Frost Number Research Articles

The application of elevation corrected MERRA2 reanalysis ground surface temperature in a permafrost model on the Qinghai-Tibet Plateau

There is an urgent need to evaluate the accuracy of reanalysis datasets to improve the reliability of climate research, hydrology, ecology, engineering work, and so on. The ground surface temperature (GST) is also regarded as a significant upper boundary condition when simulating permafrost distribution. In this study, the newest Modern-Era Retrospective Analysis for the Research and Applications Version 2 (MERRA2) reanalysis GST from the National Aeronautics and Space Administration's (NASA) Global Modeling and Assimilation Office (GMAO) is compared with GST data from 69 meteorological stations over the Qinghai-Tibet Plateau (QTP). Then, elevation correction of the MERRA2 GST was performed for different altitudes on seasonal scales. The correction indicates that the accuracy of raw MERRA2 GST data has been greatly improved after the elevation calibration. The decreased proportions of root mean square error (RMSE) for calibrated GST in winter, autumn, summer, and spring are 88.4, 92.8, 95.7, and 92.8%, respectively. The improvements in the mean bias error (MBE) in winter, autumn, summer, and spring are 88.4, 92.8, 95.7, and 92.8%, respectively. Most of the QTP presents a statistically increasing tendency of 0.2 to 0.5 °C/10a for GST at a significance level of 0.01 from 1980 to 2013. Then, the elevation corrected MERRA2 GST was applied in the surface frost number semi-physical permafrost model. The simulated results show that the permafrost area on the QTP is approximately 1.02 × 106 km2 in the early 21st century, excluding lakes and glaciers. The permafrost degradation was characterized by the disappearance of permafrost which mainly occurred in the eastern QTP.

Spatial distribution and changes of Xing'an permafrost in China over the past three decades

Climate warming causes profound consequences on permafrost distribution throughout the high-latitude regions of the globe. Xing'an permafrost in China is the southernmost part of high-latitude permafrost and is constantly changing. However, understanding on this change process of permafrost is limited. On the basis of digital elevation model (DEM) data, meteorological station, survey data and the meteorological forcing dataset in the northern northeast area in China, we calculated the mean annual ground surface temperature (MAGST), the frost number (Fn) of air temperature (Ta), and the ground surface temperature (GST) with the Fn model. The change in permafrost were analyzed from 1980 to 2010 by statistical and empirical/semi-empirical models. Comparison of the calculated results with the published frozen ground map and survey data, the description on permafrost distribution was more accurate using the Fn of GST than Ta. Permafrost zoning was performed using Fn of GST results and continuous coefficient. The area of permafrost changed from 2.21 × 105 Km2 to 4.87 × 105 Km2. The degradation trend was from low-to high-altitude areas and from continuous to discontinuous permafrost. The permafrost was significantly degraded from the 1980s to the 1990s. The degradation rate slowed down from the 2000s, and some areas have been developed. This work provides basic data and reference for regional permafrost research and project in cold areas.

Effect of climate and thaw depth on alpine vegetation variations at different permafrost degrading stages in the Tibetan Plateau, China

ABSTRACTUnderstanding the driving forces for alpine vegetation variations at different permafrost degrading stages is important when the Tibetan Plateau is experiencing climate warming. We applied the modified Frost Number model to simulate frozen ground distributions in the Tibetan Plateau and calculated the maximum thawing depth by the Stefan approach. We classified the simulated frozen ground into three subzones: seasonal frozen ground zone, changing zone, and permafrost zone. We evaluated the effects of precipitation, air temperature, and maximum thawing depth on Normalized Difference Vegetation Index (NDVI) in the subzones across five different stages from 1982 to 2012. The results show that permafrost zone, changing zone, and seasonal frozen ground zone account for about 30.6 percent, 23.3 percent, and 46.1 percent of the study area, respectively. Over the five stages, permafrost areas decreased at fast, slow, fastest, and then slowest rate from stage1 to stage 5, and the large continuous permafrost area has been degraded into pieces. Precipitation is strongly correlated with NDVI and contributes most `to the changes of NDVI. Maximum thawing depth and particularly air temperature show a much smaller correlation and contribute less to the variation rate of NDVI. The findings will have broad applications in investigating the impact of climate and environment changes on alpine vegetation variations in the Tibetan Plateau.

Study on the Permafrost Distribution Based on RS/GIS

Permafrost in Qinghai-Tibet Plateau is the world’s highest elevation and largest permafrost regions in the lower latitude. For its vast area and less measured data, traditional mapping methods rely on the observations of station have been largely restricted. So it is necessary to build permafrost distribution model. Based on the GIS, using the RS data as the main data source and considering the distribution characteristics of permafrost in Qinghai-Tibet Plateau, we build Multivariate analysis model. Considered the elevation, land-surface temperature, vegetation, soil moisture and surface albedo and other factors related to the permafrost distribution in Tibet Plateau, and selected the Qinghai Tibet highway as the study area to simulate the permafrost distribution. Compared with the Retrieval Model of Ground Temperature based on RS/GIS, elevation model and frost number model, it is found that simulation result of Multivariate analysis model fit best with the permafrost distribution map and it reflected the permafrost distribution well along the Qinghai-Tibet highway.

Simulated responses of permafrost distribution to climate change on the Qinghai\u2013Tibet Plateau

Climate warming causes changes in permafrost distribution, which affects the surface energy balance, hydrologic cycle and carbon flux in cold regions. In this study, the Surface Frost Number model was applied to examine permafrost distribution on the Qinghai–Tibet Plateau (QTP) under the four RCPs (RCP2.6, RCP4.5, RCP6.0, and RCP8.5). The Kappa statistic was used to evaluate model results by comparing simulations of baseline permafrost distribution (1981–2010) with the existing frozen soil maps. The comparison shows that the Surface Frost Number model is suitable for simulating the general characteristics of permafrost distribution on the QTP. Simulated results suggest that areas of permafrost degradation would be the smallest in the near-term (2011‒2040) with the rates of 17.17%, 18.07%, 12.95% and 15.66% under RCP2.6, RCP4.5, RCP6.0 and RCP8.5, respectively. The rate of permafrost degradation would be faster in the mid-term (2041‒2070), especially under the RCP8.5 scenario (about 41.42%). Areas of permafrost degradation would be the largest in the long-term (2071‒2099) relative to baseline conditions, with a modelled 64.31% decrease in permafrost distribution using the RCP8.5 scenario. Our results would help the decision‒making for engineering construction program on the QTP, and support local units in their efforts to adapt climate change.

The Application and Evaluation of Simple Permafrost Distribution Models on the Qinghai-Tibet Plateau

The performance of simple permafrost distribution models widely used on the Qinghai–Tibet Plateau (QTP) has not been fully evaluated. In this study, two empirical models (the elevation model and mean annual ground temperature model) and three semi-physical models (the surface frost number model, the temperature at the top of permafrost model and the Kudryavtsev model) were investigated. The simulation results from the models were compared to each other and validated against existing permafrost maps of the entire QTP and in three representative areas investigated in the field. The models generally overestimated permafrost distribution in the investigated areas, but they captured the broad characteristics of permafrost distribution on the entire QTP, and performed best in areas with colder, continuous permafrost. Large variations in performance occurred at elevations of 3800–4500 m asl and in areas with thermally unstable permafrost. The two empirical models performed best in areas where permafrost is strongly controlled by elevation, such as eastern QTP. In contrast, the three semi-physical models were better in southern island permafrost areas with relatively flat terrain, where local factors considerably impact the distribution of permafrost. Model performance could be enhanced by explicitly considering the effects of elevation zones and regional conditions. Copyright © 2017 John Wiley & Sons, Ltd.

Remote Sensing of the Mean Annual Surface Temperature and Surface Frost Number for Mapping Permafrost in China

The use of satellite-infrared sensors to map permafrost distribution is a new research topic. Two important permafrost indices, the mean annual surface temperature (MAST) and the surface frost number (SFN), are estimated using MODIS Aqua/Terra LST products based on a pragmatic scheme proposed in this study. The advantage of this approach is that it allows the full use of every value at any time and at any pixel of MODIS LST products. This scheme is simple, easy to implement, and independent of other observations. The accuracy of the method depends only on the accuracy of the MODIS LST products. Eight years of data sets from 2003 to 2010 were generated using this scheme to reflect the spatial distribution of permafrost and the surface thermal state. A comparison between the southern/lower limit of permafrost and results from the 8-year average MAST and SFN show that the 0 °C MAST isotherm and 0.5 contour of SFN agree well with the identified southern/lower limits of permafrost in China.

A comparison of permafrost prediction models along a section of Trail Ridge Road, Rocky Mountain National Park, Colorado, USA

The distribution of mountain permafrost along Trail Ridge Road (TRR) in Rocky Mountain National Park, Colorado, was modeled using ‘frost numbers’ and a ‘temperature of permafrost model’ (TTOP) in order to assess the accuracy of prediction models. The TTOP model is based on regional observations of air temperature and heat transfer functions involving vegetation, soil, and snow; whereas the frost number model is based on site-specific ratios of ground temperature measurements of frozen and thawed degree-days. Thirty HOBO© temperature data loggers were installed near the surface as well as at depth (30 to 85 cm). From mid-July 2008 to 2010, the mean annual soil temperature (MAST) for all surface sites was − 1.5 °C. Frost numbers averaged 0.56; TTOP averaged − 1.8 °C. The MAST was colder on western-facing slopes at high elevations. Surface and deeper probes had similar MASTs; however, deeper probes had less daily and seasonal variation. Another model developed at the regional scale based on proxy indicators of permafrost (rock glaciers and land cover) classified 5.1 km 2 of permafrost within the study area, whereas co-kriging interpolations of frost numbers and TTOP data indicated 2.0 km 2 and 4.6 km 2 of permafrost, respectively. Only 0.8 km 2 were common among all three models. Three boreholes drilled within 2 m of TRR indicate that permafrost does not exist at these locations despite each borehole being classified as containing permafrost by at least one model. Addressing model uncertainty is important because nutrients stored within frozen or frost-affected soils can be released and impact alpine water bodies. The uncertainty also exposes two fundamental problems: empirical models designed for high latitudes are not necessarily applicable to mountain permafrost, and the presence of mountain permafrost in the alpine tundra of the Colorado Front Range has not been validated.

Spatial modelling of palsa mires in relation to climate in northern Europe

AbstractPalsa mires are mire complexes that occur in the Northern Hemisphere, representing one of the most marginal permafrost features at the outer limit of the permafrost zone. A climate‐based spatial model is presented for the distribution of palsa mires in northern Europe. The model is based on an extensive spatial data of palsa mires and climatological variables from 1913 grid cells in an area of c. 240 000 km2. Generalized linear modelling (GLM) with curvilinear and interaction terms is used to derive the palsa mire–climate relationships. The final model correctly classified 77·6 per cent of the palsa mire presence squares. The results indicate a positive association of the distribution of palsa mires with increasing frost number and continentality, whereas precipitation and temperature showed a negative correlation with the distribution of palsa mires. Additionally, interaction of thawing degree days and summer time precipitation showed a negative association. Climatologically, the optimum areas of palsa mires occur in areas of low precipitation (<450 mm) and a mean annual temperature between −3 °C and −5 °C. Potential reasons for the performance of the model and the sensitivity of palsa mires to climate change are discussed. The application of a GIS‐based generalized linear modelling as used here provides a versatile method to study the distribution of different geomorphological phenomena across climatological gradients. Copyright © 2004 John Wiley & Sons, Ltd.

Predicting availability to consumers of spatially and temporally variable resources

Ecological dynamics in many aquatic communities are strongly influenced by spatial and temporal variability of key limiting resources, and the extent to which consumers can locate and exploit concentrations of those resources. Intuitively, resource concentrations that are `close' and `long-lived' should typically be more available to consumers than `distant' and `ephemeral' resource concentrations. The speed and accuracy with which consumers can locate concentrations of their resources is in part determined by their movement characteristics and sensory constraints, which vary with taxon, life-history stage, physiological state, environmental conditions, and other factors. This has motivated detailed observation and modelling of individual-level foraging behaviors in a wide variety of taxa. However, our abilities to develop this intuitive concept of availability into empirically-based, quantitative predictions for consumer–resource interactions remain limited, largely due to the complexities of formulating and simulating spatially explicit models of consumer–resource interactions, and the difficulty of understanding how specific simulation results relate to broader ecological situations. This paper presents a non-dimensional index, the Frost number, that provides a simple prediction of availability to consumers of spatially and temporally varying resource concentrations. This index incorporates characteristics of both resource distributions and consumer movement behaviors. When Frost numbers characterizing consumer–resource interactions are much less than unity, resource concentrations are typically unavailable to consumers because travel time to reach them exceeds the longevity of the resource. Conversely, when Frost numbers are much greater than unity, resource longevity exceeds travel time so that resource concentrations are available. The Frost number may provide a preliminary identification of the length and time scales at which resources are available to consumers in complex ecological systems, even when detailed spatial observations and simulations are not available.

A GIS-aided response model of high-altitude permafrost to global change

Two models are used to simulate the high-altitude permafrost distribution on the Qinghai-Xizang Plateau. The two models are the “altitude model”, a Gaussian distribution function used to describe the latitudinal zonation of permafrost based on the three-dimensional rules of high-altitude permafrost, and the “frost number model”, a dimensionless ratio defined by manipulation of freezing and thawing degree-day sums. The results show that the “altitude model” can simulate the high-altitude permafrost distribution under present climate conditions accurately. Given the essential hypotheses and using the GCM scenarios from HADCM2, the “altitude model” is used for predicting the permafrost distribution change on the Qinghai-Xizang Plateau. The results show that the permafrost on the plateau will not change significantly during 20–50 a, the percentage of the total disappeared area will not be over 19%. However, by the year 2099, if the air temperature increases by an average of 2.91°C on the plateau, the decrease in the area of permafrost will exceed 58%—almost all the permafrost in the southern plateau and in the eastern plateau will disappear.

A Computational Method for Prediction and Regionalization of Permafrost

The number, a dimensionless ratio defined by manipulation of either freezing and thawing degree-day sums or frost and thaw penetration depths, can be used to define an unambiguous latitudinal zonation of permafrost continuity. The index is computed using several variables influencing the depth of frost and thaw penetration, and can be related mathematically to the existence and continuity of permafrost. Although the frost number is a useful device for portraying the distribution of contemporary permafrost at continental scales, it is not capable of detecting relict permafrost and should not be mapped over small areas unless numerous climate stations are located in the region of interest.

Permafrost Distribution in Central Canada: Applications of a Climate-Based Predictive Model

Abstract A revised permafrost index, computed from mean monthly air temperatures and snowcover data, produces an unambiguous latitudinal zonation of contemporary permafrost. Isarithmic mapping of this “surface frost number'’defines a latitudinal zonation that is in substantial agreement with a previous semi-empirical mapping of permafrost in the lowlands of central Canada. A related index, the “Stefan frost number,'’employs estimates of soil properties in an approximate engineering solution for the depths of freezing and thawing. Mapping of this index by unclassed choropleth methods provides an estimate of point-to-point variations in permafrost distribution under the assumptions of homogeneous topography and vegetation. The model successfully predicts the presence of permafrost in peatlands outside the zonal limits defined by climatic criteria alone. The frost number provides an easily computed, physically based method for predicting permafrost that lends itself to a variety of cartographic representatio...