Global COSMOS Reference (draft)

Global COSMOS Reference A community reference for the processing of sensor data of the COsmic-ray Soil Moisture Observing System Version 0.9.2 December 16, 2025 doi:10.5281/zenodo.17959506 Contributing Authors Martin Schrön1,*, Steffen Zacharias1,*, Roland Baatz2, Gabriele Baroni3, Heye Bogena4, Cosimo Brogi4, Benjamin Fersch5, Trenton Franz6, Lasse Hertle1,7, David McJannet8, Sascha Oswald9, Daniel Power1, Daniel Rasche1,10, Rafael Rosolem11, and the global COSMOS community 1UFZ - Helmholtz Centre for Environmental Research Leipzig, Germany, 2ZALF Müncheberg, 3University of Bologna, 4Agrosphere Institute (IBG-3), Forschungszentrum Jülich GmbH, Jülich, Germany, 5KIT - Karlsruhe Institute of Technology, Campus Alpin, Garmisch-Partenkirchen, Germany, 6University of Nebraska, 7University Heidelberg, 8CSIRO Environment, Australia, 9Institute of Environmental Science and Geography, University of Potsdam, Germany, 10GFZ - Helmholtz Centre for Geosciences Potsdam, Germany, 11University of Bristol. *Correspondence: martin.schro[email protected], steffen.zacha[email protected] Acknowledgements The development of this reference has been supported by: (i) the European Commission’s Horizon 2020/Horizon Europe Framework Programmes: Horizon 2020 project eLTER PLUS (European long-term ecosystem, critical zone and socioecological systems research infrastructure PLUS, grant no. 871128), Horizon project ENVRINNOV (ENVironment Research infrastructures INNOVation Roadmap, grant no. 101131426), (ii) 21GRD08 SoMMet (Metrology for multiscale monitoring of soil moisture), a Joint Research Project within the Programme ’European Partnership on Metrology’ of EURAMET. Preface Over the last 15 years, the COsmic-ray Soil Moisture Observing System (COSMOS) based on CosmicRay Neutron Sensing technology (CRNS) has undergone tremendous development. The knowledge of the methodology, particularly the underlying physical principles and the environmental factors affecting its signal, has advanced immensely. The potential and limitations of CRNS for hydrological applications are much better understood today than they were a few years ago. However, enormous scientific progress comes at a cost. With the manifold of additional findings that accumulated over the last years, it is more and more difficult to gain an adequate overview of the current state of knowledge, especially for new users. This creates new challenges for further dissemination of the measurement method. At the same time, there are increased efforts to further advance the standardization of environmental observations globally. Data processing standards are being developed in this context. Nevertheless, there is presently no available standard for the processing of CRNS data that is coordinated within the international CRNS community. Against this background, CRNS scientists have joined forces to develop a reference guideline for the processing of CRNS data. The reference is defined as a comprehensive compilation of concepts for CRNS data processing that reflect an established status of knowledge that has been successfully and adequately applied in recent years by the CRNS community. It is crucial to emphasize at this point that the present reference should neither be interpreted as an exclusionary benchmark, nor as the only possible way to process CRNS data. Instead, it is to be seen as a scientific basis which individual processing approaches could build upon, and which future research can be compared against. In that sense, the reference document... 1. can serve as a basis for current and future activities of international harmonization of CRNSbase observation of soil moisture, 2. provides immediately available and clear guidance for new users for the implementation of the CRNS method, 3. can be used as a standardized benchmark to test and proof new concepts against as well as allowing for easy reproducibility of experiments. Consequently, the COSMOS reference is a living document that can be continuously developed in joint consultation. We encourage the community to continuously review and develop the state of knowledge described in this version. 2 Release notes for version 0.9.2 The is a preliminary draft. 3 Glossary COSMOS COsmic-ray Soil moisture Observing System CRNS Cosmic-Ray Neutron Sensing HDPE High-density polyethylene NMDB Neutron Monitor Database UTC Coordinated universal time 4 Contents 1 Introduction 6 2 Sensor placement 6 3 Raw data requirements 7 4 Cleaning raw data 7 5 General quality control 7 6 Uncertainty determination 8 7 Neutron count harmonization 8 8 Neutron corrections 8 8.1 Atmospheric pressure correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 8.2 Airhumiditycorrection ................................. 9 8.3 Incoming neutron correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 8.4 Biomasscorrection ................................... 12 8.5 Mobile roving corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 9 Quality control of processed neutrons 12 10 Temporal averaging 13 10.1Smoothing........................................ 13 10.2Aggregation ....................................... 13 11 Conversion to soil moisture 14 11.1 The neutron-to-soil moisture relationship . . . . . . . . . . . . . . . . . . . . . . . . 14 11.2 Correction for additional soil hydrogen sources . . . . . . . . . . . . . . . . . . . . . 14 11.3 Scaling to volumetric soil moisture . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 12 Soil moisture quality control 15 13 Soil moisture uncertainty 15 14 CRNS footprint radius and penetration depth 16 15 Sensor calibration using in-situ soil moisture 18 15.1 Vertical averaging of in-situ probes . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 15.2 Horizontal averaging of profile values . . . . . . . . . . . . . . . . . . . . . . . . . . 18 16 Conversion to snow water equivalent 19 17 Processed data requirements 20 5 1 Introduction Measured epithermal neutrons are a proxy for soil water content, but systematic factors and stochastic effects also influence the neutron signal. Research in the last decades has led to a profound understanding of these influencing factors and has facilitated a more accurate extraction of the soil moisture signal from the cosmic-ray neutron data. The commonly agreed processing framework is described below, following the scheme visualized in Fig. 1. Its technical implementation can be supported by public tools and software libraries, such as Corny, Crspy, or Neptoon. .This document applies to moderated neutron detectors. They are usually shielded by 20-25mm of polyethylene to become most sensitive to epithermal neutrons. The processing routines for bare thermal neutron detectors or leaded high-energy neutron detectors may vary. Raw sensor data Cleaning Quality control Quality control Quality control Neutron smoothing Aggregation Air humidity NMDB.eu Sampling campaign Sampling campaign Air pressure Incoming cosmic rays Biomass Soil moisture Uncertainty determination Uncertainty propagation Footprint & depth Calibration vertical average COSMOS product horizontal average Unit harmonization Neutron corrections Figure 1: General scheme for COSMOS data processing with the main processing steps (lightgrey), subtasks (white), optional steps (dashed), and dependencies on external data sources (grey). 2 Sensor placement In order to reduce the systematic uncertainties due to landscape features, it is recommended that the COSMOS station is installed at a height of 1.5-2 m above the ground. Also, the ideal surrounding landscape should be rather homogeneous and have a flat topography, a single or a dominant land use (i.e., not partly irrigated), no artificial features (i.e., buildings, high voltage power lines), and no water bodies within 100 m distance. 6 3 Raw data requirements The minimum requirements for raw data from COSMOS measurements include the following columns: Variable Units Symbol Date and time, ideally synchronized UTC t Epithermal neutron count rate counts per period or elapsed time Nraw Data that is required for the processing, but could be taken from another source: Variable Units Symbol Air pressure hPa or mbar P Air temperature °CT Air relative humidity % hrel Optional data that is helpful for the processing and sensor diagnostics: Variable Units Symbol Elapsed time since the last record sec ∆t Battery voltage V U Internal air temperature °CTint Internal air humidity % hint,rel Redundant air pressure sensors hPa or mbar Pi 4 Cleaning raw data Raw data can be inconsistent due to several reasons (transmission signal loss, power cuts, restarts). Typically, a cleaning process is necessary to provide a consistent data stream. This process involves the following steps: 1. Drop lines with inconsistent number of columns, 2. Drop lines with missing or duplicated datetime values, 3. Drop first hour of data after starting or restarting the CRNS device, as this record may have an uncertain integration period, 4. Replace non-numeric values by NaN, 5. Sort data by datetime. 5 General quality control Suspicious or unrealistic data values should be replaced by NaN or dropped. The following ranges are recommended for filtering: Variable Minimum value Maximum value tinstallation date future values Nraw 0individual P500 1100 T−50 50 hrel 0 100 hint,rel 0 80 U10.5 20 7 6 Uncertainty determination Counting neutrons is a random process. In periods of no external influences, their values follow a Poisson distribution with a well defined standard deviation, σNraw =pNraw .(1) This value represents the uncertainty, or stochastic error of a neutron measurement. It is useful for further quality control and processing, and for the calculation of the final soil moisture error. .Since the theory behind this calculation is based on the counting process itself, this step must be performed on the raw neutron counts and before any unit conversion or correction. 7 Neutron count harmonization Harmonized neutron count rates, N, should be in units of counts per hour (cph) to facilitate easy intercomparison between CRNS sites. This requires a conversion factor, u, on the raw neutron counts. The same unit conversion needs to be applied on the raw uncertainty: N=Nraw ·u , σN=σNraw ·u . (2) Units of Nraw Conversion factor u counts per hour (cph) 1 counts per second (cps) 3600 counts per elapsed time ∆t(in sec) ∆t/3600 If not explicitly provided as a column, the elapsed time ∆tis the time difference between records. 8 Neutron corrections The amount of epithermal neutrons in the environment is subject to change, even in periods of constant soil moisture. Therefore, corrections need to be applied to remove variations of neutron counts that are not related to soil moisture changes. It is recommended to address the four most important influencing factors - (i) atmospheric pressure, (ii) air humidity, (iii) incoming neutron intensity, (iv) biomass water - by introducing four correction factors, C, that act multiplicative on the neutron count rate, N, to provide the corrected neutron count rate, N′: N′=N·Cp·Ch·Cinc ·Cveg .(3) The same correction factors need to be applied on the uncertainty, σN: σN′=σN·Cp·Ch·Cinc ·Cveg .(4) These corrections need to be performed on each neutron measurement, i.e., each time step t, before any further smoothing or aggregation. 8.1 Atmospheric pressure correction Since the cosmic-ray flux through the atmosphere is attenuated by the traversed cumulative mass, measured neutron count rates can be normalized to standard atmospheric pressure following [Desilets and Zreda, 2003]: Cp=eβ(P−Pref),(5) 8 Lattice water could be determined from soil clay content, Clay (in g/g), following the empirical approach: θlatt =a+b·Clay ,(22) where a= 0.0149,b= 0.16 determined for american soil [Dong and Ochsner, 2018] or a= 0, b= 0.1783 determined for australian soil [Greacen et al., 1981]. .In forests there is an additional source of hydrogen, the water in the litter layer. This is difficult to measure at it changes in time, while it is a source of surface water that is well visible by the CRNS. Its proper treatment during data processing is currently under discussion. it is recommended to carefully interpret the resulting soil moisture product from CRNS as a combined value including both, water in the soil and in the litter layer. 11.3 Scaling to volumetric soil moisture In order to retrieve volumetric soil water content, θ(in m3/m3), the value needs to be scaled by soil bulk density, ϱb(in g/cm3): θ(N′) = θ′ grv(N′)·ϱb.(23) 12 Soil moisture quality control To indicate unrealistically high values in the CRNS-derived soil moisture time series, it is recommended to flag values greater than local soil porosity, Φ(in %). Overshoot in CRNS-derived soil moisture above soil porosity could still occur, if additional water was accumulated that has not been accounted for in the previous section, such as ponding water or intercepted water after huge rain events, or snow. These water sources are typically not recognized by in-situ soil moisture probes or infiltration models. Therefore, no general recommendation can be given, and the interpretation and usage of these values should be determined by the specific use case. Variable Minimum value Maximum value θ0 Φ 13 Soil moisture uncertainty The statistical uncertainty of CRNS-derived soil moisture can be calculated on the basis of the corrected neutron count uncertainty, σN′. Due to the non-linearity of the neutron-to-soil moisture relationship, the propagated uncertainty is highly asymmetric [Iwema et al., 2021], i.e. the error towards wetter values, σ+ θ, is typically higher than the error towards dryer values, σ− θ. The numerically simplest approach is to estimate the impact of neutron uncertainty on the soil moisture uncertainty by the finite distance method: upper error: σ+ θ=θ(N′)−θ(N′−σN′),(24) lower error: σ− θ=θ(N′)−θ(N′+σN′).(25) If a single symmetrical uncertainty value is required, the error propagation presented by [Weimar et al., 2020] could be used: σθ= ∂θ ∂N′σN′ =θ/ϱb+a2+θorg +θlatt2·ϱb a0N0 σN′.(26) It is important to note that these stochastic uncertainty estimates do not account for other (systematic) uncertainties, e.g., due to unconsidered biomass effects [Avery et al., 2016], calibration errors, and unconsidered variations in incoming neutron flux [Baroni et al., 2018], atmospheric pressure [Gugerli et al., 2019], or air humidity [Iwema et al., 2021]. 15 14 CRNS footprint radius and penetration depth The footprint radius, R86 (in m), is defined as the distance within which 86 % of the measured neutrons first probed the soil. It can be determined numerically by integrating the weighting functions, Wr(θ, h)as shown in [Köhli et al., 2015]: ZR86 0 Wrdr= 0.865 Z∞ 0 Wrdr . (27) If this calculation is not feasible, R86 can be read out from Tab. 3 as a function of θand h. This table is valid for standard air pressure and no vegetation. To adapt the values on the local conditions for air pressure Pand vegetation height Hveg, subsequent rescaling of the values is necessary, following the approach by [Köhli et al., 2015]: R86(θ, h, P, Hveg) = R86 ·Fp(P)·Fveg(Hveg, θ),(28) The corresponding functions and parameters can be found in [Schrön et al., 2017], Appendix A. .Note that the footprint estimation is based on simulations for homogeneous bare soil terrain. It will be different for more complex terrain, e.g. with strong hydrogen patterns of hydrogen pools above or below the surface. The measurement depth, D86 (in m), is the depth within which 86 % of the neutrons probed the soil. It can be calculated at each time step following [Schrön et al., 2017], Appendix A: D86 =0.01 ϱb8.321 + 0.14249 0.96655 + e−0.01 rθ+ 20.0 θ+ 0.0429,(29) where ϱb(in g/cm3) is the average soil bulk density in the upper 25cm, θis the derived volumetric soil moisture (in m3/m3), and r(in m) is the distance from the CRNS. It is recommend to set r= 1 as a proxy for the average measurement depth in the footprint. The formula also includes an additional factor, 0.01, for unit conversion to meters. .Note that this formula was derived based on simulations for average soil bulk density conditions. It may be wrong for extreme cases of highly porous media or particularly dense soil. The valid range is 1.0< ϱb<1.8g/cm3. 16 Table 3: Footprint radius, R86 (in m), as a function of volumetric soil moisture, θ(in m3/m3) as rows, and air absolute humidity, h(in g/m3), as columns. The data file is also available from [Schrön et al., 2017]. θ\h1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 0.01 231 229 227 225 223 221 219 217 214 212 210 207 205 202 200 197 195 193 190 188 186 183 181 179 177 175 172 170 168 166 0.02 226 224 222 219 217 214 212 210 207 205 203 201 198 196 194 192 190 188 186 184 181 179 177 175 174 172 170 168 166 164 0.03 229 226 223 220 218 215 212 210 208 205 203 200 198 196 194 192 189 187 185 183 181 179 177 175 173 171 170 168 166 164 0.04 231 228 225 222 220 217 214 212 209 206 204 202 199 197 195 192 190 188 186 184 182 180 178 176 174 172 170 168 167 165 0.05 233 230 227 224 221 218 215 213 210 207 205 203 200 198 195 193 191 189 187 185 182 180 178 177 175 173 171 169 167 165 0.06 233 230 227 224 221 218 216 213 210 208 205 203 200 198 196 193 191 189 187 185 183 181 179 177 175 173 171 169 167 166 0.07 233 229 226 223 221 218 215 212 210 207 205 202 200 197 195 193 191 188 186 184 182 180 178 176 174 172 171 169 167 165 0.08 231 228 225 222 219 217 214 211 209 206 203 201 199 196 194 192 190 187 185 183 181 179 177 175 173 172 170 168 166 164 0.09 229 226 223 220 217 215 212 209 207 204 202 199 197 195 192 190 188 186 184 182 180 178 176 174 172 170 168 167 165 163 0.10 226 223 221 218 215 212 210 207 204 202 200 197 195 193 190 188 186 184 182 180 178 176 174 172 170 168 167 165 163 161 0.11 223 220 218 215 212 209 207 204 202 199 197 195 192 190 188 186 184 181 179 177 175 174 172 170 168 166 164 163 161 159 0.12 220 217 214 212 209 206 204 201 199 196 194 192 190 187 185 183 181 179 177 175 173 171 169 167 166 164 162 160 159 157 0.13 217 214 211 208 206 203 201 198 196 193 191 189 186 184 182 180 178 176 174 172 170 168 167 165 163 161 160 158 156 155 0.14 213 210 207 205 202 200 197 195 192 190 188 185 183 181 179 177 175 173 171 169 167 166 164 162 160 159 157 155 154 152 0.15 209 206 204 201 198 196 194 191 189 187 184 182 180 178 176 174 172 170 168 166 164 163 161 159 157 156 154 153 151 149 0.16 205 202 200 197 195 192 190 188 185 183 181 179 177 175 173 171 169 167 165 163 161 160 158 156 155 153 151 150 148 147 0.17 201 198 196 193 191 189 186 184 182 179 177 175 173 171 169 167 165 164 162 160 158 156 155 153 152 150 148 147 145 144 0.18 197 194 192 189 187 185 182 180 178 176 174 172 170 168 166 164 162 160 158 157 155 153 152 150 149 147 145 144 142 141 0.19 193 190 188 186 183 181 179 176 174 172 170 168 166 164 162 161 159 157 155 154 152 150 149 147 146 144 143 141 140 138 0.20 189 186 184 182 179 177 175 173 171 169 167 165 163 161 159 157 155 154 152 150 149 147 146 144 143 141 140 138 137 135 0.21 185 182 180 178 176 173 171 169 167 165 163 161 159 158 156 154 152 151 149 147 146 144 143 141 140 138 137 135 134 133 0.22 181 179 176 174 172 170 168 166 164 162 160 158 156 154 152 151 149 147 146 144 143 141 140 138 137 135 134 133 131 130 0.23 177 175 172 170 168 166 164 162 160 158 156 154 153 151 149 148 146 144 143 141 140 138 137 135 134 132 131 130 129 127 0.24 173 171 169 167 165 163 161 159 157 155 153 151 149 148 146 144 143 141 140 138 137 135 134 132 131 130 128 127 126 125 0.25 170 167 165 163 161 159 157 155 153 152 150 148 146 145 143 141 140 138 137 135 134 133 131 130 128 127 126 125 123 122 0.26 166 164 162 160 158 156 154 152 150 148 147 145 143 142 140 139 137 136 134 133 131 130 128 127 126 125 123 122 121 120 0.27 163 161 158 156 155 153 151 149 147 145 144 142 140 139 137 136 134 133 131 130 129 127 126 125 123 122 121 120 119 117 0.28 159 157 155 153 151 150 148 146 144 143 141 139 138 136 135 133 132 130 129 127 126 125 124 122 121 120 119 117 116 115 0.29 156 154 152 150 148 147 145 143 141 140 138 137 135 134 132 131 129 128 126 125 124 122 121 120 119 118 116 115 114 113 0.30 153 151 149 148 146 144 142 140 139 137 136 134 133 131 130 128 127 125 124 123 121 120 119 118 117 115 114 113 112 111 0.31 150 149 147 145 143 141 140 138 136 135 133 132 130 129 127 126 125 123 122 121 119 118 117 116 115 113 112 111 110 109 0.32 148 146 144 142 141 139 137 136 134 132 131 129 128 127 125 124 122 121 120 119 117 116 115 114 113 111 110 109 108 107 0.33 145 143 142 140 138 137 135 133 132 130 129 127 126 124 123 122 120 119 118 117 115 114 113 112 111 110 109 108 107 105 0.34 143 141 139 138 136 134 133 131 130 128 127 125 124 123 121 120 119 117 116 115 114 112 111 110 109 108 107 106 105 104 0.35 141 139 137 136 134 132 131 129 128 126 125 123 122 121 119 118 117 116 114 113 112 111 110 109 108 106 105 104 103 102 0.36 139 137 135 134 132 131 129 127 126 125 123 122 120 119 118 116 115 114 113 112 110 109 108 107 106 105 104 103 102 101 0.37 137 135 134 132 130 129 127 126 124 123 122 120 119 118 116 115 114 113 111 110 109 108 107 106 105 104 103 102 101 100 0.38 136 134 132 131 129 127 126 124 123 122 120 119 117 116 115 114 112 111 110 109 108 107 106 105 104 102 101 100 100 99 0.39 134 132 131 129 128 126 124 123 122 120 119 117 116 115 114 112 111 110 109 108 107 106 104 103 102 101 100 99 98 97 0.40 133 131 129 128 126 125 123 122 120 119 118 116 115 114 113 111 110 109 108 107 106 104 103 102 101 100 99 98 97 97 0.41 132 130 128 127 125 124 122 121 119 118 117 115 114 113 112 110 109 108 107 106 105 104 102 101 100 99 98 98 97 96 0.42 131 129 127 126 124 123 121 120 118 117 116 114 113 112 111 109 108 107 106 105 104 103 102 101 100 99 98 97 96 95 0.43 130 128 127 125 123 122 120 119 118 116 115 114 112 111 110 109 108 106 105 104 103 102 101 100 99 98 97 96 95 94 0.44 129 127 126 124 123 121 120 118 117 116 114 113 112 110 109 108 107 106 105 104 102 101 100 99 98 97 96 95 94 94 0.45 129 127 125 124 122 121 119 118 116 115 114 112 111 110 109 108 106 105 104 103 102 101 100 99 98 97 96 95 94 93 0.46 128 127 125 123 122 120 119 117 116 115 113 112 111 110 108 107 106 105 104 103 101 100 99 98 97 96 95 94 94 93 0.47 128 126 125 123 122 120 119 117 116 114 113 112 110 109 108 107 106 104 103 102 101 100 99 98 97 96 95 94 93 92 0.48 128 126 124 123 121 120 118 117 116 114 113 112 110 109 108 107 105 104 103 102 101 100 99 98 97 96 95 94 93 92 0.49 128 126 124 123 121 120 118 117 115 114 113 111 110 109 108 106 105 104 103 102 101 100 99 98 97 96 95 94 93 92 0.50 128 126 124 123 121 120 118 117 115 114 113 111 110 109 108 106 105 104 103 102 101 100 99 97 96 95 94 94 93 92 17 15 Sensor calibration using in-situ soil moisture The calibration parameter N0(or N′ max) in Eq. (19) can be determined by independent measurements of average soil moisture in the CRNS footprint, θcal (in m3/m3): N′ max = 1.0746 N0=N′p0−θgrv,cal p0−p1θgrv,cal (30) where θgrv,cal =θcal/ϱb+θorg +θlatt +θlitt .(31) Here, it is important to note that the values measured by in-situ probes is volumetric soil moisture, so that it needs to be converted to gravimetric soil moisture and added on top of the other hydrogen pools in the footprint. If multiple calibration campaigns have been conducted, the final N′ max is the average of the individual values or the optimal value that minimizes the RMSE to every sampling campaign. θcal could be determined either by manual soil sampling, or by using a distributed network of soil moisture sensors (TDR or TDT). Both types of data need to be weighted horizontally and vertically to account for the spatial sensitivity of neutron measurement. The horizontal weighting function Wrand the vertical weighting function Wddepend on soil moisture and air humidity at the day of interest, and can be calculated using the functions provided by [Schrön et al., 2017], Eqs. 4 and 6. .Make sure that the neutron detector is operating properly during the soil sampling campaign, and that no significant changes of soil moisture occur during the averaging period of CRNS (e.g., 24 hours) on the calibration time, e.g. due to precipitation, or irrigation. This will reduce calibration uncertainty and eventually the uncertainty on θ. 15.1 Vertical averaging of in-situ probes For each location/profile in the footprint area, a vertically averaged value of soil moisture, θprofile (in m3/m3) needs to be determined. According to [Schrön et al., 2017], this requires knowledge of the weight wdfor each in-situ soil moisture measurement, θd(in m3/m3) at depth d: θprofile =Pθdwd Pwd .(32) It is recommended to take at least 3 measurements per profile: one below the surface, 0-10 cm, one at 10-20 cm, and one at 20-30 cm. Since typically there are very few in-situ measurements available per profile, while the depth-sensitivity of the neutrons is highly non-linear, it is recommended to integrate over the whole profile up to 1 m and define ranges within which each measurement is representative: wd=Zdj di Wddd∝Wdi−Wdj.(33) Here, the weight of an in-situ measurement at depth dis given by integrating the weighting function Wdfrom an upper depth, dito a lower depth, dj. For the uppermost measurement, di= 0 (the surface) and djwould be the half-way distance to the next measurement below that sensor. For the lowest measurement, dj= 1 (1 m depth). Since Wdhas an exponential form, the integration is trivial and simply the difference between the values of Wdat diand dj. 15.2 Horizontal averaging of profile values It is recommended to take sufficient in situ soil moisture samples such that the soil moisture in the CRNS footprint area is covered representatively, while the locations can be picked depending on local spatial heterogeneity and the resources available. The calibration samples need to be averaged using the horizontal weighting function Wraccording to [Schrön et al., 2017], section 4.5. For this, 18 Figure 2: Screenshot from the tool https://neptoon-tools.streamlit.app where a sampling scheme could be designed based on areas of equal contribution (color shades) depending on wetness conditions (slider) and on the desired number of annuli, e.g., 2 (blue), 3 (green), or 5 (brown). regions (annuli) of equal contribution (e.g., 5 annuli of 20% quantiles) to the neutron signal could be defined depending on the local conditions (i.e., atmospheric pressure, air humidity, average soil moisture) that influence the spatial sensitivity of the CRNS. All sampling points that fall within an annulus Aare arithmetically averaged and therefore receive the same weights, which are calculated according to the weighting scheme of [Schrön et al., 2017]. More specifically, Wris integrated throughout the domain to find the radii r1and r2that define the five annuli A(r1, r2)within which all samples are equally averaged: θcal =1 5 5 X A=1 θA,where θA=⟨θr⟩ ∀r∈(r1, r2)(34) with Zr2 r1 Wrdr=A 5Z∞ 0 Wrdr . (35) In particular, this method ensures that soil samples taken using the outdated COSMOS scheme (25, 75, 200) m, which assumed larger CRNS footprints, are not double weighted. Due to the long distances of this COSMOS sampling scheme, there may be no soil samples in one annulus. If this is the case (e.g., using historical soil sampling data), the samples in the next larger ring may receive double the weight. For instance, the soil samples taken at 25 m distance are also representative for the soil moisture in the first annulus around the sensor. For calibration campaigns, it is recommended to follow this approach, i.e., to find the distances ri that define the five annuli and to take an equal number of soil samples in each annulus around the sensor. To determine these annuli, online tools could be used as a guideline, such as https: //neptoon-tools.streamlit.app (see also Fig. 2). It is generally recommended that each land use class in the footprint should be equally represented, and that small irregular features should generally be avoided, such as tractor lines. 16 Conversion to snow water equivalent Conversion to snow products will be considered for future versions of this document. 19 17 Processed data requirements The minimum requirements for processed CRNS data should include the following columns: Variable Units Symbol Date and time UTC t Neutron counts cph N Corrected neutron counts cph N′ Corrected neutron uncertainty cph σN′ Air pressure hPa or mbar P Air absolute humidity g/m3h Volumetric soil moisture m3/m3θ Vol. soil moisture lower uncertainty m3/m3σ− θ Vol. soil moisture upper uncertainty m3/m3σ+ θ Vol. soil moisture symm. uncertainty m3/m3σθ Footprint radius m R86 Measurement depth m D86 Meta data should include the following parameters that are specific to the site, required to reprocess the data, and typically constant in time: Variable Units Symbol Original time resolution sec ∆t Latitude, Longitude decimal degree lat, lon Cutoff rigidity GV R Atmospheric depth g/cm2x Barometric coefficient mbar−1β Neutron monitor station name NM Reference air pressure hPa or mbar Pref Reference air humidity g/m3href Reference neutron monitor counts cps Mref Calibration date time UTC tcal Calibration wt. avg. soil moisture g/g θcal Calibration parameter cph N0 Calibration parameter cph Nmax Aggregation window hours ∆tagg Smoothing window hours w Soil (dry) bulk density g/cm3ϱb Soil porosity % Φ Lattice water g/g θlatt Organic water equivalent g/g θorg Dry aboveground biomass kg/m2B 20 References [Avery et al., 2016] Avery, W. 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