Please show the process and calculations for this.
Find the (quasi-)steady state temperature (equilibrium temperature) for Lake Boltzmann, an Oregon lake in late September, given the following information. Shortwave Input: Cloudless insolation (at a = 90) I = 1075 W/m2 Average solar angle over the day a = 24 Average daily cloud cover N= 0.25 Cloud-cover factor = (1 - kN) (multiply cloudless insolation by this factor) k = 0.22 for this cloud base altitude Cloud base altitude = 1,750 ft, Day length = 12 h Longwave Input: Assume essentially all of this comes from a mix of clouds and humid air, so approximate the value by using this equation: * = 0.90oT4 = Where Te is the cloud-base temperature Cloud base mean temperature should be estimated using the DALR as the average lapse rate and 10C as the mean surface air temperature. You should use a Stefan-Boltzmann coefficient (6) value of 5.67 x 10-8 W m-2 K4 (for all media). Evaporative Heat Output: 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 Conductive Heat Loss: Assume a Bowen Ratio" value of 0.22, meaning that conduction is 22% of the evaporative heat loss value. Longwave Output: 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 IR light the relevant range of 10 um 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 irrelevant to this heat budget with the information you are given. Just work in units of flux: W/m. 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!!) Find the (quasi-)steady state temperature (equilibrium temperature) for Lake Boltzmann, an Oregon lake in late September, given the following information. Shortwave Input: Cloudless insolation (at a = 90) I = 1075 W/m2 Average solar angle over the day a = 24 Average daily cloud cover N= 0.25 Cloud-cover factor = (1 - kN) (multiply cloudless insolation by this factor) k = 0.22 for this cloud base altitude Cloud base altitude = 1,750 ft, Day length = 12 h Longwave Input: Assume essentially all of this comes from a mix of clouds and humid air, so approximate the value by using this equation: * = 0.90oT4 = Where Te is the cloud-base temperature Cloud base mean temperature should be estimated using the DALR as the average lapse rate and 10C as the mean surface air temperature. You should use a Stefan-Boltzmann coefficient (6) value of 5.67 x 10-8 W m-2 K4 (for all media). Evaporative Heat Output: 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 Conductive Heat Loss: Assume a Bowen Ratio" value of 0.22, meaning that conduction is 22% of the evaporative heat loss value. Longwave Output: 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 IR light the relevant range of 10 um 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 irrelevant to this heat budget with the information you are given. Just work in units of flux: W/m. 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!!)
