R/estimate_formation_head.R
estimate_formation_head.Rd`estimate_formation_head` takes a vector of transmissivity and a vector of associated blended head measurements. The formation head is then determined as each interval is added. The transmissivity and blended head values should be ordered so that the monitoring interval is incrementally increased with each value. An example application would be the FLUTe reverse head methodology
estimate_formation_head(transmissivity, blended)
| transmissivity | the transmissivity distribution for each interval |
|---|---|
| blended | the blended head value |
a single value of the blended head
`estimate_formation_head` calculates the formation head using the following formula:
$$^fh_i = \frac{\sum\limits_{i=1}^{i} \Delta T_i (^bh_i - ^fh_i)}{T_i} + ^bh_1$$
where:
* \(h_{blended}\) is the blended head in the well * \(\Delta T_i\) is the difference in transmissivity between increasingly larger interval. * \(^fh_i\) is the formation head of the newly exposed interval * \(^bh_i\) is the blended head of the increasingly larger interval * \(^bh_1\) is the blended head of the first interval * \(i\) is the interval number
Keller, C. (2017). A New Rapid Method for Measuring the Vertical Head Profile. Groundwater, 55(2), 244-254.
Other blended head methods:
blended_head_change(),
estimate_blended_head(),
estimate_missing(),
plot_blended()
transmissivity <- abs(rnorm(10, sd = 100)) # random T distribution cumulative_transmissivity <- cumsum(transmissivity) head <- sort(rnorm(10)) # decreasing head with depth formation_head <- estimate_formation_head(cumulative_transmissivity, head) estimate_blended_head(transmissivity[1:3], formation_head[1:3])#> [1] -0.2792372