Ignacio Rodriguez-Iturbe talk at Berkley in 2007 about Hydrology in 21st century

A talk of one of my masters, Ignacio Rodriguez-Iturbe, where he shows some of the work we did together more than ten years ago.

Obviously he, and Andrea Rinaldo were illuminating my way: but it was also my own way. It is always a pleasure to hear "El Jefe" talk.

Ignacio's talk starts around 6:10 m. The reference for the work to which I participated it is "The Book": Fractal River Networks, chance and self organization, Cambridge University Press, 1997.  Ecohydrology is partially covered in Ecohydrology of water controlled ecosystems: soil moisture and plants dynamics.

Reproducible Research (and papers)

Many papers I read in hydrology present research that is very difficult to reproduce. Because, as a scientist, I would like to reproduce the results of what I read (this is science, indeed!) some rules should be followed. I found this group of scientists that initiated a Reproducible Research web site, especially directed to image processing colleagues, but easily extendible to Hydrology, and related fields. They offer a how to guide, which is verbatim reported here below:

"Of course, it all starts with a good description of the theory, algorithm, or experiments in the paper. A block diagram or a pseudo-code description can do miracles! Once this is done, make a web page containing the following information:

• Title 
• Authors (with links to the authors' websites) 
• Abstract 
• Full reference of your paper, with current publication status, and a PDF of your paper 
• All the code to reproduce all the results, images and tables. Make sure all the code is well documented, and that there is a readme file explaining how to execute it 
• All the data (images, measurements, etc) to reproduce all the results, images and tables. Add a readme file explaining what the data represent 
• A list of configurations on which you tested your code (software version, platform) 
• An e-mail address that people can use for comments and remarks (and to report bugs) 

Depending on the field in which you work, it can also be interesting to add the following (optional) information to the web page:

• Images (add their captions, so that people know what Figure xx is about) 
• References (with abstracts)

For every link to a file, add its size between brackets. This allows people to skip large downloads if they are on a slow connection.
For examples, see this list of reproducible papers at LCAV, EPFL. "

Obviously they also link a blog and links to various RR resources. RR, incidentally, the same as my initials.

Now there is also a book about reproducible research made with R by Christopher Gandrud. The chapter can be found here.

GEOtop history up to the first public realease: part II

First Part

GEOtop 0.75

(mostly financed by COFIN 2001, THARMIT Eu Project, CUDAM - CofinLab 2001, ASI 54/2000)

With the Master thesis of Giacomo Bertoldi [2000] it was decided to throw away the PM equation for estimating evapotranspiration (actually we kept it for comparison), and to solve directly the energy budget in any point of the basin. This was the birth of GEOTOP 0.75 which is thoroughly documented in Bertoldi et al. [2011], and BTW in Rigon et al. [2006]. GEOtop 0.75 was actually a SVAT model plus an rainfall-runoff model coupled together, and was able to predict, besides the "normal hydrological observables", soil temperature.

GEOtop 0.75 needed several parameters to be run, however the modeling could have been considered parsimonious,  if its complexity was compared with its prognostic capabilities.   The user could switch-off the SVAT part and have a parametrically parsimonious rainfall-runoff model, or vice-versa s/he could switch-off the rainfall-runoff model and have a reasonably simple SVAT model. 

Large efforts were  done in cleaning the old code and improving the input-outputs quality. Wigmosta et al. [1994] original model is very similar to the version 0.75 of GEOtop (but was mostly a case of evolutionary convergence since the comparison came after the GEOtop implementation). 

In doing this version of GEOtop, we wanted to pursue the modelling of the entire surface hydrological cycle, even if a reasonable snow modeling still had to arrive. We were also looking for having a good tool for doing eco-hydrology. The revamp of eco-hydrology was in fact already seeded in Rodriguez-Iturbe's mind when I was working with him at the Texas A&M University (1994-1996), and  I was fully aware of his ideas from the beginning of the project. . 

For validation of the model, Tom Over  had a key role.  He, besides giving a lot of ideas for making the concepts behind the model clear, suggested to use the South Great Planes 97 experiment data set: that we promptly did as it appears in the first journal paper about the model Rigon et al. [2006]. In fact, one does not realize how scarce are hydrological data if he does not have a good model to cope with them.

Based partially on GEOtop 0.75 (and on the subsequent GEOtop 0.875) came all the work by Reza Entezarolmahdi who tried to create an automatic calibration system for the model. He used MOSC-EM  which, however was never really integrated in the model.  The work of Reza was really interesting for many points of view, but probably a little early with respect to our times, and scheduling. 

GEOtop 0.875

(mostly financed by TIDE EU Project, CUDAM Cofinlab COFIN 2001, THARMIT EU project)

This version finally achieved the goal of having  a snow accumulation and melt model (derived by the Utah Energy Balance -UEB- by Tarboton and Luce, [1992]) implemented by Fabrizio Zanotti [2003] with the help of Giacomo Bertoldi.  It also included a post-processor, the S-FACTOR (implemented by Christian Tiso [2003]), which used information on soil moisture to estimate the triggering of instabilites in hillslope^1.  Both the implementations were the outcome of two M.S. thesis.  Snow-melting and soil freezing are essential components in the hydrological cycle of mountain catchments and cannot not be overlooked. Landslide and debris-flow triggering are also an issue with particular relevance in mountains areas, such that floods in mountain areas are usually the combined effect of large liquid and solid discharges whose effects cannot be separated: GEOtop with this version started to be a reasonable a tool for studying all of these phenomena.  The reader can appreciate the differences among the previous version of GEOtop 0.5 and this one. Turbulent fluxes were now evaluated with a proper schematization of PBL and heat equation was quietly included in the picture; snow was modeled with a physically based (mono layered) model. 

With the version 0.875, let say 0.875b, we  also attack the problem of a sound hillslope-hydrology modeling, as ancillary to studying hillslope stability. The following is the rational behind the project, in words I wrote at that time.

"So far , our understanding of mountain catchments in fact has been based on hillslope hydrology, as reviewed for instance in Wipkey and Kirkby [1978], and  the "perceptual" hillslope model derived from the assumptions: that it is possible to neglect the transients in the water fluxes [in the sense clarified in Iverson, 2000]; that topographic gradients dominate the hydrologic response; that hydraulic conductivity strongly decreases with depth in the soil, and, not independently, that runoff occurs mostly owing to saturation excess. 

This last assumption, in turn, is  based upon the results of a long series of experiments from the late seventies on by American geomorfologists (Dunne, Black, Dietrich, Montgomery, Torres), and was supported by many others (among these: Moore, Grayson, Sivapalan, Wood). 

These above studies and research activities changed the belief spread by Horton that runoff was mostly due to a infiltration excess mechanism. Developing hydrological models based on saturation excess ideas (which involved further simplification) originated a series of models among which the already cited TOPMODEL [Beven and Kirkby,1979; Sivapalan et al, 1991; Franchini et al, 1996] is the most successful product in the rainfall-runoff area and SHALSTAB in landslide mapping. 

 There are many aspects that could be improved with respect to these modeling strategies. 

First of all:  in characterizing  the subsurface flow field more in terms of total head, even if in simplified form as in Iverson [2000], than in terms of the topographic gradient, as a first step toward the integration of the three dimensional Richards equation."

This step was implemented by the master thesis of Davide Tamanini [2003] that made GEOtop able to simulate transient subsurface flow, and both saturation excess and infiltration excess runoff.  A first parameterization of the soil water retention curves was also implemented in the model. It is this code that was used in the first journal papers on GEOtop (Zanotti et al., 2004, Rigon et al., 2006, Bertoldi et al., 2006). Upon this code was based the work by Silvia Simoni, helped by Fabrizio Zanotti, which produced the GEOtop-SF postprocessor that was able to estimate statistics of the stability of a hillslope. This work was realised to complete Simoni Ph.D. thesis  and Simoni et al., [2008]. 

In GEOtop 0.875 the integration of Richards equation followed a custom numerical scheme that was exceedingly complicate and non standard. Moreover, the integration scheme was not fully 3D, but could have been defined 2D + 1D, where "2D" stands for the lateral flow, obtained by using the Darcy Buckingham law, and 1D was the resolution of a one dimensional Richards equation. Despite these limitations, we could obtain reasonable reproduction of soil moisture distributions,  good discharges at the outlet of basins, excellent reproduction of summer soil temperatures, and what we considered a good reproduction of turbulent heat and evapotranspiration exchanges. 

GEOtop 0.9375 and subsequent versions till the first public release

(mainly financed by Projects with Servizio geologico PAT, progetto MORFEO by ASI, and EU IRASMOS and  AQUATERRA projects)

The new development started with in mind that we had sooner or later to switch to a version of GEOtop with a full 3D integration of Richards equation. Ex-post good results in our simulations for validating the code were  not enough to really cope with mainstream literature. 

However, the first new improvement of GEOtop was in the direction to include a multiple layer  modeling of snow and a first core of the freezing soil subroutines.  This task was mainly accomplished during the Ph.S thesis of Stefano Endrizzi [2007], and greatly improved in his subsequent work at Saskatoon, working with Phil Marsh and Bill Quinton, and recently at Zurich University collaborating with  Stephan Gruber. 

Why complicating even more an already complex model ?  Moreover, why getting a new snow model, if the Utah energy balance seemed to work fine, as written in Zanotti et al., 2004?

The rational behind this choice was essentially that the snow water equivalent was not enough for comparing snow measurement in the field with model outcomes. Clearly snow water equivalent (SWE) was enough just for those willing to cope with total water volume generated after snow melting, but not sufficient for studying and understanding the processes behind snowpack evolution and ablation. Nor even for having a reasonable estimate of soil temperature under the snow, and other interesting prognostics, like snow density. 

However, Stefano's efforts were not limited to snow. He worked hard, for getting a consistent integrator of Richards equation, that he based on a Newton Krilov-method (Kelley, 2003).  Besides he decided to change the surface water flow  equation and numerics, by using the shallow water equation integrated with a robust but explicit method.  This resulted in a very stable and reliable code that constitutes the core of the first public version of GEOtop. In fact Stefano decided to move from the the fraction of geometric series of  1/2 to the integer 1.

The collaboration of Stefano and Matteo Dall'Amico produced also a consistent integrator of the freezing soil moisture, after that Matteo, in his Ph.D thesis disentangled, at least for ourselves,  a lot of thermodynamics (and together, we introduced a simple, and "normal" thermodynamic notation). This work has been documented Dall'Amico Et Al., 2011. 

Various Directions 

Up to version 0.875 version GEOtop was pretty much a home made effort, mainly pursued by Master and Ph.D students of Trento University. However, since then, either because the Ph.D students became doctors and spread around, and because others discovered the potential our work, GEOtop started to became really internationally used. Han Xunjun in China used GEOtop in his data assimilation system implementing an ensemble Kalman filter (in Python). The Lausanne group under the direction of Marc Parlange, within the collaboration of Silvia Simoni, and the direct coding efforts of Thomas Egger implemented a real time version of the model that is giving its results everyday (http://lsir-hydrosys01.epfl.ch:22006/). John Albertson and his group implemented an erosion module to be coupled with GEOtop. In Trento, a version of GEOtop, called GEOtop-EO implemented a prototype of  infrastructure that includes besides the modeling core, a geographical database, with a raster service (built upon RAMADDA) and a visualization system based on JGrass. This was done for the project MORFEO.  At Bolzano, in EURAC, Giacomo Bertoldi and Stefano Dallachiesa, endowed GEOtop with an external (so far) vegetation dynamical model (itself came from elaboration of previous work by Albertson and Montaldo). Worth to mention in this section is also the work of Emanuele Cordano. He dedicated a lot of time in defining the "keyword schemes" that eventually, after some reworking,  become the standard for the I/O of GEOtop. He also started a parallel work on Boussinessq's equation which provided to us a first better idea of what Newton's method of integration is. Moreover, he studied and implemented the first NetCDF O (output) version of GEOtop. Last, but not least, Mountain-eering made of GEOtop the center of its business plan, and supported the completion of the freezing soil module, and is going to develop a new NetCDF input/output system (helped by Emanuele), and the creation of some data assimilation scheme of snow measures. 

Credits to work of the group of Lousanne should be given to have also included in GEOtop the METEO/IO environment which was the way to link the model to a real-time acquisition system.  Stefano Endrizzi himself, when at Saskatoon, discovered the work of Liston and Elder [2006] with MICROMET, and included it in the GEOtop distribution with the permission of the Authors. 

Also other player came  to the game. Arpa Val D'Aosta decided to make of GEOtop the principal tool for doing analysis on snow and permafrost, and it is going to support its improvement and usability. The Karlshrue Institute of Technology in Garmisch-Partenkirchen (and particularly Harald Kunstmann, and coworkers) adopted for simulation for one of their TERENO experiment.  

This, just to mention partial developments, not all of them yet flowed into the main version of the model. All of these efforts, in fact, could not being really unified in a single product. 

First Part

Notes:

^1 This eventually evolved into GEOtop-SF by Silvia Simoni, documented in Simoni et. al [2008]

GEOtop History up to its first public release: Part 1

``As scientists we are intrigued by the possibility of assembling our knowledge into a neat package to show that we do, after all, understand our science and its complex interrelated phenomena.'' (W.M., Kohler, 1969).  

I robbed this statement from Keith Beven's [2000] book: Rainfall-Runoff,  the primer, because it clearly represents one of the motivations that stand behind the development of GEOtop.  

As some of you may know, versioning, at the beginning of GEOtop development followed the geometric series of two. First version was  0.5, second 0.75, third 0.875, and so on.  The message was that such a model solution is never definitive (the version 1), and, besides, I was always intrigued by the Zeno's paradox, and by the versioning system of TeX (asymptotically approaching up Pi) and LaTeX (moving up to number e).

Who follow upfor the main development decided to change the versioning with a more normal sequence. That was the first public edition. Further details of this history can be found in the presentation I gave in Princeton CHAMDA II 2004, and can be found here in a revised version. 

GEOtop 0.5

The development of the first version of GEOtop (0.5) was mostly financed by the Autonomous Province of Trento through the Serraia project, and by the Italian Ministry of Research and University through the Cofin 1999 project.

The very first step was  reading and reading again  the Dara Entekabi review of modeling the whole hydrological cycle [e.g. - Marani and Rigon (eds), 1997]^1, and the development started with  the master thesis of Paolo Verardo, and his subsequent work in 1998. Around a year was spent to implement a decent model for evapotranspiration in a complex terrain environment, according to the Penman-Monteith (PM) scheme (find the formula either in Dara's lecture above, or in my lecture here), and all the necessary incoming radiation treatments. All this work was not dedicated to the PM formula which was obviously trivial to implement, but to find a proper estimation of the radiation, which included the view angle and the shadowing routine.^2

 The  problem of data  regionalization (the only data we had were those coming from traditional hydro-meteorological stations in single points and we did not have many of them) was faced for the first time. 

A part from the geomorphological data that we extract from DEMs (the "sine qua non" basis of all our work), we had to regionalize (make spatial): air-surface temperature (varying  with the elevation of the terrain), net radiation (and eventually by the evaluation of an atmospheric thickness which has to be regionalized too), and wind speed. 

In sequence it was decided to use: kriging  techniques and the hypothesis of adiabatic temperature profile (for air temperature)^3;  Brutsaert [1983] paper results (for atmosphere emissivity)^4,  and constant (or occasionally kriged) wind speed everywhere. This was performed through the use of external programs.

The heat conduction into the ground was parametrized as a linear combination of a sinusoidal function as Entekabi suggested [1997] . That work  was also inspired by the routines  of IPW (Image Processing Workbench) [Frew, 1990]. 

Actually we tried to make IPW work concurrently with the borning GEOtop: but its pervasive scripting base (scripting is good but there is a point after which it makes the code organization unclear), the discontinued support, and ignorance of IPW code internals (and just ignorance), led us to built a new system from the scratch. 

Despite of the approximations introduced, GEOtop 0.5 model worked fairly well in estimating the net longwave and shortwave radiation in any point across a basin and at any hour of the day, and could give also what appeared to us reliable estimates of the potential evapotranspiration on a daily basis. However to obtain the real evapotranspiration was a different question (and, obviously, to validate it, even a different one).  

Marco Pegoretti [1999] added to the evapotranspiration modules a rainfall-runoff model (temporary called GEOMODEL). The approach we had to the problem of rainfall-runoff  was strongly influenced by the work of Rodriguez-Iturbe and Valdes [1979] and Gupta and Waymire [1980],  and we were reluctant to abandon the simplicity of a GIUH-based model in favor of a fully distributed model (that we made later). 

Of the many ideas behind the theory of the GIUH  derives from the observation that the river basin is a complex system (an interplay of hillslopes and channels) but, at least for the forecasting of floods,  simple models work fairly well (leading to the conclusion that dynamics simplify the complexity and wipe out part of the heterogeneity underneath)^5.

The big problem in the GIUH approach however was (and is) that the determination of the effective rainfall, i.e. the correct separation of surface runoff (interpreted as the cause of the flood surge) from subsurface flow (which must be actually treated separately and routed to the channels in a slower way), especially in dependence of storm events of diverse intensity, duration and inter-arrival time. 

A model more or less contemporary to the GIUH is the TOPMODEL by Beven and Kirkby [1979]. It is based on the paradigm that runoff production is due to saturated areas (according to Dunne and Black, 1970). Thus, once one knows which areas are saturated and describes their growing during an event, the problem of the runoff coefficient is almost solved,  and routing of water to an outlet can be accomplished by some simple mechanism (the Muskingum-Cunge model at least in the original TOPMODEL papers).^6

Thus, an idea could have been to merge the best of the two formulations, the GIUH concept with the TOPMODEL. However the hypotheses on which the TOPMODEL has been based, mainly the stationarity of the hillslope subsurface fluxes,  simplifies the life of the modeler, but introduces several limitations, and needs several work-around as described in  Beven et al., [2002] to be applied with success. In fact, when the final goal of modeling,  is not simply the production of a well-fitted flood wave, but for instance the estimation of local soil moisture contents, the TOPMODEL fails to be accurate enough [e.g., Grayson and Wilson, 2002]. 

Due to its limitations, the TOPMODEL's parameters  become "effective'' parameters, and lose their original physical significance (for instance, the hydraulic conductivity cannot be validated by local field measurements), and need to be "calibrated" ex-post. Other limitations will be mentioned below when talking about the GEOTP 0.875 version. In any case, the TOPMODEL concept has been demonstrated to be a good tool to model floods in small-to -medium catchments, and has been considered the reference hydrological model for many of the researchers during the '90s. The TOPMODEL's ability to forecast floods derives also from its account (trivial indeed) of the topology and geometry of small- catchment flow paths: it was shown, in fact, that in small watersheds (up to at least 1000 square kilometers), hillslope residence time dominates the characteristic time of flood formation and that topology and geometry of river basins are sufficient with very minimalist dynamics to explain the shape of floods [e.g. Rinaldo et al, 1991; Rigon et al, 1996, Rinaldo et al., 1995, D'Odorico, 1996; D'Odorico and Rigon, 2003]. 

Upon all the above arguments, it was decided  to build a completely new subsurface and surface model, still driven by gravity (i.e. by topographic slope as the TOPMODEL and not by the total hydraulic head) but, as a first approximation to the final wishes of having a better physically-based theory, introducing the buffer to cope with infiltration into the vadose zone.  Subsurface flow was produced only by the saturated layer (including the capillary fringe), if present, and lateral surface runoff was routed as a kinematic wave (and through Manning/Gauckler-Strikler equation for velocities). 

In doing this, it was also tried  a better characterization of flow paths, with reference to the bedrock, instead of to the surface topography [see McDonnell et al., 1996]: this could be done by measuring soil depth or interpolating it for instance as in [Heimsath et al, 1997 or Roering et al, 1999; please see the overlooked  Bertoldi et al, 2006 for the details]. 

In this separation of surface and subsurface fluxes, GEOtop 0.5 was similar to the grid bases THALES [Grayson et al., 1994a,1994b] or the more recent NEWTHALES. 

At first, the version of GEOtop by Verardo-Pregoretti-Rigon (GEOTOP 0.5) could work without an explicit channel routing by assigning a locally variable roughness and hydraulic radius; if channels were determined by accurate topographic analysis, they could be explicitly treated. 

In this case, channels routing was performed by a GIUH theory as in Rinaldo et al [1995], where channel celerity and hydrodynamic dispersion were  considered spatially uniform and constant in time. 

Instead of the effective rainfall, the spatially and temporally distributed input to channels was produced by GEOtop, i.e. the GEOMODEL produced patterns of spatially distributed soil moisture, and these patterns were used to reduce the potential evapotranspiration to its real counterpart as described in Bertoldi et al., [2002].

Second Part

Notes

^1 - MIT's group, on the other side had a long tradition in this direction of modeling that originated from Pete Eagleson work in late seventies and eighties. Dara's talk in fact inherit a lot from that work. Raphael Bras, Dara Entekabi, Valeriy Ivanov, Enrique Vivoni and others themselves  implemented a model similar, in concepts, to GEOtop, tRibs. 

^2 Today GEOtop mostly uses Xavier Corripio's schemes

^3 We still use kriging, but also Glen Liston's Micromet [Liston and Elder, 2006] and MeteoIO 

^4 Various possibilities are present now, and they derive mainly from Stefano Endrizzi Ph.D. thesis.

^5 But this is to many respect debatable, since this statement refers to the closure of the basin, and from this going back to forecasting the internal distribution of discharge is impossible. Keith Beven wrote a lot on this. 

^6 Research subsequent to TOPMODEL, including ours (e.g. Lanni et al., 2011, 2012 for a review of problems and literature, and Cordano and Rigon, 2008 for a top-down derivation of TOPMODEL related equation from Richards' one) , clarified many of the limitation behind TOPMODEL approach. 

Highest Cited WRR papers ever

I had from WRR editor, Prof. Praveen Kumar the list of highest cited Water Resources Research Papers, one of the best  Journals in the Hydrological field. I asked to have this ranking in order to have another way to select and and papers to my collection of historic and benchmark papers for Hydrology.
I was not actually expecting an answer from Praveen but it cames (and I realized later that this record is easy to obtain having a WEB of SCIENCE and SCOPUS account) Results were stored in a file that you can retrieve here.

Being the most cited does not necessarily means being the best papers. Some very good papers could have been published very recently, and still not having enough citations to rank among the first ones. Some very good  papers could be too specialistic to be read by most of us fluency.  Besides some topic are of more broad interest than others, and this increase their citations' rates.  However, after all of these disclaimers, here there are the papers, some statistics, and comments. The paper grouped, for broad sub-fields, are about:

calibration and uncertainty  8

evapotranspiration and ecohydrology 6

experimental hydrology 2

geochemistry 5

geomorphology 22

groundwater 78

infiltration and vadose zone 29

other 10

precipitation 5

mathematical ans statistical 13

surface water 23

The dominance of groundwater papers is apparent, but this is probably a inheritance of the lated eighties and nineties. While browsing the recent papers there is more equilibrium between the fields covered.

Grouped for year of publication, the are distributed as shown below. 

The figures shows that they cover all the decades of publication of WRR from 1965 to 2003.

Grouped per decades these 201 paper are

1960 16

1970  36

1980  75

1990  68

2000  6 

So, the 20 higher cited papers are (the other can be seen in the xls file):

- MUALEM, Y, NEW MODEL FOR PREDICTING HYDRAULIC CONDUCTIVITY OF UNSATURATED POROUS-MEDIA, 1976, cit: 1818

- TOPP, GC, DAVIS, JL, ANNAN, AP, ELECTROMAGNETIC DETERMINATION OF SOIL-WATER CONTENT - MEASUREMENTS IN COAXIAL TRANSMISSION-LINES, 1980, cit: 1800

- BEVEN, K, GERMANN, P, MACROPORES AND WATER-FLOW IN SOILS, 1982, cit:1058

- CLAPP, RB, HORNBERGER, GM, EMPIRICAL EQUATIONS FOR SOME SOIL HYDRAULIC-PROPERTIES,1978, cit: 1034

- GELHAR, LW, AXNESS, CL, 3-DIMENSIONAL STOCHASTIC-ANALYSIS OF MACRODISPERSION IN AQUIFERS, 1983, cit: 986

- RITCHIE, JT, MODEL FOR PREDICTING EVAPORATION FROM A ROW CROP WITH INCOMPLETE COVER, 1972,cit: 931

- DUAN, QY, SOROOSHIAN, S, GUPTA, HV EFFECTIVE AND EFFICIENT GLOBAL OPTIMIZATION FOR CONCEPTUAL RAINFALL-RUNOFF MODELS, 1992, cit: 776

- SUDICKY, EA, A NATURAL GRADIENT EXPERIMENT ON SOLUTE TRANSPORT IN A SAND AQUIFER - SPATIAL VARIABILITY OF HYDRAULIC CONDUCTIVITY AND ITS ROLE IN THE DISPERSION PROCESS,1986, cit:645

- HIRSCH, RM, SLACK, JR, SMITH, RA, TECHNIQUES OF TREND ANALYSIS FOR MONTHLY WATER-QUALITY DATA, 1982, cit:577

- Legates,  GJ, McCabe, DR, Evaluating the use of goodness-of-fit measures in hydrologic and hydroclimatic model validation, 1999, cit:573

- CELIA, MA, BOULOUTAS, ET, ZARBA, RL, A GENERAL MASS-CONSERVATIVE NUMERICAL-SOLUTION FOR THE UNSATURATED FLOW EQUATION, 1990, cit:564

- GELHAR, LW, WELTY, C, REHFELDT, KR, A CRITICAL-REVIEW OF DATA ON FIELD-SCALE DISPERSION IN AQUIFERS, 1992, cit:554

- YEH, WWG, REVIEW OF PARAMETER-IDENTIFICATION PROCEDURES IN GROUNDWATER HYDROLOGY - THE INVERSE PROBLEM, 1986, cit: 546

- COSBY, BJ, HORNBERGER, GM, GALLOWAY, JN, WRIGHT, RF, MODELING THE EFFECTS OF ACID DEPOSITION - ASSESSMENT OF A LUMPED PARAMETER MODEL OF SOIL-WATER AND STREAMWATER CHEMISTRY, 1985, cit: 530

- FREEZE, RA, STOCHASTIC-CONCEPTUAL ANALYSIS OF ONE-DIMENSIONAL GROUNDWATER FLOW IN NONUNIFORM HOMOGENEOUS MEDIA, 1975, cit: 528

- JACKSON, RD, IDSO, SB, REGINATO, RJ, PINTER, PJ, CANOPY TEMPERATURE AS A CROP WATER-STRESS INDICATOR, 1981, cit:506

- Tarboton, A new method for the determination of flow directions and upslope areas in grid digital elevation models, DG, 1997, cit: 477

- CARSEL, RF, PARRISH, RS, DEVELOPING JOINT PROBABILITY-DISTRIBUTIONS OF SOIL-WATER RETENTION CHARACTERISTICS, 1988, cit: 467

- COSBY, BJ, HORNBERGER, GM, CLAPP, RB, GINN, TR, A STATISTICAL EXPLORATION OF THE RELATIONSHIPS OF SOIL-MOISTURE CHARACTERISTICS TO THE PHYSICAL-PROPERTIES OF SOILS, 1984, cit: 451

RICHARDSON, CW, STOCHASTIC SIMULATION OF DAILY PRECIPITATION, TEMPERATURE, AND SOLAR-RADIATION, 1981, cit: 440

Reading the list of these paper is apparent that the first ones belong to a interdisciplinary area of interest that cover hydrology, soil science, and, at least, agricolture.  The inverse modelling is also a pretty relevant topic, while surface hydrology is not present (except for Tarboton's paper, which however is on DEM treatment): which is a surprise to me!

The mean number of citations is around 300. So, a high cited paper, at least for WRR should have around 200 citations (unfortunately, my papers are still away from this).  A summary of the statistics is:

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    

  184.0   208.0   241.0   302.9   318.0  1818.0    

The ten most recent papers among the most cited are:

- Houser, PR, Shuttleworth, WJ, Famiglietti, JS, Gupta, HV, Syed, KH, Goodrich, DC, Integration of soil moisture remote sensing and hydrologic modeling using data assimilation,  1998, cit: 185

- Legates, DR, McCabe, GJ, Evaluating the use of goodness-of-fit measures in hydrologic and hydroclimatic model validation,   1999, cit: 573

- Nepf, HM, Drag, turbulence, and diffusion in flow through emergent vegetation, 1999, cit: 239

- Western, AW, Grayson, RB, Bloschl, G, Willgoose, GR, McMahon, Observed spatial organization of soil moisture and its relation to terrain indices  TA 1999,  cit: 209

- Rodriguez-Iturbe, I, Ecohydrology: A hydrologic perspective of climate-soil-vegetation dynamics,   2000, cit: 213

- Iverson, RM, Landslide triggering by rain infiltration,  2000, cit:207

-McArthur, JM, Ravenscroft, P, Safiulla, S, Thirlwall,  MF, Arsenic in groundwater: Testing pollution mechanisms for sedimentary aquifers in Bangladesh  2001, cit:  279

-Zhang, L, Dawes, WR, Walker, GR, Response of mean annual evapotranspiration to vegetation changes at catchment scale,  2001, cit:  274

-Zhang, XB, Harvey, KD, Hogg, WD, Yuzyk, TR, Trends in Canadian streamflow, 2001, cit: 201

-  Vrugt, JA, Gupta, HV, Bouten, W, Sorooshian, S 2003, A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters

Neither between these appears a paper on surface waters. However, it is interesting to note that the topics covered are different from those of the highest cited papers. Meaning probably that each decade has its focus. 

Yearly citations rate show that the first group of papers are really outliers with respect to the others. However the mean number of citations per year is around 12, and if your papers has more that 5 citations per years, there is some hope that sometimes in the future it could enter in this rank.

 Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    

  4.244   7.960  10.420  12.300  14.190  56.250   

The ten papers with the highest annual average citations' rate are:

- TOPP, GC, DAVIS, JL, ANNAN, AP, ELECTROMAGNETIC DETERMINATION OF SOIL-WATER CONTENT - MEASUREMENTS IN COAXIAL TRANSMISSION-LINES,  1980, cit: 1800, citation rate: 56.25,

-  MUALEM, Y, NEW MODEL FOR PREDICTING HYDRAULIC CONDUCTIVITY OF UNSATURATED POROUS-MEDIA, 1976, citation rate: 50.5

- DR, McCabe, GJ, Evaluating the use of goodness-of-fit measures in hydrologic and hydroclimatic model validation Legates,  1999,cit: 1800,cit: , citation rate: 44.01

- DUAN, QY, SOROOSHIAN, S, GUPTA, V, EFFECTIVE AND EFFICIENT GLOBAL OPTIMIZATION FOR CONCEPTUAL RAINFALL-RUNOFF MODELS,  1992, cit: 776, citation rate:38.8

- BEVEN, K, GERMANN, P, MACROPORES AND WATER-FLOW IN SOILS,  1982, cit: 1058, citation rate: 35.3

- GELHAR, LW, AXNESS, CL , 3-DIMENSIONAL STOCHASTIC-ANALYSIS OF MACRODISPERSION IN AQUIFERS, 1983, cit: 986, citation rate: 34

- Tarboton, DG, A new method for the determination of flow directions and upslope areas in grid digital elevation models, 1997, cit: 477, citation rate: 30.4

- CLAPP, RB, HORNBERGER, GM, EMPIRICAL EQUATIONS FOR SOME SOIL HYDRAULIC-PROPERTIES, 1978 cit: 1034, citation rate: 24

- Gupta, HV, Sorooshian, S, Yapo, PO , Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information, 1998, cit. 402, citation rate: 23.3

- GELHAR, LW, WELTY, C, REHFELDT, KR, A CRITICAL-REVIEW OF DATA ON FIELD-SCALE DISPERSION IN AQUIFERS,  1992, cit: 554, citations rate: 19.2

Finally, the authors who wrote these papers are 337. Most of them appear once. Those who compare more than two times are: 

12           ABRIOLA, LM    3

12           BEVEN, K    3

12           CELIA, MA    3

12           COSBY, BJ    3

12           DAGAN, G    3

12           DIETRICH, WE    3

12           GORELICK, SM    3

12           GRAYSON, RB    3

12            IDSO, SB    3

12           KITANIDIS, PK    3

12           MCMAHON, TA    3

12           NIELSEN, DR    3

12           PAPADOPU.IS    3

12           SUDICKY, EA    3

12           VANGENUCHTEN, MT    3

12           WITHERSPOON, PA    3

12           WRIGHT, RF    3

7            FREEZE, RA    4

7            MANDELBROT, BB    4

7            RODRIGUEZ-ITURBE, I    4

7            SOROOSHIAN, S    4

3            GUPTA, HV    5

3            GUTJAHR, AL    5

3            HORNBERGER, GM    5

3            NEUMAN, SP    5

3            MONTGOMERY, DR    6

2            WALLIS, JR    6

1            GELHAR, LW   12

I must say that I know most of the Authors, many of them personally, since their work inspired mine, and just by googling their names it is clear that some of them gave some exceptional contribution even in other journals. So despite the many disclaimer citations say something. Someone of my hydrological heroes is missing: but doing benchmark papers is probably is slightly a different thing than writing a highly cited paper. 

Simulated effect of soil depth and bedrock topography on near-surface hydrologic response and shallow landslide triggering by Lanni, McDonnell, Hopp and Rigon

We have just submitted a paper  that, looked from a certain perspective, can be thought on the evolution of soil moisture content in presence of variable soil depth. In fact, variable soil depth, jointly with the fact that increases in hydraulic conductivity follows the increase in water pressure, and that hydraulic conductivity itself can often be considered negligible when the soil is unsaturated, delays the formation of a widespread water table in a hillslope. Therefore the effective contributing area above a point of a catchment is usually  not the total upstream area but just a part of it.  This obviously has consequences on the propagation of instabilities along a slope.

The Abstract of the paper:

This paper explores the effect of hillslope hydrological behavior on slope stability in the context of transient subsurface saturation development and landslide triggering. We perform a series of virtual experiments to address how subsurface topography affects the location and spatial pattern of slip surface development and pore pressure dynamics. We use a 3D Darcy-Richards equation solver (Hydrus 3-D) combined with a cellular automata slope stability model to simulate the spatial propagation of the destabilized area. Our results showed that the soil-bedrock interface and in particular, bedrock depressions, played a key role on pore pressure dynamics, acting as an impedance for the downslope drainage of perched water. Filling and spilling of depressions in the bedrock surface microtopography induced localized zones of increased pressure head such that the development of pore-pressure fields—not predictable by surface topography—lead to rapid landslide propagation. Our work suggests that landslide models should consider the subsurface topography in order to include a connectivity component in the mathematical description of hydrological processes operating at the hillslope scale. Quantitative soil- landscape methods combined with physically-based landslide models may improve our ability to predict shallow landslide potential. 

Among the original stuff presented in this paper, there is a tentativ to move away from the concept of instable points to the one of instable regions.  The traditional (simplified) approach based on the infinite slope stability (Ning Lu is discussing it here) is in fact used in modern GIS based program like SHALSTAB (here on ARCGIS or here on opensource GIS) or SINMAP to determine the instabilities of single points, which we try here to generalize a little. 

The paper draft is available here, if you are interested in. A related discussion can also be found in the previous papers by Lanni et Al., 2011 and in the draft by Cordano and Rigon, 2012.

Solving the Boussinesq's (groundwater) equation by Cordano and Rigon

Boussinesq's equation describes the motion of a free aquifer under the Dupuit hypothesis, or, if you prefer, the motion of the surface of  the water table. This paper just submitted for reviewing treats its numerical solution using a new method derived from previous work of Brugnano and Casulli (2008) and Casulli (2009). Let's talk the abstract:


This work presents with a new conservative finite-volume numerical solution for the two-dimensional groundwater flow (Boussinesq) equation, which can be used for investigations of hillslope subsurface flow processes and simulations of catchment hydrology. The Boussinesq Equation is integrated for each grid element and can take account of the local variability of topography and soil properties within the grid elements. The numerical method allows for wetting and drying of the water-table, which has been successfully simulated.
The stability and convergence of the method is shown to be guaranteed apriori by the properties of the solver itself. 
The numerics are validated against some approximate analytical solutions, and  compared to another numerical solver of the Boussinesq equation. Finally, the solver capabilities are further explored with simulations of the Panola experimental hillslope where  the bedrock topography, which is accurately known, causes complex wetting and drying patterns;  in this situation the importance of a two-dimensional description of subsurface flows to obtain properly simulated discharges becomes clear.

What is relevant in our paper, among other thing, is:

• the cleanliness of the integration method (that makes the numerics fast)
• the ability to deal with wetting and drying zones
• the accurate  treatment of boundary conditions (which could, in theory, break the conditions of integrability a-priori)

The first appendix can be used as an introduction to the Newton's method for integration of non linear equations.

As usual, the code we provide is released with a GPL v3 license, and available for download, at the moment, in the GEOtop site. Emanuele Cordano wrote also some ancillary R code which plots the analytical solutions of the equation in some simplified setting described in the paper (under Packages - boussinesq in the CRAN site).

The model was used to create the reference conditions in the paper by Lanni et Al., 2011 [pdf]. The draft of the paper for curious can be downloaded from here. The final version can be retrieved through this post.