/second/third quartiles to 6.4 years for the 5th and 95th percentiles at the shallow depth, and from 4.0 to 9.3 years at the middle depth. It should be noted that in some cases the required number of years for the 5th and 95th percentiles were less than that for the first and third quartiles; however, these conditions were exceptional.

On average, more than 5 complete years of data are necessary to represent the 5th percentile of daily soil moisture. This has significant implications for soil moisture drought monitoring, as datasets with less than 5 years of data may not accurately depict drought severity when using a percentile-based drought classification. To better illustrate this, we randomly selected n data years at each site and calculated the 5th percentile of soil moisture separately for each calendar month. We then computed the percent of daily soil moisture observations from the entire record at each site that were equal to or less than their respective 5th-percentile values based on n data years. We repeat this process 300 times using a bootstrapping procedure with resampling. The entire process is then repeated using n + 2 data years, and n is increased by 2 until all available data years are implemented.

The percent of the total record classified as extreme drought decreases substantially as the number of data years is increased (Fig. 6). At the Acme, Oklahoma, site (Fig. 6a) over 20% of January days between 1998 and 2014 exhibit extreme drought soil moisture conditions based on a 5th percentile calculated using only 2 years of observations. However, less than 10% of days are classified as extreme drought for all months at Acme when more than 8 years of data are used. A similar pattern occurs at all 15 stations, including the Borden, Ontario, site (Fig. 6b), where approximately 5% of days in the entire record are less than the 5th percentile calculated using 8 or more years. In some cases, the 5th percentile of soil moisture based on 2 years of data was larger than the first quartile of the entire record. At most sites, the 5th percentile estimated based on 4 data years was larger than 10%–12% of days in the entire record. This suggests that implementing a percentile-based drought classification procedure with a short soil moisture record may not result in an accurate depiction of drought severity. It is worth noting that drought in this paper is treated as a statistical parameter without an explicit physical meaning (i.e., without considering drought impacts). In practice, drought conditions are commonly assessed based on the impacts on, for example, vegetation or reservoir and groundwater storage. Our results show the importance of observation record length for physically based drought monitoring. From a statistical perspective, our results indicate that a record length of 6–8 years is usually sufficient to estimate 5th- and 95th-percentile values that are representative of the entire data record.

Fig. 6.

Sensitivity analysis that shows the average number of drought days (soil moisture < 5th percentile) as a function of the number of years of data used to determine the 5th-percentile threshold. Results are shown for the (a) Acme and (b) Borden sites for January, April, July, and October. Bars are shaded on the basis of the soil moisture measurement depth.

Fig. 6.

Sensitivity analysis that shows the average number of drought days (soil moisture < 5th percentile) as a function of the number of years of data used to determine the 5th-percentile threshold. Results are shown for the (a) Acme and (b) Borden sites for January, April, July, and October. Bars are shaded on the basis of the soil moisture measurement depth.

5. Discussion

The importance of soil moisture to the climate system, particularly for seasonal climate prediction and monitoring extreme climatic events, is unquestionable (Legates et al. 2011). Given the importance of soil moisture, numerous recent efforts have focused on increasing the availability and quality of soil moisture data (i.e., Robock et al. 2000; Kerr et al. 2001; Schaake et al. 2004; Dorigo et al. 2011; Entekhabi et al. 2010; Wagner et al. 2012; Quiring et al. 2016). The recent advent of datasets from models, satellite remote sensing, and in situ sensors has dramatically improved global soil moisture monitoring. However, the lack of a 30+-yr in situ soil moisture observation record at most stations around the world precludes a solid understanding of true moisture conditions and therefore impedes climate and agricultural modeling using these soil moisture datasets (Illston et al. 2004).

Given this circumstance, it is important to understand the necessary observation record length for generating a stable distribution from which in situ soil moisture can be contextualized. This study is one of the first to quantitatively assess the necessary record length and characterize how it varies in both time and space. Our results show that between 3 and 15 data years are required to generate stable soil moisture distributions; however, the majority of conditions necessitate a record length of only 3–6 years. Unsurprisingly, longer records are necessary to capture the tails of the distribution. Generally, 4–8 years of data, on average, are sufficient for determining the 5th and 95th percentiles. This range is slightly higher than the two summers’ worth of soil moisture data suggested by Findell et al. (2015) to obtain a sample whose distribution is indistinguishable from the larger population. However, Findell et al. (2015) investigated record lengths necessary for observation-based land–atmosphere interaction studies, and therefore they were only interested in warm-season climate variables. Consequently we would expect lesser observation record requirements for the summer season than the more variable winter or autumn seasons (e.g., Figs. 5b, 6b). Although the aims of this study differ from those of Findell et al. (2015), our conclusions are similar. Several (more than 2) complete years of observations are necessary to properly characterize the distribution of daily, in situ soil moisture. However, perhaps more important is the finding that under most land cover/soil texture/climate/sensor conditions, no more than 6 complete data years are required to capture the 15-yr soil moisture distribution.

Factors affecting soil moisture dynamics such as soil texture, land cover, and precipitation variability and intensity are not explicitly accounted for in this study but likely influence the statistical properties of daily soil moisture. For example, sandy soils will drain more quickly and therefore they will tend to have fewer observations at or near field capacity than loamy soils. Therefore, assessing drought severity based on soil moisture percentiles may not account for these differences in actual drought severity and ecosystem impacts. This is a limitation of any percentile-based methodology. An additional important limitation of this study is that the entire soil moisture record (between 13 and 17 years) is used as the “truth.” It is quite possible that these record lengths are not sufficient to capture the full range of soil moisture variations at these locations. It would be ideal to replicate this analysis using a 30+-yr soil moisture dataset. However, as previously mentioned, there are very few continuous, daily in situ soil moisture datasets that contain more than 20 years of data. Despite this shortcoming, we believe that this study has value because a 15-yr soil moisture dataset can be representative of a 30+-yr dataset, if hydroclimatic conditions during the shorter period have a similar mean and variance as the longer period.

We evaluated the hydroclimatic variability at the U.S. sites using three hydroclimatic indices, the 3-month standardized precipitation index (SPI), the Palmer drought severity index (PDSI), and the Palmer hydrological drought index (PHDI) (Fig. 7). The indices are taken from NOAA’s climate-division dataset, and the climate-division data are presumed to represent hydroclimate conditions at each site. The SPI, PDSI, and PHDI represent meteorological, agricultural, and hydrological drought, respectively, and typically range between −3 and 3 (SPI), between −10 and 10 (PDSI), and between −10 and 10 (PHDI). Results are presented for only 11 of the 13 U.S. stations because multiple U.S. stations share a single climate division. All stations in the United States experienced anomalously dry and wet conditions over the study period, although some more than others. For example, the Sheldon, Nevada (SCAN), station experienced three multiyear drought events, according to PDSI and PHDI, separated by much shorter periods of relatively wet conditions. Although these indices do not directly represent soil moisture, the composites in Fig. 7 suggest that all nine sites in the United States experienced a wide variety of hydroclimatological conditions between 1998 and 2015. It should be noted that all three drought indices were obtained at a 3-month resolution; however, the PDSI and PHDI typically vary on longer (6+ month) time scales than the SPI (3 months). This explains the reduced variability in the former two as compared with the latter. The roles of both climatological factors (precipitation extremes, changes in cloud cover, etc.) and hydrological/ecological factors (water table depth, soil organic-layer depth, rooting depth, etc.) in determining the number of data years necessary to represent the soil moisture climatology at a given location is worthy of further investigation and will be the focus future research.

Fig. 7.

Monthly composites of (a) 3-month SPI, (b) PDSI, and (c) PHDI during the study period 1998–2014. Data are taken from NOAA’s climate-division dataset (http://www7.ncdc.noaa.gov/CDO/CDODivisionalSelect.jsp) and are shown for the climate division in which each of the U.S. stations reside.

Fig. 7.

Monthly composites of (a) 3-month SPI, (b) PDSI, and (c) PHDI during the study period 1998–2014. Data are taken from NOAA’s climate-division dataset (http://www7.ncdc.noaa.gov/CDO/CDODivisionalSelect.jsp) and are shown for the climate division in which each of the U.S. stations reside.

6. Conclusions

Daily in situ soil moisture observations, measured at three depths in the soil column at 15 stations in the United States and Canada, are used to quantify the observation record length necessary to generate a stable soil moisture distribution. The Anderson–Darling test is implemented, both with and without a Bonferroni adjustment, to quantify the necessary record lengths for different stations, measurement depths, calendar months, and percentiles. We find the sufficient record length for generating stable distributions ranges between 3 and 15 years, with the majority of cases requiring only a 3–6-yr observation record. More years of data were necessary to properly characterize the distribution extremes (5th and 95th percentile) than the first, second, and third quartiles. Similarly, the required number of years increased with depth, with more years necessary for observations taken between 50 and 60 cm than for those taken between 20- and 30-cm and between 5- and 10-cm depths.

Overall our results suggest that 5 years of daily in situ soil moisture observations are sufficient in most conditions to create stable percentiles. These results may not apply to locations with climatic and/or edaphic conditions that differ from those used in this study.

Acknowledgments

Oklahoma Mesonet data are provided through the courtesy of the Oklahoma Mesonet, which is jointly operated by Oklahoma State University and the University of Oklahoma. Continued funding for maintenance of the network is provided by the taxpayers of Oklahoma. Data from the U.S. Department of Energy as part of the Atmospheric Radiation Measurement (ARM) Climate Research Facility (Pawhuska and Lamont, Oklahoma, sites) were used. This work used soil moisture data acquired by the FLUXNET community and in particular by Fluxnet-Canada (supported by CFCAS, NSERC, BIOCAP, Environment Canada, and NRCan). We additionally acknowledge the helpful suggestions of Drs. Mike Palecki, Jesse Bell, and Ronald Leeper and the three anonymous reviewers.

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Footnotes

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JAMC-D-16-0143.s1.

Supplemental Material