Vertical Adjustment Methods

Vertical adjustments may be required when spatial interpolation alone is insufficient to account for the spatial distribution of a given meteorological variable. Generally, when the land surface is not flat, or nearly flat, over a geographic region, the topography will alter the distribution of meteorological variables. When using MetInterp, three vertical adjustment methods are available: None, Bias, Lapse. None refers to no vertical adjustments, which can be used when geographic conditions, outside of distance between gages, do not affect the distribution of the given variable.

Bias Adjustment

Bias adjustment is generally used when accounting for topographic effects on the temporal distribution of precipitation. This process requires a bias grid, which is typically a monthly or annual normal precipitation depth. A good example is the PRISM dataset (PRISM Climate Group, Oregon State U). Prior to spatial interpolation, the Bias Adjustment method normalizes the gage values with the grid values as follows:

In the above equation, $//<![CDATA[ \begin{array}{l}z_{gage}^{norm}\end{array} //]]>$ is the normalized z value for a given gage, $//<![CDATA[ \begin{array}{l}z_{gage}\end{array} //]]>$ is the raw z value for that gage, and $//<![CDATA[ \begin{array}{l}bias_{gage}\end{array} //]]>$ is the bias value from the grid cell that the gage falls within. After normalization, the z value is interpolated spatially with the selected spatial interpolation method. After interpolation, each grid value is multiplied by corresponding bias value to bring it from normalized space to actual space. This adjustment is described below:

In the above equation, $//<![CDATA[ \begin{array}{l}z_{cell}^{norm}\end{array} //]]>$ is the z value for a given cell in normal space (from spatial interpolation of $//<![CDATA[ \begin{array}{l}z_{gage}^{norm}\end{array} //]]>$), $//<![CDATA[ \begin{array}{l}bias_{cell}\end{array} //]]>$ is the bias value for the current grid cell, and $//<![CDATA[ \begin{array}{l}z_{cell}\end{array} //]]>$ is the final adjusted value.

Lapse Adjustment

Lapse adjustment is generally used when accounting for the relationship between elevation and temperature. Generally, temperature decreases with increasing elevation. In order to account for this, an elevation grid and lapse rate must be specified. Based on that elevation and lapse rate, normalization of gage values prior to spatial interpolation, and adjustment to grid cell values after interpolation, are performed similar to bias adjustment. The normalization process converts the temperature of each grid cell to sea level (elevation zero). This is performed in the equation below:

In the above equation, $//<![CDATA[ \begin{array}{l}z_{gage}^{sl}\end{array} //]]>$ is the equivalent temperature at sea level for a given gage, $//<![CDATA[ \begin{array}{l}z_{gage}\end{array} //]]>$ is the gage observed value, and $//<![CDATA[ \begin{array}{l}LR\end{array} //]]>$ is the lapse rate. After spatial interpolation of the sea level values, grid cell values are converted to the elevation of the grid cell as follows:

IIn the above equation, $//<![CDATA[ \begin{array}{l}z_{cell}^{sl}\end{array} //]]>$ is the interpolated equivalent temperature at sea level for a given cell and  $//<![CDATA[ \begin{array}{l}z_{cell}\end{array} //]]>$ corrected value for the given cell.

There are two methods for specifying the lapse rate: static user-specified value and computed. The static user-specified lapse rate is straightforward, as the user must prescribe a single lapse rate for the entire computation. Alternatively, the computed option computes a lapse rate by computing a linear lapse rate from the gages at each time step.