GEOG 566

         Advanced spatial statistics and GIScience

June 11, 2018

Modelling snow for sheep

Filed under: 2018,Final Project @ 1:21 pm

RESEARCH QUESTION – How do seasonal snow conditions affect Dall Sheep recruitment?

Dall an emblematic species of alpine regions in high latitude North America. Their ranges extend from the mountains of the Yukon Territory, Canada, to the furthest western extent of the Brooks Range in Alaska. Populations of Dall Sheep have declined 21% range-wide since the 1990s with a major mechanism of decline thought to be the increased frequency of extreme spring snow conditions(Alaska Department of Fish and Game, 2014). During the months of April and May mature Dall sheep ewes typically give birth to one lamb. The survival of this lamb is dependent on the mother’s ability to protect it from predators and guide it to accessible forage. If successful, the lamb is ‘recruited’ into the population. Hence, a commonly used metric of animal population growth potential is the mother to child ratio, or in this case the lamb to ewe ratio (hereafter written as lamb:ewe). Extreme spring snow conditions are thought to decrease lamb survival by limiting access to forage, either by deep snow coverage or ice-layers formed in the snow subsequent to rain-on-snow events. The limited forage could cause starvation or increased use of areas where vulnerability to predation is increased. In this project I will examine this question via use of a spatially explicit snow-evolution model, SnowModel, and lamb:ewe ratios from summer sheep surveys.


In this project I used three primary datasets;

Snow / climate dataset; SnowModel (Liston and Elder, 2006)was used to simulate daily snow and climate conditions in 6 different Dall sheep domains where survey data was available. SnowModel was forced with the Modern Era Retrospective Reanalysis for Research and Applications (MERRA2) product (Gelaro et al., 2017). SnowModel effectively downscales temperature, humidity, precipitation, wind speed and direction from a 0.5º by 0.625º to a 30m resolution and physically evolves and distributes a simulated snowpack across digital elevation and landcover layers, derived from the IfSAR DTM distributed by US Geological Survey and the NLCD 2011 product distributed by the Multi-resolution Land Characteristics Consortium respectively (Homer et al., 2015). For 5 of the domains (Brooks Range, Denali, Gates of the Arctic, Lake Clark and Yukon Charley), where available, in-situ data on snow depth and snow water equivalent were used to calibrate and validate the model. The 6thdomain, in the Wrangell St Elias, in-situ data from a March 2017 field campaign was used to calibrate and validate the model and test for model performance (see below). SnowModel is run for the entire period between September 1st1980 and August 31st2017. Daily data for snow and climate above the elevation of shrubline were then aggregated into monthly and seasonal metrics e.g. mean monthly snow depth (m). Seasons in this case were taken as September to November (Fall), December to February (Winter), March to May (Spring) and June to August (Summer).

Figure 1; Map of Alaska with Dall Sheep ranges

Sheep data; Sheep data used here is from annual surveys completed by Alaska Department of Fish and Game, Bureau of Land Management, US Fish and Wildlife Service and National Park Service in the same area as the SnowModel domains. Lamb:ewe ratios were calculated from the number of lambs recorded and the number of ewes and ewe-likes. Survey methods include distance sampling, stratified random sampling, and minimum count methods either from a ground location or fixed wing aircraft.

Climate Indice data; Climate indices of larger scale weather patterns were downloaded from the National Oceanographic and Atmospheric Administration (NOAA) for 7 different indices; the Pacific Decadal Oscillation (PDO), Arctic Oscillation (AO), East Pacific / North Pacific Oscillation (EP/NP), North Pacific Pattern (NP), West Pacific Pattern (WP), Pacific North American Index (PNA), and the North Atlantic Oscillation (NAO) (


The hypotheses for this project fell were delineated by blog post, the three installments of which looked at a) model performance, b) climate indices and snow condition relationships, c) snow condition and lamb:ewe ratio relationships. They are hence;

  1. SnowModel performs best at the elevations and landcover where the greatest amount of in-situ data in available
  2. The influence of different climate indices on snow conditions is not uniform throughout Dall sheep ranges
  3. Spring snow conditions have the greatest impact on lamb:ewe ratios surveyed in summer


For hypothesis A I used a multivariate approach to test the hypothesis, using the FAMD tool of the FactoMineR library in R to test where SnowModel was over or under predicting snow depth by land cover class and other metrics of topography (elevation, slope, aspect and northerness).

For hypothesis B I used autocorrelation and crosscorrelation functions in R to test for patterns within the time series of the snow metrics and in correlation with the climate indices.

For hypothesis C I used a simple approach comparing whether snow conditions were above or below their mean to whether lamb:ewe ratios were above or below their mean to see which conditions and when might best predict levels of recruitment. This then informed a multiple logistic regression model computed in R


Hypothesis A;

The results from my hypothesis A can be best seen in figures 2 to 4;

eigenvalue variance.percent cumulative.variance.percent

Dim.1 3.1793016        24.456166                    24.45617

Dim.2 2.1249171        16.345516                    40.80168

Dim.3 1.4969078        11.514675                    52.31636

Dim.4 1.2530914         9.639165                    61.95552

Dim.5 0.9902287         7.617144                    69.57267

Figure 2; Scree plot and table from the multiple factor analysis

Figure 3; Plot of the importance of the quantitative variables importance to the 1stand 2nddimension of the factor

Figure 4; Plot of the qualititative variables importance to the 1stand 2nddimension of the factor analysis.

The factor analysis revealed that only 40% of the variation in the data could be explained by the first 2 dimensions (figure 2), with elevation being the biggest contributor to the 1stdimension, and the category of SnowModel error (diffCategory) being the biggest contributor to the 2nddimension (figures 3 and 4). However, and perhaps expectedly given its elevational transition and role in in snow accumulation processes, landcover type was a significant contributor in both dimensions. Broadly speaking as the elevation increased, and the landcover went from coniferous forest to prostrate shrub tundra and bare ground, model accuracy increased. Interestingly there is also a pattern of underprediction in bare and coniferous forest landcover and over prediction in prostrate shrub tundra and erect shrub tundra, although the magnitude of the error is greatest in the landcover classes that typically populate lower elevations. As I had greater amounts of in-situ data from higher elevations I could confirm my hypothesis, however the analysis did reveal an under and overpredict pattern between bare ground and prostrate shrub tundra that I didn’t expect.

Hypothesis B;

I conducted analyses for all 6 domains described above, however the autocorrelation of monthly and seasonal snow/climate metrics from 1980 to 2017 and cross-correlations of monthly and seasonal total snowfall from 1980 to 2017 to climate indices, did not reveal any meaningful patterns, though some statistically significant results at certain lags were observed they never rose above ~0.5 for the autocorrelation and ~0.25 for the cross correlation. This suggests that larger term patterns of climate do not explain a large proportion of the inter and intra annual variability in snow conditions in alpine areas. Of note is the stronger influence of different climate indices for different domains, although only weakly significant there appears to be a pattern dependent on latitude and continentality, please refer to blog post 2 to examine this. In the meantime hypothesis 2 can be considered open for further testing. For this post please see the examples from the Wrangell St Elias below as illustrative;

Figure 5; Autocorrelation of monthly variables 1980 to 2017, Wrangell St Elias domain


Figure 6; Autocorrelation of seasonal variables 1980 to 2017, Wrangell St Elias domain


Figure 7; Cross-correlation of monthly variables to climates indices 1980 to 2017, Wrangell St Elias domain

Hypothesis C;

To test hypothesis C a simplistic approach was utilised to confirm the occurrence of the following conditions;

  1. High month/season snowfall and low lamb:ewe ratios
  2. Low month/season air temperature and low lamb:ewe ratios
  3. High month/season snow depth and low lamb:ewe ratios
  4. Low month/season forageable area and low lamb:ewe ratios

These statements are based on what we expect the relationship between snow conditions and sheep recruitment might be – increased snowfall and snow depth, or lower air temperatures and forageable area, produce conditions where greater energy expenditure is required for survival. Dall sheep are in calorific deficit during the snow season so benign conditions mean that ewes reach the lambing period in better condition and are potentially then more able to provide for their lambs, increasing the observed lamb:ewe ratio. An alternative or complementary idea is that conditions during and after lambing are more important as lambs require a narrower range of conditions than adult sheep to survive. From the frequency of occurrence of agreement in these conditions we can select variables for use in a logistic regression model.

I will present my results only for the Wrangell St Elias domain by month, however seasonal results and other domains have been analysed but not yet interpreted.


Figure 9; Wrangell St Elias results by month

Figure 10; Log regression result

From the simple comparison we can see that spring month (March, April, May) snow conditions that are more hazardous do not always predict low lamb:ewe ratios any more than winter months (December, January, February). From the logistic regression model, where I included the variables by month that had the most frequent occurrence of meeting the conditions, February forageable area and the total amount of November snowfall came out in the final model as being strongest.


Each of my blogposts / hypotheses took me further along towards a better idea about how best to address and answer my research question. Hypothesis A described where SnowModel was performing best, and worst, and gives a quantifiable error to propagate through the analysis (although I have not done that here). Most importantly it gave me reasonable confidence that the model is doing reasonably ok in sheep territory and refined the areas where I can spend energy trying to improve it.

Hypothesis B, and its tests, were murkier, producing know results that really jumped out for their confirmation or rejection of the hypothesis. Further work would be to aggregate the indices and snow seasons further into yearly, or September to August, averages and compare them to lamb:ewe ratios as wells as snow and climate metrics.

Hypothesis C produced a model that rejected the original hypothesis, suggesting that snowfall in the autumn and the area available to forage in February is most important in. predicting lamb:ewe ratios. However, the pseudo R-sq (derived from its AIC score) of this model is not much to shout about and could likely be refined by introducing seasonal values and more variables into the analysis. Logistic regressions weren’t conducted in other domains than the Wrangell St Elias – it would be interesting to compare results to these to examine whether there are range-wide similarities.

The results from hypothesis C can be used to interpret whether years where no sheep survey took place are likely to have below and above average lamb:ewe ratios, giving an indication as to whether the observed population decline is a result of recruitment being affected by increasing occurrence of hazardous snow years.


Using R and Rstudio for the first time was a significant feature of this class for me. I began to appreciate the value of organising data according to the tidyverse philosophy and saw incremental improvement in my abilities to conduct analyses and create figures using the packages available. I’m not yet certain whether it is an overall improvement on Matlab, which I previously used, but I do prefer the ease of ggplot2 over equivalent Matlab tools.

I was pretty unversed statistically at the beginning of this class and have gained an understanding in the principles, use and concepts of Principle Component Analysis, Multiple Factor Analysis, autocorrelation and cross-correlation spatially and temporally, and multiple logistic regression. My future work will be much enhanced as a result.


Alaska Department of Fish and Game, 2014. Trends in Alaska Sheep Populations, Hunting, and Harvests. Division of Wildlife Conservation, Wildlife Management Report ADF&G/DWC/ WMR-2014-3, Juneau.

Gelaro, R., McCarty, W., Suárez, M.J., Todling, R., Molod, A., Takacs, L., Randles, C.A., Darmenov, A., Bosilovich, M.G., Reichle, R., Wargan, K., Coy, L., Cullather, R., Draper, C., Akella, S., Buchard, V., Conaty, A., da Silva, A.M., Gu, W., Kim, G.-K., Koster, R., Lucchesi, R., Merkova, D., Nielsen, J.E., Partyka, G., Pawson, S., Putman, W., Rienecker, M., Schubert, S.D., Sienkiewicz, M., Zhao, B., Gelaro, R., McCarty, W., Suárez, M.J., Todling, R., Molod, A., Takacs, L., Randles, C.A., Darmenov, A., Bosilovich, M.G., Reichle, R., Wargan, K., Coy, L., Cullather, R., Draper, C., Akella, S., Buchard, V., Conaty, A., da Silva, A.M., Gu, W., Kim, G.-K., Koster, R., Lucchesi, R., Merkova, D., Nielsen, J.E., Partyka, G., Pawson, S., Putman, W., Rienecker, M., Schubert, S.D., Sienkiewicz, M., Zhao, B., 2017. The Modern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA-2). J. Clim. 30, 5419–5454.

Homer, C., Dewitz, J., Yang, L., Jin, S., Danielson, P., 2015. Completion of the 2011 National Land Cover Database for the Conterminous United States – Representing a Decade of Land Cover Change Information. Photogramm. Eng. 11.

Liston, G.E., Elder, K., 2006. A Distributed Snow-Evolution Modeling System (SnowModel). J. Hydrometeorol. 7, 1259–1276.

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  1.   leatherl — June 15, 2018 @ 2:43 pm    

    Chris, it’s cool to see all of these different techniques combined! I’m curious if you would expect to see any autocorrelation in the sheep data or lamb:ewe ratio? Is there cross-correlation or an interannual effect of climate on sheep, or lamb:ewe ratio? Also, I’m a little unclear about the variable selection process for the final model– did you test additional regressions before selecting the variables in the model you reported in figure 9? If you were to test additional regressions to locate variables that are more significantly related, which variables would you choose?

  2.   jonesju — June 15, 2018 @ 7:17 am    

    Very good work. As I understand it, you’ve shown that the snow model has low error in vegetation types likely to be frequented by sheep, that long-term modeled snow is not cross-correlated with climate indices (but it is correlated at lag zero with some of these indices – so what does that mean?), and that there may be some predictive relationships between snow and lamb/ewe ratios. Did you succeed in running a logistic regression? I hope you will pursue this.

  3.   swanssam — June 15, 2018 @ 7:00 am    

    Hi Chris, really nicely done. I’m curious if you were surprised that climate indexes had no influence on snowpack for the range of Dall sheep that you investigated. Is Alaska as a whole largely unaffected by climate change so far, because temperatures haven’t risen to a threshold of warming yet? Or do you reckon that your time period is just to short to observe trends on such a large scale? Either way, great job and good luck in your future endeavors!

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