This study focused on the utility of coarse surface soil moisture observations for applications that require high resolution surface soil moisture information. This was accomplished by quantifying the information content of average soil moisture for three different spatial scales of 81 km2, 790 km2, and 4400 km2. In situ point ob- servations of soil moisture from 31 stations in Iowa were used to develop a spatial stochastic model that assumes hillslope-scale model parameters are independent. Soil moisture dry-downs and wetting regimes were analyzed using rain gauge and soil moisture sensor data. The statistical nature of dry-downs were parameterized using a power-law decay, and soil moisture increases due to rainfall were parameterized using a non-dimensional lo-gistic curve that is a function of soil moisture deficit. The resulting stochastic model is used to quantify the magnitude of the standard deviation, ( ) , and skewness G( ) as a function of the areal average. We show that the greatest information content (small spatial standard deviation) of average observation corresponded to values near the minimum or the maximum soil moisture with <( ) 5% , while average observations for in- termediate soil moisture values had the lowest information content with >( ) 20% . The differences in in- formation content as a function of the areal average were consistent with the statistical nature of soil moisture that can be interpreted as small range bounded variable. However, this study provides quantitative estimates for the magnitude of the sub-grid and basin scale variability, documenting the utility for applications that require high resolution information. These results form the basis for the investigation of spatial runoff production inresponse to rainfall and to inform plot scale agriculture applications. 1. Introduction Surface soil moisture is a key state variable linking short-term and long-term water and energy balances in the soil and the atmosphere (Yang et al., 2016) and land-atmosphere interactions (Entekhabi et al., 1996) that determine evaporation and evapotranspiration (Koster et al., 2004), and surface runoff production leading to extreme flooding (Grillakis et al., 2016). It also plays a major role in plant ecology, en- vironmental biology (Orchard and Cook, 1983), and carbon cycle through plant respiration (Boone et al., 1998). The most common technique for field-scale soil moisture measure- ment is using soil TDR (Time Domain Reflectometry) probes (Topp et al., 1980; Romano, 2014). However, due to high spatial variability of soil moisture in space (Western et al., 2004; Yang et al., 2017), using this measurement technique is neither feasible nor practical for larger spatial scales. Therefore, remote sensing techniques are being employed as a more efficient alternative to track soil moisture in space and time.NASA SMAP (Soil Moisture Active Passive) is the most recent satellite mission to focus on global soil moisture observations (Entekhabi et al., 2010) launched in 2015 that uses L-band (1.4 GHz) radiometer. Satellite soil moisture estimations have coarse spatial resolution (e.g. Enhanced SMAP L3 9 km) due to limitations in large antenna size needed for L-band microwave measurements (Njoku and Entekhabi,1996; Kerr, 2007). Therefore, understanding information content of the satellite soil moisture and its spatial variability for sub-grid and basin scales is essential for its hydrologic applications. Several studies focused on characterization of the measured soil moisture distribution and its spatial variability over time using field observations (e.g. Famiglietti et al. (1997), Ryu and Famiglietti (1997), Choi and Jacobs (2007), Brocca et al. (2012), Cho and Choi (2014)). Rosenbaum et al. (2012) used 150 sensor observations to study soil moisture spatial variability and showed that groundwater influencedlocations have higher spatial variability than other locations. Famiglietti et al. (2008) analyzed the soil moisture spatial variability at https://doi.org/10.1016/j.jhydrol.2019.06.026 Received 11 September 2018; Received in revised form 4 June 2019; Accepted 9 June 2019⁎Corresponding author. E-mailaddress: navid-jadidoleslam@uiowa.edu (N. Jadidoleslam).Journal of Hydrology 576 (2019) 85–97 0022-1694/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). T spatial scales ranging from 800 (m) to 50 (km). Their analysis de- monstrated that larger spatial extents have higher variability. Brocca et al. (2014) compared variability of absolute soil moisture, degree of saturation and soil moisture anomalies with respect to long-term mean for 6 observation networks with areas ranging from 250 to 150,000 km2 . In addition to studies based on observations only, there have been studies that used modeling approach to investigate soil moisture variability. For example, Teuling and Troch (2005) used a soil moisture balance model to estimate soil moisture variability in 3 different sites. Controls of soil hydraulic properties, specifically van Genuchten- Mualem parameters, on the relationship between soil moisture spatial variability with its mean has been investigated by different studies (e.g. García et al. (2014), Qu et al. (2015), Wang et al. (2015)). Zarlenga et al. (2018) adopted a stochastic model of unsaturated flow to in- vestigate the effects of a scaling triplet (spacing, extent and support introduced by Andrew and Günter (1999)) on the soil moisture spatial variability. Chaney et al. (2015) used the TOPLATS model (Sivapalan et al., 1987) to estimate watershed scale spatial variability of root-zone soilmoisture using fine scale ( 500 m) radar rainfall data. Application of three dimensional hydrologic model for estimation of soil moisture variability has also been investigated by Cornelissen et al. (2014) and Gebler et al. (2017). Reported results from those two modeling studiesindicate underestimation of spatial variability from modeled soil moisture compared to observations. For details on current status of soil moisture spatio-temporal variability research, the reader is referred to Section 3ofBrocca et al. (2017) and Section 8 in Babaeian et al. (2018). In previous studies, soil moisture sensor observations play a key role in understanding spatial and temporal variability of soil moisture and evaluation of soil moisture estimations from model simulations. These studies demonstrate the added value of field measurements of soil moisture. The main objective of this study is to investigate soil moisture variability within SMAP satellite sub-grid and basin spatial scales by analyzing soil moisture sensor and rain gauge observations and using higher resolution radar rainfall and soil properties to approximate spatial statistics of surface soil moisture. Section 2describes the domains of study and data characteristics that are used. Section 2.3, discusses the methodology for extraction of the soil dry-downs and wetting phases, the parameterization of eachphase, and a description of the soil moisture model. In Results and Discussion (Section 3), we compare stochastic model results with SMAP and soil moisture sensor(s) for one SMAP pixel within each basin and atthe basin scale. Thereafter, we investigate the soil moisture spatial statistics of the proposed model and compare it with field observations and SMAP satellite soil moisture. 2. Materials and methods 2.1. Studyarea Two watersheds (Fig. 1) located in Iowa are the focus of this study. Iowa is located in a warm and humid continental climate zone (e.g. Peel et al. (2007)) with an annual average precipitation of 870 mm (1981–2010). The Turkey River basin is located at northeast Iowa and has a drainage area of 4400 km2 . It is approximately 56% cropland, 14% pasture, 13% of the basin is forested, and the remaining area is grassland and developed. The South Fork basin is located in north- central Iowa with a drainage area of 790 km2 . Cropland dominates the land cover with 88% of the total area. The main soil texture, based on USDA classes, for the Turkey River and South Fork basins are silt-loam and loam, respectively.2.2. Data 2.2.1. Fieldmeasurements Fig. 1 shows available soil moisture and rain gauges in the state of Iowa, USA. At each site, 4 soil moisture sensors are installed at depths of 5, 10, 20 and 50 cm. This study will focus on the 5 cm depth of soil column at each site. The IFC (Iowa Flood Center) TDR probes are Campbell CS655 (Campbell Scientific Inc., 2012) and the USDA-ARS soil moisture sensors are Stevens Hydra probes (Stevens, 2018). Both soil moisture sensors have a reported accuracy from ±1 to ±3% vo- lumetric soil moisture. At each site, dual tipping bucket rain gauges are collocated with the soil moisture sensors. It has been shown that dual tipping bucket rain gauges for rainfall measurements increases the measurement reliability (Ciach et al., 1999). The temporal coverage of the soil moisture and rainfall data for different sites is shown in Fig. 2. For quality control of soil moisture data, we followed Dorigo et al. (2011) for detection of errors in soil moisture time series. We applied a manual quality control on the soil moisture sensor data. We removed the cold season time periods (No- vember 1–March 31), highlighted as gray in Fig. 2, to avoid possible erroneous soil moisture readings due to frozen top soil layer. Also, weused rainfall data from two tipping bucket rain gauges at each site to check the soil moisture time series. If there was rainfall more than 5 mm and soil moisture did not increase during a 24-h period, we avoided using the data. We did not remove temperature-related diurnal fluc- tuations in soil moisture because these fluctuations are within the specified accuracy of sensors. 2.2.2. Radarrainfall &satellite soil moisture For rainfall, we used MRMS (Multi Radar Multi Sensor), a rain gauge bias-corrected radar rainfall product (Zhang et al., 2016) that has approximately a 1-km resolution. We employed hourly rainfall from April to November 2016 as forcing for estimation of the soil moisture for each hillslope which is discussed in the Section 2.3.3. Enhanced Level 3 Version 1 (hereafter L3) SMAP (Chaubell et al., 2016) soil moisture product has approximately 9 km resolution with global revisit time of 2–3 days. SMAP soil moisture estimations are provided by NASA on EASE-Grid 2 (hereafter SMAP grid). There are 21 and 73 SMAP pixels that intersect with South Fork and Turkey River basins, respectively. We use SMAP soil moisture for comparisons with sensor observations and simulated hillslope soil moisture. 2.2.3. Soilproperties Two soil properties used in this study are porosity and residual soil moisture. These two values, for 0–5 cm soil layer, were obtained from the POLARIS soil properties database, which is a probabilistic soil series map for the contiguous United States and has a 30 (m) spatial resolution (Chaney et al., 2016). 2.3. Methods Field-scale soil moisture dynamics could be classified into two phases. Soil moisture dry-down that is due to drainage and evapora- tion/evapotranspiration while soil wetting is due to rainfall and/or ir- rigation, noting that most of the agricultural fields in Iowa are rain-fed. We analyzed the soil moisture dry-downs and wetting phases of soil moisture time series. Then, we parameterized these two phases and used the distributions of parameters for estimation of the hillslope surface soil moisture forced with MRMS rainfall. 2.3.1. Dry-downperiods The dry-down time periods of surface soil moisture were identified using local minimum and maximums of the soil moisture time series. A threshold peak prominence value of 0.02 ( m /m3 3 ) was used and the dry- down curves that last at least 12 h were selected. Also, dry-downs with more than 2 mm accumulated rainfall were excluded from the analysis.N.Jadidoleslam,et al. Journal of Hydrology 576 (2019) 85–97 86 Consequently, 2352 dry-down events are employed in the study. Rondinelli et al. (2015) and Shellito et al. (2016) used an ex- ponential equation with different mathematical forms for fitting the soil moisture dry-down curves using 3 parameters. For this study, we se- lected a power-law model with two parameters for fitting the dry-down curves, to improve flexibility and to decrease the number of parameters required, = + + SM SM SM t SM ( )[( 1)( ( ) 1)] t r r1 1 (1) where SM is soil moisture at the initiation of dry-down, SM t is soil moisture at any time t elapsed from the dry-down initiation and SM r is residual soil moisture, which is assumed as minimum soil moisture of the time series. Eq.(1)is fitted to extracted dry-down curves from soil moisture observations with a non-linear least square method to find and for each dry-down curve. Fig. 4 shows the normalized dry-down curvesbased on initial soil moisture of the dry-downs for IFC soil moisturesensors with elapsed time ( t ) in days. Each of the fitted curves have different dry-down parameters ( , ). Fitted and observed dry-down curves have a good agreement with an RMSE (root mean square error)and coefficient of determination of 0.006 cm /cm3 3 and 0.95, respec- tively. 2.3.2. Wettingphase The total rainfall and magnitude of soil moisture increase during rainfall events are found for each wetting time periods from soil moisture time series. An example of these periods are highlighted asblue in Fig. 3. Using a similar approach described in Section 2.3.1 with an inter-event dry period of 2 h, we found positive soil moisture changeand total rainfall depth. We detected 4334 wetting periods across the sensor histories. Hardie et al. (2013) investigated soil moisture change with respect to rainfall for 0–90 (cm) depths. They were able to find “weak but Fig.1. Locations of the stations used in this study for IFC (Iowa Flood Center) and ARS (Agricultural Research Service) stations shown in blue and green, respectively. (For interpretation of the