Occurrence of Wet or Dry Day

With the first-order Markov-chain model, the probability of rain on a given day is conditioned on the wet or dry status of the previous day. A wet day is defined as a day with 0.1 mm of rain or more.

The user is required to input the probability of a wet day on day $i$ given a wet day on day $i-1,Pi-1(W/W)$, and the probability of a wet day on day $i$ given a dry day on day $i-1,P_i(W/D)$, for each month of the year. From these inputs the remaining transition probabilities can be derived:

$P_i(D/W)=1-P_i(W/W)$ 1:3.1.1

$P_i(W/W)=1-P_i(W/D)$ 1:3.1.2

where $P_i(D/W)$ is the probability of a dry day on day $i$ given a wet day on day $i-1$ and $P_i(D/D)$ is the probability of a dry day on day $i$ given a dry day on day $i-1$.

To define a day as wet or dry, SWAT+ generates a random number between 0.0 and 1.0. This random number is compared to the appropriate wet-dry probability, $P_i(W/W)$or $P_i(W/D)$. If the random number is equal to or less than the wet-dry probability, the day is defined as wet. If the random number is greater than the wet-dry probability, the day is defined as dry.