In the previous update I mentioned the need to calculate the volume of water above the critical flood discharge i.e. the volume of water likely to spill onto the floodplain; a very important calculation when looking at the impact of a flood mitigation measure.
To do this, I essentially need to calculate the area of certain sections of a simulated flood hydrograph - the area under a graph. This is known as integration. The programme I am running my model in, MATLAB, allows this to be done in several different ways. However I am having problems using some of the available methods.
Therefore I am used the trapezoidal rule, which is not likely to give the most accurate estimate of the area of a graph;
http://en.wikipedia.org/wiki/Trapezoidal_rule
The following image is useful for understanding how the trapezoidal rule works
http://en.wikipedia.org/wiki/File:Trapezoidal_rule_illustration_small.svg
As it uses straight lines to approimate a curve, there are inevitably errors in area calculation - moreso than if I can use a similar but more accurate method - and therefore uncertainty in my findings. My aim is therefore to try to figure out how to use an improved method of integration. However, for the moment, the current does allow me to explore the effect of CRIMs on flood volume.
Initial results (for an uncalibrated model) on flood volume to follow soon....
Wednesday, 26 May 2010
Tuesday, 18 May 2010
Figure 1
A figure showing;
the oberserved flood hydrograph during the 2000 flood event (black).
the simulated flood hydrograph using a 30mm/day time map with no interventions(red)
the simulated flood hydrograph using a 30mm/day time map with a CRIM added along reach 127 (blue).
The figure shows how increasing the channel and floodplain roughness at reach 127 results in a decrease in flood peak of just over 3 cumecs (m3/s)
Important to note;
The observed hydrograph is taken from the Isfield gauge downstream of Uckfield, whereas the two simulated hydrographs produce hydrographs predicted for an areas just upstream of Uckfield. This will lead to a slightly greater difference between simulated and observed hydrographs
Screening simulaions - the effects of CRIMs; preliminary results
Screening simulations
These simulations involved increasing the channel and floodplain roughness along one reach at a time to simulate the adding of a CRIM (debris dam and floodplain vegetation) and looking at the impact this has on river discharge just upstream of Uckfield.
-NOTE- I will add some images showing some of my results in the next update, which I'll add after this.
Results have been produced for all rain time maps (1mm/day - 200mm/day). A potential problem I have is in deciding on an appropriate time map to use, as discussed in my previous update. It was mentioned that goodness-of-fit statistics can be misleading. Therefore I decided to look at the effect of CRIMs where time maps 30, 36, 42 and 50mm/day were applied.
- NOTE - The model may be calibrated with different time maps throughout the storm period.
My choice was based on what was felt to produce the best hydrograph when initially compared to the observed hydrgraph. As discussed previously, the hydrograph produced when using a 30mm/day time map shows an encouragingly good qualitative fit, albeit with a time lag.
Table 1. The number of reaches in the Uck catchment where, if applied to 1 individual reach, a CRIM would decrease flood peak by more than 5, 1 and 0.1 cumecs.
Table 1 shows some of my initial results. It shows for example that, using the 30mm time map, there are 11 reaches which reduce the largest flood peak by over 5 cumecs individually. It can be seen that with increased rainfall rate, more reaches have a reducing effect on the main flood peak - this is not suprising as for the higher rainfall rates initial flood peak is higher.
-NOTE- It is also important to note that there are also many reaches which increase the flood peak when a CRIM is added, and many more 'neutral' sites where the effect is insignificant. In addition to this, for various reasons some of the reaches may not be suitable for CRIMs even if the model shows that increasing roughness in that area has a positive effect on flood reduction.
For example an area of floodplain may all ready be heavily vegetated - therefore floodplain roughness cannot be increased in practice.
The results are encouraging - when looking at a qualitatively good simulation of the 2000 flood hydrograph, over 50 reaches can potentially reduce the main flood peak by over 0.1 cumecs individually.
However there are other points to consider when looking at these results;
I was quite surprised at the extent of the effect of applying CRIMs to certain reaches, largely though not exclusively located along the main Uck. Four reaches reduced the flood peak by over 10 cumecs on their own. This is an extremely large reduction.
This may be due to a model artefact. - As an additional analysis I am going to run the same simulations again but this time not increase the channel rough as much;
The default channel roughness (represented as manning's roughness, n) is 0.035;
For the results discussed here, n was increased to 0.14;
This could be potentially too high so I'll run the same simulations again, increasing channel n to 0.08. This will represent a less extreme intervention and I hope results will still be positive;
Secondly so far I have only analysed my results looking at flood peak reduction. It is not necessarily helpful to reduce the flood peak if the volume of water above critical flood discharge - the amount of water spilling onto the floodplain - remains the same over a storm event. (Though it may still be beneficial in terms of timing of flood waters)
Therefore I need to look at the volume of water above critical flood discharge. This is proving to be more difficult for me to do than hoped. I basically need to figure out how to work out the area under a section of the discharge curve. This appears to be a slightly complicated proceduce and one I haven't figured out yet.
After looking at the individual effect of adding CRIMs, I will need to look at how combinations of CRIMs affect the flood peak.
Images showing my initial results to follow....
Ed
These simulations involved increasing the channel and floodplain roughness along one reach at a time to simulate the adding of a CRIM (debris dam and floodplain vegetation) and looking at the impact this has on river discharge just upstream of Uckfield.
-NOTE- I will add some images showing some of my results in the next update, which I'll add after this.
Results have been produced for all rain time maps (1mm/day - 200mm/day). A potential problem I have is in deciding on an appropriate time map to use, as discussed in my previous update. It was mentioned that goodness-of-fit statistics can be misleading. Therefore I decided to look at the effect of CRIMs where time maps 30, 36, 42 and 50mm/day were applied.
- NOTE - The model may be calibrated with different time maps throughout the storm period.
My choice was based on what was felt to produce the best hydrograph when initially compared to the observed hydrgraph. As discussed previously, the hydrograph produced when using a 30mm/day time map shows an encouragingly good qualitative fit, albeit with a time lag.
Table 1. The number of reaches in the Uck catchment where, if applied to 1 individual reach, a CRIM would decrease flood peak by more than 5, 1 and 0.1 cumecs.
Table 1 shows some of my initial results. It shows for example that, using the 30mm time map, there are 11 reaches which reduce the largest flood peak by over 5 cumecs individually. It can be seen that with increased rainfall rate, more reaches have a reducing effect on the main flood peak - this is not suprising as for the higher rainfall rates initial flood peak is higher.
-NOTE- It is also important to note that there are also many reaches which increase the flood peak when a CRIM is added, and many more 'neutral' sites where the effect is insignificant. In addition to this, for various reasons some of the reaches may not be suitable for CRIMs even if the model shows that increasing roughness in that area has a positive effect on flood reduction.
For example an area of floodplain may all ready be heavily vegetated - therefore floodplain roughness cannot be increased in practice.
The results are encouraging - when looking at a qualitatively good simulation of the 2000 flood hydrograph, over 50 reaches can potentially reduce the main flood peak by over 0.1 cumecs individually.
However there are other points to consider when looking at these results;
I was quite surprised at the extent of the effect of applying CRIMs to certain reaches, largely though not exclusively located along the main Uck. Four reaches reduced the flood peak by over 10 cumecs on their own. This is an extremely large reduction.
This may be due to a model artefact. - As an additional analysis I am going to run the same simulations again but this time not increase the channel rough as much;
The default channel roughness (represented as manning's roughness, n) is 0.035;
For the results discussed here, n was increased to 0.14;
This could be potentially too high so I'll run the same simulations again, increasing channel n to 0.08. This will represent a less extreme intervention and I hope results will still be positive;
Secondly so far I have only analysed my results looking at flood peak reduction. It is not necessarily helpful to reduce the flood peak if the volume of water above critical flood discharge - the amount of water spilling onto the floodplain - remains the same over a storm event. (Though it may still be beneficial in terms of timing of flood waters)
Therefore I need to look at the volume of water above critical flood discharge. This is proving to be more difficult for me to do than hoped. I basically need to figure out how to work out the area under a section of the discharge curve. This appears to be a slightly complicated proceduce and one I haven't figured out yet.
After looking at the individual effect of adding CRIMs, I will need to look at how combinations of CRIMs affect the flood peak.
Images showing my initial results to follow....
Ed
Sunday, 16 May 2010
Sensitivity analysis - preliminary results
As discussed in the previous update, I aimed to carry out 2000 model runs to look at how the output (river discharge) of the model varied as model variables or parameters (such as channel roughness) were varied randomly.
The greatest difficulty with this has been just making sure that everything is set up correctly for my model runs. Sometimes this has involved quite a bit of trial and error - often a lot of model errors - to get everything right. As I can automate all my simulations it would be very annoying to find after 2000 simulations I'd made a msitake. However the simulations have now been carried out (with the help of Stuart letting me use his computer as well as mine).
I have used a number of different objective functions to analyse the accuracy of model predictions of the flood hydrograph. These basically attempt to quantify the goodness of fit of my observed (2000 flood event) and simulated hydrographs. Amongst these was the Nash-Sutcliffe model efficency (NSME), which allows measurement of the variation between the observed and the simulated hydrograph.
However Nash-Sutcliffe values were very poor for nearly all of the simulations. As were results showing the error in predicted flood peak. The low values were quite discouraging as it suggests that, at least when varying parameter values, the model is a poor respresentation of the observed flood hydrograph.
However there are several potential positives to take from the simulations;
- Firstly it is now even more clear that the model is very sensitive to rainfall rate applied. This stands to reason that a very small or very (very!) large rainfall rate is not likely to produce a flood hydrograph similar to that observed in 2000. - On reflection this is good in that it would be expected that the flood hydrograph would change quite considerably under different rainfall rates.
- Secondly the NSME statistic can give misleading results if they are not looked at closely.
For example it is biased towards the highest flows, therefore a model can be given a low NSME value even if most of the flood hydrograph is correctly predicted.
Also errors in the timing of flood peak can affect the results from using the statistic.
For example it is possible to produce a pretty good qualititative simulation of the observed hydrograph of the 2000 event using a set rainfall rate. From simply looking at this we can see that the timing of the peaks is slightly out - this can greatly affect NSME values. If the timing error if corrected for, very high NSME values can be achieved - indicating a good fit.
Therefore we believe the poor results are far from suggesting the model is not useful and it highlights the importance of not just analysing results but looking at how they are analysed.
As the model is very sensitive to rainfall rate only a small range of rainfall rate is likely to produce a good simulation of the flood hydrograph, therefore when I ran 2000 simulations very few combinations of variables produced 'good' results.
However after some extra thought usefull information can be found from the simulations. Trends in parameters values can be seen and will be looked at more closely in time. A future forward step is likely to be calibrating the model using several different rain rates as the event progresses. It is hoped this may offer up more accurate results and allow better investigation of the model parameters.
On the plus side it is now possible to run much faster simulations, using the computer power of several computers so results can be obtained much sooner.
Tomorrow I shall update you on results from my screening simulations, which are quite interesting.
Ed
The greatest difficulty with this has been just making sure that everything is set up correctly for my model runs. Sometimes this has involved quite a bit of trial and error - often a lot of model errors - to get everything right. As I can automate all my simulations it would be very annoying to find after 2000 simulations I'd made a msitake. However the simulations have now been carried out (with the help of Stuart letting me use his computer as well as mine).
I have used a number of different objective functions to analyse the accuracy of model predictions of the flood hydrograph. These basically attempt to quantify the goodness of fit of my observed (2000 flood event) and simulated hydrographs. Amongst these was the Nash-Sutcliffe model efficency (NSME), which allows measurement of the variation between the observed and the simulated hydrograph.
However Nash-Sutcliffe values were very poor for nearly all of the simulations. As were results showing the error in predicted flood peak. The low values were quite discouraging as it suggests that, at least when varying parameter values, the model is a poor respresentation of the observed flood hydrograph.
However there are several potential positives to take from the simulations;
- Firstly it is now even more clear that the model is very sensitive to rainfall rate applied. This stands to reason that a very small or very (very!) large rainfall rate is not likely to produce a flood hydrograph similar to that observed in 2000. - On reflection this is good in that it would be expected that the flood hydrograph would change quite considerably under different rainfall rates.
- Secondly the NSME statistic can give misleading results if they are not looked at closely.
For example it is biased towards the highest flows, therefore a model can be given a low NSME value even if most of the flood hydrograph is correctly predicted.
Also errors in the timing of flood peak can affect the results from using the statistic.
For example it is possible to produce a pretty good qualititative simulation of the observed hydrograph of the 2000 event using a set rainfall rate. From simply looking at this we can see that the timing of the peaks is slightly out - this can greatly affect NSME values. If the timing error if corrected for, very high NSME values can be achieved - indicating a good fit.
Therefore we believe the poor results are far from suggesting the model is not useful and it highlights the importance of not just analysing results but looking at how they are analysed.
As the model is very sensitive to rainfall rate only a small range of rainfall rate is likely to produce a good simulation of the flood hydrograph, therefore when I ran 2000 simulations very few combinations of variables produced 'good' results.
However after some extra thought usefull information can be found from the simulations. Trends in parameters values can be seen and will be looked at more closely in time. A future forward step is likely to be calibrating the model using several different rain rates as the event progresses. It is hoped this may offer up more accurate results and allow better investigation of the model parameters.
On the plus side it is now possible to run much faster simulations, using the computer power of several computers so results can be obtained much sooner.
Tomorrow I shall update you on results from my screening simulations, which are quite interesting.
Ed
Monday, 3 May 2010
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