Amount of Precipitation

Numerous probability distribution functions have been used to describe the distribution of rainfall amounts. SWAT+ provides the user with two options: a skewed distribution and an exponential distribution.

The skewed distribution was proposed by Nicks (1974) and is based on a skewed distribution used by Fiering (1967) to generate representative streamflow. The equation used to calculate the amount of precipitation on a wet day is:

Rday=μmon+2σmon([(SNDdaygmon6)gmon6+1]31gmon)R_{day}=\mu_{mon}+2*\sigma_{mon}*(\frac{[(SND_{day}-\frac{g_{mon}}{{6}})*\frac{g_{mon}}{{6}}+1]^3-1}{g_{mon}}) 1:3.1.3

where RdayR_{day} is the amount of rainfall on a given day (mm H2_2O), μmon\mu_{mon} is the mean daily rainfall (mm H2_2O) for the month, σmon\sigma_{mon} is the standard deviation of daily rainfall (mm H2_2O) for the month, SNDdaySND_{day} is the standard normal deviate calculated for the day, and gmong_{mon}is the skew coefficient for daily precipitation in the month.

The standard normal deviate for the day is calculated:

SNDday=cos(6.283rnd2)2ln(rnd1)SND_{day}=cos(6.283*rnd_2)*\sqrt{-2ln(rnd_1)} 1:3.1.4

where rnd1rnd_1 and rnd2rnd_2 are random numbers between 0.0 and 1.0.

The exponential distribution is provided as an alternative to the skewed distribution. This distribution requires fewer inputs and is most commonly used in areas where limited data on precipitation events is available. Daily precipitation is calculated with the exponential distribution using the equation:

Rday=μmon(ln(rnd1))rexpR_{day}=\mu_{mon}*(-ln(rnd_1))^{rexp} 1:3.1.5

where RdayR_{day} is the amount of rainfall on a given day (mm H2_2O), μmon\mu_{mon} is the mean daily rainfall (mm H2_2O) for the month, rnd1rnd_1 is a random number between 0.0 and 1.0, and rexprexp is an exponent that should be set between 1.0 and 2.0. As the value of rexprexp is increased, the number of extreme rainfall events during the year will increase. Testing of this equation at locations across the U.S. have shown that a value of 1.3 gives satisfactory results.

Table 1:3-1: SWAT+ input variables that pertain to generation of precipitation.

Variable NameDefinitionFile Name

PCPSIM

Precipitation input code: 1-measured, 2-generated

file.cio

PR_W(1,mon)

Pi(W/D)P_i(W/D): probability of a wet day following a dry day in month

.wgn

PR_W(2,mon)

Pi(W/W)P_i(W/W): probability of a wet day following a wet day in month

.wgn

IDIST

Rainfall distribution code: 0-skewed, 1-exponential

file.cio

REXP

rexprexp: value of exponent (required if IDIST = 1)

file.cio

PCPMM(mon)

average amount of precipitation falling in month (mm H2O)

.wgn

PCPD(mon)

average number of days of precipitation in month(μmon\mu_{mon}= PCPMM / PCPD)

.wgn

PCPSTD(mon)

σmon\sigma_{mon}: standard deviation for daily precipitation in month (mm H2_2O)

.wgn

PCPSKW(mon)

gmong_{mon}: skew coefficient for daily precipitation in month

.wgn

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