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---
##-- arkriger: August 2023
#- https://stackoverflow.com/questions/47806200/create-a-comment-box-using-rmarkdown-html-file
title: "Trend Surface Analysis with R (part I)"
output:
pdf_document: default
Expand All @@ -7,6 +9,18 @@ output:
html_notebook: default
---

<style>
p.comment {
background-color: #DBDBDB;
padding: 10px;
border: 1px solid black;
margin-left: 25px;
border-radius: 5px;
font-style: italic;
}

</style>

This Notebook (the first-of-four) serves to introduce a user to a series of exercises focused on *higher order* **_Trend Surface analysis with R_**.

It consists of two sections:
Expand All @@ -15,20 +29,26 @@ It consists of two sections:
2. Deterministic Interpolation Techniques
a) Voronoi
b) Inverse Distance Weighting

<span style="color: red;">**REQUIRED:** You are required to insert your outputs and any comment into this document. The document you submit should therefore contain the existing text in addition to:</span>

- Plots and other outputs from executing the code chunks
- Discussion of your plots and other outputs as well as conclusions reached.
- This should also include any hypotheses and assumptions made as well as factors that may affect your conclusions.

```{r install }

<div class="alert alert-danger">
<strong>REQUIRED!</strong>

You are required to insert your outputs and any comment into this document. The document you submit should therefore contain the existing text in addition to:

- Plots and other outputs from executing the code chunks
- Discussion of your plots and other outputs as well as conclusions reached.
- This should also include any hypotheses and assumptions made as well as factors that may affect your conclusions.
</div>

```{r install-load }
#- options
options(prompt="> ", continue="+ ", digits=3, width=70, show.signif.stars=F, repr.plot.width=7, repr.plot.height=7)
rm(list=ls())
# Install necessary packages: You only need to run this part once
#install.packages(c("sf", "gstat", "stars"))
#- load
library(sf) # 'simple features' representations of spatial objects
library(gstat) # geostatistics
library(stars) # gridded data structures ("rasters")
Expand All @@ -49,13 +69,13 @@ cfaq <- read.csv(file, header = 1, sep = ',', dec = '.')
#-- look
head(cfaq ,3)
```
<span style="color: orange;">**QUESTION:**</span>
<div class="alert alert-warning"> <strong>QUESTION!</strong> </div>

- **What is the purpose of producing a map of the the elevation of the top of the aquifer over the study area? In other words, who would use the map and for what purpose?**
- **Question 1.** What is the purpose of producing a map of the the elevation of the top of the aquifer over the study area? In other words, who would use the map and for what purpose?

```{ r ans-01}
[click in this cell and type your answer here]
```
<p class="comment">
[ Answer 1. click in this cell and type your answer here. your answer must be between these [] brackets ]
</p>

```{r str-cfaq }
str(cfaq)
Expand Down Expand Up @@ -105,19 +125,20 @@ range(cfaq.sf$elevation); diff(range(cfaq.sf$elevation))
range(cfaq.sf$depth); diff(range(cfaq.sf$depth))
```

<span style="color: orange;">**QUESTION:**</span>
<div class="alert alert-warning"> <strong>QUESTION!</strong> </div>

- **How many observations are there? What was recorded at each point?**
- **Question 2.** How many observations are there? What was recorded at each point?

```{ r ans-02}
[click in this cell and type your answer here]
```
<p class="comment">
[ Answer 2. click in this cell and type your answer here. your answer must be between these [] brackets ]
</p>

- **What are the geographic limits of the study area? What is its area, in km2?**
- **Question 3.** What are the geographic limits of the study area? What is its area, in km2?

<p class="comment">
[ Answer 3. click in this cell and type your answer here. your answer must be between these [] brackets ]
</p>

```{ r ans-03}
[click in this cell and type your answer here]
```
```{r plot-names }
plot(st_coordinates(cfaq.sf)[,2] ~ st_coordinates(cfaq.sf)[,1],
#plot(st_coordinates(cfaq.sf)[,1] ~ st_coordinates(cfaq.sf)[,2],
Expand All @@ -131,6 +152,7 @@ text(st_coordinates(cfaq.sf)[,1], st_coordinates(cfaq.sf)[,2],
#text(cfaqN, round(aq$z), adj=c(0.5,0.5))
title("Elevation of aquifer, m")
```

```{r plot-elevation }
plot(#st_coordinates(cfaq.sf)[,2] ~ st_coordinates(cfaq.sf)[,1],
st_coordinates(cfaq.sf)[,2] ~ st_coordinates(cfaq.sf)[,1],
Expand All @@ -151,13 +173,14 @@ plot(#st_coordinates(cfaq.sf)[,2] ~ st_coordinates(cfaq.sf)[,1],
grid()
title("Elevation of aquifer, m")
```
<span style="color: orange;">**QUESTION:**</span>

- **Describe the spatial pattern of the elevations. Do nearby points have similar values? Is there a trend across the whole area? Are there local exceptions to the trend?**
<div class="alert alert-warning"> <strong>QUESTION!</strong> </div>

```{ r ans-02}
[click in this cell and type your answer here]
```
- **Question 4.** Describe the spatial pattern of the elevations. Do nearby points have similar values? Is there a trend across the whole area? Are there local exceptions to the trend?

<p class="comment">
[ Answer 4. click in this cell and type your answer here. your answer must be between these [] brackets ]
</p>

## 2. Deterministic Interpolation Techniques

Expand All @@ -166,7 +189,9 @@ Before we delve into higher order interpolation techniques; let us first explore
a) Thiessen Polygons
b) Inverse Distance Weighting (IDW)

<span style="color: red;">**REMEMBER:**</span> our goal is to estimate values where non exist. And depending on the application (and the data we have access to) higher order methods might not be necessary!
<div class="alert alert-danger">
<strong>REMEMBER!</strong> our goal is to estimate values where non exist. And depending on the application (and the data we have access to) higher order methods might not be necessary!
</div>

### a) Thiessen Polygons

Expand Down Expand Up @@ -293,18 +318,19 @@ for (i in 1:num_plots) {
par(mfrow = c(1, 1), mar = c(5.1, 4.1, 4.1, 2.1))
```

<span style="color: orange;">**QUESTION:**</span>

- **Why do we need interpolation methods that go deeper / further than the two presented here?**
<div class="alert alert-warning"> <strong>QUESTION!</strong> </div>

```{ r ans-03}
[click in this cell and type your answer here]
```
- **Question 5.** Why do we need interpolation methods that go deeper / further than the two presented here?

- **Comment on the quality of the IDW**
<p class="comment">
[ Answer 5. click in this cell and type your answer here. your answer must be between these [] brackets ]
</p>

> <span style="color: blue;">**HINT:**</span> Think about the subjectivity of the power function and what this means. Also consider what happens when we overlay the voronoi with the various idw interpolations. What does this mean?
- **Question 6.** Comment on the quality of the IDW

<div class="alert alert-info">
<strong>HINT!</strong> Think about the subjectivity of the power function and what this means. Also consider what happens when we overlay the voronoi with the various idw interpolations. What does this mean?
</div>

```{r plot-idw-voronoi }
# Plot IDW results with overlay of original points
Expand Down Expand Up @@ -350,14 +376,16 @@ for (i in 1:num_plots) {
par(mfrow = c(1, 1), mar = c(5.1, 4.1, 4.1, 2.1))
```

```{ r ans-04}
[click in this cell and type your answer here]
```
<p class="comment">
[ Answer 6. click in this cell and type your answer here. your answer must be between these [] brackets ]
</p>

- **How can the quality of the IDW improve?**
- **Question 7.** How can the quality of the IDW improve?

> > <span style="color: blue;">**HINT:**</span> Consider the location and density of the sample (input) points
<div class="alert alert-info">
<strong>HINT!</strong> Consider the location and density of the sample (input) points
</div>

```{ r ans-05}
[click in this cell and type your answer here]
```
<p class="comment">
[ Answer 7. click in this cell and type your answer here. your answer must be between these [] brackets ]
</p>

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