When to Picnic?Peter Barnum and Vinithra VaradharajanThe Robotics Institute, Carnegie Mellon UniversityPittsburgh, PA [email protected],[email protected] IntroductionThe quantitative and reliable prediction of the level of precipitation is important for scientific, eco-nomic and ecological reasons [3]. Currently, there are many global climate models, but there is stilla great deal of uncertainty in their predictions. Not only do they not agree with themselves, they donot even predict the past correctly [7]. (This is a similar idea to having poor training error.) Suchpoor performance rates are primarily due to the vast number of local and global factors that influenceweather. Hence, the need to accurately predict precipitation levels given the datasets of historicalrecords from different areas is an ideal machine learning problem. Many supervised learning tech-niques are applicable, with different levels of accuracy. In addition, the choice of a technique alsoneeds to take into consideration that these datasets often suffer from missing values.This report discusses the use of one such machine learning technique, namely nearest neighbor, topredict the level of precipitation expected on a particular day at a particular location, given data onthe level of precipitation that occurred on previous days at the same location and at neighboringlocations.We begin by stating the problem and describing the data provided. Discussing previous work on thetopic sets the scene for our approach to the problem by discussing previous work on the topic. Thisis followed by a description of the nearest neighbor machine learning technique and how it is usedin weather prediction. We then describes the design and implementation of experiments and discussthe results obtained. The report ends with a discussion of future work and conclusions.2 Problem definitionWe use a machine learning technique to predict the level of precipitation based on historical precipi-tation data. We use the Widmann and Bretherton dataset that includes 45 years of daily precipitationdata across 50 km x 50 km from the Northwest of the US in netCDF format. The data has threedimensions: latitude, longitude and time in days. The unit for each entry is mm/day and refers to theprecipitation that occurred at a particular location, specified by the latitude and longitude values, andon a particular day, specified by the time value. Such an objective requires understanding the dataand its features, selection of a machine learning technique, application of the technique by makingassumptions and evaluation of the entire approach by analyzing the results.The data extracted from the netCDF file is scaled by a factor of 0.1 and has several missing values.The missing value is indicated by a value of 32767. The data has been prepared by descaling thedata and setting the missing value entry as 0 instead of 32767. Dealing with missing data explicitlyadds unnecessary complexity. Given this, we have no intelligent way to pick a prior, except thatthere is more often no rain than some rain.3 Related WorkPeople have tried to predict weather with various techniques and models for millenia. Early weatherprediction algorithms involved memorizing lists of predictive algorithms, such as “red sky at night,sailor’s delight”, which was probably based on a data driven approach that recognized that if the skywas red the night before, it often rained the next day. Advances in modeling have led to additionaltechniques. According to Beniston [1], a variety of models are used, based on the resolution thatis needed. For example, much more specific physical effects are used for local weather prediction,compared to global climate prediction. Wikipedia [12] divides these precisions into two categories,Global models and Regional models. Common global models are GFS, NOGAPS, GEM, ECMWF,UKMET, and GME. Common local models are WRF, NAM, NMM-WRF, AR-WRF, MM, andHIRLAM. These models predict a variety of factors, such as temperature, dew point, wind speedand direction, precipitation, and precipitation type. In contrast, our work is only trying to predict theamount of precipitation. We have at our disposal only a smaller set of features than those that thesemodels take advantage, so we cannot use these models directly.Many different machine learning methods and assumptions have been suggested to predict weatherand their accompanying difficulties have been listed. In [4], Palmer approaches the problem ofuncertainty in forecasts of weather and climate using ensembles of integrations of comprehensiveweather and climate prediction models, with explicit perturbations to both initial conditions andmodel formulation resulting in an ensemble of forecasts that can be interpreted as a probabilisticprediction. He then uses singular-vector methods to determine the linearly-unstable componentof the initial probability density function. He bases his prediction systems on timescales of days,seasons and decades. He states that many of the difficulties in forecasting predictability arise fromthe large dimensionality of the climate system. In [7], the Bayesian approach to model-based datainterpretation has been used to investigate global climate modeling and prediction. It has beenfound to be particularly useful in applications where a large amount of prior domain knowledge isavailable. The Bayesian approach can not only find the most probably model, but it can also say howaccurate the prediction is. Two methods that have been suggested specifically related to predictionof precipitation are neural networks [5, 9, 2] and prognostic equations [10]. In [3] Ehrendorferstates that quantification of atmospheric predictability asks for the rate at which two initially closetrajectories diverge for given atmospheric dynamics. Such estimates place upper bounds on timehorizons over which useful forecasts may be expected. The literature stated here has led us tobelieve that given our dataset two key features worth analyzing are the influence of time and spaceon the precipitation at a particular location.4 Using nearest neighbors for predictionAs discussed above, weather prediction is a complex and unsolved problem. The problem is com-plex, largely due to the huge number of hidden factors. It would not be unreasonable to say that ifweather was a graphical model, there would be a million latent variables for every observed one.Given this complexity, we do not want to try to use a parametric
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