since 89, I guess. I had very little trouble with them, and could dedicate the time that others were spending to fix their motherboards, cards, software and hardware to do hydrology, or just enjoy life.
He is narating here:
And talking:
What he accomplished, in the word of Anton Ego:
Yes, I think I do. After reading a lot of overheated puffery about your new cook, you know what I'm craving? A little perspective. That's it. I'd like some fresh, clear, well seasoned perspective. Can you suggest a good wine to go with that?
R.I.P.
My reflections and notes about hydrology and being a hydrologist in academia. The daily evolution of my work. Especially for my students, but also for anyone with the patience to read them.
Thursday, October 6, 2011
Sunday, October 2, 2011
Presentation about landslides triggering given at IWL2
I was trying to convey the idea that landslide triggering is tricky and complex. But simple settings have a simple behavior, especially when we look at statistics. Nevertheless complexity is behind the curtain. The right one, I mean, that depends on vegetation distribution, soils use, heterogenous soil depth, and the fact that landslides are a very local phenomenon.
Here you will find the presentation. Hopefully a paper will come out from it.
Here you will find the presentation. Hopefully a paper will come out from it.
Thursday, September 8, 2011
On the relative role of upslope and downslope topography for describing water flowpath and storage dynamics: a theoretical analysis
Hydrological studies have shown, for many years now, that catchments organize themselves. The signals that go into a basin (in our case rainfall) look different to those that come out of it (i.e.river discharge), due to hydrodynamics, flow path geometry, and topology effects (e.g. Rinaldo et al., 1991, 1995; D’Odorico and Rigon, 2003; Botter and Rinaldo, 2003). However, tracer campaigns (e.g.,isotope studies) and their interpretation have shown that the whole dynamic is more complex than first naively expected (e.g., Soulsby et al., 2009), and that “the total catchment storage is likely to be much greater than the dynamic storage inferred by hydrometric data alone, and needs to be invoked to explain some nonlinearity in rainfall-runoff responses in relation to antecedent conditions” (Birkel et al., 2011). For instance, in many catchment settings, dynamically expanding and contracting riparian saturation zones can play a major role in producing the real (proper) travel time of water (Fiori and Russo, 2008, Russo and Fiori, 2008, Tetzlaff et al., 2007). At the same time, the small-scale topographic variations in the bedrock and the filling and spilling of water into depressions and over the bedrock micro-topography (Tromp-van Meerveld and McDonnell, 2006; Hopp and McDonnell, 2009) can control the subsurface flow routing. Several researchers have also reported the role played by geological landscape features. The lack of confining layers in jointed and fractured bedrock and the local variations in its hydraulic conductivity may strongly influence water storage dynamics in the overlying soil layer (Pierson, 1977; Wilson and Dietrich, 1987; Montgomery et al., 2002).
The overall model of the spatial structure that leads to flow and storage organization (something that is crucial to prioritizing what to do and where to do it in river catchments) brings, therefore, to a system of reservoirs which, uphill, can be defined on the basis of bedrock geometry and permeability, and, close to the riparian zones, on the basis of various storage areas that interact dynamically with the stream network.
In this paper, we analyze the case where topography (i.e., lateral flow) is recognized as the predominant control for subsurface flow mechanisms. This is generally the case in mountain regions with moderate to steep topography (Tetzlaff et al., 2009a) where a shallow (highly conductive) soil layer lies on an impervious bedrock substrate (Western et al., 2004). Under these conditions, the availability of storage for water is limited almost exclusively to soil drainable porosity (e.g., Hilberts et al., 2005; Cordano and Rigon, 2008), complex riparian dynamics are less important, and can, as a first approximation, be neglected. Moreover, elevation potential dominates total hydraulic potential, and thus topography represents a good proxy (in theory) for water flow paths (e.g., Seibert et al., 2007; McNamara et al., 2005) and spatial patterns of soil moisture (e.g., Schmidt and Persson, 2003).
The fact that elevation potential dominates total hydraulic potential led to assume that local topography could represent a good way for describing hydrological processes at the hillslope/catchment scale.
Upon this belief, topographic indices have been developed and used as proxies to represent the role of topography on subsurface flow paths and soil-water storage dynamics. However, over the years these indices proved to be insufficient to explain an increasing number of case studies (e.g. Burt and Butcher, 1986; Western et al., 1999; Seibert et al., 1997) and brought to several reconsiderations of the matter, of which we briefly report.
The paper is available on Hydrological Processes Preview, and is the same paper presented in a previous post when submitted.
References
Birkel C, Tetzlaff D, Dunn SM, Soulsby C. 2011. Using time domain and geographic source tracers to conceptualise streamflow generation processes in lumped rainfall-runoff models. Water Resources Research. 47. W02515. Doi:10.1029/2010WR009547.
Botter, G, Rinaldo, A. 2003. Scale effect on geomorphologic and kinematic dispersion. Water Resour. Res. 39(10): 1286. Doi:10.1029/2003WR002154.
Burt TP, Butcher DP. 1985. Topographic controls of soil moisture distributions. J. Soil Sci. 36: 469 – 486.
Cordano E, Rigon R. 2008. A perturbative view on the subsurface water pressure response at hillslope scale, Water Resour. Res. 44. W05407. Doi:10.1029/2006WR005740.
D’Odorico P, Rigon R. 2003. Hillslope and channel contributions to the hydrologic response, Water Resour. Res. 39(5): 1113–1121. Doi:10.1029/2002WR001708.
Fiori A, Russo D. 2008. Travel Time Distribution in a Hillslope: Insight from Numerical Simulations. Water Resour. Res. 44. W12426. Doi:10.1029/2008WR007135.
Hilberts A, Troch P, Paniconi C. 2005. Storage-dependent drainable porosity for complex hillslopes. Water Resour. Res. 41. W06001. Doi:10.1029/2004WR003725.
Hopp L, McDonnell JJ. 2009. Connectivity at the hillslope scale: Identifying interactions between storm size, bedrock permeability, slope angle and soil depth. Journal of Hydrology 376(3-4): 378-391.DOI: 10.1016/j.jhydrol.2009.07.047
McNamara P, Chandler D, Seyfried M, Achet S. 2005. Soil moisture states, lateral flow, and streamflow generation in a semi-arid, snowmelt-driven catchmen. Hydrol. Process. 19: 4023– 4038.
Montgomery DR, Dietrich WE, Heffner JT. 2002. Piezometric response in shallow bedrock at CB1: Implications for runoff generation and landsliding. Water Resour. Res. 38(12): 1274. Doi:10.1029/2002WR001429.
Pierson TC. 1977. Factors controlling debris-flow initiation on forested hillslopes in the Oregon Coast Range, Ph.D. dissertation, 166 pp., Univ. of Wash., Seattle.
Rinaldo A, Marani A, Rigon R. 1991. Geomorphological dispersion. Water Resour. Res 27(4): 513–525.
Rinaldo A, Vogel GK, Rigon R, Rodriguez-Iturbe I. 1995. Can one gauge the shape of a basin?. Water Resour. Res. 31(4):1119–1127.
Russo D, Fiori A. 2008. Equivalent Vadose Zone Steady-State Flow: An Assessment its Capability to Predict Transport in a Realistic Combined Vadose Zone - Groundwater Flow System. Water Resour. Res. 44. W09436. Doi:10.1029/ 2007WR006170.
Seibert J, Bishop KH, Nyberg L. 1997. A test of TOPMODEL's ability to predict spatially distributed groundwater levels. Hydrological Processes 11: 1131–1144.
Seibert J, McGlynn BL. 2007. A new triangular multiple flow-direction algorithm for computing upslope areas from gridded digital elevation models. Water Resour. Res. 43. W04501, Doi:10.1029/2006WR005128.
Schmidt F, Persson A. 2003. Comparison of DEM Data Capture and Topographic Wetness Indices. Precision Agricolture 4: 179-192.
Soulsby C, Tetzlaff D, Hrachowitz M. 2009. Tracers and transit times: Windows for viewing catchment scale storage?. Hydrological Processes 23: 3503-3507.
Tetzlaff D, Soulsby C, Bacon PJ, Youngson AF, Gibbins CN, Malcolm IA. 2007. Connectivity between landscapes and riverscapes—A unifying theme in integrating hydrology and ecology in catchment science?. Hydrological Processes 21: 1385–1389
Tetzlaff D, Seibert J, McGuire KJ, Laudon H, Burns DA, Dunn SM, Soulsby C. 2009a. How does landscape structure influence catchment transit times across different geomorphic provinces?. Hydrological Processes 23: 945 – 953.
Tromp-van Meerveld HJ, McDonnell JJ. 2006. Threshold relations in subsurface stormflow: 2. The fill and spill hypothesis. Water Resour. Res. 42(2). DOI: 10.1029/2004WR003800.
Western AW, Grayson RB, Blöschl G, Willgoose GR, McMahon TA. 1999. Observed spatial organization of soil moisture and its relation to terrain indices. Water Resour. Res. 35 (3). DOI: 10.1029/1998WR900065.
Western AW, Zhou SL, Grayson RB, McMahon TA, Bloschl G, Wilson DJ, 2004. Spatial correlation of soil moisture in small catchments and its relationship to dominant spatial hydrological processes. Journal of Hydrology 286 (1-4): 113-134. Doi: 10.1016/j.jhydrol.2003.09.014.
Wilson CJ, Dietrich WE. 1987. The contribution of bedrock groundwater flow to storm runoff and high pore pressure development in hollows, in Erosion and Sedimentation in the Pacific Rim, IAHS Publ., vol. 165, edited by R. L. Beschta et al.: 49–60, Int. Assoc. of Hydrol Sci., Wallingford, UK
The overall model of the spatial structure that leads to flow and storage organization (something that is crucial to prioritizing what to do and where to do it in river catchments) brings, therefore, to a system of reservoirs which, uphill, can be defined on the basis of bedrock geometry and permeability, and, close to the riparian zones, on the basis of various storage areas that interact dynamically with the stream network.
In this paper, we analyze the case where topography (i.e., lateral flow) is recognized as the predominant control for subsurface flow mechanisms. This is generally the case in mountain regions with moderate to steep topography (Tetzlaff et al., 2009a) where a shallow (highly conductive) soil layer lies on an impervious bedrock substrate (Western et al., 2004). Under these conditions, the availability of storage for water is limited almost exclusively to soil drainable porosity (e.g., Hilberts et al., 2005; Cordano and Rigon, 2008), complex riparian dynamics are less important, and can, as a first approximation, be neglected. Moreover, elevation potential dominates total hydraulic potential, and thus topography represents a good proxy (in theory) for water flow paths (e.g., Seibert et al., 2007; McNamara et al., 2005) and spatial patterns of soil moisture (e.g., Schmidt and Persson, 2003).
The fact that elevation potential dominates total hydraulic potential led to assume that local topography could represent a good way for describing hydrological processes at the hillslope/catchment scale.
Upon this belief, topographic indices have been developed and used as proxies to represent the role of topography on subsurface flow paths and soil-water storage dynamics. However, over the years these indices proved to be insufficient to explain an increasing number of case studies (e.g. Burt and Butcher, 1986; Western et al., 1999; Seibert et al., 1997) and brought to several reconsiderations of the matter, of which we briefly report.
The paper is available on Hydrological Processes Preview, and is the same paper presented in a previous post when submitted.
References
Birkel C, Tetzlaff D, Dunn SM, Soulsby C. 2011. Using time domain and geographic source tracers to conceptualise streamflow generation processes in lumped rainfall-runoff models. Water Resources Research. 47. W02515. Doi:10.1029/2010WR009547.
Botter, G, Rinaldo, A. 2003. Scale effect on geomorphologic and kinematic dispersion. Water Resour. Res. 39(10): 1286. Doi:10.1029/2003WR002154.
Burt TP, Butcher DP. 1985. Topographic controls of soil moisture distributions. J. Soil Sci. 36: 469 – 486.
Cordano E, Rigon R. 2008. A perturbative view on the subsurface water pressure response at hillslope scale, Water Resour. Res. 44. W05407. Doi:10.1029/2006WR005740.
D’Odorico P, Rigon R. 2003. Hillslope and channel contributions to the hydrologic response, Water Resour. Res. 39(5): 1113–1121. Doi:10.1029/2002WR001708.
Fiori A, Russo D. 2008. Travel Time Distribution in a Hillslope: Insight from Numerical Simulations. Water Resour. Res. 44. W12426. Doi:10.1029/2008WR007135.
Hilberts A, Troch P, Paniconi C. 2005. Storage-dependent drainable porosity for complex hillslopes. Water Resour. Res. 41. W06001. Doi:10.1029/2004WR003725.
Hopp L, McDonnell JJ. 2009. Connectivity at the hillslope scale: Identifying interactions between storm size, bedrock permeability, slope angle and soil depth. Journal of Hydrology 376(3-4): 378-391.DOI: 10.1016/j.jhydrol.2009.07.047
McNamara P, Chandler D, Seyfried M, Achet S. 2005. Soil moisture states, lateral flow, and streamflow generation in a semi-arid, snowmelt-driven catchmen. Hydrol. Process. 19: 4023– 4038.
Montgomery DR, Dietrich WE, Heffner JT. 2002. Piezometric response in shallow bedrock at CB1: Implications for runoff generation and landsliding. Water Resour. Res. 38(12): 1274. Doi:10.1029/2002WR001429.
Pierson TC. 1977. Factors controlling debris-flow initiation on forested hillslopes in the Oregon Coast Range, Ph.D. dissertation, 166 pp., Univ. of Wash., Seattle.
Rinaldo A, Marani A, Rigon R. 1991. Geomorphological dispersion. Water Resour. Res 27(4): 513–525.
Rinaldo A, Vogel GK, Rigon R, Rodriguez-Iturbe I. 1995. Can one gauge the shape of a basin?. Water Resour. Res. 31(4):1119–1127.
Russo D, Fiori A. 2008. Equivalent Vadose Zone Steady-State Flow: An Assessment its Capability to Predict Transport in a Realistic Combined Vadose Zone - Groundwater Flow System. Water Resour. Res. 44. W09436. Doi:10.1029/ 2007WR006170.
Seibert J, Bishop KH, Nyberg L. 1997. A test of TOPMODEL's ability to predict spatially distributed groundwater levels. Hydrological Processes 11: 1131–1144.
Seibert J, McGlynn BL. 2007. A new triangular multiple flow-direction algorithm for computing upslope areas from gridded digital elevation models. Water Resour. Res. 43. W04501, Doi:10.1029/2006WR005128.
Schmidt F, Persson A. 2003. Comparison of DEM Data Capture and Topographic Wetness Indices. Precision Agricolture 4: 179-192.
Soulsby C, Tetzlaff D, Hrachowitz M. 2009. Tracers and transit times: Windows for viewing catchment scale storage?. Hydrological Processes 23: 3503-3507.
Tetzlaff D, Soulsby C, Bacon PJ, Youngson AF, Gibbins CN, Malcolm IA. 2007. Connectivity between landscapes and riverscapes—A unifying theme in integrating hydrology and ecology in catchment science?. Hydrological Processes 21: 1385–1389
Tetzlaff D, Seibert J, McGuire KJ, Laudon H, Burns DA, Dunn SM, Soulsby C. 2009a. How does landscape structure influence catchment transit times across different geomorphic provinces?. Hydrological Processes 23: 945 – 953.
Tromp-van Meerveld HJ, McDonnell JJ. 2006. Threshold relations in subsurface stormflow: 2. The fill and spill hypothesis. Water Resour. Res. 42(2). DOI: 10.1029/2004WR003800.
Western AW, Grayson RB, Blöschl G, Willgoose GR, McMahon TA. 1999. Observed spatial organization of soil moisture and its relation to terrain indices. Water Resour. Res. 35 (3). DOI: 10.1029/1998WR900065.
Western AW, Zhou SL, Grayson RB, McMahon TA, Bloschl G, Wilson DJ, 2004. Spatial correlation of soil moisture in small catchments and its relationship to dominant spatial hydrological processes. Journal of Hydrology 286 (1-4): 113-134. Doi: 10.1016/j.jhydrol.2003.09.014.
Wilson CJ, Dietrich WE. 1987. The contribution of bedrock groundwater flow to storm runoff and high pore pressure development in hollows, in Erosion and Sedimentation in the Pacific Rim, IAHS Publ., vol. 165, edited by R. L. Beschta et al.: 49–60, Int. Assoc. of Hydrol Sci., Wallingford, UK
Friday, August 26, 2011
A new version of GEOtop with a Draft User Manual available
Dear all,
we have updated GEOtop to the milestone version 1.45.
It is the result of the great effort of Stefano Endrizzi and Stephan
Gruber by the University of Zurich.
This new version includes:
- simplified I/O based on keywords
- other important debugged problems
The version is positioned in the trunk of the SVN in Bozen/Bolzano:
https://dev.fsc.bz.it/private/repos/geotop/trunk/GEOtop_1.45
Furthermore, the draft version of the USERS MANUAL is ready to be
downloaded from the link:
http://cl.ly/2X24303x3b0x293l112M
Please let me know your comments on the manual in order to improve the
final version.
For who who did not read previous post about, GEOtop is a process-based hydrological models that, given the meteorological data and soil parameters in input, allows to know in
each point of the domain and in each time step:
the evaporation of the soil
the transpiration of the vegetation
the radiation and energy fluxes at the Earth surface
the pore water pressure in the soil
the water-table movements in saturated zone
the water discharge in an outlet
the temperature and ice content in the soil
the height and density of the snow
the mass balance of a glacier
Furthermore, thanks to the post-process software GEOtopFS (GEOtop
Factor of Safety), it calculates:
the dynamic probability of slope instability during a precipitation
event
The wiki-page is not completely up-to-date. But we are working to get it ready.
we have updated GEOtop to the milestone version 1.45.
It is the result of the great effort of Stefano Endrizzi and Stephan
Gruber by the University of Zurich.
This new version includes:
- simplified I/O based on keywords
- other important debugged problems
The version is positioned in the trunk of the SVN in Bozen/Bolzano:
https://dev.fsc.bz.it/private/repos/geotop/trunk/GEOtop_1.45
Furthermore, the draft version of the USERS MANUAL is ready to be
downloaded from the link:
http://cl.ly/2X24303x3b0x293l112M
Please let me know your comments on the manual in order to improve the
final version.
For who who did not read previous post about, GEOtop is a process-based hydrological models that, given the meteorological data and soil parameters in input, allows to know in
each point of the domain and in each time step:
the evaporation of the soil
the transpiration of the vegetation
the radiation and energy fluxes at the Earth surface
the pore water pressure in the soil
the water-table movements in saturated zone
the water discharge in an outlet
the temperature and ice content in the soil
the height and density of the snow
the mass balance of a glacier
Furthermore, thanks to the post-process software GEOtopFS (GEOtop
Factor of Safety), it calculates:
the dynamic probability of slope instability during a precipitation
event
The wiki-page is not completely up-to-date. But we are working to get it ready.
Tuesday, August 23, 2011
A quick guide to writing a solid peer review
This recent contribution by Nicholas and Gordon can be found here from the EOS AGU Journal of July the 12th. This below the flowchart:
The paper is really a good guide. However, it does not tell all the truth. What moves me as a reviewer (not considering that I accepted duties as associate editor or editor) is the curiosity to know a piece of exciting research a little before the rest of the guys. On the other hand, the expectations, are very often, not maintained by the incoming papers, and very few reward the efforts. However, this allows you to know what people thinks is important today, as opposed to what you (me) think it is, and is all experience gained. This can be summarized as: reviewing keep you close to active research.
A second aspect is that rarely you are completely expert of the subject treated. Most of the details of a paper from Authors you did not frequent before (on a topic you supposedly know enough), refers to paper and methods that you do not completely possess. This add sweat to your work, since you need to search and look to other papers to review one. The positive of this that you increase your knowledge. And the efforts are usually paid back with self-consciousness of what you know of a subject.
With time experience and erudition grow, and therefore the task or reviewing becomes easier, because you start to recognize the presence or absence of the structural patterns that makes of a paper a good paper. Outstanding paper are obviously matter or the science they contain.
Now, going back to my reviews.
The paper is really a good guide. However, it does not tell all the truth. What moves me as a reviewer (not considering that I accepted duties as associate editor or editor) is the curiosity to know a piece of exciting research a little before the rest of the guys. On the other hand, the expectations, are very often, not maintained by the incoming papers, and very few reward the efforts. However, this allows you to know what people thinks is important today, as opposed to what you (me) think it is, and is all experience gained. This can be summarized as: reviewing keep you close to active research.
A second aspect is that rarely you are completely expert of the subject treated. Most of the details of a paper from Authors you did not frequent before (on a topic you supposedly know enough), refers to paper and methods that you do not completely possess. This add sweat to your work, since you need to search and look to other papers to review one. The positive of this that you increase your knowledge. And the efforts are usually paid back with self-consciousness of what you know of a subject.
With time experience and erudition grow, and therefore the task or reviewing becomes easier, because you start to recognize the presence or absence of the structural patterns that makes of a paper a good paper. Outstanding paper are obviously matter or the science they contain.
Now, going back to my reviews.
Monday, August 8, 2011
Doing Ph. D. Studies
I found this nice and ironic presentation of what a Ph.D is. It is entitled Ph.D. School in picture.
There you will find the explanation of the mysterious figure above. Looking at the related post is also interesting. For instance at: Successful Ph.D. students.
A other pearl from the same Author is the post about getting tenure. Worth to read carefully to the end.
There you will find the explanation of the mysterious figure above. Looking at the related post is also interesting. For instance at: Successful Ph.D. students.
A other pearl from the same Author is the post about getting tenure. Worth to read carefully to the end.
Tuesday, July 26, 2011
Quantifying uncertainty
I saw on EOS an announcement regarding a new website, QUEST, or quantifying uncertainty in ecosystem studies. Hydrology in fact needs an effort to quantify uncertainties, but this is usually ignored.
It is quite a few years that I fly around of this issue, and probably next year I would try to dig a more little deep in literature.
The sources of uncertainty in hydrological modeling are at least three:
- the input data (which can derive from chaotic dynamics)
- the approximation contained in equations
- the parameterizations of constants which can be heterogeneous (highly variable, if not random in space)
When thinking to inputs, the paradigm is rainfall. It is usually estimated just a few points in the domain with large errors. Then, the local estimates needs to be interpolated and extrapolated in space, introducing further errors. Rainfall itself is very irregular in time and space at all of the scales, which means that you can capture just the statistics of its behavior (and this left you out in the cold with other errors).
When looking at flows, i.e. at their mathematical description in equations, one has to think that they are eminently a thermodynamical product where some fluctuations need to be neglected and described with suitably averaged properties, which could be no possible (significant).
Besides, usually the system described is made up of many non-linearly connected subsystems, and in practical implementations the nonlinearities and the feedbacks are simplified or even neglected. Moreover, equations need to be discretized on grid, which introduce itself approximations.
Finally, saying that some processes are governed by heterogeneities, we also state that the information they contain is algorithmically incompressible (e.g. Chaitin), and there is no way to represent it in short strings. The latter syndrome is the one well described by Borges in "The Exactitude of Sciences", but also in Noam Chomsky's book, Rules and Representation, where at page 8 he cites Stephen Weinberg, and goes so deep in asking if we can really know reality, and what it means.
In any case, the hydrological community, started to take care of it from a long time (here it is a recent abstract with hopefully a good literary review, and here, the work by Beven, Gupta and Wagener), but they started to work especially on the assessment of parameter uncertainty (even if GLUE pretends to be of more general validity). A recent assessment is also in this work by Goetzinger and Bardossy which can provide access to further concepts and bibliography.
However, many hydrological models produce just time series, and therefore the uncertainty reduce to understand (and sometimes to compare) a couple of time series: the measured time serie and the modeled time serie. Good hydrological models are those that reproduce the time series with a good agreement. This is quantified, often but not always, with the use of indexes. The mean square error or its root, the Nash-Sutcliffe, the minimax objective function, average absolute percentage error, the index of agreement, the coefficient of determination, are a few of them.
This is certainly a narrow perspective to look at the topic. Both the measured and the simulated series are, in fact, affected by errors, and therefore one should not compare the two series directly , but the time series including their errors. I believe that this would coincide to adopting a Bayesian perspective of the problem (e.g D'Agostini 2003 - Bayesian Reasoning in Data Analysis, A critical Introduction) and will turn into data assimilation (e.g. Kalnay, Atmospheric Modeling, Data Assimilation and Predictability, 2003) with the defect that, at this point, data and models are so entangled that it would be difficult to extricate them (but not impossible, I guess).
We can also observe that a model usually produces more than a single time series. So "a prediction" becomes the "predictions" and the uncertainty spreads in all of them.
Besides, we did not mention, spatial patterns: before we claims for their uncertainty, we have to recognize that we should quantify them. How can we do ? And for extension are we able to identify spatio-temporal patterns ? And therefore when we can decide if two of these patterns are the same (neglecting noises). Indicators of statistical equality would probably give miserable scores if applied to two or three dimensional fields.
Someone has ideas ?
It is quite a few years that I fly around of this issue, and probably next year I would try to dig a more little deep in literature.
The sources of uncertainty in hydrological modeling are at least three:
- the input data (which can derive from chaotic dynamics)
- the approximation contained in equations
- the parameterizations of constants which can be heterogeneous (highly variable, if not random in space)
When thinking to inputs, the paradigm is rainfall. It is usually estimated just a few points in the domain with large errors. Then, the local estimates needs to be interpolated and extrapolated in space, introducing further errors. Rainfall itself is very irregular in time and space at all of the scales, which means that you can capture just the statistics of its behavior (and this left you out in the cold with other errors).
When looking at flows, i.e. at their mathematical description in equations, one has to think that they are eminently a thermodynamical product where some fluctuations need to be neglected and described with suitably averaged properties, which could be no possible (significant).
Besides, usually the system described is made up of many non-linearly connected subsystems, and in practical implementations the nonlinearities and the feedbacks are simplified or even neglected. Moreover, equations need to be discretized on grid, which introduce itself approximations.
Finally, saying that some processes are governed by heterogeneities, we also state that the information they contain is algorithmically incompressible (e.g. Chaitin), and there is no way to represent it in short strings. The latter syndrome is the one well described by Borges in "The Exactitude of Sciences", but also in Noam Chomsky's book, Rules and Representation, where at page 8 he cites Stephen Weinberg, and goes so deep in asking if we can really know reality, and what it means.
In any case, the hydrological community, started to take care of it from a long time (here it is a recent abstract with hopefully a good literary review, and here, the work by Beven, Gupta and Wagener), but they started to work especially on the assessment of parameter uncertainty (even if GLUE pretends to be of more general validity). A recent assessment is also in this work by Goetzinger and Bardossy which can provide access to further concepts and bibliography.
However, many hydrological models produce just time series, and therefore the uncertainty reduce to understand (and sometimes to compare) a couple of time series: the measured time serie and the modeled time serie. Good hydrological models are those that reproduce the time series with a good agreement. This is quantified, often but not always, with the use of indexes. The mean square error or its root, the Nash-Sutcliffe, the minimax objective function, average absolute percentage error, the index of agreement, the coefficient of determination, are a few of them.
This is certainly a narrow perspective to look at the topic. Both the measured and the simulated series are, in fact, affected by errors, and therefore one should not compare the two series directly , but the time series including their errors. I believe that this would coincide to adopting a Bayesian perspective of the problem (e.g D'Agostini 2003 - Bayesian Reasoning in Data Analysis, A critical Introduction) and will turn into data assimilation (e.g. Kalnay, Atmospheric Modeling, Data Assimilation and Predictability, 2003) with the defect that, at this point, data and models are so entangled that it would be difficult to extricate them (but not impossible, I guess).
We can also observe that a model usually produces more than a single time series. So "a prediction" becomes the "predictions" and the uncertainty spreads in all of them.
Besides, we did not mention, spatial patterns: before we claims for their uncertainty, we have to recognize that we should quantify them. How can we do ? And for extension are we able to identify spatio-temporal patterns ? And therefore when we can decide if two of these patterns are the same (neglecting noises). Indicators of statistical equality would probably give miserable scores if applied to two or three dimensional fields.
Someone has ideas ?
Subscribe to:
Posts (Atom)