## Tuesday, March 13, 2018

### A short introduction to precipitation and precipitation statistics

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

### Some on statistic of extreme precipitations

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

## Thursday, March 8, 2018

### Open Science Frameworks 4 Italians

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.

However, I also make a short practical presentation.

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

## Wednesday, March 7, 2018

### Water viscosity

“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.

## Monday, March 5, 2018

### Probability and Statistics basics: a very short simple overview of concepts for my students

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

Same topic as above but different class

Introduction to visual statistics, location and scale parameters.

Same topic as above but different class

Probability axioms and some derived concepts  visualised

Same topic as above, different class

Acting with Real numbers

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

## Sunday, March 4, 2018

### Random sampling (is it defined in probability theory ?)

Really random numbers are not easily obtainable (if they exists). The short story: I perceive that in probability theory the concept of random sampling is not contemplated. Randomness is used by probability theory but is not implied by its axioms.

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. "
"In most cases, theorems relating the three paradigms (often equivalence) have been proven.
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:

Definition: Given a set (having the structure of a~$\sigma$-algebra)~$\Omega$ let a partition of
~$\Omega$, 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 ${\mathcal P} (\Omega)$.

Definition: we call sequence of elements in ${\mathcal P} (\Omega)$, denoted as $\mathcal S$ a numerable set of elements in ${\mathcal P} (\Omega)$:
$${\mathcal S} := \{ x_1 \cdot \cdot \cdot\}$$
Definition: we call a sequence a random sequence~~if it ha no
description shorter that itself via a universal Turing machine (orequivalently we can adopt one of the other two definition proposed above
Theorem: A random sequence of integers, through inverting the probability P, defines a random sequence on the set ${\mathcal P} (\Omega)$.
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].

References

[1] - Pearl, J. (2009). Causal inference in statistics: An overview. Statistics Surveys, 30, 96--146.
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

## Tuesday, February 27, 2018

### Hydrology 2018: Class 0

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

• (a) Syllabus; or where I explain what the class is about, etc

## Monday, February 26, 2018

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.

Other resources can be:
Specifically for hydrologists, but maybe a little obsolete, are:

with a preference for the first one.

## Tuesday, February 20, 2018

### Costruzioni Idrauliche 2018

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".

Foreseen Schedule

T - Is a classrom lecture
L - Is a laboratory lecture

#### Storm water management systems

February

March

April

Aqueducts

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

May
• 2018-05-3 L - SWMM and python problem solving
• 2018-05-7 T - Aqueducts in 2020
• 2018-05-101 L - Working with SWMM and PYTHON
• 2018-05-14 T - External aqueducts
• 2018-05-17 L - Introduction to EPANET
• 2018-05-21 T -  Reservoirs
• 2018-05-24 L - A simple aqueduct configuration with EPANET
• 2018-05-28 - T - How to verify aqueducts
• 2018-05-31 - L - Working with EPANET to design an aqueduct
June

Tools

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/
Questions for the midterm exam

Domande della prova intermedia 2017.

## Sunday, February 18, 2018

### Conoscere, comunicare, gestire il rischio idrogeologico in ambiente montano: 3/3

On February 15, 2018, we had the second day of the workshop: "Know, communicate and manage the hydrological and geological risk in mountain environment", originally intended for journalists, technicians, as politicians. It was held at the Department of Civil, Environmental and Mechanical Engineering Department of the University of Trento. This page reports the second day.
The first part of the workshop can be found in two previous post:
• Introduction
• About Italian legislation on hazards by Eugenio Caliceti

• Planning Emergencies after natural hazards by Marta Martinengo

• The hazard map of Trentino Province by Mauro Zambotto

• Discussion after dott. Zambotto presentation

• Comments on work groups simulations by Rocco Scolozzi

### Conoscere, comunicare, gestire il rischio idrogeologico in Ambiente montano: 2/3

On February 7 and 15, 2018, it was organised a workshop entitled "Know, communicate and manage the hydrological and geological risk in mountain environment", originally intended for journalists, technicians, as politicians. It was held at the Department of Civil, Environmental and Mechanical Engineering Department of the University of Trento. The morning talks are in another post.
The Afternoon was dedicated to a Conference open to the wide public. It covered the topic of which you see the YouTube videos below.

Other two pages refer of the conference:

• The Experience of major Ugo Grisenti after the Campolongo event (August 15, 2010)
• Some images from Campolongo
• Information (about hazards) from the institutional channel by Giampaolo Pedrotti
• Andrea Selva on the information on natural hazards (from the point of view of a local newspaper)
• The judge and hazards: the experience of Carlo Ancona

## Friday, February 16, 2018

### Conoscere, comunicare, gestire il rischio idrogeologico in Ambiente montano 1/3

On Wednesday 7  and Thursday 15 February 2018 we held at our Department (DICAM) a workshop entitled: Know, communicate and manage hydro-geological risks in mountain environments. This workshop was one of the events of the Life FRANCA project. Please find below, in Italian, the YouTube of the talks.

The days were split into other two pages other than this one related to the first morning:

First day (February 7, 2018)
• Introduction to the workshop by Luigi Fraccarollo

• Introduction to Life FRANCA by Rocco Scolozzi

• A review on hydrological hazards for non specialists by Riccardo Rigon

• A little of discussion

• What is "hazard" by Giorgio Rosatti

## Monday, January 29, 2018

### Grids - Notes for an implementation

This post talks about the same subject already analyzed in a previous post but from a slightly different point of view, hoping to add clarity to the concepts. We assume to already have the grid delineated, as for instance the one in Figure. Some other program or someone else provided to us. All the information is written in a file, maybe in a redundant form, but it is there and we just have to read it.
Assume we are talking about a three-dimensional grid. Nodes, edges, faces, and volume are identified by a number (key, label) which are specified in the grid’s file.

Therefore the problem is to read this file and implement the right (Java) structures/objects to contain it, keeping in mind that our goal, besides to upload the data in memory is to estimate the time marching of a variable $A$ (and, maybe some other variable) in a given volume. Its time variation depends on fluxes of the same quantity (mass, to simplify) that are localised at the face that constitute the boundary of the volume.

Getting the things done

The simplest thing to do is then, to associate a vector whose entries are the values of $A$ for any of the volumes in the grid. Let say, that forgetting any problem which could be connected with execution speed, caching [1], boxing-unboxing of variables, we use a Hashmap to represent these values.
We will use also a Hashmap to contain the fluxes in each face. This hasmap contains $F$ elements: as many as the number of faces. The file from which we started contains all of this information and therefore we do not have any problem to build and fill these “vectors”.
Let’s give a look to what our system to solve can look like. The problem we have to solve changes but, schematically it could be:
For any volume (we omit the index, $i$ of the volume for simplicity):
$$A^t = A^{t-1} + \sum_l a_l^{t} *i_l^{t}*f_l^t/d_l$$
Where:
$t$ is time (discretized in steps) and $t-i1$ is the previous step;
$l$ is the index of faces belonging to the volume
$d_l$ is the distance between the centroids of the two volumes that share the same face;
$i_l$ is a sign, +1 or -1, which depends on the volume and the face we are considering (volume index omitted);
$a_l$ is the area of the face $l$ or some function of of it.

For generality, the r.h.s. member of the equation is evaluated at time $t$, i.e. the equation is assumed to be implicit, but at a certain moment of the resolution algorithm, the function will be expressed as depending of some previous time (even if from the point of view of internal iterations). For a more detailed case than this simplified scheme, please see, for instance [2].
The Hashmap of $A$ contains the information about the number of volumes, i.e., $V$.
(I) an indication of the faces belonging to each volumeIl vettore (hash map) and
To obtain this, we have to store information about the topology of our grid. In the previous posts, we tried to investigate and answer to the question: which is the most convenient to store these informations ? (Right, more from a conceptual point of view than from a practical one).
From our previous analysis, we know that that for encoding the number of faces for any volume, we have to introduce a second (2) container that has has many position as the number of volumes, and for any volume a variable number of slots, each for any face of that volume (if the grids is composed by volumes of the same shape, the latter number of slots is constant for the internal elements of the grids, and variable just for the boundary volumes).
In this preliminary analysis, a Hasmap seems appropriate to contain this information, letting, for the moment, unspecified what types or objects contains this topology Hashmap, but eventually, they will contain a key or a number which identifies in a unique way a given face.
In this way the information about any face is present in two slots, belonging to the volumes that share the same face.
We have then the various quantities to store in each face:

• $a_l$ (3)
• $f_l$ (4)
• $d_l$ (5)

Anyone of the above quantites require a container with as many elements as the faces. We could, then, use three Hasmaps, whose indexes (keys) coincide with the numbers (keys) that in the topology Hasmap (2) realate faces to volumes.
To elaborate our equation we need then five containers, of which the topology one has a structure to be specified later. Well, actually all the hashmap internals has to be specified.
The elements of $a$ and $d$ are geometrical quantities that can - and has- to be specified outside the temporal cycle, if the grid structure is not modified during the computation. However, to be estimated they require further topological information that we still do not have (but can be in the grid file).
To estimate faces’ area, we need to know the nodes of the grid [3] which can be a sixth (6) container, and the way they are arranged in the faces, which is a seventh (7) container. Since the choices we did, we still choose to use Hashmaps to contain them. The Hashmap of nodes just contains the number (or the key) of nodes (and is, maybe, in most problems, pleonastic). The Hasmap of faces need to contain the arrangement of nodes, ordered in one of the two direction (left-hand -rule or right-hand-rule, clockwise and counterclockwise depends on the side you observe the face, so what is clockwise from a volume is counterclockwise for the other).
The (7) container has to have as many elements as the faces and each element contains the ordered nodes (a link, a reference, to). To estimate the area of the faces we need actually the geometry of the nodes, meaning their coordinates in some coordinate system. Usually, in most of the approaches, nodes are directly identified by their coordinates, which therefore are inserted directly (in the appropriate way) in container (7) instead that the link/reference to nodes' number (key, label).
However, I think that probably keeping the geometry separated from topology could be useful, because topology has its own scope, for instance in guiding the iteration in the summation that appears in our template equation.
Therefore we need a further container (the eight, 8) for the geometry, containing the coordinates of points. This container has $N$ elements, as many are the nodes.
The container of distances, d, to be filled needs to know between which volumes distances have to be calculated. This information, about volumes adjacency, needs another, further container (the nineth, 9) with length as the faces, i.e. with F elements. Every element, in turn, must contains the index of the elements between which is estimated.
This information that goes into the container 9, should already be in the file from which we are reading all the information. However, we should recover it by scanning all the volumes and finding which have a face in common. The latter, is a calculation that can be made off-line and we can, in any case consider it an acquired.
At this stage, we do not have much information about $f_l$. Certainly it will need to know which are adjacent volumes and requires the knowledge in container (9). Because $f_l$ is time varying it implies that information in (9) has to be maintained all along the simulation.
Every other information will require a further container. To sum up, we have a container of:

1. quantity A;
2. topology of Volumes;
3. the area of faces;
4. fluxes;
5. distances between volumes’ centroids;
6. nodes number (label, key)
7. nodes that belong to a face
8. coordinates of nodes
9. topology of faces (referring to the volumes they separate)

Towards generalizations that look to information hiding and encapsulation

We can observe that we have three types of containers: the ones which contain topological information (2,6,7,9), those which contain physical quantities (1,4), those which contains geometric quantities (3,5,8).
If, instead than a 3D problems, we would have a 2D or 1D one, the number of container change, but not their types.
To go further deep, the first problem to deal with could be to understand how, in the topology container, for instance of volumes (2) how to make room for the slots indicating their faces, since they are of variable dimension. In traditional programming, usually they would have adopted a “brute force” approach: each slot would have been set to have the dimension of the larger number of elements to be contained. The empty element replaced by a conventional number to be check. Essentially all of it would have resulted in a matrix whose rows (columns) would correspond to the the number of elements (volumes, faces) and whose columns (rows) to the variable number of elements they contain (in the case of volumes, faces; in the case of faces, edges, and so on).
In a OO language, like Java, the sub-containers of variable dimensions can be appropriate object, for instance called generically “cell” containing an array of int[ ]. Therefore the global container of a topology could be a hashmap of cells.
In principle we could use the container defined above without any wrapper, directly defining them in term of standard objects in the library of Java 9.
However, we would like, maybe, to use other types eith resepcts to those we defined. For instance, in some cases, for speed reasons, we could substitute ArrayList to Hasmap or, someone of us, working on the complexity of caching could come out with some more exotic objects.
To respond to these cases, we would like then to introduce some abstraction which, without penalizing (too much) performances. Sure, we can define wrapper classes, for instance:
• for topologies (essentially used to drive iterations)
• for geometries
• for physical quantities (used to contains data, immutable for parameters, and time-varying for variables)
These three classes would allow to fit all the cases for any dimension (1D, 2D, 3D): just the number of topology element would be varying.
However, this strategy could not be open enough to extensions which do not require breaking the code (be closed to modifications).
Using instead of classes, interfaces or abstract classes could be the right solution.
Classes, or BTW, interfaces could have also the added value to contain enough field to specify the characteristics of the entities, (es. if they work in 2D or 3D, their “name”, their units, all those type of information requested by the Ugrid convention). All these types of information are, obviously, also useful to make the programs or the libraries we are going to implement more readable and easier to be inspected by an external user.
While the topology class is self-explanatory, the geometry class (interface) has a connection to its topology. Therefore the geometry class should contain a reference to its topology to make explicit its dependence. A quantity object, for the same reason, should contain a reference to both its topology and its geometry.
The simplicity to use classes directly could be tantalizing, however, the investment for generality made by interposing interfaces or abstract classes is an investment for future.
Berti [3] advise, in fact, to separate the algorithm from the data structure, allowing therefore to write a specific algorithm once forever, and changing the data it uses, as we like. This would be a ideal condition maybe impossible to gain, but working to maintain in any case the possible changes in limited parts of the codebase is an add value to keep as reference. That is why “encapsulation” is one of paradigms of OO programming.

Some final notes

1 - In using cw-complexes to manage topology there could be overhead for speed. For instance, for accessing the values in a face of a volume, vi have to

access the volume,
access the address of the face
redirect to the appropriate quantity container to access the value
It could be useful then to eliminate one phase and once accessing the volume, having directly associate to it not the address of of the faces but the values contained in it.
If we have more than one value for face to access, related to different quantities and parameters, than maybe this added computational overhead could be considered negligible with respect to the simplicity of management of many quantities. In any case, an alternative to test.

2- At any time step, it is not only requested the quantity at time $t$, $A^{t}$, but also at the previous time, $t-1$, $A^{t-1}$. The two data structures share the same topology (which could represent a memory save). During time marching an obvious attention that the programmer needs to have is not to allocate a new grid to any time step. We can limit ourself to use only two grids across the simulation.

As an example, let us assume that time $t-1$ is going to be contained in vector $A^1$ and time $t$ in $a^2$. Then the above requirement could be obtained by switching the two matrixes as schematized as follows:
• Create A1and A2,
• Set A1 to initial conditions
• For any t
• A2=f(A1)
• cwComplex.switch(A1,A2)
The switch method exchanges the names, but does now write anything in memory of $A^1$ and $A^2$. It could be schematised as follows
• cwComplex.switch(A1,A2)
• B = A1;
• A1=A2;
• A2=B;
It is clear that, in this way, all the vectors are always filled by values, while, for some operation, cleaning them could be worth.

3 - At the core of the method os solution of the equation under scrutiny, there could usually be a Newton method, e.g. [3], Appendix A, equation A8. Any efficiency improvement for the solver is then reduce to improve the speed of this core, that, eventually can be parallelised.

Bibliography

[1] - Lund, E. T. (2014). Implementing High-Performance Delaunay Triangolation in Java. Master Thesis (A. Maus, Ed.).

[2] - Cordano, E., and R. Rigon (2013), A mass-conservative method for the integration of the two-dimensional groundwater (Boussinesq) equation, Water Resour. Res., 49, doi:10.1002/wrcr.20072.

[3] - O'Rourke, J., Computational geometry in C, Cambridge University Press, 2007

[4] - Berti, G. (2000, May 25). Generic Software Components for Scientific Computing. Ph.D. Thesis

## Wednesday, January 24, 2018

### My Questions for the 23 Hydrological Questions initiative

In November 2017 IAHS launched the new initiative to generate the 23 unsolved problems in Hydrology that would revolutionise research in the 21st century with the following YouTube video:

I probably have to formulate them differently. However at present my points are

1- What future for process based modelling beyond persistent dilettantism ? How can we converge towards new types of open models infrastructures for hydrology where the crowd can contribute, big institutions do not dominate, and reinventing the wheel will not be necessary anymore ?

2 - How to solve the energy budget, the carbon budget and the sediment budget together to constrain hydrologic models results ?

3 - Which new mathematics to choose for the hydrology of this century ? Does new hydrology (Earth System Science) needs new mathematics ?

4 - Will machine learning have a real role in hydrological modelling ?

5 - How can we really cope hydrological modeling with remote sensing measures ?

6 - How plants and grass work and interact with soil and atmosphere to produce evaporation ? Can we converge to unifying concepts that overcome present fragmented understanding ?

7 - How can we detect and measure spatial hydrological patterns ?

8- Does hydrology needs non-equilibrium thermodynamics or even a new type of thermodynamics ?

9 - How can we do hydrology science more open and replicable ?

10 - How dominant hydrological processes emerge and disappear across the scales. What tools are needed to follow the entanglement of processes ? Will we be finally able to cope with  feedbacks among processes?

## Tuesday, January 23, 2018

### My Hydrology Class 2018

Foreseen schedule

February

March
• 2018-03-02 - L - A little (very little) of GIS (for those who do not know anything about GIS). Where environmental data comes from.
• 2018-03-06 - T - A little of Statistics and Probability. (YouTube 2018 contains the video of the lectures below)
• 2018-03-09 - L - Introduction to Python with Jupyter (We mostly use the three notebook below):
• 2018-03-13 - T - Ground based Precipitations and their statistics Separation snow-rainfall - measure of precipitation
• 2018-03-16 - L - Intro to Python - Simple statistics - Empirical distribution functions - Statistical distributions - Extreme precipitations datasets
• 2018-03-20 - T - Extreme precipitations. Return period. Distribution of extreme precipitations.
• 2018-03-23 -L - Estimation of Extreme Precipitation 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:
• 2018-03-27 - T - OMS console - Installation and description. GEOframe modules.

April
• 2018-04-06 - L - Extreme Precipitations estimation Personal work under the assistance of tutors
• 2018-04-10 - T - Energy Budget. Radiation. Long wave, short wave. Theory and measure.
• 2018-04-13 - L - Estimation of radiation in a single location and over an area with GEOframe tools.
• 2018-04-17 - T - Spatial interpolation of environmental data
• 2018-04-20 - L- Estimation of areal precipitation and temperature with GEOFRAME-SIK
• Intermediate Exam
May
• 2018-05-06 - L - Problem solving lab class
• 2018-05-08 - T -Water in soil. Darcy-Buckingham. Hydraulic conductivity. Soil water retention curves.
• 2018-05-11 - L- Numerical experiments on hydraulic conductivity, soil water retention curves. Grids. - Cancelled for "Festa degli Alpini"
• 2018-05-15 - T -Richards equation and its extensions
• 2018-05-18 - L - Simulations of 1d infiltration with GEOframe-Richards-1d
• 2018-05-22 -T- Elements of theory of evaporation from soils
• 2018-05-25 -L-Simulation of evaporation from soild with GEOframe-PT, Geoframe-PM and other GEOframe tools
• 2018-05-29 -T- Transpiration- Theory
June
• 2018-06-1 - L- Estimating transpiration at catchment scale with GEOframe tools
• 2018-06-5 -T- Runoff generation
• 2018-06-08-L- Estimating runoff generation with GEoframe tools.
• 2018-06-12 - Conclusive seminar on a topic to be defined
• 2018-06-15-L - Problem solving with Tutor

## Tuesday, January 9, 2018

### Project: La gestione del sedimento nella realizzazione di servizi ecosistemici e nel controllo dei processi alluvionali.

The propoposal "La gestione del sedimento nella realizzazione di servizi ecosistemici e nel controllo dei processi alluvionali" was submitted yesterday for the call of MATTM.
The call is at this link (and it is for Geologists ?!). Actually the topics require some geology and a loto of hydrology and hydraulics. This is how the world goes.
The proposal can be found in this OSF site, called: "Gestione del Sedimento".  It is in Italian, but I will provide the translation of the following:

Abstract: The management of sediments for providing  ecosystem services and control alluvional processes.

The project is about the management of sediments in mountains catchments with the quantitative determination of erosion and mass transport. The research is made looking at the applicatio of 2000/60 and 2007/60 EU directives.
In the project's first phase:
Hydrological analysis utilises a multi-model strategy based on GEOtop and GEOFRAME-NewAGE and other open-source models.
It is estimated the sediment availability and its connectivity to the river network, by using field surveys, data made available from previous research and models.
Transport of sediments will be will be obtained with obtained with biphasic models where water and sediment are treated separately.
Objective of the above phases is to localise the sources and the sediment residence time, to detect its interaction with anthropic works and infrastructures and determine how they (the sediments) can interact with the climatic forcings.

Objective of the application phase are:
• the production of flooding hazard and risk maps;
• the forecasting on the proximate and long period of the morphologic chages or river beds, under climate change simulated through “weather generators”.
• The estimation of the impact of hydraulic works, also back in the years.
In the present project we will use a connectivity index to estimate the connection between hillslope (source sediment areas) and some target catchments’ elements (the river network, specific streams, the outlet). Sediment source areas are, partially already available from existing databases (CNR IRPI, Provincia Autonoma di Trento, Regione Sicilia), from field surveys and from remote sensing. These data are partially already available from previous projects (ASI MORFEO, CLIMAWARE, AQUATERRA, GLOBAQUA) and by the local Institutions (Geological Service of Trento Province and Regione Sicilia).

Terrein analysis will be coupled with models of landslide triggering, able to account for climate and soil use variability (in space and time) as described as variation of:

• intensity and frequency of precipitation,
• precipitation from snow to rain,
• phenology of vegetation cover

Two areas will be studied, one in the Alps and another in Apennines. The first is the Avisio torrent, and in in particolar the subcatchment closed at the Stramentizzo dam (Molina di Fiemme, TN), analysed with detailed especially in some specific parts.

The Apennine basin is the Giampilieri torrent in Messina Province.

References (that appears in the State-of-Art):

Badoux, A., Andres, N., and Turowski, J.,M., Damage costs due to bedload transport processes in Switzerland, Nat. Hazards Earth Syst. Sci., 14, 279-294, 2014.

Bertoldi et al., 2006 Bertoldi, G., Rigon, R., & Over, T. (2006). Impact of Watershed Geomorphic Characteristics on the Energy and Water Budgets. Journal of Hydrometeorology, 7(3), 389–403.

Berzi, D., Fraccarollo, L., Turbulence Locality and Granularlike Fluid Shear Viscosity in Collisional Suspensions (2015), Physical Review Letters, 115 (19), art. no. 194501. Comiti F., and

Farabegoli, E; Morandi, M.C.; Onorevoli G.; and Tonidandel, D.; Shallow landsliding susceptibility in a grass mantled alpine catchment (Duron valley, Dolomites, Italy), in preparation, 2018

Mao, L., Recent advances in the dynamics of steep channels, in Gravel-bed Rivers: Processes, Tools, Environments, John Wiley&Sons, Chichester, UK, 351-377, 2012.

Bracken, C., B. Rajagopalan, and E. Zagona (2014), A hidden Markov model combined with climate indices for multidecadal streamflow simulation, Water Resour. Res., 50, 7836–7846, doi:10.1002/2014WR015567.

Montgomery D.R., and Buffington J.M., Channel-reach morphology in mountain drainage basins. Geol. Soc. Am. Bull, v. 109, no. 5, pp. 596–611, 1997.

Renard, 1997 Renard, K.G., G.R. Foster, G.A. Weesies, D.K. McCool and D.C. Yoder. 1997. Predicting Soil Erosion by Water: A Guide to Conservation Planning with the Revised Universal Soil Loss Equation (RUSLE). Agr. Handbook No. 703. Washington, D.C.: USDA, Government Printing Office.

Rigon et al., 2006, Rigon, R., Bertoldi, G., Over, T. M., & Over, T. (2006). GEOtop: a distribute hydrological model with coupled water and energy budgets. Journal of Hydrometeorology, 7, 371–388.

Rosatti, G., Zorzi, N., Zugliani, D., Piffer, S. and Rizzi, A., Web Service ecosystem for high-quality, cost-effective debris-flow hazard assessment, 33-47, Env. Modelling & Software,  2018.

Smith, T.R., e F.P. Bretherton. «Stability and the conservation of mass in drainagebasin evolution.» Water Resource Research 8 (1972): 1506-1529.

Sofia, G., Di Stefano, C, Ferro, V., Tarolli, P. (2017). Morphological similarity of channels: from hillslopes to alpine landscapes. Land Degradation & Development, 28, 1717–1728, doi:10.1002/esp.4081.

Tarolli, P. (2016). Humans and the Earth’s surface, Earth Surface Processes and Landforms, 41, 2301–2304, doi:10.1002/esp.4059.

Tucker et al., 2001 Tucker, G. E., Lancaster, S. T., Gasparini, N. M., & Bras, R. L. (2006). The Channel-Hillslope Integrated Landscape Development Model (CHILD), 1–32.

Wainwright, J., A. J. Parsons, J. R. Cooper, P. Gao, J. A. Gillies, L. Mao, J. D. Orford, and P. G. Knight (2015), The concept of transport capacity in geomorphology, Rev. Geophys., 53, 1155–1202, doi:10.1002/2014RG000474.