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Journal of Geographical Sciences >

2018 , Vol. 28 >Issue 6: 802 - 818

DOI: https://doi.org/10.1007/s11442-018-1506-9

Research Articles

Investigating long-term trends of climate change and their spatial variations caused by regional and local environments through data mining

  • XIE Yichun , 1, 2 ,
  • ZHANG Yang 3 ,
  • LAN Hai 4 ,
  • MAO Lishen 1 ,
  • ZENG Shi 5 ,
  • CHEN Yulu 1
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  • 1. Institute for Geospatial Research and Education, Eastern Michigan University, Ypsilanti, Michigan 48197, USA
  • 2. Guangzhou Institute of Geography, Guangzhou 510070, China
  • 3. Department of Computer Science, Indiana University, Bloomington, Indiana 47405, USA
  • 4. Department of Computer Science, New York University, NY 10012, USA
  • 5. Center for Advanced Spatial Analysis, University College London, London WC1E 6BT, UK

Author: Xie Yichun (1956-), PhD and Professor, specialized in urban modelling, ecological modelling and environmental modelling. E-mail:

Received date: 2017-08-23

  Accepted date: 2017-12-10

  Online published: 2018-06-20

Supported by

Guangdong Innovative and Entrepreneurial Research Team Program, No.2016ZT06D336

GDAS Special Project of Science and Technology Development, No.2017GDASCX-0101

Copyright

Journal of Geographical Sciences, All Rights Reserved
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Abstract

Climate change is a global phenomenon but is modified by regional and local environmental conditions. Moreover, climate change exhibits remarkable cyclical oscillations and disturbances, which often mask and distort the long-term trends of climate change we would like to identify. Inspired by recent advancements in data mining, we experimented with empirical mode decomposition (EMD) technique to extract long-term change trends from climate data. We applied GIS elevation model to construct 3D EMD trend surface to visualize spatial variations of climate change over regions and biomes. We then computed various time-series similarity measures and plot them to examine spatial patterns across meteorological stations. We conducted a case study in Inner Mongolia based on daily records of precipitation and temperature at 45 meteorological stations from 1959 to 2010. The EMD curves effectively illustrated the long-term trends of climate change. The EMD 3D surfaces revealed regional variations of climate change, while the EMD similarity plots disclosed cross-station deviations. In brief, the change trends of temperature were significantly different from those of precipitation. Noticeable regional patterns and local disturbances of the changes in both temperature and precipitation were identified. The trends of change were modified by regional and local topographies and land covers.

Key words： climate change; empirical mode decomposition; Inner Mongolia; similarity plot; trend surface

Cite this article

XIE Yichun , ZHANG Yang , LAN Hai , MAO Lishen , ZENG Shi , CHEN Yulu . Investigating long-term trends of climate change and their spatial variations caused by regional and local environments through data mining[J]. Journal of Geographical Sciences, 2018 , 28(6) : 802 -818 . DOI: 10.1007/s11442-018-1506-9

1 Introduction

Global climate change has been widely recognized as a new natural threat to biodiversity (Dawson et al., 2011) and human welfare (de Sherbinin, 2011) in the 21st century. Many modern techniques have been developed by scientists to collect evidences concerning climate change contained in tree rings, ice cores, greenhouse gas levels, shoreline changes, glacier and permafrost melt, radiocarbon dating, air and sea temperature, phenology, etc. Among them, weather conditions - daily temperature and rainfall - have long been recorded and analysed to provide a direct evidence of climate change. For instance, climate change has been manifested in increased global temperatures, but also in increasing frequency of extreme weather events such as floods and droughts, severe winds, and increased temperature extremes of both hot and cold (National Climate Assessment, 2014; Rahmani and Zarghami, 2015; Xia et al., 2015).
Global climate change (e.g., global warming, increased/decreased precipitation, and extreme weather event) is regarded as one of the primary factors that are impacting grassland ecosystems (Kyselý et al., 2012; Piras et al., 2015; Ribalaygua et al., 2013). For instance, the Mongolia Plateau is getting warmer and drier. The average temperature of Mongolia increased by 1.5°C to 2.5°C in the 1990s and 2000s (Lu et al., 2009), while the annual precipitation decreased by about 7.0% during the same period (Wang et al., 2013). Global climate change is assumed to affect growth condition as well as spatial distribution of plant communities (Li S et al., 2013). Drying and warming climate usually increases fluctuation of vegetation productivity (Bai, 2008; Gong, 2015) and leads to plant community degradation (Li and Xie, 2013; Xie et al., 2017).
Moreover, ecosystem researchers have recognized that different plant communities show varied responses to climate change (Brown et al., 2013). Although precipitation and temperature are two main climate factors affecting vegetation response (Han, 2016; Wang et al., 2012), plant communities respond differently to short-term or long-term changes of precipitation and temperature, respectively (Chuai, 2007; Yuan, 2015). Second, vegetation responses to climate change display significant local and regional variations (Bai, 2008; Lu et al., 2009; Xie et al., 2017). Third, climate change displays apparent regional variations. For instance, mountainous regions are usually more sensitive to climate change than flat and low elevation regions (Damsø et al., 2015). Unique locational arrangements of land masses, oceans or water bodies, dominant air flows, topographies and elevations can have significant impacts on local meteorological conditions and thus lead to distinct regional patterns of climate change (Cheng et al., 2015). Even within the same river basin, the yields of rice and wheat could display significant regional variations because of the influence of agro-climatic factors, such as variation in temperature, length of maturity period and leaf area index (Mishra et al., 2013; Swain and Thomas, 2010). Climate change in combination with land use change could make water quality and land productivity deteriorate swiftly and lead to noticeable spatial variations (Jordan et al., 2014).
Furthermore, studies of vegetation response to climate change are facing many challenges. Climate changes contain remarkable cyclical oscillations and disturbances, which often mask and distort the long-term trends we would like to identify (Kennedy et al., 2014). Annual cycles are critical phenomena of temperature and precipitation. When analysing climate change, we should bear in mind that the seasonal changes are interacting with a lot of other dynamics, such as long-term warming/cooling or drying/wetting trends, abrupt weather events (flooding, drought, hot wave, and cold front), pollutant emissions, solar activity cycles, etc. Traditional analytical methods based on the comparisons between minimum, average and maximum values of temperature and precipitation are not capable of separating long-term trends from cyclical fluctuations and abrupt changes or capturing temporal dynamics or regional patterns of climate change (Chamaille et al., 2007). As a result, it is almost impossible to study long-term interactions between meteorological conditions and the underlying landscape, vegetation and topography by simply analyzing the records of temperature and precipitation. Therefore it is desirable to apply an effective data analysis method to break down climate variations into individual processes, i.e., cyclical, long-term and abrupt components. Only with this type of data mining and pre-processing is it feasible to investigate spatial patterns and interactions between climate change and regional environmental factors.
In this paper, we will examine diverse responses of plant communities to climate change and their spatial variations, visualize temporal trajectories and spatial patterns of climate change at regional scale, and compare spatial variations of climate change across meteorological stations. Since current GIS tools are not adequately supporting analysis and visualization of temporal trajectories and spatial patterns of climate change, we integrate recent computational data mining approaches with GIS. In particular, we will synthesize advanced signal processing and denoising techniques to extract long-term trends of climate change. We will also adopt the similarity analysis and surface visualization methods often seen in big data analytics to visualize spatial variations of the identified change trends and to analyse their relationships with landscape, vegetation and topography at region, biome and weather-station scales.

2 The study area, data and method

2.1 The study area and data

Inner Mongolia Autonomous Region (IMAR, 37°24'-53°23'N, 97°12'-126°04'E) is located in China’s northern border region with a total area of about 1,180,000 km2 (Figure 1). IMAR is also located in the southern portion of the Mongolian Plateau with an average altitude of 1000-1200 m. The climate of the steppe area is a typical temperate continental climate, with an annual precipitation of 50-450 mm and an annual average temperature of 1-10℃. The climate in the study area experiences a gradual transition from humid and semi-humid regions to semi-arid and arid regions from east to west. Precipitation shows a gradual decrease from northeast to southwest, while temperatures gradually increase from the northeast toward the southwest (Li J et al., 2013).
Figure 1 The map of the study area (Meteorological stations are numbered from east to west)
Grassland is the dominant land cover in IMAR, which is concentrated in the central part of IMAR, while most of the forest is located in the northeastern section dominated by broad-leaf and needle-leaf forests and cropland in the southern and eastern regions (Li J et al., 2013). Traditionally, grazing has long been the primary economic activity in IMAR. However, since the late 20th century, due to many coupled natural and human factors, such as climate change, economic development, population growth, and overgrazing, grassland ecosystems in IMAR suffered severe degradation and even desertification in some areas. Grasslands occupy almost 40% of the earth’s land surface, support nearly one third of global population (Gibson, 2009), and boast many important ecological functions, including soil and water conservation, carbon sequestration, wildlife habitat, etc. (Carlier et al., 2009). In addition, the Mongolian Plateau is the largest stretch of grasslands remaining on the earth, in which IMAR is an important part (Xie et al., 2017). Therefore, the selection of IMAR grassland as the case study has important implications in both academic research and policy management.
The vegetation map of Inner Mongolian Autonomous Region in 2010 was provided by Inner Mongolian Institute of Grassland Surveying and Planning (Li S et al., 2013). Meteorological data was extracted from the China Meteorological Data Service Center (CMDC, 2013), consisting of 50 surface meteorological stations distributed in Inner Mongolia (Figure 1) over 50 years, 1959-2010. The data includes the longitude and latitude information of each meteorological station, daily precipitation and temperature of each meteorological station.

2.2 The research methods

The paper synthesizes three groups of methods: (1) trends analysis derived from computational data mining (empirical mode decomposition - EMD) to extract long-term trends of change from cyclical climate data; (2) similarity analysis stemmed from data mining to examine spatial variations of climate change across meteorological stations; and (3) GIS 3D and 2D visualization techniques to reveal regional and cross-station patterns of plan community responses to climate change.
(1) Trends analysis of cyclic climate change
Data mining is a newly acknowledged-field that has received vast attention from computer science and information science researchers. Data mining refers to an analytic process designed to search for consistent patterns and/or systematic relationships between variables from large volumes of data (also known as “big data”) (Jain and Srivastava, 2013). One vital goal of data mining is to construct models and then to apply these models to new data to generate predictions (Huang et al., 1998).
Signal processing and intelligent recognition is one technique within an increasingly growing data mining toolbox. Data mining in many fields involves constantly monitoring real-time conditions on the basis of signals collected by sensors. The datasets of these signals are usually recorded or saved in the form of time series. Therefore, suitable signal processing techniques are needed in order to extract information from such signals and to disclose underlying dynamics embedded in these time-series data (Gao and Yan, 2011). These techniques serve two purposes to represent the reality sensed by various sensors: first to determine the parameters to create an abstract model of the reality, and second to confirm the model that can represent the reality to certain degree (Huang et al., 1998). The challenge is to represent the real world as close as possible while eliminating as much noises and abrupt interference on data/signal as possible. In the past, many methods were developed to achieve this goal according to the special field in which the data analysis is applied. In general, these signal processing techniques could be grouped into three approaches: Fourier transform, wavelet transform, and empirical mode decomposition.
Fourier methods traditionally are used to approximate any general function as a sum of trigonometric functions (Grafakos and Teschl, 2013). Wavelet transforms, also called “mathematical microscopes (Bovik, 2009, p. 463)”, include a suite of signal processing techniques that are developed to filter signals by using a different centre frequency in the band-pass filter, in which small scales of the noise frequency can be removed to get good-quality and useful signals (Portilla et al., 2003). Wavelet-based denoising at various scales aims to achieve high resolution in both the time and frequency domains (Dai et al., 2006; Chen and Xu, 2005). The principle of EMD is to decompose the signal into a group of similar sinusoidal signals, which was defined by the signal itself, named the intrinsic mode functions (IMFS), and a residue (Huang, 1998; Gloersen and Huang, 2003; Rao and Hsu, 2008). The IMFS reveal the status of the signal in various scales, and the residue told us the trend of the signal, which is the statistic we are interested in this paper.
In recent years, due to the increasing popularity of computational data mining, the EMD method has been applied in many research fields, such as, removing noise of time series data (Huang et al., 2001; Peng et al., 2005); analysing the properties of time series data in finance (Huang et al., 2003); and applications in hydrology and environment (Rao and Hsu, 2008), goaf surface deformation (Zhang, 2011), temperature trend extraction (Xian et al., 2008), image-based land cover classification (Demir and Ertürk, 2010) and vegetation analysis (Chen and Xu, 2005; Ghasemi et al., 2013; Cheng et al., 2014). Mathematically, EMD iteratively applies an intrinsic mode function (IMF), which decomposes complex signals into a number of distinct, simple, and non-sinusoidal signals along with a trend curve. This EMD trend curve reflects the trend of change of time-series signals and is used to identify long-term trend of changes hidden in the cyclical datasets of climate change and ecological evolution.
The mathematical algorithm of EMD is not the same as Fourier method and the Discrete Wavelet Transform although they belong to the same family of time domain signal analysis techniques (Zhang et al., 2015). EMD can be applied to decompose non-linear and non-stationary datasets in comparison with Fourier. Contrasting to wavelet denoising, EMD method has similar distortion magnitude in the process of denoising signals (Luan et al., 2004). However, the application of EMD denoising does not require to set up a priori classification function as wavelet algorithm does. This enables EMD method becomes more robust and stable.
(2) Similarity measurement of spatial variations of climate change across meteorological stations
We adopt a time series analysis of climate change to characterize climate change dynamics and reveal their spatial variations across meteorological stations. Various methods have been developed based on temporal trajectories to characterize changes in ecosystem dynamics in recent years (Lhermitte et al., 2011). These methods are also suitable to the studies of climate change due to the similar nature of temporal dynamics. The key techniques in these time series analyses are methods of identifying similarities or dissimilarities between two sequences of measurements (Goshtasby, 2012; Zastrow, 2015).
(a) Euclidean distance
$d_{st}^{2}=({{x}_{s}}-{{x}_{t}})({{x}_{s}}-{{x}_{t}})\text{ }\!\!'\!\!\text{ }$. (1)
where xs is a data vector with the size of (1 × s), and xt is another data vector with the size of (1 × t). In our case, s = t. The symbol, ', represents the transposition operation of a vector (e.g. (xs - xt)' represents the transposed vector of the original vector ( xs - xt)).
(b) Standardized Euclidean distance
$d_{st}^{2}=({{x}_{s}}-{{x}_{t}}){{V}^{-1}}({{x}_{s}}-{{x}_{t}})\text{ }\!\!'\!\!\text{ }$ (2)
where V is the n-by-n diagonal matrix whose jth diagonal element is S(j)2, where S is the vector of standard deviations. Each coordinate difference between rows in X is scaled by dividing by the corresponding element of the standard deviation.
(c) City block metric
Manhattan distance assumes that in going from one pixel to the other it is only possible to travel directly along pixel grid lines and diagonal moves are not allowed. Therefore, the distance between centroid is given by:
${{d}_{st}}=\sum\limits_{j=1}^{n}{\left| {{x}_{sj}}-{{x}_{tj}} \right|}$ (3)
(d) Chebyshev distance
Chebyshev distance or the L∞ metric (Luan et al., 2004), is defined on a vector space where the distance between two vectors is the greatest of their differences along any coordinate dimension.
${{d}_{st}}={{\max }_{j}}\left\{ \left| {{x}_{sj}}-{{x}_{tj}} \right| \right\}$ (4)
(e) Cosine distance
Cosine distance measures the similarity between two vectors of an inner product space in terms of the cosine of the angle between them. This technique has been used to measure cohesion within clusters in the field of data mining.
${{d}_{st}}=1-\frac{{{x}_{s}}x{{'}_{t}}}{\sqrt{({{x}_{s}}x{{'}_{s}})({{x}_{t}}x{{'}_{t}})}}$ (5)
(f) Correlation coefficient
Pearson correlation coefficient is suitable for determining the similarity between images with intensities that are known to be linearly related (Goshtasby, 2012). The correlation coefficient between sequences X ={xi: i = 1, . . . , n} and Y = {yi: i = 1, …, n} is defined by
$r=\frac{\sum\limits_{i-1}^{n}{({{x}_{i}}-\bar{x})}({{y}_{i}}-\bar{y})}{{{\left\{ \sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}} \right\}}^{\frac{1}{2}}}{{\left\{ \sum\limits_{i=1}^{n}{{{({{y}_{i}}-\bar{y})}^{2}}} \right\}}^{\frac{1}{2}}}}$ (6)
where $\bar{x}=\frac{1}{n}\sum\limits_{i=1}^{n}{{{x}_{i}}},\ \bar{y}=\frac{1}{n}\sum\limits_{i=1}^{n}{{{y}_{i}}}$
(g) Spearman distance
A similarity measure relating to the Pearson correlation coefficient is Spearman’s rank correlation or Spearman’s Rho (Goshtasby, 2012). If image intensities do not contain ties when they are ordered from the smallest to the largest, then by replacing the intensities with their ranks and calculating the Pearson correlation coefficient between the ranks in two images, which will give Spearman rank correlation. This is equivalent to calculating (Goshtasby, 2012):
${{d}_{st}}=1-\frac{({{r}_{s}}-{{{\bar{r}}}_{s}})({{r}_{t}}-{{{\bar{r}}}_{t}})'}{\sqrt{({{r}_{s}}-{{{\bar{r}}}_{s}})({{r}_{s}}-{{{\bar{r}}}_{s}})'}\sqrt{({{r}_{t}}-{{{\bar{r}}}_{t}})({{r}_{t}}-{{{\bar{r}}}_{t}})'}}$ (7)
where
rsj is the rank of xsj taken over x1j, x2j, ...xmj
rs and rt are the coordinate-wise rank vectors of xs and xt, i.e., rs = (rs1, rs2, ... rsn)
${{\bar{r}}_{s}}=\frac{1}{n}\sum\limits_{j}{{{r}_{sj}}}=\frac{(n+1)}{2}$
${{\bar{r}}_{t}}=\frac{1}{n}\sum\limits_{j}{{{r}_{tj}}}=\frac{(n+1)}{2}$
Spearman rank correlation is less sensitive to outliers, impulse noise and occlusion. It is also less sensitive to nonlinear intensity difference between images than Pearson correlation coefficient (Goshtasby, 2012). Because of these features, Spearman rank correlation has been used to measure trends in data as a function of time or distance.
(3) Visual data mining methods for identifying regional and cross-station patterns
In geographical information science, 3D surface models are important tools in GIS for conducting spatial analysis and visualizing the outcomes of the spatial analysis (Li et al., 2005). A typical example is the digital elevation model (DEM) that represents the earth’s elevation surface. In this paper, we are using the same technique to visualize the EMD trend line as an elevation surface over the entire study area. These EMD 3D trend surfaces clearly visualize the regional patterns of climate change during the study period (1959 - 2010) over the study area and can be examined visually. In addition, 2D contour lines derived from the 3D surfaces are also plotted to provide different views of the regional patterns of climate change. The 3D and 2D surfaces clearly depict regional patterns of plant community responses to climate change and help reveal topographical impacts on varied responses of plant communities to climate change.
The similarity measures are also plotted as 2D maps to visualize spatial variations of precipitation and temperature across the meteorological stations. The 2D similarity plots visibly reveal geographical differences of precipitation and temperature in the study area.

3 The case study of climate change in Inner Mongolia

As a starting point, we calculated annual precipitation by adding daily precipitation and annual average temperature by averaging daily temperature at each station. As a result, we got 51 records of annual precipitation and annual average temperature for all 50 meteorological stations. In order to identify long-term trends of climate change at 50 stations, we ran regression analysis of precipitation against the year and temperature against the year, respectively. We then plotted the regression slopes of precipitation and temperature as curves over the stations from east to west (Figure 2). Apparently, 38 out of 50 stations observed a decline in precipitation because they had negative slopes (under the 0.000 horizontal line). Moreover, the precipitation slope curve showed obvious ups and downs, revealing significant differences of change among the stations. On the contrary, the temperature slope curve was much smoother. 44 out of 50 stations witnessed an increase in temperature.
Figure 2 Regression slopes of precipitation and temperature, 1959-2010, at meteorological stations
Next, we examined variations of climate change over three scales, regional, vegetation type, and meteorological station, by using the methods we introduced before. The daily precipitation and temperature data from 1959 to 2010 over 45 meteorological stations were analysed. Five stations were located in urban areas and were excluded from the analysis due to the paper’s focus of exploring different responses of vegetation communities to climate change. Through EMD method, we transformed the daily climate data at each station incrementally into a long-term trend curve. The trend curves of temperature and precipitation were visualized as 3D surfaces and 2D plots by all stations from east to west. Furthermore, we applied the above-mentioned eight different similarity measurements to the EMD curves for all 45 stations. For each similarity measurement, we created a similarity matrix of 45×45 stations and then examined its sensitivity of spatial variations by stations. For sensitive similarity measurements, we created 2D plots to illustrate station-wide variations.
In the first visualization, we produced a vegetation map with the meteorological stations numbered from the east to the west and with ten types of vegetation mapped in different colours. The vegetation map helped explain the east-to-west distribution patterns of different biomes. From the vegetation map we could see the “wettest” grasslands (the meadow types) matched with the Da Hinggan Mountains stretching north to south in the eastern region of the study area and the Heilongjiang River (Figure 1). The typical steppe and hay grassland are located in the northeastern-central section and the southwestern-central section. The desert-type grasslands occupy the northwestern-central section and the western section. The dryness increased toward the west. The spatial pattern of biomes deeply affected the trends of precipitation and temperature changes from 1959 to 2010.

3.1 The temporal trends of temperature changes

Several trends of temperature changes were identified on Figures 3 and 4: (1) temperature witnessed an overall and consistent increase in the past 50 years; (2) temperature changes were moderate in the first 35 years but dramatic in the recent 15 years; (3) temperature changes showed a regional pattern, becoming warmer from east to west (because the widths of cold temperature bands were decreasing from east to west but the widths of warm temperature bands were increasing); (4) the regional pattern of temperature changes revealed noticeable spatial variations; and (5) regional variations of temperature changes were impacted by biomes. For example, around station 12 in meadow area close to the Heilongjiang River (Figures 1, 3 and 4), the relative EMD value increased from 0 to 10, station 5 in mountain area from 0 to 20 and station 40 in desert area from 0 to 30. In other words, the change trends differed locally and regionally. The desert and mountain areas responded quicker to the temperature increase than the wet biomes.
Figure 3 Temperature EMD surface diagram
Figure 4 Temperature 2D contour diagram
It was clear that the EMD values constantly increased over most stations in the past 50 years (Figure 3). The range of the EMD value changes was 10 to 30, depending on the types of biome and topography where the stations were located. In general, the EMD values increased by 10-12 points before 1995 but jumped additional 18-20 points from 1995-2010 (Figure 4). Moreover, the trend curves of EMD were raised from east to west except for several unique regional patterns (Figures 3 and 4). Firstly, most of the stations of 1-12, are located in the east edges of the Hulun Buir Steppe and the valleys of Da Xinggan Mountains with relatively less productive biomes (primarily salt meadow and some typical steppe). Therefore, the EMD changes were over 16-18 points. However, there were a couple of stations (2 and 6) around the Hulun Lake, which showed that the EMD changes were less than 15 points. Secondly, from stations 16 to 32, except for stations 25 and 26, we saw a wide stretch of blue belt and the EMD increase was a little bit over 10 points (Figure 4). Most of these stations were located in Xilinhot Typical Steppe, which was the heartland of Eurasian temperate grasslands (Xie et al., 2009), and, hence, the EMD increases were moderate. Finally, from station 34 and further west, we witnessed an extensive brown and red stretch of higher EMD values, which signified apparent warming impacts. Most of these stations were located in either deserts or desert steppe with much drier environments. Therefore, the EMD curves were raised much higher than the remaining areas (Figure 3). Clearly different environments showed diverse susceptibility to climate change.

3.2 The temporal trends of precipitation change

The temporal trends and spatial patterns of precipitation changes in the past 50 years were different from those of temperature changes. First, the precipitation generally decreased from east to west but showed complicated temporal trajectories and spatial patterns. Secondly, there was a singular precipitation increase event (reflected by higher EMU values) in the past 50 years. This precipitation increase was centered on the Hulun Lake area (Xin Barag Left Banner) and extended to the east section of the Hulun Buir Steppe and the northern section of the Da Xinggan Mountains (Figures 5 and 6). This increase event started from 1975, reached the maximum around 1990-1994, and returned to normal in 2004, lasting almost 30 years. Thirdly, the precipitation variation in the west section of the Hulun Buir Steppe and the Xilin Gol Steppe gradually decreased. Moreover, the decrease was more apparent in the wetter areas. For instance, the precipitation EMD curves over the western Hulun Buir and the eastern Xilinhot (stations 14-24) declined more noticeably and quickly than those over the western Xilinhot (stations 27-32). Fourthly, over the deserts and desert steppes (stations 4-6, 25-26 and 34-44), the precipitation EMD curves did not show a clear increasing trend (Figure 6). Finally, the EMD curves over the desert areas displayed moderate temporal changes (Figure 5) although no clear linear trends were identified.
Figure 5 Precipitation surface diagram
Figure 6 Precipitation contour diagram

3.3 Similarity measurement results

We applied the above-mentioned seven similarity measurements to the EMD dataset of 45 meteorological stations. We computed the similarity measurements of the EMD values across 45 meteorological stations. In other words, we compared similarity degrees among the meteorological stations. We also calculated the root mean square error (RMSE) to examine the sensitivity levels of these similarity measures (Table 1). The values of RMSE for tem-perature were usually lower than 0.30 and showed slight changes between different simi-larity measures. Thus, the spatial variation of temperature across meteorological stations was gradual and not dramatic. However, the RMSE values for precipitation were usually above 0.38. Especially, the RMSE values of correlation distance (C.D.) and Spearman distance (S.D.) measurements were above 0.50 and almost close to 0.60. The higher RMSE values indicated that the similarity measures were poor for precipitation (Veerasamy et al., 2011), which reflected significant variations in precipitation among the meteorological stations. For the purpose of revealing spatial variations across the stations, we were reporting C.D. and S.D.measures in the following graphics.
Table 1 Seven similarity measures: Root Mean Square Errors (RMSE)
Precipitation RMSE Temperature RMSE
Chebyshev 0.4249 Chebyshev 0.3008
City block 0.3870 City block 0.2600
Correlation 0.5956 Correlation 0.2896
Cosine 0.3898 Cosine 0.2264
Euclidean distance (E.D.) 0.4170 Euclidean distance (E.D.) 0.2654
Spearman 0.5912 Spearman 0.2805
Standardized E.D. 0.4413 Standardized E.D. 0.3042
Figures 7 and 8 were the S.D. and C.D. cross-difference maps of 45 stations in precipitation, respectively. Both displayed clear and similar patterns. These maps could be clearly read in four quads. The upper left (U-L) quad revealed the similarities or differences of the stations numbered 1 to 23. In comparison, the similarities between them were the smallest. Moreover, significant different similarities were identified around stations 3, 9-11, 13, 15, and 20 in this quad. Seen from Figure 1, we found out that these stations were either far away in distance from the stations numbered around them, or these stations were located in different biomes. The lower right (L-R) quad was another extreme, displaying dense small cells and thus indicating apparent differences between these stations numbered above 23. The different similarity measures in these two quads were consistent with the biomes observed on ground. The stations in U-L were located in meadow and typical grasslands, while the stations in L-R were largely located in deserts, desert steppes and steppe deserts. The remaining two quads depicted similarity comparisons between the stations located in quads 1 and 4. In other words, the similarity differences were identical in these quads. The variations were intermediate between U-L and L-R quads.
Figure 7 Cross-station plot of Spearman distance for precipitation
Figure 8 Cross-station plot of correlation distance for precipitation
Figures 9 and 10 were the S.D. and C.D. cross-difference maps of 45 stations by temperature, respectively. The temperature similarity maps showed different characteristics from the precipitation maps. First, there were no apparent spatial patterns. Second, the similarity differences of the meteorological stations in terms of temperature were generally smaller in comparison with precipitation. Third, the S.D. temperature map was revealing more information than the C.D. map. For instance, the S.D. map indicated that there existed some temperature irregularities among the stations numbered 1 to 11. On the other hand, the C.D. map displayed more descrambled similarities.
Figure 9 Cross-station plot of Spearman distance for temperature
Figure 10 Cross-station plot of correlation distance for temperature

4 Conclusions and discussion

We developed a statistical-cum-visual method on the basis of data-mining techniques that became available in recent years in order to investigate long-term trends and examine spatial patterns of ecological, environmental and geographical processes that are signified with cyclical or seasonable dynamics. We applied the EMD technique to extract long-term climate change trends and used 3D surface maps and 2.0D contour maps to visualize differences of change trends in three scales of region, biome and station. Moreover, we experimented with another data-mining technique, the similarity measurement, and compared seven types of commonly used similarity measures. We also visualized these similarity measures by using the cross-station plots. We tested these methods through a case study of investigating climate change in Inner Mongolia based on the daily observations of precipitation and temperature from 1959 to 2010 at 45 meteorological stations.
The case study confirmed that the selected data-mining methods and geo-visualization techniques innovatively and effectively revealed long-term climate change trends and visualized spatial patterns of climate change in three scales, region, biome and station. Moreover, two data-mining methods, EMD and the similarity measurement, complemented each other, disclosing different characteristics of spatial patterns of climate change.
Temperature, during the study period (1959-2010), increased across the study area based on the EMD trend-curves. However, the increases of temperature revealed significant temporal variations and spatial patterns. Temperature increased gently before 1995 and dramatically after 1995. Temperature increased slowly in the biomes of meadow and typical grasslands but quickly in the desert-type grasslands. When the environment was drier, the temperature increased more quickly. Furthermore, the similarity measurement illustrated that temperature trend (EMD) curves showed slight variation over meteorological stations. The cross-station similarity plots of temperature by the stations did not reveal noticeable spatial patterns.
On the other hand, the change trends of precipitation in the past 50 years on the basis of EMD curves displayed complicated temporal trajectories and spatial patterns. A significant increase centre was accompanied by an overall decrease in other areas. From the perspectives of regional and biome scales, no clear linear trends were identified. Furthermore, from the station point of view, based on the similarity measures and cross-station plots, similar change trends of precipitation were found for the stations located in the meadow and typical grasslands. However, this finding didn’t hold for the stations located in desert-type grasslands.
The above findings provided very convincing evidences to support the IPCC predictions that the climate change varied significantly by location and through time. The influences of climate change showed different temporal trends and spatial disparities at varied scales. The reactions to climate change displayed different trajectories over different regions, biomes and locations. The integrated data-mining-cum-visual method was very effective in revealing change trends and their spatial patterns of climate changes. The methods developed in this study are also suitable for investigating long-term trends and spatial patterns of other ecological processes that are signified with cyclical or seasonable fluctuations.
Finally, there is a noticeable limitation of current method. Although the primary gradients of precipitation and temperature changes are from east toward west, there is a significant distance in the south-north direction. Moreover, the meteorological stations are not located in the same latitude. Using the westward locations of the meteorological stations to describe the spatial pattern of east-toward-west vegetation responses to climate change neglected spatial variations of south-toward-north changes.

The authors have declared that no competing interests exist.

References

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[1]
Bai Y, Wu J, Xing Q.et al, 2008. Primary production and rain use efficiency across a precipitation gradient on the Mongolia Plateau.Ecology, 89(8): 2140-2153.Understanding how the aboveground net primary production (ANPP) of arid and semiarid ecosystems of the world responds to variations in precipitation is crucial for assessing the impacts of climate change on terrestrial ecosystems. Rain-use efficiency (RUE) is an important measure for acquiring this understanding. However, little is known about the response pattern of RUE for the largest contiguous natural grassland region of the world, the Eurasian Steppe. Here we investigated the spatial and temporal patterns of ANPP and RUE and their key driving factors based on a long-term data set from 21 natural arid and semiarid ecosystem sites across the Inner Mongolia steppe region in northern China. Our results showed that, with increasing mean annual precipitation (MAP), (1) ANPP increased while the interannual variability of ANPP declined, (2) plant species richness increased and the relative abundance of key functional groups shifted predictably, and (3) RUE increased in space across different ecosystems but decreased with increasing annual precipitation within a given ecosystem. These results clearly indicate that the patterns of both ANPP and RUE are scale dependent, and the seemingly conflicting patterns of RUE in space vs. time suggest distinctive underlying mechanisms, involving interactions among precipitation, soil N, and biotic factors. Also, while our results supported the existence of a common maximum RUE, they also indicated that its value could be substantially increased by altering resource availability, such as adding nitrogen. Our findings have important implications for understanding and predicting ecological impacts of global climate change and for management practices in arid and semiarid ecosystems in the Inner Mongolia steppe region and beyond.

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[2]
Bovik A C, 2009. The Essential Guide to Image Processing. Burlington, MA: Academic Press (Elsevier), 853.

[3]
Brown D G, Agrawal A, Sass D A.et al, 2013. Responses to climate and economic risks and opportunities across national and ecological boundaries: Changing household strategies on the Mongolian Plateau.Environmental Research Letters, 8(045011): 9. doi: 10.1088/1748-9326/8/4/045011.Abstract Climate changes on the Mongolian Plateau are creating new challenges for the households and communities of the region. Much of the existing research on household choices in response to climate variability and change focuses on environmental risks and stresses. In contrast, our analysis highlights the importance of taking into account environmental and economic opportunities in explaining household adaptation choices. We surveyed over 750 households arrayed along an ecological gradient and matched across the national border in Mongolia and the Inner Mongolia Autonomous Region, China, asking what changes in livelihoods strategies households made over the last ten years, and analyzed these choices in two broad categories of options: diversification and livestock management. We combined these data with remotely sensed information about vegetation growth and self-reported exposure to price fluctuations. Our statistical results showed that households experiencing lower ecological and economic variability, higher average levels of vegetation growth, and with greater levels of material wealth, were often those that undertook more actions to improve their conditions in the face of variability. The findings have implications both for how interventions aimed at supporting ongoing choices might be targeted and for theory construction related to social adaptation.

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[4]
Cade B S, Noon B R, 2003. A gentle introduction to quantile regression for ecologists.Frontiers in Ecology and the Environment, 1(8): 412-420.

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[5]
Carlier L, Rotar I, Vlahova M.et al, 2009. Importance and functions of grasslands.Notulae Botanicae Horti Agrobotanici Cluj-Napoca, 37(1): 25-30.Grasslands, mixture of grass, clover and other leguminous species, dicotyledonous, herbs and shrubs, contribute to a high degree to the struggle against erosion and to the regularizing of water regimes, to the purification of fertilizers and pesticides and to biodiversity and they have aesthetic role and recreational function as far as they provide public access that other agricultural uses do not allow. Grassland will continue to be an important form of land use in Europe, but with increased diversity in management objectives and systems used. Besides its role as basic nutrient for herbivores and ruminants, grasslands have opportunities for an adding value by exploiting positive health characteristics in animal products from grassland and through the delivery of environmental benefits. But even for grassland it is very difficult to create a good frame for its different tasks (1) the provision of forage for livestock, (2) protection and conservation of soil and water resources, (3) furnishing a habitat for wildlife, both flora and fauna and (4) contribution to the attractiveness of the landscape. Nevertheless it is the only crop able to fulfil so many tasks and to fit so many requirements. In this article the focus is limited to the grass and clover components of the grasslands.

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[6]
Chamaille S, Jammesa B, Fritza H.et al, 2007. Short communication detecting climate changes of concern in highly variable environment.Journal of Arid Environments, 71(3): 321-326. doi: 10.1016/j.jaridenv.2007.05.005.Rapid climate change is happening worldwide and is affecting ecosystems processes as well as plant and animal abundances and distribution. However, the large climate variability observed in arid and semi-arid regions often impairs the statistical detection of long-term trends using standard statistical methods, especially if one is primarily interested in specific components of the climate changes. Here we highlight how quantile regression overcomes some of the confounding effects of large climate variability in long-term rainfall data. For instance, we show how quantile regressions revealed that droughts worsened in Hwange National Park (Zimbabwe) during the course of the 20th century, a change that would not have been detected using simple linear regression. We briefly discuss the implications of our findings for the management of the park.

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[7]
Chen J, Xu Y, 2005. Application of EMD to signal trend extraction.Journal of Vibration, Measurement and Diagnosis, 25(2): 101-104.This paper investigates the application of empirical mode decomposition (EMD)to signal trend extraction. EMD can decompose any signal into sum of intrinsic mode functions (IMF) plus a residual. Thus, the signal trend is defined as the residual or sum of several IMF components whose frequency content is lower than a given value. Both simulated and field measured signal are employed in this study to demonstrate the feasibility of the approach. The results show that the trend can be extracted directly from the measured signal using the EMD approach without any presumptions of the trend type. It is concluded that the EMD approach is a promising tool for signal trend extraction.

[8]
Cheng F Y, Jian S P, Yang Z M.et al, 2015. Influence of regional climate change on meteorological characteristics and their subsequent effect on ozone dispersion in Taiwan.Atmospheric Environment 103: 66-81.61Study impact of regional climate change on meteorology and O3 dispersions.61Land surface process responded to enhanced precipitation with damper soil condition.61Strength of land–sea breeze flow becomes weaker.61With reduced dispersion, pollutants tend to accumulate near emission source region.

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[9]
Cheng T, Riaño D, Ustin S L, 2014. Detecting diurnal and seasonal variation in canopy water content of nut tree orchards from airborne imaging spectroscopy data using continuous wavelet analysis.Remote Sensing of Environment, 143: 39-53.61Continuous wavelet analysis (CWA) was applied to diurnal and seasonal AVIRIS images.61The best wavelet feature (1100nm, scale 6) emphasized the NIR water absorption.61CWA outperformed existing and optimized narrowband indices for CWC prediction.61The optimal index did not use a water band and was more sensitive to seasonality.61AVIRIS data revealed significant diurnal and seasonal variation as field data did.

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[10]
Chuai X W, Huang X J, Wang W J.et al, 2013. NDVI, temperature and precipitation changes and their relationships with different vegetation types during 1998-2007 in Inner Mongolia, China.International Journal of Climatology, 33(7): 1696-1706.Based on vegetation maps of Inner Mongolia, SPOT-VEGETATION normalized difference vegetation index (NDVI) data, and temperature and precipitation data from 118 meteorological stations, this study analysed changes in NDVI, temperature and precipitation, and performed correlation analyses of NDVI, temperature and precipitation for eight different vegetation types during the growing seasons (April–October) of the period 1998–2007 in Inner Mongolia, China. We also investigated seasonal correlations and lag-time effects, and our results indicated that for different vegetation types, NDVI changes during 1998–2007 showed great variation. NDVI correlated quite differently with temperature and precipitation, with obvious seasonal differences. Lag-time effects also varied among vegetation types and seasons. On the whole, Inner Mongolia is becoming warmer, and drier for most regions, and ecological pressure in Inner Mongolia is increasing, and our focus on such issues is therefore important. Copyright 08 2012 Royal Meteorological Society

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[11]
Cianfrani C, Satizábal H F, Randin C, 2015. A spatial modelling framework for assessing climate change impacts on freshwater ecosystems: Response of brown trout (Salmo trutta L.) biomass to warming water temperature.Ecological Modelling, 313: 1-12.Mountain regions worldwide are particularly sensitive to on-going climate change. Specifically in the Alps in Switzerland, the temperature has increased twice as fast than in the rest of the Northern hemisphere. Water temperature closely follows the annual air temperature cycle, severely impacting streams and freshwater ecosystems. In the last 20 years, brown trout (Salmo trutta L.) catch has declined by approximately 40 50% in many rivers in Switzerland. Increasing water temperature has been suggested as one of the most likely cause of this decline. Temperature has a direct effect on trout population dynamics through developmental and disease control but can also indirectly impact dynamics via food-web interactions such as resource availability. We developed a spatially explicit modelling framework that allows spatial and temporal projections of trout biomass using the Aare river catchment as a model system, in order to assess the spatial and seasonal patterns of trout biomass variation. Given that biomass has a seasonal variation depending on trout life history stage, we developed seasonal biomass variation models for three periods of the year (Autumn inter, Spring and Summer). Because stream water temperature is a critical parameter for brown trout development, we first calibrated a model to predict water temperature as a function of air temperature to be able to further apply climate change scenarios. We then built a model of trout biomass variation by linking water temperature to trout biomass measurements collected by electro-fishing in 21 stations from 2009 to 2011. The different modelling components of our framework had overall a good predictive ability and we could show a seasonal effect of water temperature affecting trout biomass variation. Our statistical framework uses a minimum set of input variables that make it easily transferable to other study areas or fish species but could be improved by including effects of the biotic environment and the evolution of demographical parameters over time. However, our framework still remains informative to spatially highlight where potential changes of water temperature could affect trout biomass.

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[12]
Cleve B M, 2004. Fourier Analysis. Society for Industrial and Applied Mathematics 235-253.

[13]
CMDC (China Meteorological Data Service Center), 2013. Inner Mongolian Meteorological Stations and Data. https://data.cma.cn/en (the data was acquired in 2013).

[14]
Conners R W, Harlow C A, 1980. A theoretical comparison of texture algorithms.IEEE Transaction on Pattern Analysis and Machine Intelligence, 2(3): 204-222.An evaluation of the ability of four texture analysis algorithms to perform automatic texture discrimination will be described. The algorithms which will be examined are the spatial gray level dependence method (SGLDM), the gray level run length method (GLRLM), the gray level difference method (GLDM), and the power spectral method (PSM). The evaluation procedure employed does not depend on the set of features used with each algorithm or the pattern recognition scheme. Rather, what is examined is the amount of texturecontext information contained in the spatial gray level dependence matrices, the gray level run length matrices, the gray level difference density functions, and the power spectrum. The comparison will be performed in two steps. First, only Markov generated textures will be considered. The Markov textures employed are similar to the ones used by perceptual psychologist B. Julesz in his investigations of human texture perception. These Markov textures provide a convenient mechanism for generating certain example texture pairs which are important in the analysis process. In the second part of the analysis the results obtained by considering only Markov textures will be extended to all textures which can be represented by translation stationary random fields of order two. This generalization clearly includes a much broader class of textures than Markovian ones. The results obtained indicate that the SGLDM is the most powerful algorithm of the four considered, and that the GLDM is more powerful than the PSM.

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[15]
Coselmon M M, Balter J M, McShan D L.et al, 2004. Mutual information based CT registration of the lung at exhale and inhale breathing states using thin-plate splines.Medical Physics, 31(11): 2942-2948.Abstract The advent of dynamic radiotherapy modeling and treatment techniques requires an infrastructure to weigh the merits of various interventions (breath holding, gating, tracking). The creation of treatment planning models that account for motion and deformation can allow the relative worth of such techniques to be evaluated. In order to develop a treatment planning model of a moving and deforming organ such as the lung, registration tools that account for deformation are required. We tested the accuracy of a mutual information based image registration tool using thin-plate splines driven by the selection of control points and iterative alignment according to a simplex algorithm. Eleven patients each had sequential CT scans at breath-held normal inhale and exhale states. The exhale right lung was segmented from CT and served as the reference model. For each patient, thirty control points were used to align the inhale CT right lung to the exhale CT right lung. Alignment accuracy (the standard deviation of the difference in the actual and predicted inhale position) was determined from locations of vascular and bronchial bifurcations, and found to be 1.7, 3.1, and 3.6 mm about the RL, AP, and IS directions. The alignment accuracy was significantly different from the amount of measured movement during breathing only in the AP and IS directions. The accuracy of alignment including thin-plate splines was more accurate than using affine transformations and the same iteration and scoring methodology. This technique shows promise for the future development of dynamic models of the lung for use in four-dimensional (4-D) treatment planning.

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[16]
Dai G, Liu F, 2007. Instantaneous parameters extraction based on wavelet denoising and EMD.Acta Metrologica Sinica, 28(2): 158-162.

[17]
Dai W, Ding X, Zhu J, 2006. EMD filter method and its application in GPS multipath.Acta Geodaetica et Cartographica Sinica, 35(11): 321-327.

[18]
Damsø T, Kjær T, Christensen T B, 2016. Local climate action plans in climate change mitigation: Examining the case of Denmark. Energy Policy 89: 74-83.

[19]
Dawson I K, Vinceti B, Weber J C, 2011. Climate change and tree genetic resource management: maintaining and enhancing the productivity and value of smallholder tropical agroforestry landscapes: A review.Agroforestry Systems, 81(1): 67-78.Anthropogenic climate change has significant consequences for the sustainability and productivity of agroforestry ecosystems upon which millions of smallholders in the tropics depend and that provide valuable global services. We here consider the current state of knowledge of the impacts of climate change on tree genetic resources and implications for action in a smallholder setting. Required measures to respond to change include: (1) the facilitated translocation of environmentally-matched germplasm across appropriate geographic scales, (2) the elevation of effective population sizes of tree stands through the promotion of pollinators and other farm management interventions; and (3) the use of a wider range of lastic species and populations for planting. Key bottlenecks to response that are discussed here include limitations in the international exchange of tree seed and seedlings, and the absence of well-functioning delivery systems to provide smallholders with better-adapted planting material. Greater research on population-level environmental responses in indigenous tree species is important, and more studies of animal pollinators in farm landscapes are required. The development of well-functioning markets for new products that farmers can grow in order to mitigate and adapt to anthropogenic climate change must also consider genetic resource issues, as we describe.

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[20]
Demir B, Ertürk S, 2010. Empirical mode decomposition of hyperspectral images for support vector machine classification.IEEE Transactions on Geoscience and Remote Sensing, 48(11): 4071-4084.

[21]
Gao R X, Yan X, 2011. Wavelets: Theory and Applications for Manufacturing. Springer Science and Business Media LLC. doi: 10.1007/978-1-4419-1545-0.

[22]
Gauthier T, 2001. Detecting trends using Spearman’s rank correlation, coefficient.Environ Forensics, 2: 359-362.Spearman''s rank correlation coefficient is a useful tool for exploratory data analysis in environmental forensic investigations. In this application it is used to detect monotonic trends in chemical concentration with time or space.

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[23]
Ghasemi N, Sahebi M R, Mohammadzadeh A, 2013. Biomass estimation of a temperate deciduous forest using wavelet analysis.IEEE Transactions on Geoscience and Remote Sensing, 51(2): 765-776.The increasing concentration of greenhouse gases in the atmosphere has been identified as contributing to the increase in global mean temperature. Carbon sequestration into trees and forests is an effective and inexpensive method for decreasing the CO2 level in the atmosphere. Hence, accurate measurements of biomass levels will be important to the global carbon cycle and climate change. This study used a wavelet-based forest above-ground biomass (AGB) estimation approach in a temperate deciduous forest. Two-dimensional discrete wavelet transformations was applied to ALOS AVNIR and PALSAR to obtain wavelet coefficients, which were correlated with AGB estimates using multiple linear regression analysis. Different wavelets were tested using this approach. Moreover, vegetation indices and texture parameters were calculated and correlated with AGB estimates. The results indicated that wavelet-based modeling could improve the accuracy of biomass estimation to 75% or even higher in comparison with the accuracy of 30%-40% resulting from past studies using vegetation indices and texture measures. This study demonstrates that wavelet-based biomass estimation could be a promising approach for solving the uncertainty between reflectance or backscatter values from satellite images and forest biomass and therefore provide better biomass estimations.

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[24]
Gloersen P, Huang N E, 2003. Comparison of inter annual intrinsic modes in hemispheric sea ice covers and other geophysical parameters.IEEE Transactions on Geoscience and Remote Sensing, 41(5): 1062-1074.Recent papers have described 18-year trends and interannual oscillations in the Arctic and Antarctic sea ice extents, areas, and enclosed open water areas based on newly formulated 18.2-year ice concentration time series. They were obtained by fine-tuning the sea ice algorithm tie points individually for each of the four sensors used to acquire the data. In this paper, these analyses are extended to an examination of the intrinsic modes of these time series, obtained by means of empirical mode decomposition, which handles both nonstationary and nonlinear data as found in these time series, unlike filtering techniques based on Fourier analysis. Our analysis centers on periodicities greater than one year. Quasi-biennial and quasi-quadrennial oscillations similar to those observed earlier with a multitaper-filtered Fourier analysis technique were also observed. The intrinsic modes described feature frequency as well as amplitude modulation within their respective frequency bands. The slowest varying mode in the Antarctic sea ice cover has slightly less than a full period during this 18.2-year time period, but the change in sign of its curvature hints at a modal period of about 19 years, with important implications for the trend analyses published earlier.

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[25]
Gong Z, Kawamura K, Ishikawa N.et al, 2015. MODIS NDVI and vegetation phenology dynamics in the Inner Mongolia grassland.Solid Earth Discussions, 7(3): 2381-2411.The Inner Mongolia grassland, one of the most important grazing regions in China, has long been threatened by land degradation and desertification, mainly due to overgrazing. To understand vegetation responses over the last decade, this study evaluated trends in vegetation cover and phenology dynamics in the Inner Mongolia grassland by applying a normalized difference vegetation index (NDVI) time series obtained by the Terra Moderate Resolution Imaging Spectroradiometer (MODIS) during 2002-2014. The results showed that the cumulative annual NDVI increased to over 77.10 % in the permanent grassland region (2002-2014). The mean value of the total change showed that the start of season (SOS) date and the peak vegetation productivity date of the season (POS) had advanced by 5.79 and 2.43 days respectively. The end of season (EOS) was delayed by 5.07 days. These changes lengthened the season by 10.86 days. Our results also confirmed that grassland changes are closely related to spring precipitation (February-May) and increasing temperature during the growing period because of the global warming. Overall, productivity in the Inner Mongolia Autonomous Region tends to increase, but in some grassland areas with grazing, land degradation is ongoing.

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[26]
Goshtasby A, 2012. Advances in Computer Vision and Pattern Recognition. Springer-Verlag London Limited.

[27]
Grafakos L, Teschl G, 2013. On Fourier transforms of radial functions and distributions.Journal of Fourier Analysis Applications, 19: 167-179.AbstractWe find a formula that relates the Fourier transform of a radial function on02n with the Fourier transform of the same function defined on n. This formula enables one to explicitly calculate the Fourier transform of any radial function () in any dimension, provided one knows the Fourier transform of the one-dimensional function 66(||) and the two-dimensional function (,)66(|(,)|). We prove analogous results for radial tempered distributions.

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[28]
Han F, Kang S, Buyantuev A.et al, 2016. Effects of climate change on primary production in the Inner Mongolia Plateau, China.International Journal of Remote Sensing, 37(23): 5551-5564.

[29]
Han M, Liu Y H, Xi J H, 2007. Noise smoothing for nonlinear time series using wavelet soft threshold.IEEE Signal Processing Letters, 14(1): 62-65.In this letter, a new threshold algorithm based on wavelet analysis is applied to smooth noise for a nonlinear time series. By detailing the signals decomposed onto different scales, we smooth the details by using the updated thresholds to different characters of a noisy nonlinear signal. This method is an improvement of Donoho's wavelet methods to nonlinear signals. The approach has been successfully applied to smoothing the noisy chaotic time series generated by the Lorenz system as well as the observed annual runoff of Yellow River. For the nonlinear dynamical system, an attempt is made to analyze the noise reduced data by using multiresolution analysis, i.e., the false nearest neighbors, correlation integral, and autocorrelation function, to verify the proposed noise smoothing algorithm

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[30]
He Y, Wen H, Yuan H, 2007. Multi-wavelet-based deformation monitoring signal processing.Hydropower Automation and Dam Monitoring, 31(1): 61-71.Based on the introduction of multi-wavelet basic theory, an example is given to show the application of DGHM multi-wavelet to the de-noising of GPS signal. Owing to the characteristics of short support, orthogonality, symmetry (anti-symmetry) and second order approach, the de-noising of GPS signal with DGHM biorthogonal wavelet is better than that with traditional wavelets under the same filter length. The example indicates the unlimited potential of multi-wavelet in signal de-noising.

[31]
Huang D, Ding X, Chen Y, 2001. Wavelet filters based separation of GPS multipath effects and engineering structural vibrations. Acta Geodaetica et Cartographica Sinica, 30(1): 36-41.The recent advances in GPS technology recording at 20 samples per second allows reliable monitoring of engineering structure, such as suspension or cable-stayed bridges and tall buildings. But the coordinates conducted from GPS trajectory estimator (i.e. epoch by epoch) usually are affected by many factors, e.g. multi-path and temperature as major. To assess stress and drift conditions of engineering structure one have to separate structure vibrations from other biases. The Wavelet analysis technique has been successfully used for this purpose, and the analysis results from practical data are presented.

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[32]
Huang N E, Wu M C, Long S R.et al, 2003. A confidence limit for the empirical mode decomposition and Hilbert spectral analysis.The Royal Society, 459(2037): 2317-2345. doi: 10.1098/rspa.2003.1123.

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[33]
Huang N E, Wu M L, Qu W.et al, 2003. Applications of Hilbert-Huang transform to non-stationary financial time series analysis.Applied Stochastic Models in Business and Industry, 19: 245-268. doi: 10.1002/asmb.501.A new method, the Hilbert-Huang Transform (HHT), developed initially for natural and engineering sciences has now been applied to financial data. The HHT method is specially developed for analysing non-linear and non-stationary data. The method consists of two parts: (1) the empirical mode decomposition (EMD), and (2) the Hilbert spectral analysis. The key part of the method is the first step, the EMD, with which any complicated data set can be decomposed into a finite and often small number of intrinsic mode functions (IMF). An IMF is defined here as any function having the same number of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima, and minima respectively. The IMF also thus admits well-behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to non-linear and non-stationary processes. With the Hilbert transform, the IMF yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, which we designate as the Hilbert Spectrum. Comparisons with Wavelet and Fourier analyses show the new method offers much better temporal and frequency resolutions. The EMD is also useful as a filter to extract variability of different scales. In the present application, HHT has been used to examine the changeability of the market, as a measure of volatility of the market. Published in 2003 by John Wiley & Sons, Ltd.

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[34]
Huang S, Li P, Yang B, 2005. Study on the characteristics of multipath effects in GPS dynamic deformation monitoring.Geomatics and Information Science of Wuhan University, 30(10): 877-879.The multipath has long been considered a major error source in GPS applications. The characteristics of the GPS signal multipath effects are analyzed, based on which an experiment that considers the characteristics of dynamic deformation monitoring has been carried out. The solution results of observation data in two successive days are processed by a method, which combines the wavelet filtering and the differential correction between two successive days. The research demonstrates that the multipath errors have stronger repeatability on successive days; after significantly mitigating the influence of multipath effects, the accuracy of three-dimensional positioning for GPS dynamic deformation monitoring can attain the mm level, an obvious accuracy improving particularly in vertical component. The characteristics of GPS signal multipath, the experimental scheme and the qualitative and quantitative analysis of results are detailed.

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[35]
Jain N, Srivastava V, 2013. Data mining techniques: A survey paper.International Journal of Research in Engineering and Technology, 2(11): 2319-1163.

[36]
Jordan Y C, Ghulam A, Chu M L, 2014. Assessing the impacts of future urban development patterns and climate changes on total suspended sediment loading in surface waters using geoinformatics.Journal of Environmental Informatics, 24(2): 65-79.

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[37]
Kennedy M, Basu B, 2014. An analysis of the climate change architecture. Renewable and Sustainable Energy Reviews, 34: 185-193.This paper examines the complexity of the current negotiations to avert climate change under the United Nations Framework Convention on Climate Change. Drawing on economic game theory modelling, it interprets the latest developments within the international negotiations and provides a political economy analysis of the climate change architecture. It places the pursuit of international co-operation, via the Kyoto Protocols second commitment period, in the context of a countrys maintenance of national interest and a flexible emissions abatement strategy. Accepting that countries will reject an international agreement or obligation that is seen as inimical to their economic competitiveness, it incorporates a new game theory model, considers how learning from such models can influence agreement design and proposes a new approach from a non-monotonic polluting payoff function. Attention is placed on enabling conditions that entice countries to ratify a climate agreement, thereby encouraging participation and accelerating a near term deployment of low carbon technologies.

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[38]
Koenker R, 2005. Quantile Regression. Cambridge University Press.

[39]
Kotlyar M, Fuhrman S, Ableson A.et al, 2002. Spearman correlation identifies statistically significant gene expression clusters in spinal cord development and injury.Neurochemical Research, 27(10): 1133-1140.An important problem in the analysis of large-scale gene expression data is the validation of gene expression clusters. By examining the temporal expression patterns of 74 genes expressed in rat spinal cord under three different experimental conditions, we have found evidence that some genes cluster together under multiple conditions. Using RT-PCR data from spinal cord development and two sets of microarray data from spinal injury, we applied Spearman correlation to identify clusters and to assign P values to pairs of genes with highly similar temporal expression patterns. We found that 15% of genes occurred in statistically significant pairs in all three experimental conditions, providing both statistical and experimental support for the idea that genes that cluster together are co-regulated. In addition, we demonstrated that DNA microarray and RT-PCR data are comparable, and can be combined to confirm gene expression relationships.

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[40]
Kyselý J, Beguería S, Beranová R.et al, 2012. Different patterns of climate change scenarios for short-term and multi-day precipitation extremes in the Mediterranean.Global and Planetary Change, 98: 63-72.78 We evaluate climate-change scenarios of precipitation extremes in the Mediterranean based on an ensemble of RCMs. 78 Projected increases of short-term precipitation extremes exceed those of multi-day extremes. 78 The largest ensemble–mean increases are projected in autumn. 78 Increases are simulated even in regions and seasons in which mean precipitation declines. 78 The change in precipitation patterns may be manifested also in higher frequency and severity of flash floods.

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[41]
Lhermitte S, Verbesselt J, Verstraeten W.et al, 2011. A comparison of time series similarity measures for classification and change detection of ecosystem dynamics.Remote Sensing of Environment, 115: 3129-3152.78 A quantitative comparison of time series similarity measures D is performed. 78 Four groups of D with different sensitivities are obtained. 78 Time series characteristics, noise and variability affect the performance of D. 78 The sensitivities stress the importance of proper selection of similarity measures. 78 Understanding time series properties is crucial for classification/change detection.

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[42]
Li J, Cui Y, Liu J.et al, 2013. Estimation and analysis of net primary productivity by integrating MODIS remote sensing data with a light use efficiency model.Ecological Modelling, 252: 3-10. doi: 10.1016/j.ecolmodel.2012.11.026.Estimates of regional net primary productivity (NPP) are very useful in modeling regional and global carbon cycles. This work proposed a new method to study NPP characteristics and changes in the Inner Mongolia Autonomous Region, China. To estimate NPP accurately, we integrated photosynthetically active radiation (PAR) with a light use efficiency model, derived from Moderate Resolution Imaging Spectroradiometer atmospheric and land products. Validation analyses showed that the PAR and NPP values simulated by the model matched observed data well. Annual NPP in the study area was about 0.25 PgC a(-1) from 2003 to 2008. In spatial distribution, NPP decreased from northeast to southwest in the Inner Mongolia Autonomous Region. NPP from May to September accounted for 84.2% of annual NPP, while that from July to August accounted for 44.3%. NPP was significantly correlated to both precipitation and temperature at monthly temporal scales. NPP also changed with the fraction of absorbed PAR. (C) 2012 Elsevier B.V. All rights reserved.

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[43]
Li S, Xie Y, 2013. Investigating coupled impacts of climate change and socioeconomic transformation on desertification by using multi-temporal landsat images: A case study in Central Xilingol, China.IEEE Geoscience and Remote Sensing Letters, 10(5): 1244-1248. doi: 10.1109/LGRS.2013.2257158.A case study is conducted in Xilingol Rangeland, Inner Mongolia, China, to investigate the driving factors of temporal dynamics of desertification by using time-series Landsat images. The spectral characters of sand dunes and urban lands in the arid and semiarid grassland environments are very similar, and thus, it is hard to discriminate them with traditional image classifiers. Nine available scenes of Landsat images without cloud cover from 1985 to 2010 are chosen for the case study. An object-oriented image classification (OOIC) is developed to classify sand dunes. The classification results are assessed with the ground reference points in 1985, 2004, and 2010, the land-cover maps produced from other classifiers in literature, and Google Earth historical aerial photo archives. Second, the areas of sand dunes derived from OOIC at the nine times are extrapolated into a 26-year time-series data set from 1985 to 2010 by applying several extrapolation techniques commonly used in regional geographic studies. Afterward, six climate factors and nine socioeconomic variables during the same study period along with the sand dune area are composed into a completed data set to investigate the coupled impacts of climate change and socioeconomic transformation on the temporal dynamics of desertification. Three types of regression models (climate model, economic model, and the coupled model) are explored, respectively, to examine which factors contribute more to the desertification dynamics. The findings confirm that the desertification process in Xilingol Rangeland is very complicated although it shows a strong causal relationship with several socioeconomic factors.

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[44]
Li S, Xie Y, Brown D.et al, 2013. Spatial variability of the adaptation of grassland vegetation to climatic change in Inner Mongolia of China.Applied Geography, 43: 1-12. doi: 10.1016/j.apgeog.2013.05.008.61Panel regression models were developed to explore spatiotemporal relationships between vegetation and climate.61Vegetation growth responses to climate changes were shaped by unique characteristics of the study area.61The interactions between vegetation and climate were dependent on spatially and temporally varying contextual factors.61A ‘big-data’ was created by integrating satellite data, ground observations of climate factors and vegetation maps in GIS.

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[45]
Li Z, Zhu Q, Gold C, 2005. Digital Terrain Modeling: Principles and Methodology. CRC Press.

[46]
Liu L, Liu C, Jiang C, 2007. Novel EMD algorithm and its application.Journal of System Simulation, 19(2): 446-447.

[47]
Lu N, Wilske B, Ni J.et al, 2009. Climate change in Inner Mongolia from 1955 to 2005: Trends at regional, biome and local scales.Environmental Research Letters, 4: 045006. doi: 10.1088/1748-9326/4/4/045006.This study investigated the climate change in Inner Mongolia based on 51 meteorological stations from 1955 to 2005. The climate data was analyzed at the regional, biome (i.e. forest, grassland and desert) and station scales, with the biome scale as our primary focus. The climate records showed trends of warmer and drier conditions in the region. The annual daily mean, maximum and minimum temper...

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[48]
Luan Y, Fan Y, Xue L, 2004. Under ground space study on prediction model of trend.Term for Ground Surface Movement, 24(1): 14-18.

[49]
Mishra A, Singh R, Raghuwanshi N S.et al, 2013. Spatial variability of climate change impacts on yield of rice and wheat in the Indian Ganga Basin.Science of the Total Environment, 468: S132-S138.61Climate change impacts on crops in the Indian Ganga Basin have been analyzed.61SRES A1B emissions scenario simulations of REMO and HadRM3 GCMs for the period 2011–2040 have been used.61Projected climate showed more decrease of potential yields at higher latitudes.

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[50]
Nunes J C, Gu Y S, Delechelle E, 2005. Texture analysis based on local analysis of the bidimensional empirical mode decomposition.Machine Vision and Applications, 16(3): 177-188.The main contribution of our approach is to apply the Hilbert-Huang Transform (which consists of two parts: (a) Empirical Mode Decomposition (EMD), and (b) the Hilbert spectral analysis) to texture analysis. The EMD is locally adaptive and suitable for analysis of non-linear or non-stationary processes. This one-dimensional decomposition technique extracts a finite number of oscillatory components or ell-behaved AM-FM functions, called Intrinsic Mode Function (IMF), directly from the data. Firstly, we extend the EMD to 2D-data (i.e. images), the so called bidimensional EMD (BEMD), the process being called 2D- sifting process . The 2D-sifting process is performed in two steps: extrema detection by neighboring window or morphological operators and surface interpolation by radial basis functions or multigrid B-splines. Secondly, we analyse each 2D-IMF obtained by BEMD by studying local properties (amplitude, phase, isotropy and orientation) extracted from the monogenic signal of each one of them. The monogenic signal is a 2D-generalization of the analytic signal, where the Riesz Transform replaces the Hilbert Transform . The performance of this texture analysis method, using the BEMD and Riesz Transform, is demonstrated with both synthetic and natural images.

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[51]
Pearson K.1895. Contributions to the mathematical theory of evolution (III): Regression, heredity, and panmixia.Proceeding of the Royal Society of London, 59(353-358): 67-71.

[52]
Peng Z K, Tse P W, Chu F L, 2005. A comparison study of improved Hilbert-Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing.Original Research Article Mechanical Systems and Signal Processing, 19(5): 974-988.For rolling bearing fault detection, it is expected that a desired time–frequency analysis method should have good computation efficiency, and have good resolution in both time domain and frequency domain. As the best available time–frequency method so far, the wavelet transform still cannot fulfill the rolling bearing fault detection task very well since it has some inevitable deficiencies. The recent popular time–frequency analysis method, Hilbert–Huang transform (HHT), has good computation efficiency and does not involve the concept of the frequency resolution and the time resolution. So the HHT seems to have potential to become a perfect tool for rolling bearing fault detection. However, in practical applications, the HHT also suffers from some unsolved deficiencies. To ameliorate these deficiencies, by seeking help from the wavelet packet transform (WPT) and a simple but effective method for intrinsic mode function (IMF) selection, an improved HHT is put forward in this studying. Several numerical study cases will be used to validate the capabilities of the improved HHT. Finally, the improved HHT's performance in rolling bearing fault detection is compared with that of the wavelet based scalogram through experimental case studies. The comparison results have shown that (1) the improved HHT has better resolution both in time domain and in frequency domain than the scalogram; (2) the improved HHT has better computing efficiency than scalogram; (3) the HHT spectrum also has one unresolved and maybe inevitable deficiency—ripple phenomenon in its estimated frequency, which would mislead our analysis.

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[53]
Piras M, Mascaro G, Deidda R.et al, 2016. Impacts of climate change on precipitation and discharge extremes through the use of statistical downscaling approaches in a Mediterranean basin. Science of the Total Environment, 543: 952-964.61Statistical analysis in a basin in Sardinia shows high uncertainty of climate projections of precipitation extremes.61Soil properties and topography control the basin response to extreme storms.61Statistical downscaling of precipitation is useful to improve accuracy of physically-based hydrologic simulations.

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[54]
Portilla J, Strela V, Wainwright M J.et al, 2003. Image denoising using scale mixtures of Gaussians in the wavelet domain.IEEE Transaction on Image Processing, 12(11): 1338-1351.We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.

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[55]
Rahmani M A, Zarghami M, 2015. The use of statistical weather generator, hybrid data driven and system dynamics models for water resources management under climate change.Journal of Environmental Informatics, 25(1): 23-35.

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[56]
Rao K S, Hsu C, 2008. Antenna system supporting multiple frequency bands and multiple beams.Antennas and Propagation, 56(10): 3327-3329.

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[57]
Ribalaygua J, Pino M, Pórtoles J.et al, 2013. Climate change scenarios for temperature and precipitation in Aragón (Spain).Science of the Total Environment, 463: 1015-1030.

[58]
Sherbinin de A, Castro M, Gemenne F, 2011. Preparing for resettlement associated with climate change.Science, 334(6055): 456-457.

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[59]
Spearman C, 1904. The proof and measurement of association between two things.The American Journal of Psychology, 15(1): 72-101.Author information: (1)Telethon Institute for Child Health Research and Centre for Child Health Research, The University of Western Australia (M560), 35 Stirling Highway, Crawley, WA 6009, Australia. nickdk@ichr.uwa.edu.au

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[60]
Swain D K, Thomas D, 2010. Climate change impact assessment and evaluation of agro-adaptation measures for rice production in eastern India.Journal of Environmental Informatics, 16(2): 94-101.

[61]
Veerasamy R, Rajak H, Jain A.et al, 2011. Validation of QSAR models: Strategies and importance.International Journal of Drug Design and Discovery, 2(3): 511-519.

[62]
Wang J, Brown D, Agrawal A, 2013. Climate adaptation, local institutions, and rural livelihoods: A comparative study of herder communities in Mongolia and Inner Mongolia, China.Global Environmental Change, 23(6): 1673-1683.Climate variability has been evident on the Mongolian plateau in recent decades. Livelihood adaptation to climate variability is important for local sustainable development. This paper applies an analytical framework focused on adaptation, institutions, and livelihoods to study climate adaptation in the Mongolian grasslands. A household survey was designed and implemented in each of three broad vegetation types in Mongolia and Inner Mongolia. The analytical results show that livelihood adaptation strategies of herders vary greatly across the border between Mongolia and Inner Mongolia, China. Local institutions played important roles in shaping and facilitating livelihood adaptation strategies of herders. Mobility and communal pooling were the two key categories of adaptation strategies in Mongolia, and they were shaped and facilitated by local communal institutions. Storage, livelihood diversification, and market exchange were the three key categories of adaptation strategies in Inner Mongolia, and they were mainly shaped and facilitated by local government and market institutions. Local institutions enhanced but also at times undermined adaptive capacity of herder communities in the two countries, but in different ways. Sedentary grazing has increased livelihood vulnerability of herders to climate variability and change. With grazing sedentarization, the purchase and storage of forage has become an important strategy of herders to adapt to the highly variable climate. The multilevel statistical models of forage purchasing behaviors show that the strategies of livestock management, household financial capital, environmental (i.e., precipitation and vegetation growth) variability, and the status of pasture degradation were the major determinants of this adaptation strategy. (C) 2013 Elsevier Ltd. All rights reserved.

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[63]
Wang Z, Fang J, Tang Z.et al, 2012. Relative role of contemporary environment versus history in shaping diversity patterns of China’s woody plants.Ecography, 35(12): 1124-1133. doi: 10.1111/j.1600-0587.2011.06781.x.What determines large-scale patterns of species diversity is a central and controversial topic in biogeography and ecology. In this study, we compared the effects of contemporary environment and historical contingencies on species richness patterns of woody plants in China, using fine-resolution geographic databases of the distributions of 11 405 woody species and climate, topography, and vegetation information. Residuals of species richness-environment generalized linear models were significantly different from 0 in the majority of seven biogeographical regions, and also differed significantly between these regions, indicating significant deviation from the predicted species richness based on contemporary environment. Additionally, species richness of a given biogeographical region deviated substantially from the predictions of species richness-environment models developed for the remaining regions combined. This suggests different richness-environment relationships among regions. These results indicate important historical signals in the species richness patterns of woody plants across China. The signals are especially pronounced in the eastern Himalayas, the Mongolian Plateau, and the Tibetan Plateau, perhaps reflecting their special geological features and history. Nevertheless, partial regression indicated that historical effects were less important relative to contemporary environment. In conclusion, contemporary environment (notably climate) determines the general trend in woody-plant species richness across China, while historical contingencies generate regional deviations from this trend. Our findings imply that both species diversity and regional evolutionary and ecological histories should be taken into account for future nature conservation.

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[64]
Xia X H, Wu Q, Mou X L.et al, 2015. Potential impacts of climate change on the water quality of different water bodies.Journal of Environmental Informatics, 25(2): 85-98.

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[65]
Xian X, Lin Z S, Cheng X X.et al, 2008. Regional features of the temperature trend in China based on empirical mode decomposition.Journal of Geographical Sciences, 18(2): 166-176.By the Empirical Mode Decomposition method, we analyzed the observed monthly average temperature in more than 700 stations from 1951–2001 over China. Simultaneously, the temperature variability of each station is calculated by this method, and classification chart of long term trend and temperature variability distributing chart of China are obtained, supported by GIS, 1 km×1 km resolution. The results show that: in recent 50 years, the temperature has increased by more than 0.4°C/10a in most parts of northern China, while in Southwest China and the middle and lower Yangtze Valley, the increase is not significant. The areas with a negative temperature change rate are distributed sporadically in Southwest China. Meanwhile, the temperature data from 1881 to 2001 in nine study regions in China are also analyzed, indicating that in the past 100 years, the temperature has been increasing all the way in Northeast China, North China, South China, Northwest China and Xinjiang and declining in Southwest China. An inverse ‘V-shaped’ trend is also found in Central China. But in Tibet the change is less significant.

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[66]
Xie Y, Crary D, Bai Y.et al, 2017. Modelling grassland ecosystem responses to coupled climate and socioeconomic influences from multi-spatial-and-temporal scales. Journal of Environmental Informatics, 1684-8799. doi: 10.3808/ jei.201600337.

[67]
Xie Y, Sha Z, Yu M.et al, 2009. A comparison of two models with Landsat data for estimating above ground grassland biomass in Inner Mongolia, China.Ecological Modelling, 220: 1810-1818.Two models, artificial neural network (ANN) and multiple linear regression (MLR), were developed to estimate typical grassland aboveground dry biomass in Xilingol River Basin, Inner Mongolia, China. The normalized difference vegetation index (NDVI) and topographic variables (elevation, aspect, and slope) were combined with atmospherically corrected reflectance from the Landsat ETM+ reflective bands as the candidate input variables for building both models. Seven variables (NDVI, aspect, and bands 1, 3, 4, 5 and 7) were selected by the ANN model (implemented in Statistica 6.0 neural network module), while six (elevation, NDVI, and bands 1, 3, 5 and 7) were picked to fit the MLR function after a stepwise analysis was executed between the candidate input variables and the above ground dry biomass. Both models achieved reasonable results with RMSEs ranging from 39.88% to 50.08%. The ANN model provided a more accurate estimation (RMSE r = 39.88% for the training set, and RMSE r = 42.36% for the testing set) than MLR (RMSE r = 49.51% for the training, and RMSE r = 53.20% for the testing). The final above ground dry biomass maps of the research area were produced based on the ANN and MLR models, generating the estimated mean values of 121 and 147 g/m 2, respectively.

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[68]
Yuan X, Li L, Chen X.et al, 2015. Effects of precipitation intensity and temperature on NDVI-based grass change over northern China during the period from 1982 to 2011.Remote Sensing, 7(8): 10164-10183. doi: 10.3390/rs70810164.The knowledge about impacts of changes in precipitation regimes on terrestrial ecosystems is fundamental to improve our understanding of global environment change, particularly in the context that heavy precipitation is expected to increase according to the 5th Intergovernmental Panel on Climate Change (IPCC) assessment. Based on observed climate data and the Advanced Very High Resolution Radiometer (AVHRR) Global Inventory Modeling and Mapping Studies (GIMMS) satellite-derived normalized difference vegetation index (NDVI), here we analyzed the spatio-temporal changes in grassland NDVI, covering 1.64 × 106 km2, in northern China and their linkages to changes in precipitation and temperature during the period 1982–2011. We found that mean growing season (April–October) grass NDVI is more sensitive to heavy precipitation than to moderate or light precipitation in both relatively arid areas (RAA) and relatively humid areas (RHA), whereas the sensitivities of grass NDVI to temperature are comparable to total precipitation in RHA. Heavy precipitation showed the strongest impacts in more than half of northern China (56%), whereas impacts of light precipitation on grass NDVI were stronger in some areas (21%), mainly distributed in northwestern China, a typical arid and semi-arid area. Our findings suggest that responses of grasslands are divergent with respect to changes in precipitation intensities.

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[69]
Yue S, Pilon P, Cavadias G, 2002. Power of the Mann-Kendall and Spearman’s rho tests for detecting monotonic trends in hydrological series.Journal of Hydrology, 259(1): 254-271.In many hydrological studies, two non-parametric rank-based statistical tests, namely the Mann鈥揔endall test and Spearman's rho test are used for detecting monotonic trends in time series data. However, the power of these tests has not been well documented. This study investigates the power of the tests by Monte Carlo simulation. Simulation results indicate that their power depends on the pre-assigned significance level, magnitude of trend, sample size, and the amount of variation within a time series. That is, the bigger the absolute magnitude of trend, the more powerful are the tests; as the sample size increases, the tests become more powerful; and as the amount of variation increases within a time series, the power of the tests decrease. When a trend is present, the power is also dependent on the distribution type and skewness of the time series. The simulation results also demonstrate that these two tests have similar power in detecting a trend, to the point of being indistinguishable in practice. The two tests are implemented to assess the significance of trends in annual maximum daily streamflow data of 20 pristine basins in Ontario, Canada. Results indicate that the P-values computed by these different tests are almost identical. By the binomial distribution, the field significant downward trend was assessed at the significance level of 0.05. Results indicate that a higher number of sites show evidence of decreasing trends than one might expect due to chance alone.

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[70]
Zastrow M, 2015. Data visualization: Science on the map: Easy-to-use mapping tools give researchers the power to create beautiful visualizations of geographic data.Nature, 519: 119-120.Easy-to-use mapping tools give researchers the power to create beautiful visualizations of geographic data.

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[71]
Zhang A B, Chen T Y, Liu X X.et al, 2015. Monitoring data filter and deformation information extraction based on wavelet filter and empirical mode decomposition.Applied Mechanics and Materials, 742: 261-271.Analyses of GPS signals by wavelet algorithms and empirical mode decomposition (EMD) have demonstrated the strength of these techniques in discriminating signals from noise. However, the denoising precision seriously affects the final EMD error, especially for signals containing incremental developments in information. We present a new noise filter and trend extraction model based on the orthogonal wavelet transform and EMD. Simulated and real data are used to evaluate the proposed method. The results suggest that: 1) The orthogonal wavelet transform and EMD method can better mitigate the random errors hidden in periodic signals; 2) For signals with a linear trend, the orthogonal wavelet transform filtering method is superior to EMD. We suggest a method of trend extraction by EMD after noise filtering using the wavelet; 3) For signals with a nonlinear trend, theoretical analysis and simulation results show that the new noise filter and trend extraction model is superior to EMD and the simple combination of wavelets with EMD. The proposed approach not only extracts instantaneous features, but also reduces the number of decomposition layers of the signals and the cumulative errors in later decomposition. This method significantly improves the accuracy of the extracted deformation; 4) After mitigating the influence of multipath and other error effects with the new model, we attain millimeter accuracy for the vertical component position in GPS dynamic deformation.

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[72]
Zhang A B, Gao J X, Zhang Z J, 2011. Deformation analysis and prediction of building above old mine goaf based on multiscale method.Rock and Soil Mechanics, 32(8): 2423-2428.Deformation of ground surface above old mine goaf is a complex nonlinear process,which has complex,sudden,and long-term features.The foundation stability and residual deformation must be evaluated before building life or service facilities above old mine goaf.A new method is put forward for stability analysis and evaluation of buildings above goaf by multiscale decomposition using empirical mode decomposition(EMD) method.Trough case study,detail signals of dynamic deformation of buildings above old mine goaf are obtained using multiscale empirical mode decomposition method.Decomposition scales are analyzed so as to evaluate the deformation characteristics reflected by original data and research the deformation mechanism effectively.Precision prediction for deformation is obtained by multiscale prediction model which is better than traditional method.This prediction model can provide a theoretical basis for stability evaluation of buildings above old mine goaf.

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[73]
Zheng T, Yang L, 2007. Discussion and improvement on empirical mode decomposition algorithm.Acta Scientiarum Naturalum Universitatis Sunyatseni, 46(1): 1-6.The stopping criteria for sifting and boundary effect are studied for Empirical Mode Decomposition(EMD) algorithm.The decomposition is enhanced by combining with the alternative EMD approach and the new stopping criteria.The alternative EMD approach circumvents the problem of boundary continuation in B-Spline interpolation,where the signal is assumed to be infinitely long.A discussion for boundary continuation with finite length is presented and its algorithm is developed.This research compensates for the existing approach and can serve as an applicable method in practice.Experiments show that the proposed method is effective.

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[74]
Zheng Z, 2001. Wavelet Transformation and the Application of Its MATLAB Tools. Beijing: Earthquake Press.

[75]
Zhong P, Ding X, Zheng D, 2006. Separation of structural vibrations and GPS multipath signals using Vondrak filter.Journal of Central South University of Technology, 37(6): 1189-1195.Vondrak bandpass filter,which has good signal resolution over its signal truncation frequency band and is effective in separating structural vibrations from global positioning system(GPS) multipath effects,was applied to GPS structural deformation monitoring.Real GPS observations were used to test the performance of the proposed filter.The results show that the method has the potential to improve the quality of GPS results,which can successfully extract the desired vibration signals from the point coordinate series and separate the structural vibrations and multipath signals from the double-difference carrier-phase observation residuals series.

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