Reconstructing Precipitation Events Using Collocated Soil Moisture Information

Nathaniel Parker aDepartment of Agronomy, Kansas State University, Manhattan, Kansas

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https://orcid.org/0000-0002-4821-1179
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Andres Patrignani aDepartment of Agronomy, Kansas State University, Manhattan, Kansas

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Abstract

Complete and accurate precipitation records are important for developing reliable flood warning systems, streamflow forecasts, rainfall–runoff estimates, and numerical land surface predictions. Existing methods for flagging missing precipitation events and filling gaps in the precipitation record typically rely on precipitation from neighboring stations. In this study, we investigated an alternative method for back-calculating precipitation events using changes in root-zone soil water storage. Our hypothesis was that using a different variable (i.e., soil moisture) from the same monitoring station will be more accurate in estimating hourly precipitation than using the same variable (i.e., precipitation) from the nearest neighboring station. Precipitation events were estimated from soil moisture as the sum of hourly changes in profile soil water storage. Hourly precipitation and soil moisture observations were obtained from a mesoscale network in the central U.S. Great Plains from May 2017 to December 2020. The proposed method based on soil moisture had a minimum detectable limit of 7.6 mm (95th percentile of undetected precipitation events) due to canopy and soil interception. The method was outperformed by the nearest neighbor (NN) interpolation method when neighboring stations were at distances of <10 km. However, the proposed method outperformed the NN method in 22 out of 27 stations when nearest stations were at distances > 10 km. Using changes in soil water storage was an effective approach for flagging and estimating actual missing precipitation events caused by pluviometer malfunction, highlighting new opportunities for using readily available in situ soil moisture information for operational quality control of precipitation observations in mesoscale environmental monitoring networks.

Significance Statement

This study investigated a new method for reconstructing precipitation events using changes in root-zone soil water storage. The method consists of a new option for improving the quality control of precipitation observations collected at in situ environmental monitoring networks. Using the sum of hourly changes in soil water storage proved effective as a qualitative method for flagging missing precipitation events caused by pluviometer failure and as a quantitative method for reconstructing precipitation events. This study presents a promising application of in situ soil moisture information as an alternative method for quality control of precipitation and as a method for filling gaps in the historical precipitation record of catchment-scale hydrological networks and mesoscale environmental monitoring networks.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Andres Patrignani, andrespatrignani@ksu.edu

Abstract

Complete and accurate precipitation records are important for developing reliable flood warning systems, streamflow forecasts, rainfall–runoff estimates, and numerical land surface predictions. Existing methods for flagging missing precipitation events and filling gaps in the precipitation record typically rely on precipitation from neighboring stations. In this study, we investigated an alternative method for back-calculating precipitation events using changes in root-zone soil water storage. Our hypothesis was that using a different variable (i.e., soil moisture) from the same monitoring station will be more accurate in estimating hourly precipitation than using the same variable (i.e., precipitation) from the nearest neighboring station. Precipitation events were estimated from soil moisture as the sum of hourly changes in profile soil water storage. Hourly precipitation and soil moisture observations were obtained from a mesoscale network in the central U.S. Great Plains from May 2017 to December 2020. The proposed method based on soil moisture had a minimum detectable limit of 7.6 mm (95th percentile of undetected precipitation events) due to canopy and soil interception. The method was outperformed by the nearest neighbor (NN) interpolation method when neighboring stations were at distances of <10 km. However, the proposed method outperformed the NN method in 22 out of 27 stations when nearest stations were at distances > 10 km. Using changes in soil water storage was an effective approach for flagging and estimating actual missing precipitation events caused by pluviometer malfunction, highlighting new opportunities for using readily available in situ soil moisture information for operational quality control of precipitation observations in mesoscale environmental monitoring networks.

Significance Statement

This study investigated a new method for reconstructing precipitation events using changes in root-zone soil water storage. The method consists of a new option for improving the quality control of precipitation observations collected at in situ environmental monitoring networks. Using the sum of hourly changes in soil water storage proved effective as a qualitative method for flagging missing precipitation events caused by pluviometer failure and as a quantitative method for reconstructing precipitation events. This study presents a promising application of in situ soil moisture information as an alternative method for quality control of precipitation and as a method for filling gaps in the historical precipitation record of catchment-scale hydrological networks and mesoscale environmental monitoring networks.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Andres Patrignani, andrespatrignani@ksu.edu

1. Introduction

Precipitation is an atmospheric essential climate variable, and its accurate quantification is crucial for agricultural, hydrological, and ecological research (Bojinski et al. 2014). In the United States, precipitation has been measured using manually operated pluviometers since 1890 by the U.S. National Weather Service (NWS) Cooperative Observer Program (COOP) (Fiebrich 2009) and since 1997 by the Community Collaborative Rain, Hail and Snow (CoCoRaHS) citizen science network (Reges et al. 2016). With the advent of electronic dataloggers and the increasing need to record precipitation totals and precipitation intensity at higher temporal resolution (e.g., minute, hourly), automated pluviometers based on tipping-bucket, weighing-bucket, and siphon mechanisms have become standard instrumentation in automated weather networks (McPherson et al. 2007; Patrignani et al. 2020a; Shulski et al. 2018; Sun et al. 2018). However, human errors (in the case of manual pluviometers), and occasional instrument malfunctioning or failure due to normal wear and obstruction of the rain collector in both manual and automated pluviometers can go unnoticed, thus introducing gaps in the historical precipitation record (Shafer et al. 2000; Michaelides et al. 2009). These gaps in the historical precipitation record can ultimately propagate and affect the prediction accuracy of the soil water balance in land surface models, streamflow predictions, and runoff estimates from rainfall–runoff models (Chen et al. 2018; Tan and Yang 2020).

Detecting missing precipitation events due to malfunctioning pluviometers often requires a combination of manual and automated quality control procedures. Manual checks typically include auxiliary information collected during site visits (e.g., evidence of clogged pluviometer or faulty bearings in tipping-bucket mechanism) and corroboration with rainfall observations in nearby stations and multisensor gridded precipitation products by trained operators (Shafer et al. 2000; Patrignani et al. 2020a). Automated checks for gross errors in precipitation observations typically include (i) range tests, which are aimed at flagging observations that fall outside a pre-established range based on physically plausible values and climate extremes, and (ii) step tests, which are aimed at identifying differences between successive observations to identify suspicious changes above an allowable threshold value (Fiebrich and Crawford 2001; Shafer et al. 2000). In the absence of collocated rain gauges, missing precipitation events are typically filled by spatial interpolation of precipitation information from nearby stations (i.e., gap filling using the same variable from different locations). Common spatial interpolation methods for filling missing precipitation records include nearest neighbor (Bárdossy and Pegram 2014), Thiessen polygons (Mair and Fares 2011), and inverse distance weight (di Piazza et al. 2011). These interpolation methods are simple to implement and are available in most software packages (Kashani and Dinpashoh 2012), but do not account for the spatial autocorrelation of precipitation among neighboring stations (Mair and Fares 2011). More sophisticated spatial interpolation methods based on geostatistical principles such as ordinary kriging (Bárdossy and Pegram 2014), kriging with external drift (Verworn and Haberlandt 2011), and geographically weighted regression (di Piazza et al. 2011) can solve this problem by accounting for the spatial structure of precipitation events. But, the inherently high spatial variability and the different timing of precipitation events among neighboring stations implies that even sophisticated spatial interpolation methods can result in inaccurate estimation of missing precipitation events, particularly at subdaily scales (i.e., minute and hourly observations) (Ciach and Krajewski 2006; Teegavarapu and Pathak 2008; Cristiano et al. 2017). As an alternative, neural networks trained using time series of precipitation events for the same station have shown promising results for replacing missing precipitation events, surpassing the accuracy of geostatistical interpolation methods (Teegavarapu and Chandramouli 2005; Kashani and Dinpashoh 2012). However, artificial neural networks typically rely on continuous precipitation time series without missing records, which is the very problem they are trying to solve.

Other alternatives for filling missing precipitation events include the use of ground radars, multisensor gridded products, and remote sensors on board orbiting satellites. For instance, the hourly and daily Next-Generation Weather Radar (NEXRAD) gridded precipitation products provide quality-controlled, multisensor (radar and in situ rain gauge) precipitation data available at 4-km spatial resolution for the contiguous United States (Heiss et al. 1990; Young et al. 2000; Krajewski and Smith 2002). Multisensor gridded products provide areal average precipitation that is useful for hydrological and agricultural applications, however, gridded products may not always represent in situ precipitation amounts at the point level (Fig. 1 in the online supplemental material), and gridded products often result in large datasets that are not practical for real-time precipitation quality control on board of station dataloggers.

An alternative approach for flagging and filling missing precipitation events that can be implemented in dataloggers and postprocessing routines that has the potential to resolve uncertainties related to horizontal spatial interpolation methods and the timing of precipitation events in neighboring stations is the use of in situ soil moisture observations collected at the same station (i.e., gap filling using a different variable from the same location). The strong link between precipitation and soil moisture has been widely used to estimate surface and root-zone soil moisture from precipitation observations (Pan et al. 2003; Dorigo et al. 2013; Coopersmith et al. 2015), but recent studies have suggested the possibility of doing just the opposite, to reconstruct precipitation events from changes in soil water storage (Crow et al. 2009; Brocca et al. 2013, 2015; Pellarin et al. 2020; Parker and Patrignani 2020; Filippucci et al. 2020). The concept relies on using the soil as a natural rain gauge by relating temporal changes in the soil water storage to precipitation. While this method relies on stations equipped with collocated pluviometers and soil moisture sensors, there is growing number of statewide and nationwide mesoscale networks that monitor root-zone soil moisture. For instance, the North American Soil Moisture Database is a new high-quality observational soil moisture database that consists of ∼1800 stations across North America (Quiring et al. 2016), and similar initiatives have been developed for other parts of the world (Dorigo et al. 2011). This new wave of mesoscale networks that include soil moisture as a standard measurement opens new opportunities for leveraging readily available in situ soil moisture observations for quality control (QC) and quality assurance (QA) of other essential variables like precipitation. This is particularly relevant considering that the typical distance between neighboring stations in statewide mesoscale networks is >25 km and between 70 and 200 km in nationwide networks (Ochsner et al. 2013; Brotzge et al. 2020; Patrignani et al. 2020b). Thus, the objectives of this study were to test the accuracy of using changes in root-zone soil water storage as (i) a qualitative quality assurance method for detecting the occurrence of false-negative precipitation events due to malfunctioning pluviometers and (ii) as a quantitative method for filling gaps in the precipitation record. The scope of this study is aimed at conceptualizing and testing the proposed method using the soil as a natural rain gauge in its simplest form, solely using sensor observations and without accounting for additional soil hydraulic properties or sophisticated modeling procedures so that researchers and network managers alike can easily implement the method as part of routine operations. In other words, we evaluate whether changes in soil moisture storage at the same in situ station can be used to flag and reconstruct missing precipitation events using a mesoscale in situ network in the U.S. Great Plains as a case study scenario.

2. Materials and methods

a. Concept and assumptions

The link between the change in soil water storage and precipitation is explicit in the equation describing the soil water balance, which for a rainfed system neglecting capillary rise can be represented as
ΔS=PETRODI,
where ΔS is the change in soil water storage (mm), P is precipitation (mm), E is evaporation from the soil surface (mm), T is plant transpiration (mm), RO is surface runoff (mm), D is deep drainage (mm), and I is canopy and litter interception (mm). For the change in soil water storage to equate precipitation, ΔSP, several conditions need to be met, at least during the period of the rainfall event. For this reason, in this study we used a soil water balance at an hourly time scale. During the occurrence of a precipitation event, the air near the land surface typically approaches the saturation vapor pressure (i.e., relative humidity ∼100%), dramatically reducing the vapor pressure deficit and the atmospheric water demand (Campbell and Norman 1998). Under these conditions, evaporative and transpirational losses were assumed negligible during the precipitation event (i.e., E and T ≈ 0). Considering the typically low rainfall intensity in the U.S. Central Plains (i.e., <5 mm h−1 average peak rainfall intensity in the region) (Lee et al. 2017) and that stations of the Kansas Mesonet (see section 2b) are mostly located on landscapes with less than 1% slopes covered with natural vegetation, the runoff was also assumed to be negligible (i.e., RO ≈ 0). If we further assume that most precipitation events in this region have a duration of only a few hours (typically <3 h; Lee et al. 2017), then it results unlikely that precipitation that infiltrates the soil profile will move beyond the depth of the deepest soil moisture sensor at the stations of the Kansas Mesonet (i.e., 50-cm depth, see section 2b). Therefore, the drainage rate during the duration of precipitation events was also assumed negligible (i.e., D ≈ 0). This assumption implies that we ignored any preferential flow through macropores and soil cracks. A brief discussion is presented in section 3a(3) to discuss the magnitude of the drainage term by adding a simple hydraulic conductivity model. The soil moisture sensors of the Kansas Mesonet are installed under natural vegetation, so unlike the previous components of the soil water balance, the interception component cannot be assumed negligible (i.e., I ≠ 0). Small precipitation events that are often intercepted by vegetation canopy and litter evaporate without reaching the soil surface. Even then, the precipitation water that reaches the soil surface still needs to enter the sensing volume of the topmost (i.e., 5-cm depth) soil moisture sensor to be detected. Thus, we know a priori that the proposed approach has a detectable limit below which it cannot be used to predict the occurrence of precipitation events. Accounting for the interception component, Eq. (1) simplifies to
P=ΔS+I.

In this study, the interception component in Eq. (2) was determined from a histogram of precipitation events that did not result in a measurable change in soil water storage (i.e., undetected precipitation events). We selected the 95th percentile of the precipitation amount of undetected events by the array of soil moisture sensors as an arbitrary, but a reasonable, approximation of canopy and litter interception. As mentioned earlier, the interception term in our study also accounts for a small fraction of soil water storage present near the soil surface that is beyond the sensing volume of the topmost sensor at 5-cm depth. In this context, the magnitude of the interception term represents the minimum detectable precipitation event using the proposed method. Undoubtedly, we made some important simplifying assumptions that would not hold under most field circumstances, but we hypothesize that these assumptions hold during typical precipitation events in the central United States with the aim of generating a first-order approximation of precipitation based on changes in root-zone (i.e., top 50 cm) soil water storage.

b. Precipitation and soil moisture dataset

Hourly observations of precipitation and soil moisture were obtained from the Kansas Mesonet from the deployment of soil moisture sensors in 2017 to 31 December 2020. The Kansas Mesonet is an environmental monitoring network established in 1986 by the Kansas State Research and Extension that consists of 62 in situ stations distributed across the state of Kansas (Patrignani et al. 2020a). The stations are located in long-term sites characterized by landscapes with <1% slope and permanent natural vegetation dominated by warm-season grasses. Stations of the Kansas Mesonet are located across a precipitation gradient that ranges from 300 mm yr−1 in the western portion of the state to 1300 mm in the eastern portion of the state. Liquid precipitation is measured at all stations using a tipping-bucket rain gauge (Model TE525, Texas Electronics Inc. Dallas, Texas) with a resolution of 0.25 mm. We used hourly precipitation and soil moisture information from 30 stations of the Kansas Mesonet equipped with soil moisture records longer than one year and an additional 17 stations without soil moisture sensors were included to obtain precipitation for the nearest neighbor interpolation (Fig. 1). The use of hourly data was essential to meet the assumptions of the soil water balance components stated earlier. For this study, the minimum interevent time (MIT) that defines individual precipitation events was assumed to be 1 h (Dunkerley 2015; Medina-Cobo et al. 2016).

Fig. 1.
Fig. 1.

Distribution of the 47 stations of the Kansas Mesonet considered in this study. Filled triangles represent stations with precipitation and soil moisture records (N = 30) and open circles represent stations with precipitation and without soil moisture records (N = 17) that were considered for the nearest neighbor approach.

Citation: Journal of Hydrometeorology 22, 12; 10.1175/JHM-D-21-0168.1

In stations of the Kansas Mesonet, volumetric water content is monitored at 5-, 10-, 20-, and 50-cm depths using soil water reflectometers (Model CS655, Campbell Scientific Inc., Logan, UT) since 2017. The soil moisture sensors were calibrated using soil samples collected from all the stations monitoring soil moisture between June and November 2019. The calibration equation was obtained by relating the volumetric water content (θ) of the soil samples determined with the thermo-gravimetric method as a function of the apparent dielectric permittivity (Ka, unitless) and bulk electrical conductivity (ECb, in dS m−1) (Evett et al. 2005) reported by the soil moisture sensor at the time of soil sampling. The calibration equation used in this study is
θ=0.025+0.091Ka0.176ECb.

The RMSE of the calibration equation in our soils was 0.05 cm3 cm−3, which is 44% less than the RMSE of the sensor manufacturer’s equation based on the third-order polynomial proposed by Topp et al. (1980) (RMSE = 0.09 cm3 cm−3).

c. Computation of changes in soil water storage

After computing the volumetric water content of each soil moisture sensor, the total soil water storage (S) in the soil profile was approximated using the trapezoidal rule of integration, which is a common approach in the literature for integrating vertical measurements of soil moisture to compute profile soil water storage (e.g., Nachabe et al. 2004; Gao et al. 2019):
St=θ1,tZ1,t+i=2nθi1,t+θi,t2(Zi,tZi1,t),
where t is time in hours, Zi (mm) is the depth of the ith sensor, θi is the volumetric water content of the ith sensor, and n is the total number of sensors in the soil profile. For the 0–5-cm soil layer, we assumed that the sensor placed at 5-cm depth represents the soil moisture of the surface layer (i.e., 0–5 cm). Then, the predicted precipitation from soil moisture was computed based on the sum of hourly changes in the soil water storage for each observed precipitation event. The approach for reconstructing precipitation events from changes in soil water storage is illustrated in Fig. 2a using a 5-h precipitation event from 2300 central standard time (CST) 14 May to 0300 CST 15 May 2018 recorded at the Parsons station. Figure 2a illustrates the use of the soil profile as a natural rain gauge, in which the soil water storage at each sensor depth changes as the rainfall event progresses. Then, the sum of hourly changes in root-zone soil water storage can be used to reconstruct detailed cumulative precipitation dynamics (Fig. 2b). In this particular example, the observed total precipitation was 46.5 mm and the estimated total precipitation based on changes in soil water storage was 48.7 mm (Fig. 2b). In previous stages of this manuscript, we also considered reconstructing precipitation events using the difference in soil water storage between an hour before and an hour after the precipitation event. However, precipitation estimates were the same as using the sum of hourly changes in soil water storage. As a result, we favored the simplest approach based on the sum of hourly changes in soil water storage, which does not require knowledge of the start and end of a precipitation event, and thus can be easily implemented as a near-real-time precipitation quality control procedure on board of common dataloggers (a sample code in CRBasic is available in the supplemental material).
Fig. 2.
Fig. 2.

Example illustrating changes in profile soil moisture during (a) 5-h precipitation event at the Parsons station of the Kansas Mesonet from 2300 CST 14 May to 0300 CST 15 May 2018, and (b) the corresponding cumulative precipitation measured by the station pluviometer (Pobs) and the cumulative precipitation reconstructed using changes in soil water storage (ΔS). Times (t) are expressed in hours relative to the start of the precipitation event. Soil water content at time t = −1 h represents the water content of the soil profile at an hour before the start of the precipitation event and t = 6 h represents the soil water content at an hour after the end of the precipitation event.

Citation: Journal of Hydrometeorology 22, 12; 10.1175/JHM-D-21-0168.1

For each precipitation event, we also obtained additional metrics such as antecedent soil water storage (mm), antecedent soil water deficit (mm), and antecedent relative saturation. The antecedent soil water storage was estimated as the soil water storage an hour before a precipitation event. The antecedent soil water deficit was computed as the difference between the saturation point and the antecedent soil water storage. The saturation point was approximated as the maximum value of the soil water storage time series for each station. The antecedent relative saturation was computed as the ratio of the antecedent soil water storage to the saturation point. Before evaluating the accuracy of the proposed soil moisture–based precipitation approach, we removed precipitation events smaller than the minimum detectable threshold of 7.6 mm (see section 2a). We also removed precipitation events during the winter season with soil temperature values ≤ 1°C because of the change in the apparent dielectric permittivity of partially frozen soils that affects the estimation of volumetric water content (Fig. 2 in the supplemental material) (Zhang et al. 2003; Seyfried and Grant 2007).

The accuracy of the proposed approach for reconstructing precipitation events from changes in root-zone soil water storage was evaluated both qualitatively and quantitatively. The qualitative evaluation involved the determination of true positive precipitation events correctly detected with changes in soil moisture storage and false-negative precipitation events that were not detected with the proposed approach. For this analysis, the occurrence of a precipitation event based on soil moisture was only considered when the changes in soil water storage were greater than 1 mm to avoid including small soil moisture fluctuations due to sensor noise and thermal gradients. The quantitative evaluation of the proposed approach was done using root-mean-square error (RMSE), mean absolute error (MAE), and mean bias error (MBE). We selected RMSE because it is a commonly used error metric and allowed us to compare our findings with other studies in the literature. The MAE was also included in our analysis as a robust error metric that is less sensitive to outliers compared to RMSE (Willmott and Matsuura 2005). The MBE measures the tendency of a model to underestimate or overestimate observations and expresses the mean difference between predicted and observed variables (Harrison and Bales 2014). A negative MBE value represents underestimation, and a positive MBE represents overestimation. All data analysis was performed using MATLAB R2020b (Mathworks, Inc., Natick, Massachusetts).

d. Comparison with nearest neighbor interpolation approach

To assess the accuracy of the proposed method relative to common methods for filling missing precipitation events, we compared the quantitative accuracy of our soil moisture–based approach to the nearest neighbor interpolation approach. We evaluated the nearest neighbor approach using precipitation events greater than the minimum detectable threshold of the soil moisture approach obtained from all 47 stations considered in this study. The nearest neighbor interpolation method works by replacing missing precipitation events at a target station with precipitation records from the nearest station in terms of geographical distance. Similar to the soil moisture approach, the accuracy of the nearest neighbor approach was evaluated using RMSE, MAE, and MBE.

3. Results and discussion

a. Testing of model assumptions

1) Evaporation and transpiration assumptions

One of the assumptions of the proposed method for reconstructing precipitation events based on changes in soil water storage is that soil evaporation and plant transpiration are negligible during precipitation events. Since stations of the Kansas Mesonet also record air temperature and relative humidity at hourly intervals, we used these variables to compute the atmospheric vapor pressure deficit during the precipitation events. The median relative humidity (RH) recorded during all precipitation events was 95% (Fig. 3a) and the median resulting vapor pressure deficit was 0.1 kPa (Fig. 3b). Vapor pressure deficit is a primary driver of soil evaporation (Or et al. 2013) and plant transpiration (Sinclair et al. 2017), thus, the nearly zero vapor pressure deficit recorded during precipitation events provides some evidence for the assumption of negligible evaporation and transpiration. It is worth mentioning that while this assumption seems valid for hourly precipitation events, the assumption of negligible evaporation and transpiration will likely not hold at daily time steps, which could lead to precipitation underestimation when using the proposed soil moisture–based approach to reconstruct rainfall due to pre- and poststorm evapotranspiration resulting from hours of the day without precipitation. For instance, on 19 June 2020 at the Hays station of the Kansas Mesonet, the vapor pressure deficit increased from 0.1 to 1.0 kPa following a 4-h precipitation event (Fig. 3c). This assumption seems to work well in the U.S. Great Plains, but this assumption will need to be tested before implementation in other parts of the world.

Fig. 3.
Fig. 3.

Distribution of (a) relative humidity and (b) vapor pressure deficit for 2497 hourly precipitation events across 30 stations of the Kansas Mesonet from 15 May 2017 to 31 Dec 2020. (c) Example of the lower vapor pressure deficit (VPD) during a precipitation event recorded at the Hays station of the Kansas Mesonet on 19 Jun 2020. Times are reported in central standard time (CST).

Citation: Journal of Hydrometeorology 22, 12; 10.1175/JHM-D-21-0168.1

2) Interception assumption

The interception threshold determined based on the 95th percentile of 9031 precipitation events in all the stations monitoring soil moisture that did not result in a measurable increase in soil water storage was 7.6 mm. This value is higher than the canopy interception threshold of 4 mm determined for prairie grass in the region (Zou et al. 2015), which is not surprising since the interception threshold derived in this study comprises canopy interception and a small amount of infiltrated water that likely did not reach the sensing volume of the topmost soil moisture sensor. During these small precipitation events, all soil moisture sensors typically exhibited negative changes in volumetric soil water content. Our findings imply that a precipitation event totaling >7.6 mm is required for the proposed approach based on changes in soil water storage to work in this region. As a result, the remaining analyses in this study were performed using a total of 2497 precipitation events > 7.6 mm.

3) Drainage assumption

To test the assumption of negligible drainage we approximated the magnitude of the drainage term for a typical rainfall event using the Campbell (1974) soil hydraulic conductivity model using a unit gradient assumption (i.e., gravity-driven flow). In this case, the hourly drainage rate at 50-cm depth was assumed equal to the hydraulic conductivity for that hour. Due to the lack of site-specific soil hydraulic properties for the Kansas Mesonet, we used soil hydraulic properties for the Campbell model for U.S. soils (Rawls et al. 1982, 1992) corresponding to the predominant soil textural class at the 50-cm sensor depth across the Kansas Mesonet (i.e., silty clay loam, Ksat = 1.5 mm h−1, b = 6.6). Overall, the median duration of the 2497 precipitation events analyzed in this study was 4 h, which resulted in an estimated median drainage of 0.28 mm considering all rainfall events, suggesting that assuming negligible drainage beyond the 50-cm sensor depth during typical precipitation events results in small errors that could be considered negligible for the purposes of this study. To quantify the impact of longer precipitation events on the proposed approach, a more detailed discussion is provided in section 3d(1).

b. Distribution of precipitation events

Our study spanned an approximate area of 231 000 km2 across a gradient of 300–1300 mm in annual rainfall. Based on the minimum detectable precipitation threshold, our dataset resulted in 2497 precipitation events with a median precipitation amount of 16 mm and a median precipitation duration of 4 h (Fig. 4a). The maximum precipitation amount was 187 mm, which was recorded at the Ottawa 2SE station from 2200 CST 31 July to 0700 CST 1 August 2019. Similarly, the maximum sum of changes in soil water storage was 100 mm, a value also recorded at the Ottawa 2SE station at the time of the maximum precipitation event. The median precipitation intensity of the dataset was 3.9 mm h−1 and the maximum recorded precipitation intensity was 45.7 mm h−1 (Fig. 4b), which was recorded at the Miami station on 29 January 2020 from 0900 to 1200 CST. Based on the precipitation intensity classification system of the World Meteorological Organization (2017), 25% of the precipitation events were classified as light events (<2.5 mm h−1), 65% as moderate (from ≥2.5 to <10 mm h−1), and 10% as heavy precipitation events (≥10 mm h−1). Our findings show that precipitation events in this region of the U.S Great Plains are largely dominated by light- and moderate-intensity precipitation events, which accounted for 90% of the total precipitation events during the study period.

Fig. 4.
Fig. 4.

(a) Histogram of precipitation amount, and (b) histogram of precipitation intensity for the 2497 precipitation events in the resulting dataset across 30 stations of the Kansas Mesonet from 15 May 2017 to 31 Dec 2020. Rainfall intensity was classified as light (rainfall intensity < 2.5 mm h−1), moderate (from rainfall intensity ≥ 2.5 to <10 mm h−1), and heavy (rainfall intensity > 10 mm h−1) according to the classification by the World Meteorological Organization. The x axes of the figures were truncated for visual clarity.

Citation: Journal of Hydrometeorology 22, 12; 10.1175/JHM-D-21-0168.1

c. Qualitative analysis

Overall, using changes in root-zone soil water storage correctly flagged 2044 out of the 2497 precipitation events > 7.6 mm, while the remaining 453 precipitation events were not detected by the soil (Table 1). This represents 82% accuracy in detecting precipitation events greater than the interception threshold. The remaining 453 (18%) undetected precipitation events typically occurred when the antecedent soil moisture was at or near saturation conditions, with an average antecedent relative saturation of the 453 undetected events of 0.82. The failure of soils at or near saturation conditions in responding to precipitation events was also documented in previous studies that estimated precipitation using in situ soil moisture (Brocca et al. 2013, 2015) and satellite-based soil moisture products (Crow et al. 2011; Brocca et al. 2014, 2019; Pellarin et al. 2020).

Table 1.

Qualitative evaluation of precipitation detection by soil moisture using 2497 hourly observations that exceeded 7.6 mm from 30 stations of the Kansas Mesonet.

Table 1.

Interestingly, the proposed approach based on changes in soil water storage was able to identify actual missing precipitation events in the Kansas Mesonet precipitation record that remained unknown until this study. For example, a missing precipitation event that went unnoticed at the Gypsum station from 0000 to 0300 CST 22 April 2019 was correctly identified using the proposed approach based on changes in soil water storage (Fig. 5a). The sum of hourly changes in soil water storage for the same period totaled 24.3 mm whereas the rain gauge recorded no precipitation occurrence. Verification with a multisensor gridded precipitation product with 4-km spatial resolution generated by the U.S. National Weather Service (NWS, https://water.weather.gov/precip) for the same day revealed a precipitation event of 19.1 mm, suggesting that a missing precipitation event occurred at the Gypsum station. Further inspection of the visit sheets filled by the field technician of the Kansas Mesonet revealed that the rain gauge at the Gypsum station was clogged during a posterior station visit (Fig. 3 in the supplemental material). Similarly, a malfunctioning rain gauge failed to capture multiple precipitation events during July 2017 at the Lake City station. During the same period, the estimated precipitation based on changes in the soil water storage totaled 50.2 mm (Fig. 5b). Verification with the gridded precipitation product generated by the NWS for the corresponding days revealed multiple precipitation events totaling 50.8 mm. Again, crosschecking with a visit sheet filled by the field technician revealed that the rain gauge at the Lake City station was clogged on a posterior station visit (Fig. 4 in the supplemental material). The ability to flag missing precipitation events using the proposed approach coupled with the high (82%) accuracy of the proposed approach in flagging precipitation events shows a promising application of collocated soil moisture observations for precipitation quality control in mesoscale networks. The proposed approach could complement existing methods for precipitation QA and QC such as the use of precipitation records from neighboring stations (Einfalt and Michaelides 2008) and multisensor gridded precipitation products (Shafer et al. 2000; Patrignani et al. 2020a).

Fig. 5.
Fig. 5.

Examples of precipitation events that were effectively captured by the proposed approach based on changes in soil water storage, but that were missed due to a malfunctioning pluviometer at (a) the Gypsum station in April 2019 and (b) the Lake City station in July 2017. Both figures comprise hourly results that have been aggregated into daily intervals for visual clarity. We also retrieved the precipitation total for the same dates obtained from the U.S. National Weather Service (NWS) 4-km multisensor gridded product that in both cases provided an independent precipitation observation. Here, Pobs is the observed precipitation at the station, and ΔS is the observed change in soil profile water storage at the station. Rain gauges in both stations were fixed during a time without rainfall.

Citation: Journal of Hydrometeorology 22, 12; 10.1175/JHM-D-21-0168.1

d. Quantitative analysis

1) Accuracy of precipitation estimation using in situ soil moisture

The quantitative accuracy of the proposed approach for estimating precipitation based on the sum of hourly changes in soil water storage resulted in r = 0.57, RMSE = 14.1 mm, and MAE = 8.0 mm, with a slight tendency to underestimate the total observed precipitation with an MBE = −3.0 mm (Fig. 6a). The RMSE of the proposed in situ soil moisture–based approach is similar to the range in RMSE of 11.8–16.4 mm reported in a previous study for 5-day accumulated global precipitation derived by coupling satellite-based global soil moisture products with the SM2RAIN algorithm (Brocca et al. 2014). Considering all stations and precipitation events > 7.6 mm (i.e., interception threshold), the proposed approach based on soil moisture performed similar to the nearest neighbor interpolation technique, which resulted in r = 0.55, RMSE = 16.6 mm, and MAE = 10.6 mm (Fig. 6c). In addition, the nearest neighbor interpolation approach showed a higher precipitation underestimation than the soil moisture–based approach with MBE = −5.8 mm (Fig. 6c). The comparatively higher precipitation underestimation by the nearest neighbor interpolation than the soil moisture–based approach could be attributed to the inherently high spatial and temporal variability of precipitation events as a consequence of the distance between stations (Ciach and Krajewski 2006; Sadler et al. 2017; Patrignani et al. 2020b), especially at subdaily intervals. When we only considered precipitation events totaling less than the antecedent soil water deficit before the precipitation event, the accuracy of our approach improved by about 30%, with an RMSE of 7.7 mm and MAE of 5.5 mm (Fig. 6b). This improvement was not surprising since the soil profile had sufficient pore space to store infiltrating water, indicating that the proposed approach works best for precipitation events totaling less than the antecedent soil water deficit. Thus, the proposed approach has a minimum and a maximum precipitation detection threshold that can be obtained from the time series of soil moisture and precipitation itself.

Fig. 6.
Fig. 6.

Comparison of rain gauge observations to predicted precipitation using (a) change in soil water storage for all precipitation events (N = 2497), (b) change in soil water storage for precipitation events lower than the antecedent soil water deficit (N = 1716), and (c) nearest neighbor interpolation for precipitation events exceeding 7.6 mm from 15 May 2017 to 31 Dec 2020. The soil moisture approach used precipitation events across 30 stations monitoring soil moisture while the nearest neighbor approach used 2497 precipitation events across all 47 stations of the Kansas Mesonet, including stations with and without soil moisture sensors. Dashed lines represent the 1:1 line, and solid lines represent fitted linear regressions (in all cases the linear model had p < 0.001).

Citation: Journal of Hydrometeorology 22, 12; 10.1175/JHM-D-21-0168.1

A major limitation of the proposed approach occurs when the soil moisture is at or near saturation conditions that limit the soil’s ability to store infiltrating water, leading to precipitation underestimation. For instance, in the near-saturation scenario at the Ottawa 2SE station (Fig. 7), the inability of the soil profile to capture subsequent precipitation events after reaching near-saturation conditions on 7 October 2018 resulted in a total change in soil water storage of 72 mm, which amounts to only 29% of the observed total precipitation of 249 mm during the period. At near-saturation soil moisture conditions, the soil has negligible air-filled porosity to store additional precipitation and also the infiltrating water can drain beyond the deepest sensor depth without necessarily changing the storage of the soil profile, and if the rainfall rate exceeds the infiltrability of the soil, then part of the rainfall may also result in ponding or runoff (Brocca et al. 2014; Crow et al. 2011). The proposed soil moisture–based approach without a drainage term may have limited applicability in regions where soils are frequently at or near saturation conditions.

Fig. 7.
Fig. 7.

Example of precipitation underestimation by the proposed approach caused by the lack of response in soil water storage when the soil is at or near-saturation conditions due to several consecutive precipitation events at the Ottawa 2SE station. The Pobs is the observed precipitation, and ΔS is the change in soil profile water storage.

Citation: Journal of Hydrometeorology 22, 12; 10.1175/JHM-D-21-0168.1

Drainage beyond the deepest moisture sensor, especially under near saturation conditions, can be accounted for by adding a drainage term to the proposed equation based on hourly changes in soil water storage. In this study, the addition of a drainage term based on the Campbell model to the proposed approach resulted in RMSE = 13.0 mm and MAE = 7.7 mm, an error that is marginally lower (for a substantially more complicated method) than solely using the sum of hourly differences in soil water storage (Fig. 5 in the supplemental material). A previous study in different sites in western Europe using a single soil moisture sensor near the soil surface (i.e., 5–30 cm) and characterized by coarse-textured soils (e.g., sand and sandy loam; Brocca et al. 2013), showed that drainage accounted for up to 30% of the precipitation estimates (Brocca et al. 2014). The low drainage rates in our study are likely attributed to the deeper array of sensors and the predominantly fine-textured soils across Kansas that typically have hydraulic conductivities (Ksat ∼ 1.5 mm h−1) that are an order of magnitude lower than coarse-textured soils (e.g., Ksat for sand ∼ 25.9 mm h−1; Rawls et al. 1982).

We also observed that in precipitation events with intensities > 10 mm h−1 underestimation could have been caused by high antecedent soil moisture conditions coupled with ponding and possible runoff. The case where high-intensity precipitation events are underestimated in high antecedent soil moisture conditions was also observed by Brocca et al. (2015). Out of the 2497 precipitation events in our dataset, 781 events (31%) occurred when the antecedent soil water deficit (i.e., available air-filled porosity) before the start of the precipitation event was smaller than the total amount of the precipitation event.

On some occasions, we also found that the proposed approach overestimated the observed precipitation amount. For instance, after a 6-h precipitation event totaling 27.7 mm in a sandy loam soil with an antecedent water deficit of 39.1 mm at the Lake City station, the resulted changes in soil water storage totaled 35.5 mm, which is 28% in excess of the observed precipitation (Fig. 8a). Similarly, a 51.6-mm precipitation event in a silty clay loam with an antecedent water deficit of 81.7 mm resulted in an estimated precipitation amount of 74 mm at the Ashland Bottoms station (Fig. 8c), which is 43% in excess of the observed precipitation. One possible reason for the precipitation overestimation could be attributed to the method for computing soil water storage using the trapezoidal rule, especially in the layer between the 20- and 50-cm sensor depths, where small errors in volumetric water content could greatly affect the computed water storage in the 300-mm-thick layer. Another explanation for the overestimation might be due to additional water contribution from surface runoff, subsurface lateral flow, and water table rise (for stations located near rivers). However, because most stations of the Kansas Mesonet were deployed in vegetated landscapes with <1% slope and deep water tables, conditions prone to surface and subsurface runoff and water table rise likely occur at a few specific stations (e.g., Cherokee and Woodson stations, Table 2).

Fig. 8.
Fig. 8.

(a),(c) Time series of observed (Pobs) and predicted cumulative precipitation from changes in soil water storage (ΔS) and (b),(d) the corresponding profile soil water content dynamics for overestimated precipitation events. (top) An example for a sandy loam at the Lake City station from 2200 CST 5 Jul to 0300 CST 6 Jul 2019 and (bottom) an example for a silty clay loam soil at the Ashland Bottoms station from 0400 to 0900 CST 29 Jun 2017. Soil water content at time t = −1 h represents the water content of the soil profile at an hour before the start of the precipitation event and t = 7 h represents the soil water content at an hour after the end of the precipitation event.

Citation: Journal of Hydrometeorology 22, 12; 10.1175/JHM-D-21-0168.1

Table 2.

Comparison of precipitation estimation error between the proposed soil moisture approach (SM) and the nearest neighbor interpolation approach (NN) for all precipitation events greater than 7.6 mm at each of the 30 stations of the Kansas Mesonet that monitors root-zone soil moisture. The predicted precipitation from soil moisture was computed as the sum of hourly changes in soil water storage + interception value of 7.6 mm.

Table 2.

2) Comparison with nearest neighbor interpolation

The comparison of the nearest neighbor interpolation and the soil moisture–based approach at each individual station that monitors soil moisture showed that the nearest neighbor approach consistently outperforms the proposed soil moisture–based approach when the distance to the nearest station is ≤10 km (Table 2). At distances ≤ 10 km, the nearest neighbor approach resulted in an average r = 0.84 (SD = 0.01) and an average MAE = 5.8 mm (SD = 0.27 mm), while the soil moisture–based approach resulted in an average r = 0.53 (SD = 0.01) and average MAE = 8.5 mm (SD = 0.13 mm) (Table 2). At distances between 10 and 15 km the two methods had comparable performance and were probably within the error of the method itself (Fig. 6 in the supplemental material). On the other hand, as the distance to the nearest neighboring station increased beyond ∼10–15 km, the soil moisture–based approach outperformed the nearest neighbor approach in 22 out of 27 cases, exhibiting an average r = 0.64 (SD = 0.03) and MAE = 7.5 mm (SD = 0.37 mm) compared to the mean correlation of 0.47 (SD = 0.03) and MAE = 11.4 mm (SD = 0.36) for the nearest neighbor approach (Table 2). This suggests that for stations with the nearest neighbor station located >10–15 km, using the proposed soil moisture–based approach could be more accurate than using the nearest neighbor interpolation approach for filling the gap in missing precipitation at hourly intervals. This result is especially relevant in sparse networks where the distance to the nearest station can be several orders of magnitude larger than the range in spatial autocorrelation of precipitation events. For instance, a study in central Oklahoma using a dense network of 25 rain gauges over a 9-km2 area revealed that the distance at which precipitation events are no longer correlated is 4 km (Ciach and Krajewski 2006). In contrast, the median distance between nearest neighbor stations in the Oklahoma Mesonet (McPherson et al. 2007) is about 30 km, indicating that even in one of the densest statewide mesoscale networks in the United States there is an opportunity to further explore the use of collocated soil moisture information for QA and QC procedures and for filling missing precipitation records at hourly time scales in mesoscale environmental monitoring networks. The potential could be even greater for nationwide networks such as the Soil Climate Analysis Network (Schaefer et al. 2007) with a median distance between neighbors of 69 km and for the U.S. Climate Reference Network (Diamond et al. 2013) with a median distance of 197 km. The applicability of the proposed approach could be particularly helpful in sparse networks outside the United States in which high-resolution multisensor precipitation products are unavailable.

To illustrate the limitations of using nearest neighbors to fill precipitation gaps at subdaily time scales we analyzed two precipitation events of similar amount and duration, but with neighboring stations at different distances. For the case of close neighboring stations, during a 5-h precipitation event of 24.9 mm at the Ashland Bottoms station at 1700 CST 18 May 2017, the nearest neighbor station (i.e., Manhattan station, about 10 km away) recorded a precipitation event of 19.8 mm, which started at about an hour earlier than the soil moisture response at the Ashland Bottoms station (Fig. 9a). The resulting sum of hourly changes in soil water storage at the Ashland Bottoms stations was 20.5 mm, indicating that when stations have close neighbors, the nearest neighbor approach shows comparable precipitation amount and timing to the soil moisture approach. For the case of a station with far neighbors, during a 5-h precipitation event of 33.3 mm at the Woodson station at 1500 CST 17 April 2019, the nearest neighbor station (i.e., Parsons station, about 70 km away) recorded precipitation of 11.2 mm (Fig. 9b) and the timing of the precipitation event was delayed by 2 h. Similarly, the precipitation event at the Ottawa 2SE station (89 km away, second nearest station) started an hour earlier while the precipitation at the Butler station (97 km away, third nearest station) started 2 h earlier than the precipitation at the Woodson station (Fig. 9b). The soil moisture sensors at the Woodson station responded immediately to the precipitation event and the resulting sum of hourly changes in soil water storage was 30 mm. In other words, none of the nearest stations, which are located ≥70 km from the Woodson station was able to accurately capture both the amount and timing of the precipitation event compared to the soil moisture–based approach. Future studies should consider testing the performance of soil moisture–derived precipitation against more sophisticated spatial interpolation methods and gridded precipitation products from multisensors, radars, and remote sensing satellites.

Fig. 9.
Fig. 9.

Timing of precipitation events within the same storm for a station of the Kansas Mesonet (a) with close nearest neighboring stations (Ashland Bottoms) and (b) a station with distant nearest neighboring stations (Woodson). The figure highlights that changes in soil water storage may constitute a better alternative to estimate both the amount and timing of precipitation events in stations with distant nearest neighbors compared to using information from nearest neighboring stations. Times are reported in central standard time (CST).

Citation: Journal of Hydrometeorology 22, 12; 10.1175/JHM-D-21-0168.1

Our approach could be particularly useful in hydrological and mesoscale environmental monitoring networks equipped with collocated pluviometers and in situ soil moisture sensors. In North America, mesoscale networks that include soil moisture as a standard measurement have been expanding as a consequence of state and federal initiatives (Quiring et al. 2016). This includes recent statewide networks like the West Texas Mesonet (Schroeder et al. 2005), the Alabama Mesonet (Kimball et al. 2010), New York Mesonet (Brotzge et al. 2020), the Kentucky Mesonet (Mahmood et al. 2019), and the Manitoba Agriculture Mesonet (Ojo and Manaigre 2021) and federal networks like the U.S. Climate Reference Network (Diamond et al. 2013), the Soil Climate Analysis Network (Schaefer et al. 2007), and the National Ecological Observatory Network (Keller et al. 2008) that monitor precipitation and soil moisture at most stations. Outside North America, there is also a growing number of in situ networks that monitor soil moisture like the Czech Hydrometeorological Institute Network (Mozny et al. 2013), the Wales Soil Moisture Network (Petropoulos and McCalmont 2017), the COSMOS-U.K. network across the United Kingdom (Evans et al. 2016), and the CosmOz soil moisture monitoring network across Australia (Hawdon et al. 2014). As the number of mesoscale networks that include soil moisture observations increases, there is an increasing potential to use the proposed approach for both quality control and quality assurance of precipitation observations, and as more general method to guide the reconstruction of precipitation from soil moisture observations.

4. Conclusions

We investigated a simple approach for reconstructing precipitation events at hourly time steps based on the sum of hourly changes in root-zone soil water storage. The proposed method was tested using 30 stations of the Kansas Mesonet equipped with collocated pluviometers and an array of permanent soil moisture sensors distributed along the root zone. The use of changes in soil water storage proved effective as a qualitative method for flagging precipitation events (accuracy = 82%) and as a quantitative method (MAE = 8.0 mm, RMSE = 14.1 mm) for reconstructing precipitation events > 7.6 mm. The soil moisture approach, the soil moisture approach proved more accurate than the nearest neighbor approach at stations with the nearest station distance > 10 km. Our findings highlight a promising application of in situ soil moisture information as a practical and complementary method for operational quality control and quality assurance of precipitation and as a method to fill gaps in the historical precipitation records of in situ environmental monitoring networks without the need for horizontal spatial assumptions.

Acknowledgments

The authors wish to thank Christopher Redmond, Mary Knapp, and Randall Mai from the Kansas Mesonet for providing access to the visit sheets and precipitation and soil moisture datasets for this study. This work was supported by the USDA National Institute of Food and Agriculture Hatch Multistate projects Awards 1021229 and 1021608, by the U.S. Geological Survey Award G16AP00054, and by the Kansas State University Agricultural Experiment Station Contribution Number 22-058-J. The authors declare no conflicts of interest.

Data availability statement.

Datasets for this study are available in the supplemental materials with filename Dataset_final.mat for the soil moisture-derived precipitation, and the nearest neighbor interpolation approach. The dataset file can be accessed using MATLAB.

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