Management by Applying Novel Analytics on Satellite Data ... energy and moisture budgets, and because surface temperatur
Recent Contributions to Climate Change and Water Resource Management by Applying Novel Analytics on Satellite Data Semih Kuter 1,4, Zuhal Akyurek 2,5, Gerhard-Wilhelm Weber 3,4,* 1
Çankırı Karatekin University, Faculty of Forestry, Department of Forest Engineering, 18200, Çankırı, Turkey 2
3
Middle East Technical University, Faculty of Engineering, Department of Civil Engineering, 06800, Ankara, Turkey
Poznan University of Technology, Faculty of Engineering Management, Department of Marketing and Economic Engineering, 60-965, Poznan, Poland 4
5
Middle East Technical University, Institute of Applied Mathematics, 06800, Ankara, Turkey
Middle East Technical University, Graduate School of Natural and Applied Sciences, Department of Geodetic and Geographic Information Technologies, 06800, Ankara, Turkey
*
Corresponding Author:
[email protected]
Abstract In this presentation, we will demonstrate the integration of modern methods of Operational Research within spatial analysis including satellite data (i.e., Big Data) in order to develop better models for climate change studies and the sustainable management of water resources. As we all know, snow is an important land cover whose distribution over space and time plays a significant role in various environmental processes. Hence, snow cover mapping with high accuracy is necessary to have a real understanding for present and future climate, water cycle, and ecological changes. Thus, our basic aim is to investigate and represent the design and use of Multivariate Adaptive Regression Splines (MARS) for fractional snow cover (FSC) mapping from satellite data. Keywords: Snow cover mapping, Operational Research, MARS, climate change, snow hydrology
1. Introduction As an interdisciplinary science, Operational Research (OR) plays a key role in almost all branches of science (Kuter et al., 2017a; Kuter et al., 2018; Kuter et al., 2017b; Kuter et al., 2014; Özmen et al., 2014; Özmen et al., 2011; Weber et al., 2011), economics (Alp et al., 2011; Kürüm et al., 2012; Özmen et al., 2013; Taylan and Weber, 2008; Weber et al., 2012) and engineering (Yerlikaya-Özkurt et al., 2014, 2016) for decision making in complex real-world problems by employing scientific methods, fundamentally based on the theories of Data Mining, Statistical Learning and Inverse Problems. Besides the development of our world with its dizzying speed, serious problems, like global warming, drastic changes in weather and climate as well as increasing scarcity in fresh water supplies, etc., are at alarming levels (EWS, 2012; Mekonnen and Hoekstra, 2016; Nogué et al., 2009; Yang and Yeh, 2016). These global challenges often exhibit spatial characteristics and closely related to our nature and environment.
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Since snow can cover up to 40% of the Earth’s land surface during the Northern Hemisphere winter, the extent and variability of seasonal snow cover are important parameters in the climate system, due to their effects on energy and moisture budgets, and because surface temperature is highly dependent on the presence or absence of snow cover (Hall et al., 1995). In turn, snow-cover trends serve as key indicators of climate change. The climatological, hydrological, and ecological importance of snow cover is linked to its energy storage, high reflectance, good insulating properties, significant heat capacity, substantial water storage, and eventual release of this storage during the melting season (Czyzowska-Wisniewski et al., 2015). Since the middle of the 20th century, the snow-covered area in the Northern Hemisphere decreased about 10%, mainly due to a decrease in snow precipitation, an increased precipitation ratio of rainfall to snow, and an earlier melt in spring and summer (Czyzowska-Wisniewski et al., 2015). As stated in UNESCO (2006), UNESCO/IHP/HWRP (2009) and Wiltshire et al. (2013), Alpine regions, such as the Rocky Mountains, Tibetan Plateau, the Himalayas, the Andes, and mountains of the Middle East showed the greatest decrease in snow-covered area, resulting in a large scarcity in water availability to neighboring dry lowlands. They rely on river water discharge from mountains. These regions are occupied by one-sixth of the world’s population, and have suffered pronounced water shortages, widespread poverty, and famine. With the current high rate of population growth (Asia, South America), decline in groundwater due to extensive overpumping, and biological/chemical pollution, water shortages are likely to be the main limitations of future economic and social development, and human health in these regions. Snow cover has important implications for the hydrology and climate of mid- to high-latitude and mountain environments. As a frozen-water reservoir, snow holds precipitation until snowmelt runoff is released. Snowmelt runoff can pose a flooding hazard because it is often released rapidly during spring (Rango, 1996). However, snow is essential for the water supply of more than one sixth of world’s population that relies on fresh water from seasonal and glacial snowmelt (Barnett et al., 2005). Many and even very big Developing and Emerging Countries receive their water supply for drinking, household, agricultural and industrial purposes from the melting of snowpacks on high mountain chains. Since one-third of global water supplies are obtained from snowmelt, any change in the timing of releases will have serious repercussions for management (Jury and Vaux, 2005). Runoff predictions from snowmelt are achieved by implementing snow cover information into hydrological models. Runoff from snow also supplies the necessary water for sustaining forest ecosystems in watersheds (Douville et al., 2002). Thus, There is a strict necessity to include snow-cover extent and snow-water equivalent within hydrologic models in order to generate snowmelt runoff estimates for improved forecast accuracy for water supply, runoff rates and soil moisture recharge (Dozier, 1992). As we have tried to emphasize so far, enhanced understanding of present and future climate, water cycle, and ecological changes requires accurate assessment of seasonal snow cover. Although snow-covered area analysis based on in situ measurements (Beniston, 2003; Brown and Goodison, 1996; Laternser and Schneebeli, 2003; Marty, 2008) provides high-quality long time series data, snow cover
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mapping through field surveys is not economically and logistically practical (Gafurov and Bárdossy, 2009). Remote sensing (RS) has been providing unique opportunities for continuous monitoring of the Earth by sensors with different operational and technical characteristics installed on Earth-observing satellite platforms since the mid-60s, when the first operational snow mapping was done by National Oceanic and Atmospheric Administration (Hall and Martinec, 1985). With the development in the information technologies, more computer-demanding algorithms have started to involve in RS applications. Additionally, recent technological improvements of all kinds of measurement devices (which are Earth-observing satellite platforms in our case) create a gigantic and continuously growing supply of information (i.e., Big Data) to analyze. This situation forces us, scientists, to position the machine learning issues within the areas of data mining and model optimization, and to elaborate our work in the area of OR. Thus, it is inevitable for us to consider these global issues within an OR perspective, and in order to prevent and tackle them, we need more information about the interaction between human and environment. Hence, we require effective tools to deepen our understanding in such natural and environmental phenomena, where we have to “mine” for the inherent structure of the data in both time and spatial domains. One challenging issue in snow mapping is the trade-off between the temporal and spatial resolution of satellite imageries. Since high spatial resolution reduces the temporal resolution, it eventually limits timely detection of the changes in snow cover. Vice versa, high temporal resolution data reduce the precision of snow cover maps due to low spatial resolution. In order to deal with this problem, various Fractional Snow Cover (FSC) mapping approaches have been proposed and applied to low or moderate resolution images such as spectral unmixing (Painter et al., 2003) and empirical Normalized Difference Snow Index (NDSI) (Salomonson and Appel, 2004) methods. In contrast to binary classification approach where a pixel is labeled as either snow-covered or snow-free, the true class distribution can be well estimated in FSC mapping, even though the precise location of class fractions within each coarse resolution pixel still remains unknown (Verbeiren et al., 2008). The primary focus of this presentation is to investigate the applicability of Multivariate Adaptive Regression Splines (MARS) for FSC mapping from Moderate Resolution Imaging Spectroradiometer (MODIS) data. MARS is a nonparametric regression technique developed by Friedman (1991) and it is widely used in data mining and estimation theory in order to build flexible regression models for complex and high-dimensional nonlinear data. The main advantage of MARS is its ability to define the underlying functional relationships between dependent and independent variables by simply and smoothly connecting piecewise linear polynomial pieces, i.e., linear splines, resulting in a flexible model that can handle both linear and nonlinear behavior. 2. Multivariate Adaptive Regression Splines (MARS) In MARS, one-dimensional piecewise linear basis functions (BFs) are used to define relationships between a response variable and a set of predictors. The range of each predictor variable is cut into subsets of the full range by using knots which defines an inflection point along the range of a predictor. The slope of the linear segments between each consecutive pair of knots varies which ensures that the fully fitted function has no breaks or sudden steps. Selection of BFs is data-based and specific to the problem in MARS, which makes it a powerful
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adaptive regression procedure, suitable for solving high-dimensional and complex problems. The method is nonparametric, since it does not make any specific assumptions on the relations between the variables (Friedman, 1991; Hastie et al., 2009). MARS uses two stages when building up a regression model, namely, the “forward pass” and the “backward pass” algorithms. In the forward pass, the algorithm chooses the knot and its corresponding pair of BFs that result in the largest decrease in residual error, and the products satisfying the above mentioned condition are successively added to the model, until a predefined value Mmax is reached. During the model building, BFs are fitted in such a way that additive and interactive effects of the predictors are taken into account to determine the response variable. Since the forward pass creates an over-fit model, the backward pass is applied in order to prevent the model obtained in the forward pass from over-fitting by decreasing the complexity of the model without degrading the fit to the data. Those BFs which give the smallest increase in the residual sum of squares are removed at each step during the backward pass. Consequently, a predictor variable can be completely excluded from the model unless any of its BFs has a meaningful contribution to the predictive performance of the model. This iterative procedure continues until an optimal number of effective terms is represented in the final model. 3. Data Set and Model Building As dataset, 20 MODIS images taken over European Alps between April 2013 and December 2016 were downloaded from the web page of MODIS Level 1 and Atmosphere Archive and Distribution System (https://ladsweb.modaps.eosdis.nasa.gov) (cf. Table 1). Land cover information was acquired from MODIS MCD12Q1 product at 500 m spatial resolution produced within the frame of International Geosphere-Biosphere Programme (IGBP) (Friedl et al., 2010) (Figure 1). Table 1. Landsat 8 OLI and MODIS image pairs used in the training and the testing of MARS models. Image pair no Training scenes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Test scenes A B C D E
Date of acquisition
Scene time Landsat/MODIS
OLI tile Path/Row Processing level
Number of available pixels
18.04.2013 15.01.2014 08.03.2014 13.03.2014 07.04.2014 14.04.2014 12.12.2014 13.01.2015 10.02.2015 12.02.2015 19.02.2015 18.03.2015 20.12.2015 21.01.2016 22.12.2016
10:19/09:45 10:18/09:45 09:52/09:20 10:11/09:35 10:04/09:30 10:10/09:35 09:58/09:25 09:58/09:25 10:23/09:50 10:10/09:35 10:17/09.45 09:57/09:25 10:17/09:45 10:17/09.45 10:17/09.45
195/29 - L1T 195/29 - L1T 191/28 - L1T 194/28 - L1T 193/27 - L1T 194/28 - L1T 192/27 - L1T 192/27 - L1T 196/29 - L1T 194/29 - L1T 195/29 - L1T 192/27 - L1T 195/28 - L1T 195/29 - L1T 195/29 - L1T
47,369 63,789 75,880 66,027 82,381 73,053 41,004 53,101 78,894 39,116 66,396 70,155 37,146 57,258 69,606
16.12.2013 01.01.2014 13.03.2014 12.02.2015 24.04.2015
10:06/09:30 10:05/09:30 10:10/09:35 10:10/09:35 10:16/09:45
193/28 - L1T 193/28 - L1T 194/27 - L1T 194/28 - L1T 195/28 - L1T
59,984 38,479 81,481 53,587 64,061
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All corresponding Landsat 8 images were downloaded from the dedicated web page of the United States Geological Survey (USGS) (http://earthexplorer.usgs.gov). The scenes were selected so that they had a minimal cloud cover and were in an analysis-ready format, known as Level 1T (L1T), which incorporates precision georegistration and orthorectification employing digital topography (Wulder et al., 2012).
Fig. 1. Study area and the locations of Landsat 8 tiles.
All Landsat 8 images were classified into binary snow/nonsnow maps by using the OLI version of MODIS binary snow cover mapping algorithm SNOMAP (Hall et al., 1995). Landsat binary snow maps with 30 m resolution were used to calculate the snow cover fraction inside of a circle with 500 m radius centered at each MODIS pixel (Figure 2).
Fig. 2. Derivation of reference MODIS FSC maps from binary-classified higher resolution Landsat images. 5
Training data, for each pixel, consisted of a response variable, i.e., FSC values derived from higher resolution Landsat images, and ten predictor variables, namely, reflectance values from MODIS bands 1-7, NDSI, Normalized Difference Vegetation Index (NDVI) and land cover class. Each predictor variable, except the land cover class which was categorical, was normalized within the range of [0, 1]. The performance of MARS regression models during both training and testing stages were assessed by Root Mean Square Error (RMSE) and Correlation Coefficient (R) values: N
RMSE
yˆ i 1
yi
2
i
,
N
N
N
(1)
N
N yi yˆ i yi yˆ i
R
i 1
i 1
N y yi i 1 i 1 N
2 i
N
2
i 1
N N yˆ yˆ i i 1 i 1 N
2
,
(2)
2 i
where N is the total number of observations, yi is the ith reference value, and yˆ i is the ith predicted value. There are two basic MARS parameters to control the “model tuning” process during the training stage. The first parameter is the “maximum allowed numbers of BFs in the forward pass” (max_BFs), and the second one is the “maximum allowed degree of interactions between predictor variables” (max_INT). Increasing max_BFs brings a rise in the amount of flexibility - therefore, complexity - of the resulting model, whereas increasing max_INT provides the ability to model nonlinearities and statistical dependencies between predictor variables. Development of MARS models was performed with a basic trial-and-error procedure to decide the optimal values of these two parameters for each type of training samples. First, max_INT took the values from the set
1,2,3 , and then the value of max_BFs was incrementally varied taking within the set
for each value of
max_INT. The training data were split into two subsets in MARS as training and testing, with the corresponding sizes 70% and 30%, respectively. The MARS model that gave maximum R on 30% test data during model building was chosen for each sample type. The details of obtained MARS models are represented in Table 2.
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Table 2. Training performance of MARS models with various max_INT and max_BFs settings. Among the sequence of models for each type of sampling type and sample size, the MARS model that gave the best R value on the 30% test data in the training process was chosen. Boldface R value indicates the best MARS training performance(SR: Simple random sampling, STR_FSC: Stratified random sampling with respect to fractional snow cover , STR_FSC_LC: Stratified random sampling with respect to both fractional snow cover and land cover). Max. degree of interaction
Training (70%) Sampling type
SR
1
STR_FSC
STR_FSC_LC
SR
2
STR_FSC
STR_FSC_LC
SR
3
STR_FSC
STR_FSC_LC
Sample size Small Medium Large Small Medium Large Small Medium Large Small Medium Large Small Medium Large Small Medium Large Small Medium Large Small Medium Large Small Medium Large
Test (30%)
RMSE
R
RMSE
R
0.1399 0.1385 0.1382 0.1372 0.1376 0.1374 0.1354 0.1374 0.1368 0.1308 0.1299 0.1299 0.1277 0.1290 0.1298 0.1277 0.1290 0.1288 0.1384 0.1292 0.1288 0.1261 0.1283 0.1280 0.1265 0.1280 0.1275
0.9374 0.9388 0.9393 0.9401 0.9396 0.9398 0.9417 0.9399 0.9402 0.9455 0.9464 0.9465 0.9483 0.9470 0.9465 0.9483 0.9472 0.9472 0.9388 0.9469 0.9475 0.9496 0.9477 0.9480 0.9493 0.9480 0.9483
0.1340 0.1379 0.1362 0.1392 0.1372 0.1380 0.1393 0.1382 0.1381 0.1282 0.1301 0.1282 0.1337 0.1291 0.1303 0.1353 0.1313 0.1300 0.1323 0.1298 0.1276 0.1332 0.1286 0.1286 0.1345 0.1307 0.1287
0.9429 0.9392 0.9409 0.9380 0.9402 0.9394 0.9381 0.9391 0.9396 0.9479 0.9461 0.9478 0.9430 0.9472 0.9461 0.9417 0.9452 0.9467 0.9445 0.9463 0.9483 0.9434 0.9476 0.9475 0.9424 0.9457 0.9478
Max. number of BFs in the forward pass 40 80 80 60 80 80 40 80 80 120 160 160 160 140 160 100 160 160 20 160 160 160 160 160 100 160 160
4. Results The independent test dataset, which was not used during the training, is the most valuable to assess the performance of MARS FSC models. Table 3 represents the results of our MARS models on five individual test scenes A-E, and the combined test data, according to the best training performance of each type of model for nine different training sample types. When the performance of MARS is evaluated in terms of its computational efficiency expressed in terms of CPU times during training, as given in Tables 4, we observe that the increase in both complexity of model building and training data size result in an increase in the training time.
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Table 3. Performance of MARS models on 5 independent test scenes A-E and the combined test dataset consisting of 297,592 pixels in total. Bold face row indicates the test results of the corresponding model setting with respect to the best training performance (S: Small, M: Medium, L: Large).
MARS
Model
Sampling type / size S SR M L S STR M FSC L S STR FSC M LC L
A RMSE 0.1672 0.1656 0.1671 0.1654 0.1645 0.1660 0.1650 0.1664 0.1648
B R 0.8829 0.8832 0.8837 0.8856 0.8861 0.8853 0.8840 0.8841 0.8864
RMSE 0.1455 0.1476 0.1480 0.1682 0.1426 0.1443 0.1484 0.1465 0.1462
C R 0.9260 0.9239 0.9232 0.9036 0.9299 0.9275 0.9238 0.9247 0.9252
RMSE 0.0970 0.0952 0.0956 0.0971 0.0953 0.0951 0.0965 0.0952 0.0956
D R 0.9671 0.9682 0.9681 0.9674 0.9682 0.9680 0.9667 0.9682 0.9682
RMSE 0.1847 0.1809 0.1832 0.1889 0.1871 0.1830 0.1932 0.1819 0.1836
E R 0.8802 0.8844 0.8828 0.8774 0.8793 0.8837 0.8692 0.8841 0.8815
RMSE 0.0863 0.0860 0.0851 0.0872 0.0849 0.0853 0.0882 0.0851 0.0854
R 0.9747 0.9751 0.9755 0.9743 0.9756 0.9754 0.9735 0.9754 0.9753
Combined RMSE R 0.1367 0.9390 0.1353 0.9395 0.1363 0.9393 0.1408 0.9363 0.1357 0.9406 0.1353 0.9402 0.1388 0.9370 0.1355 0.9398 0.1356 0.9396
Table 4. Average CPU times in seconds elapsed during the training of MARS models with various settings for max_INT and max_BFs, and for different training data sizes ( * indicates the average CPU time of the final MARS model). max_INT
1
2
3
max_BFs 20 40 60 80 100 120 140 160 180 200 20 40 60 80 100 120 140 160 180 200 20 40 60 80 100 120 140 160 180 200
Small 1.20 1.41 1.88 2.50 3.14 3.88 4.75 5.16 5.02 5.10 1.39 2.90 5.65 9.86 16.04 23.60 33.19 44.04 56.05 68.73 1.61 4.24 8.53 14.13 20.67 28.16 36.69 46.23 55.47 65.97
Medium 7.92 10.63 14.37 18.53 23.33 28.57 32.50 32.61 32.68 33.00 13.20 26.64 51.36 88.22 137.73 202.97 277.50 355.13 458.39 562.30 14.61 38.41 74.34 118.05 163.81 224.01 272.39 339.47 410.31 488.34
Large 15.56 21.90 30.52 39.33 50.58 59.75 63.89 61.39 60.92 61.29 26.59 63.45 115.82 200.74 317.39 448.64 611.95 711.33 890.64 1082.95 30.43 84.88 168.50 267.58 370.92 500.24 649.34 838.27* 1037.33 1227.91
As the complexity of MARS increases, the average training time also increases. This is an expected result since increasing max_INT and max_BFs enlarge the search space of MARS, which means that more candidate BFs are included into the model, resulting in an increase of the training time. The chosen MARS model spends 838.27 seconds during training. Once the MARS models are trained, the average required time to estimate FSC values on each of the independent test datasets is less than 2.0 seconds. 5. Conclusion In this study, an alternative approach for FSC mapping was introduced by utilizing a special form of spline fitting, namely, MARS. In fact, the use of spline functions within the context of our modeling of complex environmental dynamics offers great advantages. Splines, from the viewpoint of a single dimension (i.e., input 8
variable), are piecewise polynomials. If only polynomials were used, then they would generally converge to plus or minus infinity when the absolute values of the input variables grow large. As real-world processes mostly stay in bounded margins (even if these bounds can be very large), polynomials would need to be of a high degree to “turn around” (i.e., oscillate enough) in order to stay in the margin. But with high-degree polynomials, it is not that easy to work, especially, since the real-world problems are multivariate, which can imply multiplication effects and, hence, a fast increase of the degree of the resulting polynomial. This phenomena is also known as the “curse of dimensionality”. Instead, including splines allows us to keep, in each dimension, the degree of the polynomial “pieces” very low. Splines are, indeed very “flexible”, such to say, “elastic”. Often, we are calling them “smoothing splines” since they “smoothly” approximate the discrete data. Rapid advances in RS technologies give us the opportunity of more effective planning and decision making. As our study showed us, once we manage to integrate the dynamical progress of scientific advances in OR with the spatial technologies, we can improve our ability to deal with global challenges that particularly affect the countries which are in greatest needs. So, there is still room for us to enhance our understanding of the value of spatial data and to find better methods for incorporating the modern techniques OR with RS, in order to develop sustainable economies, to increase the quality of life for the Developing Countries and provide a better future for the next generations. References 1.
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