**External aqueducts**

**Reservoirs**

Here they are the video lectures about aqueducts' reservoirs, intakes, etc.

**External aqueducts**

**Reservoirs**

A week ago I started to read “The book of why: the science of cause and effects" by Judea Pearl. (see also his website). This is part of my search for new mathematics for describing entangled hydrological and ecological processes (see also this post and links therein). It is a dissemination book and not intended to grow too technical. However, it arrives the moment when understanding technicalities becomes part of the full understanding, if you do not want to remain a tourist of the new knowledge and become instead an active user of it. Pearl says he dedicated most of his research life to these problems and, therefore, pretending to fill the gap in few weeks is a nonsense.

I require more time to go deeper but presently I have no time. Therefore let me take some annotations here for making easier future efforts.

To go to the details, one can go to the more technical book by Pearl himself, Causality. However, it happened I went to browse some chapters of the very good Shalizi's book on statistics. Chapters from the 20th are a reasonable starting point. Shalizi book itself is not fully explicative but a compromise where some theorems are not deminstrated but assumed and make explicit. Nice enough but requiring in any case the appropriate dedication. Shalizi seems to be a voracious reader, and in the bibliography of his chapter 21, he cites some fundamentals work to put in line for a full understanding the topic. His subsequent chapters also enlarge the vision to information theory, and is connections between the science of causal statistics. Cool. While postponing the study and trying to grasp concepts, I fully report the bibliography I came across here below (mostly from Shalizi's).

All of these are also a good reading for those who believe that data science is a practice which springs out from nowhere.

References

I require more time to go deeper but presently I have no time. Therefore let me take some annotations here for making easier future efforts.

To go to the details, one can go to the more technical book by Pearl himself, Causality. However, it happened I went to browse some chapters of the very good Shalizi's book on statistics. Chapters from the 20th are a reasonable starting point. Shalizi book itself is not fully explicative but a compromise where some theorems are not deminstrated but assumed and make explicit. Nice enough but requiring in any case the appropriate dedication. Shalizi seems to be a voracious reader, and in the bibliography of his chapter 21, he cites some fundamentals work to put in line for a full understanding the topic. His subsequent chapters also enlarge the vision to information theory, and is connections between the science of causal statistics. Cool. While postponing the study and trying to grasp concepts, I fully report the bibliography I came across here below (mostly from Shalizi's).

All of these are also a good reading for those who believe that data science is a practice which springs out from nowhere.

References

- Chalak, K., & White, H. (2012). Causality, Conditional Independence, an Graphical Separation in Settable Systems. Neural Computation, 1–60.
- Cover, Thomas M. and Joy A. Thomas (2006). Elements of Information Theory. New York: John Wiley, 2nd edn.
- Dinno, A. (2017). An Introduction to the Loop Analysis of Qualitatively Specified Complex Causal Systems (pp. 1–23).
- Guttorp, Peter (1995). Stochastic Modeling of Scientific Data. London: Chapman and Hall.
- Jordan, Michael I. (ed.) (1998). Learning in Graphical Models, Dordrecht. Kluwer Academic.
- Kindermann, Ross and J. Laurie Snell (1980). Markov Random Fields and their Ap- plications. Providence, Rhode Island: American Mathematical Society. URL http://www.ams.org/online_bks/conm1/.
- Lauritzen, S.L., Dawid, A.P., Larsen, B.N., Leimer, H.G. (1990), Independence properties of directed Markov fields, Networks, 20, 491-505
- Lauritzen, S.L. (1996) Graphical Models. New York: Oxford University Press.
- Loehlin, John C. (1992). Latent Variable Models: An Introduction to Factor, Path, and Structural Analysis. Hillsdale, New Jersey: Lawrence Erlbaum Associates, 2nd edn.
- Moran, P. A. P. (1961). “Path Coefficients Reconsidered.” Australian Journal of Statis- tics, 3: 87–93. doi:10.1111/j.1467-842X.1961.tb00314.x.
- Pearl, J. (2000). Causality- Models, Reasoning, and Inference (pp. 1–386). Cambridge University Press.
- Wright,S., The Method of Path Coefficients. Annals of Mathematical Statistics 5:161-215.
- Wysocki, W. (1992). “Mathematical Foundations of Multivariate Path Analysis.” In- ventiones Mathematicae, 21: 387–397. URL https://eudml.org/doc/263277.

This shows the lectures I gave this week on soil and soil water to my class of hydrology.

**Soils**

**Texture and structure of soils**

**Definitions**

**Darcy and Buckingham laws**

**Soil Water retention curves**

**Hydraulic conductivity**

**Hydraulic conductivity at saturation**

**Richards equation (first part)**

Here they are the videos of the aqueducts lectures.

**Generalities**

**Distribution Network Topologies**

**Distribution Network Equations**

**Design requirements**

**Verification of the design**
**To sum up**

This post is to contain research work and studies about river Adige as soon as they come to my attention. Please help me in finding them.

**Papers**

**Master Thesis**

**Ph.D. Thesis**

**Books**

- Chiogna, G., Santoni, E., Camin, F., Tonon, A., Majone, B., Trenti, A., & Bellin, A. (2014). Stable isotope characterization of the Vermigliana catchment. Journal of Hydrology, 509(C), 1–11. http://doi.org/10.1016/j.jhydrol.2013.11.052
- Chiogna, G., Majone, B., Paoli, K. C., Diamantini, E., Stella, E., Mallucci, S., et al. (2015). A review of hydrological and chemical stressors in the Adige catchment and its ecological status. Science of the Total Environment, 1–15. http://doi.org/10.1016/j.scitotenv.2015.06.149
- Laiti, L., Giovannini, L., Zardi, D., Belluardo, G., & Moser, D. (2018a). Estimating Hourly Beam and Diffuse Solar Radiation in an Alpine Valley: A Critical Assessment of Decomposition Models. Atmosphere, 9(4), 117–20. http://doi.org/10.3390/atmos9040117
- Laiti, L., Mallucci, S., Piccolroaz, S., Bellin, A., Zardi, D., Fiori, A., et al. (2018b). Testing the Hydrological Coherence of High-Resolution Gridded Precipitation and Temperature Data Sets. Water Resources Research, 1–30. http://doi.org/10.1002/2017WR021633
- Ranzi, R, Werth, K, Gentilini, S, Mangiapane, S, The Adige River map in 1:20,736 scale of Leopoldo de Claricini-Dornpacher (1847),
- 12th Conference of ICA-International Cartographic Association Commission on Cartographic Heritage into the Digital “Digital Approaches to Cartographic Heritage”
- At: Venice, 2017
- Tuo, Y., Marcolini, G., Disse, M., & Chiogna, G. (2018a). A multi-objective approach to improve SWAT model calibration in alpine catchments. Journal of Hydrology, 559, 347–360. http://doi.org/10.1016/j.jhydrol.2018.02.055
- Tuo, Y., Marcolini, G., Disse, M., & Chiogna, G. (2018b). Calibration of snow parameters in SWAT: comparison of three approaches in the Upper Adige River basin (Italy). Hydrological Sciences Journal, 00(00), 1–22. http://doi.org/10.1080/02626667.2018.1439172

- Francesca Bergamin (Zolezzi, G and Bertoldi, W., Supervisors), Studio dell'evoluzione morfologica del fiume Adige nell'ultimo secolo: analisi di sezioni storiche e di modello interpretativo, DICAM, Trento, AA 2016-2017
- Stefano Tasin (Rigon R., Bancheri, M.), Modellazione di portate idriche nei bacini alpini con JGrass-NewAGE, Anno Accademico, 2015-2016

- Mallucci, S. (Bellin, A. and Majone, B, Supervisors), Hydro-climatic shifts in the Alpine region under a changing climate: trends, drivers detection and scale issues
**,**Ph.D. Dissertation, 2018

- Werth, K, Ranzi, R.
**,**Il fiume Adige da Merano a Borghetto nella carta di Leopoldo De Claricini (1847). Die Etsch von Meran bis Borghetto auf der Leopold von Claricini Karte (1847). Con 14 cartine fiume Adige, ISBN: 88-99910-05-7 - EAN: 9788899910051, 2017

We announce that, parallel to this blog, it was just opened an OSF project called GEOframe that contains the complete documentation of the various components developed. Information will continue, however, to appear here too.

GEOframe is already a big tree and it will grow more and more. Click on the Figure to access the documentation site. Each OMS component will have its OMS subproject and the subproject itself contains as standard:

GEOframe is already a big tree and it will grow more and more. Click on the Figure to access the documentation site. Each OMS component will have its OMS subproject and the subproject itself contains as standard:

- The link to the component
**source code**(the URL of Github site where developers and programmer can download the code) - Github
**executable with examples**(the Github - GeoframeComponents site where to download a working example including the executables) - A link to the
**Component's documentation** **Jupiter Notebooks**: illustrating the examples' I/O**R**: Not available Yet: but the same as above but the same as above in R**GEOframe blog page**: point to the geoframe.blogspot.com page where is further documented the component (essentially this information should be the one summarised in the Wiki page of the OSF component's page

This is part of the IAHS initiative in identifying some important questions in today's hydrology. As you know from the previous post, I made my eleven question questions. From the colleagues who participated to the call they received a decent agreement. However, during the phase of thinking, there was a refocusing (which I believe was useful) and a request to look to topics or issues that could be answered or solved in a few years. More specific, less oriented to basic questions.

This brought to a different set of questions (whose formulation I did not participated actively). Finally, Gunther Blöschl (GS) writes about the final screening that happened at the Wien Symposium: "*On Saturday we had three rounds of discussions in four break out groups and one final plenary discussion. In each round we discussed the questions, merged them, split them and reworded them as needed followed by a voting on prioritising the questions. The voting was for gold/silver/bronze/remove in each of the three break out group rounds. Only the gold and silver ones were retained for the plenary with an additional round of voting (by the entire plenary) for gold, silver or removing them from the list. The idea of the process was to whittle down the 260 questions initially proposed to a more coherent and smaller set of those questions deemed most important by the participants. The process resulted in 16 gold and 29 silver questions which are posted here.* "

I think it is important to see what was chosen to have a poll about what the community (mostly the European one?) thinks it is important, even if, maybe, not fundamental.

This brought to a different set of questions (whose formulation I did not participated actively). Finally, Gunther Blöschl (GS) writes about the final screening that happened at the Wien Symposium: "

I think it is important to see what was chosen to have a poll about what the community (mostly the European one?) thinks it is important, even if, maybe, not fundamental.

More material on the main page.

Here they are the video of introduction to solar radiation for hydrologists. There is not any special in this. You can see all our contributions and literature on the topic in these posts.

**Introduction to Radiation - Planck and Stefan-Boltzmann laws **(slides here)

**Radiation from Sun to Earth **(slides here)

**Radiation vs latitude **(slides here)

**Attenuation of solar radiation by the atmosphere **(slides here)

**Copying with terrain **(slides here)

**Long wave radiation **(slides here)

Gaby Katul (GS) is one of the most prominent hydrologists around the world (if this statement can have a meaning): his production is extremely high both in quality and quantity and for any is a lighthouse to follow. His production is especially directed to study turbulence and eco-hydrology. Therefore there is no doubt that his Dalton medal, received this week at EGU general assembly is well deserved. I could not be in Wien this year. However, I asked Gaby if he can send to me his presentation that all the present qualified as outstanding.

Please clicking on the above figure access and enjoy it.

Please clicking on the above figure access and enjoy it.

In trying to move out from Penman-Monteith scheme, we arrived to the Schymasky and Or paper. It re-analyses the calculation of Transpiration of a leaf. In our work we are trying to extend their contribution to the entire canopy and subsequently to an entire catchment. As in our tradition our work is both theoretical (in the analysis of equations) and numerical up to the implementation. The results of our efforts are presented in the next poster that was shown both at the Hydromod 2018 conference and at EGU general assembly in Wien.

You can find it directly at the blog TranspirAction (by Michele Bottazzi) or clicking on the Figure above. The portrait version used in Tübingen is here.

You can find it directly at the blog TranspirAction (by Michele Bottazzi) or clicking on the Figure above. The portrait version used in Tübingen is here.

Marialaura Bancheri after her Ph.D. defense mainly worked at university of Basilicata in Potenza under the supervision of Professor Salvatore Manfreda (GS) to apply GEOframe-NewAGE infrastructures to the realtime forecasting of discharges in Basilicata region. Salvatore presented the result of their work at EGU Wien 2017. Please below, find the presentation about the system implemented.

Clicking on the figure, you can access the slides. The work in Basilicata is a great achievement, even if only a few of the potentialities of the system were exploited.

There are several ways to categorize this work. One way is to see it inserted in the GEOtop 3.0 project that aims to rebuild GEOtop physics and informatics. Another way is to see it inserted in the work to get better cryospheric parameterisations. A third way is to see it as a part of the process delineate in my professorship talk. More pragmatically, it represents a new implementation of the coupled Richards equation and energy budget by using sound numerics and OMS3.

No easy to read. It requires application.

You can see the presentation at the OSF site, here.

No easy to read. It requires application.

You can see the presentation at the OSF site, here.

In feeling that Hydrology needs new mathematical-physics, I explored several directions (Information Theory, Statistics, Causality theory, Algebraic topology, Thermodynamics -!-, and not very much the usual paraphernalia that modern physics uses whose taste I kind think to know, Petri Nets) and I arrived to category theory. Category theory is the mathematics of connections and retro-actions represented in graphical form. I arrived here because I think that expanding hydrology to Earth System Science, it opens to the world of connections, and understanding connections means understanding complexity.

For other definitions, please give a look to this new book by

Just at the first pages, it also address to other books, and I also found

I collected many other books and papers about CT. However, if you want to start, start from these two. Eventually you can subscribe to the Azimuth forum and enroll John Baez course.

Please find below the main papers and the Ph.D. dissertations related to the GEOFRAME-NewAGE system. (You can find general information on GEOFRAME NewAGE starting from this post).

12 - Bancheri, M., Serafin, F., Bottazzi, M., Abera, W., Formetta, G., & Rigon, R. (2018). The design, deployment and testing of Kriging models in GEOframe. Geoscientific Model Development Discussions, 1–31. http://doi.org/10.5194/gmd-2017-310

11 - Bancheri, M., A flexible approach to the extimation of water budgets and its connection to the travel time theory, Ph.D. Dissertation, 2017

10 - Abera, W; Formetta, G.; Brocca, L.; Rigon, R.; Water budget modelling of the Upper Blue Nile basin using the JGrass-NewAge model system and satellite data, Hydrol. Earth Syst. Sci., 21, 3145-3165, 2017,https://doi.org/10.5194/hess-21-3145-2017

9 - Abera, W; Formetta, G.; Borga, M.; Rigon, R.; Estimating the water budget components and their variability in a Pre-Alpine basin with NewAge-JGrass, Advances in Water Resources, 2017

8 - Abera, W. - Modelling water budget at a basin scale using JGrass-NewAge system, Ph.D. Dissertation, Università di Trento, 2016

7 - Formetta, G., Bancheri M., Rigon R., Performances of site-specific parameterizations of longwave radiation, Hydrol. Earth Syst. Sci., 20, 4641-4654, 2016, http://www.hydrol-earth-syst-sci.net/20/4641/2016/

doi:10.5194/hess-20-4641-2016

6 - Formetta G. , Antonello A. , Franceschi S. , David O., Rigon R., Digital watershed representation within the NewAge-JGrass system. Boletin Geologico y Minero, 125 (3): 371-381, 2014. ISSN: 0366-0176

5 - Formetta G., David O., Kampf S., Rigon R., Snow water equivalent modeling components in NewAge-JGrass, Geosci. Model Dev., 7, 725-736, 2014

4 - Formetta G., Antonello A., Franceschi S., David O., and Rigon R., Hydrological modelling with components: A GIS-based open-source framework, Environmental Modelling & Software, 5 (2014), 190-200}

3- Formetta, G., Hydrological modelling with components: the OMS3 NewAge-JGrass system, Doctoral Dissertation, Università di Trento, 2013

2 - Formetta G., Rigon R., Chavez J.L., David O., The short wave radiation model in JGrass-NewAge System, Geosci. Model Dev., 6, 915-928, 2013, www.geosci-model-dev.net/6/915/2013/, doi:10.5194/gmd-6-915-2013

1 - Formetta, G., Mantilla, R., Franceschi, S., Antonello A., Rigon R., The JGrass-NewAge system for forecasting and managing the hydrological budgets at the basin scale: models of flow generation and propagation/routing, Geoscientific Model Development, Volume: 4 Issue: 4 Pages: 943-955, DOI: 10.5194/gmd-4-943-201, 2011

NewAGE is based on the Object Modelling System whose main reference is the following:

0- David, O., Ascough, J.C. II, Lloyd, W., Green, T.R., Rojas, K.W., Leveasley, G.H., Ahuja, L.R., A software engineering perspective on environmental modeling framework design: The Object Modeling System, Environn. Modelling & Software, 201-213, 2013

P.S. - The system has been formerly named Jgrass-NewAGE but we though it was better to avoid possible misunderstandings with the GRASS community (that we deeply love) and changed the name. Besides, GEOFRAME better interprets the spirit of the new components than JGrass.

12 - Bancheri, M., Serafin, F., Bottazzi, M., Abera, W., Formetta, G., & Rigon, R. (2018). The design, deployment and testing of Kriging models in GEOframe. Geoscientific Model Development Discussions, 1–31. http://doi.org/10.5194/gmd-2017-310

11 - Bancheri, M., A flexible approach to the extimation of water budgets and its connection to the travel time theory, Ph.D. Dissertation, 2017

10 - Abera, W; Formetta, G.; Brocca, L.; Rigon, R.; Water budget modelling of the Upper Blue Nile basin using the JGrass-NewAge model system and satellite data, Hydrol. Earth Syst. Sci., 21, 3145-3165, 2017,https://doi.org/10.5194/hess-21-3145-2017

9 - Abera, W; Formetta, G.; Borga, M.; Rigon, R.; Estimating the water budget components and their variability in a Pre-Alpine basin with NewAge-JGrass, Advances in Water Resources, 2017

8 - Abera, W. - Modelling water budget at a basin scale using JGrass-NewAge system, Ph.D. Dissertation, Università di Trento, 2016

7 - Formetta, G., Bancheri M., Rigon R., Performances of site-specific parameterizations of longwave radiation, Hydrol. Earth Syst. Sci., 20, 4641-4654, 2016, http://www.hydrol-earth-syst-sci.net/20/4641/2016/

doi:10.5194/hess-20-4641-2016

6 - Formetta G. , Antonello A. , Franceschi S. , David O., Rigon R., Digital watershed representation within the NewAge-JGrass system. Boletin Geologico y Minero, 125 (3): 371-381, 2014. ISSN: 0366-0176

5 - Formetta G., David O., Kampf S., Rigon R., Snow water equivalent modeling components in NewAge-JGrass, Geosci. Model Dev., 7, 725-736, 2014

4 - Formetta G., Antonello A., Franceschi S., David O., and Rigon R., Hydrological modelling with components: A GIS-based open-source framework, Environmental Modelling & Software, 5 (2014), 190-200}

3- Formetta, G., Hydrological modelling with components: the OMS3 NewAge-JGrass system, Doctoral Dissertation, Università di Trento, 2013

2 - Formetta G., Rigon R., Chavez J.L., David O., The short wave radiation model in JGrass-NewAge System, Geosci. Model Dev., 6, 915-928, 2013, www.geosci-model-dev.net/6/915/2013/, doi:10.5194/gmd-6-915-2013

1 - Formetta, G., Mantilla, R., Franceschi, S., Antonello A., Rigon R., The JGrass-NewAge system for forecasting and managing the hydrological budgets at the basin scale: models of flow generation and propagation/routing, Geoscientific Model Development, Volume: 4 Issue: 4 Pages: 943-955, DOI: 10.5194/gmd-4-943-201, 2011

NewAGE is based on the Object Modelling System whose main reference is the following:

0- David, O., Ascough, J.C. II, Lloyd, W., Green, T.R., Rojas, K.W., Leveasley, G.H., Ahuja, L.R., A software engineering perspective on environmental modeling framework design: The Object Modeling System, Environn. Modelling & Software, 201-213, 2013

P.S. - The system has been formerly named Jgrass-NewAGE but we though it was better to avoid possible misunderstandings with the GRASS community (that we deeply love) and changed the name. Besides, GEOFRAME better interprets the spirit of the new components than JGrass.

This is one of the posters I will present next 5th of April at Hydromod2018.

It present some of our results in TT theory and conveys the fact that, given a set of equations, the travel time distribution is (obviously) set. There are no hidden degree of freedom. All of it is contained in the paper about age-ranked equations. Clicking on the Figure you have the high resolution pdf.

This is a the oster we'll present at Tübingen on April 5 during the 2018 Hydromod Conference. It argues about process-based modelling and lumped modelling, intending that the first type of models solve partial differential equations (PDEs), the second (ODEs).

Clicking on the figure above you can access the pdf of the file and read the Q-codes, if you like. Q-codes refers to other posts in abouthydrology. Therefore as an alternative you can browse the blog for them.

Everybody fight for having an oral presentation at conferences. However, a poster is often not a bad idea. A poster is like a resume. His scope is not to tell everything about your work, but to attract potentially interested people from who you can have nice conversations, learn something, start a collaboration. To get the general idea of an award winning poster, give a close look to the poster below, that is part of a dedicated page on Nature.

A less traditional layout is the one of the poster to which I dedicated the first post of this year. Finally informative guidelines by:

A less traditional layout is the one of the poster to which I dedicated the first post of this year. Finally informative guidelines by:

- Nature journal
- Cornell Center for Material Research
- Liverpool University
- Colin Purrington's templates
- McDermott poster story

Obviously, it is assumed that you have something to tell (but this is another topic).

We are arrived then to design a storm water management system. Which are the requirements ? Which are the typical case studies ? Which are the tools for making the right estimations ? These lectures start to give an answer.

**Criteri di progettazione delle Fognature pluviali**

**Esempi di due interventi di progettazione e/o riprogettazione delle fognature pluviali**

**Criteri di dimensionamento speditivo delle reti di fognatura pluviale (Parte I)**

**Criteri di dimensionamento speditivo delle reti di fognatura pluviale (Parte II)**

**Criteri di dimensionamento speditivo delle reti di fognatura pluviale (Parte III)**

**Using the linear reservoir model to infer the maximum discharge of a hydraulic network**

**Ancora sul calcolo del diametro interno (speditivo) dei tubi di fognatura**

I am sharing here the videos of my lectures, in Italian, about precipitations. They were performed during my today class of Hydrology, whose main site is here. More material on precipitations can be found in this old post.

**Precipitation: a short introduction**

**Statistical properties of precipitation on the ground**

**The concept of return period**

**Intensity-Duration-Frequency curves (and return period again)**

**Interpolating Gumbel with the maximum likelihood method**

**Interpolating Gumbel with the minimum squares method**

**Illustrating the Pearson's test**

**The Generalised extreme value distribution**

Gumbel distribution function

Interpolating Gumbel with the moments method

A deeper explanation of Pearson's test (and a little of hypothesis testing)

Alternative videos for some of the topics are available here.

These are the lectures that regard the interpolation of Intensity-Duration-Frequency (IDF) curves to rainfall estreme datas. It is covered a little of theory which will be subsequently used to practically interpolate some data sets. These lectures are part of the class of Hydraulic Constructions and Hydrology held at the University of Trento.

**Intensity-duration-frequency curves definition**

**The Gumbel distribution**

**Moments method**

**Maximum likelihood**

**Minimum squares**

For enjoinment of my students, I prepare some slides and and gave a brief introduction to the Open Science Framework in Italian that can be of help for anyone.

The slides can be found here.

Using the slides I gave this talk.

The slides can be found here.

Using the slides I gave this talk.

However, I also make a short practical presentation.

They obviously do not substitute the much more comprehensive YouTube in English

and the quite extensive help.

“Viscosity is a property of the fluid which opposes the relative motion between the two surfaces of the fluid that are moving at different velocities. In simple terms, viscosity means friction between the molecules of fluid. When the fluid is forced through a tube, the particles which compose the fluid generally move more quickly near the tube's axis and more slowly near its walls; therefore some stress (such as a pressure difference between the two ends of the tube) is needed to overcome the friction between particle layers to keep the fluid moving.” (Source Wikipedia)

One relevant point for us is that water viscosity changes with temperature in a non neglibile way between -10 and 40 centigrades, temperature that many soils can across easily in different seasons: this table shows how much. A model for water viscosity in a large range of temperatures is given by Kestin et al. [1978], which can be used in models.

Viscosity is actually so important that an entire website is dedicated to its experimental values of viscosity: viscopedia. Same information can also be read from this other informative website about water as a substance.

Viscosity variation is usually forgotten in hydrological modelling and the fact that water travels two times faster (at least) in summer than in winter is usually forgotten in any model of runoff production. It is probably time that we incorporate such effects in our modelling of infiltration, and for what regards me, in our numerical integrator of Richards equation.

When dealing with infiltration, in hydrologically realistic contexts, papers by Constanz and coworker are a standard reference, starting from Constantz [1981], Ronan et al, 1998, and Costantz and Murphy [1991]. Papers citing them are also interesting (here the Scopus list) and cover quite recent works too. We can identify two issues (the usual ones): first it is necessary to understand how viscosity variation affects equations of flow, secondly how these affect a heterogeneous landscape.

Grifoll et al (2005), in analysing the problem of water vapor transport, independently if you like or not their solutions, contains the right equations, and can be an help to write yours.

A related question is if temperature alters also the soil water retention curves. This problem is faced by a recent paper by Roshani and Sedano [2016] but it is still clearly an open problem.

I did not start really reading these papers. However, here it is their list below.

One relevant point for us is that water viscosity changes with temperature in a non neglibile way between -10 and 40 centigrades, temperature that many soils can across easily in different seasons: this table shows how much. A model for water viscosity in a large range of temperatures is given by Kestin et al. [1978], which can be used in models.

Viscosity is actually so important that an entire website is dedicated to its experimental values of viscosity: viscopedia. Same information can also be read from this other informative website about water as a substance.

Viscosity variation is usually forgotten in hydrological modelling and the fact that water travels two times faster (at least) in summer than in winter is usually forgotten in any model of runoff production. It is probably time that we incorporate such effects in our modelling of infiltration, and for what regards me, in our numerical integrator of Richards equation.

When dealing with infiltration, in hydrologically realistic contexts, papers by Constanz and coworker are a standard reference, starting from Constantz [1981], Ronan et al, 1998, and Costantz and Murphy [1991]. Papers citing them are also interesting (here the Scopus list) and cover quite recent works too. We can identify two issues (the usual ones): first it is necessary to understand how viscosity variation affects equations of flow, secondly how these affect a heterogeneous landscape.

Grifoll et al (2005), in analysing the problem of water vapor transport, independently if you like or not their solutions, contains the right equations, and can be an help to write yours.

A related question is if temperature alters also the soil water retention curves. This problem is faced by a recent paper by Roshani and Sedano [2016] but it is still clearly an open problem.

I did not start really reading these papers. However, here it is their list below.

- Constantz, J. (1981). Temperature Dependence of Unsaturated Hydraulic Conductivity of Two Soils. Soil Sci. Soc. Am. J., 46, 466–470.
- Constantz, J., & Murphy, F. (1991). The temperature dependence of ponded infiltration under isothermal conditions. Journal of Hydrology, 122, 119–128..
- Grifoll, J., Gastó, J. M., & Cohen, Y. (2005). Non-isothermal soil water transport and evaporation. Advances in Water Resources, 28(11), 1254–1266. http://doi.org/10.1016/j.advwatres.2005.04.008
- Hopmans, J. W., & Dane, J. H. 1986). Temperature Dependence of Soil Hydraulic Properties. Soil Sci. Soc. Am. J., (50), 4–9.
- Jaynes, D. B. (2002). (1990) Temperature Variations Effect on Field-Measured Infiltration, 1–8.
- Kestin, J., Sokolov, M., & Wakeham, W. A. (1978). Viscosity of Liquid Water in the Range -8 C to 150 C. J. Phys. Chem. Ref. Data, 7(3), 941–048.
- Ronan, A., Prudic, D., Thodal, C., & Constantz, J. (1998). Field study and simulation of diurnal temperature effects on infiltration and variably saturated flow beneath an ephemeral stream. Water Resources Res., 34(9), 2137–2153.
- Roshani, P., & Sedano, J. Á. I. (2016). Incorporating Temperature Effects in Soil-Water Characteristic Curves. Indian Geotechnical Journal, 46(3), 309–318. http://doi.org/10.1007/s40098-016-0201-y

These lectures cover both the class of Hydrology and Hydraulic Constructions that share the necessity to talk a little of statistics. In four steps I talk about simple concepts about statistics and probability. Very basic stuff to remind to my students what they should already know. Probably in the second series of slides I performed better.

**Samples, Population, empirical distributions**

**Introduction to visual statistics, location and scale parameters.**

**Probability axioms and some derived concepts visualised**

**Acting with Real numbers**

Same topic as above but different class

Same topic as above but different class

Same topic as above, different class

Almost the same as above bur with a couple of slides more

Really random numbers are not easily obtainable (if they exists). The short story: I perceive that

Randomly literally means that there is no law (expressed in equations) or algorithm (expressed in actions or some programing code) that connects one pick in the sequence to another. The elements in the sequence can depend on others (as described by their correlation) while this dependence does not imply causation (in the sense that one implies the other): "correlation does not imply causation".

Taking the problem from a different perspective, Judea Pearl stresses that probability is about "association'' not "causality'' (which is, in a sense, the reverse of randomness): "An associational concept is any relationship that can be defined in terms of a joint distribution of observed variables, and a causal concept is any relationship that cannot be defined from the distribution alone. Examples of associational concepts are: correlation, regression, dependence, conditional independence, like-lihood, collapsibility, propensity score, risk ratio, odds ratio, marginalization, conditionalization, ``controlling for,'' and so on.

Examples of causal concepts are:randomization, influence, effect, confounding, "holding constant,'' disturbance, spurious correlation, faithfulness/stability, instrumental variables, intervention, explanation, attribution, and so on. The former can, while the latter cannot be defined in term of distribution functions." He also writes: "Every claim invoking causal concepts must rely onsome premises that invoke such concepts; it cannot be inferred from, or even defined in terms statistical associations alone.''

Therefore Pearl, at least, in the sense that random elements in a random sequence are not causally related, supports the idea that if probability is not about causality, it is not either about ranmdomness.

Wikipedia also supports my arguments: "Axiomatic probability theory deliberately avoids a definition of a random sequence [2]. Traditional probability theory does not state if a specific sequence is random, but generally proceeds to discuss the properties of random variables and stochastic sequences assuming some definition of randomness. The Bourbaki school considered the statement ``let us consider a random sequence" abuse of language [3] "

The same Wikipedia explains very clearly which is the state of art of randomness concept but, for a more interested reader, the educational review paper by Volchan [4], is certainly informative.

I report from Wikipedia the current state of art for the extractions of random sequences:

"Three basic paradigms for dealing with random sequences have now emerged [5]:

- The frequency / measure-theoretic approach. This approach started with the work of Richard von Mises and Alonzo Church. In the 1960s Per Martin-Loef noticed that the sets coding such frequency-based stochastic properties are a special kind measure zero sets, and that a more general and smooth definition can be obtained by considering all effectively measure zero sets.
- The complexity / compressibility approach. This paradigm was championed by A. N. Kolmogorov along with contributions Levin and Gregory Chaitin. For finite random sequences, Kolmogorov defined the ``randomness'' as the entropy, Kolmogorov complexity, of a string of length K of zeros and ones as the closeness of its entropy to K, i.e. if the complexity of the string is close to K it is very random and if the complexity is far below K, it is not so random.
- The predictability approach. This paradigm was due Claus P. Schnorr and uses a slightly different definition of constructive martingales than martingales used in traditional probability theory. Schnorr showed how the existence of a selective betting strategy implied the existence of a selection rule for a biased sub-sequence. If one only requires a recursive martingale to succeed on a sequence instead of constructively succeeds on a sequence, then one gets the recursively randomness concepts. Yongge Wang that recursively randomness concept is different from Schnorr's randomness concepts. "

I do not pretend to have fully understood the previous statements. However, in summary, we have to grow quite complicate if we want to understand what randomness is.

Once clarified what it is, we can have the problem to assess what can be a random arrangement for an arbitrary set of objects, say $\Omega$. Taking example of the algorithms used to get a given random sequence of numbers from a give distribution, we can observe that probability itself can be used to infer the random sequence of a set from a random sequence in [0,1] by inverting the probability $P$.

Random sampling is significant when the set of the domain is subdivided into disjoint parts: a partition. Therefore:

~\(\Omega\), denoted as:

${\mathcal P }(\Omega):=\{ x | \cup_{x \in \mathcal P} x = \Omega\, {\rm{and}}\ \forall y,z \in \Omega,\, y\cap z = \emptyset \}$

Through probability \(P\) defined over ${\mathcal P} (\Omega)$ each element $x$ of the set is mapped into the closed interval [0,1] and it is guaranteed that $P[\cup_{x \in \mathcal P} x] = 1$

There is not necessarily an ordering in the partition of $\Omega$ but we can arbitrarily arrange the set and associate each of its element with a subset of [0,1] of Lesbesgue measure (a.k.a. length) corresponding to its probability. By using the arbitrary order of the partition, we can at the same time build the (cumulative) probability. By arranging or re-arranging the numbers in [0,1], we thus imply (since $P$ is bijective) a re-arrangement of the set ${\mathcal P} (\Omega)$.

$${\mathcal S} := \{ x_1 \cdot \cdot \cdot\}$$

description shorter that itself via a universal Turing machine (orequivalently we can adopt one of the other two definition proposed above

The prof is trivial. If there is a law that connects elements in ${\mathcal P} (\Omega)$ then through the probability $P$ a describing law is obtained also for the random sequence in [0,1], which is, therefore no more random.

So randomness of any set on which is defined a probability can be derived by getting a random sequence in [0,1].

http://doi.org/10.1214/09-SS057

[2] Inevitable Randomness in Discrete Mathematics by József Beck 2009 ISBN 0-8218-4756-2 page 44

[3] Algorithms: main ideas and applications by Vladimir Andreevich Uspenskiĭ, Alekseĭ, Lʹvovich Semenov 1993 Springer ISBN 0-7923-2210-X page 166

[4] Sergio B. Volchan, What is a random sequences, The American Mathematical Monthly, Vol. 109, 2002, pp. 46–63[5] R. Downey, Some Recent Progress in Algorithmic Randomness, in Mathematical foundations of computer science 2004: by Jiří Fiala, Václav Koubek 2004 ISBN 3-540-22823-3 page 44

The zero lecture on my hydrology class. The whole picture of the class is here instead.

There are a lot of resources to start with python, but for hydrologists, but here I tried, at least at the beginning, a list of readings to be quickly operative.

**For who loves more traditional approaches than Notebooks and require a ”books like” approach**, maybe because it happens that they never programmed before, the first information is the Python site itself. Its Italian counterpart is here.

with a preference for the first one.

- Jupyter notebooks are a splendid way to organise calculations: you have first to lear how to use them (here a manual).
- Lectures on scientific computing with Python by J.R. Johansson cover the main topics very nicely. the first four of more general interest:
- Lecture-0 Scientific Computing with Python (This is a general lecture)
- Lecture-1 Introduction to Python Programming (Just basic notions on programming)
- Lecture-2 Numpy - multidimensional data arrays (Array and vectors)
- Lecture-3 Scipy - Library of scientific algorithms (Doing science with Python)
- Lecture-4 Matplotlib - 2D and 3D plotting (No plots, no science: quite a general introduction)

- For Italians, my own introductory lectures have their place, I believe also because I used Jupyter notebooks (and Python 3) to convey previous work by Joseph Eschgfaeller (translated from Python 2.7).
- Una introduzione gentile al Python scripting (mostly a translation from JE lectures)
- Esperimenti nella lettura di un file
- Leggere un file con PANDAS (e plot dei dati con Matplotlib)
- Scipy Lecture Notes is a good (not necessarily quick) starting. The html version supports hyperlinks that the pdf one does not. You can download the chapters in pdf and at their end, you can download the Jupyter notebooks with the exercises. You can also find part of the exercises here below
- From Wes McKinney (creator of Pandas) Python for data analysis book:
- Chapter 2: Python Language Basics, IPython, and Jupyter Notebooks
- Chapter 3: Built-in Data Structures, Functions, and Files
- Chapter 4: NumPy Basics: Arrays and Vectorized Computation
- Chapter 5: Getting Started with pandas
- Chapter 6: Data Loading, Storage, and File Formats
- Chapter 7: Data Cleaning and Preparation
- Chapter 8: Data Wrangling: Join, Combine, and Reshape
- Chapter 9: Plotting and Visualization
- Chapter 10: Data Aggregation and Group Operations
- Chapter 11: Time Series
- Chapter 12: Advanced pandas
- Chapter 13: Introduction to Modeling Libraries in Python
- Chapter 14: Data Analysis Examples
- Appendix A: Advanced NumPy
- Kevin Sheppard's introduction to statistical analysis with Python also a manuscript to read.

Other resources can be:

- The main NumPy and SciPy documentation.
- Python Scientific Lecture Notes a comprehensive set of tutorials on the scientific Python ecosystem.
- Software Carpentry is an open source course on basic software development skills for people with backgrounds in science, engineering, and medicine.
- Introduction to Statistics an introduction to the basic statistical concepts, combined with a complete set of application examples for the statistical data analysis with Python (by T. Haslwanter).

- They suggests Dive into Python (EN, IT) as a good starting book, and I think it is
- Python Crash course is also a traditional type of book that covers all the traditional element of programming. It is certainly a good book but I would say that its approach does not cope exactly with the modern ‘hip’ approach that a scientist has when using python with more high level infrastructures as Pandas (and partially Numpy and Scipy are) which, for instance often do not require to explicit iterations with “for” loops.
- Think Python (EN, IT) is also an alternative to previous books
- A little different is Thinking in Python, because it is oriented to introduce topics of object oriented (OO) programming which are not usually covered in elementary programming books. Even if OO at its core is to get used to design patterns.

- Python in Hydrology
- Python programming guide for Earth Scientists
- A hands-on introduction to using Python in the Atmospheric and Oceanic sciences

with a preference for the first one.

- Soil Physics with Python: Transport in the Soil-Plant-Atmosphere System, by Bittelli et al, is al, is a book on soil science which is quite appealing (as seen the TOC): the kindle version cost reasonably but it is in Python 2.7. Its Python programs are available here.

This is the material for the 2018 class in Hydraulic constructions at University of Trento. The material, is being revised during the class and is similar to the last year class. A first difference is that slides will be loaded into an Open Science Framework (OSF) repository. More information in the Introductory class below. The name is hydraulic construction. Actually it covers the hydraulic design of a storm water management system and the hydraulic design of an Aqueduct. With hydraulic design, I mean that the class teach how to calculate the hydraulics of infrastructure. It will not teach anything else and neither will cover how to really draw them to produce a final executive project. These knowledges are communicated in the class called "Progetto di Costruzioni Idrauliche".

T - Is a classrom lecture

L - Is a laboratory lecture

- 2018-02-26
- Introductory Class. (YouTube 2018. Unfortunately non very visible)
- New goals for Urban hydrology. (YouTube 2018. Unfortunately non very visible)
- The sewage systems devices (YouTube 2018. Unfortunately non very visible)
- Local control on the hydrological cycle (YouTube 2018. unfortunately non very visible)
- The law of public works
- The past and the future

- Further readings (optional)
- Using OSF

- 2018-03-01 - L - Introduction to Python with Jupyter (We mostly use the three notebook below):
- Una introduzione gentile al Python scripting (mostly a translation from JE lectures
- Leggere file da un file Excel e fare qualche grafico
- Leggere un file con PANDAS (e plot dei dati con Matplotlib)
- Further resources are available in this other post.
- 2018-03-05 - T -
- A little of Statistics and Probability.
- Descriptive Statistics
- Statistics' statistics
- Further readings on Statistics (see also here)
- Probability's Axioms
- Distributions
- Further readings on Probability
- YouTube videos 2018
- 2018-03-08 - L -Explorative data analysis and Simple statistics with Python's Pandas
- Gaussian Distribution
- Central Limit Theorem Illustrated (and some other distributions)
- Gamma Distribution (and some other further Python)
- 2018-03-12 - T - Statistical properties of Extreme precipitations and their interpolation.
- Intensity duration frequency curves
- Gumbel distribution functions
- Moments method
- Maximum likelihood method
- Minimum squares method
- The YouTube video of the class 2018.
- Further readings ( see the Precipitations' post)
- 2018-03-15 - L - Estimation of Extremes with Python
- Exercise: Using the examples of the last Lab, draw a Gumbel distribution.
- Exercise: Select randomly from a Gumbel distribution and empirically shows the effects of the central limit theorem.
- For estimating the Gumbel distribution parameters:
- The YouTube video of the class 2018.
- 2018-03-19 - T - Element for the design of storm water management infrastructures- I.
- The storm water drainage network (SWDN)
- Urban cases
- The estimation of the flood wave (the IUH case) and the Hydraulic design of the SWDN
- YouTube Videos
- 2018-03-22 - L - Estimation of Extremes with Python - II
- 2018-03-26 - T - Elements for the design of storm water infrastructures

- 2018-04-5 - L Short introduction to QGIS for representing urban infrastructures.
- Introduction to QGIS by Elisa Stella and Daniele Dalla Torre. For other information about tools installation, see the bottom of the page.
- Using QGIS and GISWater to feed SWMM
- Material/Data of the lab

- Further Video classes on QGIS/GISWATER
- Create subcatchments
- Homogenize the subcatchment layer and insert it in the database
- Geometric information subcatchments
- Average Slope
- Impervious
- Simp, Routeto
- https://www.youtube.com/watch?v=HJIGH-ndcJ4

- 2018-04-09 - T- Pumping stormwaters.
- 2018-04-12 -L Working with SWMM for implementing a storm water management system
- 2018-04-16 - T - Pipes (slides from Roberto Magini) and infrastructures
- 2018-04-19 - L - Simple estimation of the maximum discharge via Python
- Maximum Discharge from a linear reservoir model
- Internal diameter of the pipe
- Summing discharges from pipes (I)
- Summing discharges from pipes (II)
- 2018-04-24 - Midterm written exam
- Question to be answered. Students will be required to answer to two (2) questions randomly chosen and (3) produce e code snippet in Python to perform the task required.

As a general, simple and descriptive reference, the first six chapters of Maurizio Leopardi's book can be useful :

- Utilizzo Idropotabile
- Il trasporto in pressione
- Dimensionamento idraulico delle condotte
- Acquedotto con sollevamento meccanico
- Serbatoi
- Reti di distribuzione

The state of the water supply in Italy is summarised here (Corriere della Sera, 2018-05-16)

- 2018-05-3 L - SWMM and Python problem solving
- 2018-05-7 T - Aqueducts
- Aqueducts in 2020 (YouTube)
- Equations for aqueducts networks (YouTube)
- Mass and energy Conservation (YouTube)
- 2018-05-101 L - Working with SWMM and PYTHON
- 2018-05-14 T - Design of aqueducts networks
- 2018-05-17 L - Introduction to EPANET
- 2018-05-21 T - External aqueducts & Reservoirs
- External aqueducts (YouTube)
- Reservoirs (YouTube)
- Contemporary problems in aqueduct's network management
- 2018-05-24 L - A simple aqueduct configuration with EPANET
- 2018-05-28 - T - Water Sources
- Springs (YouTube)
- Wells
- Excavations (optional)
- Surface Waters
- Generalities
- Small Intake, Grid
- Channel (Optional)
- Sand Remover (Optional)
- 2018-05-31 - L - Working with EPANET to design an aqueduct

- 2018-06-04 T - Houses' infrastructures
- 2018-06- 11 L - Problem solving with EPANET

During the class I will introduce sever tools for calculations.

- Open Science Framework (OSF): It is a tool for sharing a workflow, especially design for scientific purposes. It allows storage of files and documents and their selective publication on the web.
- Python - Python is a modern programming languages. It will be used for data treatment, estimation of the idf curves of precipitation, some hydraulic calculation and data visualisation. I will use Python mostly as a scripting language to bind and using existing tools.
- SWMM - Is an acronym for Storm Water Management System. Essentially it is a model for the estimation of runoff adjusted to Urban environment. I do not endorse very much its hydrology. However, it is the most used tools by colleagues who cares about storm water management, and I adopt it. It is not a tool for designing storm water networks, and therefore, some more work should be done with Python to fill the gaps.
- EPANET Is the tool developed by EPA to estimate water distribution networks.
- GISWATER: http://growworkinghard.altervista.org/giswater-11-install-windows/
- QGIS: http://growworkinghard.altervista.org/qgis-2-18-how-to-install-step-by-step-on-windows/

Grades (voti) of the intermediate exam.

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