DE102017110994A1 - Method for the determination of snow parameters - Google Patents

Abstract

The invention relates to a method for determining snow parameters of a snow cover S arranged on a base G, comprising the phases that in an initialization phase (I) without snow cover S on the bottom G and at least one antenna (A1) of the at least two antennas (A1, A2) the relative position between the two antennas (A1, A2) of the at least two antennas (A1, A2) connected to the two receivers (E1, E2) by means of received microwave signals from navigation satellites from differential pseudo-orange measurements and carrier-phase measurements determines the relative position between the two antennas (A1, A2) and performs parallel reference measurements on signal strength; in at least one decision-making phase (D) it is decided whether it is wet or dry snow; in at least one measurement phase (M) at least one time at which a snow cover S covers the base G and the one antenna (A1) of the at least two antennas (A1, A2), the snow-related propagation delay in the zenith direction and the integer ambiguities of the determine double-differentiated carrier phase measurements using the relative position derived in the initialization phase (I), and perform parallel measurements of signal strength; At least one of the snow snow equivalent (SWE), snow height (HS) and snowfall (LWC) parameters of the snow cover S arranged on the bottom G is determined in at least one result determination phase (R).

Description

The invention relates to a method for determining snow parameters. In particular, the invention relates to a method for determining snow parameters using microwave signals from one or more global navigation satellite systems (GNSS).

Prior art with references

It is known that signals from navigation satellites in the L-band microwave range are transmitted at a frequency between 1 and 2 GHz and can be received by GNSS receivers. From the navigation satellite signals, GNSS receivers derive measurements for carrier phase, pseudorange, and signal strength.

The carrier phase measurement includes the phase position of the receiver's measured sinusoidal carrier signal, which depends on the distance between satellite and receiver, atmospheric delays and clock errors in navigation satellites and receivers. This carrier phase measurement is continuously determined in the receiver with a control loop (Phase Locked Loop, PLL), which minimizes the deviation between measured and receiver-generated phase position.

The pseudo-orange measurement represents an estimate of the distance between satellite and receiver. This pseudo orange is determined from the transit time of the signal between satellite and receiver with another loop (Delay Locked Loop, DLL). The carrier-phase and pseudo-orange measurements are the inputs of real-time kinematic positioning (RTK) [1, 2].

The signal strength measurement is expressed as the ratio between the received signal power and the carrier-to-noise power density ratio (C / N ₀ ). This is also determined in the control loops by integration / accumulation of the received signal strength. The signal strength measurement is reduced by the liquid water content of the snow, since in the microwave range, the dielectric properties between air and water differ significantly.

By processing GNSS raw data, such as pseudorange and carrier phase measurements, using RTK positioning algorithms, the position of a GNSS antenna, even with low-cost single-frequency GNSS receivers, can be precisely determined in the millimeter to centimeter range [3 -6]. This allows accurate relative run-time determination between such GNSS receivers and a set of global navigation satellites. The quality depends on the availability and elevation of the navigation satellites within the visible range of the GNSS receiver. This applies to various local and global systems of navigation satellites (e.g., GPS, GLONASS, Galileo, BeiDou, QZSS, GAGAN) and their combination [7, 8].

It is further known that the propagation velocity of electromagnetic microwave signals in the snow (in the dry state in proportions of ice crystals and air, in the wet state additionally consisting of water) and also in most other naturally occurring media is smaller than in the air or in a vacuum. Both the attenuation of the signals as well as their reflection and refraction as well as the change in the signal propagation speed depend on the dielectric properties of the snow as well as the density and moisture content of the respective snowpack [9-11]. Snow parameters can thus be determined by the interaction of electrical microwave signals with a medium such as snow.

In the context of the method according to the invention, the term "snow parameter" includes at least the snow water equivalent (SWE) of a snow cover which describes the total water stored in liquid and solid form in the snowpack, the snow depth ("SWE"). height of snow "; HS) of a snow cover in the vertical direction and the snow light (proportion of liquid water in the snow cover," LWC ") of a snowpack in the vertical direction. The term snow cover refers to the local expression of the presence of snow in one place. The snow parameters determined by the method are assumed to be homogeneous for the area in the snowpack, which is penetrated by all navigation satellite signals.

Schmid et al. [12] describe the propagation delay of L-band microwave signals in snow, measured with an upward-looking ground radar at 1.6 GHz. In this method, in the presence of a snow cover over the ground, from a radar installed in the ground but facing towards the sky, L-band signals are emitted into the snowpack and markedly reflected at the interface between snow surface and atmosphere. The antennas of this radar record the two-way runtime of the signals through the snowpack. On the basis of an assumption of the snow density (SD) (quotient of the mass and volume of the snow cover) and the application of dielectric snow models, could under dry snow conditions the snow depth (HS) are derived [12]. If the snow density (SD) is known, the snow snow equivalent (SWE) can be determined together with the calculated snow depth (HS), as the quotient of snow depth (HS) and snow density (SD) [12]. The snow density (SD) can either be measured, modeled [12] or estimated according to [13] and / or [14]. Overall, however, deviations in the density determination have only minor effects [15].

In wet snow, the calculation of snow parameters is more complex, because in addition to the propagation delay, the signal attenuation due to the presence of liquid water has to be taken into account [10]. Koch et al. [15] using GPS signal strength data for the first time, continuously monitored snow snow cover (LWC) throughout the spring snowmelt periods mathematically and physically using a non-destructive method together with dielectric snowmaking models [11], externally measured snow depth data, and an assumption derived from the snow density (HS). To determine signal strength attenuation, at least one GPS antenna was placed on the ground under the snow cover [15, 16]. In combination with measurements of the propagation delay in snow, measured with an L-band ground radar, the snow depth (HS) and the snow water equivalent (SWE) could be determined for both dry and wet snow [16]. The combination of GNSS sensors with ground radars, however, leads to an overall high cost due to the higher cost of radar equipment. In addition, the latter have a high power consumption and are expensive to install. Thus, this approach is unsuitable for large, dense sensor networks and their operation in remote locations. In contrast, the GNSS sensors used are available at low cost; their chips are e.g. also installed in smartphones as components. GNSS sensors are capable of accepting the receiver function in low-cost, reliable, independent-of-energy, high-bandwidth systems for determining snow parameters.

Furthermore, it is known that in particular expensive, geodesic multi-frequency GNSS receivers (consisting of a high-quality clock quartz and a synchronous processing of signals at different frequencies) and antennas (with multipath suppression) have been tested for the detection of snow parameters, the snow depth (HS) was determined reflectometrically. In this procedure, at least one GNSS antenna is located above the snowpack to receive both the direct and snow-surface reflected GNSS signals (eg [16-18]). Depending on how much snow lies, the reflected signals change, from which the snow depth can be derived. However, this technique can not determine the liquid water content and the snow water equivalent (SWE) only indirectly [19]. In addition, these high-end GNSS receivers are very expensive compared to the low-cost products and therefore not suitable for rebuilding sensor networks, eg in alpine and remote regions. In addition, wide, free and flat areas of about 1000 m ^{2 are} required for the GNSS reflectometry technique [19, 20], which is scarcely to be found in alpine space, for example.

Furthermore, other mechanical, acoustic, optical but also electronic measuring techniques for determining individual snow parameters are known. However, these are not able to measure several snow parameters in parallel with a simple measuring principle and a simple device.

• [1] N. C. Talbot, Centimeters in the Field, A users Perspective of Real-Time Kinematic Positioning in a Production Environment, Proc. of the 6th Int. Techn. Meet. of the Satellite Div. of the Inst. of Navigation (ION GPS), Salt Lake City, UT, USA, 1049–1057, 1993 .
• [2] T. Takasu and A. Yasuda, Development of the low-cost RTK-GPS receiver with an open source program package RTKLIB, Proc. of Int. Symp. on GPS/GNSS., Jeju, Korea, 2009 .
• [3] P. Henkel, Tightly coupled precise point positioning and attitude determination, IEEE Transactions on Aerospace and Electronic Systems, 51(4), 3182–3197, 2015 .
• [4] P. Henkel, and C. Günther, Partial integer decorrelation: optimum trade-off between variance reduction and bias amplification, Journal of Geodesy, 84(1), 51–63, 2010 .
• [5] P. Henkel, M. Iafrancesco and A. Sperl, Precise Point Positioning with Multipath Estimation, Proc. of ION/ IEEE Position, Location and Navigation Symp. (PLANS), Savannah, GA, USA, 6 pp., 2016 .
• [6] P. Henkel, and J. Cárdenas, Method for Determining a Baseline between two Receivers, patent appl. No.: EP 12 199 772.0 , appl. date: 28.12.2012; European publication No. EP2749900 (A1) , publication date: 02.07.2014.
• [7] P. Henkel, U. Mittmann and M. Iafrancesco, Real-Time Kinematic Positioning with GPS and GLONASS, Proc. of 24-th Europ. Signal Proc. Conf. (EUSIPCO), Budapest, Hungary, 5 pp., 2016 .
• [8] N. Kubo, F. Wu, and A. Yasuda, Integral GPS and QZSS Ambiguity Resolution, Transactions Jap. Soc. Aero. Space Sci., Vol. 47, No. 155, 38–43, 2004 .
• [9] F. T., Ulaby, D. G. Long, W. J. Blackwell, C. Elachi, A. K. Fung, C. Ruf, K. Sarabandi, H. A. Zebker, and J. Van Zyl, Microwave radar and radiometric remote sensing, 2014 .
• [10] J. H. Bradford, J. T. Harper, and J. Brown, Complex dielectric permittivity measurements from ground-penetrating radar data to estimate snow liquid water content in the pendular regime, Water Resources Research, 45, W08403, 2009 .
• [11] M. E. Tiuri, A. H. Sihvola, E. G. Nyfors, and M. T. Hallikainen, The complex dielectric constant of snow at microwave frequencies, IEEE Journal of Oceanic Engineering, 9(5), 377–382, 1984 .
• [12] L. Schmid, A. Heilig, C. Mitterer, J. Schweizer, H. Maurer, R. Okorn and O. Eisen, Continuous snowpack monitoring using upward-looking ground-penetrating radar technology, Journal of Glaciology, 60, 221, 509–525, 2014 .
• [13] V., B. Meløysund, Leira, K. V. Høiseth, and K. R. Lisø, Predicting snow density using meteorological data, Meteorological Applications, 14(4), 413–423, 2007 .
• [14] T. C. Jonas, Marty, and J. Magnusson (2009), Estimating the snow water equivalent from snow depth measurements in the Swiss Alps, Journal of Hydrology, 378(1), 161–167 .
• [15] F. Koch, M. Prasch, L. Schmid, J. Schweizer, and W. Mauser, Measuring snow liquid water content with low-cost GPS receivers, Sensors, 14(11), 20975–20999, 2014 .
• [16] L. Schmid, F. Koch, A. Heilig, M. Prasch, O. Eisen, W. Mauser and J. Schweizer, A novel sensor combination (upGPR-GPS) to continuously and nondestructively derive snow cover properties, Geophysical Research Letters, 42(9), 3397–3405 2015 .
• [17] K. M. Larson, E. Gutmann, V. Zavorotny, J. Braun, M. Williams and F. Nievinski, Can we measure snow depth with GPS receivers? Geophysical Research Letters, 36(17), L17502, 2009 .
• [18] S. Jin, N. Najibi, Sensing snow height and surface temperature variations in Greenland from GPS reflected signals, Advances in Space Research, 53(11), 1623–1633, 2014 .
• [19] N. Rodriguez-Alvarenz, E. Valencia, X. Bosch-Lluis, A Camps, I. Ramos-Perez, H. Park, and M. Vall-Llossera, Snow thickness monitoring using GNSS measurements, Geoscience and Remote Sensing Letters, IEEE, 9(6), 1109–1113, 2012 .
• [20] J. L. McCreight, E. E. Small, and K. M. Larson, Snow depth, density, and SWE estimates derived from GPS reflection data: Validation in the western US, Water Resources Research, 50(8), 6892–6909, 2014 .
• [21] K. M. Larson, GPS interferometric reflectometry: applications to surface soil moisture, snow depth, and vegetation water content in the western United States, Wiley Interdisciplinary Reviews: Water, 3(6), 775–787, 2016 .

The above statements refer to the following state of the art:

• [1] NC Talbot, Centimeters in the Field, A users Perspective of Real-Time Kinematic Positioning in a Production Environment, Proc. of the 6th Int. Techn. Meet. of the Satellite Div. of the Inst. of Navigation (ION GPS), Salt Lake City, UT, USA, 1049-1057, 1993 ,
• [2] T. Takasu and A. Yasuda, Development of the low-cost RTK-GPS receiver with an open source program package RTKLIB, Proc. of Int. Symp. On GPS / GNSS., Jeju, Korea, 2009 ,
• [3] P. Henkel, Tightly coupled precise point positioning and attitude determination, IEEE Transactions on Aerospace and Electronic Systems, 51 (4), 3182-3197, 2015 ,
• [4] P. Henkel, and C. Günther, Partial integer decorrelation: optimum trade-off between variance reduction and bias amplification, Journal of Geodesy, 84 (1), 51-63, 2010 ,
• [5] P. Henkel, M. Iafrancesco and A. Sperl, Precise Point Positioning with Multipath Estimation, Proc. of ION / IEEE Position, Location and Navigation Symposium (PLANS), Savannah, GA, USA, 6 pp., 2016 ,
• [6] P. Henkel, and J. Cárdenas, Method for Determining a Baseline between Two Receivers, patent appl. No .: EP 12 199 772.0 , appl. date: 28.12.2012; European publication no. EP2749900 (A1) , publication date: 02.07.2014.
• [7] P. Henkel, U. Mittmann and M. Iafrancesco, Real-Time Kinematic Positioning with GPS and GLONASS, Proc. of 24-th Europ. Signal Proc. Conf. (EUSIPCO), Budapest, Hungary, 5 pp., 2016 ,
• [8th] N. Kubo, F. Wu, and A. Yasuda, Integral GPS and QZSS Ambiguity Resolution, Transactions Jap. Soc. Aero. Space Sci., Vol. 47, no. 155, 38-43, 2004 ,
• [9] FT, Ulaby, DG Long, WJ Blackwell, C. Elachi, AK Fung, C. Ruf, K. Sarabandi, HA Zebker, and J. Van Zyl, Microwave radar and radiometric remote sensing, 2014 ,
• [10] JH Bradford, JT Harper, and J. Brown, Complex dielectric permittivity measurements from ground-penetrating radar data to estimate snow liquid water content in the pendular regime, Water Resources Research, 45, W08403, 2009 ,
• [11] ME Tiuri, AH Sihvola, EG Nyfors, and MT Hallikainen, The complex dielectric constant of snow at microwave frequencies, IEEE Journal of Oceanic Engineering, 9 (5), 377-382, 1984 ,
• [12] L. Schmid, A. Heilig, C. Mitterer, J. Schweizer, H. Maurer, R. Okorn and O. Eisen, Continuous snowpack monitoring using upward-looking ground-penetrating radar technology, Journal of Glaciology, 60, 221, 509 -525, 2014 ,
• [13] V., B. Meløysund, Leira, KV Høiseth, and KR Lisø, Predicting snow density using meteorological data, Meteorological Applications, 14 (4), 413-423, 2007 ,
• [14] TC Jonas, Marty, and J. Magnusson (2009), Estimating the snow water equivalent from snow depth measurements in the Swiss Alps, Journal of Hydrology, 378 (1), 161-167 ,
• [15] F. Koch, M. Prasch, L. Schmid, J. Schweizer, and W. Mauser, Measuring snow liquid water content with low cost GPS receivers, Sensors, 14 (11), 20975-20999, 2014 ,
• [16] Schmid, F. Koch, A. Heilig, M. Prasch, O. Eisen, W. Mauser and J. Schweizer, A novel sensor combination (upGPR-GPS) to continuously and nondestructively derive snow cover properties, Geophysical Research Letters, 42 (9), 3397-3405 2015 ,
• [17] KM Larson, E. Gutmann, V. Zavorotny, J. Braun, M. Williams and F. Nievinski, Can we measure snow depth with GPS receivers? Geophysical Research Letters, 36 (17), L17502, 2009 ,
• [18] S. Jin, N. Najibi, Sensing snow height and surface temperature variations in Greenland from GPS reflected signals, Advances in Space Research, 53 (11), 1623-1633, 2014 ,
• [19] N. Rodriguez-Alvarenz, E. Valencia, X. Bosch-Lluis, A Camps, I. Ramos-Perez, H. Park, and M. Vall-Llossera, Snow thickness monitoring using GNSS measurements, Geoscience and Remote Sensing Letters, IEEE , 9 (6), 1109-1113, 2012 ,
• [20] JL McCreight, EE Small, and KM Larson, Snow depth, density, and SWE estimates derived from GPS reflection data: Validation in the western US, Water Resources Research, 50 (8), 6892-6909, 2014 ,
• [21] KM Larson, GPS interferometric reflectometry: applications to surface soil moisture, snow depth, and vegetation water content in the western United States, Wiley Interdisciplinary Reviews: Water, 3 (6), 775-787, 2016 ,

Task and objective

In view of the above-described disadvantages of the prior art, it was an object of the present invention to provide a new method for determining the snow parameters snow water equivalent (SWE), snow depth (HS) and snow (LWC).

In particular, it was an object of the present invention to provide a method for the determination of snow parameters snow water equivalent (SWE), snow depth (HS) and snow (LWC), which can work with easily available, inexpensive equipment and free accessible raw data, ideally via an existing communication Network can be generated and also transmitted to the receiver.

It was another object of the present invention to provide a method for determining the snow parameters snow water equivalent (SWE), snow depth (HS) and snow (LWC) which can also be implemented in remote regions, especially in regions without external power supply by using a corresponding device And still leads to reliable, quickly accessible results.

An apparatus for determining snow parameters that can be used for the method according to the present invention is described in a co-pending patent application of the present inventors entitled "Apparatus for Determining Snow Parameters".

the solution of the problem

The above-mentioned and other objects of the invention to be solved, ie to determine the sought snow parameters, is possible with a mathematical and physical derivation of quantities from the raw data received over a period of GNSS signals.

As already stated in the prior art, microwave signals in the snow, among other things, experience refraction, attenuation and propagation delays. In general, for calculating snow parameters, the microwave signals influenced by the dielectric properties of a snow cover can be used In the case of GNSS signals, these are carrier phase, pseudo orange and signal strength measurements.

The GNSS signal propagation in the microwave range is determined by the dielectric properties of a medium and thus differs between air and snow. The propagation velocity is reduced due to the snow, so that the carrier phase and pseudo-orange measurements are effectively decelerated. The dielectric properties of snow or the reduction of the propagation velocity with respect to the speed of light in vacuum depend on the moisture content and the density of the snowpack [10, 11]. In addition, the GNSS signals are refracted when entering the snow surface, whereby the strength of the refraction also depends on the moisture content of the snow cover. From these physical fundamentals, the above-described snow parameters can be derived from information of propagation delays and signal strengths of microwave signals using mathematical and physical equations [10, 12, 15, 16].

The determination of snow parameters, however, has never before been developed solely on the basis of the link between the GNSS carrier phases and the GNSS signal strength measurements (raw data). The reason for this is that prior to the application of the present invention, the propagation delay of GNSS signals in a snowpack has never been developed based on GNSS carrier phase data. The present invention therefore relates to a method of measuring snow parameters according to claim 1. Preferred embodiments of the present invention are claimed in the dependent claims 2 to 15.

A corresponding apparatus for measuring navigation satellite microwave signals (GNSS) is described and claimed in a co-pending patent application of the inventors of the present method of invention entitled "Apparatus for Determining Snow Parameters". However, the method of the invention is not limited to this device.

Advantages of the solution

The advantages achieved by the invention are that on the one hand, the snow parameters can be determined precisely with only two antennas A1, A2, which are connected to navigation signal receivers E1, E2. A further advantage is that the three snow parameters snow water equivalent, snow depth and snow light can all be determined with the same device, which was not possible before.

The apparatus for determining snow parameters which may be used for the method according to the present invention is described and claimed in a co-pending patent application of the present inventors entitled "Apparatus for Determining Snow Parameters". However, the method of the invention is not limited to this device.

Another advantage of the method according to the invention is that it is a non-destructive measuring method: the snow cover is not influenced by the measurement. In addition, freely available navigation satellite signals are usefully used in addition to their actually specific task of positioning and navigation. Consequently, it is a cost effective method. Since the navigation satellites are available worldwide and constantly, snow parameters can be continuously measured almost at any point on earth.

The invention will be described below with reference to the three 1 to 3 explained in more detail. The explanation, and in particular the reference to the figures are only illustrative and exemplary description of the invention, without the invention being limited thereto.

In the figures show:

1 a schematic illustration of the spatial arrangement of the two GNSS antennas under (A1) and over (A2) a snow cover S on the bottom G, as it can be used as an example for the determination of snow parameters. The direct distance B between the antennas is conventionally referred to as the 'baseline' (B). 1 also shows and the height H of the antenna A2 of the at least two antennas A1, A2 above the snow cover S above the ground G and the horizontal distance E of the two antennas A1 and A2 of the at least two antennas A1, A2 from each other, viewed parallel to the bottom G; and

2 a flow chart for the procedure for the determination of Snow Snow equivalent (SWE), Snow height (HS) and Snow (LWC) snow parameters under dry (DS) (solid lines) and wet (WS) (dashed lines) snow conditions. The method is subdivided into an initialization phase (I), a decision phase (D), a measurement phase (M) with several steps of the processing and a result determination phase (R); and

3 For example, the carrier phase residuals in no snow or dry snow conditions for different snow water equivalent values (SWE values) for a period of each a day. Here, a) includes a SWE value of 0 cm, ie no snow, b) an SWE value of 200 mm, c) a SWE value of 400 mm and d) a SWE value of 600 mm. The absolute value ranges of the carrier phase residuals r are proportional to the snow water equivalent (SWE).

Detailed explanation of the claims / technical description of the invention

The present invention relates to a method for determining snow parameters of a snow cover S arranged on a base G. The term "snow parameters" in the context of the present description and in the patent claims particularly (but without limitation for the method according to the invention) the parameters snow water equivalent (SWE ) snow cover S, snow depth (HS) of a snow cover S and snow light (LWC) a snow cover S understood.

The method according to the invention for the determination of snow parameters is carried out in particular (but without limiting the method according to the invention) by means of a device which may comprise: at least two receivers E1, E2 of microwave signals from navigation satellites and at least two antennas A1, A2, which coincide with the at least two receivers E1, E2 are connected.

The device useful in the method of the invention is described and claimed in detail in the co-pending patent application of the inventors entitled "Apparatus for Determining Snow Parameters," which is incorporated by reference into the present application with its full disclosure. In this case, an antenna A1 of the at least two antennas A1, A2 is fixed on a base G under a snow cover S and another antenna A2 of the at least two antennas A1, A2 is fixed at a predetermined height H above the snow cover S in such a way that the two antennas A1, A2 of the at least two antennas A1, A2 parallel to the base G have a defined distance E and perpendicular to the bottom G have a defined distance H (see 1 ).

The method according to the invention for determining snow parameters comprises four phases, which are carried out at at least one point in time (see 2 ):
The first phase comprises an initialization or calibration phase (I), in which the relative positions (Ia) between the antennas (A1, A2) of the at least two antennas (A1, A2) are determined and reference measurements for the signal strength (Ib) are performed :
The antennas (A1, A2) receive microwave signals from navigation satellites (GNSS) and the connected receivers (E1, E2) determine pseudorange and carrier phase measurements from these microwave signals. The pseudorange and carrier phase measurements from the receiver E1 are subtracted from the corresponding measurements at the receiver E2 to produce differential pseudorange and carrier phase measurements. The differential pseudo-orange and carrier-phase measurements are linearly dependent on the relative position between the two antennas, so that the relative position can be determined by linear compensation calculation. When using the differential carrier phase measurements in addition to the relative position in addition, the ambiguities of the differential carrier phase measurements must be determined. Optionally, using the differential pseudo-orange measurements, the differential multipath errors of the differential pseudo-orange measurements can also be estimated to increase accuracy. The reference measurements for signal strength are carried out analogously to [15, 16] (Ib).

In a second phase, which corresponds to a decision phase (D), it is decided whether there is a snowpack S on the ground G or does not exist. This decision is made on the basis of the differential carrier phase measurements, which are influenced by the snowpack S. The differential carrier phase measurements are also affected by the relative position between both antennas, which has already been determined in the initialization phase and can thus be corrected.

In the decision phase it is also decided if the snow is wet or dry (Db). For this purpose one or more a priori known signal strength thresholds are used, e.g. <-3dB after [15].

In a subsequent third phase, which comprises at least one measurement phase M, but which can also comprise several measurement phases M immediately after one another or at arbitrary intervals, one determines at least one time point at which a snowpack S the ground G and the one antenna A1 at least two antennas (A1, A2) covered, the snow-related propagation delay in the zenith direction. For this purpose, differential carrier phase measurements are used, which are linearly dependent on the snow-related propagation delay. Thus, the snow-related propagation delay can be derived by linear compensation calculation from the differential carrier phase measurements. Since the differential carrier phase measurements are ambiguous and the differential ambiguities take on new values each time the receivers turn off and on, they must also be determined with. The measurement phase M therefore requires a determination of the snow-related propagation delay in the zenith direction as well as the ambiguities of the differential carrier phase measurements. The differential carrier phase measurements are also linearly dependent on the differential ambiguities so that a linear compensation calculation satisfies. However, the integerity of the ambiguities should be taken into account in order to achieve the highest possible accuracy.

The individual sub-steps for deriving the snow-related propagation delay are described in detail below (preferred embodiments). In dry snow, these are the sub-steps Ma1 to Ma11; in wet snow, sub-steps Mb1 and Mb2 are additionally required.

In a subsequent fourth phase, the snow-related propagation delay transmitted in the at least one measurement phase M at the two antennas A1, A2 of the at least two antennas A1, A2 and transmitted to the connected receivers E1, E2 is additionally processed in the zenith direction and in the case of wet snow the signal strength measurement, which has been normalized to the reference measurement, which was carried out in the initialization phase I. The snow water equivalent (SWE) is determined as the result. The snow depth (HS) can be additionally calculated by adding a snow density information according to the previous version. In wet snow, the snow light (LWC) is additionally derived as a result of the decision determination phase R.

The carrier phase measurements are determined on two GNSS receivers (E1, E2), with one GNSS antenna (A1, A2) on one pole above the snow and another receiver on the bottom. The carrier phase measurements from both receivers (E1, E2) are subtracted to eliminate navigation satellite clock errors and atmospheric delays. The differential measurements thus obtained are referred to as "differential carrier phase measurements".

The snow parameters are derived from the differential carrier phase measurements which, depending on the elevation and the number of navigation satellites, can be measured with a precision of one millimeter to centimeter accuracy.

Since the carrier signals are sinusoidal and thus periodic, the carrier phase measurements are ambiguous. The ambiguities of the carrier phase measurements are integer with respect to the wavelength. Therefore, not only the snow parameters but also the integer ambiguities of the differential carrier phase measurements have to be determined.

These differential carrier phase measurements are strongly influenced by the clock errors of the two low-cost receivers. This influence can be eliminated by the selection of a reference navigation satellite and the difference between the differential carrier phase measurement of this reference navigation satellite and the differential carrier phase measurements of the other satellites. The reference navigation satellite is selected so that the elevation, signal strength and visibility are as large as possible. The thus obtained twice differentiated measurements are referred to below as double difference measurements.

• – relative Position zwischen beiden GNSS-Antennen
• – Medium zwischen beiden GNSS-Antennen (Luft, Schnee)
• – ganzzahlige Mehrdeutigkeiten der Doppeldifferenzmessungen der Trägerphasen-Messungen

The double difference measurements are influenced by the following physical quantities:

• - relative position between both GNSS antennas
• - Medium between two GNSS antennas (air, snow)
• Integer ambiguities of the double difference measurements of the carrier phase measurements

• – Änderung der Schneeeigenschaften (signifikant im Zeitraum von Stunden oder länger)
• – Änderung der Navigationssatelliten-Elevationen (signifikant im Zeitraum von Minuten oder länger)
• – Messrauschen (stets vorhanden)
• – Unzureichende Synchronisierung der GNSS-Empfänger (signifikant im Zeitraum von Mikro-Sekunden oder länger)

The double difference measurements are temporally variable, with several reasons with different variability:

• - change of snow characteristics (significant in the period of hours or longer)
• - Change of navigation satellite elevations (significant in the period of minutes or longer)
• - measurement noise (always present)
• - Insufficient synchronization of the GNSS receivers (significant in the period of micro-seconds or longer)

In further preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention without limiting the invention thereto, snow parameters of the snow cover are determined as the result of the result determination phase (R) S is the snow water equivalent (SWE), which describes the total water stored in the snowpack in liquid and solid form, the snow depth (HS), which describes the height of the snowpack in the vertical direction to the ground G, and the snow light (LWC) , which describes the percentage of liquid water in the snowpack are.

In further preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention, without limiting the invention thereto, in the case of dry snow (DS), the snow water equivalent (SWE) and snow depth (HS) and where, in the case of wet snow (WS), the snowfall (LWC) is also determined.

In the case of dry snow, the snow runtime delay, as determined from the GNSS pseudorange and carrier phase measurements in the zenith direction, is compared to the assumed velocity of L-band microwave signals in dry snow, e.g. from [16] multiplied to obtain the snow water equivalent (SWE). With the addition of optional snow density information (eg from [13, 14]), snow depth (HS), snow snow equivalent (SWE) and snow density (SD) can be determined together with the calculated snow water equivalent (SWE) [12 ].

In wet snow (WS) the calculation is more complex, since in addition to the propagation delay in the zenith direction, derived from the GNSS pseudorange and carrier phase measurements, the signal attenuation [10, 16], expressed as a reduction of the C / N ₀ [15 ], by the occurrence of liquid water must be considered. In other preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention without limiting the invention thereto, one passes as a result of the result determination phase (R) under wet snow conditions WS together the snow parameters snow snow equivalent (SWE), snow height (HS) and snowfall (LWC) together from the previously determined snow-related propagation delay and the normalized to the reference measurement signal strength measurements with the optional addition of the snow density, after which in the initialization phase (I) parallel to Determining the relative position (Ia) of the two antennas (A1, A2) of the at least two antennas (A1, A2) a normalized reference (Ib) of the signal strength detected without snow cover (S) on the bottom (G). In the measuring phase (M) parallel to the processing of the pseudo orange and carrier phase measurements under snow conditions (Ma1 Ma11) also processed the signal strength under snow conditions, which determines dampening under wet snow conditions by the occurrence of liquid water in the snow cover S. From a significant GNSS signal strength reduction (<-3dB, [15]), measured on the GNSS antenna on the ground G, which is in the case of a snowpack S under the snow cover S, the snow is defined as wet. On the basis of the snow depth information and the signal strength measurement, the liquid water content (LWC) can also be calculated according to [15, 16] using dielectric snow pattern models (eg [11]). The signal strength under snow conditions for each measured time step is related to the normalized reference (Mb1) [15, 16]. The normalized signal strength optionally linked to the dielectric properties of the snow, optionally using the assumption of a dry snow density and the propagation delay (from Ma11) (Mb2) (eg according to [16]).

In further preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention without limiting the invention thereto, in the initialization phase (I) the relative positions of the Antennas (A1, A2) of the at least two antennas (A1, A2), the ambiguities of the differential carrier phase measurements and optionally the differential Mehrwegefehler together from the differential pseudorange and carrier phase measurements by linear compensation calculation (Ia).

The determination of the snow parameters from double-differentiated carrier-phase measurements sets a general knowledge (accuracy in the range of several meters) of the absolute position (for efficient calculation of the navigation satellite elevations) and a highly accurate knowledge of the relative position between the antennas A1 and A2 of the at least two antennas (to correct the double-differentiated carrier-phase measurements). These positional data are determined in the initialization phase, i. at a time when there is no snow cover over the GNSS antenna A1 at the bottom.

The three-dimensional relative position (baseline B) between the antennas A1 and A2 of the at least two antennas is determined from the double-differentiated pseudorange and carrier phase measurements using any RTK method [1, 2, 7]. A central point of any RTK method is the exploitation of the integerity of the ambiguities of the differential carrier phase measurements. For low-cost GNSS receivers and GNSS antennas, the additional estimation of the pseudorange multipath errors in an extended RTK method is recommended. For more details on RTK positioning, see [3-6].

In further preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention without limiting the invention thereto, the elevation of the navigation satellites is determined in the measurement phase (M) at the position of at least one of the antennas (A1, A2), and also the directional vectors between navigation satellites and at least one antenna (A1, A2) from the positions of Navigation satellites and the positions of at least one antenna (A1, A2) (Ma1), and selects a satellite with the highest possible elevation, signal strength and long visibility as a reference satellite (Ma2).

In further preferred embodiments of the method according to the invention, which can be implemented together with a feature of the invention or with several features of the invention or with all features of the invention without limiting the invention thereto, one additionally determines a synchronization correction (Ma3) for each differential carrier phase -Measurement.

Since the clocks in low-cost receivers are not synchronized and drift relatively strongly, a synchronization correction is required for the double-differentiated measurements. This synchronization correction is derived from the movement of the navigation satellites within the time of the relative receiver clock error.

In further preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention without limiting the invention thereto, in the measurement phase (M) double-differentiated carrier phases are formed Measurements by subtracting the differential carrier phase measurements of the reference navigation satellite from the differential carrier phase measurements of all other navigation satellites; and, if necessary, additionally subtracting the synchronization correction and the double-differentiated distances between satellite and receiver, which are determined from the direction vectors between satellite and receiver and the relative position between the antennas (A1, A2) (Ma5); and possibly additionally correcting jumps in the double difference carrier phase measurements (Ma6); and optionally additionally determining for each time step of a measurement the subset of the navigation satellites (Ma7) available, ascending and descending in the field of view of the antennas.

To determine the snow parameters, the doubly differentiated measurements must first be corrected by some non-snow specific parameters: These include the synchronization correction and a geometry term. The latter includes the double-differentiated distances between satellite and receiver. Since the distance between satellite and receiver is large compared to the distance between the two receivers, the direction vector between satellite and receiver may be assumed to be parallel for both receivers. Thus, the double-differentiated distance can be represented as a projection of the relative position between both GNSS antennas.

In further preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention, without limiting the invention to it, one estimates in the measurement phase (M) initial (Ma8) the integer double-differentiated ambiguities of the double-differentiated carrier-phase measurements and the snow-related time delay in the zenith direction from a time series of double-differentiated carrier phase measurements by linear compensation calculation, wherein the projection of the snow-related propagation delay from the direction of incidence to the zenith direction used by the known elevations of the navigation satellites.

The corrected double-differentiated carrier phase measurements are dependent on the differential propagation delay in the snow and the double-differentiated ambiguities of the carrier phase measurements. The propagation delay in the snow, in turn, depends on the elevation of the navigation satellites and the snow depth. Since the elevation of the navigation satellites can be assumed to be known a priori, the propagation delays of the double-differential carrier phase measurements of all navigation satellites can be represented as a function of a single (i.e., scalar) propagation delay in the zenith direction. Thus, K ambiguities and 1 propagation delay in the zenith direction have to be determined from the K double-differentiated carrier-phase measurements. Since the number of unknowns exceeds the number of measurements by one, measurements of several times are required. The separability between the temporally constant carrier phase ambiguities and the snow-related propagation delays is made possible by the change in satellite geometry. The duration of an overflight of a navigation satellite is usually up to 6 hours, so that the satellite geometry changes only slowly and measurements of a longer period of several hours are required.

The integerity of the ambiguities is initially neglected, ie, a real-valued estimate of the ambiguities and snow parameters is derived from the double-differential carrier phase measurements. For this purpose, a linear compensation calculation is applied, which minimizes the quadratic deviation between measured and calculated double-differentiated measurements. The conditioning of the equation system can be done by using a rough a priori Information of the propagation delay in the snow can be significantly improved. This can be derived, for example, from the snow parameters of the previous day. In a second step, the real-valued estimates of the ambiguities are mapped to integer values. For this, a simple rounding, a sequential rounding or a systematic search can be used. The real-valued ambiguity estimates are highly correlated so that sequential rounding and systematic searching yield better results than simple rounding. The reliability of the ambiguity information can be significantly increased by the integration of a priori information about the snow-related propagation delay in the zenith direction in the ambiguity search. For this, only that ambiguity solution is used that leads to consistent snow parameters.

In further preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention, without limiting the invention to this, it is additionally determined in the measuring phase (M) (Ma9) the integer double-differentiated ambiguities of the carrier-phase measurements of the new-rising navigation satellites from the difference rounded to the nearest integer between the double-differentiated carrier-phase measurements and the double-differentiated calculated carrier-phase measurements, the double-differentiated calculated carrier-phase Measurements from the product between the projection of the snow-related propagation delay from the direction of incidence to the zenith direction can be determined by means of the known elevations of the navigation satellites and the snow-related propagation delay in the zenith direction.

The satellite geometry changes continuously due to the Earth's rotation and the orbiting navigation satellites, so that within a measurement cycle individual navigation satellites above the horizon or local surveys rise or fall. The former requires an initialization of the ambiguities of the newly-emerging navigation satellites. The ambiguities are determined by linear compensation calculation based on the elevation of the newly-rising navigation satellites and the zenith-time propagation delay known from the other navigation satellites.

In further preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention, without restricting the invention to this, in the measuring phase (M) residuals of the double differentiating carrier phase measurements by subtracting the double-differentiated carrier phase ambiguities from the double-differentiated carrier phase measurements, and determining the snow-related propagation delay in the zenith direction by linear compensation calculation from the residues of the double-differentiated carrier phase measurements Projection of the snow-related propagation delay from the direction of incidence to the zenith direction by means of the known elevations of the navigation satellites forms and uses (Ma10).

Once the ambiguities are fixed to integer values, they are subtracted from the corrected double-differentiated carrier phase measurements. The residuals of the fixed double-differentiated carrier-phase measurements thus obtained depend only on the snow-related propagation delay in the zenith direction. This propagation delay in the zenith direction is determined by linear compensation calculation from the residuals of the fixed and corrected double-differentiated carrier phase measurements. The residuals are directly proportional to the snow water equivalent (SWE). The snow water equivalent (SWE) can therefore be determined from the residuals of all navigation satellites by means of linear compensation calculation on the basis of the signal propagation speed and the known satellite geometry.

In 3 this is exemplified for continuous GNSS measurements on four days, where the SWE values are between 0 and 600 mm. This also reflects the previously described variability of the double-differentiated carrier phase measurements, in particular with regard to the influence of the snow. The arch-like courses of the residuals are due to the changes in the elevations of the navigation satellites, which lead to different maturities in the snow.

In further preferred embodiments of the method according to the invention, which may be implemented together with a feature of the invention or with several features of the invention or with all features of the invention without limiting the invention thereto, the double-differentiated ambiguities are checked and, if necessary, corrected as soon as the invention Elevation of a navigation satellite near the elevation of the reference navigation satellite is determined by means of the double-differentiated carrier-phase measurements rounded to the wavelength and then rounded to the nearest whole number (Ma11).

A correct estimation of the ambiguities is a prerequisite for a precise determination of the snow parameters. Therefore, a Plausibility check for the ambiguity estimate. This checks the residuals of the fixed double-differentiated carrier phase measurements as soon as the elevation of a navigation satellite is close to the elevation of the reference navigation satellite. At this time, the snow related propagation delays for the selected navigation satellite correspond to the propagation delay of the reference navigation satellite such that the differential snow related propagation delay is close to zero and thus the residuals of the fixed dual-differential carrier phase measurements would also have to be close to zero. If not, the ambiguity estimate is adjusted accordingly.

In further preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention without limiting the invention thereto, the accuracy of the particular snow-related propagation delay in the zenith direction is increased by averaging or filtering the particular snow-related propagation delay over time. The filtering may be, for example, a simple averaging or a low-pass filter.

In further preferred embodiments of the method according to the invention, which can be realized together with a feature of the invention or with several features of the invention or with all features of the invention, without limiting the invention thereto, wherein the over-the-snow antenna (A2) and replacing the receiver (E2) with a virtual reference station, the virtual reference station deriving pseudo-orange, carrier phase and signal strength measurements by linear combination of the pseudorange, carrier phase and signal strength measurements from a network of reference stations.

A1

Antenne auf dem Grund G unter der Schneedecke S

A2

Antenne oberhalb der Schneedecke S

G

Grund

S

Schneedecke

DS

trockene Schneebedingungen

WS

feuchte Schneebedingungen

B

Basislinie

H

Höhe (vertikaler Abstand) der einen Antenne (A2), die oberhalb der Schneedecke S über dem Grund G positioniert ist

E

Abstand E der beiden Antennen (A1, A2) der mindestens zwei Antennen (A1, A2) parallel zum Grund G

I

Initialisierungsphase

D

Entscheidungsphase

M

Messphase

R

Ergebnisermittlungsphase

r

Trägerphasenresiduen

t

Zeit

The process according to the invention has been described in detail above with reference to the figures relating to preferred embodiments of the process. However, the invention is not limited to the preferred embodiments shown in the figures and described in the description. Rather, the scope of the invention is determined by the following claims.

A1

Antenna on the ground G under the snow cover S

A2

Antenna above the snow cover S

G

reason

S

snow

DS

dry snow conditions

WS

wet snow conditions

B

baseline

H

Height (vertical distance) of the one antenna (A2), which is positioned above the snow cover S above the bottom G.

e

Distance E of the two antennas (A1, A2) of the at least two antennas (A1, A2) parallel to the base G

I

initialization

D

decision phase

M

measuring phase

R

Results analysis phase

r

Trägerphasenresiduen

t

Time

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• EP 12199772 [0013]
• EP 2749900 A1 [0013]

Cited non-patent literature

• NC Talbot, Centimeters in the Field, A users Perspective of Real-Time Kinematic Positioning in a Production Environment, Proc. of the 6th Int. Techn. Meet. of the Satellite Div. of the Inst. of Navigation (ION GPS), Salt Lake City, UT, USA, 1049-1057, 1993 [0013]
• T. Takasu and A. Yasuda, Development of the low-cost RTK-GPS receiver with an open source program package RTKLIB, Proc. of Int. Symp. On GPS / GNSS., Jeju, Korea, 2009 [0013]
• P. Henkel, Tightly coupled precise point positioning and attitude determination, IEEE Transactions on Aerospace and Electronic Systems, 51 (4), 3182-3197, 2015. [0013]
• P. Henkel, and C. Günther, Partial integer decorrelation: optimum trade-off between variance reduction and bias amplification, Journal of Geodesy, 84 (1), 51-63, 2010 [0013]
• P. Henkel, M. Iafrancesco and A. Sperl, Precise Point Positioning with Multipath Estimation, Proc. of ION / IEEE Position, Location and Navigation Symp. (PLANS), Savannah, GA, USA, 6 pp., 2016 [0013]
• P. Henkel, U. Mittmann and M. Iafrancesco, Real-Time Kinematic Positioning with GPS and GLONASS, Proc. of 24-th Europ. Signal Proc. Conf. (EUSIPCO), Budapest, Hungary, 5 pp., 2016 [0013]
• N. Kubo, F. Wu, and A. Yasuda, Integral GPS and QZSS Ambiguity Resolution, Transactions Jap. Soc. Aero. Space Sci., Vol. 47, no. 155, 38-43, 2004 [0013]
• FT, Ulaby, DG Long, WJ Blackwell, C. Elachi, AK Fung, C. Ruf, K. Sarabandi, HA Zebker, and J. Van Zyl, Microwave radar and radiometric remote sensing, 2014. [0013]
• JH Bradford, JT Harper, and J. Brown, Complex dielectric permittivity measurements from ground-penetrating radar data to estimate snow liquid water content in the pendular regime, Water Resources Research, 45, W08403, 2009. [0013]
• ME Tiuri, AH Sihvola, EG Nyfors, and MT Hallikainen, The Complex Constant Constant of Snow at Microwave Frequencies, IEEE Journal of Oceanic Engineering, 9 (5), 377-382, 1984. [0013]
• L. Schmid, A. Heilig, C. Mitterer, J. Schweizer, H. Maurer, R. Okorn and O. Eisen, Continuous snowpack monitoring using upward-looking ground-penetrating radar technology, Journal of Glaciology, 60, 221, 509 -525, 2014 [0013]
• V., B. Meløysund, Leira, KV Høiseth, and KR Lisø, Predicting snow density using meteorological data, Meteorological Applications, 14 (4), 413-423, 2007 [0013]
• TC Jonas, Marty, and J. Magnusson (2009), Estimating the snow water equivalent from snow depth measurements in the Swiss Alps, Journal of Hydrology, 378 (1), 161-167 [0013]
• F. Koch, M. Prasch, L. Schmid, J. Schweizer, and W. Mauser, Measuring snow liquid water content with low-cost GPS receivers, Sensors, 14 (11), 20975-20999, 2014 [0013]
• Schmid, F. Koch, A. Heilig, M. Prasch, O. Eisen, W. Mauser and J. Schweizer, A novel sensor combination (upGPR-GPS) to continuously and nondestructively derive snow cover properties, Geophysical Research Letters, 42 (9), 3397-3405 2015 [0013]
• KM Larson, E. Gutmann, V. Zavorotny, J. Braun, M. Williams and F. Nievinski, Can we measure snow depth with GPS receivers? Geophysical Research Letters, 36 (17), L17502, 2009 [0013]
• Greenland from GPS reflected signals, Advances in Space Research, 53 (11), 1623-1633, 2014 [0013] S.Jin, N.Najibi, Sensing snow height and surface temperature variations in Greenland.
• N. Rodriguez-Alvarenz, E. Valencia, X. Bosch-Lluis, A Camps, I. Ramos-Perez, H. Park, and M. Vall-Llossera, Snow thickness monitoring using GNSS measurements, Geoscience and Remote Sensing Letters, IEEE , 9 (6), 1109-1113, 2012 [0013]
• JL McCreight, EE Small, and KM Larson, Snow depth, density, and SWE estimates derived from GPS reflection data: Validation in the western US, Water Resources Research, 50 (8), 6892-6909, 2014 [0013]
• KM Larson, GPS interferometric reflectometry: applications to surface soil moisture, snow depth, and vegetation water content in the western United States, Wiley Interdisciplinary Reviews: Water, 3 (6), 775-787, 2016 [0013]

Claims (13)

Method for determining snow parameters of a snow cover S arranged on a ground G with at least two receivers (E1, E2) of microwave signals from navigation satellites which are each connected to one antenna (A1, A2), one antenna (A1) of the at least two antennas (A1, A2) fixed on the ground G under a snow cover S and another antenna (A2) of the at least two antennas (A1, A2) is fixed above the snow cover S; encompassing the 4 phases that one a) in an initialization phase (I) without snow cover S on the bottom G and with at least one antenna (A1) of the at least two antennas (A1, A2) determines the relative positions between the antennas (A1, A2) by means of received microwave signals from navigation satellites in which the receivers (E1, E2) derive pseudorange and carrier phase measurements from the received microwave signals, from which differentiated pseudorange and carrier phase measurements are determined by difference between the measurements of both receivers, and the relative positions from the pseudorange differential measurements and carrier phase measurements are determined by linear compensation calculation (Ia); and performs parallel reference measurements on signal strength (Ib); b) in a decision phase (D) at least one time at which a snow cover S covers the base G and the one antenna A1 of the at least two antennas (A1, A2), first by means of carrier phase measurements the presence of a snow cover (Da) and then by means of the signal strength, the occurrence of snowfall (Db) of the then received microwave signals from navigation satellites determines whether the snow is dry or moist; c) in at least one measurement phase (M) at least one time at which a snow cover S covers the base G and the one antenna A1 of the at least two antennas (A1, A2), the snow-related propagation delay in the zenith direction and the ambiguities of the differential Determine carrier phase measurements by means of the differential pseudo-orange measurements and carrier phase measurements derived from the then received microwave signals from navigation satellites; and parallel measurements of signal strength are performed; d) determines at least one snow parameter from the snow-related propagation delay determined in the measurement phase (M) in at least one result determination phase (R); and, if appropriate, further properties of the snow in the determination of the snow parameters of the snow cover S arranged on the bottom G in the measuring phase (M) and result determination phase (R). Method for determining snow parameters according to claim 1, wherein the snow parameter determined in result determination phase (R) describes the snow water equivalent (SWE), which describes the total water stored in liquid and solid form in the snowpack, the snow depth (HS), which describes the height of the snow cover in the vertical direction above the ground G, and the snow light (LWC), which describes the percentage of liquid water in the snow cover are. Method for the determination of snow parameters according to claims 1 to 2, wherein in the case of dry snow (DS) the snow water equivalent (SWE) and with optional addition of the snow density (SD) the snow height (HS) is determined and wherein in the case of wet snow ( WS) also derives the snow light (LWC) together from the previously determined snow-related propagation delay in the zenith direction and the normalized to the reference measurement signal strength measurements. Method for determining snow parameters according to one or more of claims 1 to 3, wherein in the initialization phase (I) the relative positions of the antennas (A1, A2) of the at least two antennas (A1, A2), the ambiguities of the differential carrier phase measurements and, optionally, determining the differential multipath errors together from the differential pseudorange and carrier phase measurements by linear compensation calculation (Ia). Method for determining snow parameters according to one or more of claims 1 to 3, wherein in the measuring phase (M) the elevation of the navigation satellites at the position of at least one of the antennas (A1, A2) and the direction vectors between navigation satellites and at least one antenna ( A1, A2) from the positions of the navigation satellites and the positions of at least one antenna (A1, A2) determined (Ma1), and a navigation satellite with the highest possible elevation, signal strength and long visibility as a reference satellite (Ma2) selects. Method for determining snow parameters according to one or more of claims 1 to 5, wherein additionally a synchronization correction is determined for each differential carrier phase measurement (Ma3). Method for determining snow parameters according to one or more of claims 1 to 6, wherein in the measuring phase (M) double-differentiated carrier-phase measurements are obtained by subtracting the differential carrier-phase measurements of the reference navigation satellite from the differential carrier-phase measurements of all others Navigation satellites forms (Ma4); and, if necessary, additionally subtracting the synchronization correction and the double-differentiated distances between satellite and receiver, which are determined from the direction vectors between satellite and receiver and the relative position between the antennas (A1, A2) (Ma5); and, if necessary, additionally correcting jumps in the double-differentiated carrier-phase measurements (Ma6); and optionally additionally determining for each time step of a measurement the subset of the navigation satellites (Ma7) available, ascending and descending in the field of view of the antennas. Method for determining snow parameters according to one or more of claims 1 to 7, wherein in the measurement phase (M) initial (Ma8) the integer double-differentiated ambiguities of the carrier phase measurements and the snow-related propagation delay in the zenith direction from a time series of twice Differentiated carrier phase measurements determined by linear compensation calculation, wherein one forms the projection of the snow-related propagation delay from the direction of incidence to the zenith direction by means of the known elevations of the navigation satellites. Method for the determination of snow parameters according to one or more of claims 1 to 7, wherein in the measuring phase (M) in addition (Ma9) the integer double-differentiated ambiguities of the carrier phase measurements of the newly-rising navigation satellites are rounded from the nearest integer The difference between the double-differentiated carrier phase measurements and the double-differentiated calculated carrier phase measurements determines the double-differentiated calculated carrier phase measurements from the product between the projection of the snow-related propagation delay from the direction of incidence to the zenith direction by means of the known elevations the navigation satellites and the snow-related propagation delay in the zenith direction. Method for determining snow parameters according to one or more of claims 1 to 9, wherein in the measuring phase (M) residuals of the double-differentiated carrier-phase measurement are formed by subtraction of the double-differentiated carrier-phase ambiguities from the double-differentiated carrier-phase measurements, and determining the snow-related propagation delay in the zenith direction by linear compensation calculation from the residuals of the double-differentiated carrier phase measurements, wherein the projection of the snow-related propagation delay from the direction of incidence to the zenith direction is formed and used by means of the known elevations of the navigation satellites ( Ma10). Method for determining snow parameters according to one or more of Claims 1 to 10, wherein the derived double-differentiated ambiguities of at least one double-differentiated carrier-phase measurement are checked and, if necessary, the double-differentiated ambiguities are corrected as soon as the elevation of a navigation satellite near the elevation of the reference navigation satellite is determined by means of the double-differentiated carrier-phase measurements (Ma11) which are normalized to the wavelength and then rounded to the nearest whole number. Method for determining snow parameters according to one or more of Claims 1 to 11, wherein the accuracy of the determined propagation delay in the zenith direction is increased by averaging or filtering. Method for determining snow parameters according to claim 1, wherein the snow cover installed antenna A2 and the receiver (E2) are replaced by a virtual reference station, the virtual reference station measuring pseudo orange, carrier phase and signal strength measurements from the pseudo orange, carrier phase and derives signal strength measurements from a network of reference stations.

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