!! To do - clean up layout - test

2nd year, 1st semester

Earth and Climate

Christian Schwarz

one 3-hr lecture every friday; one-day field trip to the Lesse river to perform measurements and an assignment for one point in which you discuss the measurements.

The exam is open book, but has very little available time (2025)!!. Dont waste time, prioritise the questions that you can't defend orally, and you should be fine.

2025

January

1 hour to prepare the questions, 10 min to present 2 of the 4 questions orally

Oral question
1. Graph: log-log graph of weighted percentage silt+clay M vs width-depth ratio w/d. What connection do you see? why could this be? Express the relation in an equation
2. Graphs: connection between slope/froude number vs shear velocity and number of braids in a river channel, also a graph describing the connection between ? and ?, where the planforms of the concerned rivers are indicated: braided/straight/meandering. What relation do the graphs show? Why? Which factors could be missing from these graphs?
Field trip: given is the connection between bankful discharge and width and depth. You get the equation governing the connection, of the form w = a ln(Q) +b (a&b =cte). How would you calculate flow velocity? Give an equation.
How would you measure the discharge of a river, if you can only measure flow depth? Explain how and explain the physical sense behind it.
Oral question: explain Hortonian genesis of drainage networks. How does this compare with groundwater-driven genesis?

2023

January (almost exactly the same as previous exams)

A river has a rectangular cross-section of 17m wide. The bed is sandy (density 1460 kg/m3, assume ks ~3*D90), with a grain size (D90 = 7mm) and a slope of 0.5%. (water at 10°C has a kinematic viscosity of 1.306*10-6 m2/s and a density of 999.75 kg/m3). a) Assume a discharge of 18 m3/s: what whill be the corresponding water depth? Use an iterative procedure here (accuracy 2 decimal places). ! Be careful, motivate every choice of parameters and assumptions you make!

b) Under the conditions of (a) will bed load transport occur? What is the maximum grain size the river van transport?

c) What kind of bedform do you expect?

d) Explain how the bedforms influence the shear stress using this figure... Do you have to adjust your calculation of shear stress?

Field trip: During the field excursions along the Lesse river, you measured the hydraulic geometry with increasing distance from the river’s source. Below you see figures based on the data collected during the measurements.

Use regime theory to establish a relationship between velocity and discharge; use this relationship to the calculate the velocities at the d1(blue) excursion stops (d1: stop1-4, q1,q2,q3,q4:0.07,0.31,3.28,4.66 m3 /s); tip: use the equation shown below
Use the resulting equation to estimate the discharge at stop5 (width= 25 m)
During the field trip we calculated the bankful discharge: - Why did we do this? Give at least three examples. - Looking at this cross-section. Why does it look this way? How does this form influence your river? What factors are important?

January pt 2

We have learned about different ways to characterize and compare river morphologies, explain the different methods, their assumptions and what we can learn from them in your own words?
Describe the different mechanisms creating drainage networks, and the factors influencing them
Explain the meaning of “geomorphological dominant discharge of river”, what kind of discharges is this term referring to ? How do we know this (you can describe it, show equations and draw graphs but you need explain what they mean)?
Below you find the fundamental equation describing turbulent flow:
1. Explain how this one is deduced. Since you can use your slides make sure to explain on what concepts and assumptions the equations are based on. Use your own words.
2. If you compare the velocity profile between turbulent and laminar flow, what are the main differences caused by? Does the velocity profile of turbulent and laminar flow have implications on sediment transport, yes/no, which?
3. Aside from bedload transport we also learned about suspended sediment transport, below you see a graph we discussed during the lecture showing the change in sediment concentration during a storm event, please describe the figure and give at least two reasons why it looks like that?

2021-2022

August

A river has a rectangular cross-section of 123m wide. The bed is sandy(density: 2650 kg/m3 , assume ks ≈ 3*D90) , with a grain size( D90: 0.8 cm) and a slope of 0.5%. (water at 10°C has a kinematic viscosity: 1.306 * 10-6 m2 /s and a density of 999.75 kg/m3 )

Assume a discharge of 40 m³ s-1 : what will be the corresponding water depth ? Use an iterative procedure here (accuracy 2 decimal places). ! Be careful, motivate every choice of parameters and assumptions you make ! Assume 𝑛 ≠ 𝑘𝑠 1 6 26
Under the conditions of (a) will bed load transport occur, what is the maximum grain size the river can transport ?
What kind of bedform do you expect?
If bedforms are present, would you need to adjust the total calculated shearstress in a shear stress available for transport of bed material. In the course we learned one method, explain it and discuss its implications on sediment transport?

Field trip: During the field excursions along the Lesse river, you measured the hydraulic geometry with increasing distance from the river’s source. Below you see figures based on the data collected during the measurements.

Use regime theory to establish a relationship between velocity and discharge; use this relationship to the calculate the velocities at the d1(blue) excursion stops (d1: stop1-4, q1,q2,q3,q4:0.07,0.31,3.28,4.66 m3 /s); tip: use the equation shown below
Use the resulting equation to estimate the discharge at stop5 (width= 25 m)
Discuss the implications of your results, how does the river morphology change with increasing bankfull discharge, does it get deeper or wider. Are there any other factors which could influence the relationship between discharge, width depth and velocity?
Looking at the grainsize analysis of the sediment samples collected during the excursion, we see a coarsening, increasing D50, from stop1 to stop5. Based on theoretical considerations is this what we would expect, yes/no why, please discuss?

Januari

A river has a rectangular cross-section of 11 m wide. The bed is gravelly (density: 1460 kg/m3 , assume ks ≈ 3*D90) , with a grain size( D90: 8 cm) and a slope of 0.5%. (water at 10°C has a kinematic viscosity: 1.306 * 10-6 m2 /s and a density of 999.75 kg/m3 )

Assume a discharge of 18 m³ s-1 : what will be the corresponding water depth ? Use an iterative procedure here (accuracy 2 decimal places). ! Be careful, motivate every choice of parameters and assumptions you make ! Assume 𝑛 ≠ 𝑘𝑠 1 6
Under the conditions of (a) will bed load transport occur, what is the maximum grain size the river can transport ?
What kind of bedform do you expect?
If bedforms are present, would you need to adjust the total calculated shearstress in a shear stress available for transport of bed material. In the course we learned one method, explain it and discuss its implications on sediment transport?

Field trip: During the field excursions along the Lesse river, you measured the hydraulic geometry with increasing distance from the river’s source. Below you see figures based on the data collected during the measurements.

Use regime theory to establish a relationship between velocity and discharge; use this relationship to the calculate the velocities at the d1(blue) excursion stops (d1: stop1-4, q1,q2,q3,q4:0.07,0.31,3.28,4.66 m3 /s); tip: use the equation shown below
Use the resulting equation to estimate the discharge at stop5 (width= 25 m)
Discuss the implications of your results, how does the river morphology change with increasing bankfull discharge, does it get deeper or wider. Are there any other factors which could influence the relationship between discharge, width depth and velocity?
Looking at the grainsize analysis of the sediment samples collected during the excursion, we see a coarsening, increasing D50, from stop1 to stop5. Based on theoretical considerations is this what we would expect, yes/no why, please discuss

January pt 2

We have learned about different ways to characterize and compare river morphologies, explain the different methods, their assumptions and what we can learn from them in your own words?
Describe the different mechanisms creating drainage networks, and the factors influencing them?
Explain the meaning of “geomorphological dominant discharge of river”, what kind of discharges is this term referring to ? How do we know this (you can describe it, show equations and draw graphs but you need explain what they mean)?

Below you find the fundamental equation describing turbulent flow:

Explain how this one is deduced. Since you can use your slides make sure to explain on what concepts and assumptions the equations are based on. Use your own words.
If you compare the velocity profile between turbulent and laminar flow, what are the main differences caused by? Does the velocity profile of turbulent and laminar flow have implications on sediment transport, yes/no, which?
Aside from bedload transport we also learned about suspended sediment transport, below you see a graph we discussed during the lecture showing the change in sediment concentration during a storm event, please describe the figure and give at least two reasons why it looks like that ?

In 2021-2022 Schwartz took over the course so pay attention to exam question that are older because they might not be representative

2017-2018 (Govers replaced by Lies Jacobs)

1. Given: figure of specific energy vs. water depth. Discuss this figure. What happens in the minimum and the 2 asymptots of this function? Express this mathematically. What is subcritical, critical and supercritical flow and how can you quantify it? Why would this information be useful to know?

2. Given: figure of ln(z) - velocity. How can you calculate shear velocity from this? What is the relation between the steepness of the linear relation and the shear velocity? How do you then find the shear stress and what are the units?

3. Given: figure with Shields parameter on y axis and grain size diameter on x axis, and a line that indicates initial motion of bedload and initial motion of suspended load. Why do the curve look like this? What does initiation of motion depend on in both cases? How would you expect the curve to look for sediments finer then ca. 100 µm?

4. Excursion 1: Given graph of discharge vs. nitrate concentration in the Dijle with showed rather odd results for only a small range of discharge values. How can you link the figure with the theory of statistical models in chapter 1? What would be your strategy to deal with this problem?

5. Exursion 2: Given graph of velocity measured at max. depth at each stop for the Dijle. What relation do you expect for the velocity when going downstream? Why is this (not) the case here?

6. Exercise 1: Same as 1. from 2014-2015 but with other values.

7. Exercise 2: Given a figure with log(discharge) and exceedance probability. Can you make an estimate of the geomorphic most effective discharge?

2014-2015

1. A river has a rectengular section of 10 m wide. The bed is gravelly, with a mean diameter of 0.1 m. The slope is 0.5%.

a) Assume a discharge of 15 m³/s, what will be the corresponding water depth? Use an iterative approach

b) What is the maximum grain size the river can transport?

c) Assume that the following suspended load concentrations are measured. What is then the suspended load sediment flux transported by the river?

z (m) - C (mg/L)

0.05 - 1210

0.10 - 950

0.15 - 625

0.25 - 325

0.30 - 225

0.40 - 125

0.50 - 100

0.70 - 70

0.90 - 50

2. Spring amphitheaters in Kinshasha are formed in Kalahari sands, which have a mean diameter of 300 µm. You may assume that the rainfall excess in the area is 500 mm/y. Finally assume that you have a spring amphiteater draining a surface area of 1.5 km² where the water seeps out over a surface of 150 m² and that the system is in steady state. Thus, the water draining towards the groundwater table is evacuated via the spring. The level of the springs is ca. 150 m below the level of the general topography. Can you calculate, assuming a realistic value for the hydraulic conductivity for the sands, whether or not spring erosion will occur? You will need to calculate the groundwater potential gradient from the data provided to use Dunne's formula.

3. Field trip:

a) Calculate shear velocity from ln(z) - velocity graph.

b) In your report, you calculated Manning n values for the Lesse river, which has a bed medium grain size of 50 mm. Are your n values larger ofg smaller than expected? How would you explain this?

c) Calculaten of maximum transportable grain size via diagram in excursion guide and via Shields curve.

4. Given: the fundamental equation describing turbulent flow. Explain how this is deducded. Look into your slides and make notes so that you can explain in your own words where this equation is coming from.

5. Given: the graph of exceedance probability vs. geometric length (fractal dimension). Can you explain what fractals are, how one can calculate the fractal dimension and why it does or does not work for rivers?

2013-2014

schriftelijk:

1. Gegeven: snelheidsprofiel uit excursiegids + tabel met sleepsnelheid (berekend en afgeleid van grafiek): Hoe kan je adhv de grafiek de sleepsnelheid berekenen? en hoe bereken je deze direct zonder snelheidsprofiel? Hoe zie je op de grafiek dan stop 4 en 5 een lagere U* hebben dan de andere stops?

2. oefening ivm initiëren van bronerosie. verwacht je dat er bronerosie mogelijk is? (slope, infiltratie in mm per jaar, soort ondergrond (k uit afleiden)... was gegeven)

3. oefening over suspentielading. Diepte en hoeveelheid suspensie per diepte was gegeven => wat is correctiefactor als je meet op 0.25 m? Hiervoor heb je eerst nog de verschillende snelheden nodig. bereken ook de gemiddelde snelheid.

mondeling:

4. gegeven stukje matlabcode over pca. Uitleggen wat er staat en waarvoor dit nodig is.

5. hoe kom je aan de afleiding van het snelheidsprofiel voor turbulente stroming?

2004 – 2005

Verklaar voor volgende stellingen of ze waar/niet waar zijn en leg uit waarom:
1. Als de waarschijnlijkheidsdichtheid voor een debiet van 20m³/s bij een neerslagduur van 1uur gelijk is aan 0.25 en deze van een debiet van 60m³/s bij een neerslagduur van 2uur gelijk is aan 0.10, dan kunnen we de overschrijdingskans voor een debiet van 80m³/s bij een neerslagduur van 3uur berekenen als (0.10*0.25)/((0.10+0.25)/2).
2. De patronen in een rivierbedding (ribbels, duinen, ...) kunnen weergegeven worden door een fractale dimensie.
3. We weten voor een rivier dat de meandergolflengte tijdens de laatste tussen-ijstijd 2 keer zo lang was dan deze nu is. Het debiet toen moet dus ook twee maal zo groot geweest zijn.
Een rivier heeft een rechthoekige sectie van 10m breed en 1m diep. De helling bedraagt 0.3% en de mediane korreldiameter 0.01m. De waardes voor de suspentieconcentratie op iedere hoogte (boven wateroppervlak) zijn gegeven: h (g/l) 0.05 10.6 0.10 9.7 0.15 8.0 0.20 7.5 0.30 7.3 0.40 6.8 0.50 5.7 0.60 6.3 0.70 5.4 0.80 2.4 0.90 1.2 Bereken de suspentielast gegeven de formules voor snelheidsverdeling en suspentielading uit de cursus. Bereken ook de gemiddelde snelheid van de stroming

2003 – 2004

Juist of fout en beargumenteer
1. Als de verdeling van riviernetwerken in ambilaterale klassen niet significant verschillen onder de nulhypothese dan impliceert dit dat de netwerken altijd toevallig verdeelt zijn.
2. Het vast debiet is recht evenredig met de sleepsnelheid tot de macht 3/2 en de sleepsnelheid is recht evenredig met de snelheid tot de macht 2/3. Bijgevolg is het vast debiet recht evenredig met de snelheid.
3. Ribbels en zandbanken in een rivier vertonen een fractaal karakter.
4. De wetten van Horton m.b.t. de bifurcatie ratio vertellen ons dat de evolutie van riviersegmenten in een riviernetwerk voorspeld kan worden. Ook de lengteratio en de oppervlakteratio vertellen ons iets over de hydrologische karakteristieken van het bekken.
5. De herhalingsperiode van een debiet van 60m3/s voor de Dijle is 100 jaar. Bijgevolg is de kans dat dit debiet in de komende 5 jaar overschreden zal worden 20%.
Een rivier heeft een rechthoekige sectie, 10m breed en 1m diep. De helling bedraagt 0,3% en de mediane korrelgrootte 0,01m. Volgende waarden voor de suspentieconcentratie werden gemeten over verschillende diepten: diepte (m) concentratie (g/l) 0,05 10,6 0,10 9,7 0,15 8,0 0,20 7,5 0,30 7,3 0,40 6,8 0,50 5,7 0,60 6,3 0,70 5,4 0,80 2,4 0,90 1,2 Bereken de suspentielast, het beddingstransport en de gemiddelde snelheid van de stroming.

Excursie Lesse: Teken op een log-log grafiek de evolutie van de breedte, diepte en gemiddelde snelheid van de Lesse in stroomafwaartse zin. Wat neemt het sterkst toe: de diepte of de snelheid en waarom?