Question: User: Time series for MALI.
Latitude (cm)
-30
-35
-40
-45
-50
1996
1998
2000
2002
2004
2006
2008
Rate 16.399 +- 0.131 mm/yr Time (years) Repeatability 2.7 mm
Longitude (cm)
-45
-50
-55
-60
-65
-70
-75
-80
1996
1998
2000
2002
2004
2006
2008
Rate 26.705 +- 0.164 mm/yr Time (years) Repeatability 3.7 mm
Height (cm)
-4
-2
0
2
4
6
8
10
12
1996
1998
2000
2002
2004
2006
2008
Rate -2.441 +- 0.654 mm/yr Time (years) Repeatability 9.3 mm
top-left: a line time-series plot titled "Time series for MALI." with three stacked panels showing Latitude (cm), Longitude (cm), and Height (cm) versus Time (years), each with a black noisy series, a red fitted trend line, and two thin green vertical reference lines near 1998 and 1999.top-left: Total horizontal velocity
top-right:
center: = 24(N 22 S velocity)24 + 24(E 22 W velocity)24
bottom-left:
bottom-right:The data from GPS station MALI is represented in the first screenshot. Using this data and the formula in the second screenshot, calculate the velocity of this GPS station.
1. **State the problem:** Calculate the total horizontal velocity of the GPS station MALI using the given rates for Latitude and Longitude.
2. **Given data:**
- Latitude rate = $16.399 \pm 0.131$ mm/yr
- Longitude rate = $26.705 \pm 0.164$ mm/yr
3. **Formula for total horizontal velocity:**
$$\text{Velocity} = \sqrt{(\text{Latitude rate})^2 + (\text{Longitude rate})^2}$$
4. **Substitute the values:**
$$\text{Velocity} = \sqrt{(16.399)^2 + (26.705)^2}$$
5. **Calculate squares:**
$$16.399^2 = 268.96$$
$$26.705^2 = 713.88$$
6. **Sum the squares:**
$$268.96 + 713.88 = 982.84$$
7. **Calculate the square root:**
$$\sqrt{982.84} = 31.36$$
8. **Interpretation:**
The total horizontal velocity of the GPS station MALI is approximately $31.36$ mm/yr.
9. **Note on height rate:**
Height rate is vertical and not used in horizontal velocity calculation.
**Final answer:**
$$\boxed{31.36 \text{ mm/yr}}$$