Snow pit measurements

The SnowMicroPen (SMP) measures penetration force of a cone driven into the snowpack from above. It delivers output in form of applied force at penetration depth at high resolution.

This signal is quite dense in information given that the SMP probes the mechanical failure of snow, albeit maybe a bit hard to interpret directly in the field.

For the (software) lab however, the SMP offers an objective method of measurement delivering data in a timely manner which would be an impossible undertaking by traditional methods. There exist accompanying routines to meaningfully derive some fundamental quantities like the density and grain size from this signal so that the relevance to the practitioner is immediate.

This satisfies a great variety of scientific research applications but it leaves something to be desired for daily field work where information flow may be tailored to more traditional types of information like the grain shapes.

Luckily, the SMP’s force profile is such a significant gain in information that it is possible to derive almost all data that would also be gathered in a manual snow pit from it - within certain limitations. Due to the complexity of snow, the connections between its properties and whichever set of micro-parameters are far from being fully understood. Therefore, the farther removed the derived quantities are from the raw SMP signal the more stochastic the calculation models become. For example, snowmicropyn does calculate the grain shapes for an SMP signal, but learning which SMP micro-parameters are tied to a certain snow type is left to a machine learning algorithm since this problem has not been solved reliably by other means yet.

This page is meant to describe the modules implemented in snowmicropyn that derive micro- and macro-parameters of the system and therefore transform a raw SMP signal into a full simulated snow pit.

Micromechanical properties - A shot noise model

Löwe et al. showed with a shot noise approach that some microstructural parameters of the snowpack can be be deduced from the analytical solution of a stochastic model. To this end the penetration force of the SMP cone can be interpreted as a Poisson shot noise process and can be simulated as such, giving a statistical but principally rigorous solution.

The following quantities are commonly derived from the SMP signal and are also computed as a first step in snowmicropyn (via statistical moments of the dataset):

  1. f_0

    The rupture strength.

  2. delta

    The deflection at rupture. The entire one-point statistics of the penetration force F solely depend on the product lambda*delta. Hence, to estimate both parameters a higher order correlation function is chosen: the force covariance. The simplest estimate for delta can be inferred from the slope of the correlation function at origin.

  3. lambda

    Intensity of the Poisson point process.

  4. L

    The element size. This is the average distance between neighboring elements. Since the (projected) area of the SMP A is fixed the element size and intensity can be related by lambda = A/L^3. This relation quantifies assumptions about the spatial distribution of snow grains when propagating the information from the one-dimensional force characteristics to the three-dimensional snowpack.

In short, first the non-central moments of the SMP force are estimated in a finite window. Second, an estimate of the cumulants can be obtained from their relation to the non-central moments. From these, lambda*delta and f0 can be calculated from combinations of the mean and variance, and finally delta through the covariance of the force signal.

Macro parameters - Regression

Relating stratigraphic parameters to physical properties of snow is a topic of ongoing research. However, the importance of density and grain size as fundamental characteristics of the snow samples become clear in many applications, including snow models. With these two morphometric measures, key properties such as thermal conductivity, dielectric permittivity or air permeability can be computed.

The underlying idea of the statistical model employed here is that repeated elastic increases of the force followed by small elastic deflections of length delta correspond to the SMP cone breaking through snow crystals separated by air gaps.

Ground truth measurements about density and SSA were originally sampled by means of Micro-CT. Meanwhile however snowmicropyn offers a couple of parameterizations that were obtained by various methods for different SMP devices and climate settings. In any case SMP measurements were performed at the observation sites to calibrate the density and SSA models with.

  1. Density

    The statistical model for the snow density has evolved to include more than just the (logarithm of) the penetration force. Snowmicropyn offers a comprehensive developer’s API, and depending on new publications the models may look slightly or completely different. Which parameterization to use depends on the SMP device and wide-scale snow conditions. Early successfull attempts to estimate the density are of the bilinear form:

    aa[0] + aa[1] * np.log(F_m) + aa[2] * np.log(F_m) * LL + aa[3] * LL

    and a couple of parameter sets for this model are provided in snowmicropyn. See API Reference for further details.

  2. Specific Surface Area (SSA)

    Again, snowmicropyn provides the framework to include new calibrations at hand, giving the option to choose from a number of publications. The SMP length scale L lends itself to start a regression on, and indeed already a direct comparison reveals a correlation to the length scales derived from independent measurements. To account for varying snow types (e. g. different densities in different climate settings) a linear regression for the SMP variables L and ln(F) can be used (for example). Read more at API Reference.

  3. Hardness

    The force needed for the SMP’s cone to break up the crystal structure and drive through the snow is not the same as when measuring snow hardness via the hand hardness index where snow is being displaced horizontally. The hand hardness index (from “new snow” to “ice”) is estimated with a power law fit through a graph connecting SMP to manual hand hardness index measurements using a few data points from a dedicated experiment.

  4. Grain size

    The grain size is indirectely proportional to the SSA, so we have this already.

Snow grain shapes - Machine Learning

Current theoretical efforts hope to find a fundamental model to connect an SMP measurement with the observed type of snow. Until such methods are successfull we try to simulate the model with standard machine learning techniques.

Since the micro-parameters derived by the shot noise model have a physical meaning they are used together with the force signal to fit a machine learning model to the data and predict the snow type, i. e. the grain shape.

Snowmicropyn allows the user to choose from a set of different machine learning routines together with minimalistic algorithms for data pre-processing and resampling. In the future hopefully more sophisticated functions to compare, warp and merge profiles will be offered.

Operational application

A great benefit of having a “manual-like” profile at hand after performing SMP measurements is that certain snowpack models can be started with this kind of information. It remains to be seen how quickly a snow model driven by SMP data will stabilize its own (potentially different) microstructure parameters and produce reliable output in the form of macroscopical observables like the grain shape.

Apart from a whole range of practical challenges however the path is principally clear: we can take the SMP into the field, record some bits of meta data like the slope angle and air temperature and feed this data to a computer. Snowmicropyn can then produce standardized CAAML output. This together with meteorological weather forecast data can drive climate models to analyze and predict the snow stratigraphy for the observation site fully automatically.

Summary

An SMP measurement is quick and objective, and snowmicropyn can derive the necessary snowpack properties needed to drive operational forecasting tools (with varying complexity and trustworthiness of the estimated parameters).