APPLICATION OF NON PARAMETRIC BASIS SPLINE (B-SPLINE) IN TEMPERATURE FORECASTING
APPLICATION OF NON PARAMETRIC BASIS SPLINE (B-SPLINE) IN TEMPERATURE FORECASTING
Rezzy Eko Caraka1*, Alvita Rachma Devi1
1Department of Statistics, Diponegoro University,Indonesia
*corresponding author: rezzyekocaraka@gmail.com
ABSTRACT
“Weather is important but hard to predict”—lay people and scientists alike will agree. The complexity of system limits the knowledge about it and therefore its predictability even over a few days. It is complex because many variables within the Earth’s atmosphere, such as temperature and they do so nonlinearly. B-spline as a basis for one-dimensional regression and we extend this paper by using B-spline to construct a basis for bivariate regression. This construction gives a basis in two dimensions with local support and hence a fully flexible family of fitted mortality surfaces one of the principal motivations behind the use of B-spline as the basis of regression is that it does not suffer from the lack of stability that can so bedevil ordinary polynomial regression. The essential difference is that B-spline have local non-zero support in contrast to the polynomial basis for standard regression. The optimal B-Spline models rely on the optimal knots that has a minimum Generalized Cross Validation (GCV)
Keywords: Temperature, B-Spline, Generalized Cross Validation, non-parametric
A. Introduction
Far from being future fear, global warming is happening now, and scientists have evidence that humans are to blame. For decades, cars and factories have spewed billions of tons of greenhouse gasses into the atmosphere, and these gasses caused temperatures to rise between 0.6°C and 0.9°C (1.08°F to 1.62°F) over the past century. The rate of warming in the last 50 years was double the rate observed over the last 100 years. Temperatures are certain to go up further. Several studies have looked at the potential impact of climate change.
Riebeek (2007) explained Global warmth begins with sunlight. When light from the Sun reaches the Earth, roughly 30 percent of it is reflected back into space by clouds, atmospheric particles, reflective ground surfaces, and even ocean surf. The remaining 70 percent of the light is absorbed by the land, air, and oceans, heating our planet’s surface and atmosphere and making life on Earth possible. Solar energy does not stay bound up in Earth’s environment forever. Instead, as the rocks, the air, and the sea warm, they emit thermal radiation or infrared heat. Much of this thermal radiation travels directly out to space, allowing Earth to cool.
Some of this outgoing radiation, however, is reabsorbed by water vapor, carbon dioxide, and the gasses in the atmosphere (called greenhouse gasses because of their heat-trapping capacity) and is then re-radiated back toward The Earth’s surface. On the whole, this re-absorption process is good. If there were no greenhouse gasses or clouds in the atmosphere, the Earth’s average surface temperature would be a very chilly -18°C (0°F) instead of the comfortable 15°C (59°F) that it is today. What makes scientists concerned now is that over the past 250 years, humans have been artificially raising the concentration of greenhouse gasses in the atmosphere at an ever-increasing rate. By 2004, humans were pumping out over 8 billion tons of carbon dioxide per year. Some of it was absorbed by “sinks” like forests or the ocean, and the rest accumulated in the atmosphere. We produce millions of pounds of methane by allowing our trash to decompose in landfills and by breeding large herds of methane-belching cattle. Nitrogen-based fertilizers and other soil management practices lead to the release of nitrous oxide into the atmosphere.
Green (2009) explained Policymakers need to know whether the prediction is possible and, if so, whether any proposed forecasting method will provide forecasts that are substantially more accurate than those from the relevant benchmark method. An inspection of global temperature data suggests that temperature is subject to irregular variations on all relevant time scales and that variations during the late 1900s were not unusual. In such a situation, a “no change” extrapolation is an appropriate benchmark forecasting method. We used the UK Met Office Hadley Centre’s annual average thermometer data from 1850 through 2007 to examine the performance of the benchmark method. The accuracy of forecasts from the benchmark is such that even perfect forecasts would be unlikely to help policymakers. For example, mean absolute errors for the 20- and 50-year horizons were 0.18C and 0.24C respectively. We nevertheless demonstrate the use of benchmarking with the example of the Intergovernmental Panel on Climate Change’s 1992 linear projection of long-term warming at a rate of 0.03 C per year. The small sample of errors from ex-ante projections at 0.03 C per year for 1992 through 2008 was practically indistinguishable from the benchmark errors. Validation for long-term forecasting, however, requires a much longer horizon. Again using the IPCC warming rate for our demonstration, we projected the rate successively over a period analogous to that envisaged in their scenario of exponential CO growth—the years 1851 to 1975. The errors from the projections were more than seven times greater than the errors from the benchmark method. Relative errors were larger for longer forecast horizons. Our validation exercise illustrates the importance of determining whether it is possible to obtain forecasts that are more useful than those from a simple benchmark before making expensive policy decisions.
The most obvious impact of global warming will change in both average and extreme temperature and precipitation, but warming will also enhance coastal erosion, lengthen the growing season, melt ice caps and glaciers, and alter the range of some infectious diseases, among other things. For most places, global warming will result in more hot days and fewer cool days, with the greatest warming happening over land. Longer, more intense heat waves will become more frequent. High latitudes and generally wet places will tend to receive more rainfall, while tropical regions and generally dry places will probably receive less rain. Increases in rainfall will come in the form of bigger, wetter storms, rather than in the form of more rainy days. In between those larger storms will be longer periods of light or no rain, so the frequency of drought will increase. Hurricanes will likely increase in intensity due to warmer ocean surface temperatures.
Napiorkowski, M.J. (2014) discussed Stream temperature forecasting by means of an ensemble of neural networks: Importance of input variables and ensemble size in The Valley of Biala Tarnowska River. Located in the central part of the Polish Carpathians. The source is located in the Low Beskid at altitudes of 730 meters (Carpathian belt, southern Poland). The total length of the river is 101.8 km and the catchment area to the Koszyce Wielkie gauging station (10 km to the southwest of the city of Tarnow) equals 956.9 km. Biala rnowska catchment is very narrow and extends from the border with Slovakia. The majority of the river has unregulated banks and is in a natural state. Fields, pastures, meadows, and natural vegetation predominate in the catchment of the upper and middle portion of the river. Dominant geology can be defined as sandstone and shale flysch. Biala Tanowska catchment is divided into two different parts. The south section, representing about 25% of the catchment, is a wooded mountain part with the average slope of 10‰. The north part representing almost 75% of the basin, characterized by deep river valleys (mostly agricultural hills and foothills), is generally deforested. The river slope in the northern part is in the range of 0.9–5 ‰. The highest precipitation (up to 100 mm/month), and hence frequent states are observed during summer months. Average (high/low) temperature is (1ºC/5ºC) in January and (25ºC/13ºC) in July. According to the Köppen Climate Classification Biala Tarnowska river is located within the Humid Continental Zone. It may freeze during winter months and river ice may occur between November and April. If the Biala Tarnowska River is frozen and the results forecasting performance of the neural networks is satisfactory and generally more elements in aggregated ensemble results in the better forecast. Prediction errors observed in winter are related to the river freezing and melting processes, which are very difficult to be predicted accurately.
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