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1. Introduction to Machine Learning in Meteorology
The integration of machine learning (ML) into meteorological studies is rapidly increasing, signifying a crucial shift in how weather phenomena are understood and predicted. As demonstrated in studies, meteorologists are increasingly utilizing ML methods, emphasizing the need for professionals in this field to be well-versed in these technologies. However, there is a noticeable scarcity of resources specifically tailored to meteorology that explain ML terms and methodologies.
To address this gap, this article aims to serve as a foundational resource for meteorologists, offering clear, accessible explanations of ML concepts and their applications in weather forecasting. A primary goal is to enhance the trustworthiness and adoption of ML methods by discussing them in plain language and illustrating their use with practical meteorological examples.
In operational settings, ML models are frequently perceived as black boxes, which can deter users from fully trusting and utilizing their potential. This perception stems from the opaque nature of ML methods, which can make it difficult for forecasts to align with a meteorologist’s existing knowledge. As such, this article aims to demystify ML, making it more transparent and enhancing user trust by meeting the requirements of a good forecast.
This paper is structured to provide a comprehensive overview, starting with an introduction to ML methods and common terms. It progresses into a discussion of general ML methods within a meteorological context, detailing the ML pipeline from beginning to end. Finally, it concludes with a summary and an outlook on future topics, setting the stage for further exploration of advanced ML techniques.
2. Machine Learning Methods and Terminology
This section elucidates some of the most frequently used machine learning (ML) methods, beginning with definitions of key terms. ML, in its broadest sense, refers to any empirical method where parameters are fit (i.e., learned) using a training dataset. This fitting process is designed to optimize (e.g., minimize or maximize) a predefined loss (i.e., cost) function. Within this framework, ML is divided into two primary categories: supervised and unsupervised learning.
Supervised learning involves training ML methods with specific input features and output labels. For instance, predicting tomorrow’s high temperature at a specific location using historical temperature measurements as labels. In contrast, unsupervised learning methods operate without predefined output labels, such as using self-organizing maps to identify patterns in weather data. This article will focus on supervised learning techniques.
The input features for supervised learning are often referred to as input data, predictors, or variables, and they can be mathematically represented as the vector (matrix) X. The desired output of the ML model, known as the target, predictand, or label, is mathematically written as the scalar (vector) y. To illustrate, in the meteorological example of predicting tomorrow’s high temperature, the input feature might be tomorrow’s temperature as forecasted by a numerical weather model (e.g., GFS), while the label would be tomorrow’s observed temperature.
Supervised ML methods are further subdivided into regression and classification tasks. Regression tasks involve ML methods that output a continuous range of values, such as the predicted high temperature for tomorrow (e.g., 75.0°F). Classification tasks, on the other hand, use ML methods to classify data into categories, such as predicting whether it will rain or snow tomorrow. To frame the high temperature forecast as a classification task, one might ask: “Will tomorrow be warmer than today?” This article will explore both regression and classification methods, noting that many ML methods can be adapted for either type of task.
All ML methods discussed share a common trait: they quantitatively utilize training data to optimize a set of weights (i.e., thresholds) that enable prediction. These weights are determined either by minimizing the error of the ML prediction or maximizing the probability of a class label. The following subsections will detail various ML methods, starting with simpler approaches (e.g., linear regression) and advancing to more complex ones (e.g., support vector machines).
2.1 Linear Regression: A Foundation in Prediction
One of the fundamental principles in machine learning is to begin with simpler models when addressing a task. Occam’s razor suggests that the simplest solution that effectively solves the problem or represents the data should be preferred. While this does not always mandate using the simplest ML model, it does imply that simpler models should be explored before resorting to more complex ones. Thus, linear regression is discussed first due to its simplicity and computational efficiency. It has a notable history in meteorology, forming the basis of the model output statistics product (MOS) familiar to many meteorologists.
At its core, linear regression approximates the value to be predicted (y^) by fitting weight terms (wi) according to the equation:
y^=∑i=0i=Dwixi
Here, the first predictor (x0) is always 1, allowing w0 to act as a bias term that shifts the function away from the origin as necessary. The term D represents the number of features used for the task.
The goal in machine learning is to determine wi values that minimize a user-specified loss function, which quantifies the error. For traditional linear regression, the most common loss function is the residual summed squared error (RSS):
RSS=∑j=1N(yj−y^j)2
In this equation, yj represents a true data point, y^j is the corresponding predicted data point, and N is the total number of data points in the training dataset. Linear regression using RSS is highly effective and a fast learning algorithm, making it a recommended baseline method before moving to more complex approaches.
Datasets can sometimes include irrelevant or noisy predictors, which can introduce instabilities during learning. One way to address this is to use ridge regression, a modified version of linear regression. Ridge regression minimizes both the summed squared error and the sum of the squared weights, known as an L2 penalty:
RSSridge=∑j=1N(yj−y^j)2+λ∑i=0Dwi2
Here, λ (≥0) is a user-defined parameter that regulates the weight of the penalty. Similarly, lasso regression minimizes the sum of the absolute values of the weights, a penalty known as an L1 penalty:
RSSlasso=∑j=1N(yj−y^j)2+λ∑i=0D|wi|
Both lasso and ridge regression encourage smaller learned weights, but they do so in different ways. These penalties are often combined to form the elastic-net penalty:
RSSelastic=∑j=1N(yj−y^j)2+λ∑i=0D[αwi2+(1−α)|wi|]
The addition of components to the loss function, as described in equations (3)–(5), is known as regularization and is also found in other ML methods. Recent studies have utilized linear regression for various applications, including subseasonal prediction of tropical cyclone parameters, relating mesocyclone characteristics to tornado intensity, and short-term forecasting of tropical cyclone intensity.
Caption: A visual example of linear regression with a single input predictor. The x-axis is a synthetic input feature, and the y-axis is a synthetic output label. The solid black line is the regression fit, and the red dashed lines are the residuals.
2.2 Logistic Regression: Extending Regression to Classification
Complementing linear regression, logistic regression is a classification method that builds on the same functional form as linear regression. The key differences lie in the method for determining the weights and a minor adjustment to the output. Specifically, logistic regression applies the sigmoid function to the output of the linear equation:
S(y^)=11+e−y^
The sigmoid function scales the output of the linear equation to a range between 0 and 1, allowing it to be interpreted as a probability. In the simplest classification case, involving just two classes (e.g., rain or snow), the sigmoid output can be interpreted as the probability of either class. The classification is then formulated as finding the wi that maximizes the probability of a desired class. Mathematically, the classification loss function for logistic regression can be described as:
loss=∑i=0i=D−yilog[S(y^)]+(1−yi)log[1−S(y^)]
The expression is minimized using derivatives, with more information on minimization techniques available in resources on data assimilation for numerical weather prediction.
Logistic regression has been utilized in meteorology for a long time. An early paper demonstrated its skill in predicting the probability of hail greater than 1.9 cm, while more recent applications include identifying storm mode, subseasonal prediction of surface temperature, and predicting the transition of tropical cyclones to extratropical cyclones.
2.3 Naïve Bayes: A Probabilistic Classifier
Another classification method, the naïve Bayes classifier, uses Bayes’s theorem, expressed as:
P(y|x)=P(y)P(x|y)P(x)
This equation calculates the probability of a label y (e.g., snow) given a set of input features x (e.g., temperature). It uses the probability of the label y occurring in the dataset, the probability of the input features given they belong to class y, and the overall probability of the input features. The “naïve” aspect of this algorithm comes from the assumption that all input features x are independent of each other.
The predicted class (y^) from naïve Bayes is the classification label (y) that maximizes the sum of the log of the probability of that classification [P(y)] and the sum of the log of all the probabilities of the specific inputs given the classification [P(xi|y)].
To visualize P(xi|y), consider surface weather measurements from a station where data were compiled for both raining and snowing conditions. To get P(xi|y), an underlying distribution function is assumed, commonly the normal distribution:
f(x;μ,σ)=1σ2πexp[−12(x−μσ)]
Here, μ is the mean and σ is the standard deviation of the training data. The parameters μ and σ are “learned” from the training data. If the normal distribution assumption is poor, other distributions can be used, such as multinomial or Bernoulli distributions.
Naïve Bayes classification has been popularly used in meteorology for implementing ProbSevere, which uses various severe storm parameters and observations to classify the likelihood of a storm becoming severe. Additional examples include identifying tropical cyclone secondary eyewall formation, identifying anomalous propagation in radar data, and retrieving precipitation type from geostationary satellites.
Caption: Visualizing the probability of an input feature given the class label. This example is created from 5-min weather station observations from near Marquette, MI (years included: 2005–20). The precipitation phase was determined by the present weather sensor. The histogram is the normalized number of observations in that temperature bin, while the smooth curves are the normal distribution fit to the data. Red is for raining instances and blue is for snowing instances.
2.4 Trees and Forests: Decision-Based Learning
Decision trees use a decision-making method analogous to flow charts, where the decision points are learned automatically from the data. Decision trees create splits in the data based on decisions that reduce either the Gini impurity or the entropy value after the split. Gini impurity is defined as:
Gini=∑i=0i=kpi(1−pi)
Entropy is defined as:
entropy=∑i=0i=kpilog2(pi)
Both functions measure how similar the data point labels are within each grouping of the tree after a split. The goal is to choose splits that result in leaves with minimal Gini impurity or entropy, ideally resulting in subgroups where all labels are the same. The output of this tree can be either the majority class label or the ratio of the major class, providing a probabilistic output.
While a decision tree with a single decision has limited prediction power, complexity can be increased by including greater depth (more decisions/branches). An additional step to increase complexity is to use ensembles, forming the basis of two additional tree-based methods: random forests and gradient boosted decision trees.
Random forests are collections of decision trees trained on random subsets of data and random subsets of input variables. Gradient boosted decision trees are ensembles where each tree is trained on the remaining error from the previous trees. Predictions from the ensemble of trees can be combined through a voting procedure or by averaging the probabilistic outputs from each tree.
While the discussion here has centered on classification, tree-based methods can also be used for regression. The main alteration involves substituting the loss function. For example, the residual summed squared error is a common loss function for both random forests and gradient boosted regression.
2.5 Support Vector Machines: Maximizing Margins
A support vector machine (SVM) is an ML method similar to linear and logistic regression. SVM uses a linear boundary for predictions:
y^=wTx+b
Here, w is a vector of weights, x is a vector of input features, b is a bias term, and y^ is the regression prediction. In classification, only the sign of the right side of the equation is used. The main difference between linear methods and SVM is that SVM includes margins to the linear boundary, defined as the area between the boundary and the closest training data point for each class label.
The optimization task for SVM is to maximize the margin, which can be described mathematically as:
margin=1wTw
A powerful feature of SVM is its ability to extend to additional mathematical formulations for the boundary, such as a quadratic function. Recent applications of SVM in meteorology include classifying storm mode, hindcasting tropical cyclones, and evaluating errors in quantitative precipitation retrievals.
Caption: Support vector machine classification examples. (a) Ideal (synthetic) data where the x and y axis are both input features, while the color designates what class each point belongs to. The decision boundary learned by the support vector machine is the solid black line, while the margin is shown by the dashed lines. (b) A real world example using NAM 1800 UTC forecasts of U and V wind and tipping-bucket measurements of precipitation. Blue plus markers are raining instances, and the red minus signs are non-raining instances. Black lines are the decision boundary and margins.
3. Machine Learning Applications and Discussion
This section discusses the use of various ML methods in the context of thunderstorms, using data from the Storm Event Imagery dataset (SEVIR). This dataset contains over 10,000 storm events from 2017 to 2019, including measurements from GOES-16 and NEXRAD. Each event spans four hours and includes measurements of visible reflectance, water vapor brightness temperature, infrared window brightness temperature, vertically integrated liquid (VIL), and lightning flashes.
In addition to demonstrating ML in the context of the SEVIR dataset, this section follows the general steps involved in using ML, including best practices and common pitfalls.
3.1 Problem Statements
The SEVIR data is applied to two tasks:
- Determine if an image contains a thunderstorm.
- Predict the number of lightning flashes in an image.
We assume GLM observations are unavailable, requiring the use of other measurements as features to estimate the presence and intensity of lightning.
3.2 Data Acquisition and Preprocessing
The first step in any ML project is to obtain data. The SEVIR data is publicly available on Amazon Web Services. A key question is: “How much data is needed for machine learning?” While there is no universal answer, it is generally important to gather enough diverse data to avoid bias in the ML model.
After obtaining the data, it is crucial to remove any spurious data to ensure the ML model learns from high-quality inputs. Cleaning and preparing the dataset for ML often takes a significant amount of time.
Subsequent to cleaning, the next step is to engineer the inputs (features) and outputs (labels). For these tasks, domain knowledge is essential. Relevant quantities are the magnitude of reflectance in the visible channel, the coldness of brightness temperatures in the water vapor and clean infrared channels, and the amount of vertically integrated water. Thus, we extract the following percentiles from each image and variable: 0, 1, 10, 25, 50, 75, 90, 99, and 100.
To create the labels, the number of lightning flashes in each image are summed. For Task 1, an image is classified as containing a thunderstorm if it has at least one flash in the last five minutes. For Task 2, the sum of all lightning flashes in the past five minutes is used as the regression target.
The dataset is then split into three independent subsets: training, validation, and testing sets. This is to prevent the ML model from “memorizing” the training data, a phenomenon known as over-fitting. The training dataset is the largest subset, typically 70% to 85% of the total data. The validation dataset is used to assess over-fitting and to evaluate different model configurations (hyper-parameters). The test dataset is reserved for the very end of the ML process, providing an unbiased assessment of the trained ML model’s skill on unseen data.
In meteorology, independence between the subsets is often challenging due to spatial and temporal autocorrelations. To mitigate this, time is often used to split the dataset. For example, we split the SEVIR data by training on data from January 1, 2017, to June 1, 2019, and using alternating weeks in the rest of 2019 for the validation and testing sets.
Caption: An example storm image from the SEVIR dataset. This event is from 6 Aug 2018. (a) The visible reflectance, (b) the midtropospheric water vapor brightness temperature, (c) the clean infrared brightness temperatures, (d) the vertically integrated liquid retrieved from NEXRAD, and (e) gridded GLM number of flashes. Annotated locations of representative percentiles that were engineered features used for the ML models are shown in (a).
3.3 Training and Evaluation
3.3.1 Classification: Identifying Thunderstorms
Task 1 involves classifying whether an image contains a thunderstorm. The methods available for this task include logistic regression, naïve Bayes, decision trees, random forests, gradient boosted trees, and support vector machines.
All methods are initially trained using their default hyper-parameters and one input feature: the minimum infrared brightness temperature (Tb). This is because Tb is a meteorological proxy for storm depth, which is correlated with lightning formation. Training all methods using Tb achieves an accuracy of 80% on the validation dataset.
Another common performance metric for classification tasks is the area under the curve (AUC) of the receiver operating characteristics curve (ROC). The ROC curve is calculated from the relationship between the probability of false detection (POFD) and the probability of detection (POD), which are derived from a contingency table.
An additional method for evaluating performance is a performance diagram. This diagram uses POD on the y-axis and success ratio (SR) on the x-axis, allowing for the assessment of a model’s performance. From this, we assess whether a model is overforecasting or underforecasting.
Using all available input features yields higher accuracies across all models. To prevent bias, it is good practice to normalize input features.
With the model showing good performance, we can now interrogate how the ML is making its predictions. This is to alleviate some of opaqueness of the ML black box and align with the ML user’s prior knowledge.
Techniques such as permutation importance and accumulated local effects (ALE) are used to answer these questions. Permutation importance quantifies the relative importance of an input feature by assessing the change in the evaluation metric when that variable is shuffled. ALE investigates the relationship between an input feature and the model’s output.
3.3.2 Regression: Predicting Lightning Flashes
Task 2 is to predict the number of lightning flashes within an image. The regression methods available include linear regression, decision tree, random forest, gradient boosted trees, and support vector machines.
With Tb as the lone predictor, linear methods may struggle due to the many images with zero flashes. One way to improve performance would be to only predict the number of flashes in images where there are non-zero flashes. This can be achieved leveraging the classification model that we trained earlier.
A common way to compare regression model performance is to create a one-to-one plot, which plots the predicted number of flashes against the true measured number of flashes.
To quantify each model’s performance, the following are common metrics calculated: mean bias, mean absolute error (MAE), root mean squared error (RMSE), and coefficient of determination (R2).
Using all available features increases the model’s performance. Since the initial fitting of the ML models used default parameters, there may be room for improvement.
Here, we show an example of some hyper-parameter tuning of a random forest. Hyper-parameter search systematically varies the depth of the trees from 1 to 10 and the number of trees from 1 to 100.
The best random forest model choice for predicting lightning flashes is a random forest with a maximum depth of eight and a total of 10 trees.
3.4 Testing
The test dataset is held out until the end, ensuring that there is no unintentional tuning of the final model configuration. These test results are the end performance metrics that should be interpreted as the expected ML performance on new data. For the ML models here, the metrics are very similar as the validation set.
4. Summary and Future Work
This article served as the first part of a two-part tutorial designed for the operational meteorology community. It surveyed common ML methods, all considered supervised methods, where data are trained from include pre-labeled truth data. These methods included linear regression, logistic regression, decision trees, random forests, gradient boosted decision trees, naïve Bayes, and support vector machines. The overarching goal was to introduce these methods in such a way that ML becomes more familiar to readers as they encounter them in the operational community and general meteorological literature. Moreover, this article provided ample references of published meteorological examples and open-source code to act as catalysts for readers to adapt and try ML on their own datasets and in their workflows.
The second part of this series will discuss a more complex, yet potentially more powerful, grouping of ML methods: neural networks and deep learning. Neural networks have been applied to meteorological topics for decades, and with the exponential growth of computing resources and dataset sizes, research using neural networks and deep learning in meteorology has been accelerating.
FAQ: Machine Learning in Operational Meteorology
1. What is machine learning in operational meteorology?
Machine learning in operational meteorology involves using algorithms to analyze weather data, forecast weather patterns, and improve meteorological predictions, enhancing real-time weather services.
2. How can machine learning enhance weather forecasting?
Machine learning can analyze vast datasets of historical and real-time weather information to identify patterns and make more accurate and timely weather predictions compared to traditional methods.
3. What types of machine learning models are used in meteorology?
Common machine learning models used in meteorology include linear regression, logistic regression, decision trees, random forests, neural networks, and support vector machines (SVM).
4. What data sources are used to train machine learning models for weather forecasting?
Machine learning models use data from weather stations, satellites, radar systems, climate models, and historical weather databases to train and improve their predictive capabilities.
5. What are the key benefits of using machine learning in weather prediction?
Key benefits include improved forecast accuracy, faster data processing, better handling of complex atmospheric phenomena, and the ability to generate predictions for specific locations or events.
6. How do operational meteorologists use machine learning in real-time forecasting?
Operational meteorologists use machine learning algorithms to process data from various sources in real-time, generate forecasts, and issue timely warnings about severe weather conditions.
7. What are some challenges in implementing machine learning in operational meteorology?
Challenges include data quality issues, the computational cost of training complex models, the need for expertise in both meteorology and machine learning, and the interpretability of machine learning model outputs.
8. Can machine learning models predict extreme weather events accurately?
Machine learning models can improve the prediction of extreme weather events by analyzing historical patterns and real-time data, but accuracy depends on data availability, model complexity, and the specific event characteristics.
9. How is deep learning used in operational meteorology?
Deep learning, a subset of machine learning, uses neural networks with multiple layers to analyze complex patterns in weather data, improving predictions for severe weather, climate modeling, and long-term forecasting.
10. How can I learn more about using machine learning in meteorology?
You can learn more by taking courses in data science and meteorology, reading research papers, attending conferences, and using resources like LEARNS.EDU.VN, which provides comprehensive guides and tutorials.
LEARNS.EDU.VN offers a wealth of resources to help you dive deeper into machine learning and its applications in meteorology. Whether you’re seeking to understand the basics, master advanced techniques, or explore career paths, LEARNS.EDU.VN provides expert guidance and comprehensive educational materials.
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