Snowcover simulation models

In the 1960s with the development of digital computers, researchers were able to construct conceptual simulation models of the snow accumulation and ablation

Snow and Climate: Physical Processes, Surface Energy Exchange and Modeling, ed. Richard L. Armstrong and Eric Brun. Published by Cambridge University Press. © Cambridge University Press 2008.

process. These models were developed to solve many kinds of practical hydrologic problems. In a conceptual model, each major physical process is represented by a mathematical relationship. This is in contrast to degree-day techniques, which were commonly used to estimate snow-cover outflow directly from air temperature data. Degree-day techniques do not include the snow accumulation process, nor do they explicitly account for heat deficits, liquid-water retention and transmission, and the areal extent of the snow cover.

Two of the earliest snow-cover simulation models were developed by Rockwood (1964) as part of the SSARR model U.S. Army Corps of Engineers (1972) and by Anderson and Crawford (1964) for use in conjunction with the Stanford Watershed model. Both models used air temperature as the sole index to energy exchange across the air-snow interface. This is also true of subsequent models developed by Eggleston et al. (1971) and Anderson (1973). Generalized snowmelt equations from the publication Snow Hydrology (1956), based on theoretical and empirical considerations, were used in several snow-cover simulation models (Amorocho and Espildora, 1966; Carlson etal., 1974), and as an option in the SSARR model. The net radiation balance, estimated from incoming solar radiation and air temperature, was used to compute energy exchange in the snow-cover simulation model developed by Leaf and Brink (1973). This model was developed to determine the probable hydrologic effects of forest management.

All of the models mentioned above compute snowmelt by one set of equations and the change in the heat deficit of the snow cover with a separate equation (the SSARR model does not compute the heat deficit). Thus, these models are not energy balance models. Some of these models use empirical procedures to estimate changes in the heat deficit during non-melt periods. The Eggleston et al. and the Leaf and Brink models used the one-dimensional Fourier heat-conduction equation and the assumption that the snow surface temperature (T0) equals the air temperature (Ta) to compute temperatures at one or two points within the snow cover. Quick (1967) also used the heat-conduction equation and the assumption that T0 = Ta to compute changes in the snow-cover temperature profile during periods when depth can be considered to be constant. In addition, Quick accounts for the effect of the density profile on the snow-cover temperature profile.

In the 1970s, several energy balance snow-cover models were developed (Obled, 1973; Humphrey and Skau, 1974; Outcalt etal., 1975). The energy balance included net radiation transfer, latent and sensible heat transfer, heat transfer by rain water, and the change in heat storage of the snow cover. The change in heat storage was also determined from the computed temperature profiles at the beginning (time t) and the end (time t + At) of each computational time interval (At). Finite-difference approximations to the Fourier heat-conduction equation were solved to determine the temperature profile at time t + At, knowing the profile at time t. The thermal conductivity of the snow varied with snow density. The snow surface temperature was determined by various iterative schemes that sought to reduce to an acceptable level the difference between the value of the change in the heat storage term in the energy balance equation and the value of the same term as determined from changes in snow-cover temperatures. None of these models included the densification of the snow cover. Humphrey and Skau used periodic measurements of the density profile to account for changes in snow density. The other two models merely used the measured total snow-cover density. Only Obled made comparisons between computed and observed values of snow-cover outflow and water equivalent. Humphrey and Skau, as well as Obled, showed comparisons of computed and observed snow-cover temperature profiles. Outcalt et al. only made comparisons between the computed and observed dates on which melt begins and ablation is complete.

Anderson's 1976 work evolved from an earlier study of snow-cover energy exchange (Anderson, 1968). In this earlier study, Anderson computed the change in heat storage only when an isothermal snow cover was cooling immediately following a melt period. Thus the model could only be used during extended snowmelt periods or periods of daytime melt and night-time heat loss. The model was tested on data collected as part of a lysimeter study of snowmelt at the Central Sierra Snow Laboratory (U.S. Army Corps of Engineers, 1956). The data included all the necessary meteorological input variables and snow-cover variables such as water equivalent, depth, temperature, and snow-cover outflow. There was very good agreement between computed and observed values of daily snow-cover outflow and mean night-time snow surface temperature. However, there were several problems. The period of record was quite short (17 days), plus there was some uncertainty regarding the accuracy of a portion of the data. More importantly, there was almost no variability in meteorological conditions during the period (warm days and cool nights with mostly clear skies and moderate winds). Thus, it was not possible to determine if the model was valid over a wide range of meteorological conditions.

Attempts at finding another high-quality data set that included measurements of all the necessary input and verification variables were unsuccessful. Because the data were not available to adequately test snow-cover energy exchange models, the National Oceanic and Atmospheric Administration (NOAA) and the Agricultural Research Service (ARS) (Johnson and Anderson, 1968) established a snow research station to study the physical processes in snowmelt and snow metamorphism. The station was located within the ARS's Sleepers River Research Watershed near Danville, Vermont. While not the most ideal location in terms of the amount of snow (average maximum water-equivalent of about 300 mm), the station was nearly ideal for observing the wide variety of meteorological conditions that occurred during snowmelt periods. Data collection at the NOAA-ARS snow research station began in December 1968. Measurement methods had changed over time due to advances in instrumentation and additional types of data were collected to provide more and better information for testing snow-cover energy exchange models. In addition to providing better data for model testing, this research enhanced the understanding of the energy transfer process and the numerical techniques needed to solve the basic snow-cover energy exchange equations. Clearly, a new, more theoretically sound, and more complete snow-cover energy balance model needed to be developed. The result was Anderson's point energy and mass balance model (Anderson, 1976). This model was based on surface energy balance equations and equations for energy transfer within the snow cover. The snow cover was divided into finite layers and the model included the mathematical representations of densification of the snow layers and the retention and transmission of liquid water.

It must also be mentioned that Navarre developed a numerical snow model named "Perce-Neige" (Navarre, 1975) with characteristics similar to those of Anderson's model (1976). Navarre's work was published in 1975 but only in French, which meant that very few subsequent papers on snow modeling referred to it.

From 1978 to 1983, the World Meteorological Organization (WMO) compared the various snowmelt runoff models (WMO, 1986a). The corresponding WMO report examined 11 snow models and described their degree of success in providing hydrological models with runoff data. These models used a very simple representation of internal physical processes, compared with Anderson's model (1976). Probably the simple construction of these models was due to limited computing resources at that time and to the fact that the effects of internal processes on energy balance were not considered to be as important as they are today.

During the late 1980s, with the increased knowledge of snow processes and meteorology, the availability of snow and weather data sets, and the general use of faster computers, more sophisticated snow models were developed and used in a research or operational context in the fields of hydrology, avalanche forecasting, and climate analysis. A major conceptual breakthrough came from snow metamorphism studies, in which researchers simulated layering, a fundamental characteristic of the snowpack (Fig. 4.1), (Brun et al., 1992).

The challenge remains to determine how sophisticated snow models need to be for their intended scope of use. For that purpose, ICSI (International Commission on Snow and Ice) initiated a project called SNOWMIP, which compared the results from recent snow models when used on different climate conditions (Essery and Yang, 2001). In Section 4.2, Zong-Liang Yang describes some of these models and summarizes the results of a recent worldwide investigation on existing snow models which provides a precise view of the state of the art in snow modeling. It shows a very large variability in snow model features and designs.

Section 4.3 discusses the relative importance of major energy exchange processes at the snow surface or within the snowpack in terms of their impact on snow


Figure 4.1. Simulation of temporal evolution of snowpack layering at Col de Porte during winter 1998/99. Each color represents a snow type (see Brun et al., 1992). (Plate 4.1.)


Figure 4.1. Simulation of temporal evolution of snowpack layering at Col de Porte during winter 1998/99. Each color represents a snow type (see Brun et al., 1992). (Plate 4.1.)

simulations in a stand-alone model. Section 4.4 gives an overview of the representation of snow processes in different climate models.

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