The information technology of forecast of the dynamics of lake's fields in permafrost was developed using geo-simulation approach to modeling. The model properties were determined on base of analysis of data on climatic changes and satellite images. The program complex for predicting geocryological changes under global warming using computer experiments with the model is presented. A new forecast assessments of changes of thermokarst processes on the territory of West-Siberian permafrost were obtained on base of computer experiments. model. It is shown that the gradual increase in temperature to 2 - 3 ∘ C in future decades will cause a reduction in the area of thermokarst lakes, what is an indicator of the continuing degradation of permafrost by the end of the century. The developed information technology can be used for solving problems of predicting the dynamics of greenhouse gas emissions from thermokarst ponds in Western Siberia under the impact of global warming. abstract environment.
The global warming leads to an increase of accidents on pipelines and other oil and gas facilities due to lower strength of permafrost. Moreover permafrost, as a repository of carbon conserved in the vast frozen peat bogs of northern Eurasia and America may cause even more warming if greenhouse gas release. The development of measures to reduce the damage of oil and gas companies require the use of forward-looking assessments of the dynamics of thermokarst processes. Due to considerable bogging and inaccessibility of the territory of Western Siberia, where is located the main oil and gas complex of Russia the research of these processes is impossible without the use of remote sensing data. The information technology of modeling and forecasting of the dynamics of thermokarst lakes fields was developed using satellite images for the period 1973-2010 years. An important issue is the creation of a mathematical model. The complexity of modeling the field of thermokarst lakes has led to the need to use geo-simulation approach to modeling of natural objects with a spatial structure.
We know that global warming leads to the northern territories to the growth of accidents on pipelines and other oil and gas facilities. Reducing the strength of permafrost caused by the acceleration of thermokarst processes under the influence of warming, is accompanied by the growth of economic and environmental damages on the domestic oil and gas companies, located in the permafrost zone. The development of measures to reduce the damage of oil and gas companies is impossible without predictive estimates of the dynamics of the morphological structure of thermokarst lake fields, the preparation of which requires the use of mathematical modeling of the dynamics of thermokarst processes on the territory of permafrost under a global warming.
Due to the high degree of waterlogging and remote areas of permafrost, these
studies both in our country and abroad are carried out with the use of remote
sensing data. At the same time as the most suitable geomorphological indicator
of changes in permafrost is used thermokarst lakes which is well seen on satellite
images [
Thermokarst processes can be modeled mathematically with analytical
models based on theory. Matt has shown [
However, modern forecasts of temperature changes for the north of Western
Siberia [
Geo-simulation model of lake field dynamics based on
experimental data from satellite images
Simulation modelling is one of the most important mathematical modelling
types. According to Moiseev and Svirezhev [
Creation of a geo-simulation model of thermokarst lakes fields requires
knowledge of the basic properties of these fields, which can be obtained experimentally.
Because of the inaccessibility of the northern territories of Siberia, thermokarst
experimental studies were carried out by remote sensing. For remote study
twenty-nine test sites were chosen in different zones of the West-Siberian
permafrost (sporadic, discontinuous and continuous). Remote study of the shape of
thermokarst lakes boundaries was carried out via satellite images in our research
[
To state the regularities for distribution of random coordinates of lakes and size-distribution of them, satellite images Landsat obtained in period 1984-2014 years were used. All space images are selected from the public archive - Global Land Cover Facility and these images are georeferenced in the UTM projection. Processing of space images was carried out by using the software ENVI 4.7 and ArcGIS 9.3. Lakes classification on the Landsat images was carried out by the method of a binary coding (encoding binary classification algorithm in the software ENVI 4.7). Lakes areas are defined by using ArcGIS 9.3. At each test site were identified from hundreds to thousands of lakes. Received data about lake areas were used to determine the average area of lakes and to build both distribution histograms of coordinates centers and of lakes areas for each test site. form:
Analysis of histograms of distribution of latitude and longitude values of
location of lakes centers given in [
with a probability of 95% [
= 1 ÷ ¯ ¯ = 1 ∑︁ =1
, = 1, where - a parameter of distribution law.
The value of parameter can be determined with the help of experimental data according to the formula: where (1) (2) is area of -th lake in test site; - number of lakes in this test site.
Testing correspondence of exponential law of lake area distribution given by Eq. (1) to experimental histograms shows that in all researched test sites this law corresponds to experimental data in accordance with criterion 2 with average probability 90%. Consequently, the stated law of distribution of lake area in form Eq. (1) does not contradict the experimental data. The analysis of the experimental distribution of lakes according to their areas shows that in all test sites varies in the range of 0.034 – 0.086 with average values 0.06.
Accordingly, the following fundamental principles determining substantial properties of a model of spatial-temporal structure of thermokarst lake field can be formulated: 1. Lake coastline shapes can be represented by a circle equation with centres coordinates , , and area ( - lake serial number). 2. Spatial changes in the position of centres of circles and their areas are statistically independent.
by a uniform law. 3. Random distribution of circle centres coordinates , ( = 1, ) is governed 4. Random distribution of number of circles over their areas conforms to the exponential law of distribution as in (1) with as a parameter. 5. Time changes in statistical properties of population of random circles and their dependence on climatic changes are determined by dependency of parameter on time and climatic characteristics in the following equation: = (, , ) (3) where - temperature, - level of precipitation and - time.
Model of field of thermokarst lakes is a collection of random circles, the statistical properties of which correspond to the above principles (1-5). Consequently, major elements in the model description are characteristics of lake shapes, parameters of their random location on surface and random distribution of lakes over their size (areas).
It is necessary to discuss questions of study of interrelation of climate and
geo-cryological changes in permafrost and its accounting in the model. To analyse
a correlation of area change of thermokarst lakes and climatic indices (average
annual temperature and precipitation level) an alternative approach was taken
to obtain data on air temperature and precipitation. The approach is based on
re-analysis of meteorological data [
To study the interrelation between the changes of thermokarst lake areas and
changes of air temperature and precipitation level we shall compare coefficients
of a linear trend of time changes of average values of the lakes’ areas and climate
characteristics. It is the analysis of the data obtained for developing a model
of thermokarst lake fields suitable for prediction that is of most interest. It is
necessary to study temperature dependence of parameter , which determines the
kind of law for thermokarst lakes’ distribution in accordance with their areas,
discussed in [
Previously the equation of dependence of parameter on time and climate
features was introduced in implicit form (3). To develop a model of actual
thermokarst lake dynamics it is necessary to define this dependence in explicit
form. This was the reason for doing multidimensional regression analysis [
The results of multidimensional regression analysis of the data on parameter and climate features can be presented as an equation of multiple regression in the form: = 0 + 1 × 1 + 2 × 2 + 3 × 3 (4) where 1 - average annual air temperature, 2 - precipitation level, 3 - time, - coefficients of regression equation = 0, . . . , 3.
In the result of the regression analysis of time series of the values of parameter and climate features, the following values of regression equation coefficients were obtained (4): 0 = −0.585ℎ −1; 1 = 0.00062ℎ −1/∘ ; 2 = 0.000014ℎ −1/ ; 3 = 0.00032ℎ −1/ .
The stated regression dependence of parameter on time and climate changes is a basis for developing algorithms for modelling random thermokarst lake fields, discussed in the next section. 3
Methodic questions of predicting of lake’s field based on geo-simulation modeling In a general case, mutual density of probabilities of random coordinates of centres and areas of circles imitating lakes in a mathematical model of random thermokarst lake fields can be presented in the form: (, , ) (5) where and - coordinates of circle center in a model; - area of a circle imitating a lake.
Consequently, the totality of circles in the model of lake fields will be presented as a totality of groups of three random values (, , ). To develop an algorithm for modelling thermokarst lake fields, it is necessary to take into consideration statistical connections between changes in lakes coordinates and their areas.
Further to equation (5), the random-number sequence determining characteristics of location of circles centers ( and ) is generated using the antenna of pseudo-random numbers distributed in accordance with the law of even distribution. And to form circles of random size whose areas are distributed according to the law conforming to equation (1) it is necessary to generate random-number sequences distributed in accordance with the exponential law. Consequently, together with using software generators for even distribution of pseudo-random numbers, the software realization of an imitation model of thermokarst lake fields includes creating a generator for pseudo-random number sequences, distributed in accordance with the exponential law.
We should consider a geo-simulation model of spatial structure of thermokarst lake field ( ) that is a totality of circles and reflects the state of a thermokarst lake field at the moment of time . To model the dynamics of thermokarst lake fields, we should consider a general model of spatio-temporal structure of a thermokarst lake field in the form:
= { ( 1), . . . , ( ), . . . , ( )}, = 1, . . . , which is a time sequence of geo-simulation models of a thermokarst lake field ( ), = 1, . . . , where each model relates to a particular moment of time.
Fig. 1 gives a visual presentation of the general model for spatio-temporal structure of thermokarst lake fields in the form of geo-information system (GIS) layers that relate to given time moments 1, 2, . . . , ∈ ( 1, ). (6) Legend: - time (year), = 1,
When modelling spatio-temporal structure of thermokarst lake fields it is important to take into consideration both time dependence and climate features (temperature, precipitation level). Accordingly, the dependence of parameter on time and climate features is determined by the equation of multiple regression in the form (4). This is the reason why equation (4) was used to develop an algorithm for numerical modelling dynamics of thermokarst lake fields.
The developed algorithm for modelling dynamics of thermokarst lake fields can be presented as follows: step 1 — the year of modelling is specified , = 1, . . . , ; ) of the model area (MA) under study are specified;
) in MA is specified; step 2 — the areas ( step 3 — lake density ( formula: = ×
; step 4 — the number of circles within MA is determined in accordance with step 5 — the centre of MA location in the map is specified; step 6 — parameter is determined in accordance with formula (4) for given values of temperature and time (year of modelling);
step 7 — pseudo-random number is generated, distributed in accordance with uniform law; mula:
step 8 — using the number obtained at the previous step, a pseudo-random number is calculated to characterize the value of circle area according with for = −
ln 1 (7) where - pseudo-random number distributed in accordance with uniform law in interval (0, 1), = 1, . . . , ;
step 9 — two pseudo-random numbers are generated, distributed in accordance with uniform law, determining the coordinates for circle centre location on the screen; step 10 — using the values of a number triple (, , steps 8 and 9, in accordance with equations ) obtained at previous (8) (9) and a circle is formed on the screen;
step 11 — if the number of circles obtained is less than , determined at step 4, the algorithm repeats beginning with step 7, otherwise it is completed.
The given algorithm allows formation of a model of spatial structure for a given time moment ( ), where = 1, . . . , . To make a general model of dynamics of a thermokarst lake field by means of forming a time sequence of models ( ) for a given set of moments ( = 1, . . . , ) the algorithm repeats for the number of times (m) needed.
Accuracy of modelling dynamics of thermokarst lake fields was studied in the form of computer experiment on the model. Values of parameter in this case are calculated according to the multiple regression formula (4) using the data about average annual temperature and precipitation level determined for each S by re-analysis. Then a model field is formed in accordance with the algorithm described above. Estimation showed that the error of determination of average values of lakes areas on base of modelling with use of experimental data is 17%. This may well be regarded as a suitable result of modelling thermokarst lake fields for predicting thermokarst lake fields dynamics. 4
Geo-simulation models are considered as more promising and make it possible
to study the dynamics of the thermokarst lakes fields in today’s global warming.
Recently, within the framework of the ideology of the simulation formed one of
the new areas of computer modeling, which is called geo-simulation modeling.
It is a simulation of complex objects with a spatial structure and realized with
the use of methods and means of geoinformatics. The geo-simulation model of
thermokarst lakes fields in the form of the random circles set is described in
[
The implementation of a mathematical model of thermokarst lakes fields
considered in [
The structure of the developed software package includes the following main components: 1. subsystem of geo-simulation modeling thermokarst lakes fields; 2. the subsystem of the displaying model results; 3. database (DB); 4. the subsystem of dataset formation.
The following describes components of the software package. The subsystem
of geo-simulation modeling thermokarst lakes fields, developed by the author,
it is a set of software modules that provide the input parameters of the model,
the formation of pseudo-random number sequences and output of simulation
results. The structure of the subsystem of geo-simulation modeling thermokarst
lakes fields includes the following main blocks:
input module is designed to provide the pseudo-random number sequences
values of model parameters;
generator of the pseudo-random number sequences is a major component of
the subsystem of geo-simulation modeling thermokarst lakes field and it is
designed to generate random number sequences in the algorithms
implementation for numerical simulation of thermokarst lakes fields. The numerical
simulation algorithm is described in details in [
The subsystem of the displaying model results allows showing the output given
either on a digital map by means of geographic information system (ArcGIS),
or in the form of electron tables and graphics in MSExcel. The database is a
part of the software package. It is a store spatial and attributes information on
the study sites obtained during the field experiment. Description of the database
structure and capacity is given in [
Sample of predicting of lake’s field dynamics in
West-Siberian permafrost
To generate the forecast of dynamics of the thermokarst lakes fields in permafrost
of Western Siberia for future decades, it is necessary to have projections on
climate changes in the study area. Temperature forecast for the north of Western
Siberia to 2300 are presented in [
Scenario of computer simulation experiment: Predicting the dynamics
of thermokarst lake fields on the basis of the geo-simulation model using
predictive estimates of temperature changes in the north of Western Siberia [
As shown in [
Because of the current lack of prognosis of precipitation changes in the
prediction period, at obtaining of forecast assessments of lakes area changes are used
data only about temperature changes. To substantiate the prediction
possibility without precipitation we conducted a comparison of the regression equation
coefficients (4), the values of which are given on p. 6. Comparison of these
coefficients shows that 2 ≪ 1 and 2 ≪ 3. This allows us to ignore the contribution
of term 2 × 2 in the equation (4) in the value of the parameter . Comparison
of the results of the lakes dynamics prediction by using the developed algorithm
for the period up to 2030 [
The most important result of the analysis of forecast estimates presented in Fig. 3, is the conclusion about continuation of the reduction of the average area of thermokarst lakes in the West Siberian permafrost. The graph in Fig. 3 shows that at the end of the forecast period, the average area of the lakes can be reduced to 14.5 hectares, i.e. approximately 20% compared to 2010 year. Thus, the continued increase in the coming decades the average annual temperature of surface atmosphere will be accompanied by a reduction in the average area of thermokarst lakes in the permafrost zone of Western Siberia, what is the result of permafrost degradation and reduce its strength. Designed geo-simulation model of the dynamics of thermokarst lake fields, taking into account the relationship between regional geocryological and climate changes, allowed to carry out forecasting changes of lake sizes in conditions of continuing global warming. Long-term prognosis of the dynamics of lake thermokarst-fields using this model showed that with the growth of the air temperature in West-Siberian permafrost lake areas will be reduced on average by approximately 20% by the end of the forecast period. A new forecast assessments of changes of thermokarst processes on the territory of West-Siberian permafrost were obtained using computer experiments with the model. It is shown that the gradual increase in temperature to 1∘ C by 2050 year will cause a reduction in the area of thermokarst lakes, what is an indicator of the continuing degradation of permafrost in coming decades.
The information technology of modeling and forecasting the dynamics of thermokarst lakes fields can be used for solving the problems of reducing the accident rate on the infrastructure facilities in the permafrost territories and predicting the dynamics of greenhouse gas emissions from thermokarst ponds in Western Siberia under the impact of global warming.
This research was supported by grant RFBR Project No. 15-45-00075.