An Investigation into Long-Term Precipitation Patterns in the Pacific Northwest

When modeling long-term precipitation, a question is how to account for climate change. A common approach is to analyze historical data for trends, but what happens when a simple analysis of precipitation totals doesn't show a clear signal? This post documents an investigation into a more nuanced approach for a stochastic precipitation model.

Initial Analysis of Precipitation Totals

The study focuses on the long-term precipitation record from Olympia, Washington, a representative site for the West Cascade lowlands. An initial analysis of the annual and seasonal precipitation totals from 1948 to the present revealed statistically insignificant linear trends. This finding suggested that if a climate signal exists, it might be in the more subtle, underlying patterns of how rain falls.

Figure 1 - Historical Annual Precipitation Totals by Season

A Deeper Look with a Stochastic Model

To explore these underlying patterns, I used PrecipGen, a stochastic weather generator built in the GoldSim simulation software. PrecipGen is an extension of WGEN, a Markov-chain Gamma model. This model uses four statistical parameters to describe the daily "building blocks" of precipitation:

• PWW (Probability Wet-Wet): Controls the length of wet spells.
• PWD (Probability Dry-Wet): Controls the length of dry spells.
• Alpha (Shape Parameter): Controls the shape of the rainfall distribution.
• Beta (Scale Parameter): Controls the average intensity of rainfall.

Figure 2 - Screen Capture of the Markov Chain-gamma Model in GoldSim

Standard stochastic models, like the Markov-chain model used here, are excellent at simulating short-term, year-to-year variability. However, they have a limitation: the model's parameters (PWW, PWD, Alpha, and Beta) are typically derived from the full historical record. This process effectively averages out and mutes the long-term, low-frequency fluctuations, including the very wet and dry periods that can last for years.

This shortcoming is demonstrated in the plot below. The shaded percentiles represent the range of likely outcomes from the baseline model. The historical data, however, swings outside this narrow band, proving that the model is failing to capture the full magnitude of the long-term historical cycles. This highlights the need for an enhanced model that can account for these hidden, long-term climate signals.

Figure 3 - Percentiles of Simulated Compared to Historical Precipitation

Finding a Signal in the Parameters

When I analyzed the long-term historical trends of these four parameters, a clearer signal emerged. I found statistically significant, multi-year cycles and linear trends in several of these parameters. One of the most notable findings was a consistent downward trend in the Alpha parameter, especially in the winter and spring, with an R-squared value of up to 0.60. A decreasing Alpha suggests that the rainfall distribution is becoming more skewed, which could lead to a higher probability of more intense rainfall events.

Figure 4 - Historical Trends in the Four Parameters by Season

Here is a summary of what I found in the historical trends of these 4 parameters:

• Decreasing Alpha: A consistent downward trend was found in the Alpha parameter. This indicates the shape of the rainfall distribution is becoming more skewed, leading to a higher probability of more intense downpours.
• Increasing Beta: The Beta parameter is generally increasing. This suggests greater variability in storm intensity, meaning the difference between a light shower and a heavy downpour is becoming more pronounced.
• Changing PWW & PWD: Trends in PWW and PWD indicate changes in the persistence of weather patterns. A dropping PWW suggests wet periods may not last as long, while a dropping PWD would point toward longer and more severe dry periods.

Taken together, these trends paint a picture of a future climate that is more "volatile" or "flashy", where precipitation is less consistent and more characterized by intense events, even if the total annual rainfall remains the same.

Enhancing the Model

Based on these findings, I enhanced the PrecipGen model by incorporating these parameter trends into a seasonal, mean-reverting random walk. The goal was to create a model that could account for the observed long-term changes in precipitation patterns.

The results of this trend-aware model are interesting. When comparing its output to the historical record, the new model appears better able to simulate some of the extremes seen in the past. The plot below shows the probability distribution of the maximum daily rainfall from the new model compared to a baseline model without the trends. The historical maximum of 122 mm/d, which was an outlier for the baseline model, falls within the probable range of outcomes for the new model.

Figure 5 - Examples Showing Probabilistic Precipitation Compared to Historical

Beyond a visual comparison, a statistical analysis was performed to quantitatively assess the model's performance. The table below compares metrics from the single historical record against the mean of the full ensemble of 100 simulated realizations.

Metric	Historical	Ensemble Mean
Mean of Annual Peak	64.1	56.9
Peak of all Years	122.4	190.6
Mean Winter Total	547.4	512.3
Mean Spring Total	271.0	296.8
Mean Summer Total	82.6	75.5
Mean Fall Total	383.0	387.2

Another test of the enhanced model is its ability to replicate the historical extremes that are so critical for water resource planning. The charts below demonstrate the model's improved performance. In the figure below, is a plot of the daily precipitation over time and extending beyond the historical time period to show the visual comparison of peak daily rainfall events.

Figure 6 - Time History of Simulated and Historical Daily Precipitation

The probability distribution of the peak precipitation rate shows that the new, trend-aware model generates a much more realistic range of potential peak rainfall events, a range that comfortably includes the observed historical maximum of 122 mm/d.

Join the Discussion

This study suggests that looking beyond precipitation totals to the underlying statistical parameters can reveal more significant long-term climate trends. Incorporating these trends appears to improve a stochastic model's ability to simulate long-term historical extremes. This remains an ongoing investigation, but it presents a promising avenue for improving long-term stochastic rainfall models. If you would like to learn more about this evaluation and see how you can implement the same, please let us know in the comments.