The maximum and minimum temperature recorded at a Lake is $18C$ and $15C$ in February. The mean air temperature $(T),$ pan evaporation $(E_P),$ wind speed $(u_Z),$ relative humidity $(RH),$ and net radiation $(Rn)$ in a nearby weather station were found to be $23C,15m\frac{m}{?}$ day, $23\frac{m}{s},47\%,20\mathrm{.}54M\frac{J}{m^2}\frac{?}{?}$ day, respectively. Estimate Lake evaporation $(m\frac{m}{?}$ day$)$ using:

$($a$)$ Pan Evaporation method,

$($b$)$ Aerodynamic method,

$($c$)$ Energy balance method, and

$($d$)$ Penman method of combined aerodynamic and energy balance algorithm.

Data you may need:

Saturation vapor pressure, $e_S=611e^{(\frac{19\mathrm{.}65T}{273+T})}$ where $T$ is temperature in $C$ and $e_s$ in $Pa$

$($You can also use table to read off the value of $e_s$ from internet or textbook $($Table $2\mathrm{.}9$ or Appendix A$)$ Assume, Pan Coefficient $=0\mathrm{.}7$

Bulk evaporation coefficient, $C_E=1\mathrm{.}3{10}^{-3}$

Vapor pressure at elevation $Z$;$e_Z=R{H}^{**}{e}_s$

Atmospheric pressure at sea level $=101\mathrm{.}3$kPa

Density of air $=1\mathrm{.}19k\frac{g}{m^3}$ and for water $=1000k\frac{g}{m^3}$

Bowen ratio $=0\mathrm{.}1$

Latent heat of vaporization $()=2\mathrm{.}447M\frac{J}{k}g$

Disregard the soil head index $)=(0$

Constants for the Penman method $($Table $2\mathrm{.}9)$: at $23C,=0\mathrm{.}17$ and $=0\mathrm{.}0669kP\frac{a}{}C$