A Machine Learning Exercise in Mountain Hydrology
By: Kayden H
Tags: Machine Learning, Hydrology, Snow, Remote Sensing, Editors Pick

A Machine Learning Exercise in Mountain Hydrology

Passive Reconstruction of Snowpack Cold Content

Here’s a 4-minute TLDR version of this story

Background

Mountain snowpack in the midlatitudes is a seasonal water tower that varies heavily from year to year. As a water resource, considerably large snowpacks can present a flood risk, while small snowpacks can exacerbate drought conditions in some regions. It is important, then, to be able to understand and predict the snowpack amount and when it will melt. One key requisite (though not exhaustive) is to characterize its cold content (CC), or the amount of energy required to begin melting it. It is a function of the snowpack’s density and temperature profile, which can be measured from a snow pit or stratified sensors. These measurement approaches make characterizing CC difficult over a mountain range without a complex, physically-based earth system model that requires detailed weather information. This raises the question, to what extent can a parsimonious model predict CC?

This article presents a brief investigation of a machine learning approach to CC estimation. I survey a few different models before running several data-withholding experiments using both satellite and ground measurements from a well-instrumented study site, which are then compared to published CC estimates from a physically-based model.

Study Site and Data

The Niwot Ridge Long-term Ecological Research site is located in the Rocky Mountains of Colorado, USA, just east of the Continental Divide. It contains multiple meteorological stations spanning subalpine, alpine, and high-alpine environments, with hourly measurements beginning in 1990. Snow surveys are conducted several times each month during the snow season, which record stratified measurements of snow temperature and density from which CC can be calculated. Here, I use measurements from the alpine (3528 m) site since it has the densest snow pit record to train and evaluate modeled CC with (343 pits from 1995 to 2016). Both meteorological (air temperature, relative humidity, wind speed) and snow pit measurements were obtained from Jennings et al. (2018).

Hourly snow water equivalent (SWE) measurements come from a snow pillow near the subalpine site managed by the Natural Resource Conservation Service, which oversees a vast snowpack telemetry (“snotel”) network across the Western United States. It should be noted that SWE measurements are closer to the subalpine site than to the alpine site (~ 2–3 km apart). True alpine SWE behavior may differ, especially during the melt season, which might degrade CC estimates. This limitation challenges a machine learning approach to take successful advantage of a proxy measurement of likely (but unknown) correlation to the truth.

The same might be said for satellite remote sensing measurements, since they are indirect and often constrained by other physical quantities through algorithms to derive a quantity of interest. Notwithstanding, they provide promising inroads to characterizing and understanding earth systems at a large scale. Here, I used daily 3.125-km resolution passive microwave brightness temperatures (TB, Brodzik et al. 2016) from the nearest grid point to the site. Inter-channel differences have been shown to aid remotely-sensed SWE estimates (e.g. Bair et al. 2018). TB hereafter refers to the difference between the 37-GHz and 85-GHz channels aboard the SSMI sensors. Due to frequently missing values, I used both Tropical (nighttime) and Northern (morning) passes. Missing Tropical values were infilled with bias-corrected Northern values for each snow season. Each season’s data was smoothed with a cubic spline to fill remaining gaps, which lasted no longer than 3–4 days.

Predictor Variables

All predictors (14) are listed and described in Table 1. Few are taken the day of the target measurement (Date, TB, SWE), while majority represent a summary of the prior 30 days leading up to the target measurement. Each predictor is classified by its respective data stream (meteorology, satellite, or snotel). Note that Date and Cold-hrs (a) applies to all streams. This is because SNOTEL sites often have temperature gauges collocated with a snow pillow, and to imagine a remote sensing scenario informed by air temperature and TB.

Table 1. Predictor variables used in this study and their respective data source (MET: meteorology, SAT: satellite, SNOTEL: snowpack telemetry).

Model Selection

Training data were split randomly from the 343 target points, 25 percent of which were withheld for validating the test frameworks described below. The schemes I describe were the best-performing for this specific data set after brief parameter sensitivity analyses. All predictors were standardized prior to training, and all modeling was done using Python’s sklearn library.

Principal Component Regression (PC. R)

Multicollinearity among predictors (Figure 1) warranted an exhaustion of redundant correlations before applying a linear regression. CC in this case was regressed against the first 9 principal components, which explain 99 percent of its variability.

Figure 1. Correlation matrix among predictor variables (defined in Table 1).

Support Vector Regression (SV. R)

The support vector machine framework used a Gaussian radial-basis function kernel with parameters C=10 and epsilon=1.0.

Decision Tree Ensembles

The first ensemble method (of three) was a random forest regressor (RF) having a maximum depth of 15 and minimum splitting/leaf samples of 3. The second used bootstrap aggregation (Bag) and the third used AdaBoost (AdaB) with a decision tree base estimator having a maximum depth of 15. Each approach used 1000 estimators.

Scatterplots, regression error characteristic (REC) curves, and a Taylor diagram of each case are shown in Figure 2, which demonstrate the ensemble methods to outperform the other two. Both SV. R and PC. R tend to underestimate large values of CC and sometimes return physically impossible (i.e. negative) values. Ensemble approaches avoid that tendency entirely and perform similarly. The boosting approach marginally outperforms the RF and Bag frameworks (having out-of-bag scores of 0.64), and is used in the following experiments.

Figure 2. Test model performances using all 14 predictors showing (left) observed versus estimated values, (center) the regression error characteristic curves, and (right) a Taylor diagram.

Data Withholding Experiments

Five cases of “missing data” were investigated by permuting a few of the 3 data streams (Table 1). Table 2 defines each case, which I hypothesized would have progressively poorer performance. The model setup for each used the same number of estimators, but the maximum depth was adjusted to be one more than the number of predictors in each scenario.

Table 2. Withholding experiments and their number of input variables.

Figure 3 compares model performances, which reveal how model fidelity decays without SWE information. Withholding only SWE (i.e. the SAT+MET case) leaves most predictors at work, yet CC estimates suffer much more. That and the SAT cases both tend to group their predictions toward the climatological mean of non-zero CC (~ 3.8 MJ) rather than capturing the observed tails of CC.

Figure 3. AdaBoost performances for each data withholding experiment.

This is a credit to SWE itself being part of the CC calculation. So, these results signify congruent SWE behavior at the subalpine and alpine sites kilometers apart. This also signifies the need for (microwave) satellite measurements to be augmented with supporting weather, land surface, or more diverse spectral information to be effective for snowpack characterization. Decomposing feature importance (Figure 4) emphasizes this point, revealing CC to be explained mostly by SWE, air temperature and wind speed.

Figure 4. Decision tree ensemble predictor importance for Case 0.

With SWE information on-hand, machine learning CC estimates contend with those from a physically-based snowpack model (Table 3, Jennings et al. 2018), while estimates derived from weather or satellite information alone perform less satisfactorily.

Table 3. Comparison of performance metrics relative to a physical model.

A Closing Remark

Overall, a machine learning model can begin to successfully estimate a hard-to-reach snowpack property without a physical model, but only when given detailed information about slightly less difficult-to-reach properties. Snow surveys or weather/snotel stations can’t be made every few meters of a mountain range, leaving the spatial distribution of snowpack a long-standing challenge.

References

[1] E.H. Bair, A. A. Calfa, K. Rittger, and J. Dozier, Using Machine Learning for real-time estimates of snow water equivalent in the watersheds of Afghanistan (2018), Cryosphere, 12, 1579–1594, https://doi.org/10.5194/tc-12-1579-2018.

[2] M.J. Brodzik, D. G. Long, M. A. Hardman, A. Paget, and R. Armstrong, Calibrated Enhanced-Resolution Passive Microwave Daily EASE-Grid 2.0 Brightness Temperature, ESDR, Version 1 [SSMI] (2016), NASA National Snow and Ice Data Center Distributed Active Archive Center, https://doi.org/10.5067/MEASURES/CRYOSPHERE/NSIDC-0630.001. [2020–11–27].

[3] K.S. Jennings, T. G. F. Kittel, and N. P. Molotch, anced-Observations and simulations of the seasonal evolution of snowpack cold content and its relation to snowmelt and the snowpack energy budget (2018), Cryosphere, 12, 1595–1614, https://doi.org/10.5194/tc-12-1595-2018.