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1:3.4.3.2 Solar Radiation

The continuity equation relates average daily solar radiation adjusted for wet or dry conditions to the average daily solar radiation for the month:

μradmon∗daystot=μWradmon∗dayswet+μDradmon∗daysdry\mu rad_{mon}*days_{tot}=\mu Wrad_{mon}*days_{wet}+\mu Drad_{mon}*days_{dry}μradmon​∗daystot​=μWradmon​∗dayswet​+μDradmon​∗daysdry​ 1:3.4.19

where μradmon\mu rad_{mon}μradmon​ is the average daily solar radiation for the month (MJ m−2^{-2}−2), daystotdays_{tot}daystot​ are the total number of days in the month, μWradmon\mu Wrad_{mon}μWradmon​ is the average daily solar radiation of the month on wet days (MJ m−2^{-2}−2), dayswetdays_{wet}dayswet​ are the number of wet days in the month, μDradmon\mu Drad_{mon}μDradmon​ is the average daily solar radiation of the month on dry days (MJ m−2^{-2}−2), and daysdrydays_{dry}daysdry​ are the number of dry days in the month.

The wet day average solar radiation is assumed to be less than the dry day average solar radiation by some fraction:

1:3.4.20

where is the average daily solar radiation of the month on wet days (MJ m), is the average daily solar radiation of the month on dry days (MJ m), and is a scaling factor that controls the degree of deviation in solar radiation caused by the presence or absence of precipitation. The scaling factor, , is set to 0.5 in SWAT+.

To calculate the dry day average solar radiation, equations 1:3.4.19 and 1:3.4.20 are combined and solved for :

1:3.4.21

Incorporating the modified values into equation 1:3.4.12, SWAT+ calculated the solar radiation on a wet day using the equation:

1:3.4.22

and the solar radiation on a dry day using the equation:

1:3.4.23

Table 1:3-4: SWAT+ input variables that pertain to generation of temperature and solar radiation.

Definition
Source Name
Input Name
Input File

tmp_max_ave

: standard deviation for maximum air temperature in month ()

tmpstdmx

tmp_max_sd

: average minimum air temperature for month ()

tmpmn

tmp_min_ave

: standard deviation for minimum air temperature in month ()

tmpstdmn

tmp_min_sd

: average daily solar radiation for month (MJ m)

solarav

slr_ave

: average number of days of precipitation in month

pcpd

pcp_days

μWradmon=bR∗μDradmon\mu Wrad_{mon}=b_R*\mu Drad_{mon}μWradmon​=bR​∗μDradmon​
μWradmon\mu Wrad_{mon}μWradmon​
−2^{-2}−2
μDradmon\mu Drad_{mon}μDradmon​
−2^{-2}−2
bRb_RbR​
bRb_RbR​
μDradmon\mu Drad_{mon}μDradmon​
μDradmon=μradmon∗daystotbR∗dayswet+daysdry\mu Drad_{mon}=\frac{\mu rad_{mon}*days_{tot}}{b_R*days_{wet}+days_{dry}}μDradmon​=bR​∗dayswet​+daysdry​μradmon​∗daystot​​
Hday=μWradmon+χi(3)∗σradmonH_{day}=\mu Wrad_{mon}+\chi_i(3)*\sigma rad_{mon}Hday​=μWradmon​+χi​(3)∗σradmon​
Hday=μDradmon+χi(3)∗σradmonH_{day}=\mu Drad_{mon}+\chi_i(3)*\sigma rad_{mon}Hday​=μDradmon​+χi​(3)∗σradmon​

Temperature input: 'sim' for simulated or gage name

tgage

tmp

weather-sta.cli

Solar radiation input: 'sim' for simulated or gage name

sgage

slr

weather-sta.cli

μmxmon\mu mx_{mon}μmxmon​: average maximum air temperature for month (°C\degree C°C)

tmpmx

σmxmon\sigma mx_{mon}σmxmon​
°C\degree C°C
μmnmon\mu mn_{mon}μmnmon​
°C\degree C°C
σmnmon\sigma mn_{mon}σmnmon​
°C\degree C°C
μradmon\mu rad_{mon}μradmon​
−2^{-2}−2
dayswetdays_{wet}dayswet​
weather-wgn.cli
weather-wgn.cli
weather-wgn.cli
weather-wgn.cli
weather-wgn.cli
weather-wgn.cli

1:3.4.3 Adjustment for Clear/Overcast Conditions

Maximum temperature and solar radiation will be lower on overcast days than on clear days. To incorporate the influence of wet/dry days on generated values of maximum temperature and solar radiation, the average daily maximum temperature, μmxmon\mu mx_{mon}μmxmon​, and average daily solar radiation, μradmon\mu rad_{mon}μradmon​, in equations 1:3.4.10 and 1:3.4.12 are adjusted for wet or dry conditions.

1:3.4.3.1 Maximum Temperature

The continuity equation relates average daily maximum temperature adjusted for wet or dry conditions to the average daily maximum temperature for the month:

μmxmon∗daystot=μWmxmon∗dayswet+μDmxmon∗daysdry\mu mx_{mon}*days_{tot}=\mu Wmx_{mon}*days_{wet}+\mu Dmx_{mon}*days_{dry}μmxmon​∗daystot​=μWmxmon​∗dayswet​+μDmxmon​∗daysdry​ 1:3.4.14

where μmxmon\mu mx_{mon}μmxmon​ is the average daily maximum temperature for the month (°C\degree C°C), daystotdays_{tot}daystot​ are the total number of days in the month, μWmxmon\mu Wmx_{mon}μWmxmon​ is the average daily maximum temperature of the month on wet days (°C\degree C°C), dayswetdays_{wet}dayswet​ are the number of wet days in the month, μDmxmon\mu Dmx_{mon}μDmxmon​ is the average daily maximum temperature of the month on dry days (°C\degree C°C), and daysdrydays_{dry}daysdry​ are the number of dry days in the month.

The wet day average maximum temperature is assumed to be less than the dry day average maximum temperature by some fraction of (μmxmon−μmnmon\mu mx_{mon}-\mu mn_{mon}μmxmon​−μmnmon​):

1:3.4.15

where is the average daily maximum temperature of the month on wet days (), is the average daily maximum temperature of the month on dry days (), is a scaling factor that controls the degree of deviation in temperature caused by the presence or absence of precipitation, is the average daily maximum temperature for the month(), and is the average daily minimum temperature for the month (). The scaling factor, , is set to 0.5 in SWAT+.

To calculate the dry day average maximum temperature, equations 1:3.4.14 and 1:3.4.15 are combined and solved for :

1:3.4.16

Incorporating the modified values into equation 1:3.4.10, SWAT+ calculates the maximum temperature for a wet day using the equation:

1:3.4.17

and the maximum temperature for a dry day using the equation:

1:3.4.18

μWmxmon=μDmxmon−bT∗(μmxmon−μmnmon)\mu Wmx_{mon}=\mu Dmx_{mon}-b_T*(\mu mx_{mon}-\mu mn_{mon})μWmxmon​=μDmxmon​−bT​∗(μmxmon​−μmnmon​)
μWmxmon\mu Wmx{mon}μWmxmon
°C\degree C°C
μDmxmon\mu Dmx_{mon}μDmxmon​
°C\degree C°C
bTb_TbT​
μmxmon\mu mx_{mon}μmxmon​
°C\degree C°C
μmnmon\mu mn_{mon}μmnmon​
°C\degree C°C
bTb_TbT​
μDmxmon\mu Dmx_{mon}μDmxmon​
μDmxmon=μmxmon+bT∗dayswetdaystot∗(μmxmon−μmnmon)\mu Dmx_{mon}=\mu mx_{mon}+b_T*\frac{days_{wet}}{days_{tot}}*(\mu mx_{mon}-\mu mn_{mon})μDmxmon​=μmxmon​+bT​∗daystot​dayswet​​∗(μmxmon​−μmnmon​)
Tmx=μWmxmon+χi(1)∗σmxmonT_{mx}=\mu Wmx_{mon}+\chi_i(1)*\sigma mx_{mon}Tmx​=μWmxmon​+χi​(1)∗σmxmon​
Tmx=μDmxmon+χi(1)∗σmxmonT_{mx}=\mu Dmx_{mon}+\chi_i(1)*\sigma mx_{mon}Tmx​=μDmxmon​+χi​(1)∗σmxmon​