PrecipGen: Long-Term Precipitation Forecasting

Posted by Jason Lillywhite

A GoldSim model that simulates long-term daily precipitation (PrecipGen) has been added to the GoldSim Model Library. We applied the model to locations in Logan, Utah and Dublin Ireland to help evaluate the effectiveness of this model's ability to forecast daily precipitation rates and capture long term droughts. This application is useful for GoldSim modelers looking to incorporate randomly generated rainfall forecasts in their water balance models. The model shows promise in simulating precipitation for a site that is influenced by multi-year wet and dry cycles. Informal testing has been showing signs of robustness and some refinements to the testing are currently underway.

Figure 1 - Screen Capture of PrecipGen with Results

A few years ago, the decision was made to modify the original WGEN model³ that simulates daily precipitation over long periods of time. The goal was to more accurately account for long-term changes in wet versus dry conditions in a simple but robust way that could work across multiple different climate regions. This led to the creation of PrecipGen, which builds on previous work with the addition of long-term drought-deluge cycles.

The Science Behind PrecipGen

This model simulates daily precipitation using a first-order, 2-state Markov chain-gamma model. A Markov process models the change between states randomly over time and the probability of a state change depends on the previous state. Precipitation rate is modeled by sampling from a gamma probability distribution on wet days. Leveraging the foundational work of Dee Allen Wright and the WGEN model from 1983, implemented in FORTRAN, this GoldSim iteration inherits a legacy of reliability in precipitation simulation. This implementation has the added ability to incorporate long-term cyclic behavior, based on patterns found in the historical record. 

The first step of the model is to perform a statistical analysis of the historical record. This is done using PrecipGen PAR. This model estimates the average and standard deviations of the PrecipGen parameters along with some correlation coefficients. This data can be copy-pasted into the PrecipGen model. The reason these models are kept separate is because PrecipGen PAR only needs to be run once and PrecipGen model will be run many times. 

Using input parameters from PrecipGen PAR, PrecipGen uses Stochastic elements to adjust the parameters each year by sampling from a gamma distribution with correlations. 

Testing

To perform testing, the following short-term outputs were compiled:

• Annual and Monthly Totals
• Number of Days above 50 mm
• Number of wet/dry days in a row

To test the long-term functionality, a threshold and triggering logic was developed to quantify periods of drought. The following long-term outputs were compiled:

• Drought duration for the first drought found in each realization
• Frequency of droughts during each realization
• 7-year running average
• 
  

These tests were performed in 3 different models: Historical sampling, WGEN, PrecipGen

The test model (called PrecipGen Tester.gsm) compares results of PrecipGen, WGEN, and historical sampling. Currently, testing is limited to visual inspection of results and work on further quantifying test results is currently underway. Current test results include visual inspection of: 

• Probability distribution of annual precipitation
• Average monthly precipitation
• Probability distribution of drought duration

These results are shown below for both locations.

Figure 2 - Results for Logan, Utah

Figure 3 - Results for Dublin, Ireland

In both locations, PrecipGen is able to more closely match the range of annual precipitation measured at the location and also produces a larger range of drought possibilities. 

Results and Conclusion

Initial test results indicate that PrecipGen is able to produce a closer fit distribution when compared to GoldSim's WGEN implementation. In addition to that, the PrecipGen model shows some improvement on the deviations from normal on a daily, monthly, and annual basis (not all shown here).  No site-specific calibration has been performed. Below is a comparison of these same three models with a view of the probabilistic time history of annual precipitation.

Figure 3 - Time History Probabilities for Logan, Utah

Figure 4 - Time History Probabilities for Dublin, Ireland

Many GoldSim customers use GoldSim to incorporate uncertainty and randomness in water balance models and water resources systems. PrecipGen does this by also allowing the user to define the longer-term changes. Precipitation always plays a role in these models and enabling a robust precipitation simulator for a tool like GoldSim, which is integrated with a Monte Carlo simulator engine, would greatly benefit these users. Stay tuned for upcoming updates with results from applications at other sites.

You can download the latest version of PrecipGen from our library: PrecipGen: Simulating Daily Precipitation with GoldSim – GoldSim Help Center