Can someone help me out with this problem? The problem is asking for the equilib

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Can someone help me out with this problem? The problem is asking for the equilibrium temperature of the lake. I don't know what equations to use for the individual fluxes, so I'm unable to get the net flux equation and find the temp :( Any help would be appreciated. Thanks!

Cloudless insolation (at alpha = 90 degree) ? C = 1060 W/m2 Average solar angle over the day alpha = 30 degree Average daily cloud cover N = 0.25 Cloud base altitude = 1.700 ft. so use k = 0.22 for the effect of cloud cover (Eq. 3-56) Day length = 12 h Assume essentially all of this conies from a mix of clouds and humid air. so approximate the value by using the "cloudy sky" formula (Eq 3.63 in reading) but do not apply the 0.25 factor. Cloud base mean temperature should be estimated using the DALR as the average lapse rate and 10 degree C as the mean surface air temperature. You should use a Stefan-Boltzmann coefficient (sigma) value of 5.67 times 10-8 W m-2 K-4 (for all media). (This differs a bit from a value that may appear in some versions of the written class notes) Lake has a measured evaporation rate of 4.6 mm/d. The pan correction factor has already been applied, so this is the estimate of the actual lake evaporation Use a latent heat of vaporization of 2.400 J/g at this temperature range Assume a "Bowen Ratio" value of 0.22, meaning that conduction is 22% of the evaporative heat loss value. This is governed by the water temperature, which is the variable you are solving for. Assume that water has an emissivity for longwave light of 1.0. (Water is virtually a blackbody with respect to JR light in the relevant range of 10 mu m wavelength.) NOTE 1: Remember that shortwave insolation only occur for 12 hr/d (half the day) while all the other fluxes operate continuously for 24 hr/d. Make sure your model reflects this. NOTE 2: The area, volume, depth of the lake are largely irrelevant to this heat budget with the information you are given. Just work in units of flux: W/m2. Also, although there is a sign convention that ' in" is negative and "out" is positive, adjust the final sign on your sum-of-fluxes to be positive before you take the fourth root. (We don't have an imaginary number for the temp!!)

Explanation / Answer

Q=Qsw+Qlw+Qs+QL+Qv

Q=resultant gain/loss (watt/m2)

Qsw=shortwave radiation flux

Qlw=longwave radiatiion flux

Qs=sensible heat flux/conductive heat always -ve

Ql=latent heat flux/evapaoration heat always -ve

for shortwave radiation

I=2hv^3/c^2(1/e^(hv/kT-1)

changein energy=Cp.m.(deltaT)

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