Understanding CLIGEN Parameters (In Plain English)

First published: October 2026
Last updated: October 23, 2026

[!NOTE] You do not need an advanced degree in statistics to understand or use CLIGEN parameters. This guide breaks down the core concepts into simple, intuitive ideas that every engineer and modeler can grasp.

The USDA CLIGEN (Climate Generator) model was created by the Agricultural Research Service to generate realistic daily weather inputs for hydrological, erosion, and water resources models.

Unlike simplistic tools that assume rainfall behaves like a standard bell curve (normal distribution), CLIGEN mirrors how the atmosphere actually behaves in the real world.

1. Rainfall Occurrence: The 2-State Markov Chain

In nature, weather has "memory." If it rained today, a storm front is overhead, meaning the odds of rain tomorrow are significantly higher than if today was a dry, sunny day.

CLIGEN captures this behavior using two transition probabilities calculated for each calendar month:

• $P(W|W)$ — Probability of a Wet Day given Yesterday was Wet:
  In plain English: "If it rained today, what are the odds it rains again tomorrow?"
  Typical values: Usually ranges between $0.40$ and $0.70$ ($40\% - 70\%$). High values mean storms tend to linger for several days in a row (storm clustering).
• $P(W|D)$ — Probability of a Wet Day given Yesterday was Dry:
  In plain English: "If today was dry and clear, what are the odds a brand-new storm arrives tomorrow?"
  Typical values: Usually much lower, often between $0.10$ and $0.25$ ($10\% - 25\%$).

stateDiagram-v2
    Dry --> Dry: 1 - P(W|D)
    Dry --> Wet: P(W|D) (New Storm Starts)
    Wet --> Wet: P(W|W) (Storm Persists)
    Wet --> Dry: 1 - P(W|W) (Sky Clears)

By calculating separate $P(W|W)$ and $P(W|D)$ values for each of the 12 months, the simulator perfectly replicates seasonal dry spells (long streaks of dry days) and seasonal storm clusters.

2. Rainfall Amount: The Pearson Type III Distribution

Once the model decides that a day is "Wet", it must determine: How much rain falls on that day?

Daily rainfall cannot follow a standard bell curve because: 1. Rainfall can never be negative (you cannot have $-5\text{ mm}$ of rain). 2. Most rainy days produce small or moderate showers (light rain). 3. Very rarely, an extreme downpour delivers a huge amount of water in 24 hours.

This creates a heavily skewed distribution with a long right-hand tail. CLIGEN models this using the Pearson Type III (Gamma-family) distribution, defined by three statistical properties for each month:

• $\text{Mean}$ (Average Daily Wet-Day Depth):
  The average rainfall amount on days when measurable rain occurs (ignoring all dry days).
• $\text{StdDev}$ (Standard Deviation):
  How widely storm depths vary around the monthly average.
• $\text{Skew}$ (Skewness Coefficient):
  A measure of asymmetry. Higher skewness means rare, massive downpours occur that are much larger than the average shower. Capturing true historical skewness is what allows hydrologic models to accurately evaluate flood and spillway overflow risks.

3. Daily Temperatures: Conditioned on Wet vs. Dry Days

Have you ever noticed that summer days with cloudy, rainy weather are significantly cooler than clear, sunny days? And winter nights with clouds are often milder than crisp, clear, sub-zero nights?

CLIGEN accounts for this atmospheric reality by conditioning daily temperatures on rainfall status:

• $T_{\max,\text{dry}}$: Mean maximum temperature on dry, sunny days.
• $T_{\max,\text{wet}}$: Mean maximum temperature on rainy, overcast days (almost always lower than $T_{\max,\text{dry}}$).
• $\sigma_{T_{\max}}$: Standard deviation of daily maximum temperature.
• $T_{\min}$: Mean daily minimum temperature.
• $\sigma_{T_{\min}}$: Standard deviation of daily minimum temperature.

Furthermore, CLIGEN incorporates cross-correlation between maximum and minimum temperatures: if daytime heating is unusually strong, the following nighttime minimum tends to be warmer as well.

Summary of the 12-Month Matrix

When the Climate Simulator calculates your site's parameters, it produces a clean 12-row table (one row for each month, January through December) containing: - 4 Precipitation values per month: $[P(W|W), P(W|D), \text{Mean}, \text{Skew}]$ - 5 Temperature values per month: $[T_{\max,\text{dry}}, T_{\max,\text{wet}}, \sigma_{T_{\max}}, T_{\min}, \sigma_{T_{\min}}]$

This compact set of numbers represents the complete statistical "DNA" of your site's climate, ready to drive millions of days of realistic synthetic simulation.