Yuchuan Lai

This is part of a series of studies I conducted during my PhD to investigate location-specific climate change and provide future information for engineering use.

This page discusses about Lai, Y. and D.A. Dzombak. 2020: Use of the Autoregressive Integrated Moving Average (ARIMA) Model to Forecast Near-term Regional Temperature and Precipitation. Weather and Forecasting, 35, 959–976, https://doi.org/10.1175/WAF-D-19-0158.1 as well as Lai, Y. and D.A. Dzombak. 2021. Use of Integrated Global Climate Model Simulations and Statistical Time Series Forecasting to Project Regional Temperature and Precipitation. Journal of Applied Meteorology and Climatology. 60, 695–710, https://doi.org/10.1175/JAMC-D-20-0204.1. The ARIMA forecasting model is also available at https://github.com/yuchuan-lai/scifi as a R package.

We have also published a separate paper to discuss about the comparions between the ARIMA near-term forecasts and downscaled GCM products, see https://doi.org/10.1061/AOMJAH.AOENG-0015.

See other pages about compiled historical data and using climate models to inform future conditions.

In this research, we sought to bridge the critical gap between global climate model projections and the specific, location-based needs of civil and environmental engineering. Recognizing that infrastructure design requires credible, interpretable data on temperature and precipitation extremes, our primary objective was to develop forecasting techniques that are adaptable, capable of quantifying uncertainty, and easily updated. We began by establishing a purely data-driven statistical approach for near-term forecasting (2–20 years) and subsequently expanded this framework into a hybrid model that integrates global climate simulations to project conditions over longer timeframes.

1. Objectives

Our initial goal was to create a reliable alternative to standard downscaling methods for the near-term. We identified that engineers often struggle with the uncertainties inherent in downscaled Global Climate Model (GCM) products. Therefore, we aimed to develop a method that could produce interpretable probabilistic forecasts directly from historical station-level data. Building on this, our subsequent objective was to extend these capabilities into the long term. In addition, we sought to combine the statistical forecasting skills of our initial ARIMA model with the physics-based climate change signals provided by GCMs, creating an integrated technique that reduces model bias and provides efficient, location-specific projections for engineering design values.

2. Methodology

We selected the Autoregressive Integrated Moving Average (ARIMA) framework as the core of our methodology because it effectively addresses the unique characteristics of climate time series—specifically temporal correlations and skewed distributions—which simple linear trend methods often fail to capture. To handle the non-normal distribution frequently found in precipitation data, we incorporated Box-Cox transformations prior to model fitting.

The Near-Term Approach: In our initial phase, we utilized a data-driven method relying solely on historical observations at individual cities. We applied a systematic process: testing for stationarity and trend, fitting the ARIMA model to historical data, and generating point and interval forecasts. To extend the utility of these forecasts for engineering applications, we integrated bootstrap techniques to estimate confidence intervals for specific return periods of extreme series—such as 10-year or 50-year events—and developed a resampling method to simulate future daily temperature and precipitation series.

The Hybrid G-ARIMA Approach: To facilitate long-term projections, we adopted a hybrid approach. We conceptualized regional climate time series as a combination of three components: a "climate change signal" derived from the median values of an ensemble of GCMs, a "regional deviation" modeled by ARIMA, and daily residuals. By using the ARIMA model to project how local conditions deviate from the global signal, we effectively utilized the statistical power of historical data to correct and refine the physics-based GCM trends. This allowed us to leverage the long-term trend information from different GCMs while anchoring the projections in local historical realities.

3. Results

Our evaluations demonstrated that this statistical framework offers a reliable alternative to traditional downscaling methods. In assessments of our near-term model, we found that while it did not outperform every other technique for every index, it was generally more reliable and provided more accurate interval forecasts than common methods like linear trend extrapolation or baseline historical averages. These uncertainty bounds proved critical for engineering risk assessment, particularly for annual extremes.

When we integrated GCM data into the hybrid G-ARIMA model, we observed that the technique successfully modified the underlying climate change trend from GCMs to better align with recent historical observations. Consequently, the model produced city-specific daily projections that were comparable to historical observations and demonstrated improved accuracy for several annual indices when compared to the commonly used LOCA downscaled product.

Furthermore, both iterations of our model proved highly effective for practical applications.

Interactive plot for the ARIMA forecasts

The interactive graph below presents some of our work on the use of the ARIMA model to forecast temperature and precipitation records at different U.S. cities. The forecast results are also available for downloads using the side panel.
Note that: 1) the ARIMA forecasts of the annual indices are provided by directly forecasting the time series of the annual indies; 2) the ARIMA annual forecasts of some indicies such as those related to the number of days are subject to greater uncertainty as these indices are in integer values; 3) the orders of the ARIMA model (for the autoregressive and moving average terms) were determined by fitting the historical period of records each time and consequently the different lengths of historical records (even under the same indices for the same cities) can have the different ARIMA orders, leading to likely different ARIMA forecasting results.
It may take up to a minute for the graphs to be loaded. View the webpage with the desktop version is recommended.