Simulation of snow water equivalent by mathematical models of different complexity
L. Holko1, S.A. Sokratov2, A.B. Shmakin3, Z. Kostka1
institute of Hydrology, Slovak Academy of Sciences, Slovakia; 2Moscow State University, Russia; ^Institute of Geography, Russian
Academy of Sciences, Moscow, Russia
Представлены результаты апробирования нескольких моделей накопления и таяния снежного покрова для трёх различных участков в северной Словакии: долина, открытое пространство в горах и горный лес.
Introduction
Snow water equivalent (SWE) is the most important hydrological characteristic of the snow cover, because it provides the information on the amount of water that can eventually contribute to river runoff during the snowmelt. Basic principles of snow accumulation and melt, and thus the SWE simulation were elaborated about 50 years ago [1—3, 36, 37]. However, new models which profit from the progress in knowledge and technological development (data acquisition, computing) are developed permanently. Current models of snow cover evolution strive to simulate also some internal properties of the snowpack such as snow stratigraphy, temperature distribution in the snowpack, mass and energy fluxes, etc. [e.g. 6, 19, 23]. Some models attempt to include the effects of vegetation on snow-related processes [18, 26] or consider snowdrift [14, 24, 25, 31]. Except point simulation of snow cover evolution, distributed models have been developed to simulate SWE for river basins [10, 30, 33, 39]. Koivusalo [20] has recently provided an overview of snow cover modeling for hydrology.
Most snow models similarly using the threshold air temperature (or temperatures) to determine the portion of precipitation falling as snow generally simulate snow accumulation. Algorithms of snow melting can be roughly divided into three big groups. The simplest ones (index models) are based on the relationships between snowmelt and the conventionally measured meteorological variables, e.g. air temperature (the degree-day model), wind speed, etc. These models attempt to describe the complex process of snowmelt by means of simpler relationships. Algorithms of the second group strive to solve the complex energy balance of the snow cover (the energy-based models). Some models that are denoted as the «energy-based» still employ empirical relationships for snowmelt (e.g. using the air temperature to simulate melt contributions from various energy fluxes). Other energy-based models use more sophisticated physical approach in snowmelt modeling, although in details none of them can avoid empirical relationships. This is due to computational complexity or unavailability of necessary input data. Algorithms of the third group use generalized equations based on direct empirical relationships between snowmelt and selected meteorological characteristics. They are not used so often as the algorithms of the first two groups and, strictly speaking, they may not be called «mathematical models».
The most often used are the index models. Temperature index (degree-day) models proved their efficiency and are used in operational streamflow forecasting for a long time [9, 22, 27, 38, etc.]. World Meteorological Organization [40] has compared 11 different models used in several countries. Most of them were the degree-day models and were designed to work at a basin scale. Melloh [28] reviewed 7 major operational models that are based on the investigations of the U.S. Army Corps of Engineers [36, 37] and the U.S. National Weather Service [4, 5]. Except the degree-day, they have also the option of using the energy-balance of the snowpack to calculate the snowmelt.
Along with the development of the snow models, numerous studies attempted to inter-compare their results [7, 11, 13, 16]. The comparison is based on using the same input data and comparing modeled outputs with actually measured values [15]. Bengtsson and Singh [8] highlighted that the complexity of the model should reflect basin conditions. A simple degree-day model can be suitable for large basins in which runoff permanently increases during snowmelt, but the model has to be distributed related to land cover and topography. Also for small-forested basins where most of streamflow is of groundwater origin, the degree-day model combined with a conceptual runoff model can reproduce runoff well. In catchments in which the overland flow is an important runoff component, runoff fluctuates during a day. In such conditions, a high-resolution snow model is required to simulate the runoff.
The objective of this paper was to compare the ability of snow models with different complexities to simulate snow cover characteristics (mainly SWE) under different meteorological and landscape conditions.
Study area and data
The climatic data that served as the inputs into tested models and the snow data that were used to validate them were measured at three sites in the Jalovecky creek catchment, north Slovakia (Figs 1 and 2).
The first site called Ondrasova, is situated in the Lip-tov valley at altitude 570 m a.s.l. It represents the snow formation conditions of the wide mountain valley (shallow snow cover of shorter duration). This site has the best data. Climatic data are measured there with different frequencies. Precipitation is measured daily, cloudiness and wind speed three times per day. Air temperature (at 2 m and 5 cm above the surface), air humidity, soil temperatures at
L. Holko et al.
F i g. 1. Study area and the location of the sites Ondra>ova (1), Cervenec-open area (2), Cervenec-forest (3) Рис. 1. Территория исследований и местоположение участков: Ондрашова (1), Червенец — открытый участок (2 ), Червенец-лес (3 )
depths of 5, 10, 20, 50 and 100 cm, scalar wind speed, sunshine duration and snow depth are measured continuously. Snow characteristics at the nearby snow course (depth at 20 points, water equivalent at 3 points, snow structure at one pit, snow temperature at the same pit at several depths) were measured with varying frequency.
Two other sites (Cervenec) are situated in the Western Tatra Mountains. They represent the snow formation conditions at high altitudes at the open area and in the forest. Meteorological station is situated at the open area (site Cervenec-open area). It provided continuous measurements of the air temperature (at 2 m and 15 cm above the surface), air humidity, wind speed, global radiation, soil surface temperature and soil temperature at the depth of 15 cm. Precipitation is measured by the raingauge (weekly) and storage gauge (monthly). The readings of the gauges were recalculated into daily precipitation depths according to station Ondraíová. Snow course data (varying frequency of measurements) comprised 60 measurements of snow depth (SD) and 3 measurements of snow water equivalent (SWE). Snow structure and snow temperature at several depths were measured in the snow pit. The last site (Cervenec-forest) has the most limited data. Air temperature and air humidity were measured there in hourly time step in winter 2007. Correlations with data from Cervenec-open area were used to calculate air temperature and air humidity in winter 2006. Weekly precipitation at the site Cervenec-forest is measured since January 2007. Correlation with data from Cervenec-open area was again used to calculate precipitation for winter 2006. Snow course data were measured on the same days as the ones at the Cervenec-open area site. They comprised 20 measurements of SD and 3 measurements of SWE. Snow structure and snow temperature at several depths were measured in the snow pit.
Discharge of the Jalovecky creek measured at the outlet of the mountain part of the catchment was used as additional data to identify the snowmelt events.
Winters 2006 and 2007 had different climatic and snow characteristics. Winter 2006 was cold and long at the lower elevations, although in mountains the maximum
SWE was just «normal». Winter 2007 was mild with little snow at lower elevations, but SWE values were above-average in the mountains.
Snow cover models
The temperature and temperature-wind models represented Index snow cover models. These models are lumped, i.e. they do not take into account snow layering and the snowpack is represented as one layer. Two lumped models represented the energy-based models and one distributed model, e.g. the model that simulates multi-layered snowpack. The lumped energy-based models were represented by the combined extended approach by Braun [12] — further denoted as EXT, and the UEB model [35]. The multi-layer energy-based models were represented by the SPONSOR [34], which participated recently in a large model intercomparison project [15].
The models were run in a daily time step. Basic simulated output was snow water equivalent (SWE) which was simulated by all the models. The UEB (snowpack and snow surface temperatures) and SPONSOR (snow depth, snow temperature, layers) models simulated additional outputs. The modeling strategy was aimed at proper simulation of both maximum SWE and the timing of snow-melt, because these two characteristics are the most important in snow hydrology for flood runoff forecasting. After satisfactory simulation of SWE, other measured and simulated characteristics (snow surface temperatures, snow depths) were compared.
Index models. Two index models were used — the temperature index model and the temperature-wind index model. Snow accumulation in both models was calculated identically. The snow was accumulated if the air temperature was below the threshold value determining the beginning of the snowmelt. The type of falling precipitation depended on the air temperature. Fraction of snow was calculated according to the following equation [33]:
P -
snow
TRIS + Ttrans "
(1)
where P„„„„, is the fraction of snow on the total precipita-
snuw
F i g. 2. Snow profiles Ondra>ova (a), Cervenec-open area (b),
and Cervenec-forest (c) Рис. 2. Местоположение п
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