沙漠面积预测

Summary

Land desertification is the most serious problem of land resources in the world and has greatly restricted the economic development of a country. In theory, the introduction of forest protection is of great significance to resist the desertification. The paper takes an in-depth discussion about some problems existing in the construction of the Three North Shelterbelt.

For the first question, we are going to predict the situation of desertification in 60 years with the analysis of the evolution trend about desertification before the construction of the Three North Shelterbelt in China according to the requirements of subject. Combined with the causal relationship theory of desertification development, we take double exponential smoothing on existing data with the exponential smoothing method, and get the relevant parameters of a and b, which is respectively 34.386 and 0.355. Here is the conclusion: it is expected that the desertification area is 0.65601 million square kilometers in 2075. When analyzing the influence factors of desertification, we respectively regard geography and climate, economy and society as natural factor and human factor. Then we use Mann-Whitney-Wilcoxon method to test the correlation between precipitation and the average temperature difference. It is concluded that the decrease of precipitation and the increase of air temperature have a little effect on desertification, while the human activity is the most significant one.

The second question is to evaluate the impact of the Three North Shelterbelt on the evolution of desertification. With the usage of grey system model, we analyze the desertification data correlatively, convert it into a white box system, set up differential equation model and then perform the residual test to detect the forecast accuracy. We draw the conclusion that it is expected that the desertification area is 0.620301 million square kilometers in 2050. The same method goes to the analysis of influence factors about forest construction. We analyze the correlation between the factors about rainfall and forest area, and draw the conclusion that the population factor is the most crucial one for the forest construction.

The third question is the analysis of the opportunity cost of the Three North Shelterbelt construction. We focus on the impact of the construction on the local water resources, and analyze the variation tendency and correlation relationship between forest area and the amount of local underground water resources. Here comes the conclusion: the construction of the Three North Shelterbelt consumes local groundwater resources severely and the correlation coefficient reaches to 0.717. Forest will consume 53.893-billion-cubic meters water from 2012 to 2020. Finally, we analyze the opportunity cost of the Three North Shelterbelt construction concretely with the combination of the impact of underground water and surface water on local economy and culture.

Keywords:the Three North Shelterbelt, exponential smoothing, grey system, desertification.

Content

1.Introduction (2)

1.1.Background (2)

1.2.Problem Review (3)

2.Assumption (3)

3.Symbols Definition (4)

4.Mode for growth of Gobi Desert (5)

4.1.Analysis of the Green Great Wall factors (5)

4.2.Mode based on Exponential smoothing (6)

4.3.Forecast results and analysis (8)

5.What other factors influence this growth (10)

5.1.Geographical and climate (10)

5.2.Economy and Society (14)

6.Prediction of Gobi Desert with the grey models (15)

6.1.Grey model in the growth of Gobi desert (15)

6.2.GM(1,1) forecast model (16)

6.3.Model checking and analysis (18)

6.4.Strength and weakness (20)

7.Threat assessment model of Green Great Wall (20)

7.1.Threat from different attributes. (20)

7.2.Model of correlation analysis (21)

7.3.Results and Analysis (22)

8.Model of water resource opportunity (23)

8.1.Opportunity cost of water resource (23)

8.2.Model of planting and water resource (24)

https://www.sodocs.net/doc/2217697492.html,prehensive analysis of opportunity cost (27)

9.Strengths and Weaknesses (27)

9.1.Strengths (27)

9.2.Weaknesses (28)

10.Conclusion (28)

11.Reference (29)

12.Appendix (30)

1.Introduction

1.1.Background

A desert is a barren area of land where little precipitation occurs and consequently living conditions are hostile for plant and animal life[1]. Deserts are distributed all over the world. In China, the area of desert is about 700000 square kilometers. If taking into account the 500000 square kilometers of Gobi, accounting for 13.5% of China's land area.

Desertification is a type of land degradation in which a relatively dry land region becomes increasingly arid, typically losing its bodies of water as well as vegetation and wildlife[2]. Dry climate, sparse vegetation, and excessive use, make it easier for desertification. Other factors, such as geographic, ecological, societal also play important role in desertification. In Inner Mongolia and North Africa, tens of thousands of people are forced to leave their hometown under the threat of the desertification.

The Gobi, locates at southern Mongolia and northwestern China, is a large desert region in Asia. In recent years, Gobi is expanding at a sobering speed, consume a large amount of grassland. The desertification of Gobi mainly blame on human activities. In addition, china has carried out many plans to slow the expansion of the desert.

In order to resist desertification, techniques focus on two aspects: provisioning of water, and fixation and hyper-fertilizing soil. To reach this goal, many regions make project to plant trees. In china, The Three-North Shelter Forest program, as known as the Green Great Wall, is a series of human-planted wind-breaking forest strips,

designed to hold back the expansion of the Gobi Desert. It is planned to be completed in 2050.Up to now, the Three-North Shelter Forest Program has total 270000 square kilometers preservation forest. More encouragingly, the positive factor has showed that the Gobi area is decreasing in china.

1.2.Problem Review

From the problem, we can know that it needs us to build mathematical models to predicate the growth of Gobi Desert and evaluate the influence of the Green Great Wall. So we need to do following things:

Build a mathematical model to express the Gobi Desert growth without The Green Wall and forecast the trend in the future. In this model, we will consider the problem mainly based on the condition of China.

Compared the data forecasted by ideal model and the actual data, analysis the geographic, ecological, societal, and climate factors influence this growth

Consider the Green Wall and correct the growth model.

Analysis the cultivation process of green The Great Wall, evaluate the threat level of each possible factor.

Model the water consumption of The Green Wall.

2.Assumption

Assume that the information finding on the academic papers is real and convincing.

Assuming that the desert area is only the region in China.

Assuming that the forest area has a positive correlation with planted land area and rainfall capacity.

Assuming that the forest area has a negative correlation with temperature, population and so on.

Assuming that there will not be any catastrophe of data in the grey-system model.

Assuming that the underground water keep the certain rate with total water resources.

Assuming that the variation trend of desert area and forest is smooth and steady.

3. Symbols Definition

Symbol

Explanation t

particular year

X t

the area of Gobi in particular year

1S t index smoothing value of t 2S t

secondary index smoothing value of t

smoothing factor t a

forecast beginning point

t b step increment 0k X the area of Gobi sequence 1k X itemized accumulation of 0k X

1k Z

mean sequence of 1k X

k

class ratio k

prediction residuals k forecast class ratio deviation 1^k X

forecast area of Gobi Desert k i

correlation coefficient at time k r i

series connection degree

4.Mode for growth of Gobi Desert

4.1.Analysis of the Green Great Wall factors

In order to forecast the growth of the Gobi Desert without the Green Great Wall, we assume that if we can find data showing the area of Gobi Desert without the Green Wall. We can use model to forecast the growth of Gobi Desert with such data. From the China National Forestry Bureau we learned that the government began to implement the three North Shelterbelt program from 1979. The three North Shelterbelt covering north area in 13 provinces, autonomous region. Gobi Desert is one of the important administration target of this program.

Figure 1 The three North Shelterbelt distribution

Considering that the effect of the Green Great Wall is a gradually increasing process, the impact on the Gobi Desert is very small in the beginning years. Before the tree planting area to a certain size, we can ignore its impact on the growth of Gobi

Desert. Through the discussion results there is conclusion that the growth model without the Green Wall can be concluded with the data before 1980s. Furthermore, the data before 1990s also have a certain credibility.

4.2. Mode based on Exponential smoothing

The growth of desert area is a continuous process. Since we confirmed that our model should forecast the growth of Gobi Desert. We collected the data of the critical time points. So we adopted exponential smoothing to forecast the growth of the Gobi Desert. Exponential smoothing is a rule of thumb technique for smoothing time series data. And Exponential smoothing is commonly applied to smooth data. In this discussion, the process of desertification is continuous. With the expansion of the desert, adjacent area can be influenced by the same factor. So the new desert area puts the same factors to adjacent area, which leads to the further desertification. Using the Exponential smoothing method and the unknown information can obtain prediction data.

According to the data from the desert research papers [3], we capture key information and analyze the data, we shows them in Table 1.

Data

Area (104 km 2)

Data

Growth Rate (km 2/year)

1975 30.82 1955-1975 1560 1985 33.3 1975-1989 2100 1999

38.57

1989-1999

3600

Table 1 Area and Growth Rate of Gobi Desert

From the growth rate and the desert area in 1975. Do the calculation to get the annual area of the Gobi desert from 1955 to 1975. Using exponential smoothing method to modified the data, making it more believable. We have

11

21

2

11111S t X t S t S t S t S t

After get the smoothing annual area of the Gobi desert, we can set the forecast beginning point t

a and the step increment t

b . To forecast the future growth, we have

12122^t t T t t a S t S t b S t S t a b y

At first, we set the beginning point at 1975, forecast the area of the Gobi Desert from 1975 to 1990. The data shows the phenomenon that the forecast data and real data is very close. Particularly, the real data in 1985 nearly equal to the forecast data. Data X t

1S t 2S t

Data X t

1S t 2S t

1955 27.43 27.430 27.430 1973 30.4 30.19675 30.00363 1956 27.586 27.508 27.469 1974 30.61 30.40338 30.2035 1957 27.742 27.625 27.547 1975 30.82 30.61169

30.4076

1958 27.898 27.762 27.654 1976 31.03 30.82084 30.61422 1959 28.054 27.908 27.781 1977 31.24 31.03042 30.82232 1960 28.21 28.059 27.920 1978 31.45 31.24021 31.03127 1961 28.366 28.212 28.066 1979 31.66 31.45011 31.24069 1962 28.522 28.367 28.217 1980 31.87 31.66005 31.45037 1963 28.678 28.523 28.370 1981 32.23 31.94503

31.6977

1964 28.834 28.678 28.524 1982 32.59 32.26751 31.98261 1965 28.99 28.834 28.679 1983 32.95 32.60876 32.29568 1966 29.146 28.990 28.835 1984 33.31 32.95938 32.62753 1967 29.302 29.146 28.990 1985 33.67 33.31469 32.97111 1968 29.458 29.302 29.146 1986 34.03 33.67234 33.32173 1969

29.614

29.458

29.302

1987

34.39

34.03117 33.67645

1970 29.77 29.614 29.458

1971 29.98 29.797 29.628

1972 30.19 29.994 29.811

Table 2 Forecast result from 1975 to 1987

4.3.Forecast results and analysis

In the Exponential smoothing model, if the beginning point more late, the number of data which particular in the calculation will be larger. At the same time, the outcome will be more accurate. From Table 3 we find the forecast data and real data is very close in 1985. What's more, the data shows the consistency near 1985. So we set the beginning point at 1985, forecast the area of the Gobi Desert from 2015 to 2075. The results shows in

Data Area

(104

km2)

Data

Area

(104

km2)

Data

Area

(104

km2)

Data

Area

(104

km2)

2015 44.318 2031 49.994 2047 55.669 2063 61.345 2016 44.673 2032 50.348 2048 56.024 2064 61.700 2017 45.028 2033 50.703 2049 56.379 2065 62.054 2018 45.382 2034 51.058 2050 56.733 2066 62.409 2019 45.737 2035 51.413 2051 57.088 2067 62.764 2020 46.092 2036 51.767 2052 57.443 2068 63.118 2021 46.446 2037 52.122 2053 57.798 2069 63.473 2022 46.801 2038 52.477 2054 58.152 2070 63.828 2023 47.156 2039 52.831 2055 58.507 2071 64.183 2024 47.511 2040 53.186 2056 58.862 2072 64.537 2025 47.865 2041 53.541 2057 59.216 2073 64.892 2026 48.220 2042 53.896 2058 59.571 2074 65.247

2027 48.575 2043 54.250 2059 59.926 2075 65.601 2028 48.930 2044 54.605 2060 60.281

2029 49.284 2045 54.960 2061 60.635

2030 49.639 2046 55.315 2062 60.990

Table 3 Forecast result from 2015 to 2075

Accuracy analysis The Exponential smoothing model can forecast the data of time

series accurately. To show the relatedly between the forecast data and real data directly, we plot over a range of time in Figure 1.

Figure 2 The relatedly between the forecast data and real data.

From 1975 to 2015, the prediction curves show a smooth growth trend. At four points, the real data was close to the forecast data. The model basically accords with the actual situation.

Residual analyze According to the forecast outcomes, do residual's correlation

test. The result shows in Figure 3. From the figure we can know that the deviation within the constraint curve. The forecast outcomes are realiable.

Figure 3 Residual correlation of sequence

Phenomenon explanation However, the data shows little gap in 2015.

Considering the speed of the desertification grows. In addition, the plants in the first stage of the Three North Shelterbelt comes to the aging stage around 2015.

5.What other factors influence this growth

Considering the influence factors of land desertification is complicated, there are omissions in the results from the regression analysis. Therefore, in order to facilitate the economic, social, geographical, climatic factors analysis, we will put together the geography and climate, as environmental factors, the economy and society together, as the human factor, analysis.

5.1.Geographical and climate

Through observation of the world desert in Figure 3, we can see that the vast majority of the world's deserts are located near the tropic of Cancer and the tropic and Capricorn.

N N, obviously higher While the deserts in China are mainly distributed in35~50

than the average of the global desert. This area should not be a dry climate zone in the latitude of the distribution. Considering the geographical and climatic factors, Firstly, the region far from the sea, little affected by the warm air in the ocean. Secondly, because of the high Tibetan Plateau terrain, the vast area of Northwest China and Inner Mongolia shows unique climate. In winter, in control of the Siberia-Mongolia anticyclone and cold air, climate is dry and cold. In summer, Tibet Plateau blocking the monsoon humid from the Indian Ocean, the climate is high temperature and less rainfall. So this region in extreme drought through the year. Thirdly, due to the high content of sand in the area, loose and easy to flow. Sand blown by the wind and piled up, thus forming a large desert.

Figure 4 Desert distribution in the world.

According to common sense, we can judge that the temperature rise and the decrease in precipitation may result in land desertification. Taking into account the change of temperature and precipitation is small in 20 years, and the contribution of land desertification may be weak. We have collected data of the average annual rainfall and the average temperature difference between the average temperature in the 100 years in Gobi desert between 1950~1956 and 1970~1976. Then, we use Mann-Whitney-Wilcoxon test to take nonparametric test of precipitation and temperature in two periods, Make sure if there is significant difference.

First of all, we sort the data on the basis of precipitation from low to high, the minimum value in rank1, the rank table as follows:

Data Precipitation Rank Data Precipitation Rank 1973 150 1 1951 185 8

1970 163 2 1950 190 9

1974 174 3 1975 192 10

1972 175 4 1955 195 11

1976 176 5 1953 205 12

1956 180 6 1954 209 13

1971 184

7 1952 210

14

Table 4 Rank the mixed samples of precipitation in 14 years.

Sorting data in the form, get the rank sum.

1950~1956 1970~1976

Data Precipitation Rank Data Precipitation Rank 1950 190 9 1970 163 2 1951 185 8 1971 184 7 1952 210 14 1972 175 4 1953 205 12 1973 150 1 1954 209 13 1974 174 3 1955 195 11 1975 192 10 1956 180 6 1976 176 5 rank sum 73 rank sum 32

Table 5 Mixed rank of two sample

The number of samples is enough. (17n ,27n ) Sample approximation is subject to normal distribution. Using the formula, calculate the mean value and standard deviation of sampling distribution:

(1)6(661)1123922

n n n W (1)

66(661)1212 6.2441212

n n n n W Statistics is discrete but the normal distribution is continuous. We approximate the normal distribution approximation using the continuity correction. Because 73W , we do the calculate of the p-value:

730.539(73)()( 5.365)6.244

P W P z P z

Using the standard normal distribution table and z=5.365, bilateral P-value is far less than 0.001. Therefore, at the 99.9% confidence level, we believe that the 50's and the 70's is not the same as the total precipitation, the 50's precipitation is significantly higher than the 70's.

Similarly, we analysis the temperature: Data

Temperature difference

Rank

Data

Temperature difference

Rank

1955 -0.5 1 1971 -0.15 8 1976 -0.45 2 1970 -0.1 9 1953 -0.4 4 1951 0 10 1956 -0.4 4 1972 0.03 11 1975 -0.4 5 1950 0.07 12 1973 -0.3 6 1952 0.2 13.5 1954

-0.2

7

1974

0.2

13.5

Table 6 Rank the mixed samples of temperature difference in 14 years.

1950~1956

1970~1976

Data

T emperature difference

Rank

Data

T emperature difference

Rank

1950 0.07 12 1970 -0.1 9 1951 0 10 1971 -0.15 8 1952 0.2 13.5 1972 0.03 11 1953 -0.4 4 1973 -0.3 6 1954 -0.2 7 1974 0.2 13.5 1955 -0.5 1 1975 -0.4 5 1956

-0.4

4

1976

-0.45

2

rank sum 51.5

rank sum 54.5

Table 7 Mixed rank of two sample

(1)6(661)1123922

n n n W (1)

66(661)1212 6.2441212n n n n W 54.50.539(54.5)()( 2.40)6.244

P W P z P z

Using the standard table and z=2.40, p-value=2*0.0082=0.0164<0.05, and so, at the 95% confidence level, we believe that the 50's and the 70's temperature is generally not the same, the average temperature of 50s was significantly lower than the average temperature of 70s.

5.2. Economy and Society

Overall, at a hundred years, there is little change in geography and climate, which is not a huge change in the environment. Therefore, we believe that human activity is the main factor in the growth of desertification. First, population pressure. Since the

founding of new China, due to the improvement of living conditions, the population growth rate has been greatly improved, and has caused great pressure on the environment. Secondly, over reclamation and overgrazing. Due to the population pressure and the people pursuit of economic interests. The reclamation and overgrazing phenomenon is becoming more and more serious, the biological diversity, vegetation coverage rate, the height of the grass layer decreased significantly, resulting in surface of bare patches, gradually expanded and connected, and finally the whole surface of the desert.

6.Prediction of Gobi Desert with the grey models 6.1.Grey model in the growth of Gobi desert

In the first question, the growth rate of Gobi Desert was predicted by using exponential smoothing model. In order to eliminate the influence of the Great Green Wall factors on the growth rate of Gobi desert, the data selection is prior to the implementation of the three North Shelterbelt program. Also include the period that the influence of the Green Great Wall is too little. Considering the influence factors to the three North Shelterbelt in second problem, compared with the first problem has the following advantages and challenges. First, we can use more data volume, can get more convincing prediction results. Second, the factor of green the Great Wall is difficult to quantify.

In order to establish a more comprehensive and convincing model, we first analyze the growth system of Desert Gobi. The growth process of Desert Gobi is affected by many factors, including geography, economy, climate, human activities and the Green Great Wall. Some factors in these systems is known to us, such as part of the annual growth rate and area, precipitation. Many unknown factors such as the Green Great Wall's influence on the growth speed of Gobi Desert and human activities, etc.

We know that the system information is partially known and partially unknown system called the gray system.[4] This kind of gray system is very difficult to quantify. In order to accurately describe the growth process of Gobi desert, we use GM (1,1) model of Grey system to carry on the Green Great wall factors to analysis the growth process. Seem the influence factors as the grey variable. Using the data of the Gobi Desert as forecast sample to make forecast.

6.2. GM(1,1) forecast model

Firstly, introduce the area of the Gobi Desert fifth a year from 1975 to 2015. It's know that Chinese government start the Green Great Wall from 1978. Secondly, sequence the data in Table8 Data

1975 1980 1985 1990 1995 2000 2005 2010 2015 k

1

2

3

4

5

6

7

8

9

0k X

31.22

32.27 33.32 34.97 36.77 38.57 40.97 43.37 45.77

k

0.9675 0.9685 0.9528 0.9510 0.9533 0.9414 0.9447 0.9476

Table 8 the area of Gobi sequence and class ratio

Using the grey forecast model must satisfy some conditions. Then, we test whether the data satisfy the model. Calculate the class ratio of the sequence.

001,2,3,4,5,6,7,8,9k k k X X k

Only the k all in the 22

22,n n e e

, the model can be used.

[e -2n+1e 2n+2]

=[0.81871.199]

After inspection, the data are consistent with the level of class ratio, and it can be applied to the GM model. Then do ADO to 0k X , get new number series 1k X .

Mean operation of the sequence

1k X .Then get a new number series. 1k Z .So

the establishment of grey differential equation is

1

,2,3,4,5,6,7,8,9x k az k b k

The corresponding whitening differential equation is

1

dx ax t b dt

(,)T u a b ,000(2,3,9)T Y x x x ,(1)(1)(1)1(2)1(3)1(9)z z B z

. Use least square method to solve equation. Finally, gain the predicting equation.

1

^1(1),2,3,4,5,6,7,8ab b b x

k x e k a a

Figure 5 Algorithm structure diagram

6.3. Model checking and analysis

Predict the results by using the prediction formula. According to the rule of GM model, analyzed the results are reliable or not. Residual test : According to the formula.

000^

,1,2,3,5,6,7,8,9x

k x k k k x k

If 0.2, the result ban be considered to meet the general requirements. If 0.1, the result ban be considered to meet the high requirements. Class ratio deviation test : According to the formula.

10.51(),1,2,3,5,6,7,8,910.5a

k k k a

If 0.2k , the result ban be considered to meet the general requirements. If

0.1k , the result ban be considered to meet the high requirements.

The results are calculated using MATLAB software programming. k

Data

0k X

1k Z

k

k

1 1975 31.2

2 31.22 0 2 1980 32.27 31.6892 0.0180 -0.0188

3 1985 33.32 33.369

4 0.001

5 -0.0199 4 1990 34.97 35.1387 0.0048 -0.0033 5 1995 36.77 37.0019 0.0063 -0.0015

6 2000 38.5

7 38.9639 0.0102 -0.0039 7 2005 40.97 41.029

8 0.0015 0.0087 8 2010 43.37 43.2054 0.0038 0.0052 9

2015

45.77

45.4962

0.0060

0.0022

Table 9 Model checking data

From the data that the model data have good results, the model can be used for forecasting. According to the prediction formula, we obtain the future growth trend of three North shelterbelt. Display in Table10 Data

2020

2025

2030

2035

2040

2045

2050