Meteorological Data

When simulating water temperature, the user must provide data records for the following meteorological variables:

Solar radiation,
Cloud cover,
Air temperature,
Humidity,
Atmospheric pressure, and
Wind speed.

These are needed to calculate the shortwave and surface heat flux components in the temperature module.

Meteorological data (met data) is input in HEC-ResSim at user-defined meteorological stations (met stations). Each water quality subdomain is then assigned a met station from which data will be used. An example of summary met data plots are shown for a single station below.

HEC-ResSim met data editor screenshot. Met data timeseries are shown for air temperature, wind speed, cloud cover, humidity, shortwave radiation, and atmospheric pressure.

In the event that there are few met stations, spaced far apart within the modeling domain, the user may wish to blend (spatially interpolate) met data from multiple stations to obtain a better estimate of meteorological conditions at a given location.

This spatial interpolation is done using inverse distance weighting:

$\begin{array}{l}\displaystyle \hat{Z} = \frac{\sum_{i=1}^{N} w_i Z_i}{\sum_{i=1}^{N} w_i} \hspace{1cm} w_i = \frac{1}{d_i^p}\end{array}$

where

$\begin{array}{l}\hat{Z}\end{array}$ is the blended value of the met variable,
$\begin{array}{l}Z_i\end{array}$ is the value of the met variable at met station $\begin{array}{l}i\end{array}$ ,
$\begin{array}{l}N\end{array}$ is the number of met stations used in blending,
$\begin{array}{l}w_i\end{array}$ is the weight assigned to the blended location for met station $\begin{array}{l}i\end{array}$ ,
$\begin{array}{l}d_i\end{array}$ is the distance between the blended location and met station $\begin{array}{l}i\end{array}$ , and
$\begin{array}{l}p\end{array}$ is an exponential weighting factor.

The exponential weighting factor generally takes values greater than one. In the HEC-WQ Engine, a default value of two is used (inverse distance squared weighting), and a maximum of three met stations are used in blending.

Met data records must be defined for the entirety of the simulation period. The inputs can be constant (suitable for atmospheric pressure data) or given as time series. Three additional options exist for developing met datasets as function of other time series or met station characteristics. These are explained below.

Atmospheric Pressure as a Function of Site Elevation

Atmospheric pressure may be calculated as a function of elevation using the barometric formula (NOAA, 1976).

$\begin{array}{l}\displaystyle P = P_o \exp \left( - \frac{g \, h \, M}{T_o \, R} \right)\end{array}$

where

$\begin{array}{l}P\end{array}$ is the atmospheric pressure (kPa),
$\begin{array}{l}P_o\end{array}$ is standard sea level atmospheric pressure (101.325 kPa),
$\begin{array}{l}g\end{array}$ is gravitational acceleration (m/s²),
$\begin{array}{l}z\end{array}$ is the site elevation (m),
$\begin{array}{l}M\end{array}$ is the molar mass of dry air (0.02896 kg/mol),
$\begin{array}{l}T_o\end{array}$ is the standard sea level temperature (288.15 K), and
$\begin{array}{l}R\end{array}$ is the universal gas law constant (8.3144 J/mol-K).

If no atmospheric pressure record exists for the site, this option will estimate it as a constant value based on the elevation given for the met station.

Computed Solar Radiation

If measured solar radiation data is unavailable, it may be predicted based on calculated extra-terrestrial radiation (TVA, 1972) and atmospheric attenuation (Klein, 1948).

Extra-terrestrial Solar Radiation

Predicted solar radiation reaching the top of the atmosphere, and integrated over a time period, is given as:

1)	$\begin{array}{l}\displaystyle q_o = \frac{12}{\pi} \frac{I_o}{r^2} \left( \sin\phi \sin\delta (h_e - h_b) + \cos\phi \cos\delta (\sin h_e - \sin h_b) \right)\end{array}$

where

$\begin{array}{l}q_o\end{array}$ is the predicted, extra-terrestrial, solar radiation (W/m²),
$\begin{array}{l}I_o\end{array}$ is the solar constant (1390 W/m²),
$\begin{array}{l}r\end{array}$ is the relative earth and sun distance,
$\begin{array}{l}\phi\end{array}$ is the site's latitude (radians),
$\begin{array}{l}\delta\end{array}$ is the solar declination (radians),
$\begin{array}{l}h_b\end{array}$ is the solar hour angle at the start of the period (radians), and
$\begin{array}{l}h_e\end{array}$ is the solar hour angle at the end of the period (radians).

The relative earth-sun distance is estimated with the formula:

$\begin{array}{l}\displaystyle r = 1.0 + 0.017 \cos \left( \frac{2\pi}{365} (186 - D_y) \right)\end{array}$

where $\begin{array}{l}D_y\end{array}$ is the day of the year (January 1 corresponds to $\begin{array}{l}D_y=1\end{array}$ ).

The solar declination is estimated as:

$\begin{array}{l}\displaystyle \delta = \frac{23.45 \pi}{180} \cos \left( \frac{2\pi}{365} (172 - D_y) \right)\end{array}$

and the hour angle is computed

$\begin{array}{l}\displaystyle h = \frac{12}{\pi} \left( \textrm{ST} - \textrm{DTSL} - \textrm{ET} \right)\end{array}$

where

$\begin{array}{l}\textrm{ST}\end{array}$ is the standard time,
$\begin{array}{l}\textrm{DTSL}\end{array}$ is the time difference between the local and standard meridian ( $\begin{array}{l}\textrm{DTSL} = \frac{1}{15}(\theta - \theta_{SM})\end{array}$ where $\begin{array}{l}\theta\end{array}$ is the site longitude and $\begin{array}{l}\theta_{sm}\end{array}$ is the longitude of the standard meridian), and
$\begin{array}{l}\textrm{ET}\end{array}$ is the equation of time ( $\begin{array}{l}\textrm{ET} = -60(0.12357 \sin D_y - 0.004289 \cos D_y + 0.153809 \sin 2D_y + 0.060783 \cos 2D_y)\end{array}$ ), which relates true and mean local solar noon.

A couple images of the computed shortwave solar radiation records, without any atmospheric attenuation, are shown below for a site in the mid-latitudes of the northern hemisphere.

Computed, clear-sky shortwave solar radiation for a site in the western and northern hemisphere.

Computed, clear-sky shortwave solar radiation for a site in the western and northern hemisphere. Zoom in of a few specific days.

Atmospheric Attenuation

In general, the attenuation of solar radiation through the atmosphere can be calculated following Beer's Law as:

$\begin{array}{l}\displaystyle q_s = q_o e ^{-\eta L}\end{array}$

where

$\begin{array}{l}q_s\end{array}$ is the solar radiation reaching the surface of a water body (W/m²),
$\begin{array}{l}\eta\end{array}$ is the attenuation coefficient (1/m), and
$\begin{array}{l}L\end{array}$ is the path length (m).

Klein (1948) describes a procedure for estimating the attenuation based on atmospheric dust, humidity, atmospheric pressure and cloud cover. The procedure is summarized in TVA (1972) and the resulting formulas used in the WQ Engine are given below.

2)	$\begin{array}{l}\displaystyle q = q_o \frac{a'' + 0.5 ( 1 - a' - d_s )}{1 - 0.5 R_g (1 - a' + d_s)} (1 - R_t) (1 - 0.65 C_l^2)\end{array}$

where

$\begin{array}{l}q\end{array}$ is the shortwave solar radiation penetrating the surface of the water (W/m²),
$\begin{array}{l}a'\end{array}$ is the atmospheric transmission coefficient after scattering is considered (dimensionless),
$\begin{array}{l}a''\end{array}$ is the atmospheric transmission coefficient after scattering and absorption are considered (dimensionless),
$\begin{array}{l}R_g\end{array}$ is the reflectivity of the ground (dimensionless),
$\begin{array}{l}d_s\end{array}$ is the dust scattering coefficient (dimensionless),
$\begin{array}{l}R_t\end{array}$ is the reflectivity of the water surface (dimensionless), and
$\begin{array}{l}C_l\end{array}$ is the cloud cover fraction (dimensionless, range 0-1).

The atmospheric transmission terms ( $\begin{array}{l}a\end{array}$ ) are computed using the formulas

$\begin{array}{l}a' = \exp \left( (-0.465 + 0.134 \, w) \left( 0.129 + 0.171 e^{-0.88 \, m_p} \right) m_p \right) \\ a'' = \exp \left( (-0.465 + 0.134 \, w) \left( 0.179 + 0.421 e^{-0.721 \, m_p} \right) m_p \right)\end{array}$

where the precipitable water content of the atmosphere ( $\begin{array}{l}w\end{array}$ ) is

$\begin{array}{l}\displaystyle w = 0.85 \, e^{0.11 + 0.0614 \, T_{dp}}\end{array}$

and the optical air mass ( $\begin{array}{l}m_p\end{array}$ ) is

$\begin{array}{l}\displaystyle m_p = \frac{P/P_o}{\sin \alpha + 0.15 \left( \frac{180 \, \alpha}{\pi} + 3.885\right)^{-1.253}}\end{array}$

and

$\begin{array}{l}T_{dp}\end{array}$ is the dew point temperature (deg C),
$\begin{array}{l}P\end{array}$ is the atmospheric pressure (kPa),
$\begin{array}{l}P_o\end{array}$ is standard sea level atmospheric pressure (101.325 kPa),
$\begin{array}{l}\alpha\end{array}$ is the solar altitude (radians), defined by $\begin{array}{l}\sin \alpha = \sin \phi \sin \delta + \cos \phi \cos \delta \cos h\end{array}$

In Equation 2), $\begin{array}{l}R_g\end{array}$ is the reflectivity of the ground in the vicinity of the site. For modeling of water bodies, this is taken to be equal to the reflectivity of the water surface ( $\begin{array}{l}R_t\end{array}$ ), which is defined as a function of the solar altitude and cloud cover. This accounts for the higher reflection off the water surface near dawn and dusk, and lower reflection during the middle of the day.

$\begin{array}{l}\displaystyle R_t = A_r \left( \frac{180 \, \alpha}{\pi} \right)^{B_r}\end{array}$

The values for the coefficients $\begin{array}{l}A_r\end{array}$ and $\begin{array}{l}B_r\end{array}$ are given in the table below as a function of the cloud cover.

Cloudiness $\begin{array}{l}C_l\end{array}$	Clear $\begin{array}{l}< 0.1\end{array}$	Scattered $\begin{array}{l}0.1-0.5\end{array}$	Broken $\begin{array}{l}0.5-0.9\end{array}$	Overcast $\begin{array}{l}>0.9\end{array}$
$\begin{array}{l}A_r\end{array}$	1.18	2.20	0.95	0.33
$\begin{array}{l}B_r\end{array}$	-0.77	-0.97	-0.75	-0.45

Taken together, Equation 1) and Equation 2) can be used to calculate the shortwave radiation penetrating the water surface as a function of site location, date and time, atmospheric pressure, cloud cover, and humidity.

Computed Cloud Cover

Cloud cover is not available at many met station installations. However, it may be estimated using the ratio of measured shortwave radiation reaching the earth's surface to that predicted in the absence of clouds.

$\begin{array}{l}\displaystyle \frac{q_{s,\textrm{meas}}}{q_{s,\textrm{pred}}} = 1 - 0.65 C_l^2\end{array}$

where $\begin{array}{l}q_{s,\textrm{meas}}\end{array}$ is the shortwave radiation measured at the site by an pyranometer, and $\begin{array}{l}q_{s,\textrm{pred}}\end{array}$ is the predicted shortwave radiation, which can be calculated using a variation of Equation 2).

$\begin{array}{l}\displaystyle q_{s,\textrm{pred}} = q_o \frac{a'' + 0.5 ( 1 - a' - d_s )}{1 - 0.5 R_g (1 - a' + d_s)}\end{array}$

Since predicted shortwave radiation is zero in the hours between sunset and sunrise, the measured and observed shortwave radiation values are accumulated over the day, and an aggregated cloud cover value is computed and assumed to apply over a 24 hour period.

Top panel - observed versus computed sunny day short wave solar radiation. Bottom panel - computed daily cloud cover based on the short wave radiation data.