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Edited by: Heye Reemt Bogena, Helmholtz Association of German Research Centers (HZ), Germany

Reviewed by: Martin Schrön, Helmholtz Centre for Environmental Research (UFZ), Germany; Rui Jin, Northwest Institute of Eco-Environment and Resources (CAS), China

This article was submitted to Water and Hydrocomplexity, a section of the journal Frontiers in Water

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

The Cosmic-Ray Neutron Sensor (CRNS) technique for estimating landscape average soil water content (SWC) is now a decade old and includes many practical methods for implementing measurements, such as identification of detection area and depth and determining crop biomass water equivalent. However, in order to maximize the societal relevance of CRNS SWC data, practical value-added products need to be developed that can estimate both water flux (i.e., rainfall, deep percolation, evapotranspiration) and root zone SWC changes. In particular, simple methods that can be used to estimate daily values at landscape average scales are needed by decision makers and stakeholders interested in utilizing this technique. Moreover, landscape average values are necessary for better comparisons with remote sensing products. In this work we utilize three well-established algorithms to enhance the usability of the CRNS data. The algorithms aim to: (1) temporally smooth the neutron intensity and SWC time series, (2) estimate a daily rainfall product using the Soil Moisture 2 Rain (SM2RAIN) algorithm, and (3) estimate daily root zone SWC using an exponential filter algorithm. The algorithms are tested on the CRNS site at the Hydrological Open Air Laboratory experiment in Petzenkirchen, Austria over a 3 years period. Independent observations of rainfall and point SWC data are used to calibrate the algorithms. With respect to the neutron filter, we found the Savitzky-Golay (SG) had the best results in preserving the amplitude and timing of the SWC response to rainfall as compared to the Moving Average (MA), which shifted the SWC peak by 2–4 h. With respect to daily rainfall using the SM2RAIN algorithm, we found the MA and SG filters had similar results for a range of temporal windows (3–13 h) with cumulative errors of <9% against the observations. With respect to daily root zone SWC, we found all filters behaved well (Kling-Gupta-Efficiency criteria > 0.9). A methodological framework is presented that summarizes the different processes, required data, algorithms, and products.

The Cosmic-Ray Neutron Sensor (CRNS) is an

While remote sensing has made significant progress in recent years (McCabe et al.,

The CRNS technology offers part of the solution to fill this critical measurement gap at the field scale given its ability to measure landscape average SWC over hundreds of meters horizontally and tens of centimeters vertically. Over the past decade since its development CRNS theory and best practices for equipment have greatly matured. Nonetheless, practical implementation of using the CRNS data by stakeholders requires further developing value-added products. In this methodological study, we will apply and evaluate three well-established algorithms used within the science community to increase the practical use of CRNS data. The three algorithms aim to: (1) temporally smooth the neutron intensity and SWC time series, (2) estimate a daily rainfall product using the Soil Moisture 2 Rain (SM2RAIN) algorithm (Brocca et al.,

In order to provide the reader a clear outline of the manuscript

Methodological framework describing the different processes, required data, algorithms, and products using CRNS data from Petzenkirchen, Austria.

A CRNS (Model # CRS 1000/B, HydroInnova LLC, Albuquerque, NM, USA) was installed at the study area in northeast Austria (48.1547°N, 15.1483°E, elevation 277 m, average slope of 8%) on 11 December 2013 and has continuously operated since (Franz et al.,

A network of Time-Domain Transmissivity (TDT) sensors (SPADE, Julich, Germany) were installed in the second half of 2013 and available for a portion of 2014. The TDT sensors record hourly SWC at a point and were installed at 31 sites distributed around the study area (Blöschl et al.,

Time series of TDT probes organized by depth

The CRNS technique works by counting low-energy neutrons (~0.5–1000 eV) from a moderated detector over a certain time interval (typically 1 h for stationary sensors) (see Zreda et al.,

Given the challenge of estimating landscape average rainfall from ground based observations and top down approaches using satellites, additional sources of rainfall data are greatly needed (McCabe et al.,

where ^{*} is the soil water capacity equal to soil depth times porosity, ^{b} is deep drainage and

thereby leaving three parameters to calibrate (^{*},

Given the wide array of SWC products at different scales the SM2RAIN algorithm has been applied and validated across time and space. By using the European Space Agency Climate Change Initiative (ESA CCI) soil moisture product, Ciabatta et al. (

A common problem with remotely sensed SWC data is that only the near surface (~0–3 cm) is directly observed using microwave wavelengths (Jackson et al.,

In this study, we utilized the continuous CRNS SWC data, and assumed a depth of ~0-20 cm based on expected effective depth of the site (see Franz et al., _{1}), and layer 2 is the lower soil layer of interest (here an integrated root zone storage estimate constrained by the depth of the TDT sensors in order to calibrate the exponential filter approach). For demonstration purposes here a layer 2 depth of 0–30 and 0–60 cm will be provided in the following examples. Having two different root zone depths may be important to relate the available SWC with different growth stages of crop over the growing season. SWC of layer 2 (denoted by _{2}) is described as:

where

where _{2(t)} and _{1(t)} are the Soil Water Index (SWI) of layer 2 and layer 1, respectively, _{t} is the gain. Soil water index is the SWC scaled between 0 and 1 using assumed minimum and maximum values, SWI_{t} ranges from 0 to 1 and is calculated as:

where _{t−1}is the gain of the previous time step, Δ_{t} = 1 and _{2(1)} = _{1(1)}. The characteristic time length (_{2min}, _{2max}). In order to perform the calibration we used the _{2min} from 0.01 to 0.25 every 0.005 cm^{3}/cm^{3}, _{2max} from 0.36 to 0.75 every 0.005 cm^{3}/cm^{3}, and

^{3}/cm^{3} based on the sites soil bulk density, see Franz et al.,

Summary of daily rainfall error analysis using different filtering techniques on moderated neutron counts and propagating calculated SWC data through SM2RAIN algorithm.

^{*} |
||||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 h raw data | 3104.7 | 876.7 | 39.4 | 0.598 | 4.20 | 0.79 | 0.481 | 20.00 | 3.81 | 49.92 |

MA 3 h | 2225.2 | −2.8 | 0.1 | 0.694 | 3.57 | 0.00 | 0.559 | 31.43 | 5.37 | 29.71 |

MA 6 h | 2239.5 | 11.5 | 0.5 | 0.738 | 3.34 | 0.01 | 0.623 | 56.98 | 6.97 | 50.00 |

MA 8 h^{*} |
2144.2 | −83.8 | 3.8 | 0.743 | 3.32 | −0.08 | 0.615 | 69.65 | 3.32 | 46.85 |

MA 10 h | 2090.0 | −138.0 | 6.2 | 0.721 | 3.44 | −0.12 | 0.609 | 81.58 | 0.00 | 50.00 |

MA 12 h | 2051.8 | −176.2 | 7.9 | 0.736 | 3.36 | −0.16 | 0.629 | 91.43 | 0.00 | 50.00 |

MA 24 h | 1919.5 | −308.5 | 13.8 | 0.753 | 3.27 | −0.28 | 0.641 | 139.02 | 0.00 | 50.00 |

SG 1st order, 3 h | 2062.9 | −165.2 | 7.4 | 0.686 | 3.62 | −0.15 | 0.518 | 30.28 | 8.54 | 47.32 |

SG 2nd order, 3 h | 3104.7 | 876.7 | 39.4 | 0.598 | 4.20 | 0.79 | 0.410 | 20.00 | 3.81 | 49.93 |

SG 1st order, 7 h | 2140.4 | −87.6 | 3.9 | 0.731 | 3.38 | −0.08 | 0.601 | 63.28 | 7.94 | 49.97 |

SG 2nd order, 7 h | 2162.8 | −65.2 | 2.9 | 0.701 | 3.54 | −0.06 | 0.555 | 32.35 | 4.97 | 49.70 |

SG 3rd order, 7 h | 2162.8 | −65.2 | 2.9 | 0.701 | 3.54 | −0.06 | 0.555 | 32.35 | 4.97 | 49.70 |

SG 1st order, 9 h | 2148.5 | −79.5 | 3.6 | 0.728 | 3.40 | −0.07 | 0.619 | 77.32 | 1.04 | 46.90 |

SG 2nd order, 9 h | 2023.8 | −204.2 | 9.2 | 0.713 | 3.49 | −0.18 | 0.536 | 39.60 | 4.24 | 49.93 |

SG 3rd order, 9 h | 2064.1 | −163.9 | 7.4 | 0.711 | 3.50 | −0.15 | 0.547 | 40.23 | 4.27 | 49.93 |

SG 1st order, 11 h | 2094.8 | −133.2 | 6.0 | 0.719 | 3.45 | −0.12 | 0.606 | 86.95 | 2.85 | 49.96 |

SG 2nd order, 11 h | 2116.2 | −111.8 | 5.0 | 0.704 | 3.52 | −0.10 | 0.577 | 46.68 | 3.40 | 10.36 |

SG 3rd order, 11 h | 2116.2 | −111.8 | 5.0 | 0.704 | 3.52 | −0.10 | 0.577 | 46.68 | 3.40 | 10.36 |

SG 1st order, 13 h | 2051.8 | −176.2 | 7.9 | 0.710 | 3.50 | −0.16 | 0.593 | 97.39 | 0.41 | 49.98 |

SG 2nd order, 13 h | 2193.9 | −34.1 | 1.5 | 0.733 | 3.37 | −0.03 | 0.631 | 53.17 | 2.20 | 5.62 |

SG 3rd order, 13 h^{*} |
2193.7 | −34.3 | 1.5 | 0.733 | 3.37 | −0.03 | 0.631 | 53.17 | 2.20 | 5.62 |

SG 1st order, 25 h | 1895.8 | −332.3 | 14.9 | 0.693 | 3.60 | −0.30 | 0.583 | 139.97 | 0.07 | 50.00 |

SG 2nd order, 25 h | 1965.4 | −262.6 | 11.8 | 0.702 | 3.54 | −0.24 | 0.579 | 97.91 | 0.00 | 49.99 |

SG 3rd order, 25 h | 1965.4 | −262.6 | 11.8 | 0.702 | 3.54 | −0.24 | 0.579 | 97.91 | 0.00 | 49.99 |

Time series of

Zoomed in times series of

^{*},

Comparing the three parameters with Brocca et al. (

Cumulative sums of observed rainfall and SM2RAIN estimates using three neutron filters. See

Summary of SM2RAIN algorithm statistical performance at Petzenkirchen for different integration periods.

1 h raw data | 1 | 0.598 | 4.20 | 0.41 | 3104.74 | 876.74 | 39.4 |

MA8 h | 1 | 0.743 | 3.32 | 0.62 | 2144.23 | −83.77 | 3.8 |

SG 3rd order, 13 h | 1 | 0.733 | 3.37 | 0.63 | 2193.72 | −34.28 | 1.5 |

1 h raw data | 3 | 0.635 | 2.72 | 0.45 | 3085.45 | 857.44 | 38.5 |

MA 8 h | 3 | 0.788 | 2.00 | 0.68 | 2299.48 | 71.48 | 3.2 |

SG 3rd order, 13 h | 3 | 0.788 | 1.99 | 0.68 | 2238.16 | 10.15 | 0.5 |

1 h raw data | 5 | 0.652 | 2.15 | 0.48 | 3062.31 | 834.31 | 37.4 |

MA 8 h | 5 | 0.791 | 1.55 | 0.69 | 2274.14 | 46.14 | 2.1 |

SG 3rd order, 13 h | 5 | 0.753 | 1.67 | 0.65 | 2158.14 | −69.86 | 3.1 |

_{2max} and _{1min} was lower for the 1 h neutron data due to the higher random fluctuations. As expected

Summary of calibration fit and three parameter estimates for the 0–30 and 0–60 cm exponential filter models for different neutron filters.

_{2min} (cm^{3}/cm^{3}) |
_{2max} (cm^{3}/cm^{3}) |
||||
---|---|---|---|---|---|

Daily SWC, 1 h data | 30 | 0.911 | 0.01 | 0.675 | 50 |

Daily SWC, MA 8 h | 30 | 0.909 | 0.045 | 0.68 | 48 |

Daily SWC, SG 3rd order, 13 h | 30 | 0.908 | 0.035 | 0.68 | 50 |

Daily SWC, 1 h data | 60 | 0.914 | 0.125 | 0.585 | 64 |

Daily SWC, MA 8 h | 60 | 0.913 | 0.15 | 0.59 | 62 |

Daily SWC, SG 3rd order, 13 h | 60 | 0.912 | 0.145 | 0.59 | 64 |

Comparison of SWC for the CRNS (neutron filter SG 3rd order, 13 h), fitted exponential model, and observed landscape average TDT data for the

Using the CNRS SWC data and the exponential model fits in

Time series of SWC for CRNS, 0–30 cm exponential filter product, and 0–60 cm exponential filter product for the 3 years period.

The key limitation of this work is that only a single CRNS site was used, mainly due to the challenge of having a high-density

With respect to the SM2RAIN algorithm, the CRNS data performed comparable to rain gage and satellite products for the MA and SG neutron filters. The 1 h data lead to a 39.4% overestimation of rainfall due to the random fluctuations in the neutron counts. The key assumption for the SM2RAIN method is that no surface runoff is generated during rainfall, which may be violated for certain sites. In addition, selection of the three parameters did vary with choice of neutron filter algorithm. Current versions of the SM2RAIN algorithm do include a self-calibration procedure. We did find that adding the criteria of cumulative sum percent error against the observed rainfall was helpful in selecting appropriate window sizes for evaluating the filters and conserving water mass balance.

With respect to daily root zone SWC, all three neutron filtering techniques worked well, albeit the 1 h data had a different _{2min} parameter. The main challenge of the exponential filter approach is selection of the

This methodological paper provides the background, equations, and example calculations from the Petzenkirchen CRNS study site using three well-established algorithms summarized in the methodological framework in

The datasets generated for this study can be found in the Mendeley Repository with the citation- Franz, Trenton (2020), Data for Cosmic-Ray Neutron Sensor: Practical Data Products from Cosmic-Ray Neutron Sensing for Hydrological Applications, Mendeley Data, V2, doi:

TF performed the primary data analysis and wrote the manuscript. AW and JZ assisted with data analysis and edited the manuscript. LH and GD provided funding, laboratory access, and edited the manuscript. PS and MV provided datasets from HOAL and edited the manuscript. LB provided access to SM2RAIN algorithm, assisted with data analysis, and edited the manuscript. WW edited the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors would like to acknowledge the support of the Hydrological Open Air Laboratory, the Soil and Water Management & Crop Nutrition Laboratory of the Joint Division of Nuclear Techniques in Food and Agriculture, the Vienna Doctoral Programme on Water Resources Systems and Georg Weltin in the installation and maintenance of the CRNS.

The Supplementary Material for this article can be found online at:

Containing the raw and processed data.