Description of the Water Balance Model

Water balance modeling is a tool for increasing our understanding of climate influence on natural resources. Like balancing a check book, it is a way of tracking the balance of nature’s most important asset. Most natural resources we manage are either water itself (springs, rivers, wetlands), or life that depends on water. Water and temperature interactions are based in physics that we can mathematically model. We find (and many others before us have too) that these modeled values are more strongly correlated with the things we manage than simple measures of temperature or precipitation. We use a simple model based on methods described by Thornthwaite and Mather (1955) and Lutz et al. (2010). The model tracks the fate of precipitation after it falls. After precipitation (snow or rain) hits the ground it has three options: (1) Stay put temporarily as stored snow pack or soil moisture, (2) Go up, via evaporation or through plants via transpiration. (3) Go down and become either ground water or runoff to wetlands, lakes, streams, rivers. Temperature determines the time water is stored as snow and when it melts, as well as the rate of evapotranspiration. The movement of water between compartments depends on the amount of energy (heat) in the system and the amount of water available.

Potential Evapotranspiration (PET, mm): The amount of evaporation and transpiration (movement of water into the atmosphere by plants) that would occur if soil moisture were unlimited. Temperature, wind, solar radiation, cloudiness and a variety of other factors affect PET. Sixty to ninety percent of annual precipitation is evapotranspired back to the atmosphere, mostly through plant leaves. There are many ways to calculate PET. In the current model, we used methods described by Oudin et al (2005

AET - Actual evapotransporation. AET is an estimate of the amount of water that evaporates from soil and that is transpired by plants. AET is positively correlated with primary production (plant biomass growth) across all ecosystems - deserts to the arctic - and changes in AET may be the single best indicator of how vegetation will respond to climate change. AET is limited by water availability (precipitation or soil moisture) and it increases only when water is actually available and temperatures are above freezing - conditions also required for most plant growth. In ecosystems where temperature or snow cover limits plant growth, warming temperatures will generally increase AET. In water-limited systems, AET is strongly correlated with precipitation.

Moisture Deficit (Deficit, mm): Use simple subtraction, i.e., Deficit = PET – AET. Deficit is the amount of water vegetation would use if it was available. Deficit can never be negative.

Soil water: The amount of water that is held in the soil. The model treats the soil like a bucket that can be filled by inputs (e.g. rain, snowmelt) and emptied by outputs (e.g. evaporation, transpiration). If the soil gets full, then runoff to streams results. Water holding capacity is the amount of water soil retains after it is saturated then drains. Think of a saturated sponge left on a counter without squeezing. Soil typically fills with water in winter and spring. As plants use water from soil it can be replenished by rain. If rain doesn’t fall, deficit or summer drought occurs. Plants “drink” water from soil and soil stores water, but not all soils are equal. Some are shallow, some rocky, sandy, or loamy, thus different soils store different amounts of water. In the current model, we used SSURGO soil data from the Natural Resources Conservation Service to determine the water holding capacity for each area (Soil Survey Staff, NRCS, 2018). Units = mm.

Runoff (mm): When the soil water bucket overflows, the water is lost as runoff.

Accumulated Snow Water Equivalent (SWE, mm): total SWE at each location. Estimated using equations described by Tercek and Rodman (2016) with melt threshold temperatures at each lkm grid cell provided by Jennings et al. (2018)

Literature Cited

Jennings, K., T. Winchell, B. Livneh, and N. Molotch. 2018. Spatial variation in the rain-snow temperature threshold across the northern hemisphere. Nature Communications 9:1148.

Lutz J, J. van Wagtendonk and J. Franklin. 2010. Climatic water deficit, tree species ranges, and climate change in Yosemite National Park. Journal of Biogeography 37: 936 – 950.

Millman, K. and M. Aivazis. 2011. Python for Scientists and Engineers, Computing in Science & Engi-
neering 13: 9–12.

Oudin, L., F. Hervieu, C. Michel, C. Perrin, V. Andreassian, F. Anctil, C. Loumange. 2005. Which potential evapotranspiration input for a lumped rainfall-runoff model? Part 2 = Towards a simple and efficent potential evapotranspiration model for rainfall-runoff modelling. Journal of Hydrology 303: 290 – 306.

Oudin, L., L. Moulin, H. Bendjoudi, and P. Ribstein. 2010. Estimating potential evapotranspiration without continuous daily data: possible errors and impact on water balance simulations. Hydrological Sciences Journal 55(2): 209 – 222.

Running, S. and J. Coughlan. 1988. A general model of forest ecosystem processes for regional applications I. Hydrologic balance, canopy gas exchange and primary production processes. Ecological
 Modelling 42: 125 – 154.

Soil Survey Staff, Natural Resources Conservation Service, United States Department of Agriculture. Web Soil Survey. Available online at https://websoilsurvey.nrcs.usda.gov/. Accessed 04/10/2018.

Tercek, M. and A. Rodman. 2016. Forecasts of 21st Century snowpack and implications for snowmobile and snowcoach use in Yellowstone National Park. PloS One 11(7): e0159218. doi:10.1371/journal.pone.0159218

Thornthwaite, C.W. and Mather, J.R. 1955. The water balance. Publications in Climatology, Centerton.

Thornton, P.E., Running, S.W., White, M.A. 1997. Generating surfaces of daily meteorological variables over large regions of complex terrain. Journal of Hydrology 190: 204-251. http://dx.doi.org/10.1016/S00022-1694(96)03128-9

Thornton, P.E., H. Hasenauer, and M.A. White. 2000. Simultaneous estimation of daily solar radiation and humidity from observed temperature and precipitation: An application over complex terrain in Austria. Agricultural and Forest Meteorology 104:255-271. http://dx.doi.org/10.1016/S0168- 1923(00)00170-2