2.4. Statistical Forecasting in Environmental Sciences

Regression is a Statistical Forecasting Technique!

Statistical forecasting is a method used to predict future values or trends based on historical data and statistical techniques. It relies on the assumption that historical patterns and relationships observed in the data will continue into the future. They play a crucial role in environmental science for analyzing complex datasets, identifying patterns, and making informed decisions related to environmental monitoring, management, and projections. They help researchers extract valuable insights from environmental data and support evidence-based decision-making.

Principal Component Analysis (PCA): Definition: PCA is a dimensionality reduction technique that identifies the most important variables (principal components) in a dataset while reducing redundancy. Example: In climate science, PCA can be used to reduce a large set of meteorological variables (temperature, humidity, pressure) into a smaller set of principal components that capture the most variability in weather patterns.

2.4.1. Preprocessing: Feature Selection in Environmental Forecasting

Feature selection involves choosing a subset of the most relevant and informative features (variables) from the original dataset for forecasting. In environmental sciences, datasets can be vast and include numerous variables, some of which may not contribute significantly to the forecast’s accuracy. Feature selection methods help streamline the modeling process and improve model performance by reducing noise and overfitting.

For example, when predicting air quality, a machine learning model may consider various factors like temperature, humidity, wind speed, and pollutant levels. Feature selection helps identify which of these variables are the most influential in making accurate forecasts. This not only simplifies the model but also reduces the risk of including irrelevant or redundant information.

2.4.2. Postprocessing: Enhancing Forecast Reliability

Postprocessing involves refining the output of a forecasting model to improve its reliability and applicability. In environmental forecasting, postprocessing can be especially valuable because it allows for the incorporation of domain-specific knowledge and adjustments to account for unique environmental conditions.

For instance, in hydrological forecasting, a machine learning model may predict river water levels based on various meteorological and hydrological data. Postprocessing can involve correcting the model’s predictions based on local topography, historical flood records, or expert insights to provide more accurate and actionable forecasts.

Moreover, postprocessing can involve the creation of prediction intervals, as mentioned earlier, which quantify the uncertainty associated with the forecasts. This information is critical for making decisions related to environmental management, risk assessment, and emergency response.

2.4.3. Prediction Intervals

Temporal dependency in statistical forecasting is a fundamental concept that underscores the inherent relationship between data points in a time series. As phenomena observed in a time series get closer in time, they tend to exhibit a stronger connection and dependence than those further apart. This notion is crucial in understanding the dynamics of time series data and forms the bedrock of forecasting methodologies. When dealing with time series forecasting, it becomes apparent that forecasting events or values closer in time often results in considerably less variability and, consequently, higher accuracy than attempting predictions further into the future. This principle echoes the idea that phenomena evolve over time and are influenced by recent observations. Therefore, considering temporal dependency is essential when delving into time series analysis, as it provides valuable insights into the patterns and trends that can drive accurate forecasts, making it a vital concept in the field of statistical forecasting.

Total international visitors to Australia (1980–2015) along with 10-year forecasts and 80% and 95% prediction intervals.The width of a prediction interval reflects the level of uncertainty associated with the forecast – narrower intervals indicate greater confidence, while wider intervals signify higher uncertainty. Thus, prediction intervals are a vital component of forecasting as they not only provide a point estimate but also convey the degree of uncertainty associated with the forecasted values.

Figure credit: An Easy Guide to Gradient Descent in Machine Learning, Great Learning. (link)

2.4.4. Model Output Statistics (MOS)

MOS is a statistical technique used in meteorology and atmospheric science to improve the accuracy of numerical weather predictions (NWP) by statistically post-processing the output of numerical weather models. MOS aims to correct systematic biases and errors present in raw model output and produce more accurate and reliable weather forecasts. It’s especially important for short- to medium-range forecasts, where the impact of model biases can be significant.

Here’s how MOS works:

Obtain Model Output: First, meteorologists run numerical weather models to generate forecasts for various weather parameters like temperature, humidity, wind speed, and precipitation. These models use complex mathematical equations to simulate the behavior of the atmosphere.

Collect Observation Data: Concurrently, actual weather observations are collected from weather stations, satellites, radars, and other sources. These observations serve as ground truth.

Develop Statistical Relationships: MOS techniques involve developing statistical relationships between the model output and observed data. These relationships can be simple linear regressions, more complex statistical models, or machine learning algorithms.

Apply Corrections: The statistical relationships developed in step 3 are applied to correct the raw model output. For example, if the model consistently predicts temperatures that are too high, the MOS equations adjust the model’s temperature forecasts downward.

Produce Improved Forecasts: The corrected model output, now enhanced by MOS, provides more accurate and reliable forecasts. These improved forecasts are then used for weather predictions and advisories.

MOS is particularly valuable in situations where NWP models have known biases or limitations. It helps address issues like systematic over- or under-prediction of temperature, poor handling of local terrain effects, and biases in precipitation forecasts.

Regression models are widely used in environmental sciences for statistical forecasting and prediction. They allow researchers to analyze and model the relationships between various environmental variables, leading to a better understanding of natural systems and improved forecasts.

2.4.5. Application of Regression Models in Environmental Sciences:

Climate Modeling: Predicting global temperature changes based on historical climate data. Regression Type: Time Series Regression Application: Regression models can analyze long-term temperature data to identify trends, seasonal patterns, and factors contributing to temperature variations. This information is crucial for understanding climate change.

Air Quality Forecasting: Forecasting daily air quality index (AQI) based on meteorological data and pollutant concentrations. Regression Type: Multiple Linear Regression Application: Regression models can assess the relationship between air quality parameters (e.g., PM2.5 levels, ozone concentrations) and meteorological factors (e.g., temperature, wind speed) to provide accurate AQI forecasts for public health and regulatory purposes.

Hydrological Predictions: Predicting river discharge based on rainfall, temperature, and land use data. Regression Type: Nonlinear Regression (e.g., Hydrological Models) Application: Regression models, often in the form of hydrological models, are used to simulate the behavior of watersheds, reservoirs, and river systems. They help predict river flow and flooding events, supporting flood management and water resource planning.

Species Distribution Modeling:Predicting the distribution of a specific plant species based on climate, soil, and elevation data. Regression Type: Logistic Regression (for presence-absence data) Application: Regression models, such as logistic regression, can analyze the relationship between species occurrence and environmental factors. They help ecologists understand the factors influencing species distribution and assess the impact of climate change on ecosystems.

Soil Quality Assessment:Predicting soil properties (e.g., pH, organic matter content) based on geographic location and land use. Regression Type: Geostatistical Regression (e.g., Kriging) Application: Regression models can be used to interpolate and predict soil properties at unmeasured locations, aiding in soil management and agricultural planning.

Coastal Erosion Forecasting:Predicting shoreline erosion rates based on wave energy, tidal patterns, and coastal vegetation. Regression Type: Spatial Regression Application: Regression models can assess the relationship between environmental variables and coastal erosion rates. This information is essential for coastal management and protection against sea-level rise.

Forest Fire Prediction:Forecasting the likelihood and spread of forest fires based on temperature, humidity, and vegetation data. Regression Type: Decision Tree Regression Application: Regression models, such as decision tree regression, can be employed to build predictive models for forest fire risk. They help authorities allocate resources for fire prevention and suppression.

In each of these examples, regression models provide a quantitative framework for understanding the relationships between environmental variables and making forecasts or predictions. They support evidence-based decision-making in environmental management and contribute to our ability to address environmental challenges.