Here is an example of my data set;
Date Time(GMT)Depth Temp Salinity Density Phosphate
24/06/2002 1000 1 33.855 0.01
24/06/2002
This might be not the fastest approach if your data frame is large, but a fairly strightforward one. This might change the order of your data frame and you might need to reorder by e.g. date afterwards. Instead of deleting we split the data by date, in each chunk pick a row with the maximum date and finally join the result back into a data frame
data = split(data, data$Date)
data = lapply(data, function(x) x[which.max(x$Depth), , drop=FALSE])
data = do.call("rbind", data)