Weather-Predictor

Project Abstract

Introduction

This project aims to construct an agent that can produce accurate predictions of whether it will rain tomorrow in New York based on today's temperature and humidity. This project proposes a probabilistic approach using Hidden Markov Models (HMMs) to infer latent weather states, whether there will be rain/snow or not, from historical observational data: daily average dry bulb temperature(°F) and daily average relative humidity(%). We are also using daily precipitation(inch) and daily snow depth(inch) to classify whether a day counts towards rain/snow or towards no rain/snow. By treating weather evolution as a sequence of hidden variables (rain/snow or no rain/snow) influenced by observable variables (temperature and humidity), the model leverages the HMM’s ability to decode state transitions and emission probabilities from time-series data. The framework is trained on publicly available climate records: [Climate data - New York State. (2022, July 8). Kaggle.] (https://www.kaggle.com/datasets/die9origephit/temperature-data-albany-new-york), preprocessed into discrete observation sequences. The resulting agent can probabilistically forecast near-term weather conditions, offering a lightweight, data-driven alternative to complex numerical models. This work highlights the potential of HMMs in modeling environmental systems where unobserved states drive observable outcomes, bridging the gap between interpretable stochastic models and real-world forecasting applications.

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• Performance measure: accuracy of its predictions of whether it is going to rain or snow or not.

• Environment: Only able to see the input statement and the training data.

• Actuators: the input cell (today's observations) and output cell (rain/snow or not tomorrow).

• Sensors: the input cell.

• This is a goal-based model, with the only goal of finding the probability of rain/snow for the next day given today's observations, and returning an output based on that value. This is a model-based agent. It trains on the dataset once and will answer only from its training.

Data Exploration and Preprocessing Step

We are using the dataset daily_data.csv

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There are 2668 observations in this training set, each with 19 features. The data are from January 1st, 2015 to May 31, 2022, which has some days missing, but we can ignore that since it is a large dataset. The features are:

STATION,DATE,REPORT_TYPE,SOURCE,BackupElements,BackupElevation,BackupEquipment,BackupLatitude,BackupLongitude,BackupName,DailyAverageDewPointTemperature,DailyAverageDryBulbTemperature,DailyAverageRelativeHumidity,DailyAverageSeaLevelPressure,DailyAverageStationPressure,DailyAverageWetBulbTemperature,DailyAverageWindSpeed,DailyCoolingDegreeDays,DailyDepartureFromNormalAverageTemperature,DailyHeatingDegreeDays,DailyMaximumDryBulbTemperature,DailyMinimumDryBulbTemperature,DailyPeakWindDirection,DailyPeakWindSpeed,DailyPrecipitation,DailySnowDepth,DailySnowfall,DailySustainedWindDirection,DailySustainedWindSpeed,Sunrise,Sunset,WindEquipmentChangeDate

But we will not be needing all of them. We only need the 12th, 13th, 25th, and 26th feature of each observation. The first 2568 observations will be the training data of this project and the last 100 observations will be the validation set. The data set is reliable since it was taken directly from a national weather station in Albany, New York.

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There are 4 columns that we are using:

• Daily average dry bulb temperature (°F) (column 12)
• Daily average relative humidity (%) (column 13)
• Daily Precipitation (inch) (column 25)
• Daily Snow Depth (inch) (column 26)

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Binarize features:

• Daily average dry bulb temperature: calculated median for all data points in the training set: 51.0. Any data point with a temperature higher or equal to this threshold will be classified as high, others are low

• Daily average relative humidity: calculated median for all data points in the training set: 66.0. Any data point with a humidity higher or equal to this threshold will be classified as high, others are low

• Daily Precipitation and Daily Snow Depth: any data point that has a precipitation greater than 0 OR has a precipitation greater than 0 will be classified as rain/snow, others are no rain/snow

• The median calculation step is done in the beginning of the ipynb file.

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Objective

Given:

Today's temperature and humidity

Return:

Is it going to rain/snow tomorrow

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Assumption:

Weather transitions are Markovian (tomorrow’s rain/snow or not depends only on today’s).

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Method

Use Forward Algorithm for calculating today’s state, then use the predicted state of today to predict tomorrow’s state

Note:

We are not taking Rain/Snow or not from the user input, we are predicting it. Rain/Snow or not is a hidden variable! This is because sometimes this piece of information could be missing and we also believe that the Forward-Backward Algorithm on Hidden Markov Models will produce a more accurate result than just directly returning the likelihood of Rain/Snow or not from data.

But in order to use the Forward Algorithm, we need to set up a HMM

• Hidden States: The weather (rain/snow, no rain/snow).

• Observations: The measured data (temperature, humidity).

Model Parameters:

An HMM is defined by three matrices:

1. Transition Matrix A: Probability of moving from state i to j.

• $$\text{A}_\text{ij}$$ = $$P$$(next state = j ∣ current state = i)​, (shape: 2 x 2)
• There are 2 possible states: [Rain/Snow, no Rain/Snow]

2. Emission Matrix B: Probability of observing k given state i.

• $$\text{B}_\text{ik}$$ = $$P$$(observation = k ∣ state = i), (shape: 2 x 4)
• There are 4 possible observations: [High temp High humidity, High temp Low humidity, Low temp High Humidity, Low temp, Low Humidity]

3. Initial State Distribution: Probability of starting in state i.

• $$\text{init}_\text{i}$$ = $$P$$(initial state = i), (shape: 2)

Computations of the three matrices

Compute the transition matrix A, emission matrix B, and initial distribution π directly from counts.

• $$\text{B}_\text{ik}$$ = $$\frac{\text{Number of transitions from state i to j}}{\text{Total transitions from State i}}$$

  • Example: If no Rain/Snow occurs 100 times and transitions to Rain/Snow 20 times:

    A_Rain/Snow, no Rain/Snow = $$\frac{20}{100}$$ = 0.2

• $$\text{B}_\text{ik}$$ = $$\frac{\text{Count of observation k in state i}}{\text{Total observations in state i}}$$

• $$\pi_\text{i}$$ = Frequency of state i = $$\frac{\text{Count of state i}}{\text{Total number of data}}$$

Forward Algorithm for Today’s State

1. Compute the probability of being in state i today given today’s observation:

   • This is the filtered state distribution given today’s observation. Using Bayes’ theorem:

     $$P$$(in state i today | today’s observation) = $$\frac{\text{P(today’s observation | in state i today)} \cdot \text{P(in state i today)}}{\text{P(today’s observation)}}$$

   • Let $$\alpha_{\text{observation, j}}$$ = $$B_\text{i, observation} \cdot \pi_i$$, and P(today’s observation) = $$\text{sum over j of B}_\text{j, observation} \cdot \pi_j$$

     $$P$$(in state i today | today’s observation) = $$\frac{\alpha_{\text{observation, i}}}{\text{sum over j of }\alpha_{\text{observation, j}}}$$

2. Predict Tomorrow’s State

   • Use the transition matrix A to compute the probability of transitioning to state j tomorrow:

     P(state j tomorrow | today’s observation) = sum over i of P(in state i today | today’s observation) $$\cdot$$ P(state j tomorrow | state i today)

   • P(in state i today | today’s observation) are calculated in part 1 and P(state j tomorrow | state i today) is just $$\text{A}_\text{ij}$$

     P(state j tomorrow | today’s observation) = sum over i of $$\bigg(\frac{\alpha_\text{observation, i}}{\text{sum over j of } \alpha_\text{observation, j}}\bigg)$$ $$\cdot$$ P(state j tomorrow | state i today)

3. Extract the probability of "rain/snow tomorrow":

   • P(rain/snow tomorrow | today’s observation)
   • if < 0.5, then return "most likely no rain or snow tomorrow"
   • if >= 0.5, then return "most likely will rain or snow tomorrow"

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Conclusion

The validation set claims that our agent has an accuracy of 73%, which suggests that the model has a lot of room for improvement. But this can be explained. While HMMs provide an interpretable framework for sequential data, their performance hinges on careful state definition, robust data preprocessing, and alignment with the Markov assumption. For weather prediction, integrating HMMs with complementary techniques or modern deep learning architectures may yield better results. Here are several factors that could explain the suboptimal performance:

Potential Issues and Drawbacks:

1. Oversimplified State Definitions
   • Hidden states ("rain/snow", "no rain/snow") might not align well with the observed data (temperature/humidity). For example, the temperature/humidity of a no rain/snow day during winter may overlap with the temperature/humidity of a rain/snow day in summer.
2. Violation of Markov Assumption
   • Weather depends on long-term patterns and seasonal trends, but we used HMMs which assume the next state depends ONLY on the current state.
   • HMMs Struggle with Long-Term Dependencies: They prioritize short-term transitions, making them weak at predicting infrequent or seasonal events.
3. Suboptimal Hyperparameters
   • The number of hidden and observed states might not reflect real-world weather complexity. There are definitely more than 2 features that contribute to rain/snow or not on the next day. We should consider more features and observed states to contribute to the HMM.
4. Weather is indeed not something that can be very easily predicted. We should have narrowed our data and prediction in some way, such as only analyzing and predicting Summer days.
   • Emission-Rich, Transition-Poor: If weather changes are abrupt, the transition matrix A may fail to capture rare transitions.
   • The HMM matrices are a combination of all the data throughout whole years. As stated earlier, the transition matrix and emission matrix should be very different and unique for certain periods of time, such as for the four seasons. This means that it is very likely that the matrices actually cannot represent any of the seasons at all. We need to narrow our data down more.

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Future Feature Expansions

For future improvements:

• The agent can allow users to input a whole sequence of observations (e.g., past 3 days) for more robust state inference. A longer sequence would improve the accuracy of a Forward Algorithm on HMMs.
• Adding more data to the training data would also increase the accuracy. More data enables the model to learn better transition probabilities and emission likelihoods, making it more reliable in predicting future weather states.
• Selecting more features to contribute to the HMM could improve model performance. We can include additional weather-related features (e.g., wind speed, atmospheric pressure, etc.) that may correlate with the target weather states (rain, snow, sunny). These features would broaden the model’s representation and improve predictions.
• In addition, using more recent data would be better. This is because the climate is changing, hence behaviors tens of years before are less likely suitable for the behaviors of weather today. Recent data may be more valuable for accurate forecasting.
• We should also check the observation that the user inputted. If the observation is very rare, for example, having a very extreme temperature that the training data lacks, then refuse to make the prediction and explain to the user. This would prevent the model from making unreliable predictions based on outlier data.
• Another way to improve would be not to binarize the data (and user input) and use Gaussian HMM. Using Gaussian HMM allows the model to better handle real-world features like temperature and humidity, that are typically represented with continuous numbers. This can improve the model's ability to make accurate predictions.

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Instructions

To run the agent, download the WeatherPredictor.ipynb file and the daily_data.csv file in the SAME directory. If you are using Google Colab, you will need to drag the CSV file to the "file" location in Google Colab and overwrite the file location when reading it.

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Contributors

• Tom Tang
• Guan Huang-Chen
• Xueheng Zhou
• Jefferson Umanzor-Urrutia
• Iron486 (dataset owner)